%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : ALG150+1 : TPTP v8.1.2. Released v2.7.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n023.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Wed Aug 30 16:37:59 EDT 2023 % Result : Unsatisfiable 16.98s 2.97s % Output : Proof 152.53s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : ALG150+1 : TPTP v8.1.2. Released v2.7.0. % 0.12/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.12/0.33 % Computer : n023.cluster.edu % 0.12/0.33 % Model : x86_64 x86_64 % 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.33 % Memory : 8042.1875MB % 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.33 % CPULimit : 300 % 0.12/0.33 % WCLimit : 300 % 0.12/0.33 % DateTime : Mon Aug 28 04:02:10 EDT 2023 % 0.12/0.33 % CPUTime : % 0.58/0.63 ________ _____ % 0.58/0.63 ___ __ \_________(_)________________________________ % 0.58/0.63 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.58/0.63 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.58/0.63 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.58/0.63 % 0.58/0.63 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.58/0.63 (2023-06-19) % 0.58/0.63 % 0.58/0.63 (c) Philipp Rümmer, 2009-2023 % 0.58/0.63 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.58/0.63 Amanda Stjerna. % 0.58/0.63 Free software under BSD-3-Clause. % 0.58/0.63 % 0.58/0.63 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.58/0.63 % 0.58/0.63 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.69/0.64 Running up to 7 provers in parallel. % 0.73/0.66 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.73/0.66 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.73/0.66 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.73/0.66 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.73/0.66 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.73/0.66 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.73/0.66 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 4.31/1.36 Prover 4: Preprocessing ... % 4.73/1.36 Prover 1: Preprocessing ... % 4.73/1.40 Prover 2: Preprocessing ... % 4.73/1.40 Prover 3: Preprocessing ... % 4.73/1.40 Prover 5: Preprocessing ... % 4.73/1.40 Prover 0: Preprocessing ... % 4.73/1.40 Prover 6: Preprocessing ... % 8.01/1.81 Prover 2: Constructing countermodel ... % 8.01/1.82 Prover 3: Constructing countermodel ... % 8.23/1.89 Prover 4: Constructing countermodel ... % 8.23/1.89 Prover 1: Constructing countermodel ... % 8.23/1.90 Prover 6: Constructing countermodel ... % 8.77/1.93 Prover 0: Constructing countermodel ... % 10.47/2.16 Prover 5: Constructing countermodel ... % 16.87/2.97 Prover 6: proved (2311ms) % 16.98/2.97 % 16.98/2.97 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p % 16.98/2.97 % 16.98/2.97 Prover 0: stopped % 16.98/2.99 Prover 3: stopped % 16.98/2.99 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 16.98/2.99 Prover 2: stopped % 16.98/3.00 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 16.98/3.00 Prover 5: stopped % 17.23/3.01 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 17.23/3.02 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 17.23/3.02 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 18.60/3.21 Prover 10: Preprocessing ... % 18.60/3.23 Prover 7: Preprocessing ... % 19.18/3.27 Prover 11: Preprocessing ... % 19.18/3.28 Prover 13: Preprocessing ... % 19.18/3.28 Prover 8: Preprocessing ... % 19.89/3.37 Prover 8: Constructing countermodel ... % 19.89/3.39 Prover 10: Constructing countermodel ... % 19.89/3.40 Prover 7: Constructing countermodel ... % 19.89/3.40 Prover 13: Constructing countermodel ... % 20.44/3.47 Prover 11: Constructing countermodel ... % 63.86/9.04 Prover 13: stopped % 63.86/9.05 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 64.77/9.10 Prover 16: Preprocessing ... % 65.78/9.28 Prover 16: Constructing countermodel ... % 111.51/15.05 Prover 16: stopped % 111.51/15.07 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085 % 112.29/15.17 Prover 19: Preprocessing ... % 113.15/15.29 Prover 19: Constructing countermodel ... % 118.61/16.00 Prover 1: stopped % 138.25/18.84 Prover 19: stopped % 142.70/19.59 Prover 4: Found proof (size 162954) % 142.70/19.59 Prover 4: proved (18931ms) % 142.70/19.59 Prover 11: stopped % 142.70/19.59 Prover 7: stopped % 142.70/19.59 Prover 8: stopped % 142.70/19.59 Prover 10: stopped % 142.70/19.59 % 142.70/19.59 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p % 142.70/19.59 % 144.83/20.43 % SZS output start Proof for theBenchmark % 145.04/20.53 Assumptions after simplification: % 145.04/20.53 --------------------------------- % 145.04/20.53 % 145.04/20.53 (ax1) % 145.04/20.58 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 145.04/20.58 ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: % 145.04/20.58 $i] : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: % 145.04/20.58 $i] : ? [v14: $i] : ? [v15: $i] : (op(e3, e3) = v15 & op(e3, e2) = v14 & % 145.04/20.58 op(e3, e1) = v13 & op(e3, e0) = v12 & op(e2, e3) = v11 & op(e2, e2) = v10 & % 145.04/20.58 op(e2, e1) = v9 & op(e2, e0) = v8 & op(e1, e3) = v7 & op(e1, e2) = v6 & % 145.04/20.58 op(e1, e1) = v5 & op(e1, e0) = v4 & op(e0, e3) = v3 & op(e0, e2) = v2 & % 145.04/20.58 op(e0, e1) = v1 & op(e0, e0) = v0 & $i(v15) & $i(v14) & $i(v13) & $i(v12) & % 145.04/20.58 $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) & % 145.04/20.58 $i(v3) & $i(v2) & $i(v1) & $i(v0) & (v15 = e3 | v15 = e2 | v15 = e1 | v15 = % 145.04/20.58 e0) & (v14 = e3 | v14 = e2 | v14 = e1 | v14 = e0) & (v13 = e3 | v13 = e2 | % 145.04/20.58 v13 = e1 | v13 = e0) & (v12 = e3 | v12 = e2 | v12 = e1 | v12 = e0) & (v11 % 145.04/20.58 = e3 | v11 = e2 | v11 = e1 | v11 = e0) & (v10 = e3 | v10 = e2 | v10 = e1 | % 145.04/20.58 v10 = e0) & (v9 = e3 | v9 = e2 | v9 = e1 | v9 = e0) & (v8 = e3 | v8 = e2 | % 145.04/20.58 v8 = e1 | v8 = e0) & (v7 = e3 | v7 = e2 | v7 = e1 | v7 = e0) & (v6 = e3 | % 145.04/20.58 v6 = e2 | v6 = e1 | v6 = e0) & (v5 = e3 | v5 = e2 | v5 = e1 | v5 = e0) & % 145.04/20.58 (v4 = e3 | v4 = e2 | v4 = e1 | v4 = e0) & (v3 = e3 | v3 = e2 | v3 = e1 | v3 % 145.04/20.58 = e0) & (v2 = e3 | v2 = e2 | v2 = e1 | v2 = e0) & (v1 = e3 | v1 = e2 | v1 % 145.04/20.58 = e1 | v1 = e0) & (v0 = e3 | v0 = e2 | v0 = e1 | v0 = e0)) % 145.04/20.58 % 145.04/20.58 (ax10) % 145.04/20.58 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 145.04/20.58 (op(v0, v0) = v1 & op(e2, v1) = v2 & op(e2, e2) = v0 & $i(v2) & $i(v1) & % 145.04/20.58 $i(v0) & ( ~ (v2 = e1) | ~ (v1 = e0) | ~ (v0 = e3))) % 145.04/20.58 % 145.04/20.58 (ax11) % 145.04/20.58 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 145.04/20.58 (op(v0, v0) = v1 & op(e1, v1) = v2 & op(e1, e1) = v0 & $i(v2) & $i(v1) & % 145.04/20.58 $i(v0) & ( ~ (v2 = e2) | ~ (v1 = e0) | ~ (v0 = e3))) % 145.04/20.58 % 145.04/20.58 (ax12) % 145.04/20.59 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 145.04/20.59 (op(v0, v0) = v1 & op(e3, v1) = v2 & op(e3, e3) = v0 & $i(v2) & $i(v1) & % 145.04/20.59 $i(v0) & ( ~ (v2 = e2) | ~ (v1 = e1) | ~ (v0 = e0))) % 145.04/20.59 % 145.04/20.59 (ax13) % 145.04/20.59 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 145.04/20.59 (op(v0, v0) = v1 & op(e2, v1) = v2 & op(e2, e2) = v0 & $i(v2) & $i(v1) & % 145.04/20.59 $i(v0) & ( ~ (v2 = e3) | ~ (v1 = e1) | ~ (v0 = e0))) % 145.04/20.59 % 145.04/20.59 (ax14) % 145.04/20.59 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 145.04/20.59 (op(v0, v0) = v1 & op(e3, v1) = v2 & op(e3, e3) = v0 & $i(v2) & $i(v1) & % 145.04/20.59 $i(v0) & ( ~ (v2 = e0) | ~ (v1 = e1) | ~ (v0 = e2))) % 145.04/20.59 % 145.04/20.59 (ax15) % 145.04/20.59 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 145.04/20.59 (op(v0, v0) = v1 & op(e0, v1) = v2 & op(e0, e0) = v0 & $i(v2) & $i(v1) & % 145.04/20.59 $i(v0) & ( ~ (v2 = e3) | ~ (v1 = e1) | ~ (v0 = e2))) % 145.04/20.59 % 145.04/20.59 (ax16) % 145.04/20.60 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 145.04/20.60 (op(v0, v0) = v1 & op(e2, v1) = v2 & op(e2, e2) = v0 & $i(v2) & $i(v1) & % 145.04/20.60 $i(v0) & ( ~ (v2 = e0) | ~ (v1 = e1) | ~ (v0 = e3))) % 145.04/20.60 % 145.04/20.60 (ax17) % 145.04/20.60 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 145.04/20.60 (op(v0, v0) = v1 & op(e0, v1) = v2 & op(e0, e0) = v0 & $i(v2) & $i(v1) & % 145.04/20.60 $i(v0) & ( ~ (v2 = e2) | ~ (v1 = e1) | ~ (v0 = e3))) % 145.04/20.60 % 145.04/20.60 (ax18) % 145.04/20.60 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 145.04/20.60 (op(v0, v0) = v1 & op(e3, v1) = v2 & op(e3, e3) = v0 & $i(v2) & $i(v1) & % 145.04/20.60 $i(v0) & ( ~ (v2 = e1) | ~ (v1 = e2) | ~ (v0 = e0))) % 145.04/20.60 % 145.04/20.60 (ax19) % 145.04/20.60 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 145.04/20.60 (op(v0, v0) = v1 & op(e1, v1) = v2 & op(e1, e1) = v0 & $i(v2) & $i(v1) & % 145.04/20.60 $i(v0) & ( ~ (v2 = e3) | ~ (v1 = e2) | ~ (v0 = e0))) % 145.04/20.60 % 145.04/20.60 (ax2) % 145.49/20.62 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 145.49/20.62 ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: % 145.49/20.62 $i] : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: % 145.49/20.62 $i] : ? [v14: $i] : ? [v15: $i] : (op(e3, e3) = v15 & op(e3, e2) = v14 & % 145.49/20.62 op(e3, e1) = v11 & op(e3, e0) = v6 & op(e2, e3) = v13 & op(e2, e2) = v12 & % 145.49/20.62 op(e2, e1) = v10 & op(e2, e0) = v5 & op(e1, e3) = v9 & op(e1, e2) = v8 & % 145.49/20.62 op(e1, e1) = v7 & op(e1, e0) = v4 & op(e0, e3) = v3 & op(e0, e2) = v2 & % 145.49/20.62 op(e0, e1) = v1 & op(e0, e0) = v0 & $i(v15) & $i(v14) & $i(v13) & $i(v12) & % 145.49/20.62 $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) & % 145.49/20.62 $i(v3) & $i(v2) & $i(v1) & $i(v0) & (v15 = e3 | v14 = e3 | v11 = e3 | v6 = % 145.49/20.62 e3) & (v15 = e3 | v13 = e3 | v9 = e3 | v3 = e3) & (v15 = e2 | v14 = e2 | % 145.49/20.62 v11 = e2 | v6 = e2) & (v15 = e2 | v13 = e2 | v9 = e2 | v3 = e2) & (v15 = % 145.49/20.62 e1 | v14 = e1 | v11 = e1 | v6 = e1) & (v15 = e1 | v13 = e1 | v9 = e1 | v3 % 145.49/20.62 = e1) & (v15 = e0 | v14 = e0 | v11 = e0 | v6 = e0) & (v15 = e0 | v13 = e0 % 145.49/20.62 | v9 = e0 | v3 = e0) & (v14 = e3 | v12 = e3 | v8 = e3 | v2 = e3) & (v14 = % 145.49/20.62 e2 | v12 = e2 | v8 = e2 | v2 = e2) & (v14 = e1 | v12 = e1 | v8 = e1 | v2 = % 145.49/20.62 e1) & (v14 = e0 | v12 = e0 | v8 = e0 | v2 = e0) & (v13 = e3 | v12 = e3 | % 145.49/20.62 v10 = e3 | v5 = e3) & (v13 = e2 | v12 = e2 | v10 = e2 | v5 = e2) & (v13 = % 145.49/20.62 e1 | v12 = e1 | v10 = e1 | v5 = e1) & (v13 = e0 | v12 = e0 | v10 = e0 | v5 % 145.49/20.62 = e0) & (v11 = e3 | v10 = e3 | v7 = e3 | v1 = e3) & (v11 = e2 | v10 = e2 | % 145.49/20.62 v7 = e2 | v1 = e2) & (v11 = e1 | v10 = e1 | v7 = e1 | v1 = e1) & (v11 = e0 % 145.49/20.62 | v10 = e0 | v7 = e0 | v1 = e0) & (v9 = e3 | v8 = e3 | v7 = e3 | v4 = e3) % 145.49/20.62 & (v9 = e2 | v8 = e2 | v7 = e2 | v4 = e2) & (v9 = e1 | v8 = e1 | v7 = e1 | % 145.49/20.62 v4 = e1) & (v9 = e0 | v8 = e0 | v7 = e0 | v4 = e0) & (v6 = e3 | v5 = e3 | % 145.49/20.62 v4 = e3 | v0 = e3) & (v6 = e2 | v5 = e2 | v4 = e2 | v0 = e2) & (v6 = e1 | % 145.49/20.62 v5 = e1 | v4 = e1 | v0 = e1) & (v3 = e3 | v2 = e3 | v1 = e3 | v0 = e3) & % 145.49/20.62 (v3 = e2 | v2 = e2 | v1 = e2 | v0 = e2) & (v3 = e1 | v2 = e1 | v1 = e1 | v0 % 145.49/20.62 = e1) & (v0 = e0 | ((v6 = e0 | v5 = e0 | v4 = e0) & (v3 = e0 | v2 = e0 | % 145.49/20.62 v1 = e0)))) % 145.49/20.62 % 145.49/20.62 (ax20) % 145.49/20.62 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 145.49/20.62 (op(v0, v0) = v1 & op(e3, v1) = v2 & op(e3, e3) = v0 & $i(v2) & $i(v1) & % 145.49/20.63 $i(v0) & ( ~ (v2 = e0) | ~ (v1 = e2) | ~ (v0 = e1))) % 145.49/20.63 % 145.49/20.63 (ax21) % 145.49/20.63 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 145.49/20.63 (op(v0, v0) = v1 & op(e0, v1) = v2 & op(e0, e0) = v0 & $i(v2) & $i(v1) & % 145.49/20.63 $i(v0) & ( ~ (v2 = e3) | ~ (v1 = e2) | ~ (v0 = e1))) % 145.49/20.63 % 145.49/20.63 (ax22) % 145.49/20.63 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 145.49/20.63 (op(v0, v0) = v1 & op(e1, v1) = v2 & op(e1, e1) = v0 & $i(v2) & $i(v1) & % 145.49/20.63 $i(v0) & ( ~ (v2 = e0) | ~ (v1 = e2) | ~ (v0 = e3))) % 145.49/20.63 % 145.49/20.63 (ax23) % 145.49/20.63 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 145.49/20.63 (op(v0, v0) = v1 & op(e0, v1) = v2 & op(e0, e0) = v0 & $i(v2) & $i(v1) & % 145.49/20.63 $i(v0) & ( ~ (v2 = e1) | ~ (v1 = e2) | ~ (v0 = e3))) % 145.49/20.63 % 145.49/20.63 (ax24) % 145.49/20.63 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 145.49/20.63 (op(v0, v0) = v1 & op(e2, v1) = v2 & op(e2, e2) = v0 & $i(v2) & $i(v1) & % 145.49/20.63 $i(v0) & ( ~ (v2 = e1) | ~ (v1 = e3) | ~ (v0 = e0))) % 145.49/20.63 % 145.49/20.63 (ax25) % 145.49/20.63 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 145.49/20.63 (op(v0, v0) = v1 & op(e1, v1) = v2 & op(e1, e1) = v0 & $i(v2) & $i(v1) & % 145.49/20.63 $i(v0) & ( ~ (v2 = e2) | ~ (v1 = e3) | ~ (v0 = e0))) % 145.49/20.63 % 145.49/20.63 (ax26) % 145.49/20.64 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 145.49/20.64 (op(v0, v0) = v1 & op(e2, v1) = v2 & op(e2, e2) = v0 & $i(v2) & $i(v1) & % 145.49/20.64 $i(v0) & ( ~ (v2 = e0) | ~ (v1 = e3) | ~ (v0 = e1))) % 145.49/20.64 % 145.49/20.64 (ax27) % 145.49/20.64 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 145.49/20.64 (op(v0, v0) = v1 & op(e0, v1) = v2 & op(e0, e0) = v0 & $i(v2) & $i(v1) & % 145.49/20.64 $i(v0) & ( ~ (v2 = e2) | ~ (v1 = e3) | ~ (v0 = e1))) % 145.49/20.64 % 145.49/20.64 (ax28) % 145.49/20.64 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 145.49/20.64 (op(v0, v0) = v1 & op(e1, v1) = v2 & op(e1, e1) = v0 & $i(v2) & $i(v1) & % 145.49/20.64 $i(v0) & ( ~ (v2 = e0) | ~ (v1 = e3) | ~ (v0 = e2))) % 145.49/20.64 % 145.49/20.64 (ax29) % 145.49/20.64 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 145.49/20.64 (op(v0, v0) = v1 & op(e0, v1) = v2 & op(e0, e0) = v0 & $i(v2) & $i(v1) & % 145.49/20.64 $i(v0) & ( ~ (v2 = e1) | ~ (v1 = e3) | ~ (v0 = e2))) % 145.49/20.64 % 145.49/20.64 (ax3) % 145.49/20.65 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 145.49/20.65 ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: % 145.49/20.65 $i] : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: % 145.49/20.65 $i] : ? [v14: $i] : ? [v15: $i] : ( ~ (v15 = v14) & ~ (v15 = v13) & ~ % 145.49/20.65 (v15 = v12) & ~ (v15 = v11) & ~ (v15 = v7) & ~ (v15 = v3) & ~ (v14 = % 145.49/20.65 v13) & ~ (v14 = v12) & ~ (v14 = v10) & ~ (v14 = v6) & ~ (v14 = v2) & % 145.49/20.65 ~ (v13 = v12) & ~ (v13 = v9) & ~ (v13 = v5) & ~ (v13 = v1) & ~ (v12 = % 145.49/20.65 v8) & ~ (v12 = v4) & ~ (v12 = v0) & ~ (v11 = v10) & ~ (v11 = v9) & ~ % 145.49/20.65 (v11 = v8) & ~ (v11 = v7) & ~ (v11 = v3) & ~ (v10 = v9) & ~ (v10 = v8) & % 145.49/20.65 ~ (v10 = v6) & ~ (v10 = v2) & ~ (v9 = v8) & ~ (v9 = v5) & ~ (v9 = v1) & % 145.49/20.65 ~ (v8 = v4) & ~ (v8 = v0) & ~ (v7 = v6) & ~ (v7 = v5) & ~ (v7 = v4) & % 145.49/20.65 ~ (v7 = v3) & ~ (v6 = v5) & ~ (v6 = v4) & ~ (v6 = v2) & ~ (v5 = v4) & ~ % 145.49/20.65 (v5 = v1) & ~ (v4 = v0) & ~ (v3 = v2) & ~ (v3 = v1) & ~ (v3 = v0) & ~ % 145.49/20.65 (v2 = v1) & ~ (v2 = v0) & ~ (v1 = v0) & op(e3, e3) = v15 & op(e3, e2) = % 145.49/20.65 v11 & op(e3, e1) = v7 & op(e3, e0) = v3 & op(e2, e3) = v14 & op(e2, e2) = % 145.49/20.65 v10 & op(e2, e1) = v6 & op(e2, e0) = v2 & op(e1, e3) = v13 & op(e1, e2) = v9 % 145.49/20.65 & op(e1, e1) = v5 & op(e1, e0) = v1 & op(e0, e3) = v12 & op(e0, e2) = v8 & % 145.49/20.65 op(e0, e1) = v4 & op(e0, e0) = v0 & $i(v15) & $i(v14) & $i(v13) & $i(v12) & % 145.49/20.65 $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) & % 145.49/20.65 $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 145.49/20.65 % 145.49/20.65 (ax4) % 145.49/20.65 ~ (e3 = e2) & ~ (e3 = e1) & ~ (e3 = e0) & ~ (e2 = e1) & ~ (e2 = e0) & ~ % 145.49/20.65 (e1 = e0) & $i(e3) & $i(e2) & $i(e1) & $i(e0) % 145.49/20.65 % 145.49/20.65 (ax5) % 145.49/20.66 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 145.49/20.66 ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: % 145.49/20.66 $i] : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: % 145.49/20.66 $i] : ? [v14: $i] : ? [v15: $i] : ? [v16: $i] : ? [v17: $i] : ? [v18: % 145.49/20.66 $i] : ? [v19: $i] : ? [v20: $i] : ? [v21: $i] : ? [v22: $i] : ? [v23: % 145.49/20.66 $i] : ? [v24: $i] : ? [v25: $i] : ? [v26: $i] : ? [v27: $i] : ? [v28: % 145.49/20.66 $i] : ? [v29: $i] : ? [v30: $i] : ? [v31: $i] : (op(e3, v30) = v31 & % 145.49/20.66 op(e3, v22) = v23 & op(e3, v14) = v15 & op(e3, v6) = v7 & op(e3, e3) = v30 & % 145.49/20.66 op(e3, e2) = v28 & op(e3, e1) = v26 & op(e3, e0) = v24 & op(e2, v28) = v29 & % 145.49/20.66 op(e2, v20) = v21 & op(e2, v12) = v13 & op(e2, v4) = v5 & op(e2, e3) = v22 & % 145.49/20.66 op(e2, e2) = v20 & op(e2, e1) = v18 & op(e2, e0) = v16 & op(e1, v26) = v27 & % 145.49/20.66 op(e1, v18) = v19 & op(e1, v10) = v11 & op(e1, v2) = v3 & op(e1, e3) = v14 & % 145.49/20.66 op(e1, e2) = v12 & op(e1, e1) = v10 & op(e1, e0) = v8 & op(e0, v24) = v25 & % 145.49/20.66 op(e0, v16) = v17 & op(e0, v8) = v9 & op(e0, v0) = v1 & op(e0, e3) = v6 & % 145.49/20.66 op(e0, e2) = v4 & op(e0, e1) = v2 & op(e0, e0) = v0 & $i(v31) & $i(v30) & % 145.49/20.66 $i(v29) & $i(v28) & $i(v27) & $i(v26) & $i(v25) & $i(v24) & $i(v23) & % 145.49/20.66 $i(v22) & $i(v21) & $i(v20) & $i(v19) & $i(v18) & $i(v17) & $i(v16) & % 145.49/20.66 $i(v15) & $i(v14) & $i(v13) & $i(v12) & $i(v11) & $i(v10) & $i(v9) & $i(v8) % 145.49/20.66 & $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ( % 145.49/20.66 ~ (v30 = e2) | v28 = e3) & ( ~ (v30 = e1) | v26 = e3) & ( ~ (v30 = e0) | % 145.49/20.66 v24 = e3) & ( ~ (v20 = e3) | v22 = e2) & ( ~ (v20 = e1) | v18 = e2) & ( ~ % 145.49/20.66 (v20 = e0) | v16 = e2) & ( ~ (v10 = e3) | v14 = e1) & ( ~ (v10 = e2) | v12 % 145.49/20.66 = e1) & ( ~ (v10 = e0) | v8 = e1) & ( ~ (v0 = e3) | v6 = e0) & ( ~ (v0 = % 145.49/20.66 e2) | v4 = e0) & ( ~ (v0 = e1) | v2 = e0) & (v30 = e3 | v20 = e2 | v10 = % 145.49/20.66 e1 | v0 = e0) & (( ~ (v31 = v30) & ~ (v29 = v28) & ~ (v27 = v26) & ~ % 145.49/20.66 (v25 = v24)) | ( ~ (v23 = v22) & ~ (v21 = v20) & ~ (v19 = v18) & ~ % 145.49/20.66 (v17 = v16)) | ( ~ (v15 = v14) & ~ (v13 = v12) & ~ (v11 = v10) & ~ % 145.49/20.66 (v9 = v8)) | ( ~ (v7 = v6) & ~ (v5 = v4) & ~ (v3 = v2) & ~ (v1 = % 145.49/20.66 v0)))) % 145.49/20.66 % 145.49/20.66 (ax6) % 145.49/20.66 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 145.49/20.66 (op(v0, v0) = v1 & op(e3, v1) = v2 & op(e3, e3) = v0 & $i(v2) & $i(v1) & % 145.49/20.66 $i(v0) & ( ~ (v2 = e2) | ~ (v1 = e0) | ~ (v0 = e1))) % 145.49/20.66 % 145.49/20.66 (ax7) % 145.49/20.66 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 145.49/20.66 (op(v0, v0) = v1 & op(e2, v1) = v2 & op(e2, e2) = v0 & $i(v2) & $i(v1) & % 145.49/20.66 $i(v0) & ( ~ (v2 = e3) | ~ (v1 = e0) | ~ (v0 = e1))) % 145.49/20.66 % 145.49/20.66 (ax8) % 145.49/20.66 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 145.49/20.66 (op(v0, v0) = v1 & op(e3, v1) = v2 & op(e3, e3) = v0 & $i(v2) & $i(v1) & % 145.49/20.66 $i(v0) & ( ~ (v2 = e1) | ~ (v1 = e0) | ~ (v0 = e2))) % 145.49/20.66 % 145.49/20.66 (ax9) % 145.49/20.66 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 145.49/20.66 (op(v0, v0) = v1 & op(e1, v1) = v2 & op(e1, e1) = v0 & $i(v2) & $i(v1) & % 145.49/20.66 $i(v0) & ( ~ (v2 = e3) | ~ (v1 = e0) | ~ (v0 = e2))) % 145.49/20.66 % 145.49/20.66 (function-axioms) % 145.49/20.66 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (op(v3, % 145.49/20.66 v2) = v1) | ~ (op(v3, v2) = v0)) % 145.49/20.66 % 145.49/20.66 Those formulas are unsatisfiable: % 145.49/20.66 --------------------------------- % 145.49/20.66 % 145.49/20.66 Begin of proof % 145.49/20.67 | % 145.49/20.67 | ALPHA: (ax1) implies: % 145.49/20.68 | (1) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 145.49/20.68 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ? % 145.49/20.68 | [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : ? [v14: $i] : % 145.49/20.68 | ? [v15: $i] : (op(e3, e3) = v15 & op(e3, e2) = v14 & op(e3, e1) = v13 % 145.49/20.68 | & op(e3, e0) = v12 & op(e2, e3) = v11 & op(e2, e2) = v10 & op(e2, e1) % 145.49/20.68 | = v9 & op(e2, e0) = v8 & op(e1, e3) = v7 & op(e1, e2) = v6 & op(e1, % 145.49/20.68 | e1) = v5 & op(e1, e0) = v4 & op(e0, e3) = v3 & op(e0, e2) = v2 & % 145.49/20.68 | op(e0, e1) = v1 & op(e0, e0) = v0 & $i(v15) & $i(v14) & $i(v13) & % 145.49/20.68 | $i(v12) & $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) & % 145.49/20.68 | $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & (v15 = e3 | v15 % 145.49/20.68 | = e2 | v15 = e1 | v15 = e0) & (v14 = e3 | v14 = e2 | v14 = e1 | v14 % 145.49/20.68 | = e0) & (v13 = e3 | v13 = e2 | v13 = e1 | v13 = e0) & (v12 = e3 | % 145.49/20.68 | v12 = e2 | v12 = e1 | v12 = e0) & (v11 = e3 | v11 = e2 | v11 = e1 | % 145.49/20.68 | v11 = e0) & (v10 = e3 | v10 = e2 | v10 = e1 | v10 = e0) & (v9 = e3 % 145.49/20.68 | | v9 = e2 | v9 = e1 | v9 = e0) & (v8 = e3 | v8 = e2 | v8 = e1 | v8 % 145.49/20.68 | = e0) & (v7 = e3 | v7 = e2 | v7 = e1 | v7 = e0) & (v6 = e3 | v6 = % 145.49/20.68 | e2 | v6 = e1 | v6 = e0) & (v5 = e3 | v5 = e2 | v5 = e1 | v5 = e0) & % 145.49/20.68 | (v4 = e3 | v4 = e2 | v4 = e1 | v4 = e0) & (v3 = e3 | v3 = e2 | v3 = % 145.49/20.68 | e1 | v3 = e0) & (v2 = e3 | v2 = e2 | v2 = e1 | v2 = e0) & (v1 = e3 % 145.49/20.68 | | v1 = e2 | v1 = e1 | v1 = e0) & (v0 = e3 | v0 = e2 | v0 = e1 | v0 % 145.49/20.68 | = e0)) % 145.49/20.68 | % 145.49/20.68 | ALPHA: (ax2) implies: % 145.49/20.69 | (2) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 145.49/20.69 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ? % 145.49/20.69 | [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : ? [v14: $i] : % 145.49/20.69 | ? [v15: $i] : (op(e3, e3) = v15 & op(e3, e2) = v14 & op(e3, e1) = v11 % 145.49/20.69 | & op(e3, e0) = v6 & op(e2, e3) = v13 & op(e2, e2) = v12 & op(e2, e1) % 145.49/20.69 | = v10 & op(e2, e0) = v5 & op(e1, e3) = v9 & op(e1, e2) = v8 & op(e1, % 145.49/20.69 | e1) = v7 & op(e1, e0) = v4 & op(e0, e3) = v3 & op(e0, e2) = v2 & % 145.49/20.69 | op(e0, e1) = v1 & op(e0, e0) = v0 & $i(v15) & $i(v14) & $i(v13) & % 145.49/20.69 | $i(v12) & $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) & % 145.49/20.69 | $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & (v15 = e3 | v14 % 145.49/20.69 | = e3 | v11 = e3 | v6 = e3) & (v15 = e3 | v13 = e3 | v9 = e3 | v3 = % 145.49/20.69 | e3) & (v15 = e2 | v14 = e2 | v11 = e2 | v6 = e2) & (v15 = e2 | v13 % 145.49/20.69 | = e2 | v9 = e2 | v3 = e2) & (v15 = e1 | v14 = e1 | v11 = e1 | v6 = % 145.49/20.69 | e1) & (v15 = e1 | v13 = e1 | v9 = e1 | v3 = e1) & (v15 = e0 | v14 = % 145.49/20.69 | e0 | v11 = e0 | v6 = e0) & (v15 = e0 | v13 = e0 | v9 = e0 | v3 = % 145.49/20.69 | e0) & (v14 = e3 | v12 = e3 | v8 = e3 | v2 = e3) & (v14 = e2 | v12 = % 145.49/20.69 | e2 | v8 = e2 | v2 = e2) & (v14 = e1 | v12 = e1 | v8 = e1 | v2 = e1) % 145.49/20.69 | & (v14 = e0 | v12 = e0 | v8 = e0 | v2 = e0) & (v13 = e3 | v12 = e3 | % 145.49/20.69 | v10 = e3 | v5 = e3) & (v13 = e2 | v12 = e2 | v10 = e2 | v5 = e2) & % 145.49/20.69 | (v13 = e1 | v12 = e1 | v10 = e1 | v5 = e1) & (v13 = e0 | v12 = e0 | % 145.49/20.69 | v10 = e0 | v5 = e0) & (v11 = e3 | v10 = e3 | v7 = e3 | v1 = e3) & % 145.49/20.69 | (v11 = e2 | v10 = e2 | v7 = e2 | v1 = e2) & (v11 = e1 | v10 = e1 | v7 % 145.49/20.69 | = e1 | v1 = e1) & (v11 = e0 | v10 = e0 | v7 = e0 | v1 = e0) & (v9 = % 145.49/20.69 | e3 | v8 = e3 | v7 = e3 | v4 = e3) & (v9 = e2 | v8 = e2 | v7 = e2 | % 145.49/20.69 | v4 = e2) & (v9 = e1 | v8 = e1 | v7 = e1 | v4 = e1) & (v9 = e0 | v8 % 145.49/20.69 | = e0 | v7 = e0 | v4 = e0) & (v6 = e3 | v5 = e3 | v4 = e3 | v0 = e3) % 145.49/20.69 | & (v6 = e2 | v5 = e2 | v4 = e2 | v0 = e2) & (v6 = e1 | v5 = e1 | v4 = % 145.49/20.69 | e1 | v0 = e1) & (v3 = e3 | v2 = e3 | v1 = e3 | v0 = e3) & (v3 = e2 % 145.49/20.69 | | v2 = e2 | v1 = e2 | v0 = e2) & (v3 = e1 | v2 = e1 | v1 = e1 | v0 % 145.49/20.69 | = e1) & (v0 = e0 | ((v6 = e0 | v5 = e0 | v4 = e0) & (v3 = e0 | v2 = % 145.49/20.69 | e0 | v1 = e0)))) % 145.49/20.69 | % 145.49/20.69 | ALPHA: (ax3) implies: % 145.49/20.69 | (3) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 145.49/20.69 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ? % 145.49/20.69 | [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : ? [v14: $i] : % 145.49/20.69 | ? [v15: $i] : ( ~ (v15 = v14) & ~ (v15 = v13) & ~ (v15 = v12) & ~ % 145.49/20.69 | (v15 = v11) & ~ (v15 = v7) & ~ (v15 = v3) & ~ (v14 = v13) & ~ % 145.49/20.69 | (v14 = v12) & ~ (v14 = v10) & ~ (v14 = v6) & ~ (v14 = v2) & ~ % 145.49/20.69 | (v13 = v12) & ~ (v13 = v9) & ~ (v13 = v5) & ~ (v13 = v1) & ~ (v12 % 145.49/20.69 | = v8) & ~ (v12 = v4) & ~ (v12 = v0) & ~ (v11 = v10) & ~ (v11 = % 145.49/20.69 | v9) & ~ (v11 = v8) & ~ (v11 = v7) & ~ (v11 = v3) & ~ (v10 = v9) % 145.49/20.69 | & ~ (v10 = v8) & ~ (v10 = v6) & ~ (v10 = v2) & ~ (v9 = v8) & ~ % 145.49/20.69 | (v9 = v5) & ~ (v9 = v1) & ~ (v8 = v4) & ~ (v8 = v0) & ~ (v7 = v6) % 145.49/20.69 | & ~ (v7 = v5) & ~ (v7 = v4) & ~ (v7 = v3) & ~ (v6 = v5) & ~ (v6 % 145.49/20.69 | = v4) & ~ (v6 = v2) & ~ (v5 = v4) & ~ (v5 = v1) & ~ (v4 = v0) & % 145.49/20.69 | ~ (v3 = v2) & ~ (v3 = v1) & ~ (v3 = v0) & ~ (v2 = v1) & ~ (v2 = % 145.49/20.69 | v0) & ~ (v1 = v0) & op(e3, e3) = v15 & op(e3, e2) = v11 & op(e3, % 145.49/20.69 | e1) = v7 & op(e3, e0) = v3 & op(e2, e3) = v14 & op(e2, e2) = v10 & % 145.49/20.69 | op(e2, e1) = v6 & op(e2, e0) = v2 & op(e1, e3) = v13 & op(e1, e2) = % 145.49/20.69 | v9 & op(e1, e1) = v5 & op(e1, e0) = v1 & op(e0, e3) = v12 & op(e0, % 145.49/20.69 | e2) = v8 & op(e0, e1) = v4 & op(e0, e0) = v0 & $i(v15) & $i(v14) & % 145.49/20.69 | $i(v13) & $i(v12) & $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) & % 145.49/20.69 | $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 145.49/20.69 | % 145.49/20.69 | ALPHA: (ax4) implies: % 145.49/20.69 | (4) ~ (e1 = e0) % 145.49/20.69 | (5) ~ (e2 = e0) % 145.49/20.69 | (6) ~ (e2 = e1) % 145.49/20.69 | (7) ~ (e3 = e0) % 145.49/20.69 | (8) ~ (e3 = e1) % 145.49/20.69 | (9) ~ (e3 = e2) % 145.49/20.69 | % 145.49/20.69 | ALPHA: (ax5) implies: % 145.49/20.70 | (10) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 145.49/20.70 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : % 145.49/20.70 | ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : ? [v14: % 145.49/20.70 | $i] : ? [v15: $i] : ? [v16: $i] : ? [v17: $i] : ? [v18: $i] : ? % 145.49/20.70 | [v19: $i] : ? [v20: $i] : ? [v21: $i] : ? [v22: $i] : ? [v23: $i] % 145.49/20.70 | : ? [v24: $i] : ? [v25: $i] : ? [v26: $i] : ? [v27: $i] : ? [v28: % 145.49/20.70 | $i] : ? [v29: $i] : ? [v30: $i] : ? [v31: $i] : (op(e3, v30) = % 145.49/20.70 | v31 & op(e3, v22) = v23 & op(e3, v14) = v15 & op(e3, v6) = v7 & % 145.49/20.70 | op(e3, e3) = v30 & op(e3, e2) = v28 & op(e3, e1) = v26 & op(e3, e0) % 145.49/20.70 | = v24 & op(e2, v28) = v29 & op(e2, v20) = v21 & op(e2, v12) = v13 & % 145.49/20.70 | op(e2, v4) = v5 & op(e2, e3) = v22 & op(e2, e2) = v20 & op(e2, e1) = % 145.49/20.70 | v18 & op(e2, e0) = v16 & op(e1, v26) = v27 & op(e1, v18) = v19 & % 145.49/20.70 | op(e1, v10) = v11 & op(e1, v2) = v3 & op(e1, e3) = v14 & op(e1, e2) % 145.49/20.70 | = v12 & op(e1, e1) = v10 & op(e1, e0) = v8 & op(e0, v24) = v25 & % 145.49/20.70 | op(e0, v16) = v17 & op(e0, v8) = v9 & op(e0, v0) = v1 & op(e0, e3) = % 145.49/20.70 | v6 & op(e0, e2) = v4 & op(e0, e1) = v2 & op(e0, e0) = v0 & $i(v31) & % 145.49/20.70 | $i(v30) & $i(v29) & $i(v28) & $i(v27) & $i(v26) & $i(v25) & $i(v24) % 145.49/20.70 | & $i(v23) & $i(v22) & $i(v21) & $i(v20) & $i(v19) & $i(v18) & % 145.49/20.70 | $i(v17) & $i(v16) & $i(v15) & $i(v14) & $i(v13) & $i(v12) & $i(v11) % 145.49/20.70 | & $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) & % 145.49/20.70 | $i(v3) & $i(v2) & $i(v1) & $i(v0) & ( ~ (v30 = e2) | v28 = e3) & ( ~ % 145.49/20.70 | (v30 = e1) | v26 = e3) & ( ~ (v30 = e0) | v24 = e3) & ( ~ (v20 = % 145.49/20.70 | e3) | v22 = e2) & ( ~ (v20 = e1) | v18 = e2) & ( ~ (v20 = e0) | % 145.49/20.70 | v16 = e2) & ( ~ (v10 = e3) | v14 = e1) & ( ~ (v10 = e2) | v12 = % 145.49/20.70 | e1) & ( ~ (v10 = e0) | v8 = e1) & ( ~ (v0 = e3) | v6 = e0) & ( ~ % 145.49/20.70 | (v0 = e2) | v4 = e0) & ( ~ (v0 = e1) | v2 = e0) & (v30 = e3 | v20 % 145.49/20.70 | = e2 | v10 = e1 | v0 = e0) & (( ~ (v31 = v30) & ~ (v29 = v28) & % 145.49/20.70 | ~ (v27 = v26) & ~ (v25 = v24)) | ( ~ (v23 = v22) & ~ (v21 = % 145.49/20.70 | v20) & ~ (v19 = v18) & ~ (v17 = v16)) | ( ~ (v15 = v14) & ~ % 145.49/20.70 | (v13 = v12) & ~ (v11 = v10) & ~ (v9 = v8)) | ( ~ (v7 = v6) & % 145.49/20.70 | ~ (v5 = v4) & ~ (v3 = v2) & ~ (v1 = v0)))) % 145.49/20.70 | % 145.49/20.70 | ALPHA: (ax6) implies: % 145.49/20.70 | (11) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(v0, v0) = v1 & op(e3, % 145.49/20.70 | v1) = v2 & op(e3, e3) = v0 & $i(v2) & $i(v1) & $i(v0) & ( ~ (v2 = % 145.49/20.70 | e2) | ~ (v1 = e0) | ~ (v0 = e1))) % 145.49/20.70 | % 145.49/20.70 | ALPHA: (ax7) implies: % 145.49/20.70 | (12) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(v0, v0) = v1 & op(e2, % 145.49/20.70 | v1) = v2 & op(e2, e2) = v0 & $i(v2) & $i(v1) & $i(v0) & ( ~ (v2 = % 145.49/20.71 | e3) | ~ (v1 = e0) | ~ (v0 = e1))) % 145.49/20.71 | % 145.49/20.71 | ALPHA: (ax8) implies: % 145.49/20.71 | (13) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(v0, v0) = v1 & op(e3, % 145.49/20.71 | v1) = v2 & op(e3, e3) = v0 & $i(v2) & $i(v1) & $i(v0) & ( ~ (v2 = % 145.49/20.71 | e1) | ~ (v1 = e0) | ~ (v0 = e2))) % 145.49/20.71 | % 145.49/20.71 | ALPHA: (ax9) implies: % 145.49/20.71 | (14) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(v0, v0) = v1 & op(e1, % 145.49/20.71 | v1) = v2 & op(e1, e1) = v0 & $i(v2) & $i(v1) & $i(v0) & ( ~ (v2 = % 145.49/20.71 | e3) | ~ (v1 = e0) | ~ (v0 = e2))) % 145.49/20.71 | % 145.49/20.71 | ALPHA: (ax10) implies: % 145.49/20.71 | (15) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(v0, v0) = v1 & op(e2, % 145.49/20.71 | v1) = v2 & op(e2, e2) = v0 & $i(v2) & $i(v1) & $i(v0) & ( ~ (v2 = % 145.49/20.71 | e1) | ~ (v1 = e0) | ~ (v0 = e3))) % 145.49/20.71 | % 145.49/20.71 | ALPHA: (ax11) implies: % 145.49/20.71 | (16) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(v0, v0) = v1 & op(e1, % 145.49/20.71 | v1) = v2 & op(e1, e1) = v0 & $i(v2) & $i(v1) & $i(v0) & ( ~ (v2 = % 145.49/20.71 | e2) | ~ (v1 = e0) | ~ (v0 = e3))) % 145.49/20.71 | % 145.49/20.71 | ALPHA: (ax12) implies: % 145.49/20.71 | (17) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(v0, v0) = v1 & op(e3, % 145.49/20.71 | v1) = v2 & op(e3, e3) = v0 & $i(v2) & $i(v1) & $i(v0) & ( ~ (v2 = % 145.49/20.71 | e2) | ~ (v1 = e1) | ~ (v0 = e0))) % 145.49/20.71 | % 145.49/20.71 | ALPHA: (ax13) implies: % 145.49/20.71 | (18) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(v0, v0) = v1 & op(e2, % 145.49/20.71 | v1) = v2 & op(e2, e2) = v0 & $i(v2) & $i(v1) & $i(v0) & ( ~ (v2 = % 145.49/20.71 | e3) | ~ (v1 = e1) | ~ (v0 = e0))) % 145.49/20.71 | % 145.49/20.71 | ALPHA: (ax14) implies: % 145.49/20.71 | (19) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(v0, v0) = v1 & op(e3, % 145.49/20.71 | v1) = v2 & op(e3, e3) = v0 & $i(v2) & $i(v1) & $i(v0) & ( ~ (v2 = % 145.49/20.71 | e0) | ~ (v1 = e1) | ~ (v0 = e2))) % 145.49/20.71 | % 145.49/20.71 | ALPHA: (ax15) implies: % 145.96/20.71 | (20) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(v0, v0) = v1 & op(e0, % 145.96/20.71 | v1) = v2 & op(e0, e0) = v0 & $i(v2) & $i(v1) & $i(v0) & ( ~ (v2 = % 145.96/20.71 | e3) | ~ (v1 = e1) | ~ (v0 = e2))) % 145.96/20.71 | % 145.96/20.71 | ALPHA: (ax16) implies: % 145.96/20.71 | (21) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(v0, v0) = v1 & op(e2, % 145.96/20.71 | v1) = v2 & op(e2, e2) = v0 & $i(v2) & $i(v1) & $i(v0) & ( ~ (v2 = % 145.96/20.71 | e0) | ~ (v1 = e1) | ~ (v0 = e3))) % 145.96/20.71 | % 145.96/20.71 | ALPHA: (ax17) implies: % 145.96/20.72 | (22) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(v0, v0) = v1 & op(e0, % 145.96/20.72 | v1) = v2 & op(e0, e0) = v0 & $i(v2) & $i(v1) & $i(v0) & ( ~ (v2 = % 145.96/20.72 | e2) | ~ (v1 = e1) | ~ (v0 = e3))) % 145.96/20.72 | % 145.96/20.72 | ALPHA: (ax18) implies: % 145.96/20.72 | (23) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(v0, v0) = v1 & op(e3, % 145.96/20.72 | v1) = v2 & op(e3, e3) = v0 & $i(v2) & $i(v1) & $i(v0) & ( ~ (v2 = % 145.96/20.72 | e1) | ~ (v1 = e2) | ~ (v0 = e0))) % 145.96/20.72 | % 145.96/20.72 | ALPHA: (ax19) implies: % 145.96/20.72 | (24) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(v0, v0) = v1 & op(e1, % 145.96/20.72 | v1) = v2 & op(e1, e1) = v0 & $i(v2) & $i(v1) & $i(v0) & ( ~ (v2 = % 145.96/20.72 | e3) | ~ (v1 = e2) | ~ (v0 = e0))) % 145.96/20.72 | % 145.96/20.72 | ALPHA: (ax20) implies: % 145.96/20.72 | (25) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(v0, v0) = v1 & op(e3, % 145.96/20.72 | v1) = v2 & op(e3, e3) = v0 & $i(v2) & $i(v1) & $i(v0) & ( ~ (v2 = % 145.96/20.72 | e0) | ~ (v1 = e2) | ~ (v0 = e1))) % 145.96/20.72 | % 145.96/20.72 | ALPHA: (ax21) implies: % 145.96/20.72 | (26) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(v0, v0) = v1 & op(e0, % 145.96/20.72 | v1) = v2 & op(e0, e0) = v0 & $i(v2) & $i(v1) & $i(v0) & ( ~ (v2 = % 145.96/20.72 | e3) | ~ (v1 = e2) | ~ (v0 = e1))) % 145.96/20.72 | % 145.96/20.72 | ALPHA: (ax22) implies: % 145.96/20.72 | (27) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(v0, v0) = v1 & op(e1, % 145.96/20.72 | v1) = v2 & op(e1, e1) = v0 & $i(v2) & $i(v1) & $i(v0) & ( ~ (v2 = % 145.96/20.72 | e0) | ~ (v1 = e2) | ~ (v0 = e3))) % 145.96/20.72 | % 145.96/20.72 | ALPHA: (ax23) implies: % 145.96/20.72 | (28) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(v0, v0) = v1 & op(e0, % 145.96/20.72 | v1) = v2 & op(e0, e0) = v0 & $i(v2) & $i(v1) & $i(v0) & ( ~ (v2 = % 145.96/20.72 | e1) | ~ (v1 = e2) | ~ (v0 = e3))) % 145.96/20.72 | % 145.96/20.72 | ALPHA: (ax24) implies: % 145.96/20.72 | (29) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(v0, v0) = v1 & op(e2, % 145.96/20.72 | v1) = v2 & op(e2, e2) = v0 & $i(v2) & $i(v1) & $i(v0) & ( ~ (v2 = % 145.96/20.72 | e1) | ~ (v1 = e3) | ~ (v0 = e0))) % 145.96/20.72 | % 145.96/20.72 | ALPHA: (ax25) implies: % 145.96/20.72 | (30) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(v0, v0) = v1 & op(e1, % 145.96/20.72 | v1) = v2 & op(e1, e1) = v0 & $i(v2) & $i(v1) & $i(v0) & ( ~ (v2 = % 145.96/20.72 | e2) | ~ (v1 = e3) | ~ (v0 = e0))) % 145.96/20.72 | % 145.96/20.72 | ALPHA: (ax26) implies: % 145.96/20.73 | (31) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(v0, v0) = v1 & op(e2, % 145.96/20.73 | v1) = v2 & op(e2, e2) = v0 & $i(v2) & $i(v1) & $i(v0) & ( ~ (v2 = % 145.96/20.73 | e0) | ~ (v1 = e3) | ~ (v0 = e1))) % 145.96/20.73 | % 145.96/20.73 | ALPHA: (ax27) implies: % 145.96/20.73 | (32) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(v0, v0) = v1 & op(e0, % 145.96/20.73 | v1) = v2 & op(e0, e0) = v0 & $i(v2) & $i(v1) & $i(v0) & ( ~ (v2 = % 145.96/20.73 | e2) | ~ (v1 = e3) | ~ (v0 = e1))) % 145.96/20.73 | % 145.96/20.73 | ALPHA: (ax28) implies: % 145.96/20.73 | (33) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(v0, v0) = v1 & op(e1, % 145.96/20.73 | v1) = v2 & op(e1, e1) = v0 & $i(v2) & $i(v1) & $i(v0) & ( ~ (v2 = % 145.96/20.73 | e0) | ~ (v1 = e3) | ~ (v0 = e2))) % 145.96/20.73 | % 145.96/20.73 | ALPHA: (ax29) implies: % 145.96/20.73 | (34) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(v0, v0) = v1 & op(e0, % 145.96/20.73 | v1) = v2 & op(e0, e0) = v0 & $i(v2) & $i(v1) & $i(v0) & ( ~ (v2 = % 145.96/20.73 | e1) | ~ (v1 = e3) | ~ (v0 = e2))) % 145.96/20.73 | % 145.96/20.73 | DELTA: instantiating (20) with fresh symbols all_4_0, all_4_1, all_4_2 gives: % 145.96/20.73 | (35) op(all_4_2, all_4_2) = all_4_1 & op(e0, all_4_1) = all_4_0 & op(e0, % 145.96/20.73 | e0) = all_4_2 & $i(all_4_0) & $i(all_4_1) & $i(all_4_2) & ( ~ % 145.96/20.73 | (all_4_0 = e3) | ~ (all_4_1 = e1) | ~ (all_4_2 = e2)) % 145.96/20.73 | % 145.96/20.73 | ALPHA: (35) implies: % 145.96/20.73 | (36) op(e0, e0) = all_4_2 % 145.96/20.73 | (37) op(e0, all_4_1) = all_4_0 % 145.96/20.73 | (38) op(all_4_2, all_4_2) = all_4_1 % 145.96/20.73 | (39) ~ (all_4_0 = e3) | ~ (all_4_1 = e1) | ~ (all_4_2 = e2) % 145.96/20.73 | % 145.96/20.73 | DELTA: instantiating (27) with fresh symbols all_6_0, all_6_1, all_6_2 gives: % 145.96/20.73 | (40) op(all_6_2, all_6_2) = all_6_1 & op(e1, all_6_1) = all_6_0 & op(e1, % 145.96/20.73 | e1) = all_6_2 & $i(all_6_0) & $i(all_6_1) & $i(all_6_2) & ( ~ % 145.96/20.73 | (all_6_0 = e0) | ~ (all_6_1 = e2) | ~ (all_6_2 = e3)) % 145.96/20.73 | % 145.96/20.73 | ALPHA: (40) implies: % 145.96/20.73 | (41) op(e1, e1) = all_6_2 % 145.96/20.73 | (42) op(e1, all_6_1) = all_6_0 % 145.96/20.73 | (43) op(all_6_2, all_6_2) = all_6_1 % 145.96/20.73 | (44) ~ (all_6_0 = e0) | ~ (all_6_1 = e2) | ~ (all_6_2 = e3) % 145.96/20.73 | % 145.96/20.73 | DELTA: instantiating (21) with fresh symbols all_8_0, all_8_1, all_8_2 gives: % 145.96/20.73 | (45) op(all_8_2, all_8_2) = all_8_1 & op(e2, all_8_1) = all_8_0 & op(e2, % 145.96/20.73 | e2) = all_8_2 & $i(all_8_0) & $i(all_8_1) & $i(all_8_2) & ( ~ % 145.96/20.73 | (all_8_0 = e0) | ~ (all_8_1 = e1) | ~ (all_8_2 = e3)) % 145.96/20.73 | % 145.96/20.73 | ALPHA: (45) implies: % 145.96/20.73 | (46) op(e2, e2) = all_8_2 % 145.96/20.73 | (47) op(e2, all_8_1) = all_8_0 % 145.96/20.73 | (48) op(all_8_2, all_8_2) = all_8_1 % 145.96/20.73 | (49) ~ (all_8_0 = e0) | ~ (all_8_1 = e1) | ~ (all_8_2 = e3) % 145.96/20.73 | % 145.96/20.73 | DELTA: instantiating (11) with fresh symbols all_10_0, all_10_1, all_10_2 % 145.96/20.73 | gives: % 145.96/20.73 | (50) op(all_10_2, all_10_2) = all_10_1 & op(e3, all_10_1) = all_10_0 & % 145.96/20.73 | op(e3, e3) = all_10_2 & $i(all_10_0) & $i(all_10_1) & $i(all_10_2) & ( % 145.96/20.73 | ~ (all_10_0 = e2) | ~ (all_10_1 = e0) | ~ (all_10_2 = e1)) % 145.96/20.73 | % 145.96/20.73 | ALPHA: (50) implies: % 145.96/20.73 | (51) op(e3, e3) = all_10_2 % 145.96/20.73 | (52) op(e3, all_10_1) = all_10_0 % 145.96/20.74 | (53) op(all_10_2, all_10_2) = all_10_1 % 145.96/20.74 | (54) ~ (all_10_0 = e2) | ~ (all_10_1 = e0) | ~ (all_10_2 = e1) % 145.96/20.74 | % 145.96/20.74 | DELTA: instantiating (22) with fresh symbols all_12_0, all_12_1, all_12_2 % 145.96/20.74 | gives: % 145.96/20.74 | (55) op(all_12_2, all_12_2) = all_12_1 & op(e0, all_12_1) = all_12_0 & % 145.96/20.74 | op(e0, e0) = all_12_2 & $i(all_12_0) & $i(all_12_1) & $i(all_12_2) & ( % 145.96/20.74 | ~ (all_12_0 = e2) | ~ (all_12_1 = e1) | ~ (all_12_2 = e3)) % 145.96/20.74 | % 145.96/20.74 | ALPHA: (55) implies: % 145.96/20.74 | (56) op(e0, e0) = all_12_2 % 145.96/20.74 | (57) op(e0, all_12_1) = all_12_0 % 145.96/20.74 | (58) op(all_12_2, all_12_2) = all_12_1 % 145.96/20.74 | (59) ~ (all_12_0 = e2) | ~ (all_12_1 = e1) | ~ (all_12_2 = e3) % 145.96/20.74 | % 145.96/20.74 | DELTA: instantiating (29) with fresh symbols all_14_0, all_14_1, all_14_2 % 145.96/20.74 | gives: % 145.96/20.74 | (60) op(all_14_2, all_14_2) = all_14_1 & op(e2, all_14_1) = all_14_0 & % 145.96/20.74 | op(e2, e2) = all_14_2 & $i(all_14_0) & $i(all_14_1) & $i(all_14_2) & ( % 145.96/20.74 | ~ (all_14_0 = e1) | ~ (all_14_1 = e3) | ~ (all_14_2 = e0)) % 145.96/20.74 | % 145.96/20.74 | ALPHA: (60) implies: % 145.96/20.74 | (61) op(e2, e2) = all_14_2 % 145.96/20.74 | (62) op(e2, all_14_1) = all_14_0 % 145.96/20.74 | (63) op(all_14_2, all_14_2) = all_14_1 % 145.96/20.74 | (64) ~ (all_14_0 = e1) | ~ (all_14_1 = e3) | ~ (all_14_2 = e0) % 145.96/20.74 | % 145.96/20.74 | DELTA: instantiating (23) with fresh symbols all_16_0, all_16_1, all_16_2 % 145.96/20.74 | gives: % 145.96/20.74 | (65) op(all_16_2, all_16_2) = all_16_1 & op(e3, all_16_1) = all_16_0 & % 145.96/20.74 | op(e3, e3) = all_16_2 & $i(all_16_0) & $i(all_16_1) & $i(all_16_2) & ( % 145.96/20.74 | ~ (all_16_0 = e1) | ~ (all_16_1 = e2) | ~ (all_16_2 = e0)) % 145.96/20.74 | % 145.96/20.74 | ALPHA: (65) implies: % 145.96/20.74 | (66) op(e3, e3) = all_16_2 % 145.96/20.74 | (67) op(e3, all_16_1) = all_16_0 % 145.96/20.74 | (68) op(all_16_2, all_16_2) = all_16_1 % 145.96/20.74 | (69) ~ (all_16_0 = e1) | ~ (all_16_1 = e2) | ~ (all_16_2 = e0) % 145.96/20.74 | % 145.96/20.74 | DELTA: instantiating (24) with fresh symbols all_18_0, all_18_1, all_18_2 % 145.96/20.74 | gives: % 145.96/20.74 | (70) op(all_18_2, all_18_2) = all_18_1 & op(e1, all_18_1) = all_18_0 & % 145.96/20.74 | op(e1, e1) = all_18_2 & $i(all_18_0) & $i(all_18_1) & $i(all_18_2) & ( % 145.96/20.74 | ~ (all_18_0 = e3) | ~ (all_18_1 = e2) | ~ (all_18_2 = e0)) % 145.96/20.74 | % 145.96/20.74 | ALPHA: (70) implies: % 145.96/20.74 | (71) op(e1, e1) = all_18_2 % 145.96/20.74 | (72) op(e1, all_18_1) = all_18_0 % 145.96/20.74 | (73) op(all_18_2, all_18_2) = all_18_1 % 145.96/20.74 | (74) ~ (all_18_0 = e3) | ~ (all_18_1 = e2) | ~ (all_18_2 = e0) % 145.96/20.74 | % 145.96/20.74 | DELTA: instantiating (26) with fresh symbols all_20_0, all_20_1, all_20_2 % 145.96/20.74 | gives: % 145.96/20.74 | (75) op(all_20_2, all_20_2) = all_20_1 & op(e0, all_20_1) = all_20_0 & % 145.96/20.74 | op(e0, e0) = all_20_2 & $i(all_20_0) & $i(all_20_1) & $i(all_20_2) & ( % 145.96/20.74 | ~ (all_20_0 = e3) | ~ (all_20_1 = e2) | ~ (all_20_2 = e1)) % 145.96/20.74 | % 145.96/20.74 | ALPHA: (75) implies: % 145.96/20.74 | (76) op(e0, e0) = all_20_2 % 145.96/20.74 | (77) op(e0, all_20_1) = all_20_0 % 145.96/20.74 | (78) op(all_20_2, all_20_2) = all_20_1 % 145.96/20.74 | (79) ~ (all_20_0 = e3) | ~ (all_20_1 = e2) | ~ (all_20_2 = e1) % 145.96/20.74 | % 145.96/20.74 | DELTA: instantiating (31) with fresh symbols all_22_0, all_22_1, all_22_2 % 145.96/20.74 | gives: % 145.96/20.74 | (80) op(all_22_2, all_22_2) = all_22_1 & op(e2, all_22_1) = all_22_0 & % 145.96/20.74 | op(e2, e2) = all_22_2 & $i(all_22_0) & $i(all_22_1) & $i(all_22_2) & ( % 145.96/20.74 | ~ (all_22_0 = e0) | ~ (all_22_1 = e3) | ~ (all_22_2 = e1)) % 145.96/20.74 | % 145.96/20.74 | ALPHA: (80) implies: % 145.96/20.74 | (81) op(e2, e2) = all_22_2 % 145.96/20.74 | (82) op(e2, all_22_1) = all_22_0 % 145.96/20.74 | (83) op(all_22_2, all_22_2) = all_22_1 % 145.96/20.74 | (84) ~ (all_22_0 = e0) | ~ (all_22_1 = e3) | ~ (all_22_2 = e1) % 145.96/20.74 | % 145.96/20.74 | DELTA: instantiating (13) with fresh symbols all_24_0, all_24_1, all_24_2 % 145.96/20.74 | gives: % 145.96/20.74 | (85) op(all_24_2, all_24_2) = all_24_1 & op(e3, all_24_1) = all_24_0 & % 145.96/20.74 | op(e3, e3) = all_24_2 & $i(all_24_0) & $i(all_24_1) & $i(all_24_2) & ( % 145.96/20.74 | ~ (all_24_0 = e1) | ~ (all_24_1 = e0) | ~ (all_24_2 = e2)) % 145.96/20.74 | % 145.96/20.74 | ALPHA: (85) implies: % 145.96/20.74 | (86) op(e3, e3) = all_24_2 % 145.96/20.74 | (87) op(e3, all_24_1) = all_24_0 % 145.96/20.74 | (88) op(all_24_2, all_24_2) = all_24_1 % 145.96/20.75 | (89) ~ (all_24_0 = e1) | ~ (all_24_1 = e0) | ~ (all_24_2 = e2) % 145.96/20.75 | % 145.96/20.75 | DELTA: instantiating (28) with fresh symbols all_26_0, all_26_1, all_26_2 % 145.96/20.75 | gives: % 145.96/20.75 | (90) op(all_26_2, all_26_2) = all_26_1 & op(e0, all_26_1) = all_26_0 & % 145.96/20.75 | op(e0, e0) = all_26_2 & $i(all_26_0) & $i(all_26_1) & $i(all_26_2) & ( % 145.96/20.75 | ~ (all_26_0 = e1) | ~ (all_26_1 = e2) | ~ (all_26_2 = e3)) % 145.96/20.75 | % 145.96/20.75 | ALPHA: (90) implies: % 145.96/20.75 | (91) op(e0, e0) = all_26_2 % 145.96/20.75 | (92) op(e0, all_26_1) = all_26_0 % 145.96/20.75 | (93) op(all_26_2, all_26_2) = all_26_1 % 145.96/20.75 | (94) ~ (all_26_0 = e1) | ~ (all_26_1 = e2) | ~ (all_26_2 = e3) % 145.96/20.75 | % 145.96/20.75 | DELTA: instantiating (30) with fresh symbols all_28_0, all_28_1, all_28_2 % 145.96/20.75 | gives: % 145.96/20.75 | (95) op(all_28_2, all_28_2) = all_28_1 & op(e1, all_28_1) = all_28_0 & % 145.96/20.75 | op(e1, e1) = all_28_2 & $i(all_28_0) & $i(all_28_1) & $i(all_28_2) & ( % 145.96/20.75 | ~ (all_28_0 = e2) | ~ (all_28_1 = e3) | ~ (all_28_2 = e0)) % 145.96/20.75 | % 145.96/20.75 | ALPHA: (95) implies: % 145.96/20.75 | (96) op(e1, e1) = all_28_2 % 145.96/20.75 | (97) op(e1, all_28_1) = all_28_0 % 145.96/20.75 | (98) op(all_28_2, all_28_2) = all_28_1 % 145.96/20.75 | (99) ~ (all_28_0 = e2) | ~ (all_28_1 = e3) | ~ (all_28_2 = e0) % 145.96/20.75 | % 145.96/20.75 | DELTA: instantiating (12) with fresh symbols all_30_0, all_30_1, all_30_2 % 145.96/20.75 | gives: % 145.96/20.75 | (100) op(all_30_2, all_30_2) = all_30_1 & op(e2, all_30_1) = all_30_0 & % 145.96/20.75 | op(e2, e2) = all_30_2 & $i(all_30_0) & $i(all_30_1) & $i(all_30_2) & % 145.96/20.75 | ( ~ (all_30_0 = e3) | ~ (all_30_1 = e0) | ~ (all_30_2 = e1)) % 145.96/20.75 | % 145.96/20.75 | ALPHA: (100) implies: % 145.96/20.75 | (101) op(e2, e2) = all_30_2 % 145.96/20.75 | (102) op(e2, all_30_1) = all_30_0 % 145.96/20.75 | (103) op(all_30_2, all_30_2) = all_30_1 % 145.96/20.75 | (104) ~ (all_30_0 = e3) | ~ (all_30_1 = e0) | ~ (all_30_2 = e1) % 145.96/20.75 | % 145.96/20.75 | DELTA: instantiating (19) with fresh symbols all_32_0, all_32_1, all_32_2 % 145.96/20.75 | gives: % 145.96/20.75 | (105) op(all_32_2, all_32_2) = all_32_1 & op(e3, all_32_1) = all_32_0 & % 145.96/20.75 | op(e3, e3) = all_32_2 & $i(all_32_0) & $i(all_32_1) & $i(all_32_2) & % 145.96/20.75 | ( ~ (all_32_0 = e0) | ~ (all_32_1 = e1) | ~ (all_32_2 = e2)) % 145.96/20.75 | % 145.96/20.75 | ALPHA: (105) implies: % 145.96/20.75 | (106) op(e3, e3) = all_32_2 % 145.96/20.75 | (107) op(e3, all_32_1) = all_32_0 % 145.96/20.75 | (108) op(all_32_2, all_32_2) = all_32_1 % 145.96/20.75 | (109) ~ (all_32_0 = e0) | ~ (all_32_1 = e1) | ~ (all_32_2 = e2) % 145.96/20.75 | % 145.96/20.75 | DELTA: instantiating (32) with fresh symbols all_34_0, all_34_1, all_34_2 % 145.96/20.75 | gives: % 145.96/20.75 | (110) op(all_34_2, all_34_2) = all_34_1 & op(e0, all_34_1) = all_34_0 & % 145.96/20.75 | op(e0, e0) = all_34_2 & $i(all_34_0) & $i(all_34_1) & $i(all_34_2) & % 145.96/20.75 | ( ~ (all_34_0 = e2) | ~ (all_34_1 = e3) | ~ (all_34_2 = e1)) % 145.96/20.75 | % 145.96/20.75 | ALPHA: (110) implies: % 145.96/20.75 | (111) op(e0, e0) = all_34_2 % 145.96/20.75 | (112) op(e0, all_34_1) = all_34_0 % 145.96/20.75 | (113) op(all_34_2, all_34_2) = all_34_1 % 145.96/20.75 | (114) ~ (all_34_0 = e2) | ~ (all_34_1 = e3) | ~ (all_34_2 = e1) % 145.96/20.75 | % 145.96/20.75 | DELTA: instantiating (33) with fresh symbols all_36_0, all_36_1, all_36_2 % 145.96/20.75 | gives: % 145.96/20.75 | (115) op(all_36_2, all_36_2) = all_36_1 & op(e1, all_36_1) = all_36_0 & % 145.96/20.75 | op(e1, e1) = all_36_2 & $i(all_36_0) & $i(all_36_1) & $i(all_36_2) & % 145.96/20.75 | ( ~ (all_36_0 = e0) | ~ (all_36_1 = e3) | ~ (all_36_2 = e2)) % 145.96/20.75 | % 145.96/20.75 | ALPHA: (115) implies: % 145.96/20.75 | (116) op(e1, e1) = all_36_2 % 145.96/20.75 | (117) op(e1, all_36_1) = all_36_0 % 145.96/20.75 | (118) op(all_36_2, all_36_2) = all_36_1 % 145.96/20.75 | (119) ~ (all_36_0 = e0) | ~ (all_36_1 = e3) | ~ (all_36_2 = e2) % 145.96/20.75 | % 145.96/20.75 | DELTA: instantiating (25) with fresh symbols all_38_0, all_38_1, all_38_2 % 145.96/20.75 | gives: % 145.96/20.75 | (120) op(all_38_2, all_38_2) = all_38_1 & op(e3, all_38_1) = all_38_0 & % 145.96/20.75 | op(e3, e3) = all_38_2 & $i(all_38_0) & $i(all_38_1) & $i(all_38_2) & % 145.96/20.75 | ( ~ (all_38_0 = e0) | ~ (all_38_1 = e2) | ~ (all_38_2 = e1)) % 145.96/20.75 | % 145.96/20.75 | ALPHA: (120) implies: % 145.96/20.75 | (121) op(e3, e3) = all_38_2 % 145.96/20.75 | (122) op(e3, all_38_1) = all_38_0 % 145.96/20.75 | (123) op(all_38_2, all_38_2) = all_38_1 % 145.96/20.75 | (124) ~ (all_38_0 = e0) | ~ (all_38_1 = e2) | ~ (all_38_2 = e1) % 145.96/20.75 | % 145.96/20.75 | DELTA: instantiating (14) with fresh symbols all_40_0, all_40_1, all_40_2 % 145.96/20.75 | gives: % 145.96/20.75 | (125) op(all_40_2, all_40_2) = all_40_1 & op(e1, all_40_1) = all_40_0 & % 145.96/20.75 | op(e1, e1) = all_40_2 & $i(all_40_0) & $i(all_40_1) & $i(all_40_2) & % 145.96/20.75 | ( ~ (all_40_0 = e3) | ~ (all_40_1 = e0) | ~ (all_40_2 = e2)) % 145.96/20.75 | % 145.96/20.75 | ALPHA: (125) implies: % 145.96/20.75 | (126) op(e1, e1) = all_40_2 % 145.96/20.75 | (127) op(e1, all_40_1) = all_40_0 % 145.96/20.75 | (128) op(all_40_2, all_40_2) = all_40_1 % 145.96/20.75 | (129) ~ (all_40_0 = e3) | ~ (all_40_1 = e0) | ~ (all_40_2 = e2) % 145.96/20.75 | % 145.96/20.75 | DELTA: instantiating (15) with fresh symbols all_42_0, all_42_1, all_42_2 % 145.96/20.75 | gives: % 145.96/20.76 | (130) op(all_42_2, all_42_2) = all_42_1 & op(e2, all_42_1) = all_42_0 & % 145.96/20.76 | op(e2, e2) = all_42_2 & $i(all_42_0) & $i(all_42_1) & $i(all_42_2) & % 145.96/20.76 | ( ~ (all_42_0 = e1) | ~ (all_42_1 = e0) | ~ (all_42_2 = e3)) % 145.96/20.76 | % 145.96/20.76 | ALPHA: (130) implies: % 145.96/20.76 | (131) op(e2, e2) = all_42_2 % 145.96/20.76 | (132) op(e2, all_42_1) = all_42_0 % 145.96/20.76 | (133) op(all_42_2, all_42_2) = all_42_1 % 145.96/20.76 | (134) ~ (all_42_0 = e1) | ~ (all_42_1 = e0) | ~ (all_42_2 = e3) % 145.96/20.76 | % 145.96/20.76 | DELTA: instantiating (34) with fresh symbols all_44_0, all_44_1, all_44_2 % 145.96/20.76 | gives: % 145.96/20.76 | (135) op(all_44_2, all_44_2) = all_44_1 & op(e0, all_44_1) = all_44_0 & % 145.96/20.76 | op(e0, e0) = all_44_2 & $i(all_44_0) & $i(all_44_1) & $i(all_44_2) & % 145.96/20.76 | ( ~ (all_44_0 = e1) | ~ (all_44_1 = e3) | ~ (all_44_2 = e2)) % 145.96/20.76 | % 145.96/20.76 | ALPHA: (135) implies: % 145.96/20.76 | (136) op(e0, e0) = all_44_2 % 145.96/20.76 | (137) op(e0, all_44_1) = all_44_0 % 145.96/20.76 | (138) op(all_44_2, all_44_2) = all_44_1 % 145.96/20.76 | (139) ~ (all_44_0 = e1) | ~ (all_44_1 = e3) | ~ (all_44_2 = e2) % 145.96/20.76 | % 145.96/20.76 | DELTA: instantiating (16) with fresh symbols all_46_0, all_46_1, all_46_2 % 145.96/20.76 | gives: % 145.96/20.76 | (140) op(all_46_2, all_46_2) = all_46_1 & op(e1, all_46_1) = all_46_0 & % 145.96/20.76 | op(e1, e1) = all_46_2 & $i(all_46_0) & $i(all_46_1) & $i(all_46_2) & % 145.96/20.76 | ( ~ (all_46_0 = e2) | ~ (all_46_1 = e0) | ~ (all_46_2 = e3)) % 145.96/20.76 | % 145.96/20.76 | ALPHA: (140) implies: % 145.96/20.76 | (141) op(e1, e1) = all_46_2 % 145.96/20.76 | (142) op(e1, all_46_1) = all_46_0 % 145.96/20.76 | (143) op(all_46_2, all_46_2) = all_46_1 % 145.96/20.76 | (144) ~ (all_46_0 = e2) | ~ (all_46_1 = e0) | ~ (all_46_2 = e3) % 145.96/20.76 | % 145.96/20.76 | DELTA: instantiating (18) with fresh symbols all_48_0, all_48_1, all_48_2 % 145.96/20.76 | gives: % 145.96/20.76 | (145) op(all_48_2, all_48_2) = all_48_1 & op(e2, all_48_1) = all_48_0 & % 145.96/20.76 | op(e2, e2) = all_48_2 & $i(all_48_0) & $i(all_48_1) & $i(all_48_2) & % 145.96/20.76 | ( ~ (all_48_0 = e3) | ~ (all_48_1 = e1) | ~ (all_48_2 = e0)) % 145.96/20.76 | % 145.96/20.76 | ALPHA: (145) implies: % 145.96/20.76 | (146) op(e2, e2) = all_48_2 % 145.96/20.76 | (147) op(e2, all_48_1) = all_48_0 % 145.96/20.76 | (148) op(all_48_2, all_48_2) = all_48_1 % 145.96/20.76 | (149) ~ (all_48_0 = e3) | ~ (all_48_1 = e1) | ~ (all_48_2 = e0) % 145.96/20.76 | % 145.96/20.76 | DELTA: instantiating (17) with fresh symbols all_50_0, all_50_1, all_50_2 % 145.96/20.76 | gives: % 145.96/20.76 | (150) op(all_50_2, all_50_2) = all_50_1 & op(e3, all_50_1) = all_50_0 & % 145.96/20.76 | op(e3, e3) = all_50_2 & $i(all_50_0) & $i(all_50_1) & $i(all_50_2) & % 145.96/20.76 | ( ~ (all_50_0 = e2) | ~ (all_50_1 = e1) | ~ (all_50_2 = e0)) % 145.96/20.76 | % 145.96/20.76 | ALPHA: (150) implies: % 145.96/20.76 | (151) op(e3, e3) = all_50_2 % 145.96/20.76 | (152) op(e3, all_50_1) = all_50_0 % 145.96/20.76 | (153) op(all_50_2, all_50_2) = all_50_1 % 145.96/20.76 | (154) ~ (all_50_0 = e2) | ~ (all_50_1 = e1) | ~ (all_50_2 = e0) % 145.96/20.76 | % 145.96/20.76 | DELTA: instantiating (3) with fresh symbols all_52_0, all_52_1, all_52_2, % 145.96/20.76 | all_52_3, all_52_4, all_52_5, all_52_6, all_52_7, all_52_8, all_52_9, % 145.96/20.76 | all_52_10, all_52_11, all_52_12, all_52_13, all_52_14, all_52_15 gives: % 145.96/20.76 | (155) ~ (all_52_0 = all_52_1) & ~ (all_52_0 = all_52_2) & ~ (all_52_0 = % 145.96/20.76 | all_52_3) & ~ (all_52_0 = all_52_4) & ~ (all_52_0 = all_52_8) & % 145.96/20.76 | ~ (all_52_0 = all_52_12) & ~ (all_52_1 = all_52_2) & ~ (all_52_1 = % 145.96/20.76 | all_52_3) & ~ (all_52_1 = all_52_5) & ~ (all_52_1 = all_52_9) & % 145.96/20.76 | ~ (all_52_1 = all_52_13) & ~ (all_52_2 = all_52_3) & ~ (all_52_2 = % 145.96/20.76 | all_52_6) & ~ (all_52_2 = all_52_10) & ~ (all_52_2 = all_52_14) & % 145.96/20.76 | ~ (all_52_3 = all_52_7) & ~ (all_52_3 = all_52_11) & ~ (all_52_3 = % 145.96/20.76 | all_52_15) & ~ (all_52_4 = all_52_5) & ~ (all_52_4 = all_52_6) & % 145.96/20.76 | ~ (all_52_4 = all_52_7) & ~ (all_52_4 = all_52_8) & ~ (all_52_4 = % 145.96/20.76 | all_52_12) & ~ (all_52_5 = all_52_6) & ~ (all_52_5 = all_52_7) & % 145.96/20.76 | ~ (all_52_5 = all_52_9) & ~ (all_52_5 = all_52_13) & ~ (all_52_6 = % 145.96/20.76 | all_52_7) & ~ (all_52_6 = all_52_10) & ~ (all_52_6 = all_52_14) & % 145.96/20.76 | ~ (all_52_7 = all_52_11) & ~ (all_52_7 = all_52_15) & ~ (all_52_8 % 145.96/20.76 | = all_52_9) & ~ (all_52_8 = all_52_10) & ~ (all_52_8 = all_52_11) % 145.96/20.76 | & ~ (all_52_8 = all_52_12) & ~ (all_52_9 = all_52_10) & ~ % 145.96/20.76 | (all_52_9 = all_52_11) & ~ (all_52_9 = all_52_13) & ~ (all_52_10 = % 145.96/20.76 | all_52_11) & ~ (all_52_10 = all_52_14) & ~ (all_52_11 = % 145.96/20.76 | all_52_15) & ~ (all_52_12 = all_52_13) & ~ (all_52_12 = % 145.96/20.76 | all_52_14) & ~ (all_52_12 = all_52_15) & ~ (all_52_13 = % 145.96/20.76 | all_52_14) & ~ (all_52_13 = all_52_15) & ~ (all_52_14 = % 145.96/20.76 | all_52_15) & op(e3, e3) = all_52_0 & op(e3, e2) = all_52_4 & op(e3, % 145.96/20.76 | e1) = all_52_8 & op(e3, e0) = all_52_12 & op(e2, e3) = all_52_1 & % 145.96/20.76 | op(e2, e2) = all_52_5 & op(e2, e1) = all_52_9 & op(e2, e0) = % 145.96/20.76 | all_52_13 & op(e1, e3) = all_52_2 & op(e1, e2) = all_52_6 & op(e1, % 145.96/20.76 | e1) = all_52_10 & op(e1, e0) = all_52_14 & op(e0, e3) = all_52_3 & % 145.96/20.76 | op(e0, e2) = all_52_7 & op(e0, e1) = all_52_11 & op(e0, e0) = % 145.96/20.76 | all_52_15 & $i(all_52_0) & $i(all_52_1) & $i(all_52_2) & $i(all_52_3) % 145.96/20.76 | & $i(all_52_4) & $i(all_52_5) & $i(all_52_6) & $i(all_52_7) & % 145.96/20.76 | $i(all_52_8) & $i(all_52_9) & $i(all_52_10) & $i(all_52_11) & % 145.96/20.76 | $i(all_52_12) & $i(all_52_13) & $i(all_52_14) & $i(all_52_15) % 145.96/20.76 | % 145.96/20.76 | ALPHA: (155) implies: % 145.96/20.76 | (156) ~ (all_52_14 = all_52_15) % 145.96/20.76 | (157) ~ (all_52_13 = all_52_15) % 145.96/20.76 | (158) ~ (all_52_13 = all_52_14) % 145.96/20.76 | (159) ~ (all_52_12 = all_52_15) % 145.96/20.76 | (160) ~ (all_52_12 = all_52_14) % 145.96/20.76 | (161) ~ (all_52_12 = all_52_13) % 145.96/20.76 | (162) ~ (all_52_11 = all_52_15) % 145.96/20.76 | (163) ~ (all_52_10 = all_52_14) % 145.96/20.76 | (164) ~ (all_52_10 = all_52_11) % 145.96/20.76 | (165) ~ (all_52_9 = all_52_13) % 145.96/20.76 | (166) ~ (all_52_9 = all_52_11) % 145.96/20.76 | (167) ~ (all_52_9 = all_52_10) % 145.96/20.76 | (168) ~ (all_52_8 = all_52_12) % 145.96/20.76 | (169) ~ (all_52_8 = all_52_11) % 145.96/20.76 | (170) ~ (all_52_8 = all_52_10) % 145.96/20.76 | (171) ~ (all_52_8 = all_52_9) % 145.96/20.76 | (172) ~ (all_52_7 = all_52_15) % 145.96/20.76 | (173) ~ (all_52_7 = all_52_11) % 145.96/20.76 | (174) ~ (all_52_6 = all_52_14) % 145.96/20.76 | (175) ~ (all_52_6 = all_52_10) % 145.96/20.76 | (176) ~ (all_52_6 = all_52_7) % 145.96/20.77 | (177) ~ (all_52_5 = all_52_13) % 145.96/20.77 | (178) ~ (all_52_5 = all_52_9) % 145.96/20.77 | (179) ~ (all_52_5 = all_52_7) % 145.96/20.77 | (180) ~ (all_52_5 = all_52_6) % 145.96/20.77 | (181) ~ (all_52_4 = all_52_12) % 145.96/20.77 | (182) ~ (all_52_4 = all_52_8) % 145.96/20.77 | (183) ~ (all_52_4 = all_52_7) % 145.96/20.77 | (184) ~ (all_52_4 = all_52_6) % 145.96/20.77 | (185) ~ (all_52_4 = all_52_5) % 145.96/20.77 | (186) ~ (all_52_3 = all_52_15) % 145.96/20.77 | (187) ~ (all_52_3 = all_52_11) % 145.96/20.77 | (188) ~ (all_52_3 = all_52_7) % 145.96/20.77 | (189) ~ (all_52_2 = all_52_14) % 145.96/20.77 | (190) ~ (all_52_2 = all_52_10) % 145.96/20.77 | (191) ~ (all_52_2 = all_52_6) % 145.96/20.77 | (192) ~ (all_52_2 = all_52_3) % 145.96/20.77 | (193) ~ (all_52_1 = all_52_13) % 145.96/20.77 | (194) ~ (all_52_1 = all_52_9) % 145.96/20.77 | (195) ~ (all_52_1 = all_52_5) % 145.96/20.77 | (196) ~ (all_52_1 = all_52_3) % 145.96/20.77 | (197) ~ (all_52_1 = all_52_2) % 145.96/20.77 | (198) ~ (all_52_0 = all_52_12) % 145.96/20.77 | (199) ~ (all_52_0 = all_52_8) % 145.96/20.77 | (200) ~ (all_52_0 = all_52_4) % 145.96/20.77 | (201) ~ (all_52_0 = all_52_3) % 145.96/20.77 | (202) ~ (all_52_0 = all_52_2) % 145.96/20.77 | (203) ~ (all_52_0 = all_52_1) % 145.96/20.77 | (204) op(e0, e0) = all_52_15 % 145.96/20.77 | (205) op(e0, e1) = all_52_11 % 145.96/20.77 | (206) op(e0, e2) = all_52_7 % 145.96/20.77 | (207) op(e0, e3) = all_52_3 % 145.96/20.77 | (208) op(e1, e0) = all_52_14 % 145.96/20.77 | (209) op(e1, e1) = all_52_10 % 145.96/20.77 | (210) op(e1, e2) = all_52_6 % 145.96/20.77 | (211) op(e1, e3) = all_52_2 % 145.96/20.77 | (212) op(e2, e0) = all_52_13 % 145.96/20.77 | (213) op(e2, e1) = all_52_9 % 145.96/20.77 | (214) op(e2, e2) = all_52_5 % 145.96/20.77 | (215) op(e2, e3) = all_52_1 % 145.96/20.77 | (216) op(e3, e0) = all_52_12 % 145.96/20.77 | (217) op(e3, e1) = all_52_8 % 145.96/20.77 | (218) op(e3, e2) = all_52_4 % 145.96/20.77 | (219) op(e3, e3) = all_52_0 % 145.96/20.77 | % 145.96/20.77 | DELTA: instantiating (1) with fresh symbols all_54_0, all_54_1, all_54_2, % 145.96/20.77 | all_54_3, all_54_4, all_54_5, all_54_6, all_54_7, all_54_8, all_54_9, % 145.96/20.77 | all_54_10, all_54_11, all_54_12, all_54_13, all_54_14, all_54_15 gives: % 145.96/20.77 | (220) op(e3, e3) = all_54_0 & op(e3, e2) = all_54_1 & op(e3, e1) = all_54_2 % 145.96/20.77 | & op(e3, e0) = all_54_3 & op(e2, e3) = all_54_4 & op(e2, e2) = % 145.96/20.77 | all_54_5 & op(e2, e1) = all_54_6 & op(e2, e0) = all_54_7 & op(e1, e3) % 145.96/20.77 | = all_54_8 & op(e1, e2) = all_54_9 & op(e1, e1) = all_54_10 & op(e1, % 145.96/20.77 | e0) = all_54_11 & op(e0, e3) = all_54_12 & op(e0, e2) = all_54_13 & % 145.96/20.77 | op(e0, e1) = all_54_14 & op(e0, e0) = all_54_15 & $i(all_54_0) & % 145.96/20.77 | $i(all_54_1) & $i(all_54_2) & $i(all_54_3) & $i(all_54_4) & % 145.96/20.77 | $i(all_54_5) & $i(all_54_6) & $i(all_54_7) & $i(all_54_8) & % 145.96/20.77 | $i(all_54_9) & $i(all_54_10) & $i(all_54_11) & $i(all_54_12) & % 145.96/20.77 | $i(all_54_13) & $i(all_54_14) & $i(all_54_15) & (all_54_0 = e3 | % 145.96/20.77 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0) & (all_54_1 = e3 | % 145.96/20.77 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0) & (all_54_2 = e3 | % 145.96/20.77 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0) & (all_54_3 = e3 | % 145.96/20.77 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0) & (all_54_4 = e3 | % 145.96/20.77 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0) & (all_54_5 = e3 | % 145.96/20.77 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0) & (all_54_6 = e3 | % 145.96/20.77 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0) & (all_54_7 = e3 | % 145.96/20.77 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0) & (all_54_8 = e3 | % 145.96/20.77 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0) & (all_54_9 = e3 | % 145.96/20.77 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0) & (all_54_10 = e3 | % 145.96/20.77 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0) & (all_54_11 = e3 % 145.96/20.77 | | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0) & (all_54_12 = % 145.96/20.77 | e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0) & (all_54_13 % 145.96/20.77 | = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0) & % 145.96/20.77 | (all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0) & % 145.96/20.77 | (all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0) % 145.96/20.77 | % 145.96/20.77 | ALPHA: (220) implies: % 145.96/20.77 | (221) op(e0, e0) = all_54_15 % 145.96/20.77 | (222) op(e0, e1) = all_54_14 % 145.96/20.77 | (223) op(e0, e2) = all_54_13 % 145.96/20.77 | (224) op(e0, e3) = all_54_12 % 145.96/20.77 | (225) op(e1, e0) = all_54_11 % 145.96/20.77 | (226) op(e1, e1) = all_54_10 % 145.96/20.77 | (227) op(e1, e2) = all_54_9 % 145.96/20.77 | (228) op(e1, e3) = all_54_8 % 145.96/20.77 | (229) op(e2, e0) = all_54_7 % 145.96/20.77 | (230) op(e2, e1) = all_54_6 % 145.96/20.77 | (231) op(e2, e2) = all_54_5 % 145.96/20.77 | (232) op(e2, e3) = all_54_4 % 145.96/20.77 | (233) op(e3, e0) = all_54_3 % 145.96/20.77 | (234) op(e3, e1) = all_54_2 % 145.96/20.77 | (235) op(e3, e2) = all_54_1 % 145.96/20.77 | (236) op(e3, e3) = all_54_0 % 145.96/20.77 | (237) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0 % 145.96/20.77 | (238) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0 % 145.96/20.77 | (239) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0 % 145.96/20.77 | (240) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0 % 145.96/20.77 | (241) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0 % 145.96/20.77 | (242) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 145.96/20.77 | (243) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0 % 145.96/20.77 | (244) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0 % 145.96/20.77 | (245) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0 % 145.96/20.77 | (246) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0 % 145.96/20.78 | (247) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 145.96/20.78 | (248) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0 % 145.96/20.78 | (249) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0 % 145.96/20.78 | (250) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0 % 145.96/20.78 | (251) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0 % 145.96/20.78 | (252) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 145.96/20.78 | % 145.96/20.78 | DELTA: instantiating (10) with fresh symbols all_56_0, all_56_1, all_56_2, % 145.96/20.78 | all_56_3, all_56_4, all_56_5, all_56_6, all_56_7, all_56_8, all_56_9, % 145.96/20.78 | all_56_10, all_56_11, all_56_12, all_56_13, all_56_14, all_56_15, % 145.96/20.78 | all_56_16, all_56_17, all_56_18, all_56_19, all_56_20, all_56_21, % 145.96/20.78 | all_56_22, all_56_23, all_56_24, all_56_25, all_56_26, all_56_27, % 145.96/20.78 | all_56_28, all_56_29, all_56_30, all_56_31 gives: % 145.96/20.78 | (253) op(e3, all_56_1) = all_56_0 & op(e3, all_56_9) = all_56_8 & op(e3, % 145.96/20.78 | all_56_17) = all_56_16 & op(e3, all_56_25) = all_56_24 & op(e3, e3) % 145.96/20.78 | = all_56_1 & op(e3, e2) = all_56_3 & op(e3, e1) = all_56_5 & op(e3, % 145.96/20.78 | e0) = all_56_7 & op(e2, all_56_3) = all_56_2 & op(e2, all_56_11) = % 145.96/20.78 | all_56_10 & op(e2, all_56_19) = all_56_18 & op(e2, all_56_27) = % 145.96/20.78 | all_56_26 & op(e2, e3) = all_56_9 & op(e2, e2) = all_56_11 & op(e2, % 145.96/20.78 | e1) = all_56_13 & op(e2, e0) = all_56_15 & op(e1, all_56_5) = % 145.96/20.78 | all_56_4 & op(e1, all_56_13) = all_56_12 & op(e1, all_56_21) = % 145.96/20.78 | all_56_20 & op(e1, all_56_29) = all_56_28 & op(e1, e3) = all_56_17 & % 145.96/20.78 | op(e1, e2) = all_56_19 & op(e1, e1) = all_56_21 & op(e1, e0) = % 145.96/20.78 | all_56_23 & op(e0, all_56_7) = all_56_6 & op(e0, all_56_15) = % 145.96/20.78 | all_56_14 & op(e0, all_56_23) = all_56_22 & op(e0, all_56_31) = % 145.96/20.78 | all_56_30 & op(e0, e3) = all_56_25 & op(e0, e2) = all_56_27 & op(e0, % 145.96/20.78 | e1) = all_56_29 & op(e0, e0) = all_56_31 & $i(all_56_0) & % 145.96/20.78 | $i(all_56_1) & $i(all_56_2) & $i(all_56_3) & $i(all_56_4) & % 145.96/20.78 | $i(all_56_5) & $i(all_56_6) & $i(all_56_7) & $i(all_56_8) & % 145.96/20.78 | $i(all_56_9) & $i(all_56_10) & $i(all_56_11) & $i(all_56_12) & % 145.96/20.78 | $i(all_56_13) & $i(all_56_14) & $i(all_56_15) & $i(all_56_16) & % 145.96/20.78 | $i(all_56_17) & $i(all_56_18) & $i(all_56_19) & $i(all_56_20) & % 145.96/20.78 | $i(all_56_21) & $i(all_56_22) & $i(all_56_23) & $i(all_56_24) & % 145.96/20.78 | $i(all_56_25) & $i(all_56_26) & $i(all_56_27) & $i(all_56_28) & % 145.96/20.78 | $i(all_56_29) & $i(all_56_30) & $i(all_56_31) & ( ~ (all_56_1 = e2) | % 145.96/20.78 | all_56_3 = e3) & ( ~ (all_56_1 = e1) | all_56_5 = e3) & ( ~ % 145.96/20.78 | (all_56_1 = e0) | all_56_7 = e3) & ( ~ (all_56_11 = e3) | all_56_9 % 145.96/20.78 | = e2) & ( ~ (all_56_11 = e1) | all_56_13 = e2) & ( ~ (all_56_11 = % 145.96/20.78 | e0) | all_56_15 = e2) & ( ~ (all_56_21 = e3) | all_56_17 = e1) & % 145.96/20.78 | ( ~ (all_56_21 = e2) | all_56_19 = e1) & ( ~ (all_56_21 = e0) | % 145.96/20.78 | all_56_23 = e1) & ( ~ (all_56_31 = e3) | all_56_25 = e0) & ( ~ % 145.96/20.78 | (all_56_31 = e2) | all_56_27 = e0) & ( ~ (all_56_31 = e1) | % 145.96/20.78 | all_56_29 = e0) & (all_56_1 = e3 | all_56_11 = e2 | all_56_21 = e1 % 145.96/20.78 | | all_56_31 = e0) & (( ~ (all_56_0 = all_56_1) & ~ (all_56_2 = % 145.96/20.78 | all_56_3) & ~ (all_56_4 = all_56_5) & ~ (all_56_6 = % 145.96/20.78 | all_56_7)) | ( ~ (all_56_8 = all_56_9) & ~ (all_56_10 = % 145.96/20.78 | all_56_11) & ~ (all_56_12 = all_56_13) & ~ (all_56_14 = % 145.96/20.78 | all_56_15)) | ( ~ (all_56_16 = all_56_17) & ~ (all_56_18 = % 145.96/20.78 | all_56_19) & ~ (all_56_20 = all_56_21) & ~ (all_56_22 = % 145.96/20.78 | all_56_23)) | ( ~ (all_56_24 = all_56_25) & ~ (all_56_26 = % 145.96/20.78 | all_56_27) & ~ (all_56_28 = all_56_29) & ~ (all_56_30 = % 145.96/20.78 | all_56_31))) % 145.96/20.78 | % 145.96/20.78 | ALPHA: (253) implies: % 145.96/20.78 | (254) op(e0, e0) = all_56_31 % 145.96/20.78 | (255) op(e0, e1) = all_56_29 % 145.96/20.78 | (256) op(e0, e2) = all_56_27 % 145.96/20.78 | (257) op(e0, e3) = all_56_25 % 145.96/20.78 | (258) op(e0, all_56_31) = all_56_30 % 145.96/20.78 | (259) op(e0, all_56_23) = all_56_22 % 145.96/20.78 | (260) op(e0, all_56_15) = all_56_14 % 145.96/20.78 | (261) op(e0, all_56_7) = all_56_6 % 145.96/20.78 | (262) op(e1, e0) = all_56_23 % 145.96/20.78 | (263) op(e1, e1) = all_56_21 % 145.96/20.78 | (264) op(e1, e2) = all_56_19 % 145.96/20.78 | (265) op(e1, e3) = all_56_17 % 145.96/20.78 | (266) op(e1, all_56_29) = all_56_28 % 145.96/20.78 | (267) op(e1, all_56_21) = all_56_20 % 145.96/20.78 | (268) op(e1, all_56_13) = all_56_12 % 145.96/20.78 | (269) op(e1, all_56_5) = all_56_4 % 145.96/20.78 | (270) op(e2, e0) = all_56_15 % 145.96/20.78 | (271) op(e2, e1) = all_56_13 % 145.96/20.78 | (272) op(e2, e2) = all_56_11 % 145.96/20.78 | (273) op(e2, e3) = all_56_9 % 145.96/20.78 | (274) op(e2, all_56_27) = all_56_26 % 145.96/20.78 | (275) op(e2, all_56_19) = all_56_18 % 145.96/20.78 | (276) op(e2, all_56_11) = all_56_10 % 145.96/20.78 | (277) op(e2, all_56_3) = all_56_2 % 145.96/20.78 | (278) op(e3, e0) = all_56_7 % 145.96/20.78 | (279) op(e3, e1) = all_56_5 % 145.96/20.78 | (280) op(e3, e2) = all_56_3 % 145.96/20.78 | (281) op(e3, e3) = all_56_1 % 145.96/20.78 | (282) op(e3, all_56_25) = all_56_24 % 145.96/20.78 | (283) op(e3, all_56_17) = all_56_16 % 145.96/20.78 | (284) op(e3, all_56_9) = all_56_8 % 145.96/20.78 | (285) op(e3, all_56_1) = all_56_0 % 145.96/20.78 | (286) ( ~ (all_56_0 = all_56_1) & ~ (all_56_2 = all_56_3) & ~ (all_56_4 = % 145.96/20.78 | all_56_5) & ~ (all_56_6 = all_56_7)) | ( ~ (all_56_8 = all_56_9) % 145.96/20.78 | & ~ (all_56_10 = all_56_11) & ~ (all_56_12 = all_56_13) & ~ % 145.96/20.78 | (all_56_14 = all_56_15)) | ( ~ (all_56_16 = all_56_17) & ~ % 145.96/20.78 | (all_56_18 = all_56_19) & ~ (all_56_20 = all_56_21) & ~ % 145.96/20.78 | (all_56_22 = all_56_23)) | ( ~ (all_56_24 = all_56_25) & ~ % 145.96/20.78 | (all_56_26 = all_56_27) & ~ (all_56_28 = all_56_29) & ~ % 145.96/20.78 | (all_56_30 = all_56_31)) % 145.96/20.78 | (287) all_56_1 = e3 | all_56_11 = e2 | all_56_21 = e1 | all_56_31 = e0 % 145.96/20.78 | (288) ~ (all_56_31 = e1) | all_56_29 = e0 % 145.96/20.78 | (289) ~ (all_56_31 = e2) | all_56_27 = e0 % 145.96/20.78 | (290) ~ (all_56_31 = e3) | all_56_25 = e0 % 145.96/20.78 | (291) ~ (all_56_21 = e0) | all_56_23 = e1 % 145.96/20.78 | (292) ~ (all_56_21 = e2) | all_56_19 = e1 % 145.96/20.78 | (293) ~ (all_56_21 = e3) | all_56_17 = e1 % 145.96/20.78 | (294) ~ (all_56_11 = e0) | all_56_15 = e2 % 145.96/20.78 | (295) ~ (all_56_11 = e1) | all_56_13 = e2 % 145.96/20.78 | (296) ~ (all_56_11 = e3) | all_56_9 = e2 % 145.96/20.78 | (297) ~ (all_56_1 = e0) | all_56_7 = e3 % 145.96/20.78 | (298) ~ (all_56_1 = e1) | all_56_5 = e3 % 145.96/20.78 | (299) ~ (all_56_1 = e2) | all_56_3 = e3 % 145.96/20.78 | % 145.96/20.78 | DELTA: instantiating (2) with fresh symbols all_58_0, all_58_1, all_58_2, % 145.96/20.78 | all_58_3, all_58_4, all_58_5, all_58_6, all_58_7, all_58_8, all_58_9, % 145.96/20.78 | all_58_10, all_58_11, all_58_12, all_58_13, all_58_14, all_58_15 gives: % 145.96/20.79 | (300) op(e3, e3) = all_58_0 & op(e3, e2) = all_58_1 & op(e3, e1) = all_58_4 % 145.96/20.79 | & op(e3, e0) = all_58_9 & op(e2, e3) = all_58_2 & op(e2, e2) = % 145.96/20.79 | all_58_3 & op(e2, e1) = all_58_5 & op(e2, e0) = all_58_10 & op(e1, % 145.96/20.79 | e3) = all_58_6 & op(e1, e2) = all_58_7 & op(e1, e1) = all_58_8 & % 145.96/20.79 | op(e1, e0) = all_58_11 & op(e0, e3) = all_58_12 & op(e0, e2) = % 145.96/20.79 | all_58_13 & op(e0, e1) = all_58_14 & op(e0, e0) = all_58_15 & % 145.96/20.79 | $i(all_58_0) & $i(all_58_1) & $i(all_58_2) & $i(all_58_3) & % 145.96/20.79 | $i(all_58_4) & $i(all_58_5) & $i(all_58_6) & $i(all_58_7) & % 145.96/20.79 | $i(all_58_8) & $i(all_58_9) & $i(all_58_10) & $i(all_58_11) & % 145.96/20.79 | $i(all_58_12) & $i(all_58_13) & $i(all_58_14) & $i(all_58_15) & % 145.96/20.79 | (all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3) & % 145.96/20.79 | (all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3) & % 145.96/20.79 | (all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2) & % 145.96/20.79 | (all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2) & % 145.96/20.79 | (all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1) & % 145.96/20.79 | (all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1) & % 145.96/20.79 | (all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0) & % 145.96/20.79 | (all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0) & % 145.96/20.79 | (all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3) & % 145.96/20.79 | (all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2) & % 145.96/20.79 | (all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1) & % 145.96/20.79 | (all_58_1 = e0 | all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0) & % 145.96/20.79 | (all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3) & % 145.96/20.79 | (all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2) & % 145.96/20.79 | (all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1) & % 145.96/20.79 | (all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0) & % 145.96/20.79 | (all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3) & % 145.96/20.79 | (all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2) & % 145.96/20.79 | (all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1) & % 145.96/20.79 | (all_58_4 = e0 | all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0) & % 145.96/20.79 | (all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3) & % 145.96/20.79 | (all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2) & % 145.96/20.79 | (all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1) & % 145.96/20.79 | (all_58_6 = e0 | all_58_7 = e0 | all_58_8 = e0 | all_58_11 = e0) & % 145.96/20.79 | (all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3) & % 145.96/20.79 | (all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2) & % 145.96/20.79 | (all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1) & % 145.96/20.79 | (all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3) & % 145.96/20.79 | (all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2) & % 145.96/20.79 | (all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1) & % 145.96/20.79 | (all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) % 145.96/20.79 | & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0))) % 145.96/20.79 | % 145.96/20.79 | ALPHA: (300) implies: % 145.96/20.79 | (301) op(e0, e0) = all_58_15 % 145.96/20.79 | (302) op(e0, e1) = all_58_14 % 145.96/20.79 | (303) op(e0, e2) = all_58_13 % 145.96/20.79 | (304) op(e0, e3) = all_58_12 % 145.96/20.79 | (305) op(e1, e0) = all_58_11 % 145.96/20.79 | (306) op(e1, e1) = all_58_8 % 145.96/20.79 | (307) op(e1, e2) = all_58_7 % 145.96/20.79 | (308) op(e1, e3) = all_58_6 % 145.96/20.79 | (309) op(e2, e0) = all_58_10 % 145.96/20.79 | (310) op(e2, e1) = all_58_5 % 145.96/20.79 | (311) op(e2, e2) = all_58_3 % 145.96/20.79 | (312) op(e2, e3) = all_58_2 % 145.96/20.79 | (313) op(e3, e0) = all_58_9 % 145.96/20.79 | (314) op(e3, e1) = all_58_4 % 145.96/20.79 | (315) op(e3, e2) = all_58_1 % 145.96/20.79 | (316) op(e3, e3) = all_58_0 % 145.96/20.79 | (317) all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) & % 145.96/20.79 | (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0)) % 145.96/20.79 | (318) all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1 % 145.96/20.79 | (319) all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2 % 145.96/20.79 | (320) all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3 % 145.96/20.79 | (321) all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1 % 145.96/20.79 | (322) all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2 % 145.96/20.79 | (323) all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3 % 145.96/20.79 | (324) all_58_6 = e0 | all_58_7 = e0 | all_58_8 = e0 | all_58_11 = e0 % 145.96/20.79 | (325) all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1 % 145.96/20.79 | (326) all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2 % 145.96/20.79 | (327) all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3 % 145.96/20.79 | (328) all_58_4 = e0 | all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0 % 145.96/20.79 | (329) all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1 % 145.96/20.79 | (330) all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2 % 145.96/20.79 | (331) all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3 % 145.96/20.79 | (332) all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0 % 145.96/20.79 | (333) all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1 % 145.96/20.79 | (334) all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2 % 145.96/20.79 | (335) all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3 % 145.96/20.79 | (336) all_58_1 = e0 | all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0 % 145.96/20.79 | (337) all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1 % 145.96/20.79 | (338) all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2 % 145.96/20.79 | (339) all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3 % 145.96/20.79 | (340) all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0 % 145.96/20.79 | (341) all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0 % 145.96/20.79 | (342) all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1 % 145.96/20.79 | (343) all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1 % 145.96/20.79 | (344) all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2 % 145.96/20.79 | (345) all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2 % 145.96/20.80 | (346) all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3 % 145.96/20.80 | (347) all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3 % 145.96/20.80 | % 145.96/20.80 | GROUND_INST: instantiating (function-axioms) with all_26_2, all_34_2, e0, e0, % 145.96/20.80 | simplifying with (91), (111) gives: % 145.96/20.80 | (348) all_34_2 = all_26_2 % 145.96/20.80 | % 145.96/20.80 | GROUND_INST: instantiating (function-axioms) with all_34_2, all_44_2, e0, e0, % 145.96/20.80 | simplifying with (111), (136) gives: % 145.96/20.80 | (349) all_44_2 = all_34_2 % 145.96/20.80 | % 145.96/20.80 | GROUND_INST: instantiating (function-axioms) with all_26_2, all_52_15, e0, e0, % 145.96/20.80 | simplifying with (91), (204) gives: % 145.96/20.80 | (350) all_52_15 = all_26_2 % 145.96/20.80 | % 145.96/20.80 | GROUND_INST: instantiating (function-axioms) with all_4_2, all_52_15, e0, e0, % 145.96/20.80 | simplifying with (36), (204) gives: % 145.96/20.80 | (351) all_52_15 = all_4_2 % 145.96/20.80 | % 145.96/20.80 | GROUND_INST: instantiating (function-axioms) with all_44_2, all_54_15, e0, e0, % 145.96/20.80 | simplifying with (136), (221) gives: % 145.96/20.80 | (352) all_54_15 = all_44_2 % 145.96/20.80 | % 145.96/20.80 | GROUND_INST: instantiating (function-axioms) with all_52_15, all_56_31, e0, % 145.96/20.80 | e0, simplifying with (204), (254) gives: % 145.96/20.80 | (353) all_56_31 = all_52_15 % 145.96/20.80 | % 145.96/20.80 | GROUND_INST: instantiating (function-axioms) with all_20_2, all_56_31, e0, e0, % 145.96/20.80 | simplifying with (76), (254) gives: % 145.96/20.80 | (354) all_56_31 = all_20_2 % 145.96/20.80 | % 145.96/20.80 | GROUND_INST: instantiating (function-axioms) with all_54_15, all_58_15, e0, % 145.96/20.80 | e0, simplifying with (221), (301) gives: % 145.96/20.80 | (355) all_58_15 = all_54_15 % 145.96/20.80 | % 145.96/20.80 | GROUND_INST: instantiating (function-axioms) with all_12_2, all_58_15, e0, e0, % 145.96/20.80 | simplifying with (56), (301) gives: % 145.96/20.80 | (356) all_58_15 = all_12_2 % 145.96/20.80 | % 145.96/20.80 | GROUND_INST: instantiating (function-axioms) with all_52_11, all_56_29, e1, % 145.96/20.80 | e0, simplifying with (205), (255) gives: % 145.96/20.80 | (357) all_56_29 = all_52_11 % 145.96/20.80 | % 145.96/20.80 | GROUND_INST: instantiating (function-axioms) with all_56_29, all_58_14, e1, % 145.96/20.80 | e0, simplifying with (255), (302) gives: % 145.96/20.80 | (358) all_58_14 = all_56_29 % 145.96/20.80 | % 145.96/20.80 | GROUND_INST: instantiating (function-axioms) with all_54_14, all_58_14, e1, % 145.96/20.80 | e0, simplifying with (222), (302) gives: % 145.96/20.80 | (359) all_58_14 = all_54_14 % 145.96/20.80 | % 145.96/20.80 | GROUND_INST: instantiating (function-axioms) with all_52_7, all_56_27, e2, e0, % 145.96/20.80 | simplifying with (206), (256) gives: % 145.96/20.80 | (360) all_56_27 = all_52_7 % 145.96/20.80 | % 145.96/20.80 | GROUND_INST: instantiating (function-axioms) with all_56_27, all_58_13, e2, % 145.96/20.80 | e0, simplifying with (256), (303) gives: % 145.96/20.80 | (361) all_58_13 = all_56_27 % 145.96/20.80 | % 145.96/20.80 | GROUND_INST: instantiating (function-axioms) with all_54_13, all_58_13, e2, % 145.96/20.80 | e0, simplifying with (223), (303) gives: % 145.96/20.80 | (362) all_58_13 = all_54_13 % 145.96/20.80 | % 145.96/20.80 | GROUND_INST: instantiating (function-axioms) with all_54_12, all_56_25, e3, % 145.96/20.80 | e0, simplifying with (224), (257) gives: % 145.96/20.80 | (363) all_56_25 = all_54_12 % 145.96/20.80 | % 145.96/20.80 | GROUND_INST: instantiating (function-axioms) with all_56_25, all_58_12, e3, % 145.96/20.80 | e0, simplifying with (257), (304) gives: % 145.96/20.80 | (364) all_58_12 = all_56_25 % 145.96/20.80 | % 145.96/20.80 | GROUND_INST: instantiating (function-axioms) with all_52_3, all_58_12, e3, e0, % 145.96/20.80 | simplifying with (207), (304) gives: % 145.96/20.80 | (365) all_58_12 = all_52_3 % 145.96/20.80 | % 145.96/20.80 | GROUND_INST: instantiating (function-axioms) with all_52_14, all_56_23, e0, % 145.96/20.80 | e1, simplifying with (208), (262) gives: % 145.96/20.80 | (366) all_56_23 = all_52_14 % 145.96/20.80 | % 145.96/20.80 | GROUND_INST: instantiating (function-axioms) with all_56_23, all_58_11, e0, % 145.96/20.80 | e1, simplifying with (262), (305) gives: % 145.96/20.80 | (367) all_58_11 = all_56_23 % 145.96/20.80 | % 145.96/20.80 | GROUND_INST: instantiating (function-axioms) with all_54_11, all_58_11, e0, % 145.96/20.80 | e1, simplifying with (225), (305) gives: % 145.96/20.80 | (368) all_58_11 = all_54_11 % 145.96/20.80 | % 145.96/20.80 | GROUND_INST: instantiating (function-axioms) with all_40_2, all_46_2, e1, e1, % 145.96/20.80 | simplifying with (126), (141) gives: % 145.96/20.80 | (369) all_46_2 = all_40_2 % 145.96/20.80 | % 145.96/20.80 | GROUND_INST: instantiating (function-axioms) with all_36_2, all_52_10, e1, e1, % 145.96/20.80 | simplifying with (116), (209) gives: % 145.96/20.80 | (370) all_52_10 = all_36_2 % 145.96/20.80 | % 145.96/20.80 | GROUND_INST: instantiating (function-axioms) with all_52_10, all_54_10, e1, % 145.96/20.80 | e1, simplifying with (209), (226) gives: % 145.96/20.80 | (371) all_54_10 = all_52_10 % 145.96/20.80 | % 145.96/20.80 | GROUND_INST: instantiating (function-axioms) with all_18_2, all_54_10, e1, e1, % 145.96/20.80 | simplifying with (71), (226) gives: % 145.96/20.80 | (372) all_54_10 = all_18_2 % 145.96/20.80 | % 145.96/20.80 | GROUND_INST: instantiating (function-axioms) with all_46_2, all_56_21, e1, e1, % 145.96/20.80 | simplifying with (141), (263) gives: % 145.96/20.80 | (373) all_56_21 = all_46_2 % 145.96/20.80 | % 145.96/20.80 | GROUND_INST: instantiating (function-axioms) with all_6_2, all_56_21, e1, e1, % 145.96/20.80 | simplifying with (41), (263) gives: % 145.96/20.80 | (374) all_56_21 = all_6_2 % 145.96/20.80 | % 145.96/20.80 | GROUND_INST: instantiating (function-axioms) with all_40_2, all_58_8, e1, e1, % 145.96/20.80 | simplifying with (126), (306) gives: % 145.96/20.80 | (375) all_58_8 = all_40_2 % 145.96/20.80 | % 145.96/20.80 | GROUND_INST: instantiating (function-axioms) with all_36_2, all_58_8, e1, e1, % 145.96/20.80 | simplifying with (116), (306) gives: % 145.96/20.80 | (376) all_58_8 = all_36_2 % 145.96/20.80 | % 145.96/20.80 | GROUND_INST: instantiating (function-axioms) with all_28_2, all_58_8, e1, e1, % 145.96/20.80 | simplifying with (96), (306) gives: % 145.96/20.80 | (377) all_58_8 = all_28_2 % 145.96/20.80 | % 145.96/20.80 | GROUND_INST: instantiating (function-axioms) with all_54_9, all_56_19, e2, e1, % 145.96/20.80 | simplifying with (227), (264) gives: % 145.96/20.80 | (378) all_56_19 = all_54_9 % 145.96/20.80 | % 145.96/20.80 | GROUND_INST: instantiating (function-axioms) with all_56_19, all_58_7, e2, e1, % 145.96/20.80 | simplifying with (264), (307) gives: % 145.96/20.80 | (379) all_58_7 = all_56_19 % 145.96/20.80 | % 145.96/20.80 | GROUND_INST: instantiating (function-axioms) with all_52_6, all_58_7, e2, e1, % 145.96/20.80 | simplifying with (210), (307) gives: % 145.96/20.80 | (380) all_58_7 = all_52_6 % 145.96/20.80 | % 145.96/20.80 | GROUND_INST: instantiating (function-axioms) with all_52_2, all_56_17, e3, e1, % 145.96/20.80 | simplifying with (211), (265) gives: % 145.96/20.80 | (381) all_56_17 = all_52_2 % 145.96/20.80 | % 145.96/20.80 | GROUND_INST: instantiating (function-axioms) with all_56_17, all_58_6, e3, e1, % 145.96/20.80 | simplifying with (265), (308) gives: % 145.96/20.80 | (382) all_58_6 = all_56_17 % 145.96/20.80 | % 145.96/20.80 | GROUND_INST: instantiating (function-axioms) with all_54_8, all_58_6, e3, e1, % 145.96/20.80 | simplifying with (228), (308) gives: % 145.96/20.80 | (383) all_58_6 = all_54_8 % 145.96/20.80 | % 145.96/20.80 | GROUND_INST: instantiating (function-axioms) with all_54_7, all_56_15, e0, e2, % 145.96/20.80 | simplifying with (229), (270) gives: % 145.96/20.80 | (384) all_56_15 = all_54_7 % 145.96/20.80 | % 145.96/20.80 | GROUND_INST: instantiating (function-axioms) with all_56_15, all_58_10, e0, % 145.96/20.80 | e2, simplifying with (270), (309) gives: % 145.96/20.80 | (385) all_58_10 = all_56_15 % 145.96/20.80 | % 145.96/20.80 | GROUND_INST: instantiating (function-axioms) with all_52_13, all_58_10, e0, % 145.96/20.80 | e2, simplifying with (212), (309) gives: % 145.96/20.80 | (386) all_58_10 = all_52_13 % 145.96/20.80 | % 145.96/20.80 | GROUND_INST: instantiating (function-axioms) with all_54_6, all_56_13, e1, e2, % 145.96/20.80 | simplifying with (230), (271) gives: % 145.96/20.80 | (387) all_56_13 = all_54_6 % 145.96/20.80 | % 145.96/20.80 | GROUND_INST: instantiating (function-axioms) with all_56_13, all_58_5, e1, e2, % 145.96/20.80 | simplifying with (271), (310) gives: % 145.96/20.80 | (388) all_58_5 = all_56_13 % 145.96/20.80 | % 145.96/20.81 | GROUND_INST: instantiating (function-axioms) with all_52_9, all_58_5, e1, e2, % 145.96/20.81 | simplifying with (213), (310) gives: % 145.96/20.81 | (389) all_58_5 = all_52_9 % 145.96/20.81 | % 145.96/20.81 | GROUND_INST: instantiating (function-axioms) with all_8_2, all_30_2, e2, e2, % 145.96/20.81 | simplifying with (46), (101) gives: % 145.96/20.81 | (390) all_30_2 = all_8_2 % 145.96/20.81 | % 145.96/20.81 | GROUND_INST: instantiating (function-axioms) with all_30_2, all_52_5, e2, e2, % 145.96/20.81 | simplifying with (101), (214) gives: % 145.96/20.81 | (391) all_52_5 = all_30_2 % 145.96/20.81 | % 145.96/20.81 | GROUND_INST: instantiating (function-axioms) with all_22_2, all_52_5, e2, e2, % 145.96/20.81 | simplifying with (81), (214) gives: % 145.96/20.81 | (392) all_52_5 = all_22_2 % 145.96/20.81 | % 145.96/20.81 | GROUND_INST: instantiating (function-axioms) with all_30_2, all_54_5, e2, e2, % 145.96/20.81 | simplifying with (101), (231) gives: % 145.96/20.81 | (393) all_54_5 = all_30_2 % 145.96/20.81 | % 145.96/20.81 | GROUND_INST: instantiating (function-axioms) with all_14_2, all_54_5, e2, e2, % 145.96/20.81 | simplifying with (61), (231) gives: % 145.96/20.81 | (394) all_54_5 = all_14_2 % 145.96/20.81 | % 145.96/20.81 | GROUND_INST: instantiating (function-axioms) with all_52_5, all_56_11, e2, e2, % 145.96/20.81 | simplifying with (214), (272) gives: % 145.96/20.81 | (395) all_56_11 = all_52_5 % 145.96/20.81 | % 145.96/20.81 | GROUND_INST: instantiating (function-axioms) with all_42_2, all_56_11, e2, e2, % 145.96/20.81 | simplifying with (131), (272) gives: % 145.96/20.81 | (396) all_56_11 = all_42_2 % 145.96/20.81 | % 145.96/20.81 | GROUND_INST: instantiating (function-axioms) with all_54_5, all_58_3, e2, e2, % 145.96/20.81 | simplifying with (231), (311) gives: % 145.96/20.81 | (397) all_58_3 = all_54_5 % 145.96/20.81 | % 145.96/20.81 | GROUND_INST: instantiating (function-axioms) with all_48_2, all_58_3, e2, e2, % 145.96/20.81 | simplifying with (146), (311) gives: % 145.96/20.81 | (398) all_58_3 = all_48_2 % 145.96/20.81 | % 145.96/20.81 | GROUND_INST: instantiating (function-axioms) with all_54_4, all_56_9, e3, e2, % 145.96/20.81 | simplifying with (232), (273) gives: % 145.96/20.81 | (399) all_56_9 = all_54_4 % 145.96/20.81 | % 145.96/20.81 | GROUND_INST: instantiating (function-axioms) with all_56_9, all_58_2, e3, e2, % 145.96/20.81 | simplifying with (273), (312) gives: % 145.96/20.81 | (400) all_58_2 = all_56_9 % 145.96/20.81 | % 145.96/20.81 | GROUND_INST: instantiating (function-axioms) with all_52_1, all_58_2, e3, e2, % 145.96/20.81 | simplifying with (215), (312) gives: % 145.96/20.81 | (401) all_58_2 = all_52_1 % 145.96/20.81 | % 145.96/20.81 | GROUND_INST: instantiating (function-axioms) with all_52_12, all_56_7, e0, e3, % 145.96/20.81 | simplifying with (216), (278) gives: % 145.96/20.81 | (402) all_56_7 = all_52_12 % 145.96/20.81 | % 145.96/20.81 | GROUND_INST: instantiating (function-axioms) with all_56_7, all_58_9, e0, e3, % 145.96/20.81 | simplifying with (278), (313) gives: % 145.96/20.81 | (403) all_58_9 = all_56_7 % 145.96/20.81 | % 145.96/20.81 | GROUND_INST: instantiating (function-axioms) with all_54_3, all_58_9, e0, e3, % 145.96/20.81 | simplifying with (233), (313) gives: % 145.96/20.81 | (404) all_58_9 = all_54_3 % 145.96/20.81 | % 145.96/20.81 | GROUND_INST: instantiating (function-axioms) with all_54_2, all_56_5, e1, e3, % 145.96/20.81 | simplifying with (234), (279) gives: % 145.96/20.81 | (405) all_56_5 = all_54_2 % 145.96/20.81 | % 145.96/20.81 | GROUND_INST: instantiating (function-axioms) with all_56_5, all_58_4, e1, e3, % 145.96/20.81 | simplifying with (279), (314) gives: % 145.96/20.81 | (406) all_58_4 = all_56_5 % 145.96/20.81 | % 145.96/20.81 | GROUND_INST: instantiating (function-axioms) with all_52_8, all_58_4, e1, e3, % 145.96/20.81 | simplifying with (217), (314) gives: % 145.96/20.81 | (407) all_58_4 = all_52_8 % 145.96/20.81 | % 145.96/20.81 | GROUND_INST: instantiating (function-axioms) with all_52_4, all_56_3, e2, e3, % 145.96/20.81 | simplifying with (218), (280) gives: % 145.96/20.81 | (408) all_56_3 = all_52_4 % 145.96/20.81 | % 145.96/20.81 | GROUND_INST: instantiating (function-axioms) with all_56_3, all_58_1, e2, e3, % 145.96/20.81 | simplifying with (280), (315) gives: % 145.96/20.81 | (409) all_58_1 = all_56_3 % 145.96/20.81 | % 145.96/20.81 | GROUND_INST: instantiating (function-axioms) with all_54_1, all_58_1, e2, e3, % 145.96/20.81 | simplifying with (235), (315) gives: % 145.96/20.81 | (410) all_58_1 = all_54_1 % 145.96/20.81 | % 145.96/20.81 | GROUND_INST: instantiating (function-axioms) with all_24_2, all_32_2, e3, e3, % 145.96/20.81 | simplifying with (86), (106) gives: % 145.96/20.81 | (411) all_32_2 = all_24_2 % 145.96/20.81 | % 145.96/20.81 | GROUND_INST: instantiating (function-axioms) with all_24_2, all_38_2, e3, e3, % 145.96/20.81 | simplifying with (86), (121) gives: % 145.96/20.81 | (412) all_38_2 = all_24_2 % 145.96/20.81 | % 145.96/20.81 | GROUND_INST: instantiating (function-axioms) with all_38_2, all_50_2, e3, e3, % 145.96/20.81 | simplifying with (121), (151) gives: % 145.96/20.81 | (413) all_50_2 = all_38_2 % 145.96/20.81 | % 145.96/20.81 | GROUND_INST: instantiating (function-axioms) with all_32_2, all_52_0, e3, e3, % 145.96/20.81 | simplifying with (106), (219) gives: % 145.96/20.81 | (414) all_52_0 = all_32_2 % 145.96/20.81 | % 145.96/20.81 | GROUND_INST: instantiating (function-axioms) with all_50_2, all_54_0, e3, e3, % 145.96/20.81 | simplifying with (151), (236) gives: % 145.96/20.81 | (415) all_54_0 = all_50_2 % 145.96/20.81 | % 145.96/20.81 | GROUND_INST: instantiating (function-axioms) with all_54_0, all_56_1, e3, e3, % 145.96/20.81 | simplifying with (236), (281) gives: % 145.96/20.81 | (416) all_56_1 = all_54_0 % 145.96/20.81 | % 145.96/20.81 | GROUND_INST: instantiating (function-axioms) with all_16_2, all_56_1, e3, e3, % 145.96/20.81 | simplifying with (66), (281) gives: % 145.96/20.81 | (417) all_56_1 = all_16_2 % 146.43/20.81 | % 146.43/20.81 | GROUND_INST: instantiating (function-axioms) with all_52_0, all_58_0, e3, e3, % 146.43/20.81 | simplifying with (219), (316) gives: % 146.43/20.81 | (418) all_58_0 = all_52_0 % 146.43/20.81 | % 146.43/20.81 | GROUND_INST: instantiating (function-axioms) with all_10_2, all_58_0, e3, e3, % 146.43/20.81 | simplifying with (51), (316) gives: % 146.43/20.81 | (419) all_58_0 = all_10_2 % 146.43/20.81 | % 146.43/20.81 | COMBINE_EQS: (418), (419) imply: % 146.43/20.81 | (420) all_52_0 = all_10_2 % 146.43/20.81 | % 146.43/20.81 | SIMP: (420) implies: % 146.43/20.81 | (421) all_52_0 = all_10_2 % 146.43/20.81 | % 146.43/20.81 | COMBINE_EQS: (409), (410) imply: % 146.43/20.81 | (422) all_56_3 = all_54_1 % 146.43/20.81 | % 146.43/20.81 | SIMP: (422) implies: % 146.43/20.81 | (423) all_56_3 = all_54_1 % 146.43/20.81 | % 146.43/20.81 | COMBINE_EQS: (400), (401) imply: % 146.43/20.81 | (424) all_56_9 = all_52_1 % 146.43/20.81 | % 146.43/20.81 | SIMP: (424) implies: % 146.43/20.81 | (425) all_56_9 = all_52_1 % 146.43/20.81 | % 146.43/20.81 | COMBINE_EQS: (397), (398) imply: % 146.43/20.81 | (426) all_54_5 = all_48_2 % 146.43/20.81 | % 146.43/20.81 | SIMP: (426) implies: % 146.43/20.81 | (427) all_54_5 = all_48_2 % 146.43/20.81 | % 146.43/20.81 | COMBINE_EQS: (406), (407) imply: % 146.43/20.81 | (428) all_56_5 = all_52_8 % 146.43/20.81 | % 146.43/20.81 | SIMP: (428) implies: % 146.43/20.81 | (429) all_56_5 = all_52_8 % 146.43/20.81 | % 146.43/20.81 | COMBINE_EQS: (388), (389) imply: % 146.43/20.81 | (430) all_56_13 = all_52_9 % 146.43/20.81 | % 146.43/20.81 | SIMP: (430) implies: % 146.43/20.81 | (431) all_56_13 = all_52_9 % 146.43/20.81 | % 146.43/20.81 | COMBINE_EQS: (382), (383) imply: % 146.43/20.81 | (432) all_56_17 = all_54_8 % 146.43/20.81 | % 146.43/20.81 | SIMP: (432) implies: % 146.43/20.81 | (433) all_56_17 = all_54_8 % 146.43/20.81 | % 146.43/20.81 | COMBINE_EQS: (379), (380) imply: % 146.43/20.81 | (434) all_56_19 = all_52_6 % 146.43/20.81 | % 146.43/20.81 | SIMP: (434) implies: % 146.43/20.81 | (435) all_56_19 = all_52_6 % 146.43/20.81 | % 146.43/20.81 | COMBINE_EQS: (376), (377) imply: % 146.43/20.81 | (436) all_36_2 = all_28_2 % 146.43/20.81 | % 146.43/20.81 | SIMP: (436) implies: % 146.43/20.81 | (437) all_36_2 = all_28_2 % 146.43/20.81 | % 146.43/20.81 | COMBINE_EQS: (375), (377) imply: % 146.43/20.81 | (438) all_40_2 = all_28_2 % 146.43/20.81 | % 146.43/20.81 | SIMP: (438) implies: % 146.43/20.81 | (439) all_40_2 = all_28_2 % 146.43/20.81 | % 146.43/20.81 | COMBINE_EQS: (403), (404) imply: % 146.43/20.81 | (440) all_56_7 = all_54_3 % 146.43/20.81 | % 146.43/20.81 | SIMP: (440) implies: % 146.43/20.81 | (441) all_56_7 = all_54_3 % 146.43/20.81 | % 146.43/20.81 | COMBINE_EQS: (385), (386) imply: % 146.43/20.81 | (442) all_56_15 = all_52_13 % 146.43/20.81 | % 146.43/20.81 | SIMP: (442) implies: % 146.43/20.81 | (443) all_56_15 = all_52_13 % 146.43/20.81 | % 146.43/20.81 | COMBINE_EQS: (367), (368) imply: % 146.43/20.81 | (444) all_56_23 = all_54_11 % 146.43/20.81 | % 146.43/20.81 | SIMP: (444) implies: % 146.43/20.81 | (445) all_56_23 = all_54_11 % 146.43/20.81 | % 146.43/20.81 | COMBINE_EQS: (364), (365) imply: % 146.43/20.81 | (446) all_56_25 = all_52_3 % 146.43/20.81 | % 146.43/20.81 | SIMP: (446) implies: % 146.43/20.81 | (447) all_56_25 = all_52_3 % 146.43/20.81 | % 146.43/20.81 | COMBINE_EQS: (361), (362) imply: % 146.43/20.81 | (448) all_56_27 = all_54_13 % 146.43/20.81 | % 146.43/20.81 | SIMP: (448) implies: % 146.43/20.81 | (449) all_56_27 = all_54_13 % 146.43/20.81 | % 146.43/20.81 | COMBINE_EQS: (358), (359) imply: % 146.43/20.81 | (450) all_56_29 = all_54_14 % 146.43/20.81 | % 146.43/20.81 | SIMP: (450) implies: % 146.43/20.81 | (451) all_56_29 = all_54_14 % 146.43/20.81 | % 146.43/20.81 | COMBINE_EQS: (355), (356) imply: % 146.43/20.81 | (452) all_54_15 = all_12_2 % 146.43/20.81 | % 146.43/20.81 | SIMP: (452) implies: % 146.43/20.81 | (453) all_54_15 = all_12_2 % 146.43/20.81 | % 146.43/20.81 | COMBINE_EQS: (416), (417) imply: % 146.43/20.81 | (454) all_54_0 = all_16_2 % 146.43/20.81 | % 146.43/20.81 | SIMP: (454) implies: % 146.43/20.81 | (455) all_54_0 = all_16_2 % 146.43/20.81 | % 146.43/20.81 | COMBINE_EQS: (408), (423) imply: % 146.43/20.81 | (456) all_54_1 = all_52_4 % 146.43/20.81 | % 146.43/20.81 | SIMP: (456) implies: % 146.43/20.81 | (457) all_54_1 = all_52_4 % 146.43/20.81 | % 146.43/20.81 | COMBINE_EQS: (405), (429) imply: % 146.43/20.81 | (458) all_54_2 = all_52_8 % 146.43/20.81 | % 146.43/20.81 | SIMP: (458) implies: % 146.43/20.81 | (459) all_54_2 = all_52_8 % 146.43/20.81 | % 146.43/20.81 | COMBINE_EQS: (402), (441) imply: % 146.43/20.81 | (460) all_54_3 = all_52_12 % 146.43/20.81 | % 146.43/20.81 | SIMP: (460) implies: % 146.43/20.81 | (461) all_54_3 = all_52_12 % 146.43/20.81 | % 146.43/20.81 | COMBINE_EQS: (399), (425) imply: % 146.43/20.81 | (462) all_54_4 = all_52_1 % 146.43/20.81 | % 146.43/20.81 | SIMP: (462) implies: % 146.43/20.81 | (463) all_54_4 = all_52_1 % 146.43/20.81 | % 146.43/20.81 | COMBINE_EQS: (395), (396) imply: % 146.43/20.82 | (464) all_52_5 = all_42_2 % 146.43/20.82 | % 146.43/20.82 | SIMP: (464) implies: % 146.43/20.82 | (465) all_52_5 = all_42_2 % 146.43/20.82 | % 146.43/20.82 | COMBINE_EQS: (387), (431) imply: % 146.43/20.82 | (466) all_54_6 = all_52_9 % 146.43/20.82 | % 146.43/20.82 | SIMP: (466) implies: % 146.43/20.82 | (467) all_54_6 = all_52_9 % 146.43/20.82 | % 146.43/20.82 | COMBINE_EQS: (384), (443) imply: % 146.43/20.82 | (468) all_54_7 = all_52_13 % 146.43/20.82 | % 146.43/20.82 | SIMP: (468) implies: % 146.43/20.82 | (469) all_54_7 = all_52_13 % 146.43/20.82 | % 146.43/20.82 | COMBINE_EQS: (381), (433) imply: % 146.43/20.82 | (470) all_54_8 = all_52_2 % 146.43/20.82 | % 146.43/20.82 | SIMP: (470) implies: % 146.43/20.82 | (471) all_54_8 = all_52_2 % 146.43/20.82 | % 146.43/20.82 | COMBINE_EQS: (378), (435) imply: % 146.43/20.82 | (472) all_54_9 = all_52_6 % 146.43/20.82 | % 146.43/20.82 | SIMP: (472) implies: % 146.43/20.82 | (473) all_54_9 = all_52_6 % 146.43/20.82 | % 146.43/20.82 | COMBINE_EQS: (373), (374) imply: % 146.43/20.82 | (474) all_46_2 = all_6_2 % 146.43/20.82 | % 146.43/20.82 | SIMP: (474) implies: % 146.43/20.82 | (475) all_46_2 = all_6_2 % 146.43/20.82 | % 146.43/20.82 | COMBINE_EQS: (366), (445) imply: % 146.43/20.82 | (476) all_54_11 = all_52_14 % 146.43/20.82 | % 146.43/20.82 | COMBINE_EQS: (363), (447) imply: % 146.43/20.82 | (477) all_54_12 = all_52_3 % 146.43/20.82 | % 146.43/20.82 | SIMP: (477) implies: % 146.43/20.82 | (478) all_54_12 = all_52_3 % 146.43/20.82 | % 146.43/20.82 | COMBINE_EQS: (360), (449) imply: % 146.43/20.82 | (479) all_54_13 = all_52_7 % 146.43/20.82 | % 146.43/20.82 | SIMP: (479) implies: % 146.43/20.82 | (480) all_54_13 = all_52_7 % 146.43/20.82 | % 146.43/20.82 | COMBINE_EQS: (357), (451) imply: % 146.43/20.82 | (481) all_54_14 = all_52_11 % 146.43/20.82 | % 146.43/20.82 | SIMP: (481) implies: % 146.43/20.82 | (482) all_54_14 = all_52_11 % 146.43/20.82 | % 146.43/20.82 | COMBINE_EQS: (353), (354) imply: % 146.43/20.82 | (483) all_52_15 = all_20_2 % 146.43/20.82 | % 146.43/20.82 | SIMP: (483) implies: % 146.43/20.82 | (484) all_52_15 = all_20_2 % 146.43/20.82 | % 146.43/20.82 | COMBINE_EQS: (415), (455) imply: % 146.43/20.82 | (485) all_50_2 = all_16_2 % 146.43/20.82 | % 146.43/20.82 | SIMP: (485) implies: % 146.43/20.82 | (486) all_50_2 = all_16_2 % 146.43/20.82 | % 146.43/20.82 | COMBINE_EQS: (393), (427) imply: % 146.43/20.82 | (487) all_48_2 = all_30_2 % 146.43/20.82 | % 146.43/20.82 | COMBINE_EQS: (394), (427) imply: % 146.43/20.82 | (488) all_48_2 = all_14_2 % 146.43/20.82 | % 146.43/20.82 | COMBINE_EQS: (371), (372) imply: % 146.43/20.82 | (489) all_52_10 = all_18_2 % 146.43/20.82 | % 146.43/20.82 | SIMP: (489) implies: % 146.43/20.82 | (490) all_52_10 = all_18_2 % 146.43/20.82 | % 146.43/20.82 | COMBINE_EQS: (352), (453) imply: % 146.43/20.82 | (491) all_44_2 = all_12_2 % 146.43/20.82 | % 146.43/20.82 | SIMP: (491) implies: % 146.43/20.82 | (492) all_44_2 = all_12_2 % 146.43/20.82 | % 146.43/20.82 | COMBINE_EQS: (414), (421) imply: % 146.43/20.82 | (493) all_32_2 = all_10_2 % 146.43/20.82 | % 146.43/20.82 | SIMP: (493) implies: % 146.43/20.82 | (494) all_32_2 = all_10_2 % 146.43/20.82 | % 146.43/20.82 | COMBINE_EQS: (392), (465) imply: % 146.43/20.82 | (495) all_42_2 = all_22_2 % 146.43/20.82 | % 146.43/20.82 | COMBINE_EQS: (391), (465) imply: % 146.43/20.82 | (496) all_42_2 = all_30_2 % 146.43/20.82 | % 146.43/20.82 | COMBINE_EQS: (370), (490) imply: % 146.43/20.82 | (497) all_36_2 = all_18_2 % 146.43/20.82 | % 146.43/20.82 | SIMP: (497) implies: % 146.43/20.82 | (498) all_36_2 = all_18_2 % 146.43/20.82 | % 146.43/20.82 | COMBINE_EQS: (351), (484) imply: % 146.43/20.82 | (499) all_20_2 = all_4_2 % 146.43/20.82 | % 146.43/20.82 | COMBINE_EQS: (350), (484) imply: % 146.43/20.82 | (500) all_26_2 = all_20_2 % 146.43/20.82 | % 146.43/20.82 | SIMP: (500) implies: % 146.43/20.82 | (501) all_26_2 = all_20_2 % 146.43/20.82 | % 146.43/20.82 | COMBINE_EQS: (413), (486) imply: % 146.43/20.82 | (502) all_38_2 = all_16_2 % 146.43/20.82 | % 146.43/20.82 | SIMP: (502) implies: % 146.43/20.82 | (503) all_38_2 = all_16_2 % 146.43/20.82 | % 146.43/20.82 | COMBINE_EQS: (487), (488) imply: % 146.43/20.82 | (504) all_30_2 = all_14_2 % 146.43/20.82 | % 146.43/20.82 | SIMP: (504) implies: % 146.43/20.82 | (505) all_30_2 = all_14_2 % 146.43/20.82 | % 146.43/20.82 | COMBINE_EQS: (369), (475) imply: % 146.43/20.82 | (506) all_40_2 = all_6_2 % 146.43/20.82 | % 146.43/20.82 | SIMP: (506) implies: % 146.43/20.82 | (507) all_40_2 = all_6_2 % 146.43/20.82 | % 146.43/20.82 | COMBINE_EQS: (349), (492) imply: % 146.43/20.82 | (508) all_34_2 = all_12_2 % 146.43/20.82 | % 146.43/20.82 | SIMP: (508) implies: % 146.43/20.82 | (509) all_34_2 = all_12_2 % 146.43/20.82 | % 146.43/20.82 | COMBINE_EQS: (495), (496) imply: % 146.43/20.82 | (510) all_30_2 = all_22_2 % 146.43/20.82 | % 146.43/20.82 | SIMP: (510) implies: % 146.43/20.82 | (511) all_30_2 = all_22_2 % 146.43/20.82 | % 146.43/20.82 | COMBINE_EQS: (439), (507) imply: % 146.43/20.82 | (512) all_28_2 = all_6_2 % 146.43/20.82 | % 146.43/20.82 | SIMP: (512) implies: % 146.43/20.82 | (513) all_28_2 = all_6_2 % 146.43/20.82 | % 146.43/20.82 | COMBINE_EQS: (412), (503) imply: % 146.43/20.82 | (514) all_24_2 = all_16_2 % 146.43/20.82 | % 146.43/20.82 | SIMP: (514) implies: % 146.43/20.82 | (515) all_24_2 = all_16_2 % 146.43/20.82 | % 146.43/20.82 | COMBINE_EQS: (437), (498) imply: % 146.43/20.82 | (516) all_28_2 = all_18_2 % 146.43/20.82 | % 146.43/20.82 | SIMP: (516) implies: % 146.43/20.82 | (517) all_28_2 = all_18_2 % 146.43/20.82 | % 146.43/20.82 | COMBINE_EQS: (348), (509) imply: % 146.43/20.82 | (518) all_26_2 = all_12_2 % 146.43/20.82 | % 146.43/20.82 | SIMP: (518) implies: % 146.43/20.82 | (519) all_26_2 = all_12_2 % 146.43/20.82 | % 146.43/20.82 | COMBINE_EQS: (411), (494) imply: % 146.43/20.82 | (520) all_24_2 = all_10_2 % 146.43/20.82 | % 146.43/20.82 | SIMP: (520) implies: % 146.43/20.82 | (521) all_24_2 = all_10_2 % 146.43/20.82 | % 146.43/20.82 | COMBINE_EQS: (505), (511) imply: % 146.43/20.82 | (522) all_22_2 = all_14_2 % 146.43/20.82 | % 146.43/20.82 | COMBINE_EQS: (390), (511) imply: % 146.43/20.82 | (523) all_22_2 = all_8_2 % 146.43/20.82 | % 146.43/20.82 | COMBINE_EQS: (513), (517) imply: % 146.43/20.82 | (524) all_18_2 = all_6_2 % 146.43/20.82 | % 146.43/20.82 | COMBINE_EQS: (501), (519) imply: % 146.43/20.82 | (525) all_20_2 = all_12_2 % 146.43/20.82 | % 146.43/20.82 | SIMP: (525) implies: % 146.43/20.82 | (526) all_20_2 = all_12_2 % 146.43/20.82 | % 146.43/20.82 | COMBINE_EQS: (515), (521) imply: % 146.43/20.82 | (527) all_16_2 = all_10_2 % 146.43/20.82 | % 146.43/20.82 | COMBINE_EQS: (522), (523) imply: % 146.43/20.82 | (528) all_14_2 = all_8_2 % 146.43/20.82 | % 146.43/20.82 | COMBINE_EQS: (499), (526) imply: % 146.43/20.82 | (529) all_12_2 = all_4_2 % 146.43/20.82 | % 146.43/20.82 | COMBINE_EQS: (519), (529) imply: % 146.43/20.82 | (530) all_26_2 = all_4_2 % 146.43/20.82 | % 146.43/20.82 | COMBINE_EQS: (509), (529) imply: % 146.43/20.82 | (531) all_34_2 = all_4_2 % 146.43/20.82 | % 146.43/20.82 | COMBINE_EQS: (498), (524) imply: % 146.43/20.82 | (532) all_36_2 = all_6_2 % 146.43/20.82 | % 146.43/20.82 | COMBINE_EQS: (503), (527) imply: % 146.43/20.82 | (533) all_38_2 = all_10_2 % 146.43/20.82 | % 146.43/20.82 | COMBINE_EQS: (495), (523) imply: % 146.43/20.82 | (534) all_42_2 = all_8_2 % 146.43/20.82 | % 146.43/20.82 | COMBINE_EQS: (492), (529) imply: % 146.43/20.82 | (535) all_44_2 = all_4_2 % 146.43/20.82 | % 146.43/20.82 | COMBINE_EQS: (488), (528) imply: % 146.43/20.82 | (536) all_48_2 = all_8_2 % 146.43/20.82 | % 146.43/20.82 | COMBINE_EQS: (486), (527) imply: % 146.43/20.82 | (537) all_50_2 = all_10_2 % 146.43/20.82 | % 146.43/20.82 | COMBINE_EQS: (490), (524) imply: % 146.43/20.82 | (538) all_52_10 = all_6_2 % 146.43/20.82 | % 146.43/20.82 | COMBINE_EQS: (465), (534) imply: % 146.43/20.82 | (539) all_52_5 = all_8_2 % 146.43/20.82 | % 146.43/20.82 | COMBINE_EQS: (453), (529) imply: % 146.43/20.82 | (540) all_54_15 = all_4_2 % 146.43/20.82 | % 146.43/20.82 | COMBINE_EQS: (372), (524) imply: % 146.43/20.82 | (541) all_54_10 = all_6_2 % 146.43/20.82 | % 146.43/20.82 | COMBINE_EQS: (427), (536) imply: % 146.43/20.82 | (542) all_54_5 = all_8_2 % 146.43/20.82 | % 146.43/20.82 | COMBINE_EQS: (455), (527) imply: % 146.43/20.82 | (543) all_54_0 = all_10_2 % 146.43/20.82 | % 146.43/20.82 | COMBINE_EQS: (354), (499) imply: % 146.43/20.82 | (544) all_56_31 = all_4_2 % 146.43/20.82 | % 146.43/20.82 | COMBINE_EQS: (396), (534) imply: % 146.43/20.82 | (545) all_56_11 = all_8_2 % 146.43/20.82 | % 146.43/20.82 | COMBINE_EQS: (417), (527) imply: % 146.43/20.82 | (546) all_56_1 = all_10_2 % 146.43/20.82 | % 146.43/20.82 | COMBINE_EQS: (356), (529) imply: % 146.43/20.82 | (547) all_58_15 = all_4_2 % 146.43/20.82 | % 146.43/20.82 | COMBINE_EQS: (359), (482) imply: % 146.43/20.82 | (548) all_58_14 = all_52_11 % 146.43/20.82 | % 146.43/20.82 | COMBINE_EQS: (362), (480) imply: % 146.43/20.82 | (549) all_58_13 = all_52_7 % 146.43/20.82 | % 146.43/20.82 | COMBINE_EQS: (368), (476) imply: % 146.43/20.82 | (550) all_58_11 = all_52_14 % 146.43/20.82 | % 146.43/20.82 | COMBINE_EQS: (404), (461) imply: % 146.43/20.82 | (551) all_58_9 = all_52_12 % 146.43/20.82 | % 146.43/20.82 | COMBINE_EQS: (377), (513) imply: % 146.43/20.82 | (552) all_58_8 = all_6_2 % 146.43/20.82 | % 146.43/20.82 | COMBINE_EQS: (383), (471) imply: % 146.43/20.82 | (553) all_58_6 = all_52_2 % 146.43/20.82 | % 146.43/20.82 | COMBINE_EQS: (398), (536) imply: % 146.43/20.82 | (554) all_58_3 = all_8_2 % 146.43/20.82 | % 146.43/20.82 | COMBINE_EQS: (410), (457) imply: % 146.43/20.82 | (555) all_58_1 = all_52_4 % 146.43/20.82 | % 146.43/20.82 | REDUCE: (203), (421) imply: % 146.43/20.82 | (556) ~ (all_52_1 = all_10_2) % 146.43/20.82 | % 146.43/20.82 | SIMP: (556) implies: % 146.43/20.82 | (557) ~ (all_52_1 = all_10_2) % 146.43/20.82 | % 146.43/20.82 | REDUCE: (202), (421) imply: % 146.43/20.82 | (558) ~ (all_52_2 = all_10_2) % 146.43/20.82 | % 146.43/20.82 | SIMP: (558) implies: % 146.43/20.82 | (559) ~ (all_52_2 = all_10_2) % 146.43/20.82 | % 146.43/20.82 | REDUCE: (201), (421) imply: % 146.43/20.82 | (560) ~ (all_52_3 = all_10_2) % 146.43/20.82 | % 146.43/20.82 | SIMP: (560) implies: % 146.43/20.82 | (561) ~ (all_52_3 = all_10_2) % 146.43/20.82 | % 146.43/20.82 | REDUCE: (200), (421) imply: % 146.43/20.82 | (562) ~ (all_52_4 = all_10_2) % 146.43/20.82 | % 146.43/20.82 | SIMP: (562) implies: % 146.43/20.82 | (563) ~ (all_52_4 = all_10_2) % 146.43/20.82 | % 146.43/20.82 | REDUCE: (199), (421) imply: % 146.43/20.82 | (564) ~ (all_52_8 = all_10_2) % 146.43/20.82 | % 146.43/20.82 | SIMP: (564) implies: % 146.43/20.82 | (565) ~ (all_52_8 = all_10_2) % 146.43/20.82 | % 146.43/20.82 | REDUCE: (198), (421) imply: % 146.43/20.82 | (566) ~ (all_52_12 = all_10_2) % 146.43/20.82 | % 146.43/20.82 | SIMP: (566) implies: % 146.43/20.82 | (567) ~ (all_52_12 = all_10_2) % 146.43/20.82 | % 146.43/20.83 | REDUCE: (195), (539) imply: % 146.43/20.83 | (568) ~ (all_52_1 = all_8_2) % 146.43/20.83 | % 146.43/20.83 | REDUCE: (190), (538) imply: % 146.43/20.83 | (569) ~ (all_52_2 = all_6_2) % 146.43/20.83 | % 146.43/20.83 | REDUCE: (186), (351) imply: % 146.43/20.83 | (570) ~ (all_52_3 = all_4_2) % 146.43/20.83 | % 146.43/20.83 | REDUCE: (185), (539) imply: % 146.43/20.83 | (571) ~ (all_52_4 = all_8_2) % 146.43/20.83 | % 146.43/20.83 | REDUCE: (180), (539) imply: % 146.43/20.83 | (572) ~ (all_52_6 = all_8_2) % 146.43/20.83 | % 146.43/20.83 | SIMP: (572) implies: % 146.43/20.83 | (573) ~ (all_52_6 = all_8_2) % 146.43/20.83 | % 146.43/20.83 | REDUCE: (179), (539) imply: % 146.43/20.83 | (574) ~ (all_52_7 = all_8_2) % 146.43/20.83 | % 146.43/20.83 | SIMP: (574) implies: % 146.43/20.83 | (575) ~ (all_52_7 = all_8_2) % 146.43/20.83 | % 146.43/20.83 | REDUCE: (178), (539) imply: % 146.43/20.83 | (576) ~ (all_52_9 = all_8_2) % 146.43/20.83 | % 146.43/20.83 | SIMP: (576) implies: % 146.43/20.83 | (577) ~ (all_52_9 = all_8_2) % 146.43/20.83 | % 146.43/20.83 | REDUCE: (177), (539) imply: % 146.43/20.83 | (578) ~ (all_52_13 = all_8_2) % 146.43/20.83 | % 146.43/20.83 | SIMP: (578) implies: % 146.43/20.83 | (579) ~ (all_52_13 = all_8_2) % 146.43/20.83 | % 146.43/20.83 | REDUCE: (175), (538) imply: % 146.43/20.83 | (580) ~ (all_52_6 = all_6_2) % 146.43/20.83 | % 146.43/20.83 | REDUCE: (172), (351) imply: % 146.43/20.83 | (581) ~ (all_52_7 = all_4_2) % 146.43/20.83 | % 146.43/20.83 | REDUCE: (170), (538) imply: % 146.43/20.83 | (582) ~ (all_52_8 = all_6_2) % 146.43/20.83 | % 146.43/20.83 | REDUCE: (167), (538) imply: % 146.43/20.83 | (583) ~ (all_52_9 = all_6_2) % 146.43/20.83 | % 146.43/20.83 | REDUCE: (164), (538) imply: % 146.43/20.83 | (584) ~ (all_52_11 = all_6_2) % 146.43/20.83 | % 146.43/20.83 | SIMP: (584) implies: % 146.43/20.83 | (585) ~ (all_52_11 = all_6_2) % 146.43/20.83 | % 146.43/20.83 | REDUCE: (163), (538) imply: % 146.43/20.83 | (586) ~ (all_52_14 = all_6_2) % 146.43/20.83 | % 146.43/20.83 | SIMP: (586) implies: % 146.43/20.83 | (587) ~ (all_52_14 = all_6_2) % 146.43/20.83 | % 146.43/20.83 | REDUCE: (162), (351) imply: % 146.43/20.83 | (588) ~ (all_52_11 = all_4_2) % 146.43/20.83 | % 146.43/20.83 | REDUCE: (159), (351) imply: % 146.43/20.83 | (589) ~ (all_52_12 = all_4_2) % 146.43/20.83 | % 146.43/20.83 | REDUCE: (157), (351) imply: % 146.43/20.83 | (590) ~ (all_52_13 = all_4_2) % 146.43/20.83 | % 146.43/20.83 | REDUCE: (156), (351) imply: % 146.43/20.83 | (591) ~ (all_52_14 = all_4_2) % 146.43/20.83 | % 146.43/20.83 | REDUCE: (153), (537) imply: % 146.43/20.83 | (592) op(all_10_2, all_10_2) = all_50_1 % 146.43/20.83 | % 146.43/20.83 | REDUCE: (148), (536) imply: % 146.43/20.83 | (593) op(all_8_2, all_8_2) = all_48_1 % 146.43/20.83 | % 146.43/20.83 | REDUCE: (143), (475) imply: % 146.43/20.83 | (594) op(all_6_2, all_6_2) = all_46_1 % 146.43/20.83 | % 146.43/20.83 | REDUCE: (138), (535) imply: % 146.43/20.83 | (595) op(all_4_2, all_4_2) = all_44_1 % 146.43/20.83 | % 146.43/20.83 | REDUCE: (133), (534) imply: % 146.43/20.83 | (596) op(all_8_2, all_8_2) = all_42_1 % 146.43/20.83 | % 146.43/20.83 | REDUCE: (128), (507) imply: % 146.43/20.83 | (597) op(all_6_2, all_6_2) = all_40_1 % 146.43/20.83 | % 146.43/20.83 | REDUCE: (123), (533) imply: % 146.43/20.83 | (598) op(all_10_2, all_10_2) = all_38_1 % 146.43/20.83 | % 146.43/20.83 | REDUCE: (118), (532) imply: % 146.43/20.83 | (599) op(all_6_2, all_6_2) = all_36_1 % 146.43/20.83 | % 146.43/20.83 | REDUCE: (113), (531) imply: % 146.43/20.83 | (600) op(all_4_2, all_4_2) = all_34_1 % 146.43/20.83 | % 146.43/20.83 | REDUCE: (108), (494) imply: % 146.43/20.83 | (601) op(all_10_2, all_10_2) = all_32_1 % 146.43/20.83 | % 146.43/20.83 | REDUCE: (103), (390) imply: % 146.43/20.83 | (602) op(all_8_2, all_8_2) = all_30_1 % 146.43/20.83 | % 146.43/20.83 | REDUCE: (98), (513) imply: % 146.43/20.83 | (603) op(all_6_2, all_6_2) = all_28_1 % 146.43/20.83 | % 146.43/20.83 | REDUCE: (93), (530) imply: % 146.43/20.83 | (604) op(all_4_2, all_4_2) = all_26_1 % 146.43/20.83 | % 146.43/20.83 | REDUCE: (88), (521) imply: % 146.43/20.83 | (605) op(all_10_2, all_10_2) = all_24_1 % 146.43/20.83 | % 146.43/20.83 | REDUCE: (83), (523) imply: % 146.43/20.83 | (606) op(all_8_2, all_8_2) = all_22_1 % 146.43/20.83 | % 146.43/20.83 | REDUCE: (78), (499) imply: % 146.43/20.83 | (607) op(all_4_2, all_4_2) = all_20_1 % 146.43/20.83 | % 146.43/20.83 | REDUCE: (73), (524) imply: % 146.43/20.83 | (608) op(all_6_2, all_6_2) = all_18_1 % 146.43/20.83 | % 146.43/20.83 | REDUCE: (68), (527) imply: % 146.43/20.83 | (609) op(all_10_2, all_10_2) = all_16_1 % 146.43/20.83 | % 146.43/20.83 | REDUCE: (63), (528) imply: % 146.43/20.83 | (610) op(all_8_2, all_8_2) = all_14_1 % 146.43/20.83 | % 146.43/20.83 | REDUCE: (58), (529) imply: % 146.43/20.83 | (611) op(all_4_2, all_4_2) = all_12_1 % 146.43/20.83 | % 146.43/20.83 | REDUCE: (285), (546) imply: % 146.43/20.83 | (612) op(e3, all_10_2) = all_56_0 % 146.43/20.83 | % 146.43/20.83 | REDUCE: (284), (425) imply: % 146.43/20.83 | (613) op(e3, all_52_1) = all_56_8 % 146.43/20.83 | % 146.43/20.83 | REDUCE: (283), (381) imply: % 146.43/20.83 | (614) op(e3, all_52_2) = all_56_16 % 146.43/20.83 | % 146.43/20.83 | REDUCE: (282), (447) imply: % 146.43/20.83 | (615) op(e3, all_52_3) = all_56_24 % 146.43/20.83 | % 146.43/20.83 | REDUCE: (277), (408) imply: % 146.43/20.83 | (616) op(e2, all_52_4) = all_56_2 % 146.43/20.83 | % 146.43/20.83 | REDUCE: (276), (545) imply: % 146.43/20.83 | (617) op(e2, all_8_2) = all_56_10 % 146.43/20.83 | % 146.43/20.83 | REDUCE: (275), (435) imply: % 146.43/20.83 | (618) op(e2, all_52_6) = all_56_18 % 146.43/20.83 | % 146.43/20.83 | REDUCE: (274), (360) imply: % 146.43/20.83 | (619) op(e2, all_52_7) = all_56_26 % 146.43/20.83 | % 146.43/20.83 | REDUCE: (269), (429) imply: % 146.43/20.83 | (620) op(e1, all_52_8) = all_56_4 % 146.43/20.83 | % 146.43/20.83 | REDUCE: (268), (431) imply: % 146.43/20.83 | (621) op(e1, all_52_9) = all_56_12 % 146.43/20.83 | % 146.43/20.83 | REDUCE: (267), (374) imply: % 146.43/20.83 | (622) op(e1, all_6_2) = all_56_20 % 146.43/20.83 | % 146.43/20.83 | REDUCE: (266), (357) imply: % 146.43/20.83 | (623) op(e1, all_52_11) = all_56_28 % 146.43/20.83 | % 146.43/20.83 | REDUCE: (261), (402) imply: % 146.43/20.83 | (624) op(e0, all_52_12) = all_56_6 % 146.43/20.83 | % 146.43/20.83 | REDUCE: (260), (443) imply: % 146.43/20.83 | (625) op(e0, all_52_13) = all_56_14 % 146.43/20.83 | % 146.43/20.83 | REDUCE: (259), (366) imply: % 146.43/20.83 | (626) op(e0, all_52_14) = all_56_22 % 146.43/20.83 | % 146.43/20.83 | REDUCE: (258), (544) imply: % 146.43/20.83 | (627) op(e0, all_4_2) = all_56_30 % 146.43/20.83 | % 146.43/20.83 | GROUND_INST: instantiating (function-axioms) with all_26_1, all_34_1, all_4_2, % 146.43/20.83 | all_4_2, simplifying with (600), (604) gives: % 146.43/20.83 | (628) all_34_1 = all_26_1 % 146.43/20.83 | % 146.43/20.83 | GROUND_INST: instantiating (function-axioms) with all_20_1, all_34_1, all_4_2, % 146.43/20.83 | all_4_2, simplifying with (600), (607) gives: % 146.43/20.83 | (629) all_34_1 = all_20_1 % 146.43/20.83 | % 146.43/20.83 | GROUND_INST: instantiating (function-axioms) with all_12_1, all_34_1, all_4_2, % 146.43/20.83 | all_4_2, simplifying with (600), (611) gives: % 146.43/20.83 | (630) all_34_1 = all_12_1 % 146.43/20.83 | % 146.43/20.83 | GROUND_INST: instantiating (function-axioms) with all_4_1, all_44_1, all_4_2, % 146.43/20.83 | all_4_2, simplifying with (38), (595) gives: % 146.43/20.83 | (631) all_44_1 = all_4_1 % 146.43/20.83 | % 146.43/20.83 | GROUND_INST: instantiating (function-axioms) with all_26_1, all_44_1, all_4_2, % 146.43/20.83 | all_4_2, simplifying with (595), (604) gives: % 146.43/20.83 | (632) all_44_1 = all_26_1 % 146.43/20.83 | % 146.43/20.83 | GROUND_INST: instantiating (function-axioms) with all_18_1, all_40_1, all_6_2, % 146.43/20.83 | all_6_2, simplifying with (597), (608) gives: % 146.43/20.83 | (633) all_40_1 = all_18_1 % 146.43/20.83 | % 146.43/20.83 | GROUND_INST: instantiating (function-axioms) with all_6_1, all_46_1, all_6_2, % 146.43/20.83 | all_6_2, simplifying with (43), (594) gives: % 146.43/20.83 | (634) all_46_1 = all_6_1 % 146.43/20.83 | % 146.43/20.83 | GROUND_INST: instantiating (function-axioms) with all_40_1, all_46_1, all_6_2, % 146.43/20.83 | all_6_2, simplifying with (594), (597) gives: % 146.43/20.83 | (635) all_46_1 = all_40_1 % 146.43/20.83 | % 146.43/20.83 | GROUND_INST: instantiating (function-axioms) with all_36_1, all_46_1, all_6_2, % 146.43/20.83 | all_6_2, simplifying with (594), (599) gives: % 146.43/20.83 | (636) all_46_1 = all_36_1 % 146.43/20.83 | % 146.43/20.83 | GROUND_INST: instantiating (function-axioms) with all_28_1, all_46_1, all_6_2, % 146.43/20.83 | all_6_2, simplifying with (594), (603) gives: % 146.43/20.83 | (637) all_46_1 = all_28_1 % 146.43/20.83 | % 146.43/20.83 | GROUND_INST: instantiating (function-axioms) with all_14_1, all_22_1, all_8_2, % 146.43/20.83 | all_8_2, simplifying with (606), (610) gives: % 146.43/20.83 | (638) all_22_1 = all_14_1 % 146.43/20.83 | % 146.43/20.83 | GROUND_INST: instantiating (function-axioms) with all_8_1, all_42_1, all_8_2, % 146.43/20.83 | all_8_2, simplifying with (48), (596) gives: % 146.43/20.83 | (639) all_42_1 = all_8_1 % 146.43/20.83 | % 146.43/20.83 | GROUND_INST: instantiating (function-axioms) with all_22_1, all_42_1, all_8_2, % 146.43/20.83 | all_8_2, simplifying with (596), (606) gives: % 146.43/20.83 | (640) all_42_1 = all_22_1 % 146.43/20.83 | % 146.43/20.83 | GROUND_INST: instantiating (function-axioms) with all_42_1, all_48_1, all_8_2, % 146.43/20.83 | all_8_2, simplifying with (593), (596) gives: % 146.43/20.83 | (641) all_48_1 = all_42_1 % 146.43/20.83 | % 146.43/20.83 | GROUND_INST: instantiating (function-axioms) with all_30_1, all_48_1, all_8_2, % 146.43/20.83 | all_8_2, simplifying with (593), (602) gives: % 146.43/20.83 | (642) all_48_1 = all_30_1 % 146.43/20.83 | % 146.43/20.83 | GROUND_INST: instantiating (function-axioms) with all_10_1, all_24_1, % 146.43/20.83 | all_10_2, all_10_2, simplifying with (53), (605) gives: % 146.43/20.83 | (643) all_24_1 = all_10_1 % 146.43/20.83 | % 146.43/20.83 | GROUND_INST: instantiating (function-axioms) with all_24_1, all_32_1, % 146.43/20.83 | all_10_2, all_10_2, simplifying with (601), (605) gives: % 146.43/20.83 | (644) all_32_1 = all_24_1 % 146.43/20.83 | % 146.43/20.83 | GROUND_INST: instantiating (function-axioms) with all_32_1, all_38_1, % 146.43/20.83 | all_10_2, all_10_2, simplifying with (598), (601) gives: % 146.43/20.83 | (645) all_38_1 = all_32_1 % 146.43/20.83 | % 146.43/20.83 | GROUND_INST: instantiating (function-axioms) with all_38_1, all_50_1, % 146.43/20.83 | all_10_2, all_10_2, simplifying with (592), (598) gives: % 146.43/20.83 | (646) all_50_1 = all_38_1 % 146.43/20.83 | % 146.43/20.83 | GROUND_INST: instantiating (function-axioms) with all_16_1, all_50_1, % 146.43/20.83 | all_10_2, all_10_2, simplifying with (592), (609) gives: % 146.43/20.83 | (647) all_50_1 = all_16_1 % 146.43/20.83 | % 146.43/20.83 | COMBINE_EQS: (646), (647) imply: % 146.43/20.83 | (648) all_38_1 = all_16_1 % 146.43/20.83 | % 146.43/20.83 | SIMP: (648) implies: % 146.43/20.83 | (649) all_38_1 = all_16_1 % 146.43/20.83 | % 146.43/20.83 | COMBINE_EQS: (641), (642) imply: % 146.43/20.83 | (650) all_42_1 = all_30_1 % 146.43/20.83 | % 146.43/20.83 | SIMP: (650) implies: % 146.43/20.83 | (651) all_42_1 = all_30_1 % 146.43/20.83 | % 146.43/20.83 | COMBINE_EQS: (634), (636) imply: % 146.43/20.83 | (652) all_36_1 = all_6_1 % 146.43/20.83 | % 146.43/20.83 | COMBINE_EQS: (635), (636) imply: % 146.43/20.83 | (653) all_40_1 = all_36_1 % 146.43/20.83 | % 146.43/20.83 | SIMP: (653) implies: % 146.43/20.83 | (654) all_40_1 = all_36_1 % 146.43/20.83 | % 146.43/20.83 | COMBINE_EQS: (636), (637) imply: % 146.43/20.83 | (655) all_36_1 = all_28_1 % 146.43/20.83 | % 146.43/20.83 | COMBINE_EQS: (631), (632) imply: % 146.43/20.83 | (656) all_26_1 = all_4_1 % 146.43/20.83 | % 146.43/20.83 | SIMP: (656) implies: % 146.43/20.83 | (657) all_26_1 = all_4_1 % 146.43/20.83 | % 146.43/20.83 | COMBINE_EQS: (639), (651) imply: % 146.43/20.83 | (658) all_30_1 = all_8_1 % 146.43/20.83 | % 146.43/20.83 | COMBINE_EQS: (640), (651) imply: % 146.43/20.83 | (659) all_30_1 = all_22_1 % 146.43/20.83 | % 146.43/20.83 | COMBINE_EQS: (633), (654) imply: % 146.43/20.83 | (660) all_36_1 = all_18_1 % 146.43/20.83 | % 146.43/20.83 | SIMP: (660) implies: % 146.43/20.83 | (661) all_36_1 = all_18_1 % 146.43/20.83 | % 146.43/20.83 | COMBINE_EQS: (645), (649) imply: % 146.43/20.83 | (662) all_32_1 = all_16_1 % 146.43/20.83 | % 146.43/20.83 | SIMP: (662) implies: % 146.43/20.83 | (663) all_32_1 = all_16_1 % 146.43/20.83 | % 146.43/20.83 | COMBINE_EQS: (655), (661) imply: % 146.43/20.83 | (664) all_28_1 = all_18_1 % 146.43/20.83 | % 146.43/20.83 | COMBINE_EQS: (652), (655) imply: % 146.43/20.83 | (665) all_28_1 = all_6_1 % 146.43/20.83 | % 146.43/20.83 | COMBINE_EQS: (628), (629) imply: % 146.43/20.83 | (666) all_26_1 = all_20_1 % 146.43/20.83 | % 146.43/20.83 | SIMP: (666) implies: % 146.43/20.83 | (667) all_26_1 = all_20_1 % 146.43/20.83 | % 146.43/20.83 | COMBINE_EQS: (629), (630) imply: % 146.43/20.83 | (668) all_20_1 = all_12_1 % 146.43/20.83 | % 146.43/20.83 | COMBINE_EQS: (644), (663) imply: % 146.43/20.83 | (669) all_24_1 = all_16_1 % 146.43/20.83 | % 146.43/20.83 | SIMP: (669) implies: % 146.43/20.83 | (670) all_24_1 = all_16_1 % 146.43/20.83 | % 146.43/20.83 | COMBINE_EQS: (658), (659) imply: % 146.43/20.83 | (671) all_22_1 = all_8_1 % 146.43/20.83 | % 146.43/20.83 | SIMP: (671) implies: % 146.43/20.83 | (672) all_22_1 = all_8_1 % 146.43/20.83 | % 146.43/20.83 | COMBINE_EQS: (664), (665) imply: % 146.43/20.83 | (673) all_18_1 = all_6_1 % 146.43/20.83 | % 146.43/20.83 | SIMP: (673) implies: % 146.43/20.83 | (674) all_18_1 = all_6_1 % 146.43/20.83 | % 146.43/20.83 | COMBINE_EQS: (657), (667) imply: % 146.43/20.83 | (675) all_20_1 = all_4_1 % 146.43/20.83 | % 146.43/20.83 | SIMP: (675) implies: % 146.43/20.83 | (676) all_20_1 = all_4_1 % 146.43/20.83 | % 146.43/20.83 | COMBINE_EQS: (643), (670) imply: % 146.43/20.83 | (677) all_16_1 = all_10_1 % 146.43/20.83 | % 146.43/20.83 | COMBINE_EQS: (638), (672) imply: % 146.43/20.83 | (678) all_14_1 = all_8_1 % 146.43/20.83 | % 146.43/20.83 | SIMP: (678) implies: % 146.43/20.83 | (679) all_14_1 = all_8_1 % 146.43/20.83 | % 146.43/20.83 | COMBINE_EQS: (668), (676) imply: % 146.43/20.83 | (680) all_12_1 = all_4_1 % 146.43/20.83 | % 146.43/20.83 | SIMP: (680) implies: % 146.43/20.83 | (681) all_12_1 = all_4_1 % 146.43/20.83 | % 146.43/20.83 | COMBINE_EQS: (663), (677) imply: % 146.43/20.83 | (682) all_32_1 = all_10_1 % 146.43/20.83 | % 146.43/20.83 | COMBINE_EQS: (629), (676) imply: % 146.43/20.84 | (683) all_34_1 = all_4_1 % 146.43/20.84 | % 146.43/20.84 | COMBINE_EQS: (649), (677) imply: % 146.43/20.84 | (684) all_38_1 = all_10_1 % 146.43/20.84 | % 146.43/20.84 | COMBINE_EQS: (633), (674) imply: % 146.43/20.84 | (685) all_40_1 = all_6_1 % 146.43/20.84 | % 146.43/20.84 | COMBINE_EQS: (642), (658) imply: % 146.43/20.84 | (686) all_48_1 = all_8_1 % 146.43/20.84 | % 146.43/20.84 | COMBINE_EQS: (647), (677) imply: % 146.43/20.84 | (687) all_50_1 = all_10_1 % 146.43/20.84 | % 146.43/20.84 | REDUCE: (152), (687) imply: % 146.43/20.84 | (688) op(e3, all_10_1) = all_50_0 % 146.43/20.84 | % 146.43/20.84 | REDUCE: (122), (684) imply: % 146.43/20.84 | (689) op(e3, all_10_1) = all_38_0 % 146.43/20.84 | % 146.43/20.84 | REDUCE: (107), (682) imply: % 146.43/20.84 | (690) op(e3, all_10_1) = all_32_0 % 146.43/20.84 | % 146.43/20.84 | REDUCE: (87), (643) imply: % 146.43/20.84 | (691) op(e3, all_10_1) = all_24_0 % 146.43/20.84 | % 146.43/20.84 | REDUCE: (67), (677) imply: % 146.43/20.84 | (692) op(e3, all_10_1) = all_16_0 % 146.43/20.84 | % 146.43/20.84 | REDUCE: (147), (686) imply: % 146.43/20.84 | (693) op(e2, all_8_1) = all_48_0 % 146.43/20.84 | % 146.43/20.84 | REDUCE: (132), (639) imply: % 146.43/20.84 | (694) op(e2, all_8_1) = all_42_0 % 146.43/20.84 | % 146.43/20.84 | REDUCE: (102), (658) imply: % 146.43/20.84 | (695) op(e2, all_8_1) = all_30_0 % 146.43/20.84 | % 146.43/20.84 | REDUCE: (82), (672) imply: % 146.43/20.84 | (696) op(e2, all_8_1) = all_22_0 % 146.43/20.84 | % 146.43/20.84 | REDUCE: (62), (679) imply: % 146.43/20.84 | (697) op(e2, all_8_1) = all_14_0 % 146.43/20.84 | % 146.43/20.84 | REDUCE: (142), (634) imply: % 146.43/20.84 | (698) op(e1, all_6_1) = all_46_0 % 146.43/20.84 | % 146.43/20.84 | REDUCE: (127), (685) imply: % 146.43/20.84 | (699) op(e1, all_6_1) = all_40_0 % 146.43/20.84 | % 146.43/20.84 | REDUCE: (117), (652) imply: % 146.43/20.84 | (700) op(e1, all_6_1) = all_36_0 % 146.43/20.84 | % 146.43/20.84 | REDUCE: (97), (665) imply: % 146.43/20.84 | (701) op(e1, all_6_1) = all_28_0 % 146.43/20.84 | % 146.43/20.84 | REDUCE: (72), (674) imply: % 146.43/20.84 | (702) op(e1, all_6_1) = all_18_0 % 146.43/20.84 | % 146.43/20.84 | REDUCE: (137), (631) imply: % 146.43/20.84 | (703) op(e0, all_4_1) = all_44_0 % 146.43/20.84 | % 146.43/20.84 | REDUCE: (112), (683) imply: % 146.43/20.84 | (704) op(e0, all_4_1) = all_34_0 % 146.43/20.84 | % 146.43/20.84 | REDUCE: (92), (657) imply: % 146.43/20.84 | (705) op(e0, all_4_1) = all_26_0 % 146.43/20.84 | % 146.43/20.84 | REDUCE: (77), (676) imply: % 146.43/20.84 | (706) op(e0, all_4_1) = all_20_0 % 146.43/20.84 | % 146.43/20.84 | REDUCE: (57), (681) imply: % 146.43/20.84 | (707) op(e0, all_4_1) = all_12_0 % 146.43/20.84 | % 146.43/20.84 | GROUND_INST: instantiating (function-axioms) with all_12_0, all_26_0, all_4_1, % 146.43/20.84 | e0, simplifying with (705), (707) gives: % 146.43/20.84 | (708) all_26_0 = all_12_0 % 146.43/20.84 | % 146.43/20.84 | GROUND_INST: instantiating (function-axioms) with all_4_0, all_44_0, all_4_1, % 146.43/20.84 | e0, simplifying with (37), (703) gives: % 146.43/20.84 | (709) all_44_0 = all_4_0 % 146.43/20.84 | % 146.43/20.84 | GROUND_INST: instantiating (function-axioms) with all_34_0, all_44_0, all_4_1, % 146.43/20.84 | e0, simplifying with (703), (704) gives: % 146.43/20.84 | (710) all_44_0 = all_34_0 % 146.43/20.84 | % 146.43/20.84 | GROUND_INST: instantiating (function-axioms) with all_26_0, all_44_0, all_4_1, % 146.43/20.84 | e0, simplifying with (703), (705) gives: % 146.43/20.84 | (711) all_44_0 = all_26_0 % 146.43/20.84 | % 146.43/20.84 | GROUND_INST: instantiating (function-axioms) with all_20_0, all_44_0, all_4_1, % 146.43/20.84 | e0, simplifying with (703), (706) gives: % 146.43/20.84 | (712) all_44_0 = all_20_0 % 146.43/20.84 | % 146.43/20.84 | GROUND_INST: instantiating (function-axioms) with all_6_0, all_40_0, all_6_1, % 146.43/20.84 | e1, simplifying with (42), (699) gives: % 146.43/20.84 | (713) all_40_0 = all_6_0 % 146.43/20.84 | % 146.43/20.84 | GROUND_INST: instantiating (function-axioms) with all_28_0, all_40_0, all_6_1, % 146.43/20.84 | e1, simplifying with (699), (701) gives: % 146.43/20.84 | (714) all_40_0 = all_28_0 % 146.43/20.84 | % 146.43/20.84 | GROUND_INST: instantiating (function-axioms) with all_36_0, all_46_0, all_6_1, % 146.43/20.84 | e1, simplifying with (698), (700) gives: % 146.43/20.84 | (715) all_46_0 = all_36_0 % 146.43/20.84 | % 146.43/20.84 | GROUND_INST: instantiating (function-axioms) with all_28_0, all_46_0, all_6_1, % 146.43/20.84 | e1, simplifying with (698), (701) gives: % 146.43/20.84 | (716) all_46_0 = all_28_0 % 146.43/20.84 | % 146.43/20.84 | GROUND_INST: instantiating (function-axioms) with all_18_0, all_46_0, all_6_1, % 146.43/20.84 | e1, simplifying with (698), (702) gives: % 146.43/20.84 | (717) all_46_0 = all_18_0 % 146.43/20.84 | % 146.43/20.84 | GROUND_INST: instantiating (function-axioms) with all_8_0, all_30_0, all_8_1, % 146.43/20.84 | e2, simplifying with (47), (695) gives: % 146.43/20.84 | (718) all_30_0 = all_8_0 % 146.43/20.84 | % 146.43/20.84 | GROUND_INST: instantiating (function-axioms) with all_14_0, all_30_0, all_8_1, % 146.43/20.84 | e2, simplifying with (695), (697) gives: % 146.43/20.84 | (719) all_30_0 = all_14_0 % 146.43/20.84 | % 146.43/20.84 | GROUND_INST: instantiating (function-axioms) with all_42_0, all_48_0, all_8_1, % 146.43/20.84 | e2, simplifying with (693), (694) gives: % 146.43/20.84 | (720) all_48_0 = all_42_0 % 146.43/20.84 | % 146.43/20.84 | GROUND_INST: instantiating (function-axioms) with all_30_0, all_48_0, all_8_1, % 146.43/20.84 | e2, simplifying with (693), (695) gives: % 146.43/20.84 | (721) all_48_0 = all_30_0 % 146.43/20.84 | % 146.43/20.84 | GROUND_INST: instantiating (function-axioms) with all_22_0, all_48_0, all_8_1, % 146.43/20.84 | e2, simplifying with (693), (696) gives: % 146.43/20.84 | (722) all_48_0 = all_22_0 % 146.43/20.84 | % 146.43/20.84 | GROUND_INST: instantiating (function-axioms) with all_10_0, all_38_0, % 146.43/20.84 | all_10_1, e3, simplifying with (52), (689) gives: % 146.43/20.84 | (723) all_38_0 = all_10_0 % 146.43/20.84 | % 146.43/20.84 | GROUND_INST: instantiating (function-axioms) with all_32_0, all_38_0, % 146.43/20.84 | all_10_1, e3, simplifying with (689), (690) gives: % 146.43/20.84 | (724) all_38_0 = all_32_0 % 146.43/20.84 | % 146.43/20.84 | GROUND_INST: instantiating (function-axioms) with all_24_0, all_38_0, % 146.43/20.84 | all_10_1, e3, simplifying with (689), (691) gives: % 146.43/20.84 | (725) all_38_0 = all_24_0 % 146.43/20.84 | % 146.43/20.84 | GROUND_INST: instantiating (function-axioms) with all_32_0, all_50_0, % 146.43/20.84 | all_10_1, e3, simplifying with (688), (690) gives: % 146.43/20.84 | (726) all_50_0 = all_32_0 % 146.43/20.84 | % 146.43/20.84 | GROUND_INST: instantiating (function-axioms) with all_16_0, all_50_0, % 146.43/20.84 | all_10_1, e3, simplifying with (688), (692) gives: % 146.43/20.84 | (727) all_50_0 = all_16_0 % 146.43/20.84 | % 146.43/20.84 | COMBINE_EQS: (726), (727) imply: % 146.43/20.84 | (728) all_32_0 = all_16_0 % 146.43/20.84 | % 146.43/20.84 | SIMP: (728) implies: % 146.43/20.84 | (729) all_32_0 = all_16_0 % 146.43/20.84 | % 146.43/20.84 | COMBINE_EQS: (720), (722) imply: % 146.43/20.84 | (730) all_42_0 = all_22_0 % 146.43/20.84 | % 146.43/20.84 | COMBINE_EQS: (720), (721) imply: % 146.43/20.84 | (731) all_42_0 = all_30_0 % 146.43/20.84 | % 146.43/20.84 | COMBINE_EQS: (715), (717) imply: % 146.43/20.84 | (732) all_36_0 = all_18_0 % 146.43/20.84 | % 146.43/20.84 | COMBINE_EQS: (715), (716) imply: % 146.43/20.84 | (733) all_36_0 = all_28_0 % 146.43/20.84 | % 146.43/20.84 | COMBINE_EQS: (709), (710) imply: % 146.43/20.84 | (734) all_34_0 = all_4_0 % 146.43/20.84 | % 146.43/20.84 | COMBINE_EQS: (710), (711) imply: % 146.43/20.84 | (735) all_34_0 = all_26_0 % 146.43/20.84 | % 146.43/20.84 | COMBINE_EQS: (710), (712) imply: % 146.43/20.84 | (736) all_34_0 = all_20_0 % 146.43/20.84 | % 146.43/20.84 | COMBINE_EQS: (730), (731) imply: % 146.43/20.84 | (737) all_30_0 = all_22_0 % 146.43/20.84 | % 146.43/20.84 | SIMP: (737) implies: % 146.43/20.84 | (738) all_30_0 = all_22_0 % 146.43/20.84 | % 146.43/20.84 | COMBINE_EQS: (713), (714) imply: % 146.43/20.84 | (739) all_28_0 = all_6_0 % 146.43/20.84 | % 146.43/20.84 | SIMP: (739) implies: % 146.43/20.84 | (740) all_28_0 = all_6_0 % 146.43/20.84 | % 146.43/20.84 | COMBINE_EQS: (723), (725) imply: % 146.43/20.84 | (741) all_24_0 = all_10_0 % 146.43/20.84 | % 146.43/20.84 | COMBINE_EQS: (724), (725) imply: % 146.43/20.84 | (742) all_32_0 = all_24_0 % 146.43/20.84 | % 146.43/20.84 | SIMP: (742) implies: % 146.43/20.84 | (743) all_32_0 = all_24_0 % 146.43/20.84 | % 146.43/20.84 | COMBINE_EQS: (732), (733) imply: % 146.43/20.84 | (744) all_28_0 = all_18_0 % 146.43/20.84 | % 146.43/20.84 | SIMP: (744) implies: % 146.43/20.84 | (745) all_28_0 = all_18_0 % 146.43/20.84 | % 146.43/20.84 | COMBINE_EQS: (734), (736) imply: % 146.43/20.84 | (746) all_20_0 = all_4_0 % 146.43/20.84 | % 146.43/20.84 | COMBINE_EQS: (735), (736) imply: % 146.43/20.84 | (747) all_26_0 = all_20_0 % 146.43/20.84 | % 146.43/20.84 | SIMP: (747) implies: % 146.43/20.84 | (748) all_26_0 = all_20_0 % 146.43/20.84 | % 146.43/20.84 | COMBINE_EQS: (729), (743) imply: % 146.43/20.84 | (749) all_24_0 = all_16_0 % 146.43/20.84 | % 146.43/20.84 | SIMP: (749) implies: % 146.43/20.84 | (750) all_24_0 = all_16_0 % 146.43/20.84 | % 146.43/20.84 | COMBINE_EQS: (719), (738) imply: % 146.43/20.84 | (751) all_22_0 = all_14_0 % 146.43/20.84 | % 146.43/20.84 | COMBINE_EQS: (718), (738) imply: % 146.43/20.84 | (752) all_22_0 = all_8_0 % 146.43/20.84 | % 146.43/20.84 | COMBINE_EQS: (740), (745) imply: % 146.43/20.84 | (753) all_18_0 = all_6_0 % 146.43/20.84 | % 146.43/20.84 | COMBINE_EQS: (708), (748) imply: % 146.43/20.84 | (754) all_20_0 = all_12_0 % 146.43/20.84 | % 146.43/20.84 | SIMP: (754) implies: % 146.43/20.84 | (755) all_20_0 = all_12_0 % 146.43/20.84 | % 146.43/20.84 | COMBINE_EQS: (741), (750) imply: % 146.43/20.84 | (756) all_16_0 = all_10_0 % 146.43/20.84 | % 146.43/20.84 | SIMP: (756) implies: % 146.43/20.84 | (757) all_16_0 = all_10_0 % 146.43/20.84 | % 146.43/20.84 | COMBINE_EQS: (751), (752) imply: % 146.43/20.84 | (758) all_14_0 = all_8_0 % 146.43/20.84 | % 146.43/20.84 | COMBINE_EQS: (746), (755) imply: % 146.43/20.84 | (759) all_12_0 = all_4_0 % 146.43/20.84 | % 146.43/20.84 | COMBINE_EQS: (708), (759) imply: % 146.43/20.84 | (760) all_26_0 = all_4_0 % 146.43/20.84 | % 146.43/20.84 | COMBINE_EQS: (729), (757) imply: % 146.43/20.84 | (761) all_32_0 = all_10_0 % 146.43/20.84 | % 146.43/20.84 | COMBINE_EQS: (732), (753) imply: % 146.43/20.84 | (762) all_36_0 = all_6_0 % 146.43/20.84 | % 146.43/20.84 | COMBINE_EQS: (730), (752) imply: % 146.43/20.84 | (763) all_42_0 = all_8_0 % 146.43/20.84 | % 146.43/20.84 | COMBINE_EQS: (715), (762) imply: % 146.43/20.84 | (764) all_46_0 = all_6_0 % 146.43/20.84 | % 146.43/20.84 | COMBINE_EQS: (720), (763) imply: % 146.43/20.84 | (765) all_48_0 = all_8_0 % 146.43/20.84 | % 146.43/20.84 | COMBINE_EQS: (727), (757) imply: % 146.43/20.84 | (766) all_50_0 = all_10_0 % 146.43/20.84 | % 146.43/20.84 | BETA: splitting (39) gives: % 146.43/20.84 | % 146.43/20.84 | Case 1: % 146.43/20.84 | | % 146.43/20.84 | | (767) ~ (all_4_0 = e3) % 146.43/20.84 | | % 146.43/20.84 | | BETA: splitting (44) gives: % 146.43/20.84 | | % 146.43/20.84 | | Case 1: % 146.43/20.84 | | | % 146.43/20.84 | | | (768) ~ (all_6_1 = e2) % 146.43/20.84 | | | % 146.43/20.84 | | | BETA: splitting (49) gives: % 146.43/20.84 | | | % 146.43/20.84 | | | Case 1: % 146.43/20.84 | | | | % 146.43/20.84 | | | | (769) ~ (all_8_1 = e1) % 146.43/20.84 | | | | % 146.43/20.84 | | | | BETA: splitting (54) gives: % 146.43/20.84 | | | | % 146.43/20.84 | | | | Case 1: % 146.43/20.84 | | | | | % 146.43/20.84 | | | | | (770) ~ (all_10_0 = e2) % 146.43/20.84 | | | | | % 146.43/20.84 | | | | | BETA: splitting (59) gives: % 146.43/20.84 | | | | | % 146.43/20.84 | | | | | Case 1: % 146.43/20.84 | | | | | | % 146.43/20.84 | | | | | | (771) ~ (all_12_0 = e2) % 146.43/20.84 | | | | | | % 146.43/20.84 | | | | | | REDUCE: (759), (771) imply: % 146.43/20.84 | | | | | | (772) ~ (all_4_0 = e2) % 146.43/20.84 | | | | | | % 146.43/20.84 | | | | | | BETA: splitting (64) gives: % 146.43/20.84 | | | | | | % 146.43/20.84 | | | | | | Case 1: % 146.43/20.84 | | | | | | | % 146.43/20.84 | | | | | | | (773) ~ (all_14_0 = e1) % 146.43/20.84 | | | | | | | % 146.43/20.84 | | | | | | | REDUCE: (758), (773) imply: % 146.43/20.84 | | | | | | | (774) ~ (all_8_0 = e1) % 146.43/20.84 | | | | | | | % 146.43/20.84 | | | | | | | BETA: splitting (69) gives: % 146.43/20.84 | | | | | | | % 146.43/20.84 | | | | | | | Case 1: % 146.43/20.84 | | | | | | | | % 146.43/20.84 | | | | | | | | (775) ~ (all_16_0 = e1) % 146.43/20.84 | | | | | | | | % 146.43/20.84 | | | | | | | | REDUCE: (757), (775) imply: % 146.43/20.84 | | | | | | | | (776) ~ (all_10_0 = e1) % 146.43/20.84 | | | | | | | | % 146.43/20.84 | | | | | | | | BETA: splitting (84) gives: % 146.43/20.84 | | | | | | | | % 146.43/20.84 | | | | | | | | Case 1: % 146.43/20.84 | | | | | | | | | % 146.43/20.84 | | | | | | | | | (777) ~ (all_22_1 = e3) % 146.43/20.84 | | | | | | | | | % 146.43/20.84 | | | | | | | | | REDUCE: (672), (777) imply: % 146.43/20.84 | | | | | | | | | (778) ~ (all_8_1 = e3) % 146.43/20.84 | | | | | | | | | % 146.43/20.84 | | | | | | | | | BETA: splitting (94) gives: % 146.43/20.84 | | | | | | | | | % 146.43/20.84 | | | | | | | | | Case 1: % 146.43/20.84 | | | | | | | | | | % 146.43/20.84 | | | | | | | | | | (779) ~ (all_26_0 = e1) % 146.43/20.84 | | | | | | | | | | % 146.43/20.84 | | | | | | | | | | REDUCE: (760), (779) imply: % 146.43/20.84 | | | | | | | | | | (780) ~ (all_4_0 = e1) % 146.43/20.84 | | | | | | | | | | % 146.43/20.84 | | | | | | | | | | BETA: splitting (99) gives: % 146.43/20.84 | | | | | | | | | | % 146.43/20.84 | | | | | | | | | | Case 1: % 146.43/20.84 | | | | | | | | | | | % 146.43/20.84 | | | | | | | | | | | (781) ~ (all_28_0 = e2) % 146.43/20.84 | | | | | | | | | | | % 146.43/20.84 | | | | | | | | | | | REDUCE: (740), (781) imply: % 146.43/20.84 | | | | | | | | | | | (782) ~ (all_6_0 = e2) % 146.43/20.84 | | | | | | | | | | | % 146.43/20.84 | | | | | | | | | | | BETA: splitting (104) gives: % 146.43/20.84 | | | | | | | | | | | % 146.43/20.84 | | | | | | | | | | | Case 1: % 146.43/20.84 | | | | | | | | | | | | % 146.43/20.84 | | | | | | | | | | | | (783) ~ (all_30_0 = e3) % 146.43/20.84 | | | | | | | | | | | | % 146.43/20.84 | | | | | | | | | | | | REDUCE: (718), (783) imply: % 146.43/20.84 | | | | | | | | | | | | (784) ~ (all_8_0 = e3) % 146.43/20.84 | | | | | | | | | | | | % 146.43/20.84 | | | | | | | | | | | | BETA: splitting (109) gives: % 146.43/20.84 | | | | | | | | | | | | % 146.43/20.84 | | | | | | | | | | | | Case 1: % 146.43/20.84 | | | | | | | | | | | | | % 146.43/20.84 | | | | | | | | | | | | | (785) ~ (all_32_1 = e1) % 146.43/20.84 | | | | | | | | | | | | | % 146.43/20.84 | | | | | | | | | | | | | REDUCE: (682), (785) imply: % 146.43/20.84 | | | | | | | | | | | | | (786) ~ (all_10_1 = e1) % 146.43/20.84 | | | | | | | | | | | | | % 146.43/20.84 | | | | | | | | | | | | | BETA: splitting (119) gives: % 146.43/20.84 | | | | | | | | | | | | | % 146.43/20.84 | | | | | | | | | | | | | Case 1: % 146.43/20.84 | | | | | | | | | | | | | | % 146.43/20.84 | | | | | | | | | | | | | | (787) ~ (all_36_1 = e3) % 146.43/20.84 | | | | | | | | | | | | | | % 146.43/20.84 | | | | | | | | | | | | | | REDUCE: (652), (787) imply: % 146.43/20.84 | | | | | | | | | | | | | | (788) ~ (all_6_1 = e3) % 146.43/20.84 | | | | | | | | | | | | | | % 146.43/20.84 | | | | | | | | | | | | | | BETA: splitting (124) gives: % 146.43/20.84 | | | | | | | | | | | | | | % 146.43/20.84 | | | | | | | | | | | | | | Case 1: % 146.43/20.84 | | | | | | | | | | | | | | | % 146.43/20.84 | | | | | | | | | | | | | | | (789) ~ (all_38_1 = e2) % 146.43/20.84 | | | | | | | | | | | | | | | % 146.43/20.84 | | | | | | | | | | | | | | | REDUCE: (684), (789) imply: % 146.43/20.84 | | | | | | | | | | | | | | | (790) ~ (all_10_1 = e2) % 146.43/20.84 | | | | | | | | | | | | | | | % 146.43/20.84 | | | | | | | | | | | | | | | BETA: splitting (129) gives: % 146.43/20.84 | | | | | | | | | | | | | | | % 146.43/20.84 | | | | | | | | | | | | | | | Case 1: % 146.43/20.84 | | | | | | | | | | | | | | | | % 146.43/20.84 | | | | | | | | | | | | | | | | (791) ~ (all_40_0 = e3) % 146.43/20.84 | | | | | | | | | | | | | | | | % 146.43/20.84 | | | | | | | | | | | | | | | | REDUCE: (713), (791) imply: % 146.43/20.84 | | | | | | | | | | | | | | | | (792) ~ (all_6_0 = e3) % 146.43/20.84 | | | | | | | | | | | | | | | | % 146.43/20.84 | | | | | | | | | | | | | | | | BETA: splitting (288) gives: % 146.43/20.84 | | | | | | | | | | | | | | | | % 146.43/20.84 | | | | | | | | | | | | | | | | Case 1: % 146.43/20.84 | | | | | | | | | | | | | | | | | % 146.43/20.84 | | | | | | | | | | | | | | | | | (793) ~ (all_56_31 = e1) % 146.43/20.84 | | | | | | | | | | | | | | | | | % 146.43/20.84 | | | | | | | | | | | | | | | | | REDUCE: (544), (793) imply: % 146.43/20.84 | | | | | | | | | | | | | | | | | (794) ~ (all_4_2 = e1) % 146.43/20.84 | | | | | | | | | | | | | | | | | % 146.43/20.84 | | | | | | | | | | | | | | | | | BETA: splitting (290) gives: % 146.43/20.84 | | | | | | | | | | | | | | | | | % 146.43/20.84 | | | | | | | | | | | | | | | | | Case 1: % 146.43/20.84 | | | | | | | | | | | | | | | | | | % 146.43/20.84 | | | | | | | | | | | | | | | | | | (795) ~ (all_56_31 = e3) % 146.43/20.84 | | | | | | | | | | | | | | | | | | % 146.43/20.84 | | | | | | | | | | | | | | | | | | REDUCE: (544), (795) imply: % 146.43/20.84 | | | | | | | | | | | | | | | | | | (796) ~ (all_4_2 = e3) % 146.43/20.84 | | | | | | | | | | | | | | | | | | % 146.43/20.84 | | | | | | | | | | | | | | | | | | BETA: splitting (289) gives: % 146.43/20.84 | | | | | | | | | | | | | | | | | | % 146.43/20.84 | | | | | | | | | | | | | | | | | | Case 1: % 146.43/20.84 | | | | | | | | | | | | | | | | | | | % 146.43/20.84 | | | | | | | | | | | | | | | | | | | (797) ~ (all_56_31 = e2) % 146.43/20.84 | | | | | | | | | | | | | | | | | | | % 146.43/20.84 | | | | | | | | | | | | | | | | | | | REDUCE: (544), (797) imply: % 146.43/20.84 | | | | | | | | | | | | | | | | | | | (798) ~ (all_4_2 = e2) % 146.43/20.84 | | | | | | | | | | | | | | | | | | | % 146.43/20.84 | | | | | | | | | | | | | | | | | | | BETA: splitting (237) gives: % 146.43/20.84 | | | | | | | | | | | | | | | | | | | % 146.43/20.84 | | | | | | | | | | | | | | | | | | | Case 1: % 146.43/20.84 | | | | | | | | | | | | | | | | | | | | % 146.43/20.84 | | | | | | | | | | | | | | | | | | | | (799) all_54_15 = e3 % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (540), (796), (799) are inconsistent by sub-proof % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | #740. % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | % 146.43/20.85 | | | | | | | | | | | | | | | | | | | Case 2: % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | (800) ~ (all_54_15 = e3) % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | (801) all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0 % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | BETA: splitting (801) gives: % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | Case 1: % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | (802) all_54_15 = e2 % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (540), (798), (802) are inconsistent by sub-proof % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | #739. % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | Case 2: % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | (803) ~ (all_54_15 = e2) % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | (804) all_54_15 = e1 | all_54_15 = e0 % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (804) gives: % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | Case 1: % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | | (805) all_54_15 = e1 % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (540), (794), (805) are inconsistent by sub-proof % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | | #738. % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | Case 2: % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | | (806) all_54_15 = e0 % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (540), (806) imply: % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | | (807) all_4_2 = e0 % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | | SIMP: (807) implies: % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | | (808) all_4_2 = e0 % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (544), (808) imply: % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | | (809) all_56_31 = e0 % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (547), (808) imply: % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | | (810) all_58_15 = e0 % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (570), (808) imply: % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | | (811) ~ (all_52_3 = e0) % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (581), (808) imply: % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | | (812) ~ (all_52_7 = e0) % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (588), (808) imply: % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | | (813) ~ (all_52_11 = e0) % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (589), (808) imply: % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | | (814) ~ (all_52_12 = e0) % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (590), (808) imply: % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | | (815) ~ (all_52_13 = e0) % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (591), (808) imply: % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | | (816) ~ (all_52_14 = e0) % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (38), (808) imply: % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | | (817) op(e0, e0) = all_4_1 % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (627), (808) imply: % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | | (818) op(e0, e0) = all_56_30 % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (36), (808) imply: % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | | (819) op(e0, e0) = e0 % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_4_1, % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | | all_56_30, e0, e0, simplifying with (817), (818) % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | | gives: % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | | (820) all_56_30 = all_4_1 % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | | all_56_30, e0, e0, simplifying with (818), (819) % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | | gives: % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | | (821) all_56_30 = e0 % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (820), (821) imply: % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | | (822) all_4_1 = e0 % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | | SIMP: (822) implies: % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | | (823) all_4_1 = e0 % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (37), (823) imply: % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | | (824) op(e0, e0) = all_4_0 % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_4_0, % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | | e0, e0, simplifying with (819), (824) gives: % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | | (825) all_4_0 = e0 % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (772), (825) imply: % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | | (826) ~ (e2 = e0) % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (780), (825) imply: % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | | (827) ~ (e1 = e0) % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (296) gives: % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | | | (828) ~ (all_56_11 = e3) % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (545), (828) imply: % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | | | (829) ~ (all_8_2 = e3) % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (298) gives: % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | | | | (830) ~ (all_56_1 = e1) % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (546), (830) imply: % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | | | | (831) ~ (all_10_2 = e1) % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (299) gives: % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | (832) ~ (all_56_1 = e2) % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (546), (832) imply: % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | (833) ~ (all_10_2 = e2) % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (294) gives: % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | (834) ~ (all_56_11 = e0) % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (545), (834) imply: % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | (835) ~ (all_8_2 = e0) % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (295) gives: % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | (836) ~ (all_56_11 = e1) % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (545), (836) imply: % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | (837) ~ (all_8_2 = e1) % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (41), (42), (43), (46), (48), (51), (53), % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | (158), (160), (161), (168), (169), (173), (174), % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | (176), (181), (182), (183), (184), (188), (189), % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | (191), (192), (208), (237), (238), (239), (240), % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | (241), (242), (243), (244), (245), (247), (249), % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | (250), (251), (252), (286), (287), (291), (292), % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | (293), (297), (318), (319), (321), (322), (326), % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | (332), (337), (343), (344), (365), (366), (374), % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | (381), (386), (389), (401), (402), (407), (419), % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | (435), (457), (459), (461), (469), (471), (473), % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | (476), (478), (480), (482), (540), (541), (542), % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | (543), (544), (545), (546), (547), (548), (549), % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | (550), (551), (553), (554), (555), (557), (559), % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | (561), (563), (565), (567), (568), (569), (571), % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | (573), (575), (579), (580), (585), (587), (589), % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | (591), (612), (617), (621), (622), (768), (782), % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | (786), (788), (794), (796), (798), (809), (811), % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | (812), (813), (814), (815), (816), (821), (829), % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | (831), (833), (835), (837), (function-axioms) are % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #640. % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | (838) all_56_13 = e2 % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | (839) all_56_11 = e1 % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (545), (839) imply: % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | (840) all_8_2 = e1 % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (431), (838) imply: % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | (841) all_52_9 = e2 % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (389), (841) imply: % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | (842) all_58_5 = e2 % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (554), (840) imply: % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | (843) all_58_3 = e1 % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (571), (840) imply: % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | (844) ~ (all_52_4 = e1) % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (575), (840) imply: % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | (845) ~ (all_52_7 = e1) % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (165), (841) imply: % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | (846) ~ (all_52_13 = e2) % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (846) implies: % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | (847) ~ (all_52_13 = e2) % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (579), (840) imply: % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | (848) ~ (all_52_13 = e1) % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (48), (840) imply: % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | (849) op(e1, e1) = all_8_1 % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (332) gives: % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (850) all_58_2 = e0 % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (401), (850) imply: % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (851) all_52_1 = e0 % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (193), (851) imply: % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (852) ~ (all_52_13 = e0) % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (557), (851) imply: % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (853) ~ (all_10_2 = e0) % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (853) implies: % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (854) ~ (all_10_2 = e0) % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (252) gives: % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (855) all_54_0 = e3 % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (543), (855) imply: % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (856) all_10_2 = e3 % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (856) implies: % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (857) all_10_2 = e3 % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (559), (857) imply: % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (858) ~ (all_52_2 = e3) % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (245) gives: % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (859) all_54_7 = e3 % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (469), (859) imply: % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (860) all_52_13 = e3 % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (860) implies: % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (861) all_52_13 = e3 % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (158), (861) imply: % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (862) ~ (all_52_14 = e3) % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (862) implies: % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (863) ~ (all_52_14 = e3) % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (212), (861) imply: % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (864) op(e2, e0) = e3 % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_6_2, % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_1, e1, e1, simplifying with (41), (849) % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (865) all_8_1 = all_6_2 % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (778), (865) imply: % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (866) ~ (all_6_2 = e3) % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (47), (865) imply: % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (867) op(e2, all_6_2) = all_8_0 % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (327) gives: % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (868) all_58_6 = e3 % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (553), (868) imply: % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (869) all_52_2 = e3 % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (858), (869) imply: % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (870) $false % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (870) is inconsistent. % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (871) all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3 % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (871) gives: % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (872) all_58_7 = e3 % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (380), (872) imply: % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (873) all_52_6 = e3 % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (184), (873) imply: % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (874) ~ (all_52_4 = e3) % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (176), (873) imply: % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (875) ~ (all_52_7 = e3) % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (875) implies: % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (876) ~ (all_52_7 = e3) % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (239) gives: % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (877) all_54_13 = e3 % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (480), (876), (877) are inconsistent by sub-proof % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #668. % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (878) all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0 % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (878) gives: % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (879) all_54_13 = e2 % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (480), (879) imply: % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (880) all_52_7 = e2 % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (880) implies: % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (881) all_52_7 = e2 % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (183), (881) imply: % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (882) ~ (all_52_4 = e2) % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (251) gives: % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (883) all_54_1 = e3 % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (457), (874), (883) are inconsistent by sub-proof % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #722. % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (884) all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0 % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (182), (328), (407), (457), (548), (552), (616), % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (784), (813), (842), (844), (864), (867), (882), % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (884), (function-axioms) are inconsistent by % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #637. % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (885) all_54_13 = e1 | all_54_13 = e0 % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (480), (812), (845), (885) are inconsistent by % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #711. % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (886) all_58_8 = e3 | all_58_11 = e3 % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (550), (552), (863), (866), (886) are inconsistent % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #636. % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (887) all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0 % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (469), (815), (847), (848), (887) are inconsistent % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #649. % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (888) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (543), (831), (833), (854), (888) are inconsistent % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #731. % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (889) all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0 % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (889) gives: % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (890) all_58_3 = e0 % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (843), (890) imply: % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (891) e1 = e0 % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4), (891) imply: % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (892) $false % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (892) is inconsistent. % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (893) all_58_5 = e0 | all_58_10 = e0 % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (893) gives: % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (894) all_58_5 = e0 % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (842), (894) imply: % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (895) e2 = e0 % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5), (895) imply: % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (896) $false % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (896) is inconsistent. % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (897) all_58_10 = e0 % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (386), (897) imply: % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (898) all_52_13 = e0 % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (815), (898) imply: % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (899) $false % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (899) is inconsistent. % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | (900) all_56_15 = e2 % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | (901) all_56_11 = e0 % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (545), (901) imply: % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | (902) all_8_2 = e0 % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (443), (900) imply: % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | (903) all_52_13 = e2 % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (386), (903) imply: % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | (904) all_58_10 = e2 % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (554), (902) imply: % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | (905) all_58_3 = e0 % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (193), (903) imply: % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | (906) ~ (all_52_1 = e2) % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (568), (902) imply: % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | (907) ~ (all_52_1 = e0) % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (571), (902) imply: % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | (908) ~ (all_52_4 = e0) % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (165), (903) imply: % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | (909) ~ (all_52_9 = e2) % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (577), (902) imply: % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | (910) ~ (all_52_9 = e0) % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (161), (903) imply: % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | (911) ~ (all_52_12 = e2) % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (158), (903) imply: % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | (912) ~ (all_52_14 = e2) % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (912) implies: % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | (913) ~ (all_52_14 = e2) % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (46), (902) imply: % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | (914) op(e2, e2) = e0 % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (625), (903) imply: % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | (915) op(e0, e2) = all_56_14 % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_7, % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_14, e2, e0, simplifying with (206), (915) % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | (916) all_56_14 = all_52_7 % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (291) gives: % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | (917) ~ (all_56_21 = e0) % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (374), (917) imply: % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | (918) ~ (all_6_2 = e0) % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (324) gives: % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (919) all_58_6 = e0 % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (553), (919) imply: % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (920) all_52_2 = e0 % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (920) implies: % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (921) all_52_2 = e0 % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (192), (921) imply: % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (922) ~ (all_52_3 = e0) % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (189), (921) imply: % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (923) ~ (all_52_14 = e0) % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (569), (921) imply: % 146.43/20.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (924) ~ (all_6_2 = e0) % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (328) gives: % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (925) all_58_4 = e0 % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (407), (925) imply: % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (926) all_52_8 = e0 % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (168), (926) imply: % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (927) ~ (all_52_12 = e0) % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (565), (926) imply: % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (928) ~ (all_10_2 = e0) % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (928) implies: % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (929) ~ (all_10_2 = e0) % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (620), (926) imply: % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (930) op(e1, e0) = all_56_4 % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (252) gives: % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (931) all_54_0 = e3 % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (543), (931) imply: % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (932) all_10_2 = e3 % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (419), (932) imply: % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (933) all_58_0 = e3 % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (557), (932) imply: % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (934) ~ (all_52_1 = e3) % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (561), (932) imply: % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (935) ~ (all_52_3 = e3) % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (563), (932) imply: % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (936) ~ (all_52_4 = e3) % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (567), (932) imply: % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (937) ~ (all_52_12 = e3) % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (249) gives: % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (938) all_54_3 = e3 % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (461), (937), (938) are inconsistent by sub-proof % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #659. % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (939) ~ (all_54_3 = e3) % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (940) all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0 % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (940) gives: % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (941) all_54_3 = e2 % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (461), (911), (941) are inconsistent by sub-proof % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #658. % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (942) all_54_3 = e1 | all_54_3 = e0 % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (323) gives: % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (943) all_58_9 = e3 % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (551), (943) imply: % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (944) all_52_12 = e3 % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (937), (944) imply: % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (945) $false % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (945) is inconsistent. % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (946) all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3 % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (335) gives: % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (947) all_58_2 = e3 % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (401), (947) imply: % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (948) all_52_1 = e3 % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (934), (948) imply: % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (949) $false % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (949) is inconsistent. % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (950) ~ (all_58_2 = e3) % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (951) all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3 % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (942) gives: % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (952) all_54_3 = e1 % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (461), (952) imply: % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (953) all_52_12 = e1 % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (953) implies: % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (954) all_52_12 = e1 % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (181), (954) imply: % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (955) ~ (all_52_4 = e1) % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (251) gives: % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (956) all_54_1 = e3 % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (457), (936), (956) are inconsistent by sub-proof % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #722. % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (957) all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0 % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (946) gives: % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (958) all_58_10 = e3 % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (904), (958) are inconsistent by sub-proof % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #635. % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (959) all_58_11 = e3 | all_58_15 = e3 % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (248) gives: % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (960) all_54_4 = e3 % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (463), (934), (960) are inconsistent by sub-proof % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #634. % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (961) all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0 % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (961) gives: % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (962) all_54_4 = e2 % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (463), (906), (962) are inconsistent by sub-proof % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #633. % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (963) all_54_4 = e1 | all_54_4 = e0 % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (959) gives: % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (964) all_58_11 = e3 % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (550), (964) imply: % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (965) all_52_14 = e3 % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (208), (965) imply: % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (966) op(e1, e0) = e3 % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (951) gives: % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (967) all_58_3 = e3 % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (905), (967) are inconsistent by sub-proof % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #632. % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (968) all_58_5 = e3 | all_58_10 = e3 % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (968) gives: % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (969) all_58_5 = e3 % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (389), (969) imply: % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (970) all_52_9 = e3 % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (344) gives: % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (971) all_58_0 = e2 % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (933), (971) imply: % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (972) e3 = e2 % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (9), (972) imply: % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (973) $false % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (973) is inconsistent. % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (974) all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2 % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (963) gives: % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (975) all_54_4 = e1 % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (463), (975) imply: % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (976) all_52_1 = e1 % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (401), (976) imply: % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (977) all_58_2 = e1 % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (957) gives: % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (978) all_54_1 = e2 % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (457), (978) imply: % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (979) all_52_4 = e2 % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (979) implies: % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (980) all_52_4 = e2 % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (616), (980) imply: % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (981) op(e2, e2) = all_56_2 % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (974) gives: % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (982) all_58_2 = e2 % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (977), (982) are inconsistent by sub-proof % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #631. % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (983) all_58_6 = e2 | all_58_12 = e2 % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (983) gives: % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (984) all_58_6 = e2 % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (919), (984) imply: % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (985) e2 = e0 % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (985) implies: % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (986) e2 = e0 % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5), (986) imply: % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (987) $false % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (987) is inconsistent. % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (988) all_58_12 = e2 % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (365), (988) imply: % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (989) all_52_3 = e2 % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (187), (989) imply: % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (990) ~ (all_52_11 = e2) % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (990) implies: % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (991) ~ (all_52_11 = e2) % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (935), (989) imply: % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (992) ~ (e3 = e2) % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (330) gives: % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (993) all_58_4 = e2 % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (925), (993) are inconsistent by sub-proof % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #630. % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (994) all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2 % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (994) gives: % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (995) all_58_5 = e2 % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (969), (995) imply: % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (996) e3 = e2 % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (9), (996) imply: % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (997) $false % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (997) is inconsistent. % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (998) all_58_8 = e2 | all_58_14 = e2 % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (998) gives: % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (999) all_58_8 = e2 % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (552), (999) imply: % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1000) all_6_2 = e2 % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (43), (1000) imply: % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1001) op(e2, e2) = all_6_1 % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_56_4, % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0, e1, simplifying with (930), (966) gives: % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1002) all_56_4 = e3 % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_56_2, % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2, e2, simplifying with (914), (981) gives: % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1003) all_56_2 = e0 % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_6_1, % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_2, e2, e2, simplifying with (981), (1001) % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1004) all_56_2 = all_6_1 % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1003), (1004) imply: % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1005) all_6_1 = e0 % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (42), (1005) imply: % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1006) op(e1, e0) = all_6_0 % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_6_0, % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0, e1, simplifying with (966), (1006) gives: % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1007) all_6_0 = e3 % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (792), (1007) imply: % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1008) $false % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1008) is inconsistent. % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1009) all_58_14 = e2 % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (548), (991), (1009) are inconsistent by sub-proof % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #629. % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1010) all_54_1 = e1 | all_54_1 = e0 % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (457), (908), (955), (1010) are inconsistent by % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #628. % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1011) all_54_4 = e0 % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (463), (1011) imply: % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1012) all_52_1 = e0 % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (907), (1012) imply: % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1013) $false % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1013) is inconsistent. % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1014) all_58_10 = e3 % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (904), (1014) are inconsistent by sub-proof % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #635. % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1015) all_58_15 = e3 % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (810), (1015) imply: % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1016) e3 = e0 % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1016) implies: % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1017) e3 = e0 % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7), (1017) imply: % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1018) $false % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1018) is inconsistent. % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 146.43/20.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1019) all_54_3 = e0 % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (461), (814), (1019) are inconsistent by sub-proof % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #656. % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1020) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (543), (831), (833), (929), (1020) are % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #731. % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1021) all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0 % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (389), (548), (552), (813), (910), (918), (1021) % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #626. % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1022) ~ (all_58_6 = e0) % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (328), (340), (365), (389), (401), (407), (419), % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (548), (552), (553), (565), (811), (813), (907), % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (910), (918), (1022) are inconsistent by sub-proof % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | #623. % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1023) all_56_23 = e1 % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1024) all_56_21 = e0 % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (374), (1024) imply: % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1025) all_6_2 = e0 % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1025) implies: % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1026) all_6_2 = e0 % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (366), (1023) imply: % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1027) all_52_14 = e1 % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1027) implies: % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1028) all_52_14 = e1 % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (552), (1026) imply: % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1029) all_58_8 = e0 % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (189), (1028) imply: % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1030) ~ (all_52_2 = e1) % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (569), (1026) imply: % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1031) ~ (all_52_2 = e0) % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (174), (1028) imply: % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1032) ~ (all_52_6 = e1) % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (580), (1026) imply: % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1033) ~ (all_52_6 = e0) % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (582), (1026) imply: % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1034) ~ (all_52_8 = e0) % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (160), (1028) imply: % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1035) ~ (all_52_12 = e1) % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (626), (1028) imply: % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1036) op(e0, e1) = all_56_22 % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (171), (176), (181), (182), (183), (184), % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | (187), (188), (191), (192), (194), (196), (197), % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | (205), (207), (210), (211), (213), (215), (217), % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | (218), (239), (240), (243), (244), (246), (248), % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | (249), (250), (251), (286), (318), (319), (329), % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | (330), (335), (337), (338), (340), (345), (365), % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | (380), (381), (389), (401), (402), (407), (408), % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | (425), (429), (431), (435), (457), (459), (461), % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | (463), (467), (471), (473), (478), (480), (547), % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | (548), (549), (551), (553), (555), (613), (614), % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | (616), (618), (620), (621), (624), (794), (809), % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | (811), (812), (814), (821), (900), (904), (905), % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | (906), (907), (908), (909), (910), (911), (916), % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1023), (1029), (1030), (1031), (1032), (1033), % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1034), (1035), (1036), (function-axioms) are % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #607. % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | (1037) all_56_3 = e3 % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | (1038) all_56_1 = e2 % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (546), (1038) imply: % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | (1039) all_10_2 = e2 % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (408), (1037) imply: % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | (1040) all_52_4 = e3 % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (419), (1039) imply: % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | (1041) all_58_0 = e2 % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (181), (1040) imply: % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | (1042) ~ (all_52_12 = e3) % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1042) implies: % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | (1043) ~ (all_52_12 = e3) % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (571), (1040) imply: % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | (1044) ~ (all_8_2 = e3) % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (567), (1039) imply: % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | (1045) ~ (all_52_12 = e2) % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (53), (1039) imply: % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | (1046) op(e2, e2) = all_10_1 % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (249) gives: % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | (1047) all_54_3 = e3 % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (461), (1047) imply: % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | (1048) all_52_12 = e3 % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1043), (1048) imply: % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | (1049) $false % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1049) is inconsistent. % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | (1050) all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0 % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1050) gives: % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1051) all_54_3 = e2 % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (461), (1051) imply: % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1052) all_52_12 = e2 % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1045), (1052) imply: % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1053) $false % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1053) is inconsistent. % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1054) all_54_3 = e1 | all_54_3 = e0 % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1054) gives: % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1055) all_54_3 = e1 % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (461), (1055) imply: % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1056) all_52_12 = e1 % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (216), (1056) imply: % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1057) op(e3, e0) = e1 % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_8_2, % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_10_1, e2, e2, simplifying with (46), (1046) % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1058) all_10_1 = all_8_2 % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (790), (1058) imply: % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1059) ~ (all_8_2 = e2) % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (786), (1058) imply: % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1060) ~ (all_8_2 = e1) % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (52), (1058) imply: % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1061) op(e3, all_8_2) = all_10_0 % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (247) gives: % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1062) all_54_5 = e3 % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (542), (829), (1062) are inconsistent by sub-proof % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #737. % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1063) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1063) gives: % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1064) all_54_5 = e2 % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (542), (1059), (1064) are inconsistent by % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #648. % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1065) ~ (all_54_5 = e2) % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1066) all_54_5 = e1 | all_54_5 = e0 % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1066) gives: % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1067) all_54_5 = e1 % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (542), (1060), (1067) are inconsistent by % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #647. % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1068) all_54_5 = e0 % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (542), (1068) imply: % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1069) all_8_2 = e0 % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1069) implies: % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1070) all_8_2 = e0 % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (568), (1070) imply: % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1071) ~ (all_52_1 = e0) % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1061), (1070) imply: % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1072) op(e3, e0) = all_10_0 % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (340) gives: % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1073) all_58_0 = e0 % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1041), (1073) imply: % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1074) e2 = e0 % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5), (1074) imply: % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1075) $false % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1075) is inconsistent. % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1076) all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0 % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1076) gives: % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1077) all_58_2 = e0 % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (401), (1077) imply: % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1078) all_52_1 = e0 % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1071), (1078) imply: % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1079) $false % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1079) is inconsistent. % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1080) all_58_6 = e0 | all_58_12 = e0 % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1080) gives: % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1081) all_58_6 = e0 % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (553), (1081) imply: % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1082) all_52_2 = e0 % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (614), (1082) imply: % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1083) op(e3, e0) = all_56_16 % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1, % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_16, e0, e3, simplifying with (1057), (1083) % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1084) all_56_16 = e1 % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_10_0, % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_16, e0, e3, simplifying with (1072), (1083) % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1085) all_56_16 = all_10_0 % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1084), (1085) imply: % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1086) all_10_0 = e1 % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1086) implies: % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1087) all_10_0 = e1 % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (776), (1087) imply: % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1088) $false % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1088) is inconsistent. % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1089) all_58_12 = e0 % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (365), (1089) imply: % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1090) all_52_3 = e0 % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (811), (1090) imply: % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1091) $false % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1091) is inconsistent. % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 146.43/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1092) all_54_3 = e0 % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (461), (1092) imply: % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1093) all_52_12 = e0 % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (814), (1093) imply: % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1094) $false % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1094) is inconsistent. % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | (1095) all_56_5 = e3 % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | (1096) all_56_1 = e1 % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (546), (1096) imply: % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | (1097) all_10_2 = e1 % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (429), (1095) imply: % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | (1098) all_52_8 = e3 % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (419), (1097) imply: % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | (1099) all_58_0 = e1 % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (182), (1098) imply: % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | (1100) ~ (all_52_4 = e3) % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (563), (1097) imply: % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | (1101) ~ (all_52_4 = e1) % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (168), (1098) imply: % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | (1102) ~ (all_52_12 = e3) % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1102) implies: % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | (1103) ~ (all_52_12 = e3) % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (582), (1098) imply: % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | (1104) ~ (all_6_2 = e3) % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1104) implies: % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | (1105) ~ (all_6_2 = e3) % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (567), (1097) imply: % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | (1106) ~ (all_52_12 = e1) % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (53), (1097) imply: % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | (1107) op(e1, e1) = all_10_1 % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (249) gives: % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | (1108) all_54_3 = e3 % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (461), (1108) imply: % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | (1109) all_52_12 = e3 % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1103), (1109) imply: % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | (1110) $false % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1110) is inconsistent. % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | (1111) all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0 % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (341) gives: % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | (1112) all_58_0 = e0 % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1099), (1112) imply: % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | (1113) e1 = e0 % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4), (1113) imply: % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | (1114) $false % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1114) is inconsistent. % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | (1115) all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0 % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1115) gives: % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1116) all_58_1 = e0 % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (555), (1116) imply: % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1117) all_52_4 = e0 % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (183), (1117) imply: % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1118) ~ (all_52_7 = e0) % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (181), (1117) imply: % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1119) ~ (all_52_12 = e0) % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (571), (1117) imply: % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1120) ~ (all_8_2 = e0) % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1120) implies: % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1121) ~ (all_8_2 = e0) % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1111) gives: % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1122) all_54_3 = e2 % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (461), (1122) imply: % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1123) all_52_12 = e2 % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1123) implies: % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1124) all_52_12 = e2 % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (216), (1124) imply: % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1125) op(e3, e0) = e2 % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_6_2, % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_10_1, e1, e1, simplifying with (41), (1107) % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1126) all_10_1 = all_6_2 % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (790), (1126) imply: % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1127) ~ (all_6_2 = e2) % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (786), (1126) imply: % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1128) ~ (all_6_2 = e1) % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (52), (1126) imply: % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1129) op(e3, all_6_2) = all_10_0 % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (242) gives: % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1130) all_54_10 = e3 % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (541), (1105), (1130) are inconsistent by % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #736. % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1131) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1131) gives: % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1132) all_54_10 = e2 % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (541), (1127), (1132) are inconsistent by % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #735. % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1133) all_54_10 = e1 | all_54_10 = e0 % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1133) gives: % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1134) all_54_10 = e1 % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (541), (1128), (1134) are inconsistent by % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #606. % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1135) all_54_10 = e0 % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (541), (1135) imply: % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1136) all_6_2 = e0 % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1136) implies: % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1137) all_6_2 = e0 % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (569), (1137) imply: % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1138) ~ (all_52_2 = e0) % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (580), (1137) imply: % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1139) ~ (all_52_6 = e0) % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1129), (1137) imply: % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1140) op(e3, e0) = all_10_0 % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (332) gives: % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1141) all_58_2 = e0 % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (401), (1141) imply: % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1142) all_52_1 = e0 % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (613), (1142) imply: % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1143) op(e3, e0) = all_56_8 % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, all_56_8, % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0, e3, simplifying with (1125), (1143) gives: % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1144) all_56_8 = e2 % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_10_0, % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_8, e0, e3, simplifying with (1140), (1143) % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1145) all_56_8 = all_10_0 % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1144), (1145) imply: % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1146) all_10_0 = e2 % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1146) implies: % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1147) all_10_0 = e2 % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (770), (1147) imply: % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1148) $false % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1148) is inconsistent. % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1149) ~ (all_58_2 = e0) % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (336), (340), (365), (380), (401), (419), (549), % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (553), (554), (555), (563), (811), (812), (1121), % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1138), (1139), (1149) are inconsistent by % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #602. % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1150) all_54_3 = e1 | all_54_3 = e0 % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (461), (814), (1106), (1150) are inconsistent by % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #655. % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1151) ~ (all_58_1 = e0) % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (555), (1151) imply: % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1152) ~ (all_52_4 = e0) % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1111) gives: % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1153) all_54_3 = e2 % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (461), (1153) imply: % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1154) all_52_12 = e2 % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (181), (1154) imply: % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1155) ~ (all_52_4 = e2) % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (251), (457), (1100), (1101), (1152), (1155) are % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #717. % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1156) all_54_3 = e1 | all_54_3 = e0 % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (461), (814), (1106), (1156) are inconsistent by % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #655. % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | End of split % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | (1157) all_56_11 = e3 % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | (1158) all_56_9 = e2 % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (425), (1158) imply: % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | (1159) all_52_1 = e2 % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (545), (1157) imply: % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | (1160) all_8_2 = e3 % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (554), (1160) imply: % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | (1161) all_58_3 = e3 % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (197), (1159) imply: % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | (1162) ~ (all_52_2 = e2) % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1162) implies: % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | (1163) ~ (all_52_2 = e2) % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (196), (1159) imply: % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | (1164) ~ (all_52_3 = e2) % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1164) implies: % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | (1165) ~ (all_52_3 = e2) % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (193), (1159) imply: % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | (1166) ~ (all_52_13 = e2) % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1166) implies: % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | (1167) ~ (all_52_13 = e2) % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (557), (1159) imply: % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | (1168) ~ (all_10_2 = e2) % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1168) implies: % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | (1169) ~ (all_10_2 = e2) % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (579), (1160) imply: % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | (1170) ~ (all_52_13 = e3) % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (48), (1160) imply: % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | (1171) op(e3, e3) = all_8_1 % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (245) gives: % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | (1172) all_54_7 = e3 % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (469), (1170), (1172) are inconsistent by % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #601. % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | (1173) all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0 % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1173) gives: % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | (1174) all_54_7 = e2 % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (469), (1167), (1174) are inconsistent by % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #652. % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | (1175) all_54_7 = e1 | all_54_7 = e0 % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1175) gives: % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | (1176) all_54_7 = e1 % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (469), (1176) imply: % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | (1177) all_52_13 = e1 % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1177) implies: % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | (1178) all_52_13 = e1 % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (212), (1178) imply: % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | (1179) op(e2, e0) = e1 % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_10_2, % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_1, e3, e3, simplifying with (51), (1171) % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | (1180) all_10_2 = all_8_1 % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (543), (1180) imply: % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | (1181) all_54_0 = all_8_1 % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (559), (1180) imply: % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | (1182) ~ (all_52_2 = all_8_1) % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (563), (1180) imply: % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | (1183) ~ (all_52_4 = all_8_1) % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1169), (1180) imply: % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | (1184) ~ (all_8_1 = e2) % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (252) gives: % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1185) all_54_0 = e3 % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (778), (1181), (1185) are inconsistent by % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #600. % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1186) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1186) gives: % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1187) all_54_0 = e2 % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1181), (1184), (1187) are inconsistent by % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #599. % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 146.43/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.80/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1188) all_54_0 = e1 | all_54_0 = e0 % 146.80/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.80/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1188) gives: % 146.80/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.80/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 146.80/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.80/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1189) all_54_0 = e1 % 146.80/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.80/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (769), (1181), (1189) are inconsistent by % 146.80/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #598. % 146.80/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.80/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 146.80/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.80/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1190) all_54_0 = e0 % 146.80/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.80/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1181), (1190) imply: % 146.80/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1191) all_8_1 = e0 % 146.80/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.80/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1191) implies: % 146.80/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1192) all_8_1 = e0 % 146.80/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.80/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1182), (1192) imply: % 146.80/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1193) ~ (all_52_2 = e0) % 146.80/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.80/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1183), (1192) imply: % 146.80/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1194) ~ (all_52_4 = e0) % 146.80/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.80/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (47), (1192) imply: % 146.80/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1195) op(e2, e0) = all_8_0 % 146.80/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.80/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (324) gives: % 146.80/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.80/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 146.80/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.80/20.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1196) all_58_6 = e0 % 146.80/20.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.80/20.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (553), (1196) imply: % 146.80/20.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1197) all_52_2 = e0 % 146.80/20.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.80/20.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1193), (1197) imply: % 146.80/20.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1198) $false % 146.80/20.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.80/20.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1198) is inconsistent. % 146.80/20.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.80/20.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 146.80/20.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.80/20.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1199) all_58_7 = e0 | all_58_8 = e0 | all_58_11 = e0 % 146.80/20.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.80/20.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (336) gives: % 146.80/20.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.80/20.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 146.80/20.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.80/20.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1200) all_58_1 = e0 % 146.80/20.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.80/20.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (555), (1200) imply: % 146.80/20.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1201) all_52_4 = e0 % 146.80/20.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.80/20.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1194), (1201) imply: % 146.80/20.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1202) $false % 146.80/20.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.80/20.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1202) is inconsistent. % 146.80/20.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.80/20.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 146.80/20.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.80/20.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1203) all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0 % 146.80/20.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.80/20.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1203) gives: % 146.80/20.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.80/20.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 146.80/20.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.80/20.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1204) all_58_3 = e0 % 146.80/20.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.80/20.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (193), (294), (344), (365), (401), (419), (443), % 146.80/20.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (553), (1157), (1161), (1163), (1165), (1169), % 146.80/20.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1204) are inconsistent by sub-proof #595. % 146.80/20.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.80/20.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 146.80/20.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.80/20.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1205) all_58_7 = e0 | all_58_13 = e0 % 146.80/20.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.80/20.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1199) gives: % 146.80/20.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.80/20.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 146.80/20.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.80/20.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1206) all_58_7 = e0 % 146.80/20.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.80/20.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (380), (1206) imply: % 146.80/20.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1207) all_52_6 = e0 % 146.80/20.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.80/20.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (618), (1207) imply: % 146.80/20.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1208) op(e2, e0) = all_56_18 % 146.80/20.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.80/20.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1, % 146.80/20.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_18, e0, e2, simplifying with (1179), (1208) % 146.80/20.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 146.80/20.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1209) all_56_18 = e1 % 146.80/20.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.80/20.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_8_0, % 146.80/20.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_18, e0, e2, simplifying with (1195), (1208) % 146.80/20.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 146.80/20.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1210) all_56_18 = all_8_0 % 146.80/20.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.80/20.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1209), (1210) imply: % 146.80/20.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1211) all_8_0 = e1 % 146.80/20.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.80/20.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1211) implies: % 146.80/20.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1212) all_8_0 = e1 % 146.80/20.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.80/20.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (774), (1212) imply: % 146.80/20.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1213) $false % 146.80/20.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.80/20.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1213) is inconsistent. % 146.80/20.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.80/20.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 146.80/20.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.80/20.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1214) ~ (all_58_7 = e0) % 146.80/20.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.80/20.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (380), (1214) imply: % 146.80/20.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1215) ~ (all_52_6 = e0) % 146.80/20.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.80/20.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (380), (549), (812), (1205), (1215) are % 146.80/20.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #604. % 146.80/20.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.80/20.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 146.80/20.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.80/20.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 146.80/20.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.80/20.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 146.80/20.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.80/20.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 146.80/20.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.80/20.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 146.80/20.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.80/20.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 146.80/20.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.80/20.90 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 146.80/20.90 | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.80/20.90 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 146.80/20.90 | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.80/20.90 | | | | | | | | | | | | | | | | | | | | | | | | | | (1216) all_54_7 = e0 % 146.80/20.90 | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.80/20.90 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (469), (815), (1216) are inconsistent by sub-proof % 146.80/20.90 | | | | | | | | | | | | | | | | | | | | | | | | | | #650. % 146.80/20.90 | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.80/20.90 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 146.80/20.90 | | | | | | | | | | | | | | | | | | | | | | | | | % 146.80/20.90 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 146.80/20.90 | | | | | | | | | | | | | | | | | | | | | | | | % 146.80/20.90 | | | | | | | | | | | | | | | | | | | | | | | End of split % 146.80/20.90 | | | | | | | | | | | | | | | | | | | | | | | % 146.80/20.90 | | | | | | | | | | | | | | | | | | | | | | End of split % 146.80/20.90 | | | | | | | | | | | | | | | | | | | | | | % 146.80/20.90 | | | | | | | | | | | | | | | | | | | | | End of split % 146.80/20.90 | | | | | | | | | | | | | | | | | | | | | % 146.80/20.90 | | | | | | | | | | | | | | | | | | | | End of split % 146.80/20.90 | | | | | | | | | | | | | | | | | | | | % 146.80/20.90 | | | | | | | | | | | | | | | | | | | End of split % 146.80/20.90 | | | | | | | | | | | | | | | | | | | % 146.80/20.90 | | | | | | | | | | | | | | | | | | Case 2: % 146.80/20.90 | | | | | | | | | | | | | | | | | | | % 146.80/20.90 | | | | | | | | | | | | | | | | | | | (1217) all_56_31 = e2 % 146.80/20.90 | | | | | | | | | | | | | | | | | | | (1218) all_56_27 = e0 % 146.80/20.90 | | | | | | | | | | | | | | | | | | | % 146.80/20.90 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (360), (1218) imply: % 146.80/20.90 | | | | | | | | | | | | | | | | | | | (1219) all_52_7 = e0 % 146.80/20.90 | | | | | | | | | | | | | | | | | | | % 146.80/20.90 | | | | | | | | | | | | | | | | | | | SIMP: (1219) implies: % 146.80/20.90 | | | | | | | | | | | | | | | | | | | (1220) all_52_7 = e0 % 146.80/20.90 | | | | | | | | | | | | | | | | | | | % 146.80/20.90 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (544), (1217) imply: % 146.80/20.90 | | | | | | | | | | | | | | | | | | | (1221) all_4_2 = e2 % 146.80/20.90 | | | | | | | | | | | | | | | | | | | % 146.80/20.90 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (547), (1221) imply: % 146.80/20.90 | | | | | | | | | | | | | | | | | | | (1222) all_58_15 = e2 % 146.80/20.90 | | | | | | | | | | | | | | | | | | | % 146.80/20.90 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (549), (1220) imply: % 146.80/20.90 | | | | | | | | | | | | | | | | | | | (1223) all_58_13 = e0 % 146.80/20.90 | | | | | | | | | | | | | | | | | | | % 146.80/20.90 | | | | | | | | | | | | | | | | | | | REDUCE: (173), (1220) imply: % 146.80/20.90 | | | | | | | | | | | | | | | | | | | (1224) ~ (all_52_11 = e0) % 146.80/20.90 | | | | | | | | | | | | | | | | | | | % 146.80/20.90 | | | | | | | | | | | | | | | | | | | SIMP: (1224) implies: % 146.80/20.90 | | | | | | | | | | | | | | | | | | | (1225) ~ (all_52_11 = e0) % 146.80/20.90 | | | | | | | | | | | | | | | | | | | % 146.80/20.90 | | | | | | | | | | | | | | | | | | | REDUCE: (575), (1220) imply: % 146.80/20.90 | | | | | | | | | | | | | | | | | | | (1226) ~ (all_8_2 = e0) % 146.80/20.90 | | | | | | | | | | | | | | | | | | | % 146.80/20.90 | | | | | | | | | | | | | | | | | | | SIMP: (1226) implies: % 146.80/20.90 | | | | | | | | | | | | | | | | | | | (1227) ~ (all_8_2 = e0) % 146.80/20.90 | | | | | | | | | | | | | | | | | | | % 146.80/20.90 | | | | | | | | | | | | | | | | | | | REDUCE: (581), (1220), (1221) imply: % 146.80/20.90 | | | | | | | | | | | | | | | | | | | (1228) ~ (e2 = e0) % 146.80/20.90 | | | | | | | | | | | | | | | | | | | % 146.80/20.90 | | | | | | | | | | | | | | | | | | | REDUCE: (588), (1221) imply: % 146.80/20.90 | | | | | | | | | | | | | | | | | | | (1229) ~ (all_52_11 = e2) % 146.80/20.90 | | | | | | | | | | | | | | | | | | | % 146.80/20.90 | | | | | | | | | | | | | | | | | | | REDUCE: (589), (1221) imply: % 146.80/20.90 | | | | | | | | | | | | | | | | | | | (1230) ~ (all_52_12 = e2) % 146.80/20.90 | | | | | | | | | | | | | | | | | | | % 146.80/20.90 | | | | | | | | | | | | | | | | | | | REDUCE: (590), (1221) imply: % 146.80/20.90 | | | | | | | | | | | | | | | | | | | (1231) ~ (all_52_13 = e2) % 146.80/20.90 | | | | | | | | | | | | | | | | | | | % 146.80/20.90 | | | | | | | | | | | | | | | | | | | REDUCE: (38), (1221) imply: % 146.80/20.90 | | | | | | | | | | | | | | | | | | | (1232) op(e2, e2) = all_4_1 % 146.80/20.90 | | | | | | | | | | | | | | | | | | | % 146.80/20.90 | | | | | | | | | | | | | | | | | | | REDUCE: (619), (1220) imply: % 146.80/20.90 | | | | | | | | | | | | | | | | | | | (1233) op(e2, e0) = all_56_26 % 146.80/20.90 | | | | | | | | | | | | | | | | | | | % 146.80/20.90 | | | | | | | | | | | | | | | | | | | REDUCE: (36), (1221) imply: % 146.80/20.90 | | | | | | | | | | | | | | | | | | | (1234) op(e0, e0) = e2 % 146.80/20.90 | | | | | | | | | | | | | | | | | | | % 146.80/20.90 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (36), (37), (41), (42), (43), (46), % 146.80/20.90 | | | | | | | | | | | | | | | | | | | (47), (48), (51), (53), (158), (160), (161), % 146.80/20.90 | | | | | | | | | | | | | | | | | | | (166), (168), (171), (174), (181), (182), (189), % 146.80/20.90 | | | | | | | | | | | | | | | | | | | (191), (193), (194), (196), (205), (208), (212), % 146.80/20.90 | | | | | | | | | | | | | | | | | | | (237), (238), (241), (242), (243), (245), (247), % 146.80/20.90 | | | | | | | | | | | | | | | | | | | (248), (251), (252), (287), (291), (292), (293), % 146.80/20.90 | | | | | | | | | | | | | | | | | | | (295), (297), (298), (299), (317), (318), (321), % 146.80/20.90 | | | | | | | | | | | | | | | | | | | (328), (330), (331), (332), (333), (337), (343), % 146.80/20.90 | | | | | | | | | | | | | | | | | | | (345), (365), (374), (381), (386), (389), (401), % 146.80/20.90 | | | | | | | | | | | | | | | | | | | (402), (407), (408), (419), (429), (431), (435), % 146.80/20.90 | | | | | | | | | | | | | | | | | | | (457), (463), (469), (473), (476), (482), (540), % 146.80/20.90 | | | | | | | | | | | | | | | | | | | (541), (542), (543), (544), (545), (546), (547), % 146.80/20.90 | | | | | | | | | | | | | | | | | | | (548), (550), (551), (552), (554), (555), (557), % 146.80/20.90 | | | | | | | | | | | | | | | | | | | (559), (561), (563), (565), (567), (568), (569), % 146.80/20.90 | | | | | | | | | | | | | | | | | | | (571), (573), (577), (579), (580), (582), (583), % 146.80/20.90 | | | | | | | | | | | | | | | | | | | (585), (587), (589), (590), (591), (621), (624), % 146.80/20.90 | | | | | | | | | | | | | | | | | | | (625), (626), (767), (768), (769), (774), (778), % 146.80/20.90 | | | | | | | | | | | | | | | | | | | (782), (786), (788), (790), (794), (1222), (1223), % 146.80/20.90 | | | | | | | | | | | | | | | | | | | (1225), (1227), (1229), (1230), (1231), (1232), % 146.80/20.90 | | | | | | | | | | | | | | | | | | | (1233), (1234), (function-axioms) are inconsistent % 146.80/20.90 | | | | | | | | | | | | | | | | | | | by sub-proof #564. % 146.80/20.90 | | | | | | | | | | | | | | | | | | | % 146.80/20.90 | | | | | | | | | | | | | | | | | | End of split % 146.80/20.90 | | | | | | | | | | | | | | | | | | % 146.80/20.90 | | | | | | | | | | | | | | | | | Case 2: % 146.80/20.90 | | | | | | | | | | | | | | | | | | % 146.80/20.90 | | | | | | | | | | | | | | | | | | (1235) all_56_31 = e3 % 146.80/20.90 | | | | | | | | | | | | | | | | | | (1236) all_56_25 = e0 % 146.80/20.90 | | | | | | | | | | | | | | | | | | % 146.80/20.90 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (447), (1236) imply: % 146.80/20.90 | | | | | | | | | | | | | | | | | | (1237) all_52_3 = e0 % 146.80/20.90 | | | | | | | | | | | | | | | | | | % 146.80/20.90 | | | | | | | | | | | | | | | | | | SIMP: (1237) implies: % 146.80/20.90 | | | | | | | | | | | | | | | | | | (1238) all_52_3 = e0 % 146.80/20.90 | | | | | | | | | | | | | | | | | | % 146.80/20.90 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (544), (1235) imply: % 146.80/20.90 | | | | | | | | | | | | | | | | | | (1239) all_4_2 = e3 % 146.80/20.90 | | | | | | | | | | | | | | | | | | % 146.80/20.90 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (365), (1238) imply: % 146.80/20.90 | | | | | | | | | | | | | | | | | | (1240) all_58_12 = e0 % 146.80/20.90 | | | | | | | | | | | | | | | | | | % 146.80/20.90 | | | | | | | | | | | | | | | | | | REDUCE: (192), (1238) imply: % 146.80/20.90 | | | | | | | | | | | | | | | | | | (1241) ~ (all_52_2 = e0) % 146.80/20.90 | | | | | | | | | | | | | | | | | | % 146.80/20.90 | | | | | | | | | | | | | | | | | | REDUCE: (188), (1238) imply: % 146.80/20.90 | | | | | | | | | | | | | | | | | | (1242) ~ (all_52_7 = e0) % 146.80/20.90 | | | | | | | | | | | | | | | | | | % 146.80/20.90 | | | | | | | | | | | | | | | | | | SIMP: (1242) implies: % 146.80/20.90 | | | | | | | | | | | | | | | | | | (1243) ~ (all_52_7 = e0) % 146.80/20.90 | | | | | | | | | | | | | | | | | | % 146.80/20.90 | | | | | | | | | | | | | | | | | | REDUCE: (187), (1238) imply: % 146.80/20.90 | | | | | | | | | | | | | | | | | | (1244) ~ (all_52_11 = e0) % 146.80/20.90 | | | | | | | | | | | | | | | | | | % 146.80/20.90 | | | | | | | | | | | | | | | | | | SIMP: (1244) implies: % 146.80/20.90 | | | | | | | | | | | | | | | | | | (1245) ~ (all_52_11 = e0) % 146.80/20.90 | | | | | | | | | | | | | | | | | | % 146.80/20.90 | | | | | | | | | | | | | | | | | | REDUCE: (561), (1238) imply: % 146.80/20.90 | | | | | | | | | | | | | | | | | | (1246) ~ (all_10_2 = e0) % 146.80/20.90 | | | | | | | | | | | | | | | | | | % 146.80/20.90 | | | | | | | | | | | | | | | | | | SIMP: (1246) implies: % 146.80/20.90 | | | | | | | | | | | | | | | | | | (1247) ~ (all_10_2 = e0) % 146.80/20.90 | | | | | | | | | | | | | | | | | | % 146.80/20.90 | | | | | | | | | | | | | | | | | | REDUCE: (570), (1238), (1239) imply: % 146.80/20.90 | | | | | | | | | | | | | | | | | | (1248) ~ (e3 = e0) % 146.80/20.90 | | | | | | | | | | | | | | | | | | % 146.80/20.90 | | | | | | | | | | | | | | | | | | REDUCE: (581), (1239) imply: % 146.80/20.90 | | | | | | | | | | | | | | | | | | (1249) ~ (all_52_7 = e3) % 146.80/20.90 | | | | | | | | | | | | | | | | | | % 146.80/20.90 | | | | | | | | | | | | | | | | | | REDUCE: (588), (1239) imply: % 146.80/20.90 | | | | | | | | | | | | | | | | | | (1250) ~ (all_52_11 = e3) % 146.80/20.90 | | | | | | | | | | | | | | | | | | % 146.80/20.90 | | | | | | | | | | | | | | | | | | REDUCE: (591), (1239) imply: % 146.80/20.90 | | | | | | | | | | | | | | | | | | (1251) ~ (all_52_14 = e3) % 146.80/20.90 | | | | | | | | | | | | | | | | | | % 146.80/20.90 | | | | | | | | | | | | | | | | | | REDUCE: (38), (1239) imply: % 146.80/20.90 | | | | | | | | | | | | | | | | | | (1252) op(e3, e3) = all_4_1 % 146.80/20.90 | | | | | | | | | | | | | | | | | | % 146.80/20.90 | | | | | | | | | | | | | | | | | | REDUCE: (36), (1239) imply: % 146.80/20.90 | | | | | | | | | | | | | | | | | | (1253) op(e0, e0) = e3 % 146.80/20.90 | | | | | | | | | | | | | | | | | | % 146.80/20.91 | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (8), (9), (37), (38), (43), (46), (47), % 146.80/20.91 | | | | | | | | | | | | | | | | | | (48), (51), (53), (160), (165), (168), (169), % 146.80/20.91 | | | | | | | | | | | | | | | | | | (171), (174), (176), (181), (182), (183), (184), % 146.80/20.91 | | | | | | | | | | | | | | | | | | (191), (193), (194), (196), (197), (205), (238), % 146.80/20.91 | | | | | | | | | | | | | | | | | | (241), (242), (243), (244), (246), (247), (248), % 146.80/20.91 | | | | | | | | | | | | | | | | | | (250), (251), (252), (287), (291), (292), (293), % 146.80/20.91 | | | | | | | | | | | | | | | | | | (294), (296), (298), (299), (318), (320), (321), % 146.80/20.91 | | | | | | | | | | | | | | | | | | (328), (335), (336), (339), (343), (345), (365), % 146.80/20.91 | | | | | | | | | | | | | | | | | | (374), (380), (381), (386), (389), (401), (407), % 146.80/20.91 | | | | | | | | | | | | | | | | | | (419), (425), (429), (435), (457), (459), (463), % 146.80/20.91 | | | | | | | | | | | | | | | | | | (467), (471), (473), (476), (482), (541), (542), % 146.80/20.91 | | | | | | | | | | | | | | | | | | (543), (545), (546), (547), (548), (549), (550), % 146.80/20.91 | | | | | | | | | | | | | | | | | | (551), (554), (555), (557), (559), (568), (569), % 146.80/20.91 | | | | | | | | | | | | | | | | | | (571), (573), (575), (577), (580), (582), (585), % 146.80/20.91 | | | | | | | | | | | | | | | | | | (587), (613), (617), (625), (768), (769), (772), % 146.80/20.91 | | | | | | | | | | | | | | | | | | (774), (778), (788), (790), (794), (1235), (1240), % 146.80/20.91 | | | | | | | | | | | | | | | | | | (1241), (1243), (1245), (1247), (1249), (1250), % 146.80/20.91 | | | | | | | | | | | | | | | | | | (1251), (1252), (1253), (function-axioms) are % 146.80/20.91 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #538. % 146.80/20.91 | | | | | | | | | | | | | | | | | | % 146.80/20.91 | | | | | | | | | | | | | | | | | End of split % 146.80/20.91 | | | | | | | | | | | | | | | | | % 146.80/20.91 | | | | | | | | | | | | | | | | Case 2: % 146.80/20.91 | | | | | | | | | | | | | | | | | % 146.80/20.91 | | | | | | | | | | | | | | | | | (1254) all_56_31 = e1 % 146.80/20.91 | | | | | | | | | | | | | | | | | (1255) all_56_29 = e0 % 146.80/20.91 | | | | | | | | | | | | | | | | | % 146.80/20.91 | | | | | | | | | | | | | | | | | COMBINE_EQS: (357), (1255) imply: % 146.80/20.91 | | | | | | | | | | | | | | | | | (1256) all_52_11 = e0 % 146.80/20.91 | | | | | | | | | | | | | | | | | % 146.80/20.91 | | | | | | | | | | | | | | | | | SIMP: (1256) implies: % 146.80/20.91 | | | | | | | | | | | | | | | | | (1257) all_52_11 = e0 % 146.80/20.91 | | | | | | | | | | | | | | | | | % 146.80/20.91 | | | | | | | | | | | | | | | | | COMBINE_EQS: (544), (1254) imply: % 146.80/20.91 | | | | | | | | | | | | | | | | | (1258) all_4_2 = e1 % 146.80/20.91 | | | | | | | | | | | | | | | | | % 146.80/20.91 | | | | | | | | | | | | | | | | | COMBINE_EQS: (548), (1257) imply: % 146.80/20.91 | | | | | | | | | | | | | | | | | (1259) all_58_14 = e0 % 146.80/20.91 | | | | | | | | | | | | | | | | | % 146.80/20.91 | | | | | | | | | | | | | | | | | REDUCE: (187), (1257) imply: % 146.80/20.91 | | | | | | | | | | | | | | | | | (1260) ~ (all_52_3 = e0) % 146.80/20.91 | | | | | | | | | | | | | | | | | % 146.80/20.91 | | | | | | | | | | | | | | | | | REDUCE: (173), (1257) imply: % 146.80/20.91 | | | | | | | | | | | | | | | | | (1261) ~ (all_52_7 = e0) % 146.80/20.91 | | | | | | | | | | | | | | | | | % 146.80/20.91 | | | | | | | | | | | | | | | | | REDUCE: (581), (1258) imply: % 146.80/20.91 | | | | | | | | | | | | | | | | | (1262) ~ (all_52_7 = e1) % 146.80/20.91 | | | | | | | | | | | | | | | | | % 146.80/20.91 | | | | | | | | | | | | | | | | | REDUCE: (166), (1257) imply: % 146.80/20.91 | | | | | | | | | | | | | | | | | (1263) ~ (all_52_9 = e0) % 146.80/20.91 | | | | | | | | | | | | | | | | | % 146.80/20.91 | | | | | | | | | | | | | | | | | REDUCE: (585), (1257) imply: % 146.80/20.91 | | | | | | | | | | | | | | | | | (1264) ~ (all_6_2 = e0) % 146.80/20.91 | | | | | | | | | | | | | | | | | % 146.80/20.91 | | | | | | | | | | | | | | | | | SIMP: (1264) implies: % 146.80/20.91 | | | | | | | | | | | | | | | | | (1265) ~ (all_6_2 = e0) % 146.80/20.91 | | | | | | | | | | | | | | | | | % 146.80/20.91 | | | | | | | | | | | | | | | | | REDUCE: (589), (1258) imply: % 146.80/20.91 | | | | | | | | | | | | | | | | | (1266) ~ (all_52_12 = e1) % 146.80/20.91 | | | | | | | | | | | | | | | | | % 146.80/20.91 | | | | | | | | | | | | | | | | | REDUCE: (590), (1258) imply: % 146.80/20.91 | | | | | | | | | | | | | | | | | (1267) ~ (all_52_13 = e1) % 146.80/20.91 | | | | | | | | | | | | | | | | | % 146.80/20.91 | | | | | | | | | | | | | | | | | REDUCE: (38), (1258) imply: % 146.80/20.91 | | | | | | | | | | | | | | | | | (1268) op(e1, e1) = all_4_1 % 146.80/20.91 | | | | | | | | | | | | | | | | | % 146.80/20.91 | | | | | | | | | | | | | | | | | REDUCE: (36), (1258) imply: % 146.80/20.91 | | | | | | | | | | | | | | | | | (1269) op(e0, e0) = e1 % 146.80/20.91 | | | | | | | | | | | | | | | | | % 146.80/20.91 | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (37), (41), (42), (43), (48), (53), (161), % 146.80/20.91 | | | | | | | | | | | | | | | | | (165), (168), (176), (181), (192), (194), (206), % 146.80/20.91 | | | | | | | | | | | | | | | | | (207), (239), (240), (242), (245), (246), (247), % 146.80/20.91 | | | | | | | | | | | | | | | | | (249), (252), (292), (293), (294), (295), (296), % 146.80/20.91 | | | | | | | | | | | | | | | | | (297), (298), (299), (330), (331), (332), (333), % 146.80/20.91 | | | | | | | | | | | | | | | | | (337), (343), (374), (380), (381), (386), (389), % 146.80/20.91 | | | | | | | | | | | | | | | | | (401), (402), (407), (408), (419), (425), (431), % 146.80/20.91 | | | | | | | | | | | | | | | | | (435), (461), (467), (469), (478), (480), (541), % 146.80/20.91 | | | | | | | | | | | | | | | | | (542), (543), (545), (546), (549), (551), (552), % 146.80/20.91 | | | | | | | | | | | | | | | | | (554), (555), (557), (563), (567), (571), (577), % 146.80/20.91 | | | | | | | | | | | | | | | | | (579), (580), (582), (583), (622), (625), (767), % 146.80/20.91 | | | | | | | | | | | | | | | | | (769), (772), (786), (792), (1259), (1260), % 146.80/20.91 | | | | | | | | | | | | | | | | | (1261), (1262), (1263), (1265), (1266), (1267), % 146.80/20.91 | | | | | | | | | | | | | | | | | (1268), (1269), (function-axioms) are inconsistent % 146.80/20.91 | | | | | | | | | | | | | | | | | by sub-proof #517. % 146.80/20.91 | | | | | | | | | | | | | | | | | % 146.80/20.91 | | | | | | | | | | | | | | | | End of split % 146.80/20.91 | | | | | | | | | | | | | | | | % 146.80/20.91 | | | | | | | | | | | | | | | Case 2: % 146.80/20.91 | | | | | | | | | | | | | | | | % 146.80/20.91 | | | | | | | | | | | | | | | | (1270) all_40_0 = e3 % 146.80/20.91 | | | | | | | | | | | | | | | | (1271) ~ (all_40_1 = e0) | ~ (all_40_2 = e2) % 146.80/20.91 | | | | | | | | | | | | | | | | % 146.80/20.91 | | | | | | | | | | | | | | | | COMBINE_EQS: (713), (1270) imply: % 146.80/20.91 | | | | | | | | | | | | | | | | (1272) all_6_0 = e3 % 146.80/20.91 | | | | | | | | | | | | | | | | % 146.80/20.91 | | | | | | | | | | | | | | | | REDUCE: (42), (1272) imply: % 146.80/20.91 | | | | | | | | | | | | | | | | (1273) op(e1, all_6_1) = e3 % 146.80/20.91 | | | | | | | | | | | | | | | | % 146.80/20.91 | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8), (9), (36), (37), (38), (41), (42), (43), % 146.80/20.91 | | | | | | | | | | | | | | | | (46), (47), (48), (51), (53), (158), (160), (161), % 146.80/20.91 | | | | | | | | | | | | | | | | (165), (168), (169), (171), (173), (174), (176), % 146.80/20.91 | | | | | | | | | | | | | | | | (181), (182), (183), (184), (187), (188), (189), % 146.80/20.91 | | | | | | | | | | | | | | | | (191), (192), (193), (194), (196), (197), (205), % 146.80/20.91 | | | | | | | | | | | | | | | | (206), (207), (208), (237), (238), (239), (240), % 146.80/20.91 | | | | | | | | | | | | | | | | (241), (242), (243), (244), (246), (247), (248), % 146.80/20.91 | | | | | | | | | | | | | | | | (249), (250), (251), (252), (287), (288), (290), % 146.80/20.91 | | | | | | | | | | | | | | | | (291), (292), (293), (294), (296), (297), (298), % 146.80/20.91 | | | | | | | | | | | | | | | | (299), (318), (320), (321), (324), (326), (328), % 146.80/20.91 | | | | | | | | | | | | | | | | (332), (335), (336), (339), (340), (343), (344), % 146.80/20.91 | | | | | | | | | | | | | | | | (345), (357), (365), (366), (374), (380), (381), % 146.80/20.91 | | | | | | | | | | | | | | | | (386), (389), (401), (402), (407), (408), (419), % 146.80/20.91 | | | | | | | | | | | | | | | | (425), (429), (435), (443), (447), (457), (459), % 146.80/20.91 | | | | | | | | | | | | | | | | (461), (463), (467), (471), (473), (476), (478), % 146.80/20.91 | | | | | | | | | | | | | | | | (480), (482), (507), (540), (541), (542), (543), % 146.80/20.91 | | | | | | | | | | | | | | | | (544), (545), (546), (547), (548), (549), (550), % 146.80/20.91 | | | | | | | | | | | | | | | | (551), (552), (553), (554), (555), (557), (559), % 146.80/20.91 | | | | | | | | | | | | | | | | (561), (563), (565), (567), (568), (569), (570), % 146.80/20.91 | | | | | | | | | | | | | | | | (571), (573), (575), (577), (580), (581), (582), % 146.80/20.91 | | | | | | | | | | | | | | | | (585), (587), (588), (589), (590), (591), (613), % 146.80/20.91 | | | | | | | | | | | | | | | | (617), (621), (622), (625), (685), (767), (768), % 146.80/20.91 | | | | | | | | | | | | | | | | (769), (772), (774), (778), (782), (786), (788), % 146.80/20.91 | | | | | | | | | | | | | | | | (790), (1271), (1273), (function-axioms) are % 146.80/20.91 | | | | | | | | | | | | | | | | inconsistent by sub-proof #498. % 146.80/20.91 | | | | | | | | | | | | | | | | % 146.80/20.91 | | | | | | | | | | | | | | | End of split % 146.80/20.91 | | | | | | | | | | | | | | | % 146.80/20.91 | | | | | | | | | | | | | | Case 2: % 146.80/20.91 | | | | | | | | | | | | | | | % 146.80/20.91 | | | | | | | | | | | | | | | (1274) all_38_1 = e2 % 146.80/20.91 | | | | | | | | | | | | | | | (1275) ~ (all_38_0 = e0) | ~ (all_38_2 = e1) % 146.80/20.91 | | | | | | | | | | | | | | | % 146.80/20.91 | | | | | | | | | | | | | | | COMBINE_EQS: (684), (1274) imply: % 146.80/20.91 | | | | | | | | | | | | | | | (1276) all_10_1 = e2 % 146.80/20.91 | | | | | | | | | | | | | | | % 146.80/20.91 | | | | | | | | | | | | | | | SIMP: (1276) implies: % 146.80/20.91 | | | | | | | | | | | | | | | (1277) all_10_1 = e2 % 146.80/20.91 | | | | | | | | | | | | | | | % 146.80/20.91 | | | | | | | | | | | | | | | REDUCE: (53), (1277) imply: % 146.80/20.91 | | | | | | | | | | | | | | | (1278) op(all_10_2, all_10_2) = e2 % 146.80/20.91 | | | | | | | | | | | | | | | % 146.80/20.91 | | | | | | | | | | | | | | | REDUCE: (52), (1277) imply: % 146.80/20.91 | | | | | | | | | | | | | | | (1279) op(e3, e2) = all_10_0 % 146.80/20.91 | | | | | | | | | | | | | | | % 146.80/20.91 | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_4, % 146.80/20.91 | | | | | | | | | | | | | | | all_10_0, e2, e3, simplifying with (218), (1279) % 146.80/20.91 | | | | | | | | | | | | | | | gives: % 146.80/20.91 | | | | | | | | | | | | | | | (1280) all_52_4 = all_10_0 % 146.80/20.91 | | | | | | | | | | | | | | | % 146.80/20.91 | | | | | | | | | | | | | | | COMBINE_EQS: (457), (1280) imply: % 146.80/20.92 | | | | | | | | | | | | | | | (1281) all_54_1 = all_10_0 % 146.80/20.92 | | | | | | | | | | | | | | | % 146.80/20.92 | | | | | | | | | | | | | | | COMBINE_EQS: (408), (1280) imply: % 146.80/20.92 | | | | | | | | | | | | | | | (1282) all_56_3 = all_10_0 % 146.80/20.92 | | | | | | | | | | | | | | | % 146.80/20.92 | | | | | | | | | | | | | | | COMBINE_EQS: (555), (1280) imply: % 146.80/20.92 | | | | | | | | | | | | | | | (1283) all_58_1 = all_10_0 % 146.80/20.92 | | | | | | | | | | | | | | | % 146.80/20.92 | | | | | | | | | | | | | | | REDUCE: (183), (1280) imply: % 146.80/20.92 | | | | | | | | | | | | | | | (1284) ~ (all_52_7 = all_10_0) % 146.80/20.92 | | | | | | | | | | | | | | | % 146.80/20.92 | | | | | | | | | | | | | | | SIMP: (1284) implies: % 146.80/20.92 | | | | | | | | | | | | | | | (1285) ~ (all_52_7 = all_10_0) % 146.80/20.92 | | | | | | | | | | | | | | | % 146.80/20.92 | | | | | | | | | | | | | | | REDUCE: (182), (1280) imply: % 146.80/20.92 | | | | | | | | | | | | | | | (1286) ~ (all_52_8 = all_10_0) % 146.80/20.92 | | | | | | | | | | | | | | | % 146.80/20.92 | | | | | | | | | | | | | | | SIMP: (1286) implies: % 146.80/20.92 | | | | | | | | | | | | | | | (1287) ~ (all_52_8 = all_10_0) % 146.80/20.92 | | | | | | | | | | | | | | | % 146.80/20.92 | | | | | | | | | | | | | | | REDUCE: (181), (1280) imply: % 146.80/20.92 | | | | | | | | | | | | | | | (1288) ~ (all_52_12 = all_10_0) % 146.80/20.92 | | | | | | | | | | | | | | | % 146.80/20.92 | | | | | | | | | | | | | | | SIMP: (1288) implies: % 146.80/20.92 | | | | | | | | | | | | | | | (1289) ~ (all_52_12 = all_10_0) % 146.80/20.92 | | | | | | | | | | | | | | | % 146.80/20.92 | | | | | | | | | | | | | | | REDUCE: (563), (1280) imply: % 146.80/20.92 | | | | | | | | | | | | | | | (1290) ~ (all_10_0 = all_10_2) % 146.80/20.92 | | | | | | | | | | | | | | | % 146.80/20.92 | | | | | | | | | | | | | | | REDUCE: (571), (1280) imply: % 146.80/20.92 | | | | | | | | | | | | | | | (1291) ~ (all_10_0 = all_8_2) % 146.80/20.92 | | | | | | | | | | | | | | | % 146.80/20.92 | | | | | | | | | | | | | | | REDUCE: (616), (1280) imply: % 146.80/20.92 | | | | | | | | | | | | | | | (1292) op(e2, all_10_0) = all_56_2 % 146.80/20.92 | | | | | | | | | | | | | | | % 146.80/20.92 | | | | | | | | | | | | | | | BETA: splitting (129) gives: % 146.80/20.92 | | | | | | | | | | | | | | | % 146.80/20.92 | | | | | | | | | | | | | | | Case 1: % 146.80/20.92 | | | | | | | | | | | | | | | | % 146.80/20.92 | | | | | | | | | | | | | | | | (1293) ~ (all_40_0 = e3) % 146.80/20.92 | | | | | | | | | | | | | | | | % 146.80/20.92 | | | | | | | | | | | | | | | | REDUCE: (713), (1293) imply: % 146.80/20.92 | | | | | | | | | | | | | | | | (1294) ~ (all_6_0 = e3) % 146.80/20.92 | | | | | | | | | | | | | | | | % 146.80/20.92 | | | | | | | | | | | | | | | | BETA: splitting (288) gives: % 146.80/20.92 | | | | | | | | | | | | | | | | % 146.80/20.92 | | | | | | | | | | | | | | | | Case 1: % 146.80/20.92 | | | | | | | | | | | | | | | | | % 146.80/20.92 | | | | | | | | | | | | | | | | | (1295) ~ (all_56_31 = e1) % 146.80/20.92 | | | | | | | | | | | | | | | | | % 146.80/20.92 | | | | | | | | | | | | | | | | | REDUCE: (544), (1295) imply: % 146.80/20.92 | | | | | | | | | | | | | | | | | (1296) ~ (all_4_2 = e1) % 146.80/20.92 | | | | | | | | | | | | | | | | | % 146.80/20.92 | | | | | | | | | | | | | | | | | BETA: splitting (292) gives: % 146.80/20.92 | | | | | | | | | | | | | | | | | % 146.80/20.92 | | | | | | | | | | | | | | | | | Case 1: % 146.80/20.92 | | | | | | | | | | | | | | | | | | % 146.80/20.92 | | | | | | | | | | | | | | | | | | (1297) ~ (all_56_21 = e2) % 146.80/20.92 | | | | | | | | | | | | | | | | | | % 146.80/20.92 | | | | | | | | | | | | | | | | | | REDUCE: (374), (1297) imply: % 146.80/20.92 | | | | | | | | | | | | | | | | | | (1298) ~ (all_6_2 = e2) % 146.80/20.92 | | | | | | | | | | | | | | | | | | % 146.80/20.92 | | | | | | | | | | | | | | | | | | BETA: splitting (290) gives: % 146.80/20.92 | | | | | | | | | | | | | | | | | | % 146.80/20.92 | | | | | | | | | | | | | | | | | | Case 1: % 146.80/20.92 | | | | | | | | | | | | | | | | | | | % 146.80/20.92 | | | | | | | | | | | | | | | | | | | (1299) ~ (all_56_31 = e3) % 146.80/20.92 | | | | | | | | | | | | | | | | | | | % 146.80/20.92 | | | | | | | | | | | | | | | | | | | REDUCE: (544), (1299) imply: % 146.80/20.92 | | | | | | | | | | | | | | | | | | | (1300) ~ (all_4_2 = e3) % 146.80/20.92 | | | | | | | | | | | | | | | | | | | % 146.80/20.95 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (37), (38), (41), (42), (43), (46), (47), % 146.80/20.95 | | | | | | | | | | | | | | | | | | | (48), (51), (53), (158), (160), (161), (165), % 146.80/20.95 | | | | | | | | | | | | | | | | | | | (168), (169), (173), (174), (176), (181), (182), % 146.80/20.95 | | | | | | | | | | | | | | | | | | | (183), (184), (188), (189), (191), (192), (193), % 146.80/20.95 | | | | | | | | | | | | | | | | | | | (196), (208), (212), (237), (238), (239), (240), % 146.80/20.95 | | | | | | | | | | | | | | | | | | | (241), (242), (243), (244), (245), (247), (249), % 146.80/20.95 | | | | | | | | | | | | | | | | | | | (250), (251), (252), (286), (287), (289), (291), % 146.80/20.95 | | | | | | | | | | | | | | | | | | | (292), (293), (294), (295), (296), (297), (298), % 146.80/20.95 | | | | | | | | | | | | | | | | | | | (299), (318), (319), (321), (322), (326), (328), % 146.80/20.95 | | | | | | | | | | | | | | | | | | | (330), (332), (333), (336), (337), (340), (342), % 146.80/20.95 | | | | | | | | | | | | | | | | | | | (343), (344), (360), (365), (366), (374), (380), % 146.80/20.95 | | | | | | | | | | | | | | | | | | | (381), (386), (389), (401), (402), (407), (419), % 146.80/20.95 | | | | | | | | | | | | | | | | | | | (425), (429), (431), (435), (443), (457), (459), % 146.80/20.95 | | | | | | | | | | | | | | | | | | | (461), (469), (471), (473), (476), (478), (480), % 146.80/20.95 | | | | | | | | | | | | | | | | | | | (482), (533), (540), (541), (542), (543), (544), % 146.80/20.95 | | | | | | | | | | | | | | | | | | | (545), (546), (547), (548), (549), (550), (551), % 146.80/20.95 | | | | | | | | | | | | | | | | | | | (552), (553), (554), (555), (557), (559), (561), % 146.80/20.95 | | | | | | | | | | | | | | | | | | | (563), (565), (567), (568), (569), (570), (571), % 146.80/20.95 | | | | | | | | | | | | | | | | | | | (573), (575), (577), (579), (580), (581), (582), % 146.80/20.95 | | | | | | | | | | | | | | | | | | | (583), (585), (587), (588), (589), (590), (591), % 146.80/20.95 | | | | | | | | | | | | | | | | | | | (612), (617), (618), (621), (622), (627), (723), % 146.80/20.95 | | | | | | | | | | | | | | | | | | | (767), (768), (769), (770), (776), (778), (782), % 146.80/20.95 | | | | | | | | | | | | | | | | | | | (784), (786), (788), (1275), (1278), (1281), % 146.80/20.95 | | | | | | | | | | | | | | | | | | | (1282), (1283), (1285), (1287), (1289), (1290), % 146.80/20.95 | | | | | | | | | | | | | | | | | | | (1291), (1292), (1294), (1296), (1298), (1300), % 146.80/20.95 | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 146.80/20.95 | | | | | | | | | | | | | | | | | | | #476. % 146.80/20.95 | | | | | | | | | | | | | | | | | | | % 146.80/20.95 | | | | | | | | | | | | | | | | | | Case 2: % 146.80/20.95 | | | | | | | | | | | | | | | | | | | % 146.80/20.95 | | | | | | | | | | | | | | | | | | | (1301) all_56_31 = e3 % 146.80/20.95 | | | | | | | | | | | | | | | | | | | (1302) all_56_25 = e0 % 146.80/20.95 | | | | | | | | | | | | | | | | | | | % 146.80/20.95 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (447), (1302) imply: % 146.80/20.95 | | | | | | | | | | | | | | | | | | | (1303) all_52_3 = e0 % 146.80/20.95 | | | | | | | | | | | | | | | | | | | % 146.80/20.95 | | | | | | | | | | | | | | | | | | | SIMP: (1303) implies: % 146.80/20.95 | | | | | | | | | | | | | | | | | | | (1304) all_52_3 = e0 % 146.80/20.95 | | | | | | | | | | | | | | | | | | | % 146.80/20.95 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (544), (1301) imply: % 146.80/20.95 | | | | | | | | | | | | | | | | | | | (1305) all_4_2 = e3 % 146.80/20.95 | | | | | | | | | | | | | | | | | | | % 146.80/20.95 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (547), (1305) imply: % 146.80/20.95 | | | | | | | | | | | | | | | | | | | (1306) all_58_15 = e3 % 146.80/20.95 | | | | | | | | | | | | | | | | | | | % 146.80/20.95 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (365), (1304) imply: % 146.80/20.95 | | | | | | | | | | | | | | | | | | | (1307) all_58_12 = e0 % 146.80/20.95 | | | | | | | | | | | | | | | | | | | % 146.80/20.95 | | | | | | | | | | | | | | | | | | | REDUCE: (188), (1304) imply: % 146.80/20.95 | | | | | | | | | | | | | | | | | | | (1308) ~ (all_52_7 = e0) % 146.80/20.95 | | | | | | | | | | | | | | | | | | | % 146.80/20.95 | | | | | | | | | | | | | | | | | | | SIMP: (1308) implies: % 146.80/20.95 | | | | | | | | | | | | | | | | | | | (1309) ~ (all_52_7 = e0) % 146.80/20.95 | | | | | | | | | | | | | | | | | | | % 146.80/20.95 | | | | | | | | | | | | | | | | | | | REDUCE: (187), (1304) imply: % 146.80/20.95 | | | | | | | | | | | | | | | | | | | (1310) ~ (all_52_11 = e0) % 146.80/20.95 | | | | | | | | | | | | | | | | | | | % 146.80/20.95 | | | | | | | | | | | | | | | | | | | SIMP: (1310) implies: % 146.80/20.95 | | | | | | | | | | | | | | | | | | | (1311) ~ (all_52_11 = e0) % 146.80/20.95 | | | | | | | | | | | | | | | | | | | % 146.80/20.95 | | | | | | | | | | | | | | | | | | | REDUCE: (561), (1304) imply: % 146.80/20.95 | | | | | | | | | | | | | | | | | | | (1312) ~ (all_10_2 = e0) % 146.80/20.95 | | | | | | | | | | | | | | | | | | | % 146.80/20.95 | | | | | | | | | | | | | | | | | | | SIMP: (1312) implies: % 146.80/20.95 | | | | | | | | | | | | | | | | | | | (1313) ~ (all_10_2 = e0) % 146.80/20.95 | | | | | | | | | | | | | | | | | | | % 146.80/20.95 | | | | | | | | | | | | | | | | | | | REDUCE: (588), (1305) imply: % 146.80/20.95 | | | | | | | | | | | | | | | | | | | (1314) ~ (all_52_11 = e3) % 146.80/20.95 | | | | | | | | | | | | | | | | | | | % 146.80/20.95 | | | | | | | | | | | | | | | | | | | REDUCE: (38), (1305) imply: % 146.80/20.95 | | | | | | | | | | | | | | | | | | | (1315) op(e3, e3) = all_4_1 % 146.80/20.95 | | | | | | | | | | | | | | | | | | | % 146.80/20.95 | | | | | | | | | | | | | | | | | | | REDUCE: (36), (1305) imply: % 146.80/20.95 | | | | | | | | | | | | | | | | | | | (1316) op(e0, e0) = e3 % 146.80/20.95 | | | | | | | | | | | | | | | | | | | % 146.80/20.95 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (37), (41), (42), (43), (46), (47), (48), (51), % 146.80/20.95 | | | | | | | | | | | | | | | | | | | (169), (193), (206), (238), (242), (247), (251), % 146.80/20.95 | | | | | | | | | | | | | | | | | | | (252), (291), (293), (294), (296), (298), (318), % 146.80/20.95 | | | | | | | | | | | | | | | | | | | (321), (322), (342), (345), (374), (381), (386), % 146.80/20.95 | | | | | | | | | | | | | | | | | | | (401), (407), (419), (425), (482), (533), (541), % 146.80/20.95 | | | | | | | | | | | | | | | | | | | (542), (543), (545), (546), (547), (548), (549), % 146.80/20.95 | | | | | | | | | | | | | | | | | | | (550), (551), (553), (557), (559), (567), (568), % 146.80/20.95 | | | | | | | | | | | | | | | | | | | (569), (575), (579), (585), (587), (612), (617), % 146.80/20.95 | | | | | | | | | | | | | | | | | | | (622), (626), (723), (768), (770), (774), (778), % 146.80/20.95 | | | | | | | | | | | | | | | | | | | (780), (784), (788), (1275), (1278), (1281), % 146.80/20.95 | | | | | | | | | | | | | | | | | | | (1283), (1285), (1290), (1291), (1296), (1298), % 146.80/20.95 | | | | | | | | | | | | | | | | | | | (1306), (1307), (1309), (1311), (1313), (1314), % 146.80/20.95 | | | | | | | | | | | | | | | | | | | (1315), (1316), (function-axioms) are inconsistent % 146.80/20.95 | | | | | | | | | | | | | | | | | | | by sub-proof #467. % 146.80/20.95 | | | | | | | | | | | | | | | | | | | % 146.80/20.95 | | | | | | | | | | | | | | | | | | End of split % 146.80/20.95 | | | | | | | | | | | | | | | | | | % 146.80/20.95 | | | | | | | | | | | | | | | | | Case 2: % 146.80/20.95 | | | | | | | | | | | | | | | | | | % 146.80/20.95 | | | | | | | | | | | | | | | | | | (1317) all_56_21 = e2 % 146.80/20.95 | | | | | | | | | | | | | | | | | | (1318) all_56_19 = e1 % 146.80/20.95 | | | | | | | | | | | | | | | | | | % 146.80/20.95 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (435), (1318) imply: % 146.80/20.95 | | | | | | | | | | | | | | | | | | (1319) all_52_6 = e1 % 146.80/20.95 | | | | | | | | | | | | | | | | | | % 146.80/20.95 | | | | | | | | | | | | | | | | | | SIMP: (1319) implies: % 146.80/20.95 | | | | | | | | | | | | | | | | | | (1320) all_52_6 = e1 % 146.80/20.95 | | | | | | | | | | | | | | | | | | % 146.80/20.95 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (374), (1317) imply: % 146.80/20.95 | | | | | | | | | | | | | | | | | | (1321) all_6_2 = e2 % 146.80/20.95 | | | | | | | | | | | | | | | | | | % 146.80/20.95 | | | | | | | | | | | | | | | | | | SIMP: (1321) implies: % 146.80/20.95 | | | | | | | | | | | | | | | | | | (1322) all_6_2 = e2 % 146.80/20.95 | | | | | | | | | | | | | | | | | | % 146.80/20.95 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (380), (1320) imply: % 146.80/20.95 | | | | | | | | | | | | | | | | | | (1323) all_58_7 = e1 % 146.80/20.95 | | | | | | | | | | | | | | | | | | % 146.80/20.95 | | | | | | | | | | | | | | | | | | REDUCE: (569), (1322) imply: % 146.80/20.95 | | | | | | | | | | | | | | | | | | (1324) ~ (all_52_2 = e2) % 146.80/20.95 | | | | | | | | | | | | | | | | | | % 146.80/20.95 | | | | | | | | | | | | | | | | | | REDUCE: (573), (1320) imply: % 146.80/20.95 | | | | | | | | | | | | | | | | | | (1325) ~ (all_8_2 = e1) % 146.80/20.95 | | | | | | | | | | | | | | | | | | % 146.80/20.95 | | | | | | | | | | | | | | | | | | SIMP: (1325) implies: % 146.80/20.95 | | | | | | | | | | | | | | | | | | (1326) ~ (all_8_2 = e1) % 146.80/20.95 | | | | | | | | | | | | | | | | | | % 146.80/20.95 | | | | | | | | | | | | | | | | | | REDUCE: (580), (1320), (1322) imply: % 146.80/20.95 | | | | | | | | | | | | | | | | | | (1327) ~ (e2 = e1) % 146.80/20.95 | | | | | | | | | | | | | | | | | | % 146.80/20.95 | | | | | | | | | | | | | | | | | | REDUCE: (582), (1322) imply: % 146.80/20.95 | | | | | | | | | | | | | | | | | | (1328) ~ (all_52_8 = e2) % 146.80/20.95 | | | | | | | | | | | | | | | | | | % 146.80/20.95 | | | | | | | | | | | | | | | | | | REDUCE: (43), (1322) imply: % 146.80/20.95 | | | | | | | | | | | | | | | | | | (1329) op(e2, e2) = all_6_1 % 146.80/20.95 | | | | | | | | | | | | | | | | | | % 146.80/20.95 | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (46), (188), (193), (247), (252), (294), % 146.80/20.95 | | | | | | | | | | | | | | | | | | (297), (298), (299), (338), (339), (344), (345), % 146.80/20.95 | | | | | | | | | | | | | | | | | | (365), (401), (402), (407), (419), (429), (443), % 146.80/20.95 | | | | | | | | | | | | | | | | | | (542), (543), (545), (546), (549), (551), (553), % 146.80/20.95 | | | | | | | | | | | | | | | | | | (554), (575), (619), (768), (770), (788), (1278), % 146.80/20.95 | | | | | | | | | | | | | | | | | | (1282), (1283), (1285), (1287), (1289), (1290), % 146.80/20.95 | | | | | | | | | | | | | | | | | | (1323), (1324), (1326), (1328), (1329), % 146.80/20.95 | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 146.80/20.95 | | | | | | | | | | | | | | | | | | #464. % 146.80/20.95 | | | | | | | | | | | | | | | | | | % 146.80/20.95 | | | | | | | | | | | | | | | | | End of split % 146.80/20.95 | | | | | | | | | | | | | | | | | % 146.80/20.95 | | | | | | | | | | | | | | | | Case 2: % 146.80/20.95 | | | | | | | | | | | | | | | | | % 146.80/20.95 | | | | | | | | | | | | | | | | | (1330) all_56_31 = e1 % 146.80/20.95 | | | | | | | | | | | | | | | | | (1331) all_56_29 = e0 % 146.80/20.95 | | | | | | | | | | | | | | | | | % 146.80/20.95 | | | | | | | | | | | | | | | | | COMBINE_EQS: (357), (1331) imply: % 146.80/20.95 | | | | | | | | | | | | | | | | | (1332) all_52_11 = e0 % 146.80/20.95 | | | | | | | | | | | | | | | | | % 146.80/20.96 | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (36), (37), (38), (41), (42), (43), (48), % 146.80/20.96 | | | | | | | | | | | | | | | | | (53), (161), (165), (166), (168), (173), (176), % 146.80/20.96 | | | | | | | | | | | | | | | | | (181), (187), (192), (194), (206), (207), (239), % 146.80/20.96 | | | | | | | | | | | | | | | | | (240), (242), (245), (246), (247), (249), (252), % 146.80/20.96 | | | | | | | | | | | | | | | | | (292), (293), (294), (295), (296), (297), (298), % 146.80/20.96 | | | | | | | | | | | | | | | | | (299), (330), (331), (332), (333), (337), (343), % 146.80/20.96 | | | | | | | | | | | | | | | | | (374), (380), (381), (386), (389), (401), (402), % 146.80/20.96 | | | | | | | | | | | | | | | | | (407), (408), (419), (425), (431), (435), (461), % 146.80/20.96 | | | | | | | | | | | | | | | | | (467), (469), (478), (480), (541), (542), (543), % 146.80/20.96 | | | | | | | | | | | | | | | | | (544), (545), (546), (548), (549), (551), (552), % 146.80/20.96 | | | | | | | | | | | | | | | | | (554), (555), (557), (563), (567), (571), (577), % 146.80/20.96 | | | | | | | | | | | | | | | | | (579), (580), (581), (582), (583), (585), (589), % 146.80/20.96 | | | | | | | | | | | | | | | | | (590), (622), (625), (767), (769), (772), (786), % 146.80/20.96 | | | | | | | | | | | | | | | | | (1294), (1330), (1332), (function-axioms) are % 146.80/20.96 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #463. % 146.80/20.96 | | | | | | | | | | | | | | | | | % 146.80/20.96 | | | | | | | | | | | | | | | | End of split % 146.80/20.96 | | | | | | | | | | | | | | | | % 146.80/20.96 | | | | | | | | | | | | | | | Case 2: % 146.80/20.96 | | | | | | | | | | | | | | | | % 146.80/20.96 | | | | | | | | | | | | | | | | (1333) all_40_0 = e3 % 146.80/20.96 | | | | | | | | | | | | | | | | (1334) ~ (all_40_1 = e0) | ~ (all_40_2 = e2) % 146.80/20.96 | | | | | | | | | | | | | | | | % 146.80/20.96 | | | | | | | | | | | | | | | | COMBINE_EQS: (713), (1333) imply: % 146.80/20.96 | | | | | | | | | | | | | | | | (1335) all_6_0 = e3 % 146.80/20.96 | | | | | | | | | | | | | | | | % 146.80/20.96 | | | | | | | | | | | | | | | | SIMP: (1335) implies: % 146.80/20.96 | | | | | | | | | | | | | | | | (1336) all_6_0 = e3 % 146.80/20.96 | | | | | | | | | | | | | | | | % 146.80/20.96 | | | | | | | | | | | | | | | | REDUCE: (42), (1336) imply: % 146.80/20.96 | | | | | | | | | | | | | | | | (1337) op(e1, all_6_1) = e3 % 146.80/20.96 | | | | | | | | | | | | | | | | % 146.80/20.96 | | | | | | | | | | | | | | | | BETA: splitting (288) gives: % 146.80/20.96 | | | | | | | | | | | | | | | | % 146.80/20.96 | | | | | | | | | | | | | | | | Case 1: % 146.80/20.96 | | | | | | | | | | | | | | | | | % 146.80/20.96 | | | | | | | | | | | | | | | | | (1338) ~ (all_56_31 = e1) % 146.80/20.96 | | | | | | | | | | | | | | | | | % 146.80/20.96 | | | | | | | | | | | | | | | | | REDUCE: (544), (1338) imply: % 146.80/20.96 | | | | | | | | | | | | | | | | | (1339) ~ (all_4_2 = e1) % 146.80/20.96 | | | | | | | | | | | | | | | | | % 146.80/20.96 | | | | | | | | | | | | | | | | | BETA: splitting (292) gives: % 146.80/20.96 | | | | | | | | | | | | | | | | | % 146.80/20.96 | | | | | | | | | | | | | | | | | Case 1: % 146.80/20.96 | | | | | | | | | | | | | | | | | | % 146.80/20.96 | | | | | | | | | | | | | | | | | | (1340) ~ (all_56_21 = e2) % 146.80/20.96 | | | | | | | | | | | | | | | | | | % 146.80/20.96 | | | | | | | | | | | | | | | | | | REDUCE: (374), (1340) imply: % 146.80/20.96 | | | | | | | | | | | | | | | | | | (1341) ~ (all_6_2 = e2) % 146.80/20.96 | | | | | | | | | | | | | | | | | | % 146.80/20.96 | | | | | | | | | | | | | | | | | | BETA: splitting (290) gives: % 146.80/20.96 | | | | | | | | | | | | | | | | | | % 146.80/20.96 | | | | | | | | | | | | | | | | | | Case 1: % 146.80/20.96 | | | | | | | | | | | | | | | | | | | % 146.80/20.96 | | | | | | | | | | | | | | | | | | | (1342) ~ (all_56_31 = e3) % 146.80/20.96 | | | | | | | | | | | | | | | | | | | % 146.80/20.96 | | | | | | | | | | | | | | | | | | | REDUCE: (544), (1342) imply: % 146.80/20.96 | | | | | | | | | | | | | | | | | | | (1343) ~ (all_4_2 = e3) % 146.80/20.96 | | | | | | | | | | | | | | | | | | | % 146.80/20.96 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (36), (41), (42), (43), (46), (51), (53), % 146.80/20.96 | | | | | | | | | | | | | | | | | | | (158), (160), (161), (174), (176), (181), (183), % 146.80/20.96 | | | | | | | | | | | | | | | | | | | (184), (189), (191), (208), (237), (239), (241), % 146.80/20.96 | | | | | | | | | | | | | | | | | | | (242), (243), (247), (249), (251), (252), (287), % 146.80/20.96 | | | | | | | | | | | | | | | | | | | (291), (292), (293), (294), (297), (299), (321), % 146.80/20.96 | | | | | | | | | | | | | | | | | | | (324), (326), (328), (332), (340), (344), (365), % 146.80/20.96 | | | | | | | | | | | | | | | | | | | (366), (374), (380), (381), (386), (389), (401), % 146.80/20.96 | | | | | | | | | | | | | | | | | | | (402), (407), (408), (419), (435), (443), (457), % 146.80/20.96 | | | | | | | | | | | | | | | | | | | (461), (473), (476), (480), (507), (540), (541), % 146.80/20.96 | | | | | | | | | | | | | | | | | | | (542), (543), (544), (545), (546), (547), (548), % 146.80/20.96 | | | | | | | | | | | | | | | | | | | (550), (551), (552), (553), (554), (557), (559), % 146.80/20.96 | | | | | | | | | | | | | | | | | | | (563), (565), (567), (568), (569), (570), (571), % 146.80/20.96 | | | | | | | | | | | | | | | | | | | (573), (577), (580), (581), (587), (588), (589), % 146.80/20.96 | | | | | | | | | | | | | | | | | | | (590), (591), (621), (622), (685), (768), (782), % 146.80/20.96 | | | | | | | | | | | | | | | | | | | (786), (788), (1334), (1337), (1339), (1343), % 146.80/20.96 | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 146.80/20.96 | | | | | | | | | | | | | | | | | | | #504. % 146.80/20.96 | | | | | | | | | | | | | | | | | | | % 146.80/20.96 | | | | | | | | | | | | | | | | | | Case 2: % 146.80/20.96 | | | | | | | | | | | | | | | | | | | % 146.80/20.96 | | | | | | | | | | | | | | | | | | | (1344) all_56_31 = e3 % 146.80/20.96 | | | | | | | | | | | | | | | | | | | (1345) all_56_25 = e0 % 146.80/20.96 | | | | | | | | | | | | | | | | | | | % 146.80/20.96 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (447), (1345) imply: % 146.80/20.96 | | | | | | | | | | | | | | | | | | | (1346) all_52_3 = e0 % 146.80/20.96 | | | | | | | | | | | | | | | | | | | % 146.80/20.96 | | | | | | | | | | | | | | | | | | | SIMP: (1346) implies: % 146.80/20.96 | | | | | | | | | | | | | | | | | | | (1347) all_52_3 = e0 % 146.80/20.96 | | | | | | | | | | | | | | | | | | | % 146.80/20.96 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (544), (1344) imply: % 146.80/20.96 | | | | | | | | | | | | | | | | | | | (1348) all_4_2 = e3 % 146.80/20.96 | | | | | | | | | | | | | | | | | | | % 146.80/20.96 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (547), (1348) imply: % 146.80/20.96 | | | | | | | | | | | | | | | | | | | (1349) all_58_15 = e3 % 146.80/20.96 | | | | | | | | | | | | | | | | | | | % 146.80/20.96 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (365), (1347) imply: % 146.80/20.96 | | | | | | | | | | | | | | | | | | | (1350) all_58_12 = e0 % 146.80/20.96 | | | | | | | | | | | | | | | | | | | % 146.80/20.96 | | | | | | | | | | | | | | | | | | | REDUCE: (188), (1347) imply: % 146.80/20.96 | | | | | | | | | | | | | | | | | | | (1351) ~ (all_52_7 = e0) % 146.80/20.96 | | | | | | | | | | | | | | | | | | | % 146.80/20.96 | | | | | | | | | | | | | | | | | | | SIMP: (1351) implies: % 146.80/20.96 | | | | | | | | | | | | | | | | | | | (1352) ~ (all_52_7 = e0) % 146.80/20.96 | | | | | | | | | | | | | | | | | | | % 146.80/20.96 | | | | | | | | | | | | | | | | | | | REDUCE: (187), (1347) imply: % 146.80/20.96 | | | | | | | | | | | | | | | | | | | (1353) ~ (all_52_11 = e0) % 146.80/20.96 | | | | | | | | | | | | | | | | | | | % 146.80/20.96 | | | | | | | | | | | | | | | | | | | SIMP: (1353) implies: % 146.80/20.96 | | | | | | | | | | | | | | | | | | | (1354) ~ (all_52_11 = e0) % 146.80/20.96 | | | | | | | | | | | | | | | | | | | % 146.80/20.96 | | | | | | | | | | | | | | | | | | | REDUCE: (561), (1347) imply: % 146.80/20.96 | | | | | | | | | | | | | | | | | | | (1355) ~ (all_10_2 = e0) % 146.80/20.96 | | | | | | | | | | | | | | | | | | | % 146.80/20.96 | | | | | | | | | | | | | | | | | | | SIMP: (1355) implies: % 146.80/20.96 | | | | | | | | | | | | | | | | | | | (1356) ~ (all_10_2 = e0) % 146.80/20.96 | | | | | | | | | | | | | | | | | | | % 146.80/20.96 | | | | | | | | | | | | | | | | | | | REDUCE: (588), (1348) imply: % 146.80/20.96 | | | | | | | | | | | | | | | | | | | (1357) ~ (all_52_11 = e3) % 146.80/20.96 | | | | | | | | | | | | | | | | | | | % 146.80/20.96 | | | | | | | | | | | | | | | | | | | REDUCE: (38), (1348) imply: % 146.80/20.96 | | | | | | | | | | | | | | | | | | | (1358) op(e3, e3) = all_4_1 % 146.80/20.96 | | | | | | | | | | | | | | | | | | | % 146.80/20.96 | | | | | | | | | | | | | | | | | | | REDUCE: (36), (1348) imply: % 146.80/20.96 | | | | | | | | | | | | | | | | | | | (1359) op(e0, e0) = e3 % 146.80/20.96 | | | | | | | | | | | | | | | | | | | % 146.80/20.96 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (37), (41), (42), (43), (46), (47), (48), (51), % 146.80/20.96 | | | | | | | | | | | | | | | | | | | (169), (193), (206), (238), (242), (247), (251), % 146.80/20.96 | | | | | | | | | | | | | | | | | | | (252), (291), (293), (294), (296), (298), (318), % 146.80/20.96 | | | | | | | | | | | | | | | | | | | (321), (322), (342), (345), (374), (381), (386), % 146.80/20.96 | | | | | | | | | | | | | | | | | | | (401), (407), (419), (425), (482), (533), (541), % 146.80/20.96 | | | | | | | | | | | | | | | | | | | (542), (543), (545), (546), (547), (548), (549), % 146.80/20.96 | | | | | | | | | | | | | | | | | | | (550), (551), (553), (557), (559), (567), (568), % 146.80/20.96 | | | | | | | | | | | | | | | | | | | (569), (575), (579), (585), (587), (612), (617), % 146.80/20.96 | | | | | | | | | | | | | | | | | | | (622), (626), (723), (768), (770), (774), (778), % 146.80/20.96 | | | | | | | | | | | | | | | | | | | (780), (784), (788), (1275), (1278), (1281), % 146.80/20.96 | | | | | | | | | | | | | | | | | | | (1283), (1285), (1290), (1291), (1339), (1341), % 146.80/20.96 | | | | | | | | | | | | | | | | | | | (1349), (1350), (1352), (1354), (1356), (1357), % 146.80/20.96 | | | | | | | | | | | | | | | | | | | (1358), (1359), (function-axioms) are inconsistent % 146.80/20.96 | | | | | | | | | | | | | | | | | | | by sub-proof #467. % 146.80/20.96 | | | | | | | | | | | | | | | | | | | % 146.80/20.96 | | | | | | | | | | | | | | | | | | End of split % 146.80/20.96 | | | | | | | | | | | | | | | | | | % 146.80/20.96 | | | | | | | | | | | | | | | | | Case 2: % 146.80/20.96 | | | | | | | | | | | | | | | | | | % 146.80/20.96 | | | | | | | | | | | | | | | | | | (1360) all_56_21 = e2 % 146.80/20.96 | | | | | | | | | | | | | | | | | | (1361) all_56_19 = e1 % 146.80/20.96 | | | | | | | | | | | | | | | | | | % 146.80/20.96 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (435), (1361) imply: % 146.80/20.96 | | | | | | | | | | | | | | | | | | (1362) all_52_6 = e1 % 146.80/20.96 | | | | | | | | | | | | | | | | | | % 146.80/20.96 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (374), (1360) imply: % 146.80/20.96 | | | | | | | | | | | | | | | | | | (1363) all_6_2 = e2 % 146.80/20.96 | | | | | | | | | | | | | | | | | | % 146.80/20.96 | | | | | | | | | | | | | | | | | | REF_CLOSE: (43), (46), (247), (507), (542), (573), (685), % 146.80/20.96 | | | | | | | | | | | | | | | | | | (768), (788), (1334), (1362), (1363), % 146.80/20.96 | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 146.80/20.96 | | | | | | | | | | | | | | | | | | #506. % 146.80/20.96 | | | | | | | | | | | | | | | | | | % 146.80/20.96 | | | | | | | | | | | | | | | | | End of split % 146.80/20.96 | | | | | | | | | | | | | | | | | % 146.80/20.96 | | | | | | | | | | | | | | | | Case 2: % 146.80/20.96 | | | | | | | | | | | | | | | | | % 146.80/20.96 | | | | | | | | | | | | | | | | | (1364) all_56_31 = e1 % 146.80/20.96 | | | | | | | | | | | | | | | | | (1365) all_56_29 = e0 % 146.80/20.96 | | | | | | | | | | | | | | | | | % 146.80/20.96 | | | | | | | | | | | | | | | | | COMBINE_EQS: (357), (1365) imply: % 146.80/20.96 | | | | | | | | | | | | | | | | | (1366) all_52_11 = e0 % 146.80/20.96 | | | | | | | | | | | | | | | | | % 146.80/20.96 | | | | | | | | | | | | | | | | | SIMP: (1366) implies: % 146.80/20.96 | | | | | | | | | | | | | | | | | (1367) all_52_11 = e0 % 146.80/20.96 | | | | | | | | | | | | | | | | | % 146.80/20.96 | | | | | | | | | | | | | | | | | REF_CLOSE: (37), (38), (41), (43), (173), (176), (187), % 146.80/20.96 | | | | | | | | | | | | | | | | | (192), (206), (207), (239), (240), (242), (292), % 146.80/20.96 | | | | | | | | | | | | | | | | | (293), (374), (381), (435), (478), (480), (541), % 146.80/20.96 | | | | | | | | | | | | | | | | | (544), (585), (622), (767), (772), (788), (1337), % 146.80/20.96 | | | | | | | | | | | | | | | | | (1364), (1367), (function-axioms) are inconsistent % 146.80/20.96 | | | | | | | | | | | | | | | | | by sub-proof #462. % 146.80/20.96 | | | | | | | | | | | | | | | | | % 146.80/20.96 | | | | | | | | | | | | | | | | End of split % 146.80/20.96 | | | | | | | | | | | | | | | | % 146.80/20.96 | | | | | | | | | | | | | | | End of split % 146.80/20.96 | | | | | | | | | | | | | | | % 146.80/20.96 | | | | | | | | | | | | | | End of split % 146.80/20.96 | | | | | | | | | | | | | | % 146.80/20.96 | | | | | | | | | | | | | Case 2: % 146.80/20.96 | | | | | | | | | | | | | | % 146.80/20.96 | | | | | | | | | | | | | | (1368) all_36_1 = e3 % 146.80/20.96 | | | | | | | | | | | | | | (1369) ~ (all_36_0 = e0) | ~ (all_36_2 = e2) % 146.80/20.96 | | | | | | | | | | | | | | % 146.80/20.96 | | | | | | | | | | | | | | COMBINE_EQS: (652), (1368) imply: % 146.80/20.96 | | | | | | | | | | | | | | (1370) all_6_1 = e3 % 146.80/20.96 | | | | | | | | | | | | | | % 146.80/20.96 | | | | | | | | | | | | | | REDUCE: (43), (1370) imply: % 146.80/20.96 | | | | | | | | | | | | | | (1371) op(all_6_2, all_6_2) = e3 % 146.80/20.96 | | | | | | | | | | | | | | % 146.80/20.96 | | | | | | | | | | | | | | REDUCE: (42), (1370) imply: % 146.80/20.96 | | | | | | | | | | | | | | (1372) op(e1, e3) = all_6_0 % 146.80/20.96 | | | | | | | | | | | | | | % 146.80/20.96 | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_2, % 146.80/20.96 | | | | | | | | | | | | | | all_6_0, e3, e1, simplifying with (211), (1372) % 146.80/20.96 | | | | | | | | | | | | | | gives: % 146.80/20.96 | | | | | | | | | | | | | | (1373) all_52_2 = all_6_0 % 146.80/20.96 | | | | | | | | | | | | | | % 146.80/20.96 | | | | | | | | | | | | | | COMBINE_EQS: (471), (1373) imply: % 146.80/20.96 | | | | | | | | | | | | | | (1374) all_54_8 = all_6_0 % 146.80/20.96 | | | | | | | | | | | | | | % 146.80/20.96 | | | | | | | | | | | | | | COMBINE_EQS: (381), (1373) imply: % 146.80/20.96 | | | | | | | | | | | | | | (1375) all_56_17 = all_6_0 % 146.80/20.96 | | | | | | | | | | | | | | % 146.80/20.96 | | | | | | | | | | | | | | COMBINE_EQS: (553), (1373) imply: % 146.80/20.96 | | | | | | | | | | | | | | (1376) all_58_6 = all_6_0 % 146.80/20.96 | | | | | | | | | | | | | | % 146.80/20.96 | | | | | | | | | | | | | | REDUCE: (197), (1373) imply: % 146.80/20.96 | | | | | | | | | | | | | | (1377) ~ (all_52_1 = all_6_0) % 146.80/20.96 | | | | | | | | | | | | | | % 146.80/20.96 | | | | | | | | | | | | | | REDUCE: (192), (1373) imply: % 146.80/20.96 | | | | | | | | | | | | | | (1378) ~ (all_52_3 = all_6_0) % 146.80/20.96 | | | | | | | | | | | | | | % 146.80/20.96 | | | | | | | | | | | | | | SIMP: (1378) implies: % 146.80/20.96 | | | | | | | | | | | | | | (1379) ~ (all_52_3 = all_6_0) % 146.80/20.96 | | | | | | | | | | | | | | % 146.80/20.96 | | | | | | | | | | | | | | REDUCE: (191), (1373) imply: % 146.80/20.96 | | | | | | | | | | | | | | (1380) ~ (all_52_6 = all_6_0) % 146.80/20.96 | | | | | | | | | | | | | | % 146.80/20.96 | | | | | | | | | | | | | | SIMP: (1380) implies: % 146.80/20.96 | | | | | | | | | | | | | | (1381) ~ (all_52_6 = all_6_0) % 146.80/20.96 | | | | | | | | | | | | | | % 146.80/20.96 | | | | | | | | | | | | | | REDUCE: (189), (1373) imply: % 146.80/20.96 | | | | | | | | | | | | | | (1382) ~ (all_52_14 = all_6_0) % 146.80/20.96 | | | | | | | | | | | | | | % 146.80/20.96 | | | | | | | | | | | | | | SIMP: (1382) implies: % 146.80/20.96 | | | | | | | | | | | | | | (1383) ~ (all_52_14 = all_6_0) % 146.80/20.96 | | | | | | | | | | | | | | % 146.80/20.96 | | | | | | | | | | | | | | REDUCE: (559), (1373) imply: % 146.80/20.96 | | | | | | | | | | | | | | (1384) ~ (all_10_2 = all_6_0) % 146.80/20.96 | | | | | | | | | | | | | | % 146.80/20.96 | | | | | | | | | | | | | | SIMP: (1384) implies: % 146.80/20.96 | | | | | | | | | | | | | | (1385) ~ (all_10_2 = all_6_0) % 146.80/20.96 | | | | | | | | | | | | | | % 146.80/20.96 | | | | | | | | | | | | | | REDUCE: (569), (1373) imply: % 146.80/20.97 | | | | | | | | | | | | | | (1386) ~ (all_6_0 = all_6_2) % 146.80/20.97 | | | | | | | | | | | | | | % 146.80/20.97 | | | | | | | | | | | | | | BETA: splitting (124) gives: % 146.80/20.97 | | | | | | | | | | | | | | % 146.80/20.97 | | | | | | | | | | | | | | Case 1: % 146.80/20.97 | | | | | | | | | | | | | | | % 146.80/20.97 | | | | | | | | | | | | | | | (1387) ~ (all_38_1 = e2) % 146.80/20.97 | | | | | | | | | | | | | | | % 146.80/20.97 | | | | | | | | | | | | | | | REDUCE: (684), (1387) imply: % 146.80/20.97 | | | | | | | | | | | | | | | (1388) ~ (all_10_1 = e2) % 146.80/20.97 | | | | | | | | | | | | | | | % 146.80/20.97 | | | | | | | | | | | | | | | BETA: splitting (292) gives: % 146.80/20.97 | | | | | | | | | | | | | | | % 146.80/20.97 | | | | | | | | | | | | | | | Case 1: % 146.80/20.97 | | | | | | | | | | | | | | | | % 146.80/20.97 | | | | | | | | | | | | | | | | (1389) ~ (all_56_21 = e2) % 146.80/20.97 | | | | | | | | | | | | | | | | % 146.80/20.97 | | | | | | | | | | | | | | | | REDUCE: (374), (1389) imply: % 146.80/20.97 | | | | | | | | | | | | | | | | (1390) ~ (all_6_2 = e2) % 146.80/20.97 | | | | | | | | | | | | | | | | % 146.80/20.97 | | | | | | | | | | | | | | | | BETA: splitting (288) gives: % 146.80/20.97 | | | | | | | | | | | | | | | | % 146.80/20.97 | | | | | | | | | | | | | | | | Case 1: % 146.80/20.97 | | | | | | | | | | | | | | | | | % 146.80/20.97 | | | | | | | | | | | | | | | | | (1391) ~ (all_56_31 = e1) % 146.80/20.97 | | | | | | | | | | | | | | | | | % 146.80/20.97 | | | | | | | | | | | | | | | | | REDUCE: (544), (1391) imply: % 146.80/20.97 | | | | | | | | | | | | | | | | | (1392) ~ (all_4_2 = e1) % 146.80/20.97 | | | | | | | | | | | | | | | | | % 146.80/20.97 | | | | | | | | | | | | | | | | | BETA: splitting (294) gives: % 146.80/20.97 | | | | | | | | | | | | | | | | | % 146.80/20.97 | | | | | | | | | | | | | | | | | Case 1: % 146.80/20.97 | | | | | | | | | | | | | | | | | | % 146.80/20.97 | | | | | | | | | | | | | | | | | | (1393) ~ (all_56_11 = e0) % 146.80/20.97 | | | | | | | | | | | | | | | | | | % 146.80/20.97 | | | | | | | | | | | | | | | | | | REDUCE: (545), (1393) imply: % 146.80/20.97 | | | | | | | | | | | | | | | | | | (1394) ~ (all_8_2 = e0) % 146.80/20.97 | | | | | | | | | | | | | | | | | | % 146.80/20.97 | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (36), (38), (41), (46), (47), (48), (51), % 146.80/20.97 | | | | | | | | | | | | | | | | | | (52), (53), (161), (168), (171), (174), (181), % 146.80/20.97 | | | | | | | | | | | | | | | | | | (182), (193), (194), (212), (237), (242), (243), % 146.80/20.97 | | | | | | | | | | | | | | | | | | (244), (245), (247), (251), (252), (287), (291), % 146.80/20.97 | | | | | | | | | | | | | | | | | | (293), (295), (296), (297), (298), (299), (318), % 146.80/20.97 | | | | | | | | | | | | | | | | | | (320), (321), (326), (329), (330), (331), (335), % 146.80/20.97 | | | | | | | | | | | | | | | | | | (337), (343), (344), (365), (366), (374), (380), % 146.80/20.97 | | | | | | | | | | | | | | | | | | (386), (389), (401), (402), (407), (408), (419), % 146.80/20.97 | | | | | | | | | | | | | | | | | | (425), (429), (431), (457), (469), (473), (540), % 146.80/20.97 | | | | | | | | | | | | | | | | | | (541), (542), (543), (544), (545), (546), (547), % 146.80/20.97 | | | | | | | | | | | | | | | | | | (548), (549), (550), (551), (552), (554), (555), % 146.80/20.97 | | | | | | | | | | | | | | | | | | (557), (561), (563), (565), (568), (571), (573), % 146.80/20.97 | | | | | | | | | | | | | | | | | | (575), (577), (580), (582), (583), (585), (587), % 146.80/20.97 | | | | | | | | | | | | | | | | | | (589), (590), (612), (622), (623), (627), (769), % 146.80/20.97 | | | | | | | | | | | | | | | | | | (774), (776), (778), (782), (786), (1371), (1374), % 146.80/20.97 | | | | | | | | | | | | | | | | | | (1375), (1376), (1377), (1381), (1383), (1385), % 146.80/20.97 | | | | | | | | | | | | | | | | | | (1386), (1388), (1390), (1392), (1394), % 146.80/20.97 | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 146.80/20.97 | | | | | | | | | | | | | | | | | | #442. % 146.80/20.97 | | | | | | | | | | | | | | | | | | % 146.80/20.97 | | | | | | | | | | | | | | | | | Case 2: % 146.80/20.97 | | | | | | | | | | | | | | | | | | % 146.80/20.97 | | | | | | | | | | | | | | | | | | (1395) all_56_15 = e2 % 146.80/20.97 | | | | | | | | | | | | | | | | | | (1396) all_56_11 = e0 % 146.80/20.97 | | | | | | | | | | | | | | | | | | % 146.80/20.97 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (545), (1396) imply: % 146.80/20.97 | | | | | | | | | | | | | | | | | | (1397) all_8_2 = e0 % 146.80/20.97 | | | | | | | | | | | | | | | | | | % 146.80/20.97 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (443), (1395) imply: % 146.80/20.97 | | | | | | | | | | | | | | | | | | (1398) all_52_13 = e2 % 146.80/20.97 | | | | | | | | | | | | | | | | | | % 146.80/20.97 | | | | | | | | | | | | | | | | | | REDUCE: (568), (1397) imply: % 146.80/20.97 | | | | | | | | | | | | | | | | | | (1399) ~ (all_52_1 = e0) % 146.80/20.97 | | | | | | | | | | | | | | | | | | % 146.80/20.97 | | | | | | | | | | | | | | | | | | REDUCE: (577), (1397) imply: % 146.80/20.97 | | | | | | | | | | | | | | | | | | (1400) ~ (all_52_9 = e0) % 146.80/20.97 | | | | | | | | | | | | | | | | | | % 146.80/20.97 | | | | | | | | | | | | | | | | | | REDUCE: (590), (1398) imply: % 146.80/20.97 | | | | | | | | | | | | | | | | | | (1401) ~ (all_4_2 = e2) % 146.80/20.97 | | | | | | | | | | | | | | | | | | % 146.80/20.97 | | | | | | | | | | | | | | | | | | SIMP: (1401) implies: % 146.80/20.97 | | | | | | | | | | | | | | | | | | (1402) ~ (all_4_2 = e2) % 146.80/20.97 | | | | | | | | | | | | | | | | | | % 146.80/20.97 | | | | | | | | | | | | | | | | | | REDUCE: (48), (1397) imply: % 146.80/20.97 | | | | | | | | | | | | | | | | | | (1403) op(e0, e0) = all_8_1 % 146.80/20.97 | | | | | | | | | | | | | | | | | | % 146.80/20.97 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_4_2, % 146.80/20.97 | | | | | | | | | | | | | | | | | | all_8_1, e0, e0, simplifying with (36), (1403) % 146.80/20.97 | | | | | | | | | | | | | | | | | | gives: % 146.80/20.97 | | | | | | | | | | | | | | | | | | (1404) all_8_1 = all_4_2 % 146.80/20.97 | | | | | | | | | | | | | | | | | | % 146.80/20.97 | | | | | | | | | | | | | | | | | | REDUCE: (778), (1404) imply: % 146.80/20.97 | | | | | | | | | | | | | | | | | | (1405) ~ (all_4_2 = e3) % 146.80/20.97 | | | | | | | | | | | | | | | | | | % 146.80/20.97 | | | | | | | | | | | | | | | | | | BETA: splitting (237) gives: % 146.80/20.97 | | | | | | | | | | | | | | | | | | % 146.80/20.97 | | | | | | | | | | | | | | | | | | Case 1: % 146.80/20.97 | | | | | | | | | | | | | | | | | | | % 146.80/20.97 | | | | | | | | | | | | | | | | | | | (1406) all_54_15 = e3 % 146.80/20.97 | | | | | | | | | | | | | | | | | | | % 146.80/20.97 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (540), (1405), (1406) are inconsistent by % 146.80/20.97 | | | | | | | | | | | | | | | | | | | sub-proof #740. % 146.80/20.97 | | | | | | | | | | | | | | | | | | | % 146.80/20.97 | | | | | | | | | | | | | | | | | | Case 2: % 146.80/20.97 | | | | | | | | | | | | | | | | | | | % 146.80/20.97 | | | | | | | | | | | | | | | | | | | (1407) all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0 % 146.80/20.97 | | | | | | | | | | | | | | | | | | | % 146.80/20.97 | | | | | | | | | | | | | | | | | | | BETA: splitting (1407) gives: % 146.80/20.97 | | | | | | | | | | | | | | | | | | | % 146.80/20.97 | | | | | | | | | | | | | | | | | | | Case 1: % 146.80/20.97 | | | | | | | | | | | | | | | | | | | | % 146.80/20.97 | | | | | | | | | | | | | | | | | | | | (1408) all_54_15 = e2 % 146.80/20.97 | | | | | | | | | | | | | | | | | | | | % 146.80/20.97 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (540), (1402), (1408) are inconsistent by % 146.80/20.97 | | | | | | | | | | | | | | | | | | | | sub-proof #739. % 146.80/20.97 | | | | | | | | | | | | | | | | | | | | % 146.80/20.97 | | | | | | | | | | | | | | | | | | | Case 2: % 146.80/20.97 | | | | | | | | | | | | | | | | | | | | % 146.80/20.97 | | | | | | | | | | | | | | | | | | | | (1409) all_54_15 = e1 | all_54_15 = e0 % 146.80/20.97 | | | | | | | | | | | | | | | | | | | | % 146.80/20.97 | | | | | | | | | | | | | | | | | | | | BETA: splitting (1409) gives: % 146.80/20.97 | | | | | | | | | | | | | | | | | | | | % 146.80/20.97 | | | | | | | | | | | | | | | | | | | | Case 1: % 146.80/20.97 | | | | | | | | | | | | | | | | | | | | | % 146.80/20.97 | | | | | | | | | | | | | | | | | | | | | (1410) all_54_15 = e1 % 146.80/20.97 | | | | | | | | | | | | | | | | | | | | | % 146.80/20.97 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (540), (1392), (1410) are inconsistent by % 146.80/20.97 | | | | | | | | | | | | | | | | | | | | | sub-proof #738. % 146.80/20.97 | | | | | | | | | | | | | | | | | | | | | % 146.80/20.97 | | | | | | | | | | | | | | | | | | | | Case 2: % 146.80/20.97 | | | | | | | | | | | | | | | | | | | | | % 146.80/20.97 | | | | | | | | | | | | | | | | | | | | | (1411) all_54_15 = e0 % 146.80/20.97 | | | | | | | | | | | | | | | | | | | | | % 146.80/20.97 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (540), (1411) imply: % 146.80/20.97 | | | | | | | | | | | | | | | | | | | | | (1412) all_4_2 = e0 % 146.80/20.97 | | | | | | | | | | | | | | | | | | | | | % 146.80/20.97 | | | | | | | | | | | | | | | | | | | | | SIMP: (1412) implies: % 146.80/20.97 | | | | | | | | | | | | | | | | | | | | | (1413) all_4_2 = e0 % 146.80/20.97 | | | | | | | | | | | | | | | | | | | | | % 146.80/20.97 | | | | | | | | | | | | | | | | | | | | | REDUCE: (570), (1413) imply: % 146.80/20.97 | | | | | | | | | | | | | | | | | | | | | (1414) ~ (all_52_3 = e0) % 146.80/20.97 | | | | | | | | | | | | | | | | | | | | | % 146.80/20.97 | | | | | | | | | | | | | | | | | | | | | REDUCE: (588), (1413) imply: % 146.80/20.97 | | | | | | | | | | | | | | | | | | | | | (1415) ~ (all_52_11 = e0) % 146.80/20.97 | | | | | | | | | | | | | | | | | | | | | % 146.80/20.97 | | | | | | | | | | | | | | | | | | | | | REDUCE: (38), (1413) imply: % 146.80/20.97 | | | | | | | | | | | | | | | | | | | | | (1416) op(e0, e0) = all_4_1 % 146.80/20.97 | | | | | | | | | | | | | | | | | | | | | % 146.80/20.97 | | | | | | | | | | | | | | | | | | | | | REDUCE: (627), (1413) imply: % 146.80/20.97 | | | | | | | | | | | | | | | | | | | | | (1417) op(e0, e0) = all_56_30 % 146.80/20.97 | | | | | | | | | | | | | | | | | | | | | % 146.80/20.97 | | | | | | | | | | | | | | | | | | | | | REDUCE: (36), (1413) imply: % 146.80/20.97 | | | | | | | | | | | | | | | | | | | | | (1418) op(e0, e0) = e0 % 146.80/20.97 | | | | | | | | | | | | | | | | | | | | | % 146.80/20.97 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_4_1, % 146.80/20.97 | | | | | | | | | | | | | | | | | | | | | all_56_30, e0, e0, simplifying with (1416), (1417) % 146.80/20.97 | | | | | | | | | | | | | | | | | | | | | gives: % 146.80/20.97 | | | | | | | | | | | | | | | | | | | | | (1419) all_56_30 = all_4_1 % 146.80/20.97 | | | | | | | | | | | | | | | | | | | | | % 146.80/20.97 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, % 146.80/20.97 | | | | | | | | | | | | | | | | | | | | | all_56_30, e0, e0, simplifying with (1417), (1418) % 146.80/20.97 | | | | | | | | | | | | | | | | | | | | | gives: % 146.80/20.97 | | | | | | | | | | | | | | | | | | | | | (1420) all_56_30 = e0 % 146.80/20.97 | | | | | | | | | | | | | | | | | | | | | % 146.80/20.97 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1419), (1420) imply: % 146.80/20.97 | | | | | | | | | | | | | | | | | | | | | (1421) all_4_1 = e0 % 146.80/20.97 | | | | | | | | | | | | | | | | | | | | | % 146.80/20.97 | | | | | | | | | | | | | | | | | | | | | SIMP: (1421) implies: % 146.80/20.97 | | | | | | | | | | | | | | | | | | | | | (1422) all_4_1 = e0 % 146.80/20.97 | | | | | | | | | | | | | | | | | | | | | % 146.80/20.97 | | | | | | | | | | | | | | | | | | | | | REDUCE: (37), (1422) imply: % 146.80/20.97 | | | | | | | | | | | | | | | | | | | | | (1423) op(e0, e0) = all_4_0 % 146.80/20.97 | | | | | | | | | | | | | | | | | | | | | % 146.80/20.97 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_4_0, % 146.80/20.97 | | | | | | | | | | | | | | | | | | | | | e0, e0, simplifying with (1418), (1423) gives: % 146.80/20.97 | | | | | | | | | | | | | | | | | | | | | (1424) all_4_0 = e0 % 146.80/20.97 | | | | | | | | | | | | | | | | | | | | | % 146.80/20.97 | | | | | | | | | | | | | | | | | | | | | REDUCE: (767), (1424) imply: % 146.80/20.97 | | | | | | | | | | | | | | | | | | | | | (1425) ~ (e3 = e0) % 146.80/20.97 | | | | | | | | | | | | | | | | | | | | | % 146.80/20.97 | | | | | | | | | | | | | | | | | | | | | REDUCE: (780), (1424) imply: % 146.80/20.97 | | | | | | | | | | | | | | | | | | | | | (1426) ~ (e1 = e0) % 146.80/20.97 | | | | | | | | | | | | | | | | | | | | | % 146.80/20.97 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (291) gives: % 146.80/20.97 | | | | | | | | | | | | | | | | | | | | | % 146.80/20.97 | | | | | | | | | | | | | | | | | | | | | Case 1: % 146.80/20.97 | | | | | | | | | | | | | | | | | | | | | | % 146.80/20.97 | | | | | | | | | | | | | | | | | | | | | | (1427) ~ (all_56_21 = e0) % 146.80/20.97 | | | | | | | | | | | | | | | | | | | | | | % 146.80/20.97 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (374), (1427) imply: % 146.80/20.97 | | | | | | | | | | | | | | | | | | | | | | (1428) ~ (all_6_2 = e0) % 146.80/20.97 | | | | | | | | | | | | | | | | | | | | | | % 146.80/20.97 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (328) gives: % 146.80/20.97 | | | | | | | | | | | | | | | | | | | | | | % 146.80/20.97 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 146.80/20.97 | | | | | | | | | | | | | | | | | | | | | | | % 146.80/20.97 | | | | | | | | | | | | | | | | | | | | | | | (1429) all_58_4 = e0 % 146.80/20.97 | | | | | | | | | | | | | | | | | | | | | | | % 146.80/20.97 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (407), (1429) imply: % 146.80/20.97 | | | | | | | | | | | | | | | | | | | | | | | (1430) all_52_8 = e0 % 146.80/20.97 | | | | | | | | | | | | | | | | | | | | | | | % 146.80/20.97 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (565), (1430) imply: % 146.80/20.97 | | | | | | | | | | | | | | | | | | | | | | | (1431) ~ (all_10_2 = e0) % 146.80/20.97 | | | | | | | | | | | | | | | | | | | | | | | % 146.80/20.97 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1431) implies: % 146.80/20.97 | | | | | | | | | | | | | | | | | | | | | | | (1432) ~ (all_10_2 = e0) % 146.80/20.97 | | | | | | | | | | | | | | | | | | | | | | | % 146.80/20.97 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (582), (1430) imply: % 146.80/20.97 | | | | | | | | | | | | | | | | | | | | | | | (1433) ~ (all_6_2 = e0) % 146.80/20.97 | | | | | | | | | | | | | | | | | | | | | | | % 146.80/20.97 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (340) gives: % 146.80/20.97 | | | | | | | | | | | | | | | | | | | | | | | % 146.80/20.97 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 146.80/20.97 | | | | | | | | | | | | | | | | | | | | | | | | % 146.80/20.97 | | | | | | | | | | | | | | | | | | | | | | | | (1434) all_58_0 = e0 % 146.80/20.97 | | | | | | | | | | | | | | | | | | | | | | | | % 146.80/20.97 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (419), (1434) imply: % 146.80/20.97 | | | | | | | | | | | | | | | | | | | | | | | | (1435) all_10_2 = e0 % 146.80/20.97 | | | | | | | | | | | | | | | | | | | | | | | | % 146.80/20.97 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1432), (1435) imply: % 146.80/20.97 | | | | | | | | | | | | | | | | | | | | | | | | (1436) $false % 146.80/20.97 | | | | | | | | | | | | | | | | | | | | | | | | % 146.80/20.97 | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1436) is inconsistent. % 146.80/20.97 | | | | | | | | | | | | | | | | | | | | | | | | % 146.80/20.97 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 146.80/20.97 | | | | | | | | | | | | | | | | | | | | | | | | % 146.80/20.97 | | | | | | | | | | | | | | | | | | | | | | | | (1437) all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0 % 146.80/20.97 | | | | | | | | | | | | | | | | | | | | | | | | % 146.80/20.97 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1437) gives: % 146.80/20.97 | | | | | | | | | | | | | | | | | | | | | | | | % 146.80/20.97 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 146.80/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | % 146.80/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | (1438) all_58_2 = e0 % 146.80/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | % 146.80/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (401), (1438) imply: % 146.80/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | (1439) all_52_1 = e0 % 146.80/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | % 146.80/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1399), (1439) imply: % 146.80/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | (1440) $false % 146.80/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | % 146.80/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1440) is inconsistent. % 146.80/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | % 146.80/20.97 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 146.80/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | % 146.80/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | (1441) all_58_6 = e0 | all_58_12 = e0 % 146.80/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | % 146.80/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1441) gives: % 146.80/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | % 146.80/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 146.80/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.80/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | (1442) all_58_6 = e0 % 146.80/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.80/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1376), (1442) imply: % 146.80/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | (1443) all_6_0 = e0 % 146.80/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.80/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1443) implies: % 146.80/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | (1444) all_6_0 = e0 % 146.80/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.80/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1375), (1444) imply: % 146.80/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | (1445) all_56_17 = e0 % 146.80/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.80/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (41), (242), (293), (374), (541), (622), % 146.80/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | (1371), (1390), (1428), (1445), (function-axioms) % 146.80/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #441. % 146.80/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.80/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 146.80/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.80/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | (1446) all_58_12 = e0 % 146.80/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.80/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (365), (1446) imply: % 146.80/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | (1447) all_52_3 = e0 % 146.80/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.80/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1447) implies: % 146.80/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | (1448) all_52_3 = e0 % 146.80/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.80/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1414), (1448) imply: % 146.80/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | (1449) $false % 146.80/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.80/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1449) is inconsistent. % 146.80/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.80/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 146.80/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | % 146.80/20.97 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 146.80/20.97 | | | | | | | | | | | | | | | | | | | | | | | | % 146.80/20.97 | | | | | | | | | | | | | | | | | | | | | | | End of split % 146.80/20.97 | | | | | | | | | | | | | | | | | | | | | | | % 146.80/20.97 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 146.80/20.97 | | | | | | | | | | | | | | | | | | | | | | | % 146.80/20.97 | | | | | | | | | | | | | | | | | | | | | | | (1450) all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0 % 146.80/20.97 | | | | | | | | | | | | | | | | | | | | | | | % 146.80/20.97 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (389), (548), (552), (1400), (1415), (1428), % 146.80/20.97 | | | | | | | | | | | | | | | | | | | | | | | (1450) are inconsistent by sub-proof #626. % 146.80/20.97 | | | | | | | | | | | | | | | | | | | | | | | % 146.80/20.97 | | | | | | | | | | | | | | | | | | | | | | End of split % 146.80/20.97 | | | | | | | | | | | | | | | | | | | | | | % 146.80/20.97 | | | | | | | | | | | | | | | | | | | | | Case 2: % 146.80/20.97 | | | | | | | | | | | | | | | | | | | | | | % 146.80/20.97 | | | | | | | | | | | | | | | | | | | | | | (1451) all_56_21 = e0 % 146.80/20.97 | | | | | | | | | | | | | | | | | | | | | | % 146.80/20.97 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (374), (1451) imply: % 146.80/20.97 | | | | | | | | | | | | | | | | | | | | | | (1452) all_6_2 = e0 % 146.80/20.97 | | | | | | | | | | | | | | | | | | | | | | % 146.80/20.97 | | | | | | | | | | | | | | | | | | | | | | SIMP: (1452) implies: % 146.80/20.97 | | | | | | | | | | | | | | | | | | | | | | (1453) all_6_2 = e0 % 146.80/20.97 | | | | | | | | | | | | | | | | | | | | | | % 146.80/20.97 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1371), (1453) imply: % 146.80/20.97 | | | | | | | | | | | | | | | | | | | | | | (1454) op(e0, e0) = e3 % 146.80/20.97 | | | | | | | | | | | | | | | | | | | | | | % 146.80/20.97 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (1416), (1417), (1418), (1454), % 146.80/20.97 | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 146.80/20.97 | | | | | | | | | | | | | | | | | | | | | | #454. % 146.80/20.97 | | | | | | | | | | | | | | | | | | | | | | % 146.80/20.97 | | | | | | | | | | | | | | | | | | | | | End of split % 146.80/20.97 | | | | | | | | | | | | | | | | | | | | | % 146.80/20.97 | | | | | | | | | | | | | | | | | | | | End of split % 146.80/20.97 | | | | | | | | | | | | | | | | | | | | % 146.80/20.97 | | | | | | | | | | | | | | | | | | | End of split % 146.80/20.97 | | | | | | | | | | | | | | | | | | | % 146.80/20.97 | | | | | | | | | | | | | | | | | | End of split % 146.80/20.97 | | | | | | | | | | | | | | | | | | % 146.80/20.97 | | | | | | | | | | | | | | | | | End of split % 146.80/20.97 | | | | | | | | | | | | | | | | | % 146.80/20.97 | | | | | | | | | | | | | | | | Case 2: % 146.80/20.97 | | | | | | | | | | | | | | | | | % 146.80/20.97 | | | | | | | | | | | | | | | | | (1455) all_56_31 = e1 % 146.80/20.97 | | | | | | | | | | | | | | | | | (1456) all_56_29 = e0 % 146.80/20.97 | | | | | | | | | | | | | | | | | % 146.80/20.97 | | | | | | | | | | | | | | | | | COMBINE_EQS: (357), (1456) imply: % 146.80/20.97 | | | | | | | | | | | | | | | | | (1457) all_52_11 = e0 % 146.80/20.97 | | | | | | | | | | | | | | | | | % 146.80/20.97 | | | | | | | | | | | | | | | | | SIMP: (1457) implies: % 146.80/20.97 | | | | | | | | | | | | | | | | | (1458) all_52_11 = e0 % 146.80/20.97 | | | | | | | | | | | | | | | | | % 146.80/20.97 | | | | | | | | | | | | | | | | | REF_CLOSE: (37), (38), (41), (187), (207), (240), (242), % 146.80/20.97 | | | | | | | | | | | | | | | | | (293), (374), (478), (541), (544), (585), (622), % 146.80/20.97 | | | | | | | | | | | | | | | | | (767), (772), (1371), (1375), (1379), (1390), % 146.80/20.97 | | | | | | | | | | | | | | | | | (1455), (1458), (function-axioms) are inconsistent % 146.80/20.97 | | | | | | | | | | | | | | | | | by sub-proof #436. % 146.80/20.97 | | | | | | | | | | | | | | | | | % 146.80/20.97 | | | | | | | | | | | | | | | | End of split % 146.80/20.97 | | | | | | | | | | | | | | | | % 146.80/20.97 | | | | | | | | | | | | | | | Case 2: % 146.80/20.97 | | | | | | | | | | | | | | | | % 146.80/20.97 | | | | | | | | | | | | | | | | (1459) all_56_21 = e2 % 146.80/20.97 | | | | | | | | | | | | | | | | (1460) all_56_19 = e1 % 146.80/20.97 | | | | | | | | | | | | | | | | % 146.80/20.97 | | | | | | | | | | | | | | | | COMBINE_EQS: (435), (1460) imply: % 146.80/20.97 | | | | | | | | | | | | | | | | (1461) all_52_6 = e1 % 146.80/20.97 | | | | | | | | | | | | | | | | % 146.80/20.97 | | | | | | | | | | | | | | | | SIMP: (1461) implies: % 146.80/20.97 | | | | | | | | | | | | | | | | (1462) all_52_6 = e1 % 146.80/20.97 | | | | | | | | | | | | | | | | % 146.80/20.97 | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (46), (48), (244), (287), (324), (374), % 146.80/20.97 | | | | | | | | | | | | | | | | (380), (532), (544), (545), (546), (550), (552), % 146.80/20.97 | | | | | | | | | | | | | | | | (580), (591), (617), (762), (1369), (1371), % 146.80/20.97 | | | | | | | | | | | | | | | | (1374), (1376), (1381), (1383), (1385), (1386), % 146.80/20.97 | | | | | | | | | | | | | | | | (1459), (1462), (function-axioms) are inconsistent % 146.80/20.97 | | | | | | | | | | | | | | | | by sub-proof #431. % 146.80/20.97 | | | | | | | | | | | | | | | | % 146.80/20.97 | | | | | | | | | | | | | | | End of split % 146.80/20.97 | | | | | | | | | | | | | | | % 146.80/20.97 | | | | | | | | | | | | | | Case 2: % 146.80/20.97 | | | | | | | | | | | | | | | % 146.80/20.97 | | | | | | | | | | | | | | | (1463) all_38_1 = e2 % 146.80/20.97 | | | | | | | | | | | | | | | (1464) ~ (all_38_0 = e0) | ~ (all_38_2 = e1) % 146.80/20.97 | | | | | | | | | | | | | | | % 146.80/20.97 | | | | | | | | | | | | | | | COMBINE_EQS: (684), (1463) imply: % 146.80/20.97 | | | | | | | | | | | | | | | (1465) all_10_1 = e2 % 146.80/20.97 | | | | | | | | | | | | | | | % 146.80/20.97 | | | | | | | | | | | | | | | REDUCE: (53), (1465) imply: % 146.80/20.97 | | | | | | | | | | | | | | | (1466) op(all_10_2, all_10_2) = e2 % 146.80/20.97 | | | | | | | | | | | | | | | % 146.80/20.97 | | | | | | | | | | | | | | | REDUCE: (52), (1465) imply: % 146.80/20.97 | | | | | | | | | | | | | | | (1467) op(e3, e2) = all_10_0 % 146.80/20.97 | | | | | | | | | | | | | | | % 146.80/20.98 | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (36), (37), (38), (41), (46), (48), % 146.80/20.98 | | | | | | | | | | | | | | | (51), (53), (158), (166), (174), (181), (182), % 146.80/20.98 | | | | | | | | | | | | | | | (184), (187), (188), (194), (196), (207), (218), % 146.80/20.98 | | | | | | | | | | | | | | | (238), (240), (241), (242), (243), (244), (247), % 146.80/20.98 | | | | | | | | | | | | | | | (248), (251), (252), (287), (288), (290), (291), % 146.80/20.98 | | | | | | | | | | | | | | | (292), (293), (294), (295), (296), (297), (298), % 146.80/20.98 | | | | | | | | | | | | | | | (299), (324), (326), (336), (344), (357), (365), % 146.80/20.98 | | | | | | | | | | | | | | | (366), (374), (380), (401), (402), (408), (419), % 146.80/20.98 | | | | | | | | | | | | | | | (425), (429), (431), (435), (443), (447), (457), % 146.80/20.98 | | | | | | | | | | | | | | | (463), (473), (476), (478), (482), (532), (533), % 146.80/20.98 | | | | | | | | | | | | | | | (541), (542), (543), (544), (545), (546), (549), % 146.80/20.98 | | | | | | | | | | | | | | | (550), (552), (554), (555), (557), (561), (563), % 146.80/20.98 | | | | | | | | | | | | | | | (568), (570), (571), (573), (580), (585), (587), % 146.80/20.98 | | | | | | | | | | | | | | | (588), (591), (612), (617), (618), (622), (627), % 146.80/20.98 | | | | | | | | | | | | | | | (723), (762), (767), (770), (772), (776), (782), % 146.80/20.98 | | | | | | | | | | | | | | | (1369), (1371), (1374), (1375), (1376), (1377), % 146.80/20.98 | | | | | | | | | | | | | | | (1379), (1381), (1383), (1385), (1386), (1464), % 146.80/20.98 | | | | | | | | | | | | | | | (1466), (1467), (function-axioms) are inconsistent % 146.80/20.98 | | | | | | | | | | | | | | | by sub-proof #411. % 146.80/20.98 | | | | | | | | | | | | | | | % 146.80/20.98 | | | | | | | | | | | | | | End of split % 146.80/20.98 | | | | | | | | | | | | | | % 146.80/20.98 | | | | | | | | | | | | | End of split % 146.80/20.98 | | | | | | | | | | | | | % 146.80/20.98 | | | | | | | | | | | | Case 2: % 146.80/20.98 | | | | | | | | | | | | | % 146.80/20.98 | | | | | | | | | | | | | (1468) all_32_1 = e1 % 146.80/20.98 | | | | | | | | | | | | | (1469) ~ (all_32_0 = e0) | ~ (all_32_2 = e2) % 146.80/20.98 | | | | | | | | | | | | | % 146.80/20.98 | | | | | | | | | | | | | COMBINE_EQS: (682), (1468) imply: % 146.80/20.98 | | | | | | | | | | | | | (1470) all_10_1 = e1 % 146.80/20.98 | | | | | | | | | | | | | % 146.80/20.98 | | | | | | | | | | | | | SIMP: (1470) implies: % 146.80/20.98 | | | | | | | | | | | | | (1471) all_10_1 = e1 % 146.80/20.98 | | | | | | | | | | | | | % 146.80/20.98 | | | | | | | | | | | | | REDUCE: (53), (1471) imply: % 146.80/20.98 | | | | | | | | | | | | | (1472) op(all_10_2, all_10_2) = e1 % 146.80/20.98 | | | | | | | | | | | | | % 146.80/20.98 | | | | | | | | | | | | | REDUCE: (52), (1471) imply: % 146.80/20.98 | | | | | | | | | | | | | (1473) op(e3, e1) = all_10_0 % 146.80/20.98 | | | | | | | | | | | | | % 146.80/20.98 | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_8, % 146.80/20.98 | | | | | | | | | | | | | all_10_0, e1, e3, simplifying with (217), (1473) % 146.80/20.98 | | | | | | | | | | | | | gives: % 146.80/20.98 | | | | | | | | | | | | | (1474) all_52_8 = all_10_0 % 146.80/20.98 | | | | | | | | | | | | | % 146.80/20.98 | | | | | | | | | | | | | COMBINE_EQS: (459), (1474) imply: % 146.80/20.98 | | | | | | | | | | | | | (1475) all_54_2 = all_10_0 % 146.80/20.98 | | | | | | | | | | | | | % 146.80/20.98 | | | | | | | | | | | | | COMBINE_EQS: (429), (1474) imply: % 146.80/20.98 | | | | | | | | | | | | | (1476) all_56_5 = all_10_0 % 146.80/20.98 | | | | | | | | | | | | | % 146.80/20.98 | | | | | | | | | | | | | COMBINE_EQS: (407), (1474) imply: % 146.80/20.98 | | | | | | | | | | | | | (1477) all_58_4 = all_10_0 % 146.80/20.98 | | | | | | | | | | | | | % 146.80/20.98 | | | | | | | | | | | | | REDUCE: (182), (1474) imply: % 146.80/20.98 | | | | | | | | | | | | | (1478) ~ (all_52_4 = all_10_0) % 146.80/20.98 | | | | | | | | | | | | | % 146.80/20.98 | | | | | | | | | | | | | REDUCE: (171), (1474) imply: % 146.80/20.98 | | | | | | | | | | | | | (1479) ~ (all_52_9 = all_10_0) % 146.80/20.98 | | | | | | | | | | | | | % 146.80/20.98 | | | | | | | | | | | | | SIMP: (1479) implies: % 146.80/20.98 | | | | | | | | | | | | | (1480) ~ (all_52_9 = all_10_0) % 146.80/20.98 | | | | | | | | | | | | | % 146.80/20.98 | | | | | | | | | | | | | REDUCE: (169), (1474) imply: % 146.80/20.98 | | | | | | | | | | | | | (1481) ~ (all_52_11 = all_10_0) % 146.80/20.98 | | | | | | | | | | | | | % 146.80/20.98 | | | | | | | | | | | | | SIMP: (1481) implies: % 146.80/20.98 | | | | | | | | | | | | | (1482) ~ (all_52_11 = all_10_0) % 146.80/20.98 | | | | | | | | | | | | | % 146.80/20.98 | | | | | | | | | | | | | REDUCE: (168), (1474) imply: % 146.80/20.98 | | | | | | | | | | | | | (1483) ~ (all_52_12 = all_10_0) % 146.80/20.98 | | | | | | | | | | | | | % 146.80/20.98 | | | | | | | | | | | | | SIMP: (1483) implies: % 146.80/20.98 | | | | | | | | | | | | | (1484) ~ (all_52_12 = all_10_0) % 146.80/20.98 | | | | | | | | | | | | | % 146.80/20.98 | | | | | | | | | | | | | REDUCE: (565), (1474) imply: % 146.80/20.98 | | | | | | | | | | | | | (1485) ~ (all_10_0 = all_10_2) % 146.80/20.98 | | | | | | | | | | | | | % 146.80/20.98 | | | | | | | | | | | | | REDUCE: (582), (1474) imply: % 146.80/20.98 | | | | | | | | | | | | | (1486) ~ (all_10_0 = all_6_2) % 146.80/20.98 | | | | | | | | | | | | | % 146.80/20.98 | | | | | | | | | | | | | BETA: splitting (119) gives: % 146.80/20.98 | | | | | | | | | | | | | % 146.80/20.98 | | | | | | | | | | | | | Case 1: % 146.80/20.98 | | | | | | | | | | | | | | % 146.80/20.98 | | | | | | | | | | | | | | (1487) ~ (all_36_1 = e3) % 146.80/20.98 | | | | | | | | | | | | | | % 146.80/20.98 | | | | | | | | | | | | | | REDUCE: (652), (1487) imply: % 146.80/20.98 | | | | | | | | | | | | | | (1488) ~ (all_6_1 = e3) % 146.80/20.98 | | | | | | | | | | | | | | % 146.80/20.98 | | | | | | | | | | | | | | BETA: splitting (288) gives: % 146.80/20.98 | | | | | | | | | | | | | | % 146.80/20.98 | | | | | | | | | | | | | | Case 1: % 146.80/20.98 | | | | | | | | | | | | | | | % 146.80/20.98 | | | | | | | | | | | | | | | (1489) ~ (all_56_31 = e1) % 146.80/20.98 | | | | | | | | | | | | | | | % 146.80/20.98 | | | | | | | | | | | | | | | REDUCE: (544), (1489) imply: % 146.80/20.98 | | | | | | | | | | | | | | | (1490) ~ (all_4_2 = e1) % 146.80/20.98 | | | | | | | | | | | | | | | % 146.80/20.98 | | | | | | | | | | | | | | | BETA: splitting (292) gives: % 146.80/20.98 | | | | | | | | | | | | | | | % 146.80/20.98 | | | | | | | | | | | | | | | Case 1: % 146.80/20.98 | | | | | | | | | | | | | | | | % 146.80/20.98 | | | | | | | | | | | | | | | | (1491) ~ (all_56_21 = e2) % 146.80/20.98 | | | | | | | | | | | | | | | | % 146.80/20.98 | | | | | | | | | | | | | | | | REDUCE: (374), (1491) imply: % 146.80/20.98 | | | | | | | | | | | | | | | | (1492) ~ (all_6_2 = e2) % 146.80/20.98 | | | | | | | | | | | | | | | | % 147.23/20.98 | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (36), (37), (38), (41), (46), (47), % 147.23/20.98 | | | | | | | | | | | | | | | | (48), (51), (161), (165), (166), (193), (194), % 147.23/20.98 | | | | | | | | | | | | | | | | (196), (205), (237), (246), (247), (248), (250), % 147.23/20.98 | | | | | | | | | | | | | | | | (252), (293), (294), (295), (296), (297), (298), % 147.23/20.98 | | | | | | | | | | | | | | | | (299), (318), (320), (321), (328), (329), (330), % 147.23/20.98 | | | | | | | | | | | | | | | | (331), (335), (340), (341), (345), (365), (374), % 147.23/20.98 | | | | | | | | | | | | | | | | (386), (389), (401), (402), (408), (419), (425), % 147.23/20.98 | | | | | | | | | | | | | | | | (431), (443), (463), (467), (494), (540), (542), % 147.23/20.98 | | | | | | | | | | | | | | | | (543), (545), (546), (547), (548), (549), (550), % 147.23/20.98 | | | | | | | | | | | | | | | | (551), (552), (555), (557), (561), (563), (567), % 147.23/20.98 | | | | | | | | | | | | | | | | (568), (571), (577), (581), (585), (587), (589), % 147.23/20.98 | | | | | | | | | | | | | | | | (590), (612), (613), (617), (625), (627), (761), % 147.23/20.98 | | | | | | | | | | | | | | | | (767), (769), (770), (772), (774), (776), (778), % 147.23/20.98 | | | | | | | | | | | | | | | | (780), (784), (1469), (1472), (1475), (1476), % 147.23/20.98 | | | | | | | | | | | | | | | | (1477), (1478), (1480), (1482), (1484), (1485), % 147.23/20.98 | | | | | | | | | | | | | | | | (1486), (1490), (1492), (function-axioms) are % 147.23/20.98 | | | | | | | | | | | | | | | | inconsistent by sub-proof #383. % 147.23/20.98 | | | | | | | | | | | | | | | | % 147.23/20.98 | | | | | | | | | | | | | | | Case 2: % 147.23/20.98 | | | | | | | | | | | | | | | | % 147.23/20.98 | | | | | | | | | | | | | | | | (1493) all_56_21 = e2 % 147.23/20.98 | | | | | | | | | | | | | | | | (1494) all_56_19 = e1 % 147.23/20.98 | | | | | | | | | | | | | | | | % 147.23/20.98 | | | | | | | | | | | | | | | | COMBINE_EQS: (435), (1494) imply: % 147.23/20.98 | | | | | | | | | | | | | | | | (1495) all_52_6 = e1 % 147.23/20.98 | | | | | | | | | | | | | | | | % 147.23/20.98 | | | | | | | | | | | | | | | | SIMP: (1495) implies: % 147.23/20.98 | | | | | | | | | | | | | | | | (1496) all_52_6 = e1 % 147.23/20.98 | | | | | | | | | | | | | | | | % 147.23/20.98 | | | | | | | | | | | | | | | | COMBINE_EQS: (374), (1493) imply: % 147.23/20.98 | | | | | | | | | | | | | | | | (1497) all_6_2 = e2 % 147.23/20.98 | | | | | | | | | | | | | | | | % 147.23/20.98 | | | | | | | | | | | | | | | | SIMP: (1497) implies: % 147.23/20.98 | | | | | | | | | | | | | | | | (1498) all_6_2 = e2 % 147.23/20.98 | | | | | | | | | | | | | | | | % 147.23/20.98 | | | | | | | | | | | | | | | | REDUCE: (573), (1496) imply: % 147.23/20.98 | | | | | | | | | | | | | | | | (1499) ~ (all_8_2 = e1) % 147.23/20.98 | | | | | | | | | | | | | | | | % 147.23/20.98 | | | | | | | | | | | | | | | | SIMP: (1499) implies: % 147.23/20.98 | | | | | | | | | | | | | | | | (1500) ~ (all_8_2 = e1) % 147.23/20.98 | | | | | | | | | | | | | | | | % 147.23/20.98 | | | | | | | | | | | | | | | | REDUCE: (43), (1498) imply: % 147.23/20.98 | | | | | | | | | | | | | | | | (1501) op(e2, e2) = all_6_1 % 147.23/20.98 | | | | | | | | | | | | | | | | % 147.23/20.98 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_8_2, % 147.23/20.98 | | | | | | | | | | | | | | | | all_6_1, e2, e2, simplifying with (46), (1501) % 147.23/20.98 | | | | | | | | | | | | | | | | gives: % 147.23/20.98 | | | | | | | | | | | | | | | | (1502) all_8_2 = all_6_1 % 147.23/20.98 | | | | | | | | | | | | | | | | % 147.23/20.98 | | | | | | | | | | | | | | | | COMBINE_EQS: (542), (1502) imply: % 147.23/20.98 | | | | | | | | | | | | | | | | (1503) all_54_5 = all_6_1 % 147.23/20.98 | | | | | | | | | | | | | | | | % 147.23/20.98 | | | | | | | | | | | | | | | | COMBINE_EQS: (545), (1502) imply: % 147.23/20.98 | | | | | | | | | | | | | | | | (1504) all_56_11 = all_6_1 % 147.23/20.98 | | | | | | | | | | | | | | | | % 147.23/20.98 | | | | | | | | | | | | | | | | REDUCE: (571), (1502) imply: % 147.23/20.98 | | | | | | | | | | | | | | | | (1505) ~ (all_52_4 = all_6_1) % 147.23/20.98 | | | | | | | | | | | | | | | | % 147.23/20.98 | | | | | | | | | | | | | | | | REDUCE: (1500), (1502) imply: % 147.23/20.98 | | | | | | | | | | | | | | | | (1506) ~ (all_6_1 = e1) % 147.23/20.98 | | | | | | | | | | | | | | | | % 147.23/20.98 | | | | | | | | | | | | | | | | REDUCE: (48), (1502) imply: % 147.23/20.98 | | | | | | | | | | | | | | | | (1507) op(all_6_1, all_6_1) = all_8_1 % 147.23/20.98 | | | | | | | | | | | | | | | | % 147.23/20.98 | | | | | | | | | | | | | | | | BETA: splitting (247) gives: % 147.23/20.98 | | | | | | | | | | | | | | | | % 147.23/20.98 | | | | | | | | | | | | | | | | Case 1: % 147.23/20.98 | | | | | | | | | | | | | | | | | % 147.23/20.98 | | | | | | | | | | | | | | | | | (1508) all_54_5 = e3 % 147.23/20.98 | | | | | | | | | | | | | | | | | % 147.23/20.98 | | | | | | | | | | | | | | | | | REF_CLOSE: (1488), (1503), (1508) are inconsistent by % 147.23/20.98 | | | | | | | | | | | | | | | | | sub-proof #509. % 147.23/20.98 | | | | | | | | | | | | | | | | | % 147.23/20.98 | | | | | | | | | | | | | | | | Case 2: % 147.23/20.98 | | | | | | | | | | | | | | | | | % 147.23/20.98 | | | | | | | | | | | | | | | | | (1509) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 147.23/20.98 | | | | | | | | | | | | | | | | | % 147.23/20.98 | | | | | | | | | | | | | | | | | BETA: splitting (1509) gives: % 147.23/20.98 | | | | | | | | | | | | | | | | | % 147.23/20.98 | | | | | | | | | | | | | | | | | Case 1: % 147.23/20.98 | | | | | | | | | | | | | | | | | | % 147.23/20.98 | | | | | | | | | | | | | | | | | | (1510) all_54_5 = e2 % 147.23/20.98 | | | | | | | | | | | | | | | | | | % 147.23/20.98 | | | | | | | | | | | | | | | | | | REF_CLOSE: (768), (1503), (1510) are inconsistent by % 147.23/20.98 | | | | | | | | | | | | | | | | | | sub-proof #466. % 147.23/20.98 | | | | | | | | | | | | | | | | | | % 147.23/20.98 | | | | | | | | | | | | | | | | | Case 2: % 147.23/20.98 | | | | | | | | | | | | | | | | | | % 147.23/20.98 | | | | | | | | | | | | | | | | | | (1511) all_54_5 = e1 | all_54_5 = e0 % 147.23/20.98 | | | | | | | | | | | | | | | | | | % 147.23/20.98 | | | | | | | | | | | | | | | | | | BETA: splitting (1511) gives: % 147.23/20.98 | | | | | | | | | | | | | | | | | | % 147.23/20.98 | | | | | | | | | | | | | | | | | | Case 1: % 147.23/20.98 | | | | | | | | | | | | | | | | | | | % 147.23/20.98 | | | | | | | | | | | | | | | | | | | (1512) all_54_5 = e1 % 147.23/20.98 | | | | | | | | | | | | | | | | | | | % 147.23/20.98 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1503), (1506), (1512) are inconsistent by % 147.23/20.98 | | | | | | | | | | | | | | | | | | | sub-proof #465. % 147.23/20.98 | | | | | | | | | | | | | | | | | | | % 147.23/20.98 | | | | | | | | | | | | | | | | | | Case 2: % 147.23/20.98 | | | | | | | | | | | | | | | | | | | % 147.23/20.98 | | | | | | | | | | | | | | | | | | | (1513) all_54_5 = e0 % 147.23/20.98 | | | | | | | | | | | | | | | | | | | % 147.23/20.98 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1503), (1513) imply: % 147.23/20.98 | | | | | | | | | | | | | | | | | | | (1514) all_6_1 = e0 % 147.23/20.98 | | | | | | | | | | | | | | | | | | | % 147.23/20.98 | | | | | | | | | | | | | | | | | | | SIMP: (1514) implies: % 147.23/20.98 | | | | | | | | | | | | | | | | | | | (1515) all_6_1 = e0 % 147.23/20.98 | | | | | | | | | | | | | | | | | | | % 147.23/20.98 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1504), (1515) imply: % 147.23/20.98 | | | | | | | | | | | | | | | | | | | (1516) all_56_11 = e0 % 147.23/20.98 | | | | | | | | | | | | | | | | | | | % 147.23/20.98 | | | | | | | | | | | | | | | | | | | REDUCE: (1505), (1515) imply: % 147.23/20.98 | | | | | | | | | | | | | | | | | | | (1517) ~ (all_52_4 = e0) % 147.23/20.98 | | | | | | | | | | | | | | | | | | | % 147.23/20.98 | | | | | | | | | | | | | | | | | | | REDUCE: (1507), (1515) imply: % 147.23/20.98 | | | | | | | | | | | | | | | | | | | (1518) op(e0, e0) = all_8_1 % 147.23/20.98 | | | | | | | | | | | | | | | | | | | % 147.23/20.98 | | | | | | | | | | | | | | | | | | | BETA: splitting (294) gives: % 147.23/20.98 | | | | | | | | | | | | | | | | | | | % 147.23/20.98 | | | | | | | | | | | | | | | | | | | Case 1: % 147.23/20.98 | | | | | | | | | | | | | | | | | | | | % 147.23/20.98 | | | | | | | | | | | | | | | | | | | | (1519) ~ (all_56_11 = e0) % 147.23/20.98 | | | | | | | | | | | | | | | | | | | | % 147.23/20.98 | | | | | | | | | | | | | | | | | | | | REDUCE: (1516), (1519) imply: % 147.23/20.98 | | | | | | | | | | | | | | | | | | | | (1520) $false % 147.23/20.98 | | | | | | | | | | | | | | | | | | | | % 147.23/20.98 | | | | | | | | | | | | | | | | | | | | CLOSE: (1520) is inconsistent. % 147.23/20.98 | | | | | | | | | | | | | | | | | | | | % 147.23/20.98 | | | | | | | | | | | | | | | | | | | Case 2: % 147.23/20.98 | | | | | | | | | | | | | | | | | | | | % 147.23/20.98 | | | | | | | | | | | | | | | | | | | | (1521) all_56_15 = e2 % 147.23/20.98 | | | | | | | | | | | | | | | | | | | | % 147.23/20.98 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (443), (1521) imply: % 147.23/20.98 | | | | | | | | | | | | | | | | | | | | (1522) all_52_13 = e2 % 147.23/20.98 | | | | | | | | | | | | | | | | | | | | % 147.24/20.98 | | | | | | | | | | | | | | | | | | | | REDUCE: (161), (1522) imply: % 147.24/20.98 | | | | | | | | | | | | | | | | | | | | (1523) ~ (all_52_12 = e2) % 147.24/20.98 | | | | | | | | | | | | | | | | | | | | % 147.24/20.98 | | | | | | | | | | | | | | | | | | | | REDUCE: (590), (1522) imply: % 147.24/20.98 | | | | | | | | | | | | | | | | | | | | (1524) ~ (all_4_2 = e2) % 147.24/20.98 | | | | | | | | | | | | | | | | | | | | % 147.24/20.98 | | | | | | | | | | | | | | | | | | | | SIMP: (1524) implies: % 147.24/20.98 | | | | | | | | | | | | | | | | | | | | (1525) ~ (all_4_2 = e2) % 147.24/20.98 | | | | | | | | | | | | | | | | | | | | % 147.24/20.98 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (37), (38), (51), (237), (250), (252), % 147.24/20.98 | | | | | | | | | | | | | | | | | | | | (298), (299), (340), (341), (345), (408), (419), % 147.24/20.98 | | | | | | | | | | | | | | | | | | | | (494), (540), (543), (546), (551), (555), (563), % 147.24/20.98 | | | | | | | | | | | | | | | | | | | | (567), (589), (612), (627), (761), (767), (769), % 147.24/20.98 | | | | | | | | | | | | | | | | | | | | (770), (776), (778), (780), (1469), (1472), % 147.24/20.98 | | | | | | | | | | | | | | | | | | | | (1475), (1476), (1477), (1478), (1485), (1517), % 147.24/20.98 | | | | | | | | | | | | | | | | | | | | (1518), (1523), (1525), (function-axioms) are % 147.24/20.98 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #385. % 147.24/20.98 | | | | | | | | | | | | | | | | | | | | % 147.24/20.98 | | | | | | | | | | | | | | | | | | | End of split % 147.24/20.98 | | | | | | | | | | | | | | | | | | | % 147.24/20.98 | | | | | | | | | | | | | | | | | | End of split % 147.24/20.98 | | | | | | | | | | | | | | | | | | % 147.24/20.98 | | | | | | | | | | | | | | | | | End of split % 147.24/20.98 | | | | | | | | | | | | | | | | | % 147.24/20.98 | | | | | | | | | | | | | | | | End of split % 147.24/20.98 | | | | | | | | | | | | | | | | % 147.24/20.98 | | | | | | | | | | | | | | | End of split % 147.24/20.98 | | | | | | | | | | | | | | | % 147.24/20.98 | | | | | | | | | | | | | | Case 2: % 147.24/20.98 | | | | | | | | | | | | | | | % 147.24/20.98 | | | | | | | | | | | | | | | (1526) all_56_31 = e1 % 147.24/20.98 | | | | | | | | | | | | | | | (1527) all_56_29 = e0 % 147.24/20.98 | | | | | | | | | | | | | | | % 147.24/20.98 | | | | | | | | | | | | | | | COMBINE_EQS: (357), (1527) imply: % 147.24/20.98 | | | | | | | | | | | | | | | (1528) all_52_11 = e0 % 147.24/20.98 | | | | | | | | | | | | | | | % 147.24/20.99 | | | | | | | | | | | | | | | REF_CLOSE: (38), (41), (48), (250), (252), (297), (299), % 147.24/20.99 | | | | | | | | | | | | | | | (337), (380), (402), (408), (543), (544), (546), % 147.24/20.99 | | | | | | | | | | | | | | | (549), (554), (555), (563), (580), (581), (622), % 147.24/20.99 | | | | | | | | | | | | | | | (769), (770), (776), (1472), (1475), (1478), % 147.24/20.99 | | | | | | | | | | | | | | | (1482), (1484), (1485), (1526), (1528), % 147.24/20.99 | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 147.24/20.99 | | | | | | | | | | | | | | | #381. % 147.24/20.99 | | | | | | | | | | | | | | | % 147.24/20.99 | | | | | | | | | | | | | | End of split % 147.24/20.99 | | | | | | | | | | | | | | % 147.24/20.99 | | | | | | | | | | | | | Case 2: % 147.24/20.99 | | | | | | | | | | | | | | % 147.24/20.99 | | | | | | | | | | | | | | (1529) all_36_1 = e3 % 147.24/20.99 | | | | | | | | | | | | | | (1530) ~ (all_36_0 = e0) | ~ (all_36_2 = e2) % 147.24/20.99 | | | | | | | | | | | | | | % 147.24/20.99 | | | | | | | | | | | | | | COMBINE_EQS: (652), (1529) imply: % 147.24/20.99 | | | | | | | | | | | | | | (1531) all_6_1 = e3 % 147.24/20.99 | | | | | | | | | | | | | | % 147.24/20.99 | | | | | | | | | | | | | | REDUCE: (43), (1531) imply: % 147.24/20.99 | | | | | | | | | | | | | | (1532) op(all_6_2, all_6_2) = e3 % 147.24/20.99 | | | | | | | | | | | | | | % 147.24/20.99 | | | | | | | | | | | | | | REDUCE: (42), (1531) imply: % 147.24/20.99 | | | | | | | | | | | | | | (1533) op(e1, e3) = all_6_0 % 147.24/20.99 | | | | | | | | | | | | | | % 147.24/20.99 | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_2, % 147.24/20.99 | | | | | | | | | | | | | | all_6_0, e3, e1, simplifying with (211), (1533) % 147.24/20.99 | | | | | | | | | | | | | | gives: % 147.24/20.99 | | | | | | | | | | | | | | (1534) all_52_2 = all_6_0 % 147.24/20.99 | | | | | | | | | | | | | | % 147.24/20.99 | | | | | | | | | | | | | | COMBINE_EQS: (471), (1534) imply: % 147.24/20.99 | | | | | | | | | | | | | | (1535) all_54_8 = all_6_0 % 147.24/20.99 | | | | | | | | | | | | | | % 147.24/20.99 | | | | | | | | | | | | | | COMBINE_EQS: (553), (1534) imply: % 147.24/20.99 | | | | | | | | | | | | | | (1536) all_58_6 = all_6_0 % 147.24/20.99 | | | | | | | | | | | | | | % 147.24/20.99 | | | | | | | | | | | | | | REDUCE: (191), (1534) imply: % 147.24/20.99 | | | | | | | | | | | | | | (1537) ~ (all_52_6 = all_6_0) % 147.24/20.99 | | | | | | | | | | | | | | % 147.24/20.99 | | | | | | | | | | | | | | SIMP: (1537) implies: % 147.24/20.99 | | | | | | | | | | | | | | (1538) ~ (all_52_6 = all_6_0) % 147.24/20.99 | | | | | | | | | | | | | | % 147.24/20.99 | | | | | | | | | | | | | | REDUCE: (189), (1534) imply: % 147.24/20.99 | | | | | | | | | | | | | | (1539) ~ (all_52_14 = all_6_0) % 147.24/20.99 | | | | | | | | | | | | | | % 147.24/20.99 | | | | | | | | | | | | | | SIMP: (1539) implies: % 147.24/20.99 | | | | | | | | | | | | | | (1540) ~ (all_52_14 = all_6_0) % 147.24/20.99 | | | | | | | | | | | | | | % 147.24/20.99 | | | | | | | | | | | | | | REDUCE: (559), (1534) imply: % 147.24/20.99 | | | | | | | | | | | | | | (1541) ~ (all_10_2 = all_6_0) % 147.24/20.99 | | | | | | | | | | | | | | % 147.24/20.99 | | | | | | | | | | | | | | SIMP: (1541) implies: % 147.24/20.99 | | | | | | | | | | | | | | (1542) ~ (all_10_2 = all_6_0) % 147.24/20.99 | | | | | | | | | | | | | | % 147.24/20.99 | | | | | | | | | | | | | | REDUCE: (569), (1534) imply: % 147.24/20.99 | | | | | | | | | | | | | | (1543) ~ (all_6_0 = all_6_2) % 147.24/20.99 | | | | | | | | | | | | | | % 147.24/20.99 | | | | | | | | | | | | | | BETA: splitting (292) gives: % 147.24/20.99 | | | | | | | | | | | | | | % 147.24/20.99 | | | | | | | | | | | | | | Case 1: % 147.24/20.99 | | | | | | | | | | | | | | | % 147.24/20.99 | | | | | | | | | | | | | | | (1544) ~ (all_56_21 = e2) % 147.24/20.99 | | | | | | | | | | | | | | | % 147.24/20.99 | | | | | | | | | | | | | | | REDUCE: (374), (1544) imply: % 147.24/20.99 | | | | | | | | | | | | | | | (1545) ~ (all_6_2 = e2) % 147.24/20.99 | | | | | | | | | | | | | | | % 147.24/20.99 | | | | | | | | | | | | | | | BETA: splitting (294) gives: % 147.24/20.99 | | | | | | | | | | | | | | | % 147.24/20.99 | | | | | | | | | | | | | | | Case 1: % 147.24/20.99 | | | | | | | | | | | | | | | | % 147.24/20.99 | | | | | | | | | | | | | | | | (1546) ~ (all_56_11 = e0) % 147.24/20.99 | | | | | | | | | | | | | | | | % 147.24/20.99 | | | | | | | | | | | | | | | | REDUCE: (545), (1546) imply: % 147.24/20.99 | | | | | | | | | | | | | | | | (1547) ~ (all_8_2 = e0) % 147.24/20.99 | | | | | | | | | | | | | | | | % 147.24/20.99 | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (37), (38), (41), (46), (47), (48), % 147.24/20.99 | | | | | | | | | | | | | | | | (51), (165), (166), (193), (194), (196), (205), % 147.24/20.99 | | | | | | | | | | | | | | | | (246), (247), (248), (250), (252), (288), (293), % 147.24/20.99 | | | | | | | | | | | | | | | | (295), (296), (297), (298), (299), (318), (320), % 147.24/20.99 | | | | | | | | | | | | | | | | (321), (328), (329), (330), (331), (335), (337), % 147.24/20.99 | | | | | | | | | | | | | | | | (345), (357), (365), (374), (380), (386), (389), % 147.24/20.99 | | | | | | | | | | | | | | | | (401), (402), (408), (419), (425), (431), (463), % 147.24/20.99 | | | | | | | | | | | | | | | | (467), (494), (542), (543), (544), (545), (546), % 147.24/20.99 | | | | | | | | | | | | | | | | (547), (548), (549), (550), (551), (552), (554), % 147.24/20.99 | | | | | | | | | | | | | | | | (555), (557), (561), (563), (567), (568), (571), % 147.24/20.99 | | | | | | | | | | | | | | | | (577), (580), (581), (585), (587), (612), (613), % 147.24/20.99 | | | | | | | | | | | | | | | | (617), (622), (625), (761), (769), (770), (772), % 147.24/20.99 | | | | | | | | | | | | | | | | (774), (776), (784), (1469), (1472), (1475), % 147.24/20.99 | | | | | | | | | | | | | | | | (1476), (1477), (1478), (1480), (1482), (1484), % 147.24/20.99 | | | | | | | | | | | | | | | | (1485), (1486), (1545), (1547), (function-axioms) % 147.24/20.99 | | | | | | | | | | | | | | | | are inconsistent by sub-proof #380. % 147.24/20.99 | | | | | | | | | | | | | | | | % 147.24/20.99 | | | | | | | | | | | | | | | Case 2: % 147.24/20.99 | | | | | | | | | | | | | | | | % 147.24/20.99 | | | | | | | | | | | | | | | | (1548) all_56_15 = e2 % 147.24/20.99 | | | | | | | | | | | | | | | | (1549) all_56_11 = e0 % 147.24/20.99 | | | | | | | | | | | | | | | | % 147.24/20.99 | | | | | | | | | | | | | | | | REF_CLOSE: (36), (37), (38), (48), (51), (161), (237), (250), % 147.24/20.99 | | | | | | | | | | | | | | | | (252), (298), (299), (340), (341), (345), (408), % 147.24/20.99 | | | | | | | | | | | | | | | | (419), (443), (494), (540), (543), (545), (546), % 147.24/20.99 | | | | | | | | | | | | | | | | (551), (555), (563), (567), (571), (589), (590), % 147.24/20.99 | | | | | | | | | | | | | | | | (612), (627), (761), (767), (769), (770), (776), % 147.24/20.99 | | | | | | | | | | | | | | | | (778), (780), (1469), (1472), (1475), (1476), % 147.24/20.99 | | | | | | | | | | | | | | | | (1477), (1478), (1485), (1548), (1549), % 147.24/20.99 | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 147.24/20.99 | | | | | | | | | | | | | | | | #384. % 147.24/20.99 | | | | | | | | | | | | | | | | % 147.24/20.99 | | | | | | | | | | | | | | | End of split % 147.24/20.99 | | | | | | | | | | | | | | | % 147.24/20.99 | | | | | | | | | | | | | | Case 2: % 147.24/20.99 | | | | | | | | | | | | | | | % 147.24/20.99 | | | | | | | | | | | | | | | (1550) all_56_21 = e2 % 147.24/20.99 | | | | | | | | | | | | | | | (1551) all_56_19 = e1 % 147.24/20.99 | | | | | | | | | | | | | | | % 147.24/20.99 | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (46), (48), (244), (287), (324), (374), % 147.24/20.99 | | | | | | | | | | | | | | | (380), (435), (532), (544), (545), (546), (550), % 147.24/20.99 | | | | | | | | | | | | | | | (552), (580), (591), (617), (762), (1530), (1532), % 147.24/20.99 | | | | | | | | | | | | | | | (1535), (1536), (1538), (1540), (1542), (1543), % 147.24/20.99 | | | | | | | | | | | | | | | (1550), (1551), (function-axioms) are inconsistent % 147.24/20.99 | | | | | | | | | | | | | | | by sub-proof #412. % 147.24/20.99 | | | | | | | | | | | | | | | % 147.24/20.99 | | | | | | | | | | | | | | End of split % 147.24/20.99 | | | | | | | | | | | | | | % 147.24/20.99 | | | | | | | | | | | | | End of split % 147.24/20.99 | | | | | | | | | | | | | % 147.24/20.99 | | | | | | | | | | | | End of split % 147.24/20.99 | | | | | | | | | | | | % 147.24/20.99 | | | | | | | | | | | Case 2: % 147.24/20.99 | | | | | | | | | | | | % 147.24/20.99 | | | | | | | | | | | | (1552) all_30_0 = e3 % 147.24/20.99 | | | | | | | | | | | | (1553) ~ (all_30_1 = e0) | ~ (all_30_2 = e1) % 147.24/20.99 | | | | | | | | | | | | % 147.24/20.99 | | | | | | | | | | | | COMBINE_EQS: (718), (1552) imply: % 147.24/20.99 | | | | | | | | | | | | (1554) all_8_0 = e3 % 147.24/20.99 | | | | | | | | | | | | % 147.24/20.99 | | | | | | | | | | | | REF_CLOSE: (9), (36), (41), (46), (47), (48), (51), (212), % 147.24/20.99 | | | | | | | | | | | | (237), (242), (247), (252), (294), (295), (296), % 147.24/20.99 | | | | | | | | | | | | (390), (425), (431), (443), (540), (541), (542), % 147.24/20.99 | | | | | | | | | | | | (543), (545), (557), (579), (583), (590), (617), % 147.24/20.99 | | | | | | | | | | | | (658), (769), (778), (1553), (1554), % 147.24/20.99 | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 147.24/20.99 | | | | | | | | | | | | #379. % 147.24/20.99 | | | | | | | | | | | | % 147.24/20.99 | | | | | | | | | | | End of split % 147.24/20.99 | | | | | | | | | | | % 147.24/20.99 | | | | | | | | | | Case 2: % 147.24/20.99 | | | | | | | | | | | % 147.24/20.99 | | | | | | | | | | | (1555) all_28_0 = e2 % 147.24/20.99 | | | | | | | | | | | (1556) ~ (all_28_1 = e3) | ~ (all_28_2 = e0) % 147.24/20.99 | | | | | | | | | | | % 147.24/20.99 | | | | | | | | | | | COMBINE_EQS: (740), (1555) imply: % 147.24/20.99 | | | | | | | | | | | (1557) all_6_0 = e2 % 147.24/20.99 | | | | | | | | | | | % 147.24/20.99 | | | | | | | | | | | SIMP: (1557) implies: % 147.24/20.99 | | | | | | | | | | | (1558) all_6_0 = e2 % 147.24/20.99 | | | | | | | | | | | % 147.24/20.99 | | | | | | | | | | | REF_CLOSE: (6), (8), (36), (37), (38), (41), (42), (43), % 147.24/20.99 | | | | | | | | | | | (46), (51), (144), (158), (173), (174), (176), % 147.24/20.99 | | | | | | | | | | | (187), (192), (206), (207), (208), (211), (237), % 147.24/20.99 | | | | | | | | | | | (239), (240), (242), (247), (252), (288), (289), % 147.24/20.99 | | | | | | | | | | | (290), (291), (292), (293), (294), (297), (321), % 147.24/20.99 | | | | | | | | | | | (341), (357), (366), (374), (381), (386), (402), % 147.24/20.99 | | | | | | | | | | | (407), (419), (435), (443), (475), (478), (480), % 147.24/20.99 | | | | | | | | | | | (513), (540), (541), (542), (543), (544), (545), % 147.24/20.99 | | | | | | | | | | | (546), (547), (550), (551), (555), (559), (569), % 147.24/20.99 | | | | | | | | | | | (571), (573), (580), (585), (620), (622), (627), % 147.24/20.99 | | | | | | | | | | | (634), (665), (764), (767), (768), (772), (1556), % 147.24/20.99 | | | | | | | | | | | (1558), (function-axioms) are inconsistent by % 147.24/20.99 | | | | | | | | | | | sub-proof #364. % 147.24/20.99 | | | | | | | | | | | % 147.24/20.99 | | | | | | | | | | End of split % 147.24/20.99 | | | | | | | | | | % 147.24/20.99 | | | | | | | | | Case 2: % 147.24/20.99 | | | | | | | | | | % 147.24/20.99 | | | | | | | | | | (1559) all_26_0 = e1 % 147.24/20.99 | | | | | | | | | | (1560) ~ (all_26_1 = e2) | ~ (all_26_2 = e3) % 147.24/20.99 | | | | | | | | | | % 147.24/20.99 | | | | | | | | | | COMBINE_EQS: (760), (1559) imply: % 147.24/20.99 | | | | | | | | | | (1561) all_4_0 = e1 % 147.24/20.99 | | | | | | | | | | % 147.24/20.99 | | | | | | | | | | SIMP: (1561) implies: % 147.24/20.99 | | | | | | | | | | (1562) all_4_0 = e1 % 147.24/20.99 | | | | | | | | | | % 147.24/20.99 | | | | | | | | | | REDUCE: (767), (1562) imply: % 147.24/20.99 | | | | | | | | | | (1563) ~ (e3 = e1) % 147.24/20.99 | | | | | | | | | | % 147.24/20.99 | | | | | | | | | | REDUCE: (772), (1562) imply: % 147.24/20.99 | | | | | | | | | | (1564) ~ (e2 = e1) % 147.24/20.99 | | | | | | | | | | % 147.24/20.99 | | | | | | | | | | REDUCE: (37), (1562) imply: % 147.24/20.99 | | | | | | | | | | (1565) op(e0, all_4_1) = e1 % 147.24/20.99 | | | | | | | | | | % 147.24/20.99 | | | | | | | | | | BETA: splitting (99) gives: % 147.24/20.99 | | | | | | | | | | % 147.24/20.99 | | | | | | | | | | Case 1: % 147.24/20.99 | | | | | | | | | | | % 147.24/20.99 | | | | | | | | | | | (1566) ~ (all_28_0 = e2) % 147.24/20.99 | | | | | | | | | | | % 147.24/20.99 | | | | | | | | | | | REDUCE: (740), (1566) imply: % 147.24/20.99 | | | | | | | | | | | (1567) ~ (all_6_0 = e2) % 147.24/20.99 | | | | | | | | | | | % 147.24/20.99 | | | | | | | | | | | BETA: splitting (104) gives: % 147.24/20.99 | | | | | | | | | | | % 147.24/20.99 | | | | | | | | | | | Case 1: % 147.24/20.99 | | | | | | | | | | | | % 147.24/20.99 | | | | | | | | | | | | (1568) ~ (all_30_0 = e3) % 147.24/20.99 | | | | | | | | | | | | % 147.24/20.99 | | | | | | | | | | | | REDUCE: (718), (1568) imply: % 147.24/20.99 | | | | | | | | | | | | (1569) ~ (all_8_0 = e3) % 147.24/20.99 | | | | | | | | | | | | % 147.24/20.99 | | | | | | | | | | | | BETA: splitting (109) gives: % 147.24/20.99 | | | | | | | | | | | | % 147.24/20.99 | | | | | | | | | | | | Case 1: % 147.24/20.99 | | | | | | | | | | | | | % 147.24/20.99 | | | | | | | | | | | | | (1570) ~ (all_32_1 = e1) % 147.24/20.99 | | | | | | | | | | | | | % 147.24/20.99 | | | | | | | | | | | | | REDUCE: (682), (1570) imply: % 147.24/20.99 | | | | | | | | | | | | | (1571) ~ (all_10_1 = e1) % 147.24/20.99 | | | | | | | | | | | | | % 147.24/20.99 | | | | | | | | | | | | | BETA: splitting (119) gives: % 147.24/20.99 | | | | | | | | | | | | | % 147.24/20.99 | | | | | | | | | | | | | Case 1: % 147.24/20.99 | | | | | | | | | | | | | | % 147.24/20.99 | | | | | | | | | | | | | | (1572) ~ (all_36_1 = e3) % 147.24/20.99 | | | | | | | | | | | | | | % 147.24/20.99 | | | | | | | | | | | | | | REDUCE: (652), (1572) imply: % 147.24/20.99 | | | | | | | | | | | | | | (1573) ~ (all_6_1 = e3) % 147.24/20.99 | | | | | | | | | | | | | | % 147.24/20.99 | | | | | | | | | | | | | | BETA: splitting (124) gives: % 147.24/20.99 | | | | | | | | | | | | | | % 147.24/20.99 | | | | | | | | | | | | | | Case 1: % 147.24/20.99 | | | | | | | | | | | | | | | % 147.24/20.99 | | | | | | | | | | | | | | | (1574) ~ (all_38_1 = e2) % 147.24/20.99 | | | | | | | | | | | | | | | % 147.24/20.99 | | | | | | | | | | | | | | | REDUCE: (684), (1574) imply: % 147.24/20.99 | | | | | | | | | | | | | | | (1575) ~ (all_10_1 = e2) % 147.24/20.99 | | | | | | | | | | | | | | | % 147.24/20.99 | | | | | | | | | | | | | | | BETA: splitting (129) gives: % 147.24/20.99 | | | | | | | | | | | | | | | % 147.24/20.99 | | | | | | | | | | | | | | | Case 1: % 147.24/20.99 | | | | | | | | | | | | | | | | % 147.24/20.99 | | | | | | | | | | | | | | | | (1576) ~ (all_40_0 = e3) % 147.24/20.99 | | | | | | | | | | | | | | | | % 147.24/20.99 | | | | | | | | | | | | | | | | REDUCE: (713), (1576) imply: % 147.24/20.99 | | | | | | | | | | | | | | | | (1577) ~ (all_6_0 = e3) % 147.24/20.99 | | | | | | | | | | | | | | | | % 147.24/20.99 | | | | | | | | | | | | | | | | BETA: splitting (288) gives: % 147.24/20.99 | | | | | | | | | | | | | | | | % 147.24/20.99 | | | | | | | | | | | | | | | | Case 1: % 147.24/20.99 | | | | | | | | | | | | | | | | | % 147.24/20.99 | | | | | | | | | | | | | | | | | (1578) ~ (all_56_31 = e1) % 147.24/20.99 | | | | | | | | | | | | | | | | | % 147.24/20.99 | | | | | | | | | | | | | | | | | REDUCE: (544), (1578) imply: % 147.24/20.99 | | | | | | | | | | | | | | | | | (1579) ~ (all_4_2 = e1) % 147.24/20.99 | | | | | | | | | | | | | | | | | % 147.24/20.99 | | | | | | | | | | | | | | | | | BETA: splitting (290) gives: % 147.24/20.99 | | | | | | | | | | | | | | | | | % 147.24/20.99 | | | | | | | | | | | | | | | | | Case 1: % 147.24/20.99 | | | | | | | | | | | | | | | | | | % 147.24/20.99 | | | | | | | | | | | | | | | | | | (1580) ~ (all_56_31 = e3) % 147.24/20.99 | | | | | | | | | | | | | | | | | | % 147.24/20.99 | | | | | | | | | | | | | | | | | | REDUCE: (544), (1580) imply: % 147.24/20.99 | | | | | | | | | | | | | | | | | | (1581) ~ (all_4_2 = e3) % 147.24/20.99 | | | | | | | | | | | | | | | | | | % 147.24/20.99 | | | | | | | | | | | | | | | | | | BETA: splitting (289) gives: % 147.24/20.99 | | | | | | | | | | | | | | | | | | % 147.24/20.99 | | | | | | | | | | | | | | | | | | Case 1: % 147.24/20.99 | | | | | | | | | | | | | | | | | | | % 147.24/20.99 | | | | | | | | | | | | | | | | | | | (1582) ~ (all_56_31 = e2) % 147.24/20.99 | | | | | | | | | | | | | | | | | | | % 147.24/20.99 | | | | | | | | | | | | | | | | | | | REDUCE: (544), (1582) imply: % 147.24/20.99 | | | | | | | | | | | | | | | | | | | (1583) ~ (all_4_2 = e2) % 147.24/20.99 | | | | | | | | | | | | | | | | | | | % 147.24/20.99 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (38), (237), (540), (627), (1565), (1579), % 147.24/20.99 | | | | | | | | | | | | | | | | | | | (1581), (1583), (function-axioms) are inconsistent % 147.24/20.99 | | | | | | | | | | | | | | | | | | | by sub-proof #363. % 147.24/20.99 | | | | | | | | | | | | | | | | | | | % 147.24/20.99 | | | | | | | | | | | | | | | | | | Case 2: % 147.24/20.99 | | | | | | | | | | | | | | | | | | | % 147.24/20.99 | | | | | | | | | | | | | | | | | | | (1584) all_56_31 = e2 % 147.24/20.99 | | | | | | | | | | | | | | | | | | | (1585) all_56_27 = e0 % 147.24/20.99 | | | | | | | | | | | | | | | | | | | % 147.24/20.99 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (360), (1585) imply: % 147.24/20.99 | | | | | | | | | | | | | | | | | | | (1586) all_52_7 = e0 % 147.24/20.99 | | | | | | | | | | | | | | | | | | | % 147.24/20.99 | | | | | | | | | | | | | | | | | | | SIMP: (1586) implies: % 147.24/20.99 | | | | | | | | | | | | | | | | | | | (1587) all_52_7 = e0 % 147.24/20.99 | | | | | | | | | | | | | | | | | | | % 147.24/20.99 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (544), (1584) imply: % 147.24/20.99 | | | | | | | | | | | | | | | | | | | (1588) all_4_2 = e2 % 147.24/20.99 | | | | | | | | | | | | | | | | | | | % 147.24/20.99 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (547), (1588) imply: % 147.24/20.99 | | | | | | | | | | | | | | | | | | | (1589) all_58_15 = e2 % 147.24/20.99 | | | | | | | | | | | | | | | | | | | % 147.24/20.99 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (549), (1587) imply: % 147.24/20.99 | | | | | | | | | | | | | | | | | | | (1590) all_58_13 = e0 % 147.24/20.99 | | | | | | | | | | | | | | | | | | | % 147.24/20.99 | | | | | | | | | | | | | | | | | | | REDUCE: (173), (1587) imply: % 147.24/20.99 | | | | | | | | | | | | | | | | | | | (1591) ~ (all_52_11 = e0) % 147.24/20.99 | | | | | | | | | | | | | | | | | | | % 147.24/20.99 | | | | | | | | | | | | | | | | | | | SIMP: (1591) implies: % 147.24/21.00 | | | | | | | | | | | | | | | | | | | (1592) ~ (all_52_11 = e0) % 147.24/21.00 | | | | | | | | | | | | | | | | | | | % 147.24/21.00 | | | | | | | | | | | | | | | | | | | REDUCE: (575), (1587) imply: % 147.24/21.00 | | | | | | | | | | | | | | | | | | | (1593) ~ (all_8_2 = e0) % 147.24/21.00 | | | | | | | | | | | | | | | | | | | % 147.24/21.00 | | | | | | | | | | | | | | | | | | | SIMP: (1593) implies: % 147.24/21.00 | | | | | | | | | | | | | | | | | | | (1594) ~ (all_8_2 = e0) % 147.24/21.00 | | | | | | | | | | | | | | | | | | | % 147.24/21.00 | | | | | | | | | | | | | | | | | | | REDUCE: (581), (1587), (1588) imply: % 147.24/21.00 | | | | | | | | | | | | | | | | | | | (1595) ~ (e2 = e0) % 147.24/21.00 | | | | | | | | | | | | | | | | | | | % 147.24/21.00 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (36), (37), (38), (41), (42), (43), (46), % 147.24/21.00 | | | | | | | | | | | | | | | | | | | (47), (48), (51), (53), (158), (160), (161), % 147.24/21.00 | | | | | | | | | | | | | | | | | | | (166), (168), (171), (174), (181), (182), (189), % 147.24/21.00 | | | | | | | | | | | | | | | | | | | (191), (193), (194), (196), (205), (208), (212), % 147.24/21.00 | | | | | | | | | | | | | | | | | | | (237), (238), (241), (242), (243), (245), (247), % 147.24/21.00 | | | | | | | | | | | | | | | | | | | (248), (251), (252), (287), (291), (292), (293), % 147.24/21.00 | | | | | | | | | | | | | | | | | | | (295), (297), (298), (299), (317), (318), (321), % 147.24/21.00 | | | | | | | | | | | | | | | | | | | (328), (330), (331), (332), (333), (337), (343), % 147.24/21.00 | | | | | | | | | | | | | | | | | | | (345), (365), (374), (381), (386), (389), (401), % 147.24/21.00 | | | | | | | | | | | | | | | | | | | (402), (407), (408), (419), (429), (431), (435), % 147.24/21.00 | | | | | | | | | | | | | | | | | | | (457), (463), (469), (473), (476), (482), (540), % 147.24/21.00 | | | | | | | | | | | | | | | | | | | (541), (542), (543), (544), (545), (546), (547), % 147.24/21.00 | | | | | | | | | | | | | | | | | | | (548), (550), (551), (552), (554), (555), (557), % 147.24/21.00 | | | | | | | | | | | | | | | | | | | (559), (561), (563), (565), (567), (568), (569), % 147.24/21.00 | | | | | | | | | | | | | | | | | | | (571), (573), (577), (579), (580), (582), (583), % 147.24/21.00 | | | | | | | | | | | | | | | | | | | (585), (587), (588), (589), (590), (591), (619), % 147.24/21.00 | | | | | | | | | | | | | | | | | | | (621), (624), (625), (626), (767), (768), (769), % 147.24/21.00 | | | | | | | | | | | | | | | | | | | (774), (778), (1567), (1571), (1573), (1575), % 147.24/21.00 | | | | | | | | | | | | | | | | | | | (1579), (1587), (1588), (1589), (1590), (1592), % 147.24/21.00 | | | | | | | | | | | | | | | | | | | (1594), (1595), (function-axioms) are inconsistent % 147.24/21.00 | | | | | | | | | | | | | | | | | | | by sub-proof #362. % 147.24/21.00 | | | | | | | | | | | | | | | | | | | % 147.24/21.00 | | | | | | | | | | | | | | | | | | End of split % 147.24/21.00 | | | | | | | | | | | | | | | | | | % 147.24/21.00 | | | | | | | | | | | | | | | | | Case 2: % 147.24/21.00 | | | | | | | | | | | | | | | | | | % 147.24/21.00 | | | | | | | | | | | | | | | | | | (1596) all_56_31 = e3 % 147.24/21.00 | | | | | | | | | | | | | | | | | | (1597) all_56_25 = e0 % 147.24/21.00 | | | | | | | | | | | | | | | | | | % 147.31/21.00 | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (9), (36), (37), (38), (43), (46), (47), % 147.31/21.00 | | | | | | | | | | | | | | | | | | (48), (51), (53), (160), (165), (168), (169), % 147.31/21.00 | | | | | | | | | | | | | | | | | | (171), (174), (176), (181), (182), (183), (184), % 147.31/21.00 | | | | | | | | | | | | | | | | | | (187), (188), (191), (192), (193), (194), (196), % 147.31/21.00 | | | | | | | | | | | | | | | | | | (197), (205), (238), (241), (242), (243), (244), % 147.31/21.00 | | | | | | | | | | | | | | | | | | (246), (247), (248), (250), (251), (252), (287), % 147.31/21.00 | | | | | | | | | | | | | | | | | | (291), (292), (293), (294), (296), (298), (299), % 147.31/21.00 | | | | | | | | | | | | | | | | | | (318), (320), (321), (328), (335), (336), (339), % 147.31/21.00 | | | | | | | | | | | | | | | | | | (343), (345), (365), (374), (380), (381), (386), % 147.31/21.00 | | | | | | | | | | | | | | | | | | (389), (401), (407), (419), (425), (429), (435), % 147.31/21.00 | | | | | | | | | | | | | | | | | | (447), (457), (459), (463), (467), (471), (473), % 147.31/21.00 | | | | | | | | | | | | | | | | | | (476), (482), (541), (542), (543), (544), (545), % 147.31/21.00 | | | | | | | | | | | | | | | | | | (546), (547), (548), (549), (550), (551), (554), % 147.31/21.00 | | | | | | | | | | | | | | | | | | (555), (557), (559), (561), (568), (569), (570), % 147.31/21.00 | | | | | | | | | | | | | | | | | | (571), (573), (575), (577), (580), (581), (582), % 147.31/21.00 | | | | | | | | | | | | | | | | | | (585), (587), (588), (591), (613), (617), (625), % 147.31/21.00 | | | | | | | | | | | | | | | | | | (768), (769), (772), (774), (778), (1573), (1575), % 147.31/21.00 | | | | | | | | | | | | | | | | | | (1579), (1596), (1597), (function-axioms) are % 147.31/21.00 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #503. % 147.31/21.00 | | | | | | | | | | | | | | | | | | % 147.31/21.00 | | | | | | | | | | | | | | | | | End of split % 147.31/21.00 | | | | | | | | | | | | | | | | | % 147.31/21.00 | | | | | | | | | | | | | | | | Case 2: % 147.31/21.00 | | | | | | | | | | | | | | | | | % 147.31/21.00 | | | | | | | | | | | | | | | | | (1598) all_56_31 = e1 % 147.31/21.00 | | | | | | | | | | | | | | | | | (1599) all_56_29 = e0 % 147.31/21.00 | | | | | | | | | | | | | | | | | % 147.31/21.00 | | | | | | | | | | | | | | | | | COMBINE_EQS: (357), (1599) imply: % 147.31/21.00 | | | | | | | | | | | | | | | | | (1600) all_52_11 = e0 % 147.31/21.00 | | | | | | | | | | | | | | | | | % 147.31/21.00 | | | | | | | | | | | | | | | | | SIMP: (1600) implies: % 147.31/21.00 | | | | | | | | | | | | | | | | | (1601) all_52_11 = e0 % 147.31/21.00 | | | | | | | | | | | | | | | | | % 147.31/21.00 | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (36), (37), (38), (41), (42), (43), (48), % 147.31/21.00 | | | | | | | | | | | | | | | | | (53), (161), (165), (166), (168), (173), (176), % 147.31/21.00 | | | | | | | | | | | | | | | | | (181), (187), (192), (194), (206), (207), (239), % 147.31/21.00 | | | | | | | | | | | | | | | | | (240), (242), (245), (246), (247), (249), (252), % 147.31/21.00 | | | | | | | | | | | | | | | | | (292), (293), (294), (295), (296), (297), (298), % 147.31/21.00 | | | | | | | | | | | | | | | | | (299), (330), (331), (332), (333), (337), (343), % 147.31/21.00 | | | | | | | | | | | | | | | | | (374), (380), (381), (386), (389), (401), (402), % 147.31/21.00 | | | | | | | | | | | | | | | | | (407), (408), (419), (425), (431), (435), (461), % 147.31/21.00 | | | | | | | | | | | | | | | | | (467), (469), (478), (480), (541), (542), (543), % 147.31/21.00 | | | | | | | | | | | | | | | | | (544), (545), (546), (548), (549), (551), (552), % 147.31/21.00 | | | | | | | | | | | | | | | | | (554), (555), (557), (563), (567), (571), (577), % 147.31/21.00 | | | | | | | | | | | | | | | | | (579), (580), (581), (582), (583), (585), (589), % 147.31/21.00 | | | | | | | | | | | | | | | | | (590), (622), (625), (767), (769), (772), (1571), % 147.31/21.00 | | | | | | | | | | | | | | | | | (1577), (1598), (1601), (function-axioms) are % 147.31/21.00 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #463. % 147.31/21.00 | | | | | | | | | | | | | | | | | % 147.31/21.00 | | | | | | | | | | | | | | | | End of split % 147.31/21.00 | | | | | | | | | | | | | | | | % 147.31/21.00 | | | | | | | | | | | | | | | Case 2: % 147.31/21.00 | | | | | | | | | | | | | | | | % 147.31/21.00 | | | | | | | | | | | | | | | | (1602) all_40_0 = e3 % 147.31/21.00 | | | | | | | | | | | | | | | | (1603) ~ (all_40_1 = e0) | ~ (all_40_2 = e2) % 147.31/21.00 | | | | | | | | | | | | | | | | % 147.31/21.00 | | | | | | | | | | | | | | | | COMBINE_EQS: (713), (1602) imply: % 147.31/21.00 | | | | | | | | | | | | | | | | (1604) all_6_0 = e3 % 147.31/21.00 | | | | | | | | | | | | | | | | % 147.31/21.00 | | | | | | | | | | | | | | | | REDUCE: (42), (1604) imply: % 147.31/21.00 | | | | | | | | | | | | | | | | (1605) op(e1, all_6_1) = e3 % 147.31/21.00 | | | | | | | | | | | | | | | | % 147.31/21.01 | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8), (9), (36), (37), (38), (41), (42), (43), % 147.31/21.01 | | | | | | | | | | | | | | | | (46), (47), (48), (51), (53), (158), (160), (161), % 147.31/21.01 | | | | | | | | | | | | | | | | (165), (168), (169), (171), (173), (174), (176), % 147.31/21.01 | | | | | | | | | | | | | | | | (181), (182), (183), (184), (187), (188), (189), % 147.31/21.01 | | | | | | | | | | | | | | | | (191), (192), (193), (194), (196), (197), (205), % 147.31/21.01 | | | | | | | | | | | | | | | | (206), (207), (208), (237), (238), (239), (240), % 147.31/21.01 | | | | | | | | | | | | | | | | (241), (242), (243), (244), (246), (247), (248), % 147.31/21.01 | | | | | | | | | | | | | | | | (249), (250), (251), (252), (287), (288), (290), % 147.31/21.01 | | | | | | | | | | | | | | | | (291), (292), (293), (294), (296), (297), (298), % 147.31/21.01 | | | | | | | | | | | | | | | | (299), (318), (320), (321), (324), (326), (328), % 147.31/21.01 | | | | | | | | | | | | | | | | (332), (335), (336), (339), (340), (343), (344), % 147.31/21.01 | | | | | | | | | | | | | | | | (345), (357), (365), (366), (374), (380), (381), % 147.31/21.01 | | | | | | | | | | | | | | | | (386), (389), (401), (402), (407), (408), (419), % 147.31/21.01 | | | | | | | | | | | | | | | | (425), (429), (435), (443), (447), (457), (459), % 147.31/21.01 | | | | | | | | | | | | | | | | (461), (463), (467), (471), (473), (476), (478), % 147.31/21.01 | | | | | | | | | | | | | | | | (480), (482), (507), (540), (541), (542), (543), % 147.31/21.01 | | | | | | | | | | | | | | | | (544), (545), (546), (547), (548), (549), (550), % 147.31/21.01 | | | | | | | | | | | | | | | | (551), (552), (553), (554), (555), (557), (559), % 147.31/21.01 | | | | | | | | | | | | | | | | (561), (563), (565), (567), (568), (569), (570), % 147.31/21.01 | | | | | | | | | | | | | | | | (571), (573), (575), (577), (580), (581), (582), % 147.31/21.01 | | | | | | | | | | | | | | | | (585), (587), (588), (589), (590), (591), (613), % 147.31/21.01 | | | | | | | | | | | | | | | | (617), (621), (622), (625), (685), (767), (768), % 147.31/21.01 | | | | | | | | | | | | | | | | (769), (772), (774), (778), (1567), (1571), % 147.31/21.01 | | | | | | | | | | | | | | | | (1573), (1575), (1603), (1605), (function-axioms) % 147.31/21.01 | | | | | | | | | | | | | | | | are inconsistent by sub-proof #498. % 147.31/21.01 | | | | | | | | | | | | | | | | % 147.31/21.01 | | | | | | | | | | | | | | | End of split % 147.31/21.01 | | | | | | | | | | | | | | | % 147.31/21.01 | | | | | | | | | | | | | | Case 2: % 147.31/21.01 | | | | | | | | | | | | | | | % 147.31/21.01 | | | | | | | | | | | | | | | (1606) all_38_1 = e2 % 147.31/21.01 | | | | | | | | | | | | | | | (1607) ~ (all_38_0 = e0) | ~ (all_38_2 = e1) % 147.31/21.01 | | | | | | | | | | | | | | | % 147.31/21.01 | | | | | | | | | | | | | | | COMBINE_EQS: (684), (1606) imply: % 147.31/21.01 | | | | | | | | | | | | | | | (1608) all_10_1 = e2 % 147.31/21.01 | | | | | | | | | | | | | | | % 147.31/21.01 | | | | | | | | | | | | | | | SIMP: (1608) implies: % 147.31/21.01 | | | | | | | | | | | | | | | (1609) all_10_1 = e2 % 147.31/21.01 | | | | | | | | | | | | | | | % 147.31/21.01 | | | | | | | | | | | | | | | REDUCE: (53), (1609) imply: % 147.31/21.01 | | | | | | | | | | | | | | | (1610) op(all_10_2, all_10_2) = e2 % 147.31/21.01 | | | | | | | | | | | | | | | % 147.31/21.01 | | | | | | | | | | | | | | | REDUCE: (52), (1609) imply: % 147.31/21.01 | | | | | | | | | | | | | | | (1611) op(e3, e2) = all_10_0 % 147.31/21.01 | | | | | | | | | | | | | | | % 147.31/21.01 | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_4, % 147.31/21.01 | | | | | | | | | | | | | | | all_10_0, e2, e3, simplifying with (218), (1611) % 147.31/21.01 | | | | | | | | | | | | | | | gives: % 147.31/21.01 | | | | | | | | | | | | | | | (1612) all_52_4 = all_10_0 % 147.31/21.01 | | | | | | | | | | | | | | | % 147.31/21.01 | | | | | | | | | | | | | | | COMBINE_EQS: (457), (1612) imply: % 147.31/21.01 | | | | | | | | | | | | | | | (1613) all_54_1 = all_10_0 % 147.31/21.01 | | | | | | | | | | | | | | | % 147.31/21.01 | | | | | | | | | | | | | | | COMBINE_EQS: (408), (1612) imply: % 147.31/21.01 | | | | | | | | | | | | | | | (1614) all_56_3 = all_10_0 % 147.31/21.01 | | | | | | | | | | | | | | | % 147.31/21.01 | | | | | | | | | | | | | | | COMBINE_EQS: (555), (1612) imply: % 147.31/21.01 | | | | | | | | | | | | | | | (1615) all_58_1 = all_10_0 % 147.31/21.01 | | | | | | | | | | | | | | | % 147.31/21.01 | | | | | | | | | | | | | | | REDUCE: (183), (1612) imply: % 147.31/21.01 | | | | | | | | | | | | | | | (1616) ~ (all_52_7 = all_10_0) % 147.31/21.01 | | | | | | | | | | | | | | | % 147.31/21.01 | | | | | | | | | | | | | | | SIMP: (1616) implies: % 147.31/21.01 | | | | | | | | | | | | | | | (1617) ~ (all_52_7 = all_10_0) % 147.31/21.01 | | | | | | | | | | | | | | | % 147.31/21.01 | | | | | | | | | | | | | | | REDUCE: (182), (1612) imply: % 147.31/21.01 | | | | | | | | | | | | | | | (1618) ~ (all_52_8 = all_10_0) % 147.31/21.01 | | | | | | | | | | | | | | | % 147.31/21.01 | | | | | | | | | | | | | | | SIMP: (1618) implies: % 147.31/21.01 | | | | | | | | | | | | | | | (1619) ~ (all_52_8 = all_10_0) % 147.31/21.01 | | | | | | | | | | | | | | | % 147.31/21.01 | | | | | | | | | | | | | | | REDUCE: (181), (1612) imply: % 147.31/21.01 | | | | | | | | | | | | | | | (1620) ~ (all_52_12 = all_10_0) % 147.31/21.01 | | | | | | | | | | | | | | | % 147.31/21.01 | | | | | | | | | | | | | | | SIMP: (1620) implies: % 147.31/21.01 | | | | | | | | | | | | | | | (1621) ~ (all_52_12 = all_10_0) % 147.31/21.01 | | | | | | | | | | | | | | | % 147.31/21.01 | | | | | | | | | | | | | | | REDUCE: (563), (1612) imply: % 147.31/21.01 | | | | | | | | | | | | | | | (1622) ~ (all_10_0 = all_10_2) % 147.31/21.01 | | | | | | | | | | | | | | | % 147.31/21.01 | | | | | | | | | | | | | | | REDUCE: (571), (1612) imply: % 147.31/21.01 | | | | | | | | | | | | | | | (1623) ~ (all_10_0 = all_8_2) % 147.31/21.01 | | | | | | | | | | | | | | | % 147.31/21.01 | | | | | | | | | | | | | | | REDUCE: (616), (1612) imply: % 147.31/21.01 | | | | | | | | | | | | | | | (1624) op(e2, all_10_0) = all_56_2 % 147.31/21.01 | | | | | | | | | | | | | | | % 147.31/21.01 | | | | | | | | | | | | | | | BETA: splitting (129) gives: % 147.31/21.01 | | | | | | | | | | | | | | | % 147.31/21.01 | | | | | | | | | | | | | | | Case 1: % 147.31/21.01 | | | | | | | | | | | | | | | | % 147.31/21.01 | | | | | | | | | | | | | | | | (1625) ~ (all_40_0 = e3) % 147.31/21.01 | | | | | | | | | | | | | | | | % 147.31/21.01 | | | | | | | | | | | | | | | | REDUCE: (713), (1625) imply: % 147.31/21.01 | | | | | | | | | | | | | | | | (1626) ~ (all_6_0 = e3) % 147.31/21.01 | | | | | | | | | | | | | | | | % 147.31/21.01 | | | | | | | | | | | | | | | | BETA: splitting (288) gives: % 147.31/21.01 | | | | | | | | | | | | | | | | % 147.31/21.01 | | | | | | | | | | | | | | | | Case 1: % 147.31/21.01 | | | | | | | | | | | | | | | | | % 147.31/21.01 | | | | | | | | | | | | | | | | | (1627) ~ (all_56_31 = e1) % 147.31/21.01 | | | | | | | | | | | | | | | | | % 147.31/21.01 | | | | | | | | | | | | | | | | | REDUCE: (544), (1627) imply: % 147.31/21.01 | | | | | | | | | | | | | | | | | (1628) ~ (all_4_2 = e1) % 147.31/21.01 | | | | | | | | | | | | | | | | | % 147.31/21.01 | | | | | | | | | | | | | | | | | BETA: splitting (290) gives: % 147.31/21.01 | | | | | | | | | | | | | | | | | % 147.31/21.01 | | | | | | | | | | | | | | | | | Case 1: % 147.31/21.01 | | | | | | | | | | | | | | | | | | % 147.31/21.01 | | | | | | | | | | | | | | | | | | (1629) ~ (all_56_31 = e3) % 147.31/21.01 | | | | | | | | | | | | | | | | | | % 147.31/21.01 | | | | | | | | | | | | | | | | | | REDUCE: (544), (1629) imply: % 147.31/21.01 | | | | | | | | | | | | | | | | | | (1630) ~ (all_4_2 = e3) % 147.31/21.01 | | | | | | | | | | | | | | | | | | % 147.31/21.01 | | | | | | | | | | | | | | | | | | BETA: splitting (292) gives: % 147.31/21.01 | | | | | | | | | | | | | | | | | | % 147.31/21.01 | | | | | | | | | | | | | | | | | | Case 1: % 147.31/21.01 | | | | | | | | | | | | | | | | | | | % 147.31/21.01 | | | | | | | | | | | | | | | | | | | (1631) ~ (all_56_21 = e2) % 147.31/21.01 | | | | | | | | | | | | | | | | | | | % 147.31/21.01 | | | | | | | | | | | | | | | | | | | REDUCE: (374), (1631) imply: % 147.31/21.01 | | | | | | | | | | | | | | | | | | | (1632) ~ (all_6_2 = e2) % 147.31/21.01 | | | | | | | | | | | | | | | | | | | % 147.31/21.01 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (37), (38), (41), (42), (43), (46), (47), % 147.31/21.01 | | | | | | | | | | | | | | | | | | | (48), (51), (53), (158), (160), (161), (165), % 147.31/21.01 | | | | | | | | | | | | | | | | | | | (168), (169), (173), (174), (176), (181), (182), % 147.31/21.01 | | | | | | | | | | | | | | | | | | | (183), (184), (188), (189), (191), (192), (193), % 147.31/21.01 | | | | | | | | | | | | | | | | | | | (196), (208), (212), (237), (238), (239), (240), % 147.31/21.01 | | | | | | | | | | | | | | | | | | | (241), (242), (243), (244), (245), (247), (249), % 147.31/21.01 | | | | | | | | | | | | | | | | | | | (250), (251), (252), (286), (287), (289), (291), % 147.31/21.01 | | | | | | | | | | | | | | | | | | | (292), (293), (294), (295), (296), (297), (298), % 147.31/21.01 | | | | | | | | | | | | | | | | | | | (299), (318), (319), (321), (322), (326), (328), % 147.31/21.01 | | | | | | | | | | | | | | | | | | | (330), (332), (333), (336), (337), (340), (342), % 147.31/21.01 | | | | | | | | | | | | | | | | | | | (343), (344), (360), (365), (366), (374), (380), % 147.31/21.01 | | | | | | | | | | | | | | | | | | | (381), (386), (389), (401), (402), (407), (419), % 147.31/21.01 | | | | | | | | | | | | | | | | | | | (425), (429), (431), (435), (443), (457), (459), % 147.31/21.01 | | | | | | | | | | | | | | | | | | | (461), (469), (471), (473), (476), (478), (480), % 147.31/21.01 | | | | | | | | | | | | | | | | | | | (482), (533), (540), (541), (542), (543), (544), % 147.31/21.01 | | | | | | | | | | | | | | | | | | | (545), (546), (547), (548), (549), (550), (551), % 147.31/21.01 | | | | | | | | | | | | | | | | | | | (552), (553), (554), (555), (557), (559), (561), % 147.31/21.01 | | | | | | | | | | | | | | | | | | | (563), (565), (567), (568), (569), (570), (571), % 147.31/21.01 | | | | | | | | | | | | | | | | | | | (573), (575), (577), (579), (580), (581), (582), % 147.31/21.01 | | | | | | | | | | | | | | | | | | | (583), (585), (587), (588), (589), (590), (591), % 147.31/21.01 | | | | | | | | | | | | | | | | | | | (612), (617), (618), (621), (622), (627), (723), % 147.31/21.01 | | | | | | | | | | | | | | | | | | | (767), (768), (769), (770), (776), (778), (1567), % 147.31/21.01 | | | | | | | | | | | | | | | | | | | (1569), (1571), (1573), (1607), (1610), (1613), % 147.31/21.01 | | | | | | | | | | | | | | | | | | | (1614), (1615), (1617), (1619), (1621), (1622), % 147.31/21.01 | | | | | | | | | | | | | | | | | | | (1623), (1624), (1626), (1628), (1630), (1632), % 147.31/21.01 | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 147.31/21.01 | | | | | | | | | | | | | | | | | | | #476. % 147.31/21.01 | | | | | | | | | | | | | | | | | | | % 147.31/21.01 | | | | | | | | | | | | | | | | | | Case 2: % 147.31/21.01 | | | | | | | | | | | | | | | | | | | % 147.31/21.01 | | | | | | | | | | | | | | | | | | | (1633) all_56_21 = e2 % 147.31/21.01 | | | | | | | | | | | | | | | | | | | (1634) all_56_19 = e1 % 147.31/21.01 | | | | | | | | | | | | | | | | | | | % 147.31/21.01 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (435), (1634) imply: % 147.31/21.01 | | | | | | | | | | | | | | | | | | | (1635) all_52_6 = e1 % 147.31/21.01 | | | | | | | | | | | | | | | | | | | % 147.31/21.01 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (374), (1633) imply: % 147.31/21.01 | | | | | | | | | | | | | | | | | | | (1636) all_6_2 = e2 % 147.31/21.01 | | | | | | | | | | | | | | | | | | | % 147.31/21.01 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (43), (46), (188), (193), (247), (252), (294), % 147.31/21.01 | | | | | | | | | | | | | | | | | | | (297), (298), (299), (338), (339), (344), (345), % 147.31/21.01 | | | | | | | | | | | | | | | | | | | (365), (380), (401), (402), (407), (419), (429), % 147.31/21.01 | | | | | | | | | | | | | | | | | | | (443), (542), (543), (545), (546), (549), (551), % 147.31/21.01 | | | | | | | | | | | | | | | | | | | (553), (554), (569), (573), (575), (580), (582), % 147.31/21.01 | | | | | | | | | | | | | | | | | | | (619), (768), (770), (1573), (1610), (1614), % 147.31/21.01 | | | | | | | | | | | | | | | | | | | (1615), (1617), (1619), (1621), (1622), (1635), % 147.31/21.01 | | | | | | | | | | | | | | | | | | | (1636), (function-axioms) are inconsistent by % 147.31/21.01 | | | | | | | | | | | | | | | | | | | sub-proof #361. % 147.31/21.01 | | | | | | | | | | | | | | | | | | | % 147.31/21.01 | | | | | | | | | | | | | | | | | | End of split % 147.31/21.01 | | | | | | | | | | | | | | | | | | % 147.31/21.01 | | | | | | | | | | | | | | | | | Case 2: % 147.31/21.01 | | | | | | | | | | | | | | | | | | % 147.36/21.01 | | | | | | | | | | | | | | | | | | (1637) all_56_31 = e3 % 147.36/21.01 | | | | | | | | | | | | | | | | | | (1638) all_56_25 = e0 % 147.36/21.01 | | | | | | | | | | | | | | | | | | % 147.36/21.01 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (447), (1638) imply: % 147.36/21.01 | | | | | | | | | | | | | | | | | | (1639) all_52_3 = e0 % 147.36/21.01 | | | | | | | | | | | | | | | | | | % 147.36/21.01 | | | | | | | | | | | | | | | | | | SIMP: (1639) implies: % 147.36/21.01 | | | | | | | | | | | | | | | | | | (1640) all_52_3 = e0 % 147.36/21.01 | | | | | | | | | | | | | | | | | | % 147.36/21.01 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (544), (1637) imply: % 147.36/21.01 | | | | | | | | | | | | | | | | | | (1641) all_4_2 = e3 % 147.36/21.01 | | | | | | | | | | | | | | | | | | % 147.36/21.01 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (530), (1641) imply: % 147.36/21.01 | | | | | | | | | | | | | | | | | | (1642) all_26_2 = e3 % 147.36/21.01 | | | | | | | | | | | | | | | | | | % 147.36/21.01 | | | | | | | | | | | | | | | | | | REDUCE: (188), (1640) imply: % 147.36/21.01 | | | | | | | | | | | | | | | | | | (1643) ~ (all_52_7 = e0) % 147.36/21.01 | | | | | | | | | | | | | | | | | | % 147.36/21.01 | | | | | | | | | | | | | | | | | | SIMP: (1643) implies: % 147.36/21.01 | | | | | | | | | | | | | | | | | | (1644) ~ (all_52_7 = e0) % 147.36/21.01 | | | | | | | | | | | | | | | | | | % 147.36/21.01 | | | | | | | | | | | | | | | | | | REDUCE: (187), (1640) imply: % 147.36/21.01 | | | | | | | | | | | | | | | | | | (1645) ~ (all_52_11 = e0) % 147.36/21.01 | | | | | | | | | | | | | | | | | | % 147.36/21.01 | | | | | | | | | | | | | | | | | | SIMP: (1645) implies: % 147.36/21.01 | | | | | | | | | | | | | | | | | | (1646) ~ (all_52_11 = e0) % 147.36/21.01 | | | | | | | | | | | | | | | | | | % 147.36/21.01 | | | | | | | | | | | | | | | | | | REDUCE: (561), (1640) imply: % 147.36/21.01 | | | | | | | | | | | | | | | | | | (1647) ~ (all_10_2 = e0) % 147.36/21.01 | | | | | | | | | | | | | | | | | | % 147.36/21.01 | | | | | | | | | | | | | | | | | | SIMP: (1647) implies: % 147.36/21.01 | | | | | | | | | | | | | | | | | | (1648) ~ (all_10_2 = e0) % 147.36/21.01 | | | | | | | | | | | | | | | | | | % 147.36/21.01 | | | | | | | | | | | | | | | | | | REDUCE: (588), (1641) imply: % 147.36/21.01 | | | | | | | | | | | | | | | | | | (1649) ~ (all_52_11 = e3) % 147.36/21.01 | | | | | | | | | | | | | | | | | | % 147.36/21.01 | | | | | | | | | | | | | | | | | | REDUCE: (591), (1641) imply: % 147.36/21.01 | | | | | | | | | | | | | | | | | | (1650) ~ (all_52_14 = e3) % 147.36/21.01 | | | | | | | | | | | | | | | | | | % 147.36/21.01 | | | | | | | | | | | | | | | | | | REDUCE: (38), (1641) imply: % 147.36/21.01 | | | | | | | | | | | | | | | | | | (1651) op(e3, e3) = all_4_1 % 147.36/21.01 | | | | | | | | | | | | | | | | | | % 147.36/21.01 | | | | | | | | | | | | | | | | | | REDUCE: (36), (1641) imply: % 147.36/21.01 | | | | | | | | | | | | | | | | | | (1652) op(e0, e0) = e3 % 147.36/21.01 | | | | | | | | | | | | | | | | | | % 147.36/21.01 | | | | | | | | | | | | | | | | | | REF_CLOSE: (41), (43), (46), (48), (51), (160), (168), (169), % 147.36/21.01 | | | | | | | | | | | | | | | | | | (174), (188), (193), (238), (241), (242), (247), % 147.36/21.01 | | | | | | | | | | | | | | | | | | (250), (252), (291), (292), (293), (294), (297), % 147.36/21.01 | | | | | | | | | | | | | | | | | | (298), (299), (336), (338), (339), (343), (344), % 147.36/21.01 | | | | | | | | | | | | | | | | | | (345), (365), (374), (380), (381), (401), (402), % 147.36/21.01 | | | | | | | | | | | | | | | | | | (407), (419), (429), (435), (443), (459), (476), % 147.36/21.01 | | | | | | | | | | | | | | | | | | (482), (541), (542), (543), (545), (546), (549), % 147.36/21.01 | | | | | | | | | | | | | | | | | | (551), (553), (554), (559), (565), (567), (569), % 147.36/21.01 | | | | | | | | | | | | | | | | | | (573), (575), (580), (582), (585), (587), (619), % 147.36/21.01 | | | | | | | | | | | | | | | | | | (622), (657), (768), (770), (778), (1560), (1573), % 147.36/21.01 | | | | | | | | | | | | | | | | | | (1610), (1614), (1615), (1617), (1619), (1621), % 147.36/21.02 | | | | | | | | | | | | | | | | | | (1622), (1642), (1644), (1646), (1648), (1649), % 147.36/21.02 | | | | | | | | | | | | | | | | | | (1650), (1651), (1652), (function-axioms) are % 147.36/21.02 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #360. % 147.36/21.02 | | | | | | | | | | | | | | | | | | % 147.36/21.02 | | | | | | | | | | | | | | | | | End of split % 147.36/21.02 | | | | | | | | | | | | | | | | | % 147.36/21.02 | | | | | | | | | | | | | | | | Case 2: % 147.36/21.02 | | | | | | | | | | | | | | | | | % 147.36/21.02 | | | | | | | | | | | | | | | | | (1653) all_56_31 = e1 % 147.36/21.02 | | | | | | | | | | | | | | | | | (1654) all_56_29 = e0 % 147.36/21.02 | | | | | | | | | | | | | | | | | % 147.36/21.02 | | | | | | | | | | | | | | | | | COMBINE_EQS: (357), (1654) imply: % 147.36/21.02 | | | | | | | | | | | | | | | | | (1655) all_52_11 = e0 % 147.36/21.02 | | | | | | | | | | | | | | | | | % 147.36/21.02 | | | | | | | | | | | | | | | | | SIMP: (1655) implies: % 147.36/21.02 | | | | | | | | | | | | | | | | | (1656) all_52_11 = e0 % 147.36/21.02 | | | | | | | | | | | | | | | | | % 147.36/21.02 | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (36), (37), (38), (41), (42), (43), (48), % 147.36/21.02 | | | | | | | | | | | | | | | | | (53), (161), (165), (166), (168), (173), (176), % 147.36/21.02 | | | | | | | | | | | | | | | | | (181), (187), (192), (194), (206), (207), (239), % 147.36/21.02 | | | | | | | | | | | | | | | | | (240), (242), (245), (246), (247), (249), (252), % 147.36/21.02 | | | | | | | | | | | | | | | | | (292), (293), (294), (295), (296), (297), (298), % 147.36/21.02 | | | | | | | | | | | | | | | | | (299), (330), (331), (332), (333), (337), (343), % 147.36/21.02 | | | | | | | | | | | | | | | | | (374), (380), (381), (386), (389), (401), (402), % 147.36/21.02 | | | | | | | | | | | | | | | | | (407), (408), (419), (425), (431), (435), (461), % 147.36/21.02 | | | | | | | | | | | | | | | | | (467), (469), (478), (480), (541), (542), (543), % 147.36/21.02 | | | | | | | | | | | | | | | | | (544), (545), (546), (548), (549), (551), (552), % 147.36/21.02 | | | | | | | | | | | | | | | | | (554), (555), (557), (563), (567), (571), (577), % 147.36/21.02 | | | | | | | | | | | | | | | | | (579), (580), (581), (582), (583), (585), (589), % 147.36/21.02 | | | | | | | | | | | | | | | | | (590), (622), (625), (767), (769), (772), (1571), % 147.36/21.02 | | | | | | | | | | | | | | | | | (1626), (1653), (1656), (function-axioms) are % 147.36/21.02 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #463. % 147.36/21.02 | | | | | | | | | | | | | | | | | % 147.36/21.02 | | | | | | | | | | | | | | | | End of split % 147.36/21.02 | | | | | | | | | | | | | | | | % 147.36/21.02 | | | | | | | | | | | | | | | Case 2: % 147.36/21.02 | | | | | | | | | | | | | | | | % 147.36/21.02 | | | | | | | | | | | | | | | | (1657) all_40_0 = e3 % 147.36/21.02 | | | | | | | | | | | | | | | | (1658) ~ (all_40_1 = e0) | ~ (all_40_2 = e2) % 147.36/21.02 | | | | | | | | | | | | | | | | % 147.36/21.02 | | | | | | | | | | | | | | | | COMBINE_EQS: (713), (1657) imply: % 147.36/21.02 | | | | | | | | | | | | | | | | (1659) all_6_0 = e3 % 147.36/21.02 | | | | | | | | | | | | | | | | % 147.36/21.02 | | | | | | | | | | | | | | | | SIMP: (1659) implies: % 147.36/21.02 | | | | | | | | | | | | | | | | (1660) all_6_0 = e3 % 147.36/21.02 | | | | | | | | | | | | | | | | % 147.36/21.02 | | | | | | | | | | | | | | | | REDUCE: (42), (1660) imply: % 147.36/21.02 | | | | | | | | | | | | | | | | (1661) op(e1, all_6_1) = e3 % 147.36/21.02 | | | | | | | | | | | | | | | | % 147.36/21.02 | | | | | | | | | | | | | | | | BETA: splitting (288) gives: % 147.36/21.02 | | | | | | | | | | | | | | | | % 147.36/21.02 | | | | | | | | | | | | | | | | Case 1: % 147.36/21.02 | | | | | | | | | | | | | | | | | % 147.36/21.02 | | | | | | | | | | | | | | | | | (1662) ~ (all_56_31 = e1) % 147.36/21.02 | | | | | | | | | | | | | | | | | % 147.36/21.02 | | | | | | | | | | | | | | | | | REDUCE: (544), (1662) imply: % 147.36/21.02 | | | | | | | | | | | | | | | | | (1663) ~ (all_4_2 = e1) % 147.36/21.02 | | | | | | | | | | | | | | | | | % 147.36/21.02 | | | | | | | | | | | | | | | | | BETA: splitting (290) gives: % 147.36/21.02 | | | | | | | | | | | | | | | | | % 147.36/21.02 | | | | | | | | | | | | | | | | | Case 1: % 147.36/21.02 | | | | | | | | | | | | | | | | | | % 147.36/21.02 | | | | | | | | | | | | | | | | | | (1664) ~ (all_56_31 = e3) % 147.36/21.02 | | | | | | | | | | | | | | | | | | % 147.36/21.02 | | | | | | | | | | | | | | | | | | REDUCE: (544), (1664) imply: % 147.36/21.02 | | | | | | | | | | | | | | | | | | (1665) ~ (all_4_2 = e3) % 147.36/21.02 | | | | | | | | | | | | | | | | | | % 147.36/21.02 | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (36), (41), (42), (43), (46), (51), (53), % 147.36/21.02 | | | | | | | | | | | | | | | | | | (158), (160), (161), (174), (176), (181), (183), % 147.36/21.02 | | | | | | | | | | | | | | | | | | (184), (189), (191), (208), (237), (239), (241), % 147.36/21.02 | | | | | | | | | | | | | | | | | | (242), (243), (247), (249), (251), (252), (287), % 147.36/21.02 | | | | | | | | | | | | | | | | | | (291), (292), (293), (294), (297), (299), (321), % 147.36/21.02 | | | | | | | | | | | | | | | | | | (324), (326), (328), (332), (340), (344), (365), % 147.36/21.02 | | | | | | | | | | | | | | | | | | (366), (374), (380), (381), (386), (389), (401), % 147.36/21.02 | | | | | | | | | | | | | | | | | | (402), (407), (408), (419), (435), (443), (457), % 147.36/21.02 | | | | | | | | | | | | | | | | | | (461), (473), (476), (480), (507), (540), (541), % 147.36/21.02 | | | | | | | | | | | | | | | | | | (542), (543), (544), (545), (546), (547), (548), % 147.36/21.02 | | | | | | | | | | | | | | | | | | (550), (551), (552), (553), (554), (557), (559), % 147.36/21.02 | | | | | | | | | | | | | | | | | | (563), (565), (567), (568), (569), (570), (571), % 147.36/21.02 | | | | | | | | | | | | | | | | | | (573), (577), (580), (581), (587), (588), (589), % 147.36/21.02 | | | | | | | | | | | | | | | | | | (590), (591), (621), (622), (685), (768), (1567), % 147.36/21.02 | | | | | | | | | | | | | | | | | | (1571), (1573), (1658), (1661), (1663), (1665), % 147.36/21.02 | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 147.36/21.02 | | | | | | | | | | | | | | | | | | #504. % 147.36/21.02 | | | | | | | | | | | | | | | | | | % 147.36/21.02 | | | | | | | | | | | | | | | | | Case 2: % 147.36/21.02 | | | | | | | | | | | | | | | | | | % 147.36/21.02 | | | | | | | | | | | | | | | | | | (1666) all_56_31 = e3 % 147.36/21.02 | | | | | | | | | | | | | | | | | | (1667) all_56_25 = e0 % 147.36/21.02 | | | | | | | | | | | | | | | | | | % 147.36/21.02 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (447), (1667) imply: % 147.36/21.02 | | | | | | | | | | | | | | | | | | (1668) all_52_3 = e0 % 147.36/21.02 | | | | | | | | | | | | | | | | | | % 147.36/21.02 | | | | | | | | | | | | | | | | | | SIMP: (1668) implies: % 147.36/21.02 | | | | | | | | | | | | | | | | | | (1669) all_52_3 = e0 % 147.36/21.02 | | | | | | | | | | | | | | | | | | % 147.36/21.02 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (544), (1666) imply: % 147.36/21.02 | | | | | | | | | | | | | | | | | | (1670) all_4_2 = e3 % 147.36/21.02 | | | | | | | | | | | | | | | | | | % 147.36/21.02 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (530), (1670) imply: % 147.36/21.02 | | | | | | | | | | | | | | | | | | (1671) all_26_2 = e3 % 147.36/21.02 | | | | | | | | | | | | | | | | | | % 147.36/21.02 | | | | | | | | | | | | | | | | | | REDUCE: (188), (1669) imply: % 147.36/21.02 | | | | | | | | | | | | | | | | | | (1672) ~ (all_52_7 = e0) % 147.36/21.02 | | | | | | | | | | | | | | | | | | % 147.36/21.02 | | | | | | | | | | | | | | | | | | SIMP: (1672) implies: % 147.36/21.02 | | | | | | | | | | | | | | | | | | (1673) ~ (all_52_7 = e0) % 147.36/21.02 | | | | | | | | | | | | | | | | | | % 147.36/21.02 | | | | | | | | | | | | | | | | | | REDUCE: (187), (1669) imply: % 147.36/21.02 | | | | | | | | | | | | | | | | | | (1674) ~ (all_52_11 = e0) % 147.36/21.02 | | | | | | | | | | | | | | | | | | % 147.36/21.02 | | | | | | | | | | | | | | | | | | SIMP: (1674) implies: % 147.36/21.02 | | | | | | | | | | | | | | | | | | (1675) ~ (all_52_11 = e0) % 147.36/21.02 | | | | | | | | | | | | | | | | | | % 147.36/21.02 | | | | | | | | | | | | | | | | | | REDUCE: (561), (1669) imply: % 147.36/21.02 | | | | | | | | | | | | | | | | | | (1676) ~ (all_10_2 = e0) % 147.36/21.02 | | | | | | | | | | | | | | | | | | % 147.36/21.02 | | | | | | | | | | | | | | | | | | SIMP: (1676) implies: % 147.36/21.02 | | | | | | | | | | | | | | | | | | (1677) ~ (all_10_2 = e0) % 147.36/21.02 | | | | | | | | | | | | | | | | | | % 147.36/21.02 | | | | | | | | | | | | | | | | | | REDUCE: (588), (1670) imply: % 147.36/21.02 | | | | | | | | | | | | | | | | | | (1678) ~ (all_52_11 = e3) % 147.36/21.02 | | | | | | | | | | | | | | | | | | % 147.36/21.02 | | | | | | | | | | | | | | | | | | REDUCE: (591), (1670) imply: % 147.36/21.02 | | | | | | | | | | | | | | | | | | (1679) ~ (all_52_14 = e3) % 147.36/21.02 | | | | | | | | | | | | | | | | | | % 147.36/21.02 | | | | | | | | | | | | | | | | | | REDUCE: (38), (1670) imply: % 147.36/21.02 | | | | | | | | | | | | | | | | | | (1680) op(e3, e3) = all_4_1 % 147.36/21.02 | | | | | | | | | | | | | | | | | | % 147.36/21.02 | | | | | | | | | | | | | | | | | | REDUCE: (36), (1670) imply: % 147.36/21.02 | | | | | | | | | | | | | | | | | | (1681) op(e0, e0) = e3 % 147.36/21.02 | | | | | | | | | | | | | | | | | | % 147.36/21.02 | | | | | | | | | | | | | | | | | | REF_CLOSE: (41), (43), (46), (48), (51), (160), (168), (169), % 147.36/21.02 | | | | | | | | | | | | | | | | | | (174), (188), (193), (238), (241), (242), (247), % 147.36/21.02 | | | | | | | | | | | | | | | | | | (250), (252), (291), (292), (293), (294), (297), % 147.36/21.02 | | | | | | | | | | | | | | | | | | (298), (299), (336), (338), (339), (343), (344), % 147.36/21.02 | | | | | | | | | | | | | | | | | | (345), (365), (374), (380), (381), (401), (402), % 147.36/21.02 | | | | | | | | | | | | | | | | | | (407), (419), (429), (435), (443), (459), (476), % 147.36/21.02 | | | | | | | | | | | | | | | | | | (482), (541), (542), (543), (545), (546), (549), % 147.36/21.02 | | | | | | | | | | | | | | | | | | (551), (553), (554), (559), (565), (567), (569), % 147.36/21.02 | | | | | | | | | | | | | | | | | | (573), (575), (580), (582), (585), (587), (619), % 147.36/21.02 | | | | | | | | | | | | | | | | | | (622), (657), (768), (770), (778), (1560), (1573), % 147.36/21.02 | | | | | | | | | | | | | | | | | | (1610), (1614), (1615), (1617), (1619), (1621), % 147.36/21.02 | | | | | | | | | | | | | | | | | | (1622), (1671), (1673), (1675), (1677), (1678), % 147.36/21.02 | | | | | | | | | | | | | | | | | | (1679), (1680), (1681), (function-axioms) are % 147.36/21.02 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #360. % 147.36/21.02 | | | | | | | | | | | | | | | | | | % 147.36/21.02 | | | | | | | | | | | | | | | | | End of split % 147.36/21.02 | | | | | | | | | | | | | | | | | % 147.36/21.02 | | | | | | | | | | | | | | | | Case 2: % 147.36/21.02 | | | | | | | | | | | | | | | | | % 147.36/21.02 | | | | | | | | | | | | | | | | | (1682) all_56_31 = e1 % 147.36/21.02 | | | | | | | | | | | | | | | | | (1683) all_56_29 = e0 % 147.36/21.02 | | | | | | | | | | | | | | | | | % 147.36/21.02 | | | | | | | | | | | | | | | | | COMBINE_EQS: (357), (1683) imply: % 147.36/21.02 | | | | | | | | | | | | | | | | | (1684) all_52_11 = e0 % 147.36/21.02 | | | | | | | | | | | | | | | | | % 147.36/21.02 | | | | | | | | | | | | | | | | | SIMP: (1684) implies: % 147.36/21.02 | | | | | | | | | | | | | | | | | (1685) all_52_11 = e0 % 147.36/21.02 | | | | | | | | | | | | | | | | | % 147.36/21.02 | | | | | | | | | | | | | | | | | REF_CLOSE: (37), (38), (41), (43), (173), (176), (187), % 147.36/21.02 | | | | | | | | | | | | | | | | | (192), (206), (207), (239), (240), (242), (292), % 147.36/21.02 | | | | | | | | | | | | | | | | | (293), (374), (381), (435), (478), (480), (541), % 147.36/21.02 | | | | | | | | | | | | | | | | | (544), (585), (622), (767), (772), (1573), (1661), % 147.36/21.02 | | | | | | | | | | | | | | | | | (1682), (1685), (function-axioms) are inconsistent % 147.36/21.02 | | | | | | | | | | | | | | | | | by sub-proof #462. % 147.36/21.02 | | | | | | | | | | | | | | | | | % 147.36/21.02 | | | | | | | | | | | | | | | | End of split % 147.36/21.02 | | | | | | | | | | | | | | | | % 147.36/21.02 | | | | | | | | | | | | | | | End of split % 147.36/21.02 | | | | | | | | | | | | | | | % 147.36/21.02 | | | | | | | | | | | | | | End of split % 147.36/21.02 | | | | | | | | | | | | | | % 147.36/21.02 | | | | | | | | | | | | | Case 2: % 147.36/21.02 | | | | | | | | | | | | | | % 147.36/21.02 | | | | | | | | | | | | | | (1686) all_36_1 = e3 % 147.36/21.02 | | | | | | | | | | | | | | (1687) ~ (all_36_0 = e0) | ~ (all_36_2 = e2) % 147.36/21.02 | | | | | | | | | | | | | | % 147.36/21.02 | | | | | | | | | | | | | | COMBINE_EQS: (652), (1686) imply: % 147.36/21.02 | | | | | | | | | | | | | | (1688) all_6_1 = e3 % 147.36/21.02 | | | | | | | | | | | | | | % 147.36/21.02 | | | | | | | | | | | | | | REDUCE: (43), (1688) imply: % 147.36/21.02 | | | | | | | | | | | | | | (1689) op(all_6_2, all_6_2) = e3 % 147.36/21.02 | | | | | | | | | | | | | | % 147.36/21.02 | | | | | | | | | | | | | | REDUCE: (42), (1688) imply: % 147.36/21.02 | | | | | | | | | | | | | | (1690) op(e1, e3) = all_6_0 % 147.36/21.02 | | | | | | | | | | | | | | % 147.36/21.02 | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_2, % 147.36/21.02 | | | | | | | | | | | | | | all_6_0, e3, e1, simplifying with (211), (1690) % 147.36/21.02 | | | | | | | | | | | | | | gives: % 147.36/21.02 | | | | | | | | | | | | | | (1691) all_52_2 = all_6_0 % 147.36/21.02 | | | | | | | | | | | | | | % 147.36/21.02 | | | | | | | | | | | | | | COMBINE_EQS: (471), (1691) imply: % 147.36/21.02 | | | | | | | | | | | | | | (1692) all_54_8 = all_6_0 % 147.36/21.02 | | | | | | | | | | | | | | % 147.36/21.02 | | | | | | | | | | | | | | COMBINE_EQS: (381), (1691) imply: % 147.36/21.02 | | | | | | | | | | | | | | (1693) all_56_17 = all_6_0 % 147.36/21.02 | | | | | | | | | | | | | | % 147.36/21.02 | | | | | | | | | | | | | | COMBINE_EQS: (553), (1691) imply: % 147.36/21.02 | | | | | | | | | | | | | | (1694) all_58_6 = all_6_0 % 147.36/21.02 | | | | | | | | | | | | | | % 147.36/21.02 | | | | | | | | | | | | | | REDUCE: (197), (1691) imply: % 147.36/21.02 | | | | | | | | | | | | | | (1695) ~ (all_52_1 = all_6_0) % 147.36/21.02 | | | | | | | | | | | | | | % 147.36/21.02 | | | | | | | | | | | | | | REDUCE: (192), (1691) imply: % 147.36/21.02 | | | | | | | | | | | | | | (1696) ~ (all_52_3 = all_6_0) % 147.36/21.02 | | | | | | | | | | | | | | % 147.36/21.02 | | | | | | | | | | | | | | SIMP: (1696) implies: % 147.36/21.02 | | | | | | | | | | | | | | (1697) ~ (all_52_3 = all_6_0) % 147.36/21.02 | | | | | | | | | | | | | | % 147.36/21.02 | | | | | | | | | | | | | | REDUCE: (191), (1691) imply: % 147.36/21.02 | | | | | | | | | | | | | | (1698) ~ (all_52_6 = all_6_0) % 147.36/21.02 | | | | | | | | | | | | | | % 147.36/21.02 | | | | | | | | | | | | | | SIMP: (1698) implies: % 147.36/21.02 | | | | | | | | | | | | | | (1699) ~ (all_52_6 = all_6_0) % 147.36/21.02 | | | | | | | | | | | | | | % 147.36/21.02 | | | | | | | | | | | | | | REDUCE: (189), (1691) imply: % 147.36/21.02 | | | | | | | | | | | | | | (1700) ~ (all_52_14 = all_6_0) % 147.36/21.02 | | | | | | | | | | | | | | % 147.36/21.02 | | | | | | | | | | | | | | SIMP: (1700) implies: % 147.36/21.02 | | | | | | | | | | | | | | (1701) ~ (all_52_14 = all_6_0) % 147.36/21.02 | | | | | | | | | | | | | | % 147.36/21.02 | | | | | | | | | | | | | | REDUCE: (559), (1691) imply: % 147.36/21.02 | | | | | | | | | | | | | | (1702) ~ (all_10_2 = all_6_0) % 147.36/21.02 | | | | | | | | | | | | | | % 147.36/21.02 | | | | | | | | | | | | | | SIMP: (1702) implies: % 147.36/21.02 | | | | | | | | | | | | | | (1703) ~ (all_10_2 = all_6_0) % 147.36/21.02 | | | | | | | | | | | | | | % 147.36/21.02 | | | | | | | | | | | | | | REDUCE: (569), (1691) imply: % 147.36/21.02 | | | | | | | | | | | | | | (1704) ~ (all_6_0 = all_6_2) % 147.36/21.02 | | | | | | | | | | | | | | % 147.36/21.02 | | | | | | | | | | | | | | BETA: splitting (124) gives: % 147.36/21.02 | | | | | | | | | | | | | | % 147.36/21.02 | | | | | | | | | | | | | | Case 1: % 147.36/21.02 | | | | | | | | | | | | | | | % 147.36/21.02 | | | | | | | | | | | | | | | (1705) ~ (all_38_1 = e2) % 147.36/21.02 | | | | | | | | | | | | | | | % 147.36/21.02 | | | | | | | | | | | | | | | REDUCE: (684), (1705) imply: % 147.36/21.03 | | | | | | | | | | | | | | | (1706) ~ (all_10_1 = e2) % 147.36/21.03 | | | | | | | | | | | | | | | % 147.36/21.03 | | | | | | | | | | | | | | | BETA: splitting (292) gives: % 147.36/21.03 | | | | | | | | | | | | | | | % 147.36/21.03 | | | | | | | | | | | | | | | Case 1: % 147.36/21.03 | | | | | | | | | | | | | | | | % 147.36/21.03 | | | | | | | | | | | | | | | | (1707) ~ (all_56_21 = e2) % 147.36/21.03 | | | | | | | | | | | | | | | | % 147.36/21.03 | | | | | | | | | | | | | | | | REDUCE: (374), (1707) imply: % 147.36/21.03 | | | | | | | | | | | | | | | | (1708) ~ (all_6_2 = e2) % 147.36/21.03 | | | | | | | | | | | | | | | | % 147.36/21.03 | | | | | | | | | | | | | | | | BETA: splitting (294) gives: % 147.36/21.03 | | | | | | | | | | | | | | | | % 147.36/21.03 | | | | | | | | | | | | | | | | Case 1: % 147.36/21.03 | | | | | | | | | | | | | | | | | % 147.36/21.03 | | | | | | | | | | | | | | | | | (1709) ~ (all_56_11 = e0) % 147.36/21.03 | | | | | | | | | | | | | | | | | % 147.36/21.03 | | | | | | | | | | | | | | | | | REDUCE: (545), (1709) imply: % 147.36/21.03 | | | | | | | | | | | | | | | | | (1710) ~ (all_8_2 = e0) % 147.36/21.03 | | | | | | | | | | | | | | | | | % 147.36/21.03 | | | | | | | | | | | | | | | | | BETA: splitting (288) gives: % 147.36/21.03 | | | | | | | | | | | | | | | | | % 147.36/21.03 | | | | | | | | | | | | | | | | | Case 1: % 147.36/21.03 | | | | | | | | | | | | | | | | | | % 147.36/21.03 | | | | | | | | | | | | | | | | | | (1711) ~ (all_56_31 = e1) % 147.36/21.03 | | | | | | | | | | | | | | | | | | % 147.36/21.03 | | | | | | | | | | | | | | | | | | REDUCE: (544), (1711) imply: % 147.36/21.03 | | | | | | | | | | | | | | | | | | (1712) ~ (all_4_2 = e1) % 147.36/21.03 | | | | | | | | | | | | | | | | | | % 147.36/21.03 | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (36), (38), (41), (46), (47), (48), (51), % 147.36/21.03 | | | | | | | | | | | | | | | | | | (52), (53), (161), (168), (171), (174), (181), % 147.36/21.03 | | | | | | | | | | | | | | | | | | (182), (193), (194), (212), (237), (242), (243), % 147.36/21.03 | | | | | | | | | | | | | | | | | | (244), (245), (247), (251), (252), (287), (291), % 147.36/21.03 | | | | | | | | | | | | | | | | | | (293), (295), (296), (297), (298), (299), (318), % 147.36/21.03 | | | | | | | | | | | | | | | | | | (320), (321), (326), (329), (330), (331), (335), % 147.36/21.03 | | | | | | | | | | | | | | | | | | (337), (343), (344), (365), (366), (374), (380), % 147.36/21.03 | | | | | | | | | | | | | | | | | | (386), (389), (401), (402), (407), (408), (419), % 147.36/21.03 | | | | | | | | | | | | | | | | | | (425), (429), (431), (457), (469), (473), (540), % 147.36/21.03 | | | | | | | | | | | | | | | | | | (541), (542), (543), (544), (545), (546), (547), % 147.36/21.03 | | | | | | | | | | | | | | | | | | (548), (549), (550), (551), (552), (554), (555), % 147.36/21.03 | | | | | | | | | | | | | | | | | | (557), (561), (563), (565), (568), (571), (573), % 147.36/21.03 | | | | | | | | | | | | | | | | | | (575), (577), (580), (582), (583), (585), (587), % 147.36/21.03 | | | | | | | | | | | | | | | | | | (589), (590), (612), (622), (623), (627), (769), % 147.36/21.03 | | | | | | | | | | | | | | | | | | (774), (776), (778), (1567), (1571), (1689), % 147.36/21.03 | | | | | | | | | | | | | | | | | | (1692), (1693), (1694), (1695), (1699), (1701), % 147.36/21.03 | | | | | | | | | | | | | | | | | | (1703), (1704), (1706), (1708), (1710), (1712), % 147.36/21.03 | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 147.36/21.03 | | | | | | | | | | | | | | | | | | #442. % 147.36/21.03 | | | | | | | | | | | | | | | | | | % 147.36/21.03 | | | | | | | | | | | | | | | | | Case 2: % 147.36/21.03 | | | | | | | | | | | | | | | | | | % 147.36/21.03 | | | | | | | | | | | | | | | | | | (1713) all_56_31 = e1 % 147.36/21.03 | | | | | | | | | | | | | | | | | | (1714) all_56_29 = e0 % 147.36/21.03 | | | | | | | | | | | | | | | | | | % 147.36/21.03 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (357), (1714) imply: % 147.36/21.03 | | | | | | | | | | | | | | | | | | (1715) all_52_11 = e0 % 147.36/21.03 | | | | | | | | | | | | | | | | | | % 147.36/21.03 | | | | | | | | | | | | | | | | | | SIMP: (1715) implies: % 147.36/21.03 | | | | | | | | | | | | | | | | | | (1716) all_52_11 = e0 % 147.36/21.03 | | | | | | | | | | | | | | | | | | % 147.36/21.03 | | | | | | | | | | | | | | | | | | REF_CLOSE: (37), (38), (41), (187), (207), (240), (242), % 147.36/21.03 | | | | | | | | | | | | | | | | | | (293), (374), (478), (541), (544), (585), (622), % 147.36/21.03 | | | | | | | | | | | | | | | | | | (767), (772), (1689), (1693), (1697), (1708), % 147.36/21.03 | | | | | | | | | | | | | | | | | | (1713), (1716), (function-axioms) are inconsistent % 147.36/21.03 | | | | | | | | | | | | | | | | | | by sub-proof #436. % 147.36/21.03 | | | | | | | | | | | | | | | | | | % 147.36/21.03 | | | | | | | | | | | | | | | | | End of split % 147.36/21.03 | | | | | | | | | | | | | | | | | % 147.36/21.03 | | | | | | | | | | | | | | | | Case 2: % 147.36/21.03 | | | | | | | | | | | | | | | | | % 147.36/21.03 | | | | | | | | | | | | | | | | | (1717) all_56_15 = e2 % 147.36/21.03 | | | | | | | | | | | | | | | | | (1718) all_56_11 = e0 % 147.36/21.03 | | | | | | | | | | | | | | | | | % 147.36/21.03 | | | | | | | | | | | | | | | | | COMBINE_EQS: (545), (1718) imply: % 147.36/21.03 | | | | | | | | | | | | | | | | | (1719) all_8_2 = e0 % 147.36/21.03 | | | | | | | | | | | | | | | | | % 147.36/21.03 | | | | | | | | | | | | | | | | | COMBINE_EQS: (443), (1717) imply: % 147.36/21.03 | | | | | | | | | | | | | | | | | (1720) all_52_13 = e2 % 147.36/21.03 | | | | | | | | | | | | | | | | | % 147.36/21.03 | | | | | | | | | | | | | | | | | REDUCE: (158), (1720) imply: % 147.36/21.03 | | | | | | | | | | | | | | | | | (1721) ~ (all_52_14 = e2) % 147.36/21.03 | | | | | | | | | | | | | | | | | % 147.36/21.03 | | | | | | | | | | | | | | | | | SIMP: (1721) implies: % 147.36/21.03 | | | | | | | | | | | | | | | | | (1722) ~ (all_52_14 = e2) % 147.36/21.03 | | | | | | | | | | | | | | | | | % 147.36/21.03 | | | | | | | | | | | | | | | | | REDUCE: (590), (1720) imply: % 147.36/21.03 | | | | | | | | | | | | | | | | | (1723) ~ (all_4_2 = e2) % 147.36/21.03 | | | | | | | | | | | | | | | | | % 147.36/21.03 | | | | | | | | | | | | | | | | | SIMP: (1723) implies: % 147.36/21.03 | | | | | | | | | | | | | | | | | (1724) ~ (all_4_2 = e2) % 147.36/21.03 | | | | | | | | | | | | | | | | | % 147.36/21.03 | | | | | | | | | | | | | | | | | REDUCE: (48), (1719) imply: % 147.36/21.03 | | | | | | | | | | | | | | | | | (1725) op(e0, e0) = all_8_1 % 147.36/21.03 | | | | | | | | | | | | | | | | | % 147.36/21.03 | | | | | | | | | | | | | | | | | BETA: splitting (326) gives: % 147.36/21.03 | | | | | | | | | | | | | | | | | % 147.36/21.03 | | | | | | | | | | | | | | | | | Case 1: % 147.36/21.03 | | | | | | | | | | | | | | | | | | % 147.36/21.03 | | | | | | | | | | | | | | | | | | (1726) all_58_6 = e2 % 147.36/21.03 | | | | | | | | | | | | | | | | | | % 147.36/21.03 | | | | | | | | | | | | | | | | | | REF_CLOSE: (1567), (1694), (1726) are inconsistent by % 147.36/21.03 | | | | | | | | | | | | | | | | | | sub-proof #461. % 147.36/21.03 | | | | | | | | | | | | | | | | | | % 147.36/21.03 | | | | | | | | | | | | | | | | | Case 2: % 147.36/21.03 | | | | | | | | | | | | | | | | | | % 147.36/21.03 | | | | | | | | | | | | | | | | | | (1727) all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2 % 147.36/21.03 | | | | | | | | | | | | | | | | | | % 147.36/21.03 | | | | | | | | | | | | | | | | | | BETA: splitting (1727) gives: % 147.36/21.03 | | | | | | | | | | | | | | | | | | % 147.36/21.03 | | | | | | | | | | | | | | | | | | Case 1: % 147.36/21.03 | | | | | | | | | | | | | | | | | | | % 147.36/21.03 | | | | | | | | | | | | | | | | | | | % 147.36/21.03 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_4_2, % 147.36/21.03 | | | | | | | | | | | | | | | | | | | all_8_1, e0, e0, simplifying with (36), (1725) % 147.36/21.03 | | | | | | | | | | | | | | | | | | | gives: % 147.36/21.03 | | | | | | | | | | | | | | | | | | | (1728) all_8_1 = all_4_2 % 147.36/21.03 | | | | | | | | | | | | | | | | | | | % 147.36/21.03 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (38), (237), (540), (627), (769), (778), (1565), % 147.36/21.03 | | | | | | | | | | | | | | | | | | | (1724), (1725), (1728), (function-axioms) are % 147.36/21.03 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #359. % 147.36/21.03 | | | | | | | | | | | | | | | | | | | % 147.36/21.03 | | | | | | | | | | | | | | | | | | Case 2: % 147.36/21.03 | | | | | | | | | | | | | | | | | | | % 147.36/21.03 | | | | | | | | | | | | | | | | | | | (1729) all_58_8 = e2 | all_58_11 = e2 % 147.36/21.03 | | | | | | | | | | | | | | | | | | | % 147.36/21.03 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (550), (552), (1708), (1722), (1729) are % 147.36/21.03 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #511. % 147.36/21.03 | | | | | | | | | | | | | | | | | | | % 147.36/21.03 | | | | | | | | | | | | | | | | | | End of split % 147.36/21.03 | | | | | | | | | | | | | | | | | | % 147.36/21.03 | | | | | | | | | | | | | | | | | End of split % 147.36/21.03 | | | | | | | | | | | | | | | | | % 147.36/21.03 | | | | | | | | | | | | | | | | End of split % 147.36/21.03 | | | | | | | | | | | | | | | | % 147.36/21.03 | | | | | | | | | | | | | | | Case 2: % 147.36/21.03 | | | | | | | | | | | | | | | | % 147.36/21.03 | | | | | | | | | | | | | | | | (1730) all_56_21 = e2 % 147.36/21.03 | | | | | | | | | | | | | | | | (1731) all_56_19 = e1 % 147.36/21.03 | | | | | | | | | | | | | | | | % 147.36/21.03 | | | | | | | | | | | | | | | | COMBINE_EQS: (435), (1731) imply: % 147.36/21.03 | | | | | | | | | | | | | | | | (1732) all_52_6 = e1 % 147.36/21.03 | | | | | | | | | | | | | | | | % 147.36/21.03 | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (46), (48), (244), (287), (324), (374), % 147.36/21.03 | | | | | | | | | | | | | | | | (380), (532), (544), (545), (546), (550), (552), % 147.36/21.03 | | | | | | | | | | | | | | | | (580), (591), (617), (762), (1687), (1689), % 147.36/21.03 | | | | | | | | | | | | | | | | (1692), (1694), (1699), (1701), (1703), (1704), % 147.36/21.03 | | | | | | | | | | | | | | | | (1730), (1732), (function-axioms) are inconsistent % 147.36/21.03 | | | | | | | | | | | | | | | | by sub-proof #431. % 147.36/21.03 | | | | | | | | | | | | | | | | % 147.36/21.03 | | | | | | | | | | | | | | | End of split % 147.36/21.03 | | | | | | | | | | | | | | | % 147.36/21.03 | | | | | | | | | | | | | | Case 2: % 147.36/21.03 | | | | | | | | | | | | | | | % 147.36/21.03 | | | | | | | | | | | | | | | (1733) all_38_1 = e2 % 147.36/21.03 | | | | | | | | | | | | | | | (1734) ~ (all_38_0 = e0) | ~ (all_38_2 = e1) % 147.36/21.03 | | | | | | | | | | | | | | | % 147.36/21.03 | | | | | | | | | | | | | | | COMBINE_EQS: (684), (1733) imply: % 147.36/21.03 | | | | | | | | | | | | | | | (1735) all_10_1 = e2 % 147.36/21.03 | | | | | | | | | | | | | | | % 147.36/21.03 | | | | | | | | | | | | | | | REDUCE: (53), (1735) imply: % 147.36/21.03 | | | | | | | | | | | | | | | (1736) op(all_10_2, all_10_2) = e2 % 147.36/21.03 | | | | | | | | | | | | | | | % 147.36/21.03 | | | | | | | | | | | | | | | REDUCE: (52), (1735) imply: % 147.36/21.03 | | | | | | | | | | | | | | | (1737) op(e3, e2) = all_10_0 % 147.36/21.03 | | | | | | | | | | | | | | | % 147.36/21.03 | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (36), (37), (38), (41), (46), (48), % 147.36/21.03 | | | | | | | | | | | | | | | (51), (53), (158), (166), (174), (181), (182), % 147.36/21.03 | | | | | | | | | | | | | | | (184), (187), (188), (194), (196), (207), (218), % 147.36/21.03 | | | | | | | | | | | | | | | (238), (240), (241), (242), (243), (244), (247), % 147.36/21.03 | | | | | | | | | | | | | | | (248), (251), (252), (287), (288), (290), (291), % 147.36/21.03 | | | | | | | | | | | | | | | (292), (293), (294), (295), (296), (297), (298), % 147.36/21.03 | | | | | | | | | | | | | | | (299), (324), (326), (336), (344), (357), (365), % 147.36/21.03 | | | | | | | | | | | | | | | (366), (374), (380), (401), (402), (408), (419), % 147.36/21.03 | | | | | | | | | | | | | | | (425), (429), (431), (435), (443), (447), (457), % 147.36/21.03 | | | | | | | | | | | | | | | (463), (473), (476), (478), (482), (532), (533), % 147.36/21.03 | | | | | | | | | | | | | | | (541), (542), (543), (544), (545), (546), (549), % 147.36/21.03 | | | | | | | | | | | | | | | (550), (552), (554), (555), (557), (561), (563), % 147.36/21.03 | | | | | | | | | | | | | | | (568), (570), (571), (573), (580), (585), (587), % 147.36/21.03 | | | | | | | | | | | | | | | (588), (591), (612), (617), (618), (622), (627), % 147.36/21.03 | | | | | | | | | | | | | | | (723), (762), (767), (770), (772), (776), (1567), % 147.36/21.03 | | | | | | | | | | | | | | | (1687), (1689), (1692), (1693), (1694), (1695), % 147.36/21.03 | | | | | | | | | | | | | | | (1697), (1699), (1701), (1703), (1704), (1734), % 147.36/21.03 | | | | | | | | | | | | | | | (1736), (1737), (function-axioms) are inconsistent % 147.36/21.03 | | | | | | | | | | | | | | | by sub-proof #411. % 147.36/21.03 | | | | | | | | | | | | | | | % 147.36/21.03 | | | | | | | | | | | | | | End of split % 147.36/21.03 | | | | | | | | | | | | | | % 147.36/21.03 | | | | | | | | | | | | | End of split % 147.36/21.03 | | | | | | | | | | | | | % 147.36/21.03 | | | | | | | | | | | | Case 2: % 147.36/21.03 | | | | | | | | | | | | | % 147.36/21.03 | | | | | | | | | | | | | (1738) all_32_1 = e1 % 147.36/21.03 | | | | | | | | | | | | | (1739) ~ (all_32_0 = e0) | ~ (all_32_2 = e2) % 147.36/21.03 | | | | | | | | | | | | | % 147.36/21.03 | | | | | | | | | | | | | COMBINE_EQS: (682), (1738) imply: % 147.36/21.03 | | | | | | | | | | | | | (1740) all_10_1 = e1 % 147.36/21.03 | | | | | | | | | | | | | % 147.36/21.03 | | | | | | | | | | | | | SIMP: (1740) implies: % 147.36/21.03 | | | | | | | | | | | | | (1741) all_10_1 = e1 % 147.36/21.03 | | | | | | | | | | | | | % 147.36/21.03 | | | | | | | | | | | | | REDUCE: (53), (1741) imply: % 147.36/21.03 | | | | | | | | | | | | | (1742) op(all_10_2, all_10_2) = e1 % 147.36/21.03 | | | | | | | | | | | | | % 147.36/21.03 | | | | | | | | | | | | | REDUCE: (52), (1741) imply: % 147.36/21.03 | | | | | | | | | | | | | (1743) op(e3, e1) = all_10_0 % 147.36/21.03 | | | | | | | | | | | | | % 147.36/21.03 | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_8, % 147.36/21.03 | | | | | | | | | | | | | all_10_0, e1, e3, simplifying with (217), (1743) % 147.36/21.03 | | | | | | | | | | | | | gives: % 147.36/21.03 | | | | | | | | | | | | | (1744) all_52_8 = all_10_0 % 147.36/21.03 | | | | | | | | | | | | | % 147.36/21.03 | | | | | | | | | | | | | COMBINE_EQS: (459), (1744) imply: % 147.36/21.03 | | | | | | | | | | | | | (1745) all_54_2 = all_10_0 % 147.36/21.03 | | | | | | | | | | | | | % 147.36/21.03 | | | | | | | | | | | | | COMBINE_EQS: (429), (1744) imply: % 147.36/21.03 | | | | | | | | | | | | | (1746) all_56_5 = all_10_0 % 147.36/21.03 | | | | | | | | | | | | | % 147.36/21.03 | | | | | | | | | | | | | COMBINE_EQS: (407), (1744) imply: % 147.36/21.03 | | | | | | | | | | | | | (1747) all_58_4 = all_10_0 % 147.36/21.03 | | | | | | | | | | | | | % 147.36/21.03 | | | | | | | | | | | | | REDUCE: (182), (1744) imply: % 147.36/21.03 | | | | | | | | | | | | | (1748) ~ (all_52_4 = all_10_0) % 147.36/21.03 | | | | | | | | | | | | | % 147.36/21.03 | | | | | | | | | | | | | REDUCE: (171), (1744) imply: % 147.36/21.03 | | | | | | | | | | | | | (1749) ~ (all_52_9 = all_10_0) % 147.36/21.03 | | | | | | | | | | | | | % 147.36/21.03 | | | | | | | | | | | | | SIMP: (1749) implies: % 147.36/21.03 | | | | | | | | | | | | | (1750) ~ (all_52_9 = all_10_0) % 147.36/21.03 | | | | | | | | | | | | | % 147.36/21.03 | | | | | | | | | | | | | REDUCE: (169), (1744) imply: % 147.36/21.03 | | | | | | | | | | | | | (1751) ~ (all_52_11 = all_10_0) % 147.36/21.03 | | | | | | | | | | | | | % 147.36/21.03 | | | | | | | | | | | | | SIMP: (1751) implies: % 147.36/21.03 | | | | | | | | | | | | | (1752) ~ (all_52_11 = all_10_0) % 147.36/21.03 | | | | | | | | | | | | | % 147.36/21.03 | | | | | | | | | | | | | REDUCE: (168), (1744) imply: % 147.36/21.03 | | | | | | | | | | | | | (1753) ~ (all_52_12 = all_10_0) % 147.36/21.03 | | | | | | | | | | | | | % 147.36/21.03 | | | | | | | | | | | | | SIMP: (1753) implies: % 147.36/21.03 | | | | | | | | | | | | | (1754) ~ (all_52_12 = all_10_0) % 147.36/21.03 | | | | | | | | | | | | | % 147.36/21.03 | | | | | | | | | | | | | REDUCE: (565), (1744) imply: % 147.36/21.03 | | | | | | | | | | | | | (1755) ~ (all_10_0 = all_10_2) % 147.36/21.03 | | | | | | | | | | | | | % 147.36/21.03 | | | | | | | | | | | | | REDUCE: (582), (1744) imply: % 147.36/21.03 | | | | | | | | | | | | | (1756) ~ (all_10_0 = all_6_2) % 147.36/21.03 | | | | | | | | | | | | | % 147.36/21.03 | | | | | | | | | | | | | BETA: splitting (119) gives: % 147.36/21.03 | | | | | | | | | | | | | % 147.36/21.03 | | | | | | | | | | | | | Case 1: % 147.36/21.03 | | | | | | | | | | | | | | % 147.36/21.03 | | | | | | | | | | | | | | (1757) ~ (all_36_1 = e3) % 147.36/21.03 | | | | | | | | | | | | | | % 147.36/21.03 | | | | | | | | | | | | | | REDUCE: (652), (1757) imply: % 147.36/21.03 | | | | | | | | | | | | | | (1758) ~ (all_6_1 = e3) % 147.36/21.03 | | | | | | | | | | | | | | % 147.36/21.03 | | | | | | | | | | | | | | BETA: splitting (292) gives: % 147.36/21.03 | | | | | | | | | | | | | | % 147.36/21.03 | | | | | | | | | | | | | | Case 1: % 147.36/21.03 | | | | | | | | | | | | | | | % 147.36/21.03 | | | | | | | | | | | | | | | (1759) ~ (all_56_21 = e2) % 147.36/21.03 | | | | | | | | | | | | | | | % 147.36/21.03 | | | | | | | | | | | | | | | REDUCE: (374), (1759) imply: % 147.36/21.03 | | | | | | | | | | | | | | | (1760) ~ (all_6_2 = e2) % 147.36/21.03 | | | | | | | | | | | | | | | % 147.36/21.03 | | | | | | | | | | | | | | | BETA: splitting (294) gives: % 147.36/21.03 | | | | | | | | | | | | | | | % 147.36/21.03 | | | | | | | | | | | | | | | Case 1: % 147.36/21.03 | | | | | | | | | | | | | | | | % 147.36/21.03 | | | | | | | | | | | | | | | | (1761) ~ (all_56_11 = e0) % 147.36/21.03 | | | | | | | | | | | | | | | | % 147.36/21.03 | | | | | | | | | | | | | | | | REDUCE: (545), (1761) imply: % 147.36/21.03 | | | | | | | | | | | | | | | | (1762) ~ (all_8_2 = e0) % 147.36/21.03 | | | | | | | | | | | | | | | | % 147.36/21.04 | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (37), (38), (41), (46), (47), (48), % 147.36/21.04 | | | | | | | | | | | | | | | | (51), (165), (166), (193), (194), (196), (205), % 147.36/21.04 | | | | | | | | | | | | | | | | (246), (247), (248), (250), (252), (288), (293), % 147.36/21.04 | | | | | | | | | | | | | | | | (295), (296), (297), (298), (299), (318), (320), % 147.36/21.04 | | | | | | | | | | | | | | | | (321), (328), (329), (330), (331), (335), (337), % 147.36/21.04 | | | | | | | | | | | | | | | | (345), (357), (365), (374), (380), (386), (389), % 147.36/21.04 | | | | | | | | | | | | | | | | (401), (402), (408), (419), (425), (431), (463), % 147.36/21.04 | | | | | | | | | | | | | | | | (467), (494), (542), (543), (544), (545), (546), % 147.36/21.04 | | | | | | | | | | | | | | | | (547), (548), (549), (550), (551), (552), (554), % 147.36/21.04 | | | | | | | | | | | | | | | | (555), (557), (561), (563), (567), (568), (571), % 147.36/21.04 | | | | | | | | | | | | | | | | (577), (580), (581), (585), (587), (612), (613), % 147.36/21.04 | | | | | | | | | | | | | | | | (617), (622), (625), (761), (769), (770), (772), % 147.36/21.04 | | | | | | | | | | | | | | | | (774), (776), (1569), (1739), (1742), (1745), % 147.36/21.04 | | | | | | | | | | | | | | | | (1746), (1747), (1748), (1750), (1752), (1754), % 147.36/21.04 | | | | | | | | | | | | | | | | (1755), (1756), (1760), (1762), (function-axioms) % 147.36/21.04 | | | | | | | | | | | | | | | | are inconsistent by sub-proof #380. % 147.36/21.04 | | | | | | | | | | | | | | | | % 147.36/21.04 | | | | | | | | | | | | | | | Case 2: % 147.36/21.04 | | | | | | | | | | | | | | | | % 147.36/21.04 | | | | | | | | | | | | | | | | (1763) all_56_11 = e0 % 147.36/21.04 | | | | | | | | | | | | | | | | % 147.36/21.04 | | | | | | | | | | | | | | | | REF_CLOSE: (36), (38), (48), (237), (294), (443), (540), % 147.36/21.04 | | | | | | | | | | | | | | | | (545), (590), (627), (769), (778), (1565), (1763), % 147.36/21.04 | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 147.36/21.04 | | | | | | | | | | | | | | | | #357. % 147.36/21.04 | | | | | | | | | | | | | | | | % 147.36/21.04 | | | | | | | | | | | | | | | End of split % 147.36/21.04 | | | | | | | | | | | | | | | % 147.36/21.04 | | | | | | | | | | | | | | Case 2: % 147.36/21.04 | | | | | | | | | | | | | | | % 147.36/21.04 | | | | | | | | | | | | | | | (1764) all_56_21 = e2 % 147.36/21.04 | | | | | | | | | | | | | | | (1765) all_56_19 = e1 % 147.36/21.04 | | | | | | | | | | | | | | | % 147.36/21.04 | | | | | | | | | | | | | | | COMBINE_EQS: (435), (1765) imply: % 147.36/21.04 | | | | | | | | | | | | | | | (1766) all_52_6 = e1 % 147.36/21.04 | | | | | | | | | | | | | | | % 147.36/21.04 | | | | | | | | | | | | | | | COMBINE_EQS: (374), (1764) imply: % 147.36/21.04 | | | | | | | | | | | | | | | (1767) all_6_2 = e2 % 147.36/21.04 | | | | | | | | | | | | | | | % 147.36/21.04 | | | | | | | | | | | | | | | SIMP: (1767) implies: % 147.36/21.04 | | | | | | | | | | | | | | | (1768) all_6_2 = e2 % 147.36/21.04 | | | | | | | | | | | | | | | % 147.36/21.04 | | | | | | | | | | | | | | | REDUCE: (573), (1766) imply: % 147.36/21.04 | | | | | | | | | | | | | | | (1769) ~ (all_8_2 = e1) % 147.36/21.04 | | | | | | | | | | | | | | | % 147.36/21.04 | | | | | | | | | | | | | | | SIMP: (1769) implies: % 147.36/21.04 | | | | | | | | | | | | | | | (1770) ~ (all_8_2 = e1) % 147.36/21.04 | | | | | | | | | | | | | | | % 147.36/21.04 | | | | | | | | | | | | | | | REDUCE: (43), (1768) imply: % 147.36/21.04 | | | | | | | | | | | | | | | (1771) op(e2, e2) = all_6_1 % 147.36/21.04 | | | | | | | | | | | | | | | % 147.36/21.04 | | | | | | | | | | | | | | | REF_CLOSE: (36), (38), (46), (48), (237), (247), (294), % 147.36/21.04 | | | | | | | | | | | | | | | (443), (540), (542), (545), (590), (627), (768), % 147.36/21.04 | | | | | | | | | | | | | | | (769), (778), (1565), (1758), (1770), (1771), % 147.36/21.04 | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 147.36/21.04 | | | | | | | | | | | | | | | #356. % 147.36/21.04 | | | | | | | | | | | | | | | % 147.36/21.04 | | | | | | | | | | | | | | End of split % 147.36/21.04 | | | | | | | | | | | | | | % 147.36/21.04 | | | | | | | | | | | | | Case 2: % 147.36/21.04 | | | | | | | | | | | | | | % 147.36/21.04 | | | | | | | | | | | | | | (1772) all_36_1 = e3 % 147.36/21.04 | | | | | | | | | | | | | | (1773) ~ (all_36_0 = e0) | ~ (all_36_2 = e2) % 147.36/21.04 | | | | | | | | | | | | | | % 147.36/21.04 | | | | | | | | | | | | | | COMBINE_EQS: (652), (1772) imply: % 147.36/21.04 | | | | | | | | | | | | | | (1774) all_6_1 = e3 % 147.36/21.04 | | | | | | | | | | | | | | % 147.36/21.04 | | | | | | | | | | | | | | SIMP: (1774) implies: % 147.36/21.04 | | | | | | | | | | | | | | (1775) all_6_1 = e3 % 147.36/21.04 | | | | | | | | | | | | | | % 147.36/21.04 | | | | | | | | | | | | | | REDUCE: (43), (1775) imply: % 147.36/21.04 | | | | | | | | | | | | | | (1776) op(all_6_2, all_6_2) = e3 % 147.36/21.04 | | | | | | | | | | | | | | % 147.36/21.04 | | | | | | | | | | | | | | REDUCE: (42), (1775) imply: % 147.36/21.04 | | | | | | | | | | | | | | (1777) op(e1, e3) = all_6_0 % 147.36/21.04 | | | | | | | | | | | | | | % 147.36/21.04 | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_2, % 147.36/21.04 | | | | | | | | | | | | | | all_6_0, e3, e1, simplifying with (211), (1777) % 147.36/21.04 | | | | | | | | | | | | | | gives: % 147.36/21.04 | | | | | | | | | | | | | | (1778) all_52_2 = all_6_0 % 147.36/21.04 | | | | | | | | | | | | | | % 147.36/21.04 | | | | | | | | | | | | | | COMBINE_EQS: (471), (1778) imply: % 147.36/21.04 | | | | | | | | | | | | | | (1779) all_54_8 = all_6_0 % 147.36/21.04 | | | | | | | | | | | | | | % 147.36/21.04 | | | | | | | | | | | | | | COMBINE_EQS: (553), (1778) imply: % 147.36/21.04 | | | | | | | | | | | | | | (1780) all_58_6 = all_6_0 % 147.36/21.04 | | | | | | | | | | | | | | % 147.36/21.04 | | | | | | | | | | | | | | REDUCE: (191), (1778) imply: % 147.36/21.04 | | | | | | | | | | | | | | (1781) ~ (all_52_6 = all_6_0) % 147.36/21.04 | | | | | | | | | | | | | | % 147.36/21.04 | | | | | | | | | | | | | | SIMP: (1781) implies: % 147.36/21.04 | | | | | | | | | | | | | | (1782) ~ (all_52_6 = all_6_0) % 147.36/21.04 | | | | | | | | | | | | | | % 147.36/21.04 | | | | | | | | | | | | | | REDUCE: (189), (1778) imply: % 147.36/21.04 | | | | | | | | | | | | | | (1783) ~ (all_52_14 = all_6_0) % 147.36/21.04 | | | | | | | | | | | | | | % 147.36/21.04 | | | | | | | | | | | | | | SIMP: (1783) implies: % 147.36/21.04 | | | | | | | | | | | | | | (1784) ~ (all_52_14 = all_6_0) % 147.36/21.04 | | | | | | | | | | | | | | % 147.36/21.04 | | | | | | | | | | | | | | REDUCE: (559), (1778) imply: % 147.36/21.04 | | | | | | | | | | | | | | (1785) ~ (all_10_2 = all_6_0) % 147.36/21.04 | | | | | | | | | | | | | | % 147.36/21.04 | | | | | | | | | | | | | | SIMP: (1785) implies: % 147.36/21.04 | | | | | | | | | | | | | | (1786) ~ (all_10_2 = all_6_0) % 147.36/21.04 | | | | | | | | | | | | | | % 147.36/21.04 | | | | | | | | | | | | | | REDUCE: (569), (1778) imply: % 147.36/21.04 | | | | | | | | | | | | | | (1787) ~ (all_6_0 = all_6_2) % 147.36/21.04 | | | | | | | | | | | | | | % 147.36/21.04 | | | | | | | | | | | | | | BETA: splitting (288) gives: % 147.36/21.04 | | | | | | | | | | | | | | % 147.36/21.04 | | | | | | | | | | | | | | Case 1: % 147.36/21.04 | | | | | | | | | | | | | | | % 147.36/21.04 | | | | | | | | | | | | | | | (1788) ~ (all_56_31 = e1) % 147.36/21.04 | | | | | | | | | | | | | | | % 147.36/21.04 | | | | | | | | | | | | | | | REDUCE: (544), (1788) imply: % 147.36/21.04 | | | | | | | | | | | | | | | (1789) ~ (all_4_2 = e1) % 147.36/21.04 | | | | | | | | | | | | | | | % 147.36/21.04 | | | | | | | | | | | | | | | BETA: splitting (290) gives: % 147.36/21.04 | | | | | | | | | | | | | | | % 147.36/21.04 | | | | | | | | | | | | | | | Case 1: % 147.36/21.04 | | | | | | | | | | | | | | | | % 147.36/21.04 | | | | | | | | | | | | | | | | (1790) ~ (all_56_31 = e3) % 147.36/21.04 | | | | | | | | | | | | | | | | % 147.36/21.04 | | | | | | | | | | | | | | | | REDUCE: (544), (1790) imply: % 147.36/21.04 | | | | | | | | | | | | | | | | (1791) ~ (all_4_2 = e3) % 147.36/21.04 | | | | | | | | | | | | | | | | % 147.36/21.04 | | | | | | | | | | | | | | | | BETA: splitting (292) gives: % 147.36/21.04 | | | | | | | | | | | | | | | | % 147.36/21.04 | | | | | | | | | | | | | | | | Case 1: % 147.36/21.04 | | | | | | | | | | | | | | | | | % 147.36/21.04 | | | | | | | | | | | | | | | | | (1792) ~ (all_56_21 = e2) % 147.36/21.04 | | | | | | | | | | | | | | | | | % 147.36/21.04 | | | | | | | | | | | | | | | | | REDUCE: (374), (1792) imply: % 147.36/21.04 | | | | | | | | | | | | | | | | | (1793) ~ (all_6_2 = e2) % 147.36/21.04 | | | | | | | | | | | | | | | | | % 147.36/21.04 | | | | | | | | | | | | | | | | | BETA: splitting (294) gives: % 147.36/21.04 | | | | | | | | | | | | | | | | | % 147.36/21.04 | | | | | | | | | | | | | | | | | Case 1: % 147.36/21.04 | | | | | | | | | | | | | | | | | | % 147.36/21.04 | | | | | | | | | | | | | | | | | | (1794) ~ (all_56_11 = e0) % 147.36/21.04 | | | | | | | | | | | | | | | | | | % 147.36/21.04 | | | | | | | | | | | | | | | | | | REDUCE: (545), (1794) imply: % 147.36/21.04 | | | | | | | | | | | | | | | | | | (1795) ~ (all_8_2 = e0) % 147.36/21.04 | | | | | | | | | | | | | | | | | | % 147.36/21.04 | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (37), (38), (41), (46), (47), (48), % 147.36/21.04 | | | | | | | | | | | | | | | | | | (51), (165), (166), (193), (194), (196), (205), % 147.36/21.04 | | | | | | | | | | | | | | | | | | (246), (247), (248), (250), (252), (288), (293), % 147.36/21.04 | | | | | | | | | | | | | | | | | | (295), (296), (297), (298), (299), (318), (320), % 147.36/21.04 | | | | | | | | | | | | | | | | | | (321), (328), (329), (330), (331), (335), (337), % 147.36/21.04 | | | | | | | | | | | | | | | | | | (345), (357), (365), (374), (380), (386), (389), % 147.36/21.04 | | | | | | | | | | | | | | | | | | (401), (402), (408), (419), (425), (431), (463), % 147.36/21.04 | | | | | | | | | | | | | | | | | | (467), (494), (542), (543), (544), (545), (546), % 147.36/21.04 | | | | | | | | | | | | | | | | | | (547), (548), (549), (550), (551), (552), (554), % 147.36/21.04 | | | | | | | | | | | | | | | | | | (555), (557), (561), (563), (567), (568), (571), % 147.36/21.04 | | | | | | | | | | | | | | | | | | (577), (580), (581), (585), (587), (612), (613), % 147.36/21.04 | | | | | | | | | | | | | | | | | | (617), (622), (625), (761), (769), (770), (772), % 147.36/21.04 | | | | | | | | | | | | | | | | | | (774), (776), (1569), (1739), (1742), (1745), % 147.36/21.04 | | | | | | | | | | | | | | | | | | (1746), (1747), (1748), (1750), (1752), (1754), % 147.36/21.04 | | | | | | | | | | | | | | | | | | (1755), (1756), (1793), (1795), (function-axioms) % 147.36/21.04 | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #380. % 147.36/21.04 | | | | | | | | | | | | | | | | | | % 147.36/21.04 | | | | | | | | | | | | | | | | | Case 2: % 147.36/21.04 | | | | | | | | | | | | | | | | | | % 147.36/21.04 | | | | | | | | | | | | | | | | | | (1796) all_56_15 = e2 % 147.36/21.04 | | | | | | | | | | | | | | | | | | % 147.36/21.04 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (443), (1796) imply: % 147.36/21.04 | | | | | | | | | | | | | | | | | | (1797) all_52_13 = e2 % 147.36/21.04 | | | | | | | | | | | | | | | | | | % 147.36/21.04 | | | | | | | | | | | | | | | | | | REDUCE: (590), (1797) imply: % 147.36/21.04 | | | | | | | | | | | | | | | | | | (1798) ~ (all_4_2 = e2) % 147.36/21.04 | | | | | | | | | | | | | | | | | | % 147.36/21.04 | | | | | | | | | | | | | | | | | | SIMP: (1798) implies: % 147.36/21.04 | | | | | | | | | | | | | | | | | | (1799) ~ (all_4_2 = e2) % 147.36/21.04 | | | | | | | | | | | | | | | | | | % 147.36/21.04 | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (38), (237), (540), (627), (1565), (1789), % 147.36/21.04 | | | | | | | | | | | | | | | | | | (1791), (1799), (function-axioms) are inconsistent % 147.36/21.04 | | | | | | | | | | | | | | | | | | by sub-proof #363. % 147.36/21.04 | | | | | | | | | | | | | | | | | | % 147.36/21.04 | | | | | | | | | | | | | | | | | End of split % 147.36/21.04 | | | | | | | | | | | | | | | | | % 147.36/21.04 | | | | | | | | | | | | | | | | Case 2: % 147.36/21.04 | | | | | | | | | | | | | | | | | % 147.36/21.04 | | | | | | | | | | | | | | | | | (1800) all_56_21 = e2 % 147.36/21.04 | | | | | | | | | | | | | | | | | (1801) all_56_19 = e1 % 147.36/21.04 | | | | | | | | | | | | | | | | | % 147.36/21.04 | | | | | | | | | | | | | | | | | COMBINE_EQS: (435), (1801) imply: % 147.36/21.04 | | | | | | | | | | | | | | | | | (1802) all_52_6 = e1 % 147.36/21.04 | | | | | | | | | | | | | | | | | % 147.36/21.04 | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (46), (48), (244), (287), (324), (374), % 147.36/21.04 | | | | | | | | | | | | | | | | | (380), (532), (544), (545), (546), (550), (552), % 147.36/21.04 | | | | | | | | | | | | | | | | | (580), (591), (617), (762), (1773), (1776), % 147.36/21.04 | | | | | | | | | | | | | | | | | (1779), (1780), (1782), (1784), (1786), (1787), % 147.36/21.04 | | | | | | | | | | | | | | | | | (1800), (1802), (function-axioms) are inconsistent % 147.36/21.04 | | | | | | | | | | | | | | | | | by sub-proof #431. % 147.36/21.04 | | | | | | | | | | | | | | | | | % 147.36/21.04 | | | | | | | | | | | | | | | | End of split % 147.36/21.04 | | | | | | | | | | | | | | | | % 147.36/21.04 | | | | | | | | | | | | | | | Case 2: % 147.36/21.04 | | | | | | | | | | | | | | | | % 147.36/21.04 | | | | | | | | | | | | | | | | (1803) all_56_31 = e3 % 147.36/21.04 | | | | | | | | | | | | | | | | (1804) all_56_25 = e0 % 147.36/21.04 | | | | | | | | | | | | | | | | % 147.36/21.04 | | | | | | | | | | | | | | | | COMBINE_EQS: (447), (1804) imply: % 147.36/21.04 | | | | | | | | | | | | | | | | (1805) all_52_3 = e0 % 147.36/21.04 | | | | | | | | | | | | | | | | % 147.36/21.04 | | | | | | | | | | | | | | | | SIMP: (1805) implies: % 147.36/21.04 | | | | | | | | | | | | | | | | (1806) all_52_3 = e0 % 147.36/21.04 | | | | | | | | | | | | | | | | % 147.36/21.04 | | | | | | | | | | | | | | | | COMBINE_EQS: (544), (1803) imply: % 147.36/21.04 | | | | | | | | | | | | | | | | (1807) all_4_2 = e3 % 147.36/21.04 | | | | | | | | | | | | | | | | % 147.36/21.04 | | | | | | | | | | | | | | | | COMBINE_EQS: (530), (1807) imply: % 147.36/21.04 | | | | | | | | | | | | | | | | (1808) all_26_2 = e3 % 147.36/21.04 | | | | | | | | | | | | | | | | % 147.36/21.04 | | | | | | | | | | | | | | | | COMBINE_EQS: (365), (1806) imply: % 147.36/21.04 | | | | | | | | | | | | | | | | (1809) all_58_12 = e0 % 147.36/21.04 | | | | | | | | | | | | | | | | % 147.36/21.04 | | | | | | | | | | | | | | | | REDUCE: (561), (1806) imply: % 147.36/21.04 | | | | | | | | | | | | | | | | (1810) ~ (all_10_2 = e0) % 147.36/21.04 | | | | | | | | | | | | | | | | % 147.36/21.04 | | | | | | | | | | | | | | | | SIMP: (1810) implies: % 147.36/21.04 | | | | | | | | | | | | | | | | (1811) ~ (all_10_2 = e0) % 147.36/21.04 | | | | | | | | | | | | | | | | % 147.36/21.04 | | | | | | | | | | | | | | | | REDUCE: (38), (1807) imply: % 147.36/21.04 | | | | | | | | | | | | | | | | (1812) op(e3, e3) = all_4_1 % 147.36/21.04 | | | | | | | | | | | | | | | | % 147.36/21.04 | | | | | | | | | | | | | | | | BETA: splitting (1560) gives: % 147.36/21.04 | | | | | | | | | | | | | | | | % 147.36/21.04 | | | | | | | | | | | | | | | | Case 1: % 147.36/21.04 | | | | | | | | | | | | | | | | | % 147.36/21.04 | | | | | | | | | | | | | | | | | (1813) ~ (all_26_1 = e2) % 147.36/21.04 | | | | | | | | | | | | | | | | | % 147.36/21.04 | | | | | | | | | | | | | | | | | REDUCE: (657), (1813) imply: % 147.36/21.04 | | | | | | | | | | | | | | | | | (1814) ~ (all_4_1 = e2) % 147.36/21.04 | | | | | | | | | | | | | | | | | % 147.36/21.04 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_10_2, % 147.36/21.04 | | | | | | | | | | | | | | | | | all_4_1, e3, e3, simplifying with (51), (1812) % 147.36/21.04 | | | | | | | | | | | | | | | | | gives: % 147.36/21.04 | | | | | | | | | | | | | | | | | (1815) all_10_2 = all_4_1 % 147.36/21.04 | | | | | | | | | | | | | | | | | % 147.36/21.04 | | | | | | | | | | | | | | | | | COMBINE_EQS: (543), (1815) imply: % 147.36/21.04 | | | | | | | | | | | | | | | | | (1816) all_54_0 = all_4_1 % 147.36/21.04 | | | | | | | | | | | | | | | | | % 147.36/21.04 | | | | | | | | | | | | | | | | | COMBINE_EQS: (546), (1815) imply: % 147.36/21.04 | | | | | | | | | | | | | | | | | (1817) all_56_1 = all_4_1 % 147.36/21.04 | | | | | | | | | | | | | | | | | % 147.36/21.04 | | | | | | | | | | | | | | | | | COMBINE_EQS: (419), (1815) imply: % 147.36/21.04 | | | | | | | | | | | | | | | | | (1818) all_58_0 = all_4_1 % 147.36/21.04 | | | | | | | | | | | | | | | | | % 147.36/21.04 | | | | | | | | | | | | | | | | | REDUCE: (1755), (1815) imply: % 147.36/21.04 | | | | | | | | | | | | | | | | | (1819) ~ (all_10_0 = all_4_1) % 147.36/21.04 | | | | | | | | | | | | | | | | | % 147.36/21.04 | | | | | | | | | | | | | | | | | REDUCE: (1811), (1815) imply: % 147.36/21.04 | | | | | | | | | | | | | | | | | (1820) ~ (all_4_1 = e0) % 147.36/21.04 | | | | | | | | | | | | | | | | | % 147.36/21.04 | | | | | | | | | | | | | | | | | BETA: splitting (344) gives: % 147.36/21.04 | | | | | | | | | | | | | | | | | % 147.36/21.04 | | | | | | | | | | | | | | | | | Case 1: % 147.36/21.04 | | | | | | | | | | | | | | | | | | % 147.36/21.04 | | | | | | | | | | | | | | | | | | (1821) all_58_0 = e2 % 147.36/21.04 | | | | | | | | | | | | | | | | | | % 147.36/21.04 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1818), (1821) imply: % 147.36/21.04 | | | | | | | | | | | | | | | | | | (1822) all_4_1 = e2 % 147.36/21.04 | | | | | | | | | | | | | | | | | | % 147.36/21.04 | | | | | | | | | | | | | | | | | | REDUCE: (1814), (1822) imply: % 147.36/21.04 | | | | | | | | | | | | | | | | | | (1823) $false % 147.36/21.04 | | | | | | | | | | | | | | | | | | % 147.36/21.04 | | | | | | | | | | | | | | | | | | CLOSE: (1823) is inconsistent. % 147.36/21.04 | | | | | | | | | | | | | | | | | | % 147.36/21.04 | | | | | | | | | | | | | | | | | Case 2: % 147.36/21.04 | | | | | | | | | | | | | | | | | | % 147.36/21.04 | | | | | | | | | | | | | | | | | | (1824) all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2 % 147.36/21.04 | | | | | | | | | | | | | | | | | | % 147.36/21.04 | | | | | | | | | | | | | | | | | | BETA: splitting (1824) gives: % 147.36/21.04 | | | | | | | | | | | | | | | | | | % 147.36/21.04 | | | | | | | | | | | | | | | | | | Case 1: % 147.36/21.04 | | | | | | | | | | | | | | | | | | | % 147.36/21.04 | | | | | | | | | | | | | | | | | | | (1825) all_58_2 = e2 % 147.36/21.04 | | | | | | | | | | | | | | | | | | | % 147.36/21.04 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (401), (1825) imply: % 147.36/21.04 | | | | | | | | | | | | | | | | | | | (1826) all_52_1 = e2 % 147.36/21.04 | | | | | | | | | | | | | | | | | | | % 147.36/21.04 | | | | | | | | | | | | | | | | | | | REDUCE: (194), (1826) imply: % 147.36/21.04 | | | | | | | | | | | | | | | | | | | (1827) ~ (all_52_9 = e2) % 147.36/21.04 | | | | | | | | | | | | | | | | | | | % 147.36/21.04 | | | | | | | | | | | | | | | | | | | SIMP: (1827) implies: % 147.36/21.04 | | | | | | | | | | | | | | | | | | | (1828) ~ (all_52_9 = e2) % 147.36/21.04 | | | | | | | | | | | | | | | | | | | % 147.36/21.04 | | | | | | | | | | | | | | | | | | | REDUCE: (193), (1826) imply: % 147.36/21.04 | | | | | | | | | | | | | | | | | | | (1829) ~ (all_52_13 = e2) % 147.36/21.04 | | | | | | | | | | | | | | | | | | | % 147.36/21.04 | | | | | | | | | | | | | | | | | | | SIMP: (1829) implies: % 147.36/21.04 | | | | | | | | | | | | | | | | | | | (1830) ~ (all_52_13 = e2) % 147.36/21.04 | | | | | | | | | | | | | | | | | | | % 147.36/21.04 | | | | | | | | | | | | | | | | | | | REDUCE: (568), (1826) imply: % 147.36/21.04 | | | | | | | | | | | | | | | | | | | (1831) ~ (all_8_2 = e2) % 147.36/21.04 | | | | | | | | | | | | | | | | | | | % 147.36/21.04 | | | | | | | | | | | | | | | | | | | SIMP: (1831) implies: % 147.36/21.04 | | | | | | | | | | | | | | | | | | | (1832) ~ (all_8_2 = e2) % 147.36/21.04 | | | | | | | | | | | | | | | | | | | % 147.36/21.04 | | | | | | | | | | | | | | | | | | | BETA: splitting (294) gives: % 147.36/21.04 | | | | | | | | | | | | | | | | | | | % 147.36/21.04 | | | | | | | | | | | | | | | | | | | Case 1: % 147.36/21.04 | | | | | | | | | | | | | | | | | | | | % 147.36/21.04 | | | | | | | | | | | | | | | | | | | | (1833) ~ (all_56_11 = e0) % 147.36/21.04 | | | | | | | | | | | | | | | | | | | | % 147.36/21.04 | | | | | | | | | | | | | | | | | | | | REDUCE: (545), (1833) imply: % 147.36/21.04 | | | | | | | | | | | | | | | | | | | | (1834) ~ (all_8_2 = e0) % 147.36/21.04 | | | | | | | | | | | | | | | | | | | | % 147.36/21.04 | | | | | | | | | | | | | | | | | | | | BETA: splitting (295) gives: % 147.36/21.04 | | | | | | | | | | | | | | | | | | | | % 147.36/21.04 | | | | | | | | | | | | | | | | | | | | Case 1: % 147.36/21.04 | | | | | | | | | | | | | | | | | | | | | % 147.36/21.04 | | | | | | | | | | | | | | | | | | | | | (1835) ~ (all_56_11 = e1) % 147.36/21.04 | | | | | | | | | | | | | | | | | | | | | % 147.36/21.04 | | | | | | | | | | | | | | | | | | | | | REDUCE: (545), (1835) imply: % 147.36/21.04 | | | | | | | | | | | | | | | | | | | | | (1836) ~ (all_8_2 = e1) % 147.36/21.04 | | | | | | | | | | | | | | | | | | | | | % 147.36/21.04 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (247) gives: % 147.36/21.04 | | | | | | | | | | | | | | | | | | | | | % 147.36/21.04 | | | | | | | | | | | | | | | | | | | | | Case 1: % 147.36/21.04 | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.04 | | | | | | | | | | | | | | | | | | | | | | (1837) all_54_5 = e3 % 147.36/21.04 | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.04 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (542), (1837) imply: % 147.36/21.04 | | | | | | | | | | | | | | | | | | | | | | (1838) all_8_2 = e3 % 147.36/21.04 | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.04 | | | | | | | | | | | | | | | | | | | | | | SIMP: (1838) implies: % 147.36/21.04 | | | | | | | | | | | | | | | | | | | | | | (1839) all_8_2 = e3 % 147.36/21.04 | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.04 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (48), (1839) imply: % 147.36/21.04 | | | | | | | | | | | | | | | | | | | | | | (1840) op(e3, e3) = all_8_1 % 147.36/21.04 | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.04 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_4_1, % 147.36/21.04 | | | | | | | | | | | | | | | | | | | | | | all_8_1, e3, e3, simplifying with (1812), (1840) % 147.36/21.04 | | | | | | | | | | | | | | | | | | | | | | gives: % 147.36/21.04 | | | | | | | | | | | | | | | | | | | | | | (1841) all_8_1 = all_4_1 % 147.36/21.04 | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.04 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (769), (1841) imply: % 147.36/21.04 | | | | | | | | | | | | | | | | | | | | | | (1842) ~ (all_4_1 = e1) % 147.36/21.04 | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.04 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (51), (250), (252), (298), (299), (331), % 147.36/21.04 | | | | | | | | | | | | | | | | | | | | | | (408), (494), (543), (546), (612), (761), (770), % 147.36/21.04 | | | | | | | | | | | | | | | | | | | | | | (776), (1739), (1742), (1745), (1746), (1747), % 147.36/21.04 | | | | | | | | | | | | | | | | | | | | | | (1748), (1811), (1816), (1817), (1819), (1820), % 147.36/21.04 | | | | | | | | | | | | | | | | | | | | | | (1842), (function-axioms) are inconsistent by % 147.36/21.04 | | | | | | | | | | | | | | | | | | | | | | sub-proof #354. % 147.36/21.04 | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.04 | | | | | | | | | | | | | | | | | | | | | Case 2: % 147.36/21.04 | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.04 | | | | | | | | | | | | | | | | | | | | | | (1843) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 147.36/21.04 | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.04 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (542), (1832), (1834), (1836), (1843) are % 147.36/21.04 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #644. % 147.36/21.04 | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.04 | | | | | | | | | | | | | | | | | | | | | End of split % 147.36/21.04 | | | | | | | | | | | | | | | | | | | | | % 147.36/21.04 | | | | | | | | | | | | | | | | | | | | Case 2: % 147.36/21.04 | | | | | | | | | | | | | | | | | | | | | % 147.36/21.04 | | | | | | | | | | | | | | | | | | | | | (1844) all_56_13 = e2 % 147.36/21.04 | | | | | | | | | | | | | | | | | | | | | % 147.36/21.04 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (431), (1828), (1844) are inconsistent by % 147.36/21.04 | | | | | | | | | | | | | | | | | | | | | sub-proof #353. % 147.36/21.04 | | | | | | | | | | | | | | | | | | | | | % 147.36/21.04 | | | | | | | | | | | | | | | | | | | | End of split % 147.36/21.04 | | | | | | | | | | | | | | | | | | | | % 147.36/21.04 | | | | | | | | | | | | | | | | | | | Case 2: % 147.36/21.04 | | | | | | | | | | | | | | | | | | | | % 147.36/21.04 | | | | | | | | | | | | | | | | | | | | (1845) all_56_15 = e2 % 147.36/21.04 | | | | | | | | | | | | | | | | | | | | % 147.36/21.04 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (443), (1830), (1845) are inconsistent by % 147.36/21.04 | | | | | | | | | | | | | | | | | | | | sub-proof #352. % 147.36/21.04 | | | | | | | | | | | | | | | | | | | | % 147.36/21.04 | | | | | | | | | | | | | | | | | | | End of split % 147.36/21.04 | | | | | | | | | | | | | | | | | | | % 147.36/21.04 | | | | | | | | | | | | | | | | | | Case 2: % 147.36/21.04 | | | | | | | | | | | | | | | | | | | % 147.36/21.04 | | | | | | | | | | | | | | | | | | | (1846) all_58_6 = e2 | all_58_12 = e2 % 147.36/21.04 | | | | | | | | | | | | | | | | | | | % 147.36/21.04 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (1567), (1780), (1809), (1846) are % 147.36/21.04 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #422. % 147.36/21.04 | | | | | | | | | | | | | | | | | | | % 147.36/21.04 | | | | | | | | | | | | | | | | | | End of split % 147.36/21.04 | | | | | | | | | | | | | | | | | | % 147.36/21.04 | | | | | | | | | | | | | | | | | End of split % 147.36/21.04 | | | | | | | | | | | | | | | | | % 147.36/21.04 | | | | | | | | | | | | | | | | Case 2: % 147.36/21.04 | | | | | | | | | | | | | | | | | % 147.36/21.04 | | | | | | | | | | | | | | | | | (1847) ~ (all_26_2 = e3) % 147.36/21.04 | | | | | | | | | | | | | | | | | % 147.36/21.04 | | | | | | | | | | | | | | | | | REDUCE: (1808), (1847) imply: % 147.36/21.04 | | | | | | | | | | | | | | | | | (1848) $false % 147.36/21.04 | | | | | | | | | | | | | | | | | % 147.36/21.04 | | | | | | | | | | | | | | | | | CLOSE: (1848) is inconsistent. % 147.36/21.04 | | | | | | | | | | | | | | | | | % 147.36/21.04 | | | | | | | | | | | | | | | | End of split % 147.36/21.04 | | | | | | | | | | | | | | | | % 147.36/21.04 | | | | | | | | | | | | | | | End of split % 147.36/21.04 | | | | | | | | | | | | | | | % 147.36/21.04 | | | | | | | | | | | | | | Case 2: % 147.36/21.04 | | | | | | | | | | | | | | | % 147.36/21.04 | | | | | | | | | | | | | | | (1849) all_56_31 = e1 % 147.36/21.04 | | | | | | | | | | | | | | | (1850) all_56_29 = e0 % 147.36/21.04 | | | | | | | | | | | | | | | % 147.36/21.04 | | | | | | | | | | | | | | | COMBINE_EQS: (357), (1850) imply: % 147.36/21.04 | | | | | | | | | | | | | | | (1851) all_52_11 = e0 % 147.36/21.04 | | | | | | | | | | | | | | | % 147.36/21.04 | | | | | | | | | | | | | | | SIMP: (1851) implies: % 147.36/21.04 | | | | | | | | | | | | | | | (1852) all_52_11 = e0 % 147.36/21.04 | | | | | | | | | | | | | | | % 147.36/21.04 | | | | | | | | | | | | | | | COMBINE_EQS: (544), (1849) imply: % 147.36/21.04 | | | | | | | | | | | | | | | (1853) all_4_2 = e1 % 147.36/21.04 | | | | | | | | | | | | | | | % 147.36/21.04 | | | | | | | | | | | | | | | REDUCE: (1752), (1852) imply: % 147.36/21.04 | | | | | | | | | | | | | | | (1854) ~ (all_10_0 = e0) % 147.36/21.04 | | | | | | | | | | | | | | | % 147.36/21.04 | | | | | | | | | | | | | | | SIMP: (1854) implies: % 147.36/21.04 | | | | | | | | | | | | | | | (1855) ~ (all_10_0 = e0) % 147.36/21.04 | | | | | | | | | | | | | | | % 147.36/21.04 | | | | | | | | | | | | | | | REDUCE: (585), (1852) imply: % 147.36/21.04 | | | | | | | | | | | | | | | (1856) ~ (all_6_2 = e0) % 147.36/21.04 | | | | | | | | | | | | | | | % 147.36/21.04 | | | | | | | | | | | | | | | SIMP: (1856) implies: % 147.36/21.04 | | | | | | | | | | | | | | | (1857) ~ (all_6_2 = e0) % 147.36/21.04 | | | | | | | | | | | | | | | % 147.36/21.05 | | | | | | | | | | | | | | | REDUCE: (38), (1853) imply: % 147.36/21.05 | | | | | | | | | | | | | | | (1858) op(e1, e1) = all_4_1 % 147.36/21.05 | | | | | | | | | | | | | | | % 147.36/21.05 | | | | | | | | | | | | | | | REDUCE: (627), (1853) imply: % 147.36/21.05 | | | | | | | | | | | | | | | (1859) op(e0, e1) = all_56_30 % 147.36/21.05 | | | | | | | | | | | | | | | % 147.36/21.05 | | | | | | | | | | | | | | | REDUCE: (205), (1852) imply: % 147.36/21.05 | | | | | | | | | | | | | | | (1860) op(e0, e1) = e0 % 147.36/21.05 | | | | | | | | | | | | | | | % 147.36/21.05 | | | | | | | | | | | | | | | REF_CLOSE: (41), (250), (252), (297), (299), (402), (408), % 147.36/21.05 | | | | | | | | | | | | | | | (543), (546), (770), (776), (1565), (1742), % 147.36/21.05 | | | | | | | | | | | | | | | (1745), (1748), (1754), (1755), (1855), (1857), % 147.36/21.05 | | | | | | | | | | | | | | | (1858), (1859), (1860), (function-axioms) are % 147.36/21.05 | | | | | | | | | | | | | | | inconsistent by sub-proof #350. % 147.36/21.05 | | | | | | | | | | | | | | | % 147.36/21.05 | | | | | | | | | | | | | | End of split % 147.36/21.05 | | | | | | | | | | | | | | % 147.36/21.05 | | | | | | | | | | | | | End of split % 147.36/21.05 | | | | | | | | | | | | | % 147.36/21.05 | | | | | | | | | | | | End of split % 147.36/21.05 | | | | | | | | | | | | % 147.36/21.05 | | | | | | | | | | | Case 2: % 147.36/21.05 | | | | | | | | | | | | % 147.36/21.05 | | | | | | | | | | | | (1861) all_30_0 = e3 % 147.36/21.05 | | | | | | | | | | | | (1862) ~ (all_30_1 = e0) | ~ (all_30_2 = e1) % 147.36/21.05 | | | | | | | | | | | | % 147.36/21.05 | | | | | | | | | | | | COMBINE_EQS: (718), (1861) imply: % 147.36/21.05 | | | | | | | | | | | | (1863) all_8_0 = e3 % 147.36/21.05 | | | | | | | | | | | | % 147.36/21.05 | | | | | | | | | | | | SIMP: (1863) implies: % 147.36/21.05 | | | | | | | | | | | | (1864) all_8_0 = e3 % 147.36/21.05 | | | | | | | | | | | | % 147.36/21.05 | | | | | | | | | | | | REF_CLOSE: (9), (36), (41), (46), (47), (48), (51), (212), % 147.36/21.05 | | | | | | | | | | | | (237), (242), (247), (252), (294), (295), (296), % 147.36/21.05 | | | | | | | | | | | | (390), (425), (431), (443), (540), (541), (542), % 147.36/21.05 | | | | | | | | | | | | (543), (545), (557), (579), (583), (590), (617), % 147.36/21.05 | | | | | | | | | | | | (658), (769), (778), (1862), (1864), % 147.36/21.05 | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 147.36/21.05 | | | | | | | | | | | | #379. % 147.36/21.05 | | | | | | | | | | | | % 147.36/21.05 | | | | | | | | | | | End of split % 147.36/21.05 | | | | | | | | | | | % 147.36/21.05 | | | | | | | | | | Case 2: % 147.36/21.05 | | | | | | | | | | | % 147.36/21.05 | | | | | | | | | | | (1865) all_28_0 = e2 % 147.36/21.05 | | | | | | | | | | | (1866) ~ (all_28_1 = e3) | ~ (all_28_2 = e0) % 147.36/21.05 | | | | | | | | | | | % 147.36/21.05 | | | | | | | | | | | COMBINE_EQS: (740), (1865) imply: % 147.36/21.05 | | | | | | | | | | | (1867) all_6_0 = e2 % 147.36/21.05 | | | | | | | | | | | % 147.36/21.05 | | | | | | | | | | | SIMP: (1867) implies: % 147.36/21.05 | | | | | | | | | | | (1868) all_6_0 = e2 % 147.36/21.05 | | | | | | | | | | | % 147.36/21.05 | | | | | | | | | | | REF_CLOSE: (6), (8), (36), (37), (38), (41), (42), (43), % 147.36/21.05 | | | | | | | | | | | (46), (51), (144), (158), (173), (174), (176), % 147.36/21.05 | | | | | | | | | | | (187), (192), (206), (207), (208), (211), (237), % 147.36/21.05 | | | | | | | | | | | (239), (240), (242), (247), (252), (288), (289), % 147.36/21.05 | | | | | | | | | | | (290), (291), (292), (293), (294), (297), (321), % 147.36/21.05 | | | | | | | | | | | (341), (357), (366), (374), (381), (386), (402), % 147.36/21.05 | | | | | | | | | | | (407), (419), (435), (443), (475), (478), (480), % 147.36/21.05 | | | | | | | | | | | (513), (540), (541), (542), (543), (544), (545), % 147.36/21.05 | | | | | | | | | | | (546), (547), (550), (551), (555), (559), (569), % 147.36/21.05 | | | | | | | | | | | (571), (573), (580), (585), (620), (622), (627), % 147.36/21.05 | | | | | | | | | | | (634), (665), (764), (767), (768), (772), (1866), % 147.36/21.05 | | | | | | | | | | | (1868), (function-axioms) are inconsistent by % 147.36/21.05 | | | | | | | | | | | sub-proof #364. % 147.36/21.05 | | | | | | | | | | | % 147.36/21.05 | | | | | | | | | | End of split % 147.36/21.05 | | | | | | | | | | % 147.36/21.05 | | | | | | | | | End of split % 147.36/21.05 | | | | | | | | | % 147.36/21.05 | | | | | | | | Case 2: % 147.36/21.05 | | | | | | | | | % 147.36/21.05 | | | | | | | | | (1869) all_22_1 = e3 % 147.36/21.05 | | | | | | | | | (1870) ~ (all_22_0 = e0) | ~ (all_22_2 = e1) % 147.36/21.05 | | | | | | | | | % 147.36/21.05 | | | | | | | | | COMBINE_EQS: (672), (1869) imply: % 147.36/21.05 | | | | | | | | | (1871) all_8_1 = e3 % 147.36/21.05 | | | | | | | | | % 147.36/21.05 | | | | | | | | | REDUCE: (48), (1871) imply: % 147.36/21.05 | | | | | | | | | (1872) op(all_8_2, all_8_2) = e3 % 147.36/21.05 | | | | | | | | | % 147.36/21.05 | | | | | | | | | REDUCE: (47), (1871) imply: % 147.36/21.05 | | | | | | | | | (1873) op(e2, e3) = all_8_0 % 147.36/21.05 | | | | | | | | | % 147.36/21.05 | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (36), (37), (38), (41), (42), % 147.36/21.05 | | | | | | | | | (43), (46), (48), (51), (52), (53), (94), (99), % 147.36/21.05 | | | | | | | | | (119), (139), (144), (158), (160), (161), (165), % 147.36/21.05 | | | | | | | | | (166), (168), (169), (171), (173), (174), (176), % 147.36/21.05 | | | | | | | | | (181), (182), (183), (184), (187), (188), (189), % 147.36/21.05 | | | | | | | | | (191), (192), (193), (194), (197), (205), (206), % 147.36/21.05 | | | | | | | | | (207), (208), (210), (211), (212), (213), (215), % 147.36/21.05 | | | | | | | | | (216), (217), (218), (237), (238), (239), (240), % 147.36/21.05 | | | | | | | | | (241), (242), (243), (244), (245), (246), (247), % 147.36/21.05 | | | | | | | | | (248), (249), (250), (251), (252), (286), (287), % 147.36/21.05 | | | | | | | | | (288), (289), (290), (291), (292), (293), (294), % 147.36/21.05 | | | | | | | | | (295), (296), (297), (317), (318), (319), (320), % 147.36/21.05 | | | | | | | | | (321), (322), (323), (324), (326), (327), (329), % 147.36/21.05 | | | | | | | | | (330), (331), (332), (333), (336), (337), (338), % 147.36/21.05 | | | | | | | | | (339), (341), (342), (344), (357), (360), (365), % 147.36/21.05 | | | | | | | | | (366), (374), (380), (381), (386), (389), (401), % 147.36/21.05 | | | | | | | | | (402), (407), (419), (425), (431), (435), (443), % 147.36/21.05 | | | | | | | | | (447), (457), (459), (461), (463), (467), (469), % 147.36/21.05 | | | | | | | | | (471), (473), (475), (476), (478), (480), (482), % 147.36/21.05 | | | | | | | | | (513), (523), (530), (532), (535), (540), (541), % 147.36/21.05 | | | | | | | | | (542), (543), (544), (545), (546), (547), (548), % 147.36/21.05 | | | | | | | | | (549), (550), (551), (552), (553), (554), (555), % 147.36/21.05 | | | | | | | | | (557), (559), (561), (563), (565), (567), (568), % 147.36/21.05 | | | | | | | | | (569), (570), (571), (573), (575), (577), (579), % 147.36/21.05 | | | | | | | | | (580), (583), (585), (587), (588), (590), (591), % 147.36/21.05 | | | | | | | | | (612), (613), (614), (615), (617), (618), (619), % 147.36/21.05 | | | | | | | | | (620), (621), (622), (623), (625), (626), (627), % 147.36/21.05 | | | | | | | | | (631), (634), (652), (657), (665), (709), (740), % 147.36/21.05 | | | | | | | | | (752), (760), (762), (764), (767), (768), (770), % 147.36/21.05 | | | | | | | | | (772), (774), (1870), (1872), (1873), % 147.36/21.05 | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 147.36/21.05 | | | | | | | | | #307. % 147.36/21.05 | | | | | | | | | % 147.36/21.05 | | | | | | | | End of split % 147.36/21.05 | | | | | | | | % 147.36/21.05 | | | | | | | Case 2: % 147.36/21.05 | | | | | | | | % 147.36/21.05 | | | | | | | | (1874) all_16_0 = e1 % 147.36/21.05 | | | | | | | | (1875) ~ (all_16_1 = e2) | ~ (all_16_2 = e0) % 147.36/21.05 | | | | | | | | % 147.36/21.05 | | | | | | | | COMBINE_EQS: (757), (1874) imply: % 147.36/21.05 | | | | | | | | (1876) all_10_0 = e1 % 147.36/21.05 | | | | | | | | % 147.36/21.05 | | | | | | | | COMBINE_EQS: (741), (1876) imply: % 147.36/21.05 | | | | | | | | (1877) all_24_0 = e1 % 147.36/21.05 | | | | | | | | % 147.36/21.05 | | | | | | | | REDUCE: (770), (1876) imply: % 147.36/21.05 | | | | | | | | (1878) ~ (e2 = e1) % 147.36/21.05 | | | | | | | | % 147.36/21.05 | | | | | | | | REDUCE: (52), (1876) imply: % 147.36/21.05 | | | | | | | | (1879) op(e3, all_10_1) = e1 % 147.36/21.05 | | | | | | | | % 147.36/21.05 | | | | | | | | BETA: splitting (84) gives: % 147.36/21.05 | | | | | | | | % 147.36/21.05 | | | | | | | | Case 1: % 147.36/21.05 | | | | | | | | | % 147.36/21.05 | | | | | | | | | (1880) ~ (all_22_1 = e3) % 147.36/21.05 | | | | | | | | | % 147.36/21.05 | | | | | | | | | REDUCE: (672), (1880) imply: % 147.36/21.05 | | | | | | | | | (1881) ~ (all_8_1 = e3) % 147.36/21.05 | | | | | | | | | % 147.36/21.05 | | | | | | | | | BETA: splitting (89) gives: % 147.36/21.05 | | | | | | | | | % 147.36/21.05 | | | | | | | | | Case 1: % 147.36/21.05 | | | | | | | | | | % 147.36/21.05 | | | | | | | | | | (1882) ~ (all_24_0 = e1) % 147.36/21.05 | | | | | | | | | | % 147.36/21.05 | | | | | | | | | | REDUCE: (1877), (1882) imply: % 147.36/21.05 | | | | | | | | | | (1883) $false % 147.36/21.05 | | | | | | | | | | % 147.36/21.05 | | | | | | | | | | CLOSE: (1883) is inconsistent. % 147.36/21.05 | | | | | | | | | | % 147.36/21.05 | | | | | | | | | Case 2: % 147.36/21.05 | | | | | | | | | | % 147.36/21.05 | | | | | | | | | | (1884) ~ (all_24_1 = e0) | ~ (all_24_2 = e2) % 147.36/21.05 | | | | | | | | | | % 147.36/21.05 | | | | | | | | | | BETA: splitting (94) gives: % 147.36/21.05 | | | | | | | | | | % 147.36/21.05 | | | | | | | | | | Case 1: % 147.36/21.05 | | | | | | | | | | | % 147.36/21.05 | | | | | | | | | | | (1885) ~ (all_26_0 = e1) % 147.36/21.05 | | | | | | | | | | | % 147.36/21.05 | | | | | | | | | | | REDUCE: (760), (1885) imply: % 147.36/21.05 | | | | | | | | | | | (1886) ~ (all_4_0 = e1) % 147.36/21.05 | | | | | | | | | | | % 147.36/21.05 | | | | | | | | | | | BETA: splitting (99) gives: % 147.36/21.05 | | | | | | | | | | | % 147.36/21.05 | | | | | | | | | | | Case 1: % 147.36/21.05 | | | | | | | | | | | | % 147.36/21.05 | | | | | | | | | | | | (1887) ~ (all_28_0 = e2) % 147.36/21.05 | | | | | | | | | | | | % 147.36/21.05 | | | | | | | | | | | | REDUCE: (740), (1887) imply: % 147.36/21.05 | | | | | | | | | | | | (1888) ~ (all_6_0 = e2) % 147.36/21.05 | | | | | | | | | | | | % 147.36/21.05 | | | | | | | | | | | | BETA: splitting (119) gives: % 147.36/21.05 | | | | | | | | | | | | % 147.36/21.05 | | | | | | | | | | | | Case 1: % 147.36/21.05 | | | | | | | | | | | | | % 147.36/21.05 | | | | | | | | | | | | | (1889) ~ (all_36_1 = e3) % 147.36/21.05 | | | | | | | | | | | | | % 147.36/21.05 | | | | | | | | | | | | | REDUCE: (652), (1889) imply: % 147.36/21.05 | | | | | | | | | | | | | (1890) ~ (all_6_1 = e3) % 147.36/21.05 | | | | | | | | | | | | | % 147.36/21.05 | | | | | | | | | | | | | BETA: splitting (129) gives: % 147.36/21.05 | | | | | | | | | | | | | % 147.36/21.05 | | | | | | | | | | | | | Case 1: % 147.36/21.05 | | | | | | | | | | | | | | % 147.36/21.05 | | | | | | | | | | | | | | (1891) ~ (all_40_0 = e3) % 147.36/21.05 | | | | | | | | | | | | | | % 147.36/21.05 | | | | | | | | | | | | | | REDUCE: (713), (1891) imply: % 147.36/21.05 | | | | | | | | | | | | | | (1892) ~ (all_6_0 = e3) % 147.36/21.05 | | | | | | | | | | | | | | % 147.36/21.05 | | | | | | | | | | | | | | BETA: splitting (288) gives: % 147.36/21.05 | | | | | | | | | | | | | | % 147.36/21.05 | | | | | | | | | | | | | | Case 1: % 147.36/21.05 | | | | | | | | | | | | | | | % 147.36/21.05 | | | | | | | | | | | | | | | (1893) ~ (all_56_31 = e1) % 147.36/21.05 | | | | | | | | | | | | | | | % 147.36/21.05 | | | | | | | | | | | | | | | REDUCE: (544), (1893) imply: % 147.36/21.05 | | | | | | | | | | | | | | | (1894) ~ (all_4_2 = e1) % 147.36/21.05 | | | | | | | | | | | | | | | % 147.36/21.05 | | | | | | | | | | | | | | | BETA: splitting (292) gives: % 147.36/21.05 | | | | | | | | | | | | | | | % 147.36/21.05 | | | | | | | | | | | | | | | Case 1: % 147.36/21.05 | | | | | | | | | | | | | | | | % 147.36/21.05 | | | | | | | | | | | | | | | | (1895) ~ (all_56_21 = e2) % 147.36/21.05 | | | | | | | | | | | | | | | | % 147.36/21.05 | | | | | | | | | | | | | | | | REDUCE: (374), (1895) imply: % 147.36/21.05 | | | | | | | | | | | | | | | | (1896) ~ (all_6_2 = e2) % 147.36/21.05 | | | | | | | | | | | | | | | | % 147.36/21.06 | | | | | | | | | | | | | | | | REF_CLOSE: (8), (36), (37), (38), (41), (42), (43), (46), % 147.36/21.06 | | | | | | | | | | | | | | | | (47), (48), (51), (53), (158), (160), (161), % 147.36/21.06 | | | | | | | | | | | | | | | | (165), (168), (169), (171), (173), (174), (176), % 147.36/21.06 | | | | | | | | | | | | | | | | (181), (182), (183), (184), (187), (188), (189), % 147.36/21.06 | | | | | | | | | | | | | | | | (191), (192), (193), (194), (196), (197), (205), % 147.36/21.06 | | | | | | | | | | | | | | | | (206), (207), (208), (210), (211), (213), (215), % 147.36/21.06 | | | | | | | | | | | | | | | | (216), (217), (218), (237), (238), (239), (240), % 147.36/21.06 | | | | | | | | | | | | | | | | (241), (242), (243), (244), (245), (246), (247), % 147.36/21.06 | | | | | | | | | | | | | | | | (248), (249), (250), (251), (252), (286), (287), % 147.36/21.06 | | | | | | | | | | | | | | | | (289), (290), (291), (293), (294), (295), (296), % 147.36/21.06 | | | | | | | | | | | | | | | | (297), (298), (299), (317), (318), (319), (320), % 147.36/21.06 | | | | | | | | | | | | | | | | (321), (322), (324), (326), (327), (328), (329), % 147.36/21.06 | | | | | | | | | | | | | | | | (330), (332), (333), (335), (336), (337), (338), % 147.36/21.06 | | | | | | | | | | | | | | | | (340), (341), (342), (343), (345), (347), (360), % 147.36/21.06 | | | | | | | | | | | | | | | | (365), (366), (374), (380), (381), (386), (389), % 147.36/21.06 | | | | | | | | | | | | | | | | (401), (402), (407), (408), (419), (425), (429), % 147.36/21.06 | | | | | | | | | | | | | | | | (431), (435), (443), (447), (457), (459), (461), % 147.36/21.06 | | | | | | | | | | | | | | | | (463), (467), (469), (471), (473), (476), (478), % 147.36/21.06 | | | | | | | | | | | | | | | | (480), (482), (521), (527), (540), (541), (542), % 147.36/21.06 | | | | | | | | | | | | | | | | (543), (544), (545), (546), (547), (548), (549), % 147.36/21.06 | | | | | | | | | | | | | | | | (550), (551), (552), (553), (554), (555), (557), % 147.36/21.06 | | | | | | | | | | | | | | | | (559), (561), (563), (565), (567), (568), (569), % 147.36/21.06 | | | | | | | | | | | | | | | | (570), (571), (573), (575), (577), (579), (580), % 147.36/21.06 | | | | | | | | | | | | | | | | (581), (582), (583), (585), (587), (588), (589), % 147.36/21.06 | | | | | | | | | | | | | | | | (590), (591), (612), (613), (614), (615), (616), % 147.36/21.06 | | | | | | | | | | | | | | | | (617), (618), (620), (621), (622), (624), (625), % 147.36/21.06 | | | | | | | | | | | | | | | | (626), (627), (643), (677), (768), (769), (772), % 147.36/21.06 | | | | | | | | | | | | | | | | (774), (1875), (1879), (1881), (1884), (1886), % 147.36/21.06 | | | | | | | | | | | | | | | | (1888), (1890), (1894), (1896), (function-axioms) % 147.36/21.06 | | | | | | | | | | | | | | | | are inconsistent by sub-proof #285. % 147.36/21.06 | | | | | | | | | | | | | | | | % 147.36/21.06 | | | | | | | | | | | | | | | Case 2: % 147.36/21.06 | | | | | | | | | | | | | | | | % 147.36/21.06 | | | | | | | | | | | | | | | | (1897) all_56_21 = e2 % 147.36/21.06 | | | | | | | | | | | | | | | | (1898) all_56_19 = e1 % 147.36/21.06 | | | | | | | | | | | | | | | | % 147.36/21.06 | | | | | | | | | | | | | | | | COMBINE_EQS: (435), (1898) imply: % 147.36/21.06 | | | | | | | | | | | | | | | | (1899) all_52_6 = e1 % 147.36/21.06 | | | | | | | | | | | | | | | | % 147.36/21.06 | | | | | | | | | | | | | | | | COMBINE_EQS: (374), (1897) imply: % 147.36/21.06 | | | | | | | | | | | | | | | | (1900) all_6_2 = e2 % 147.36/21.06 | | | | | | | | | | | | | | | | % 147.36/21.06 | | | | | | | | | | | | | | | | REDUCE: (174), (1899) imply: % 147.36/21.06 | | | | | | | | | | | | | | | | (1901) ~ (all_52_14 = e1) % 147.36/21.06 | | | | | | | | | | | | | | | | % 147.36/21.06 | | | | | | | | | | | | | | | | SIMP: (1901) implies: % 147.36/21.06 | | | | | | | | | | | | | | | | (1902) ~ (all_52_14 = e1) % 147.36/21.06 | | | | | | | | | | | | | | | | % 147.36/21.06 | | | | | | | | | | | | | | | | REDUCE: (573), (1899) imply: % 147.36/21.06 | | | | | | | | | | | | | | | | (1903) ~ (all_8_2 = e1) % 147.36/21.06 | | | | | | | | | | | | | | | | % 147.36/21.06 | | | | | | | | | | | | | | | | SIMP: (1903) implies: % 147.36/21.06 | | | | | | | | | | | | | | | | (1904) ~ (all_8_2 = e1) % 147.36/21.06 | | | | | | | | | | | | | | | | % 147.36/21.06 | | | | | | | | | | | | | | | | REDUCE: (43), (1900) imply: % 147.36/21.06 | | | | | | | | | | | | | | | | (1905) op(e2, e2) = all_6_1 % 147.36/21.06 | | | | | | | | | | | | | | | | % 147.36/21.06 | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (9), (36), (42), (46), (48), (208), % 147.36/21.06 | | | | | | | | | | | | | | | | (247), (294), (297), (321), (323), (341), (386), % 147.36/21.06 | | | | | | | | | | | | | | | | (402), (407), (419), (443), (542), (545), (546), % 147.36/21.06 | | | | | | | | | | | | | | | | (547), (550), (551), (555), (571), (620), (768), % 147.36/21.06 | | | | | | | | | | | | | | | | (1881), (1890), (1892), (1894), (1902), (1904), % 147.36/21.06 | | | | | | | | | | | | | | | | (1905), (function-axioms) are inconsistent by % 147.36/21.06 | | | | | | | | | | | | | | | | sub-proof #283. % 147.36/21.06 | | | | | | | | | | | | | | | | % 147.36/21.06 | | | | | | | | | | | | | | | End of split % 147.36/21.06 | | | | | | | | | | | | | | | % 147.36/21.06 | | | | | | | | | | | | | | Case 2: % 147.36/21.06 | | | | | | | | | | | | | | | % 147.36/21.06 | | | | | | | | | | | | | | | (1906) all_56_31 = e1 % 147.36/21.06 | | | | | | | | | | | | | | | (1907) all_56_29 = e0 % 147.36/21.06 | | | | | | | | | | | | | | | % 147.36/21.06 | | | | | | | | | | | | | | | COMBINE_EQS: (357), (1907) imply: % 147.36/21.06 | | | | | | | | | | | | | | | (1908) all_52_11 = e0 % 147.36/21.06 | | | | | | | | | | | | | | | % 147.36/21.06 | | | | | | | | | | | | | | | SIMP: (1908) implies: % 147.36/21.06 | | | | | | | | | | | | | | | (1909) all_52_11 = e0 % 147.36/21.06 | | | | | | | | | | | | | | | % 147.36/21.06 | | | | | | | | | | | | | | | COMBINE_EQS: (544), (1906) imply: % 147.36/21.06 | | | | | | | | | | | | | | | (1910) all_4_2 = e1 % 147.36/21.06 | | | | | | | | | | | | | | | % 147.36/21.06 | | | | | | | | | | | | | | | COMBINE_EQS: (547), (1910) imply: % 147.36/21.06 | | | | | | | | | | | | | | | (1911) all_58_15 = e1 % 147.36/21.06 | | | | | | | | | | | | | | | % 147.36/21.06 | | | | | | | | | | | | | | | COMBINE_EQS: (548), (1909) imply: % 147.36/21.06 | | | | | | | | | | | | | | | (1912) all_58_14 = e0 % 147.36/21.06 | | | | | | | | | | | | | | | % 147.36/21.06 | | | | | | | | | | | | | | | REDUCE: (187), (1909) imply: % 147.36/21.06 | | | | | | | | | | | | | | | (1913) ~ (all_52_3 = e0) % 147.36/21.06 | | | | | | | | | | | | | | | % 147.36/21.06 | | | | | | | | | | | | | | | REDUCE: (570), (1910) imply: % 147.36/21.06 | | | | | | | | | | | | | | | (1914) ~ (all_52_3 = e1) % 147.36/21.06 | | | | | | | | | | | | | | | % 147.36/21.06 | | | | | | | | | | | | | | | REDUCE: (173), (1909) imply: % 147.36/21.06 | | | | | | | | | | | | | | | (1915) ~ (all_52_7 = e0) % 147.36/21.06 | | | | | | | | | | | | | | | % 147.36/21.06 | | | | | | | | | | | | | | | REDUCE: (581), (1910) imply: % 147.36/21.06 | | | | | | | | | | | | | | | (1916) ~ (all_52_7 = e1) % 147.36/21.06 | | | | | | | | | | | | | | | % 147.36/21.06 | | | | | | | | | | | | | | | REDUCE: (166), (1909) imply: % 147.36/21.06 | | | | | | | | | | | | | | | (1917) ~ (all_52_9 = e0) % 147.36/21.06 | | | | | | | | | | | | | | | % 147.36/21.06 | | | | | | | | | | | | | | | REDUCE: (585), (1909) imply: % 147.36/21.06 | | | | | | | | | | | | | | | (1918) ~ (all_6_2 = e0) % 147.36/21.06 | | | | | | | | | | | | | | | % 147.36/21.06 | | | | | | | | | | | | | | | SIMP: (1918) implies: % 147.36/21.06 | | | | | | | | | | | | | | | (1919) ~ (all_6_2 = e0) % 147.36/21.06 | | | | | | | | | | | | | | | % 147.36/21.06 | | | | | | | | | | | | | | | REDUCE: (589), (1910) imply: % 147.36/21.06 | | | | | | | | | | | | | | | (1920) ~ (all_52_12 = e1) % 147.36/21.06 | | | | | | | | | | | | | | | % 147.36/21.06 | | | | | | | | | | | | | | | REDUCE: (590), (1910) imply: % 147.36/21.06 | | | | | | | | | | | | | | | (1921) ~ (all_52_13 = e1) % 147.36/21.06 | | | | | | | | | | | | | | | % 147.36/21.06 | | | | | | | | | | | | | | | REDUCE: (38), (1910) imply: % 147.36/21.06 | | | | | | | | | | | | | | | (1922) op(e1, e1) = all_4_1 % 147.36/21.06 | | | | | | | | | | | | | | | % 147.36/21.06 | | | | | | | | | | | | | | | REDUCE: (627), (1910) imply: % 147.36/21.06 | | | | | | | | | | | | | | | (1923) op(e0, e1) = all_56_30 % 147.36/21.06 | | | | | | | | | | | | | | | % 147.36/21.06 | | | | | | | | | | | | | | | REDUCE: (205), (1909) imply: % 147.36/21.06 | | | | | | | | | | | | | | | (1924) op(e0, e1) = e0 % 147.36/21.06 | | | | | | | | | | | | | | | % 147.36/21.06 | | | | | | | | | | | | | | | REDUCE: (36), (1910) imply: % 147.36/21.06 | | | | | | | | | | | | | | | (1925) op(e0, e0) = e1 % 147.36/21.06 | | | | | | | | | | | | | | | % 147.36/21.06 | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, % 147.36/21.06 | | | | | | | | | | | | | | | all_56_30, e1, e0, simplifying with (1923), (1924) % 147.36/21.06 | | | | | | | | | | | | | | | gives: % 147.36/21.06 | | | | | | | | | | | | | | | (1926) all_56_30 = e0 % 147.36/21.06 | | | | | | | | | | | | | | | % 147.36/21.06 | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_6_2, % 147.36/21.06 | | | | | | | | | | | | | | | all_4_1, e1, e1, simplifying with (41), (1922) % 147.36/21.06 | | | | | | | | | | | | | | | gives: % 147.36/21.06 | | | | | | | | | | | | | | | (1927) all_6_2 = all_4_1 % 147.36/21.06 | | | | | | | | | | | | | | | % 147.36/21.06 | | | | | | | | | | | | | | | COMBINE_EQS: (541), (1927) imply: % 147.36/21.06 | | | | | | | | | | | | | | | (1928) all_54_10 = all_4_1 % 147.36/21.06 | | | | | | | | | | | | | | | % 147.36/21.06 | | | | | | | | | | | | | | | COMBINE_EQS: (374), (1927) imply: % 147.36/21.06 | | | | | | | | | | | | | | | (1929) all_56_21 = all_4_1 % 147.36/21.06 | | | | | | | | | | | | | | | % 147.36/21.06 | | | | | | | | | | | | | | | COMBINE_EQS: (552), (1927) imply: % 147.36/21.06 | | | | | | | | | | | | | | | (1930) all_58_8 = all_4_1 % 147.36/21.06 | | | | | | | | | | | | | | | % 147.36/21.06 | | | | | | | | | | | | | | | REDUCE: (569), (1927) imply: % 147.36/21.06 | | | | | | | | | | | | | | | (1931) ~ (all_52_2 = all_4_1) % 147.36/21.06 | | | | | | | | | | | | | | | % 147.36/21.06 | | | | | | | | | | | | | | | REDUCE: (580), (1927) imply: % 147.36/21.06 | | | | | | | | | | | | | | | (1932) ~ (all_52_6 = all_4_1) % 147.36/21.06 | | | | | | | | | | | | | | | % 147.36/21.06 | | | | | | | | | | | | | | | REDUCE: (582), (1927) imply: % 147.36/21.06 | | | | | | | | | | | | | | | (1933) ~ (all_52_8 = all_4_1) % 147.36/21.06 | | | | | | | | | | | | | | | % 147.36/21.06 | | | | | | | | | | | | | | | REDUCE: (583), (1927) imply: % 147.36/21.06 | | | | | | | | | | | | | | | (1934) ~ (all_52_9 = all_4_1) % 147.36/21.06 | | | | | | | | | | | | | | | % 147.36/21.06 | | | | | | | | | | | | | | | REDUCE: (587), (1927) imply: % 147.36/21.06 | | | | | | | | | | | | | | | (1935) ~ (all_52_14 = all_4_1) % 147.36/21.06 | | | | | | | | | | | | | | | % 147.36/21.06 | | | | | | | | | | | | | | | REDUCE: (1919), (1927) imply: % 147.36/21.06 | | | | | | | | | | | | | | | (1936) ~ (all_4_1 = e0) % 147.36/21.06 | | | | | | | | | | | | | | | % 147.36/21.06 | | | | | | | | | | | | | | | REDUCE: (43), (1927) imply: % 147.36/21.06 | | | | | | | | | | | | | | | (1937) op(all_4_1, all_4_1) = all_6_1 % 147.36/21.06 | | | | | | | | | | | | | | | % 147.36/21.06 | | | | | | | | | | | | | | | REDUCE: (622), (1927) imply: % 147.36/21.06 | | | | | | | | | | | | | | | (1938) op(e1, all_4_1) = all_56_20 % 147.36/21.06 | | | | | | | | | | | | | | | % 147.36/21.06 | | | | | | | | | | | | | | | BETA: splitting (292) gives: % 147.36/21.06 | | | | | | | | | | | | | | | % 147.36/21.06 | | | | | | | | | | | | | | | Case 1: % 147.36/21.06 | | | | | | | | | | | | | | | | % 147.36/21.06 | | | | | | | | | | | | | | | | (1939) ~ (all_56_21 = e2) % 147.36/21.06 | | | | | | | | | | | | | | | | % 147.36/21.06 | | | | | | | | | | | | | | | | REDUCE: (1929), (1939) imply: % 147.36/21.06 | | | | | | | | | | | | | | | | (1940) ~ (all_4_1 = e2) % 147.36/21.06 | | | | | | | | | | | | | | | | % 147.36/21.06 | | | | | | | | | | | | | | | | BETA: splitting (294) gives: % 147.36/21.06 | | | | | | | | | | | | | | | | % 147.36/21.06 | | | | | | | | | | | | | | | | Case 1: % 147.36/21.06 | | | | | | | | | | | | | | | | | % 147.36/21.06 | | | | | | | | | | | | | | | | | (1941) ~ (all_56_11 = e0) % 147.36/21.06 | | | | | | | | | | | | | | | | | % 147.36/21.06 | | | | | | | | | | | | | | | | | REDUCE: (545), (1941) imply: % 147.36/21.06 | | | | | | | | | | | | | | | | | (1942) ~ (all_8_2 = e0) % 147.36/21.06 | | | | | | | | | | | | | | | | | % 147.36/21.06 | | | | | | | | | | | | | | | | | BETA: splitting (293) gives: % 147.36/21.06 | | | | | | | | | | | | | | | | | % 147.36/21.06 | | | | | | | | | | | | | | | | | Case 1: % 147.36/21.06 | | | | | | | | | | | | | | | | | | % 147.36/21.06 | | | | | | | | | | | | | | | | | | (1943) ~ (all_56_21 = e3) % 147.36/21.06 | | | | | | | | | | | | | | | | | | % 147.36/21.06 | | | | | | | | | | | | | | | | | | REDUCE: (1929), (1943) imply: % 147.36/21.06 | | | | | | | | | | | | | | | | | | (1944) ~ (all_4_1 = e3) % 147.36/21.06 | | | | | | | | | | | | | | | | | | % 147.36/21.06 | | | | | | | | | | | | | | | | | | BETA: splitting (242) gives: % 147.36/21.06 | | | | | | | | | | | | | | | | | | % 147.36/21.06 | | | | | | | | | | | | | | | | | | Case 1: % 147.36/21.06 | | | | | | | | | | | | | | | | | | | % 147.36/21.06 | | | | | | | | | | | | | | | | | | | (1945) all_54_10 = e3 % 147.36/21.06 | | | | | | | | | | | | | | | | | | | % 147.36/21.06 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1928), (1944), (1945) are inconsistent by % 147.36/21.06 | | | | | | | | | | | | | | | | | | | sub-proof #282. % 147.36/21.06 | | | | | | | | | | | | | | | | | | | % 147.36/21.06 | | | | | | | | | | | | | | | | | | Case 2: % 147.36/21.06 | | | | | | | | | | | | | | | | | | | % 147.36/21.06 | | | | | | | | | | | | | | | | | | | (1946) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 147.36/21.06 | | | | | | | | | | | | | | | | | | | % 147.36/21.06 | | | | | | | | | | | | | | | | | | | BETA: splitting (1946) gives: % 147.36/21.06 | | | | | | | | | | | | | | | | | | | % 147.36/21.06 | | | | | | | | | | | | | | | | | | | Case 1: % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | (1947) all_54_10 = e2 % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1928), (1940), (1947) are inconsistent by % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | sub-proof #281. % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | % 147.36/21.06 | | | | | | | | | | | | | | | | | | | Case 2: % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | (1948) ~ (all_54_10 = e2) % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | (1949) all_54_10 = e1 | all_54_10 = e0 % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | BETA: splitting (1949) gives: % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | Case 1: % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | (1950) all_54_10 = e1 % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1928), (1950) imply: % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | (1951) all_4_1 = e1 % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | SIMP: (1951) implies: % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | (1952) all_4_1 = e1 % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | REDUCE: (1931), (1952) imply: % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | (1953) ~ (all_52_2 = e1) % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | REDUCE: (1932), (1952) imply: % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | (1954) ~ (all_52_6 = e1) % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | REDUCE: (1933), (1952) imply: % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | (1955) ~ (all_52_8 = e1) % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | REDUCE: (1934), (1952) imply: % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | (1956) ~ (all_52_9 = e1) % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | REDUCE: (1935), (1952) imply: % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | (1957) ~ (all_52_14 = e1) % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | REDUCE: (1937), (1952) imply: % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | (1958) op(e1, e1) = all_6_1 % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | REDUCE: (1938), (1952) imply: % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | (1959) op(e1, e1) = all_56_20 % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | REDUCE: (1922), (1952) imply: % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | (1960) op(e1, e1) = e1 % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | REDUCE: (37), (1952) imply: % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | (1961) op(e0, e1) = all_4_0 % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_4_0, % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | e1, e0, simplifying with (1924), (1961) gives: % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | (1962) all_4_0 = e0 % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_6_1, % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | all_56_20, e1, e1, simplifying with (1958), (1959) % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | gives: % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | (1963) all_56_20 = all_6_1 % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1, % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | all_56_20, e1, e1, simplifying with (1959), (1960) % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | gives: % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | (1964) all_56_20 = e1 % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1963), (1964) imply: % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | (1965) all_6_1 = e1 % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | REDUCE: (772), (1962) imply: % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | (1966) ~ (e2 = e0) % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | REDUCE: (1886), (1962) imply: % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | (1967) ~ (e1 = e0) % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | REDUCE: (42), (1965) imply: % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | (1968) op(e1, e1) = all_6_0 % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1, all_6_0, % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | e1, e1, simplifying with (1960), (1968) gives: % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | (1969) all_6_0 = e1 % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | REDUCE: (1892), (1969) imply: % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | (1970) ~ (e3 = e1) % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (297) gives: % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | Case 1: % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | | (1971) ~ (all_56_1 = e0) % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (546), (1971) imply: % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | | (1972) ~ (all_10_2 = e0) % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (48), (161), (165), (168), (181), (194), % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | | (245), (246), (247), (249), (252), (296), (298), % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | | (299), (330), (337), (343), (380), (389), (407), % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | | (408), (419), (425), (461), (467), (469), (542), % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | | (543), (545), (546), (549), (551), (554), (555), % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | | (563), (567), (571), (577), (579), (769), (1912), % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | | (1916), (1917), (1920), (1921), (1930), (1940), % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | | (1942), (1954), (1955), (1956), (1959), (1960), % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | | (1972), (function-axioms) are inconsistent by % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | | sub-proof #531. % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | Case 2: % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | | (1973) all_56_7 = e3 % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | | (1974) all_56_1 = e0 % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (546), (1974) imply: % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | | (1975) all_10_2 = e0 % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (402), (1973) imply: % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | | (1976) all_52_12 = e3 % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (551), (1976) imply: % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | | (1977) all_58_9 = e3 % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (419), (1975) imply: % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | | (1978) all_58_0 = e0 % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (557), (1975) imply: % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | | (1979) ~ (all_52_1 = e0) % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (559), (1975) imply: % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | | (1980) ~ (all_52_2 = e0) % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (563), (1975) imply: % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | | (1981) ~ (all_52_4 = e0) % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (160), (1976) imply: % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | | (1982) ~ (all_52_14 = e3) % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | | SIMP: (1982) implies: % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | | (1983) ~ (all_52_14 = e3) % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (53), (1975) imply: % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | | (1984) op(e0, e0) = all_10_1 % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (342) gives: % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | | | (1985) all_58_0 = e1 % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (1978), (1985) are inconsistent by sub-proof % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | | | #730. % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | | | (1986) all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1 % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1986) gives: % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | | | | (1987) all_58_2 = e1 % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (401), (1987) imply: % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | | | | (1988) all_52_1 = e1 % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (425), (1988) imply: % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | | | | (1989) all_56_9 = e1 % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (613), (1988) imply: % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | | | | (1990) op(e3, e1) = all_56_8 % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (296) gives: % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | | | | | (1991) ~ (all_56_11 = e3) % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (545), (1991) imply: % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | | | | | (1992) ~ (all_8_2 = e3) % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (247) gives: % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | | | | | | (1993) all_54_5 = e3 % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (542), (1992), (1993) are inconsistent by % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #737. % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | | | | | | (1994) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (337) gives: % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1995) all_58_1 = e1 % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (555), (1995) imply: % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1996) all_52_4 = e1 % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (184), (1996) imply: % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1997) ~ (all_52_6 = e1) % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (571), (1996) imply: % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1998) ~ (all_8_2 = e1) % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1998) implies: % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1999) ~ (all_8_2 = e1) % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (345) gives: % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2000) all_58_0 = e2 % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (340), (365), (401), (553), (1913), (1979), % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1980), (2000) are inconsistent by sub-proof #613. % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2001) all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2 % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2001) gives: % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2002) all_58_1 = e2 % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (1995), (2002) are inconsistent by sub-proof % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #594. % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2003) all_58_4 = e2 | all_58_9 = e2 % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2003) gives: % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2004) all_58_4 = e2 % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (407), (2004) imply: % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2005) all_52_8 = e2 % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (217), (2005) imply: % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2006) op(e3, e1) = e2 % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (336) gives: % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2007) all_58_1 = e0 % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1995), (2007) imply: % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2008) e1 = e0 % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4), (2008) imply: % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2009) $false % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2009) is inconsistent. % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2010) all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0 % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2010) gives: % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2011) all_58_3 = e0 % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (554), (2011) imply: % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2012) all_8_2 = e0 % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1942), (2012) imply: % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2013) $false % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2013) is inconsistent. % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2014) all_58_7 = e0 | all_58_13 = e0 % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2014) gives: % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2015) all_58_7 = e0 % 147.36/21.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (380), (2015) imply: % 147.36/21.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2016) all_52_6 = e0 % 147.36/21.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (174), (2016) imply: % 147.36/21.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2017) ~ (all_52_14 = e0) % 147.36/21.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2017) implies: % 147.36/21.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2018) ~ (all_52_14 = e0) % 147.36/21.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (573), (2016) imply: % 147.36/21.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2019) ~ (all_8_2 = e0) % 147.36/21.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (241) gives: % 147.36/21.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 147.36/21.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2020) all_54_11 = e3 % 147.36/21.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (476), (1983), (2020) are inconsistent by % 147.36/21.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #416. % 147.36/21.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 147.36/21.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2021) all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0 % 147.36/21.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2021) gives: % 147.36/21.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 147.36/21.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2022) all_54_11 = e2 % 147.36/21.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (476), (2022) imply: % 147.36/21.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2023) all_52_14 = e2 % 147.36/21.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2023) implies: % 147.36/21.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2024) all_52_14 = e2 % 147.36/21.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (550), (2024) imply: % 147.36/21.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2025) all_58_11 = e2 % 147.36/21.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (46), (48), (317), (334), (386), % 147.36/21.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (542), (554), (617), (625), (769), (1879), (1911), % 147.36/21.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1925), (1942), (1977), (1984), (1987), (1990), % 147.36/21.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1994), (1999), (2006), (2025), (function-axioms) % 147.36/21.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #278. % 147.36/21.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 147.36/21.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2026) all_54_11 = e1 | all_54_11 = e0 % 147.36/21.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (476), (1957), (2018), (2026) are inconsistent by % 147.36/21.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #688. % 147.36/21.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 147.36/21.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 147.36/21.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 147.36/21.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2027) all_58_13 = e0 % 147.36/21.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (549), (2027) imply: % 147.36/21.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2028) all_52_7 = e0 % 147.36/21.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1915), (2028) imply: % 147.36/21.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2029) $false % 147.36/21.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2029) is inconsistent. % 147.36/21.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 147.36/21.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 147.36/21.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 147.36/21.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 147.36/21.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2030) all_58_9 = e2 % 147.36/21.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1977), (2030) imply: % 147.36/21.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2031) e3 = e2 % 147.36/21.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (9), (2031) imply: % 147.36/21.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2032) $false % 147.36/21.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2032) is inconsistent. % 147.36/21.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 147.36/21.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 147.36/21.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 147.36/21.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.07 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 147.36/21.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2033) all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1 % 147.36/21.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (48), (380), (549), (554), (769), (1916), (1954), % 147.36/21.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1959), (1960), (2033), (function-axioms) are % 147.36/21.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #533. % 147.36/21.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.07 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 147.36/21.07 | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.07 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 147.36/21.07 | | | | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.07 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 147.36/21.07 | | | | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.07 | | | | | | | | | | | | | | | | | | | | | | | | | (2034) all_56_9 = e2 % 147.36/21.07 | | | | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.07 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (1989), (2034) are inconsistent by sub-proof % 147.36/21.07 | | | | | | | | | | | | | | | | | | | | | | | | | #496. % 147.36/21.07 | | | | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.07 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 147.36/21.07 | | | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.07 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 147.36/21.07 | | | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.07 | | | | | | | | | | | | | | | | | | | | | | | | (2035) all_58_6 = e1 | all_58_12 = e1 % 147.36/21.07 | | | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.07 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2035) gives: % 147.36/21.07 | | | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.07 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 147.36/21.07 | | | | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.07 | | | | | | | | | | | | | | | | | | | | | | | | | (2036) all_58_6 = e1 % 147.36/21.07 | | | | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.07 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (553), (1953), (2036) are inconsistent by % 147.36/21.07 | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #472. % 147.36/21.07 | | | | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.07 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 147.36/21.07 | | | | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.07 | | | | | | | | | | | | | | | | | | | | | | | | | (2037) all_58_12 = e1 % 147.36/21.07 | | | | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.07 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (365), (2037) imply: % 147.36/21.07 | | | | | | | | | | | | | | | | | | | | | | | | | (2038) all_52_3 = e1 % 147.36/21.07 | | | | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.07 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1914), (2038) imply: % 147.36/21.07 | | | | | | | | | | | | | | | | | | | | | | | | | (2039) $false % 147.36/21.07 | | | | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.07 | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2039) is inconsistent. % 147.36/21.07 | | | | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.07 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 147.36/21.07 | | | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.07 | | | | | | | | | | | | | | | | | | | | | | | End of split % 147.36/21.07 | | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.07 | | | | | | | | | | | | | | | | | | | | | | End of split % 147.36/21.07 | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.07 | | | | | | | | | | | | | | | | | | | | | End of split % 147.36/21.07 | | | | | | | | | | | | | | | | | | | | | % 147.36/21.07 | | | | | | | | | | | | | | | | | | | | Case 2: % 147.36/21.07 | | | | | | | | | | | | | | | | | | | | | % 147.36/21.07 | | | | | | | | | | | | | | | | | | | | | (2040) all_54_10 = e0 % 147.36/21.07 | | | | | | | | | | | | | | | | | | | | | % 147.36/21.07 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1928), (1936), (2040) are inconsistent by % 147.36/21.07 | | | | | | | | | | | | | | | | | | | | | sub-proof #277. % 147.36/21.07 | | | | | | | | | | | | | | | | | | | | | % 147.36/21.07 | | | | | | | | | | | | | | | | | | | | End of split % 147.36/21.07 | | | | | | | | | | | | | | | | | | | | % 147.36/21.07 | | | | | | | | | | | | | | | | | | | End of split % 147.36/21.07 | | | | | | | | | | | | | | | | | | | % 147.36/21.07 | | | | | | | | | | | | | | | | | | End of split % 147.36/21.07 | | | | | | | | | | | | | | | | | | % 147.36/21.07 | | | | | | | | | | | | | | | | | Case 2: % 147.36/21.07 | | | | | | | | | | | | | | | | | | % 147.36/21.07 | | | | | | | | | | | | | | | | | | (2041) all_56_21 = e3 % 147.36/21.07 | | | | | | | | | | | | | | | | | | (2042) all_56_17 = e1 % 147.36/21.07 | | | | | | | | | | | | | | | | | | % 147.36/21.07 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (381), (2042) imply: % 147.36/21.07 | | | | | | | | | | | | | | | | | | (2043) all_52_2 = e1 % 147.36/21.07 | | | | | | | | | | | | | | | | | | % 147.36/21.07 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1929), (2041) imply: % 147.36/21.07 | | | | | | | | | | | | | | | | | | (2044) all_4_1 = e3 % 147.36/21.07 | | | | | | | | | | | | | | | | | | % 147.36/21.07 | | | | | | | | | | | | | | | | | | REF_CLOSE: (37), (192), (207), (240), (478), (767), (772), % 147.36/21.07 | | | | | | | | | | | | | | | | | | (1913), (2043), (2044), (function-axioms) are % 147.36/21.07 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #521. % 147.36/21.07 | | | | | | | | | | | | | | | | | | % 147.36/21.07 | | | | | | | | | | | | | | | | | End of split % 147.36/21.07 | | | | | | | | | | | | | | | | | % 147.36/21.07 | | | | | | | | | | | | | | | | Case 2: % 147.36/21.07 | | | | | | | | | | | | | | | | | % 147.36/21.07 | | | | | | | | | | | | | | | | | (2045) all_56_11 = e0 % 147.36/21.07 | | | | | | | | | | | | | | | | | % 147.36/21.07 | | | | | | | | | | | | | | | | | COMBINE_EQS: (545), (2045) imply: % 147.36/21.07 | | | | | | | | | | | | | | | | | (2046) all_8_2 = e0 % 147.36/21.07 | | | | | | | | | | | | | | | | | % 147.36/21.07 | | | | | | | | | | | | | | | | | REDUCE: (48), (2046) imply: % 147.36/21.07 | | | | | | | | | | | | | | | | | (2047) op(e0, e0) = all_8_1 % 147.36/21.07 | | | | | | | | | | | | | | | | | % 147.36/21.07 | | | | | | | | | | | | | | | | | REF_CLOSE: (769), (1925), (2047), (function-axioms) are % 147.36/21.07 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #519. % 147.36/21.07 | | | | | | | | | | | | | | | | | % 147.36/21.07 | | | | | | | | | | | | | | | | End of split % 147.36/21.07 | | | | | | | | | | | | | | | | % 147.36/21.07 | | | | | | | | | | | | | | | Case 2: % 147.36/21.07 | | | | | | | | | | | | | | | | % 147.36/21.07 | | | | | | | | | | | | | | | | (2048) all_56_21 = e2 % 147.36/21.07 | | | | | | | | | | | | | | | | (2049) all_56_19 = e1 % 147.36/21.07 | | | | | | | | | | | | | | | | % 147.36/21.07 | | | | | | | | | | | | | | | | COMBINE_EQS: (435), (2049) imply: % 147.36/21.07 | | | | | | | | | | | | | | | | (2050) all_52_6 = e1 % 147.36/21.07 | | | | | | | | | | | | | | | | % 147.36/21.07 | | | | | | | | | | | | | | | | COMBINE_EQS: (1929), (2048) imply: % 147.36/21.07 | | | | | | | | | | | | | | | | (2051) all_4_1 = e2 % 147.36/21.07 | | | | | | | | | | | | | | | | % 147.36/21.07 | | | | | | | | | | | | | | | | REF_CLOSE: (37), (176), (206), (239), (480), (767), (772), % 147.36/21.07 | | | | | | | | | | | | | | | | (1915), (2050), (2051), (function-axioms) are % 147.36/21.07 | | | | | | | | | | | | | | | | inconsistent by sub-proof #501. % 147.36/21.07 | | | | | | | | | | | | | | | | % 147.36/21.07 | | | | | | | | | | | | | | | End of split % 147.36/21.07 | | | | | | | | | | | | | | | % 147.36/21.07 | | | | | | | | | | | | | | End of split % 147.36/21.07 | | | | | | | | | | | | | | % 147.36/21.07 | | | | | | | | | | | | | Case 2: % 147.36/21.07 | | | | | | | | | | | | | | % 147.36/21.07 | | | | | | | | | | | | | | (2052) all_40_0 = e3 % 147.36/21.07 | | | | | | | | | | | | | | (2053) ~ (all_40_1 = e0) | ~ (all_40_2 = e2) % 147.36/21.07 | | | | | | | | | | | | | | % 147.36/21.07 | | | | | | | | | | | | | | COMBINE_EQS: (713), (2052) imply: % 147.36/21.07 | | | | | | | | | | | | | | (2054) all_6_0 = e3 % 147.36/21.07 | | | | | | | | | | | | | | % 147.36/21.07 | | | | | | | | | | | | | | SIMP: (2054) implies: % 147.36/21.07 | | | | | | | | | | | | | | (2055) all_6_0 = e3 % 147.36/21.07 | | | | | | | | | | | | | | % 147.36/21.07 | | | | | | | | | | | | | | REDUCE: (42), (2055) imply: % 147.36/21.07 | | | | | | | | | | | | | | (2056) op(e1, all_6_1) = e3 % 147.36/21.07 | | | | | | | | | | | | | | % 147.36/21.07 | | | | | | | | | | | | | | BETA: splitting (288) gives: % 147.36/21.07 | | | | | | | | | | | | | | % 147.36/21.07 | | | | | | | | | | | | | | Case 1: % 147.36/21.07 | | | | | | | | | | | | | | | % 147.36/21.07 | | | | | | | | | | | | | | | (2057) ~ (all_56_31 = e1) % 147.36/21.07 | | | | | | | | | | | | | | | % 147.36/21.07 | | | | | | | | | | | | | | | REDUCE: (544), (2057) imply: % 147.36/21.07 | | | | | | | | | | | | | | | (2058) ~ (all_4_2 = e1) % 147.36/21.07 | | | | | | | | | | | | | | | % 147.36/21.07 | | | | | | | | | | | | | | | BETA: splitting (292) gives: % 147.36/21.07 | | | | | | | | | | | | | | | % 147.36/21.07 | | | | | | | | | | | | | | | Case 1: % 147.36/21.07 | | | | | | | | | | | | | | | | % 147.36/21.07 | | | | | | | | | | | | | | | | (2059) ~ (all_56_21 = e2) % 147.36/21.07 | | | | | | | | | | | | | | | | % 147.36/21.07 | | | | | | | | | | | | | | | | REDUCE: (374), (2059) imply: % 147.36/21.07 | | | | | | | | | | | | | | | | (2060) ~ (all_6_2 = e2) % 147.36/21.07 | | | | | | | | | | | | | | | | % 147.36/21.07 | | | | | | | | | | | | | | | | REF_CLOSE: (8), (36), (37), (38), (41), (42), (43), (46), % 147.36/21.07 | | | | | | | | | | | | | | | | (47), (48), (51), (53), (158), (160), (161), % 147.36/21.07 | | | | | | | | | | | | | | | | (165), (168), (169), (171), (173), (174), (176), % 147.36/21.07 | | | | | | | | | | | | | | | | (181), (182), (183), (184), (187), (188), (189), % 147.36/21.07 | | | | | | | | | | | | | | | | (191), (192), (193), (194), (196), (197), (205), % 147.36/21.07 | | | | | | | | | | | | | | | | (206), (207), (208), (210), (211), (213), (215), % 147.36/21.07 | | | | | | | | | | | | | | | | (216), (217), (218), (237), (238), (239), (240), % 147.36/21.07 | | | | | | | | | | | | | | | | (241), (242), (243), (244), (245), (246), (247), % 147.36/21.07 | | | | | | | | | | | | | | | | (248), (249), (250), (251), (252), (286), (287), % 147.36/21.07 | | | | | | | | | | | | | | | | (289), (290), (291), (293), (294), (295), (296), % 147.36/21.07 | | | | | | | | | | | | | | | | (297), (298), (299), (317), (318), (319), (320), % 147.36/21.07 | | | | | | | | | | | | | | | | (321), (322), (324), (326), (327), (328), (329), % 147.36/21.07 | | | | | | | | | | | | | | | | (330), (332), (333), (335), (336), (337), (338), % 147.36/21.07 | | | | | | | | | | | | | | | | (340), (341), (342), (343), (345), (347), (360), % 147.36/21.07 | | | | | | | | | | | | | | | | (365), (366), (374), (380), (381), (386), (389), % 147.36/21.07 | | | | | | | | | | | | | | | | (401), (402), (407), (408), (419), (425), (429), % 147.36/21.07 | | | | | | | | | | | | | | | | (431), (435), (443), (447), (457), (459), (461), % 147.36/21.07 | | | | | | | | | | | | | | | | (463), (467), (469), (471), (473), (476), (478), % 147.36/21.07 | | | | | | | | | | | | | | | | (480), (482), (521), (527), (540), (541), (542), % 147.36/21.07 | | | | | | | | | | | | | | | | (543), (544), (545), (546), (547), (548), (549), % 147.36/21.07 | | | | | | | | | | | | | | | | (550), (551), (552), (553), (554), (555), (557), % 147.36/21.07 | | | | | | | | | | | | | | | | (559), (561), (563), (565), (567), (568), (569), % 147.36/21.07 | | | | | | | | | | | | | | | | (570), (571), (573), (575), (577), (579), (580), % 147.36/21.07 | | | | | | | | | | | | | | | | (581), (582), (583), (585), (587), (588), (589), % 147.36/21.07 | | | | | | | | | | | | | | | | (590), (591), (612), (613), (614), (615), (616), % 147.36/21.07 | | | | | | | | | | | | | | | | (617), (618), (620), (621), (622), (624), (625), % 147.36/21.07 | | | | | | | | | | | | | | | | (626), (627), (643), (677), (768), (769), (772), % 147.36/21.07 | | | | | | | | | | | | | | | | (774), (1875), (1879), (1881), (1884), (1886), % 147.36/21.07 | | | | | | | | | | | | | | | | (1888), (1890), (2058), (2060), (function-axioms) % 147.36/21.07 | | | | | | | | | | | | | | | | are inconsistent by sub-proof #285. % 147.36/21.07 | | | | | | | | | | | | | | | | % 147.36/21.07 | | | | | | | | | | | | | | | Case 2: % 147.36/21.07 | | | | | | | | | | | | | | | | % 147.36/21.07 | | | | | | | | | | | | | | | | (2061) all_56_21 = e2 % 147.36/21.07 | | | | | | | | | | | | | | | | (2062) all_56_19 = e1 % 147.36/21.07 | | | | | | | | | | | | | | | | % 147.36/21.07 | | | | | | | | | | | | | | | | REF_CLOSE: (43), (46), (247), (374), (435), (507), (542), % 147.36/21.07 | | | | | | | | | | | | | | | | (573), (685), (768), (1890), (2053), (2061), % 147.36/21.07 | | | | | | | | | | | | | | | | (2062), (function-axioms) are inconsistent by % 147.36/21.07 | | | | | | | | | | | | | | | | sub-proof #276. % 147.36/21.07 | | | | | | | | | | | | | | | | % 147.36/21.07 | | | | | | | | | | | | | | | End of split % 147.36/21.07 | | | | | | | | | | | | | | | % 147.36/21.07 | | | | | | | | | | | | | | Case 2: % 147.36/21.07 | | | | | | | | | | | | | | | % 147.36/21.07 | | | | | | | | | | | | | | | (2063) all_56_31 = e1 % 147.36/21.07 | | | | | | | | | | | | | | | (2064) all_56_29 = e0 % 147.36/21.07 | | | | | | | | | | | | | | | % 147.36/21.07 | | | | | | | | | | | | | | | COMBINE_EQS: (357), (2064) imply: % 147.36/21.07 | | | | | | | | | | | | | | | (2065) all_52_11 = e0 % 147.36/21.07 | | | | | | | | | | | | | | | % 147.36/21.07 | | | | | | | | | | | | | | | SIMP: (2065) implies: % 147.36/21.07 | | | | | | | | | | | | | | | (2066) all_52_11 = e0 % 147.36/21.07 | | | | | | | | | | | | | | | % 147.36/21.07 | | | | | | | | | | | | | | | REF_CLOSE: (37), (38), (41), (43), (173), (176), (187), % 147.36/21.07 | | | | | | | | | | | | | | | (192), (206), (207), (239), (240), (242), (292), % 147.36/21.07 | | | | | | | | | | | | | | | (293), (374), (381), (435), (478), (480), (541), % 147.36/21.07 | | | | | | | | | | | | | | | (544), (585), (622), (767), (772), (1890), (2056), % 147.36/21.07 | | | | | | | | | | | | | | | (2063), (2066), (function-axioms) are inconsistent % 147.36/21.07 | | | | | | | | | | | | | | | by sub-proof #462. % 147.36/21.07 | | | | | | | | | | | | | | | % 147.36/21.07 | | | | | | | | | | | | | | End of split % 147.36/21.07 | | | | | | | | | | | | | | % 147.36/21.07 | | | | | | | | | | | | | End of split % 147.36/21.07 | | | | | | | | | | | | | % 147.36/21.07 | | | | | | | | | | | | Case 2: % 147.36/21.07 | | | | | | | | | | | | | % 147.36/21.07 | | | | | | | | | | | | | (2067) all_36_1 = e3 % 147.36/21.07 | | | | | | | | | | | | | (2068) ~ (all_36_0 = e0) | ~ (all_36_2 = e2) % 147.36/21.07 | | | | | | | | | | | | | % 147.36/21.07 | | | | | | | | | | | | | COMBINE_EQS: (652), (2067) imply: % 147.36/21.07 | | | | | | | | | | | | | (2069) all_6_1 = e3 % 147.36/21.07 | | | | | | | | | | | | | % 147.36/21.07 | | | | | | | | | | | | | REDUCE: (43), (2069) imply: % 147.36/21.07 | | | | | | | | | | | | | (2070) op(all_6_2, all_6_2) = e3 % 147.36/21.07 | | | | | | | | | | | | | % 147.36/21.07 | | | | | | | | | | | | | REDUCE: (42), (2069) imply: % 147.36/21.07 | | | | | | | | | | | | | (2071) op(e1, e3) = all_6_0 % 147.36/21.07 | | | | | | | | | | | | | % 147.36/21.07 | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_2, % 147.36/21.07 | | | | | | | | | | | | | all_6_0, e3, e1, simplifying with (211), (2071) % 147.36/21.07 | | | | | | | | | | | | | gives: % 147.36/21.07 | | | | | | | | | | | | | (2072) all_52_2 = all_6_0 % 147.36/21.07 | | | | | | | | | | | | | % 147.36/21.07 | | | | | | | | | | | | | COMBINE_EQS: (471), (2072) imply: % 147.36/21.07 | | | | | | | | | | | | | (2073) all_54_8 = all_6_0 % 147.36/21.07 | | | | | | | | | | | | | % 147.36/21.07 | | | | | | | | | | | | | COMBINE_EQS: (381), (2072) imply: % 147.36/21.07 | | | | | | | | | | | | | (2074) all_56_17 = all_6_0 % 147.36/21.07 | | | | | | | | | | | | | % 147.36/21.07 | | | | | | | | | | | | | COMBINE_EQS: (553), (2072) imply: % 147.36/21.07 | | | | | | | | | | | | | (2075) all_58_6 = all_6_0 % 147.36/21.07 | | | | | | | | | | | | | % 147.36/21.07 | | | | | | | | | | | | | REDUCE: (197), (2072) imply: % 147.36/21.07 | | | | | | | | | | | | | (2076) ~ (all_52_1 = all_6_0) % 147.36/21.07 | | | | | | | | | | | | | % 147.36/21.07 | | | | | | | | | | | | | REDUCE: (192), (2072) imply: % 147.36/21.07 | | | | | | | | | | | | | (2077) ~ (all_52_3 = all_6_0) % 147.36/21.07 | | | | | | | | | | | | | % 147.36/21.07 | | | | | | | | | | | | | SIMP: (2077) implies: % 147.36/21.07 | | | | | | | | | | | | | (2078) ~ (all_52_3 = all_6_0) % 147.36/21.07 | | | | | | | | | | | | | % 147.36/21.07 | | | | | | | | | | | | | REDUCE: (191), (2072) imply: % 147.36/21.07 | | | | | | | | | | | | | (2079) ~ (all_52_6 = all_6_0) % 147.36/21.07 | | | | | | | | | | | | | % 147.36/21.07 | | | | | | | | | | | | | SIMP: (2079) implies: % 147.36/21.07 | | | | | | | | | | | | | (2080) ~ (all_52_6 = all_6_0) % 147.36/21.07 | | | | | | | | | | | | | % 147.36/21.07 | | | | | | | | | | | | | REDUCE: (189), (2072) imply: % 147.36/21.07 | | | | | | | | | | | | | (2081) ~ (all_52_14 = all_6_0) % 147.36/21.07 | | | | | | | | | | | | | % 147.36/21.07 | | | | | | | | | | | | | SIMP: (2081) implies: % 147.36/21.07 | | | | | | | | | | | | | (2082) ~ (all_52_14 = all_6_0) % 147.36/21.07 | | | | | | | | | | | | | % 147.36/21.07 | | | | | | | | | | | | | REDUCE: (559), (2072) imply: % 147.36/21.07 | | | | | | | | | | | | | (2083) ~ (all_10_2 = all_6_0) % 147.36/21.07 | | | | | | | | | | | | | % 147.36/21.07 | | | | | | | | | | | | | SIMP: (2083) implies: % 147.36/21.07 | | | | | | | | | | | | | (2084) ~ (all_10_2 = all_6_0) % 147.36/21.07 | | | | | | | | | | | | | % 147.36/21.07 | | | | | | | | | | | | | REDUCE: (569), (2072) imply: % 147.36/21.07 | | | | | | | | | | | | | (2085) ~ (all_6_0 = all_6_2) % 147.36/21.07 | | | | | | | | | | | | | % 147.36/21.07 | | | | | | | | | | | | | REDUCE: (614), (2072) imply: % 147.36/21.07 | | | | | | | | | | | | | (2086) op(e3, all_6_0) = all_56_16 % 147.36/21.07 | | | | | | | | | | | | | % 147.36/21.07 | | | | | | | | | | | | | BETA: splitting (288) gives: % 147.36/21.07 | | | | | | | | | | | | | % 147.36/21.07 | | | | | | | | | | | | | Case 1: % 147.36/21.07 | | | | | | | | | | | | | | % 147.36/21.07 | | | | | | | | | | | | | | (2087) ~ (all_56_31 = e1) % 147.36/21.07 | | | | | | | | | | | | | | % 147.36/21.07 | | | | | | | | | | | | | | REDUCE: (544), (2087) imply: % 147.36/21.07 | | | | | | | | | | | | | | (2088) ~ (all_4_2 = e1) % 147.36/21.07 | | | | | | | | | | | | | | % 147.36/21.07 | | | | | | | | | | | | | | BETA: splitting (290) gives: % 147.36/21.07 | | | | | | | | | | | | | | % 147.36/21.07 | | | | | | | | | | | | | | Case 1: % 147.36/21.07 | | | | | | | | | | | | | | | % 147.36/21.07 | | | | | | | | | | | | | | | (2089) ~ (all_56_31 = e3) % 147.36/21.07 | | | | | | | | | | | | | | | % 147.36/21.07 | | | | | | | | | | | | | | | REDUCE: (544), (2089) imply: % 147.36/21.07 | | | | | | | | | | | | | | | (2090) ~ (all_4_2 = e3) % 147.36/21.07 | | | | | | | | | | | | | | | % 147.36/21.08 | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (36), (38), (41), (46), (48), (51), % 147.36/21.08 | | | | | | | | | | | | | | | (168), (174), (181), (242), (243), (244), (287), % 147.36/21.08 | | | | | | | | | | | | | | | (291), (292), (293), (295), (320), (321), (323), % 147.36/21.08 | | | | | | | | | | | | | | | (324), (329), (337), (365), (366), (374), (380), % 147.36/21.08 | | | | | | | | | | | | | | | (389), (407), (431), (435), (473), (532), (541), % 147.36/21.08 | | | | | | | | | | | | | | | (544), (545), (546), (547), (548), (549), (550), % 147.36/21.08 | | | | | | | | | | | | | | | (551), (552), (554), (555), (561), (567), (573), % 147.36/21.08 | | | | | | | | | | | | | | | (575), (577), (580), (585), (587), (591), (617), % 147.36/21.08 | | | | | | | | | | | | | | | (622), (623), (627), (762), (1881), (1888), % 147.36/21.08 | | | | | | | | | | | | | | | (2068), (2070), (2073), (2074), (2075), (2080), % 147.36/21.08 | | | | | | | | | | | | | | | (2082), (2084), (2085), (2088), (2090), % 147.36/21.08 | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 147.36/21.08 | | | | | | | | | | | | | | | #274. % 147.36/21.08 | | | | | | | | | | | | | | | % 147.36/21.08 | | | | | | | | | | | | | | Case 2: % 147.36/21.08 | | | | | | | | | | | | | | | % 147.36/21.08 | | | | | | | | | | | | | | | (2091) all_56_31 = e3 % 147.36/21.08 | | | | | | | | | | | | | | | (2092) all_56_25 = e0 % 147.36/21.08 | | | | | | | | | | | | | | | % 147.36/21.08 | | | | | | | | | | | | | | | COMBINE_EQS: (447), (2092) imply: % 147.36/21.08 | | | | | | | | | | | | | | | (2093) all_52_3 = e0 % 147.36/21.08 | | | | | | | | | | | | | | | % 147.36/21.08 | | | | | | | | | | | | | | | SIMP: (2093) implies: % 147.36/21.08 | | | | | | | | | | | | | | | (2094) all_52_3 = e0 % 147.36/21.08 | | | | | | | | | | | | | | | % 147.36/21.08 | | | | | | | | | | | | | | | COMBINE_EQS: (544), (2091) imply: % 147.36/21.08 | | | | | | | | | | | | | | | (2095) all_4_2 = e3 % 147.36/21.08 | | | | | | | | | | | | | | | % 147.36/21.08 | | | | | | | | | | | | | | | COMBINE_EQS: (547), (2095) imply: % 147.36/21.08 | | | | | | | | | | | | | | | (2096) all_58_15 = e3 % 147.36/21.08 | | | | | | | | | | | | | | | % 147.36/21.08 | | | | | | | | | | | | | | | COMBINE_EQS: (365), (2094) imply: % 147.36/21.08 | | | | | | | | | | | | | | | (2097) all_58_12 = e0 % 147.36/21.08 | | | | | | | | | | | | | | | % 147.36/21.08 | | | | | | | | | | | | | | | REDUCE: (188), (2094) imply: % 147.36/21.08 | | | | | | | | | | | | | | | (2098) ~ (all_52_7 = e0) % 147.36/21.08 | | | | | | | | | | | | | | | % 147.36/21.08 | | | | | | | | | | | | | | | SIMP: (2098) implies: % 147.36/21.08 | | | | | | | | | | | | | | | (2099) ~ (all_52_7 = e0) % 147.36/21.08 | | | | | | | | | | | | | | | % 147.36/21.08 | | | | | | | | | | | | | | | REDUCE: (187), (2094) imply: % 147.36/21.08 | | | | | | | | | | | | | | | (2100) ~ (all_52_11 = e0) % 147.36/21.08 | | | | | | | | | | | | | | | % 147.36/21.08 | | | | | | | | | | | | | | | SIMP: (2100) implies: % 147.36/21.08 | | | | | | | | | | | | | | | (2101) ~ (all_52_11 = e0) % 147.36/21.08 | | | | | | | | | | | | | | | % 147.36/21.08 | | | | | | | | | | | | | | | REDUCE: (2078), (2094) imply: % 147.36/21.08 | | | | | | | | | | | | | | | (2102) ~ (all_6_0 = e0) % 147.36/21.08 | | | | | | | | | | | | | | | % 147.36/21.08 | | | | | | | | | | | | | | | SIMP: (2102) implies: % 147.36/21.08 | | | | | | | | | | | | | | | (2103) ~ (all_6_0 = e0) % 147.36/21.08 | | | | | | | | | | | | | | | % 147.36/21.08 | | | | | | | | | | | | | | | REDUCE: (570), (2094), (2095) imply: % 147.36/21.08 | | | | | | | | | | | | | | | (2104) ~ (e3 = e0) % 147.36/21.08 | | | | | | | | | | | | | | | % 147.36/21.08 | | | | | | | | | | | | | | | REDUCE: (581), (2095) imply: % 147.36/21.08 | | | | | | | | | | | | | | | (2105) ~ (all_52_7 = e3) % 147.36/21.08 | | | | | | | | | | | | | | | % 147.36/21.08 | | | | | | | | | | | | | | | REDUCE: (590), (2095) imply: % 147.36/21.08 | | | | | | | | | | | | | | | (2106) ~ (all_52_13 = e3) % 147.36/21.08 | | | | | | | | | | | | | | | % 147.36/21.08 | | | | | | | | | | | | | | | REDUCE: (38), (2095) imply: % 147.36/21.08 | | | | | | | | | | | | | | | (2107) op(e3, e3) = all_4_1 % 147.36/21.08 | | | | | | | | | | | | | | | % 147.36/21.08 | | | | | | | | | | | | | | | REDUCE: (615), (2094) imply: % 147.36/21.08 | | | | | | | | | | | | | | | (2108) op(e3, e0) = all_56_24 % 147.36/21.08 | | | | | | | | | | | | | | | % 147.36/21.08 | | | | | | | | | | | | | | | REDUCE: (627), (2095) imply: % 147.36/21.08 | | | | | | | | | | | | | | | (2109) op(e0, e3) = all_56_30 % 147.36/21.08 | | | | | | | | | | | | | | | % 147.36/21.08 | | | | | | | | | | | | | | | REDUCE: (207), (2094) imply: % 147.36/21.08 | | | | | | | | | | | | | | | (2110) op(e0, e3) = e0 % 147.36/21.08 | | | | | | | | | | | | | | | % 147.36/21.08 | | | | | | | | | | | | | | | REDUCE: (36), (2095) imply: % 147.36/21.08 | | | | | | | | | | | | | | | (2111) op(e0, e0) = e3 % 147.36/21.08 | | | | | | | | | | | | | | | % 147.36/21.08 | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, % 147.36/21.08 | | | | | | | | | | | | | | | all_56_30, e3, e0, simplifying with (2109), (2110) % 147.36/21.08 | | | | | | | | | | | | | | | gives: % 147.36/21.08 | | | | | | | | | | | | | | | (2112) all_56_30 = e0 % 147.36/21.08 | | | | | | | | | | | | | | | % 147.36/21.08 | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_12, % 147.36/21.08 | | | | | | | | | | | | | | | all_56_24, e0, e3, simplifying with (216), (2108) % 147.36/21.08 | | | | | | | | | | | | | | | gives: % 147.36/21.08 | | | | | | | | | | | | | | | (2113) all_56_24 = all_52_12 % 147.36/21.08 | | | | | | | | | | | | | | | % 147.36/21.08 | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_10_2, % 147.36/21.08 | | | | | | | | | | | | | | | all_4_1, e3, e3, simplifying with (51), (2107) % 147.36/21.08 | | | | | | | | | | | | | | | gives: % 147.36/21.08 | | | | | | | | | | | | | | | (2114) all_10_2 = all_4_1 % 147.36/21.08 | | | | | | | | | | | | | | | % 147.36/21.08 | | | | | | | | | | | | | | | COMBINE_EQS: (546), (2114) imply: % 147.36/21.08 | | | | | | | | | | | | | | | (2115) all_56_1 = all_4_1 % 147.36/21.08 | | | | | | | | | | | | | | | % 147.36/21.08 | | | | | | | | | | | | | | | COMBINE_EQS: (419), (2114) imply: % 147.36/21.08 | | | | | | | | | | | | | | | (2116) all_58_0 = all_4_1 % 147.36/21.08 | | | | | | | | | | | | | | | % 147.36/21.08 | | | | | | | | | | | | | | | REDUCE: (563), (2114) imply: % 147.36/21.08 | | | | | | | | | | | | | | | (2117) ~ (all_52_4 = all_4_1) % 147.36/21.08 | | | | | | | | | | | | | | | % 147.36/21.08 | | | | | | | | | | | | | | | REDUCE: (565), (2114) imply: % 147.36/21.08 | | | | | | | | | | | | | | | (2118) ~ (all_52_8 = all_4_1) % 147.36/21.08 | | | | | | | | | | | | | | | % 147.36/21.08 | | | | | | | | | | | | | | | REDUCE: (567), (2114) imply: % 147.36/21.08 | | | | | | | | | | | | | | | (2119) ~ (all_52_12 = all_4_1) % 147.36/21.08 | | | | | | | | | | | | | | | % 147.36/21.08 | | | | | | | | | | | | | | | REDUCE: (2084), (2114) imply: % 147.36/21.08 | | | | | | | | | | | | | | | (2120) ~ (all_6_0 = all_4_1) % 147.36/21.08 | | | | | | | | | | | | | | | % 147.36/21.08 | | | | | | | | | | | | | | | SIMP: (2120) implies: % 147.36/21.08 | | | | | | | | | | | | | | | (2121) ~ (all_6_0 = all_4_1) % 147.36/21.08 | | | | | | | | | | | | | | | % 147.36/21.08 | | | | | | | | | | | | | | | REDUCE: (53), (2114) imply: % 147.36/21.08 | | | | | | | | | | | | | | | (2122) op(all_4_1, all_4_1) = all_10_1 % 147.36/21.08 | | | | | | | | | | | | | | | % 147.36/21.08 | | | | | | | | | | | | | | | REDUCE: (612), (2114) imply: % 147.36/21.08 | | | | | | | | | | | | | | | (2123) op(e3, all_4_1) = all_56_0 % 147.36/21.08 | | | | | | | | | | | | | | | % 147.36/21.08 | | | | | | | | | | | | | | | BETA: splitting (292) gives: % 147.36/21.08 | | | | | | | | | | | | | | | % 147.36/21.08 | | | | | | | | | | | | | | | Case 1: % 147.36/21.08 | | | | | | | | | | | | | | | | % 147.36/21.08 | | | | | | | | | | | | | | | | (2124) ~ (all_56_21 = e2) % 147.36/21.08 | | | | | | | | | | | | | | | | % 147.36/21.08 | | | | | | | | | | | | | | | | REDUCE: (374), (2124) imply: % 147.36/21.08 | | | | | | | | | | | | | | | | (2125) ~ (all_6_2 = e2) % 147.36/21.08 | | | | | | | | | | | | | | | | % 147.36/21.08 | | | | | | | | | | | | | | | | BETA: splitting (291) gives: % 147.36/21.08 | | | | | | | | | | | | | | | | % 147.36/21.08 | | | | | | | | | | | | | | | | Case 1: % 147.36/21.08 | | | | | | | | | | | | | | | | | % 147.36/21.08 | | | | | | | | | | | | | | | | | (2126) ~ (all_56_21 = e0) % 147.36/21.08 | | | | | | | | | | | | | | | | | % 147.36/21.08 | | | | | | | | | | | | | | | | | REDUCE: (374), (2126) imply: % 147.36/21.08 | | | | | | | | | | | | | | | | | (2127) ~ (all_6_2 = e0) % 147.36/21.08 | | | | | | | | | | | | | | | | | % 147.36/21.08 | | | | | | | | | | | | | | | | | BETA: splitting (294) gives: % 147.36/21.08 | | | | | | | | | | | | | | | | | % 147.36/21.08 | | | | | | | | | | | | | | | | | Case 1: % 147.36/21.08 | | | | | | | | | | | | | | | | | | % 147.36/21.08 | | | | | | | | | | | | | | | | | | (2128) ~ (all_56_11 = e0) % 147.36/21.08 | | | | | | | | | | | | | | | | | | % 147.36/21.08 | | | | | | | | | | | | | | | | | | REDUCE: (545), (2128) imply: % 147.36/21.08 | | | | | | | | | | | | | | | | | | (2129) ~ (all_8_2 = e0) % 147.36/21.08 | | | | | | | | | | | | | | | | | | % 147.36/21.08 | | | | | | | | | | | | | | | | | | BETA: splitting (295) gives: % 147.36/21.08 | | | | | | | | | | | | | | | | | | % 147.36/21.08 | | | | | | | | | | | | | | | | | | Case 1: % 147.36/21.08 | | | | | | | | | | | | | | | | | | | % 147.36/21.08 | | | | | | | | | | | | | | | | | | | (2130) ~ (all_56_11 = e1) % 147.36/21.08 | | | | | | | | | | | | | | | | | | | % 147.36/21.08 | | | | | | | | | | | | | | | | | | | REDUCE: (545), (2130) imply: % 147.36/21.08 | | | | | | | | | | | | | | | | | | | (2131) ~ (all_8_2 = e1) % 147.36/21.08 | | | | | | | | | | | | | | | | | | | % 147.36/21.08 | | | | | | | | | | | | | | | | | | | BETA: splitting (293) gives: % 147.36/21.08 | | | | | | | | | | | | | | | | | | | % 147.36/21.08 | | | | | | | | | | | | | | | | | | | Case 1: % 147.36/21.08 | | | | | | | | | | | | | | | | | | | | % 147.36/21.08 | | | | | | | | | | | | | | | | | | | | (2132) ~ (all_56_21 = e3) % 147.36/21.08 | | | | | | | | | | | | | | | | | | | | % 147.36/21.08 | | | | | | | | | | | | | | | | | | | | REDUCE: (374), (2132) imply: % 147.36/21.08 | | | | | | | | | | | | | | | | | | | | (2133) ~ (all_6_2 = e3) % 147.36/21.08 | | | | | | | | | | | | | | | | | | | | % 147.36/21.08 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (41), (242), (541), (622), (2070), (2125), (2127), % 147.36/21.08 | | | | | | | | | | | | | | | | | | | | (2133), (function-axioms) are inconsistent by % 147.36/21.08 | | | | | | | | | | | | | | | | | | | | sub-proof #459. % 147.36/21.08 | | | | | | | | | | | | | | | | | | | | % 147.36/21.08 | | | | | | | | | | | | | | | | | | | Case 2: % 147.36/21.08 | | | | | | | | | | | | | | | | | | | | % 147.36/21.08 | | | | | | | | | | | | | | | | | | | | (2134) all_56_21 = e3 % 147.36/21.08 | | | | | | | | | | | | | | | | | | | | (2135) all_56_17 = e1 % 147.36/21.08 | | | | | | | | | | | | | | | | | | | | % 147.36/21.08 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2074), (2135) imply: % 147.36/21.08 | | | | | | | | | | | | | | | | | | | | (2136) all_6_0 = e1 % 147.36/21.08 | | | | | | | | | | | | | | | | | | | | % 147.36/21.08 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (374), (2134) imply: % 147.36/21.08 | | | | | | | | | | | | | | | | | | | | (2137) all_6_2 = e3 % 147.36/21.08 | | | | | | | | | | | | | | | | | | | | % 147.36/21.08 | | | | | | | | | | | | | | | | | | | | SIMP: (2137) implies: % 147.36/21.08 | | | | | | | | | | | | | | | | | | | | (2138) all_6_2 = e3 % 147.36/21.08 | | | | | | | | | | | | | | | | | | | | % 147.36/21.08 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (552), (2138) imply: % 147.36/21.08 | | | | | | | | | | | | | | | | | | | | (2139) all_58_8 = e3 % 147.36/21.08 | | | | | | | | | | | | | | | | | | | | % 147.36/21.08 | | | | | | | | | | | | | | | | | | | | REDUCE: (2076), (2136) imply: % 147.36/21.08 | | | | | | | | | | | | | | | | | | | | (2140) ~ (all_52_1 = e1) % 147.36/21.08 | | | | | | | | | | | | | | | | | | | | % 147.36/21.08 | | | | | | | | | | | | | | | | | | | | REDUCE: (2080), (2136) imply: % 147.36/21.08 | | | | | | | | | | | | | | | | | | | | (2141) ~ (all_52_6 = e1) % 147.36/21.08 | | | | | | | | | | | | | | | | | | | | % 147.36/21.08 | | | | | | | | | | | | | | | | | | | | REDUCE: (580), (2138) imply: % 147.36/21.08 | | | | | | | | | | | | | | | | | | | | (2142) ~ (all_52_6 = e3) % 147.36/21.08 | | | | | | | | | | | | | | | | | | | | % 147.36/21.08 | | | | | | | | | | | | | | | | | | | | REDUCE: (583), (2138) imply: % 147.36/21.08 | | | | | | | | | | | | | | | | | | | | (2143) ~ (all_52_9 = e3) % 147.36/21.08 | | | | | | | | | | | | | | | | | | | | % 147.36/21.08 | | | | | | | | | | | | | | | | | | | | REDUCE: (585), (2138) imply: % 147.36/21.08 | | | | | | | | | | | | | | | | | | | | (2144) ~ (all_52_11 = e3) % 147.36/21.08 | | | | | | | | | | | | | | | | | | | | % 147.36/21.08 | | | | | | | | | | | | | | | | | | | | REDUCE: (2082), (2136) imply: % 147.36/21.08 | | | | | | | | | | | | | | | | | | | | (2145) ~ (all_52_14 = e1) % 147.36/21.08 | | | | | | | | | | | | | | | | | | | | % 147.36/21.08 | | | | | | | | | | | | | | | | | | | | REDUCE: (587), (2138) imply: % 147.36/21.08 | | | | | | | | | | | | | | | | | | | | (2146) ~ (all_52_14 = e3) % 147.36/21.08 | | | | | | | | | | | | | | | | | | | | % 147.36/21.08 | | | | | | | | | | | | | | | | | | | | REDUCE: (2070), (2138) imply: % 147.36/21.08 | | | | | | | | | | | | | | | | | | | | (2147) op(e3, e3) = e3 % 147.36/21.08 | | | | | | | | | | | | | | | | | | | | % 147.36/21.08 | | | | | | | | | | | | | | | | | | | | REDUCE: (2086), (2136) imply: % 147.36/21.08 | | | | | | | | | | | | | | | | | | | | (2148) op(e3, e1) = all_56_16 % 147.36/21.08 | | | | | | | | | | | | | | | | | | | | % 147.36/21.08 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_8, % 147.36/21.08 | | | | | | | | | | | | | | | | | | | | all_56_16, e1, e3, simplifying with (217), (2148) % 147.36/21.08 | | | | | | | | | | | | | | | | | | | | gives: % 147.36/21.08 | | | | | | | | | | | | | | | | | | | | (2149) all_56_16 = all_52_8 % 147.36/21.08 | | | | | | | | | | | | | | | | | | | | % 147.36/21.08 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_4_1, e3, % 147.36/21.08 | | | | | | | | | | | | | | | | | | | | e3, e3, simplifying with (2107), (2147) gives: % 147.36/21.08 | | | | | | | | | | | | | | | | | | | | (2150) all_4_1 = e3 % 147.36/21.08 | | | | | | | | | | | | | | | | | | | | % 147.36/21.08 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2115), (2150) imply: % 147.36/21.08 | | | | | | | | | | | | | | | | | | | | (2151) all_56_1 = e3 % 147.36/21.08 | | | | | | | | | | | | | | | | | | | | % 147.36/21.08 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2116), (2150) imply: % 147.36/21.08 | | | | | | | | | | | | | | | | | | | | (2152) all_58_0 = e3 % 147.36/21.08 | | | | | | | | | | | | | | | | | | | | % 147.36/21.08 | | | | | | | | | | | | | | | | | | | | REDUCE: (2117), (2150) imply: % 147.36/21.08 | | | | | | | | | | | | | | | | | | | | (2153) ~ (all_52_4 = e3) % 147.36/21.08 | | | | | | | | | | | | | | | | | | | | % 147.36/21.08 | | | | | | | | | | | | | | | | | | | | REDUCE: (2118), (2150) imply: % 147.36/21.08 | | | | | | | | | | | | | | | | | | | | (2154) ~ (all_52_8 = e3) % 147.36/21.08 | | | | | | | | | | | | | | | | | | | | % 147.36/21.08 | | | | | | | | | | | | | | | | | | | | REDUCE: (2119), (2150) imply: % 147.36/21.08 | | | | | | | | | | | | | | | | | | | | (2155) ~ (all_52_12 = e3) % 147.36/21.08 | | | | | | | | | | | | | | | | | | | | % 147.36/21.08 | | | | | | | | | | | | | | | | | | | | REDUCE: (2122), (2150) imply: % 147.36/21.08 | | | | | | | | | | | | | | | | | | | | (2156) op(e3, e3) = all_10_1 % 147.36/21.08 | | | | | | | | | | | | | | | | | | | | % 147.36/21.08 | | | | | | | | | | | | | | | | | | | | REDUCE: (2123), (2150) imply: % 147.36/21.08 | | | | | | | | | | | | | | | | | | | | (2157) op(e3, e3) = all_56_0 % 147.36/21.08 | | | | | | | | | | | | | | | | | | | | % 147.36/21.08 | | | | | | | | | | | | | | | | | | | | REDUCE: (37), (2150) imply: % 147.36/21.08 | | | | | | | | | | | | | | | | | | | | (2158) op(e0, e3) = all_4_0 % 147.36/21.08 | | | | | | | | | | | | | | | | | | | | % 147.36/21.08 | | | | | | | | | | | | | | | | | | | | BETA: splitting (344) gives: % 147.36/21.08 | | | | | | | | | | | | | | | | | | | | % 147.36/21.08 | | | | | | | | | | | | | | | | | | | | Case 1: % 147.36/21.08 | | | | | | | | | | | | | | | | | | | | | % 147.36/21.08 | | | | | | | | | | | | | | | | | | | | | (2159) all_58_0 = e2 % 147.36/21.08 | | | | | | | | | | | | | | | | | | | | | % 147.36/21.08 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2152), (2159) imply: % 147.36/21.08 | | | | | | | | | | | | | | | | | | | | | (2160) e3 = e2 % 147.36/21.08 | | | | | | | | | | | | | | | | | | | | | % 147.36/21.08 | | | | | | | | | | | | | | | | | | | | | REDUCE: (9), (2160) imply: % 147.36/21.08 | | | | | | | | | | | | | | | | | | | | | (2161) $false % 147.36/21.08 | | | | | | | | | | | | | | | | | | | | | % 147.36/21.08 | | | | | | | | | | | | | | | | | | | | | CLOSE: (2161) is inconsistent. % 147.36/21.08 | | | | | | | | | | | | | | | | | | | | | % 147.36/21.08 | | | | | | | | | | | | | | | | | | | | Case 2: % 147.36/21.08 | | | | | | | | | | | | | | | | | | | | | % 147.36/21.08 | | | | | | | | | | | | | | | | | | | | | (2162) all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2 % 147.36/21.08 | | | | | | | | | | | | | | | | | | | | | % 147.36/21.08 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2162) gives: % 147.36/21.08 | | | | | | | | | | | | | | | | | | | | | % 147.36/21.08 | | | | | | | | | | | | | | | | | | | | | Case 1: % 147.36/21.08 | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.08 | | | | | | | | | | | | | | | | | | | | | | (2163) all_58_2 = e2 % 147.36/21.08 | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.08 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (401), (2163) imply: % 147.36/21.08 | | | | | | | | | | | | | | | | | | | | | | (2164) all_52_1 = e2 % 147.36/21.08 | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.08 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (425), (2164) imply: % 147.36/21.08 | | | | | | | | | | | | | | | | | | | | | | (2165) all_56_9 = e2 % 147.36/21.08 | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.08 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (194), (2164) imply: % 147.36/21.08 | | | | | | | | | | | | | | | | | | | | | | (2166) ~ (all_52_9 = e2) % 147.36/21.08 | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.08 | | | | | | | | | | | | | | | | | | | | | | SIMP: (2166) implies: % 147.36/21.08 | | | | | | | | | | | | | | | | | | | | | | (2167) ~ (all_52_9 = e2) % 147.36/21.08 | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.08 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (193), (2164) imply: % 147.36/21.08 | | | | | | | | | | | | | | | | | | | | | | (2168) ~ (all_52_13 = e2) % 147.36/21.08 | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.08 | | | | | | | | | | | | | | | | | | | | | | SIMP: (2168) implies: % 147.36/21.08 | | | | | | | | | | | | | | | | | | | | | | (2169) ~ (all_52_13 = e2) % 147.36/21.08 | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.08 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (568), (2164) imply: % 147.36/21.08 | | | | | | | | | | | | | | | | | | | | | | (2170) ~ (all_8_2 = e2) % 147.36/21.08 | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.08 | | | | | | | | | | | | | | | | | | | | | | SIMP: (2170) implies: % 147.36/21.08 | | | | | | | | | | | | | | | | | | | | | | (2171) ~ (all_8_2 = e2) % 147.36/21.08 | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.08 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (613), (2164) imply: % 147.36/21.08 | | | | | | | | | | | | | | | | | | | | | | (2172) op(e3, e2) = all_56_8 % 147.36/21.08 | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.08 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (247) gives: % 147.36/21.08 | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.08 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 147.36/21.08 | | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.08 | | | | | | | | | | | | | | | | | | | | | | | (2173) all_54_5 = e3 % 147.36/21.08 | | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.08 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (542), (2173) imply: % 147.36/21.08 | | | | | | | | | | | | | | | | | | | | | | | (2174) all_8_2 = e3 % 147.36/21.08 | | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.08 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (554), (2174) imply: % 147.36/21.08 | | | | | | | | | | | | | | | | | | | | | | | (2175) all_58_3 = e3 % 147.36/21.08 | | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.08 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (41), (52), (158), (160), (165), (168), % 147.36/21.08 | | | | | | | | | | | | | | | | | | | | | | | (169), (171), (173), (174), (176), (181), (182), % 147.36/21.08 | | | | | | | | | | | | | | | | | | | | | | | (183), (184), (205), (206), (208), (210), (212), % 147.36/21.08 | | | | | | | | | | | | | | | | | | | | | | | (213), (218), (238), (239), (241), (242), (243), % 147.36/21.08 | | | | | | | | | | | | | | | | | | | | | | | (245), (246), (249), (250), (251), (286), (293), % 147.36/21.08 | | | | | | | | | | | | | | | | | | | | | | | (317), (318), (319), (321), (322), (329), (330), % 147.36/21.08 | | | | | | | | | | | | | | | | | | | | | | | (332), (336), (337), (338), (341), (357), (360), % 147.36/21.08 | | | | | | | | | | | | | | | | | | | | | | | (366), (374), (380), (386), (389), (407), (431), % 147.36/21.08 | | | | | | | | | | | | | | | | | | | | | | | (435), (443), (457), (459), (461), (467), (469), % 147.36/21.08 | | | | | | | | | | | | | | | | | | | | | | | (473), (476), (480), (482), (541), (547), (548), % 147.36/21.08 | | | | | | | | | | | | | | | | | | | | | | | (549), (550), (551), (552), (554), (555), (618), % 147.36/21.08 | | | | | | | | | | | | | | | | | | | | | | | (619), (621), (622), (623), (625), (626), (767), % 147.36/21.08 | | | | | | | | | | | | | | | | | | | | | | | (770), (772), (1886), (2070), (2088), (2092), % 147.36/21.08 | | | | | | | | | | | | | | | | | | | | | | | (2096), (2097), (2099), (2101), (2105), (2106), % 147.36/21.08 | | | | | | | | | | | | | | | | | | | | | | | (2110), (2113), (2125), (2127), (2129), (2135), % 147.36/21.08 | | | | | | | | | | | | | | | | | | | | | | | (2139), (2141), (2142), (2143), (2144), (2145), % 147.36/21.08 | | | | | | | | | | | | | | | | | | | | | | | (2146), (2147), (2149), (2151), (2152), (2153), % 147.36/21.08 | | | | | | | | | | | | | | | | | | | | | | | (2154), (2155), (2156), (2157), (2158), (2163), % 147.36/21.08 | | | | | | | | | | | | | | | | | | | | | | | (2165), (2167), (2169), (2172), (2175), % 147.36/21.08 | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 147.36/21.08 | | | | | | | | | | | | | | | | | | | | | | | #323. % 147.36/21.08 | | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.08 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 147.36/21.08 | | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.08 | | | | | | | | | | | | | | | | | | | | | | | (2176) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 147.36/21.08 | | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.08 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (542), (2129), (2131), (2171), (2176) are % 147.36/21.08 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #644. % 147.36/21.08 | | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.08 | | | | | | | | | | | | | | | | | | | | | | End of split % 147.36/21.08 | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.08 | | | | | | | | | | | | | | | | | | | | | Case 2: % 147.36/21.08 | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.08 | | | | | | | | | | | | | | | | | | | | | | (2177) all_58_6 = e2 | all_58_12 = e2 % 147.36/21.08 | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.08 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (1888), (2075), (2097), (2177) are % 147.36/21.08 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #422. % 147.36/21.08 | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.08 | | | | | | | | | | | | | | | | | | | | | End of split % 147.36/21.08 | | | | | | | | | | | | | | | | | | | | | % 147.36/21.08 | | | | | | | | | | | | | | | | | | | | End of split % 147.36/21.08 | | | | | | | | | | | | | | | | | | | | % 147.36/21.08 | | | | | | | | | | | | | | | | | | | End of split % 147.36/21.08 | | | | | | | | | | | | | | | | | | | % 147.36/21.08 | | | | | | | | | | | | | | | | | | Case 2: % 147.36/21.08 | | | | | | | | | | | | | | | | | | | % 147.36/21.08 | | | | | | | | | | | | | | | | | | | (2178) all_56_13 = e2 % 147.36/21.08 | | | | | | | | | | | | | | | | | | | (2179) all_56_11 = e1 % 147.36/21.08 | | | | | | | | | | | | | | | | | | | % 147.36/21.08 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (545), (2179) imply: % 147.36/21.08 | | | | | | | | | | | | | | | | | | | (2180) all_8_2 = e1 % 147.36/21.08 | | | | | | | | | | | | | | | | | | | % 147.36/21.08 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (431), (2178) imply: % 147.36/21.08 | | | | | | | | | | | | | | | | | | | (2181) all_52_9 = e2 % 147.36/21.08 | | | | | | | | | | | | | | | | | | | % 147.36/21.08 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (389), (2181) imply: % 147.36/21.08 | | | | | | | | | | | | | | | | | | | (2182) all_58_5 = e2 % 147.36/21.08 | | | | | | | | | | | | | | | | | | | % 147.36/21.08 | | | | | | | | | | | | | | | | | | | REDUCE: (571), (2180) imply: % 147.36/21.08 | | | | | | | | | | | | | | | | | | | (2183) ~ (all_52_4 = e1) % 147.36/21.08 | | | | | | | | | | | | | | | | | | | % 147.36/21.08 | | | | | | | | | | | | | | | | | | | REDUCE: (583), (2181) imply: % 147.36/21.08 | | | | | | | | | | | | | | | | | | | (2184) ~ (all_6_2 = e2) % 147.36/21.08 | | | | | | | | | | | | | | | | | | | % 147.36/21.08 | | | | | | | | | | | | | | | | | | | REDUCE: (48), (2180) imply: % 147.36/21.08 | | | | | | | | | | | | | | | | | | | (2185) op(e1, e1) = all_8_1 % 147.36/21.08 | | | | | | | | | | | | | | | | | | | % 147.36/21.08 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (41), (242), (298), (328), (343), (407), % 147.36/21.08 | | | | | | | | | | | | | | | | | | | (419), (429), (541), (546), (548), (552), (555), % 147.36/21.08 | | | | | | | | | | | | | | | | | | | (582), (769), (1881), (2101), (2125), (2127), % 147.36/21.08 | | | | | | | | | | | | | | | | | | | (2182), (2183), (2185), (function-axioms) are % 147.36/21.08 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #571. % 147.36/21.08 | | | | | | | | | | | | | | | | | | | % 147.36/21.08 | | | | | | | | | | | | | | | | | | End of split % 147.36/21.08 | | | | | | | | | | | | | | | | | | % 147.36/21.08 | | | | | | | | | | | | | | | | | Case 2: % 147.36/21.08 | | | | | | | | | | | | | | | | | | % 147.36/21.08 | | | | | | | | | | | | | | | | | | (2186) all_56_11 = e0 % 147.36/21.08 | | | | | | | | | | | | | | | | | | % 147.36/21.08 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (545), (2186) imply: % 147.36/21.08 | | | | | | | | | | | | | | | | | | (2187) all_8_2 = e0 % 147.36/21.08 | | | | | | | | | | | | | | | | | | % 147.36/21.08 | | | | | | | | | | | | | | | | | | REDUCE: (48), (2187) imply: % 147.36/21.08 | | | | | | | | | | | | | | | | | | (2188) op(e0, e0) = all_8_1 % 147.36/21.08 | | | | | | | | | | | | | | | | | | % 147.36/21.08 | | | | | | | | | | | | | | | | | | REF_CLOSE: (1881), (2111), (2188), (function-axioms) are % 147.36/21.08 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #546. % 147.36/21.08 | | | | | | | | | | | | | | | | | | % 147.36/21.08 | | | | | | | | | | | | | | | | | End of split % 147.36/21.08 | | | | | | | | | | | | | | | | | % 147.36/21.08 | | | | | | | | | | | | | | | | Case 2: % 147.36/21.08 | | | | | | | | | | | | | | | | | % 147.36/21.08 | | | | | | | | | | | | | | | | | (2189) all_56_23 = e1 % 147.36/21.08 | | | | | | | | | | | | | | | | | (2190) all_56_21 = e0 % 147.36/21.08 | | | | | | | | | | | | | | | | | % 147.36/21.08 | | | | | | | | | | | | | | | | | REF_CLOSE: (174), (243), (244), (287), (366), (374), (473), % 147.36/21.08 | | | | | | | | | | | | | | | | | (545), (573), (580), (587), (1888), (2073), % 147.36/21.08 | | | | | | | | | | | | | | | | | (2080), (2082), (2085), (2091), (2115), (2121), % 147.36/21.08 | | | | | | | | | | | | | | | | | (2189), (2190) are inconsistent by sub-proof #320. % 147.36/21.08 | | | | | | | | | | | | | | | | | % 147.36/21.08 | | | | | | | | | | | | | | | | End of split % 147.36/21.08 | | | | | | | | | | | | | | | | % 147.36/21.08 | | | | | | | | | | | | | | | Case 2: % 147.36/21.08 | | | | | | | | | | | | | | | | % 147.36/21.08 | | | | | | | | | | | | | | | | (2191) all_56_21 = e2 % 147.36/21.08 | | | | | | | | | | | | | | | | (2192) all_56_19 = e1 % 147.36/21.08 | | | | | | | | | | | | | | | | % 147.36/21.08 | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (46), (48), (244), (287), (324), (374), % 147.36/21.08 | | | | | | | | | | | | | | | | (380), (435), (544), (545), (546), (550), (552), % 147.36/21.08 | | | | | | | | | | | | | | | | (580), (591), (617), (2070), (2073), (2075), % 147.36/21.08 | | | | | | | | | | | | | | | | (2080), (2082), (2084), (2085), (2103), (2191), % 147.36/21.08 | | | | | | | | | | | | | | | | (2192), (function-axioms) are inconsistent by % 147.36/21.08 | | | | | | | | | | | | | | | | sub-proof #319. % 147.36/21.08 | | | | | | | | | | | | | | | | % 147.36/21.08 | | | | | | | | | | | | | | | End of split % 147.36/21.08 | | | | | | | | | | | | | | | % 147.36/21.09 | | | | | | | | | | | | | | End of split % 147.36/21.09 | | | | | | | | | | | | | | % 147.36/21.09 | | | | | | | | | | | | | Case 2: % 147.36/21.09 | | | | | | | | | | | | | | % 147.36/21.09 | | | | | | | | | | | | | | (2193) all_56_31 = e1 % 147.36/21.09 | | | | | | | | | | | | | | (2194) all_56_29 = e0 % 147.36/21.09 | | | | | | | | | | | | | | % 147.36/21.09 | | | | | | | | | | | | | | REF_CLOSE: (37), (38), (41), (46), (48), (187), (207), (240), % 147.36/21.09 | | | | | | | | | | | | | | (242), (244), (287), (292), (293), (324), (357), % 147.36/21.09 | | | | | | | | | | | | | | (374), (380), (435), (478), (532), (541), (544), % 147.36/21.09 | | | | | | | | | | | | | | (545), (546), (550), (552), (580), (585), (588), % 147.36/21.09 | | | | | | | | | | | | | | (591), (617), (622), (762), (767), (772), (2068), % 147.36/21.09 | | | | | | | | | | | | | | (2070), (2073), (2074), (2075), (2078), (2080), % 147.36/21.09 | | | | | | | | | | | | | | (2082), (2084), (2085), (2193), (2194), % 147.36/21.09 | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 147.36/21.09 | | | | | | | | | | | | | | #316. % 147.36/21.09 | | | | | | | | | | | | | | % 147.36/21.09 | | | | | | | | | | | | | End of split % 147.36/21.09 | | | | | | | | | | | | | % 147.36/21.09 | | | | | | | | | | | | End of split % 147.36/21.09 | | | | | | | | | | | | % 147.36/21.09 | | | | | | | | | | | Case 2: % 147.36/21.09 | | | | | | | | | | | | % 147.36/21.09 | | | | | | | | | | | | (2195) all_28_0 = e2 % 147.36/21.09 | | | | | | | | | | | | (2196) ~ (all_28_1 = e3) | ~ (all_28_2 = e0) % 147.36/21.09 | | | | | | | | | | | | % 147.36/21.09 | | | | | | | | | | | | COMBINE_EQS: (740), (2195) imply: % 147.36/21.09 | | | | | | | | | | | | (2197) all_6_0 = e2 % 147.36/21.09 | | | | | | | | | | | | % 147.36/21.09 | | | | | | | | | | | | REF_CLOSE: (6), (8), (36), (37), (38), (41), (42), (43), % 147.36/21.09 | | | | | | | | | | | | (46), (51), (144), (158), (173), (174), (176), % 147.36/21.09 | | | | | | | | | | | | (187), (192), (206), (207), (208), (211), (237), % 147.36/21.09 | | | | | | | | | | | | (239), (240), (242), (247), (252), (288), (289), % 147.36/21.09 | | | | | | | | | | | | (290), (291), (292), (293), (294), (297), (321), % 147.36/21.09 | | | | | | | | | | | | (341), (357), (366), (374), (381), (386), (402), % 147.36/21.09 | | | | | | | | | | | | (407), (419), (435), (443), (475), (478), (480), % 147.36/21.09 | | | | | | | | | | | | (513), (540), (541), (542), (543), (544), (545), % 147.36/21.09 | | | | | | | | | | | | (546), (547), (550), (551), (555), (559), (569), % 147.36/21.09 | | | | | | | | | | | | (571), (573), (580), (585), (620), (622), (627), % 147.36/21.09 | | | | | | | | | | | | (634), (665), (764), (767), (768), (772), (2196), % 147.36/21.09 | | | | | | | | | | | | (2197), (function-axioms) are inconsistent by % 147.36/21.09 | | | | | | | | | | | | sub-proof #364. % 147.36/21.09 | | | | | | | | | | | | % 147.36/21.09 | | | | | | | | | | | End of split % 147.36/21.09 | | | | | | | | | | | % 147.36/21.09 | | | | | | | | | | Case 2: % 147.36/21.09 | | | | | | | | | | | % 147.36/21.09 | | | | | | | | | | | (2198) all_26_0 = e1 % 147.36/21.09 | | | | | | | | | | | (2199) ~ (all_26_1 = e2) | ~ (all_26_2 = e3) % 147.36/21.09 | | | | | | | | | | | % 147.36/21.09 | | | | | | | | | | | COMBINE_EQS: (760), (2198) imply: % 147.36/21.09 | | | | | | | | | | | (2200) all_4_0 = e1 % 147.36/21.09 | | | | | | | | | | | % 147.36/21.09 | | | | | | | | | | | REDUCE: (767), (2200) imply: % 147.36/21.09 | | | | | | | | | | | (2201) ~ (e3 = e1) % 147.36/21.09 | | | | | | | | | | | % 147.36/21.09 | | | | | | | | | | | REDUCE: (37), (2200) imply: % 147.36/21.09 | | | | | | | | | | | (2202) op(e0, all_4_1) = e1 % 147.36/21.09 | | | | | | | | | | | % 147.36/21.09 | | | | | | | | | | | BETA: splitting (99) gives: % 147.36/21.09 | | | | | | | | | | | % 147.36/21.09 | | | | | | | | | | | Case 1: % 147.36/21.09 | | | | | | | | | | | | % 147.36/21.09 | | | | | | | | | | | | (2203) ~ (all_28_0 = e2) % 147.36/21.09 | | | | | | | | | | | | % 147.36/21.09 | | | | | | | | | | | | REDUCE: (740), (2203) imply: % 147.36/21.09 | | | | | | | | | | | | (2204) ~ (all_6_0 = e2) % 147.36/21.09 | | | | | | | | | | | | % 147.36/21.09 | | | | | | | | | | | | BETA: splitting (119) gives: % 147.36/21.09 | | | | | | | | | | | | % 147.36/21.09 | | | | | | | | | | | | Case 1: % 147.36/21.09 | | | | | | | | | | | | | % 147.36/21.09 | | | | | | | | | | | | | (2205) ~ (all_36_1 = e3) % 147.36/21.09 | | | | | | | | | | | | | % 147.36/21.09 | | | | | | | | | | | | | REDUCE: (652), (2205) imply: % 147.36/21.09 | | | | | | | | | | | | | (2206) ~ (all_6_1 = e3) % 147.36/21.09 | | | | | | | | | | | | | % 147.36/21.09 | | | | | | | | | | | | | BETA: splitting (292) gives: % 147.36/21.09 | | | | | | | | | | | | | % 147.36/21.09 | | | | | | | | | | | | | Case 1: % 147.36/21.09 | | | | | | | | | | | | | | % 147.36/21.09 | | | | | | | | | | | | | | (2207) ~ (all_56_21 = e2) % 147.36/21.09 | | | | | | | | | | | | | | % 147.36/21.09 | | | | | | | | | | | | | | REDUCE: (374), (2207) imply: % 147.36/21.09 | | | | | | | | | | | | | | (2208) ~ (all_6_2 = e2) % 147.36/21.09 | | | | | | | | | | | | | | % 147.36/21.09 | | | | | | | | | | | | | | BETA: splitting (294) gives: % 147.36/21.09 | | | | | | | | | | | | | | % 147.36/21.09 | | | | | | | | | | | | | | Case 1: % 147.36/21.09 | | | | | | | | | | | | | | | % 147.36/21.09 | | | | | | | | | | | | | | | (2209) ~ (all_56_11 = e0) % 147.36/21.09 | | | | | | | | | | | | | | | % 147.36/21.09 | | | | | | | | | | | | | | | REDUCE: (545), (2209) imply: % 147.36/21.09 | | | | | | | | | | | | | | | (2210) ~ (all_8_2 = e0) % 147.36/21.09 | | | | | | | | | | | | | | | % 147.36/21.09 | | | | | | | | | | | | | | | BETA: splitting (293) gives: % 147.36/21.09 | | | | | | | | | | | | | | | % 147.36/21.09 | | | | | | | | | | | | | | | Case 1: % 147.36/21.09 | | | | | | | | | | | | | | | | % 147.36/21.09 | | | | | | | | | | | | | | | | (2211) ~ (all_56_21 = e3) % 147.36/21.09 | | | | | | | | | | | | | | | | % 147.36/21.09 | | | | | | | | | | | | | | | | REDUCE: (374), (2211) imply: % 147.36/21.09 | | | | | | | | | | | | | | | | (2212) ~ (all_6_2 = e3) % 147.36/21.09 | | | | | | | | | | | | | | | | % 147.36/21.09 | | | | | | | | | | | | | | | | BETA: splitting (296) gives: % 147.36/21.09 | | | | | | | | | | | | | | | | % 147.36/21.09 | | | | | | | | | | | | | | | | Case 1: % 147.36/21.09 | | | | | | | | | | | | | | | | | % 147.36/21.09 | | | | | | | | | | | | | | | | | (2213) ~ (all_56_11 = e3) % 147.36/21.09 | | | | | | | | | | | | | | | | | % 147.36/21.09 | | | | | | | | | | | | | | | | | REDUCE: (545), (2213) imply: % 147.36/21.09 | | | | | | | | | | | | | | | | | (2214) ~ (all_8_2 = e3) % 147.36/21.09 | | | | | | | | | | | | | | | | | % 147.36/21.09 | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (36), (37), (38), (41), (43), (46), (48), % 147.36/21.09 | | | | | | | | | | | | | | | | | (51), (53), (158), (160), (161), (168), (173), % 147.36/21.09 | | | | | | | | | | | | | | | | | (174), (176), (181), (182), (183), (184), (188), % 147.36/21.09 | | | | | | | | | | | | | | | | | (189), (191), (192), (196), (197), (216), (217), % 147.36/21.09 | | | | | | | | | | | | | | | | | (218), (237), (239), (240), (241), (242), (243), % 147.36/21.09 | | | | | | | | | | | | | | | | | (244), (245), (247), (248), (249), (250), (251), % 147.36/21.09 | | | | | | | | | | | | | | | | | (252), (288), (291), (295), (297), (298), (299), % 147.36/21.09 | | | | | | | | | | | | | | | | | (317), (318), (319), (320), (322), (324), (325), % 147.36/21.09 | | | | | | | | | | | | | | | | | (327), (334), (336), (340), (342), (344), (357), % 147.36/21.09 | | | | | | | | | | | | | | | | | (365), (366), (374), (380), (386), (401), (402), % 147.36/21.09 | | | | | | | | | | | | | | | | | (408), (419), (429), (431), (457), (459), (461), % 147.36/21.09 | | | | | | | | | | | | | | | | | (463), (469), (471), (473), (476), (478), (480), % 147.36/21.09 | | | | | | | | | | | | | | | | | (521), (527), (540), (541), (542), (543), (544), % 147.36/21.09 | | | | | | | | | | | | | | | | | (545), (546), (547), (548), (549), (550), (551), % 147.36/21.09 | | | | | | | | | | | | | | | | | (552), (553), (554), (555), (557), (559), (561), % 147.36/21.09 | | | | | | | | | | | | | | | | | (563), (565), (567), (568), (569), (570), (571), % 147.36/21.09 | | | | | | | | | | | | | | | | | (573), (575), (579), (580), (581), (582), (583), % 147.36/21.09 | | | | | | | | | | | | | | | | | (585), (587), (589), (590), (591), (612), (613), % 147.36/21.09 | | | | | | | | | | | | | | | | | (615), (617), (622), (625), (627), (643), (677), % 147.36/21.09 | | | | | | | | | | | | | | | | | (768), (769), (1875), (1879), (1881), (1884), % 147.36/21.09 | | | | | | | | | | | | | | | | | (2206), (2208), (2210), (2212), (2214), % 147.36/21.09 | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 147.36/21.09 | | | | | | | | | | | | | | | | | #265. % 147.36/21.09 | | | | | | | | | | | | | | | | | % 147.36/21.09 | | | | | | | | | | | | | | | | Case 2: % 147.36/21.09 | | | | | | | | | | | | | | | | | % 147.36/21.09 | | | | | | | | | | | | | | | | | (2215) all_56_11 = e3 % 147.36/21.09 | | | | | | | | | | | | | | | | | (2216) all_56_9 = e2 % 147.36/21.09 | | | | | | | | | | | | | | | | | % 147.36/21.09 | | | | | | | | | | | | | | | | | COMBINE_EQS: (425), (2216) imply: % 147.36/21.09 | | | | | | | | | | | | | | | | | (2217) all_52_1 = e2 % 147.36/21.09 | | | | | | | | | | | | | | | | | % 147.36/21.09 | | | | | | | | | | | | | | | | | COMBINE_EQS: (545), (2215) imply: % 147.36/21.09 | | | | | | | | | | | | | | | | | (2218) all_8_2 = e3 % 147.36/21.09 | | | | | | | | | | | | | | | | | % 147.36/21.09 | | | | | | | | | | | | | | | | | REDUCE: (196), (2217) imply: % 147.36/21.09 | | | | | | | | | | | | | | | | | (2219) ~ (all_52_3 = e2) % 147.36/21.09 | | | | | | | | | | | | | | | | | % 147.36/21.09 | | | | | | | | | | | | | | | | | SIMP: (2219) implies: % 147.36/21.09 | | | | | | | | | | | | | | | | | (2220) ~ (all_52_3 = e2) % 147.36/21.09 | | | | | | | | | | | | | | | | | % 147.36/21.09 | | | | | | | | | | | | | | | | | REDUCE: (557), (2217) imply: % 147.36/21.09 | | | | | | | | | | | | | | | | | (2221) ~ (all_10_2 = e2) % 147.36/21.09 | | | | | | | | | | | | | | | | | % 147.36/21.09 | | | | | | | | | | | | | | | | | SIMP: (2221) implies: % 147.36/21.09 | | | | | | | | | | | | | | | | | (2222) ~ (all_10_2 = e2) % 147.36/21.09 | | | | | | | | | | | | | | | | | % 147.36/21.09 | | | | | | | | | | | | | | | | | REDUCE: (573), (2218) imply: % 147.36/21.09 | | | | | | | | | | | | | | | | | (2223) ~ (all_52_6 = e3) % 147.36/21.09 | | | | | | | | | | | | | | | | | % 147.36/21.09 | | | | | | | | | | | | | | | | | REDUCE: (48), (2218) imply: % 147.36/21.09 | | | | | | | | | | | | | | | | | (2224) op(e3, e3) = all_8_1 % 147.36/21.09 | | | | | | | | | | | | | | | | | % 147.36/21.09 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_10_2, % 147.36/21.09 | | | | | | | | | | | | | | | | | all_8_1, e3, e3, simplifying with (51), (2224) % 147.36/21.09 | | | | | | | | | | | | | | | | | gives: % 147.36/21.09 | | | | | | | | | | | | | | | | | (2225) all_10_2 = all_8_1 % 147.36/21.09 | | | | | | | | | | | | | | | | | % 147.36/21.09 | | | | | | | | | | | | | | | | | COMBINE_EQS: (527), (2225) imply: % 147.36/21.09 | | | | | | | | | | | | | | | | | (2226) all_16_2 = all_8_1 % 147.36/21.09 | | | | | | | | | | | | | | | | | % 147.36/21.09 | | | | | | | | | | | | | | | | | COMBINE_EQS: (543), (2225) imply: % 147.36/21.09 | | | | | | | | | | | | | | | | | (2227) all_54_0 = all_8_1 % 147.36/21.09 | | | | | | | | | | | | | | | | | % 147.36/21.09 | | | | | | | | | | | | | | | | | COMBINE_EQS: (546), (2225) imply: % 147.36/21.09 | | | | | | | | | | | | | | | | | (2228) all_56_1 = all_8_1 % 147.36/21.09 | | | | | | | | | | | | | | | | | % 147.36/21.09 | | | | | | | | | | | | | | | | | REDUCE: (561), (2225) imply: % 147.36/21.09 | | | | | | | | | | | | | | | | | (2229) ~ (all_52_3 = all_8_1) % 147.36/21.09 | | | | | | | | | | | | | | | | | % 147.36/21.09 | | | | | | | | | | | | | | | | | REDUCE: (2222), (2225) imply: % 147.36/21.09 | | | | | | | | | | | | | | | | | (2230) ~ (all_8_1 = e2) % 147.36/21.09 | | | | | | | | | | | | | | | | | % 147.36/21.09 | | | | | | | | | | | | | | | | | REDUCE: (53), (2225) imply: % 147.36/21.09 | | | | | | | | | | | | | | | | | (2231) op(all_8_1, all_8_1) = all_10_1 % 147.36/21.09 | | | | | | | | | | | | | | | | | % 147.36/21.09 | | | | | | | | | | | | | | | | | BETA: splitting (252) gives: % 147.36/21.09 | | | | | | | | | | | | | | | | | % 147.36/21.09 | | | | | | | | | | | | | | | | | Case 1: % 147.36/21.09 | | | | | | | | | | | | | | | | | | % 147.36/21.09 | | | | | | | | | | | | | | | | | | (2232) all_54_0 = e3 % 147.36/21.09 | | | | | | | | | | | | | | | | | | % 147.36/21.09 | | | | | | | | | | | | | | | | | | REF_CLOSE: (1881), (2227), (2232) are inconsistent by % 147.36/21.09 | | | | | | | | | | | | | | | | | | sub-proof #600. % 147.36/21.09 | | | | | | | | | | | | | | | | | | % 147.36/21.09 | | | | | | | | | | | | | | | | | Case 2: % 147.36/21.09 | | | | | | | | | | | | | | | | | | % 147.36/21.09 | | | | | | | | | | | | | | | | | | (2233) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 147.36/21.09 | | | | | | | | | | | | | | | | | | % 147.36/21.09 | | | | | | | | | | | | | | | | | | BETA: splitting (2233) gives: % 147.36/21.09 | | | | | | | | | | | | | | | | | | % 147.36/21.09 | | | | | | | | | | | | | | | | | | Case 1: % 147.36/21.09 | | | | | | | | | | | | | | | | | | | % 147.36/21.09 | | | | | | | | | | | | | | | | | | | (2234) all_54_0 = e2 % 147.36/21.09 | | | | | | | | | | | | | | | | | | | % 147.36/21.09 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2227), (2230), (2234) are inconsistent by % 147.36/21.09 | | | | | | | | | | | | | | | | | | | sub-proof #599. % 147.36/21.09 | | | | | | | | | | | | | | | | | | | % 147.36/21.09 | | | | | | | | | | | | | | | | | | Case 2: % 147.36/21.09 | | | | | | | | | | | | | | | | | | | % 147.36/21.09 | | | | | | | | | | | | | | | | | | | (2235) all_54_0 = e1 | all_54_0 = e0 % 147.36/21.09 | | | | | | | | | | | | | | | | | | | % 147.36/21.09 | | | | | | | | | | | | | | | | | | | BETA: splitting (2235) gives: % 147.36/21.09 | | | | | | | | | | | | | | | | | | | % 147.36/21.09 | | | | | | | | | | | | | | | | | | | Case 1: % 147.36/21.09 | | | | | | | | | | | | | | | | | | | | % 147.36/21.09 | | | | | | | | | | | | | | | | | | | | (2236) all_54_0 = e1 % 147.36/21.09 | | | | | | | | | | | | | | | | | | | | % 147.36/21.09 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (769), (2227), (2236) are inconsistent by % 147.36/21.09 | | | | | | | | | | | | | | | | | | | | sub-proof #598. % 147.36/21.09 | | | | | | | | | | | | | | | | | | | | % 147.36/21.09 | | | | | | | | | | | | | | | | | | | Case 2: % 147.36/21.09 | | | | | | | | | | | | | | | | | | | | % 147.36/21.09 | | | | | | | | | | | | | | | | | | | | (2237) all_54_0 = e0 % 147.36/21.09 | | | | | | | | | | | | | | | | | | | | % 147.36/21.09 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2227), (2237) imply: % 147.36/21.09 | | | | | | | | | | | | | | | | | | | | (2238) all_8_1 = e0 % 147.36/21.09 | | | | | | | | | | | | | | | | | | | | % 147.36/21.09 | | | | | | | | | | | | | | | | | | | | SIMP: (2238) implies: % 147.36/21.09 | | | | | | | | | | | | | | | | | | | | (2239) all_8_1 = e0 % 147.36/21.09 | | | | | | | | | | | | | | | | | | | | % 147.36/21.09 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2226), (2239) imply: % 147.36/21.09 | | | | | | | | | | | | | | | | | | | | (2240) all_16_2 = e0 % 147.36/21.09 | | | | | | | | | | | | | | | | | | | | % 147.36/21.09 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2228), (2239) imply: % 147.36/21.09 | | | | | | | | | | | | | | | | | | | | (2241) all_56_1 = e0 % 147.36/21.09 | | | | | | | | | | | | | | | | | | | | % 147.36/21.09 | | | | | | | | | | | | | | | | | | | | REDUCE: (2229), (2239) imply: % 147.36/21.09 | | | | | | | | | | | | | | | | | | | | (2242) ~ (all_52_3 = e0) % 147.36/21.09 | | | | | | | | | | | | | | | | | | | | % 147.36/21.09 | | | | | | | | | | | | | | | | | | | | REDUCE: (2231), (2239) imply: % 147.36/21.09 | | | | | | | | | | | | | | | | | | | | (2243) op(e0, e0) = all_10_1 % 147.36/21.09 | | | | | | | | | | | | | | | | | | | | % 147.36/21.09 | | | | | | | | | | | | | | | | | | | | BETA: splitting (1875) gives: % 147.36/21.09 | | | | | | | | | | | | | | | | | | | | % 147.36/21.09 | | | | | | | | | | | | | | | | | | | | Case 1: % 147.36/21.09 | | | | | | | | | | | | | | | | | | | | | % 147.36/21.09 | | | | | | | | | | | | | | | | | | | | | (2244) ~ (all_16_1 = e2) % 147.36/21.09 | | | | | | | | | | | | | | | | | | | | | % 147.36/21.09 | | | | | | | | | | | | | | | | | | | | | REDUCE: (677), (2244) imply: % 147.36/21.09 | | | | | | | | | | | | | | | | | | | | | (2245) ~ (all_10_1 = e2) % 147.36/21.09 | | | | | | | | | | | | | | | | | | | | | % 147.36/21.09 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (297) gives: % 147.36/21.09 | | | | | | | | | | | | | | | | | | | | | % 147.36/21.09 | | | | | | | | | | | | | | | | | | | | | Case 1: % 147.36/21.09 | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.09 | | | | | | | | | | | | | | | | | | | | | | (2246) ~ (all_56_1 = e0) % 147.36/21.09 | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.09 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2241), (2246) imply: % 147.36/21.09 | | | | | | | | | | | | | | | | | | | | | | (2247) $false % 147.36/21.09 | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.09 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2247) is inconsistent. % 147.36/21.09 | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.09 | | | | | | | | | | | | | | | | | | | | | Case 2: % 147.36/21.09 | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.09 | | | | | | | | | | | | | | | | | | | | | | (2248) all_56_7 = e3 % 147.36/21.09 | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.09 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (402), (2248) imply: % 147.36/21.09 | | | | | | | | | | | | | | | | | | | | | | (2249) all_52_12 = e3 % 147.36/21.09 | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.09 | | | | | | | | | | | | | | | | | | | | | | SIMP: (2249) implies: % 147.36/21.09 | | | | | | | | | | | | | | | | | | | | | | (2250) all_52_12 = e3 % 147.36/21.09 | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.09 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (160), (2250) imply: % 147.36/21.09 | | | | | | | | | | | | | | | | | | | | | | (2251) ~ (all_52_14 = e3) % 147.36/21.09 | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.09 | | | | | | | | | | | | | | | | | | | | | | SIMP: (2251) implies: % 147.36/21.09 | | | | | | | | | | | | | | | | | | | | | | (2252) ~ (all_52_14 = e3) % 147.36/21.09 | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.09 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (589), (2250) imply: % 147.36/21.09 | | | | | | | | | | | | | | | | | | | | | | (2253) ~ (all_4_2 = e3) % 147.36/21.09 | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.09 | | | | | | | | | | | | | | | | | | | | | | SIMP: (2253) implies: % 147.36/21.09 | | | | | | | | | | | | | | | | | | | | | | (2254) ~ (all_4_2 = e3) % 147.36/21.09 | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.09 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (327) gives: % 147.36/21.09 | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.09 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 147.36/21.09 | | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.09 | | | | | | | | | | | | | | | | | | | | | | | (2255) all_58_6 = e3 % 147.36/21.09 | | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.09 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (553), (2255) imply: % 147.36/21.09 | | | | | | | | | | | | | | | | | | | | | | | (2256) all_52_2 = e3 % 147.36/21.09 | | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.09 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2256) implies: % 147.36/21.09 | | | | | | | | | | | | | | | | | | | | | | | (2257) all_52_2 = e3 % 147.36/21.09 | | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.09 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (192), (2257) imply: % 147.36/21.09 | | | | | | | | | | | | | | | | | | | | | | | (2258) ~ (all_52_3 = e3) % 147.36/21.09 | | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.09 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2258) implies: % 147.36/21.09 | | | | | | | | | | | | | | | | | | | | | | | (2259) ~ (all_52_3 = e3) % 147.36/21.09 | | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.09 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (318) gives: % 147.36/21.09 | | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.09 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 147.36/21.09 | | | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.09 | | | | | | | | | | | | | | | | | | | | | | | | (2260) all_58_12 = e1 % 147.36/21.09 | | | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.09 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (365), (2260) imply: % 147.36/21.09 | | | | | | | | | | | | | | | | | | | | | | | | (2261) all_52_3 = e1 % 147.36/21.09 | | | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.09 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2261) implies: % 147.36/21.09 | | | | | | | | | | | | | | | | | | | | | | | | (2262) all_52_3 = e1 % 147.36/21.09 | | | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.09 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (570), (2262) imply: % 147.36/21.09 | | | | | | | | | | | | | | | | | | | | | | | | (2263) ~ (all_4_2 = e1) % 147.36/21.09 | | | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.09 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2263) implies: % 147.36/21.09 | | | | | | | | | | | | | | | | | | | | | | | | (2264) ~ (all_4_2 = e1) % 147.36/21.09 | | | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.09 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_4_2, % 147.36/21.09 | | | | | | | | | | | | | | | | | | | | | | | | all_10_1, e0, e0, simplifying with (36), (2243) % 147.36/21.09 | | | | | | | | | | | | | | | | | | | | | | | | gives: % 147.36/21.09 | | | | | | | | | | | | | | | | | | | | | | | | (2265) all_10_1 = all_4_2 % 147.36/21.09 | | | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.09 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2245), (2265) imply: % 147.36/21.09 | | | | | | | | | | | | | | | | | | | | | | | | (2266) ~ (all_4_2 = e2) % 147.36/21.09 | | | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.09 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (38), (237), (540), (627), (2202), (2254), % 147.36/21.09 | | | | | | | | | | | | | | | | | | | | | | | | (2264), (2266), (function-axioms) are inconsistent % 147.36/21.09 | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #363. % 147.36/21.09 | | | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.09 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 147.36/21.09 | | | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.09 | | | | | | | | | | | | | | | | | | | | | | | | (2267) ~ (all_58_12 = e1) % 147.36/21.09 | | | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.09 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (365), (2267) imply: % 147.36/21.09 | | | | | | | | | | | | | | | | | | | | | | | | (2268) ~ (all_52_3 = e1) % 147.36/21.09 | | | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.09 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (240), (478), (2220), (2242), (2259), (2268) are % 147.36/21.09 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #300. % 147.36/21.09 | | | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.09 | | | | | | | | | | | | | | | | | | | | | | | End of split % 147.36/21.09 | | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.09 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 147.36/21.09 | | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.09 | | | | | | | | | | | | | | | | | | | | | | | (2269) all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3 % 147.36/21.09 | | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.09 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2269) gives: % 147.36/21.09 | | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.09 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 147.36/21.09 | | | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.09 | | | | | | | | | | | | | | | | | | | | | | | | (2270) all_58_7 = e3 % 147.36/21.09 | | | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.09 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (380), (2270) imply: % 147.36/21.09 | | | | | | | | | | | | | | | | | | | | | | | | (2271) all_52_6 = e3 % 147.36/21.09 | | | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.09 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2223), (2271) imply: % 147.36/21.09 | | | | | | | | | | | | | | | | | | | | | | | | (2272) $false % 147.36/21.09 | | | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.09 | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2272) is inconsistent. % 147.36/21.09 | | | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.09 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 147.36/21.09 | | | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.09 | | | | | | | | | | | | | | | | | | | | | | | | (2273) all_58_8 = e3 | all_58_11 = e3 % 147.36/21.09 | | | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.09 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (550), (552), (2212), (2252), (2273) are % 147.36/21.09 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #636. % 147.36/21.09 | | | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.09 | | | | | | | | | | | | | | | | | | | | | | | End of split % 147.36/21.09 | | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.09 | | | | | | | | | | | | | | | | | | | | | | End of split % 147.36/21.09 | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.09 | | | | | | | | | | | | | | | | | | | | | End of split % 147.36/21.09 | | | | | | | | | | | | | | | | | | | | | % 147.36/21.09 | | | | | | | | | | | | | | | | | | | | Case 2: % 147.36/21.09 | | | | | | | | | | | | | | | | | | | | | % 147.36/21.09 | | | | | | | | | | | | | | | | | | | | | (2274) ~ (all_16_2 = e0) % 147.36/21.09 | | | | | | | | | | | | | | | | | | | | | % 147.36/21.09 | | | | | | | | | | | | | | | | | | | | | REDUCE: (2240), (2274) imply: % 147.36/21.09 | | | | | | | | | | | | | | | | | | | | | (2275) $false % 147.36/21.09 | | | | | | | | | | | | | | | | | | | | | % 147.36/21.09 | | | | | | | | | | | | | | | | | | | | | CLOSE: (2275) is inconsistent. % 147.36/21.09 | | | | | | | | | | | | | | | | | | | | | % 147.36/21.09 | | | | | | | | | | | | | | | | | | | | End of split % 147.36/21.09 | | | | | | | | | | | | | | | | | | | | % 147.36/21.09 | | | | | | | | | | | | | | | | | | | End of split % 147.36/21.09 | | | | | | | | | | | | | | | | | | | % 147.36/21.09 | | | | | | | | | | | | | | | | | | End of split % 147.36/21.09 | | | | | | | | | | | | | | | | | | % 147.36/21.09 | | | | | | | | | | | | | | | | | End of split % 147.36/21.09 | | | | | | | | | | | | | | | | | % 147.36/21.09 | | | | | | | | | | | | | | | | End of split % 147.36/21.09 | | | | | | | | | | | | | | | | % 147.36/21.09 | | | | | | | | | | | | | | | Case 2: % 147.36/21.09 | | | | | | | | | | | | | | | | % 147.36/21.09 | | | | | | | | | | | | | | | | (2276) all_56_21 = e3 % 147.36/21.09 | | | | | | | | | | | | | | | | (2277) all_56_17 = e1 % 147.36/21.09 | | | | | | | | | | | | | | | | % 147.36/21.09 | | | | | | | | | | | | | | | | COMBINE_EQS: (381), (2277) imply: % 147.36/21.09 | | | | | | | | | | | | | | | | (2278) all_52_2 = e1 % 147.36/21.09 | | | | | | | | | | | | | | | | % 147.36/21.09 | | | | | | | | | | | | | | | | COMBINE_EQS: (374), (2276) imply: % 147.36/21.09 | | | | | | | | | | | | | | | | (2279) all_6_2 = e3 % 147.36/21.09 | | | | | | | | | | | | | | | | % 147.36/21.09 | | | | | | | | | | | | | | | | REDUCE: (191), (2278) imply: % 147.36/21.09 | | | | | | | | | | | | | | | | (2280) ~ (all_52_6 = e1) % 147.36/21.09 | | | | | | | | | | | | | | | | % 147.36/21.09 | | | | | | | | | | | | | | | | SIMP: (2280) implies: % 147.36/21.09 | | | | | | | | | | | | | | | | (2281) ~ (all_52_6 = e1) % 147.36/21.09 | | | | | | | | | | | | | | | | % 147.36/21.09 | | | | | | | | | | | | | | | | REDUCE: (189), (2278) imply: % 147.36/21.09 | | | | | | | | | | | | | | | | (2282) ~ (all_52_14 = e1) % 147.36/21.09 | | | | | | | | | | | | | | | | % 147.36/21.10 | | | | | | | | | | | | | | | | SIMP: (2282) implies: % 147.36/21.10 | | | | | | | | | | | | | | | | (2283) ~ (all_52_14 = e1) % 147.36/21.10 | | | | | | | | | | | | | | | | % 147.36/21.10 | | | | | | | | | | | | | | | | REDUCE: (559), (2278) imply: % 147.36/21.10 | | | | | | | | | | | | | | | | (2284) ~ (all_10_2 = e1) % 147.36/21.10 | | | | | | | | | | | | | | | | % 147.36/21.10 | | | | | | | | | | | | | | | | SIMP: (2284) implies: % 147.36/21.10 | | | | | | | | | | | | | | | | (2285) ~ (all_10_2 = e1) % 147.36/21.10 | | | | | | | | | | | | | | | | % 147.36/21.10 | | | | | | | | | | | | | | | | REDUCE: (580), (2279) imply: % 147.36/21.10 | | | | | | | | | | | | | | | | (2286) ~ (all_52_6 = e3) % 147.36/21.10 | | | | | | | | | | | | | | | | % 147.36/21.10 | | | | | | | | | | | | | | | | REDUCE: (587), (2279) imply: % 147.36/21.10 | | | | | | | | | | | | | | | | (2287) ~ (all_52_14 = e3) % 147.36/21.10 | | | | | | | | | | | | | | | | % 147.36/21.10 | | | | | | | | | | | | | | | | REDUCE: (43), (2279) imply: % 147.36/21.10 | | | | | | | | | | | | | | | | (2288) op(e3, e3) = all_6_1 % 147.36/21.10 | | | | | | | | | | | | | | | | % 147.36/21.10 | | | | | | | | | | | | | | | | REF_CLOSE: (8), (42), (51), (174), (208), (241), (243), % 147.36/21.10 | | | | | | | | | | | | | | | | (252), (287), (473), (476), (527), (543), (544), % 147.36/21.10 | | | | | | | | | | | | | | | | (545), (546), (573), (591), (768), (1875), (2204), % 147.36/21.10 | | | | | | | | | | | | | | | | (2206), (2276), (2281), (2283), (2285), (2286), % 147.36/21.10 | | | | | | | | | | | | | | | | (2287), (2288), (function-axioms) are inconsistent % 147.36/21.10 | | | | | | | | | | | | | | | | by sub-proof #264. % 147.36/21.10 | | | | | | | | | | | | | | | | % 147.36/21.10 | | | | | | | | | | | | | | | End of split % 147.36/21.10 | | | | | | | | | | | | | | | % 147.36/21.10 | | | | | | | | | | | | | | Case 2: % 147.36/21.10 | | | | | | | | | | | | | | | % 147.36/21.10 | | | | | | | | | | | | | | | (2289) all_56_11 = e0 % 147.36/21.10 | | | | | | | | | | | | | | | % 147.36/21.10 | | | | | | | | | | | | | | | REF_CLOSE: (36), (38), (48), (237), (294), (443), (540), % 147.36/21.10 | | | | | | | | | | | | | | | (545), (590), (627), (769), (1881), (2202), % 147.36/21.10 | | | | | | | | | | | | | | | (2289), (function-axioms) are inconsistent by % 147.36/21.10 | | | | | | | | | | | | | | | sub-proof #357. % 147.36/21.10 | | | | | | | | | | | | | | | % 147.36/21.10 | | | | | | | | | | | | | | End of split % 147.36/21.10 | | | | | | | | | | | | | | % 147.36/21.10 | | | | | | | | | | | | | Case 2: % 147.36/21.10 | | | | | | | | | | | | | | % 147.36/21.10 | | | | | | | | | | | | | | (2290) all_56_21 = e2 % 147.36/21.10 | | | | | | | | | | | | | | (2291) all_56_19 = e1 % 147.36/21.10 | | | | | | | | | | | | | | % 147.36/21.10 | | | | | | | | | | | | | | COMBINE_EQS: (435), (2291) imply: % 147.36/21.10 | | | | | | | | | | | | | | (2292) all_52_6 = e1 % 147.36/21.10 | | | | | | | | | | | | | | % 147.36/21.10 | | | | | | | | | | | | | | COMBINE_EQS: (374), (2290) imply: % 147.36/21.10 | | | | | | | | | | | | | | (2293) all_6_2 = e2 % 147.36/21.10 | | | | | | | | | | | | | | % 147.36/21.10 | | | | | | | | | | | | | | REF_CLOSE: (36), (38), (43), (46), (48), (237), (247), (294), % 147.36/21.10 | | | | | | | | | | | | | | (443), (540), (542), (545), (573), (590), (627), % 147.36/21.10 | | | | | | | | | | | | | | (768), (769), (1881), (2202), (2206), (2292), % 147.36/21.10 | | | | | | | | | | | | | | (2293), (function-axioms) are inconsistent by % 147.36/21.10 | | | | | | | | | | | | | | sub-proof #263. % 147.36/21.10 | | | | | | | | | | | | | | % 147.36/21.10 | | | | | | | | | | | | | End of split % 147.36/21.10 | | | | | | | | | | | | | % 147.36/21.10 | | | | | | | | | | | | Case 2: % 147.36/21.10 | | | | | | | | | | | | | % 147.36/21.10 | | | | | | | | | | | | | (2294) all_36_1 = e3 % 147.36/21.10 | | | | | | | | | | | | | (2295) ~ (all_36_0 = e0) | ~ (all_36_2 = e2) % 147.36/21.10 | | | | | | | | | | | | | % 147.36/21.10 | | | | | | | | | | | | | COMBINE_EQS: (652), (2294) imply: % 147.36/21.10 | | | | | | | | | | | | | (2296) all_6_1 = e3 % 147.36/21.10 | | | | | | | | | | | | | % 147.36/21.10 | | | | | | | | | | | | | SIMP: (2296) implies: % 147.36/21.10 | | | | | | | | | | | | | (2297) all_6_1 = e3 % 147.36/21.10 | | | | | | | | | | | | | % 147.36/21.10 | | | | | | | | | | | | | REF_CLOSE: (5), (36), (37), (38), (41), (42), (43), (46), % 147.36/21.10 | | | | | | | | | | | | | (48), (51), (174), (176), (187), (188), (189), % 147.36/21.10 | | | | | | | | | | | | | (191), (192), (194), (207), (211), (237), (240), % 147.36/21.10 | | | | | | | | | | | | | (242), (243), (244), (247), (287), (288), (289), % 147.36/21.10 | | | | | | | | | | | | | (290), (291), (292), (293), (294), (295), (324), % 147.36/21.10 | | | | | | | | | | | | | (344), (357), (360), (365), (366), (374), (380), % 147.36/21.10 | | | | | | | | | | | | | (381), (401), (419), (431), (435), (443), (447), % 147.36/21.10 | | | | | | | | | | | | | (471), (473), (478), (530), (532), (540), (541), % 147.36/21.10 | | | | | | | | | | | | | (542), (544), (545), (546), (550), (552), (553), % 147.36/21.10 | | | | | | | | | | | | | (559), (561), (568), (569), (570), (573), (580), % 147.36/21.10 | | | | | | | | | | | | | (585), (587), (588), (590), (591), (617), (622), % 147.36/21.10 | | | | | | | | | | | | | (627), (657), (762), (767), (769), (772), (1881), % 147.36/21.10 | | | | | | | | | | | | | (2199), (2202), (2204), (2295), (2297), % 147.36/21.10 | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 147.36/21.10 | | | | | | | | | | | | | #261. % 147.36/21.10 | | | | | | | | | | | | | % 147.36/21.10 | | | | | | | | | | | | End of split % 147.36/21.10 | | | | | | | | | | | | % 147.36/21.10 | | | | | | | | | | | Case 2: % 147.36/21.10 | | | | | | | | | | | | % 147.36/21.10 | | | | | | | | | | | | (2298) all_28_0 = e2 % 147.36/21.10 | | | | | | | | | | | | (2299) ~ (all_28_1 = e3) | ~ (all_28_2 = e0) % 147.36/21.10 | | | | | | | | | | | | % 147.36/21.10 | | | | | | | | | | | | COMBINE_EQS: (740), (2298) imply: % 147.36/21.10 | | | | | | | | | | | | (2300) all_6_0 = e2 % 147.36/21.10 | | | | | | | | | | | | % 147.36/21.10 | | | | | | | | | | | | REF_CLOSE: (6), (8), (36), (37), (38), (41), (42), (43), % 147.36/21.10 | | | | | | | | | | | | (46), (51), (144), (158), (173), (174), (176), % 147.36/21.10 | | | | | | | | | | | | (187), (192), (206), (207), (208), (211), (237), % 147.36/21.10 | | | | | | | | | | | | (239), (240), (242), (247), (252), (288), (289), % 147.36/21.10 | | | | | | | | | | | | (290), (291), (292), (293), (294), (297), (321), % 147.36/21.10 | | | | | | | | | | | | (341), (357), (366), (374), (381), (386), (402), % 147.36/21.10 | | | | | | | | | | | | (407), (419), (435), (443), (475), (478), (480), % 147.36/21.10 | | | | | | | | | | | | (513), (540), (541), (542), (543), (544), (545), % 147.36/21.10 | | | | | | | | | | | | (546), (547), (550), (551), (555), (559), (569), % 147.36/21.10 | | | | | | | | | | | | (571), (573), (580), (585), (620), (622), (627), % 147.36/21.10 | | | | | | | | | | | | (634), (665), (764), (767), (768), (772), (2299), % 147.36/21.10 | | | | | | | | | | | | (2300), (function-axioms) are inconsistent by % 147.36/21.10 | | | | | | | | | | | | sub-proof #364. % 147.36/21.10 | | | | | | | | | | | | % 147.36/21.10 | | | | | | | | | | | End of split % 147.36/21.10 | | | | | | | | | | | % 147.36/21.10 | | | | | | | | | | End of split % 147.36/21.10 | | | | | | | | | | % 147.36/21.10 | | | | | | | | | End of split % 147.36/21.10 | | | | | | | | | % 147.36/21.10 | | | | | | | | Case 2: % 147.36/21.10 | | | | | | | | | % 147.36/21.10 | | | | | | | | | (2301) all_22_1 = e3 % 147.36/21.10 | | | | | | | | | (2302) ~ (all_22_0 = e0) | ~ (all_22_2 = e1) % 147.36/21.10 | | | | | | | | | % 147.36/21.10 | | | | | | | | | COMBINE_EQS: (672), (2301) imply: % 147.36/21.10 | | | | | | | | | (2303) all_8_1 = e3 % 147.36/21.10 | | | | | | | | | % 147.36/21.10 | | | | | | | | | SIMP: (2303) implies: % 147.36/21.10 | | | | | | | | | (2304) all_8_1 = e3 % 147.36/21.10 | | | | | | | | | % 147.36/21.10 | | | | | | | | | REDUCE: (48), (2304) imply: % 147.36/21.10 | | | | | | | | | (2305) op(all_8_2, all_8_2) = e3 % 147.36/21.10 | | | | | | | | | % 147.36/21.10 | | | | | | | | | REDUCE: (47), (2304) imply: % 147.36/21.10 | | | | | | | | | (2306) op(e2, e3) = all_8_0 % 147.36/21.10 | | | | | | | | | % 147.36/21.10 | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (36), (37), (38), (41), (42), % 147.36/21.10 | | | | | | | | | (43), (46), (48), (51), (52), (53), (94), (99), % 147.36/21.10 | | | | | | | | | (119), (139), (144), (158), (160), (161), (165), % 147.36/21.10 | | | | | | | | | (166), (168), (169), (171), (173), (174), (176), % 147.36/21.10 | | | | | | | | | (181), (182), (183), (184), (187), (188), (189), % 147.36/21.10 | | | | | | | | | (191), (192), (193), (194), (197), (205), (206), % 147.36/21.10 | | | | | | | | | (207), (208), (210), (211), (212), (213), (215), % 147.36/21.10 | | | | | | | | | (216), (217), (218), (237), (238), (239), (240), % 147.36/21.10 | | | | | | | | | (241), (242), (243), (244), (245), (246), (247), % 147.36/21.10 | | | | | | | | | (248), (249), (250), (251), (252), (286), (287), % 147.36/21.10 | | | | | | | | | (288), (289), (290), (291), (292), (293), (294), % 147.36/21.10 | | | | | | | | | (295), (296), (297), (317), (318), (319), (320), % 147.36/21.10 | | | | | | | | | (321), (322), (323), (324), (326), (327), (329), % 147.36/21.10 | | | | | | | | | (330), (331), (332), (333), (336), (337), (338), % 147.36/21.10 | | | | | | | | | (339), (341), (342), (344), (357), (360), (365), % 147.36/21.10 | | | | | | | | | (366), (374), (380), (381), (386), (389), (401), % 147.36/21.10 | | | | | | | | | (402), (407), (419), (425), (431), (435), (443), % 147.36/21.10 | | | | | | | | | (447), (457), (459), (461), (463), (467), (469), % 147.36/21.10 | | | | | | | | | (471), (473), (475), (476), (478), (480), (482), % 147.36/21.10 | | | | | | | | | (513), (523), (530), (532), (535), (540), (541), % 147.36/21.10 | | | | | | | | | (542), (543), (544), (545), (546), (547), (548), % 147.36/21.10 | | | | | | | | | (549), (550), (551), (552), (553), (554), (555), % 147.36/21.10 | | | | | | | | | (557), (559), (561), (563), (565), (567), (568), % 147.36/21.10 | | | | | | | | | (569), (570), (571), (573), (575), (577), (579), % 147.36/21.10 | | | | | | | | | (580), (583), (585), (587), (588), (590), (591), % 147.36/21.10 | | | | | | | | | (612), (613), (614), (615), (617), (618), (619), % 147.36/21.10 | | | | | | | | | (620), (621), (622), (623), (625), (626), (627), % 147.36/21.10 | | | | | | | | | (631), (634), (652), (657), (665), (709), (740), % 147.36/21.10 | | | | | | | | | (752), (760), (762), (764), (767), (768), (770), % 147.36/21.10 | | | | | | | | | (772), (774), (2302), (2305), (2306), % 147.36/21.10 | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 147.36/21.10 | | | | | | | | | #307. % 147.36/21.10 | | | | | | | | | % 147.36/21.10 | | | | | | | | End of split % 147.36/21.10 | | | | | | | | % 147.36/21.10 | | | | | | | End of split % 147.36/21.10 | | | | | | | % 147.36/21.10 | | | | | | Case 2: % 147.36/21.10 | | | | | | | % 147.36/21.10 | | | | | | | (2307) all_14_0 = e1 % 147.36/21.10 | | | | | | | (2308) ~ (all_14_1 = e3) | ~ (all_14_2 = e0) % 147.36/21.10 | | | | | | | % 147.36/21.10 | | | | | | | COMBINE_EQS: (758), (2307) imply: % 147.36/21.10 | | | | | | | (2309) all_8_0 = e1 % 147.36/21.10 | | | | | | | % 147.36/21.10 | | | | | | | SIMP: (2309) implies: % 147.36/21.10 | | | | | | | (2310) all_8_0 = e1 % 147.36/21.10 | | | | | | | % 147.36/21.10 | | | | | | | COMBINE_EQS: (763), (2310) imply: % 147.36/21.10 | | | | | | | (2311) all_42_0 = e1 % 147.36/21.10 | | | | | | | % 147.36/21.10 | | | | | | | REDUCE: (47), (2310) imply: % 147.36/21.10 | | | | | | | (2312) op(e2, all_8_1) = e1 % 147.36/21.10 | | | | | | | % 147.36/21.10 | | | | | | | BETA: splitting (69) gives: % 147.36/21.10 | | | | | | | % 147.36/21.10 | | | | | | | Case 1: % 147.36/21.10 | | | | | | | | % 147.36/21.10 | | | | | | | | (2313) ~ (all_16_0 = e1) % 147.36/21.10 | | | | | | | | % 147.36/21.10 | | | | | | | | REDUCE: (757), (2313) imply: % 147.36/21.10 | | | | | | | | (2314) ~ (all_10_0 = e1) % 147.36/21.10 | | | | | | | | % 147.36/21.10 | | | | | | | | BETA: splitting (99) gives: % 147.36/21.10 | | | | | | | | % 147.36/21.10 | | | | | | | | Case 1: % 147.36/21.10 | | | | | | | | | % 147.36/21.10 | | | | | | | | | (2315) ~ (all_28_0 = e2) % 147.36/21.10 | | | | | | | | | % 147.36/21.10 | | | | | | | | | REDUCE: (740), (2315) imply: % 147.36/21.10 | | | | | | | | | (2316) ~ (all_6_0 = e2) % 147.36/21.10 | | | | | | | | | % 147.36/21.10 | | | | | | | | | BETA: splitting (109) gives: % 147.36/21.10 | | | | | | | | | % 147.36/21.10 | | | | | | | | | Case 1: % 147.36/21.10 | | | | | | | | | | % 147.36/21.10 | | | | | | | | | | (2317) ~ (all_32_1 = e1) % 147.36/21.10 | | | | | | | | | | % 147.36/21.10 | | | | | | | | | | REDUCE: (682), (2317) imply: % 147.36/21.10 | | | | | | | | | | (2318) ~ (all_10_1 = e1) % 147.36/21.10 | | | | | | | | | | % 147.36/21.10 | | | | | | | | | | BETA: splitting (119) gives: % 147.36/21.10 | | | | | | | | | | % 147.36/21.10 | | | | | | | | | | Case 1: % 147.36/21.10 | | | | | | | | | | | % 147.36/21.10 | | | | | | | | | | | (2319) ~ (all_36_1 = e3) % 147.36/21.10 | | | | | | | | | | | % 147.36/21.10 | | | | | | | | | | | REDUCE: (652), (2319) imply: % 147.36/21.10 | | | | | | | | | | | (2320) ~ (all_6_1 = e3) % 147.36/21.10 | | | | | | | | | | | % 147.36/21.10 | | | | | | | | | | | BETA: splitting (134) gives: % 147.36/21.10 | | | | | | | | | | | % 147.36/21.10 | | | | | | | | | | | Case 1: % 147.36/21.10 | | | | | | | | | | | | % 147.36/21.10 | | | | | | | | | | | | (2321) ~ (all_42_0 = e1) % 147.36/21.10 | | | | | | | | | | | | % 147.36/21.10 | | | | | | | | | | | | REDUCE: (2311), (2321) imply: % 147.36/21.10 | | | | | | | | | | | | (2322) $false % 147.36/21.10 | | | | | | | | | | | | % 147.36/21.10 | | | | | | | | | | | | CLOSE: (2322) is inconsistent. % 147.36/21.10 | | | | | | | | | | | | % 147.36/21.10 | | | | | | | | | | | Case 2: % 147.36/21.10 | | | | | | | | | | | | % 147.36/21.10 | | | | | | | | | | | | (2323) ~ (all_42_1 = e0) | ~ (all_42_2 = e3) % 147.36/21.10 | | | | | | | | | | | | % 147.36/21.10 | | | | | | | | | | | | BETA: splitting (294) gives: % 147.36/21.10 | | | | | | | | | | | | % 147.36/21.10 | | | | | | | | | | | | Case 1: % 147.36/21.10 | | | | | | | | | | | | | % 147.36/21.10 | | | | | | | | | | | | | (2324) ~ (all_56_11 = e0) % 147.36/21.10 | | | | | | | | | | | | | % 147.36/21.10 | | | | | | | | | | | | | REDUCE: (545), (2324) imply: % 147.36/21.10 | | | | | | | | | | | | | (2325) ~ (all_8_2 = e0) % 147.36/21.10 | | | | | | | | | | | | | % 147.36/21.10 | | | | | | | | | | | | | BETA: splitting (293) gives: % 147.36/21.10 | | | | | | | | | | | | | % 147.36/21.10 | | | | | | | | | | | | | Case 1: % 147.36/21.10 | | | | | | | | | | | | | | % 147.36/21.10 | | | | | | | | | | | | | | (2326) ~ (all_56_21 = e3) % 147.36/21.10 | | | | | | | | | | | | | | % 147.36/21.10 | | | | | | | | | | | | | | REDUCE: (374), (2326) imply: % 147.36/21.10 | | | | | | | | | | | | | | (2327) ~ (all_6_2 = e3) % 147.36/21.10 | | | | | | | | | | | | | | % 147.36/21.10 | | | | | | | | | | | | | | REF_CLOSE: (6), (41), (46), (48), (51), (212), (215), (242), % 147.36/21.10 | | | | | | | | | | | | | | (247), (252), (295), (296), (425), (431), (534), % 147.36/21.10 | | | | | | | | | | | | | | (541), (542), (543), (545), (557), (579), (583), % 147.36/21.10 | | | | | | | | | | | | | | (617), (639), (769), (2312), (2323), (2325), % 147.36/21.10 | | | | | | | | | | | | | | (2327), (function-axioms) are inconsistent by % 147.36/21.10 | | | | | | | | | | | | | | sub-proof #254. % 147.36/21.10 | | | | | | | | | | | | | | % 147.36/21.10 | | | | | | | | | | | | | Case 2: % 147.36/21.10 | | | | | | | | | | | | | | % 147.36/21.10 | | | | | | | | | | | | | | (2328) all_56_21 = e3 % 147.36/21.10 | | | | | | | | | | | | | | (2329) all_56_17 = e1 % 147.36/21.10 | | | | | | | | | | | | | | % 147.36/21.10 | | | | | | | | | | | | | | COMBINE_EQS: (381), (2329) imply: % 147.36/21.10 | | | | | | | | | | | | | | (2330) all_52_2 = e1 % 147.36/21.10 | | | | | | | | | | | | | | % 147.36/21.10 | | | | | | | | | | | | | | COMBINE_EQS: (374), (2328) imply: % 147.36/21.10 | | | | | | | | | | | | | | (2331) all_6_2 = e3 % 147.36/21.10 | | | | | | | | | | | | | | % 147.36/21.10 | | | | | | | | | | | | | | SIMP: (2331) implies: % 147.36/21.10 | | | | | | | | | | | | | | (2332) all_6_2 = e3 % 147.36/21.10 | | | | | | | | | | | | | | % 147.36/21.10 | | | | | | | | | | | | | | REDUCE: (191), (2330) imply: % 147.36/21.11 | | | | | | | | | | | | | | (2333) ~ (all_52_6 = e1) % 147.36/21.11 | | | | | | | | | | | | | | % 147.36/21.11 | | | | | | | | | | | | | | SIMP: (2333) implies: % 147.36/21.11 | | | | | | | | | | | | | | (2334) ~ (all_52_6 = e1) % 147.36/21.11 | | | | | | | | | | | | | | % 147.36/21.11 | | | | | | | | | | | | | | REDUCE: (189), (2330) imply: % 147.36/21.11 | | | | | | | | | | | | | | (2335) ~ (all_52_14 = e1) % 147.36/21.11 | | | | | | | | | | | | | | % 147.36/21.11 | | | | | | | | | | | | | | SIMP: (2335) implies: % 147.36/21.11 | | | | | | | | | | | | | | (2336) ~ (all_52_14 = e1) % 147.36/21.11 | | | | | | | | | | | | | | % 147.36/21.11 | | | | | | | | | | | | | | REDUCE: (559), (2330) imply: % 147.36/21.11 | | | | | | | | | | | | | | (2337) ~ (all_10_2 = e1) % 147.36/21.11 | | | | | | | | | | | | | | % 147.36/21.11 | | | | | | | | | | | | | | SIMP: (2337) implies: % 147.36/21.11 | | | | | | | | | | | | | | (2338) ~ (all_10_2 = e1) % 147.36/21.11 | | | | | | | | | | | | | | % 147.36/21.11 | | | | | | | | | | | | | | REDUCE: (569), (2330), (2332) imply: % 147.36/21.11 | | | | | | | | | | | | | | (2339) ~ (e3 = e1) % 147.36/21.11 | | | | | | | | | | | | | | % 147.36/21.11 | | | | | | | | | | | | | | REDUCE: (580), (2332) imply: % 147.36/21.11 | | | | | | | | | | | | | | (2340) ~ (all_52_6 = e3) % 147.36/21.11 | | | | | | | | | | | | | | % 147.36/21.11 | | | | | | | | | | | | | | REDUCE: (43), (2332) imply: % 147.36/21.11 | | | | | | | | | | | | | | (2341) op(e3, e3) = all_6_1 % 147.36/21.11 | | | | | | | | | | | | | | % 147.36/21.11 | | | | | | | | | | | | | | REF_CLOSE: (8), (36), (42), (51), (53), (158), (160), (161), % 147.36/21.11 | | | | | | | | | | | | | | (174), (208), (241), (243), (252), (287), (297), % 147.36/21.11 | | | | | | | | | | | | | | (321), (332), (386), (389), (401), (402), (473), % 147.36/21.11 | | | | | | | | | | | | | | (476), (543), (544), (545), (546), (547), (550), % 147.36/21.11 | | | | | | | | | | | | | | (551), (554), (557), (573), (591), (621), (768), % 147.36/21.11 | | | | | | | | | | | | | | (2316), (2318), (2320), (2325), (2328), (2334), % 147.36/21.11 | | | | | | | | | | | | | | (2336), (2338), (2340), (2341), (function-axioms) % 147.36/21.11 | | | | | | | | | | | | | | are inconsistent by sub-proof #670. % 147.36/21.11 | | | | | | | | | | | | | | % 147.36/21.11 | | | | | | | | | | | | | End of split % 147.36/21.11 | | | | | | | | | | | | | % 147.36/21.11 | | | | | | | | | | | | Case 2: % 147.36/21.11 | | | | | | | | | | | | | % 147.36/21.11 | | | | | | | | | | | | | (2342) all_56_15 = e2 % 147.36/21.11 | | | | | | | | | | | | | (2343) all_56_11 = e0 % 147.36/21.11 | | | | | | | | | | | | | % 147.36/21.11 | | | | | | | | | | | | | REF_CLOSE: (6), (36), (48), (212), (237), (443), (528), % 147.36/21.11 | | | | | | | | | | | | | (540), (545), (590), (617), (679), (769), (2308), % 147.36/21.11 | | | | | | | | | | | | | (2312), (2342), (2343), (function-axioms) are % 147.36/21.11 | | | | | | | | | | | | | inconsistent by sub-proof #251. % 147.36/21.11 | | | | | | | | | | | | | % 147.36/21.11 | | | | | | | | | | | | End of split % 147.36/21.11 | | | | | | | | | | | | % 147.36/21.11 | | | | | | | | | | | End of split % 147.36/21.11 | | | | | | | | | | | % 147.36/21.11 | | | | | | | | | | Case 2: % 147.36/21.11 | | | | | | | | | | | % 147.36/21.11 | | | | | | | | | | | (2344) all_36_1 = e3 % 147.36/21.11 | | | | | | | | | | | % 147.36/21.11 | | | | | | | | | | | COMBINE_EQS: (652), (2344) imply: % 147.36/21.11 | | | | | | | | | | | (2345) all_6_1 = e3 % 147.36/21.11 | | | | | | | | | | | % 147.36/21.11 | | | | | | | | | | | REF_CLOSE: (6), (36), (41), (42), (46), (48), (51), (134), % 147.36/21.11 | | | | | | | | | | | (197), (211), (212), (215), (237), (242), (247), % 147.36/21.11 | | | | | | | | | | | (252), (293), (294), (295), (296), (374), (381), % 147.36/21.11 | | | | | | | | | | | (425), (431), (443), (528), (534), (540), (541), % 147.36/21.11 | | | | | | | | | | | (542), (543), (545), (557), (579), (583), (590), % 147.36/21.11 | | | | | | | | | | | (617), (639), (679), (769), (2308), (2311), % 147.36/21.11 | | | | | | | | | | | (2312), (2345), (function-axioms) are inconsistent % 147.36/21.11 | | | | | | | | | | | by sub-proof #249. % 147.36/21.11 | | | | | | | | | | | % 147.36/21.11 | | | | | | | | | | End of split % 147.36/21.11 | | | | | | | | | | % 147.36/21.11 | | | | | | | | | Case 2: % 147.36/21.11 | | | | | | | | | | % 147.36/21.11 | | | | | | | | | | (2346) all_32_1 = e1 % 147.36/21.11 | | | | | | | | | | % 147.36/21.11 | | | | | | | | | | COMBINE_EQS: (682), (2346) imply: % 147.36/21.11 | | | | | | | | | | (2347) all_10_1 = e1 % 147.36/21.11 | | | | | | | | | | % 147.36/21.11 | | | | | | | | | | SIMP: (2347) implies: % 147.36/21.11 | | | | | | | | | | (2348) all_10_1 = e1 % 147.36/21.11 | | | | | | | | | | % 147.36/21.11 | | | | | | | | | | REDUCE: (53), (2348) imply: % 147.36/21.11 | | | | | | | | | | (2349) op(all_10_2, all_10_2) = e1 % 147.36/21.11 | | | | | | | | | | % 147.36/21.11 | | | | | | | | | | REDUCE: (52), (2348) imply: % 147.36/21.11 | | | | | | | | | | (2350) op(e3, e1) = all_10_0 % 147.36/21.11 | | | | | | | | | | % 147.36/21.11 | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_8, % 147.36/21.11 | | | | | | | | | | all_10_0, e1, e3, simplifying with (217), (2350) % 147.36/21.11 | | | | | | | | | | gives: % 147.36/21.11 | | | | | | | | | | (2351) all_52_8 = all_10_0 % 147.36/21.11 | | | | | | | | | | % 147.36/21.11 | | | | | | | | | | COMBINE_EQS: (459), (2351) imply: % 147.36/21.11 | | | | | | | | | | (2352) all_54_2 = all_10_0 % 147.36/21.11 | | | | | | | | | | % 147.36/21.11 | | | | | | | | | | REDUCE: (182), (2351) imply: % 147.36/21.11 | | | | | | | | | | (2353) ~ (all_52_4 = all_10_0) % 147.36/21.11 | | | | | | | | | | % 147.36/21.11 | | | | | | | | | | REDUCE: (169), (2351) imply: % 147.36/21.11 | | | | | | | | | | (2354) ~ (all_52_11 = all_10_0) % 147.36/21.11 | | | | | | | | | | % 147.36/21.11 | | | | | | | | | | SIMP: (2354) implies: % 147.36/21.11 | | | | | | | | | | (2355) ~ (all_52_11 = all_10_0) % 147.36/21.11 | | | | | | | | | | % 147.36/21.11 | | | | | | | | | | REDUCE: (168), (2351) imply: % 147.36/21.11 | | | | | | | | | | (2356) ~ (all_52_12 = all_10_0) % 147.36/21.11 | | | | | | | | | | % 147.36/21.11 | | | | | | | | | | SIMP: (2356) implies: % 147.36/21.11 | | | | | | | | | | (2357) ~ (all_52_12 = all_10_0) % 147.36/21.11 | | | | | | | | | | % 147.36/21.11 | | | | | | | | | | REDUCE: (565), (2351) imply: % 147.36/21.11 | | | | | | | | | | (2358) ~ (all_10_0 = all_10_2) % 147.36/21.11 | | | | | | | | | | % 147.36/21.11 | | | | | | | | | | REDUCE: (582), (2351) imply: % 147.36/21.11 | | | | | | | | | | (2359) ~ (all_10_0 = all_6_2) % 147.36/21.11 | | | | | | | | | | % 147.36/21.11 | | | | | | | | | | BETA: splitting (134) gives: % 147.36/21.11 | | | | | | | | | | % 147.36/21.11 | | | | | | | | | | Case 1: % 147.36/21.11 | | | | | | | | | | | % 147.36/21.11 | | | | | | | | | | | (2360) ~ (all_42_0 = e1) % 147.36/21.11 | | | | | | | | | | | % 147.36/21.11 | | | | | | | | | | | REDUCE: (2311), (2360) imply: % 147.36/21.11 | | | | | | | | | | | (2361) $false % 147.36/21.11 | | | | | | | | | | | % 147.36/21.11 | | | | | | | | | | | CLOSE: (2361) is inconsistent. % 147.36/21.11 | | | | | | | | | | | % 147.36/21.11 | | | | | | | | | | Case 2: % 147.36/21.11 | | | | | | | | | | | % 147.36/21.11 | | | | | | | | | | | (2362) ~ (all_42_1 = e0) | ~ (all_42_2 = e3) % 147.36/21.11 | | | | | | | | | | | % 147.36/21.11 | | | | | | | | | | | BETA: splitting (288) gives: % 147.36/21.11 | | | | | | | | | | | % 147.36/21.11 | | | | | | | | | | | Case 1: % 147.36/21.11 | | | | | | | | | | | | % 147.36/21.11 | | | | | | | | | | | | (2363) ~ (all_56_31 = e1) % 147.36/21.11 | | | | | | | | | | | | % 147.36/21.11 | | | | | | | | | | | | REDUCE: (544), (2363) imply: % 147.36/21.11 | | | | | | | | | | | | (2364) ~ (all_4_2 = e1) % 147.36/21.11 | | | | | | | | | | | | % 147.36/21.11 | | | | | | | | | | | | BETA: splitting (290) gives: % 147.36/21.11 | | | | | | | | | | | | % 147.36/21.11 | | | | | | | | | | | | Case 1: % 147.36/21.11 | | | | | | | | | | | | | % 147.36/21.11 | | | | | | | | | | | | | (2365) ~ (all_56_31 = e3) % 147.36/21.11 | | | | | | | | | | | | | % 147.36/21.11 | | | | | | | | | | | | | REDUCE: (544), (2365) imply: % 147.36/21.11 | | | | | | | | | | | | | (2366) ~ (all_4_2 = e3) % 147.36/21.11 | | | | | | | | | | | | | % 147.36/21.11 | | | | | | | | | | | | | BETA: splitting (291) gives: % 147.36/21.11 | | | | | | | | | | | | | % 147.36/21.11 | | | | | | | | | | | | | Case 1: % 147.36/21.11 | | | | | | | | | | | | | | % 147.36/21.11 | | | | | | | | | | | | | | (2367) ~ (all_56_21 = e0) % 147.36/21.11 | | | | | | | | | | | | | | % 147.36/21.11 | | | | | | | | | | | | | | REDUCE: (374), (2367) imply: % 147.36/21.11 | | | | | | | | | | | | | | (2368) ~ (all_6_2 = e0) % 147.36/21.11 | | | | | | | | | | | | | | % 147.36/21.11 | | | | | | | | | | | | | | REF_CLOSE: (6), (36), (41), (46), (48), (51), (189), (193), % 147.36/21.11 | | | | | | | | | | | | | | (194), (197), (212), (215), (237), (242), (247), % 147.36/21.11 | | | | | | | | | | | | | | (248), (252), (293), (294), (295), (296), (321), % 147.36/21.11 | | | | | | | | | | | | | | (323), (332), (374), (381), (386), (401), (425), % 147.36/21.11 | | | | | | | | | | | | | | (431), (443), (463), (528), (534), (540), (541), % 147.36/21.11 | | | | | | | | | | | | | | (542), (543), (545), (547), (550), (551), (557), % 147.36/21.11 | | | | | | | | | | | | | | (569), (579), (583), (587), (590), (617), (639), % 147.36/21.11 | | | | | | | | | | | | | | (679), (769), (2308), (2312), (2362), (2364), % 147.36/21.11 | | | | | | | | | | | | | | (2366), (2368), (function-axioms) are inconsistent % 147.36/21.11 | | | | | | | | | | | | | | by sub-proof #246. % 147.36/21.11 | | | | | | | | | | | | | | % 147.36/21.11 | | | | | | | | | | | | | Case 2: % 147.36/21.11 | | | | | | | | | | | | | | % 147.36/21.11 | | | | | | | | | | | | | | (2369) all_56_21 = e0 % 147.36/21.11 | | | | | | | | | | | | | | % 147.36/21.11 | | | | | | | | | | | | | | COMBINE_EQS: (374), (2369) imply: % 147.36/21.11 | | | | | | | | | | | | | | (2370) all_6_2 = e0 % 147.36/21.11 | | | | | | | | | | | | | | % 147.36/21.11 | | | | | | | | | | | | | | SIMP: (2370) implies: % 147.36/21.11 | | | | | | | | | | | | | | (2371) all_6_2 = e0 % 147.36/21.11 | | | | | | | | | | | | | | % 147.36/21.11 | | | | | | | | | | | | | | REDUCE: (2359), (2371) imply: % 147.36/21.11 | | | | | | | | | | | | | | (2372) ~ (all_10_0 = e0) % 147.36/21.11 | | | | | | | | | | | | | | % 147.36/21.11 | | | | | | | | | | | | | | REDUCE: (41), (2371) imply: % 147.36/21.11 | | | | | | | | | | | | | | (2373) op(e1, e1) = e0 % 147.36/21.11 | | | | | | | | | | | | | | % 147.36/21.11 | | | | | | | | | | | | | | REF_CLOSE: (250), (252), (297), (299), (402), (408), (543), % 147.36/21.11 | | | | | | | | | | | | | | (546), (770), (2314), (2349), (2352), (2353), % 147.36/21.11 | | | | | | | | | | | | | | (2357), (2358), (2372), (2373), (function-axioms) % 147.36/21.11 | | | | | | | | | | | | | | are inconsistent by sub-proof #245. % 147.36/21.11 | | | | | | | | | | | | | | % 147.36/21.11 | | | | | | | | | | | | | End of split % 147.36/21.11 | | | | | | | | | | | | | % 147.36/21.11 | | | | | | | | | | | | Case 2: % 147.36/21.11 | | | | | | | | | | | | | % 147.36/21.11 | | | | | | | | | | | | | (2374) all_56_31 = e3 % 147.36/21.11 | | | | | | | | | | | | | (2375) all_56_25 = e0 % 147.36/21.11 | | | | | | | | | | | | | % 147.77/21.11 | | | | | | | | | | | | | REF_CLOSE: (5), (6), (36), (38), (46), (48), (51), (173), % 147.77/21.11 | | | | | | | | | | | | | (188), (194), (196), (215), (239), (247), (248), % 147.77/21.11 | | | | | | | | | | | | | (252), (287), (294), (295), (296), (318), (319), % 147.77/21.11 | | | | | | | | | | | | | (335), (365), (374), (401), (425), (431), (447), % 147.77/21.11 | | | | | | | | | | | | | (463), (480), (528), (534), (542), (543), (544), % 147.77/21.11 | | | | | | | | | | | | | (545), (546), (547), (548), (549), (557), (568), % 147.77/21.11 | | | | | | | | | | | | | (575), (581), (585), (617), (639), (679), (769), % 147.77/21.11 | | | | | | | | | | | | | (2308), (2312), (2362), (2374), (2375), % 147.77/21.11 | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 147.77/21.11 | | | | | | | | | | | | | #243. % 147.77/21.11 | | | | | | | | | | | | | % 147.77/21.11 | | | | | | | | | | | | End of split % 147.77/21.11 | | | | | | | | | | | | % 147.77/21.11 | | | | | | | | | | | Case 2: % 147.77/21.11 | | | | | | | | | | | | % 147.77/21.11 | | | | | | | | | | | | (2376) all_56_31 = e1 % 147.77/21.11 | | | | | | | | | | | | (2377) all_56_29 = e0 % 147.77/21.11 | | | | | | | | | | | | % 147.77/21.11 | | | | | | | | | | | | COMBINE_EQS: (357), (2377) imply: % 147.77/21.11 | | | | | | | | | | | | (2378) all_52_11 = e0 % 147.77/21.11 | | | | | | | | | | | | % 147.77/21.11 | | | | | | | | | | | | SIMP: (2378) implies: % 147.77/21.11 | | | | | | | | | | | | (2379) all_52_11 = e0 % 147.77/21.11 | | | | | | | | | | | | % 147.77/21.11 | | | | | | | | | | | | REF_CLOSE: (38), (41), (48), (250), (252), (297), (299), % 147.77/21.11 | | | | | | | | | | | | (337), (380), (402), (408), (543), (544), (546), % 147.77/21.11 | | | | | | | | | | | | (549), (554), (555), (563), (580), (581), (622), % 147.77/21.11 | | | | | | | | | | | | (769), (770), (2314), (2349), (2352), (2353), % 147.77/21.11 | | | | | | | | | | | | (2355), (2357), (2358), (2376), (2379), % 147.77/21.11 | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 147.77/21.11 | | | | | | | | | | | | #381. % 147.77/21.11 | | | | | | | | | | | | % 147.77/21.11 | | | | | | | | | | | End of split % 147.77/21.11 | | | | | | | | | | | % 147.77/21.11 | | | | | | | | | | End of split % 147.77/21.11 | | | | | | | | | | % 147.77/21.11 | | | | | | | | | End of split % 147.77/21.11 | | | | | | | | | % 147.77/21.11 | | | | | | | | Case 2: % 147.77/21.11 | | | | | | | | | % 147.77/21.11 | | | | | | | | | (2380) all_28_0 = e2 % 147.77/21.11 | | | | | | | | | % 147.77/21.11 | | | | | | | | | COMBINE_EQS: (740), (2380) imply: % 147.77/21.11 | | | | | | | | | (2381) all_6_0 = e2 % 147.77/21.11 | | | | | | | | | % 147.77/21.11 | | | | | | | | | REF_CLOSE: (6), (36), (41), (42), (43), (46), (48), (51), % 147.77/21.11 | | | | | | | | | (134), (144), (211), (212), (215), (237), (242), % 147.77/21.11 | | | | | | | | | (247), (252), (293), (294), (295), (296), (374), % 147.77/21.11 | | | | | | | | | (381), (425), (431), (443), (475), (528), (534), % 147.77/21.11 | | | | | | | | | (540), (541), (542), (543), (545), (557), (559), % 147.77/21.11 | | | | | | | | | (577), (579), (583), (590), (617), (622), (634), % 147.77/21.11 | | | | | | | | | (639), (679), (764), (768), (769), (2308), (2311), % 147.77/21.11 | | | | | | | | | (2312), (2381), (function-axioms) are inconsistent % 147.77/21.11 | | | | | | | | | by sub-proof #242. % 147.77/21.11 | | | | | | | | | % 147.77/21.11 | | | | | | | | End of split % 147.77/21.11 | | | | | | | | % 147.77/21.11 | | | | | | | Case 2: % 147.77/21.11 | | | | | | | | % 147.77/21.11 | | | | | | | | (2382) all_16_0 = e1 % 147.77/21.11 | | | | | | | | % 147.77/21.11 | | | | | | | | COMBINE_EQS: (757), (2382) imply: % 147.77/21.11 | | | | | | | | (2383) all_10_0 = e1 % 147.77/21.11 | | | | | | | | % 147.77/21.11 | | | | | | | | REDUCE: (770), (2383) imply: % 147.77/21.11 | | | | | | | | (2384) ~ (e2 = e1) % 147.77/21.11 | | | | | | | | % 147.77/21.11 | | | | | | | | REDUCE: (52), (2383) imply: % 147.77/21.11 | | | | | | | | (2385) op(e3, all_10_1) = e1 % 147.77/21.11 | | | | | | | | % 147.77/21.11 | | | | | | | | BETA: splitting (94) gives: % 147.77/21.11 | | | | | | | | % 147.77/21.11 | | | | | | | | Case 1: % 147.77/21.11 | | | | | | | | | % 147.77/21.11 | | | | | | | | | (2386) ~ (all_26_0 = e1) % 147.77/21.11 | | | | | | | | | % 147.77/21.11 | | | | | | | | | REDUCE: (760), (2386) imply: % 147.77/21.11 | | | | | | | | | (2387) ~ (all_4_0 = e1) % 147.77/21.11 | | | | | | | | | % 147.77/21.11 | | | | | | | | | BETA: splitting (99) gives: % 147.77/21.11 | | | | | | | | | % 147.77/21.11 | | | | | | | | | Case 1: % 147.77/21.11 | | | | | | | | | | % 147.77/21.11 | | | | | | | | | | (2388) ~ (all_28_0 = e2) % 147.77/21.11 | | | | | | | | | | % 147.77/21.11 | | | | | | | | | | REDUCE: (740), (2388) imply: % 147.77/21.11 | | | | | | | | | | (2389) ~ (all_6_0 = e2) % 147.77/21.11 | | | | | | | | | | % 147.77/21.11 | | | | | | | | | | BETA: splitting (119) gives: % 147.77/21.11 | | | | | | | | | | % 147.77/21.11 | | | | | | | | | | Case 1: % 147.77/21.11 | | | | | | | | | | | % 147.77/21.11 | | | | | | | | | | | (2390) ~ (all_36_1 = e3) % 147.77/21.11 | | | | | | | | | | | % 147.77/21.11 | | | | | | | | | | | REDUCE: (652), (2390) imply: % 147.77/21.11 | | | | | | | | | | | (2391) ~ (all_6_1 = e3) % 147.77/21.11 | | | | | | | | | | | % 147.77/21.11 | | | | | | | | | | | BETA: splitting (134) gives: % 147.77/21.11 | | | | | | | | | | | % 147.77/21.11 | | | | | | | | | | | Case 1: % 147.77/21.11 | | | | | | | | | | | | % 147.77/21.11 | | | | | | | | | | | | (2392) ~ (all_42_0 = e1) % 147.77/21.11 | | | | | | | | | | | | % 147.77/21.11 | | | | | | | | | | | | REDUCE: (2311), (2392) imply: % 147.77/21.11 | | | | | | | | | | | | (2393) $false % 147.77/21.11 | | | | | | | | | | | | % 147.77/21.11 | | | | | | | | | | | | CLOSE: (2393) is inconsistent. % 147.77/21.11 | | | | | | | | | | | | % 147.77/21.11 | | | | | | | | | | | Case 2: % 147.77/21.11 | | | | | | | | | | | | % 147.77/21.11 | | | | | | | | | | | | (2394) ~ (all_42_1 = e0) | ~ (all_42_2 = e3) % 147.77/21.11 | | | | | | | | | | | | % 147.77/21.11 | | | | | | | | | | | | BETA: splitting (292) gives: % 147.77/21.11 | | | | | | | | | | | | % 147.77/21.11 | | | | | | | | | | | | Case 1: % 147.77/21.11 | | | | | | | | | | | | | % 147.77/21.11 | | | | | | | | | | | | | (2395) ~ (all_56_21 = e2) % 147.77/21.11 | | | | | | | | | | | | | % 147.77/21.11 | | | | | | | | | | | | | REDUCE: (374), (2395) imply: % 147.77/21.11 | | | | | | | | | | | | | (2396) ~ (all_6_2 = e2) % 147.77/21.11 | | | | | | | | | | | | | % 147.77/21.11 | | | | | | | | | | | | | BETA: splitting (288) gives: % 147.77/21.11 | | | | | | | | | | | | | % 147.77/21.11 | | | | | | | | | | | | | Case 1: % 147.77/21.11 | | | | | | | | | | | | | | % 147.77/21.11 | | | | | | | | | | | | | | (2397) ~ (all_56_31 = e1) % 147.77/21.11 | | | | | | | | | | | | | | % 147.77/21.11 | | | | | | | | | | | | | | REDUCE: (544), (2397) imply: % 147.77/21.11 | | | | | | | | | | | | | | (2398) ~ (all_4_2 = e1) % 147.77/21.11 | | | | | | | | | | | | | | % 147.77/21.11 | | | | | | | | | | | | | | BETA: splitting (290) gives: % 147.77/21.11 | | | | | | | | | | | | | | % 147.77/21.11 | | | | | | | | | | | | | | Case 1: % 147.77/21.11 | | | | | | | | | | | | | | | % 147.77/21.11 | | | | | | | | | | | | | | | (2399) ~ (all_56_31 = e3) % 147.77/21.11 | | | | | | | | | | | | | | | % 147.77/21.11 | | | | | | | | | | | | | | | REDUCE: (544), (2399) imply: % 147.77/21.11 | | | | | | | | | | | | | | | (2400) ~ (all_4_2 = e3) % 147.77/21.11 | | | | | | | | | | | | | | | % 147.77/21.11 | | | | | | | | | | | | | | | BETA: splitting (291) gives: % 147.77/21.11 | | | | | | | | | | | | | | | % 147.77/21.11 | | | | | | | | | | | | | | | Case 1: % 147.77/21.11 | | | | | | | | | | | | | | | | % 147.77/21.11 | | | | | | | | | | | | | | | | (2401) ~ (all_56_21 = e0) % 147.77/21.11 | | | | | | | | | | | | | | | | % 147.77/21.11 | | | | | | | | | | | | | | | | REDUCE: (374), (2401) imply: % 147.77/21.11 | | | | | | | | | | | | | | | | (2402) ~ (all_6_2 = e0) % 147.77/21.11 | | | | | | | | | | | | | | | | % 147.77/21.11 | | | | | | | | | | | | | | | | REF_CLOSE: (6), (36), (41), (46), (48), (51), (189), (193), % 147.77/21.11 | | | | | | | | | | | | | | | | (194), (197), (212), (215), (237), (242), (247), % 147.77/21.11 | | | | | | | | | | | | | | | | (248), (252), (293), (294), (295), (296), (321), % 147.77/21.11 | | | | | | | | | | | | | | | | (323), (332), (374), (381), (386), (401), (425), % 147.77/21.11 | | | | | | | | | | | | | | | | (431), (443), (463), (528), (534), (540), (541), % 147.77/21.11 | | | | | | | | | | | | | | | | (542), (543), (545), (547), (550), (551), (557), % 147.77/21.11 | | | | | | | | | | | | | | | | (569), (579), (583), (587), (590), (617), (639), % 147.77/21.11 | | | | | | | | | | | | | | | | (679), (769), (2308), (2312), (2394), (2398), % 147.77/21.11 | | | | | | | | | | | | | | | | (2400), (2402), (function-axioms) are inconsistent % 147.77/21.11 | | | | | | | | | | | | | | | | by sub-proof #246. % 147.77/21.11 | | | | | | | | | | | | | | | | % 147.77/21.11 | | | | | | | | | | | | | | | Case 2: % 147.77/21.11 | | | | | | | | | | | | | | | | % 147.77/21.11 | | | | | | | | | | | | | | | | (2403) all_56_23 = e1 % 147.77/21.11 | | | | | | | | | | | | | | | | (2404) all_56_21 = e0 % 147.77/21.11 | | | | | | | | | | | | | | | | % 147.77/21.11 | | | | | | | | | | | | | | | | COMBINE_EQS: (374), (2404) imply: % 147.77/21.11 | | | | | | | | | | | | | | | | (2405) all_6_2 = e0 % 147.77/21.11 | | | | | | | | | | | | | | | | % 147.77/21.11 | | | | | | | | | | | | | | | | COMBINE_EQS: (366), (2403) imply: % 147.77/21.11 | | | | | | | | | | | | | | | | (2406) all_52_14 = e1 % 147.77/21.11 | | | | | | | | | | | | | | | | % 147.77/21.11 | | | | | | | | | | | | | | | | REDUCE: (189), (2406) imply: % 147.77/21.11 | | | | | | | | | | | | | | | | (2407) ~ (all_52_2 = e1) % 147.77/21.11 | | | | | | | | | | | | | | | | % 147.77/21.11 | | | | | | | | | | | | | | | | REDUCE: (569), (2405) imply: % 147.77/21.11 | | | | | | | | | | | | | | | | (2408) ~ (all_52_2 = e0) % 147.77/21.11 | | | | | | | | | | | | | | | | % 147.77/21.11 | | | | | | | | | | | | | | | | REDUCE: (174), (2406) imply: % 147.77/21.11 | | | | | | | | | | | | | | | | (2409) ~ (all_52_6 = e1) % 147.77/21.11 | | | | | | | | | | | | | | | | % 147.77/21.11 | | | | | | | | | | | | | | | | REDUCE: (580), (2405) imply: % 147.77/21.11 | | | | | | | | | | | | | | | | (2410) ~ (all_52_6 = e0) % 147.77/21.11 | | | | | | | | | | | | | | | | % 147.77/21.11 | | | | | | | | | | | | | | | | REDUCE: (160), (2406) imply: % 147.77/21.11 | | | | | | | | | | | | | | | | (2411) ~ (all_52_12 = e1) % 147.77/21.11 | | | | | | | | | | | | | | | | % 147.77/21.11 | | | | | | | | | | | | | | | | REDUCE: (158), (2406) imply: % 147.77/21.11 | | | | | | | | | | | | | | | | (2412) ~ (all_52_13 = e1) % 147.77/21.11 | | | | | | | | | | | | | | | | % 147.77/21.11 | | | | | | | | | | | | | | | | REDUCE: (591), (2406) imply: % 147.77/21.11 | | | | | | | | | | | | | | | | (2413) ~ (all_4_2 = e1) % 147.77/21.11 | | | | | | | | | | | | | | | | % 147.77/21.11 | | | | | | | | | | | | | | | | REDUCE: (43), (2405) imply: % 147.77/21.11 | | | | | | | | | | | | | | | | (2414) op(e0, e0) = all_6_1 % 147.77/21.11 | | | | | | | | | | | | | | | | % 147.77/21.11 | | | | | | | | | | | | | | | | REDUCE: (41), (2405) imply: % 147.77/21.11 | | | | | | | | | | | | | | | | (2415) op(e1, e1) = e0 % 147.77/21.11 | | | | | | | | | | | | | | | | % 147.77/21.11 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_4_2, % 147.77/21.11 | | | | | | | | | | | | | | | | all_6_1, e0, e0, simplifying with (36), (2414) % 147.77/21.11 | | | | | | | | | | | | | | | | gives: % 147.77/21.11 | | | | | | | | | | | | | | | | (2416) all_6_1 = all_4_2 % 147.77/21.11 | | | | | | | | | | | | | | | | % 147.77/21.11 | | | | | | | | | | | | | | | | REDUCE: (768), (2416) imply: % 147.77/21.11 | | | | | | | | | | | | | | | | (2417) ~ (all_4_2 = e2) % 147.77/21.11 | | | | | | | | | | | | | | | | % 147.77/21.11 | | | | | | | | | | | | | | | | BETA: splitting (237) gives: % 147.77/21.11 | | | | | | | | | | | | | | | | % 147.77/21.11 | | | | | | | | | | | | | | | | Case 1: % 147.77/21.12 | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | (2418) all_54_15 = e3 % 147.77/21.12 | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | REF_CLOSE: (540), (2400), (2418) are inconsistent by % 147.77/21.12 | | | | | | | | | | | | | | | | | sub-proof #740. % 147.77/21.12 | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | Case 2: % 147.77/21.12 | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | (2419) all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0 % 147.77/21.12 | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | BETA: splitting (2419) gives: % 147.77/21.12 | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | Case 1: % 147.77/21.12 | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | (2420) all_54_15 = e2 % 147.77/21.12 | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | REF_CLOSE: (540), (2417), (2420) are inconsistent by % 147.77/21.12 | | | | | | | | | | | | | | | | | | sub-proof #739. % 147.77/21.12 | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | Case 2: % 147.77/21.12 | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | (2421) ~ (all_54_15 = e2) % 147.77/21.12 | | | | | | | | | | | | | | | | | | (2422) all_54_15 = e1 | all_54_15 = e0 % 147.77/21.12 | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | BETA: splitting (2422) gives: % 147.77/21.12 | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | Case 1: % 147.77/21.12 | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | (2423) all_54_15 = e1 % 147.77/21.12 | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (540), (2398), (2423) are inconsistent by % 147.77/21.12 | | | | | | | | | | | | | | | | | | | sub-proof #738. % 147.77/21.12 | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | Case 2: % 147.77/21.12 | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | (2424) all_54_15 = e0 % 147.77/21.12 | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (540), (2424) imply: % 147.77/21.12 | | | | | | | | | | | | | | | | | | | (2425) all_4_2 = e0 % 147.77/21.12 | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | SIMP: (2425) implies: % 147.77/21.12 | | | | | | | | | | | | | | | | | | | (2426) all_4_2 = e0 % 147.77/21.12 | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | REDUCE: (570), (2426) imply: % 147.77/21.12 | | | | | | | | | | | | | | | | | | | (2427) ~ (all_52_3 = e0) % 147.77/21.12 | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | REDUCE: (581), (2426) imply: % 147.77/21.12 | | | | | | | | | | | | | | | | | | | (2428) ~ (all_52_7 = e0) % 147.77/21.12 | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | REDUCE: (589), (2426) imply: % 147.77/21.12 | | | | | | | | | | | | | | | | | | | (2429) ~ (all_52_12 = e0) % 147.77/21.12 | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | REDUCE: (38), (2426) imply: % 147.77/21.12 | | | | | | | | | | | | | | | | | | | (2430) op(e0, e0) = all_4_1 % 147.77/21.12 | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | REDUCE: (627), (2426) imply: % 147.77/21.12 | | | | | | | | | | | | | | | | | | | (2431) op(e0, e0) = all_56_30 % 147.77/21.12 | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | REDUCE: (36), (2426) imply: % 147.77/21.12 | | | | | | | | | | | | | | | | | | | (2432) op(e0, e0) = e0 % 147.77/21.12 | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_4_1, % 147.77/21.12 | | | | | | | | | | | | | | | | | | | all_56_30, e0, e0, simplifying with (2430), (2431) % 147.77/21.12 | | | | | | | | | | | | | | | | | | | gives: % 147.77/21.12 | | | | | | | | | | | | | | | | | | | (2433) all_56_30 = all_4_1 % 147.77/21.12 | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, % 147.77/21.12 | | | | | | | | | | | | | | | | | | | all_56_30, e0, e0, simplifying with (2431), (2432) % 147.77/21.12 | | | | | | | | | | | | | | | | | | | gives: % 147.77/21.12 | | | | | | | | | | | | | | | | | | | (2434) all_56_30 = e0 % 147.77/21.12 | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2433), (2434) imply: % 147.77/21.12 | | | | | | | | | | | | | | | | | | | (2435) all_4_1 = e0 % 147.77/21.12 | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | SIMP: (2435) implies: % 147.77/21.12 | | | | | | | | | | | | | | | | | | | (2436) all_4_1 = e0 % 147.77/21.12 | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | REDUCE: (37), (2436) imply: % 147.77/21.12 | | | | | | | | | | | | | | | | | | | (2437) op(e0, e0) = all_4_0 % 147.77/21.12 | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_4_0, % 147.77/21.12 | | | | | | | | | | | | | | | | | | | e0, e0, simplifying with (2432), (2437) gives: % 147.77/21.12 | | | | | | | | | | | | | | | | | | | (2438) all_4_0 = e0 % 147.77/21.12 | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | REDUCE: (2387), (2438) imply: % 147.77/21.12 | | | | | | | | | | | | | | | | | | | (2439) ~ (e1 = e0) % 147.77/21.12 | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | BETA: splitting (299) gives: % 147.77/21.12 | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | Case 1: % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | (2440) ~ (all_56_1 = e2) % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | REDUCE: (546), (2440) imply: % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | (2441) ~ (all_10_2 = e2) % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | BETA: splitting (294) gives: % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | Case 1: % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | (2442) ~ (all_56_11 = e0) % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | REDUCE: (545), (2442) imply: % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | (2443) ~ (all_8_2 = e0) % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (332) gives: % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | Case 1: % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | (2444) all_58_2 = e0 % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (401), (2444) imply: % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | (2445) all_52_1 = e0 % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (197), (2445) imply: % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | (2446) ~ (all_52_2 = e0) % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (196), (2445) imply: % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | (2447) ~ (all_52_3 = e0) % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (557), (2445) imply: % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | (2448) ~ (all_10_2 = e0) % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | SIMP: (2448) implies: % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | (2449) ~ (all_10_2 = e0) % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (568), (2445) imply: % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | (2450) ~ (all_8_2 = e0) % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (613), (2445) imply: % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | (2451) op(e3, e0) = all_56_8 % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (341) gives: % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | (2452) all_58_0 = e0 % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (419), (2452) imply: % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | (2453) all_10_2 = e0 % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2449), (2453) imply: % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | (2454) $false % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2454) is inconsistent. % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | (2455) all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0 % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2455) gives: % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | (2456) all_58_1 = e0 % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (555), (2456) imply: % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | (2457) all_52_4 = e0 % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (181), (2457) imply: % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | (2458) ~ (all_52_12 = e0) % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (616), (2457) imply: % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | (2459) op(e2, e0) = all_56_2 % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_13, % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | all_56_2, e0, e2, simplifying with (212), (2459) % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | gives: % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | (2460) all_56_2 = all_52_13 % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_12, % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | all_56_8, e0, e3, simplifying with (216), (2451) % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | gives: % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | (2461) all_56_8 = all_52_12 % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (298) gives: % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | (2462) ~ (all_56_1 = e1) % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (546), (2462) imply: % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | (2463) ~ (all_10_2 = e1) % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (343) gives: % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | (2464) all_58_0 = e1 % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (419), (2464) imply: % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | (2465) all_10_2 = e1 % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2463), (2465) imply: % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | (2466) $false % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2466) is inconsistent. % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | (2467) ~ (all_58_0 = e1) % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | (2468) all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1 % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (252) gives: % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2469) all_54_0 = e3 % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (543), (2469) imply: % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2470) all_10_2 = e3 % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2470) implies: % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2471) all_10_2 = e3 % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (419), (2471) imply: % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2472) all_58_0 = e3 % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (559), (2471) imply: % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2473) ~ (all_52_2 = e3) % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (567), (2471) imply: % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2474) ~ (all_52_12 = e3) % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (244) gives: % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2475) all_54_8 = e3 % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (471), (2475) imply: % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2476) all_52_2 = e3 % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2473), (2476) imply: % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2477) $false % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2477) is inconsistent. % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2478) all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0 % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2478) gives: % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2479) all_54_8 = e2 % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (471), (2479) imply: % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2480) all_52_2 = e2 % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (553), (2480) imply: % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2481) all_58_6 = e2 % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (249) gives: % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2482) all_54_3 = e3 % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (461), (2474), (2482) are inconsistent by % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #659. % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2483) all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0 % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (342) gives: % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2484) all_58_0 = e1 % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2472), (2484) imply: % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2485) e3 = e1 % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8), (2485) imply: % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2486) $false % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2486) is inconsistent. % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2487) all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1 % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2487) gives: % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2488) all_58_2 = e1 % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (2444), (2488) are inconsistent by sub-proof % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #241. % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2489) all_58_6 = e1 | all_58_12 = e1 % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2489) gives: % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2490) all_58_6 = e1 % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2481), (2490) imply: % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2491) e2 = e1 % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2491) implies: % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2492) e2 = e1 % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6), (2492) imply: % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2493) $false % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2493) is inconsistent. % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2494) all_58_12 = e1 % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (365), (2494) imply: % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2495) all_52_3 = e1 % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (188), (2495) imply: % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2496) ~ (all_52_7 = e1) % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2496) implies: % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2497) ~ (all_52_7 = e1) % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (337) gives: % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2498) all_58_1 = e1 % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (2456), (2498) are inconsistent by sub-proof % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #703. % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2499) ~ (all_58_1 = e1) % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2500) all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1 % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (322) gives: % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2501) all_58_9 = e2 % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (551), (2501) imply: % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2502) all_52_12 = e2 % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2468) gives: % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2503) all_58_1 = e1 % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (2456), (2503) are inconsistent by sub-proof % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #703. % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2504) all_58_4 = e1 | all_58_9 = e1 % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2504) gives: % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2505) all_58_4 = e1 % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (407), (2505) imply: % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2506) all_52_8 = e1 % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (620), (2506) imply: % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2507) op(e1, e1) = all_56_4 % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2500) gives: % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2508) all_58_3 = e1 % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (554), (2508) imply: % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2509) all_8_2 = e1 % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (545), (2509) imply: % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2510) all_56_11 = e1 % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (48), (2509) imply: % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2511) op(e1, e1) = all_8_1 % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (295) gives: % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2512) ~ (all_56_11 = e1) % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2510), (2512) imply: % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2513) $false % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2513) is inconsistent. % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_56_4, % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1, e1, simplifying with (2415), (2507) gives: % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2514) all_56_4 = e0 % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_8_1, % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_4, e1, e1, simplifying with (2507), (2511) % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2515) all_56_4 = all_8_1 % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2514), (2515) imply: % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2516) all_8_1 = e0 % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2516) implies: % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2517) all_8_1 = e0 % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2312), (2517) imply: % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2518) op(e2, e0) = e1 % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (212), (2412), (2518), (function-axioms) are % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #258. % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2519) all_58_7 = e1 | all_58_13 = e1 % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (380), (549), (2409), (2497), (2519) are % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #534. % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2520) all_58_9 = e1 % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2501), (2520) imply: % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2521) e2 = e1 % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6), (2521) imply: % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2522) $false % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2522) is inconsistent. % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2523) ~ (all_58_9 = e2) % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (551), (2523) imply: % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2524) ~ (all_52_12 = e2) % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (461), (2411), (2429), (2483), (2524) are % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #326. % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2525) all_54_8 = e1 | all_54_8 = e0 % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (471), (2407), (2408), (2525) are inconsistent by % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #664. % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2526) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (543), (2441), (2449), (2463), (2526) are % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #731. % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | (2527) all_56_5 = e3 % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | (2528) all_56_1 = e1 % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (546), (2528) imply: % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | (2529) all_10_2 = e1 % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (429), (2527) imply: % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | (2530) all_52_8 = e3 % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (168), (2530) imply: % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | (2531) ~ (all_52_12 = e3) % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2531) implies: % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | (2532) ~ (all_52_12 = e3) % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (53), (2529) imply: % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | (2533) op(e1, e1) = all_10_1 % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (216), (249), (322), (461), (551), (2385), (2411), % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | (2415), (2429), (2532), (2533), (function-axioms) % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #290. % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | (2534) ~ (all_58_1 = e0) % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (555), (2534) imply: % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | (2535) ~ (all_52_4 = e0) % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (336), (380), (549), (554), (555), (2410), (2428), % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | (2443), (2535) are inconsistent by sub-proof #240. % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | End of split % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | End of split % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | Case 2: % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | (2536) ~ (all_58_2 = e0) % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (336), (340), (365), (380), (401), (419), (549), % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | (553), (554), (555), (563), (2408), (2410), % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | (2427), (2428), (2443), (2536) are inconsistent by % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | sub-proof #602. % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | End of split % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | Case 2: % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | (2537) all_56_15 = e2 % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | (2538) all_56_11 = e0 % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (545), (2538) imply: % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | (2539) all_8_2 = e0 % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (443), (2537) imply: % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | (2540) all_52_13 = e2 % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (528), (2539) imply: % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | (2541) all_14_2 = e0 % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (36), (48), (212), (237), (540), (617), % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | (679), (769), (2308), (2312), (2417), (2539), % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | (2540), (2541), (function-axioms) are inconsistent % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | by sub-proof #252. % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | End of split % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | Case 2: % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | (2542) all_56_3 = e3 % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | (2543) all_56_1 = e2 % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (546), (2543) imply: % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | (2544) all_10_2 = e2 % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (408), (2542) imply: % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | (2545) all_52_4 = e3 % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | REDUCE: (181), (2545) imply: % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | (2546) ~ (all_52_12 = e3) % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | SIMP: (2546) implies: % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | (2547) ~ (all_52_12 = e3) % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | REDUCE: (567), (2544) imply: % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | (2548) ~ (all_52_12 = e2) % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (249), (461), (2411), (2429), (2547), (2548) are % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #653. % 147.77/21.12 | | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | | End of split % 147.77/21.12 | | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | | End of split % 147.77/21.12 | | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | | End of split % 147.77/21.12 | | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | | End of split % 147.77/21.12 | | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | End of split % 147.77/21.12 | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | Case 2: % 147.77/21.12 | | | | | | | | | | | | | | | % 147.77/21.12 | | | | | | | | | | | | | | | (2549) all_56_31 = e3 % 147.77/21.12 | | | | | | | | | | | | | | | (2550) all_56_25 = e0 % 147.77/21.12 | | | | | | | | | | | | | | | % 147.77/21.13 | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (36), (38), (46), (48), (51), (173), % 147.77/21.13 | | | | | | | | | | | | | | | (188), (194), (196), (215), (239), (247), (248), % 147.77/21.13 | | | | | | | | | | | | | | | (252), (287), (294), (295), (296), (318), (319), % 147.77/21.13 | | | | | | | | | | | | | | | (335), (365), (374), (401), (425), (431), (447), % 147.77/21.13 | | | | | | | | | | | | | | | (463), (480), (528), (534), (542), (543), (544), % 147.77/21.13 | | | | | | | | | | | | | | | (545), (546), (547), (548), (549), (557), (568), % 147.77/21.13 | | | | | | | | | | | | | | | (575), (581), (585), (617), (639), (679), (769), % 147.77/21.13 | | | | | | | | | | | | | | | (2308), (2312), (2394), (2549), (2550), % 147.77/21.13 | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 147.77/21.13 | | | | | | | | | | | | | | | #243. % 147.77/21.13 | | | | | | | | | | | | | | | % 147.77/21.13 | | | | | | | | | | | | | | End of split % 147.77/21.13 | | | | | | | | | | | | | | % 147.77/21.13 | | | | | | | | | | | | | Case 2: % 147.77/21.13 | | | | | | | | | | | | | | % 147.77/21.13 | | | | | | | | | | | | | | (2551) all_56_31 = e1 % 147.77/21.13 | | | | | | | | | | | | | | (2552) all_56_29 = e0 % 147.77/21.13 | | | | | | | | | | | | | | % 147.77/21.13 | | | | | | | | | | | | | | COMBINE_EQS: (357), (2552) imply: % 147.77/21.13 | | | | | | | | | | | | | | (2553) all_52_11 = e0 % 147.77/21.13 | | | | | | | | | | | | | | % 147.77/21.13 | | | | | | | | | | | | | | SIMP: (2553) implies: % 147.77/21.13 | | | | | | | | | | | | | | (2554) all_52_11 = e0 % 147.77/21.13 | | | | | | | | | | | | | | % 147.77/21.13 | | | | | | | | | | | | | | COMBINE_EQS: (544), (2551) imply: % 147.77/21.13 | | | | | | | | | | | | | | (2555) all_4_2 = e1 % 147.77/21.13 | | | | | | | | | | | | | | % 147.77/21.13 | | | | | | | | | | | | | | REDUCE: (187), (2554) imply: % 147.77/21.13 | | | | | | | | | | | | | | (2556) ~ (all_52_3 = e0) % 147.77/21.13 | | | | | | | | | | | | | | % 147.77/21.13 | | | | | | | | | | | | | | REDUCE: (585), (2554) imply: % 147.77/21.13 | | | | | | | | | | | | | | (2557) ~ (all_6_2 = e0) % 147.77/21.13 | | | | | | | | | | | | | | % 147.77/21.13 | | | | | | | | | | | | | | SIMP: (2557) implies: % 147.77/21.13 | | | | | | | | | | | | | | (2558) ~ (all_6_2 = e0) % 147.77/21.13 | | | | | | | | | | | | | | % 147.77/21.13 | | | | | | | | | | | | | | REDUCE: (590), (2555) imply: % 147.77/21.13 | | | | | | | | | | | | | | (2559) ~ (all_52_13 = e1) % 147.77/21.13 | | | | | | | | | | | | | | % 147.77/21.13 | | | | | | | | | | | | | | REDUCE: (38), (2555) imply: % 147.77/21.13 | | | | | | | | | | | | | | (2560) op(e1, e1) = all_4_1 % 147.77/21.13 | | | | | | | | | | | | | | % 147.77/21.13 | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_6_2, % 147.77/21.13 | | | | | | | | | | | | | | all_4_1, e1, e1, simplifying with (41), (2560) % 147.77/21.13 | | | | | | | | | | | | | | gives: % 147.77/21.13 | | | | | | | | | | | | | | (2561) all_6_2 = all_4_1 % 147.77/21.13 | | | | | | | | | | | | | | % 147.77/21.13 | | | | | | | | | | | | | | COMBINE_EQS: (541), (2561) imply: % 147.77/21.13 | | | | | | | | | | | | | | (2562) all_54_10 = all_4_1 % 147.77/21.13 | | | | | | | | | | | | | | % 147.77/21.13 | | | | | | | | | | | | | | COMBINE_EQS: (374), (2561) imply: % 147.77/21.13 | | | | | | | | | | | | | | (2563) all_56_21 = all_4_1 % 147.77/21.13 | | | | | | | | | | | | | | % 147.77/21.13 | | | | | | | | | | | | | | REDUCE: (2396), (2561) imply: % 147.77/21.13 | | | | | | | | | | | | | | (2564) ~ (all_4_1 = e2) % 147.77/21.13 | | | | | | | | | | | | | | % 147.77/21.13 | | | | | | | | | | | | | | REDUCE: (2558), (2561) imply: % 147.77/21.13 | | | | | | | | | | | | | | (2565) ~ (all_4_1 = e0) % 147.77/21.13 | | | | | | | | | | | | | | % 147.77/21.13 | | | | | | | | | | | | | | REDUCE: (43), (2561) imply: % 147.77/21.13 | | | | | | | | | | | | | | (2566) op(all_4_1, all_4_1) = all_6_1 % 147.77/21.13 | | | | | | | | | | | | | | % 147.77/21.13 | | | | | | | | | | | | | | REDUCE: (622), (2561) imply: % 147.77/21.13 | | | | | | | | | | | | | | (2567) op(e1, all_4_1) = all_56_20 % 147.77/21.13 | | | | | | | | | | | | | | % 147.77/21.13 | | | | | | | | | | | | | | BETA: splitting (294) gives: % 147.77/21.13 | | | | | | | | | | | | | | % 147.77/21.13 | | | | | | | | | | | | | | Case 1: % 147.77/21.13 | | | | | | | | | | | | | | | % 147.77/21.13 | | | | | | | | | | | | | | | (2568) ~ (all_56_11 = e0) % 147.77/21.13 | | | | | | | | | | | | | | | % 147.77/21.13 | | | | | | | | | | | | | | | REDUCE: (545), (2568) imply: % 147.77/21.13 | | | | | | | | | | | | | | | (2569) ~ (all_8_2 = e0) % 147.77/21.13 | | | | | | | | | | | | | | | % 147.77/21.13 | | | | | | | | | | | | | | | REF_CLOSE: (37), (42), (46), (48), (51), (192), (207), (215), % 147.77/21.13 | | | | | | | | | | | | | | | (240), (242), (247), (252), (293), (295), (296), % 147.77/21.13 | | | | | | | | | | | | | | | (381), (425), (478), (534), (542), (543), (545), % 147.77/21.13 | | | | | | | | | | | | | | | (557), (617), (639), (767), (769), (772), (2312), % 147.77/21.13 | | | | | | | | | | | | | | | (2389), (2394), (2556), (2560), (2562), (2563), % 147.77/21.13 | | | | | | | | | | | | | | | (2564), (2565), (2566), (2567), (2569), % 147.77/21.13 | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 147.77/21.13 | | | | | | | | | | | | | | | #239. % 147.77/21.13 | | | | | | | | | | | | | | | % 147.77/21.13 | | | | | | | | | | | | | | Case 2: % 147.77/21.13 | | | | | | | | | | | | | | | % 147.77/21.13 | | | | | | | | | | | | | | | (2570) all_56_15 = e2 % 147.77/21.13 | | | | | | | | | | | | | | | (2571) all_56_11 = e0 % 147.77/21.13 | | | | | | | | | | | | | | | % 147.77/21.13 | | | | | | | | | | | | | | | REF_CLOSE: (36), (48), (212), (237), (294), (443), (528), % 147.77/21.13 | | | | | | | | | | | | | | | (540), (545), (590), (617), (679), (769), (2308), % 147.77/21.13 | | | | | | | | | | | | | | | (2312), (2559), (2570), (2571), (function-axioms) % 147.77/21.13 | | | | | | | | | | | | | | | are inconsistent by sub-proof #236. % 147.77/21.13 | | | | | | | | | | | | | | | % 147.77/21.13 | | | | | | | | | | | | | | End of split % 147.77/21.13 | | | | | | | | | | | | | | % 147.77/21.13 | | | | | | | | | | | | | End of split % 147.77/21.13 | | | | | | | | | | | | | % 147.77/21.13 | | | | | | | | | | | | Case 2: % 147.77/21.13 | | | | | | | | | | | | | % 147.77/21.13 | | | | | | | | | | | | | (2572) all_56_21 = e2 % 147.77/21.13 | | | | | | | | | | | | | (2573) all_56_19 = e1 % 147.77/21.13 | | | | | | | | | | | | | % 147.77/21.13 | | | | | | | | | | | | | COMBINE_EQS: (435), (2573) imply: % 147.77/21.13 | | | | | | | | | | | | | (2574) all_52_6 = e1 % 147.77/21.13 | | | | | | | | | | | | | % 147.77/21.13 | | | | | | | | | | | | | COMBINE_EQS: (374), (2572) imply: % 147.77/21.13 | | | | | | | | | | | | | (2575) all_6_2 = e2 % 147.77/21.13 | | | | | | | | | | | | | % 147.77/21.13 | | | | | | | | | | | | | REDUCE: (573), (2574) imply: % 147.77/21.13 | | | | | | | | | | | | | (2576) ~ (all_8_2 = e1) % 147.77/21.13 | | | | | | | | | | | | | % 147.77/21.13 | | | | | | | | | | | | | SIMP: (2576) implies: % 147.77/21.13 | | | | | | | | | | | | | (2577) ~ (all_8_2 = e1) % 147.77/21.13 | | | | | | | | | | | | | % 147.77/21.13 | | | | | | | | | | | | | REDUCE: (43), (2575) imply: % 147.77/21.13 | | | | | | | | | | | | | (2578) op(e2, e2) = all_6_1 % 147.77/21.13 | | | | | | | | | | | | | % 147.77/21.13 | | | | | | | | | | | | | REF_CLOSE: (6), (36), (46), (48), (212), (237), (247), (294), % 147.77/21.13 | | | | | | | | | | | | | (443), (528), (540), (542), (545), (590), (617), % 147.77/21.13 | | | | | | | | | | | | | (679), (768), (769), (2308), (2312), (2391), % 147.77/21.13 | | | | | | | | | | | | | (2577), (2578), (function-axioms) are inconsistent % 147.77/21.13 | | | | | | | | | | | | | by sub-proof #235. % 147.77/21.13 | | | | | | | | | | | | | % 147.77/21.13 | | | | | | | | | | | | End of split % 147.77/21.13 | | | | | | | | | | | | % 147.77/21.13 | | | | | | | | | | | End of split % 147.77/21.13 | | | | | | | | | | | % 147.77/21.13 | | | | | | | | | | Case 2: % 147.77/21.13 | | | | | | | | | | | % 147.77/21.13 | | | | | | | | | | | (2579) all_36_1 = e3 % 147.77/21.13 | | | | | | | | | | | % 147.77/21.13 | | | | | | | | | | | COMBINE_EQS: (652), (2579) imply: % 147.77/21.13 | | | | | | | | | | | (2580) all_6_1 = e3 % 147.77/21.13 | | | | | | | | | | | % 147.77/21.13 | | | | | | | | | | | SIMP: (2580) implies: % 147.77/21.13 | | | | | | | | | | | (2581) all_6_1 = e3 % 147.77/21.13 | | | | | | | | | | | % 147.77/21.13 | | | | | | | | | | | REF_CLOSE: (6), (36), (41), (42), (46), (48), (51), (134), % 147.77/21.13 | | | | | | | | | | | (197), (211), (212), (215), (237), (242), (247), % 147.77/21.13 | | | | | | | | | | | (252), (293), (294), (295), (296), (374), (381), % 147.77/21.13 | | | | | | | | | | | (425), (431), (443), (528), (534), (540), (541), % 147.77/21.13 | | | | | | | | | | | (542), (543), (545), (557), (579), (583), (590), % 147.77/21.13 | | | | | | | | | | | (617), (639), (679), (769), (2308), (2311), % 147.77/21.13 | | | | | | | | | | | (2312), (2581), (function-axioms) are inconsistent % 147.77/21.13 | | | | | | | | | | | by sub-proof #249. % 147.77/21.13 | | | | | | | | | | | % 147.77/21.13 | | | | | | | | | | End of split % 147.77/21.13 | | | | | | | | | | % 147.77/21.13 | | | | | | | | | Case 2: % 147.77/21.13 | | | | | | | | | | % 147.77/21.13 | | | | | | | | | | (2582) all_28_0 = e2 % 147.77/21.13 | | | | | | | | | | % 147.77/21.13 | | | | | | | | | | COMBINE_EQS: (740), (2582) imply: % 147.77/21.13 | | | | | | | | | | (2583) all_6_0 = e2 % 147.77/21.13 | | | | | | | | | | % 147.77/21.13 | | | | | | | | | | SIMP: (2583) implies: % 147.77/21.13 | | | | | | | | | | (2584) all_6_0 = e2 % 147.77/21.13 | | | | | | | | | | % 147.77/21.13 | | | | | | | | | | REF_CLOSE: (6), (36), (41), (42), (43), (46), (48), (51), % 147.77/21.13 | | | | | | | | | | (134), (144), (211), (212), (215), (237), (242), % 147.77/21.13 | | | | | | | | | | (247), (252), (293), (294), (295), (296), (374), % 147.77/21.13 | | | | | | | | | | (381), (425), (431), (443), (475), (528), (534), % 147.77/21.13 | | | | | | | | | | (540), (541), (542), (543), (545), (557), (559), % 147.77/21.13 | | | | | | | | | | (577), (579), (583), (590), (617), (622), (634), % 147.77/21.13 | | | | | | | | | | (639), (679), (764), (768), (769), (2308), (2311), % 147.77/21.13 | | | | | | | | | | (2312), (2584), (function-axioms) are inconsistent % 147.77/21.13 | | | | | | | | | | by sub-proof #242. % 147.77/21.13 | | | | | | | | | | % 147.77/21.13 | | | | | | | | | End of split % 147.77/21.13 | | | | | | | | | % 147.77/21.13 | | | | | | | | Case 2: % 147.77/21.13 | | | | | | | | | % 147.77/21.13 | | | | | | | | | (2585) all_26_0 = e1 % 147.77/21.13 | | | | | | | | | (2586) ~ (all_26_1 = e2) | ~ (all_26_2 = e3) % 147.77/21.13 | | | | | | | | | % 147.77/21.13 | | | | | | | | | COMBINE_EQS: (760), (2585) imply: % 147.77/21.13 | | | | | | | | | (2587) all_4_0 = e1 % 147.77/21.13 | | | | | | | | | % 147.77/21.13 | | | | | | | | | SIMP: (2587) implies: % 147.77/21.13 | | | | | | | | | (2588) all_4_0 = e1 % 147.77/21.13 | | | | | | | | | % 147.77/21.13 | | | | | | | | | REDUCE: (37), (2588) imply: % 147.77/21.13 | | | | | | | | | (2589) op(e0, all_4_1) = e1 % 147.77/21.13 | | | | | | | | | % 147.77/21.13 | | | | | | | | | BETA: splitting (99) gives: % 147.77/21.13 | | | | | | | | | % 147.77/21.13 | | | | | | | | | Case 1: % 147.77/21.13 | | | | | | | | | | % 147.77/21.13 | | | | | | | | | | (2590) ~ (all_28_0 = e2) % 147.77/21.13 | | | | | | | | | | % 147.77/21.13 | | | | | | | | | | REDUCE: (740), (2590) imply: % 147.77/21.13 | | | | | | | | | | (2591) ~ (all_6_0 = e2) % 147.77/21.13 | | | | | | | | | | % 147.77/21.13 | | | | | | | | | | BETA: splitting (119) gives: % 147.77/21.13 | | | | | | | | | | % 147.77/21.13 | | | | | | | | | | Case 1: % 147.77/21.13 | | | | | | | | | | | % 147.77/21.13 | | | | | | | | | | | (2592) ~ (all_36_1 = e3) % 147.77/21.13 | | | | | | | | | | | % 147.77/21.13 | | | | | | | | | | | REDUCE: (652), (2592) imply: % 147.77/21.13 | | | | | | | | | | | (2593) ~ (all_6_1 = e3) % 147.77/21.13 | | | | | | | | | | | % 147.77/21.13 | | | | | | | | | | | BETA: splitting (134) gives: % 147.77/21.13 | | | | | | | | | | | % 147.77/21.13 | | | | | | | | | | | Case 1: % 147.77/21.13 | | | | | | | | | | | | % 147.77/21.13 | | | | | | | | | | | | (2594) ~ (all_42_0 = e1) % 147.77/21.13 | | | | | | | | | | | | % 147.77/21.13 | | | | | | | | | | | | REDUCE: (2311), (2594) imply: % 147.77/21.13 | | | | | | | | | | | | (2595) $false % 147.77/21.13 | | | | | | | | | | | | % 147.77/21.13 | | | | | | | | | | | | CLOSE: (2595) is inconsistent. % 147.77/21.13 | | | | | | | | | | | | % 147.77/21.13 | | | | | | | | | | | Case 2: % 147.77/21.13 | | | | | | | | | | | | % 147.77/21.13 | | | | | | | | | | | | (2596) ~ (all_42_1 = e0) | ~ (all_42_2 = e3) % 147.77/21.13 | | | | | | | | | | | | % 147.77/21.13 | | | | | | | | | | | | BETA: splitting (288) gives: % 147.77/21.13 | | | | | | | | | | | | % 147.77/21.13 | | | | | | | | | | | | Case 1: % 147.77/21.13 | | | | | | | | | | | | | % 147.77/21.13 | | | | | | | | | | | | | (2597) ~ (all_56_31 = e1) % 147.77/21.13 | | | | | | | | | | | | | % 147.77/21.13 | | | | | | | | | | | | | REDUCE: (544), (2597) imply: % 147.77/21.13 | | | | | | | | | | | | | (2598) ~ (all_4_2 = e1) % 147.77/21.13 | | | | | | | | | | | | | % 147.77/21.13 | | | | | | | | | | | | | BETA: splitting (290) gives: % 147.77/21.13 | | | | | | | | | | | | | % 147.77/21.13 | | | | | | | | | | | | | Case 1: % 147.77/21.13 | | | | | | | | | | | | | | % 147.77/21.13 | | | | | | | | | | | | | | (2599) ~ (all_56_31 = e3) % 147.77/21.13 | | | | | | | | | | | | | | % 147.77/21.13 | | | | | | | | | | | | | | REDUCE: (544), (2599) imply: % 147.77/21.13 | | | | | | | | | | | | | | (2600) ~ (all_4_2 = e3) % 147.77/21.13 | | | | | | | | | | | | | | % 147.77/21.13 | | | | | | | | | | | | | | BETA: splitting (289) gives: % 147.77/21.13 | | | | | | | | | | | | | | % 147.77/21.13 | | | | | | | | | | | | | | Case 1: % 147.77/21.13 | | | | | | | | | | | | | | | % 147.77/21.13 | | | | | | | | | | | | | | | (2601) ~ (all_56_31 = e2) % 147.77/21.13 | | | | | | | | | | | | | | | % 147.77/21.13 | | | | | | | | | | | | | | | REDUCE: (544), (2601) imply: % 147.77/21.13 | | | | | | | | | | | | | | | (2602) ~ (all_4_2 = e2) % 147.77/21.13 | | | | | | | | | | | | | | | % 147.77/21.13 | | | | | | | | | | | | | | | REF_CLOSE: (36), (38), (237), (540), (627), (2589), (2598), % 147.77/21.13 | | | | | | | | | | | | | | | (2600), (2602), (function-axioms) are inconsistent % 147.77/21.13 | | | | | | | | | | | | | | | by sub-proof #363. % 147.77/21.13 | | | | | | | | | | | | | | | % 147.77/21.13 | | | | | | | | | | | | | | Case 2: % 147.77/21.13 | | | | | | | | | | | | | | | % 147.77/21.13 | | | | | | | | | | | | | | | (2603) all_56_31 = e2 % 147.77/21.13 | | | | | | | | | | | | | | | (2604) all_56_27 = e0 % 147.77/21.13 | | | | | | | | | | | | | | | % 147.77/21.13 | | | | | | | | | | | | | | | REF_CLOSE: (36), (41), (43), (46), (48), (51), (189), (193), % 147.77/21.13 | | | | | | | | | | | | | | | (194), (197), (215), (242), (247), (248), (252), % 147.77/21.13 | | | | | | | | | | | | | | | (291), (293), (295), (296), (321), (323), (332), % 147.77/21.13 | | | | | | | | | | | | | | | (360), (374), (381), (386), (401), (425), (431), % 147.77/21.13 | | | | | | | | | | | | | | | (463), (534), (541), (542), (543), (544), (545), % 147.77/21.13 | | | | | | | | | | | | | | | (547), (550), (551), (557), (569), (575), (579), % 147.77/21.13 | | | | | | | | | | | | | | | (583), (587), (617), (639), (768), (769), (2312), % 147.77/21.13 | | | | | | | | | | | | | | | (2596), (2598), (2600), (2603), (2604), % 147.77/21.13 | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 147.77/21.13 | | | | | | | | | | | | | | | #234. % 147.77/21.13 | | | | | | | | | | | | | | | % 147.77/21.13 | | | | | | | | | | | | | | End of split % 147.77/21.13 | | | | | | | | | | | | | | % 147.77/21.13 | | | | | | | | | | | | | Case 2: % 147.77/21.13 | | | | | | | | | | | | | | % 147.77/21.13 | | | | | | | | | | | | | | (2605) all_56_31 = e3 % 147.77/21.13 | | | | | | | | | | | | | | (2606) all_56_25 = e0 % 147.77/21.13 | | | | | | | | | | | | | | % 147.77/21.13 | | | | | | | | | | | | | | COMBINE_EQS: (447), (2606) imply: % 147.77/21.13 | | | | | | | | | | | | | | (2607) all_52_3 = e0 % 147.77/21.13 | | | | | | | | | | | | | | % 147.77/21.13 | | | | | | | | | | | | | | COMBINE_EQS: (544), (2605) imply: % 147.77/21.13 | | | | | | | | | | | | | | (2608) all_4_2 = e3 % 147.77/21.13 | | | | | | | | | | | | | | % 147.77/21.13 | | | | | | | | | | | | | | COMBINE_EQS: (530), (2608) imply: % 147.77/21.13 | | | | | | | | | | | | | | (2609) all_26_2 = e3 % 147.77/21.13 | | | | | | | | | | | | | | % 147.77/21.13 | | | | | | | | | | | | | | COMBINE_EQS: (547), (2608) imply: % 147.77/21.13 | | | | | | | | | | | | | | (2610) all_58_15 = e3 % 147.77/21.13 | | | | | | | | | | | | | | % 147.77/21.13 | | | | | | | | | | | | | | COMBINE_EQS: (365), (2607) imply: % 147.77/21.13 | | | | | | | | | | | | | | (2611) all_58_12 = e0 % 147.77/21.13 | | | | | | | | | | | | | | % 147.77/21.13 | | | | | | | | | | | | | | REDUCE: (196), (2607) imply: % 147.77/21.13 | | | | | | | | | | | | | | (2612) ~ (all_52_1 = e0) % 147.77/21.13 | | | | | | | | | | | | | | % 147.77/21.13 | | | | | | | | | | | | | | REDUCE: (188), (2607) imply: % 147.77/21.13 | | | | | | | | | | | | | | (2613) ~ (all_52_7 = e0) % 147.77/21.13 | | | | | | | | | | | | | | % 147.77/21.13 | | | | | | | | | | | | | | SIMP: (2613) implies: % 147.77/21.13 | | | | | | | | | | | | | | (2614) ~ (all_52_7 = e0) % 147.77/21.13 | | | | | | | | | | | | | | % 147.77/21.13 | | | | | | | | | | | | | | REDUCE: (581), (2608) imply: % 147.77/21.13 | | | | | | | | | | | | | | (2615) ~ (all_52_7 = e3) % 147.77/21.13 | | | | | | | | | | | | | | % 147.77/21.13 | | | | | | | | | | | | | | REDUCE: (38), (2608) imply: % 147.77/21.13 | | | | | | | | | | | | | | (2616) op(e3, e3) = all_4_1 % 147.77/21.13 | | | | | | | | | | | | | | % 147.77/21.13 | | | | | | | | | | | | | | REDUCE: (36), (2608) imply: % 147.77/21.13 | | | | | | | | | | | | | | (2617) op(e0, e0) = e3 % 147.77/21.13 | | | | | | | | | | | | | | % 147.77/21.13 | | | | | | | | | | | | | | BETA: splitting (2586) gives: % 147.77/21.13 | | | | | | | | | | | | | | % 147.77/21.13 | | | | | | | | | | | | | | Case 1: % 147.77/21.13 | | | | | | | | | | | | | | | % 147.77/21.13 | | | | | | | | | | | | | | | % 147.77/21.13 | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_10_2, % 147.77/21.13 | | | | | | | | | | | | | | | all_4_1, e3, e3, simplifying with (51), (2616) % 147.77/21.13 | | | | | | | | | | | | | | | gives: % 147.77/21.13 | | | | | | | | | | | | | | | (2618) all_10_2 = all_4_1 % 147.77/21.13 | | | | | | | | | | | | | | | % 147.77/21.13 | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (46), (48), (51), (173), (194), (215), % 147.77/21.13 | | | | | | | | | | | | | | | (239), (247), (248), (252), (287), (294), (295), % 147.77/21.13 | | | | | | | | | | | | | | | (296), (318), (319), (335), (374), (401), (425), % 147.77/21.13 | | | | | | | | | | | | | | | (431), (463), (480), (528), (534), (542), (543), % 147.77/21.13 | | | | | | | | | | | | | | | (545), (546), (548), (549), (557), (568), (575), % 147.77/21.13 | | | | | | | | | | | | | | | (585), (617), (639), (679), (769), (2308), (2312), % 147.77/21.13 | | | | | | | | | | | | | | | (2596), (2605), (2610), (2611), (2612), (2614), % 147.77/21.13 | | | | | | | | | | | | | | | (2615), (2617), (2618), (function-axioms) are % 147.77/21.13 | | | | | | | | | | | | | | | inconsistent by sub-proof #244. % 147.77/21.13 | | | | | | | | | | | | | | | % 147.77/21.13 | | | | | | | | | | | | | | Case 2: % 147.77/21.13 | | | | | | | | | | | | | | | % 147.77/21.13 | | | | | | | | | | | | | | | (2619) ~ (all_26_2 = e3) % 147.77/21.13 | | | | | | | | | | | | | | | % 147.77/21.13 | | | | | | | | | | | | | | | REDUCE: (2609), (2619) imply: % 147.77/21.13 | | | | | | | | | | | | | | | (2620) $false % 147.77/21.13 | | | | | | | | | | | | | | | % 147.77/21.13 | | | | | | | | | | | | | | | CLOSE: (2620) is inconsistent. % 147.77/21.13 | | | | | | | | | | | | | | | % 147.77/21.13 | | | | | | | | | | | | | | End of split % 147.77/21.13 | | | | | | | | | | | | | | % 147.77/21.13 | | | | | | | | | | | | | End of split % 147.77/21.13 | | | | | | | | | | | | | % 147.77/21.13 | | | | | | | | | | | | Case 2: % 147.77/21.13 | | | | | | | | | | | | | % 147.77/21.13 | | | | | | | | | | | | | (2621) all_56_31 = e1 % 147.77/21.13 | | | | | | | | | | | | | (2622) all_56_29 = e0 % 147.77/21.13 | | | | | | | | | | | | | % 147.77/21.13 | | | | | | | | | | | | | COMBINE_EQS: (357), (2622) imply: % 147.77/21.13 | | | | | | | | | | | | | (2623) all_52_11 = e0 % 147.77/21.13 | | | | | | | | | | | | | % 147.77/21.13 | | | | | | | | | | | | | SIMP: (2623) implies: % 147.77/21.13 | | | | | | | | | | | | | (2624) all_52_11 = e0 % 147.77/21.13 | | | | | | | | | | | | | % 147.77/21.13 | | | | | | | | | | | | | COMBINE_EQS: (544), (2621) imply: % 147.77/21.13 | | | | | | | | | | | | | (2625) all_4_2 = e1 % 147.77/21.13 | | | | | | | | | | | | | % 147.77/21.13 | | | | | | | | | | | | | REDUCE: (187), (2624) imply: % 147.77/21.13 | | | | | | | | | | | | | (2626) ~ (all_52_3 = e0) % 147.77/21.13 | | | | | | | | | | | | | % 147.77/21.13 | | | | | | | | | | | | | REDUCE: (585), (2624) imply: % 147.77/21.13 | | | | | | | | | | | | | (2627) ~ (all_6_2 = e0) % 147.77/21.13 | | | | | | | | | | | | | % 147.77/21.13 | | | | | | | | | | | | | SIMP: (2627) implies: % 147.77/21.13 | | | | | | | | | | | | | (2628) ~ (all_6_2 = e0) % 147.77/21.13 | | | | | | | | | | | | | % 147.77/21.13 | | | | | | | | | | | | | REDUCE: (590), (2625) imply: % 147.77/21.13 | | | | | | | | | | | | | (2629) ~ (all_52_13 = e1) % 147.77/21.13 | | | | | | | | | | | | | % 147.77/21.13 | | | | | | | | | | | | | REDUCE: (38), (2625) imply: % 147.77/21.13 | | | | | | | | | | | | | (2630) op(e1, e1) = all_4_1 % 147.77/21.13 | | | | | | | | | | | | | % 147.77/21.13 | | | | | | | | | | | | | REF_CLOSE: (36), (37), (41), (42), (43), (46), (48), (51), % 147.77/21.13 | | | | | | | | | | | | | (192), (207), (212), (215), (237), (240), (242), % 147.77/21.13 | | | | | | | | | | | | | (247), (252), (292), (293), (294), (295), (296), % 147.77/21.13 | | | | | | | | | | | | | (374), (381), (425), (435), (443), (478), (528), % 147.77/21.13 | | | | | | | | | | | | | (534), (540), (541), (542), (543), (545), (557), % 147.77/21.13 | | | | | | | | | | | | | (573), (580), (590), (617), (622), (639), (679), % 147.77/21.13 | | | | | | | | | | | | | (767), (768), (769), (772), (2308), (2312), % 147.77/21.13 | | | | | | | | | | | | | (2591), (2593), (2596), (2626), (2628), (2629), % 147.77/21.13 | | | | | | | | | | | | | (2630), (function-axioms) are inconsistent by % 147.77/21.13 | | | | | | | | | | | | | sub-proof #232. % 147.77/21.13 | | | | | | | | | | | | | % 147.77/21.13 | | | | | | | | | | | | End of split % 147.77/21.13 | | | | | | | | | | | | % 147.77/21.13 | | | | | | | | | | | End of split % 147.77/21.13 | | | | | | | | | | | % 147.77/21.13 | | | | | | | | | | Case 2: % 147.77/21.13 | | | | | | | | | | | % 147.77/21.13 | | | | | | | | | | | (2631) all_36_1 = e3 % 147.77/21.13 | | | | | | | | | | | % 147.77/21.13 | | | | | | | | | | | COMBINE_EQS: (652), (2631) imply: % 147.77/21.13 | | | | | | | | | | | (2632) all_6_1 = e3 % 147.77/21.13 | | | | | | | | | | | % 147.77/21.13 | | | | | | | | | | | SIMP: (2632) implies: % 147.77/21.13 | | | | | | | | | | | (2633) all_6_1 = e3 % 147.77/21.13 | | | | | | | | | | | % 147.77/21.14 | | | | | | | | | | | REF_CLOSE: (6), (36), (41), (42), (46), (48), (51), (134), % 147.77/21.14 | | | | | | | | | | | (197), (211), (212), (215), (237), (242), (247), % 147.77/21.14 | | | | | | | | | | | (252), (293), (294), (295), (296), (374), (381), % 147.77/21.14 | | | | | | | | | | | (425), (431), (443), (528), (534), (540), (541), % 147.77/21.14 | | | | | | | | | | | (542), (543), (545), (557), (579), (583), (590), % 147.77/21.14 | | | | | | | | | | | (617), (639), (679), (769), (2308), (2311), % 147.77/21.14 | | | | | | | | | | | (2312), (2633), (function-axioms) are inconsistent % 147.77/21.14 | | | | | | | | | | | by sub-proof #249. % 147.77/21.14 | | | | | | | | | | | % 147.77/21.14 | | | | | | | | | | End of split % 147.77/21.14 | | | | | | | | | | % 147.77/21.14 | | | | | | | | | Case 2: % 147.77/21.14 | | | | | | | | | | % 147.77/21.14 | | | | | | | | | | (2634) all_28_0 = e2 % 147.77/21.14 | | | | | | | | | | % 147.77/21.14 | | | | | | | | | | COMBINE_EQS: (740), (2634) imply: % 147.77/21.14 | | | | | | | | | | (2635) all_6_0 = e2 % 147.77/21.14 | | | | | | | | | | % 147.77/21.14 | | | | | | | | | | REF_CLOSE: (6), (36), (41), (42), (43), (46), (48), (51), % 147.77/21.14 | | | | | | | | | | (134), (144), (211), (212), (215), (237), (242), % 147.77/21.14 | | | | | | | | | | (247), (252), (293), (294), (295), (296), (374), % 147.77/21.14 | | | | | | | | | | (381), (425), (431), (443), (475), (528), (534), % 147.77/21.14 | | | | | | | | | | (540), (541), (542), (543), (545), (557), (559), % 147.77/21.14 | | | | | | | | | | (577), (579), (583), (590), (617), (622), (634), % 147.77/21.14 | | | | | | | | | | (639), (679), (764), (768), (769), (2308), (2311), % 147.77/21.14 | | | | | | | | | | (2312), (2635), (function-axioms) are inconsistent % 147.77/21.14 | | | | | | | | | | by sub-proof #242. % 147.77/21.14 | | | | | | | | | | % 147.77/21.14 | | | | | | | | | End of split % 147.77/21.14 | | | | | | | | | % 147.77/21.14 | | | | | | | | End of split % 147.77/21.14 | | | | | | | | % 147.77/21.14 | | | | | | | End of split % 147.77/21.14 | | | | | | | % 147.77/21.14 | | | | | | End of split % 147.77/21.14 | | | | | | % 147.77/21.14 | | | | | Case 2: % 147.77/21.14 | | | | | | % 147.77/21.14 | | | | | | (2636) all_12_0 = e2 % 147.77/21.14 | | | | | | (2637) ~ (all_12_1 = e1) | ~ (all_12_2 = e3) % 147.77/21.14 | | | | | | % 147.77/21.14 | | | | | | COMBINE_EQS: (759), (2636) imply: % 147.77/21.14 | | | | | | (2638) all_4_0 = e2 % 147.77/21.14 | | | | | | % 147.77/21.14 | | | | | | COMBINE_EQS: (734), (2638) imply: % 147.77/21.14 | | | | | | (2639) all_34_0 = e2 % 147.77/21.14 | | | | | | % 147.77/21.14 | | | | | | REDUCE: (767), (2638) imply: % 147.77/21.14 | | | | | | (2640) ~ (e3 = e2) % 147.77/21.14 | | | | | | % 147.77/21.14 | | | | | | REDUCE: (37), (2638) imply: % 147.77/21.14 | | | | | | (2641) op(e0, all_4_1) = e2 % 147.77/21.14 | | | | | | % 147.77/21.14 | | | | | | BETA: splitting (64) gives: % 147.77/21.14 | | | | | | % 147.77/21.14 | | | | | | Case 1: % 147.77/21.14 | | | | | | | % 147.77/21.14 | | | | | | | (2642) ~ (all_14_0 = e1) % 147.77/21.14 | | | | | | | % 147.77/21.14 | | | | | | | REDUCE: (758), (2642) imply: % 147.77/21.14 | | | | | | | (2643) ~ (all_8_0 = e1) % 147.77/21.14 | | | | | | | % 147.77/21.14 | | | | | | | BETA: splitting (69) gives: % 147.77/21.14 | | | | | | | % 147.77/21.14 | | | | | | | Case 1: % 147.77/21.14 | | | | | | | | % 147.77/21.14 | | | | | | | | (2644) ~ (all_16_0 = e1) % 147.77/21.14 | | | | | | | | % 147.77/21.14 | | | | | | | | REDUCE: (757), (2644) imply: % 147.77/21.14 | | | | | | | | (2645) ~ (all_10_0 = e1) % 147.77/21.14 | | | | | | | | % 147.77/21.14 | | | | | | | | BETA: splitting (84) gives: % 147.77/21.14 | | | | | | | | % 147.77/21.14 | | | | | | | | Case 1: % 147.77/21.14 | | | | | | | | | % 147.77/21.14 | | | | | | | | | (2646) ~ (all_22_1 = e3) % 147.77/21.14 | | | | | | | | | % 147.77/21.14 | | | | | | | | | REDUCE: (672), (2646) imply: % 147.77/21.14 | | | | | | | | | (2647) ~ (all_8_1 = e3) % 147.77/21.14 | | | | | | | | | % 147.77/21.14 | | | | | | | | | BETA: splitting (99) gives: % 147.77/21.14 | | | | | | | | | % 147.77/21.14 | | | | | | | | | Case 1: % 147.77/21.14 | | | | | | | | | | % 147.77/21.14 | | | | | | | | | | (2648) ~ (all_28_0 = e2) % 147.77/21.14 | | | | | | | | | | % 147.77/21.14 | | | | | | | | | | REDUCE: (740), (2648) imply: % 147.77/21.14 | | | | | | | | | | (2649) ~ (all_6_0 = e2) % 147.77/21.14 | | | | | | | | | | % 147.77/21.14 | | | | | | | | | | BETA: splitting (104) gives: % 147.77/21.14 | | | | | | | | | | % 147.77/21.14 | | | | | | | | | | Case 1: % 147.77/21.14 | | | | | | | | | | | % 147.77/21.14 | | | | | | | | | | | (2650) ~ (all_30_0 = e3) % 147.77/21.14 | | | | | | | | | | | % 147.77/21.14 | | | | | | | | | | | REDUCE: (718), (2650) imply: % 147.77/21.14 | | | | | | | | | | | (2651) ~ (all_8_0 = e3) % 147.77/21.14 | | | | | | | | | | | % 147.77/21.14 | | | | | | | | | | | BETA: splitting (109) gives: % 147.77/21.14 | | | | | | | | | | | % 147.77/21.14 | | | | | | | | | | | Case 1: % 147.77/21.14 | | | | | | | | | | | | % 147.77/21.14 | | | | | | | | | | | | (2652) ~ (all_32_1 = e1) % 147.77/21.14 | | | | | | | | | | | | % 147.77/21.14 | | | | | | | | | | | | REDUCE: (682), (2652) imply: % 147.77/21.14 | | | | | | | | | | | | (2653) ~ (all_10_1 = e1) % 147.77/21.14 | | | | | | | | | | | | % 147.77/21.14 | | | | | | | | | | | | BETA: splitting (114) gives: % 147.77/21.14 | | | | | | | | | | | | % 147.77/21.14 | | | | | | | | | | | | Case 1: % 147.77/21.14 | | | | | | | | | | | | | % 147.77/21.14 | | | | | | | | | | | | | (2654) ~ (all_34_0 = e2) % 147.77/21.14 | | | | | | | | | | | | | % 147.77/21.14 | | | | | | | | | | | | | REDUCE: (2639), (2654) imply: % 147.77/21.14 | | | | | | | | | | | | | (2655) $false % 147.77/21.14 | | | | | | | | | | | | | % 147.77/21.14 | | | | | | | | | | | | | CLOSE: (2655) is inconsistent. % 147.77/21.14 | | | | | | | | | | | | | % 147.77/21.14 | | | | | | | | | | | | Case 2: % 147.77/21.14 | | | | | | | | | | | | | % 147.77/21.14 | | | | | | | | | | | | | (2656) ~ (all_34_1 = e3) | ~ (all_34_2 = e1) % 147.77/21.14 | | | | | | | | | | | | | % 147.77/21.14 | | | | | | | | | | | | | BETA: splitting (119) gives: % 147.77/21.14 | | | | | | | | | | | | | % 147.77/21.14 | | | | | | | | | | | | | Case 1: % 147.77/21.14 | | | | | | | | | | | | | | % 147.77/21.14 | | | | | | | | | | | | | | (2657) ~ (all_36_1 = e3) % 147.77/21.14 | | | | | | | | | | | | | | % 147.77/21.14 | | | | | | | | | | | | | | REDUCE: (652), (2657) imply: % 147.77/21.14 | | | | | | | | | | | | | | (2658) ~ (all_6_1 = e3) % 147.77/21.14 | | | | | | | | | | | | | | % 147.77/21.14 | | | | | | | | | | | | | | BETA: splitting (124) gives: % 147.77/21.14 | | | | | | | | | | | | | | % 147.77/21.14 | | | | | | | | | | | | | | Case 1: % 147.77/21.14 | | | | | | | | | | | | | | | % 147.77/21.14 | | | | | | | | | | | | | | | (2659) ~ (all_38_1 = e2) % 147.77/21.14 | | | | | | | | | | | | | | | % 147.77/21.14 | | | | | | | | | | | | | | | REDUCE: (684), (2659) imply: % 147.77/21.14 | | | | | | | | | | | | | | | (2660) ~ (all_10_1 = e2) % 147.77/21.14 | | | | | | | | | | | | | | | % 147.77/21.14 | | | | | | | | | | | | | | | BETA: splitting (129) gives: % 147.77/21.14 | | | | | | | | | | | | | | | % 147.77/21.14 | | | | | | | | | | | | | | | Case 1: % 147.77/21.14 | | | | | | | | | | | | | | | | % 147.77/21.14 | | | | | | | | | | | | | | | | (2661) ~ (all_40_0 = e3) % 147.77/21.14 | | | | | | | | | | | | | | | | % 147.77/21.14 | | | | | | | | | | | | | | | | REDUCE: (713), (2661) imply: % 147.77/21.14 | | | | | | | | | | | | | | | | (2662) ~ (all_6_0 = e3) % 147.77/21.14 | | | | | | | | | | | | | | | | % 147.77/21.14 | | | | | | | | | | | | | | | | BETA: splitting (288) gives: % 147.77/21.14 | | | | | | | | | | | | | | | | % 147.77/21.14 | | | | | | | | | | | | | | | | Case 1: % 147.77/21.14 | | | | | | | | | | | | | | | | | % 147.77/21.14 | | | | | | | | | | | | | | | | | (2663) ~ (all_56_31 = e1) % 147.77/21.14 | | | | | | | | | | | | | | | | | % 147.77/21.14 | | | | | | | | | | | | | | | | | REDUCE: (544), (2663) imply: % 147.77/21.14 | | | | | | | | | | | | | | | | | (2664) ~ (all_4_2 = e1) % 147.77/21.14 | | | | | | | | | | | | | | | | | % 147.77/21.14 | | | | | | | | | | | | | | | | | BETA: splitting (292) gives: % 147.77/21.14 | | | | | | | | | | | | | | | | | % 147.77/21.14 | | | | | | | | | | | | | | | | | Case 1: % 147.77/21.14 | | | | | | | | | | | | | | | | | | % 147.77/21.14 | | | | | | | | | | | | | | | | | | (2665) ~ (all_56_21 = e2) % 147.77/21.14 | | | | | | | | | | | | | | | | | | % 147.77/21.14 | | | | | | | | | | | | | | | | | | REDUCE: (374), (2665) imply: % 147.77/21.14 | | | | | | | | | | | | | | | | | | (2666) ~ (all_6_2 = e2) % 147.77/21.14 | | | | | | | | | | | | | | | | | | % 147.77/21.14 | | | | | | | | | | | | | | | | | | BETA: splitting (294) gives: % 147.77/21.14 | | | | | | | | | | | | | | | | | | % 147.77/21.14 | | | | | | | | | | | | | | | | | | Case 1: % 147.77/21.14 | | | | | | | | | | | | | | | | | | | % 147.77/21.14 | | | | | | | | | | | | | | | | | | | (2667) ~ (all_56_11 = e0) % 147.77/21.14 | | | | | | | | | | | | | | | | | | | % 147.77/21.14 | | | | | | | | | | | | | | | | | | | REDUCE: (545), (2667) imply: % 147.77/21.14 | | | | | | | | | | | | | | | | | | | (2668) ~ (all_8_2 = e0) % 147.77/21.14 | | | | | | | | | | | | | | | | | | | % 147.77/21.14 | | | | | | | | | | | | | | | | | | | BETA: splitting (293) gives: % 147.77/21.14 | | | | | | | | | | | | | | | | | | | % 147.77/21.14 | | | | | | | | | | | | | | | | | | | Case 1: % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | (2669) ~ (all_56_21 = e3) % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | REDUCE: (374), (2669) imply: % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | (2670) ~ (all_6_2 = e3) % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | BETA: splitting (290) gives: % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | Case 1: % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | (2671) ~ (all_56_31 = e3) % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | REDUCE: (544), (2671) imply: % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | (2672) ~ (all_4_2 = e3) % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (291) gives: % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | Case 1: % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | (2673) ~ (all_56_21 = e0) % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (374), (2673) imply: % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | (2674) ~ (all_6_2 = e0) % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (242) gives: % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | (2675) all_54_10 = e3 % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (541), (2670), (2675) are inconsistent by % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | sub-proof #736. % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | (2676) ~ (all_54_10 = e3) % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | (2677) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2677) gives: % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | (2678) all_54_10 = e2 % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (541), (2666), (2678) are inconsistent by % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #735. % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | (2679) ~ (all_54_10 = e2) % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | (2680) all_54_10 = e1 | all_54_10 = e0 % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2680) gives: % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | (2681) all_54_10 = e1 % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (541), (2681) imply: % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | (2682) all_6_2 = e1 % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2682) implies: % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | (2683) all_6_2 = e1 % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (43), (2683) imply: % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | (2684) op(e1, e1) = all_6_1 % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (622), (2683) imply: % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | (2685) op(e1, e1) = all_56_20 % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (41), (2683) imply: % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | (2686) op(e1, e1) = e1 % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_6_1, % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_20, e1, e1, simplifying with (2684), (2685) % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | (2687) all_56_20 = all_6_1 % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1, % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_20, e1, e1, simplifying with (2685), (2686) % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | (2688) all_56_20 = e1 % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2687), (2688) imply: % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | (2689) all_6_1 = e1 % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2689) implies: % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | (2690) all_6_1 = e1 % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (42), (2690) imply: % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | (2691) op(e1, e1) = all_6_0 % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1, all_6_0, % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | e1, e1, simplifying with (2686), (2691) gives: % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | (2692) all_6_0 = e1 % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (296) gives: % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | | (2693) ~ (all_56_11 = e3) % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (545), (2693) imply: % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | | (2694) ~ (all_8_2 = e3) % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (295) gives: % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2695) ~ (all_56_11 = e1) % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (545), (2695) imply: % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2696) ~ (all_8_2 = e1) % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (247) gives: % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2697) all_54_5 = e3 % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (542), (2694), (2697) are inconsistent by % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #737. % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2698) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2698) gives: % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2699) all_54_5 = e2 % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (542), (2699) imply: % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2700) all_8_2 = e2 % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2700) implies: % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2701) all_8_2 = e2 % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (575), (2701) imply: % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2702) ~ (all_52_7 = e2) % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (289) gives: % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2703) ~ (all_56_31 = e2) % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (544), (2703) imply: % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2704) ~ (all_4_2 = e2) % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (38), (237), (540), (627), (2641), (2664), % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2672), (2704), (function-axioms) are inconsistent % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #229. % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2705) all_56_31 = e2 % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2706) all_56_27 = e0 % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (360), (2706) imply: % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2707) all_52_7 = e0 % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2707) implies: % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2708) all_52_7 = e0 % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (544), (2705) imply: % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2709) all_4_2 = e2 % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (547), (2709) imply: % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2710) all_58_15 = e2 % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (549), (2708) imply: % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2711) all_58_13 = e0 % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (173), (2708) imply: % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2712) ~ (all_52_11 = e0) % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2712) implies: % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2713) ~ (all_52_11 = e0) % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2702), (2708) imply: % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2714) ~ (e2 = e0) % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (36), (37), (38), (41), (42), (43), (46), % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (47), (48), (51), (53), (158), (160), (161), % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (166), (168), (171), (174), (181), (182), (189), % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (191), (193), (194), (196), (205), (208), (212), % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (237), (238), (241), (242), (243), (245), (247), % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (248), (251), (252), (287), (291), (292), (293), % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (295), (297), (298), (299), (317), (318), (321), % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (328), (330), (331), (332), (333), (337), (343), % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (345), (365), (374), (381), (386), (389), (401), % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (402), (407), (408), (419), (429), (431), (435), % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (457), (463), (469), (473), (476), (482), (540), % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (541), (542), (543), (544), (545), (546), (547), % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (548), (550), (551), (552), (554), (555), (557), % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (559), (561), (563), (565), (567), (568), (569), % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (571), (573), (577), (579), (580), (582), (583), % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (585), (587), (588), (589), (590), (591), (619), % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (621), (624), (625), (626), (767), (768), (769), % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2643), (2647), (2649), (2653), (2658), (2660), % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2664), (2668), (2708), (2709), (2710), (2711), % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2713), (2714), (function-axioms) are inconsistent % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #362. % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2715) all_54_5 = e1 | all_54_5 = e0 % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (542), (2668), (2696), (2715) are inconsistent by % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #645. % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2716) all_56_11 = e1 % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (545), (2716) imply: % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2717) all_8_2 = e1 % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (48), (769), (2685), (2686), (2717), % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | #535. % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | | (2718) all_56_11 = e3 % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | | (2719) all_56_9 = e2 % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (425), (2719) imply: % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | | (2720) all_52_1 = e2 % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (545), (2718) imply: % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | | (2721) all_8_2 = e3 % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (194), (2720) imply: % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | | (2722) ~ (all_52_9 = e2) % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2722) implies: % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | | (2723) ~ (all_52_9 = e2) % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (193), (2720) imply: % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | | (2724) ~ (all_52_13 = e2) % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2724) implies: % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | | (2725) ~ (all_52_13 = e2) % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (557), (2720) imply: % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | | (2726) ~ (all_10_2 = e2) % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2726) implies: % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | | (2727) ~ (all_10_2 = e2) % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (577), (2721) imply: % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | | (2728) ~ (all_52_9 = e3) % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (48), (2721) imply: % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | | (2729) op(e3, e3) = all_8_1 % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (36), (47), (51), (53), (161), (168), (181), % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | | (182), (212), (237), (245), (251), (252), (297), % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | | (330), (331), (343), (389), (402), (407), (419), % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | | (457), (469), (540), (543), (546), (552), (555), % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | | (563), (589), (590), (769), (2643), (2647), % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | | (2653), (2660), (2666), (2670), (2723), (2725), % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | | (2727), (2728), (2729), (function-axioms) are % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #588. % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | (2730) all_54_10 = e0 % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (541), (2674), (2730) are inconsistent by % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #705. % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | End of split % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | End of split % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | Case 2: % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | (2731) all_56_23 = e1 % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | (2732) all_56_21 = e0 % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (38), (43), (237), (366), (374), (540), % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | (591), (627), (768), (2641), (2658), (2731), % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | (2732), (function-axioms) are inconsistent by % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | sub-proof #227. % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | End of split % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | Case 2: % 147.77/21.14 | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | (2733) all_56_31 = e3 % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | (2734) all_56_25 = e0 % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (447), (2734) imply: % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | (2735) all_52_3 = e0 % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | SIMP: (2735) implies: % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | (2736) all_52_3 = e0 % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (544), (2733) imply: % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | (2737) all_4_2 = e3 % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (529), (2737) imply: % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | (2738) all_12_2 = e3 % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (547), (2737) imply: % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | (2739) all_58_15 = e3 % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (365), (2736) imply: % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | (2740) all_58_12 = e0 % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | REDUCE: (188), (2736) imply: % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | (2741) ~ (all_52_7 = e0) % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | SIMP: (2741) implies: % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | (2742) ~ (all_52_7 = e0) % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | REDUCE: (561), (2736) imply: % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | (2743) ~ (all_10_2 = e0) % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | SIMP: (2743) implies: % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | (2744) ~ (all_10_2 = e0) % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | REDUCE: (581), (2737) imply: % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | (2745) ~ (all_52_7 = e3) % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | REDUCE: (590), (2737) imply: % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | (2746) ~ (all_52_13 = e3) % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | REDUCE: (38), (2737) imply: % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | (2747) op(e3, e3) = all_4_1 % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | REDUCE: (36), (2737) imply: % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | (2748) op(e0, e0) = e3 % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2637) gives: % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | Case 1: % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | (2749) ~ (all_12_1 = e1) % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (681), (2749) imply: % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | (2750) ~ (all_4_1 = e1) % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_10_2, % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | all_4_1, e3, e3, simplifying with (51), (2747) % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | gives: % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | (2751) all_10_2 = all_4_1 % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (543), (2751) imply: % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | (2752) all_54_0 = all_4_1 % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (419), (2751) imply: % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | (2753) all_58_0 = all_4_1 % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (557), (2751) imply: % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | (2754) ~ (all_52_1 = all_4_1) % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (563), (2751) imply: % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | (2755) ~ (all_52_4 = all_4_1) % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (565), (2751) imply: % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | (2756) ~ (all_52_8 = all_4_1) % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2744), (2751) imply: % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | (2757) ~ (all_4_1 = e0) % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (53), (2751) imply: % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | (2758) op(all_4_1, all_4_1) = all_10_1 % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (296) gives: % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | (2759) ~ (all_56_11 = e3) % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (545), (2759) imply: % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | (2760) ~ (all_8_2 = e3) % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (291) gives: % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | (2761) ~ (all_56_21 = e0) % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (374), (2761) imply: % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | (2762) ~ (all_6_2 = e0) % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (242) gives: % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | (2763) all_54_10 = e3 % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (541), (2763) imply: % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | (2764) all_6_2 = e3 % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2670), (2764) imply: % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | (2765) $false % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2765) is inconsistent. % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | (2766) ~ (all_54_10 = e3) % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | (2767) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2767) gives: % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | (2768) all_54_10 = e2 % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (541), (2768) imply: % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | (2769) all_6_2 = e2 % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2666), (2769) imply: % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | (2770) $false % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2770) is inconsistent. % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | (2771) ~ (all_54_10 = e2) % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | (2772) all_54_10 = e1 | all_54_10 = e0 % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2772) gives: % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2773) all_54_10 = e1 % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (541), (2773) imply: % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2774) all_6_2 = e1 % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (569), (2774) imply: % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2775) ~ (all_52_2 = e1) % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (582), (2774) imply: % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2776) ~ (all_52_8 = e1) % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (585), (2774) imply: % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2777) ~ (all_52_11 = e1) % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2670), (2774) imply: % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2778) ~ (e3 = e1) % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2666), (2774) imply: % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2779) ~ (e2 = e1) % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (342) gives: % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2780) all_58_0 = e1 % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2753), (2780) imply: % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2781) all_4_1 = e1 % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2750), (2781) imply: % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2782) $false % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2782) is inconsistent. % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2783) all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1 % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (318) gives: % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2784) all_58_12 = e1 % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2740), (2784) imply: % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2785) e1 = e0 % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4), (2785) imply: % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2786) $false % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2786) is inconsistent. % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2787) all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1 % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2787) gives: % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2788) all_58_13 = e1 % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (549), (2788) imply: % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2789) all_52_7 = e1 % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2789) implies: % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2790) all_52_7 = e1 % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (183), (2790) imply: % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2791) ~ (all_52_4 = e1) % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (173), (2790) imply: % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2792) ~ (all_52_11 = e1) % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (319) gives: % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2793) all_58_12 = e2 % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2740), (2793) imply: % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2794) e2 = e0 % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5), (2794) imply: % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2795) $false % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2795) is inconsistent. % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2796) all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2 % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2783) gives: % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2797) all_58_2 = e1 % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (401), (2797) imply: % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2798) all_52_1 = e1 % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (568), (2798) imply: % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2799) ~ (all_8_2 = e1) % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2799) implies: % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2800) ~ (all_8_2 = e1) % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2754), (2798) imply: % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2801) ~ (all_4_1 = e1) % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (335) gives: % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2802) all_58_2 = e3 % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2797), (2802) imply: % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2803) e3 = e1 % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2803) implies: % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2804) e3 = e1 % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8), (2804) imply: % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2805) $false % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2805) is inconsistent. % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2806) all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3 % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2796) gives: % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2807) all_58_13 = e2 % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2788), (2807) imply: % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2808) e2 = e1 % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6), (2808) imply: % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2809) $false % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2809) is inconsistent. % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2810) all_58_14 = e2 | all_58_15 = e2 % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (247) gives: % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2811) all_54_5 = e3 % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (542), (2760), (2811) are inconsistent by % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #737. % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2812) ~ (all_54_5 = e3) % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2813) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2810) gives: % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2814) all_58_14 = e2 % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (548), (2814) imply: % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2815) all_52_11 = e2 % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2815) implies: % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2816) all_52_11 = e2 % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (169), (2816) imply: % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2817) ~ (all_52_8 = e2) % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2806) gives: % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2818) all_58_3 = e3 % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (554), (2818) imply: % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2819) all_8_2 = e3 % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2760), (2819) imply: % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2820) $false % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2820) is inconsistent. % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2821) all_58_5 = e3 | all_58_10 = e3 % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2821) gives: % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2822) all_58_5 = e3 % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (389), (2822) imply: % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2823) all_52_9 = e3 % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (171), (2823) imply: % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2824) ~ (all_52_8 = e3) % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2813) gives: % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2825) all_54_5 = e2 % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (542), (2825) imply: % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2826) all_8_2 = e2 % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (571), (2826) imply: % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2827) ~ (all_52_4 = e2) % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (46), (2826) imply: % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2828) op(e2, e2) = e2 % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (345) gives: % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2829) all_58_0 = e2 % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2753), (2829) imply: % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2830) all_4_1 = e2 % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2660), (2758), (2828), (2830), (function-axioms) % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #555. % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2831) ~ (all_58_0 = e2) % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2753), (2831) imply: % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2832) ~ (all_4_1 = e2) % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (250) gives: % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2833) all_54_2 = e3 % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (459), (2824), (2833) are inconsistent by % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #728. % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2834) all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0 % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2834) gives: % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2835) all_54_2 = e2 % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (459), (2817), (2835) are inconsistent by % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #727. % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2836) all_54_2 = e1 | all_54_2 = e0 % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2836) gives: % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2837) all_54_2 = e1 % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (459), (2776), (2837) are inconsistent by % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #726. % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2838) all_54_2 = e0 % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (459), (2838) imply: % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2839) all_52_8 = e0 % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2839) implies: % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2840) all_52_8 = e0 % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (182), (2840) imply: % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2841) ~ (all_52_4 = e0) % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2756), (2840) imply: % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2842) ~ (all_4_1 = e0) % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (252) gives: % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2843) all_54_0 = e3 % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2752), (2843) imply: % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2844) all_4_1 = e3 % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2844) implies: % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2845) all_4_1 = e3 % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2755), (2845) imply: % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2846) ~ (all_52_4 = e3) % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (251), (457), (2791), (2827), (2841), (2846) are % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #717. % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2847) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2750), (2752), (2757), (2832), (2847) are % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #549. % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2848) all_54_5 = e1 | all_54_5 = e0 % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (542), (2668), (2800), (2848) are inconsistent by % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #645. % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2849) all_58_10 = e3 % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (386), (2849) imply: % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2850) all_52_13 = e3 % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2746), (2850) imply: % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2851) $false % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2851) is inconsistent. % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2852) all_58_15 = e2 % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2739), (2852) imply: % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2853) e3 = e2 % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (9), (2853) imply: % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2854) $false % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2854) is inconsistent. % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2855) all_58_6 = e1 | all_58_12 = e1 % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (547), (548), (553), (2664), (2740), (2775), % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2777), (2787), (2788), (2855) are inconsistent by % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #471. % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2856) all_58_14 = e1 | all_58_15 = e1 % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (548), (2739), (2777), (2856) are % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #226. % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2857) all_54_10 = e0 % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (541), (2857) imply: % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2858) all_6_2 = e0 % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2762), (2858) imply: % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2859) $false % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2859) is inconsistent. % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | (2860) all_56_21 = e0 % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (43), (374), (2658), (2748), (2860), % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | #539. % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | End of split % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | (2861) all_56_11 = e3 % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | (2862) all_56_9 = e2 % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (425), (2862) imply: % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | (2863) all_52_1 = e2 % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (545), (2861) imply: % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | (2864) all_8_2 = e3 % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2754), (2863) imply: % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | (2865) ~ (all_4_1 = e2) % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2865) implies: % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | (2866) ~ (all_4_1 = e2) % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (48), (2864) imply: % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | (2867) op(e3, e3) = all_8_1 % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (252) gives: % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | (2868) all_54_0 = e3 % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2752), (2868) imply: % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | (2869) all_4_1 = e3 % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2747), (2869) imply: % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | (2870) op(e3, e3) = e3 % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2647), (2747), (2867), (2870), (function-axioms) % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #443. % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | (2871) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2750), (2752), (2757), (2866), (2871) are % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #549. % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | End of split % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | End of split % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | Case 2: % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | (2872) ~ (all_12_2 = e3) % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2738), (2872) imply: % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | (2873) $false % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2873) is inconsistent. % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | End of split % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | End of split % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | Case 2: % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | (2874) all_56_21 = e3 % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | (2875) all_56_17 = e1 % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (42), (43), (51), (158), (160), (161), (174), % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | (189), (191), (208), (241), (243), (252), (287), % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | (297), (321), (332), (374), (381), (386), (389), % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | (401), (402), (473), (476), (543), (544), (545), % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | (546), (547), (550), (551), (554), (557), (559), % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | (569), (573), (580), (591), (621), (768), (2649), % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | (2658), (2664), (2668), (2874), (2875), % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | #225. % 147.77/21.15 | | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | End of split % 147.77/21.15 | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | Case 2: % 147.77/21.15 | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | (2876) all_56_15 = e2 % 147.77/21.15 | | | | | | | | | | | | | | | | | | | (2877) all_56_11 = e0 % 147.77/21.15 | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (38), (48), (237), (443), (540), (545), % 147.77/21.15 | | | | | | | | | | | | | | | | | | | (590), (627), (769), (2641), (2647), (2876), % 147.77/21.15 | | | | | | | | | | | | | | | | | | | (2877), (function-axioms) are inconsistent by % 147.77/21.15 | | | | | | | | | | | | | | | | | | | sub-proof #224. % 147.77/21.15 | | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | End of split % 147.77/21.15 | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | Case 2: % 147.77/21.15 | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | (2878) all_56_21 = e2 % 147.77/21.15 | | | | | | | | | | | | | | | | | | (2879) all_56_19 = e1 % 147.77/21.15 | | | | | | | | | | | | | | | | | | % 147.77/21.15 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (435), (2879) imply: % 147.77/21.15 | | | | | | | | | | | | | | | | | | (2880) all_52_6 = e1 % 147.77/21.15 | | | | | | | | | | | | | | | | | | % 147.77/21.16 | | | | | | | | | | | | | | | | | | SIMP: (2880) implies: % 147.77/21.16 | | | | | | | | | | | | | | | | | | (2881) all_52_6 = e1 % 147.77/21.16 | | | | | | | | | | | | | | | | | | % 147.77/21.16 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (374), (2878) imply: % 147.77/21.16 | | | | | | | | | | | | | | | | | | (2882) all_6_2 = e2 % 147.77/21.16 | | | | | | | | | | | | | | | | | | % 147.77/21.16 | | | | | | | | | | | | | | | | | | SIMP: (2882) implies: % 147.77/21.16 | | | | | | | | | | | | | | | | | | (2883) all_6_2 = e2 % 147.77/21.16 | | | | | | | | | | | | | | | | | | % 147.77/21.16 | | | | | | | | | | | | | | | | | | REDUCE: (174), (2881) imply: % 147.77/21.16 | | | | | | | | | | | | | | | | | | (2884) ~ (all_52_14 = e1) % 147.77/21.16 | | | | | | | | | | | | | | | | | | % 147.77/21.16 | | | | | | | | | | | | | | | | | | SIMP: (2884) implies: % 147.77/21.16 | | | | | | | | | | | | | | | | | | (2885) ~ (all_52_14 = e1) % 147.77/21.16 | | | | | | | | | | | | | | | | | | % 147.77/21.16 | | | | | | | | | | | | | | | | | | REDUCE: (573), (2881) imply: % 147.77/21.16 | | | | | | | | | | | | | | | | | | (2886) ~ (all_8_2 = e1) % 147.77/21.16 | | | | | | | | | | | | | | | | | | % 147.77/21.16 | | | | | | | | | | | | | | | | | | SIMP: (2886) implies: % 147.77/21.16 | | | | | | | | | | | | | | | | | | (2887) ~ (all_8_2 = e1) % 147.77/21.16 | | | | | | | | | | | | | | | | | | % 147.77/21.16 | | | | | | | | | | | | | | | | | | REDUCE: (580), (2881), (2883) imply: % 147.77/21.16 | | | | | | | | | | | | | | | | | | (2888) ~ (e2 = e1) % 147.77/21.16 | | | | | | | | | | | | | | | | | | % 147.77/21.16 | | | | | | | | | | | | | | | | | | REDUCE: (43), (2883) imply: % 147.77/21.16 | | | | | | | | | | | | | | | | | | (2889) op(e2, e2) = all_6_1 % 147.77/21.16 | | | | | | | | | | | | | | | | | | % 147.77/21.16 | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (9), (36), (42), (46), (48), (208), % 147.77/21.16 | | | | | | | | | | | | | | | | | | (247), (294), (297), (321), (323), (341), (386), % 147.77/21.16 | | | | | | | | | | | | | | | | | | (402), (407), (419), (443), (542), (545), (546), % 147.77/21.16 | | | | | | | | | | | | | | | | | | (547), (550), (551), (555), (571), (620), (768), % 147.77/21.16 | | | | | | | | | | | | | | | | | | (2647), (2658), (2662), (2664), (2885), (2887), % 147.77/21.16 | | | | | | | | | | | | | | | | | | (2889), (function-axioms) are inconsistent by % 147.77/21.16 | | | | | | | | | | | | | | | | | | sub-proof #283. % 147.77/21.16 | | | | | | | | | | | | | | | | | | % 147.77/21.16 | | | | | | | | | | | | | | | | | End of split % 147.77/21.16 | | | | | | | | | | | | | | | | | % 147.77/21.16 | | | | | | | | | | | | | | | | Case 2: % 147.77/21.16 | | | | | | | | | | | | | | | | | % 147.77/21.16 | | | | | | | | | | | | | | | | | (2890) all_56_31 = e1 % 147.77/21.16 | | | | | | | | | | | | | | | | | (2891) all_56_29 = e0 % 147.77/21.16 | | | | | | | | | | | | | | | | | % 147.77/21.16 | | | | | | | | | | | | | | | | | COMBINE_EQS: (357), (2891) imply: % 147.77/21.16 | | | | | | | | | | | | | | | | | (2892) all_52_11 = e0 % 147.77/21.16 | | | | | | | | | | | | | | | | | % 147.77/21.16 | | | | | | | | | | | | | | | | | SIMP: (2892) implies: % 147.77/21.16 | | | | | | | | | | | | | | | | | (2893) all_52_11 = e0 % 147.77/21.16 | | | | | | | | | | | | | | | | | % 147.77/21.16 | | | | | | | | | | | | | | | | | COMBINE_EQS: (544), (2890) imply: % 147.77/21.16 | | | | | | | | | | | | | | | | | (2894) all_4_2 = e1 % 147.77/21.16 | | | | | | | | | | | | | | | | | % 147.77/21.16 | | | | | | | | | | | | | | | | | COMBINE_EQS: (531), (2894) imply: % 147.77/21.16 | | | | | | | | | | | | | | | | | (2895) all_34_2 = e1 % 147.77/21.16 | | | | | | | | | | | | | | | | | % 147.77/21.16 | | | | | | | | | | | | | | | | | COMBINE_EQS: (548), (2893) imply: % 147.77/21.16 | | | | | | | | | | | | | | | | | (2896) all_58_14 = e0 % 147.77/21.16 | | | | | | | | | | | | | | | | | % 147.77/21.16 | | | | | | | | | | | | | | | | | REDUCE: (581), (2894) imply: % 147.77/21.16 | | | | | | | | | | | | | | | | | (2897) ~ (all_52_7 = e1) % 147.77/21.16 | | | | | | | | | | | | | | | | | % 147.77/21.16 | | | | | | | | | | | | | | | | | REDUCE: (166), (2893) imply: % 147.77/21.16 | | | | | | | | | | | | | | | | | (2898) ~ (all_52_9 = e0) % 147.77/21.16 | | | | | | | | | | | | | | | | | % 147.77/21.16 | | | | | | | | | | | | | | | | | REDUCE: (585), (2893) imply: % 147.77/21.16 | | | | | | | | | | | | | | | | | (2899) ~ (all_6_2 = e0) % 147.77/21.16 | | | | | | | | | | | | | | | | | % 147.77/21.16 | | | | | | | | | | | | | | | | | SIMP: (2899) implies: % 147.77/21.16 | | | | | | | | | | | | | | | | | (2900) ~ (all_6_2 = e0) % 147.77/21.16 | | | | | | | | | | | | | | | | | % 147.77/21.16 | | | | | | | | | | | | | | | | | REDUCE: (589), (2894) imply: % 147.77/21.16 | | | | | | | | | | | | | | | | | (2901) ~ (all_52_12 = e1) % 147.77/21.16 | | | | | | | | | | | | | | | | | % 147.77/21.16 | | | | | | | | | | | | | | | | | REDUCE: (590), (2894) imply: % 147.77/21.16 | | | | | | | | | | | | | | | | | (2902) ~ (all_52_13 = e1) % 147.77/21.16 | | | | | | | | | | | | | | | | | % 147.77/21.16 | | | | | | | | | | | | | | | | | REDUCE: (38), (2894) imply: % 147.77/21.16 | | | | | | | | | | | | | | | | | (2903) op(e1, e1) = all_4_1 % 147.77/21.16 | | | | | | | | | | | | | | | | | % 147.77/21.16 | | | | | | | | | | | | | | | | | REDUCE: (623), (2893) imply: % 147.77/21.16 | | | | | | | | | | | | | | | | | (2904) op(e1, e0) = all_56_28 % 147.77/21.16 | | | | | | | | | | | | | | | | | % 147.77/21.16 | | | | | | | | | | | | | | | | | REDUCE: (36), (2894) imply: % 147.77/21.16 | | | | | | | | | | | | | | | | | (2905) op(e0, e0) = e1 % 147.77/21.16 | | | | | | | | | | | | | | | | | % 147.77/21.16 | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (36), (41), (42), (43), (46), (48), % 147.77/21.16 | | | | | | | | | | | | | | | | | (53), (161), (165), (168), (174), (181), (194), % 147.77/21.16 | | | | | | | | | | | | | | | | | (208), (242), (245), (246), (247), (249), (252), % 147.77/21.16 | | | | | | | | | | | | | | | | | (289), (292), (294), (295), (296), (297), (298), % 147.77/21.16 | | | | | | | | | | | | | | | | | (299), (321), (323), (330), (331), (332), (333), % 147.77/21.16 | | | | | | | | | | | | | | | | | (337), (341), (343), (360), (374), (380), (386), % 147.77/21.16 | | | | | | | | | | | | | | | | | (389), (401), (402), (407), (408), (419), (425), % 147.77/21.16 | | | | | | | | | | | | | | | | | (431), (435), (443), (461), (467), (469), (541), % 147.77/21.16 | | | | | | | | | | | | | | | | | (542), (543), (545), (546), (547), (549), (550), % 147.77/21.16 | | | | | | | | | | | | | | | | | (551), (552), (554), (555), (557), (563), (567), % 147.77/21.16 | | | | | | | | | | | | | | | | | (571), (573), (575), (577), (579), (580), (582), % 147.77/21.16 | | | | | | | | | | | | | | | | | (583), (620), (622), (625), (683), (768), (769), % 147.77/21.16 | | | | | | | | | | | | | | | | | (2647), (2653), (2656), (2658), (2662), (2895), % 147.77/21.16 | | | | | | | | | | | | | | | | | (2896), (2897), (2898), (2900), (2901), (2902), % 147.77/21.16 | | | | | | | | | | | | | | | | | (2903), (2904), (2905), (function-axioms) are % 147.77/21.16 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #221. % 147.77/21.16 | | | | | | | | | | | | | | | | | % 147.77/21.16 | | | | | | | | | | | | | | | | End of split % 147.77/21.16 | | | | | | | | | | | | | | | | % 147.77/21.16 | | | | | | | | | | | | | | | Case 2: % 147.77/21.16 | | | | | | | | | | | | | | | | % 147.77/21.16 | | | | | | | | | | | | | | | | (2906) all_40_0 = e3 % 147.77/21.16 | | | | | | | | | | | | | | | | (2907) ~ (all_40_1 = e0) | ~ (all_40_2 = e2) % 147.77/21.16 | | | | | | | | | | | | | | | | % 147.77/21.16 | | | | | | | | | | | | | | | | COMBINE_EQS: (713), (2906) imply: % 147.77/21.16 | | | | | | | | | | | | | | | | (2908) all_6_0 = e3 % 147.77/21.16 | | | | | | | | | | | | | | | | % 147.77/21.16 | | | | | | | | | | | | | | | | SIMP: (2908) implies: % 147.77/21.16 | | | | | | | | | | | | | | | | (2909) all_6_0 = e3 % 147.77/21.16 | | | | | | | | | | | | | | | | % 147.77/21.16 | | | | | | | | | | | | | | | | REDUCE: (42), (2909) imply: % 147.77/21.16 | | | | | | | | | | | | | | | | (2910) op(e1, all_6_1) = e3 % 147.77/21.16 | | | | | | | | | | | | | | | | % 147.77/21.16 | | | | | | | | | | | | | | | | REF_CLOSE: (8), (36), (38), (41), (42), (43), (46), (48), % 147.77/21.16 | | | | | | | | | | | | | | | | (51), (53), (158), (160), (161), (173), (174), % 147.77/21.16 | | | | | | | | | | | | | | | | (176), (181), (183), (184), (187), (188), (189), % 147.77/21.16 | | | | | | | | | | | | | | | | (191), (196), (208), (237), (238), (239), (241), % 147.77/21.16 | | | | | | | | | | | | | | | | (242), (243), (247), (249), (251), (252), (287), % 147.77/21.16 | | | | | | | | | | | | | | | | (288), (290), (291), (292), (293), (294), (297), % 147.77/21.16 | | | | | | | | | | | | | | | | (299), (321), (324), (326), (328), (332), (340), % 147.77/21.16 | | | | | | | | | | | | | | | | (344), (357), (365), (366), (374), (380), (381), % 147.77/21.16 | | | | | | | | | | | | | | | | (386), (389), (401), (402), (407), (408), (419), % 147.77/21.16 | | | | | | | | | | | | | | | | (435), (443), (447), (457), (461), (473), (476), % 147.77/21.16 | | | | | | | | | | | | | | | | (480), (482), (507), (531), (540), (541), (542), % 147.77/21.16 | | | | | | | | | | | | | | | | (543), (544), (545), (546), (547), (548), (550), % 147.77/21.16 | | | | | | | | | | | | | | | | (551), (552), (553), (554), (557), (559), (561), % 147.77/21.16 | | | | | | | | | | | | | | | | (563), (565), (567), (568), (569), (570), (571), % 147.77/21.16 | | | | | | | | | | | | | | | | (573), (577), (580), (581), (583), (585), (587), % 147.77/21.16 | | | | | | | | | | | | | | | | (588), (589), (590), (591), (621), (622), (625), % 147.77/21.16 | | | | | | | | | | | | | | | | (683), (685), (768), (2647), (2649), (2653), % 147.77/21.16 | | | | | | | | | | | | | | | | (2656), (2658), (2907), (2910), (function-axioms) % 147.77/21.16 | | | | | | | | | | | | | | | | are inconsistent by sub-proof #217. % 147.77/21.16 | | | | | | | | | | | | | | | | % 147.77/21.16 | | | | | | | | | | | | | | | End of split % 147.77/21.16 | | | | | | | | | | | | | | | % 147.77/21.16 | | | | | | | | | | | | | | Case 2: % 147.77/21.16 | | | | | | | | | | | | | | | % 147.77/21.16 | | | | | | | | | | | | | | | (2911) all_38_1 = e2 % 147.77/21.16 | | | | | | | | | | | | | | | (2912) ~ (all_38_0 = e0) | ~ (all_38_2 = e1) % 147.77/21.16 | | | | | | | | | | | | | | | % 147.77/21.16 | | | | | | | | | | | | | | | COMBINE_EQS: (684), (2911) imply: % 147.77/21.16 | | | | | | | | | | | | | | | (2913) all_10_1 = e2 % 147.77/21.16 | | | | | | | | | | | | | | | % 147.77/21.16 | | | | | | | | | | | | | | | REDUCE: (53), (2913) imply: % 147.77/21.16 | | | | | | | | | | | | | | | (2914) op(all_10_2, all_10_2) = e2 % 147.77/21.16 | | | | | | | | | | | | | | | % 147.77/21.16 | | | | | | | | | | | | | | | REDUCE: (52), (2913) imply: % 147.77/21.16 | | | | | | | | | | | | | | | (2915) op(e3, e2) = all_10_0 % 147.77/21.16 | | | | | | | | | | | | | | | % 147.77/21.16 | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_4, % 147.77/21.16 | | | | | | | | | | | | | | | all_10_0, e2, e3, simplifying with (218), (2915) % 147.77/21.16 | | | | | | | | | | | | | | | gives: % 147.77/21.16 | | | | | | | | | | | | | | | (2916) all_52_4 = all_10_0 % 147.77/21.16 | | | | | | | | | | | | | | | % 147.77/21.16 | | | | | | | | | | | | | | | COMBINE_EQS: (457), (2916) imply: % 147.77/21.16 | | | | | | | | | | | | | | | (2917) all_54_1 = all_10_0 % 147.77/21.16 | | | | | | | | | | | | | | | % 147.77/21.16 | | | | | | | | | | | | | | | COMBINE_EQS: (408), (2916) imply: % 147.77/21.16 | | | | | | | | | | | | | | | (2918) all_56_3 = all_10_0 % 147.77/21.16 | | | | | | | | | | | | | | | % 147.77/21.16 | | | | | | | | | | | | | | | COMBINE_EQS: (555), (2916) imply: % 147.77/21.16 | | | | | | | | | | | | | | | (2919) all_58_1 = all_10_0 % 147.77/21.16 | | | | | | | | | | | | | | | % 147.77/21.16 | | | | | | | | | | | | | | | REDUCE: (183), (2916) imply: % 147.77/21.16 | | | | | | | | | | | | | | | (2920) ~ (all_52_7 = all_10_0) % 147.77/21.16 | | | | | | | | | | | | | | | % 147.77/21.16 | | | | | | | | | | | | | | | SIMP: (2920) implies: % 147.77/21.16 | | | | | | | | | | | | | | | (2921) ~ (all_52_7 = all_10_0) % 147.77/21.16 | | | | | | | | | | | | | | | % 147.77/21.16 | | | | | | | | | | | | | | | REDUCE: (182), (2916) imply: % 147.77/21.16 | | | | | | | | | | | | | | | (2922) ~ (all_52_8 = all_10_0) % 147.77/21.16 | | | | | | | | | | | | | | | % 147.77/21.16 | | | | | | | | | | | | | | | SIMP: (2922) implies: % 147.77/21.16 | | | | | | | | | | | | | | | (2923) ~ (all_52_8 = all_10_0) % 147.77/21.16 | | | | | | | | | | | | | | | % 147.77/21.16 | | | | | | | | | | | | | | | REDUCE: (181), (2916) imply: % 147.77/21.16 | | | | | | | | | | | | | | | (2924) ~ (all_52_12 = all_10_0) % 147.77/21.16 | | | | | | | | | | | | | | | % 147.77/21.16 | | | | | | | | | | | | | | | SIMP: (2924) implies: % 147.77/21.16 | | | | | | | | | | | | | | | (2925) ~ (all_52_12 = all_10_0) % 147.77/21.16 | | | | | | | | | | | | | | | % 147.77/21.16 | | | | | | | | | | | | | | | REDUCE: (563), (2916) imply: % 147.77/21.16 | | | | | | | | | | | | | | | (2926) ~ (all_10_0 = all_10_2) % 147.77/21.16 | | | | | | | | | | | | | | | % 147.77/21.16 | | | | | | | | | | | | | | | REDUCE: (571), (2916) imply: % 147.77/21.16 | | | | | | | | | | | | | | | (2927) ~ (all_10_0 = all_8_2) % 147.77/21.16 | | | | | | | | | | | | | | | % 147.77/21.16 | | | | | | | | | | | | | | | REDUCE: (616), (2916) imply: % 147.77/21.16 | | | | | | | | | | | | | | | (2928) op(e2, all_10_0) = all_56_2 % 147.77/21.16 | | | | | | | | | | | | | | | % 147.77/21.16 | | | | | | | | | | | | | | | BETA: splitting (129) gives: % 147.77/21.16 | | | | | | | | | | | | | | | % 147.77/21.16 | | | | | | | | | | | | | | | Case 1: % 147.77/21.16 | | | | | | | | | | | | | | | | % 147.77/21.16 | | | | | | | | | | | | | | | | (2929) ~ (all_40_0 = e3) % 147.77/21.16 | | | | | | | | | | | | | | | | % 147.77/21.16 | | | | | | | | | | | | | | | | REDUCE: (713), (2929) imply: % 147.77/21.16 | | | | | | | | | | | | | | | | (2930) ~ (all_6_0 = e3) % 147.77/21.16 | | | | | | | | | | | | | | | | % 147.77/21.16 | | | | | | | | | | | | | | | | BETA: splitting (288) gives: % 147.77/21.16 | | | | | | | | | | | | | | | | % 147.77/21.16 | | | | | | | | | | | | | | | | Case 1: % 147.77/21.16 | | | | | | | | | | | | | | | | | % 147.77/21.16 | | | | | | | | | | | | | | | | | (2931) ~ (all_56_31 = e1) % 147.77/21.16 | | | | | | | | | | | | | | | | | % 147.77/21.16 | | | | | | | | | | | | | | | | | REDUCE: (544), (2931) imply: % 147.77/21.16 | | | | | | | | | | | | | | | | | (2932) ~ (all_4_2 = e1) % 147.77/21.16 | | | | | | | | | | | | | | | | | % 147.77/21.16 | | | | | | | | | | | | | | | | | BETA: splitting (292) gives: % 147.77/21.16 | | | | | | | | | | | | | | | | | % 147.77/21.16 | | | | | | | | | | | | | | | | | Case 1: % 147.77/21.16 | | | | | | | | | | | | | | | | | | % 147.77/21.16 | | | | | | | | | | | | | | | | | | (2933) ~ (all_56_21 = e2) % 147.77/21.16 | | | | | | | | | | | | | | | | | | % 147.77/21.16 | | | | | | | | | | | | | | | | | | REDUCE: (374), (2933) imply: % 147.77/21.16 | | | | | | | | | | | | | | | | | | (2934) ~ (all_6_2 = e2) % 147.77/21.16 | | | | | | | | | | | | | | | | | | % 147.77/21.16 | | | | | | | | | | | | | | | | | | BETA: splitting (294) gives: % 147.77/21.16 | | | | | | | | | | | | | | | | | | % 147.77/21.16 | | | | | | | | | | | | | | | | | | Case 1: % 147.77/21.16 | | | | | | | | | | | | | | | | | | | % 147.77/21.16 | | | | | | | | | | | | | | | | | | | (2935) ~ (all_56_11 = e0) % 147.77/21.16 | | | | | | | | | | | | | | | | | | | % 147.77/21.16 | | | | | | | | | | | | | | | | | | | REDUCE: (545), (2935) imply: % 147.77/21.16 | | | | | | | | | | | | | | | | | | | (2936) ~ (all_8_2 = e0) % 147.77/21.16 | | | | | | | | | | | | | | | | | | | % 147.77/21.16 | | | | | | | | | | | | | | | | | | | BETA: splitting (293) gives: % 147.77/21.16 | | | | | | | | | | | | | | | | | | | % 147.77/21.16 | | | | | | | | | | | | | | | | | | | Case 1: % 147.77/21.16 | | | | | | | | | | | | | | | | | | | | % 147.77/21.16 | | | | | | | | | | | | | | | | | | | | (2937) ~ (all_56_21 = e3) % 147.77/21.16 | | | | | | | | | | | | | | | | | | | | % 147.77/21.16 | | | | | | | | | | | | | | | | | | | | REDUCE: (374), (2937) imply: % 147.77/21.16 | | | | | | | | | | | | | | | | | | | | (2938) ~ (all_6_2 = e3) % 147.77/21.16 | | | | | | | | | | | | | | | | | | | | % 147.77/21.16 | | | | | | | | | | | | | | | | | | | | BETA: splitting (296) gives: % 147.77/21.16 | | | | | | | | | | | | | | | | | | | | % 147.77/21.16 | | | | | | | | | | | | | | | | | | | | Case 1: % 147.77/21.16 | | | | | | | | | | | | | | | | | | | | | % 147.77/21.16 | | | | | | | | | | | | | | | | | | | | | (2939) ~ (all_56_11 = e3) % 147.77/21.16 | | | | | | | | | | | | | | | | | | | | | % 147.77/21.16 | | | | | | | | | | | | | | | | | | | | | REDUCE: (545), (2939) imply: % 147.77/21.16 | | | | | | | | | | | | | | | | | | | | | (2940) ~ (all_8_2 = e3) % 147.77/21.16 | | | | | | | | | | | | | | | | | | | | | % 147.77/21.16 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (298) gives: % 147.77/21.16 | | | | | | | | | | | | | | | | | | | | | % 147.77/21.16 | | | | | | | | | | | | | | | | | | | | | Case 1: % 147.77/21.16 | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.16 | | | | | | | | | | | | | | | | | | | | | | (2941) ~ (all_56_1 = e1) % 147.77/21.16 | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.16 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (546), (2941) imply: % 147.77/21.16 | | | | | | | | | | | | | | | | | | | | | | (2942) ~ (all_10_2 = e1) % 147.77/21.16 | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.16 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (295) gives: % 147.77/21.16 | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.16 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 147.77/21.16 | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.16 | | | | | | | | | | | | | | | | | | | | | | | (2943) ~ (all_56_11 = e1) % 147.77/21.16 | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.16 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (545), (2943) imply: % 147.77/21.16 | | | | | | | | | | | | | | | | | | | | | | | (2944) ~ (all_8_2 = e1) % 147.77/21.16 | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.16 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (247) gives: % 147.77/21.16 | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.16 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 147.77/21.16 | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.16 | | | | | | | | | | | | | | | | | | | | | | | | (2945) all_54_5 = e3 % 147.77/21.16 | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.16 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (542), (2940), (2945) are inconsistent by % 147.77/21.16 | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #737. % 147.77/21.16 | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.16 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 147.77/21.16 | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.16 | | | | | | | | | | | | | | | | | | | | | | | | (2946) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 147.77/21.16 | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.16 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2946) gives: % 147.77/21.16 | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.16 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 147.77/21.16 | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.16 | | | | | | | | | | | | | | | | | | | | | | | | | (2947) all_54_5 = e2 % 147.77/21.16 | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.16 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (542), (2947) imply: % 147.77/21.16 | | | | | | | | | | | | | | | | | | | | | | | | | (2948) all_8_2 = e2 % 147.77/21.16 | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.16 | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2948) implies: % 147.77/21.16 | | | | | | | | | | | | | | | | | | | | | | | | | (2949) all_8_2 = e2 % 147.77/21.16 | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.16 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (568), (2949) imply: % 147.77/21.16 | | | | | | | | | | | | | | | | | | | | | | | | | (2950) ~ (all_52_1 = e2) % 147.77/21.16 | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.16 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (577), (2949) imply: % 147.77/21.16 | | | | | | | | | | | | | | | | | | | | | | | | | (2951) ~ (all_52_9 = e2) % 147.77/21.16 | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.16 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (579), (2949) imply: % 147.77/21.16 | | | | | | | | | | | | | | | | | | | | | | | | | (2952) ~ (all_52_13 = e2) % 147.77/21.16 | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.16 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (299) gives: % 147.77/21.16 | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.16 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 147.77/21.16 | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.16 | | | | | | | | | | | | | | | | | | | | | | | | | | (2953) ~ (all_56_1 = e2) % 147.77/21.16 | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.16 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (546), (2953) imply: % 147.77/21.16 | | | | | | | | | | | | | | | | | | | | | | | | | | (2954) ~ (all_10_2 = e2) % 147.77/21.16 | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.16 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (290) gives: % 147.77/21.16 | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.16 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 147.77/21.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2955) ~ (all_56_31 = e3) % 147.77/21.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (544), (2955) imply: % 147.77/21.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2956) ~ (all_4_2 = e3) % 147.77/21.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (37), (38), (41), (42), (43), (46), (47), % 147.77/21.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | (48), (51), (53), (158), (160), (161), (165), % 147.77/21.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | (168), (169), (173), (174), (176), (181), (182), % 147.77/21.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | (183), (184), (188), (189), (191), (192), (193), % 147.77/21.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | (196), (208), (212), (237), (238), (239), (240), % 147.77/21.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | (241), (242), (243), (244), (245), (247), (249), % 147.77/21.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | (250), (251), (252), (286), (287), (289), (291), % 147.77/21.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | (292), (293), (294), (295), (296), (297), (298), % 147.77/21.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | (299), (318), (319), (321), (322), (326), (328), % 147.77/21.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | (330), (332), (333), (336), (337), (340), (342), % 147.77/21.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | (343), (344), (360), (365), (366), (374), (380), % 147.77/21.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | (381), (386), (389), (401), (402), (407), (419), % 147.77/21.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | (425), (429), (431), (435), (443), (457), (459), % 147.77/21.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | (461), (469), (471), (473), (476), (478), (480), % 147.77/21.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | (482), (533), (540), (541), (542), (543), (544), % 147.77/21.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | (545), (546), (547), (548), (549), (550), (551), % 147.77/21.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | (552), (553), (554), (555), (557), (559), (561), % 147.77/21.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | (563), (565), (567), (568), (569), (570), (571), % 147.77/21.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | (573), (575), (577), (579), (580), (581), (582), % 147.77/21.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | (583), (585), (587), (588), (589), (590), (591), % 147.77/21.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | (612), (617), (618), (621), (622), (627), (723), % 147.77/21.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | (767), (768), (769), (770), (2645), (2647), % 147.77/21.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2649), (2651), (2653), (2658), (2912), (2914), % 147.77/21.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2917), (2918), (2919), (2921), (2923), (2925), % 147.77/21.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2926), (2927), (2928), (2930), (2932), (2934), % 147.77/21.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2956), (function-axioms) are inconsistent by % 147.77/21.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #476. % 147.77/21.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.16 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 147.77/21.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2957) all_56_31 = e3 % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2958) all_56_25 = e0 % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (447), (2958) imply: % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2959) all_52_3 = e0 % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2959) implies: % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2960) all_52_3 = e0 % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (544), (2957) imply: % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2961) all_4_2 = e3 % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (196), (2960) imply: % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2962) ~ (all_52_1 = e0) % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (192), (2960) imply: % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2963) ~ (all_52_2 = e0) % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (561), (2960) imply: % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2964) ~ (all_10_2 = e0) % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2964) implies: % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2965) ~ (all_10_2 = e0) % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (590), (2961) imply: % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2966) ~ (all_52_13 = e3) % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (591), (2961) imply: % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2967) ~ (all_52_14 = e3) % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (36), (2961) imply: % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2968) op(e0, e0) = e3 % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (43), (158), (165), (191), (193), (197), (244), % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | (245), (248), (252), (324), (327), (332), (380), % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | (386), (389), (401), (463), (469), (471), (543), % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | (550), (552), (553), (554), (557), (559), (625), % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2658), (2936), (2938), (2942), (2950), (2952), % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2954), (2962), (2963), (2965), (2966), (2967), % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2968), (function-axioms) are inconsistent by % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #215. % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | (2969) all_56_3 = e3 % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | (2970) all_56_1 = e2 % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (546), (2970) imply: % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | (2971) all_10_2 = e2 % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2918), (2969) imply: % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | (2972) all_10_0 = e3 % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2921), (2972) imply: % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | (2973) ~ (all_52_7 = e3) % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2923), (2972) imply: % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | (2974) ~ (all_52_8 = e3) % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (565), (2971) imply: % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | (2975) ~ (all_52_8 = e2) % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (567), (2971) imply: % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | (2976) ~ (all_52_12 = e2) % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (51), (2971) imply: % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | (2977) op(e3, e3) = e2 % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (9), (36), (38), (166), (173), % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | (176), (187), (189), (194), (206), (237), (239), % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | (242), (291), (322), (324), (327), (330), (331), % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | (344), (346), (365), (366), (374), (380), (386), % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | (389), (401), (407), (480), (529), (540), (541), % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | (547), (548), (550), (551), (552), (553), (569), % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | (570), (581), (587), (588), (591), (614), (626), % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | (627), (681), (2637), (2641), (2932), (2934), % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | (2938), (2950), (2951), (2952), (2973), (2974), % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | (2975), (2976), (2977), (function-axioms) are % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #212. % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | (2978) all_54_5 = e1 | all_54_5 = e0 % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (542), (2936), (2944), (2978) are inconsistent by % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #645. % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | End of split % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | (2979) all_56_13 = e2 % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | (2980) all_56_11 = e1 % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (545), (2980) imply: % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | (2981) all_8_2 = e1 % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (431), (2979) imply: % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | (2982) all_52_9 = e2 % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (583), (2982) imply: % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | (2983) ~ (all_6_2 = e2) % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (48), (2981) imply: % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | (2984) op(e1, e1) = all_8_1 % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_6_2, % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | all_8_1, e1, e1, simplifying with (41), (2984) % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | gives: % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | (2985) all_8_1 = all_6_2 % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (769), (2985) imply: % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | (2986) ~ (all_6_2 = e1) % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (242) gives: % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | (2987) all_54_10 = e3 % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (541), (2938), (2987) are inconsistent by % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #736. % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | (2988) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2988) gives: % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | (2989) all_54_10 = e2 % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (541), (2934), (2989) are inconsistent by % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #735. % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | (2990) ~ (all_54_10 = e2) % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | (2991) all_54_10 = e1 | all_54_10 = e0 % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2991) gives: % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | (2992) all_54_10 = e1 % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (541), (2986), (2992) are inconsistent by % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #606. % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | (2993) all_54_10 = e0 % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (541), (2993) imply: % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | (2994) all_6_2 = e0 % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2994) implies: % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | (2995) all_6_2 = e0 % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (374), (2995) imply: % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | (2996) all_56_21 = e0 % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (552), (2995) imply: % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | (2997) all_58_8 = e0 % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (569), (2995) imply: % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | (2998) ~ (all_52_2 = e0) % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (580), (2995) imply: % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | (2999) ~ (all_52_6 = e0) % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (43), (2995) imply: % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | (3000) op(e0, e0) = all_6_1 % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (291) gives: % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3001) ~ (all_56_21 = e0) % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2996), (3001) imply: % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3002) $false % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3002) is inconsistent. % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3003) all_56_23 = e1 % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (366), (3003) imply: % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3004) all_52_14 = e1 % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3004) implies: % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3005) all_52_14 = e1 % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (550), (3005) imply: % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3006) all_58_11 = e1 % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (189), (3005) imply: % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3007) ~ (all_52_2 = e1) % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (160), (3005) imply: % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3008) ~ (all_52_12 = e1) % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (158), (3005) imply: % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3009) ~ (all_52_13 = e1) % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (591), (3005) imply: % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3010) ~ (all_4_2 = e1) % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_4_2, % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_6_1, e0, e0, simplifying with (36), (3000) % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3011) all_6_1 = all_4_2 % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2658), (3011) imply: % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3012) ~ (all_4_2 = e3) % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (768), (3011) imply: % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3013) ~ (all_4_2 = e2) % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (237) gives: % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3014) all_54_15 = e3 % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (540), (3014) imply: % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3015) all_4_2 = e3 % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3012), (3015) imply: % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3016) $false % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3016) is inconsistent. % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3017) ~ (all_54_15 = e3) % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3018) all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0 % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3018) gives: % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3019) all_54_15 = e2 % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (540), (3019) imply: % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3020) all_4_2 = e2 % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3013), (3020) imply: % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3021) $false % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3021) is inconsistent. % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3022) all_54_15 = e1 | all_54_15 = e0 % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3022) gives: % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3023) all_54_15 = e1 % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (540), (3023) imply: % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3024) all_4_2 = e1 % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2932), (3024) imply: % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3025) $false % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3025) is inconsistent. % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3026) all_54_15 = e0 % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (540), (3026) imply: % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3027) all_4_2 = e0 % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (570), (3027) imply: % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3028) ~ (all_52_3 = e0) % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (581), (3027) imply: % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3029) ~ (all_52_7 = e0) % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3012), (3027) imply: % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3030) ~ (e3 = e0) % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (332) gives: % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3031) all_58_2 = e0 % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (401), (3031) imply: % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3032) all_52_1 = e0 % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (197), (3032) imply: % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3033) ~ (all_52_2 = e0) % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (196), (3032) imply: % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3034) ~ (all_52_3 = e0) % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (193), (3032) imply: % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3035) ~ (all_52_13 = e0) % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3035) implies: % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3036) ~ (all_52_13 = e0) % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (568), (3032) imply: % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3037) ~ (all_8_2 = e0) % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (336) gives: % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3038) all_58_1 = e0 % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2919), (3038) imply: % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3039) all_10_0 = e0 % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (723), (3039) imply: % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3040) all_38_0 = e0 % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2918), (3039) imply: % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3041) all_56_3 = e0 % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2925), (3039) imply: % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3042) ~ (all_52_12 = e0) % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2926), (3039) imply: % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3043) ~ (all_10_2 = e0) % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3043) implies: % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3044) ~ (all_10_2 = e0) % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2645), (3039) imply: % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3045) ~ (e1 = e0) % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (299) gives: % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3046) ~ (all_56_1 = e2) % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (546), (3046) imply: % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3047) ~ (all_10_2 = e2) % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2912) gives: % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3048) ~ (all_38_2 = e1) % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (252) gives: % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3049) all_54_0 = e3 % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (543), (3049) imply: % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3050) all_10_2 = e3 % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3050) implies: % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3051) all_10_2 = e3 % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (559), (3051) imply: % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3052) ~ (all_52_2 = e3) % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (561), (3051) imply: % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3053) ~ (all_52_3 = e3) % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (567), (3051) imply: % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3054) ~ (all_52_12 = e3) % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (249) gives: % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3055) all_54_3 = e3 % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (461), (3054), (3055) are inconsistent by % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #659. % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3056) ~ (all_54_3 = e3) % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3057) all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0 % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (244) gives: % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3058) all_54_8 = e3 % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (471), (3052), (3058) are inconsistent by % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #345. % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3059) ~ (all_54_8 = e3) % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3060) all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0 % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (323) gives: % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3061) all_58_9 = e3 % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (551), (3061) imply: % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3062) all_52_12 = e3 % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3062) implies: % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3063) all_52_12 = e3 % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3054), (3063) imply: % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3064) $false % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3064) is inconsistent. % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3065) all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3 % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3065) gives: % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3066) all_58_10 = e3 % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (386), (3066) imply: % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3067) all_52_13 = e3 % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3067) implies: % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3068) all_52_13 = e3 % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (212), (3068) imply: % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3069) op(e2, e0) = e3 % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (327) gives: % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3070) all_58_6 = e3 % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (553), (3052), (3070) are inconsistent by % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #346. % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3071) all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3 % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3071) gives: % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3072) all_58_7 = e3 % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (380), (3072) imply: % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3073) all_52_6 = e3 % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (176), (3073) imply: % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3074) ~ (all_52_7 = e3) % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3074) implies: % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3075) ~ (all_52_7 = e3) % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (573), (3073) imply: % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3076) ~ (all_8_2 = e3) % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (322) gives: % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3077) all_58_9 = e2 % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (551), (3077) imply: % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3078) all_52_12 = e2 % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3078) implies: % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3079) all_52_12 = e2 % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (168), (3079) imply: % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3080) ~ (all_52_8 = e2) % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (330) gives: % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3081) all_58_4 = e2 % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (407), (3081) imply: % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3082) all_52_8 = e2 % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3082) implies: % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3083) all_52_8 = e2 % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3080), (3083) imply: % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3084) $false % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3084) is inconsistent. % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3085) all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2 % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3085) gives: % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3086) all_58_5 = e2 % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (389), (3086) imply: % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3087) all_52_9 = e2 % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (577), (2982) imply: % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3088) ~ (all_8_2 = e2) % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3088) implies: % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3089) ~ (all_8_2 = e2) % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (247) gives: % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3090) all_54_5 = e3 % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (542), (2940), (3090) are inconsistent by % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #737. % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3091) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (333) gives: % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3092) all_58_2 = e1 % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3031), (3092) imply: % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3093) e1 = e0 % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4), (3093) imply: % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3094) $false % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3094) is inconsistent. % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3095) all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1 % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3095) gives: % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3096) all_58_3 = e1 % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (41), (47), (242), (328), (336), (380), (407), % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (541), (548), (549), (552), (554), (580), (585), % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (769), (770), (2647), (2651), (2919), (2923), % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2928), (2934), (2936), (2984), (3029), (3069), % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3086), (function-axioms) are inconsistent by % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #485. % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3097) ~ (all_58_3 = e1) % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (554), (3097) imply: % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3098) ~ (all_8_2 = e1) % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (542), (2936), (3089), (3091), (3098) are % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #279. % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 147.77/21.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3099) ~ (all_58_5 = e2) % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (389), (3099) imply: % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3100) ~ (all_52_9 = e2) % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (295) gives: % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3101) ~ (all_56_11 = e1) % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (545), (3101) imply: % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3102) ~ (all_8_2 = e1) % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (247) gives: % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3103) all_54_5 = e3 % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (542), (2940), (3103) are inconsistent by % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #737. % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3104) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (326) gives: % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3105) all_58_6 = e2 % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (553), (3105) imply: % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3106) all_52_2 = e2 % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3106) implies: % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3107) all_52_2 = e2 % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (192), (3107) imply: % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3108) ~ (all_52_3 = e2) % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3108) implies: % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3109) ~ (all_52_3 = e2) % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (319) gives: % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3110) all_58_12 = e2 % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (365), (3110) imply: % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3111) all_52_3 = e2 % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3111) implies: % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3112) all_52_3 = e2 % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3109), (3112) imply: % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3113) $false % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3113) is inconsistent. % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3114) all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2 % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3114) gives: % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3115) all_58_13 = e2 % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (549), (3115) imply: % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3116) all_52_7 = e2 % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3116) implies: % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3117) all_52_7 = e2 % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (575), (3117) imply: % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3118) ~ (all_8_2 = e2) % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3118) implies: % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3119) ~ (all_8_2 = e2) % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (542), (2936), (3102), (3104), (3119) are % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #279. % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3120) ~ (all_58_13 = e2) % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (549), (3120) imply: % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3121) ~ (all_52_7 = e2) % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (188), (192), (239), (240), (244), (326), (471), % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (478), (480), (553), (2998), (3007), (3028), % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3029), (3052), (3053), (3075), (3121) are % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #661. % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3122) ~ (all_58_6 = e2) % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (553), (3122) imply: % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3123) ~ (all_52_2 = e2) % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (471), (2998), (3007), (3060), (3123) are % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #270. % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (431), (2979), (3100) are inconsistent by % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #353. % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3124) ~ (all_58_9 = e2) % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (551), (3124) imply: % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3125) ~ (all_52_12 = e2) % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (461), (3008), (3042), (3057), (3125) are % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #326. % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3126) all_58_8 = e3 | all_58_11 = e3 % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (2997), (3006), (3126) are inconsistent % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #343. % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3127) ~ (all_58_10 = e3) % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (386), (3127) imply: % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3128) ~ (all_52_13 = e3) % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (245) gives: % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3129) all_54_7 = e3 % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (469), (3128), (3129) are inconsistent by % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #601. % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3130) all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0 % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3130) gives: % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3131) all_54_7 = e2 % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (469), (3131) imply: % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3132) all_52_13 = e2 % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3132) implies: % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3133) all_52_13 = e2 % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (161), (3133) imply: % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3134) ~ (all_52_12 = e2) % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (461), (3008), (3042), (3057), (3134) are % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #326. % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3135) all_54_7 = e1 | all_54_7 = e0 % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3135) gives: % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3136) all_54_7 = e1 % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (469), (3009), (3136) are inconsistent by % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #651. % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3137) all_54_7 = e0 % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (469), (3036), (3137) are inconsistent by % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #650. % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3138) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (543), (2942), (3044), (3047), (3138) are % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #731. % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3139) all_38_2 = e1 % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2912), (3040), (3139) are inconsistent by % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #487. % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3140) all_56_3 = e3 % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3041), (3140) imply: % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3141) e3 = e0 % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7), (3141) imply: % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3142) $false % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3142) is inconsistent. % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3143) all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0 % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (380), (549), (554), (2936), (2999), (3029), % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3143) are inconsistent by sub-proof #603. % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3144) ~ (all_58_2 = e0) % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (336), (340), (365), (380), (401), (419), (549), % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (553), (554), (555), (563), (2936), (2998), % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2999), (3028), (3029), (3144) are inconsistent by % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #602. % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | End of split % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | End of split % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | Case 2: % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | (3145) all_56_5 = e3 % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | (3146) all_56_1 = e1 % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (251), (429), (533), (546), (723), (770), (2912), % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | (2917), (2923), (2926), (3145), (3146) are % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #211. % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | End of split % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | Case 2: % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | (3147) all_56_11 = e3 % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | (3148) all_56_9 = e2 % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (425), (3148) imply: % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | (3149) all_52_1 = e2 % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (545), (3147) imply: % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | (3150) all_8_2 = e3 % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | REDUCE: (557), (3149) imply: % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | (3151) ~ (all_10_2 = e2) % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | SIMP: (3151) implies: % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | (3152) ~ (all_10_2 = e2) % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | REDUCE: (577), (3150) imply: % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | (3153) ~ (all_52_9 = e3) % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | REDUCE: (2927), (3150) imply: % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | (3154) ~ (all_10_0 = e3) % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | REDUCE: (48), (3150) imply: % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | (3155) op(e3, e3) = all_8_1 % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (251) gives: % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | Case 1: % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | (3156) all_54_1 = e3 % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2917), (3154), (3156) are inconsistent by % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | sub-proof #493. % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | Case 2: % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | (3157) all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0 % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3157) gives: % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | (3158) all_54_1 = e2 % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (770), (2917), (3158) are inconsistent by % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | sub-proof #492. % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | (3159) all_54_1 = e1 | all_54_1 = e0 % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3159) gives: % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | (3160) all_54_1 = e1 % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2645), (2917), (3160) are inconsistent by % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #491. % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | (3161) all_54_1 = e0 % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2917), (3161) imply: % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | (3162) all_10_0 = e0 % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3162) implies: % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | (3163) all_10_0 = e0 % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2921), (3163) imply: % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | (3164) ~ (all_52_7 = e0) % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2926), (3163) imply: % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | (3165) ~ (all_10_2 = e0) % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3165) implies: % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | (3166) ~ (all_10_2 = e0) % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (289) gives: % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | (3167) ~ (all_56_31 = e2) % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (544), (3167) imply: % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | (3168) ~ (all_4_2 = e2) % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (252) gives: % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | (3169) all_54_0 = e3 % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (543), (3169) imply: % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | (3170) all_10_2 = e3 % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3170) implies: % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | (3171) all_10_2 = e3 % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (565), (3171) imply: % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | (3172) ~ (all_52_8 = e3) % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (331) gives: % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3173) all_58_4 = e3 % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (407), (3173) imply: % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3174) all_52_8 = e3 % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3172), (3174) imply: % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3175) $false % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3175) is inconsistent. % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3176) all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3 % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (38), (237), (389), (540), (548), (552), % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | (588), (627), (2641), (2932), (2938), (3153), % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3168), (3176), (function-axioms) are inconsistent % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #210. % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | (3177) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3177) gives: % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3178) all_54_0 = e2 % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (543), (3152), (3178) are inconsistent by % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #734. % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3179) all_54_0 = e1 | all_54_0 = e0 % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (51), (543), (769), (3155), (3166), (3179), % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | #552. % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | (3180) all_56_27 = e0 % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (360), (3164), (3180) are inconsistent by % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #223. % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | End of split % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | End of split % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | End of split % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | End of split % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | | Case 2: % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | (3181) all_56_21 = e3 % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | (3182) all_56_17 = e1 % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (381), (3182) imply: % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | (3183) all_52_2 = e1 % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (374), (3181) imply: % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | (3184) all_6_2 = e3 % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (43), (51), (251), (252), (297), (402), (543), % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | (546), (559), (768), (770), (2645), (2658), % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | (2917), (2925), (2926), (3183), (3184), % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | #488. % 147.77/21.18 | | | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | | End of split % 147.77/21.18 | | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | Case 2: % 147.77/21.18 | | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | | (3185) all_56_15 = e2 % 147.77/21.18 | | | | | | | | | | | | | | | | | | | (3186) all_56_11 = e0 % 147.77/21.18 | | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (46), (158), (251), (252), (297), (298), (326), % 147.77/21.18 | | | | | | | | | | | | | | | | | | | (380), (402), (429), (443), (543), (545), (546), % 147.77/21.18 | | | | | | | | | | | | | | | | | | | (550), (552), (553), (559), (618), (770), (2645), % 147.77/21.18 | | | | | | | | | | | | | | | | | | | (2914), (2917), (2923), (2925), (2926), (2927), % 147.77/21.18 | | | | | | | | | | | | | | | | | | | (2934), (3185), (3186), (function-axioms) are % 147.77/21.18 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #480. % 147.77/21.18 | | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | End of split % 147.77/21.18 | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | Case 2: % 147.77/21.18 | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | (3187) all_56_21 = e2 % 147.77/21.18 | | | | | | | | | | | | | | | | | | (3188) all_56_19 = e1 % 147.77/21.18 | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (435), (3188) imply: % 147.77/21.18 | | | | | | | | | | | | | | | | | | (3189) all_52_6 = e1 % 147.77/21.18 | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (374), (3187) imply: % 147.77/21.18 | | | | | | | | | | | | | | | | | | (3190) all_6_2 = e2 % 147.77/21.18 | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (36), (42), (43), (46), (48), (174), % 147.77/21.18 | | | | | | | | | | | | | | | | | | (208), (247), (289), (294), (297), (321), (323), % 147.77/21.18 | | | | | | | | | | | | | | | | | | (341), (360), (386), (402), (407), (419), (443), % 147.77/21.18 | | | | | | | | | | | | | | | | | | (542), (545), (546), (547), (550), (551), (555), % 147.77/21.18 | | | | | | | | | | | | | | | | | | (571), (573), (575), (580), (620), (768), (769), % 147.77/21.18 | | | | | | | | | | | | | | | | | | (2647), (2658), (2930), (3189), (3190), % 147.77/21.18 | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 147.77/21.18 | | | | | | | | | | | | | | | | | | #209. % 147.77/21.18 | | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | End of split % 147.77/21.18 | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | Case 2: % 147.77/21.18 | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | (3191) all_56_31 = e1 % 147.77/21.18 | | | | | | | | | | | | | | | | | (3192) all_56_29 = e0 % 147.77/21.18 | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | COMBINE_EQS: (357), (3192) imply: % 147.77/21.18 | | | | | | | | | | | | | | | | | (3193) all_52_11 = e0 % 147.77/21.18 | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | SIMP: (3193) implies: % 147.77/21.18 | | | | | | | | | | | | | | | | | (3194) all_52_11 = e0 % 147.77/21.18 | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | COMBINE_EQS: (544), (3191) imply: % 147.77/21.18 | | | | | | | | | | | | | | | | | (3195) all_4_2 = e1 % 147.77/21.18 | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | COMBINE_EQS: (531), (3195) imply: % 147.77/21.18 | | | | | | | | | | | | | | | | | (3196) all_34_2 = e1 % 147.77/21.18 | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | COMBINE_EQS: (548), (3194) imply: % 147.77/21.18 | | | | | | | | | | | | | | | | | (3197) all_58_14 = e0 % 147.77/21.18 | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | REDUCE: (581), (3195) imply: % 147.77/21.18 | | | | | | | | | | | | | | | | | (3198) ~ (all_52_7 = e1) % 147.77/21.18 | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | REDUCE: (166), (3194) imply: % 147.77/21.18 | | | | | | | | | | | | | | | | | (3199) ~ (all_52_9 = e0) % 147.77/21.18 | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | REDUCE: (585), (3194) imply: % 147.77/21.18 | | | | | | | | | | | | | | | | | (3200) ~ (all_6_2 = e0) % 147.77/21.18 | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | SIMP: (3200) implies: % 147.77/21.18 | | | | | | | | | | | | | | | | | (3201) ~ (all_6_2 = e0) % 147.77/21.18 | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | REDUCE: (589), (3195) imply: % 147.77/21.18 | | | | | | | | | | | | | | | | | (3202) ~ (all_52_12 = e1) % 147.77/21.18 | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | REDUCE: (590), (3195) imply: % 147.77/21.18 | | | | | | | | | | | | | | | | | (3203) ~ (all_52_13 = e1) % 147.77/21.18 | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | REDUCE: (38), (3195) imply: % 147.77/21.18 | | | | | | | | | | | | | | | | | (3204) op(e1, e1) = all_4_1 % 147.77/21.18 | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | REDUCE: (623), (3194) imply: % 147.77/21.18 | | | | | | | | | | | | | | | | | (3205) op(e1, e0) = all_56_28 % 147.77/21.18 | | | | | | | | | | | | | | | | | % 147.77/21.18 | | | | | | | | | | | | | | | | | REDUCE: (36), (3195) imply: % 147.77/21.18 | | | | | | | | | | | | | | | | | (3206) op(e0, e0) = e1 % 147.77/21.18 | | | | | | | | | | | | | | | | | % 147.77/21.19 | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (36), (41), (42), (43), (46), (48), % 147.77/21.19 | | | | | | | | | | | | | | | | | (53), (161), (165), (168), (174), (181), (194), % 147.77/21.19 | | | | | | | | | | | | | | | | | (208), (242), (245), (246), (247), (249), (252), % 147.77/21.19 | | | | | | | | | | | | | | | | | (289), (292), (294), (295), (296), (297), (298), % 147.77/21.19 | | | | | | | | | | | | | | | | | (299), (321), (323), (330), (331), (332), (333), % 147.77/21.19 | | | | | | | | | | | | | | | | | (337), (341), (343), (360), (374), (380), (386), % 147.77/21.19 | | | | | | | | | | | | | | | | | (389), (401), (402), (407), (408), (419), (425), % 147.77/21.19 | | | | | | | | | | | | | | | | | (431), (435), (443), (461), (467), (469), (541), % 147.77/21.19 | | | | | | | | | | | | | | | | | (542), (543), (545), (546), (547), (549), (550), % 147.77/21.19 | | | | | | | | | | | | | | | | | (551), (552), (554), (555), (557), (563), (567), % 147.77/21.19 | | | | | | | | | | | | | | | | | (571), (573), (575), (577), (579), (580), (582), % 147.77/21.19 | | | | | | | | | | | | | | | | | (583), (620), (622), (625), (683), (768), (769), % 147.77/21.19 | | | | | | | | | | | | | | | | | (2647), (2653), (2656), (2658), (2930), (3196), % 147.77/21.19 | | | | | | | | | | | | | | | | | (3197), (3198), (3199), (3201), (3202), (3203), % 147.77/21.19 | | | | | | | | | | | | | | | | | (3204), (3205), (3206), (function-axioms) are % 147.77/21.19 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #221. % 147.77/21.19 | | | | | | | | | | | | | | | | | % 147.77/21.19 | | | | | | | | | | | | | | | | End of split % 147.77/21.19 | | | | | | | | | | | | | | | | % 147.77/21.19 | | | | | | | | | | | | | | | Case 2: % 147.77/21.19 | | | | | | | | | | | | | | | | % 147.77/21.19 | | | | | | | | | | | | | | | | (3207) all_40_0 = e3 % 147.77/21.19 | | | | | | | | | | | | | | | | (3208) ~ (all_40_1 = e0) | ~ (all_40_2 = e2) % 147.77/21.19 | | | | | | | | | | | | | | | | % 147.77/21.19 | | | | | | | | | | | | | | | | COMBINE_EQS: (713), (3207) imply: % 147.77/21.19 | | | | | | | | | | | | | | | | (3209) all_6_0 = e3 % 147.77/21.19 | | | | | | | | | | | | | | | | % 147.77/21.19 | | | | | | | | | | | | | | | | SIMP: (3209) implies: % 147.77/21.19 | | | | | | | | | | | | | | | | (3210) all_6_0 = e3 % 147.77/21.19 | | | | | | | | | | | | | | | | % 147.77/21.19 | | | | | | | | | | | | | | | | REDUCE: (42), (3210) imply: % 147.77/21.19 | | | | | | | | | | | | | | | | (3211) op(e1, all_6_1) = e3 % 147.77/21.19 | | | | | | | | | | | | | | | | % 147.77/21.19 | | | | | | | | | | | | | | | | REF_CLOSE: (8), (36), (38), (41), (42), (43), (46), (48), % 147.77/21.19 | | | | | | | | | | | | | | | | (51), (53), (158), (160), (161), (173), (174), % 147.77/21.19 | | | | | | | | | | | | | | | | (176), (181), (183), (184), (187), (188), (189), % 147.77/21.19 | | | | | | | | | | | | | | | | (191), (196), (208), (237), (238), (239), (241), % 147.77/21.19 | | | | | | | | | | | | | | | | (242), (243), (247), (249), (251), (252), (287), % 147.77/21.19 | | | | | | | | | | | | | | | | (288), (290), (291), (292), (293), (294), (297), % 147.77/21.19 | | | | | | | | | | | | | | | | (299), (321), (324), (326), (328), (332), (340), % 147.77/21.19 | | | | | | | | | | | | | | | | (344), (357), (365), (366), (374), (380), (381), % 147.77/21.19 | | | | | | | | | | | | | | | | (386), (389), (401), (402), (407), (408), (419), % 147.77/21.19 | | | | | | | | | | | | | | | | (435), (443), (447), (457), (461), (473), (476), % 147.77/21.19 | | | | | | | | | | | | | | | | (480), (482), (507), (531), (540), (541), (542), % 147.77/21.19 | | | | | | | | | | | | | | | | (543), (544), (545), (546), (547), (548), (550), % 147.77/21.19 | | | | | | | | | | | | | | | | (551), (552), (553), (554), (557), (559), (561), % 147.77/21.19 | | | | | | | | | | | | | | | | (563), (565), (567), (568), (569), (570), (571), % 147.77/21.19 | | | | | | | | | | | | | | | | (573), (577), (580), (581), (583), (585), (587), % 147.77/21.19 | | | | | | | | | | | | | | | | (588), (589), (590), (591), (621), (622), (625), % 147.77/21.19 | | | | | | | | | | | | | | | | (683), (685), (768), (2647), (2649), (2653), % 147.77/21.19 | | | | | | | | | | | | | | | | (2656), (2658), (3208), (3211), (function-axioms) % 147.77/21.19 | | | | | | | | | | | | | | | | are inconsistent by sub-proof #217. % 147.77/21.19 | | | | | | | | | | | | | | | | % 147.77/21.19 | | | | | | | | | | | | | | | End of split % 147.77/21.19 | | | | | | | | | | | | | | | % 147.77/21.19 | | | | | | | | | | | | | | End of split % 147.77/21.19 | | | | | | | | | | | | | | % 147.77/21.19 | | | | | | | | | | | | | Case 2: % 147.77/21.19 | | | | | | | | | | | | | | % 147.77/21.19 | | | | | | | | | | | | | | (3212) all_36_1 = e3 % 147.77/21.19 | | | | | | | | | | | | | | (3213) ~ (all_36_0 = e0) | ~ (all_36_2 = e2) % 147.77/21.19 | | | | | | | | | | | | | | % 147.77/21.19 | | | | | | | | | | | | | | COMBINE_EQS: (652), (3212) imply: % 147.77/21.19 | | | | | | | | | | | | | | (3214) all_6_1 = e3 % 147.77/21.19 | | | | | | | | | | | | | | % 147.77/21.19 | | | | | | | | | | | | | | SIMP: (3214) implies: % 147.77/21.19 | | | | | | | | | | | | | | (3215) all_6_1 = e3 % 147.77/21.19 | | | | | | | | | | | | | | % 147.77/21.19 | | | | | | | | | | | | | | REDUCE: (43), (3215) imply: % 147.77/21.19 | | | | | | | | | | | | | | (3216) op(all_6_2, all_6_2) = e3 % 147.77/21.19 | | | | | | | | | | | | | | % 147.77/21.19 | | | | | | | | | | | | | | REDUCE: (42), (3215) imply: % 147.77/21.19 | | | | | | | | | | | | | | (3217) op(e1, e3) = all_6_0 % 147.77/21.19 | | | | | | | | | | | | | | % 147.77/21.19 | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_2, % 147.77/21.19 | | | | | | | | | | | | | | all_6_0, e3, e1, simplifying with (211), (3217) % 147.77/21.19 | | | | | | | | | | | | | | gives: % 147.77/21.19 | | | | | | | | | | | | | | (3218) all_52_2 = all_6_0 % 147.77/21.19 | | | | | | | | | | | | | | % 147.77/21.19 | | | | | | | | | | | | | | COMBINE_EQS: (471), (3218) imply: % 147.77/21.19 | | | | | | | | | | | | | | (3219) all_54_8 = all_6_0 % 147.77/21.19 | | | | | | | | | | | | | | % 147.77/21.19 | | | | | | | | | | | | | | COMBINE_EQS: (381), (3218) imply: % 147.77/21.19 | | | | | | | | | | | | | | (3220) all_56_17 = all_6_0 % 147.77/21.19 | | | | | | | | | | | | | | % 147.77/21.19 | | | | | | | | | | | | | | COMBINE_EQS: (553), (3218) imply: % 147.77/21.19 | | | | | | | | | | | | | | (3221) all_58_6 = all_6_0 % 147.77/21.19 | | | | | | | | | | | | | | % 147.77/21.19 | | | | | | | | | | | | | | REDUCE: (197), (3218) imply: % 147.77/21.19 | | | | | | | | | | | | | | (3222) ~ (all_52_1 = all_6_0) % 147.77/21.19 | | | | | | | | | | | | | | % 147.77/21.19 | | | | | | | | | | | | | | REDUCE: (192), (3218) imply: % 147.77/21.19 | | | | | | | | | | | | | | (3223) ~ (all_52_3 = all_6_0) % 147.77/21.19 | | | | | | | | | | | | | | % 147.77/21.19 | | | | | | | | | | | | | | SIMP: (3223) implies: % 147.77/21.19 | | | | | | | | | | | | | | (3224) ~ (all_52_3 = all_6_0) % 147.77/21.19 | | | | | | | | | | | | | | % 147.77/21.19 | | | | | | | | | | | | | | REDUCE: (191), (3218) imply: % 147.77/21.19 | | | | | | | | | | | | | | (3225) ~ (all_52_6 = all_6_0) % 147.77/21.19 | | | | | | | | | | | | | | % 147.77/21.19 | | | | | | | | | | | | | | SIMP: (3225) implies: % 147.77/21.19 | | | | | | | | | | | | | | (3226) ~ (all_52_6 = all_6_0) % 147.77/21.19 | | | | | | | | | | | | | | % 147.77/21.19 | | | | | | | | | | | | | | REDUCE: (189), (3218) imply: % 147.77/21.19 | | | | | | | | | | | | | | (3227) ~ (all_52_14 = all_6_0) % 147.77/21.19 | | | | | | | | | | | | | | % 147.77/21.19 | | | | | | | | | | | | | | SIMP: (3227) implies: % 147.77/21.19 | | | | | | | | | | | | | | (3228) ~ (all_52_14 = all_6_0) % 147.77/21.19 | | | | | | | | | | | | | | % 147.77/21.19 | | | | | | | | | | | | | | REDUCE: (559), (3218) imply: % 147.77/21.19 | | | | | | | | | | | | | | (3229) ~ (all_10_2 = all_6_0) % 147.77/21.19 | | | | | | | | | | | | | | % 147.77/21.19 | | | | | | | | | | | | | | SIMP: (3229) implies: % 147.77/21.19 | | | | | | | | | | | | | | (3230) ~ (all_10_2 = all_6_0) % 147.77/21.19 | | | | | | | | | | | | | | % 147.77/21.19 | | | | | | | | | | | | | | REDUCE: (569), (3218) imply: % 147.77/21.19 | | | | | | | | | | | | | | (3231) ~ (all_6_0 = all_6_2) % 147.77/21.19 | | | | | | | | | | | | | | % 147.77/21.19 | | | | | | | | | | | | | | BETA: splitting (124) gives: % 147.77/21.19 | | | | | | | | | | | | | | % 147.77/21.19 | | | | | | | | | | | | | | Case 1: % 147.77/21.19 | | | | | | | | | | | | | | | % 147.77/21.19 | | | | | | | | | | | | | | | (3232) ~ (all_38_1 = e2) % 147.77/21.19 | | | | | | | | | | | | | | | % 147.77/21.19 | | | | | | | | | | | | | | | REDUCE: (684), (3232) imply: % 147.77/21.19 | | | | | | | | | | | | | | | (3233) ~ (all_10_1 = e2) % 147.77/21.19 | | | | | | | | | | | | | | | % 147.77/21.19 | | | | | | | | | | | | | | | BETA: splitting (288) gives: % 147.77/21.19 | | | | | | | | | | | | | | | % 147.77/21.19 | | | | | | | | | | | | | | | Case 1: % 147.77/21.19 | | | | | | | | | | | | | | | | % 147.77/21.19 | | | | | | | | | | | | | | | | (3234) ~ (all_56_31 = e1) % 147.77/21.19 | | | | | | | | | | | | | | | | % 147.77/21.19 | | | | | | | | | | | | | | | | REDUCE: (544), (3234) imply: % 147.77/21.19 | | | | | | | | | | | | | | | | (3235) ~ (all_4_2 = e1) % 147.77/21.19 | | | | | | | | | | | | | | | | % 147.77/21.19 | | | | | | | | | | | | | | | | BETA: splitting (290) gives: % 147.77/21.19 | | | | | | | | | | | | | | | | % 147.77/21.19 | | | | | | | | | | | | | | | | Case 1: % 147.77/21.19 | | | | | | | | | | | | | | | | | % 147.77/21.19 | | | | | | | | | | | | | | | | | (3236) ~ (all_56_31 = e3) % 147.77/21.19 | | | | | | | | | | | | | | | | | % 147.77/21.19 | | | | | | | | | | | | | | | | | REDUCE: (544), (3236) imply: % 147.77/21.19 | | | | | | | | | | | | | | | | | (3237) ~ (all_4_2 = e3) % 147.77/21.19 | | | | | | | | | | | | | | | | | % 147.77/21.19 | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (38), (41), (46), (48), (51), (174), (176), % 147.77/21.19 | | | | | | | | | | | | | | | | | (188), (207), (237), (240), (242), (243), (244), % 147.77/21.19 | | | | | | | | | | | | | | | | | (287), (289), (291), (292), (293), (324), (360), % 147.77/21.19 | | | | | | | | | | | | | | | | | (366), (374), (380), (435), (473), (478), (532), % 147.77/21.19 | | | | | | | | | | | | | | | | | (540), (541), (544), (545), (546), (550), (552), % 147.77/21.19 | | | | | | | | | | | | | | | | | (561), (570), (573), (580), (587), (591), (617), % 147.77/21.19 | | | | | | | | | | | | | | | | | (622), (627), (762), (2641), (2649), (3213), % 147.77/21.19 | | | | | | | | | | | | | | | | | (3216), (3219), (3220), (3221), (3224), (3226), % 147.77/21.19 | | | | | | | | | | | | | | | | | (3228), (3230), (3231), (3235), (3237), % 147.77/21.19 | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 147.77/21.19 | | | | | | | | | | | | | | | | | #208. % 147.77/21.19 | | | | | | | | | | | | | | | | | % 147.77/21.19 | | | | | | | | | | | | | | | | Case 2: % 147.77/21.19 | | | | | | | | | | | | | | | | | % 147.77/21.19 | | | | | | | | | | | | | | | | | (3238) all_56_31 = e3 % 147.77/21.19 | | | | | | | | | | | | | | | | | (3239) all_56_25 = e0 % 147.77/21.19 | | | | | | | | | | | | | | | | | % 147.77/21.19 | | | | | | | | | | | | | | | | | COMBINE_EQS: (447), (3239) imply: % 147.77/21.19 | | | | | | | | | | | | | | | | | (3240) all_52_3 = e0 % 147.77/21.19 | | | | | | | | | | | | | | | | | % 147.77/21.19 | | | | | | | | | | | | | | | | | SIMP: (3240) implies: % 147.77/21.19 | | | | | | | | | | | | | | | | | (3241) all_52_3 = e0 % 147.77/21.19 | | | | | | | | | | | | | | | | | % 147.77/21.19 | | | | | | | | | | | | | | | | | COMBINE_EQS: (544), (3238) imply: % 147.77/21.19 | | | | | | | | | | | | | | | | | (3242) all_4_2 = e3 % 147.77/21.19 | | | | | | | | | | | | | | | | | % 147.77/21.19 | | | | | | | | | | | | | | | | | REDUCE: (3224), (3241) imply: % 147.77/21.19 | | | | | | | | | | | | | | | | | (3243) ~ (all_6_0 = e0) % 147.77/21.19 | | | | | | | | | | | | | | | | | % 147.77/21.19 | | | | | | | | | | | | | | | | | SIMP: (3243) implies: % 147.77/21.19 | | | | | | | | | | | | | | | | | (3244) ~ (all_6_0 = e0) % 147.77/21.19 | | | | | | | | | | | | | | | | | % 147.77/21.19 | | | | | | | | | | | | | | | | | REDUCE: (38), (3242) imply: % 147.77/21.19 | | | | | | | | | | | | | | | | | (3245) op(e3, e3) = all_4_1 % 147.77/21.19 | | | | | | | | | | | | | | | | | % 147.77/21.19 | | | | | | | | | | | | | | | | | REDUCE: (36), (3242) imply: % 147.77/21.19 | | | | | | | | | | | | | | | | | (3246) op(e0, e0) = e3 % 147.77/21.19 | | | | | | | | | | | | | | | | | % 147.77/21.19 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_10_2, % 147.77/21.19 | | | | | | | | | | | | | | | | | all_4_1, e3, e3, simplifying with (51), (3245) % 147.77/21.19 | | | | | | | | | | | | | | | | | gives: % 147.77/21.19 | | | | | | | | | | | | | | | | | (3247) all_10_2 = all_4_1 % 147.77/21.19 | | | | | | | | | | | | | | | | | % 147.77/21.19 | | | | | | | | | | | | | | | | | COMBINE_EQS: (546), (3247) imply: % 147.77/21.19 | | | | | | | | | | | | | | | | | (3248) all_56_1 = all_4_1 % 147.77/21.19 | | | | | | | | | | | | | | | | | % 147.77/21.19 | | | | | | | | | | | | | | | | | REDUCE: (3230), (3247) imply: % 147.77/21.19 | | | | | | | | | | | | | | | | | (3249) ~ (all_6_0 = all_4_1) % 147.77/21.19 | | | | | | | | | | | | | | | | | % 147.77/21.19 | | | | | | | | | | | | | | | | | SIMP: (3249) implies: % 147.77/21.19 | | | | | | | | | | | | | | | | | (3250) ~ (all_6_0 = all_4_1) % 147.77/21.19 | | | | | | | | | | | | | | | | | % 147.77/21.19 | | | | | | | | | | | | | | | | | BETA: splitting (291) gives: % 147.77/21.19 | | | | | | | | | | | | | | | | | % 147.77/21.19 | | | | | | | | | | | | | | | | | Case 1: % 147.77/21.19 | | | | | | | | | | | | | | | | | | % 147.77/21.19 | | | | | | | | | | | | | | | | | | (3251) ~ (all_56_21 = e0) % 147.77/21.19 | | | | | | | | | | | | | | | | | | % 147.77/21.19 | | | | | | | | | | | | | | | | | | REDUCE: (374), (3251) imply: % 147.77/21.19 | | | | | | | | | | | | | | | | | | (3252) ~ (all_6_2 = e0) % 147.77/21.19 | | | | | | | | | | | | | | | | | | % 147.77/21.19 | | | | | | | | | | | | | | | | | | BETA: splitting (292) gives: % 147.77/21.19 | | | | | | | | | | | | | | | | | | % 147.77/21.19 | | | | | | | | | | | | | | | | | | Case 1: % 147.77/21.19 | | | | | | | | | | | | | | | | | | | % 147.77/21.19 | | | | | | | | | | | | | | | | | | | (3253) ~ (all_56_21 = e2) % 147.77/21.19 | | | | | | | | | | | | | | | | | | | % 147.77/21.19 | | | | | | | | | | | | | | | | | | | REDUCE: (374), (3253) imply: % 147.77/21.19 | | | | | | | | | | | | | | | | | | | (3254) ~ (all_6_2 = e2) % 147.77/21.19 | | | | | | | | | | | | | | | | | | | % 147.77/21.19 | | | | | | | | | | | | | | | | | | | BETA: splitting (294) gives: % 147.77/21.19 | | | | | | | | | | | | | | | | | | | % 147.77/21.19 | | | | | | | | | | | | | | | | | | | Case 1: % 147.77/21.19 | | | | | | | | | | | | | | | | | | | | % 147.77/21.19 | | | | | | | | | | | | | | | | | | | | (3255) ~ (all_56_11 = e0) % 147.77/21.19 | | | | | | | | | | | | | | | | | | | | % 147.77/21.19 | | | | | | | | | | | | | | | | | | | | REDUCE: (545), (3255) imply: % 147.77/21.19 | | | | | | | | | | | | | | | | | | | | (3256) ~ (all_8_2 = e0) % 147.77/21.19 | | | | | | | | | | | | | | | | | | | | % 147.77/21.19 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (36), (38), (41), (46), (47), (48), (51), % 147.77/21.19 | | | | | | | | | | | | | | | | | | | | (52), (53), (161), (168), (171), (174), (181), % 147.77/21.19 | | | | | | | | | | | | | | | | | | | | (182), (193), (194), (212), (237), (242), (243), % 147.77/21.19 | | | | | | | | | | | | | | | | | | | | (244), (245), (247), (251), (252), (287), (291), % 147.77/21.19 | | | | | | | | | | | | | | | | | | | | (293), (295), (296), (297), (298), (299), (318), % 147.77/21.19 | | | | | | | | | | | | | | | | | | | | (320), (321), (326), (329), (330), (331), (335), % 147.77/21.19 | | | | | | | | | | | | | | | | | | | | (337), (343), (344), (365), (366), (374), (380), % 147.77/21.19 | | | | | | | | | | | | | | | | | | | | (386), (389), (401), (402), (407), (408), (419), % 147.77/21.19 | | | | | | | | | | | | | | | | | | | | (425), (429), (431), (457), (469), (473), (540), % 147.77/21.19 | | | | | | | | | | | | | | | | | | | | (541), (542), (543), (544), (545), (546), (547), % 147.77/21.19 | | | | | | | | | | | | | | | | | | | | (548), (549), (550), (551), (552), (554), (555), % 147.77/21.19 | | | | | | | | | | | | | | | | | | | | (557), (561), (563), (565), (568), (571), (573), % 147.77/21.19 | | | | | | | | | | | | | | | | | | | | (575), (577), (580), (582), (583), (585), (587), % 147.77/21.19 | | | | | | | | | | | | | | | | | | | | (589), (590), (612), (622), (623), (627), (769), % 147.77/21.19 | | | | | | | | | | | | | | | | | | | | (2643), (2645), (2647), (2649), (2653), (3216), % 147.77/21.19 | | | | | | | | | | | | | | | | | | | | (3219), (3220), (3221), (3222), (3226), (3228), % 147.77/21.19 | | | | | | | | | | | | | | | | | | | | (3230), (3231), (3233), (3235), (3254), (3256), % 147.77/21.19 | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 147.77/21.19 | | | | | | | | | | | | | | | | | | | | #442. % 147.77/21.19 | | | | | | | | | | | | | | | | | | | | % 147.77/21.19 | | | | | | | | | | | | | | | | | | | Case 2: % 147.77/21.19 | | | | | | | | | | | | | | | | | | | | % 147.77/21.19 | | | | | | | | | | | | | | | | | | | | (3257) all_56_11 = e0 % 147.77/21.19 | | | | | | | | | | | | | | | | | | | | % 147.77/21.19 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (545), (3257) imply: % 147.77/21.19 | | | | | | | | | | | | | | | | | | | | (3258) all_8_2 = e0 % 147.77/21.19 | | | | | | | | | | | | | | | | | | | | % 147.77/21.19 | | | | | | | | | | | | | | | | | | | | REDUCE: (48), (3258) imply: % 147.77/21.19 | | | | | | | | | | | | | | | | | | | | (3259) op(e0, e0) = all_8_1 % 147.77/21.19 | | | | | | | | | | | | | | | | | | | | % 147.77/21.19 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2647), (3246), (3259), (function-axioms) are % 147.77/21.19 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #546. % 147.77/21.19 | | | | | | | | | | | | | | | | | | | | % 147.77/21.19 | | | | | | | | | | | | | | | | | | | End of split % 147.77/21.19 | | | | | | | | | | | | | | | | | | | % 147.77/21.19 | | | | | | | | | | | | | | | | | | Case 2: % 147.77/21.19 | | | | | | | | | | | | | | | | | | | % 147.77/21.19 | | | | | | | | | | | | | | | | | | | (3260) all_56_21 = e2 % 147.77/21.19 | | | | | | | | | | | | | | | | | | | (3261) all_56_19 = e1 % 147.77/21.19 | | | | | | | | | | | | | | | | | | | % 147.77/21.19 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (46), (48), (244), (287), (324), (374), % 147.77/21.19 | | | | | | | | | | | | | | | | | | | (380), (435), (544), (545), (546), (550), (552), % 147.77/21.19 | | | | | | | | | | | | | | | | | | | (580), (591), (617), (3216), (3219), (3221), % 147.77/21.19 | | | | | | | | | | | | | | | | | | | (3226), (3228), (3230), (3231), (3244), (3252), % 147.77/21.19 | | | | | | | | | | | | | | | | | | | (3260), (3261), (function-axioms) are inconsistent % 147.77/21.19 | | | | | | | | | | | | | | | | | | | by sub-proof #207. % 147.77/21.19 | | | | | | | | | | | | | | | | | | | % 147.77/21.19 | | | | | | | | | | | | | | | | | | End of split % 147.77/21.19 | | | | | | | | | | | | | | | | | | % 147.77/21.19 | | | | | | | | | | | | | | | | | Case 2: % 147.77/21.19 | | | | | | | | | | | | | | | | | | % 147.77/21.19 | | | | | | | | | | | | | | | | | | (3262) all_56_23 = e1 % 147.77/21.19 | | | | | | | | | | | | | | | | | | (3263) all_56_21 = e0 % 147.77/21.19 | | | | | | | | | | | | | | | | | | % 147.77/21.19 | | | | | | | | | | | | | | | | | | REF_CLOSE: (174), (243), (244), (287), (366), (374), (473), % 147.77/21.19 | | | | | | | | | | | | | | | | | | (545), (573), (580), (587), (2649), (3219), % 147.77/21.19 | | | | | | | | | | | | | | | | | | (3226), (3228), (3231), (3238), (3248), (3250), % 147.77/21.19 | | | | | | | | | | | | | | | | | | (3262), (3263) are inconsistent by sub-proof #320. % 147.77/21.19 | | | | | | | | | | | | | | | | | | % 147.77/21.19 | | | | | | | | | | | | | | | | | End of split % 147.77/21.19 | | | | | | | | | | | | | | | | | % 147.77/21.19 | | | | | | | | | | | | | | | | End of split % 147.77/21.19 | | | | | | | | | | | | | | | | % 147.77/21.19 | | | | | | | | | | | | | | | Case 2: % 147.77/21.19 | | | | | | | | | | | | | | | | % 147.77/21.19 | | | | | | | | | | | | | | | | (3264) all_56_31 = e1 % 147.77/21.19 | | | | | | | | | | | | | | | | (3265) all_56_29 = e0 % 147.77/21.19 | | | | | | | | | | | | | | | | % 147.77/21.19 | | | | | | | | | | | | | | | | COMBINE_EQS: (357), (3265) imply: % 147.77/21.19 | | | | | | | | | | | | | | | | (3266) all_52_11 = e0 % 147.77/21.19 | | | | | | | | | | | | | | | | % 147.77/21.19 | | | | | | | | | | | | | | | | SIMP: (3266) implies: % 147.77/21.19 | | | | | | | | | | | | | | | | (3267) all_52_11 = e0 % 147.77/21.19 | | | | | | | | | | | | | | | | % 147.77/21.19 | | | | | | | | | | | | | | | | COMBINE_EQS: (544), (3264) imply: % 147.77/21.19 | | | | | | | | | | | | | | | | (3268) all_4_2 = e1 % 147.77/21.19 | | | | | | | | | | | | | | | | % 147.77/21.19 | | | | | | | | | | | | | | | | COMBINE_EQS: (531), (3268) imply: % 147.77/21.19 | | | | | | | | | | | | | | | | (3269) all_34_2 = e1 % 147.77/21.19 | | | | | | | | | | | | | | | | % 147.77/21.19 | | | | | | | | | | | | | | | | REDUCE: (585), (3267) imply: % 147.77/21.19 | | | | | | | | | | | | | | | | (3270) ~ (all_6_2 = e0) % 147.77/21.19 | | | | | | | | | | | | | | | | % 147.77/21.19 | | | | | | | | | | | | | | | | SIMP: (3270) implies: % 147.77/21.19 | | | | | | | | | | | | | | | | (3271) ~ (all_6_2 = e0) % 147.77/21.19 | | | | | | | | | | | | | | | | % 147.77/21.19 | | | | | | | | | | | | | | | | REDUCE: (588), (3267), (3268) imply: % 147.77/21.19 | | | | | | | | | | | | | | | | (3272) ~ (e1 = e0) % 147.77/21.19 | | | | | | | | | | | | | | | | % 147.77/21.19 | | | | | | | | | | | | | | | | REDUCE: (38), (3268) imply: % 147.77/21.19 | | | | | | | | | | | | | | | | (3273) op(e1, e1) = all_4_1 % 147.77/21.19 | | | | | | | | | | | | | | | | % 147.77/21.19 | | | | | | | | | | | | | | | | REF_CLOSE: (4), (41), (46), (48), (242), (244), (287), (292), % 147.77/21.19 | | | | | | | | | | | | | | | | (324), (374), (380), (435), (532), (541), (544), % 147.77/21.19 | | | | | | | | | | | | | | | | (545), (546), (550), (552), (580), (591), (617), % 147.77/21.19 | | | | | | | | | | | | | | | | (622), (683), (762), (2656), (3213), (3216), % 147.77/21.19 | | | | | | | | | | | | | | | | (3219), (3221), (3226), (3228), (3230), (3231), % 147.77/21.19 | | | | | | | | | | | | | | | | (3269), (3271), (3273), (function-axioms) are % 147.77/21.19 | | | | | | | | | | | | | | | | inconsistent by sub-proof #206. % 147.77/21.19 | | | | | | | | | | | | | | | | % 147.77/21.19 | | | | | | | | | | | | | | | End of split % 147.77/21.19 | | | | | | | | | | | | | | | % 148.11/21.19 | | | | | | | | | | | | | | Case 2: % 148.11/21.19 | | | | | | | | | | | | | | | % 148.11/21.19 | | | | | | | | | | | | | | | (3274) all_38_1 = e2 % 148.11/21.19 | | | | | | | | | | | | | | | (3275) ~ (all_38_0 = e0) | ~ (all_38_2 = e1) % 148.11/21.19 | | | | | | | | | | | | | | | % 148.11/21.19 | | | | | | | | | | | | | | | COMBINE_EQS: (684), (3274) imply: % 148.11/21.19 | | | | | | | | | | | | | | | (3276) all_10_1 = e2 % 148.11/21.19 | | | | | | | | | | | | | | | % 148.11/21.19 | | | | | | | | | | | | | | | REDUCE: (53), (3276) imply: % 148.11/21.19 | | | | | | | | | | | | | | | (3277) op(all_10_2, all_10_2) = e2 % 148.11/21.19 | | | | | | | | | | | | | | | % 148.11/21.19 | | | | | | | | | | | | | | | REDUCE: (52), (3276) imply: % 148.11/21.19 | | | | | | | | | | | | | | | (3278) op(e3, e2) = all_10_0 % 148.11/21.19 | | | | | | | | | | | | | | | % 148.11/21.19 | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_4, % 148.11/21.19 | | | | | | | | | | | | | | | all_10_0, e2, e3, simplifying with (218), (3278) % 148.11/21.19 | | | | | | | | | | | | | | | gives: % 148.11/21.19 | | | | | | | | | | | | | | | (3279) all_52_4 = all_10_0 % 148.11/21.19 | | | | | | | | | | | | | | | % 148.11/21.19 | | | | | | | | | | | | | | | COMBINE_EQS: (457), (3279) imply: % 148.11/21.19 | | | | | | | | | | | | | | | (3280) all_54_1 = all_10_0 % 148.11/21.19 | | | | | | | | | | | | | | | % 148.11/21.19 | | | | | | | | | | | | | | | COMBINE_EQS: (408), (3279) imply: % 148.11/21.19 | | | | | | | | | | | | | | | (3281) all_56_3 = all_10_0 % 148.11/21.19 | | | | | | | | | | | | | | | % 148.11/21.19 | | | | | | | | | | | | | | | COMBINE_EQS: (555), (3279) imply: % 148.11/21.19 | | | | | | | | | | | | | | | (3282) all_58_1 = all_10_0 % 148.11/21.20 | | | | | | | | | | | | | | | % 148.11/21.20 | | | | | | | | | | | | | | | REDUCE: (184), (3279) imply: % 148.11/21.20 | | | | | | | | | | | | | | | (3283) ~ (all_52_6 = all_10_0) % 148.11/21.20 | | | | | | | | | | | | | | | % 148.11/21.20 | | | | | | | | | | | | | | | SIMP: (3283) implies: % 148.11/21.20 | | | | | | | | | | | | | | | (3284) ~ (all_52_6 = all_10_0) % 148.11/21.20 | | | | | | | | | | | | | | | % 148.11/21.20 | | | | | | | | | | | | | | | REDUCE: (182), (3279) imply: % 148.11/21.20 | | | | | | | | | | | | | | | (3285) ~ (all_52_8 = all_10_0) % 148.11/21.20 | | | | | | | | | | | | | | | % 148.11/21.20 | | | | | | | | | | | | | | | SIMP: (3285) implies: % 148.11/21.20 | | | | | | | | | | | | | | | (3286) ~ (all_52_8 = all_10_0) % 148.11/21.20 | | | | | | | | | | | | | | | % 148.11/21.20 | | | | | | | | | | | | | | | REDUCE: (181), (3279) imply: % 148.11/21.20 | | | | | | | | | | | | | | | (3287) ~ (all_52_12 = all_10_0) % 148.11/21.20 | | | | | | | | | | | | | | | % 148.11/21.20 | | | | | | | | | | | | | | | SIMP: (3287) implies: % 148.11/21.20 | | | | | | | | | | | | | | | (3288) ~ (all_52_12 = all_10_0) % 148.11/21.20 | | | | | | | | | | | | | | | % 148.11/21.20 | | | | | | | | | | | | | | | REDUCE: (563), (3279) imply: % 148.11/21.20 | | | | | | | | | | | | | | | (3289) ~ (all_10_0 = all_10_2) % 148.11/21.20 | | | | | | | | | | | | | | | % 148.11/21.20 | | | | | | | | | | | | | | | REDUCE: (571), (3279) imply: % 148.11/21.20 | | | | | | | | | | | | | | | (3290) ~ (all_10_0 = all_8_2) % 148.11/21.20 | | | | | | | | | | | | | | | % 148.11/21.20 | | | | | | | | | | | | | | | BETA: splitting (288) gives: % 148.11/21.20 | | | | | | | | | | | | | | | % 148.11/21.20 | | | | | | | | | | | | | | | Case 1: % 148.11/21.20 | | | | | | | | | | | | | | | | % 148.11/21.20 | | | | | | | | | | | | | | | | (3291) ~ (all_56_31 = e1) % 148.11/21.20 | | | | | | | | | | | | | | | | % 148.11/21.20 | | | | | | | | | | | | | | | | REDUCE: (544), (3291) imply: % 148.11/21.20 | | | | | | | | | | | | | | | | (3292) ~ (all_4_2 = e1) % 148.11/21.20 | | | | | | | | | | | | | | | | % 148.11/21.20 | | | | | | | | | | | | | | | | BETA: splitting (290) gives: % 148.11/21.20 | | | | | | | | | | | | | | | | % 148.11/21.20 | | | | | | | | | | | | | | | | Case 1: % 148.11/21.20 | | | | | | | | | | | | | | | | | % 148.11/21.20 | | | | | | | | | | | | | | | | | (3293) ~ (all_56_31 = e3) % 148.11/21.20 | | | | | | | | | | | | | | | | | % 148.11/21.20 | | | | | | | | | | | | | | | | | REDUCE: (544), (3293) imply: % 148.11/21.20 | | | | | | | | | | | | | | | | | (3294) ~ (all_4_2 = e3) % 148.11/21.20 | | | | | | | | | | | | | | | | | % 148.11/21.20 | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (38), (41), (46), (48), (51), (174), (176), % 148.11/21.20 | | | | | | | | | | | | | | | | | (188), (207), (237), (240), (242), (243), (244), % 148.11/21.20 | | | | | | | | | | | | | | | | | (287), (289), (291), (292), (293), (324), (360), % 148.11/21.20 | | | | | | | | | | | | | | | | | (366), (374), (380), (435), (473), (478), (532), % 148.11/21.20 | | | | | | | | | | | | | | | | | (540), (541), (544), (545), (546), (550), (552), % 148.11/21.20 | | | | | | | | | | | | | | | | | (561), (570), (573), (580), (587), (591), (617), % 148.11/21.20 | | | | | | | | | | | | | | | | | (622), (627), (762), (2641), (2649), (3213), % 148.11/21.20 | | | | | | | | | | | | | | | | | (3216), (3219), (3220), (3221), (3224), (3226), % 148.11/21.20 | | | | | | | | | | | | | | | | | (3228), (3230), (3231), (3292), (3294), % 148.11/21.20 | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 148.11/21.20 | | | | | | | | | | | | | | | | | #208. % 148.11/21.20 | | | | | | | | | | | | | | | | | % 148.11/21.20 | | | | | | | | | | | | | | | | Case 2: % 148.11/21.20 | | | | | | | | | | | | | | | | | % 148.11/21.20 | | | | | | | | | | | | | | | | | (3295) all_56_31 = e3 % 148.11/21.20 | | | | | | | | | | | | | | | | | (3296) all_56_25 = e0 % 148.11/21.20 | | | | | | | | | | | | | | | | | % 148.11/21.20 | | | | | | | | | | | | | | | | | COMBINE_EQS: (447), (3296) imply: % 148.11/21.20 | | | | | | | | | | | | | | | | | (3297) all_52_3 = e0 % 148.11/21.20 | | | | | | | | | | | | | | | | | % 148.11/21.20 | | | | | | | | | | | | | | | | | SIMP: (3297) implies: % 148.11/21.20 | | | | | | | | | | | | | | | | | (3298) all_52_3 = e0 % 148.11/21.20 | | | | | | | | | | | | | | | | | % 148.11/21.20 | | | | | | | | | | | | | | | | | COMBINE_EQS: (544), (3295) imply: % 148.11/21.20 | | | | | | | | | | | | | | | | | (3299) all_4_2 = e3 % 148.11/21.20 | | | | | | | | | | | | | | | | | % 148.11/21.20 | | | | | | | | | | | | | | | | | REDUCE: (3224), (3298) imply: % 148.11/21.20 | | | | | | | | | | | | | | | | | (3300) ~ (all_6_0 = e0) % 148.11/21.20 | | | | | | | | | | | | | | | | | % 148.11/21.20 | | | | | | | | | | | | | | | | | SIMP: (3300) implies: % 148.11/21.20 | | | | | | | | | | | | | | | | | (3301) ~ (all_6_0 = e0) % 148.11/21.20 | | | | | | | | | | | | | | | | | % 148.11/21.20 | | | | | | | | | | | | | | | | | REDUCE: (38), (3299) imply: % 148.11/21.20 | | | | | | | | | | | | | | | | | (3302) op(e3, e3) = all_4_1 % 148.11/21.20 | | | | | | | | | | | | | | | | | % 148.11/21.20 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_10_2, % 148.11/21.20 | | | | | | | | | | | | | | | | | all_4_1, e3, e3, simplifying with (51), (3302) % 148.11/21.20 | | | | | | | | | | | | | | | | | gives: % 148.11/21.20 | | | | | | | | | | | | | | | | | (3303) all_10_2 = all_4_1 % 148.11/21.20 | | | | | | | | | | | | | | | | | % 148.11/21.20 | | | | | | | | | | | | | | | | | COMBINE_EQS: (546), (3303) imply: % 148.11/21.20 | | | | | | | | | | | | | | | | | (3304) all_56_1 = all_4_1 % 148.11/21.20 | | | | | | | | | | | | | | | | | % 148.11/21.20 | | | | | | | | | | | | | | | | | REDUCE: (3230), (3303) imply: % 148.11/21.20 | | | | | | | | | | | | | | | | | (3305) ~ (all_6_0 = all_4_1) % 148.11/21.20 | | | | | | | | | | | | | | | | | % 148.11/21.20 | | | | | | | | | | | | | | | | | SIMP: (3305) implies: % 148.11/21.20 | | | | | | | | | | | | | | | | | (3306) ~ (all_6_0 = all_4_1) % 148.11/21.20 | | | | | | | | | | | | | | | | | % 148.11/21.20 | | | | | | | | | | | | | | | | | BETA: splitting (291) gives: % 148.11/21.20 | | | | | | | | | | | | | | | | | % 148.11/21.20 | | | | | | | | | | | | | | | | | Case 1: % 148.11/21.20 | | | | | | | | | | | | | | | | | | % 148.11/21.20 | | | | | | | | | | | | | | | | | | (3307) ~ (all_56_21 = e0) % 148.11/21.20 | | | | | | | | | | | | | | | | | | % 148.11/21.20 | | | | | | | | | | | | | | | | | | REDUCE: (374), (3307) imply: % 148.11/21.20 | | | | | | | | | | | | | | | | | | (3308) ~ (all_6_2 = e0) % 148.11/21.20 | | | | | | | | | | | | | | | | | | % 148.11/21.20 | | | | | | | | | | | | | | | | | | BETA: splitting (292) gives: % 148.11/21.20 | | | | | | | | | | | | | | | | | | % 148.11/21.20 | | | | | | | | | | | | | | | | | | Case 1: % 148.11/21.20 | | | | | | | | | | | | | | | | | | | % 148.11/21.20 | | | | | | | | | | | | | | | | | | | (3309) ~ (all_56_21 = e2) % 148.11/21.20 | | | | | | | | | | | | | | | | | | | % 148.11/21.20 | | | | | | | | | | | | | | | | | | | REDUCE: (374), (3309) imply: % 148.11/21.20 | | | | | | | | | | | | | | | | | | | (3310) ~ (all_6_2 = e2) % 148.11/21.20 | | | | | | | | | | | | | | | | | | | % 148.11/21.20 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (38), (41), (46), (48), (51), (53), (158), % 148.11/21.20 | | | | | | | | | | | | | | | | | | | (166), (174), (187), (188), (194), (196), (238), % 148.11/21.20 | | | | | | | | | | | | | | | | | | | (241), (242), (243), (244), (247), (248), (251), % 148.11/21.20 | | | | | | | | | | | | | | | | | | | (252), (287), (290), (291), (293), (294), (295), % 148.11/21.20 | | | | | | | | | | | | | | | | | | | (296), (297), (298), (299), (326), (336), (344), % 148.11/21.20 | | | | | | | | | | | | | | | | | | | (365), (366), (374), (380), (401), (402), (419), % 148.11/21.20 | | | | | | | | | | | | | | | | | | | (425), (429), (431), (443), (447), (463), (473), % 148.11/21.20 | | | | | | | | | | | | | | | | | | | (476), (482), (533), (541), (542), (543), (544), % 148.11/21.20 | | | | | | | | | | | | | | | | | | | (545), (546), (549), (550), (552), (554), (557), % 148.11/21.20 | | | | | | | | | | | | | | | | | | | (561), (568), (570), (573), (580), (585), (587), % 148.11/21.20 | | | | | | | | | | | | | | | | | | | (588), (591), (612), (618), (622), (627), (723), % 148.11/21.20 | | | | | | | | | | | | | | | | | | | (770), (2645), (2649), (3216), (3219), (3220), % 148.11/21.20 | | | | | | | | | | | | | | | | | | | (3221), (3222), (3224), (3226), (3228), (3230), % 148.11/21.20 | | | | | | | | | | | | | | | | | | | (3231), (3275), (3277), (3280), (3281), (3282), % 148.11/21.20 | | | | | | | | | | | | | | | | | | | (3284), (3286), (3288), (3289), (3290), (3292), % 148.11/21.20 | | | | | | | | | | | | | | | | | | | (3310), (function-axioms) are inconsistent by % 148.11/21.20 | | | | | | | | | | | | | | | | | | | sub-proof #413. % 148.11/21.20 | | | | | | | | | | | | | | | | | | | % 148.11/21.20 | | | | | | | | | | | | | | | | | | Case 2: % 148.11/21.20 | | | | | | | | | | | | | | | | | | | % 148.11/21.20 | | | | | | | | | | | | | | | | | | | (3311) all_56_21 = e2 % 148.11/21.20 | | | | | | | | | | | | | | | | | | | (3312) all_56_19 = e1 % 148.11/21.20 | | | | | | | | | | | | | | | | | | | % 148.11/21.20 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (46), (48), (244), (287), (324), (374), % 148.11/21.20 | | | | | | | | | | | | | | | | | | | (380), (435), (544), (545), (546), (550), (552), % 148.11/21.20 | | | | | | | | | | | | | | | | | | | (580), (591), (617), (3216), (3219), (3221), % 148.11/21.20 | | | | | | | | | | | | | | | | | | | (3226), (3228), (3230), (3231), (3301), (3308), % 148.11/21.20 | | | | | | | | | | | | | | | | | | | (3311), (3312), (function-axioms) are inconsistent % 148.11/21.20 | | | | | | | | | | | | | | | | | | | by sub-proof #207. % 148.11/21.20 | | | | | | | | | | | | | | | | | | | % 148.11/21.20 | | | | | | | | | | | | | | | | | | End of split % 148.11/21.20 | | | | | | | | | | | | | | | | | | % 148.11/21.20 | | | | | | | | | | | | | | | | | Case 2: % 148.11/21.20 | | | | | | | | | | | | | | | | | | % 148.11/21.20 | | | | | | | | | | | | | | | | | | (3313) all_56_23 = e1 % 148.11/21.20 | | | | | | | | | | | | | | | | | | (3314) all_56_21 = e0 % 148.11/21.20 | | | | | | | | | | | | | | | | | | % 148.11/21.20 | | | | | | | | | | | | | | | | | | REF_CLOSE: (174), (243), (244), (287), (366), (374), (473), % 148.11/21.20 | | | | | | | | | | | | | | | | | | (545), (573), (580), (587), (2649), (3219), % 148.11/21.20 | | | | | | | | | | | | | | | | | | (3226), (3228), (3231), (3295), (3304), (3306), % 148.11/21.20 | | | | | | | | | | | | | | | | | | (3313), (3314) are inconsistent by sub-proof #320. % 148.11/21.20 | | | | | | | | | | | | | | | | | | % 148.11/21.20 | | | | | | | | | | | | | | | | | End of split % 148.11/21.20 | | | | | | | | | | | | | | | | | % 148.11/21.20 | | | | | | | | | | | | | | | | End of split % 148.11/21.20 | | | | | | | | | | | | | | | | % 148.11/21.20 | | | | | | | | | | | | | | | Case 2: % 148.11/21.20 | | | | | | | | | | | | | | | | % 148.11/21.20 | | | | | | | | | | | | | | | | (3315) all_56_31 = e1 % 148.11/21.20 | | | | | | | | | | | | | | | | (3316) all_56_29 = e0 % 148.11/21.20 | | | | | | | | | | | | | | | | % 148.11/21.20 | | | | | | | | | | | | | | | | REF_CLOSE: (38), (41), (46), (48), (242), (244), (287), % 148.11/21.20 | | | | | | | | | | | | | | | | (292), (324), (357), (374), (380), (435), (531), % 148.11/21.20 | | | | | | | | | | | | | | | | (532), (541), (544), (545), (546), (550), (552), % 148.11/21.20 | | | | | | | | | | | | | | | | (580), (585), (588), (591), (617), (622), (683), % 148.11/21.20 | | | | | | | | | | | | | | | | (762), (2656), (3213), (3216), (3219), (3221), % 148.11/21.20 | | | | | | | | | | | | | | | | (3226), (3228), (3230), (3231), (3315), (3316), % 148.11/21.20 | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 148.11/21.20 | | | | | | | | | | | | | | | | #205. % 148.11/21.20 | | | | | | | | | | | | | | | | % 148.11/21.20 | | | | | | | | | | | | | | | End of split % 148.11/21.20 | | | | | | | | | | | | | | | % 148.11/21.20 | | | | | | | | | | | | | | End of split % 148.11/21.20 | | | | | | | | | | | | | | % 148.11/21.20 | | | | | | | | | | | | | End of split % 148.11/21.20 | | | | | | | | | | | | | % 148.11/21.20 | | | | | | | | | | | | End of split % 148.11/21.20 | | | | | | | | | | | | % 148.11/21.20 | | | | | | | | | | | Case 2: % 148.11/21.20 | | | | | | | | | | | | % 148.11/21.20 | | | | | | | | | | | | (3317) all_32_1 = e1 % 148.11/21.20 | | | | | | | | | | | | (3318) ~ (all_32_0 = e0) | ~ (all_32_2 = e2) % 148.11/21.20 | | | | | | | | | | | | % 148.11/21.20 | | | | | | | | | | | | COMBINE_EQS: (682), (3317) imply: % 148.11/21.20 | | | | | | | | | | | | (3319) all_10_1 = e1 % 148.11/21.20 | | | | | | | | | | | | % 148.11/21.20 | | | | | | | | | | | | SIMP: (3319) implies: % 148.11/21.20 | | | | | | | | | | | | (3320) all_10_1 = e1 % 148.11/21.20 | | | | | | | | | | | | % 148.11/21.20 | | | | | | | | | | | | REDUCE: (53), (3320) imply: % 148.11/21.20 | | | | | | | | | | | | (3321) op(all_10_2, all_10_2) = e1 % 148.11/21.20 | | | | | | | | | | | | % 148.11/21.20 | | | | | | | | | | | | REDUCE: (52), (3320) imply: % 148.11/21.20 | | | | | | | | | | | | (3322) op(e3, e1) = all_10_0 % 148.11/21.20 | | | | | | | | | | | | % 148.11/21.20 | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_8, % 148.11/21.20 | | | | | | | | | | | | all_10_0, e1, e3, simplifying with (217), (3322) % 148.11/21.20 | | | | | | | | | | | | gives: % 148.11/21.20 | | | | | | | | | | | | (3323) all_52_8 = all_10_0 % 148.11/21.20 | | | | | | | | | | | | % 148.11/21.20 | | | | | | | | | | | | COMBINE_EQS: (459), (3323) imply: % 148.11/21.20 | | | | | | | | | | | | (3324) all_54_2 = all_10_0 % 148.11/21.20 | | | | | | | | | | | | % 148.11/21.20 | | | | | | | | | | | | COMBINE_EQS: (429), (3323) imply: % 148.11/21.20 | | | | | | | | | | | | (3325) all_56_5 = all_10_0 % 148.11/21.20 | | | | | | | | | | | | % 148.11/21.20 | | | | | | | | | | | | COMBINE_EQS: (407), (3323) imply: % 148.11/21.20 | | | | | | | | | | | | (3326) all_58_4 = all_10_0 % 148.11/21.20 | | | | | | | | | | | | % 148.11/21.20 | | | | | | | | | | | | REDUCE: (182), (3323) imply: % 148.11/21.20 | | | | | | | | | | | | (3327) ~ (all_52_4 = all_10_0) % 148.11/21.20 | | | | | | | | | | | | % 148.11/21.20 | | | | | | | | | | | | REDUCE: (169), (3323) imply: % 148.11/21.20 | | | | | | | | | | | | (3328) ~ (all_52_11 = all_10_0) % 148.11/21.20 | | | | | | | | | | | | % 148.11/21.20 | | | | | | | | | | | | SIMP: (3328) implies: % 148.11/21.20 | | | | | | | | | | | | (3329) ~ (all_52_11 = all_10_0) % 148.11/21.20 | | | | | | | | | | | | % 148.11/21.20 | | | | | | | | | | | | REDUCE: (168), (3323) imply: % 148.11/21.20 | | | | | | | | | | | | (3330) ~ (all_52_12 = all_10_0) % 148.11/21.20 | | | | | | | | | | | | % 148.11/21.20 | | | | | | | | | | | | SIMP: (3330) implies: % 148.11/21.20 | | | | | | | | | | | | (3331) ~ (all_52_12 = all_10_0) % 148.11/21.20 | | | | | | | | | | | | % 148.11/21.20 | | | | | | | | | | | | REDUCE: (565), (3323) imply: % 148.11/21.20 | | | | | | | | | | | | (3332) ~ (all_10_0 = all_10_2) % 148.11/21.20 | | | | | | | | | | | | % 148.11/21.20 | | | | | | | | | | | | REDUCE: (582), (3323) imply: % 148.11/21.20 | | | | | | | | | | | | (3333) ~ (all_10_0 = all_6_2) % 148.11/21.20 | | | | | | | | | | | | % 148.11/21.20 | | | | | | | | | | | | BETA: splitting (119) gives: % 148.11/21.20 | | | | | | | | | | | | % 148.11/21.20 | | | | | | | | | | | | Case 1: % 148.11/21.20 | | | | | | | | | | | | | % 148.11/21.20 | | | | | | | | | | | | | (3334) ~ (all_36_1 = e3) % 148.11/21.20 | | | | | | | | | | | | | % 148.11/21.20 | | | | | | | | | | | | | REDUCE: (652), (3334) imply: % 148.11/21.20 | | | | | | | | | | | | | (3335) ~ (all_6_1 = e3) % 148.11/21.20 | | | | | | | | | | | | | % 148.11/21.20 | | | | | | | | | | | | | BETA: splitting (129) gives: % 148.11/21.20 | | | | | | | | | | | | | % 148.11/21.20 | | | | | | | | | | | | | Case 1: % 148.11/21.20 | | | | | | | | | | | | | | % 148.11/21.20 | | | | | | | | | | | | | | (3336) ~ (all_40_0 = e3) % 148.11/21.20 | | | | | | | | | | | | | | % 148.11/21.20 | | | | | | | | | | | | | | REDUCE: (713), (3336) imply: % 148.11/21.20 | | | | | | | | | | | | | | (3337) ~ (all_6_0 = e3) % 148.11/21.20 | | | | | | | | | | | | | | % 148.11/21.20 | | | | | | | | | | | | | | BETA: splitting (292) gives: % 148.11/21.20 | | | | | | | | | | | | | | % 148.11/21.20 | | | | | | | | | | | | | | Case 1: % 148.11/21.20 | | | | | | | | | | | | | | | % 148.11/21.20 | | | | | | | | | | | | | | | (3338) ~ (all_56_21 = e2) % 148.11/21.20 | | | | | | | | | | | | | | | % 148.11/21.20 | | | | | | | | | | | | | | | REDUCE: (374), (3338) imply: % 148.11/21.20 | | | | | | | | | | | | | | | (3339) ~ (all_6_2 = e2) % 148.11/21.20 | | | | | | | | | | | | | | | % 148.11/21.20 | | | | | | | | | | | | | | | REF_CLOSE: (7), (36), (38), (41), (48), (51), (173), (237), % 148.11/21.20 | | | | | | | | | | | | | | | (250), (252), (288), (289), (290), (291), (297), % 148.11/21.20 | | | | | | | | | | | | | | | (298), (299), (328), (330), (331), (337), (357), % 148.11/21.20 | | | | | | | | | | | | | | | (360), (374), (380), (389), (402), (408), (447), % 148.11/21.20 | | | | | | | | | | | | | | | (494), (529), (540), (543), (544), (546), (548), % 148.11/21.20 | | | | | | | | | | | | | | | (549), (552), (554), (555), (561), (563), (570), % 148.11/21.20 | | | | | | | | | | | | | | | (580), (581), (588), (612), (622), (627), (681), % 148.11/21.20 | | | | | | | | | | | | | | | (761), (769), (770), (2637), (2641), (2645), % 148.11/21.20 | | | | | | | | | | | | | | | (3318), (3321), (3324), (3325), (3326), (3327), % 148.11/21.20 | | | | | | | | | | | | | | | (3329), (3331), (3332), (3333), (3339), % 148.11/21.20 | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 148.11/21.20 | | | | | | | | | | | | | | | #203. % 148.11/21.20 | | | | | | | | | | | | | | | % 148.11/21.20 | | | | | | | | | | | | | | Case 2: % 148.11/21.20 | | | | | | | | | | | | | | | % 148.11/21.20 | | | | | | | | | | | | | | | (3340) all_56_21 = e2 % 148.11/21.20 | | | | | | | | | | | | | | | (3341) all_56_19 = e1 % 148.11/21.20 | | | | | | | | | | | | | | | % 148.11/21.20 | | | | | | | | | | | | | | | COMBINE_EQS: (435), (3341) imply: % 148.11/21.20 | | | | | | | | | | | | | | | (3342) all_52_6 = e1 % 148.11/21.20 | | | | | | | | | | | | | | | % 148.11/21.20 | | | | | | | | | | | | | | | COMBINE_EQS: (374), (3340) imply: % 148.11/21.20 | | | | | | | | | | | | | | | (3343) all_6_2 = e2 % 148.11/21.20 | | | | | | | | | | | | | | | % 148.11/21.20 | | | | | | | | | | | | | | | SIMP: (3343) implies: % 148.11/21.20 | | | | | | | | | | | | | | | (3344) all_6_2 = e2 % 148.11/21.20 | | | | | | | | | | | | | | | % 148.11/21.20 | | | | | | | | | | | | | | | REDUCE: (174), (3342) imply: % 148.11/21.20 | | | | | | | | | | | | | | | (3345) ~ (all_52_14 = e1) % 148.11/21.20 | | | | | | | | | | | | | | | % 148.11/21.20 | | | | | | | | | | | | | | | SIMP: (3345) implies: % 148.11/21.20 | | | | | | | | | | | | | | | (3346) ~ (all_52_14 = e1) % 148.11/21.20 | | | | | | | | | | | | | | | % 148.11/21.20 | | | | | | | | | | | | | | | REDUCE: (573), (3342) imply: % 148.11/21.20 | | | | | | | | | | | | | | | (3347) ~ (all_8_2 = e1) % 148.11/21.20 | | | | | | | | | | | | | | | % 148.11/21.20 | | | | | | | | | | | | | | | SIMP: (3347) implies: % 148.11/21.20 | | | | | | | | | | | | | | | (3348) ~ (all_8_2 = e1) % 148.11/21.20 | | | | | | | | | | | | | | | % 148.11/21.20 | | | | | | | | | | | | | | | REDUCE: (580), (3342), (3344) imply: % 148.11/21.20 | | | | | | | | | | | | | | | (3349) ~ (e2 = e1) % 148.11/21.20 | | | | | | | | | | | | | | | % 148.11/21.20 | | | | | | | | | | | | | | | REDUCE: (43), (3344) imply: % 148.11/21.20 | | | | | | | | | | | | | | | (3350) op(e2, e2) = all_6_1 % 148.11/21.20 | | | | | | | | | | | | | | | % 148.11/21.20 | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (9), (36), (42), (46), (48), (208), % 148.11/21.20 | | | | | | | | | | | | | | | (247), (289), (294), (297), (321), (323), (341), % 148.11/21.20 | | | | | | | | | | | | | | | (360), (386), (402), (407), (419), (443), (542), % 148.11/21.20 | | | | | | | | | | | | | | | (545), (546), (547), (550), (551), (555), (571), % 148.11/21.20 | | | | | | | | | | | | | | | (575), (620), (768), (769), (2647), (3335), % 148.11/21.20 | | | | | | | | | | | | | | | (3337), (3346), (3348), (3350), (function-axioms) % 148.11/21.20 | | | | | | | | | | | | | | | are inconsistent by sub-proof #222. % 148.11/21.20 | | | | | | | | | | | | | | | % 148.11/21.20 | | | | | | | | | | | | | | End of split % 148.11/21.20 | | | | | | | | | | | | | | % 148.11/21.20 | | | | | | | | | | | | | Case 2: % 148.11/21.20 | | | | | | | | | | | | | | % 148.11/21.20 | | | | | | | | | | | | | | (3351) ~ (all_40_1 = e0) | ~ (all_40_2 = e2) % 148.11/21.20 | | | | | | | | | | | | | | % 148.11/21.20 | | | | | | | | | | | | | | BETA: splitting (292) gives: % 148.11/21.20 | | | | | | | | | | | | | | % 148.11/21.20 | | | | | | | | | | | | | | Case 1: % 148.11/21.20 | | | | | | | | | | | | | | | % 148.11/21.20 | | | | | | | | | | | | | | | (3352) ~ (all_56_21 = e2) % 148.11/21.20 | | | | | | | | | | | | | | | % 148.11/21.20 | | | | | | | | | | | | | | | REDUCE: (374), (3352) imply: % 148.11/21.20 | | | | | | | | | | | | | | | (3353) ~ (all_6_2 = e2) % 148.11/21.20 | | | | | | | | | | | | | | | % 148.11/21.20 | | | | | | | | | | | | | | | REF_CLOSE: (7), (36), (38), (41), (48), (51), (173), (237), % 148.11/21.20 | | | | | | | | | | | | | | | (250), (252), (288), (289), (290), (291), (297), % 148.11/21.20 | | | | | | | | | | | | | | | (298), (299), (328), (330), (331), (337), (357), % 148.11/21.20 | | | | | | | | | | | | | | | (360), (374), (380), (389), (402), (408), (447), % 148.11/21.20 | | | | | | | | | | | | | | | (494), (529), (540), (543), (544), (546), (548), % 148.11/21.20 | | | | | | | | | | | | | | | (549), (552), (554), (555), (561), (563), (570), % 148.11/21.20 | | | | | | | | | | | | | | | (580), (581), (588), (612), (622), (627), (681), % 148.11/21.20 | | | | | | | | | | | | | | | (761), (769), (770), (2637), (2641), (2645), % 148.11/21.20 | | | | | | | | | | | | | | | (3318), (3321), (3324), (3325), (3326), (3327), % 148.11/21.20 | | | | | | | | | | | | | | | (3329), (3331), (3332), (3333), (3353), % 148.11/21.20 | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 148.11/21.20 | | | | | | | | | | | | | | | #203. % 148.11/21.20 | | | | | | | | | | | | | | | % 148.11/21.20 | | | | | | | | | | | | | | Case 2: % 148.11/21.20 | | | | | | | | | | | | | | | % 148.11/21.20 | | | | | | | | | | | | | | | (3354) all_56_21 = e2 % 148.11/21.20 | | | | | | | | | | | | | | | (3355) all_56_19 = e1 % 148.11/21.20 | | | | | | | | | | | | | | | % 148.11/21.20 | | | | | | | | | | | | | | | COMBINE_EQS: (435), (3355) imply: % 148.11/21.20 | | | | | | | | | | | | | | | (3356) all_52_6 = e1 % 148.11/21.20 | | | | | | | | | | | | | | | % 148.11/21.20 | | | | | | | | | | | | | | | COMBINE_EQS: (374), (3354) imply: % 148.11/21.20 | | | | | | | | | | | | | | | (3357) all_6_2 = e2 % 148.11/21.20 | | | | | | | | | | | | | | | % 148.11/21.20 | | | | | | | | | | | | | | | REF_CLOSE: (43), (46), (247), (507), (542), (573), (685), % 148.11/21.20 | | | | | | | | | | | | | | | (768), (3335), (3351), (3356), (3357), % 148.11/21.20 | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 148.11/21.20 | | | | | | | | | | | | | | | #506. % 148.11/21.20 | | | | | | | | | | | | | | | % 148.11/21.20 | | | | | | | | | | | | | | End of split % 148.11/21.20 | | | | | | | | | | | | | | % 148.11/21.20 | | | | | | | | | | | | | End of split % 148.11/21.20 | | | | | | | | | | | | | % 148.11/21.20 | | | | | | | | | | | | Case 2: % 148.11/21.20 | | | | | | | | | | | | | % 148.11/21.20 | | | | | | | | | | | | | (3358) all_36_1 = e3 % 148.11/21.20 | | | | | | | | | | | | | (3359) ~ (all_36_0 = e0) | ~ (all_36_2 = e2) % 148.11/21.20 | | | | | | | | | | | | | % 148.11/21.20 | | | | | | | | | | | | | COMBINE_EQS: (652), (3358) imply: % 148.11/21.20 | | | | | | | | | | | | | (3360) all_6_1 = e3 % 148.11/21.20 | | | | | | | | | | | | | % 148.11/21.20 | | | | | | | | | | | | | SIMP: (3360) implies: % 148.11/21.20 | | | | | | | | | | | | | (3361) all_6_1 = e3 % 148.11/21.20 | | | | | | | | | | | | | % 148.11/21.20 | | | | | | | | | | | | | REDUCE: (43), (3361) imply: % 148.11/21.20 | | | | | | | | | | | | | (3362) op(all_6_2, all_6_2) = e3 % 148.11/21.20 | | | | | | | | | | | | | % 148.11/21.20 | | | | | | | | | | | | | REDUCE: (42), (3361) imply: % 148.11/21.20 | | | | | | | | | | | | | (3363) op(e1, e3) = all_6_0 % 148.11/21.20 | | | | | | | | | | | | | % 148.11/21.21 | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (36), (38), (41), (46), (48), (51), % 148.11/21.21 | | | | | | | | | | | | | (173), (189), (191), (211), (237), (244), (250), % 148.11/21.21 | | | | | | | | | | | | | (252), (287), (288), (289), (290), (291), (292), % 148.11/21.21 | | | | | | | | | | | | | (297), (298), (299), (324), (328), (330), (331), % 148.11/21.21 | | | | | | | | | | | | | (337), (357), (360), (374), (380), (389), (402), % 148.11/21.21 | | | | | | | | | | | | | (408), (435), (447), (471), (494), (529), (532), % 148.11/21.21 | | | | | | | | | | | | | (540), (543), (544), (545), (546), (548), (549), % 148.11/21.21 | | | | | | | | | | | | | (550), (552), (553), (554), (555), (559), (561), % 148.11/21.21 | | | | | | | | | | | | | (563), (569), (570), (580), (581), (588), (591), % 148.11/21.21 | | | | | | | | | | | | | (612), (617), (622), (627), (681), (761), (762), % 148.11/21.21 | | | | | | | | | | | | | (769), (770), (2637), (2641), (2645), (3318), % 148.11/21.21 | | | | | | | | | | | | | (3321), (3324), (3325), (3326), (3327), (3329), % 148.11/21.21 | | | | | | | | | | | | | (3331), (3332), (3333), (3359), (3362), (3363), % 148.11/21.21 | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 148.11/21.21 | | | | | | | | | | | | | #202. % 148.11/21.21 | | | | | | | | | | | | | % 148.11/21.21 | | | | | | | | | | | | End of split % 148.11/21.21 | | | | | | | | | | | | % 148.11/21.21 | | | | | | | | | | | End of split % 148.11/21.21 | | | | | | | | | | | % 148.11/21.21 | | | | | | | | | | Case 2: % 148.11/21.21 | | | | | | | | | | | % 148.11/21.21 | | | | | | | | | | | (3364) all_30_0 = e3 % 148.11/21.21 | | | | | | | | | | | (3365) ~ (all_30_1 = e0) | ~ (all_30_2 = e1) % 148.11/21.21 | | | | | | | | | | | % 148.11/21.21 | | | | | | | | | | | COMBINE_EQS: (718), (3364) imply: % 148.11/21.21 | | | | | | | | | | | (3366) all_8_0 = e3 % 148.11/21.21 | | | | | | | | | | | % 148.11/21.21 | | | | | | | | | | | SIMP: (3366) implies: % 148.11/21.21 | | | | | | | | | | | (3367) all_8_0 = e3 % 148.11/21.21 | | | | | | | | | | | % 148.11/21.21 | | | | | | | | | | | REF_CLOSE: (9), (36), (41), (46), (47), (48), (51), (212), % 148.11/21.21 | | | | | | | | | | | (237), (242), (247), (252), (294), (295), (296), % 148.11/21.21 | | | | | | | | | | | (390), (425), (431), (443), (540), (541), (542), % 148.11/21.21 | | | | | | | | | | | (543), (545), (557), (579), (583), (590), (617), % 148.11/21.21 | | | | | | | | | | | (658), (769), (2647), (3365), (3367), % 148.11/21.21 | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 148.11/21.21 | | | | | | | | | | | #379. % 148.11/21.21 | | | | | | | | | | | % 148.11/21.21 | | | | | | | | | | End of split % 148.11/21.21 | | | | | | | | | | % 148.11/21.21 | | | | | | | | | Case 2: % 148.11/21.21 | | | | | | | | | | % 148.11/21.21 | | | | | | | | | | (3368) all_28_0 = e2 % 148.11/21.21 | | | | | | | | | | (3369) ~ (all_28_1 = e3) | ~ (all_28_2 = e0) % 148.11/21.21 | | | | | | | | | | % 148.11/21.21 | | | | | | | | | | COMBINE_EQS: (740), (3368) imply: % 148.11/21.21 | | | | | | | | | | (3370) all_6_0 = e2 % 148.11/21.21 | | | | | | | | | | % 148.11/21.21 | | | | | | | | | | SIMP: (3370) implies: % 148.11/21.21 | | | | | | | | | | (3371) all_6_0 = e2 % 148.11/21.21 | | | | | | | | | | % 148.11/21.21 | | | | | | | | | | REF_CLOSE: (6), (8), (36), (37), (38), (41), (42), (43), % 148.11/21.21 | | | | | | | | | | (46), (48), (51), (144), (158), (169), (171), % 148.11/21.21 | | | | | | | | | | (174), (208), (211), (237), (242), (247), (250), % 148.11/21.21 | | | | | | | | | | (252), (287), (288), (289), (290), (291), (292), % 148.11/21.21 | | | | | | | | | | (293), (294), (297), (321), (332), (333), (341), % 148.11/21.21 | | | | | | | | | | (357), (366), (374), (381), (386), (389), (401), % 148.11/21.21 | | | | | | | | | | (402), (407), (419), (435), (443), (459), (475), % 148.11/21.21 | | | | | | | | | | (513), (540), (541), (542), (543), (544), (545), % 148.11/21.21 | | | | | | | | | | (546), (547), (550), (551), (554), (555), (559), % 148.11/21.21 | | | | | | | | | | (565), (568), (569), (571), (573), (580), (582), % 148.11/21.21 | | | | | | | | | | (585), (588), (590), (620), (622), (627), (634), % 148.11/21.21 | | | | | | | | | | (665), (764), (768), (769), (3369), (3371), % 148.11/21.21 | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 148.11/21.21 | | | | | | | | | | #200. % 148.11/21.21 | | | | | | | | | | % 148.11/21.21 | | | | | | | | | End of split % 148.11/21.21 | | | | | | | | | % 148.11/21.21 | | | | | | | | Case 2: % 148.11/21.21 | | | | | | | | | % 148.11/21.21 | | | | | | | | | (3372) all_22_1 = e3 % 148.11/21.21 | | | | | | | | | (3373) ~ (all_22_0 = e0) | ~ (all_22_2 = e1) % 148.11/21.21 | | | | | | | | | % 148.11/21.21 | | | | | | | | | COMBINE_EQS: (672), (3372) imply: % 148.11/21.21 | | | | | | | | | (3374) all_8_1 = e3 % 148.11/21.21 | | | | | | | | | % 148.11/21.21 | | | | | | | | | SIMP: (3374) implies: % 148.11/21.21 | | | | | | | | | (3375) all_8_1 = e3 % 148.11/21.21 | | | | | | | | | % 148.11/21.21 | | | | | | | | | REDUCE: (48), (3375) imply: % 148.11/21.21 | | | | | | | | | (3376) op(all_8_2, all_8_2) = e3 % 148.11/21.21 | | | | | | | | | % 148.11/21.21 | | | | | | | | | REDUCE: (47), (3375) imply: % 148.11/21.21 | | | | | | | | | (3377) op(e2, e3) = all_8_0 % 148.11/21.21 | | | | | | | | | % 148.11/21.21 | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_1, % 148.11/21.21 | | | | | | | | | all_8_0, e3, e2, simplifying with (215), (3377) % 148.11/21.21 | | | | | | | | | gives: % 148.11/21.21 | | | | | | | | | (3378) all_52_1 = all_8_0 % 148.11/21.21 | | | | | | | | | % 148.11/21.21 | | | | | | | | | COMBINE_EQS: (463), (3378) imply: % 148.11/21.21 | | | | | | | | | (3379) all_54_4 = all_8_0 % 148.11/21.21 | | | | | | | | | % 148.11/21.21 | | | | | | | | | COMBINE_EQS: (425), (3378) imply: % 148.11/21.21 | | | | | | | | | (3380) all_56_9 = all_8_0 % 148.11/21.21 | | | | | | | | | % 148.11/21.21 | | | | | | | | | COMBINE_EQS: (401), (3378) imply: % 148.11/21.21 | | | | | | | | | (3381) all_58_2 = all_8_0 % 148.11/21.21 | | | | | | | | | % 148.11/21.21 | | | | | | | | | REDUCE: (197), (3378) imply: % 148.11/21.21 | | | | | | | | | (3382) ~ (all_52_2 = all_8_0) % 148.11/21.21 | | | | | | | | | % 148.11/21.21 | | | | | | | | | SIMP: (3382) implies: % 148.11/21.21 | | | | | | | | | (3383) ~ (all_52_2 = all_8_0) % 148.11/21.21 | | | | | | | | | % 148.11/21.21 | | | | | | | | | REDUCE: (196), (3378) imply: % 148.11/21.21 | | | | | | | | | (3384) ~ (all_52_3 = all_8_0) % 148.11/21.21 | | | | | | | | | % 148.11/21.21 | | | | | | | | | SIMP: (3384) implies: % 148.11/21.21 | | | | | | | | | (3385) ~ (all_52_3 = all_8_0) % 148.11/21.21 | | | | | | | | | % 148.11/21.21 | | | | | | | | | REDUCE: (194), (3378) imply: % 148.11/21.21 | | | | | | | | | (3386) ~ (all_52_9 = all_8_0) % 148.11/21.21 | | | | | | | | | % 148.11/21.21 | | | | | | | | | SIMP: (3386) implies: % 148.11/21.21 | | | | | | | | | (3387) ~ (all_52_9 = all_8_0) % 148.11/21.21 | | | | | | | | | % 148.11/21.21 | | | | | | | | | REDUCE: (193), (3378) imply: % 148.11/21.21 | | | | | | | | | (3388) ~ (all_52_13 = all_8_0) % 148.11/21.21 | | | | | | | | | % 148.11/21.21 | | | | | | | | | SIMP: (3388) implies: % 148.11/21.21 | | | | | | | | | (3389) ~ (all_52_13 = all_8_0) % 148.11/21.21 | | | | | | | | | % 148.11/21.21 | | | | | | | | | REDUCE: (557), (3378) imply: % 148.11/21.21 | | | | | | | | | (3390) ~ (all_10_2 = all_8_0) % 148.11/21.21 | | | | | | | | | % 148.11/21.21 | | | | | | | | | SIMP: (3390) implies: % 148.11/21.21 | | | | | | | | | (3391) ~ (all_10_2 = all_8_0) % 148.11/21.21 | | | | | | | | | % 148.11/21.21 | | | | | | | | | REDUCE: (568), (3378) imply: % 148.11/21.21 | | | | | | | | | (3392) ~ (all_8_0 = all_8_2) % 148.11/21.21 | | | | | | | | | % 148.11/21.21 | | | | | | | | | BETA: splitting (99) gives: % 148.11/21.21 | | | | | | | | | % 148.11/21.21 | | | | | | | | | Case 1: % 148.11/21.21 | | | | | | | | | | % 148.11/21.21 | | | | | | | | | | (3393) ~ (all_28_0 = e2) % 148.11/21.21 | | | | | | | | | | % 148.11/21.21 | | | | | | | | | | REDUCE: (740), (3393) imply: % 148.11/21.21 | | | | | | | | | | (3394) ~ (all_6_0 = e2) % 148.11/21.21 | | | | | | | | | | % 148.11/21.21 | | | | | | | | | | BETA: splitting (109) gives: % 148.11/21.21 | | | | | | | | | | % 148.11/21.21 | | | | | | | | | | Case 1: % 148.11/21.21 | | | | | | | | | | | % 148.11/21.21 | | | | | | | | | | | (3395) ~ (all_32_1 = e1) % 148.11/21.21 | | | | | | | | | | | % 148.11/21.21 | | | | | | | | | | | REDUCE: (682), (3395) imply: % 148.11/21.21 | | | | | | | | | | | (3396) ~ (all_10_1 = e1) % 148.11/21.21 | | | | | | | | | | | % 148.11/21.21 | | | | | | | | | | | BETA: splitting (114) gives: % 148.11/21.21 | | | | | | | | | | | % 148.11/21.21 | | | | | | | | | | | Case 1: % 148.11/21.21 | | | | | | | | | | | | % 148.11/21.21 | | | | | | | | | | | | (3397) ~ (all_34_0 = e2) % 148.11/21.21 | | | | | | | | | | | | % 148.11/21.21 | | | | | | | | | | | | REDUCE: (2639), (3397) imply: % 148.11/21.21 | | | | | | | | | | | | (3398) $false % 148.11/21.21 | | | | | | | | | | | | % 148.11/21.21 | | | | | | | | | | | | CLOSE: (3398) is inconsistent. % 148.11/21.21 | | | | | | | | | | | | % 148.11/21.21 | | | | | | | | | | | Case 2: % 148.11/21.21 | | | | | | | | | | | | % 148.11/21.21 | | | | | | | | | | | | (3399) ~ (all_34_1 = e3) | ~ (all_34_2 = e1) % 148.11/21.21 | | | | | | | | | | | | % 148.11/21.21 | | | | | | | | | | | | BETA: splitting (119) gives: % 148.11/21.21 | | | | | | | | | | | | % 148.11/21.21 | | | | | | | | | | | | Case 1: % 148.11/21.21 | | | | | | | | | | | | | % 148.11/21.21 | | | | | | | | | | | | | (3400) ~ (all_36_1 = e3) % 148.11/21.21 | | | | | | | | | | | | | % 148.11/21.21 | | | | | | | | | | | | | REDUCE: (652), (3400) imply: % 148.11/21.21 | | | | | | | | | | | | | (3401) ~ (all_6_1 = e3) % 148.11/21.21 | | | | | | | | | | | | | % 148.11/21.21 | | | | | | | | | | | | | BETA: splitting (129) gives: % 148.11/21.21 | | | | | | | | | | | | | % 148.11/21.21 | | | | | | | | | | | | | Case 1: % 148.11/21.21 | | | | | | | | | | | | | | % 148.11/21.21 | | | | | | | | | | | | | | (3402) ~ (all_40_0 = e3) % 148.11/21.21 | | | | | | | | | | | | | | % 148.11/21.21 | | | | | | | | | | | | | | REDUCE: (713), (3402) imply: % 148.11/21.21 | | | | | | | | | | | | | | (3403) ~ (all_6_0 = e3) % 148.11/21.21 | | | | | | | | | | | | | | % 148.11/21.21 | | | | | | | | | | | | | | BETA: splitting (288) gives: % 148.11/21.21 | | | | | | | | | | | | | | % 148.11/21.21 | | | | | | | | | | | | | | Case 1: % 148.11/21.21 | | | | | | | | | | | | | | | % 148.11/21.21 | | | | | | | | | | | | | | | (3404) ~ (all_56_31 = e1) % 148.11/21.21 | | | | | | | | | | | | | | | % 148.11/21.21 | | | | | | | | | | | | | | | REDUCE: (544), (3404) imply: % 148.11/21.21 | | | | | | | | | | | | | | | (3405) ~ (all_4_2 = e1) % 148.11/21.21 | | | | | | | | | | | | | | | % 148.11/21.21 | | | | | | | | | | | | | | | REF_CLOSE: (4), (36), (38), (42), (43), (46), (51), (166), % 148.11/21.21 | | | | | | | | | | | | | | | (169), (173), (189), (205), (207), (208), (237), % 148.11/21.21 | | | | | | | | | | | | | | | (238), (241), (242), (247), (248), (252), (287), % 148.11/21.21 | | | | | | | | | | | | | | | (289), (290), (291), (292), (293), (294), (295), % 148.11/21.21 | | | | | | | | | | | | | | | (296), (298), (321), (333), (342), (360), (365), % 148.11/21.21 | | | | | | | | | | | | | | | (366), (374), (381), (386), (389), (419), (429), % 148.11/21.21 | | | | | | | | | | | | | | | (431), (435), (443), (447), (476), (482), (529), % 148.11/21.21 | | | | | | | | | | | | | | | (540), (541), (542), (543), (544), (545), (546), % 148.11/21.21 | | | | | | | | | | | | | | | (547), (550), (551), (553), (554), (559), (561), % 148.11/21.21 | | | | | | | | | | | | | | | (569), (573), (575), (579), (580), (583), (585), % 148.11/21.21 | | | | | | | | | | | | | | | (587), (588), (591), (617), (624), (625), (627), % 148.11/21.21 | | | | | | | | | | | | | | | (681), (768), (2637), (2641), (2643), (3376), % 148.11/21.21 | | | | | | | | | | | | | | | (3379), (3380), (3381), (3385), (3389), (3391), % 148.11/21.21 | | | | | | | | | | | | | | | (3392), (3394), (3401), (3405), (function-axioms) % 148.11/21.21 | | | | | | | | | | | | | | | are inconsistent by sub-proof #194. % 148.11/21.21 | | | | | | | | | | | | | | | % 148.11/21.21 | | | | | | | | | | | | | | Case 2: % 148.11/21.21 | | | | | | | | | | | | | | | % 148.11/21.21 | | | | | | | | | | | | | | | (3406) all_56_31 = e1 % 148.11/21.21 | | | | | | | | | | | | | | | (3407) all_56_29 = e0 % 148.11/21.21 | | | | | | | | | | | | | | | % 148.11/21.21 | | | | | | | | | | | | | | | COMBINE_EQS: (357), (3407) imply: % 148.11/21.21 | | | | | | | | | | | | | | | (3408) all_52_11 = e0 % 148.11/21.21 | | | | | | | | | | | | | | | % 148.11/21.21 | | | | | | | | | | | | | | | SIMP: (3408) implies: % 148.11/21.21 | | | | | | | | | | | | | | | (3409) all_52_11 = e0 % 148.11/21.21 | | | | | | | | | | | | | | | % 148.11/21.21 | | | | | | | | | | | | | | | COMBINE_EQS: (544), (3406) imply: % 148.11/21.21 | | | | | | | | | | | | | | | (3410) all_4_2 = e1 % 148.11/21.21 | | | | | | | | | | | | | | | % 148.11/21.21 | | | | | | | | | | | | | | | COMBINE_EQS: (531), (3410) imply: % 148.11/21.21 | | | | | | | | | | | | | | | (3411) all_34_2 = e1 % 148.11/21.21 | | | | | | | | | | | | | | | % 148.11/21.21 | | | | | | | | | | | | | | | COMBINE_EQS: (548), (3409) imply: % 148.11/21.21 | | | | | | | | | | | | | | | (3412) all_58_14 = e0 % 148.11/21.21 | | | | | | | | | | | | | | | % 148.11/21.21 | | | | | | | | | | | | | | | REDUCE: (581), (3410) imply: % 148.11/21.21 | | | | | | | | | | | | | | | (3413) ~ (all_52_7 = e1) % 148.11/21.21 | | | | | | | | | | | | | | | % 148.11/21.21 | | | | | | | | | | | | | | | REDUCE: (166), (3409) imply: % 148.11/21.21 | | | | | | | | | | | | | | | (3414) ~ (all_52_9 = e0) % 148.11/21.21 | | | | | | | | | | | | | | | % 148.11/21.21 | | | | | | | | | | | | | | | REDUCE: (585), (3409) imply: % 148.11/21.21 | | | | | | | | | | | | | | | (3415) ~ (all_6_2 = e0) % 148.11/21.21 | | | | | | | | | | | | | | | % 148.11/21.21 | | | | | | | | | | | | | | | SIMP: (3415) implies: % 148.11/21.21 | | | | | | | | | | | | | | | (3416) ~ (all_6_2 = e0) % 148.11/21.21 | | | | | | | | | | | | | | | % 148.11/21.21 | | | | | | | | | | | | | | | REDUCE: (588), (3409), (3410) imply: % 148.11/21.21 | | | | | | | | | | | | | | | (3417) ~ (e1 = e0) % 148.11/21.21 | | | | | | | | | | | | | | | % 148.11/21.21 | | | | | | | | | | | | | | | REDUCE: (589), (3410) imply: % 148.11/21.21 | | | | | | | | | | | | | | | (3418) ~ (all_52_12 = e1) % 148.11/21.21 | | | | | | | | | | | | | | | % 148.11/21.21 | | | | | | | | | | | | | | | REDUCE: (590), (3410) imply: % 148.11/21.21 | | | | | | | | | | | | | | | (3419) ~ (all_52_13 = e1) % 148.11/21.21 | | | | | | | | | | | | | | | % 148.11/21.21 | | | | | | | | | | | | | | | REDUCE: (38), (3410) imply: % 148.11/21.21 | | | | | | | | | | | | | | | (3420) op(e1, e1) = all_4_1 % 148.11/21.21 | | | | | | | | | | | | | | | % 148.11/21.21 | | | | | | | | | | | | | | | REDUCE: (36), (3410) imply: % 148.11/21.21 | | | | | | | | | | | | | | | (3421) op(e0, e0) = e1 % 148.11/21.21 | | | | | | | | | | | | | | | % 148.11/21.21 | | | | | | | | | | | | | | | BETA: splitting (3399) gives: % 148.11/21.21 | | | | | | | | | | | | | | | % 148.11/21.21 | | | | | | | | | | | | | | | Case 1: % 148.11/21.21 | | | | | | | | | | | | | | | | % 148.11/21.21 | | | | | | | | | | | | | | | | (3422) ~ (all_34_1 = e3) % 148.11/21.21 | | | | | | | | | | | | | | | | % 148.11/21.21 | | | | | | | | | | | | | | | | REDUCE: (683), (3422) imply: % 148.11/21.21 | | | | | | | | | | | | | | | | (3423) ~ (all_4_1 = e3) % 148.11/21.21 | | | | | | | | | | | | | | | | % 148.11/21.21 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_6_2, % 148.11/21.21 | | | | | | | | | | | | | | | | all_4_1, e1, e1, simplifying with (41), (3420) % 148.11/21.21 | | | | | | | | | | | | | | | | gives: % 148.11/21.21 | | | | | | | | | | | | | | | | (3424) all_6_2 = all_4_1 % 148.11/21.21 | | | | | | | | | | | | | | | | % 148.11/21.21 | | | | | | | | | | | | | | | | COMBINE_EQS: (541), (3424) imply: % 148.11/21.21 | | | | | | | | | | | | | | | | (3425) all_54_10 = all_4_1 % 148.11/21.21 | | | | | | | | | | | | | | | | % 148.11/21.21 | | | | | | | | | | | | | | | | COMBINE_EQS: (374), (3424) imply: % 148.11/21.21 | | | | | | | | | | | | | | | | (3426) all_56_21 = all_4_1 % 148.11/21.21 | | | | | | | | | | | | | | | | % 148.11/21.21 | | | | | | | | | | | | | | | | COMBINE_EQS: (552), (3424) imply: % 148.11/21.21 | | | | | | | | | | | | | | | | (3427) all_58_8 = all_4_1 % 148.11/21.21 | | | | | | | | | | | | | | | | % 148.11/21.21 | | | | | | | | | | | | | | | | REDUCE: (580), (3424) imply: % 148.11/21.21 | | | | | | | | | | | | | | | | (3428) ~ (all_52_6 = all_4_1) % 148.11/21.21 | | | | | | | | | | | | | | | | % 148.11/21.21 | | | | | | | | | | | | | | | | REDUCE: (582), (3424) imply: % 148.11/21.21 | | | | | | | | | | | | | | | | (3429) ~ (all_52_8 = all_4_1) % 148.11/21.21 | | | | | | | | | | | | | | | | % 148.11/21.21 | | | | | | | | | | | | | | | | REDUCE: (583), (3424) imply: % 148.11/21.21 | | | | | | | | | | | | | | | | (3430) ~ (all_52_9 = all_4_1) % 148.11/21.21 | | | | | | | | | | | | | | | | % 148.11/21.21 | | | | | | | | | | | | | | | | REDUCE: (3416), (3424) imply: % 148.11/21.21 | | | | | | | | | | | | | | | | (3431) ~ (all_4_1 = e0) % 148.11/21.21 | | | | | | | | | | | | | | | | % 148.11/21.21 | | | | | | | | | | | | | | | | REDUCE: (43), (3424) imply: % 148.11/21.21 | | | | | | | | | | | | | | | | (3432) op(all_4_1, all_4_1) = all_6_1 % 148.11/21.21 | | | | | | | | | | | | | | | | % 148.11/21.21 | | | | | | | | | | | | | | | | REDUCE: (622), (3424) imply: % 148.11/21.21 | | | | | | | | | | | | | | | | (3433) op(e1, all_4_1) = all_56_20 % 148.11/21.21 | | | | | | | | | | | | | | | | % 148.11/21.21 | | | | | | | | | | | | | | | | BETA: splitting (294) gives: % 148.11/21.21 | | | | | | | | | | | | | | | | % 148.11/21.21 | | | | | | | | | | | | | | | | Case 1: % 148.11/21.21 | | | | | | | | | | | | | | | | | % 148.11/21.21 | | | | | | | | | | | | | | | | | (3434) ~ (all_56_11 = e0) % 148.11/21.21 | | | | | | | | | | | | | | | | | % 148.11/21.21 | | | | | | | | | | | | | | | | | REDUCE: (545), (3434) imply: % 148.11/21.21 | | | | | | | | | | | | | | | | | (3435) ~ (all_8_2 = e0) % 148.11/21.21 | | | | | | | | | | | | | | | | | % 148.11/21.21 | | | | | | | | | | | | | | | | | BETA: splitting (292) gives: % 148.11/21.21 | | | | | | | | | | | | | | | | | % 148.11/21.21 | | | | | | | | | | | | | | | | | Case 1: % 148.11/21.21 | | | | | | | | | | | | | | | | | | % 148.11/21.21 | | | | | | | | | | | | | | | | | | (3436) ~ (all_56_21 = e2) % 148.11/21.21 | | | | | | | | | | | | | | | | | | % 148.11/21.21 | | | | | | | | | | | | | | | | | | REDUCE: (3426), (3436) imply: % 148.11/21.21 | | | | | | | | | | | | | | | | | | (3437) ~ (all_4_1 = e2) % 148.11/21.21 | | | | | | | | | | | | | | | | | | % 148.11/21.21 | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (42), (48), (53), (161), (165), (168), (181), % 148.11/21.21 | | | | | | | | | | | | | | | | | | (194), (242), (245), (246), (247), (249), (252), % 148.11/21.21 | | | | | | | | | | | | | | | | | | (295), (296), (297), (298), (299), (330), (331), % 148.11/21.21 | | | | | | | | | | | | | | | | | | (332), (333), (337), (343), (380), (386), (389), % 148.11/21.21 | | | | | | | | | | | | | | | | | | (401), (402), (407), (408), (419), (425), (431), % 148.11/21.21 | | | | | | | | | | | | | | | | | | (461), (467), (469), (542), (543), (545), (546), % 148.11/21.21 | | | | | | | | | | | | | | | | | | (549), (551), (554), (555), (557), (563), (567), % 148.11/21.21 | | | | | | | | | | | | | | | | | | (571), (577), (579), (625), (769), (3396), (3403), % 148.11/21.21 | | | | | | | | | | | | | | | | | | (3412), (3413), (3414), (3418), (3419), (3420), % 148.11/21.21 | | | | | | | | | | | | | | | | | | (3421), (3423), (3425), (3427), (3428), (3429), % 148.11/21.21 | | | | | | | | | | | | | | | | | | (3430), (3431), (3432), (3433), (3435), (3437), % 148.11/21.21 | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 148.11/21.21 | | | | | | | | | | | | | | | | | | #525. % 148.11/21.21 | | | | | | | | | | | | | | | | | | % 148.11/21.21 | | | | | | | | | | | | | | | | | Case 2: % 148.11/21.21 | | | | | | | | | | | | | | | | | | % 148.11/21.21 | | | | | | | | | | | | | | | | | | (3438) all_56_21 = e2 % 148.11/21.21 | | | | | | | | | | | | | | | | | | (3439) all_56_19 = e1 % 148.11/21.21 | | | | | | | | | | | | | | | | | | % 148.11/21.21 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (435), (3439) imply: % 148.11/21.21 | | | | | | | | | | | | | | | | | | (3440) all_52_6 = e1 % 148.11/21.21 | | | | | | | | | | | | | | | | | | % 148.11/21.21 | | | | | | | | | | | | | | | | | | SIMP: (3440) implies: % 148.11/21.21 | | | | | | | | | | | | | | | | | | (3441) all_52_6 = e1 % 148.11/21.21 | | | | | | | | | | | | | | | | | | % 148.11/21.21 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3426), (3438) imply: % 148.11/21.21 | | | | | | | | | | | | | | | | | | (3442) all_4_1 = e2 % 148.11/21.21 | | | | | | | | | | | | | | | | | | % 148.11/21.21 | | | | | | | | | | | | | | | | | | SIMP: (3442) implies: % 148.11/21.21 | | | | | | | | | | | | | | | | | | (3443) all_4_1 = e2 % 148.11/21.21 | | | | | | | | | | | | | | | | | | % 148.11/21.21 | | | | | | | | | | | | | | | | | | REDUCE: (573), (3441) imply: % 148.11/21.21 | | | | | | | | | | | | | | | | | | (3444) ~ (all_8_2 = e1) % 148.11/21.21 | | | | | | | | | | | | | | | | | | % 148.11/21.21 | | | | | | | | | | | | | | | | | | SIMP: (3444) implies: % 148.11/21.21 | | | | | | | | | | | | | | | | | | (3445) ~ (all_8_2 = e1) % 148.11/21.21 | | | | | | | | | | | | | | | | | | % 148.11/21.21 | | | | | | | | | | | | | | | | | | REDUCE: (3428), (3441), (3443) imply: % 148.11/21.21 | | | | | | | | | | | | | | | | | | (3446) ~ (e2 = e1) % 148.11/21.21 | | | | | | | | | | | | | | | | | | % 148.11/21.21 | | | | | | | | | | | | | | | | | | REDUCE: (3432), (3443) imply: % 148.11/21.21 | | | | | | | | | | | | | | | | | | (3447) op(e2, e2) = all_6_1 % 148.11/21.21 | | | | | | | | | | | | | | | | | | % 148.11/21.21 | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (36), (38), (46), (247), (248), (287), (294), % 148.11/21.21 | | | | | | | | | | | | | | | | | | (333), (374), (386), (389), (443), (542), (544), % 148.11/21.21 | | | | | | | | | | | | | | | | | | (545), (546), (554), (579), (583), (627), (768), % 148.11/21.21 | | | | | | | | | | | | | | | | | | (2643), (3376), (3379), (3381), (3389), (3391), % 148.11/21.21 | | | | | | | | | | | | | | | | | | (3392), (3401), (3445), (3447), (function-axioms) % 148.11/21.21 | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #335. % 148.11/21.21 | | | | | | | | | | | | | | | | | | % 148.11/21.21 | | | | | | | | | | | | | | | | | End of split % 148.11/21.21 | | | | | | | | | | | | | | | | | % 148.11/21.21 | | | | | | | | | | | | | | | | Case 2: % 148.11/21.21 | | | | | | | | | | | | | | | | | % 148.11/21.21 | | | | | | | | | | | | | | | | | (3448) all_56_15 = e2 % 148.11/21.21 | | | | | | | | | | | | | | | | | (3449) all_56_11 = e0 % 148.11/21.21 | | | | | | | | | | | | | | | | | % 148.11/21.21 | | | | | | | | | | | | | | | | | COMBINE_EQS: (545), (3449) imply: % 148.11/21.21 | | | | | | | | | | | | | | | | | (3450) all_8_2 = e0 % 148.11/21.21 | | | | | | | | | | | | | | | | | % 148.11/21.21 | | | | | | | | | | | | | | | | | COMBINE_EQS: (443), (3448) imply: % 148.11/21.21 | | | | | | | | | | | | | | | | | (3451) all_52_13 = e2 % 148.11/21.21 | | | | | | | | | | | | | | | | | % 148.11/21.21 | | | | | | | | | | | | | | | | | COMBINE_EQS: (386), (3451) imply: % 148.11/21.21 | | | | | | | | | | | | | | | | | (3452) all_58_10 = e2 % 148.11/21.21 | | | | | | | | | | | | | | | | | % 148.11/21.21 | | | | | | | | | | | | | | | | | COMBINE_EQS: (554), (3450) imply: % 148.11/21.21 | | | | | | | | | | | | | | | | | (3453) all_58_3 = e0 % 148.11/21.21 | | | | | | | | | | | | | | | | | % 148.11/21.21 | | | | | | | | | | | | | | | | | REDUCE: (3389), (3451) imply: % 148.11/21.21 | | | | | | | | | | | | | | | | | (3454) ~ (all_8_0 = e2) % 148.11/21.21 | | | | | | | | | | | | | | | | | % 148.11/21.21 | | | | | | | | | | | | | | | | | SIMP: (3454) implies: % 148.11/21.21 | | | | | | | | | | | | | | | | | (3455) ~ (all_8_0 = e2) % 148.11/21.21 | | | | | | | | | | | | | | | | | % 148.11/21.21 | | | | | | | | | | | | | | | | | REDUCE: (3392), (3450) imply: % 148.11/21.21 | | | | | | | | | | | | | | | | | (3456) ~ (all_8_0 = e0) % 148.11/21.21 | | | | | | | | | | | | | | | | | % 148.11/21.21 | | | | | | | | | | | | | | | | | REDUCE: (3376), (3450) imply: % 148.11/21.21 | | | | | | | | | | | | | | | | | (3457) op(e0, e0) = e3 % 148.11/21.21 | | | | | | | | | | | | | | | | | % 148.11/21.21 | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (36), (38), (248), (287), (333), % 148.11/21.21 | | | | | | | | | | | | | | | | | (374), (389), (544), (546), (583), (627), (2643), % 148.11/21.21 | | | | | | | | | | | | | | | | | (3379), (3381), (3391), (3449), (3452), (3453), % 148.11/21.21 | | | | | | | | | | | | | | | | | (3455), (3456), (3457), (function-axioms) are % 148.11/21.21 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #337. % 148.11/21.21 | | | | | | | | | | | | | | | | | % 148.11/21.21 | | | | | | | | | | | | | | | | End of split % 148.11/21.21 | | | | | | | | | | | | | | | | % 148.11/21.21 | | | | | | | | | | | | | | | Case 2: % 148.11/21.21 | | | | | | | | | | | | | | | | % 148.11/21.21 | | | | | | | | | | | | | | | | (3458) ~ (all_34_2 = e1) % 148.11/21.21 | | | | | | | | | | | | | | | | % 148.11/21.21 | | | | | | | | | | | | | | | | REDUCE: (3411), (3458) imply: % 148.11/21.21 | | | | | | | | | | | | | | | | (3459) $false % 148.11/21.21 | | | | | | | | | | | | | | | | % 148.11/21.22 | | | | | | | | | | | | | | | | CLOSE: (3459) is inconsistent. % 148.11/21.22 | | | | | | | | | | | | | | | | % 148.11/21.22 | | | | | | | | | | | | | | | End of split % 148.11/21.22 | | | | | | | | | | | | | | | % 148.11/21.22 | | | | | | | | | | | | | | End of split % 148.11/21.22 | | | | | | | | | | | | | | % 148.11/21.22 | | | | | | | | | | | | | Case 2: % 148.11/21.22 | | | | | | | | | | | | | | % 148.11/21.22 | | | | | | | | | | | | | | (3460) all_40_0 = e3 % 148.11/21.22 | | | | | | | | | | | | | | (3461) ~ (all_40_1 = e0) | ~ (all_40_2 = e2) % 148.11/21.22 | | | | | | | | | | | | | | % 148.11/21.22 | | | | | | | | | | | | | | COMBINE_EQS: (713), (3460) imply: % 148.11/21.22 | | | | | | | | | | | | | | (3462) all_6_0 = e3 % 148.11/21.22 | | | | | | | | | | | | | | % 148.11/21.22 | | | | | | | | | | | | | | SIMP: (3462) implies: % 148.11/21.22 | | | | | | | | | | | | | | (3463) all_6_0 = e3 % 148.11/21.22 | | | | | | | | | | | | | | % 148.11/21.22 | | | | | | | | | | | | | | REDUCE: (42), (3463) imply: % 148.11/21.22 | | | | | | | | | | | | | | (3464) op(e1, all_6_1) = e3 % 148.11/21.22 | | | | | | | | | | | | | | % 148.11/21.22 | | | | | | | | | | | | | | BETA: splitting (288) gives: % 148.11/21.22 | | | | | | | | | | | | | | % 148.11/21.22 | | | | | | | | | | | | | | Case 1: % 148.11/21.22 | | | | | | | | | | | | | | | % 148.11/21.22 | | | | | | | | | | | | | | | (3465) ~ (all_56_31 = e1) % 148.11/21.22 | | | | | | | | | | | | | | | % 148.11/21.22 | | | | | | | | | | | | | | | REDUCE: (544), (3465) imply: % 148.11/21.22 | | | | | | | | | | | | | | | (3466) ~ (all_4_2 = e1) % 148.11/21.22 | | | | | | | | | | | | | | | % 148.11/21.22 | | | | | | | | | | | | | | | REF_CLOSE: (4), (36), (38), (42), (43), (46), (51), (166), % 148.11/21.22 | | | | | | | | | | | | | | | (169), (173), (189), (205), (207), (208), (237), % 148.11/21.22 | | | | | | | | | | | | | | | (238), (241), (242), (247), (248), (252), (287), % 148.11/21.22 | | | | | | | | | | | | | | | (289), (290), (291), (292), (293), (294), (295), % 148.11/21.22 | | | | | | | | | | | | | | | (296), (298), (321), (333), (342), (360), (365), % 148.11/21.22 | | | | | | | | | | | | | | | (366), (374), (381), (386), (389), (419), (429), % 148.11/21.22 | | | | | | | | | | | | | | | (431), (435), (443), (447), (476), (482), (529), % 148.11/21.22 | | | | | | | | | | | | | | | (540), (541), (542), (543), (544), (545), (546), % 148.11/21.22 | | | | | | | | | | | | | | | (547), (550), (551), (553), (554), (559), (561), % 148.11/21.22 | | | | | | | | | | | | | | | (569), (573), (575), (579), (580), (583), (585), % 148.11/21.22 | | | | | | | | | | | | | | | (587), (588), (591), (617), (624), (625), (627), % 148.11/21.22 | | | | | | | | | | | | | | | (681), (768), (2637), (2641), (2643), (3376), % 148.11/21.22 | | | | | | | | | | | | | | | (3379), (3380), (3381), (3385), (3389), (3391), % 148.11/21.22 | | | | | | | | | | | | | | | (3392), (3394), (3401), (3466), (function-axioms) % 148.11/21.22 | | | | | | | | | | | | | | | are inconsistent by sub-proof #194. % 148.11/21.22 | | | | | | | | | | | | | | | % 148.11/21.22 | | | | | | | | | | | | | | Case 2: % 148.11/21.22 | | | | | | | | | | | | | | | % 148.11/21.22 | | | | | | | | | | | | | | | (3467) all_56_31 = e1 % 148.11/21.22 | | | | | | | | | | | | | | | (3468) all_56_29 = e0 % 148.11/21.22 | | | | | | | | | | | | | | | % 148.11/21.22 | | | | | | | | | | | | | | | REF_CLOSE: (38), (41), (43), (46), (242), (247), (292), % 148.11/21.22 | | | | | | | | | | | | | | | (357), (374), (435), (507), (531), (541), (542), % 148.11/21.22 | | | | | | | | | | | | | | | (544), (573), (585), (622), (683), (685), (768), % 148.11/21.22 | | | | | | | | | | | | | | | (3399), (3401), (3461), (3464), (3467), (3468), % 148.11/21.22 | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 148.11/21.22 | | | | | | | | | | | | | | | #193. % 148.11/21.22 | | | | | | | | | | | | | | | % 148.11/21.22 | | | | | | | | | | | | | | End of split % 148.11/21.22 | | | | | | | | | | | | | | % 148.11/21.22 | | | | | | | | | | | | | End of split % 148.11/21.22 | | | | | | | | | | | | | % 148.11/21.22 | | | | | | | | | | | | Case 2: % 148.11/21.22 | | | | | | | | | | | | | % 148.11/21.22 | | | | | | | | | | | | | (3469) all_36_1 = e3 % 148.11/21.22 | | | | | | | | | | | | | (3470) ~ (all_36_0 = e0) | ~ (all_36_2 = e2) % 148.11/21.22 | | | | | | | | | | | | | % 148.11/21.22 | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (36), (38), (41), (42), (43), (46), % 148.11/21.22 | | | | | | | | | | | | | (48), (51), (165), (174), (189), (191), (207), % 148.11/21.22 | | | | | | | | | | | | | (211), (242), (243), (244), (245), (247), (248), % 148.11/21.22 | | | | | | | | | | | | | (287), (290), (291), (292), (293), (294), (295), % 148.11/21.22 | | | | | | | | | | | | | (296), (320), (324), (331), (332), (333), (365), % 148.11/21.22 | | | | | | | | | | | | | (366), (374), (380), (381), (386), (389), (407), % 148.11/21.22 | | | | | | | | | | | | | (431), (435), (443), (447), (469), (471), (473), % 148.11/21.22 | | | | | | | | | | | | | (523), (532), (541), (542), (544), (545), (546), % 148.11/21.22 | | | | | | | | | | | | | (547), (548), (549), (550), (552), (553), (554), % 148.11/21.22 | | | | | | | | | | | | | (559), (561), (565), (569), (573), (575), (577), % 148.11/21.22 | | | | | | | | | | | | | (579), (580), (583), (585), (587), (588), (590), % 148.11/21.22 | | | | | | | | | | | | | (591), (617), (622), (627), (652), (752), (762), % 148.11/21.22 | | | | | | | | | | | | | (2641), (2643), (3373), (3376), (3379), (3380), % 148.11/21.22 | | | | | | | | | | | | | (3381), (3383), (3385), (3387), (3389), (3391), % 148.11/21.22 | | | | | | | | | | | | | (3392), (3469), (3470), (function-axioms) are % 148.11/21.22 | | | | | | | | | | | | | inconsistent by sub-proof #191. % 148.11/21.22 | | | | | | | | | | | | | % 148.11/21.22 | | | | | | | | | | | | End of split % 148.11/21.22 | | | | | | | | | | | | % 148.11/21.22 | | | | | | | | | | | End of split % 148.11/21.22 | | | | | | | | | | | % 148.11/21.22 | | | | | | | | | | Case 2: % 148.11/21.22 | | | | | | | | | | | % 148.11/21.22 | | | | | | | | | | | (3471) all_32_1 = e1 % 148.11/21.22 | | | | | | | | | | | (3472) ~ (all_32_0 = e0) | ~ (all_32_2 = e2) % 148.11/21.22 | | | | | | | | | | | % 148.11/21.22 | | | | | | | | | | | COMBINE_EQS: (682), (3471) imply: % 148.11/21.22 | | | | | | | | | | | (3473) all_10_1 = e1 % 148.11/21.22 | | | | | | | | | | | % 148.11/21.22 | | | | | | | | | | | REDUCE: (53), (3473) imply: % 148.11/21.22 | | | | | | | | | | | (3474) op(all_10_2, all_10_2) = e1 % 148.11/21.22 | | | | | | | | | | | % 148.11/21.22 | | | | | | | | | | | REDUCE: (52), (3473) imply: % 148.11/21.22 | | | | | | | | | | | (3475) op(e3, e1) = all_10_0 % 148.11/21.22 | | | | | | | | | | | % 148.11/21.22 | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_8, % 148.11/21.22 | | | | | | | | | | | all_10_0, e1, e3, simplifying with (217), (3475) % 148.11/21.22 | | | | | | | | | | | gives: % 148.11/21.22 | | | | | | | | | | | (3476) all_52_8 = all_10_0 % 148.11/21.22 | | | | | | | | | | | % 148.11/21.22 | | | | | | | | | | | COMBINE_EQS: (459), (3476) imply: % 148.11/21.22 | | | | | | | | | | | (3477) all_54_2 = all_10_0 % 148.11/21.22 | | | | | | | | | | | % 148.11/21.22 | | | | | | | | | | | COMBINE_EQS: (429), (3476) imply: % 148.11/21.22 | | | | | | | | | | | (3478) all_56_5 = all_10_0 % 148.11/21.22 | | | | | | | | | | | % 148.11/21.22 | | | | | | | | | | | COMBINE_EQS: (407), (3476) imply: % 148.11/21.22 | | | | | | | | | | | (3479) all_58_4 = all_10_0 % 148.11/21.22 | | | | | | | | | | | % 148.11/21.22 | | | | | | | | | | | REDUCE: (182), (3476) imply: % 148.11/21.22 | | | | | | | | | | | (3480) ~ (all_52_4 = all_10_0) % 148.11/21.22 | | | | | | | | | | | % 148.11/21.22 | | | | | | | | | | | REDUCE: (169), (3476) imply: % 148.11/21.22 | | | | | | | | | | | (3481) ~ (all_52_11 = all_10_0) % 148.11/21.22 | | | | | | | | | | | % 148.11/21.22 | | | | | | | | | | | SIMP: (3481) implies: % 148.11/21.22 | | | | | | | | | | | (3482) ~ (all_52_11 = all_10_0) % 148.11/21.22 | | | | | | | | | | | % 148.11/21.22 | | | | | | | | | | | REDUCE: (168), (3476) imply: % 148.11/21.22 | | | | | | | | | | | (3483) ~ (all_52_12 = all_10_0) % 148.11/21.22 | | | | | | | | | | | % 148.11/21.22 | | | | | | | | | | | SIMP: (3483) implies: % 148.11/21.22 | | | | | | | | | | | (3484) ~ (all_52_12 = all_10_0) % 148.11/21.22 | | | | | | | | | | | % 148.11/21.22 | | | | | | | | | | | REDUCE: (565), (3476) imply: % 148.11/21.22 | | | | | | | | | | | (3485) ~ (all_10_0 = all_10_2) % 148.11/21.22 | | | | | | | | | | | % 148.11/21.22 | | | | | | | | | | | REDUCE: (582), (3476) imply: % 148.11/21.22 | | | | | | | | | | | (3486) ~ (all_10_0 = all_6_2) % 148.11/21.22 | | | | | | | | | | | % 148.11/21.22 | | | | | | | | | | | BETA: splitting (119) gives: % 148.11/21.22 | | | | | | | | | | | % 148.11/21.22 | | | | | | | | | | | Case 1: % 148.11/21.22 | | | | | | | | | | | | % 148.11/21.22 | | | | | | | | | | | | (3487) ~ (all_36_1 = e3) % 148.11/21.22 | | | | | | | | | | | | % 148.11/21.22 | | | | | | | | | | | | REDUCE: (652), (3487) imply: % 148.11/21.22 | | | | | | | | | | | | (3488) ~ (all_6_1 = e3) % 148.11/21.22 | | | | | | | | | | | | % 148.11/21.22 | | | | | | | | | | | | BETA: splitting (288) gives: % 148.11/21.22 | | | | | | | | | | | | % 148.11/21.22 | | | | | | | | | | | | Case 1: % 148.11/21.22 | | | | | | | | | | | | | % 148.11/21.22 | | | | | | | | | | | | | (3489) ~ (all_56_31 = e1) % 148.11/21.22 | | | | | | | | | | | | | % 148.11/21.22 | | | | | | | | | | | | | REDUCE: (544), (3489) imply: % 148.11/21.22 | | | | | | | | | | | | | (3490) ~ (all_4_2 = e1) % 148.11/21.22 | | | | | | | | | | | | | % 148.11/21.22 | | | | | | | | | | | | | REF_CLOSE: (4), (36), (38), (42), (43), (46), (51), (166), % 148.11/21.22 | | | | | | | | | | | | | (169), (173), (189), (205), (207), (208), (237), % 148.11/21.22 | | | | | | | | | | | | | (238), (241), (242), (247), (248), (252), (287), % 148.11/21.22 | | | | | | | | | | | | | (289), (290), (291), (292), (293), (294), (295), % 148.11/21.22 | | | | | | | | | | | | | (296), (298), (321), (333), (342), (360), (365), % 148.11/21.22 | | | | | | | | | | | | | (366), (374), (381), (386), (389), (419), (429), % 148.11/21.22 | | | | | | | | | | | | | (431), (435), (443), (447), (476), (482), (529), % 148.11/21.22 | | | | | | | | | | | | | (540), (541), (542), (543), (544), (545), (546), % 148.11/21.22 | | | | | | | | | | | | | (547), (550), (551), (553), (554), (559), (561), % 148.11/21.22 | | | | | | | | | | | | | (569), (573), (575), (579), (580), (583), (585), % 148.11/21.22 | | | | | | | | | | | | | (587), (588), (591), (617), (624), (625), (627), % 148.11/21.22 | | | | | | | | | | | | | (681), (768), (2637), (2641), (2643), (3376), % 148.11/21.22 | | | | | | | | | | | | | (3379), (3380), (3381), (3385), (3389), (3391), % 148.11/21.22 | | | | | | | | | | | | | (3392), (3394), (3488), (3490), (function-axioms) % 148.11/21.22 | | | | | | | | | | | | | are inconsistent by sub-proof #194. % 148.11/21.22 | | | | | | | | | | | | | % 148.11/21.22 | | | | | | | | | | | | Case 2: % 148.11/21.22 | | | | | | | | | | | | | % 148.11/21.22 | | | | | | | | | | | | | (3491) all_56_31 = e1 % 148.11/21.22 | | | | | | | | | | | | | (3492) all_56_29 = e0 % 148.11/21.22 | | | | | | | | | | | | | % 148.11/21.22 | | | | | | | | | | | | | COMBINE_EQS: (357), (3492) imply: % 148.11/21.22 | | | | | | | | | | | | | (3493) all_52_11 = e0 % 148.11/21.22 | | | | | | | | | | | | | % 148.11/21.22 | | | | | | | | | | | | | SIMP: (3493) implies: % 148.11/21.22 | | | | | | | | | | | | | (3494) all_52_11 = e0 % 148.11/21.22 | | | | | | | | | | | | | % 148.11/21.22 | | | | | | | | | | | | | REF_CLOSE: (38), (41), (48), (250), (252), (297), (299), % 148.11/21.22 | | | | | | | | | | | | | (337), (380), (402), (408), (543), (544), (546), % 148.11/21.22 | | | | | | | | | | | | | (549), (554), (555), (563), (580), (581), (622), % 148.11/21.22 | | | | | | | | | | | | | (769), (770), (2645), (3474), (3477), (3480), % 148.11/21.22 | | | | | | | | | | | | | (3482), (3484), (3485), (3491), (3494), % 148.11/21.22 | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 148.11/21.22 | | | | | | | | | | | | | #381. % 148.11/21.22 | | | | | | | | | | | | | % 148.11/21.22 | | | | | | | | | | | | End of split % 148.11/21.22 | | | | | | | | | | | | % 148.11/21.22 | | | | | | | | | | | Case 2: % 148.11/21.22 | | | | | | | | | | | | % 148.11/21.22 | | | | | | | | | | | | (3495) all_36_1 = e3 % 148.11/21.22 | | | | | | | | | | | | (3496) ~ (all_36_0 = e0) | ~ (all_36_2 = e2) % 148.11/21.22 | | | | | | | | | | | | % 148.11/21.22 | | | | | | | | | | | | COMBINE_EQS: (652), (3495) imply: % 148.11/21.22 | | | | | | | | | | | | (3497) all_6_1 = e3 % 148.11/21.22 | | | | | | | | | | | | % 148.11/21.22 | | | | | | | | | | | | SIMP: (3497) implies: % 148.11/21.22 | | | | | | | | | | | | (3498) all_6_1 = e3 % 148.11/21.22 | | | | | | | | | | | | % 148.11/21.22 | | | | | | | | | | | | REDUCE: (43), (3498) imply: % 148.11/21.22 | | | | | | | | | | | | (3499) op(all_6_2, all_6_2) = e3 % 148.11/21.22 | | | | | | | | | | | | % 148.11/21.22 | | | | | | | | | | | | REDUCE: (42), (3498) imply: % 148.11/21.22 | | | | | | | | | | | | (3500) op(e1, e3) = all_6_0 % 148.11/21.22 | | | | | | | | | | | | % 148.11/21.22 | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (36), (38), (41), (46), (48), (51), % 148.11/21.22 | | | | | | | | | | | | (173), (189), (191), (211), (237), (244), (250), % 148.11/21.22 | | | | | | | | | | | | (252), (287), (288), (289), (290), (291), (292), % 148.11/21.22 | | | | | | | | | | | | (297), (298), (299), (324), (328), (330), (331), % 148.11/21.22 | | | | | | | | | | | | (337), (357), (360), (374), (380), (389), (402), % 148.11/21.22 | | | | | | | | | | | | (408), (435), (447), (471), (494), (529), (532), % 148.11/21.22 | | | | | | | | | | | | (540), (543), (544), (545), (546), (548), (549), % 148.11/21.22 | | | | | | | | | | | | (550), (552), (553), (554), (555), (559), (561), % 148.11/21.22 | | | | | | | | | | | | (563), (569), (570), (580), (581), (588), (591), % 148.11/21.22 | | | | | | | | | | | | (612), (617), (622), (627), (681), (761), (762), % 148.11/21.22 | | | | | | | | | | | | (769), (770), (2637), (2641), (2645), (3472), % 148.11/21.22 | | | | | | | | | | | | (3474), (3477), (3478), (3479), (3480), (3482), % 148.11/21.22 | | | | | | | | | | | | (3484), (3485), (3486), (3496), (3499), (3500), % 148.11/21.22 | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 148.11/21.22 | | | | | | | | | | | | #202. % 148.11/21.22 | | | | | | | | | | | | % 148.11/21.22 | | | | | | | | | | | End of split % 148.11/21.22 | | | | | | | | | | | % 148.11/21.22 | | | | | | | | | | End of split % 148.11/21.22 | | | | | | | | | | % 148.11/21.22 | | | | | | | | | Case 2: % 148.11/21.22 | | | | | | | | | | % 148.11/21.22 | | | | | | | | | | (3501) all_28_0 = e2 % 148.11/21.22 | | | | | | | | | | (3502) ~ (all_28_1 = e3) | ~ (all_28_2 = e0) % 148.11/21.22 | | | | | | | | | | % 148.11/21.22 | | | | | | | | | | COMBINE_EQS: (740), (3501) imply: % 148.11/21.22 | | | | | | | | | | (3503) all_6_0 = e2 % 148.11/21.22 | | | | | | | | | | % 148.11/21.22 | | | | | | | | | | REF_CLOSE: (6), (8), (36), (37), (38), (41), (42), (43), % 148.11/21.22 | | | | | | | | | | (46), (48), (51), (144), (158), (169), (171), % 148.11/21.22 | | | | | | | | | | (174), (208), (211), (237), (242), (247), (250), % 148.11/21.22 | | | | | | | | | | (252), (287), (288), (289), (290), (291), (292), % 148.11/21.22 | | | | | | | | | | (293), (294), (297), (321), (332), (333), (341), % 148.11/21.22 | | | | | | | | | | (357), (366), (374), (381), (386), (389), (401), % 148.11/21.22 | | | | | | | | | | (402), (407), (419), (435), (443), (459), (475), % 148.11/21.22 | | | | | | | | | | (513), (540), (541), (542), (543), (544), (545), % 148.11/21.22 | | | | | | | | | | (546), (547), (550), (551), (554), (555), (559), % 148.11/21.22 | | | | | | | | | | (565), (568), (569), (571), (573), (580), (582), % 148.11/21.22 | | | | | | | | | | (585), (588), (590), (620), (622), (627), (634), % 148.11/21.22 | | | | | | | | | | (665), (764), (768), (769), (3502), (3503), % 148.11/21.22 | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 148.11/21.22 | | | | | | | | | | #200. % 148.11/21.22 | | | | | | | | | | % 148.11/21.22 | | | | | | | | | End of split % 148.11/21.22 | | | | | | | | | % 148.11/21.22 | | | | | | | | End of split % 148.11/21.22 | | | | | | | | % 148.11/21.22 | | | | | | | Case 2: % 148.11/21.22 | | | | | | | | % 148.11/21.22 | | | | | | | | (3504) all_16_0 = e1 % 148.11/21.22 | | | | | | | | (3505) ~ (all_16_1 = e2) | ~ (all_16_2 = e0) % 148.11/21.22 | | | | | | | | % 148.11/21.22 | | | | | | | | COMBINE_EQS: (757), (3504) imply: % 148.11/21.22 | | | | | | | | (3506) all_10_0 = e1 % 148.11/21.22 | | | | | | | | % 148.11/21.22 | | | | | | | | COMBINE_EQS: (741), (3506) imply: % 148.11/21.22 | | | | | | | | (3507) all_24_0 = e1 % 148.11/21.22 | | | | | | | | % 148.11/21.22 | | | | | | | | REDUCE: (770), (3506) imply: % 148.11/21.22 | | | | | | | | (3508) ~ (e2 = e1) % 148.11/21.22 | | | | | | | | % 148.11/21.22 | | | | | | | | REDUCE: (52), (3506) imply: % 148.11/21.22 | | | | | | | | (3509) op(e3, all_10_1) = e1 % 148.11/21.22 | | | | | | | | % 148.11/21.22 | | | | | | | | BETA: splitting (84) gives: % 148.11/21.22 | | | | | | | | % 148.11/21.22 | | | | | | | | Case 1: % 148.11/21.22 | | | | | | | | | % 148.11/21.22 | | | | | | | | | (3510) ~ (all_22_1 = e3) % 148.11/21.22 | | | | | | | | | % 148.11/21.22 | | | | | | | | | REDUCE: (672), (3510) imply: % 148.11/21.22 | | | | | | | | | (3511) ~ (all_8_1 = e3) % 148.11/21.22 | | | | | | | | | % 148.11/21.22 | | | | | | | | | BETA: splitting (89) gives: % 148.11/21.22 | | | | | | | | | % 148.11/21.22 | | | | | | | | | Case 1: % 148.11/21.22 | | | | | | | | | | % 148.11/21.22 | | | | | | | | | | (3512) ~ (all_24_0 = e1) % 148.11/21.22 | | | | | | | | | | % 148.11/21.22 | | | | | | | | | | REDUCE: (3507), (3512) imply: % 148.11/21.22 | | | | | | | | | | (3513) $false % 148.11/21.22 | | | | | | | | | | % 148.11/21.22 | | | | | | | | | | CLOSE: (3513) is inconsistent. % 148.11/21.22 | | | | | | | | | | % 148.11/21.22 | | | | | | | | | Case 2: % 148.11/21.22 | | | | | | | | | | % 148.11/21.22 | | | | | | | | | | (3514) ~ (all_24_1 = e0) | ~ (all_24_2 = e2) % 148.11/21.22 | | | | | | | | | | % 148.11/21.22 | | | | | | | | | | BETA: splitting (99) gives: % 148.11/21.22 | | | | | | | | | | % 148.11/21.22 | | | | | | | | | | Case 1: % 148.11/21.22 | | | | | | | | | | | % 148.11/21.22 | | | | | | | | | | | (3515) ~ (all_28_0 = e2) % 148.11/21.22 | | | | | | | | | | | % 148.11/21.22 | | | | | | | | | | | REDUCE: (740), (3515) imply: % 148.11/21.22 | | | | | | | | | | | (3516) ~ (all_6_0 = e2) % 148.11/21.22 | | | | | | | | | | | % 148.11/21.22 | | | | | | | | | | | BETA: splitting (114) gives: % 148.11/21.22 | | | | | | | | | | | % 148.11/21.22 | | | | | | | | | | | Case 1: % 148.11/21.22 | | | | | | | | | | | | % 148.11/21.22 | | | | | | | | | | | | (3517) ~ (all_34_0 = e2) % 148.11/21.22 | | | | | | | | | | | | % 148.11/21.22 | | | | | | | | | | | | REDUCE: (2639), (3517) imply: % 148.11/21.22 | | | | | | | | | | | | (3518) $false % 148.11/21.22 | | | | | | | | | | | | % 148.11/21.22 | | | | | | | | | | | | CLOSE: (3518) is inconsistent. % 148.11/21.22 | | | | | | | | | | | | % 148.11/21.22 | | | | | | | | | | | Case 2: % 148.11/21.22 | | | | | | | | | | | | % 148.11/21.22 | | | | | | | | | | | | (3519) ~ (all_34_1 = e3) | ~ (all_34_2 = e1) % 148.11/21.22 | | | | | | | | | | | | % 148.11/21.22 | | | | | | | | | | | | BETA: splitting (119) gives: % 148.11/21.22 | | | | | | | | | | | | % 148.11/21.22 | | | | | | | | | | | | Case 1: % 148.11/21.22 | | | | | | | | | | | | | % 148.11/21.22 | | | | | | | | | | | | | (3520) ~ (all_36_1 = e3) % 148.11/21.22 | | | | | | | | | | | | | % 148.11/21.22 | | | | | | | | | | | | | REDUCE: (652), (3520) imply: % 148.11/21.22 | | | | | | | | | | | | | (3521) ~ (all_6_1 = e3) % 148.11/21.22 | | | | | | | | | | | | | % 148.11/21.22 | | | | | | | | | | | | | BETA: splitting (129) gives: % 148.11/21.22 | | | | | | | | | | | | | % 148.11/21.22 | | | | | | | | | | | | | Case 1: % 148.11/21.22 | | | | | | | | | | | | | | % 148.11/21.22 | | | | | | | | | | | | | | (3522) ~ (all_40_0 = e3) % 148.11/21.22 | | | | | | | | | | | | | | % 148.11/21.22 | | | | | | | | | | | | | | REDUCE: (713), (3522) imply: % 148.11/21.22 | | | | | | | | | | | | | | (3523) ~ (all_6_0 = e3) % 148.11/21.22 | | | | | | | | | | | | | | % 148.11/21.22 | | | | | | | | | | | | | | BETA: splitting (292) gives: % 148.11/21.22 | | | | | | | | | | | | | | % 148.11/21.22 | | | | | | | | | | | | | | Case 1: % 148.11/21.22 | | | | | | | | | | | | | | | % 148.11/21.22 | | | | | | | | | | | | | | | (3524) ~ (all_56_21 = e2) % 148.11/21.22 | | | | | | | | | | | | | | | % 148.11/21.22 | | | | | | | | | | | | | | | REDUCE: (374), (3524) imply: % 148.11/21.22 | | | | | | | | | | | | | | | (3525) ~ (all_6_2 = e2) % 148.11/21.22 | | | | | | | | | | | | | | | % 148.11/21.22 | | | | | | | | | | | | | | | BETA: splitting (294) gives: % 148.11/21.22 | | | | | | | | | | | | | | | % 148.11/21.22 | | | | | | | | | | | | | | | Case 1: % 148.11/21.22 | | | | | | | | | | | | | | | | % 148.11/21.22 | | | | | | | | | | | | | | | | (3526) ~ (all_56_11 = e0) % 148.11/21.22 | | | | | | | | | | | | | | | | % 148.11/21.22 | | | | | | | | | | | | | | | | REDUCE: (545), (3526) imply: % 148.11/21.23 | | | | | | | | | | | | | | | | (3527) ~ (all_8_2 = e0) % 148.11/21.23 | | | | | | | | | | | | | | | | % 148.11/21.23 | | | | | | | | | | | | | | | | BETA: splitting (293) gives: % 148.11/21.23 | | | | | | | | | | | | | | | | % 148.11/21.23 | | | | | | | | | | | | | | | | Case 1: % 148.11/21.23 | | | | | | | | | | | | | | | | | % 148.11/21.23 | | | | | | | | | | | | | | | | | (3528) ~ (all_56_21 = e3) % 148.11/21.23 | | | | | | | | | | | | | | | | | % 148.11/21.23 | | | | | | | | | | | | | | | | | REDUCE: (374), (3528) imply: % 148.11/21.23 | | | | | | | | | | | | | | | | | (3529) ~ (all_6_2 = e3) % 148.11/21.23 | | | | | | | | | | | | | | | | | % 148.11/21.23 | | | | | | | | | | | | | | | | | BETA: splitting (296) gives: % 148.11/21.23 | | | | | | | | | | | | | | | | | % 148.11/21.23 | | | | | | | | | | | | | | | | | Case 1: % 148.11/21.23 | | | | | | | | | | | | | | | | | | % 148.11/21.23 | | | | | | | | | | | | | | | | | | (3530) ~ (all_56_11 = e3) % 148.11/21.23 | | | | | | | | | | | | | | | | | | % 148.11/21.23 | | | | | | | | | | | | | | | | | | REDUCE: (545), (3530) imply: % 148.11/21.23 | | | | | | | | | | | | | | | | | | (3531) ~ (all_8_2 = e3) % 148.11/21.23 | | | | | | | | | | | | | | | | | | % 148.11/21.23 | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (36), (37), (38), (41), (43), (46), (48), % 148.11/21.23 | | | | | | | | | | | | | | | | | | (51), (53), (158), (160), (161), (168), (173), % 148.11/21.23 | | | | | | | | | | | | | | | | | | (174), (176), (181), (182), (183), (184), (188), % 148.11/21.23 | | | | | | | | | | | | | | | | | | (189), (191), (192), (196), (197), (216), (217), % 148.11/21.23 | | | | | | | | | | | | | | | | | | (218), (237), (239), (240), (241), (242), (243), % 148.11/21.23 | | | | | | | | | | | | | | | | | | (244), (245), (247), (248), (249), (250), (251), % 148.11/21.23 | | | | | | | | | | | | | | | | | | (252), (288), (291), (295), (297), (298), (299), % 148.11/21.23 | | | | | | | | | | | | | | | | | | (317), (318), (319), (320), (322), (324), (325), % 148.11/21.23 | | | | | | | | | | | | | | | | | | (327), (334), (336), (340), (342), (344), (357), % 148.11/21.23 | | | | | | | | | | | | | | | | | | (365), (366), (374), (380), (386), (401), (402), % 148.11/21.23 | | | | | | | | | | | | | | | | | | (408), (419), (429), (431), (457), (459), (461), % 148.11/21.23 | | | | | | | | | | | | | | | | | | (463), (469), (471), (473), (476), (478), (480), % 148.11/21.23 | | | | | | | | | | | | | | | | | | (521), (527), (540), (541), (542), (543), (544), % 148.11/21.23 | | | | | | | | | | | | | | | | | | (545), (546), (547), (548), (549), (550), (551), % 148.11/21.23 | | | | | | | | | | | | | | | | | | (552), (553), (554), (555), (557), (559), (561), % 148.11/21.23 | | | | | | | | | | | | | | | | | | (563), (565), (567), (568), (569), (570), (571), % 148.11/21.23 | | | | | | | | | | | | | | | | | | (573), (575), (579), (580), (581), (582), (583), % 148.11/21.23 | | | | | | | | | | | | | | | | | | (585), (587), (589), (590), (591), (612), (613), % 148.11/21.23 | | | | | | | | | | | | | | | | | | (615), (617), (622), (625), (627), (643), (677), % 148.11/21.23 | | | | | | | | | | | | | | | | | | (768), (769), (3505), (3509), (3511), (3514), % 148.11/21.23 | | | | | | | | | | | | | | | | | | (3521), (3525), (3527), (3529), (3531), % 148.11/21.23 | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 148.11/21.23 | | | | | | | | | | | | | | | | | | #265. % 148.11/21.23 | | | | | | | | | | | | | | | | | | % 148.11/21.23 | | | | | | | | | | | | | | | | | Case 2: % 148.11/21.23 | | | | | | | | | | | | | | | | | | % 148.11/21.23 | | | | | | | | | | | | | | | | | | (3532) all_56_11 = e3 % 148.11/21.23 | | | | | | | | | | | | | | | | | | (3533) all_56_9 = e2 % 148.11/21.23 | | | | | | | | | | | | | | | | | | % 148.11/21.23 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (425), (3533) imply: % 148.11/21.23 | | | | | | | | | | | | | | | | | | (3534) all_52_1 = e2 % 148.11/21.23 | | | | | | | | | | | | | | | | | | % 148.11/21.23 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (545), (3532) imply: % 148.11/21.23 | | | | | | | | | | | | | | | | | | (3535) all_8_2 = e3 % 148.11/21.23 | | | | | | | | | | | | | | | | | | % 148.11/21.23 | | | | | | | | | | | | | | | | | | REDUCE: (197), (3534) imply: % 148.11/21.23 | | | | | | | | | | | | | | | | | | (3536) ~ (all_52_2 = e2) % 148.11/21.23 | | | | | | | | | | | | | | | | | | % 148.11/21.23 | | | | | | | | | | | | | | | | | | SIMP: (3536) implies: % 148.11/21.23 | | | | | | | | | | | | | | | | | | (3537) ~ (all_52_2 = e2) % 148.11/21.23 | | | | | | | | | | | | | | | | | | % 148.11/21.23 | | | | | | | | | | | | | | | | | | REDUCE: (196), (3534) imply: % 148.11/21.23 | | | | | | | | | | | | | | | | | | (3538) ~ (all_52_3 = e2) % 148.11/21.23 | | | | | | | | | | | | | | | | | | % 148.11/21.23 | | | | | | | | | | | | | | | | | | SIMP: (3538) implies: % 148.11/21.23 | | | | | | | | | | | | | | | | | | (3539) ~ (all_52_3 = e2) % 148.11/21.23 | | | | | | | | | | | | | | | | | | % 148.11/21.23 | | | | | | | | | | | | | | | | | | REDUCE: (194), (3534) imply: % 148.11/21.23 | | | | | | | | | | | | | | | | | | (3540) ~ (all_52_9 = e2) % 148.11/21.23 | | | | | | | | | | | | | | | | | | % 148.11/21.23 | | | | | | | | | | | | | | | | | | SIMP: (3540) implies: % 148.11/21.23 | | | | | | | | | | | | | | | | | | (3541) ~ (all_52_9 = e2) % 148.11/21.23 | | | | | | | | | | | | | | | | | | % 148.11/21.23 | | | | | | | | | | | | | | | | | | REDUCE: (557), (3534) imply: % 148.11/21.23 | | | | | | | | | | | | | | | | | | (3542) ~ (all_10_2 = e2) % 148.11/21.23 | | | | | | | | | | | | | | | | | | % 148.11/21.23 | | | | | | | | | | | | | | | | | | SIMP: (3542) implies: % 148.11/21.23 | | | | | | | | | | | | | | | | | | (3543) ~ (all_10_2 = e2) % 148.11/21.23 | | | | | | | | | | | | | | | | | | % 148.11/21.23 | | | | | | | | | | | | | | | | | | REDUCE: (577), (3535) imply: % 148.11/21.23 | | | | | | | | | | | | | | | | | | (3544) ~ (all_52_9 = e3) % 148.11/21.23 | | | | | | | | | | | | | | | | | | % 148.11/21.23 | | | | | | | | | | | | | | | | | | REDUCE: (48), (3535) imply: % 148.11/21.23 | | | | | | | | | | | | | | | | | | (3545) op(e3, e3) = all_8_1 % 148.11/21.23 | | | | | | | | | | | | | | | | | | % 148.11/21.23 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_10_2, % 148.11/21.23 | | | | | | | | | | | | | | | | | | all_8_1, e3, e3, simplifying with (51), (3545) % 148.11/21.23 | | | | | | | | | | | | | | | | | | gives: % 148.11/21.23 | | | | | | | | | | | | | | | | | | (3546) all_10_2 = all_8_1 % 148.11/21.23 | | | | | | | | | | | | | | | | | | % 148.11/21.23 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (527), (3546) imply: % 148.11/21.23 | | | | | | | | | | | | | | | | | | (3547) all_16_2 = all_8_1 % 148.11/21.23 | | | | | | | | | | | | | | | | | | % 148.11/21.23 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (543), (3546) imply: % 148.11/21.23 | | | | | | | | | | | | | | | | | | (3548) all_54_0 = all_8_1 % 148.11/21.23 | | | | | | | | | | | | | | | | | | % 148.11/21.23 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (546), (3546) imply: % 148.11/21.23 | | | | | | | | | | | | | | | | | | (3549) all_56_1 = all_8_1 % 148.11/21.23 | | | | | | | | | | | | | | | | | | % 148.11/21.23 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (419), (3546) imply: % 148.11/21.23 | | | | | | | | | | | | | | | | | | (3550) all_58_0 = all_8_1 % 148.11/21.23 | | | | | | | | | | | | | | | | | | % 148.11/21.23 | | | | | | | | | | | | | | | | | | REDUCE: (563), (3546) imply: % 148.11/21.23 | | | | | | | | | | | | | | | | | | (3551) ~ (all_52_4 = all_8_1) % 148.11/21.23 | | | | | | | | | | | | | | | | | | % 148.11/21.23 | | | | | | | | | | | | | | | | | | REDUCE: (3543), (3546) imply: % 148.11/21.23 | | | | | | | | | | | | | | | | | | (3552) ~ (all_8_1 = e2) % 148.11/21.23 | | | | | | | | | | | | | | | | | | % 148.11/21.23 | | | | | | | | | | | | | | | | | | REDUCE: (53), (3546) imply: % 148.11/21.23 | | | | | | | | | | | | | | | | | | (3553) op(all_8_1, all_8_1) = all_10_1 % 148.11/21.23 | | | | | | | | | | | | | | | | | | % 148.11/21.23 | | | | | | | | | | | | | | | | | | BETA: splitting (252) gives: % 148.11/21.23 | | | | | | | | | | | | | | | | | | % 148.11/21.23 | | | | | | | | | | | | | | | | | | Case 1: % 148.11/21.23 | | | | | | | | | | | | | | | | | | | % 148.11/21.23 | | | | | | | | | | | | | | | | | | | (3554) all_54_0 = e3 % 148.11/21.23 | | | | | | | | | | | | | | | | | | | % 148.11/21.23 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3511), (3548), (3554) are inconsistent by % 148.11/21.23 | | | | | | | | | | | | | | | | | | | sub-proof #600. % 148.11/21.23 | | | | | | | | | | | | | | | | | | | % 148.11/21.23 | | | | | | | | | | | | | | | | | | Case 2: % 148.11/21.23 | | | | | | | | | | | | | | | | | | | % 148.11/21.23 | | | | | | | | | | | | | | | | | | | (3555) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 148.11/21.23 | | | | | | | | | | | | | | | | | | | % 148.11/21.23 | | | | | | | | | | | | | | | | | | | BETA: splitting (3555) gives: % 148.11/21.23 | | | | | | | | | | | | | | | | | | | % 148.11/21.23 | | | | | | | | | | | | | | | | | | | Case 1: % 148.11/21.23 | | | | | | | | | | | | | | | | | | | | % 148.11/21.23 | | | | | | | | | | | | | | | | | | | | (3556) all_54_0 = e2 % 148.11/21.23 | | | | | | | | | | | | | | | | | | | | % 148.11/21.23 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3548), (3552), (3556) are inconsistent by % 148.11/21.23 | | | | | | | | | | | | | | | | | | | | sub-proof #599. % 148.11/21.23 | | | | | | | | | | | | | | | | | | | | % 148.11/21.23 | | | | | | | | | | | | | | | | | | | Case 2: % 148.11/21.23 | | | | | | | | | | | | | | | | | | | | % 148.11/21.23 | | | | | | | | | | | | | | | | | | | | (3557) all_54_0 = e1 | all_54_0 = e0 % 148.11/21.23 | | | | | | | | | | | | | | | | | | | | % 148.11/21.23 | | | | | | | | | | | | | | | | | | | | BETA: splitting (3557) gives: % 148.11/21.23 | | | | | | | | | | | | | | | | | | | | % 148.11/21.23 | | | | | | | | | | | | | | | | | | | | Case 1: % 148.11/21.23 | | | | | | | | | | | | | | | | | | | | | % 148.11/21.23 | | | | | | | | | | | | | | | | | | | | | (3558) all_54_0 = e1 % 148.11/21.23 | | | | | | | | | | | | | | | | | | | | | % 148.11/21.23 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (769), (3548), (3558) are inconsistent by % 148.11/21.23 | | | | | | | | | | | | | | | | | | | | | sub-proof #598. % 148.11/21.23 | | | | | | | | | | | | | | | | | | | | | % 148.11/21.23 | | | | | | | | | | | | | | | | | | | | Case 2: % 148.11/21.23 | | | | | | | | | | | | | | | | | | | | | % 148.11/21.23 | | | | | | | | | | | | | | | | | | | | | (3559) all_54_0 = e0 % 148.11/21.23 | | | | | | | | | | | | | | | | | | | | | % 148.11/21.23 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3548), (3559) imply: % 148.11/21.23 | | | | | | | | | | | | | | | | | | | | | (3560) all_8_1 = e0 % 148.11/21.23 | | | | | | | | | | | | | | | | | | | | | % 148.11/21.23 | | | | | | | | | | | | | | | | | | | | | SIMP: (3560) implies: % 148.11/21.23 | | | | | | | | | | | | | | | | | | | | | (3561) all_8_1 = e0 % 148.11/21.23 | | | | | | | | | | | | | | | | | | | | | % 148.11/21.23 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3547), (3561) imply: % 148.11/21.23 | | | | | | | | | | | | | | | | | | | | | (3562) all_16_2 = e0 % 148.11/21.23 | | | | | | | | | | | | | | | | | | | | | % 148.11/21.23 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3549), (3561) imply: % 148.11/21.23 | | | | | | | | | | | | | | | | | | | | | (3563) all_56_1 = e0 % 148.11/21.23 | | | | | | | | | | | | | | | | | | | | | % 148.11/21.23 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3550), (3561) imply: % 148.11/21.23 | | | | | | | | | | | | | | | | | | | | | (3564) all_58_0 = e0 % 148.11/21.23 | | | | | | | | | | | | | | | | | | | | | % 148.11/21.23 | | | | | | | | | | | | | | | | | | | | | REDUCE: (3551), (3561) imply: % 148.11/21.23 | | | | | | | | | | | | | | | | | | | | | (3565) ~ (all_52_4 = e0) % 148.11/21.23 | | | | | | | | | | | | | | | | | | | | | % 148.11/21.23 | | | | | | | | | | | | | | | | | | | | | REDUCE: (769), (3561) imply: % 148.11/21.23 | | | | | | | | | | | | | | | | | | | | | (3566) ~ (e1 = e0) % 148.11/21.23 | | | | | | | | | | | | | | | | | | | | | % 148.11/21.23 | | | | | | | | | | | | | | | | | | | | | REDUCE: (3553), (3561) imply: % 148.11/21.23 | | | | | | | | | | | | | | | | | | | | | (3567) op(e0, e0) = all_10_1 % 148.11/21.23 | | | | | | | | | | | | | | | | | | | | | % 148.11/21.23 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (297) gives: % 148.11/21.23 | | | | | | | | | | | | | | | | | | | | | % 148.11/21.23 | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.11/21.23 | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.23 | | | | | | | | | | | | | | | | | | | | | | (3568) ~ (all_56_1 = e0) % 148.11/21.23 | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.23 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3563), (3568) imply: % 148.11/21.23 | | | | | | | | | | | | | | | | | | | | | | (3569) $false % 148.11/21.23 | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.23 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3569) is inconsistent. % 148.11/21.23 | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.23 | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.11/21.23 | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.23 | | | | | | | | | | | | | | | | | | | | | | (3570) all_56_7 = e3 % 148.11/21.23 | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.23 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (402), (3570) imply: % 148.11/21.23 | | | | | | | | | | | | | | | | | | | | | | (3571) all_52_12 = e3 % 148.11/21.23 | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.23 | | | | | | | | | | | | | | | | | | | | | | SIMP: (3571) implies: % 148.11/21.23 | | | | | | | | | | | | | | | | | | | | | | (3572) all_52_12 = e3 % 148.11/21.23 | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.23 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (181), (3572) imply: % 148.11/21.23 | | | | | | | | | | | | | | | | | | | | | | (3573) ~ (all_52_4 = e3) % 148.11/21.23 | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.23 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (168), (3572) imply: % 148.11/21.23 | | | | | | | | | | | | | | | | | | | | | | (3574) ~ (all_52_8 = e3) % 148.11/21.23 | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.23 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (331) gives: % 148.11/21.23 | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.23 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.11/21.23 | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.23 | | | | | | | | | | | | | | | | | | | | | | | (3575) all_58_4 = e3 % 148.11/21.23 | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.23 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (407), (3575) imply: % 148.11/21.23 | | | | | | | | | | | | | | | | | | | | | | | (3576) all_52_8 = e3 % 148.11/21.23 | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.23 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3576) implies: % 148.11/21.23 | | | | | | | | | | | | | | | | | | | | | | | (3577) all_52_8 = e3 % 148.11/21.23 | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.23 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3574), (3577) imply: % 148.11/21.23 | | | | | | | | | | | | | | | | | | | | | | | (3578) $false % 148.11/21.23 | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.23 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3578) is inconsistent. % 148.11/21.23 | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.23 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.11/21.23 | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.23 | | | | | | | | | | | | | | | | | | | | | | | (3579) all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3 % 148.11/21.23 | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.23 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3579) gives: % 148.11/21.23 | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.23 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.11/21.23 | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.23 | | | | | | | | | | | | | | | | | | | | | | | | (3580) all_58_5 = e3 % 148.11/21.23 | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.23 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (389), (3580) imply: % 148.11/21.23 | | | | | | | | | | | | | | | | | | | | | | | | (3581) all_52_9 = e3 % 148.11/21.23 | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.23 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3581) implies: % 148.11/21.23 | | | | | | | | | | | | | | | | | | | | | | | | (3582) all_52_9 = e3 % 148.11/21.23 | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.23 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3544), (3582) imply: % 148.11/21.23 | | | | | | | | | | | | | | | | | | | | | | | | (3583) $false % 148.11/21.23 | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.23 | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3583) is inconsistent. % 148.11/21.23 | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.23 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.11/21.23 | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.23 | | | | | | | | | | | | | | | | | | | | | | | | (3584) all_58_8 = e3 | all_58_14 = e3 % 148.11/21.23 | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.23 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3584) gives: % 148.11/21.23 | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.23 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.11/21.23 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.23 | | | | | | | | | | | | | | | | | | | | | | | | | (3585) all_58_8 = e3 % 148.11/21.23 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.23 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (552), (3585) imply: % 148.11/21.23 | | | | | | | | | | | | | | | | | | | | | | | | | (3586) all_6_2 = e3 % 148.11/21.23 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.23 | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3586) implies: % 148.11/21.23 | | | | | | | | | | | | | | | | | | | | | | | | | (3587) all_6_2 = e3 % 148.11/21.23 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.23 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3529), (3587) imply: % 148.11/21.23 | | | | | | | | | | | | | | | | | | | | | | | | | (3588) $false % 148.11/21.23 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.23 | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3588) is inconsistent. % 148.11/21.23 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.23 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.11/21.23 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.23 | | | | | | | | | | | | | | | | | | | | | | | | | (3589) all_58_14 = e3 % 148.11/21.23 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.23 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (548), (3589) imply: % 148.11/21.23 | | | | | | | | | | | | | | | | | | | | | | | | | (3590) all_52_11 = e3 % 148.11/21.23 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.23 | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3590) implies: % 148.11/21.23 | | | | | | | | | | | | | | | | | | | | | | | | | (3591) all_52_11 = e3 % 148.11/21.23 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.23 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (357), (3591) imply: % 148.11/21.23 | | | | | | | | | | | | | | | | | | | | | | | | | (3592) all_56_29 = e3 % 148.11/21.23 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.23 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (585), (3591) imply: % 148.11/21.23 | | | | | | | | | | | | | | | | | | | | | | | | | (3593) ~ (all_6_2 = e3) % 148.11/21.23 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.23 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (288) gives: % 148.11/21.23 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.23 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.11/21.23 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.23 | | | | | | | | | | | | | | | | | | | | | | | | | | (3594) ~ (all_56_31 = e1) % 148.11/21.23 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.23 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (544), (3594) imply: % 148.11/21.23 | | | | | | | | | | | | | | | | | | | | | | | | | | (3595) ~ (all_4_2 = e1) % 148.11/21.23 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.23 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (9), (36), (38), (182), (237), (251), (330), % 148.11/21.23 | | | | | | | | | | | | | | | | | | | | | | | | | | (343), (389), (407), (457), (540), (548), (552), % 148.11/21.23 | | | | | | | | | | | | | | | | | | | | | | | | | | (555), (588), (627), (677), (2641), (3505), % 148.11/21.23 | | | | | | | | | | | | | | | | | | | | | | | | | | (3525), (3529), (3541), (3544), (3562), (3564), % 148.11/21.23 | | | | | | | | | | | | | | | | | | | | | | | | | | (3565), (3567), (3573), (3579), (3595), % 148.11/21.23 | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 148.11/21.23 | | | | | | | | | | | | | | | | | | | | | | | | | | #190. % 148.11/21.23 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.23 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.11/21.23 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.23 | | | | | | | | | | | | | | | | | | | | | | | | | | (3596) all_56_29 = e0 % 148.11/21.23 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.23 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3592), (3596) imply: % 148.11/21.23 | | | | | | | | | | | | | | | | | | | | | | | | | | (3597) e3 = e0 % 148.11/21.23 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.23 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (193), (294), (344), (365), (401), (419), (443), % 148.11/21.23 | | | | | | | | | | | | | | | | | | | | | | | | | | (553), (3532), (3537), (3539), (3543), (3597) are % 148.11/21.23 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #189. % 148.11/21.23 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.23 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.11/21.23 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.23 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.11/21.23 | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.23 | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.11/21.23 | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.23 | | | | | | | | | | | | | | | | | | | | | | End of split % 148.11/21.23 | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.23 | | | | | | | | | | | | | | | | | | | | | End of split % 148.11/21.23 | | | | | | | | | | | | | | | | | | | | | % 148.11/21.23 | | | | | | | | | | | | | | | | | | | | End of split % 148.11/21.23 | | | | | | | | | | | | | | | | | | | | % 148.11/21.23 | | | | | | | | | | | | | | | | | | | End of split % 148.11/21.23 | | | | | | | | | | | | | | | | | | | % 148.11/21.23 | | | | | | | | | | | | | | | | | | End of split % 148.11/21.23 | | | | | | | | | | | | | | | | | | % 148.11/21.23 | | | | | | | | | | | | | | | | | End of split % 148.11/21.23 | | | | | | | | | | | | | | | | | % 148.11/21.23 | | | | | | | | | | | | | | | | Case 2: % 148.11/21.23 | | | | | | | | | | | | | | | | | % 148.11/21.23 | | | | | | | | | | | | | | | | | (3598) all_56_21 = e3 % 148.11/21.23 | | | | | | | | | | | | | | | | | (3599) all_56_17 = e1 % 148.11/21.23 | | | | | | | | | | | | | | | | | % 148.11/21.23 | | | | | | | | | | | | | | | | | COMBINE_EQS: (381), (3599) imply: % 148.11/21.23 | | | | | | | | | | | | | | | | | (3600) all_52_2 = e1 % 148.11/21.23 | | | | | | | | | | | | | | | | | % 148.11/21.23 | | | | | | | | | | | | | | | | | COMBINE_EQS: (374), (3598) imply: % 148.11/21.23 | | | | | | | | | | | | | | | | | (3601) all_6_2 = e3 % 148.11/21.23 | | | | | | | | | | | | | | | | | % 148.11/21.23 | | | | | | | | | | | | | | | | | REF_CLOSE: (42), (43), (51), (174), (189), (191), (208), % 148.11/21.23 | | | | | | | | | | | | | | | | | (241), (243), (252), (287), (473), (476), (527), % 148.11/21.23 | | | | | | | | | | | | | | | | | (543), (544), (545), (546), (559), (569), (573), % 148.11/21.23 | | | | | | | | | | | | | | | | | (580), (587), (591), (768), (3505), (3516), % 148.11/21.23 | | | | | | | | | | | | | | | | | (3521), (3598), (3600), (3601), (function-axioms) % 148.11/21.23 | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #188. % 148.11/21.23 | | | | | | | | | | | | | | | | | % 148.11/21.23 | | | | | | | | | | | | | | | | End of split % 148.11/21.23 | | | | | | | | | | | | | | | | % 148.11/21.23 | | | | | | | | | | | | | | | Case 2: % 148.11/21.23 | | | | | | | | | | | | | | | | % 148.11/21.23 | | | | | | | | | | | | | | | | (3602) all_56_15 = e2 % 148.11/21.23 | | | | | | | | | | | | | | | | (3603) all_56_11 = e0 % 148.11/21.23 | | | | | | | | | | | | | | | | % 148.11/21.23 | | | | | | | | | | | | | | | | REF_CLOSE: (36), (38), (48), (237), (443), (540), (545), % 148.11/21.23 | | | | | | | | | | | | | | | | (590), (627), (769), (2641), (3511), (3602), % 148.11/21.23 | | | | | | | | | | | | | | | | (3603), (function-axioms) are inconsistent by % 148.11/21.23 | | | | | | | | | | | | | | | | sub-proof #224. % 148.11/21.23 | | | | | | | | | | | | | | | | % 148.11/21.23 | | | | | | | | | | | | | | | End of split % 148.11/21.23 | | | | | | | | | | | | | | | % 148.11/21.23 | | | | | | | | | | | | | | Case 2: % 148.11/21.23 | | | | | | | | | | | | | | | % 148.11/21.23 | | | | | | | | | | | | | | | (3604) all_56_21 = e2 % 148.11/21.23 | | | | | | | | | | | | | | | (3605) all_56_19 = e1 % 148.11/21.23 | | | | | | | | | | | | | | | % 148.11/21.23 | | | | | | | | | | | | | | | COMBINE_EQS: (435), (3605) imply: % 148.11/21.23 | | | | | | | | | | | | | | | (3606) all_52_6 = e1 % 148.11/21.23 | | | | | | | | | | | | | | | % 148.11/21.23 | | | | | | | | | | | | | | | COMBINE_EQS: (374), (3604) imply: % 148.11/21.23 | | | | | | | | | | | | | | | (3607) all_6_2 = e2 % 148.11/21.23 | | | | | | | | | | | | | | | % 148.11/21.23 | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (36), (42), (43), (46), (48), (174), % 148.11/21.23 | | | | | | | | | | | | | | | (208), (247), (289), (294), (297), (321), (323), % 148.11/21.23 | | | | | | | | | | | | | | | (341), (360), (386), (402), (407), (419), (443), % 148.11/21.23 | | | | | | | | | | | | | | | (542), (545), (546), (547), (550), (551), (555), % 148.11/21.23 | | | | | | | | | | | | | | | (571), (573), (575), (580), (620), (768), (769), % 148.11/21.23 | | | | | | | | | | | | | | | (3511), (3521), (3523), (3606), (3607), % 148.11/21.23 | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 148.11/21.23 | | | | | | | | | | | | | | | #209. % 148.11/21.23 | | | | | | | | | | | | | | | % 148.11/21.23 | | | | | | | | | | | | | | End of split % 148.11/21.23 | | | | | | | | | | | | | | % 148.11/21.23 | | | | | | | | | | | | | Case 2: % 148.11/21.23 | | | | | | | | | | | | | | % 148.11/21.23 | | | | | | | | | | | | | | (3608) all_40_0 = e3 % 148.11/21.23 | | | | | | | | | | | | | | (3609) ~ (all_40_1 = e0) | ~ (all_40_2 = e2) % 148.11/21.23 | | | | | | | | | | | | | | % 148.11/21.23 | | | | | | | | | | | | | | COMBINE_EQS: (713), (3608) imply: % 148.11/21.23 | | | | | | | | | | | | | | (3610) all_6_0 = e3 % 148.11/21.23 | | | | | | | | | | | | | | % 148.11/21.23 | | | | | | | | | | | | | | SIMP: (3610) implies: % 148.11/21.23 | | | | | | | | | | | | | | (3611) all_6_0 = e3 % 148.11/21.23 | | | | | | | | | | | | | | % 148.11/21.23 | | | | | | | | | | | | | | REDUCE: (42), (3611) imply: % 148.11/21.23 | | | | | | | | | | | | | | (3612) op(e1, all_6_1) = e3 % 148.11/21.23 | | | | | | | | | | | | | | % 148.11/21.23 | | | | | | | | | | | | | | BETA: splitting (292) gives: % 148.11/21.23 | | | | | | | | | | | | | | % 148.11/21.23 | | | | | | | | | | | | | | Case 1: % 148.11/21.23 | | | | | | | | | | | | | | | % 148.11/21.23 | | | | | | | | | | | | | | | (3613) ~ (all_56_21 = e2) % 148.11/21.23 | | | | | | | | | | | | | | | % 148.11/21.23 | | | | | | | | | | | | | | | REDUCE: (374), (3613) imply: % 148.11/21.23 | | | | | | | | | | | | | | | (3614) ~ (all_6_2 = e2) % 148.11/21.23 | | | | | | | | | | | | | | | % 148.11/21.23 | | | | | | | | | | | | | | | BETA: splitting (294) gives: % 148.11/21.23 | | | | | | | | | | | | | | | % 148.11/21.23 | | | | | | | | | | | | | | | Case 1: % 148.11/21.23 | | | | | | | | | | | | | | | | % 148.11/21.23 | | | | | | | | | | | | | | | | (3615) ~ (all_56_11 = e0) % 148.11/21.23 | | | | | | | | | | | | | | | | % 148.11/21.23 | | | | | | | | | | | | | | | | REDUCE: (545), (3615) imply: % 148.11/21.23 | | | | | | | | | | | | | | | | (3616) ~ (all_8_2 = e0) % 148.11/21.23 | | | | | | | | | | | | | | | | % 148.11/21.23 | | | | | | | | | | | | | | | | BETA: splitting (288) gives: % 148.11/21.23 | | | | | | | | | | | | | | | | % 148.11/21.23 | | | | | | | | | | | | | | | | Case 1: % 148.11/21.23 | | | | | | | | | | | | | | | | | % 148.11/21.23 | | | | | | | | | | | | | | | | | (3617) ~ (all_56_31 = e1) % 148.11/21.23 | | | | | | | | | | | | | | | | | % 148.11/21.23 | | | | | | | | | | | | | | | | | REDUCE: (544), (3617) imply: % 148.11/21.23 | | | | | | | | | | | | | | | | | (3618) ~ (all_4_2 = e1) % 148.11/21.23 | | | | | | | | | | | | | | | | | % 148.11/21.23 | | | | | | | | | | | | | | | | | BETA: splitting (293) gives: % 148.11/21.23 | | | | | | | | | | | | | | | | | % 148.11/21.23 | | | | | | | | | | | | | | | | | Case 1: % 148.11/21.23 | | | | | | | | | | | | | | | | | | % 148.11/21.23 | | | | | | | | | | | | | | | | | | (3619) ~ (all_56_21 = e3) % 148.11/21.23 | | | | | | | | | | | | | | | | | | % 148.11/21.23 | | | | | | | | | | | | | | | | | | REDUCE: (374), (3619) imply: % 148.11/21.23 | | | | | | | | | | | | | | | | | | (3620) ~ (all_6_2 = e3) % 148.11/21.23 | | | | | | | | | | | | | | | | | | % 148.11/21.23 | | | | | | | | | | | | | | | | | | BETA: splitting (296) gives: % 148.11/21.23 | | | | | | | | | | | | | | | | | | % 148.11/21.23 | | | | | | | | | | | | | | | | | | Case 1: % 148.11/21.23 | | | | | | | | | | | | | | | | | | | % 148.11/21.23 | | | | | | | | | | | | | | | | | | | (3621) ~ (all_56_11 = e3) % 148.11/21.23 | | | | | | | | | | | | | | | | | | | % 148.11/21.23 | | | | | | | | | | | | | | | | | | | REDUCE: (545), (3621) imply: % 148.11/21.23 | | | | | | | | | | | | | | | | | | | (3622) ~ (all_8_2 = e3) % 148.11/21.23 | | | | | | | | | | | | | | | | | | | % 148.11/21.23 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (36), (37), (38), (41), (43), (46), (48), % 148.11/21.23 | | | | | | | | | | | | | | | | | | | (51), (53), (158), (160), (161), (168), (173), % 148.11/21.23 | | | | | | | | | | | | | | | | | | | (174), (176), (181), (182), (183), (184), (188), % 148.11/21.23 | | | | | | | | | | | | | | | | | | | (189), (191), (192), (196), (197), (216), (217), % 148.11/21.23 | | | | | | | | | | | | | | | | | | | (218), (237), (239), (240), (241), (242), (243), % 148.11/21.23 | | | | | | | | | | | | | | | | | | | (244), (245), (247), (248), (249), (250), (251), % 148.11/21.23 | | | | | | | | | | | | | | | | | | | (252), (288), (291), (295), (297), (298), (299), % 148.11/21.23 | | | | | | | | | | | | | | | | | | | (317), (318), (319), (320), (322), (324), (325), % 148.11/21.23 | | | | | | | | | | | | | | | | | | | (327), (334), (336), (340), (342), (344), (357), % 148.11/21.23 | | | | | | | | | | | | | | | | | | | (365), (366), (374), (380), (386), (401), (402), % 148.11/21.23 | | | | | | | | | | | | | | | | | | | (408), (419), (429), (431), (457), (459), (461), % 148.11/21.23 | | | | | | | | | | | | | | | | | | | (463), (469), (471), (473), (476), (478), (480), % 148.11/21.23 | | | | | | | | | | | | | | | | | | | (521), (527), (540), (541), (542), (543), (544), % 148.11/21.23 | | | | | | | | | | | | | | | | | | | (545), (546), (547), (548), (549), (550), (551), % 148.11/21.23 | | | | | | | | | | | | | | | | | | | (552), (553), (554), (555), (557), (559), (561), % 148.11/21.23 | | | | | | | | | | | | | | | | | | | (563), (565), (567), (568), (569), (570), (571), % 148.11/21.23 | | | | | | | | | | | | | | | | | | | (573), (575), (579), (580), (581), (582), (583), % 148.11/21.23 | | | | | | | | | | | | | | | | | | | (585), (587), (589), (590), (591), (612), (613), % 148.11/21.23 | | | | | | | | | | | | | | | | | | | (615), (617), (622), (625), (627), (643), (677), % 148.11/21.23 | | | | | | | | | | | | | | | | | | | (768), (769), (3505), (3509), (3511), (3514), % 148.11/21.23 | | | | | | | | | | | | | | | | | | | (3521), (3614), (3616), (3620), (3622), % 148.11/21.23 | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 148.11/21.23 | | | | | | | | | | | | | | | | | | | #265. % 148.11/21.23 | | | | | | | | | | | | | | | | | | | % 148.11/21.23 | | | | | | | | | | | | | | | | | | Case 2: % 148.11/21.23 | | | | | | | | | | | | | | | | | | | % 148.11/21.24 | | | | | | | | | | | | | | | | | | | (3623) all_56_11 = e3 % 148.11/21.24 | | | | | | | | | | | | | | | | | | | (3624) all_56_9 = e2 % 148.11/21.24 | | | | | | | | | | | | | | | | | | | % 148.11/21.24 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (425), (3624) imply: % 148.11/21.24 | | | | | | | | | | | | | | | | | | | (3625) all_52_1 = e2 % 148.11/21.24 | | | | | | | | | | | | | | | | | | | % 148.11/21.24 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (545), (3623) imply: % 148.11/21.24 | | | | | | | | | | | | | | | | | | | (3626) all_8_2 = e3 % 148.11/21.24 | | | | | | | | | | | | | | | | | | | % 148.11/21.24 | | | | | | | | | | | | | | | | | | | REDUCE: (194), (3625) imply: % 148.11/21.24 | | | | | | | | | | | | | | | | | | | (3627) ~ (all_52_9 = e2) % 148.11/21.24 | | | | | | | | | | | | | | | | | | | % 148.11/21.24 | | | | | | | | | | | | | | | | | | | SIMP: (3627) implies: % 148.11/21.24 | | | | | | | | | | | | | | | | | | | (3628) ~ (all_52_9 = e2) % 148.11/21.24 | | | | | | | | | | | | | | | | | | | % 148.11/21.24 | | | | | | | | | | | | | | | | | | | REDUCE: (557), (3625) imply: % 148.11/21.24 | | | | | | | | | | | | | | | | | | | (3629) ~ (all_10_2 = e2) % 148.11/21.24 | | | | | | | | | | | | | | | | | | | % 148.11/21.24 | | | | | | | | | | | | | | | | | | | SIMP: (3629) implies: % 148.11/21.24 | | | | | | | | | | | | | | | | | | | (3630) ~ (all_10_2 = e2) % 148.11/21.24 | | | | | | | | | | | | | | | | | | | % 148.11/21.24 | | | | | | | | | | | | | | | | | | | REDUCE: (577), (3626) imply: % 148.11/21.24 | | | | | | | | | | | | | | | | | | | (3631) ~ (all_52_9 = e3) % 148.11/21.24 | | | | | | | | | | | | | | | | | | | % 148.11/21.24 | | | | | | | | | | | | | | | | | | | REDUCE: (48), (3626) imply: % 148.11/21.24 | | | | | | | | | | | | | | | | | | | (3632) op(e3, e3) = all_8_1 % 148.11/21.24 | | | | | | | | | | | | | | | | | | | % 148.11/21.24 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_10_2, % 148.11/21.24 | | | | | | | | | | | | | | | | | | | all_8_1, e3, e3, simplifying with (51), (3632) % 148.11/21.24 | | | | | | | | | | | | | | | | | | | gives: % 148.11/21.24 | | | | | | | | | | | | | | | | | | | (3633) all_10_2 = all_8_1 % 148.11/21.24 | | | | | | | | | | | | | | | | | | | % 148.11/21.24 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (527), (3633) imply: % 148.11/21.24 | | | | | | | | | | | | | | | | | | | (3634) all_16_2 = all_8_1 % 148.11/21.24 | | | | | | | | | | | | | | | | | | | % 148.11/21.24 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (543), (3633) imply: % 148.11/21.24 | | | | | | | | | | | | | | | | | | | (3635) all_54_0 = all_8_1 % 148.11/21.24 | | | | | | | | | | | | | | | | | | | % 148.11/21.24 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (546), (3633) imply: % 148.11/21.24 | | | | | | | | | | | | | | | | | | | (3636) all_56_1 = all_8_1 % 148.11/21.24 | | | | | | | | | | | | | | | | | | | % 148.11/21.24 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (419), (3633) imply: % 148.11/21.24 | | | | | | | | | | | | | | | | | | | (3637) all_58_0 = all_8_1 % 148.11/21.24 | | | | | | | | | | | | | | | | | | | % 148.11/21.24 | | | | | | | | | | | | | | | | | | | REDUCE: (563), (3633) imply: % 148.11/21.24 | | | | | | | | | | | | | | | | | | | (3638) ~ (all_52_4 = all_8_1) % 148.11/21.24 | | | | | | | | | | | | | | | | | | | % 148.11/21.24 | | | | | | | | | | | | | | | | | | | REDUCE: (3630), (3633) imply: % 148.11/21.24 | | | | | | | | | | | | | | | | | | | (3639) ~ (all_8_1 = e2) % 148.11/21.24 | | | | | | | | | | | | | | | | | | | % 148.11/21.24 | | | | | | | | | | | | | | | | | | | REDUCE: (53), (3633) imply: % 148.11/21.24 | | | | | | | | | | | | | | | | | | | (3640) op(all_8_1, all_8_1) = all_10_1 % 148.11/21.24 | | | | | | | | | | | | | | | | | | | % 148.11/21.24 | | | | | | | | | | | | | | | | | | | BETA: splitting (252) gives: % 148.11/21.24 | | | | | | | | | | | | | | | | | | | % 148.11/21.24 | | | | | | | | | | | | | | | | | | | Case 1: % 148.11/21.24 | | | | | | | | | | | | | | | | | | | | % 148.11/21.24 | | | | | | | | | | | | | | | | | | | | (3641) all_54_0 = e3 % 148.11/21.24 | | | | | | | | | | | | | | | | | | | | % 148.11/21.24 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3511), (3635), (3641) are inconsistent by % 148.11/21.24 | | | | | | | | | | | | | | | | | | | | sub-proof #600. % 148.11/21.24 | | | | | | | | | | | | | | | | | | | | % 148.11/21.24 | | | | | | | | | | | | | | | | | | | Case 2: % 148.11/21.24 | | | | | | | | | | | | | | | | | | | | % 148.11/21.24 | | | | | | | | | | | | | | | | | | | | (3642) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 148.11/21.24 | | | | | | | | | | | | | | | | | | | | % 148.11/21.24 | | | | | | | | | | | | | | | | | | | | BETA: splitting (3642) gives: % 148.11/21.24 | | | | | | | | | | | | | | | | | | | | % 148.11/21.24 | | | | | | | | | | | | | | | | | | | | Case 1: % 148.11/21.24 | | | | | | | | | | | | | | | | | | | | | % 148.11/21.24 | | | | | | | | | | | | | | | | | | | | | (3643) all_54_0 = e2 % 148.11/21.24 | | | | | | | | | | | | | | | | | | | | | % 148.11/21.24 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3635), (3639), (3643) are inconsistent by % 148.11/21.24 | | | | | | | | | | | | | | | | | | | | | sub-proof #599. % 148.11/21.24 | | | | | | | | | | | | | | | | | | | | | % 148.11/21.24 | | | | | | | | | | | | | | | | | | | | Case 2: % 148.11/21.24 | | | | | | | | | | | | | | | | | | | | | % 148.11/21.24 | | | | | | | | | | | | | | | | | | | | | (3644) all_54_0 = e1 | all_54_0 = e0 % 148.11/21.24 | | | | | | | | | | | | | | | | | | | | | % 148.11/21.24 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3644) gives: % 148.11/21.24 | | | | | | | | | | | | | | | | | | | | | % 148.11/21.24 | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.11/21.24 | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.24 | | | | | | | | | | | | | | | | | | | | | | (3645) all_54_0 = e1 % 148.11/21.24 | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.24 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (769), (3635), (3645) are inconsistent by % 148.11/21.24 | | | | | | | | | | | | | | | | | | | | | | sub-proof #598. % 148.11/21.24 | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.24 | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.11/21.24 | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.24 | | | | | | | | | | | | | | | | | | | | | | (3646) all_54_0 = e0 % 148.11/21.24 | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.24 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3635), (3646) imply: % 148.11/21.24 | | | | | | | | | | | | | | | | | | | | | | (3647) all_8_1 = e0 % 148.11/21.24 | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.24 | | | | | | | | | | | | | | | | | | | | | | SIMP: (3647) implies: % 148.11/21.24 | | | | | | | | | | | | | | | | | | | | | | (3648) all_8_1 = e0 % 148.11/21.24 | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.24 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3634), (3648) imply: % 148.11/21.24 | | | | | | | | | | | | | | | | | | | | | | (3649) all_16_2 = e0 % 148.11/21.24 | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.24 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3636), (3648) imply: % 148.11/21.24 | | | | | | | | | | | | | | | | | | | | | | (3650) all_56_1 = e0 % 148.11/21.24 | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.24 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3637), (3648) imply: % 148.11/21.24 | | | | | | | | | | | | | | | | | | | | | | (3651) all_58_0 = e0 % 148.11/21.24 | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.24 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3638), (3648) imply: % 148.11/21.24 | | | | | | | | | | | | | | | | | | | | | | (3652) ~ (all_52_4 = e0) % 148.11/21.24 | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.24 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (769), (3648) imply: % 148.11/21.24 | | | | | | | | | | | | | | | | | | | | | | (3653) ~ (e1 = e0) % 148.11/21.24 | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.24 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3640), (3648) imply: % 148.11/21.24 | | | | | | | | | | | | | | | | | | | | | | (3654) op(e0, e0) = all_10_1 % 148.11/21.24 | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.24 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (297) gives: % 148.11/21.24 | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.24 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.11/21.24 | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.24 | | | | | | | | | | | | | | | | | | | | | | | (3655) ~ (all_56_1 = e0) % 148.11/21.24 | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.24 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3650), (3655) imply: % 148.11/21.24 | | | | | | | | | | | | | | | | | | | | | | | (3656) $false % 148.11/21.24 | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.24 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3656) is inconsistent. % 148.11/21.24 | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.24 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.11/21.24 | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.24 | | | | | | | | | | | | | | | | | | | | | | | (3657) all_56_7 = e3 % 148.11/21.24 | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.24 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (402), (3657) imply: % 148.11/21.24 | | | | | | | | | | | | | | | | | | | | | | | (3658) all_52_12 = e3 % 148.11/21.24 | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.24 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (181), (3658) imply: % 148.11/21.24 | | | | | | | | | | | | | | | | | | | | | | | (3659) ~ (all_52_4 = e3) % 148.11/21.24 | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.24 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (168), (3658) imply: % 148.11/21.24 | | | | | | | | | | | | | | | | | | | | | | | (3660) ~ (all_52_8 = e3) % 148.11/21.24 | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.24 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (331) gives: % 148.11/21.24 | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.24 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.11/21.24 | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.24 | | | | | | | | | | | | | | | | | | | | | | | | (3661) all_58_4 = e3 % 148.11/21.24 | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.24 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (407), (3661) imply: % 148.11/21.24 | | | | | | | | | | | | | | | | | | | | | | | | (3662) all_52_8 = e3 % 148.11/21.24 | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.24 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3660), (3662) imply: % 148.11/21.24 | | | | | | | | | | | | | | | | | | | | | | | | (3663) $false % 148.11/21.24 | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.24 | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3663) is inconsistent. % 148.11/21.24 | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.24 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.11/21.24 | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.24 | | | | | | | | | | | | | | | | | | | | | | | | (3664) all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3 % 148.11/21.24 | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.24 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (9), (36), (38), (182), (237), (251), (330), % 148.11/21.24 | | | | | | | | | | | | | | | | | | | | | | | | (343), (389), (407), (457), (540), (548), (552), % 148.11/21.24 | | | | | | | | | | | | | | | | | | | | | | | | (555), (588), (627), (677), (2641), (3505), % 148.11/21.24 | | | | | | | | | | | | | | | | | | | | | | | | (3614), (3618), (3620), (3628), (3631), (3649), % 148.11/21.24 | | | | | | | | | | | | | | | | | | | | | | | | (3651), (3652), (3654), (3659), (3664), % 148.11/21.24 | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 148.11/21.24 | | | | | | | | | | | | | | | | | | | | | | | | #190. % 148.11/21.24 | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.24 | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.11/21.24 | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.24 | | | | | | | | | | | | | | | | | | | | | | End of split % 148.11/21.24 | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.24 | | | | | | | | | | | | | | | | | | | | | End of split % 148.11/21.24 | | | | | | | | | | | | | | | | | | | | | % 148.11/21.24 | | | | | | | | | | | | | | | | | | | | End of split % 148.11/21.24 | | | | | | | | | | | | | | | | | | | | % 148.11/21.24 | | | | | | | | | | | | | | | | | | | End of split % 148.11/21.24 | | | | | | | | | | | | | | | | | | | % 148.11/21.24 | | | | | | | | | | | | | | | | | | End of split % 148.11/21.24 | | | | | | | | | | | | | | | | | | % 148.11/21.24 | | | | | | | | | | | | | | | | | Case 2: % 148.11/21.24 | | | | | | | | | | | | | | | | | | % 148.11/21.24 | | | | | | | | | | | | | | | | | | (3665) all_56_21 = e3 % 148.11/21.24 | | | | | | | | | | | | | | | | | | (3666) all_56_17 = e1 % 148.11/21.24 | | | | | | | | | | | | | | | | | | % 148.11/21.24 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (381), (3666) imply: % 148.11/21.24 | | | | | | | | | | | | | | | | | | (3667) all_52_2 = e1 % 148.11/21.24 | | | | | | | | | | | | | | | | | | % 148.11/21.24 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (374), (3665) imply: % 148.11/21.24 | | | | | | | | | | | | | | | | | | (3668) all_6_2 = e3 % 148.11/21.24 | | | | | | | | | | | | | | | | | | % 148.11/21.24 | | | | | | | | | | | | | | | | | | SIMP: (3668) implies: % 148.11/21.24 | | | | | | | | | | | | | | | | | | (3669) all_6_2 = e3 % 148.11/21.24 | | | | | | | | | | | | | | | | | | % 148.11/21.24 | | | | | | | | | | | | | | | | | | REF_CLOSE: (42), (43), (51), (174), (189), (191), (208), % 148.11/21.24 | | | | | | | | | | | | | | | | | | (241), (243), (252), (287), (473), (476), (527), % 148.11/21.24 | | | | | | | | | | | | | | | | | | (543), (544), (545), (546), (559), (569), (573), % 148.11/21.24 | | | | | | | | | | | | | | | | | | (580), (587), (591), (768), (3505), (3516), % 148.11/21.24 | | | | | | | | | | | | | | | | | | (3521), (3665), (3667), (3669), (function-axioms) % 148.11/21.24 | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #188. % 148.11/21.24 | | | | | | | | | | | | | | | | | | % 148.11/21.24 | | | | | | | | | | | | | | | | | End of split % 148.11/21.24 | | | | | | | | | | | | | | | | | % 148.11/21.24 | | | | | | | | | | | | | | | | Case 2: % 148.11/21.24 | | | | | | | | | | | | | | | | | % 148.11/21.24 | | | | | | | | | | | | | | | | | (3670) all_56_31 = e1 % 148.11/21.24 | | | | | | | | | | | | | | | | | (3671) all_56_29 = e0 % 148.11/21.24 | | | | | | | | | | | | | | | | | % 148.11/21.24 | | | | | | | | | | | | | | | | | REF_CLOSE: (38), (41), (43), (46), (242), (247), (292), % 148.11/21.24 | | | | | | | | | | | | | | | | | (357), (374), (435), (507), (531), (541), (542), % 148.11/21.24 | | | | | | | | | | | | | | | | | (544), (573), (585), (622), (683), (685), (768), % 148.11/21.24 | | | | | | | | | | | | | | | | | (3519), (3521), (3609), (3612), (3670), (3671), % 148.11/21.24 | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 148.11/21.24 | | | | | | | | | | | | | | | | | #193. % 148.11/21.24 | | | | | | | | | | | | | | | | | % 148.11/21.24 | | | | | | | | | | | | | | | | End of split % 148.11/21.24 | | | | | | | | | | | | | | | | % 148.11/21.24 | | | | | | | | | | | | | | | Case 2: % 148.11/21.24 | | | | | | | | | | | | | | | | % 148.11/21.24 | | | | | | | | | | | | | | | | (3672) all_56_15 = e2 % 148.11/21.24 | | | | | | | | | | | | | | | | (3673) all_56_11 = e0 % 148.11/21.24 | | | | | | | | | | | | | | | | % 148.11/21.24 | | | | | | | | | | | | | | | | REF_CLOSE: (36), (38), (48), (237), (443), (540), (545), % 148.11/21.24 | | | | | | | | | | | | | | | | (590), (627), (769), (2641), (3511), (3672), % 148.11/21.24 | | | | | | | | | | | | | | | | (3673), (function-axioms) are inconsistent by % 148.11/21.24 | | | | | | | | | | | | | | | | sub-proof #224. % 148.11/21.24 | | | | | | | | | | | | | | | | % 148.11/21.24 | | | | | | | | | | | | | | | End of split % 148.11/21.24 | | | | | | | | | | | | | | | % 148.11/21.24 | | | | | | | | | | | | | | Case 2: % 148.11/21.24 | | | | | | | | | | | | | | | % 148.11/21.24 | | | | | | | | | | | | | | | (3674) all_56_21 = e2 % 148.11/21.24 | | | | | | | | | | | | | | | (3675) all_56_19 = e1 % 148.11/21.24 | | | | | | | | | | | | | | | % 148.11/21.24 | | | | | | | | | | | | | | | COMBINE_EQS: (435), (3675) imply: % 148.11/21.24 | | | | | | | | | | | | | | | (3676) all_52_6 = e1 % 148.11/21.24 | | | | | | | | | | | | | | | % 148.11/21.24 | | | | | | | | | | | | | | | COMBINE_EQS: (374), (3674) imply: % 148.11/21.24 | | | | | | | | | | | | | | | (3677) all_6_2 = e2 % 148.11/21.24 | | | | | | | | | | | | | | | % 148.11/21.24 | | | | | | | | | | | | | | | REF_CLOSE: (43), (46), (247), (507), (542), (573), (685), % 148.11/21.24 | | | | | | | | | | | | | | | (768), (3521), (3609), (3676), (3677), % 148.11/21.24 | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 148.11/21.24 | | | | | | | | | | | | | | | #506. % 148.11/21.24 | | | | | | | | | | | | | | | % 148.11/21.24 | | | | | | | | | | | | | | End of split % 148.11/21.24 | | | | | | | | | | | | | | % 148.11/21.24 | | | | | | | | | | | | | End of split % 148.11/21.24 | | | | | | | | | | | | | % 148.11/21.24 | | | | | | | | | | | | Case 2: % 148.11/21.24 | | | | | | | | | | | | | % 148.11/21.24 | | | | | | | | | | | | | (3678) all_36_1 = e3 % 148.11/21.24 | | | | | | | | | | | | | (3679) ~ (all_36_0 = e0) | ~ (all_36_2 = e2) % 148.11/21.24 | | | | | | | | | | | | | % 148.11/21.24 | | | | | | | | | | | | | COMBINE_EQS: (652), (3678) imply: % 148.11/21.24 | | | | | | | | | | | | | (3680) all_6_1 = e3 % 148.11/21.24 | | | | | | | | | | | | | % 148.11/21.24 | | | | | | | | | | | | | SIMP: (3680) implies: % 148.11/21.24 | | | | | | | | | | | | | (3681) all_6_1 = e3 % 148.11/21.24 | | | | | | | | | | | | | % 148.11/21.24 | | | | | | | | | | | | | REDUCE: (43), (3681) imply: % 148.11/21.24 | | | | | | | | | | | | | (3682) op(all_6_2, all_6_2) = e3 % 148.11/21.24 | | | | | | | | | | | | | % 148.11/21.24 | | | | | | | | | | | | | REDUCE: (42), (3681) imply: % 148.11/21.24 | | | | | | | | | | | | | (3683) op(e1, e3) = all_6_0 % 148.11/21.24 | | | | | | | | | | | | | % 148.11/21.24 | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_2, % 148.11/21.24 | | | | | | | | | | | | | all_6_0, e3, e1, simplifying with (211), (3683) % 148.11/21.24 | | | | | | | | | | | | | gives: % 148.11/21.24 | | | | | | | | | | | | | (3684) all_52_2 = all_6_0 % 148.11/21.24 | | | | | | | | | | | | | % 148.11/21.24 | | | | | | | | | | | | | COMBINE_EQS: (471), (3684) imply: % 148.11/21.24 | | | | | | | | | | | | | (3685) all_54_8 = all_6_0 % 148.11/21.24 | | | | | | | | | | | | | % 148.11/21.24 | | | | | | | | | | | | | COMBINE_EQS: (381), (3684) imply: % 148.11/21.24 | | | | | | | | | | | | | (3686) all_56_17 = all_6_0 % 148.11/21.24 | | | | | | | | | | | | | % 148.11/21.24 | | | | | | | | | | | | | COMBINE_EQS: (553), (3684) imply: % 148.11/21.24 | | | | | | | | | | | | | (3687) all_58_6 = all_6_0 % 148.11/21.24 | | | | | | | | | | | | | % 148.11/21.24 | | | | | | | | | | | | | REDUCE: (197), (3684) imply: % 148.11/21.24 | | | | | | | | | | | | | (3688) ~ (all_52_1 = all_6_0) % 148.11/21.24 | | | | | | | | | | | | | % 148.11/21.24 | | | | | | | | | | | | | REDUCE: (192), (3684) imply: % 148.11/21.24 | | | | | | | | | | | | | (3689) ~ (all_52_3 = all_6_0) % 148.11/21.24 | | | | | | | | | | | | | % 148.11/21.24 | | | | | | | | | | | | | SIMP: (3689) implies: % 148.11/21.24 | | | | | | | | | | | | | (3690) ~ (all_52_3 = all_6_0) % 148.11/21.24 | | | | | | | | | | | | | % 148.11/21.24 | | | | | | | | | | | | | REDUCE: (191), (3684) imply: % 148.11/21.24 | | | | | | | | | | | | | (3691) ~ (all_52_6 = all_6_0) % 148.11/21.24 | | | | | | | | | | | | | % 148.11/21.24 | | | | | | | | | | | | | SIMP: (3691) implies: % 148.11/21.24 | | | | | | | | | | | | | (3692) ~ (all_52_6 = all_6_0) % 148.11/21.24 | | | | | | | | | | | | | % 148.11/21.24 | | | | | | | | | | | | | REDUCE: (189), (3684) imply: % 148.11/21.24 | | | | | | | | | | | | | (3693) ~ (all_52_14 = all_6_0) % 148.11/21.24 | | | | | | | | | | | | | % 148.11/21.24 | | | | | | | | | | | | | SIMP: (3693) implies: % 148.11/21.24 | | | | | | | | | | | | | (3694) ~ (all_52_14 = all_6_0) % 148.11/21.24 | | | | | | | | | | | | | % 148.11/21.24 | | | | | | | | | | | | | REDUCE: (559), (3684) imply: % 148.11/21.24 | | | | | | | | | | | | | (3695) ~ (all_10_2 = all_6_0) % 148.11/21.24 | | | | | | | | | | | | | % 148.11/21.24 | | | | | | | | | | | | | SIMP: (3695) implies: % 148.11/21.24 | | | | | | | | | | | | | (3696) ~ (all_10_2 = all_6_0) % 148.11/21.24 | | | | | | | | | | | | | % 148.11/21.24 | | | | | | | | | | | | | REDUCE: (569), (3684) imply: % 148.11/21.24 | | | | | | | | | | | | | (3697) ~ (all_6_0 = all_6_2) % 148.11/21.24 | | | | | | | | | | | | | % 148.11/21.24 | | | | | | | | | | | | | BETA: splitting (292) gives: % 148.11/21.24 | | | | | | | | | | | | | % 148.11/21.24 | | | | | | | | | | | | | Case 1: % 148.11/21.24 | | | | | | | | | | | | | | % 148.11/21.24 | | | | | | | | | | | | | | (3698) ~ (all_56_21 = e2) % 148.11/21.24 | | | | | | | | | | | | | | % 148.11/21.24 | | | | | | | | | | | | | | REDUCE: (374), (3698) imply: % 148.11/21.24 | | | | | | | | | | | | | | (3699) ~ (all_6_2 = e2) % 148.11/21.24 | | | | | | | | | | | | | | % 148.11/21.24 | | | | | | | | | | | | | | BETA: splitting (294) gives: % 148.11/21.24 | | | | | | | | | | | | | | % 148.11/21.24 | | | | | | | | | | | | | | Case 1: % 148.11/21.24 | | | | | | | | | | | | | | | % 148.11/21.24 | | | | | | | | | | | | | | | (3700) ~ (all_56_11 = e0) % 148.11/21.24 | | | | | | | | | | | | | | | % 148.11/21.24 | | | | | | | | | | | | | | | REDUCE: (545), (3700) imply: % 148.11/21.24 | | | | | | | | | | | | | | | (3701) ~ (all_8_2 = e0) % 148.11/21.24 | | | | | | | | | | | | | | | % 148.11/21.24 | | | | | | | | | | | | | | | BETA: splitting (293) gives: % 148.11/21.24 | | | | | | | | | | | | | | | % 148.11/21.24 | | | | | | | | | | | | | | | Case 1: % 148.11/21.24 | | | | | | | | | | | | | | | | % 148.11/21.24 | | | | | | | | | | | | | | | | (3702) ~ (all_56_21 = e3) % 148.11/21.24 | | | | | | | | | | | | | | | | % 148.11/21.24 | | | | | | | | | | | | | | | | REDUCE: (374), (3702) imply: % 148.11/21.24 | | | | | | | | | | | | | | | | (3703) ~ (all_6_2 = e3) % 148.11/21.24 | | | | | | | | | | | | | | | | % 148.11/21.24 | | | | | | | | | | | | | | | | REF_CLOSE: (36), (38), (41), (48), (51), (174), (194), (242), % 148.11/21.24 | | | | | | | | | | | | | | | | (243), (244), (247), (252), (287), (290), (291), % 148.11/21.24 | | | | | | | | | | | | | | | | (295), (296), (326), (342), (344), (365), (366), % 148.11/21.24 | | | | | | | | | | | | | | | | (374), (380), (401), (425), (431), (447), (473), % 148.11/21.24 | | | | | | | | | | | | | | | | (541), (542), (543), (544), (545), (546), (550), % 148.11/21.24 | | | | | | | | | | | | | | | | (552), (557), (561), (568), (573), (577), (580), % 148.11/21.24 | | | | | | | | | | | | | | | | (583), (587), (622), (627), (769), (3511), (3516), % 148.11/21.24 | | | | | | | | | | | | | | | | (3682), (3685), (3687), (3688), (3690), (3692), % 148.11/21.24 | | | | | | | | | | | | | | | | (3694), (3696), (3697), (3699), (3701), (3703), % 148.11/21.24 | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 148.11/21.24 | | | | | | | | | | | | | | | | #185. % 148.11/21.24 | | | | | | | | | | | | | | | | % 148.11/21.24 | | | | | | | | | | | | | | | Case 2: % 148.11/21.24 | | | | | | | | | | | | | | | | % 148.11/21.24 | | | | | | | | | | | | | | | | (3704) all_56_21 = e3 % 148.11/21.24 | | | | | | | | | | | | | | | | (3705) all_56_17 = e1 % 148.11/21.24 | | | | | | | | | | | | | | | | % 148.11/21.24 | | | | | | | | | | | | | | | | REF_CLOSE: (51), (53), (374), (612), (3509), (3682), (3686), % 148.11/21.24 | | | | | | | | | | | | | | | | (3696), (3704), (3705), (function-axioms) are % 148.11/21.24 | | | | | | | | | | | | | | | | inconsistent by sub-proof #184. % 148.11/21.24 | | | | | | | | | | | | | | | | % 148.11/21.24 | | | | | | | | | | | | | | | End of split % 148.11/21.24 | | | | | | | | | | | | | | | % 148.11/21.24 | | | | | | | | | | | | | | Case 2: % 148.11/21.24 | | | | | | | | | | | | | | | % 148.11/21.24 | | | | | | | | | | | | | | | (3706) all_56_15 = e2 % 148.11/21.24 | | | | | | | | | | | | | | | (3707) all_56_11 = e0 % 148.11/21.24 | | | | | | | | | | | | | | | % 148.11/21.24 | | | | | | | | | | | | | | | COMBINE_EQS: (545), (3707) imply: % 148.11/21.24 | | | | | | | | | | | | | | | (3708) all_8_2 = e0 % 148.11/21.24 | | | | | | | | | | | | | | | % 148.11/21.24 | | | | | | | | | | | | | | | COMBINE_EQS: (443), (3706) imply: % 148.11/21.24 | | | | | | | | | | | | | | | (3709) all_52_13 = e2 % 148.11/21.24 | | | | | | | | | | | | | | | % 148.11/21.24 | | | | | | | | | | | | | | | REDUCE: (573), (3708) imply: % 148.11/21.24 | | | | | | | | | | | | | | | (3710) ~ (all_52_6 = e0) % 148.11/21.24 | | | | | | | | | | | | | | | % 148.11/21.24 | | | | | | | | | | | | | | | REDUCE: (158), (3709) imply: % 148.11/21.24 | | | | | | | | | | | | | | | (3711) ~ (all_52_14 = e2) % 148.11/21.24 | | | | | | | | | | | | | | | % 148.11/21.24 | | | | | | | | | | | | | | | SIMP: (3711) implies: % 148.11/21.24 | | | | | | | | | | | | | | | (3712) ~ (all_52_14 = e2) % 148.11/21.24 | | | | | | | | | | | | | | | % 148.11/21.24 | | | | | | | | | | | | | | | REDUCE: (48), (3708) imply: % 148.11/21.24 | | | | | | | | | | | | | | | (3713) op(e0, e0) = all_8_1 % 148.11/21.24 | | | | | | | | | | | | | | | % 148.11/21.24 | | | | | | | | | | | | | | | REF_CLOSE: (4), (36), (38), (41), (46), (48), (51), (168), % 148.11/21.24 | | | | | | | | | | | | | | | (174), (181), (242), (243), (244), (287), (291), % 148.11/21.24 | | | | | | | | | | | | | | | (292), (293), (295), (320), (321), (323), (324), % 148.11/21.24 | | | | | | | | | | | | | | | (326), (329), (337), (365), (366), (374), (380), % 148.11/21.24 | | | | | | | | | | | | | | | (389), (407), (431), (435), (473), (532), (541), % 148.11/21.24 | | | | | | | | | | | | | | | (544), (545), (546), (547), (548), (549), (550), % 148.11/21.24 | | | | | | | | | | | | | | | (551), (552), (554), (555), (561), (567), (573), % 148.11/21.24 | | | | | | | | | | | | | | | (575), (577), (580), (585), (587), (591), (617), % 148.11/21.24 | | | | | | | | | | | | | | | (622), (623), (627), (762), (769), (3511), (3516), % 148.11/21.24 | | | | | | | | | | | | | | | (3679), (3682), (3685), (3686), (3687), (3692), % 148.11/21.24 | | | | | | | | | | | | | | | (3694), (3696), (3697), (3699), (3710), (3712), % 148.11/21.24 | | | | | | | | | | | | | | | (3713), (function-axioms) are inconsistent by % 148.11/21.24 | | | | | | | | | | | | | | | sub-proof #183. % 148.11/21.24 | | | | | | | | | | | | | | | % 148.11/21.24 | | | | | | | | | | | | | | End of split % 148.11/21.24 | | | | | | | | | | | | | | % 148.11/21.24 | | | | | | | | | | | | | Case 2: % 148.11/21.24 | | | | | | | | | | | | | | % 148.11/21.24 | | | | | | | | | | | | | | (3714) all_56_21 = e2 % 148.11/21.24 | | | | | | | | | | | | | | (3715) all_56_19 = e1 % 148.11/21.24 | | | | | | | | | | | | | | % 148.11/21.24 | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (46), (48), (244), (287), (324), (374), % 148.11/21.24 | | | | | | | | | | | | | | (380), (435), (532), (544), (545), (546), (550), % 148.11/21.24 | | | | | | | | | | | | | | (552), (580), (591), (617), (762), (3679), (3682), % 148.11/21.24 | | | | | | | | | | | | | | (3685), (3687), (3692), (3694), (3696), (3697), % 148.11/21.24 | | | | | | | | | | | | | | (3714), (3715), (function-axioms) are inconsistent % 148.11/21.24 | | | | | | | | | | | | | | by sub-proof #412. % 148.11/21.24 | | | | | | | | | | | | | | % 148.11/21.24 | | | | | | | | | | | | | End of split % 148.11/21.24 | | | | | | | | | | | | | % 148.11/21.24 | | | | | | | | | | | | End of split % 148.11/21.24 | | | | | | | | | | | | % 148.11/21.24 | | | | | | | | | | | End of split % 148.11/21.24 | | | | | | | | | | | % 148.11/21.24 | | | | | | | | | | Case 2: % 148.11/21.24 | | | | | | | | | | | % 148.11/21.24 | | | | | | | | | | | (3716) all_28_0 = e2 % 148.11/21.24 | | | | | | | | | | | (3717) ~ (all_28_1 = e3) | ~ (all_28_2 = e0) % 148.11/21.24 | | | | | | | | | | | % 148.11/21.24 | | | | | | | | | | | COMBINE_EQS: (740), (3716) imply: % 148.11/21.24 | | | | | | | | | | | (3718) all_6_0 = e2 % 148.11/21.24 | | | | | | | | | | | % 148.11/21.24 | | | | | | | | | | | REF_CLOSE: (6), (8), (36), (37), (38), (41), (42), (43), % 148.11/21.24 | | | | | | | | | | | (46), (48), (51), (144), (158), (169), (171), % 148.11/21.24 | | | | | | | | | | | (174), (208), (211), (237), (242), (247), (250), % 148.11/21.24 | | | | | | | | | | | (252), (287), (288), (289), (290), (291), (292), % 148.11/21.24 | | | | | | | | | | | (293), (294), (297), (321), (332), (333), (341), % 148.11/21.24 | | | | | | | | | | | (357), (366), (374), (381), (386), (389), (401), % 148.11/21.24 | | | | | | | | | | | (402), (407), (419), (435), (443), (459), (475), % 148.11/21.24 | | | | | | | | | | | (513), (540), (541), (542), (543), (544), (545), % 148.11/21.24 | | | | | | | | | | | (546), (547), (550), (551), (554), (555), (559), % 148.11/21.24 | | | | | | | | | | | (565), (568), (569), (571), (573), (580), (582), % 148.11/21.24 | | | | | | | | | | | (585), (588), (590), (620), (622), (627), (634), % 148.11/21.24 | | | | | | | | | | | (665), (764), (768), (769), (3717), (3718), % 148.11/21.24 | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 148.11/21.24 | | | | | | | | | | | #200. % 148.11/21.24 | | | | | | | | | | | % 148.11/21.24 | | | | | | | | | | End of split % 148.11/21.24 | | | | | | | | | | % 148.11/21.24 | | | | | | | | | End of split % 148.11/21.24 | | | | | | | | | % 148.11/21.24 | | | | | | | | Case 2: % 148.11/21.24 | | | | | | | | | % 148.11/21.24 | | | | | | | | | (3719) all_22_1 = e3 % 148.11/21.24 | | | | | | | | | (3720) ~ (all_22_0 = e0) | ~ (all_22_2 = e1) % 148.11/21.24 | | | | | | | | | % 148.11/21.25 | | | | | | | | | REF_CLOSE: (4), (5), (6), (36), (37), (38), (41), (42), (43), % 148.11/21.25 | | | | | | | | | (46), (47), (48), (51), (53), (99), (114), (119), % 148.11/21.25 | | | | | | | | | (144), (158), (165), (166), (169), (171), (173), % 148.11/21.25 | | | | | | | | | (174), (187), (189), (191), (193), (194), (196), % 148.11/21.25 | | | | | | | | | (197), (205), (207), (208), (211), (215), (237), % 148.11/21.25 | | | | | | | | | (238), (240), (241), (242), (243), (244), (245), % 148.11/21.25 | | | | | | | | | (247), (248), (250), (252), (287), (288), (289), % 148.11/21.25 | | | | | | | | | (290), (291), (292), (293), (294), (295), (296), % 148.11/21.25 | | | | | | | | | (297), (298), (320), (321), (324), (329), (331), % 148.11/21.25 | | | | | | | | | (332), (333), (341), (342), (357), (360), (365), % 148.11/21.25 | | | | | | | | | (366), (374), (380), (381), (386), (389), (401), % 148.11/21.25 | | | | | | | | | (402), (407), (419), (425), (429), (431), (435), % 148.11/21.25 | | | | | | | | | (443), (447), (459), (463), (469), (471), (473), % 148.11/21.25 | | | | | | | | | (475), (476), (478), (482), (513), (523), (529), % 148.11/21.25 | | | | | | | | | (531), (532), (540), (541), (542), (543), (544), % 148.11/21.25 | | | | | | | | | (545), (546), (547), (548), (549), (550), (551), % 148.11/21.25 | | | | | | | | | (552), (553), (554), (555), (557), (559), (561), % 148.11/21.25 | | | | | | | | | (565), (568), (569), (570), (571), (573), (575), % 148.11/21.25 | | | | | | | | | (577), (579), (580), (582), (583), (585), (587), % 148.11/21.25 | | | | | | | | | (588), (590), (591), (617), (620), (622), (624), % 148.11/21.25 | | | | | | | | | (625), (627), (634), (652), (665), (672), (681), % 148.11/21.25 | | | | | | | | | (683), (740), (752), (762), (764), (768), (769), % 148.11/21.25 | | | | | | | | | (2637), (2639), (2641), (2643), (3719), (3720), % 148.11/21.25 | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 148.11/21.25 | | | | | | | | | #178. % 148.11/21.25 | | | | | | | | | % 148.11/21.25 | | | | | | | | End of split % 148.11/21.25 | | | | | | | | % 148.11/21.25 | | | | | | | End of split % 148.11/21.25 | | | | | | | % 148.11/21.25 | | | | | | Case 2: % 148.11/21.25 | | | | | | | % 148.11/21.25 | | | | | | | (3721) all_14_0 = e1 % 148.11/21.25 | | | | | | | (3722) ~ (all_14_1 = e3) | ~ (all_14_2 = e0) % 148.11/21.25 | | | | | | | % 148.11/21.25 | | | | | | | REF_CLOSE: (5), (6), (36), (38), (41), (42), (43), (46), (47), % 148.11/21.25 | | | | | | | (48), (51), (114), (119), (134), (173), (188), (189), % 148.11/21.25 | | | | | | | (193), (194), (196), (197), (205), (211), (212), (215), % 148.11/21.25 | | | | | | | (237), (239), (242), (247), (248), (252), (287), (288), % 148.11/21.25 | | | | | | | (289), (290), (291), (292), (293), (294), (295), (296), % 148.11/21.25 | | | | | | | (318), (319), (321), (323), (332), (335), (357), (360), % 148.11/21.25 | | | | | | | (365), (374), (381), (386), (401), (425), (431), (435), % 148.11/21.25 | | | | | | | (443), (447), (463), (480), (528), (529), (531), (534), % 148.11/21.25 | | | | | | | (540), (541), (542), (543), (544), (545), (546), (547), % 148.11/21.25 | | | | | | | (548), (549), (550), (551), (557), (568), (569), (573), % 148.11/21.25 | | | | | | | (575), (579), (580), (581), (583), (585), (587), (590), % 148.11/21.25 | | | | | | | (617), (622), (627), (639), (652), (679), (683), (758), % 148.11/21.25 | | | | | | | (763), (768), (769), (2637), (2639), (2641), (3721), % 148.11/21.25 | | | | | | | (3722), (function-axioms) are inconsistent by sub-proof % 148.11/21.25 | | | | | | | #176. % 148.11/21.25 | | | | | | | % 148.11/21.25 | | | | | | End of split % 148.11/21.25 | | | | | | % 148.11/21.25 | | | | | End of split % 148.11/21.25 | | | | | % 148.11/21.25 | | | | Case 2: % 148.11/21.25 | | | | | % 148.11/21.25 | | | | | (3723) all_10_0 = e2 % 148.11/21.25 | | | | | (3724) ~ (all_10_1 = e0) | ~ (all_10_2 = e1) % 148.11/21.25 | | | | | % 148.11/21.25 | | | | | COMBINE_EQS: (766), (3723) imply: % 148.11/21.25 | | | | | (3725) all_50_0 = e2 % 148.11/21.25 | | | | | % 148.11/21.25 | | | | | REDUCE: (52), (3723) imply: % 148.11/21.25 | | | | | (3726) op(e3, all_10_1) = e2 % 148.11/21.25 | | | | | % 148.11/21.25 | | | | | BETA: splitting (59) gives: % 148.11/21.25 | | | | | % 148.11/21.25 | | | | | Case 1: % 148.11/21.25 | | | | | | % 148.11/21.25 | | | | | | (3727) ~ (all_12_0 = e2) % 148.11/21.25 | | | | | | % 148.11/21.25 | | | | | | REDUCE: (759), (3727) imply: % 148.11/21.25 | | | | | | (3728) ~ (all_4_0 = e2) % 148.11/21.25 | | | | | | % 148.11/21.25 | | | | | | BETA: splitting (64) gives: % 148.11/21.25 | | | | | | % 148.11/21.25 | | | | | | Case 1: % 148.11/21.25 | | | | | | | % 148.11/21.25 | | | | | | | (3729) ~ (all_14_0 = e1) % 148.11/21.25 | | | | | | | % 148.11/21.25 | | | | | | | REDUCE: (758), (3729) imply: % 148.11/21.25 | | | | | | | (3730) ~ (all_8_0 = e1) % 148.11/21.25 | | | | | | | % 148.11/21.25 | | | | | | | BETA: splitting (84) gives: % 148.11/21.25 | | | | | | | % 148.11/21.25 | | | | | | | Case 1: % 148.11/21.25 | | | | | | | | % 148.11/21.25 | | | | | | | | (3731) ~ (all_22_1 = e3) % 148.11/21.25 | | | | | | | | % 148.11/21.25 | | | | | | | | REDUCE: (672), (3731) imply: % 148.11/21.25 | | | | | | | | (3732) ~ (all_8_1 = e3) % 148.11/21.25 | | | | | | | | % 148.11/21.25 | | | | | | | | BETA: splitting (94) gives: % 148.11/21.25 | | | | | | | | % 148.11/21.25 | | | | | | | | Case 1: % 148.11/21.25 | | | | | | | | | % 148.11/21.25 | | | | | | | | | (3733) ~ (all_26_0 = e1) % 148.11/21.25 | | | | | | | | | % 148.11/21.25 | | | | | | | | | REDUCE: (760), (3733) imply: % 148.11/21.25 | | | | | | | | | (3734) ~ (all_4_0 = e1) % 148.11/21.25 | | | | | | | | | % 148.11/21.25 | | | | | | | | | BETA: splitting (99) gives: % 148.11/21.25 | | | | | | | | | % 148.11/21.25 | | | | | | | | | Case 1: % 148.11/21.25 | | | | | | | | | | % 148.11/21.25 | | | | | | | | | | (3735) ~ (all_28_0 = e2) % 148.11/21.25 | | | | | | | | | | % 148.11/21.25 | | | | | | | | | | REDUCE: (740), (3735) imply: % 148.11/21.25 | | | | | | | | | | (3736) ~ (all_6_0 = e2) % 148.11/21.25 | | | | | | | | | | % 148.11/21.25 | | | | | | | | | | BETA: splitting (104) gives: % 148.11/21.25 | | | | | | | | | | % 148.11/21.25 | | | | | | | | | | Case 1: % 148.11/21.25 | | | | | | | | | | | % 148.11/21.25 | | | | | | | | | | | (3737) ~ (all_30_0 = e3) % 148.11/21.25 | | | | | | | | | | | % 148.11/21.25 | | | | | | | | | | | REDUCE: (718), (3737) imply: % 148.11/21.25 | | | | | | | | | | | (3738) ~ (all_8_0 = e3) % 148.11/21.25 | | | | | | | | | | | % 148.11/21.25 | | | | | | | | | | | BETA: splitting (119) gives: % 148.11/21.25 | | | | | | | | | | | % 148.11/21.25 | | | | | | | | | | | Case 1: % 148.11/21.25 | | | | | | | | | | | | % 148.11/21.25 | | | | | | | | | | | | (3739) ~ (all_36_1 = e3) % 148.11/21.25 | | | | | | | | | | | | % 148.11/21.25 | | | | | | | | | | | | REDUCE: (652), (3739) imply: % 148.11/21.25 | | | | | | | | | | | | (3740) ~ (all_6_1 = e3) % 148.11/21.25 | | | | | | | | | | | | % 148.11/21.25 | | | | | | | | | | | | BETA: splitting (129) gives: % 148.11/21.25 | | | | | | | | | | | | % 148.11/21.25 | | | | | | | | | | | | Case 1: % 148.11/21.25 | | | | | | | | | | | | | % 148.11/21.25 | | | | | | | | | | | | | (3741) ~ (all_40_0 = e3) % 148.11/21.25 | | | | | | | | | | | | | % 148.11/21.25 | | | | | | | | | | | | | REDUCE: (713), (3741) imply: % 148.11/21.25 | | | | | | | | | | | | | (3742) ~ (all_6_0 = e3) % 148.11/21.25 | | | | | | | | | | | | | % 148.11/21.25 | | | | | | | | | | | | | BETA: splitting (154) gives: % 148.11/21.25 | | | | | | | | | | | | | % 148.11/21.25 | | | | | | | | | | | | | Case 1: % 148.11/21.25 | | | | | | | | | | | | | | % 148.11/21.25 | | | | | | | | | | | | | | (3743) ~ (all_50_0 = e2) % 148.11/21.25 | | | | | | | | | | | | | | % 148.11/21.25 | | | | | | | | | | | | | | REDUCE: (3725), (3743) imply: % 148.11/21.25 | | | | | | | | | | | | | | (3744) $false % 148.11/21.25 | | | | | | | | | | | | | | % 148.11/21.25 | | | | | | | | | | | | | | CLOSE: (3744) is inconsistent. % 148.11/21.25 | | | | | | | | | | | | | | % 148.11/21.25 | | | | | | | | | | | | | Case 2: % 148.11/21.25 | | | | | | | | | | | | | | % 148.11/21.25 | | | | | | | | | | | | | | (3745) ~ (all_50_1 = e1) | ~ (all_50_2 = e0) % 148.11/21.25 | | | | | | | | | | | | | | % 148.11/21.25 | | | | | | | | | | | | | | BETA: splitting (288) gives: % 148.11/21.25 | | | | | | | | | | | | | | % 148.11/21.25 | | | | | | | | | | | | | | Case 1: % 148.11/21.25 | | | | | | | | | | | | | | | % 148.11/21.25 | | | | | | | | | | | | | | | (3746) ~ (all_56_31 = e1) % 148.11/21.25 | | | | | | | | | | | | | | | % 148.11/21.25 | | | | | | | | | | | | | | | REDUCE: (544), (3746) imply: % 148.11/21.25 | | | | | | | | | | | | | | | (3747) ~ (all_4_2 = e1) % 148.11/21.25 | | | | | | | | | | | | | | | % 148.11/21.25 | | | | | | | | | | | | | | | BETA: splitting (290) gives: % 148.11/21.25 | | | | | | | | | | | | | | | % 148.11/21.25 | | | | | | | | | | | | | | | Case 1: % 148.11/21.25 | | | | | | | | | | | | | | | | % 148.11/21.25 | | | | | | | | | | | | | | | | (3748) ~ (all_56_31 = e3) % 148.11/21.25 | | | | | | | | | | | | | | | | % 148.11/21.25 | | | | | | | | | | | | | | | | REDUCE: (544), (3748) imply: % 148.11/21.25 | | | | | | | | | | | | | | | | (3749) ~ (all_4_2 = e3) % 148.11/21.25 | | | | | | | | | | | | | | | | % 148.11/21.25 | | | | | | | | | | | | | | | | BETA: splitting (289) gives: % 148.11/21.25 | | | | | | | | | | | | | | | | % 148.11/21.25 | | | | | | | | | | | | | | | | Case 1: % 148.11/21.25 | | | | | | | | | | | | | | | | | % 148.11/21.25 | | | | | | | | | | | | | | | | | (3750) ~ (all_56_31 = e2) % 148.11/21.25 | | | | | | | | | | | | | | | | | % 148.11/21.25 | | | | | | | | | | | | | | | | | REDUCE: (544), (3750) imply: % 148.11/21.25 | | | | | | | | | | | | | | | | | (3751) ~ (all_4_2 = e2) % 148.11/21.25 | | | | | | | | | | | | | | | | | % 148.11/21.25 | | | | | | | | | | | | | | | | | BETA: splitting (237) gives: % 148.11/21.25 | | | | | | | | | | | | | | | | | % 148.11/21.25 | | | | | | | | | | | | | | | | | Case 1: % 148.11/21.25 | | | | | | | | | | | | | | | | | | % 148.11/21.25 | | | | | | | | | | | | | | | | | | (3752) all_54_15 = e3 % 148.11/21.25 | | | | | | | | | | | | | | | | | | % 148.11/21.25 | | | | | | | | | | | | | | | | | | REF_CLOSE: (540), (3749), (3752) are inconsistent by % 148.11/21.25 | | | | | | | | | | | | | | | | | | sub-proof #740. % 148.11/21.25 | | | | | | | | | | | | | | | | | | % 148.11/21.25 | | | | | | | | | | | | | | | | | Case 2: % 148.11/21.25 | | | | | | | | | | | | | | | | | | % 148.11/21.25 | | | | | | | | | | | | | | | | | | (3753) all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0 % 148.11/21.25 | | | | | | | | | | | | | | | | | | % 148.11/21.25 | | | | | | | | | | | | | | | | | | BETA: splitting (3753) gives: % 148.11/21.25 | | | | | | | | | | | | | | | | | | % 148.11/21.25 | | | | | | | | | | | | | | | | | | Case 1: % 148.11/21.25 | | | | | | | | | | | | | | | | | | | % 148.11/21.25 | | | | | | | | | | | | | | | | | | | (3754) all_54_15 = e2 % 148.11/21.25 | | | | | | | | | | | | | | | | | | | % 148.11/21.25 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (540), (3751), (3754) are inconsistent by % 148.11/21.25 | | | | | | | | | | | | | | | | | | | sub-proof #739. % 148.11/21.25 | | | | | | | | | | | | | | | | | | | % 148.11/21.25 | | | | | | | | | | | | | | | | | | Case 2: % 148.11/21.25 | | | | | | | | | | | | | | | | | | | % 148.11/21.25 | | | | | | | | | | | | | | | | | | | (3755) all_54_15 = e1 | all_54_15 = e0 % 148.11/21.25 | | | | | | | | | | | | | | | | | | | % 148.11/21.25 | | | | | | | | | | | | | | | | | | | BETA: splitting (3755) gives: % 148.11/21.25 | | | | | | | | | | | | | | | | | | | % 148.11/21.25 | | | | | | | | | | | | | | | | | | | Case 1: % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | (3756) all_54_15 = e1 % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (540), (3747), (3756) are inconsistent by % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | sub-proof #738. % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | % 148.11/21.25 | | | | | | | | | | | | | | | | | | | Case 2: % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | (3757) all_54_15 = e0 % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (540), (3757) imply: % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | (3758) all_4_2 = e0 % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | SIMP: (3758) implies: % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | (3759) all_4_2 = e0 % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | REDUCE: (570), (3759) imply: % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | (3760) ~ (all_52_3 = e0) % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | REDUCE: (581), (3759) imply: % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | (3761) ~ (all_52_7 = e0) % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | REDUCE: (588), (3759) imply: % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | (3762) ~ (all_52_11 = e0) % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | REDUCE: (589), (3759) imply: % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | (3763) ~ (all_52_12 = e0) % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | REDUCE: (590), (3759) imply: % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | (3764) ~ (all_52_13 = e0) % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | REDUCE: (591), (3759) imply: % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | (3765) ~ (all_52_14 = e0) % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | REDUCE: (38), (3759) imply: % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | (3766) op(e0, e0) = all_4_1 % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | REDUCE: (627), (3759) imply: % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | (3767) op(e0, e0) = all_56_30 % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | REDUCE: (36), (3759) imply: % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | (3768) op(e0, e0) = e0 % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_4_1, % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | all_56_30, e0, e0, simplifying with (3766), (3767) % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | gives: % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | (3769) all_56_30 = all_4_1 % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | all_56_30, e0, e0, simplifying with (3767), (3768) % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | gives: % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | (3770) all_56_30 = e0 % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3769), (3770) imply: % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | (3771) all_4_1 = e0 % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | SIMP: (3771) implies: % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | (3772) all_4_1 = e0 % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | REDUCE: (37), (3772) imply: % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | (3773) op(e0, e0) = all_4_0 % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_4_0, % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | e0, e0, simplifying with (3768), (3773) gives: % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | (3774) all_4_0 = e0 % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | REDUCE: (767), (3774) imply: % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | (3775) ~ (e3 = e0) % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | BETA: splitting (295) gives: % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | Case 1: % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | (3776) ~ (all_56_11 = e1) % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | REDUCE: (545), (3776) imply: % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | (3777) ~ (all_8_2 = e1) % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (298) gives: % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | (3778) ~ (all_56_1 = e1) % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (546), (3778) imply: % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | (3779) ~ (all_10_2 = e1) % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (297) gives: % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | (3780) ~ (all_56_1 = e0) % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (546), (3780) imply: % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | (3781) ~ (all_10_2 = e0) % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (299) gives: % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | (3782) ~ (all_56_1 = e2) % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (546), (3782) imply: % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | (3783) ~ (all_10_2 = e2) % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (252) gives: % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | | (3784) all_54_0 = e3 % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (543), (3784) imply: % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | | (3785) all_10_2 = e3 % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3785) implies: % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | | (3786) all_10_2 = e3 % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (53), (3786) imply: % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | | (3787) op(e3, e3) = all_10_1 % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (612), (3786) imply: % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | | (3788) op(e3, e3) = all_56_0 % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (51), (3786) imply: % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | | (3789) op(e3, e3) = e3 % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_10_1, % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_0, e3, e3, simplifying with (3787), (3788) % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | | (3790) all_56_0 = all_10_1 % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_56_0, % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | | e3, e3, simplifying with (3788), (3789) gives: % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | | (3791) all_56_0 = e3 % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3790), (3791) imply: % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | | (3792) all_10_1 = e3 % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (3726), (3787), (3788), (3792), % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | | #175. % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | | (3793) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (543), (3779), (3781), (3783), (3793) are % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #731. % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | (3794) all_56_3 = e3 % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | (3795) all_56_1 = e2 % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (546), (3795) imply: % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | (3796) all_10_2 = e2 % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (408), (3794) imply: % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | (3797) all_52_4 = e3 % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (555), (3797) imply: % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | (3798) all_58_1 = e3 % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (419), (3796) imply: % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | (3799) all_58_0 = e2 % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (559), (3796) imply: % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | (3800) ~ (all_52_2 = e2) % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (561), (3796) imply: % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | (3801) ~ (all_52_3 = e2) % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (184), (3797) imply: % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | (3802) ~ (all_52_6 = e3) % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3802) implies: % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | (3803) ~ (all_52_6 = e3) % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (181), (3797) imply: % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | (3804) ~ (all_52_12 = e3) % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3804) implies: % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | (3805) ~ (all_52_12 = e3) % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (567), (3796) imply: % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | (3806) ~ (all_52_12 = e2) % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (53), (3796) imply: % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | (3807) op(e2, e2) = all_10_1 % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (51), (3796) imply: % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | (3808) op(e3, e3) = e2 % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (249) gives: % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | | (3809) all_54_3 = e3 % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (461), (3809) imply: % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | | (3810) all_52_12 = e3 % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3805), (3810) imply: % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | | (3811) $false % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3811) is inconsistent. % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | | (3812) all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0 % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (341) gives: % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | | | (3813) all_58_0 = e0 % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3799), (3813) imply: % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | | | (3814) e2 = e0 % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5), (3814) imply: % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | | | (3815) $false % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3815) is inconsistent. % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | | | (3816) all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0 % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3812) gives: % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3817) all_54_3 = e2 % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (461), (3817) imply: % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3818) all_52_12 = e2 % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3806), (3818) imply: % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3819) $false % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3819) is inconsistent. % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3820) all_54_3 = e1 | all_54_3 = e0 % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3820) gives: % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3821) all_54_3 = e1 % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (461), (3821) imply: % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3822) all_52_12 = e1 % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (551), (3822) imply: % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3823) all_58_9 = e1 % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (216), (3822) imply: % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3824) op(e3, e0) = e1 % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3816) gives: % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3825) all_58_1 = e0 % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3798), (3825) imply: % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3826) e3 = e0 % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7), (3826) imply: % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3827) $false % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3827) is inconsistent. % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3828) all_58_4 = e0 | all_58_9 = e0 % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3828) gives: % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3829) all_58_4 = e0 % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (407), (3829) imply: % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3830) all_52_8 = e0 % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (582), (3830) imply: % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3831) ~ (all_6_2 = e0) % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3831) implies: % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3832) ~ (all_6_2 = e0) % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (620), (3830) imply: % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3833) op(e1, e0) = all_56_4 % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_14, % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_4, e0, e1, simplifying with (208), (3833) % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3834) all_56_4 = all_52_14 % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_8_2, % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_10_1, e2, e2, simplifying with (46), (3807) % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3835) all_10_1 = all_8_2 % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3726), (3835) imply: % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3836) op(e3, all_8_2) = e2 % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (293) gives: % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3837) ~ (all_56_21 = e3) % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (374), (3837) imply: % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3838) ~ (all_6_2 = e3) % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (292) gives: % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3839) ~ (all_56_21 = e2) % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (374), (3839) imply: % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3840) ~ (all_6_2 = e2) % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (242) gives: % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3841) all_54_10 = e3 % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (541), (3838), (3841) are inconsistent by % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #736. % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3842) ~ (all_54_10 = e3) % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3843) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 148.11/21.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3843) gives: % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3844) all_54_10 = e2 % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (541), (3840), (3844) are inconsistent by % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #735. % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3845) ~ (all_54_10 = e2) % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3846) all_54_10 = e1 | all_54_10 = e0 % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3846) gives: % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3847) all_54_10 = e1 % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (541), (3847) imply: % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3848) all_6_2 = e1 % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3848) implies: % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3849) all_6_2 = e1 % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (569), (3849) imply: % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3850) ~ (all_52_2 = e1) % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (580), (3849) imply: % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3851) ~ (all_52_6 = e1) % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3838), (3849) imply: % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3852) ~ (e3 = e1) % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3840), (3849) imply: % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3853) ~ (e2 = e1) % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (337) gives: % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3854) all_58_1 = e1 % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3798), (3854) imply: % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3855) e3 = e1 % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8), (3855) imply: % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3856) $false % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3856) is inconsistent. % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3857) all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1 % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3857) gives: % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3858) all_58_3 = e1 % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (554), (3858) imply: % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3859) all_8_2 = e1 % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3777), (3859) imply: % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3860) $false % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3860) is inconsistent. % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3861) all_58_7 = e1 | all_58_13 = e1 % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3861) gives: % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3862) all_58_7 = e1 % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (380), (3862) imply: % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3863) all_52_6 = e1 % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3851), (3863) imply: % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3864) $false % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3864) is inconsistent. % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3865) all_58_13 = e1 % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (549), (3865) imply: % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3866) all_52_7 = e1 % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3866) implies: % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3867) all_52_7 = e1 % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (188), (3867) imply: % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3868) ~ (all_52_3 = e1) % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (240) gives: % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3869) all_54_12 = e3 % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (478), (3869) imply: % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3870) all_52_3 = e3 % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (192), (3870) imply: % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3871) ~ (all_52_2 = e3) % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (244) gives: % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3872) all_54_8 = e3 % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (471), (3871), (3872) are inconsistent by % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #345. % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3873) ~ (all_54_8 = e3) % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3874) all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0 % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3874) gives: % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3875) all_54_8 = e2 % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (471), (3800), (3875) are inconsistent by % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #666. % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3876) ~ (all_54_8 = e2) % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3877) all_54_8 = e1 | all_54_8 = e0 % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3877) gives: % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3878) all_54_8 = e1 % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (471), (3850), (3878) are inconsistent by % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #665. % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3879) all_54_8 = e0 % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (471), (3879) imply: % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3880) all_52_2 = e0 % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3880) implies: % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3881) all_52_2 = e0 % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (197), (3881) imply: % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3882) ~ (all_52_1 = e0) % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3800), (3881) imply: % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3883) ~ (e2 = e0) % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (614), (3881) imply: % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3884) op(e3, e0) = all_56_16 % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (336) gives: % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3885) all_58_1 = e0 % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3798), (3885) imply: % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3886) e3 = e0 % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7), (3886) imply: % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3887) $false % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3887) is inconsistent. % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3888) all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0 % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3888) gives: % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3889) all_58_3 = e0 % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (554), (3889) imply: % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3890) all_8_2 = e0 % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3836), (3890) imply: % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3891) op(e3, e0) = e2 % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1, % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_16, e0, e3, simplifying with (3824), (3884) % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3892) all_56_16 = e1 % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_16, e0, e3, simplifying with (3884), (3891) % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3893) all_56_16 = e2 % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3892), (3893) imply: % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3894) e2 = e1 % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6), (3894) imply: % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3895) $false % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3895) is inconsistent. % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3896) all_58_7 = e0 | all_58_13 = e0 % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (191), (340), (365), (380), (401), (549), % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (553), (3760), (3761), (3799), (3882), (3896) are % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #174. % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3897) all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0 % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (478), (3760), (3801), (3868), (3897) are % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #615. % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3898) all_54_10 = e0 % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (541), (3832), (3898) are inconsistent by % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #705. % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3899) all_56_21 = e2 % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3900) all_56_19 = e1 % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (435), (3900) imply: % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3901) all_52_6 = e1 % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3901) implies: % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3902) all_52_6 = e1 % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (374), (3899) imply: % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3903) all_6_2 = e2 % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (174), (3902) imply: % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3904) ~ (all_52_14 = e1) % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3904) implies: % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3905) ~ (all_52_14 = e1) % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (42), (43), (46), (48), (208), (247), (289), % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (294), (297), (321), (323), (341), (360), (386), % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (402), (407), (419), (443), (542), (545), (546), % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (547), (550), (551), (555), (571), (573), (575), % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (580), (620), (768), (769), (3732), (3740), % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3742), (3803), (3838), (3902), (3903), (3905), % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #173. % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3906) all_56_21 = e3 % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3907) all_56_17 = e1 % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (381), (3907) imply: % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3908) all_52_2 = e1 % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3908) implies: % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3909) all_52_2 = e1 % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (374), (3906) imply: % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3910) all_6_2 = e3 % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (192), (3909) imply: % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3911) ~ (all_52_3 = e1) % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3911) implies: % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3912) ~ (all_52_3 = e1) % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (43), (3910) imply: % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3913) op(e3, e3) = all_6_1 % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (240) gives: % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3914) all_54_12 = e3 % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (478), (3914) imply: % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3915) all_52_3 = e3 % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (615), (3915) imply: % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3916) op(e3, e3) = all_56_24 % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (768), (3808), (3913), (3916), (function-axioms) % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #302. % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3917) all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0 % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (478), (3760), (3801), (3912), (3917) are % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #615. % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3918) all_58_9 = e0 % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3823), (3918) imply: % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3919) e1 = e0 % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4), (3919) imply: % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3920) $false % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3920) is inconsistent. % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3921) all_54_3 = e0 % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (461), (3921) imply: % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3922) all_52_12 = e0 % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3763), (3922) imply: % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3923) $false % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3923) is inconsistent. % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | (3924) all_56_7 = e3 % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | (3925) all_56_1 = e0 % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (546), (3925) imply: % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | (3926) all_10_2 = e0 % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (402), (3924) imply: % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | (3927) all_52_12 = e3 % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (53), (3926) imply: % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | (3928) op(e0, e0) = all_10_1 % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (612), (3926) imply: % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | (3929) op(e3, e0) = all_56_0 % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (216), (3927) imply: % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | (3930) op(e3, e0) = e3 % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_10_1, % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | e0, e0, simplifying with (3768), (3928) gives: % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | (3931) all_10_1 = e0 % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_56_0, % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | e0, e3, simplifying with (3929), (3930) gives: % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | (3932) all_56_0 = e3 % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3726), (3931) imply: % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | (3933) op(e3, e0) = e2 % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, e2, e0, % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | e3, simplifying with (3930), (3933) gives: % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | (3934) e3 = e2 % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (9), (3934) imply: % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | (3935) $false % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3935) is inconsistent. % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | End of split % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | (3936) all_56_5 = e3 % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | (3937) all_56_1 = e1 % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (546), (3937) imply: % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | (3938) all_10_2 = e1 % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (429), (3936) imply: % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | (3939) all_52_8 = e3 % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (407), (3939) imply: % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | (3940) all_58_4 = e3 % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (557), (3938) imply: % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | (3941) ~ (all_52_1 = e1) % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (182), (3939) imply: % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | (3942) ~ (all_52_4 = e3) % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (563), (3938) imply: % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | (3943) ~ (all_52_4 = e1) % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (168), (3939) imply: % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | (3944) ~ (all_52_12 = e3) % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | SIMP: (3944) implies: % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | (3945) ~ (all_52_12 = e3) % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (567), (3938) imply: % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | (3946) ~ (all_52_12 = e1) % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (53), (3938) imply: % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | (3947) op(e1, e1) = all_10_1 % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (612), (3938) imply: % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | (3948) op(e3, e1) = all_56_0 % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (217), (3939) imply: % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | (3949) op(e3, e1) = e3 % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3724) gives: % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | (3950) ~ (all_10_2 = e1) % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3938), (3950) imply: % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | (3951) $false % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3951) is inconsistent. % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | (3952) ~ (all_10_1 = e0) % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (249) gives: % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | (3953) all_54_3 = e3 % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (461), (3945), (3953) are inconsistent by % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #659. % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | (3954) all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0 % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3954) gives: % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | (3955) all_54_3 = e2 % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (461), (3955) imply: % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | (3956) all_52_12 = e2 % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3956) implies: % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | (3957) all_52_12 = e2 % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (181), (3957) imply: % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | (3958) ~ (all_52_4 = e2) % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (160), (3957) imply: % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | (3959) ~ (all_52_14 = e2) % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3959) implies: % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | (3960) ~ (all_52_14 = e2) % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (251) gives: % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | (3961) all_54_1 = e3 % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (457), (3942), (3961) are inconsistent by % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #722. % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | (3962) ~ (all_54_1 = e3) % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | (3963) all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0 % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3963) gives: % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3964) all_54_1 = e2 % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (457), (3958), (3964) are inconsistent by % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #721. % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3965) all_54_1 = e1 | all_54_1 = e0 % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3965) gives: % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3966) all_54_1 = e1 % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (457), (3943), (3966) are inconsistent by % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #720. % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3967) all_54_1 = e0 % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (457), (3967) imply: % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3968) all_52_4 = e0 % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3968) implies: % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3969) all_52_4 = e0 % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3943), (3969) imply: % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3970) ~ (e1 = e0) % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_6_2, % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_10_1, e1, e1, simplifying with (41), (3947) % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3971) all_10_1 = all_6_2 % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_56_0, % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1, e3, simplifying with (3948), (3949) gives: % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3972) all_56_0 = e3 % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3952), (3971) imply: % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3973) ~ (all_6_2 = e0) % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (328) gives: % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3974) all_58_4 = e0 % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3940), (3974) imply: % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3975) e3 = e0 % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7), (3975) imply: % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3976) $false % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3976) is inconsistent. % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3977) all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0 % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3977) gives: % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3978) all_58_5 = e0 % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (389), (3978) imply: % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3979) all_52_9 = e0 % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (333) gives: % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3980) all_58_2 = e1 % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (401), (3980) imply: % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3981) all_52_1 = e1 % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3941), (3981) imply: % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3982) $false % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3982) is inconsistent. % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3983) all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1 % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3983) gives: % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3984) all_58_3 = e1 % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (554), (3984) imply: % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3985) all_8_2 = e1 % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3777), (3985) imply: % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3986) $false % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3986) is inconsistent. % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3987) all_58_5 = e1 | all_58_10 = e1 % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3987) gives: % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.11/21.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3988) all_58_5 = e1 % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (3978), (3988) are inconsistent by sub-proof % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #172. % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3989) all_58_10 = e1 % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (386), (3989) imply: % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3990) all_52_13 = e1 % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (158), (3990) imply: % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3991) ~ (all_52_14 = e1) % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3991) implies: % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3992) ~ (all_52_14 = e1) % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (241) gives: % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3993) all_54_11 = e3 % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (476), (3993) imply: % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3994) all_52_14 = e3 % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3994) implies: % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3995) all_52_14 = e3 % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (174), (3995) imply: % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3996) ~ (all_52_6 = e3) % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (587), (3995) imply: % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3997) ~ (all_6_2 = e3) % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3997) implies: % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3998) ~ (all_6_2 = e3) % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (292) gives: % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3999) ~ (all_56_21 = e2) % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (374), (3999) imply: % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4000) ~ (all_6_2 = e2) % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (242), (541), (3726), (3947), (3948), (3949), % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3952), (3971), (3998), (4000), (function-axioms) % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #169. % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4001) all_56_21 = e2 % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4002) all_56_19 = e1 % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (435), (4002) imply: % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4003) all_52_6 = e1 % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4003) implies: % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4004) all_52_6 = e1 % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (374), (4001) imply: % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4005) all_6_2 = e2 % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (42), (43), (46), (48), (208), (247), (289), % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (294), (297), (321), (323), (341), (360), (386), % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (402), (407), (419), (443), (542), (545), (546), % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (547), (550), (551), (555), (571), (573), (575), % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (580), (620), (768), (769), (3732), (3740), % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3742), (3992), (3996), (3998), (4004), (4005), % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #173. % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4006) all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0 % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (476), (3765), (3960), (3992), (4006) are % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #687. % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4007) all_58_8 = e0 | all_58_14 = e0 % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (548), (552), (3762), (3973), (4007) are % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #627. % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | (4008) all_54_3 = e1 | all_54_3 = e0 % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (461), (3763), (3946), (4008) are inconsistent by % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #655. % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | End of split % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | End of split % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | Case 2: % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | (4009) all_56_13 = e2 % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | (4010) all_56_11 = e1 % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (545), (4010) imply: % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | (4011) all_8_2 = e1 % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (431), (4009) imply: % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | (4012) all_52_9 = e2 % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (389), (4012) imply: % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | (4013) all_58_5 = e2 % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | REDUCE: (571), (4011) imply: % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | (4014) ~ (all_52_4 = e1) % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | REDUCE: (165), (4012) imply: % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | (4015) ~ (all_52_13 = e2) % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | SIMP: (4015) implies: % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | (4016) ~ (all_52_13 = e2) % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | REDUCE: (583), (4012) imply: % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | (4017) ~ (all_6_2 = e2) % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | SIMP: (4017) implies: % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | (4018) ~ (all_6_2 = e2) % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | REDUCE: (579), (4011) imply: % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | (4019) ~ (all_52_13 = e1) % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | REDUCE: (48), (4011) imply: % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | (4020) op(e1, e1) = all_8_1 % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (245) gives: % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | (4021) all_54_7 = e3 % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (469), (4021) imply: % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | (4022) all_52_13 = e3 % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | SIMP: (4022) implies: % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | (4023) all_52_13 = e3 % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (161), (4023) imply: % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | (4024) ~ (all_52_12 = e3) % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (212), (4023) imply: % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | (4025) op(e2, e0) = e3 % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_6_2, % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | all_8_1, e1, e1, simplifying with (41), (4020) % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | gives: % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | (4026) all_8_1 = all_6_2 % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3732), (4026) imply: % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | (4027) ~ (all_6_2 = e3) % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (769), (4026) imply: % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | (4028) ~ (all_6_2 = e1) % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (47), (4026) imply: % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | (4029) op(e2, all_6_2) = all_8_0 % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (242) gives: % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | (4030) all_54_10 = e3 % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (541), (4027), (4030) are inconsistent by % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | sub-proof #736. % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | (4031) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4031) gives: % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | (4032) all_54_10 = e2 % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (541), (4018), (4032) are inconsistent by % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #735. % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | (4033) all_54_10 = e1 | all_54_10 = e0 % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4033) gives: % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | (4034) all_54_10 = e1 % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (541), (4028), (4034) are inconsistent by % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #606. % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | (4035) all_54_10 = e0 % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (541), (4035) imply: % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | (4036) all_6_2 = e0 % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4036) implies: % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | (4037) all_6_2 = e0 % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (374), (4037) imply: % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | (4038) all_56_21 = e0 % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (291) gives: % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | (4039) ~ (all_56_21 = e0) % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4038), (4039) imply: % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | (4040) $false % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (4040) is inconsistent. % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | (4041) all_56_23 = e1 % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (366), (4041) imply: % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | (4042) all_52_14 = e1 % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4042) implies: % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | (4043) all_52_14 = e1 % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (160), (4043) imply: % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | (4044) ~ (all_52_12 = e1) % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (249) gives: % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4045) all_54_3 = e3 % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (461), (4024), (4045) are inconsistent by % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #659. % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4046) ~ (all_54_3 = e3) % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4047) all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0 % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (322) gives: % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4048) all_58_9 = e2 % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (551), (4048) imply: % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4049) all_52_12 = e2 % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (181), (4049) imply: % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4050) ~ (all_52_4 = e2) % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (567), (4049) imply: % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4051) ~ (all_10_2 = e2) % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4051) implies: % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4052) ~ (all_10_2 = e2) % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (251) gives: % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4053) all_54_1 = e3 % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (457), (4053) imply: % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4054) all_52_4 = e3 % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4054) implies: % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4055) all_52_4 = e3 % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (182), (4055) imply: % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4056) ~ (all_52_8 = e3) % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4056) implies: % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4057) ~ (all_52_8 = e3) % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (563), (4055) imply: % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4058) ~ (all_10_2 = e3) % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4058) implies: % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4059) ~ (all_10_2 = e3) % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (298) gives: % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4060) ~ (all_56_1 = e1) % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (546), (4060) imply: % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4061) ~ (all_10_2 = e1) % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (252), (297), (402), (543), (546), (4024), (4052), % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4059), (4061) are inconsistent by sub-proof #707. % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4062) all_56_5 = e3 % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (429), (4057), (4062) are inconsistent by % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #481. % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4063) all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0 % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (182), (328), (407), (457), (548), (552), (616), % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3738), (3762), (4013), (4014), (4025), (4029), % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4050), (4063), (function-axioms) are inconsistent % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #637. % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4064) ~ (all_58_9 = e2) % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (551), (4064) imply: % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4065) ~ (all_52_12 = e2) % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (461), (3763), (4044), (4047), (4065) are % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #326. % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | End of split % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | (4066) all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0 % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (469), (3764), (4016), (4019), (4066) are % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #649. % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | End of split % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | End of split % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | | | End of split % 148.11/21.27 | | | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | | End of split % 148.11/21.27 | | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | End of split % 148.11/21.27 | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | Case 2: % 148.11/21.27 | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | (4067) all_56_31 = e2 % 148.11/21.27 | | | | | | | | | | | | | | | | | (4068) all_56_27 = e0 % 148.11/21.27 | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | COMBINE_EQS: (360), (4068) imply: % 148.11/21.27 | | | | | | | | | | | | | | | | | (4069) all_52_7 = e0 % 148.11/21.27 | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | SIMP: (4069) implies: % 148.11/21.27 | | | | | | | | | | | | | | | | | (4070) all_52_7 = e0 % 148.11/21.27 | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | COMBINE_EQS: (544), (4067) imply: % 148.11/21.27 | | | | | | | | | | | | | | | | | (4071) all_4_2 = e2 % 148.11/21.27 | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | COMBINE_EQS: (547), (4071) imply: % 148.11/21.27 | | | | | | | | | | | | | | | | | (4072) all_58_15 = e2 % 148.11/21.27 | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | COMBINE_EQS: (549), (4070) imply: % 148.11/21.27 | | | | | | | | | | | | | | | | | (4073) all_58_13 = e0 % 148.11/21.27 | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | REDUCE: (188), (4070) imply: % 148.11/21.27 | | | | | | | | | | | | | | | | | (4074) ~ (all_52_3 = e0) % 148.11/21.27 | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | REDUCE: (570), (4071) imply: % 148.11/21.27 | | | | | | | | | | | | | | | | | (4075) ~ (all_52_3 = e2) % 148.11/21.27 | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | REDUCE: (176), (4070) imply: % 148.11/21.27 | | | | | | | | | | | | | | | | | (4076) ~ (all_52_6 = e0) % 148.11/21.27 | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | REDUCE: (173), (4070) imply: % 148.11/21.27 | | | | | | | | | | | | | | | | | (4077) ~ (all_52_11 = e0) % 148.11/21.27 | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | SIMP: (4077) implies: % 148.11/21.27 | | | | | | | | | | | | | | | | | (4078) ~ (all_52_11 = e0) % 148.11/21.27 | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | REDUCE: (575), (4070) imply: % 148.11/21.27 | | | | | | | | | | | | | | | | | (4079) ~ (all_8_2 = e0) % 148.11/21.27 | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | SIMP: (4079) implies: % 148.11/21.27 | | | | | | | | | | | | | | | | | (4080) ~ (all_8_2 = e0) % 148.11/21.27 | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | REDUCE: (588), (4071) imply: % 148.11/21.27 | | | | | | | | | | | | | | | | | (4081) ~ (all_52_11 = e2) % 148.11/21.27 | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | REDUCE: (589), (4071) imply: % 148.11/21.27 | | | | | | | | | | | | | | | | | (4082) ~ (all_52_12 = e2) % 148.11/21.27 | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | REDUCE: (590), (4071) imply: % 148.11/21.27 | | | | | | | | | | | | | | | | | (4083) ~ (all_52_13 = e2) % 148.11/21.27 | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | REDUCE: (591), (4071) imply: % 148.11/21.27 | | | | | | | | | | | | | | | | | (4084) ~ (all_52_14 = e2) % 148.11/21.27 | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | REDUCE: (38), (4071) imply: % 148.11/21.27 | | | | | | | | | | | | | | | | | (4085) op(e2, e2) = all_4_1 % 148.11/21.27 | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | REDUCE: (36), (4071) imply: % 148.11/21.27 | | | | | | | | | | | | | | | | | (4086) op(e0, e0) = e2 % 148.11/21.27 | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_8_2, % 148.11/21.27 | | | | | | | | | | | | | | | | | all_4_1, e2, e2, simplifying with (46), (4085) % 148.11/21.27 | | | | | | | | | | | | | | | | | gives: % 148.11/21.27 | | | | | | | | | | | | | | | | | (4087) all_8_2 = all_4_1 % 148.11/21.27 | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | COMBINE_EQS: (542), (4087) imply: % 148.11/21.27 | | | | | | | | | | | | | | | | | (4088) all_54_5 = all_4_1 % 148.11/21.27 | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | COMBINE_EQS: (545), (4087) imply: % 148.11/21.27 | | | | | | | | | | | | | | | | | (4089) all_56_11 = all_4_1 % 148.11/21.27 | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | COMBINE_EQS: (554), (4087) imply: % 148.11/21.27 | | | | | | | | | | | | | | | | | (4090) all_58_3 = all_4_1 % 148.11/21.27 | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | REDUCE: (571), (4087) imply: % 148.11/21.27 | | | | | | | | | | | | | | | | | (4091) ~ (all_52_4 = all_4_1) % 148.11/21.27 | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | REDUCE: (573), (4087) imply: % 148.11/21.27 | | | | | | | | | | | | | | | | | (4092) ~ (all_52_6 = all_4_1) % 148.11/21.27 | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | REDUCE: (577), (4087) imply: % 148.11/21.27 | | | | | | | | | | | | | | | | | (4093) ~ (all_52_9 = all_4_1) % 148.11/21.27 | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | REDUCE: (579), (4087) imply: % 148.11/21.27 | | | | | | | | | | | | | | | | | (4094) ~ (all_52_13 = all_4_1) % 148.11/21.27 | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | REDUCE: (4080), (4087) imply: % 148.11/21.27 | | | | | | | | | | | | | | | | | (4095) ~ (all_4_1 = e0) % 148.11/21.27 | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | BETA: splitting (291) gives: % 148.11/21.27 | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | Case 1: % 148.11/21.27 | | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | | (4096) ~ (all_56_21 = e0) % 148.11/21.27 | | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | | REDUCE: (374), (4096) imply: % 148.11/21.27 | | | | | | | | | | | | | | | | | | (4097) ~ (all_6_2 = e0) % 148.11/21.27 | | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | | BETA: splitting (292) gives: % 148.11/21.27 | | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | | Case 1: % 148.11/21.27 | | | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | | | (4098) ~ (all_56_21 = e2) % 148.11/21.27 | | | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | | | REDUCE: (374), (4098) imply: % 148.11/21.27 | | | | | | | | | | | | | | | | | | | (4099) ~ (all_6_2 = e2) % 148.11/21.27 | | | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | | | BETA: splitting (293) gives: % 148.11/21.27 | | | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | | | Case 1: % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | (4100) ~ (all_56_21 = e3) % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | REDUCE: (374), (4100) imply: % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | (4101) ~ (all_6_2 = e3) % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | BETA: splitting (242) gives: % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | Case 1: % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | (4102) all_54_10 = e3 % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (541), (4102) imply: % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | (4103) all_6_2 = e3 % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | REDUCE: (4101), (4103) imply: % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | (4104) $false % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | CLOSE: (4104) is inconsistent. % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | Case 2: % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | (4105) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4105) gives: % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | (4106) all_54_10 = e2 % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (541), (4106) imply: % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | (4107) all_6_2 = e2 % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4099), (4107) imply: % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | (4108) $false % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (4108) is inconsistent. % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | (4109) ~ (all_54_10 = e2) % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | (4110) all_54_10 = e1 | all_54_10 = e0 % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4110) gives: % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | (4111) all_54_10 = e1 % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (541), (4111) imply: % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | (4112) all_6_2 = e1 % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (585), (4112) imply: % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | (4113) ~ (all_52_11 = e1) % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (318) gives: % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | (4114) all_58_12 = e1 % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (365), (4114) imply: % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | (4115) all_52_3 = e1 % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (561), (4115) imply: % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | (4116) ~ (all_10_2 = e1) % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4116) implies: % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | (4117) ~ (all_10_2 = e1) % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (207), (4115) imply: % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | (4118) op(e0, e3) = e1 % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (296) gives: % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | (4119) ~ (all_56_11 = e3) % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4089), (4119) imply: % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | (4120) ~ (all_4_1 = e3) % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (37), (51), (53), (158), (166), (181), (191), % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | (193), (196), (197), (205), (218), (238), (240), % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | (247), (248), (252), (287), (297), (299), (318), % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | (320), (321), (326), (327), (330), (335), (339), % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | (365), (374), (380), (386), (389), (401), (402), % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | (407), (408), (463), (478), (482), (543), (546), % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | (547), (548), (550), (551), (552), (553), (555), % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | (557), (559), (561), (563), (565), (567), (585), % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | (587), (612), (614), (624), (767), (3726), (3747), % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | (4067), (4072), (4073), (4074), (4075), (4076), % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | (4078), (4081), (4082), (4083), (4084), (4086), % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | (4088), (4089), (4090), (4091), (4092), (4093), % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | (4094), (4095), (4099), (4117), (4120), % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | #164. % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | (4121) all_56_11 = e3 % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (37), (3734), (4089), (4118), (4121), % 148.11/21.27 | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 148.11/21.28 | | | | | | | | | | | | | | | | | | | | | | | | | #295. % 148.11/21.28 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.28 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.11/21.28 | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.28 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.11/21.28 | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.28 | | | | | | | | | | | | | | | | | | | | | | | | (4122) all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1 % 148.11/21.28 | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.28 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (547), (548), (3747), (4073), (4113), (4122) % 148.11/21.28 | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #575. % 148.11/21.28 | | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.28 | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.11/21.28 | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.28 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.11/21.28 | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.28 | | | | | | | | | | | | | | | | | | | | | | | (4123) all_54_10 = e0 % 148.11/21.28 | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.28 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (541), (4123) imply: % 148.11/21.28 | | | | | | | | | | | | | | | | | | | | | | | (4124) all_6_2 = e0 % 148.11/21.28 | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.28 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4097), (4124) imply: % 148.11/21.28 | | | | | | | | | | | | | | | | | | | | | | | (4125) $false % 148.11/21.28 | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.28 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (4125) is inconsistent. % 148.11/21.28 | | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.28 | | | | | | | | | | | | | | | | | | | | | | End of split % 148.11/21.28 | | | | | | | | | | | | | | | | | | | | | | % 148.11/21.28 | | | | | | | | | | | | | | | | | | | | | End of split % 148.11/21.28 | | | | | | | | | | | | | | | | | | | | | % 148.11/21.28 | | | | | | | | | | | | | | | | | | | | End of split % 148.11/21.28 | | | | | | | | | | | | | | | | | | | | % 148.11/21.28 | | | | | | | | | | | | | | | | | | | Case 2: % 148.11/21.28 | | | | | | | | | | | | | | | | | | | | % 148.11/21.28 | | | | | | | | | | | | | | | | | | | | (4126) all_56_21 = e3 % 148.11/21.28 | | | | | | | | | | | | | | | | | | | | (4127) all_56_17 = e1 % 148.11/21.28 | | | | | | | | | | | | | | | | | | | | % 148.11/21.28 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (42), (43), (51), (158), (160), (161), (174), % 148.11/21.28 | | | | | | | | | | | | | | | | | | | | (189), (191), (208), (241), (243), (252), (287), % 148.11/21.28 | | | | | | | | | | | | | | | | | | | | (297), (321), (332), (374), (381), (386), (389), % 148.11/21.28 | | | | | | | | | | | | | | | | | | | | (401), (402), (473), (476), (543), (544), (545), % 148.11/21.28 | | | | | | | | | | | | | | | | | | | | (546), (547), (550), (551), (554), (557), (559), % 148.11/21.28 | | | | | | | | | | | | | | | | | | | | (569), (573), (580), (591), (621), (768), (3736), % 148.11/21.28 | | | | | | | | | | | | | | | | | | | | (3740), (3747), (4080), (4126), (4127), % 148.11/21.28 | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 148.11/21.28 | | | | | | | | | | | | | | | | | | | | #225. % 148.11/21.28 | | | | | | | | | | | | | | | | | | | | % 148.11/21.28 | | | | | | | | | | | | | | | | | | | End of split % 148.11/21.28 | | | | | | | | | | | | | | | | | | | % 148.11/21.28 | | | | | | | | | | | | | | | | | | Case 2: % 148.11/21.28 | | | | | | | | | | | | | | | | | | | % 148.11/21.28 | | | | | | | | | | | | | | | | | | | (4128) all_56_21 = e2 % 148.11/21.28 | | | | | | | | | | | | | | | | | | | (4129) all_56_19 = e1 % 148.11/21.28 | | | | | | | | | | | | | | | | | | | % 148.11/21.28 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (43), (247), (374), (435), (768), (3740), (4085), % 148.11/21.28 | | | | | | | | | | | | | | | | | | | (4088), (4092), (4095), (4128), (4129), % 148.11/21.28 | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 148.11/21.28 | | | | | | | | | | | | | | | | | | | #566. % 148.11/21.28 | | | | | | | | | | | | | | | | | | | % 148.11/21.28 | | | | | | | | | | | | | | | | | | End of split % 148.11/21.28 | | | | | | | | | | | | | | | | | | % 148.11/21.28 | | | | | | | | | | | | | | | | | Case 2: % 148.11/21.28 | | | | | | | | | | | | | | | | | | % 148.11/21.28 | | | | | | | | | | | | | | | | | | (4130) all_56_21 = e0 % 148.11/21.28 | | | | | | | | | | | | | | | | | | % 148.11/21.28 | | | | | | | | | | | | | | | | | | REF_CLOSE: (43), (374), (768), (4086), (4130), % 148.11/21.28 | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 148.11/21.28 | | | | | | | | | | | | | | | | | | #565. % 148.11/21.28 | | | | | | | | | | | | | | | | | | % 148.11/21.28 | | | | | | | | | | | | | | | | | End of split % 148.11/21.28 | | | | | | | | | | | | | | | | | % 148.11/21.28 | | | | | | | | | | | | | | | | End of split % 148.11/21.28 | | | | | | | | | | | | | | | | % 148.11/21.28 | | | | | | | | | | | | | | | Case 2: % 148.11/21.28 | | | | | | | | | | | | | | | | % 148.11/21.28 | | | | | | | | | | | | | | | | (4131) all_56_31 = e3 % 148.11/21.28 | | | | | | | | | | | | | | | | (4132) all_56_25 = e0 % 148.11/21.28 | | | | | | | | | | | | | | | | % 148.11/21.28 | | | | | | | | | | | | | | | | COMBINE_EQS: (447), (4132) imply: % 148.11/21.28 | | | | | | | | | | | | | | | | (4133) all_52_3 = e0 % 148.11/21.28 | | | | | | | | | | | | | | | | % 148.11/21.28 | | | | | | | | | | | | | | | | SIMP: (4133) implies: % 148.11/21.28 | | | | | | | | | | | | | | | | (4134) all_52_3 = e0 % 148.11/21.28 | | | | | | | | | | | | | | | | % 148.11/21.28 | | | | | | | | | | | | | | | | COMBINE_EQS: (544), (4131) imply: % 148.11/21.28 | | | | | | | | | | | | | | | | (4135) all_4_2 = e3 % 148.11/21.28 | | | | | | | | | | | | | | | | % 148.11/21.28 | | | | | | | | | | | | | | | | COMBINE_EQS: (547), (4135) imply: % 148.11/21.28 | | | | | | | | | | | | | | | | (4136) all_58_15 = e3 % 148.11/21.28 | | | | | | | | | | | | | | | | % 148.11/21.28 | | | | | | | | | | | | | | | | COMBINE_EQS: (365), (4134) imply: % 148.11/21.28 | | | | | | | | | | | | | | | | (4137) all_58_12 = e0 % 148.11/21.28 | | | | | | | | | | | | | | | | % 148.11/21.28 | | | | | | | | | | | | | | | | REDUCE: (196), (4134) imply: % 148.11/21.28 | | | | | | | | | | | | | | | | (4138) ~ (all_52_1 = e0) % 148.11/21.28 | | | | | | | | | | | | | | | | % 148.11/21.28 | | | | | | | | | | | | | | | | REDUCE: (192), (4134) imply: % 148.11/21.28 | | | | | | | | | | | | | | | | (4139) ~ (all_52_2 = e0) % 148.11/21.28 | | | | | | | | | | | | | | | | % 148.11/21.28 | | | | | | | | | | | | | | | | REDUCE: (187), (4134) imply: % 148.11/21.28 | | | | | | | | | | | | | | | | (4140) ~ (all_52_11 = e0) % 148.11/21.28 | | | | | | | | | | | | | | | | % 148.11/21.28 | | | | | | | | | | | | | | | | SIMP: (4140) implies: % 148.11/21.28 | | | | | | | | | | | | | | | | (4141) ~ (all_52_11 = e0) % 148.11/21.28 | | | | | | | | | | | | | | | | % 148.11/21.28 | | | | | | | | | | | | | | | | REDUCE: (561), (4134) imply: % 148.11/21.28 | | | | | | | | | | | | | | | | (4142) ~ (all_10_2 = e0) % 148.11/21.28 | | | | | | | | | | | | | | | | % 148.11/21.28 | | | | | | | | | | | | | | | | SIMP: (4142) implies: % 148.11/21.28 | | | | | | | | | | | | | | | | (4143) ~ (all_10_2 = e0) % 148.11/21.28 | | | | | | | | | | | | | | | | % 148.11/21.28 | | | | | | | | | | | | | | | | REDUCE: (588), (4135) imply: % 148.11/21.28 | | | | | | | | | | | | | | | | (4144) ~ (all_52_11 = e3) % 148.11/21.28 | | | | | | | | | | | | | | | | % 148.11/21.28 | | | | | | | | | | | | | | | | REDUCE: (591), (4135) imply: % 148.11/21.28 | | | | | | | | | | | | | | | | (4145) ~ (all_52_14 = e3) % 148.11/21.28 | | | | | | | | | | | | | | | | % 148.11/21.28 | | | | | | | | | | | | | | | | REDUCE: (38), (4135) imply: % 148.11/21.28 | | | | | | | | | | | | | | | | (4146) op(e3, e3) = all_4_1 % 148.11/21.28 | | | | | | | | | | | | | | | | % 148.11/21.28 | | | | | | | | | | | | | | | | REDUCE: (36), (4135) imply: % 148.11/21.28 | | | | | | | | | | | | | | | | (4147) op(e0, e0) = e3 % 148.11/21.28 | | | | | | | | | | | | | | | | % 148.11/21.28 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_10_2, % 148.11/21.28 | | | | | | | | | | | | | | | | all_4_1, e3, e3, simplifying with (51), (4146) % 148.11/21.28 | | | | | | | | | | | | | | | | gives: % 148.11/21.28 | | | | | | | | | | | | | | | | (4148) all_10_2 = all_4_1 % 148.11/21.28 | | | | | | | | | | | | | | | | % 148.11/21.28 | | | | | | | | | | | | | | | | BETA: splitting (292) gives: % 148.11/21.28 | | | | | | | | | | | | | | | | % 148.11/21.28 | | | | | | | | | | | | | | | | Case 1: % 148.11/21.28 | | | | | | | | | | | | | | | | | % 148.11/21.28 | | | | | | | | | | | | | | | | | (4149) ~ (all_56_21 = e2) % 148.11/21.28 | | | | | | | | | | | | | | | | | % 148.11/21.28 | | | | | | | | | | | | | | | | | REDUCE: (374), (4149) imply: % 148.11/21.28 | | | | | | | | | | | | | | | | | (4150) ~ (all_6_2 = e2) % 148.11/21.28 | | | | | | | | | | | | | | | | | % 148.11/21.28 | | | | | | | | | | | | | | | | | BETA: splitting (294) gives: % 148.11/21.28 | | | | | | | | | | | | | | | | | % 148.11/21.28 | | | | | | | | | | | | | | | | | Case 1: % 148.11/21.28 | | | | | | | | | | | | | | | | | | % 148.11/21.28 | | | | | | | | | | | | | | | | | | (4151) ~ (all_56_11 = e0) % 148.11/21.28 | | | | | | | | | | | | | | | | | | % 148.11/21.28 | | | | | | | | | | | | | | | | | | REDUCE: (545), (4151) imply: % 148.11/21.28 | | | | | | | | | | | | | | | | | | (4152) ~ (all_8_2 = e0) % 148.11/21.28 | | | | | | | | | | | | | | | | | | % 148.11/21.28 | | | | | | | | | | | | | | | | | | REF_CLOSE: (37), (38), (43), (46), (47), (48), (51), (160), % 148.11/21.28 | | | | | | | | | | | | | | | | | | (165), (168), (169), (171), (174), (176), (181), % 148.11/21.28 | | | | | | | | | | | | | | | | | | (182), (183), (184), (193), (194), (196), (197), % 148.11/21.28 | | | | | | | | | | | | | | | | | | (205), (206), (238), (241), (242), (243), (244), % 148.11/21.28 | | | | | | | | | | | | | | | | | | (246), (247), (248), (250), (251), (252), (291), % 148.11/21.28 | | | | | | | | | | | | | | | | | | (293), (296), (298), (299), (318), (320), (321), % 148.11/21.28 | | | | | | | | | | | | | | | | | | (322), (328), (335), (343), (345), (365), (374), % 148.11/21.28 | | | | | | | | | | | | | | | | | | (381), (386), (389), (401), (407), (419), (425), % 148.11/21.28 | | | | | | | | | | | | | | | | | | (429), (457), (459), (463), (467), (471), (473), % 148.11/21.28 | | | | | | | | | | | | | | | | | | (476), (482), (541), (542), (543), (545), (546), % 148.11/21.28 | | | | | | | | | | | | | | | | | | (547), (548), (549), (550), (551), (555), (557), % 148.11/21.28 | | | | | | | | | | | | | | | | | | (559), (568), (569), (571), (573), (575), (577), % 148.11/21.28 | | | | | | | | | | | | | | | | | | (579), (582), (585), (587), (613), (617), (625), % 148.11/21.28 | | | | | | | | | | | | | | | | | | (626), (768), (769), (3728), (3730), (3734), % 148.11/21.28 | | | | | | | | | | | | | | | | | | (3740), (3747), (4136), (4137), (4138), (4139), % 148.11/21.28 | | | | | | | | | | | | | | | | | | (4141), (4143), (4144), (4145), (4146), (4147), % 148.11/21.28 | | | | | | | | | | | | | | | | | | (4150), (4152), (function-axioms) are inconsistent % 148.11/21.28 | | | | | | | | | | | | | | | | | | by sub-proof #288. % 148.11/21.28 | | | | | | | | | | | | | | | | | | % 148.11/21.28 | | | | | | | | | | | | | | | | | Case 2: % 148.11/21.28 | | | | | | | | | | | | | | | | | | % 148.11/21.28 | | | | | | | | | | | | | | | | | | (4153) all_56_11 = e0 % 148.11/21.28 | | | | | | | | | | | | | | | | | | % 148.11/21.28 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (545), (4153) imply: % 148.11/21.28 | | | | | | | | | | | | | | | | | | (4154) all_8_2 = e0 % 148.11/21.28 | | | | | | | | | | | | | | | | | | % 148.11/21.28 | | | | | | | | | | | | | | | | | | REDUCE: (48), (4154) imply: % 148.11/21.28 | | | | | | | | | | | | | | | | | | (4155) op(e0, e0) = all_8_1 % 148.11/21.28 | | | | | | | | | | | | | | | | | | % 148.11/21.28 | | | | | | | | | | | | | | | | | | REF_CLOSE: (3732), (4147), (4155), (function-axioms) are % 148.11/21.28 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #546. % 148.11/21.28 | | | | | | | | | | | | | | | | | | % 148.11/21.28 | | | | | | | | | | | | | | | | | End of split % 148.11/21.28 | | | | | | | | | | | | | | | | | % 148.11/21.28 | | | | | | | | | | | | | | | | Case 2: % 148.11/21.28 | | | | | | | | | | | | | | | | | % 148.11/21.28 | | | | | | | | | | | | | | | | | (4156) all_56_21 = e2 % 148.11/21.28 | | | | | | | | | | | | | | | | | (4157) all_56_19 = e1 % 148.11/21.28 | | | | | | | | | | | | | | | | | % 148.11/21.28 | | | | | | | | | | | | | | | | | COMBINE_EQS: (435), (4157) imply: % 148.11/21.28 | | | | | | | | | | | | | | | | | (4158) all_52_6 = e1 % 148.11/21.28 | | | | | | | | | | | | | | | | | % 148.11/21.28 | | | | | | | | | | | | | | | | | SIMP: (4158) implies: % 148.11/21.28 | | | | | | | | | | | | | | | | | (4159) all_52_6 = e1 % 148.11/21.28 | | | | | | | | | | | | | | | | | % 148.11/21.28 | | | | | | | | | | | | | | | | | COMBINE_EQS: (374), (4156) imply: % 148.11/21.28 | | | | | | | | | | | | | | | | | (4160) all_6_2 = e2 % 148.11/21.28 | | | | | | | | | | | | | | | | | % 148.11/21.28 | | | | | | | | | | | | | | | | | SIMP: (4160) implies: % 148.11/21.28 | | | | | | | | | | | | | | | | | (4161) all_6_2 = e2 % 148.11/21.28 | | | | | | | | | | | | | | | | | % 148.11/21.28 | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (36), (42), (43), (46), (48), (174), % 148.11/21.28 | | | | | | | | | | | | | | | | | (208), (247), (289), (294), (297), (321), (323), % 148.11/21.28 | | | | | | | | | | | | | | | | | (341), (360), (386), (402), (407), (419), (443), % 148.11/21.28 | | | | | | | | | | | | | | | | | (542), (545), (546), (547), (550), (551), (555), % 148.11/21.28 | | | | | | | | | | | | | | | | | (571), (573), (575), (580), (620), (768), (769), % 148.11/21.28 | | | | | | | | | | | | | | | | | (3732), (3740), (3742), (4159), (4161), % 148.11/21.28 | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 148.11/21.28 | | | | | | | | | | | | | | | | | #209. % 148.11/21.28 | | | | | | | | | | | | | | | | | % 148.11/21.28 | | | | | | | | | | | | | | | | End of split % 148.11/21.28 | | | | | | | | | | | | | | | | % 148.11/21.28 | | | | | | | | | | | | | | | End of split % 148.11/21.28 | | | | | | | | | | | | | | | % 148.11/21.28 | | | | | | | | | | | | | | Case 2: % 148.11/21.28 | | | | | | | | | | | | | | | % 148.11/21.28 | | | | | | | | | | | | | | | (4162) all_56_31 = e1 % 148.11/21.28 | | | | | | | | | | | | | | | (4163) all_56_29 = e0 % 148.11/21.28 | | | | | | | | | | | | | | | % 148.11/21.28 | | | | | | | | | | | | | | | COMBINE_EQS: (357), (4163) imply: % 148.11/21.28 | | | | | | | | | | | | | | | (4164) all_52_11 = e0 % 148.11/21.28 | | | | | | | | | | | | | | | % 148.11/21.28 | | | | | | | | | | | | | | | COMBINE_EQS: (544), (4162) imply: % 148.11/21.28 | | | | | | | | | | | | | | | (4165) all_4_2 = e1 % 148.11/21.28 | | | | | | | | | | | | | | | % 148.11/21.28 | | | | | | | | | | | | | | | COMBINE_EQS: (548), (4164) imply: % 148.11/21.28 | | | | | | | | | | | | | | | (4166) all_58_14 = e0 % 148.11/21.28 | | | | | | | | | | | | | | | % 148.11/21.28 | | | | | | | | | | | | | | | REDUCE: (187), (4164) imply: % 148.11/21.28 | | | | | | | | | | | | | | | (4167) ~ (all_52_3 = e0) % 148.11/21.28 | | | | | | | | | | | | | | | % 148.11/21.28 | | | | | | | | | | | | | | | REDUCE: (173), (4164) imply: % 148.11/21.28 | | | | | | | | | | | | | | | (4168) ~ (all_52_7 = e0) % 148.11/21.28 | | | | | | | | | | | | | | | % 148.11/21.28 | | | | | | | | | | | | | | | REDUCE: (581), (4165) imply: % 148.11/21.28 | | | | | | | | | | | | | | | (4169) ~ (all_52_7 = e1) % 148.11/21.28 | | | | | | | | | | | | | | | % 148.11/21.28 | | | | | | | | | | | | | | | REDUCE: (166), (4164) imply: % 148.11/21.28 | | | | | | | | | | | | | | | (4170) ~ (all_52_9 = e0) % 148.11/21.28 | | | | | | | | | | | | | | | % 148.11/21.28 | | | | | | | | | | | | | | | REDUCE: (585), (4164) imply: % 148.11/21.28 | | | | | | | | | | | | | | | (4171) ~ (all_6_2 = e0) % 148.11/21.28 | | | | | | | | | | | | | | | % 148.11/21.28 | | | | | | | | | | | | | | | SIMP: (4171) implies: % 148.11/21.28 | | | | | | | | | | | | | | | (4172) ~ (all_6_2 = e0) % 148.11/21.28 | | | | | | | | | | | | | | | % 148.11/21.28 | | | | | | | | | | | | | | | REDUCE: (590), (4165) imply: % 148.11/21.28 | | | | | | | | | | | | | | | (4173) ~ (all_52_13 = e1) % 148.11/21.28 | | | | | | | | | | | | | | | % 148.11/21.28 | | | | | | | | | | | | | | | REDUCE: (38), (4165) imply: % 148.11/21.28 | | | | | | | | | | | | | | | (4174) op(e1, e1) = all_4_1 % 148.11/21.28 | | | | | | | | | | | | | | | % 148.11/21.28 | | | | | | | | | | | | | | | REDUCE: (36), (4165) imply: % 148.11/21.28 | | | | | | | | | | | | | | | (4175) op(e0, e0) = e1 % 148.11/21.28 | | | | | | | | | | | | | | | % 148.11/21.28 | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_6_2, % 148.11/21.28 | | | | | | | | | | | | | | | all_4_1, e1, e1, simplifying with (41), (4174) % 148.11/21.28 | | | | | | | | | | | | | | | gives: % 148.11/21.28 | | | | | | | | | | | | | | | (4176) all_6_2 = all_4_1 % 148.11/21.28 | | | | | | | | | | | | | | | % 148.11/21.28 | | | | | | | | | | | | | | | COMBINE_EQS: (541), (4176) imply: % 148.11/21.28 | | | | | | | | | | | | | | | (4177) all_54_10 = all_4_1 % 148.11/21.28 | | | | | | | | | | | | | | | % 148.11/21.28 | | | | | | | | | | | | | | | COMBINE_EQS: (374), (4176) imply: % 148.11/21.28 | | | | | | | | | | | | | | | (4178) all_56_21 = all_4_1 % 148.11/21.28 | | | | | | | | | | | | | | | % 148.11/21.28 | | | | | | | | | | | | | | | COMBINE_EQS: (552), (4176) imply: % 148.11/21.28 | | | | | | | | | | | | | | | (4179) all_58_8 = all_4_1 % 148.11/21.28 | | | | | | | | | | | | | | | % 148.11/21.28 | | | | | | | | | | | | | | | REDUCE: (580), (4176) imply: % 148.11/21.28 | | | | | | | | | | | | | | | (4180) ~ (all_52_6 = all_4_1) % 148.11/21.28 | | | | | | | | | | | | | | | % 148.11/21.28 | | | | | | | | | | | | | | | REDUCE: (583), (4176) imply: % 148.11/21.28 | | | | | | | | | | | | | | | (4181) ~ (all_52_9 = all_4_1) % 148.11/21.28 | | | | | | | | | | | | | | | % 148.11/21.28 | | | | | | | | | | | | | | | REDUCE: (4172), (4176) imply: % 148.11/21.28 | | | | | | | | | | | | | | | (4182) ~ (all_4_1 = e0) % 148.11/21.28 | | | | | | | | | | | | | | | % 148.11/21.28 | | | | | | | | | | | | | | | REDUCE: (43), (4176) imply: % 148.46/21.28 | | | | | | | | | | | | | | | (4183) op(all_4_1, all_4_1) = all_6_1 % 148.46/21.28 | | | | | | | | | | | | | | | % 148.46/21.28 | | | | | | | | | | | | | | | REDUCE: (622), (4176) imply: % 148.46/21.28 | | | | | | | | | | | | | | | (4184) op(e1, all_4_1) = all_56_20 % 148.46/21.28 | | | | | | | | | | | | | | | % 148.46/21.28 | | | | | | | | | | | | | | | BETA: splitting (292) gives: % 148.46/21.28 | | | | | | | | | | | | | | | % 148.46/21.28 | | | | | | | | | | | | | | | Case 1: % 148.46/21.28 | | | | | | | | | | | | | | | | % 148.46/21.28 | | | | | | | | | | | | | | | | (4185) ~ (all_56_21 = e2) % 148.46/21.28 | | | | | | | | | | | | | | | | % 148.46/21.28 | | | | | | | | | | | | | | | | REDUCE: (4178), (4185) imply: % 148.46/21.28 | | | | | | | | | | | | | | | | (4186) ~ (all_4_1 = e2) % 148.46/21.28 | | | | | | | | | | | | | | | | % 148.46/21.28 | | | | | | | | | | | | | | | | BETA: splitting (294) gives: % 148.46/21.28 | | | | | | | | | | | | | | | | % 148.46/21.28 | | | | | | | | | | | | | | | | Case 1: % 148.46/21.28 | | | | | | | | | | | | | | | | | % 148.46/21.28 | | | | | | | | | | | | | | | | | (4187) ~ (all_56_11 = e0) % 148.46/21.28 | | | | | | | | | | | | | | | | | % 148.46/21.28 | | | | | | | | | | | | | | | | | REDUCE: (545), (4187) imply: % 148.46/21.28 | | | | | | | | | | | | | | | | | (4188) ~ (all_8_2 = e0) % 148.46/21.28 | | | | | | | | | | | | | | | | | % 148.46/21.28 | | | | | | | | | | | | | | | | | BETA: splitting (293) gives: % 148.46/21.28 | | | | | | | | | | | | | | | | | % 148.46/21.28 | | | | | | | | | | | | | | | | | Case 1: % 148.46/21.28 | | | | | | | | | | | | | | | | | | % 148.46/21.28 | | | | | | | | | | | | | | | | | | (4189) ~ (all_56_21 = e3) % 148.46/21.28 | | | | | | | | | | | | | | | | | | % 148.46/21.28 | | | | | | | | | | | | | | | | | | REDUCE: (4178), (4189) imply: % 148.46/21.28 | | | | | | | | | | | | | | | | | | (4190) ~ (all_4_1 = e3) % 148.46/21.28 | | | | | | | | | | | | | | | | | | % 148.46/21.28 | | | | | | | | | | | | | | | | | | BETA: splitting (242) gives: % 148.46/21.28 | | | | | | | | | | | | | | | | | | % 148.46/21.28 | | | | | | | | | | | | | | | | | | Case 1: % 148.46/21.28 | | | | | | | | | | | | | | | | | | | % 148.46/21.28 | | | | | | | | | | | | | | | | | | | (4191) all_54_10 = e3 % 148.46/21.28 | | | | | | | | | | | | | | | | | | | % 148.46/21.28 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4177), (4191) imply: % 148.46/21.28 | | | | | | | | | | | | | | | | | | | (4192) all_4_1 = e3 % 148.46/21.28 | | | | | | | | | | | | | | | | | | | % 148.46/21.28 | | | | | | | | | | | | | | | | | | | REDUCE: (4190), (4192) imply: % 148.46/21.28 | | | | | | | | | | | | | | | | | | | (4193) $false % 148.46/21.28 | | | | | | | | | | | | | | | | | | | % 148.46/21.28 | | | | | | | | | | | | | | | | | | | CLOSE: (4193) is inconsistent. % 148.46/21.28 | | | | | | | | | | | | | | | | | | | % 148.46/21.28 | | | | | | | | | | | | | | | | | | Case 2: % 148.46/21.28 | | | | | | | | | | | | | | | | | | | % 148.46/21.28 | | | | | | | | | | | | | | | | | | | (4194) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 148.46/21.28 | | | | | | | | | | | | | | | | | | | % 148.46/21.28 | | | | | | | | | | | | | | | | | | | BETA: splitting (4194) gives: % 148.46/21.28 | | | | | | | | | | | | | | | | | | | % 148.46/21.28 | | | | | | | | | | | | | | | | | | | Case 1: % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | (4195) all_54_10 = e2 % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4177), (4195) imply: % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | (4196) all_4_1 = e2 % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | REDUCE: (4186), (4196) imply: % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | (4197) $false % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | CLOSE: (4197) is inconsistent. % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | % 148.46/21.28 | | | | | | | | | | | | | | | | | | | Case 2: % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | (4198) ~ (all_54_10 = e2) % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | (4199) all_54_10 = e1 | all_54_10 = e0 % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | BETA: splitting (4199) gives: % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | Case 1: % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | | % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | | (4200) all_54_10 = e1 % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | | % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4177), (4200) imply: % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | | (4201) all_4_1 = e1 % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | | % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | | REDUCE: (4180), (4201) imply: % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | | (4202) ~ (all_52_6 = e1) % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | | % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | | REDUCE: (4181), (4201) imply: % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | | (4203) ~ (all_52_9 = e1) % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | | % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | | REDUCE: (4183), (4201) imply: % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | | (4204) op(e1, e1) = all_6_1 % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | | % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | | REDUCE: (4184), (4201) imply: % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | | (4205) op(e1, e1) = all_56_20 % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | | % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | | REDUCE: (4174), (4201) imply: % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | | (4206) op(e1, e1) = e1 % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | | % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_6_1, % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | | all_56_20, e1, e1, simplifying with (4204), (4205) % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | | gives: % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | | (4207) all_56_20 = all_6_1 % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | | % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1, % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | | all_56_20, e1, e1, simplifying with (4205), (4206) % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | | gives: % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | | (4208) all_56_20 = e1 % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | | % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4207), (4208) imply: % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | | (4209) all_6_1 = e1 % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | | % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | | SIMP: (4209) implies: % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | | (4210) all_6_1 = e1 % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | | % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | | REDUCE: (42), (4210) imply: % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | | (4211) op(e1, e1) = all_6_0 % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | | % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1, all_6_0, % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | | e1, e1, simplifying with (4206), (4211) gives: % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | | (4212) all_6_0 = e1 % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | | % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | | REDUCE: (3742), (4212) imply: % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | | (4213) ~ (e3 = e1) % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | | % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | | REDUCE: (3736), (4212) imply: % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | | (4214) ~ (e2 = e1) % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | | % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (337) gives: % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | | % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | | | % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | | | (4215) all_58_1 = e1 % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | | | % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (555), (4215) imply: % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | | | (4216) all_52_4 = e1 % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | | | % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (408), (4216) imply: % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | | | (4217) all_56_3 = e1 % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | | | % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (181), (4216) imply: % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | | | (4218) ~ (all_52_12 = e1) % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | | | % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | | | SIMP: (4218) implies: % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | | | (4219) ~ (all_52_12 = e1) % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | | | % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (571), (4216) imply: % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | | | (4220) ~ (all_8_2 = e1) % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | | | % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | | | SIMP: (4220) implies: % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | | | (4221) ~ (all_8_2 = e1) % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | | | % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (299) gives: % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | | | % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | | | | % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | | | | (4222) ~ (all_56_1 = e2) % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | | | | % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (546), (4222) imply: % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | | | | (4223) ~ (all_10_2 = e2) % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | | | | % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (333) gives: % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | | | | % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | | | | | % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | | | | | (4224) all_58_2 = e1 % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | | | | | % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (401), (4224) imply: % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | | | | | (4225) all_52_1 = e1 % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | | | | | % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (425), (4225) imply: % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | | | | | (4226) all_56_9 = e1 % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | | | | | % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (194), (4225) imply: % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | | | | | (4227) ~ (all_52_9 = e1) % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | | | | | % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (193), (4225) imply: % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | | | | | (4228) ~ (all_52_13 = e1) % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | | | | | % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (557), (4225) imply: % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | | | | | (4229) ~ (all_10_2 = e1) % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | | | | | % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4229) implies: % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | | | | | (4230) ~ (all_10_2 = e1) % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | | | | | % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (296) gives: % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | | | | | % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | | | | | | (4231) ~ (all_56_11 = e3) % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (545), (4231) imply: % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | | | | | | (4232) ~ (all_8_2 = e3) % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (247) gives: % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | | | | | | | (4233) all_54_5 = e3 % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (542), (4232), (4233) are inconsistent by % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #737. % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | | | | | | | (4234) ~ (all_54_5 = e3) % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | | | | | | | (4235) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4235) gives: % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4236) all_54_5 = e2 % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (542), (4236) imply: % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4237) all_8_2 = e2 % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4237) implies: % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4238) all_8_2 = e2 % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (577), (4238) imply: % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4239) ~ (all_52_9 = e2) % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (579), (4238) imply: % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4240) ~ (all_52_13 = e2) % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (246) gives: % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4241) all_54_6 = e3 % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (467), (4241) imply: % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4242) all_52_9 = e3 % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4242) implies: % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4243) all_52_9 = e3 % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (165), (4243) imply: % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4244) ~ (all_52_13 = e3) % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4244) implies: % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4245) ~ (all_52_13 = e3) % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (245) gives: % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4246) all_54_7 = e3 % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (469), (4246) imply: % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4247) all_52_13 = e3 % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4245), (4247) imply: % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4248) $false % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (4248) is inconsistent. % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4249) all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0 % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4249) gives: % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4250) all_54_7 = e2 % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (469), (4250) imply: % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4251) all_52_13 = e2 % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4240), (4251) imply: % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4252) $false % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (4252) is inconsistent. % 148.46/21.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4253) all_54_7 = e1 | all_54_7 = e0 % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (340) gives: % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4254) all_58_0 = e0 % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (419), (4254) imply: % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4255) all_10_2 = e0 % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (537), (4255) imply: % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4256) all_50_2 = e0 % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (53), (4255) imply: % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4257) op(e0, e0) = all_10_1 % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4253) gives: % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4258) all_54_7 = e1 % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (469), (4173), (4258) are inconsistent by % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #651. % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4259) all_54_7 = e0 % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (469), (4259) imply: % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4260) all_52_13 = e0 % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4260) implies: % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4261) all_52_13 = e0 % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (625), (4261) imply: % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4262) op(e0, e0) = all_56_14 % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3745) gives: % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4263) ~ (all_50_1 = e1) % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (687), (4263) imply: % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4264) ~ (all_10_1 = e1) % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4175), (4257), (4262), (4264), (function-axioms) % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #530. % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4265) ~ (all_50_2 = e0) % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4256), (4265) imply: % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4266) $false % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (4266) is inconsistent. % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4267) ~ (all_58_0 = e0) % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (419), (4267) imply: % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4268) ~ (all_10_2 = e0) % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (161), (165), (168), (245), (246), (247), (249), % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (252), (330), (389), (407), (461), (467), (469), % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (542), (543), (567), (577), (579), (4166), (4170), % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4173), (4179), (4186), (4188), (4203), (4219), % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4221), (4223), (4230), (4232), (4268) are % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #536. % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4269) all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0 % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (467), (4170), (4203), (4239), (4269) are % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #608. % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4270) all_54_5 = e1 | all_54_5 = e0 % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (542), (4188), (4221), (4270) are inconsistent by % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #645. % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | | | | | (4271) all_56_9 = e2 % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (4226), (4271) are inconsistent by sub-proof % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | | | | | #496. % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | | | | (4272) all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1 % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (386), (389), (554), (4173), (4203), (4221), % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | | | | (4272) are inconsistent by sub-proof #495. % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | | | (4273) all_56_3 = e3 % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4217), (4273) imply: % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | | | (4274) e3 = e1 % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8), (4274) imply: % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | | | (4275) $false % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (4275) is inconsistent. % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | | End of split % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | | (4276) all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1 % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (48), (380), (549), (554), (769), (4169), (4202), % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | | (4205), (4206), (4276), (function-axioms) are % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #533. % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | End of split % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | Case 2: % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | (4277) all_54_10 = e0 % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4177), (4277) imply: % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | (4278) all_4_1 = e0 % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | REDUCE: (4182), (4278) imply: % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | (4279) $false % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | CLOSE: (4279) is inconsistent. % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | End of split % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | | | | | | | End of split % 148.46/21.29 | | | | | | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | | | | | | End of split % 148.46/21.29 | | | | | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | | | | | Case 2: % 148.46/21.29 | | | | | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | | | | | | (4280) all_56_21 = e3 % 148.46/21.29 | | | | | | | | | | | | | | | | | | (4281) all_56_17 = e1 % 148.46/21.29 | | | | | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | | | | | | REF_CLOSE: (37), (192), (207), (240), (381), (478), (767), % 148.46/21.29 | | | | | | | | | | | | | | | | | | (3728), (4167), (4178), (4280), (4281), % 148.46/21.29 | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 148.46/21.29 | | | | | | | | | | | | | | | | | | #365. % 148.46/21.29 | | | | | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | | | | | End of split % 148.46/21.29 | | | | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | | | | Case 2: % 148.46/21.29 | | | | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | | | | | (4282) all_56_11 = e0 % 148.46/21.29 | | | | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | | | | | COMBINE_EQS: (545), (4282) imply: % 148.46/21.29 | | | | | | | | | | | | | | | | | (4283) all_8_2 = e0 % 148.46/21.29 | | | | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | | | | | REDUCE: (48), (4283) imply: % 148.46/21.29 | | | | | | | | | | | | | | | | | (4284) op(e0, e0) = all_8_1 % 148.46/21.29 | | | | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | | | | | REF_CLOSE: (769), (4175), (4284), (function-axioms) are % 148.46/21.29 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #519. % 148.46/21.29 | | | | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | | | | End of split % 148.46/21.29 | | | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | | | Case 2: % 148.46/21.29 | | | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | | | | (4285) all_56_21 = e2 % 148.46/21.29 | | | | | | | | | | | | | | | | (4286) all_56_19 = e1 % 148.46/21.29 | | | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | | | | REF_CLOSE: (37), (176), (206), (239), (435), (480), (767), % 148.46/21.29 | | | | | | | | | | | | | | | | (3728), (4168), (4178), (4285), (4286), % 148.46/21.29 | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 148.46/21.29 | | | | | | | | | | | | | | | | #500. % 148.46/21.29 | | | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | | | End of split % 148.46/21.29 | | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | | End of split % 148.46/21.29 | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | End of split % 148.46/21.29 | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | Case 2: % 148.46/21.29 | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | (4287) all_40_0 = e3 % 148.46/21.29 | | | | | | | | | | | | | (4288) ~ (all_40_1 = e0) | ~ (all_40_2 = e2) % 148.46/21.29 | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | COMBINE_EQS: (713), (4287) imply: % 148.46/21.29 | | | | | | | | | | | | | (4289) all_6_0 = e3 % 148.46/21.29 | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | REDUCE: (42), (4289) imply: % 148.46/21.29 | | | | | | | | | | | | | (4290) op(e1, all_6_1) = e3 % 148.46/21.29 | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | BETA: splitting (154) gives: % 148.46/21.29 | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | Case 1: % 148.46/21.29 | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | | (4291) ~ (all_50_0 = e2) % 148.46/21.29 | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | | REDUCE: (3725), (4291) imply: % 148.46/21.29 | | | | | | | | | | | | | | (4292) $false % 148.46/21.29 | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | | CLOSE: (4292) is inconsistent. % 148.46/21.29 | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | Case 2: % 148.46/21.29 | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | | (4293) ~ (all_50_1 = e1) | ~ (all_50_2 = e0) % 148.46/21.29 | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | | BETA: splitting (292) gives: % 148.46/21.29 | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | | Case 1: % 148.46/21.29 | | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | | | (4294) ~ (all_56_21 = e2) % 148.46/21.29 | | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | | | REDUCE: (374), (4294) imply: % 148.46/21.29 | | | | | | | | | | | | | | | (4295) ~ (all_6_2 = e2) % 148.46/21.29 | | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | | | BETA: splitting (294) gives: % 148.46/21.29 | | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | | | Case 1: % 148.46/21.29 | | | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | | | | (4296) ~ (all_56_11 = e0) % 148.46/21.29 | | | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | | | | REDUCE: (545), (4296) imply: % 148.46/21.29 | | | | | | | | | | | | | | | | (4297) ~ (all_8_2 = e0) % 148.46/21.29 | | | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | | | | BETA: splitting (288) gives: % 148.46/21.29 | | | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | | | | Case 1: % 148.46/21.29 | | | | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | | | | | (4298) ~ (all_56_31 = e1) % 148.46/21.29 | | | | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | | | | | REDUCE: (544), (4298) imply: % 148.46/21.29 | | | | | | | | | | | | | | | | | (4299) ~ (all_4_2 = e1) % 148.46/21.29 | | | | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | | | | | BETA: splitting (291) gives: % 148.46/21.29 | | | | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | | | | | Case 1: % 148.46/21.29 | | | | | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | | | | | | (4300) ~ (all_56_21 = e0) % 148.46/21.29 | | | | | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | | | | | | REDUCE: (374), (4300) imply: % 148.46/21.29 | | | | | | | | | | | | | | | | | | (4301) ~ (all_6_2 = e0) % 148.46/21.29 | | | | | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | | | | | | BETA: splitting (293) gives: % 148.46/21.29 | | | | | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | | | | | | Case 1: % 148.46/21.29 | | | | | | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | | | | | | | (4302) ~ (all_56_21 = e3) % 148.46/21.29 | | | | | | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | | | | | | | REDUCE: (374), (4302) imply: % 148.46/21.29 | | | | | | | | | | | | | | | | | | | (4303) ~ (all_6_2 = e3) % 148.46/21.29 | | | | | | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (41), (43), (242), (541), (622), (3740), (4290), % 148.46/21.29 | | | | | | | | | | | | | | | | | | | (4295), (4301), (4303), (function-axioms) are % 148.46/21.29 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #514. % 148.46/21.29 | | | | | | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | | | | | | Case 2: % 148.46/21.29 | | | | | | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | | | | | | | (4304) all_56_21 = e3 % 148.46/21.29 | | | | | | | | | | | | | | | | | | | (4305) all_56_17 = e1 % 148.46/21.29 | | | | | | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (42), (43), (51), (158), (160), (161), (174), % 148.46/21.29 | | | | | | | | | | | | | | | | | | | (189), (191), (208), (241), (243), (252), (287), % 148.46/21.29 | | | | | | | | | | | | | | | | | | | (297), (321), (332), (374), (381), (386), (389), % 148.46/21.29 | | | | | | | | | | | | | | | | | | | (401), (402), (473), (476), (543), (544), (545), % 148.46/21.29 | | | | | | | | | | | | | | | | | | | (546), (547), (550), (551), (554), (557), (559), % 148.46/21.29 | | | | | | | | | | | | | | | | | | | (569), (573), (580), (591), (621), (768), (3736), % 148.46/21.29 | | | | | | | | | | | | | | | | | | | (3740), (4297), (4299), (4304), (4305), % 148.46/21.29 | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 148.46/21.29 | | | | | | | | | | | | | | | | | | | #225. % 148.46/21.29 | | | | | | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | | | | | | End of split % 148.46/21.29 | | | | | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | | | | | Case 2: % 148.46/21.29 | | | | | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | | | | | | (4306) all_56_23 = e1 % 148.46/21.29 | | | | | | | | | | | | | | | | | | (4307) all_56_21 = e0 % 148.46/21.29 | | | | | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (374), (4307) imply: % 148.46/21.29 | | | | | | | | | | | | | | | | | | (4308) all_6_2 = e0 % 148.46/21.29 | | | | | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | | | | | | SIMP: (4308) implies: % 148.46/21.29 | | | | | | | | | | | | | | | | | | (4309) all_6_2 = e0 % 148.46/21.29 | | | | | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (366), (4306) imply: % 148.46/21.29 | | | | | | | | | | | | | | | | | | (4310) all_52_14 = e1 % 148.46/21.29 | | | | | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | | | | | | SIMP: (4310) implies: % 148.46/21.29 | | | | | | | | | | | | | | | | | | (4311) all_52_14 = e1 % 148.46/21.29 | | | | | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | | | | | | REDUCE: (591), (4311) imply: % 148.46/21.29 | | | | | | | | | | | | | | | | | | (4312) ~ (all_4_2 = e1) % 148.46/21.29 | | | | | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | | | | | | REDUCE: (43), (4309) imply: % 148.46/21.29 | | | | | | | | | | | | | | | | | | (4313) op(e0, e0) = all_6_1 % 148.46/21.29 | | | | | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | | | | | | REDUCE: (622), (4309) imply: % 148.46/21.29 | | | | | | | | | | | | | | | | | | (4314) op(e1, e0) = all_56_20 % 148.46/21.29 | | | | | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | | | | | | REDUCE: (208), (4311) imply: % 148.46/21.29 | | | | | | | | | | | | | | | | | | (4315) op(e1, e0) = e1 % 148.46/21.29 | | | | | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (36), (237), (540), (768), (3740), (4290), % 148.46/21.29 | | | | | | | | | | | | | | | | | | (4299), (4313), (4314), (4315), (function-axioms) % 148.46/21.29 | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #505. % 148.46/21.29 | | | | | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | | | | | End of split % 148.46/21.29 | | | | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | | | | Case 2: % 148.46/21.29 | | | | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | | | | | (4316) all_56_31 = e1 % 148.46/21.29 | | | | | | | | | | | | | | | | | (4317) all_56_29 = e0 % 148.46/21.29 | | | | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | | | | | COMBINE_EQS: (357), (4317) imply: % 148.46/21.29 | | | | | | | | | | | | | | | | | (4318) all_52_11 = e0 % 148.46/21.29 | | | | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | | | | | REF_CLOSE: (37), (38), (41), (43), (173), (176), (187), % 148.46/21.29 | | | | | | | | | | | | | | | | | (192), (206), (207), (239), (240), (242), (292), % 148.46/21.29 | | | | | | | | | | | | | | | | | (293), (374), (381), (435), (478), (480), (541), % 148.46/21.29 | | | | | | | | | | | | | | | | | (544), (585), (622), (767), (3728), (3740), % 148.46/21.29 | | | | | | | | | | | | | | | | | (4290), (4316), (4318), (function-axioms) are % 148.46/21.29 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #462. % 148.46/21.29 | | | | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | | | | End of split % 148.46/21.29 | | | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | | | Case 2: % 148.46/21.29 | | | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | | | | (4319) all_56_15 = e2 % 148.46/21.29 | | | | | | | | | | | | | | | | (4320) all_56_11 = e0 % 148.46/21.29 | | | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | | | | COMBINE_EQS: (545), (4320) imply: % 148.46/21.29 | | | | | | | | | | | | | | | | (4321) all_8_2 = e0 % 148.46/21.29 | | | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | | | | COMBINE_EQS: (443), (4319) imply: % 148.46/21.29 | | | | | | | | | | | | | | | | (4322) all_52_13 = e2 % 148.46/21.29 | | | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | | | | REDUCE: (568), (4321) imply: % 148.46/21.29 | | | | | | | | | | | | | | | | (4323) ~ (all_52_1 = e0) % 148.46/21.29 | | | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | | | | REDUCE: (571), (4321) imply: % 148.46/21.29 | | | | | | | | | | | | | | | | (4324) ~ (all_52_4 = e0) % 148.46/21.29 | | | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | | | | REDUCE: (161), (4322) imply: % 148.46/21.29 | | | | | | | | | | | | | | | | (4325) ~ (all_52_12 = e2) % 148.46/21.29 | | | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | | | | REDUCE: (158), (4322) imply: % 148.46/21.29 | | | | | | | | | | | | | | | | (4326) ~ (all_52_14 = e2) % 148.46/21.29 | | | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | | | | SIMP: (4326) implies: % 148.46/21.29 | | | | | | | | | | | | | | | | (4327) ~ (all_52_14 = e2) % 148.46/21.29 | | | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | | | | REDUCE: (590), (4322) imply: % 148.46/21.29 | | | | | | | | | | | | | | | | (4328) ~ (all_4_2 = e2) % 148.46/21.29 | | | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | | | | SIMP: (4328) implies: % 148.46/21.29 | | | | | | | | | | | | | | | | (4329) ~ (all_4_2 = e2) % 148.46/21.29 | | | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | | | | REDUCE: (48), (4321) imply: % 148.46/21.29 | | | | | | | | | | | | | | | | (4330) op(e0, e0) = all_8_1 % 148.46/21.29 | | | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_4_2, % 148.46/21.29 | | | | | | | | | | | | | | | | all_8_1, e0, e0, simplifying with (36), (4330) % 148.46/21.29 | | | | | | | | | | | | | | | | gives: % 148.46/21.29 | | | | | | | | | | | | | | | | (4331) all_8_1 = all_4_2 % 148.46/21.29 | | | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | | | | REDUCE: (3732), (4331) imply: % 148.46/21.29 | | | | | | | | | | | | | | | | (4332) ~ (all_4_2 = e3) % 148.46/21.29 | | | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | | | | REDUCE: (769), (4331) imply: % 148.46/21.29 | | | | | | | | | | | | | | | | (4333) ~ (all_4_2 = e1) % 148.46/21.29 | | | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | | | | BETA: splitting (237) gives: % 148.46/21.29 | | | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | | | | Case 1: % 148.46/21.29 | | | | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | | | | | (4334) all_54_15 = e3 % 148.46/21.29 | | | | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | | | | | REF_CLOSE: (540), (4332), (4334) are inconsistent by % 148.46/21.29 | | | | | | | | | | | | | | | | | sub-proof #740. % 148.46/21.29 | | | | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | | | | Case 2: % 148.46/21.29 | | | | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | | | | | (4335) all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0 % 148.46/21.29 | | | | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | | | | | BETA: splitting (4335) gives: % 148.46/21.29 | | | | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | | | | | Case 1: % 148.46/21.29 | | | | | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | | | | | | (4336) all_54_15 = e2 % 148.46/21.29 | | | | | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | | | | | | REF_CLOSE: (540), (4329), (4336) are inconsistent by % 148.46/21.29 | | | | | | | | | | | | | | | | | | sub-proof #739. % 148.46/21.29 | | | | | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | | | | | Case 2: % 148.46/21.29 | | | | | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | | | | | | (4337) all_54_15 = e1 | all_54_15 = e0 % 148.46/21.29 | | | | | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | | | | | | BETA: splitting (4337) gives: % 148.46/21.29 | | | | | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | | | | | | Case 1: % 148.46/21.29 | | | | | | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | | | | | | | (4338) all_54_15 = e1 % 148.46/21.29 | | | | | | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (540), (4333), (4338) are inconsistent by % 148.46/21.29 | | | | | | | | | | | | | | | | | | | sub-proof #738. % 148.46/21.29 | | | | | | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | | | | | | Case 2: % 148.46/21.29 | | | | | | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | | | | | | | (4339) all_54_15 = e0 % 148.46/21.29 | | | | | | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (540), (4339) imply: % 148.46/21.29 | | | | | | | | | | | | | | | | | | | (4340) all_4_2 = e0 % 148.46/21.29 | | | | | | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | | | | | | | SIMP: (4340) implies: % 148.46/21.29 | | | | | | | | | | | | | | | | | | | (4341) all_4_2 = e0 % 148.46/21.29 | | | | | | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | | | | | | | REDUCE: (570), (4341) imply: % 148.46/21.29 | | | | | | | | | | | | | | | | | | | (4342) ~ (all_52_3 = e0) % 148.46/21.29 | | | | | | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | | | | | | | REDUCE: (581), (4341) imply: % 148.46/21.29 | | | | | | | | | | | | | | | | | | | (4343) ~ (all_52_7 = e0) % 148.46/21.29 | | | | | | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | | | | | | | REDUCE: (589), (4341) imply: % 148.46/21.29 | | | | | | | | | | | | | | | | | | | (4344) ~ (all_52_12 = e0) % 148.46/21.29 | | | | | | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | | | | | | | REDUCE: (38), (4341) imply: % 148.46/21.29 | | | | | | | | | | | | | | | | | | | (4345) op(e0, e0) = all_4_1 % 148.46/21.29 | | | | | | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | | | | | | | REDUCE: (627), (4341) imply: % 148.46/21.29 | | | | | | | | | | | | | | | | | | | (4346) op(e0, e0) = all_56_30 % 148.46/21.29 | | | | | | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | | | | | | | REDUCE: (36), (4341) imply: % 148.46/21.29 | | | | | | | | | | | | | | | | | | | (4347) op(e0, e0) = e0 % 148.46/21.29 | | | | | | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_4_1, % 148.46/21.29 | | | | | | | | | | | | | | | | | | | all_56_30, e0, e0, simplifying with (4345), (4346) % 148.46/21.29 | | | | | | | | | | | | | | | | | | | gives: % 148.46/21.29 | | | | | | | | | | | | | | | | | | | (4348) all_56_30 = all_4_1 % 148.46/21.29 | | | | | | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, % 148.46/21.29 | | | | | | | | | | | | | | | | | | | all_56_30, e0, e0, simplifying with (4346), (4347) % 148.46/21.29 | | | | | | | | | | | | | | | | | | | gives: % 148.46/21.29 | | | | | | | | | | | | | | | | | | | (4349) all_56_30 = e0 % 148.46/21.29 | | | | | | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4348), (4349) imply: % 148.46/21.29 | | | | | | | | | | | | | | | | | | | (4350) all_4_1 = e0 % 148.46/21.29 | | | | | | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | | | | | | | SIMP: (4350) implies: % 148.46/21.29 | | | | | | | | | | | | | | | | | | | (4351) all_4_1 = e0 % 148.46/21.29 | | | | | | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | | | | | | | REDUCE: (37), (4351) imply: % 148.46/21.29 | | | | | | | | | | | | | | | | | | | (4352) op(e0, e0) = all_4_0 % 148.46/21.29 | | | | | | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_4_0, % 148.46/21.29 | | | | | | | | | | | | | | | | | | | e0, e0, simplifying with (4347), (4352) gives: % 148.46/21.29 | | | | | | | | | | | | | | | | | | | (4353) all_4_0 = e0 % 148.46/21.29 | | | | | | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | | | | | | | REDUCE: (3728), (4353) imply: % 148.46/21.29 | | | | | | | | | | | | | | | | | | | (4354) ~ (e2 = e0) % 148.46/21.29 | | | | | | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | | | | | | | REDUCE: (3734), (4353) imply: % 148.46/21.29 | | | | | | | | | | | | | | | | | | | (4355) ~ (e1 = e0) % 148.46/21.29 | | | | | | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | | | | | | | BETA: splitting (297) gives: % 148.46/21.29 | | | | | | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | | | | | | | Case 1: % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | (4356) ~ (all_56_1 = e0) % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | REDUCE: (546), (4356) imply: % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | (4357) ~ (all_10_2 = e0) % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | BETA: splitting (341) gives: % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | Case 1: % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | (4358) all_58_0 = e0 % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (419), (4358) imply: % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | (4359) all_10_2 = e0 % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | REDUCE: (4357), (4359) imply: % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | (4360) $false % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | CLOSE: (4360) is inconsistent. % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | Case 2: % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | (4361) all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0 % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4361) gives: % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | | (4362) all_58_1 = e0 % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (555), (4362) imply: % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | | (4363) all_52_4 = e0 % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4324), (4363) imply: % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | | (4364) $false % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (4364) is inconsistent. % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | | (4365) all_58_4 = e0 | all_58_9 = e0 % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4365) gives: % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | | | (4366) all_58_4 = e0 % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (407), (4366) imply: % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | | | (4367) all_52_8 = e0 % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (171), (4367) imply: % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | | | (4368) ~ (all_52_9 = e0) % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4368) implies: % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | | | (4369) ~ (all_52_9 = e0) % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (169), (4367) imply: % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | | | (4370) ~ (all_52_11 = e0) % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4370) implies: % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | | | (4371) ~ (all_52_11 = e0) % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (168), (4367) imply: % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | | | (4372) ~ (all_52_12 = e0) % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (582), (4367) imply: % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | | | (4373) ~ (all_6_2 = e0) % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4373) implies: % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | | | (4374) ~ (all_6_2 = e0) % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (41), (43), (160), (176), (181), (183), % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | | | (184), (189), (239), (241), (242), (249), (251), % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | | | (252), (293), (297), (299), (324), (326), (328), % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | | | (340), (344), (365), (374), (380), (381), (389), % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | | | (401), (402), (407), (408), (419), (457), (461), % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | | | (476), (480), (541), (543), (546), (548), (550), % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | | | (552), (553), (563), (565), (567), (569), (587), % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | | | (622), (3740), (4290), (4295), (4323), (4324), % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | | | (4325), (4327), (4342), (4343), (4344), (4369), % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | | | (4371), (4374), (function-axioms) are inconsistent % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #510. % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | | | % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.46/21.29 | | | | | | | | | | | | | | | | | | | | | | | % 148.46/21.30 | | | | | | | | | | | | | | | | | | | | | | | (4375) all_58_9 = e0 % 148.46/21.30 | | | | | | | | | | | | | | | | | | | | | | | % 148.46/21.30 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (551), (4375) imply: % 148.46/21.30 | | | | | | | | | | | | | | | | | | | | | | | (4376) all_52_12 = e0 % 148.46/21.30 | | | | | | | | | | | | | | | | | | | | | | | % 148.46/21.30 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4344), (4376) imply: % 148.46/21.30 | | | | | | | | | | | | | | | | | | | | | | | (4377) $false % 148.46/21.30 | | | | | | | | | | | | | | | | | | | | | | | % 148.46/21.30 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (4377) is inconsistent. % 148.46/21.30 | | | | | | | | | | | | | | | | | | | | | | | % 148.46/21.30 | | | | | | | | | | | | | | | | | | | | | | End of split % 148.46/21.30 | | | | | | | | | | | | | | | | | | | | | | % 148.46/21.30 | | | | | | | | | | | | | | | | | | | | | End of split % 148.46/21.30 | | | | | | | | | | | | | | | | | | | | | % 148.46/21.30 | | | | | | | | | | | | | | | | | | | | End of split % 148.46/21.30 | | | | | | | | | | | | | | | | | | | | % 148.46/21.30 | | | | | | | | | | | | | | | | | | | Case 2: % 148.46/21.30 | | | | | | | | | | | | | | | | | | | | % 148.46/21.30 | | | | | | | | | | | | | | | | | | | | (4378) all_56_1 = e0 % 148.46/21.30 | | | | | | | | | | | | | | | | | | | | % 148.46/21.30 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (546), (4378) imply: % 148.46/21.30 | | | | | | | | | | | | | | | | | | | | (4379) all_10_2 = e0 % 148.46/21.30 | | | | | | | | | | | | | | | | | | | | % 148.46/21.30 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (537), (4379) imply: % 148.46/21.30 | | | | | | | | | | | | | | | | | | | | (4380) all_50_2 = e0 % 148.46/21.30 | | | | | | | | | | | | | | | | | | | | % 148.46/21.30 | | | | | | | | | | | | | | | | | | | | BETA: splitting (4293) gives: % 148.46/21.30 | | | | | | | | | | | | | | | | | | | | % 148.46/21.30 | | | | | | | | | | | | | | | | | | | | Case 1: % 148.46/21.30 | | | | | | | | | | | | | | | | | | | | | % 148.46/21.30 | | | | | | | | | | | | | | | | | | | | | (4381) ~ (all_50_1 = e1) % 148.46/21.30 | | | | | | | | | | | | | | | | | | | | | % 148.46/21.30 | | | | | | | | | | | | | | | | | | | | | REDUCE: (687), (4381) imply: % 148.46/21.30 | | | | | | | | | | | | | | | | | | | | | (4382) ~ (all_10_1 = e1) % 148.46/21.30 | | | | | | | | | | | | | | | | | | | | | % 148.46/21.30 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (36), (38), (41), (42), (43), (46), (48), % 148.46/21.30 | | | | | | | | | | | | | | | | | | | | | (51), (53), (158), (160), (161), (173), (174), % 148.46/21.30 | | | | | | | | | | | | | | | | | | | | | (176), (181), (183), (184), (187), (188), (189), % 148.46/21.30 | | | | | | | | | | | | | | | | | | | | | (191), (196), (208), (237), (238), (239), (241), % 148.46/21.30 | | | | | | | | | | | | | | | | | | | | | (242), (243), (247), (249), (251), (252), (287), % 148.46/21.30 | | | | | | | | | | | | | | | | | | | | | (290), (291), (292), (293), (294), (297), (299), % 148.46/21.30 | | | | | | | | | | | | | | | | | | | | | (321), (324), (326), (328), (332), (340), (344), % 148.46/21.30 | | | | | | | | | | | | | | | | | | | | | (365), (366), (374), (380), (381), (386), (389), % 148.46/21.30 | | | | | | | | | | | | | | | | | | | | | (401), (402), (407), (408), (419), (435), (443), % 148.46/21.30 | | | | | | | | | | | | | | | | | | | | | (447), (457), (461), (473), (476), (480), (482), % 148.46/21.30 | | | | | | | | | | | | | | | | | | | | | (507), (540), (541), (542), (543), (544), (545), % 148.46/21.30 | | | | | | | | | | | | | | | | | | | | | (546), (547), (548), (550), (551), (552), (553), % 148.46/21.30 | | | | | | | | | | | | | | | | | | | | | (554), (557), (559), (561), (563), (565), (567), % 148.46/21.30 | | | | | | | | | | | | | | | | | | | | | (568), (569), (570), (571), (573), (577), (580), % 148.46/21.30 | | | | | | | | | | | | | | | | | | | | | (581), (583), (585), (587), (588), (589), (590), % 148.46/21.30 | | | | | | | | | | | | | | | | | | | | | (591), (621), (622), (625), (685), (768), (3732), % 148.46/21.30 | | | | | | | | | | | | | | | | | | | | | (3736), (3740), (4288), (4290), (4295), (4333), % 148.46/21.30 | | | | | | | | | | | | | | | | | | | | | (4382), (function-axioms) are inconsistent by % 148.46/21.30 | | | | | | | | | | | | | | | | | | | | | sub-proof #219. % 148.46/21.30 | | | | | | | | | | | | | | | | | | | | | % 148.46/21.30 | | | | | | | | | | | | | | | | | | | | Case 2: % 148.46/21.30 | | | | | | | | | | | | | | | | | | | | | % 148.46/21.30 | | | | | | | | | | | | | | | | | | | | | (4383) ~ (all_50_2 = e0) % 148.46/21.30 | | | | | | | | | | | | | | | | | | | | | % 148.46/21.30 | | | | | | | | | | | | | | | | | | | | | REDUCE: (4380), (4383) imply: % 148.46/21.30 | | | | | | | | | | | | | | | | | | | | | (4384) $false % 148.46/21.30 | | | | | | | | | | | | | | | | | | | | | % 148.46/21.30 | | | | | | | | | | | | | | | | | | | | | CLOSE: (4384) is inconsistent. % 148.46/21.30 | | | | | | | | | | | | | | | | | | | | | % 148.46/21.30 | | | | | | | | | | | | | | | | | | | | End of split % 148.46/21.30 | | | | | | | | | | | | | | | | | | | | % 148.46/21.30 | | | | | | | | | | | | | | | | | | | End of split % 148.46/21.30 | | | | | | | | | | | | | | | | | | | % 148.46/21.30 | | | | | | | | | | | | | | | | | | End of split % 148.46/21.30 | | | | | | | | | | | | | | | | | | % 148.46/21.30 | | | | | | | | | | | | | | | | | End of split % 148.46/21.30 | | | | | | | | | | | | | | | | | % 148.46/21.30 | | | | | | | | | | | | | | | | End of split % 148.46/21.30 | | | | | | | | | | | | | | | | % 148.46/21.30 | | | | | | | | | | | | | | | End of split % 148.46/21.30 | | | | | | | | | | | | | | | % 148.46/21.30 | | | | | | | | | | | | | | Case 2: % 148.46/21.30 | | | | | | | | | | | | | | | % 148.46/21.30 | | | | | | | | | | | | | | | (4385) all_56_21 = e2 % 148.46/21.30 | | | | | | | | | | | | | | | (4386) all_56_19 = e1 % 148.46/21.30 | | | | | | | | | | | | | | | % 148.46/21.30 | | | | | | | | | | | | | | | COMBINE_EQS: (435), (4386) imply: % 148.46/21.30 | | | | | | | | | | | | | | | (4387) all_52_6 = e1 % 148.46/21.30 | | | | | | | | | | | | | | | % 148.46/21.30 | | | | | | | | | | | | | | | COMBINE_EQS: (374), (4385) imply: % 148.46/21.30 | | | | | | | | | | | | | | | (4388) all_6_2 = e2 % 148.46/21.30 | | | | | | | | | | | | | | | % 148.46/21.30 | | | | | | | | | | | | | | | REF_CLOSE: (43), (46), (247), (507), (542), (573), (685), % 148.46/21.30 | | | | | | | | | | | | | | | (768), (3740), (4288), (4387), (4388), % 148.46/21.30 | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 148.46/21.30 | | | | | | | | | | | | | | | #506. % 148.46/21.30 | | | | | | | | | | | | | | | % 148.46/21.30 | | | | | | | | | | | | | | End of split % 148.46/21.30 | | | | | | | | | | | | | | % 148.46/21.30 | | | | | | | | | | | | | End of split % 148.46/21.30 | | | | | | | | | | | | | % 148.46/21.30 | | | | | | | | | | | | End of split % 148.46/21.30 | | | | | | | | | | | | % 148.46/21.30 | | | | | | | | | | | Case 2: % 148.46/21.30 | | | | | | | | | | | | % 148.46/21.30 | | | | | | | | | | | | (4389) all_36_1 = e3 % 148.46/21.30 | | | | | | | | | | | | (4390) ~ (all_36_0 = e0) | ~ (all_36_2 = e2) % 148.46/21.30 | | | | | | | | | | | | % 148.46/21.30 | | | | | | | | | | | | COMBINE_EQS: (652), (4389) imply: % 148.46/21.30 | | | | | | | | | | | | (4391) all_6_1 = e3 % 148.46/21.30 | | | | | | | | | | | | % 148.46/21.30 | | | | | | | | | | | | REDUCE: (43), (4391) imply: % 148.46/21.30 | | | | | | | | | | | | (4392) op(all_6_2, all_6_2) = e3 % 148.46/21.30 | | | | | | | | | | | | % 148.46/21.30 | | | | | | | | | | | | REDUCE: (42), (4391) imply: % 148.46/21.30 | | | | | | | | | | | | (4393) op(e1, e3) = all_6_0 % 148.46/21.30 | | | | | | | | | | | | % 148.46/21.30 | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_2, % 148.46/21.30 | | | | | | | | | | | | all_6_0, e3, e1, simplifying with (211), (4393) % 148.46/21.30 | | | | | | | | | | | | gives: % 148.46/21.30 | | | | | | | | | | | | (4394) all_52_2 = all_6_0 % 148.46/21.30 | | | | | | | | | | | | % 148.46/21.30 | | | | | | | | | | | | COMBINE_EQS: (471), (4394) imply: % 148.46/21.30 | | | | | | | | | | | | (4395) all_54_8 = all_6_0 % 148.46/21.30 | | | | | | | | | | | | % 148.46/21.30 | | | | | | | | | | | | COMBINE_EQS: (381), (4394) imply: % 148.46/21.30 | | | | | | | | | | | | (4396) all_56_17 = all_6_0 % 148.46/21.30 | | | | | | | | | | | | % 148.46/21.30 | | | | | | | | | | | | COMBINE_EQS: (553), (4394) imply: % 148.46/21.30 | | | | | | | | | | | | (4397) all_58_6 = all_6_0 % 148.46/21.30 | | | | | | | | | | | | % 148.46/21.30 | | | | | | | | | | | | REDUCE: (197), (4394) imply: % 148.46/21.30 | | | | | | | | | | | | (4398) ~ (all_52_1 = all_6_0) % 148.46/21.30 | | | | | | | | | | | | % 148.46/21.30 | | | | | | | | | | | | REDUCE: (192), (4394) imply: % 148.46/21.30 | | | | | | | | | | | | (4399) ~ (all_52_3 = all_6_0) % 148.46/21.30 | | | | | | | | | | | | % 148.46/21.30 | | | | | | | | | | | | SIMP: (4399) implies: % 148.46/21.30 | | | | | | | | | | | | (4400) ~ (all_52_3 = all_6_0) % 148.46/21.30 | | | | | | | | | | | | % 148.46/21.30 | | | | | | | | | | | | REDUCE: (191), (4394) imply: % 148.46/21.30 | | | | | | | | | | | | (4401) ~ (all_52_6 = all_6_0) % 148.46/21.30 | | | | | | | | | | | | % 148.46/21.30 | | | | | | | | | | | | SIMP: (4401) implies: % 148.46/21.30 | | | | | | | | | | | | (4402) ~ (all_52_6 = all_6_0) % 148.46/21.30 | | | | | | | | | | | | % 148.46/21.30 | | | | | | | | | | | | REDUCE: (189), (4394) imply: % 148.46/21.30 | | | | | | | | | | | | (4403) ~ (all_52_14 = all_6_0) % 148.46/21.30 | | | | | | | | | | | | % 148.46/21.30 | | | | | | | | | | | | SIMP: (4403) implies: % 148.46/21.30 | | | | | | | | | | | | (4404) ~ (all_52_14 = all_6_0) % 148.46/21.30 | | | | | | | | | | | | % 148.46/21.30 | | | | | | | | | | | | REDUCE: (559), (4394) imply: % 148.46/21.30 | | | | | | | | | | | | (4405) ~ (all_10_2 = all_6_0) % 148.46/21.30 | | | | | | | | | | | | % 148.46/21.30 | | | | | | | | | | | | SIMP: (4405) implies: % 148.46/21.30 | | | | | | | | | | | | (4406) ~ (all_10_2 = all_6_0) % 148.46/21.30 | | | | | | | | | | | | % 148.46/21.30 | | | | | | | | | | | | REDUCE: (569), (4394) imply: % 148.46/21.30 | | | | | | | | | | | | (4407) ~ (all_6_0 = all_6_2) % 148.46/21.30 | | | | | | | | | | | | % 148.46/21.30 | | | | | | | | | | | | BETA: splitting (292) gives: % 148.46/21.30 | | | | | | | | | | | | % 148.46/21.30 | | | | | | | | | | | | Case 1: % 148.46/21.30 | | | | | | | | | | | | | % 148.46/21.30 | | | | | | | | | | | | | (4408) ~ (all_56_21 = e2) % 148.46/21.30 | | | | | | | | | | | | | % 148.46/21.30 | | | | | | | | | | | | | REDUCE: (374), (4408) imply: % 148.46/21.30 | | | | | | | | | | | | | (4409) ~ (all_6_2 = e2) % 148.46/21.30 | | | | | | | | | | | | | % 148.46/21.30 | | | | | | | | | | | | | BETA: splitting (294) gives: % 148.46/21.30 | | | | | | | | | | | | | % 148.46/21.30 | | | | | | | | | | | | | Case 1: % 148.46/21.30 | | | | | | | | | | | | | | % 148.46/21.30 | | | | | | | | | | | | | | (4410) ~ (all_56_11 = e0) % 148.46/21.30 | | | | | | | | | | | | | | % 148.46/21.30 | | | | | | | | | | | | | | REDUCE: (545), (4410) imply: % 148.46/21.30 | | | | | | | | | | | | | | (4411) ~ (all_8_2 = e0) % 148.46/21.30 | | | | | | | | | | | | | | % 148.46/21.30 | | | | | | | | | | | | | | BETA: splitting (293) gives: % 148.46/21.30 | | | | | | | | | | | | | | % 148.46/21.30 | | | | | | | | | | | | | | Case 1: % 148.46/21.30 | | | | | | | | | | | | | | | % 148.46/21.30 | | | | | | | | | | | | | | | (4412) ~ (all_56_21 = e3) % 148.46/21.30 | | | | | | | | | | | | | | | % 148.46/21.30 | | | | | | | | | | | | | | | REDUCE: (374), (4412) imply: % 148.46/21.30 | | | | | | | | | | | | | | | (4413) ~ (all_6_2 = e3) % 148.46/21.30 | | | | | | | | | | | | | | | % 148.46/21.30 | | | | | | | | | | | | | | | REF_CLOSE: (36), (38), (41), (48), (51), (174), (194), (242), % 148.46/21.30 | | | | | | | | | | | | | | | (243), (244), (247), (252), (287), (290), (291), % 148.46/21.30 | | | | | | | | | | | | | | | (295), (296), (326), (342), (344), (365), (366), % 148.46/21.30 | | | | | | | | | | | | | | | (374), (380), (401), (425), (431), (447), (473), % 148.46/21.30 | | | | | | | | | | | | | | | (541), (542), (543), (544), (545), (546), (550), % 148.46/21.30 | | | | | | | | | | | | | | | (552), (557), (561), (568), (573), (577), (580), % 148.46/21.30 | | | | | | | | | | | | | | | (583), (587), (622), (627), (769), (3732), (3736), % 148.46/21.30 | | | | | | | | | | | | | | | (4392), (4395), (4397), (4398), (4400), (4402), % 148.46/21.30 | | | | | | | | | | | | | | | (4404), (4406), (4407), (4409), (4411), (4413), % 148.46/21.30 | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 148.46/21.30 | | | | | | | | | | | | | | | #185. % 148.46/21.30 | | | | | | | | | | | | | | | % 148.46/21.30 | | | | | | | | | | | | | | Case 2: % 148.46/21.30 | | | | | | | | | | | | | | | % 148.46/21.30 | | | | | | | | | | | | | | | (4414) all_56_21 = e3 % 148.46/21.30 | | | | | | | | | | | | | | | % 148.46/21.30 | | | | | | | | | | | | | | | REF_CLOSE: (51), (53), (374), (612), (3726), (4392), (4409), % 148.46/21.30 | | | | | | | | | | | | | | | (4414), (function-axioms) are inconsistent by % 148.46/21.30 | | | | | | | | | | | | | | | sub-proof #163. % 148.46/21.30 | | | | | | | | | | | | | | | % 148.46/21.30 | | | | | | | | | | | | | | End of split % 148.46/21.30 | | | | | | | | | | | | | | % 148.46/21.30 | | | | | | | | | | | | | Case 2: % 148.46/21.30 | | | | | | | | | | | | | | % 148.46/21.30 | | | | | | | | | | | | | | (4415) all_56_15 = e2 % 148.46/21.30 | | | | | | | | | | | | | | (4416) all_56_11 = e0 % 148.46/21.30 | | | | | | | | | | | | | | % 148.46/21.30 | | | | | | | | | | | | | | REF_CLOSE: (4), (36), (38), (41), (46), (48), (51), (158), % 148.46/21.30 | | | | | | | | | | | | | | (168), (174), (181), (242), (243), (244), (287), % 148.46/21.30 | | | | | | | | | | | | | | (291), (292), (293), (295), (320), (321), (323), % 148.46/21.30 | | | | | | | | | | | | | | (324), (326), (329), (337), (365), (366), (374), % 148.46/21.30 | | | | | | | | | | | | | | (380), (389), (407), (431), (435), (443), (473), % 148.46/21.30 | | | | | | | | | | | | | | (532), (541), (544), (545), (546), (547), (548), % 148.46/21.30 | | | | | | | | | | | | | | (549), (550), (551), (552), (554), (555), (561), % 148.46/21.30 | | | | | | | | | | | | | | (567), (573), (575), (577), (580), (585), (587), % 148.46/21.30 | | | | | | | | | | | | | | (591), (617), (622), (623), (627), (762), (769), % 148.46/21.30 | | | | | | | | | | | | | | (3732), (3736), (4390), (4392), (4395), (4396), % 148.46/21.30 | | | | | | | | | | | | | | (4397), (4402), (4404), (4406), (4407), (4409), % 148.46/21.30 | | | | | | | | | | | | | | (4415), (4416), (function-axioms) are inconsistent % 148.46/21.30 | | | | | | | | | | | | | | by sub-proof #162. % 148.46/21.30 | | | | | | | | | | | | | | % 148.46/21.30 | | | | | | | | | | | | | End of split % 148.46/21.30 | | | | | | | | | | | | | % 148.46/21.30 | | | | | | | | | | | | Case 2: % 148.46/21.30 | | | | | | | | | | | | | % 148.46/21.30 | | | | | | | | | | | | | (4417) all_56_21 = e2 % 148.46/21.30 | | | | | | | | | | | | | (4418) all_56_19 = e1 % 148.46/21.30 | | | | | | | | | | | | | % 148.46/21.30 | | | | | | | | | | | | | REF_CLOSE: (4), (5), (46), (48), (244), (287), (324), (374), % 148.46/21.30 | | | | | | | | | | | | | (380), (435), (532), (544), (545), (546), (550), % 148.46/21.30 | | | | | | | | | | | | | (552), (580), (591), (617), (762), (4390), (4392), % 148.46/21.30 | | | | | | | | | | | | | (4395), (4397), (4402), (4404), (4406), (4407), % 148.46/21.30 | | | | | | | | | | | | | (4417), (4418), (function-axioms) are inconsistent % 148.46/21.30 | | | | | | | | | | | | | by sub-proof #412. % 148.46/21.30 | | | | | | | | | | | | | % 148.46/21.30 | | | | | | | | | | | | End of split % 148.46/21.30 | | | | | | | | | | | | % 148.46/21.30 | | | | | | | | | | | End of split % 148.46/21.30 | | | | | | | | | | | % 148.46/21.30 | | | | | | | | | | Case 2: % 148.46/21.30 | | | | | | | | | | | % 148.46/21.30 | | | | | | | | | | | (4419) all_30_0 = e3 % 148.46/21.30 | | | | | | | | | | | (4420) ~ (all_30_1 = e0) | ~ (all_30_2 = e1) % 148.46/21.30 | | | | | | | | | | | % 148.46/21.30 | | | | | | | | | | | COMBINE_EQS: (718), (4419) imply: % 148.46/21.30 | | | | | | | | | | | (4421) all_8_0 = e3 % 148.46/21.30 | | | | | | | | | | | % 148.46/21.30 | | | | | | | | | | | REF_CLOSE: (9), (36), (41), (46), (47), (48), (51), (212), % 148.46/21.30 | | | | | | | | | | | (237), (242), (247), (252), (294), (295), (296), % 148.46/21.30 | | | | | | | | | | | (390), (425), (431), (443), (540), (541), (542), % 148.46/21.30 | | | | | | | | | | | (543), (545), (557), (579), (583), (590), (617), % 148.46/21.30 | | | | | | | | | | | (658), (769), (3732), (4420), (4421), % 148.46/21.30 | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 148.46/21.30 | | | | | | | | | | | #379. % 148.46/21.30 | | | | | | | | | | | % 148.46/21.30 | | | | | | | | | | End of split % 148.46/21.30 | | | | | | | | | | % 148.46/21.30 | | | | | | | | | Case 2: % 148.46/21.30 | | | | | | | | | | % 148.46/21.30 | | | | | | | | | | (4422) all_28_0 = e2 % 148.46/21.30 | | | | | | | | | | (4423) ~ (all_28_1 = e3) | ~ (all_28_2 = e0) % 148.46/21.30 | | | | | | | | | | % 148.46/21.30 | | | | | | | | | | COMBINE_EQS: (740), (4422) imply: % 148.46/21.30 | | | | | | | | | | (4424) all_6_0 = e2 % 148.46/21.30 | | | | | | | | | | % 148.46/21.30 | | | | | | | | | | SIMP: (4424) implies: % 148.46/21.30 | | | | | | | | | | (4425) all_6_0 = e2 % 148.46/21.30 | | | | | | | | | | % 148.46/21.30 | | | | | | | | | | REF_CLOSE: (6), (8), (36), (37), (38), (41), (42), (43), % 148.46/21.30 | | | | | | | | | | (46), (51), (144), (158), (173), (174), (176), % 148.46/21.30 | | | | | | | | | | (187), (192), (206), (207), (208), (211), (237), % 148.46/21.30 | | | | | | | | | | (239), (240), (242), (247), (252), (288), (289), % 148.46/21.30 | | | | | | | | | | (290), (291), (292), (293), (294), (297), (321), % 148.46/21.30 | | | | | | | | | | (341), (357), (366), (374), (381), (386), (402), % 148.46/21.30 | | | | | | | | | | (407), (419), (435), (443), (475), (478), (480), % 148.46/21.30 | | | | | | | | | | (513), (540), (541), (542), (543), (544), (545), % 148.46/21.30 | | | | | | | | | | (546), (547), (550), (551), (555), (559), (569), % 148.46/21.30 | | | | | | | | | | (571), (573), (580), (585), (620), (622), (627), % 148.46/21.30 | | | | | | | | | | (634), (665), (764), (767), (768), (3728), (4423), % 148.46/21.30 | | | | | | | | | | (4425), (function-axioms) are inconsistent by % 148.46/21.30 | | | | | | | | | | sub-proof #364. % 148.46/21.30 | | | | | | | | | | % 148.46/21.30 | | | | | | | | | End of split % 148.46/21.30 | | | | | | | | | % 148.46/21.30 | | | | | | | | Case 2: % 148.46/21.30 | | | | | | | | | % 148.46/21.30 | | | | | | | | | (4426) all_26_0 = e1 % 148.46/21.30 | | | | | | | | | (4427) ~ (all_26_1 = e2) | ~ (all_26_2 = e3) % 148.46/21.30 | | | | | | | | | % 148.46/21.30 | | | | | | | | | COMBINE_EQS: (760), (4426) imply: % 148.46/21.30 | | | | | | | | | (4428) all_4_0 = e1 % 148.46/21.30 | | | | | | | | | % 148.46/21.30 | | | | | | | | | COMBINE_EQS: (709), (4428) imply: % 148.46/21.30 | | | | | | | | | (4429) all_44_0 = e1 % 148.46/21.30 | | | | | | | | | % 148.46/21.30 | | | | | | | | | REDUCE: (767), (4428) imply: % 148.46/21.30 | | | | | | | | | (4430) ~ (e3 = e1) % 148.46/21.30 | | | | | | | | | % 148.46/21.30 | | | | | | | | | REDUCE: (3728), (4428) imply: % 148.46/21.30 | | | | | | | | | (4431) ~ (e2 = e1) % 148.46/21.30 | | | | | | | | | % 148.46/21.30 | | | | | | | | | REDUCE: (37), (4428) imply: % 148.46/21.30 | | | | | | | | | (4432) op(e0, all_4_1) = e1 % 148.46/21.30 | | | | | | | | | % 148.46/21.30 | | | | | | | | | BETA: splitting (99) gives: % 148.46/21.30 | | | | | | | | | % 148.46/21.30 | | | | | | | | | Case 1: % 148.46/21.30 | | | | | | | | | | % 148.46/21.30 | | | | | | | | | | (4433) ~ (all_28_0 = e2) % 148.46/21.30 | | | | | | | | | | % 148.46/21.30 | | | | | | | | | | REDUCE: (740), (4433) imply: % 148.46/21.30 | | | | | | | | | | (4434) ~ (all_6_0 = e2) % 148.46/21.30 | | | | | | | | | | % 148.46/21.30 | | | | | | | | | | BETA: splitting (119) gives: % 148.46/21.30 | | | | | | | | | | % 148.46/21.30 | | | | | | | | | | Case 1: % 148.46/21.30 | | | | | | | | | | | % 148.46/21.30 | | | | | | | | | | | (4435) ~ (all_36_1 = e3) % 148.46/21.30 | | | | | | | | | | | % 148.46/21.30 | | | | | | | | | | | REDUCE: (652), (4435) imply: % 148.46/21.30 | | | | | | | | | | | (4436) ~ (all_6_1 = e3) % 148.46/21.30 | | | | | | | | | | | % 148.46/21.30 | | | | | | | | | | | BETA: splitting (139) gives: % 148.46/21.30 | | | | | | | | | | | % 148.46/21.30 | | | | | | | | | | | Case 1: % 148.46/21.30 | | | | | | | | | | | | % 148.46/21.30 | | | | | | | | | | | | (4437) ~ (all_44_0 = e1) % 148.46/21.30 | | | | | | | | | | | | % 148.46/21.30 | | | | | | | | | | | | REDUCE: (4429), (4437) imply: % 148.46/21.30 | | | | | | | | | | | | (4438) $false % 148.46/21.30 | | | | | | | | | | | | % 148.46/21.30 | | | | | | | | | | | | CLOSE: (4438) is inconsistent. % 148.46/21.30 | | | | | | | | | | | | % 148.46/21.30 | | | | | | | | | | | Case 2: % 148.46/21.30 | | | | | | | | | | | | % 148.46/21.30 | | | | | | | | | | | | (4439) ~ (all_44_1 = e3) | ~ (all_44_2 = e2) % 148.46/21.30 | | | | | | | | | | | | % 148.46/21.30 | | | | | | | | | | | | BETA: splitting (292) gives: % 148.46/21.30 | | | | | | | | | | | | % 148.46/21.30 | | | | | | | | | | | | Case 1: % 148.46/21.30 | | | | | | | | | | | | | % 148.46/21.30 | | | | | | | | | | | | | (4440) ~ (all_56_21 = e2) % 148.46/21.30 | | | | | | | | | | | | | % 148.46/21.30 | | | | | | | | | | | | | REDUCE: (374), (4440) imply: % 148.46/21.30 | | | | | | | | | | | | | (4441) ~ (all_6_2 = e2) % 148.46/21.30 | | | | | | | | | | | | | % 148.46/21.30 | | | | | | | | | | | | | BETA: splitting (294) gives: % 148.46/21.30 | | | | | | | | | | | | | % 148.46/21.30 | | | | | | | | | | | | | Case 1: % 148.46/21.30 | | | | | | | | | | | | | | % 148.46/21.30 | | | | | | | | | | | | | | (4442) ~ (all_56_11 = e0) % 148.46/21.30 | | | | | | | | | | | | | | % 148.46/21.30 | | | | | | | | | | | | | | REDUCE: (545), (4442) imply: % 148.46/21.30 | | | | | | | | | | | | | | (4443) ~ (all_8_2 = e0) % 148.46/21.30 | | | | | | | | | | | | | | % 148.46/21.30 | | | | | | | | | | | | | | BETA: splitting (288) gives: % 148.46/21.30 | | | | | | | | | | | | | | % 148.46/21.30 | | | | | | | | | | | | | | Case 1: % 148.46/21.30 | | | | | | | | | | | | | | | % 148.46/21.30 | | | | | | | | | | | | | | | (4444) ~ (all_56_31 = e1) % 148.46/21.30 | | | | | | | | | | | | | | | % 148.46/21.30 | | | | | | | | | | | | | | | REDUCE: (544), (4444) imply: % 148.46/21.30 | | | | | | | | | | | | | | | (4445) ~ (all_4_2 = e1) % 148.46/21.30 | | | | | | | | | | | | | | | % 148.46/21.30 | | | | | | | | | | | | | | | BETA: splitting (290) gives: % 148.46/21.30 | | | | | | | | | | | | | | | % 148.46/21.30 | | | | | | | | | | | | | | | Case 1: % 148.46/21.30 | | | | | | | | | | | | | | | | % 148.46/21.30 | | | | | | | | | | | | | | | | (4446) ~ (all_56_31 = e3) % 148.46/21.30 | | | | | | | | | | | | | | | | % 148.46/21.30 | | | | | | | | | | | | | | | | REDUCE: (544), (4446) imply: % 148.46/21.30 | | | | | | | | | | | | | | | | (4447) ~ (all_4_2 = e3) % 148.46/21.30 | | | | | | | | | | | | | | | | % 148.46/21.30 | | | | | | | | | | | | | | | | BETA: splitting (289) gives: % 148.46/21.30 | | | | | | | | | | | | | | | | % 148.46/21.30 | | | | | | | | | | | | | | | | Case 1: % 148.46/21.30 | | | | | | | | | | | | | | | | | % 148.46/21.30 | | | | | | | | | | | | | | | | | (4448) ~ (all_56_31 = e2) % 148.46/21.30 | | | | | | | | | | | | | | | | | % 148.46/21.30 | | | | | | | | | | | | | | | | | REDUCE: (544), (4448) imply: % 148.46/21.30 | | | | | | | | | | | | | | | | | (4449) ~ (all_4_2 = e2) % 148.46/21.30 | | | | | | | | | | | | | | | | | % 148.46/21.30 | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (38), (237), (540), (627), (4432), (4445), % 148.46/21.30 | | | | | | | | | | | | | | | | | (4447), (4449), (function-axioms) are inconsistent % 148.46/21.30 | | | | | | | | | | | | | | | | | by sub-proof #363. % 148.46/21.30 | | | | | | | | | | | | | | | | | % 148.46/21.30 | | | | | | | | | | | | | | | | Case 2: % 148.46/21.30 | | | | | | | | | | | | | | | | | % 148.46/21.30 | | | | | | | | | | | | | | | | | (4450) all_56_31 = e2 % 148.46/21.30 | | | | | | | | | | | | | | | | | (4451) all_56_27 = e0 % 148.46/21.30 | | | | | | | | | | | | | | | | | % 148.46/21.30 | | | | | | | | | | | | | | | | | COMBINE_EQS: (360), (4451) imply: % 148.46/21.30 | | | | | | | | | | | | | | | | | (4452) all_52_7 = e0 % 148.46/21.30 | | | | | | | | | | | | | | | | | % 148.46/21.30 | | | | | | | | | | | | | | | | | SIMP: (4452) implies: % 148.46/21.30 | | | | | | | | | | | | | | | | | (4453) all_52_7 = e0 % 148.46/21.30 | | | | | | | | | | | | | | | | | % 148.46/21.30 | | | | | | | | | | | | | | | | | COMBINE_EQS: (544), (4450) imply: % 148.46/21.30 | | | | | | | | | | | | | | | | | (4454) all_4_2 = e2 % 148.46/21.30 | | | | | | | | | | | | | | | | | % 148.46/21.30 | | | | | | | | | | | | | | | | | COMBINE_EQS: (535), (4454) imply: % 148.46/21.30 | | | | | | | | | | | | | | | | | (4455) all_44_2 = e2 % 148.46/21.30 | | | | | | | | | | | | | | | | | % 148.46/21.30 | | | | | | | | | | | | | | | | | COMBINE_EQS: (547), (4454) imply: % 148.46/21.30 | | | | | | | | | | | | | | | | | (4456) all_58_15 = e2 % 148.46/21.30 | | | | | | | | | | | | | | | | | % 148.46/21.30 | | | | | | | | | | | | | | | | | COMBINE_EQS: (549), (4453) imply: % 148.46/21.30 | | | | | | | | | | | | | | | | | (4457) all_58_13 = e0 % 148.46/21.30 | | | | | | | | | | | | | | | | | % 148.46/21.30 | | | | | | | | | | | | | | | | | REDUCE: (188), (4453) imply: % 148.46/21.30 | | | | | | | | | | | | | | | | | (4458) ~ (all_52_3 = e0) % 148.46/21.30 | | | | | | | | | | | | | | | | | % 148.46/21.30 | | | | | | | | | | | | | | | | | REDUCE: (570), (4454) imply: % 148.46/21.30 | | | | | | | | | | | | | | | | | (4459) ~ (all_52_3 = e2) % 148.46/21.30 | | | | | | | | | | | | | | | | | % 148.46/21.30 | | | | | | | | | | | | | | | | | REDUCE: (176), (4453) imply: % 148.46/21.30 | | | | | | | | | | | | | | | | | (4460) ~ (all_52_6 = e0) % 148.46/21.30 | | | | | | | | | | | | | | | | | % 148.46/21.30 | | | | | | | | | | | | | | | | | REDUCE: (173), (4453) imply: % 148.46/21.30 | | | | | | | | | | | | | | | | | (4461) ~ (all_52_11 = e0) % 148.46/21.30 | | | | | | | | | | | | | | | | | % 148.46/21.30 | | | | | | | | | | | | | | | | | SIMP: (4461) implies: % 148.46/21.30 | | | | | | | | | | | | | | | | | (4462) ~ (all_52_11 = e0) % 148.46/21.30 | | | | | | | | | | | | | | | | | % 148.46/21.30 | | | | | | | | | | | | | | | | | REDUCE: (575), (4453) imply: % 148.46/21.30 | | | | | | | | | | | | | | | | | (4463) ~ (all_8_2 = e0) % 148.46/21.30 | | | | | | | | | | | | | | | | | % 148.46/21.30 | | | | | | | | | | | | | | | | | REDUCE: (581), (4453), (4454) imply: % 148.46/21.30 | | | | | | | | | | | | | | | | | (4464) ~ (e2 = e0) % 148.46/21.30 | | | | | | | | | | | | | | | | | % 148.46/21.30 | | | | | | | | | | | | | | | | | REDUCE: (588), (4454) imply: % 148.46/21.30 | | | | | | | | | | | | | | | | | (4465) ~ (all_52_11 = e2) % 148.46/21.30 | | | | | | | | | | | | | | | | | % 148.46/21.30 | | | | | | | | | | | | | | | | | REDUCE: (589), (4454) imply: % 148.46/21.30 | | | | | | | | | | | | | | | | | (4466) ~ (all_52_12 = e2) % 148.46/21.30 | | | | | | | | | | | | | | | | | % 148.46/21.30 | | | | | | | | | | | | | | | | | REDUCE: (590), (4454) imply: % 148.54/21.30 | | | | | | | | | | | | | | | | | (4467) ~ (all_52_13 = e2) % 148.54/21.30 | | | | | | | | | | | | | | | | | % 148.54/21.30 | | | | | | | | | | | | | | | | | REDUCE: (591), (4454) imply: % 148.54/21.30 | | | | | | | | | | | | | | | | | (4468) ~ (all_52_14 = e2) % 148.54/21.30 | | | | | | | | | | | | | | | | | % 148.54/21.30 | | | | | | | | | | | | | | | | | REDUCE: (4447), (4454) imply: % 148.54/21.30 | | | | | | | | | | | | | | | | | (4469) ~ (e3 = e2) % 148.54/21.30 | | | | | | | | | | | | | | | | | % 148.54/21.30 | | | | | | | | | | | | | | | | | REDUCE: (38), (4454) imply: % 148.54/21.30 | | | | | | | | | | | | | | | | | (4470) op(e2, e2) = all_4_1 % 148.54/21.30 | | | | | | | | | | | | | | | | | % 148.54/21.30 | | | | | | | | | | | | | | | | | REDUCE: (36), (4454) imply: % 148.54/21.30 | | | | | | | | | | | | | | | | | (4471) op(e0, e0) = e2 % 148.54/21.30 | | | | | | | | | | | | | | | | | % 148.54/21.30 | | | | | | | | | | | | | | | | | BETA: splitting (4439) gives: % 148.54/21.30 | | | | | | | | | | | | | | | | | % 148.54/21.30 | | | | | | | | | | | | | | | | | Case 1: % 148.54/21.30 | | | | | | | | | | | | | | | | | | % 148.54/21.30 | | | | | | | | | | | | | | | | | | (4472) ~ (all_44_1 = e3) % 148.54/21.30 | | | | | | | | | | | | | | | | | | % 148.54/21.30 | | | | | | | | | | | | | | | | | | REDUCE: (631), (4472) imply: % 148.54/21.31 | | | | | | | | | | | | | | | | | | (4473) ~ (all_4_1 = e3) % 148.54/21.31 | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_8_2, % 148.54/21.31 | | | | | | | | | | | | | | | | | | all_4_1, e2, e2, simplifying with (46), (4470) % 148.54/21.31 | | | | | | | | | | | | | | | | | | gives: % 148.54/21.31 | | | | | | | | | | | | | | | | | | (4474) all_8_2 = all_4_1 % 148.54/21.31 | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (542), (4474) imply: % 148.54/21.31 | | | | | | | | | | | | | | | | | | (4475) all_54_5 = all_4_1 % 148.54/21.31 | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (545), (4474) imply: % 148.54/21.31 | | | | | | | | | | | | | | | | | | (4476) all_56_11 = all_4_1 % 148.54/21.31 | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (554), (4474) imply: % 148.54/21.31 | | | | | | | | | | | | | | | | | | (4477) all_58_3 = all_4_1 % 148.54/21.31 | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | REDUCE: (571), (4474) imply: % 148.54/21.31 | | | | | | | | | | | | | | | | | | (4478) ~ (all_52_4 = all_4_1) % 148.54/21.31 | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | REDUCE: (573), (4474) imply: % 148.54/21.31 | | | | | | | | | | | | | | | | | | (4479) ~ (all_52_6 = all_4_1) % 148.54/21.31 | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | REDUCE: (577), (4474) imply: % 148.54/21.31 | | | | | | | | | | | | | | | | | | (4480) ~ (all_52_9 = all_4_1) % 148.54/21.31 | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | REDUCE: (579), (4474) imply: % 148.54/21.31 | | | | | | | | | | | | | | | | | | (4481) ~ (all_52_13 = all_4_1) % 148.54/21.31 | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | REDUCE: (4443), (4474) imply: % 148.54/21.31 | | | | | | | | | | | | | | | | | | (4482) ~ (all_4_1 = e0) % 148.54/21.31 | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | BETA: splitting (298) gives: % 148.54/21.31 | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | Case 1: % 148.54/21.31 | | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | | (4483) ~ (all_56_1 = e1) % 148.54/21.31 | | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | | REDUCE: (546), (4483) imply: % 148.54/21.31 | | | | | | | | | | | | | | | | | | | (4484) ~ (all_10_2 = e1) % 148.54/21.31 | | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (37), (51), (53), (158), (166), (181), (191), % 148.54/21.31 | | | | | | | | | | | | | | | | | | | (193), (196), (197), (205), (218), (238), (240), % 148.54/21.31 | | | | | | | | | | | | | | | | | | | (247), (248), (252), (287), (297), (299), (318), % 148.54/21.31 | | | | | | | | | | | | | | | | | | | (320), (321), (326), (327), (330), (335), (339), % 148.54/21.31 | | | | | | | | | | | | | | | | | | | (365), (374), (380), (386), (389), (401), (402), % 148.54/21.31 | | | | | | | | | | | | | | | | | | | (407), (408), (463), (478), (482), (543), (546), % 148.54/21.31 | | | | | | | | | | | | | | | | | | | (547), (548), (550), (551), (552), (553), (555), % 148.54/21.31 | | | | | | | | | | | | | | | | | | | (557), (559), (561), (563), (565), (567), (585), % 148.54/21.31 | | | | | | | | | | | | | | | | | | | (587), (612), (614), (624), (767), (3726), (4441), % 148.54/21.31 | | | | | | | | | | | | | | | | | | | (4445), (4450), (4456), (4457), (4458), (4459), % 148.54/21.31 | | | | | | | | | | | | | | | | | | | (4460), (4462), (4465), (4466), (4467), (4468), % 148.54/21.31 | | | | | | | | | | | | | | | | | | | (4471), (4473), (4475), (4476), (4477), (4478), % 148.54/21.31 | | | | | | | | | | | | | | | | | | | (4479), (4480), (4481), (4482), (4484), % 148.54/21.31 | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 148.54/21.31 | | | | | | | | | | | | | | | | | | | #164. % 148.54/21.31 | | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | Case 2: % 148.54/21.31 | | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | | (4485) all_56_5 = e3 % 148.54/21.31 | | | | | | | | | | | | | | | | | | | (4486) all_56_1 = e1 % 148.54/21.31 | | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (546), (4486) imply: % 148.54/21.31 | | | | | | | | | | | | | | | | | | | (4487) all_10_2 = e1 % 148.54/21.31 | | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (429), (4485) imply: % 148.54/21.31 | | | | | | | | | | | | | | | | | | | (4488) all_52_8 = e3 % 148.54/21.31 | | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (407), (4488) imply: % 148.54/21.31 | | | | | | | | | | | | | | | | | | | (4489) all_58_4 = e3 % 148.54/21.31 | | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | | REDUCE: (171), (4488) imply: % 148.54/21.31 | | | | | | | | | | | | | | | | | | | (4490) ~ (all_52_9 = e3) % 148.54/21.31 | | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | | SIMP: (4490) implies: % 148.54/21.31 | | | | | | | | | | | | | | | | | | | (4491) ~ (all_52_9 = e3) % 148.54/21.31 | | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | | REDUCE: (53), (4487) imply: % 148.54/21.31 | | | | | | | | | | | | | | | | | | | (4492) op(e1, e1) = all_10_1 % 148.54/21.31 | | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | | REDUCE: (612), (4487) imply: % 148.54/21.31 | | | | | | | | | | | | | | | | | | | (4493) op(e3, e1) = all_56_0 % 148.54/21.31 | | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | | REDUCE: (217), (4488) imply: % 148.54/21.31 | | | | | | | | | | | | | | | | | | | (4494) op(e3, e1) = e3 % 148.54/21.31 | | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | | BETA: splitting (330) gives: % 148.54/21.31 | | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | | Case 1: % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | (4495) all_58_4 = e2 % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4489), (4495) imply: % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | (4496) e3 = e2 % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | REDUCE: (9), (4496) imply: % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | (4497) $false % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | CLOSE: (4497) is inconsistent. % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | | Case 2: % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | (4498) all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2 % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | BETA: splitting (4498) gives: % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | Case 1: % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | (4499) all_58_5 = e2 % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (389), (4499) imply: % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | (4500) all_52_9 = e2 % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | REDUCE: (4480), (4500) imply: % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | (4501) ~ (all_4_1 = e2) % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | SIMP: (4501) implies: % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | (4502) ~ (all_4_1 = e2) % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (287) gives: % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | (4503) all_56_1 = e3 % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (4486), (4503) are inconsistent by sub-proof % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | #182. % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | (4504) all_56_11 = e2 | all_56_21 = e1 | all_56_31 = e0 % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4504) gives: % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | (4505) all_56_11 = e2 % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4476), (4505) imply: % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | (4506) all_4_1 = e2 % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4502), (4506) imply: % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | (4507) $false % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (4507) is inconsistent. % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | (4508) all_56_21 = e1 | all_56_31 = e0 % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4508) gives: % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | (4509) all_56_21 = e1 % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (374), (4509) imply: % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | (4510) all_6_2 = e1 % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4510) implies: % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | (4511) all_6_2 = e1 % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (41), (4511) imply: % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | (4512) op(e1, e1) = e1 % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (3726), (4492), (4493), (4494), (4512), % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | #171. % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | (4513) all_56_31 = e0 % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (4450), (4513) are inconsistent by sub-proof % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | #166. % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | End of split % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | End of split % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | Case 2: % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | (4514) all_58_8 = e2 | all_58_14 = e2 % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (548), (552), (4441), (4465), (4514) are % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #478. % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | End of split % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | | End of split % 148.54/21.31 | | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | End of split % 148.54/21.31 | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | Case 2: % 148.54/21.31 | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | (4515) ~ (all_44_2 = e2) % 148.54/21.31 | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | REDUCE: (4455), (4515) imply: % 148.54/21.31 | | | | | | | | | | | | | | | | | | (4516) $false % 148.54/21.31 | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | CLOSE: (4516) is inconsistent. % 148.54/21.31 | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | End of split % 148.54/21.31 | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | End of split % 148.54/21.31 | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | Case 2: % 148.54/21.31 | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | (4517) all_56_31 = e3 % 148.54/21.31 | | | | | | | | | | | | | | | | (4518) all_56_25 = e0 % 148.54/21.31 | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | COMBINE_EQS: (447), (4518) imply: % 148.54/21.31 | | | | | | | | | | | | | | | | (4519) all_52_3 = e0 % 148.54/21.31 | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | SIMP: (4519) implies: % 148.54/21.31 | | | | | | | | | | | | | | | | (4520) all_52_3 = e0 % 148.54/21.31 | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | COMBINE_EQS: (544), (4517) imply: % 148.54/21.31 | | | | | | | | | | | | | | | | (4521) all_4_2 = e3 % 148.54/21.31 | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | COMBINE_EQS: (530), (4521) imply: % 148.54/21.31 | | | | | | | | | | | | | | | | (4522) all_26_2 = e3 % 148.54/21.31 | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | REDUCE: (196), (4520) imply: % 148.54/21.31 | | | | | | | | | | | | | | | | (4523) ~ (all_52_1 = e0) % 148.54/21.31 | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | REDUCE: (192), (4520) imply: % 148.54/21.31 | | | | | | | | | | | | | | | | (4524) ~ (all_52_2 = e0) % 148.54/21.31 | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | REDUCE: (187), (4520) imply: % 148.54/21.31 | | | | | | | | | | | | | | | | (4525) ~ (all_52_11 = e0) % 148.54/21.31 | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | SIMP: (4525) implies: % 148.54/21.31 | | | | | | | | | | | | | | | | (4526) ~ (all_52_11 = e0) % 148.54/21.31 | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | REDUCE: (561), (4520) imply: % 148.54/21.31 | | | | | | | | | | | | | | | | (4527) ~ (all_10_2 = e0) % 148.54/21.31 | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | SIMP: (4527) implies: % 148.54/21.31 | | | | | | | | | | | | | | | | (4528) ~ (all_10_2 = e0) % 148.54/21.31 | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | REDUCE: (588), (4521) imply: % 148.54/21.31 | | | | | | | | | | | | | | | | (4529) ~ (all_52_11 = e3) % 148.54/21.31 | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | REDUCE: (590), (4521) imply: % 148.54/21.31 | | | | | | | | | | | | | | | | (4530) ~ (all_52_13 = e3) % 148.54/21.31 | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | REDUCE: (591), (4521) imply: % 148.54/21.31 | | | | | | | | | | | | | | | | (4531) ~ (all_52_14 = e3) % 148.54/21.31 | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | REDUCE: (38), (4521) imply: % 148.54/21.31 | | | | | | | | | | | | | | | | (4532) op(e3, e3) = all_4_1 % 148.54/21.31 | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | REDUCE: (36), (4521) imply: % 148.54/21.31 | | | | | | | | | | | | | | | | (4533) op(e0, e0) = e3 % 148.54/21.31 | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | BETA: splitting (4427) gives: % 148.54/21.31 | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | Case 1: % 148.54/21.31 | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | (4534) ~ (all_26_1 = e2) % 148.54/21.31 | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | REDUCE: (657), (4534) imply: % 148.54/21.31 | | | | | | | | | | | | | | | | | (4535) ~ (all_4_1 = e2) % 148.54/21.31 | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_10_2, % 148.54/21.31 | | | | | | | | | | | | | | | | | all_4_1, e3, e3, simplifying with (51), (4532) % 148.54/21.31 | | | | | | | | | | | | | | | | | gives: % 148.54/21.31 | | | | | | | | | | | | | | | | | (4536) all_10_2 = all_4_1 % 148.54/21.31 | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | COMBINE_EQS: (543), (4536) imply: % 148.54/21.31 | | | | | | | | | | | | | | | | | (4537) all_54_0 = all_4_1 % 148.54/21.31 | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | COMBINE_EQS: (546), (4536) imply: % 148.54/21.31 | | | | | | | | | | | | | | | | | (4538) all_56_1 = all_4_1 % 148.54/21.31 | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | REDUCE: (557), (4536) imply: % 148.54/21.31 | | | | | | | | | | | | | | | | | (4539) ~ (all_52_1 = all_4_1) % 148.54/21.31 | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | REDUCE: (559), (4536) imply: % 148.54/21.31 | | | | | | | | | | | | | | | | | (4540) ~ (all_52_2 = all_4_1) % 148.54/21.31 | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | REDUCE: (4528), (4536) imply: % 148.54/21.31 | | | | | | | | | | | | | | | | | (4541) ~ (all_4_1 = e0) % 148.54/21.31 | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | REDUCE: (53), (4536) imply: % 148.54/21.31 | | | | | | | | | | | | | | | | | (4542) op(all_4_1, all_4_1) = all_10_1 % 148.54/21.31 | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | REDUCE: (612), (4536) imply: % 148.54/21.31 | | | | | | | | | | | | | | | | | (4543) op(e3, all_4_1) = all_56_0 % 148.54/21.31 | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | BETA: splitting (293) gives: % 148.54/21.31 | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | Case 1: % 148.54/21.31 | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | (4544) ~ (all_56_21 = e3) % 148.54/21.31 | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | REDUCE: (374), (4544) imply: % 148.54/21.31 | | | | | | | | | | | | | | | | | | (4545) ~ (all_6_2 = e3) % 148.54/21.31 | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | BETA: splitting (291) gives: % 148.54/21.31 | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | Case 1: % 148.54/21.31 | | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | | (4546) ~ (all_56_21 = e0) % 148.54/21.31 | | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | | REDUCE: (374), (4546) imply: % 148.54/21.31 | | | | | | | | | | | | | | | | | | | (4547) ~ (all_6_2 = e0) % 148.54/21.31 | | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | | BETA: splitting (242) gives: % 148.54/21.31 | | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | | Case 1: % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | (4548) all_54_10 = e3 % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (541), (4545), (4548) are inconsistent by % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | sub-proof #736. % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | | Case 2: % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | (4549) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | BETA: splitting (4549) gives: % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | Case 1: % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | (4550) all_54_10 = e2 % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (541), (4441), (4550) are inconsistent by % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | sub-proof #735. % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | Case 2: % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | (4551) all_54_10 = e1 | all_54_10 = e0 % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4551) gives: % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | (4552) all_54_10 = e1 % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (541), (4552) imply: % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | (4553) all_6_2 = e1 % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | SIMP: (4553) implies: % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | (4554) all_6_2 = e1 % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (552), (4554) imply: % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | (4555) all_58_8 = e1 % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (569), (4554) imply: % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | (4556) ~ (all_52_2 = e1) % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (585), (4554) imply: % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | (4557) ~ (all_52_11 = e1) % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives: % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | (4558) all_54_14 = e3 % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (482), (4529), (4558) are inconsistent by % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | sub-proof #729. % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | (4559) all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0 % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4559) gives: % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | (4560) all_54_14 = e2 % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (482), (4560) imply: % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | (4561) all_52_11 = e2 % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4561) implies: % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | (4562) all_52_11 = e2 % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (169), (4562) imply: % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | (4563) ~ (all_52_8 = e2) % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (298) gives: % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | (4564) ~ (all_56_1 = e1) % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4538), (4564) imply: % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | (4565) ~ (all_4_1 = e1) % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (252) gives: % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | | (4566) all_54_0 = e3 % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4537), (4566) imply: % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | | (4567) all_4_1 = e3 % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4567) implies: % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | | (4568) all_4_1 = e3 % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4539), (4568) imply: % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | | (4569) ~ (all_52_1 = e3) % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4540), (4568) imply: % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | | (4570) ~ (all_52_2 = e3) % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (327) gives: % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4571) all_58_6 = e3 % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (553), (4570), (4571) are inconsistent by % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #346. % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4572) ~ (all_58_6 = e3) % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4573) all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3 % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (244) gives: % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4574) all_54_8 = e3 % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (471), (4574) imply: % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4575) all_52_2 = e3 % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4570), (4575) imply: % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4576) $false % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (4576) is inconsistent. % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4577) all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0 % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4573) gives: % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4578) all_58_7 = e3 % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (380), (4578) imply: % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4579) all_52_6 = e3 % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (573), (4579) imply: % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4580) ~ (all_8_2 = e3) % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4580) implies: % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4581) ~ (all_8_2 = e3) % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4577) gives: % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4582) all_54_8 = e2 % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (471), (4582) imply: % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4583) all_52_2 = e2 % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (197), (4583) imply: % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4584) ~ (all_52_1 = e2) % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (247) gives: % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4585) all_54_5 = e3 % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (542), (4581), (4585) are inconsistent by % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #737. % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4586) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (248) gives: % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4587) all_54_4 = e3 % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (463), (4569), (4587) are inconsistent by % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #634. % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4588) all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0 % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4588) gives: % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4589) all_54_4 = e2 % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (463), (4584), (4589) are inconsistent by % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #633. % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4590) all_54_4 = e1 | all_54_4 = e0 % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4590) gives: % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4591) all_54_4 = e1 % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (463), (4591) imply: % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4592) all_52_1 = e1 % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4592) implies: % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4593) all_52_1 = e1 % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (193), (4593) imply: % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4594) ~ (all_52_13 = e1) % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4594) implies: % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4595) ~ (all_52_13 = e1) % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (568), (4593) imply: % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4596) ~ (all_8_2 = e1) % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4596) implies: % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4597) ~ (all_8_2 = e1) % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4586) gives: % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4598) all_54_5 = e2 % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (542), (4598) imply: % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4599) all_8_2 = e2 % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4599) implies: % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4600) all_8_2 = e2 % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (579), (4600) imply: % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4601) ~ (all_52_13 = e2) % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (43), (158), (165), (244), (245), (324), (332), % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (386), (389), (401), (469), (471), (550), (552), % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (553), (554), (625), (4436), (4443), (4523), % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4524), (4530), (4533), (4556), (4570), (4578), % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4595), (4601), (function-axioms) are inconsistent % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #216. % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4602) all_54_5 = e1 | all_54_5 = e0 % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (542), (4443), (4597), (4602) are inconsistent by % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #645. % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4603) all_54_4 = e0 % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (463), (4523), (4603) are inconsistent by % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #614. % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4604) all_54_8 = e1 | all_54_8 = e0 % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (471), (4524), (4556), (4604) are inconsistent by % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #664. % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4605) all_58_8 = e3 | all_58_11 = e3 % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (550), (4531), (4555), (4605) are % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #160. % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | | (4606) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4535), (4537), (4541), (4565), (4606) are % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #549. % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | (4607) all_56_5 = e3 % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | (4608) all_56_1 = e1 % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4538), (4608) imply: % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | (4609) all_4_1 = e1 % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (429), (4607) imply: % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | (4610) all_52_8 = e3 % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4610) implies: % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | (4611) all_52_8 = e3 % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4542), (4609) imply: % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | (4612) op(e1, e1) = all_10_1 % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4543), (4609) imply: % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | (4613) op(e3, e1) = all_56_0 % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (217), (4611) imply: % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | (4614) op(e3, e1) = e3 % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (41), (541), (3726), (4547), (4551), (4612), % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | (4613), (4614), (function-axioms) are inconsistent % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #170. % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | (4615) all_54_14 = e1 | all_54_14 = e0 % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (482), (4526), (4557), (4615) are inconsistent by % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #714. % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | | % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | End of split % 148.54/21.31 | | | | | | | | | | | | | | | | | | | | | | % 148.54/21.32 | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.54/21.32 | | | | | | | | | | | | | | | | | | | | | | % 148.54/21.32 | | | | | | | | | | | | | | | | | | | | | | (4616) all_54_10 = e0 % 148.54/21.32 | | | | | | | | | | | | | | | | | | | | | | % 148.54/21.32 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (541), (4547), (4616) are inconsistent by % 148.54/21.32 | | | | | | | | | | | | | | | | | | | | | | sub-proof #705. % 148.54/21.32 | | | | | | | | | | | | | | | | | | | | | | % 148.54/21.32 | | | | | | | | | | | | | | | | | | | | | End of split % 148.54/21.32 | | | | | | | | | | | | | | | | | | | | | % 148.54/21.32 | | | | | | | | | | | | | | | | | | | | End of split % 148.54/21.32 | | | | | | | | | | | | | | | | | | | | % 148.54/21.32 | | | | | | | | | | | | | | | | | | | End of split % 148.54/21.32 | | | | | | | | | | | | | | | | | | | % 148.54/21.32 | | | | | | | | | | | | | | | | | | Case 2: % 148.54/21.32 | | | | | | | | | | | | | | | | | | | % 148.54/21.32 | | | | | | | | | | | | | | | | | | | (4617) all_56_21 = e0 % 148.54/21.32 | | | | | | | | | | | | | | | | | | | % 148.54/21.32 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (43), (374), (4436), (4533), (4617), % 148.54/21.32 | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 148.54/21.32 | | | | | | | | | | | | | | | | | | | #539. % 148.54/21.32 | | | | | | | | | | | | | | | | | | | % 148.54/21.32 | | | | | | | | | | | | | | | | | | End of split % 148.54/21.32 | | | | | | | | | | | | | | | | | | % 148.54/21.32 | | | | | | | | | | | | | | | | | Case 2: % 148.54/21.32 | | | | | | | | | | | | | | | | | | % 148.54/21.32 | | | | | | | | | | | | | | | | | | (4618) all_56_21 = e3 % 148.54/21.32 | | | | | | | | | | | | | | | | | | (4619) all_56_17 = e1 % 148.54/21.32 | | | | | | | | | | | | | | | | | | % 148.54/21.32 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (381), (4619) imply: % 148.54/21.32 | | | | | | | | | | | | | | | | | | (4620) all_52_2 = e1 % 148.54/21.32 | | | | | | | | | | | | | | | | | | % 148.54/21.32 | | | | | | | | | | | | | | | | | | SIMP: (4620) implies: % 148.54/21.32 | | | | | | | | | | | | | | | | | | (4621) all_52_2 = e1 % 148.54/21.32 | | | | | | | | | | | | | | | | | | % 148.54/21.32 | | | | | | | | | | | | | | | | | | REF_CLOSE: (43), (238), (252), (374), (482), (585), (768), % 148.54/21.32 | | | | | | | | | | | | | | | | | | (4436), (4532), (4537), (4540), (4541), (4618), % 148.54/21.32 | | | | | | | | | | | | | | | | | | (4621), (function-axioms) are inconsistent by % 148.54/21.32 | | | | | | | | | | | | | | | | | | sub-proof #468. % 148.54/21.32 | | | | | | | | | | | | | | | | | | % 148.54/21.32 | | | | | | | | | | | | | | | | | End of split % 148.54/21.32 | | | | | | | | | | | | | | | | | % 148.54/21.32 | | | | | | | | | | | | | | | | Case 2: % 148.54/21.32 | | | | | | | | | | | | | | | | | % 148.54/21.32 | | | | | | | | | | | | | | | | | (4622) ~ (all_26_2 = e3) % 148.54/21.32 | | | | | | | | | | | | | | | | | % 148.54/21.32 | | | | | | | | | | | | | | | | | REDUCE: (4522), (4622) imply: % 148.54/21.32 | | | | | | | | | | | | | | | | | (4623) $false % 148.54/21.32 | | | | | | | | | | | | | | | | | % 148.54/21.32 | | | | | | | | | | | | | | | | | CLOSE: (4623) is inconsistent. % 148.54/21.32 | | | | | | | | | | | | | | | | | % 148.54/21.32 | | | | | | | | | | | | | | | | End of split % 148.54/21.32 | | | | | | | | | | | | | | | | % 148.54/21.32 | | | | | | | | | | | | | | | End of split % 148.54/21.32 | | | | | | | | | | | | | | | % 148.54/21.32 | | | | | | | | | | | | | | Case 2: % 148.54/21.32 | | | | | | | | | | | | | | | % 148.54/21.32 | | | | | | | | | | | | | | | (4624) all_56_31 = e1 % 148.54/21.32 | | | | | | | | | | | | | | | (4625) all_56_29 = e0 % 148.54/21.32 | | | | | | | | | | | | | | | % 148.54/21.32 | | | | | | | | | | | | | | | COMBINE_EQS: (357), (4625) imply: % 148.54/21.32 | | | | | | | | | | | | | | | (4626) all_52_11 = e0 % 148.54/21.32 | | | | | | | | | | | | | | | % 148.54/21.32 | | | | | | | | | | | | | | | SIMP: (4626) implies: % 148.54/21.32 | | | | | | | | | | | | | | | (4627) all_52_11 = e0 % 148.54/21.32 | | | | | | | | | | | | | | | % 148.54/21.32 | | | | | | | | | | | | | | | COMBINE_EQS: (544), (4624) imply: % 148.54/21.32 | | | | | | | | | | | | | | | (4628) all_4_2 = e1 % 148.54/21.32 | | | | | | | | | | | | | | | % 148.54/21.32 | | | | | | | | | | | | | | | REDUCE: (585), (4627) imply: % 148.54/21.32 | | | | | | | | | | | | | | | (4629) ~ (all_6_2 = e0) % 148.54/21.32 | | | | | | | | | | | | | | | % 148.54/21.32 | | | | | | | | | | | | | | | SIMP: (4629) implies: % 148.54/21.32 | | | | | | | | | | | | | | | (4630) ~ (all_6_2 = e0) % 148.54/21.32 | | | | | | | | | | | | | | | % 148.54/21.32 | | | | | | | | | | | | | | | REDUCE: (38), (4628) imply: % 148.54/21.32 | | | | | | | | | | | | | | | (4631) op(e1, e1) = all_4_1 % 148.54/21.32 | | | | | | | | | | | | | | | % 148.54/21.32 | | | | | | | | | | | | | | | REDUCE: (627), (4628) imply: % 148.54/21.32 | | | | | | | | | | | | | | | (4632) op(e0, e1) = all_56_30 % 148.54/21.32 | | | | | | | | | | | | | | | % 148.54/21.32 | | | | | | | | | | | | | | | REDUCE: (205), (4627) imply: % 148.54/21.32 | | | | | | | | | | | | | | | (4633) op(e0, e1) = e0 % 148.54/21.32 | | | | | | | | | | | | | | | % 148.54/21.32 | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, % 148.54/21.32 | | | | | | | | | | | | | | | all_56_30, e1, e0, simplifying with (4632), (4633) % 148.54/21.32 | | | | | | | | | | | | | | | gives: % 148.54/21.32 | | | | | | | | | | | | | | | (4634) all_56_30 = e0 % 148.54/21.32 | | | | | | | | | | | | | | | % 148.54/21.32 | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_6_2, % 148.54/21.32 | | | | | | | | | | | | | | | all_4_1, e1, e1, simplifying with (41), (4631) % 148.54/21.32 | | | | | | | | | | | | | | | gives: % 148.54/21.32 | | | | | | | | | | | | | | | (4635) all_6_2 = all_4_1 % 148.54/21.32 | | | | | | | | | | | | | | | % 148.54/21.32 | | | | | | | | | | | | | | | COMBINE_EQS: (541), (4635) imply: % 148.54/21.32 | | | | | | | | | | | | | | | (4636) all_54_10 = all_4_1 % 148.54/21.32 | | | | | | | | | | | | | | | % 148.54/21.32 | | | | | | | | | | | | | | | COMBINE_EQS: (374), (4635) imply: % 148.54/21.32 | | | | | | | | | | | | | | | (4637) all_56_21 = all_4_1 % 148.54/21.32 | | | | | | | | | | | | | | | % 148.54/21.32 | | | | | | | | | | | | | | | REDUCE: (4441), (4635) imply: % 148.54/21.32 | | | | | | | | | | | | | | | (4638) ~ (all_4_1 = e2) % 148.54/21.32 | | | | | | | | | | | | | | | % 148.54/21.32 | | | | | | | | | | | | | | | REDUCE: (4630), (4635) imply: % 148.54/21.32 | | | | | | | | | | | | | | | (4639) ~ (all_4_1 = e0) % 148.54/21.32 | | | | | | | | | | | | | | | % 148.54/21.32 | | | | | | | | | | | | | | | BETA: splitting (293) gives: % 148.54/21.32 | | | | | | | | | | | | | | | % 148.54/21.32 | | | | | | | | | | | | | | | Case 1: % 148.54/21.32 | | | | | | | | | | | | | | | | % 148.54/21.32 | | | | | | | | | | | | | | | | (4640) ~ (all_56_21 = e3) % 148.54/21.32 | | | | | | | | | | | | | | | | % 148.54/21.32 | | | | | | | | | | | | | | | | REDUCE: (4637), (4640) imply: % 148.54/21.32 | | | | | | | | | | | | | | | | (4641) ~ (all_4_1 = e3) % 148.54/21.32 | | | | | | | | | | | | | | | | % 148.54/21.32 | | | | | | | | | | | | | | | | BETA: splitting (242) gives: % 148.54/21.32 | | | | | | | | | | | | | | | | % 148.54/21.32 | | | | | | | | | | | | | | | | Case 1: % 148.54/21.32 | | | | | | | | | | | | | | | | | % 148.54/21.32 | | | | | | | | | | | | | | | | | (4642) all_54_10 = e3 % 148.54/21.32 | | | | | | | | | | | | | | | | | % 148.54/21.32 | | | | | | | | | | | | | | | | | COMBINE_EQS: (4636), (4642) imply: % 148.54/21.32 | | | | | | | | | | | | | | | | | (4643) all_4_1 = e3 % 148.54/21.32 | | | | | | | | | | | | | | | | | % 148.54/21.32 | | | | | | | | | | | | | | | | | REDUCE: (4641), (4643) imply: % 148.54/21.32 | | | | | | | | | | | | | | | | | (4644) $false % 148.54/21.32 | | | | | | | | | | | | | | | | | % 148.54/21.32 | | | | | | | | | | | | | | | | | CLOSE: (4644) is inconsistent. % 148.54/21.32 | | | | | | | | | | | | | | | | | % 148.54/21.32 | | | | | | | | | | | | | | | | Case 2: % 148.54/21.32 | | | | | | | | | | | | | | | | | % 148.54/21.32 | | | | | | | | | | | | | | | | | (4645) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 148.54/21.32 | | | | | | | | | | | | | | | | | % 148.54/21.32 | | | | | | | | | | | | | | | | | BETA: splitting (4645) gives: % 148.54/21.32 | | | | | | | | | | | | | | | | | % 148.54/21.32 | | | | | | | | | | | | | | | | | Case 1: % 148.54/21.32 | | | | | | | | | | | | | | | | | | % 148.54/21.32 | | | | | | | | | | | | | | | | | | (4646) all_54_10 = e2 % 148.54/21.32 | | | | | | | | | | | | | | | | | | % 148.54/21.32 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4636), (4646) imply: % 148.54/21.32 | | | | | | | | | | | | | | | | | | (4647) all_4_1 = e2 % 148.54/21.32 | | | | | | | | | | | | | | | | | | % 148.54/21.32 | | | | | | | | | | | | | | | | | | REDUCE: (4638), (4647) imply: % 148.54/21.32 | | | | | | | | | | | | | | | | | | (4648) $false % 148.54/21.32 | | | | | | | | | | | | | | | | | | % 148.54/21.32 | | | | | | | | | | | | | | | | | | CLOSE: (4648) is inconsistent. % 148.54/21.32 | | | | | | | | | | | | | | | | | | % 148.54/21.32 | | | | | | | | | | | | | | | | | Case 2: % 148.54/21.32 | | | | | | | | | | | | | | | | | | % 148.54/21.32 | | | | | | | | | | | | | | | | | | (4649) all_54_10 = e1 | all_54_10 = e0 % 148.54/21.32 | | | | | | | | | | | | | | | | | | % 148.54/21.32 | | | | | | | | | | | | | | | | | | BETA: splitting (4649) gives: % 148.54/21.32 | | | | | | | | | | | | | | | | | | % 148.54/21.32 | | | | | | | | | | | | | | | | | | Case 1: % 148.54/21.32 | | | | | | | | | | | | | | | | | | | % 148.54/21.32 | | | | | | | | | | | | | | | | | | | (4650) all_54_10 = e1 % 148.54/21.32 | | | | | | | | | | | | | | | | | | | % 148.54/21.32 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4636), (4650) imply: % 148.54/21.32 | | | | | | | | | | | | | | | | | | | (4651) all_4_1 = e1 % 148.54/21.32 | | | | | | | | | | | | | | | | | | | % 148.54/21.32 | | | | | | | | | | | | | | | | | | | REDUCE: (4432), (4651) imply: % 148.54/21.32 | | | | | | | | | | | | | | | | | | | (4652) op(e0, e1) = e1 % 148.54/21.32 | | | | | | | | | | | | | | | | | | | % 148.54/21.32 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (4633), (4652), (function-axioms) are % 148.54/21.32 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #351. % 148.54/21.32 | | | | | | | | | | | | | | | | | | | % 148.54/21.32 | | | | | | | | | | | | | | | | | | Case 2: % 148.54/21.32 | | | | | | | | | | | | | | | | | | | % 148.54/21.32 | | | | | | | | | | | | | | | | | | | (4653) all_54_10 = e0 % 148.54/21.32 | | | | | | | | | | | | | | | | | | | % 148.54/21.32 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4636), (4653) imply: % 148.54/21.32 | | | | | | | | | | | | | | | | | | | (4654) all_4_1 = e0 % 148.54/21.32 | | | | | | | | | | | | | | | | | | | % 148.54/21.32 | | | | | | | | | | | | | | | | | | | REDUCE: (4639), (4654) imply: % 148.54/21.32 | | | | | | | | | | | | | | | | | | | (4655) $false % 148.54/21.32 | | | | | | | | | | | | | | | | | | | % 148.54/21.32 | | | | | | | | | | | | | | | | | | | CLOSE: (4655) is inconsistent. % 148.54/21.32 | | | | | | | | | | | | | | | | | | | % 148.54/21.32 | | | | | | | | | | | | | | | | | | End of split % 148.54/21.32 | | | | | | | | | | | | | | | | | | % 148.54/21.32 | | | | | | | | | | | | | | | | | End of split % 148.54/21.32 | | | | | | | | | | | | | | | | | % 148.54/21.32 | | | | | | | | | | | | | | | | End of split % 148.54/21.32 | | | | | | | | | | | | | | | | % 148.54/21.32 | | | | | | | | | | | | | | | Case 2: % 148.54/21.32 | | | | | | | | | | | | | | | | % 148.54/21.32 | | | | | | | | | | | | | | | | (4656) all_56_21 = e3 % 148.54/21.32 | | | | | | | | | | | | | | | | (4657) all_56_17 = e1 % 148.54/21.32 | | | | | | | | | | | | | | | | % 148.54/21.32 | | | | | | | | | | | | | | | | COMBINE_EQS: (381), (4657) imply: % 148.54/21.32 | | | | | | | | | | | | | | | | (4658) all_52_2 = e1 % 148.54/21.32 | | | | | | | | | | | | | | | | % 148.54/21.32 | | | | | | | | | | | | | | | | COMBINE_EQS: (4637), (4656) imply: % 148.54/21.32 | | | | | | | | | | | | | | | | (4659) all_4_1 = e3 % 148.54/21.32 | | | | | | | | | | | | | | | | % 148.54/21.32 | | | | | | | | | | | | | | | | SIMP: (4659) implies: % 148.54/21.32 | | | | | | | | | | | | | | | | (4660) all_4_1 = e3 % 148.54/21.32 | | | | | | | | | | | | | | | | % 148.54/21.32 | | | | | | | | | | | | | | | | REF_CLOSE: (192), (207), (4432), (4658), (4660), % 148.54/21.32 | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 148.54/21.32 | | | | | | | | | | | | | | | | #159. % 148.54/21.32 | | | | | | | | | | | | | | | | % 148.54/21.32 | | | | | | | | | | | | | | | End of split % 148.54/21.32 | | | | | | | | | | | | | | | % 148.54/21.32 | | | | | | | | | | | | | | End of split % 148.54/21.32 | | | | | | | | | | | | | | % 148.54/21.32 | | | | | | | | | | | | | Case 2: % 148.54/21.32 | | | | | | | | | | | | | | % 148.54/21.32 | | | | | | | | | | | | | | (4661) all_56_11 = e0 % 148.54/21.32 | | | | | | | | | | | | | | % 148.54/21.32 | | | | | | | | | | | | | | REF_CLOSE: (36), (38), (48), (237), (294), (443), (540), % 148.54/21.32 | | | | | | | | | | | | | | (545), (590), (627), (769), (3732), (4432), % 148.54/21.32 | | | | | | | | | | | | | | (4661), (function-axioms) are inconsistent by % 148.54/21.32 | | | | | | | | | | | | | | sub-proof #357. % 148.54/21.32 | | | | | | | | | | | | | | % 148.54/21.32 | | | | | | | | | | | | | End of split % 148.54/21.32 | | | | | | | | | | | | | % 148.54/21.32 | | | | | | | | | | | | Case 2: % 148.54/21.32 | | | | | | | | | | | | | % 148.54/21.32 | | | | | | | | | | | | | (4662) all_56_21 = e2 % 148.54/21.32 | | | | | | | | | | | | | (4663) all_56_19 = e1 % 148.54/21.32 | | | | | | | | | | | | | % 148.54/21.32 | | | | | | | | | | | | | COMBINE_EQS: (435), (4663) imply: % 148.54/21.32 | | | | | | | | | | | | | (4664) all_52_6 = e1 % 148.54/21.32 | | | | | | | | | | | | | % 148.54/21.32 | | | | | | | | | | | | | COMBINE_EQS: (374), (4662) imply: % 148.54/21.32 | | | | | | | | | | | | | (4665) all_6_2 = e2 % 148.54/21.32 | | | | | | | | | | | | | % 148.54/21.32 | | | | | | | | | | | | | SIMP: (4665) implies: % 148.54/21.32 | | | | | | | | | | | | | (4666) all_6_2 = e2 % 148.54/21.32 | | | | | | | | | | | | | % 148.54/21.32 | | | | | | | | | | | | | REF_CLOSE: (36), (38), (43), (46), (48), (237), (247), (294), % 148.54/21.32 | | | | | | | | | | | | | (443), (540), (542), (545), (573), (590), (627), % 148.54/21.32 | | | | | | | | | | | | | (768), (769), (3732), (4432), (4436), (4664), % 148.54/21.32 | | | | | | | | | | | | | (4666), (function-axioms) are inconsistent by % 148.54/21.32 | | | | | | | | | | | | | sub-proof #263. % 148.54/21.32 | | | | | | | | | | | | | % 148.54/21.32 | | | | | | | | | | | | End of split % 148.54/21.32 | | | | | | | | | | | | % 148.54/21.32 | | | | | | | | | | | End of split % 148.54/21.32 | | | | | | | | | | | % 148.54/21.32 | | | | | | | | | | Case 2: % 148.54/21.32 | | | | | | | | | | | % 148.54/21.32 | | | | | | | | | | | (4667) all_36_1 = e3 % 148.54/21.32 | | | | | | | | | | | (4668) ~ (all_36_0 = e0) | ~ (all_36_2 = e2) % 148.54/21.32 | | | | | | | | | | | % 148.54/21.32 | | | | | | | | | | | COMBINE_EQS: (652), (4667) imply: % 148.54/21.32 | | | | | | | | | | | (4669) all_6_1 = e3 % 148.54/21.32 | | | | | | | | | | | % 148.54/21.32 | | | | | | | | | | | REF_CLOSE: (5), (36), (37), (38), (41), (42), (43), (46), % 148.54/21.32 | | | | | | | | | | | (48), (51), (174), (176), (187), (188), (189), % 148.54/21.32 | | | | | | | | | | | (191), (192), (194), (207), (211), (237), (240), % 148.54/21.32 | | | | | | | | | | | (242), (243), (244), (247), (287), (288), (289), % 148.54/21.32 | | | | | | | | | | | (290), (291), (292), (293), (294), (295), (324), % 148.54/21.32 | | | | | | | | | | | (344), (357), (360), (365), (366), (374), (380), % 148.54/21.32 | | | | | | | | | | | (381), (401), (419), (431), (435), (443), (447), % 148.54/21.32 | | | | | | | | | | | (471), (473), (478), (530), (532), (540), (541), % 148.54/21.32 | | | | | | | | | | | (542), (544), (545), (546), (550), (552), (553), % 148.54/21.32 | | | | | | | | | | | (559), (561), (568), (569), (570), (573), (580), % 148.54/21.32 | | | | | | | | | | | (585), (587), (588), (590), (591), (617), (622), % 148.54/21.32 | | | | | | | | | | | (627), (657), (762), (767), (769), (3728), (3732), % 148.54/21.32 | | | | | | | | | | | (4427), (4432), (4434), (4668), (4669), % 148.54/21.32 | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 148.54/21.32 | | | | | | | | | | | #261. % 148.54/21.32 | | | | | | | | | | | % 148.54/21.32 | | | | | | | | | | End of split % 148.54/21.32 | | | | | | | | | | % 148.54/21.32 | | | | | | | | | Case 2: % 148.54/21.32 | | | | | | | | | | % 148.54/21.32 | | | | | | | | | | (4670) all_28_0 = e2 % 148.54/21.32 | | | | | | | | | | (4671) ~ (all_28_1 = e3) | ~ (all_28_2 = e0) % 148.54/21.32 | | | | | | | | | | % 148.54/21.32 | | | | | | | | | | COMBINE_EQS: (740), (4670) imply: % 148.54/21.32 | | | | | | | | | | (4672) all_6_0 = e2 % 148.54/21.32 | | | | | | | | | | % 148.62/21.32 | | | | | | | | | | REF_CLOSE: (6), (8), (36), (37), (38), (41), (42), (43), % 148.62/21.32 | | | | | | | | | | (46), (51), (144), (158), (173), (174), (176), % 148.62/21.32 | | | | | | | | | | (187), (192), (206), (207), (208), (211), (237), % 148.62/21.32 | | | | | | | | | | (239), (240), (242), (247), (252), (288), (289), % 148.62/21.32 | | | | | | | | | | (290), (291), (292), (293), (294), (297), (321), % 148.62/21.32 | | | | | | | | | | (341), (357), (366), (374), (381), (386), (402), % 148.62/21.32 | | | | | | | | | | (407), (419), (435), (443), (475), (478), (480), % 148.62/21.32 | | | | | | | | | | (513), (540), (541), (542), (543), (544), (545), % 148.62/21.32 | | | | | | | | | | (546), (547), (550), (551), (555), (559), (569), % 148.62/21.32 | | | | | | | | | | (571), (573), (580), (585), (620), (622), (627), % 148.62/21.32 | | | | | | | | | | (634), (665), (764), (767), (768), (3728), (4671), % 148.62/21.32 | | | | | | | | | | (4672), (function-axioms) are inconsistent by % 148.62/21.32 | | | | | | | | | | sub-proof #364. % 148.62/21.32 | | | | | | | | | | % 148.62/21.32 | | | | | | | | | End of split % 148.62/21.32 | | | | | | | | | % 148.62/21.32 | | | | | | | | End of split % 148.62/21.32 | | | | | | | | % 148.62/21.32 | | | | | | | Case 2: % 148.62/21.32 | | | | | | | | % 148.62/21.32 | | | | | | | | (4673) all_22_1 = e3 % 148.62/21.32 | | | | | | | | (4674) ~ (all_22_0 = e0) | ~ (all_22_2 = e1) % 148.62/21.32 | | | | | | | | % 148.62/21.32 | | | | | | | | COMBINE_EQS: (672), (4673) imply: % 148.62/21.32 | | | | | | | | (4675) all_8_1 = e3 % 148.62/21.32 | | | | | | | | % 148.62/21.32 | | | | | | | | SIMP: (4675) implies: % 148.62/21.32 | | | | | | | | (4676) all_8_1 = e3 % 148.62/21.32 | | | | | | | | % 148.62/21.32 | | | | | | | | REDUCE: (48), (4676) imply: % 148.62/21.32 | | | | | | | | (4677) op(all_8_2, all_8_2) = e3 % 148.62/21.32 | | | | | | | | % 148.62/21.32 | | | | | | | | REDUCE: (47), (4676) imply: % 148.62/21.32 | | | | | | | | (4678) op(e2, e3) = all_8_0 % 148.62/21.32 | | | | | | | | % 148.62/21.32 | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_1, % 148.62/21.32 | | | | | | | | all_8_0, e3, e2, simplifying with (215), (4678) % 148.62/21.32 | | | | | | | | gives: % 148.62/21.32 | | | | | | | | (4679) all_52_1 = all_8_0 % 148.62/21.32 | | | | | | | | % 148.62/21.32 | | | | | | | | COMBINE_EQS: (463), (4679) imply: % 148.62/21.32 | | | | | | | | (4680) all_54_4 = all_8_0 % 148.62/21.32 | | | | | | | | % 148.62/21.32 | | | | | | | | COMBINE_EQS: (425), (4679) imply: % 148.62/21.32 | | | | | | | | (4681) all_56_9 = all_8_0 % 148.62/21.32 | | | | | | | | % 148.62/21.32 | | | | | | | | COMBINE_EQS: (401), (4679) imply: % 148.62/21.32 | | | | | | | | (4682) all_58_2 = all_8_0 % 148.62/21.32 | | | | | | | | % 148.62/21.32 | | | | | | | | REDUCE: (197), (4679) imply: % 148.62/21.32 | | | | | | | | (4683) ~ (all_52_2 = all_8_0) % 148.62/21.32 | | | | | | | | % 148.62/21.32 | | | | | | | | SIMP: (4683) implies: % 148.62/21.32 | | | | | | | | (4684) ~ (all_52_2 = all_8_0) % 148.62/21.32 | | | | | | | | % 148.62/21.32 | | | | | | | | REDUCE: (194), (4679) imply: % 148.62/21.32 | | | | | | | | (4685) ~ (all_52_9 = all_8_0) % 148.62/21.32 | | | | | | | | % 148.62/21.32 | | | | | | | | SIMP: (4685) implies: % 148.62/21.32 | | | | | | | | (4686) ~ (all_52_9 = all_8_0) % 148.62/21.32 | | | | | | | | % 148.62/21.32 | | | | | | | | REDUCE: (193), (4679) imply: % 148.62/21.32 | | | | | | | | (4687) ~ (all_52_13 = all_8_0) % 148.62/21.32 | | | | | | | | % 148.62/21.32 | | | | | | | | SIMP: (4687) implies: % 148.62/21.32 | | | | | | | | (4688) ~ (all_52_13 = all_8_0) % 148.62/21.32 | | | | | | | | % 148.62/21.32 | | | | | | | | REDUCE: (557), (4679) imply: % 148.62/21.32 | | | | | | | | (4689) ~ (all_10_2 = all_8_0) % 148.62/21.32 | | | | | | | | % 148.62/21.32 | | | | | | | | SIMP: (4689) implies: % 148.62/21.32 | | | | | | | | (4690) ~ (all_10_2 = all_8_0) % 148.62/21.32 | | | | | | | | % 148.62/21.32 | | | | | | | | REDUCE: (568), (4679) imply: % 148.62/21.32 | | | | | | | | (4691) ~ (all_8_0 = all_8_2) % 148.62/21.32 | | | | | | | | % 148.62/21.32 | | | | | | | | BETA: splitting (94) gives: % 148.62/21.32 | | | | | | | | % 148.62/21.32 | | | | | | | | Case 1: % 148.62/21.32 | | | | | | | | | % 148.62/21.32 | | | | | | | | | (4692) ~ (all_26_0 = e1) % 148.62/21.32 | | | | | | | | | % 148.62/21.32 | | | | | | | | | REDUCE: (760), (4692) imply: % 148.62/21.32 | | | | | | | | | (4693) ~ (all_4_0 = e1) % 148.62/21.32 | | | | | | | | | % 148.62/21.32 | | | | | | | | | BETA: splitting (99) gives: % 148.62/21.32 | | | | | | | | | % 148.62/21.32 | | | | | | | | | Case 1: % 148.62/21.32 | | | | | | | | | | % 148.62/21.32 | | | | | | | | | | (4694) ~ (all_28_0 = e2) % 148.62/21.32 | | | | | | | | | | % 148.62/21.32 | | | | | | | | | | REDUCE: (740), (4694) imply: % 148.62/21.32 | | | | | | | | | | (4695) ~ (all_6_0 = e2) % 148.62/21.32 | | | | | | | | | | % 148.62/21.32 | | | | | | | | | | BETA: splitting (119) gives: % 148.62/21.32 | | | | | | | | | | % 148.62/21.32 | | | | | | | | | | Case 1: % 148.62/21.32 | | | | | | | | | | | % 148.62/21.32 | | | | | | | | | | | (4696) ~ (all_36_1 = e3) % 148.62/21.32 | | | | | | | | | | | % 148.62/21.32 | | | | | | | | | | | REF_CLOSE: (4), (6), (36), (37), (38), (41), (42), (43), % 148.62/21.32 | | | | | | | | | | | (46), (51), (165), (174), (176), (189), (191), % 148.62/21.32 | | | | | | | | | | | (207), (208), (241), (242), (243), (244), (245), % 148.62/21.32 | | | | | | | | | | | (247), (248), (252), (287), (291), (292), (293), % 148.62/21.32 | | | | | | | | | | | (294), (295), (296), (319), (320), (327), (333), % 148.62/21.32 | | | | | | | | | | | (342), (365), (366), (374), (380), (381), (386), % 148.62/21.32 | | | | | | | | | | | (389), (419), (431), (435), (443), (469), (471), % 148.62/21.32 | | | | | | | | | | | (473), (476), (523), (541), (542), (543), (544), % 148.62/21.32 | | | | | | | | | | | (545), (546), (547), (548), (549), (550), (552), % 148.62/21.32 | | | | | | | | | | | (553), (554), (559), (561), (569), (573), (575), % 148.62/21.32 | | | | | | | | | | | (577), (579), (580), (583), (585), (587), (590), % 148.62/21.32 | | | | | | | | | | | (591), (617), (618), (622), (626), (627), (652), % 148.62/21.32 | | | | | | | | | | | (752), (768), (3730), (4674), (4677), (4680), % 148.62/21.32 | | | | | | | | | | | (4681), (4682), (4684), (4686), (4688), (4690), % 148.62/21.32 | | | | | | | | | | | (4691), (4693), (4695), (4696), (function-axioms) % 148.62/21.32 | | | | | | | | | | | are inconsistent by sub-proof #333. % 148.62/21.32 | | | | | | | | | | | % 148.62/21.32 | | | | | | | | | | Case 2: % 148.62/21.32 | | | | | | | | | | | % 148.62/21.32 | | | | | | | | | | | (4697) all_36_1 = e3 % 148.62/21.32 | | | | | | | | | | | (4698) ~ (all_36_0 = e0) | ~ (all_36_2 = e2) % 148.62/21.32 | | | | | | | | | | | % 148.62/21.32 | | | | | | | | | | | COMBINE_EQS: (652), (4697) imply: % 148.62/21.32 | | | | | | | | | | | (4699) all_6_1 = e3 % 148.62/21.32 | | | | | | | | | | | % 148.62/21.32 | | | | | | | | | | | SIMP: (4699) implies: % 148.62/21.32 | | | | | | | | | | | (4700) all_6_1 = e3 % 148.62/21.32 | | | | | | | | | | | % 148.62/21.32 | | | | | | | | | | | REDUCE: (43), (4700) imply: % 148.62/21.32 | | | | | | | | | | | (4701) op(all_6_2, all_6_2) = e3 % 148.62/21.32 | | | | | | | | | | | % 148.62/21.32 | | | | | | | | | | | REDUCE: (42), (4700) imply: % 148.62/21.32 | | | | | | | | | | | (4702) op(e1, e3) = all_6_0 % 148.62/21.32 | | | | | | | | | | | % 148.62/21.32 | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_2, % 148.62/21.32 | | | | | | | | | | | all_6_0, e3, e1, simplifying with (211), (4702) % 148.62/21.32 | | | | | | | | | | | gives: % 148.62/21.32 | | | | | | | | | | | (4703) all_52_2 = all_6_0 % 148.62/21.32 | | | | | | | | | | | % 148.62/21.32 | | | | | | | | | | | COMBINE_EQS: (471), (4703) imply: % 148.62/21.32 | | | | | | | | | | | (4704) all_54_8 = all_6_0 % 148.62/21.32 | | | | | | | | | | | % 148.62/21.32 | | | | | | | | | | | COMBINE_EQS: (553), (4703) imply: % 148.62/21.32 | | | | | | | | | | | (4705) all_58_6 = all_6_0 % 148.62/21.32 | | | | | | | | | | | % 148.62/21.32 | | | | | | | | | | | REDUCE: (191), (4703) imply: % 148.62/21.32 | | | | | | | | | | | (4706) ~ (all_52_6 = all_6_0) % 148.62/21.32 | | | | | | | | | | | % 148.62/21.32 | | | | | | | | | | | SIMP: (4706) implies: % 148.62/21.32 | | | | | | | | | | | (4707) ~ (all_52_6 = all_6_0) % 148.62/21.32 | | | | | | | | | | | % 148.62/21.32 | | | | | | | | | | | REDUCE: (189), (4703) imply: % 148.62/21.32 | | | | | | | | | | | (4708) ~ (all_52_14 = all_6_0) % 148.62/21.32 | | | | | | | | | | | % 148.62/21.32 | | | | | | | | | | | SIMP: (4708) implies: % 148.62/21.32 | | | | | | | | | | | (4709) ~ (all_52_14 = all_6_0) % 148.62/21.32 | | | | | | | | | | | % 148.62/21.32 | | | | | | | | | | | REDUCE: (559), (4703) imply: % 148.62/21.32 | | | | | | | | | | | (4710) ~ (all_10_2 = all_6_0) % 148.62/21.32 | | | | | | | | | | | % 148.62/21.32 | | | | | | | | | | | SIMP: (4710) implies: % 148.62/21.32 | | | | | | | | | | | (4711) ~ (all_10_2 = all_6_0) % 148.62/21.32 | | | | | | | | | | | % 148.62/21.32 | | | | | | | | | | | REDUCE: (569), (4703) imply: % 148.62/21.32 | | | | | | | | | | | (4712) ~ (all_6_0 = all_6_2) % 148.62/21.32 | | | | | | | | | | | % 148.62/21.32 | | | | | | | | | | | BETA: splitting (292) gives: % 148.62/21.32 | | | | | | | | | | | % 148.62/21.32 | | | | | | | | | | | Case 1: % 148.62/21.32 | | | | | | | | | | | | % 148.62/21.32 | | | | | | | | | | | | (4713) ~ (all_56_21 = e2) % 148.62/21.32 | | | | | | | | | | | | % 148.62/21.32 | | | | | | | | | | | | REDUCE: (374), (4713) imply: % 148.62/21.32 | | | | | | | | | | | | (4714) ~ (all_6_2 = e2) % 148.62/21.32 | | | | | | | | | | | | % 148.62/21.32 | | | | | | | | | | | | BETA: splitting (294) gives: % 148.62/21.32 | | | | | | | | | | | | % 148.62/21.32 | | | | | | | | | | | | Case 1: % 148.62/21.32 | | | | | | | | | | | | | % 148.62/21.32 | | | | | | | | | | | | | (4715) ~ (all_56_11 = e0) % 148.62/21.32 | | | | | | | | | | | | | % 148.62/21.32 | | | | | | | | | | | | | REDUCE: (545), (4715) imply: % 148.62/21.32 | | | | | | | | | | | | | (4716) ~ (all_8_2 = e0) % 148.62/21.32 | | | | | | | | | | | | | % 148.62/21.32 | | | | | | | | | | | | | BETA: splitting (293) gives: % 148.62/21.32 | | | | | | | | | | | | | % 148.62/21.32 | | | | | | | | | | | | | Case 1: % 148.62/21.32 | | | | | | | | | | | | | | % 148.62/21.32 | | | | | | | | | | | | | | (4717) ~ (all_56_21 = e3) % 148.62/21.32 | | | | | | | | | | | | | | % 148.62/21.32 | | | | | | | | | | | | | | REDUCE: (374), (4717) imply: % 148.62/21.32 | | | | | | | | | | | | | | (4718) ~ (all_6_2 = e3) % 148.62/21.32 | | | | | | | | | | | | | | % 148.62/21.32 | | | | | | | | | | | | | | BETA: splitting (296) gives: % 148.62/21.32 | | | | | | | | | | | | | | % 148.62/21.32 | | | | | | | | | | | | | | Case 1: % 148.62/21.32 | | | | | | | | | | | | | | | % 148.62/21.32 | | | | | | | | | | | | | | | (4719) ~ (all_56_11 = e3) % 148.62/21.32 | | | | | | | | | | | | | | | % 148.62/21.32 | | | | | | | | | | | | | | | REDUCE: (545), (4719) imply: % 148.62/21.32 | | | | | | | | | | | | | | | (4720) ~ (all_8_2 = e3) % 148.62/21.32 | | | | | | | | | | | | | | | % 148.62/21.32 | | | | | | | | | | | | | | | BETA: splitting (295) gives: % 148.62/21.32 | | | | | | | | | | | | | | | % 148.62/21.32 | | | | | | | | | | | | | | | Case 1: % 148.62/21.32 | | | | | | | | | | | | | | | | % 148.62/21.32 | | | | | | | | | | | | | | | | (4721) ~ (all_56_11 = e1) % 148.62/21.32 | | | | | | | | | | | | | | | | % 148.62/21.32 | | | | | | | | | | | | | | | | REDUCE: (545), (4721) imply: % 148.62/21.32 | | | | | | | | | | | | | | | | (4722) ~ (all_8_2 = e1) % 148.62/21.32 | | | | | | | | | | | | | | | | % 148.62/21.32 | | | | | | | | | | | | | | | | REF_CLOSE: (46), (247), (542), (617), (4677), (4716), (4720), % 148.62/21.32 | | | | | | | | | | | | | | | | (4722), (function-axioms) are inconsistent by % 148.62/21.32 | | | | | | | | | | | | | | | | sub-proof #347. % 148.62/21.32 | | | | | | | | | | | | | | | | % 148.62/21.32 | | | | | | | | | | | | | | | Case 2: % 148.62/21.32 | | | | | | | | | | | | | | | | % 148.62/21.32 | | | | | | | | | | | | | | | | (4723) all_56_13 = e2 % 148.62/21.32 | | | | | | | | | | | | | | | | (4724) all_56_11 = e1 % 148.62/21.32 | | | | | | | | | | | | | | | | % 148.62/21.32 | | | | | | | | | | | | | | | | COMBINE_EQS: (545), (4724) imply: % 148.62/21.32 | | | | | | | | | | | | | | | | (4725) all_8_2 = e1 % 148.62/21.32 | | | | | | | | | | | | | | | | % 148.62/21.32 | | | | | | | | | | | | | | | | COMBINE_EQS: (431), (4723) imply: % 148.62/21.32 | | | | | | | | | | | | | | | | (4726) all_52_9 = e2 % 148.62/21.32 | | | | | | | | | | | | | | | | % 148.62/21.32 | | | | | | | | | | | | | | | | COMBINE_EQS: (523), (4725) imply: % 148.62/21.32 | | | | | | | | | | | | | | | | (4727) all_22_2 = e1 % 148.62/21.32 | | | | | | | | | | | | | | | | % 148.62/21.32 | | | | | | | | | | | | | | | | REDUCE: (165), (4726) imply: % 148.62/21.32 | | | | | | | | | | | | | | | | (4728) ~ (all_52_13 = e2) % 148.62/21.32 | | | | | | | | | | | | | | | | % 148.62/21.32 | | | | | | | | | | | | | | | | SIMP: (4728) implies: % 148.62/21.32 | | | | | | | | | | | | | | | | (4729) ~ (all_52_13 = e2) % 148.62/21.32 | | | | | | | | | | | | | | | | % 148.62/21.32 | | | | | | | | | | | | | | | | REDUCE: (4686), (4726) imply: % 148.62/21.32 | | | | | | | | | | | | | | | | (4730) ~ (all_8_0 = e2) % 148.62/21.32 | | | | | | | | | | | | | | | | % 148.62/21.32 | | | | | | | | | | | | | | | | SIMP: (4730) implies: % 148.62/21.32 | | | | | | | | | | | | | | | | (4731) ~ (all_8_0 = e2) % 148.62/21.32 | | | | | | | | | | | | | | | | % 148.62/21.32 | | | | | | | | | | | | | | | | REDUCE: (579), (4725) imply: % 148.62/21.32 | | | | | | | | | | | | | | | | (4732) ~ (all_52_13 = e1) % 148.62/21.32 | | | | | | | | | | | | | | | | % 148.62/21.32 | | | | | | | | | | | | | | | | REDUCE: (4677), (4725) imply: % 148.62/21.32 | | | | | | | | | | | | | | | | (4733) op(e1, e1) = e3 % 148.62/21.32 | | | | | | | | | | | | | | | | % 148.62/21.32 | | | | | | | | | | | | | | | | REF_CLOSE: (6), (41), (245), (248), (287), (374), (469), % 148.62/21.32 | | | | | | | | | | | | | | | | (544), (546), (590), (622), (752), (3730), (4674), % 148.62/21.32 | | | | | | | | | | | | | | | | (4680), (4688), (4690), (4718), (4724), (4727), % 148.62/21.32 | | | | | | | | | | | | | | | | (4729), (4731), (4732), (4733), (function-axioms) % 148.62/21.32 | | | | | | | | | | | | | | | | are inconsistent by sub-proof #341. % 148.62/21.32 | | | | | | | | | | | | | | | | % 148.62/21.33 | | | | | | | | | | | | | | | End of split % 148.62/21.33 | | | | | | | | | | | | | | | % 148.62/21.33 | | | | | | | | | | | | | | Case 2: % 148.62/21.33 | | | | | | | | | | | | | | | % 148.62/21.33 | | | | | | | | | | | | | | | (4734) all_56_11 = e3 % 148.62/21.33 | | | | | | | | | | | | | | | (4735) all_56_9 = e2 % 148.62/21.33 | | | | | | | | | | | | | | | % 148.62/21.33 | | | | | | | | | | | | | | | COMBINE_EQS: (4681), (4735) imply: % 148.62/21.33 | | | | | | | | | | | | | | | (4736) all_8_0 = e2 % 148.62/21.33 | | | | | | | | | | | | | | | % 148.62/21.33 | | | | | | | | | | | | | | | COMBINE_EQS: (545), (4734) imply: % 148.62/21.33 | | | | | | | | | | | | | | | (4737) all_8_2 = e3 % 148.62/21.33 | | | | | | | | | | | | | | | % 148.62/21.33 | | | | | | | | | | | | | | | REDUCE: (573), (4737) imply: % 148.62/21.33 | | | | | | | | | | | | | | | (4738) ~ (all_52_6 = e3) % 148.62/21.33 | | | | | | | | | | | | | | | % 148.62/21.33 | | | | | | | | | | | | | | | REDUCE: (4686), (4736) imply: % 148.62/21.33 | | | | | | | | | | | | | | | (4739) ~ (all_52_9 = e2) % 148.62/21.33 | | | | | | | | | | | | | | | % 148.62/21.33 | | | | | | | | | | | | | | | REDUCE: (577), (4737) imply: % 148.62/21.33 | | | | | | | | | | | | | | | (4740) ~ (all_52_9 = e3) % 148.62/21.33 | | | | | | | | | | | | | | | % 148.62/21.33 | | | | | | | | | | | | | | | REDUCE: (4688), (4736) imply: % 148.62/21.33 | | | | | | | | | | | | | | | (4741) ~ (all_52_13 = e2) % 148.62/21.33 | | | | | | | | | | | | | | | % 148.62/21.33 | | | | | | | | | | | | | | | REDUCE: (4690), (4736) imply: % 148.62/21.33 | | | | | | | | | | | | | | | (4742) ~ (all_10_2 = e2) % 148.62/21.33 | | | | | | | | | | | | | | | % 148.62/21.33 | | | | | | | | | | | | | | | REDUCE: (4677), (4737) imply: % 148.62/21.33 | | | | | | | | | | | | | | | (4743) op(e3, e3) = e3 % 148.62/21.33 | | | | | | | | | | | | | | | % 148.62/21.33 | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_10_2, e3, % 148.62/21.33 | | | | | | | | | | | | | | | e3, e3, simplifying with (51), (4743) gives: % 148.62/21.33 | | | | | | | | | | | | | | | (4744) all_10_2 = e3 % 148.62/21.33 | | | | | | | | | | | | | | | % 148.62/21.33 | | | | | | | | | | | | | | | COMBINE_EQS: (419), (4744) imply: % 148.62/21.33 | | | | | | | | | | | | | | | (4745) all_58_0 = e3 % 148.62/21.33 | | | | | | | | | | | | | | | % 148.62/21.33 | | | | | | | | | | | | | | | REDUCE: (559), (4744) imply: % 148.62/21.33 | | | | | | | | | | | | | | | (4746) ~ (all_52_2 = e3) % 148.62/21.33 | | | | | | | | | | | | | | | % 148.62/21.33 | | | | | | | | | | | | | | | REDUCE: (565), (4744) imply: % 148.62/21.33 | | | | | | | | | | | | | | | (4747) ~ (all_52_8 = e3) % 148.62/21.33 | | | | | | | | | | | | | | | % 148.62/21.33 | | | | | | | | | | | | | | | REDUCE: (53), (4744) imply: % 148.62/21.33 | | | | | | | | | | | | | | | (4748) op(e3, e3) = all_10_1 % 148.62/21.33 | | | | | | | | | | | | | | | % 148.62/21.33 | | | | | | | | | | | | | | | REDUCE: (612), (4744) imply: % 148.62/21.33 | | | | | | | | | | | | | | | (4749) op(e3, e3) = all_56_0 % 148.62/21.33 | | | | | | | | | | | | | | | % 148.62/21.33 | | | | | | | | | | | | | | | BETA: splitting (331) gives: % 148.62/21.33 | | | | | | | | | | | | | | | % 148.62/21.33 | | | | | | | | | | | | | | | Case 1: % 148.62/21.33 | | | | | | | | | | | | | | | | % 148.62/21.33 | | | | | | | | | | | | | | | | (4750) all_58_4 = e3 % 148.62/21.33 | | | | | | | | | | | | | | | | % 148.62/21.33 | | | | | | | | | | | | | | | | COMBINE_EQS: (407), (4750) imply: % 148.62/21.33 | | | | | | | | | | | | | | | | (4751) all_52_8 = e3 % 148.62/21.33 | | | | | | | | | | | | | | | | % 148.62/21.33 | | | | | | | | | | | | | | | | REDUCE: (4747), (4751) imply: % 148.62/21.33 | | | | | | | | | | | | | | | | (4752) $false % 148.62/21.33 | | | | | | | | | | | | | | | | % 148.62/21.33 | | | | | | | | | | | | | | | | CLOSE: (4752) is inconsistent. % 148.62/21.33 | | | | | | | | | | | | | | | | % 148.62/21.33 | | | | | | | | | | | | | | | Case 2: % 148.62/21.33 | | | | | | | | | | | | | | | | % 148.62/21.33 | | | | | | | | | | | | | | | | (4753) all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3 % 148.62/21.33 | | | | | | | | | | | | | | | | % 148.62/21.33 | | | | | | | | | | | | | | | | BETA: splitting (327) gives: % 148.62/21.33 | | | | | | | | | | | | | | | | % 148.62/21.33 | | | | | | | | | | | | | | | | Case 1: % 148.62/21.33 | | | | | | | | | | | | | | | | | % 148.62/21.33 | | | | | | | | | | | | | | | | | (4754) all_58_6 = e3 % 148.62/21.33 | | | | | | | | | | | | | | | | | % 148.62/21.33 | | | | | | | | | | | | | | | | | COMBINE_EQS: (553), (4754) imply: % 148.62/21.33 | | | | | | | | | | | | | | | | | (4755) all_52_2 = e3 % 148.62/21.33 | | | | | | | | | | | | | | | | | % 148.62/21.33 | | | | | | | | | | | | | | | | | REDUCE: (4746), (4755) imply: % 148.62/21.33 | | | | | | | | | | | | | | | | | (4756) $false % 148.62/21.33 | | | | | | | | | | | | | | | | | % 148.62/21.33 | | | | | | | | | | | | | | | | | CLOSE: (4756) is inconsistent. % 148.62/21.33 | | | | | | | | | | | | | | | | | % 148.62/21.33 | | | | | | | | | | | | | | | | Case 2: % 148.62/21.33 | | | | | | | | | | | | | | | | | % 148.62/21.33 | | | | | | | | | | | | | | | | | (4757) all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3 % 148.62/21.33 | | | | | | | | | | | | | | | | | % 148.62/21.33 | | | | | | | | | | | | | | | | | BETA: splitting (4757) gives: % 148.62/21.33 | | | | | | | | | | | | | | | | | % 148.62/21.33 | | | | | | | | | | | | | | | | | Case 1: % 148.62/21.33 | | | | | | | | | | | | | | | | | | % 148.62/21.33 | | | | | | | | | | | | | | | | | | (4758) all_58_7 = e3 % 148.62/21.33 | | | | | | | | | | | | | | | | | | % 148.62/21.33 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (380), (4758) imply: % 148.62/21.33 | | | | | | | | | | | | | | | | | | (4759) all_52_6 = e3 % 148.62/21.33 | | | | | | | | | | | | | | | | | | % 148.62/21.33 | | | | | | | | | | | | | | | | | | REDUCE: (4738), (4759) imply: % 148.62/21.33 | | | | | | | | | | | | | | | | | | (4760) $false % 148.62/21.33 | | | | | | | | | | | | | | | | | | % 148.62/21.33 | | | | | | | | | | | | | | | | | | CLOSE: (4760) is inconsistent. % 148.62/21.33 | | | | | | | | | | | | | | | | | | % 148.62/21.33 | | | | | | | | | | | | | | | | | Case 2: % 148.62/21.33 | | | | | | | | | | | | | | | | | | % 148.62/21.33 | | | | | | | | | | | | | | | | | | (4761) all_58_8 = e3 | all_58_11 = e3 % 148.62/21.33 | | | | | | | | | | | | | | | | | | % 148.62/21.33 | | | | | | | | | | | | | | | | | | BETA: splitting (4761) gives: % 148.62/21.33 | | | | | | | | | | | | | | | | | | % 148.62/21.33 | | | | | | | | | | | | | | | | | | Case 1: % 148.62/21.33 | | | | | | | | | | | | | | | | | | | % 148.62/21.33 | | | | | | | | | | | | | | | | | | | (4762) all_58_8 = e3 % 148.62/21.33 | | | | | | | | | | | | | | | | | | | % 148.62/21.33 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (552), (4762) imply: % 148.62/21.33 | | | | | | | | | | | | | | | | | | | (4763) all_6_2 = e3 % 148.62/21.33 | | | | | | | | | | | | | | | | | | | % 148.62/21.33 | | | | | | | | | | | | | | | | | | | REDUCE: (4718), (4763) imply: % 148.62/21.33 | | | | | | | | | | | | | | | | | | | (4764) $false % 148.62/21.33 | | | | | | | | | | | | | | | | | | | % 148.62/21.33 | | | | | | | | | | | | | | | | | | | CLOSE: (4764) is inconsistent. % 148.62/21.33 | | | | | | | | | | | | | | | | | | | % 148.62/21.33 | | | | | | | | | | | | | | | | | | Case 2: % 148.62/21.33 | | | | | | | | | | | | | | | | | | | % 148.62/21.33 | | | | | | | | | | | | | | | | | | | (4765) all_58_11 = e3 % 148.62/21.33 | | | | | | | | | | | | | | | | | | | % 148.62/21.33 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (550), (4765) imply: % 148.62/21.33 | | | | | | | | | | | | | | | | | | | (4766) all_52_14 = e3 % 148.62/21.33 | | | | | | | | | | | | | | | | | | | % 148.62/21.33 | | | | | | | | | | | | | | | | | | | REDUCE: (587), (4766) imply: % 148.62/21.33 | | | | | | | | | | | | | | | | | | | (4767) ~ (all_6_2 = e3) % 148.62/21.33 | | | | | | | | | | | | | | | | | | | % 148.62/21.33 | | | | | | | | | | | | | | | | | | | BETA: splitting (4753) gives: % 148.62/21.33 | | | | | | | | | | | | | | | | | | | % 148.62/21.33 | | | | | | | | | | | | | | | | | | | Case 1: % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | (4768) all_58_5 = e3 % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (389), (4768) imply: % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | (4769) all_52_9 = e3 % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | REDUCE: (4740), (4769) imply: % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | (4770) $false % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | CLOSE: (4770) is inconsistent. % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | % 148.62/21.33 | | | | | | | | | | | | | | | | | | | Case 2: % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | (4771) all_58_8 = e3 | all_58_14 = e3 % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | BETA: splitting (4771) gives: % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | Case 1: % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | | % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | | (4772) all_58_8 = e3 % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | | % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (552), (4772) imply: % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | | (4773) all_6_2 = e3 % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | | % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | | REDUCE: (4718), (4773) imply: % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | | (4774) $false % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | | % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | | CLOSE: (4774) is inconsistent. % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | | % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | Case 2: % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | | % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | | (4775) all_58_14 = e3 % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | | % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (548), (4775) imply: % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | | (4776) all_52_11 = e3 % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | | % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | | REDUCE: (173), (4776) imply: % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | | (4777) ~ (all_52_7 = e3) % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | | % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | | REDUCE: (588), (4776) imply: % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | | (4778) ~ (all_4_2 = e3) % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | | % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | | SIMP: (4778) implies: % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | | (4779) ~ (all_4_2 = e3) % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | | % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (330) gives: % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | | % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | | | % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | | | (4780) all_58_4 = e2 % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | | | % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (407), (4780) imply: % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | | | (4781) all_52_8 = e2 % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | | | % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (168), (4781) imply: % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | | | (4782) ~ (all_52_12 = e2) % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | | | % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | | | SIMP: (4782) implies: % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | | | (4783) ~ (all_52_12 = e2) % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | | | % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4747), (4781) imply: % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | | | (4784) ~ (e3 = e2) % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | | | % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (322) gives: % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | | | % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | | | | % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | | | | (4785) all_58_9 = e2 % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | | | | % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (551), (4785) imply: % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | | | | (4786) all_52_12 = e2 % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | | | | % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4783), (4786) imply: % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | | | | (4787) $false % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | | | | % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (4787) is inconsistent. % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | | | | % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | | | | % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | | | | (4788) all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2 % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | | | | % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4788) gives: % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | | | | % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | | | | | % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | | | | | (4789) all_58_10 = e2 % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | | | | | % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (386), (4789) imply: % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | | | | | (4790) all_52_13 = e2 % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | | | | | % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4741), (4790) imply: % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | | | | | (4791) $false % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | | | | | % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (4791) is inconsistent. % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | | | | | % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | | | | | % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | | | | | (4792) all_58_11 = e2 | all_58_15 = e2 % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | | | | | % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4792) gives: % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | | | | | % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | | | | | | (4793) all_58_11 = e2 % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4765), (4793) imply: % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | | | | | | (4794) e3 = e2 % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4775), (4794) imply: % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | | | | | | (4795) all_58_14 = e2 % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (552), (4718), (4771), (4795) are % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #591. % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | | | | | | (4796) all_58_15 = e2 % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (547), (4796) imply: % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | | | | | | (4797) all_4_2 = e2 % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (544), (4797) imply: % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | | | | | | (4798) all_56_31 = e2 % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (581), (4797) imply: % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | | | | | | (4799) ~ (all_52_7 = e2) % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (289) gives: % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | | | | | | | (4800) ~ (all_56_31 = e2) % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4798), (4800) imply: % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | | | | | | | (4801) $false % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (4801) is inconsistent. % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | | | | | | | (4802) all_56_27 = e0 % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (360), (4802) imply: % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | | | | | | | (4803) all_52_7 = e0 % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4803) implies: % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | | | | | | | (4804) all_52_7 = e0 % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (183), (4804) imply: % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | | | | | | | (4805) ~ (all_52_4 = e0) % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4777), (4804) imply: % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | | | | | | | (4806) ~ (e3 = e0) % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4799), (4804) imply: % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | | | | | | | (4807) ~ (e2 = e0) % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (341) gives: % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4808) all_58_0 = e0 % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4745), (4808) imply: % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4809) e3 = e0 % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7), (4809) imply: % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4810) $false % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (4810) is inconsistent. % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4811) all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0 % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4811) gives: % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4812) all_58_1 = e0 % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (555), (4812) imply: % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4813) all_52_4 = e0 % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4805), (4813) imply: % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4814) $false % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (4814) is inconsistent. % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4815) all_58_4 = e0 | all_58_9 = e0 % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4815) gives: % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4816) all_58_4 = e0 % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (4780), (4816) are inconsistent by sub-proof % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #630. % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4817) all_58_9 = e0 % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (9), (321), (3726), (4743), (4748), (4749), % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4817), (function-axioms) are inconsistent by % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #158. % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | | | | | % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | | | | % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | | | End of split % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | | | % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | | | % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | | | (4818) all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2 % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | | | % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (389), (552), (4714), (4718), (4739), (4771), % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | | | (4818) are inconsistent by sub-proof #589. % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | | | % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | | End of split % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | | % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | End of split % 148.62/21.33 | | | | | | | | | | | | | | | | | | | | % 148.62/21.33 | | | | | | | | | | | | | | | | | | | End of split % 148.62/21.33 | | | | | | | | | | | | | | | | | | | % 148.62/21.33 | | | | | | | | | | | | | | | | | | End of split % 148.62/21.33 | | | | | | | | | | | | | | | | | | % 148.62/21.33 | | | | | | | | | | | | | | | | | End of split % 148.62/21.33 | | | | | | | | | | | | | | | | | % 148.62/21.33 | | | | | | | | | | | | | | | | End of split % 148.62/21.33 | | | | | | | | | | | | | | | | % 148.62/21.33 | | | | | | | | | | | | | | | End of split % 148.62/21.33 | | | | | | | | | | | | | | | % 148.62/21.33 | | | | | | | | | | | | | | End of split % 148.62/21.33 | | | | | | | | | | | | | | % 148.62/21.33 | | | | | | | | | | | | | Case 2: % 148.62/21.33 | | | | | | | | | | | | | | % 148.62/21.33 | | | | | | | | | | | | | | (4819) all_56_21 = e3 % 148.62/21.33 | | | | | | | | | | | | | | % 148.62/21.33 | | | | | | | | | | | | | | REF_CLOSE: (51), (53), (374), (612), (3726), (4701), (4714), % 148.62/21.33 | | | | | | | | | | | | | | (4819), (function-axioms) are inconsistent by % 148.62/21.33 | | | | | | | | | | | | | | sub-proof #163. % 148.62/21.33 | | | | | | | | | | | | | | % 148.62/21.33 | | | | | | | | | | | | | End of split % 148.62/21.33 | | | | | | | | | | | | | % 148.62/21.33 | | | | | | | | | | | | Case 2: % 148.62/21.33 | | | | | | | | | | | | | % 148.62/21.33 | | | | | | | | | | | | | (4820) all_56_15 = e2 % 148.62/21.33 | | | | | | | | | | | | | (4821) all_56_11 = e0 % 148.62/21.33 | | | | | | | | | | | | | % 148.62/21.33 | | | | | | | | | | | | | COMBINE_EQS: (545), (4821) imply: % 148.62/21.33 | | | | | | | | | | | | | (4822) all_8_2 = e0 % 148.62/21.33 | | | | | | | | | | | | | % 148.62/21.33 | | | | | | | | | | | | | COMBINE_EQS: (443), (4820) imply: % 148.62/21.33 | | | | | | | | | | | | | (4823) all_52_13 = e2 % 148.62/21.33 | | | | | | | | | | | | | % 148.62/21.33 | | | | | | | | | | | | | SIMP: (4823) implies: % 148.62/21.33 | | | | | | | | | | | | | (4824) all_52_13 = e2 % 148.62/21.33 | | | | | | | | | | | | | % 148.62/21.33 | | | | | | | | | | | | | REF_CLOSE: (4), (6), (36), (38), (248), (287), (333), (374), % 148.62/21.33 | | | | | | | | | | | | | (386), (389), (544), (545), (546), (554), (579), % 148.62/21.33 | | | | | | | | | | | | | (583), (627), (3730), (4677), (4680), (4682), % 148.62/21.33 | | | | | | | | | | | | | (4688), (4690), (4691), (4822), (4824), % 148.62/21.33 | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 148.62/21.33 | | | | | | | | | | | | | #336. % 148.62/21.33 | | | | | | | | | | | | | % 148.62/21.33 | | | | | | | | | | | | End of split % 148.62/21.33 | | | | | | | | | | | | % 148.62/21.33 | | | | | | | | | | | Case 2: % 148.62/21.33 | | | | | | | | | | | | % 148.62/21.33 | | | | | | | | | | | | (4825) all_56_21 = e2 % 148.62/21.33 | | | | | | | | | | | | (4826) all_56_19 = e1 % 148.62/21.33 | | | | | | | | | | | | % 148.62/21.33 | | | | | | | | | | | | COMBINE_EQS: (435), (4826) imply: % 148.62/21.33 | | | | | | | | | | | | (4827) all_52_6 = e1 % 148.62/21.33 | | | | | | | | | | | | % 148.62/21.33 | | | | | | | | | | | | REF_CLOSE: (4), (5), (46), (48), (244), (287), (324), (374), % 148.62/21.33 | | | | | | | | | | | | (380), (532), (544), (545), (546), (550), (552), % 148.62/21.33 | | | | | | | | | | | | (580), (591), (617), (762), (4698), (4701), % 148.62/21.33 | | | | | | | | | | | | (4704), (4705), (4707), (4709), (4711), (4712), % 148.62/21.33 | | | | | | | | | | | | (4825), (4827), (function-axioms) are inconsistent % 148.62/21.33 | | | | | | | | | | | | by sub-proof #431. % 148.62/21.33 | | | | | | | | | | | | % 148.62/21.33 | | | | | | | | | | | End of split % 148.62/21.33 | | | | | | | | | | | % 148.62/21.33 | | | | | | | | | | End of split % 148.62/21.33 | | | | | | | | | | % 148.62/21.33 | | | | | | | | | Case 2: % 148.62/21.33 | | | | | | | | | | % 148.62/21.33 | | | | | | | | | | (4828) all_28_0 = e2 % 148.62/21.33 | | | | | | | | | | (4829) ~ (all_28_1 = e3) | ~ (all_28_2 = e0) % 148.62/21.33 | | | | | | | | | | % 148.62/21.33 | | | | | | | | | | COMBINE_EQS: (740), (4828) imply: % 148.62/21.33 | | | | | | | | | | (4830) all_6_0 = e2 % 148.62/21.33 | | | | | | | | | | % 148.62/21.33 | | | | | | | | | | SIMP: (4830) implies: % 148.62/21.33 | | | | | | | | | | (4831) all_6_0 = e2 % 148.62/21.33 | | | | | | | | | | % 148.62/21.33 | | | | | | | | | | REF_CLOSE: (6), (8), (36), (37), (38), (41), (42), (43), % 148.62/21.33 | | | | | | | | | | (46), (51), (144), (158), (173), (174), (176), % 148.62/21.33 | | | | | | | | | | (187), (192), (206), (207), (208), (211), (237), % 148.62/21.33 | | | | | | | | | | (239), (240), (242), (247), (252), (288), (289), % 148.62/21.33 | | | | | | | | | | (290), (291), (292), (293), (294), (297), (321), % 148.62/21.33 | | | | | | | | | | (341), (357), (366), (374), (381), (386), (402), % 148.62/21.33 | | | | | | | | | | (407), (419), (435), (443), (475), (478), (480), % 148.62/21.33 | | | | | | | | | | (513), (540), (541), (542), (543), (544), (545), % 148.62/21.33 | | | | | | | | | | (546), (547), (550), (551), (555), (559), (569), % 148.62/21.33 | | | | | | | | | | (571), (573), (580), (585), (620), (622), (627), % 148.62/21.33 | | | | | | | | | | (634), (665), (764), (767), (768), (3728), (4829), % 148.62/21.33 | | | | | | | | | | (4831), (function-axioms) are inconsistent by % 148.62/21.33 | | | | | | | | | | sub-proof #364. % 148.62/21.33 | | | | | | | | | | % 148.62/21.33 | | | | | | | | | End of split % 148.62/21.33 | | | | | | | | | % 148.62/21.33 | | | | | | | | Case 2: % 148.62/21.33 | | | | | | | | | % 148.62/21.33 | | | | | | | | | (4832) all_26_0 = e1 % 148.62/21.33 | | | | | | | | | (4833) ~ (all_26_1 = e2) | ~ (all_26_2 = e3) % 148.62/21.33 | | | | | | | | | % 148.62/21.33 | | | | | | | | | COMBINE_EQS: (760), (4832) imply: % 148.62/21.33 | | | | | | | | | (4834) all_4_0 = e1 % 148.62/21.33 | | | | | | | | | % 148.62/21.33 | | | | | | | | | COMBINE_EQS: (709), (4834) imply: % 148.62/21.33 | | | | | | | | | (4835) all_44_0 = e1 % 148.62/21.33 | | | | | | | | | % 148.62/21.33 | | | | | | | | | REDUCE: (767), (4834) imply: % 148.62/21.33 | | | | | | | | | (4836) ~ (e3 = e1) % 148.62/21.33 | | | | | | | | | % 148.62/21.33 | | | | | | | | | REDUCE: (3728), (4834) imply: % 148.62/21.33 | | | | | | | | | (4837) ~ (e2 = e1) % 148.62/21.33 | | | | | | | | | % 148.62/21.33 | | | | | | | | | REDUCE: (37), (4834) imply: % 148.62/21.33 | | | | | | | | | (4838) op(e0, all_4_1) = e1 % 148.62/21.33 | | | | | | | | | % 148.67/21.33 | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (36), (37), (38), (41), (42), % 148.67/21.33 | | | | | | | | | (43), (46), (48), (51), (99), (119), (139), (144), % 148.67/21.33 | | | | | | | | | (158), (165), (166), (168), (169), (173), (174), % 148.67/21.33 | | | | | | | | | (176), (187), (188), (189), (191), (192), (206), % 148.67/21.33 | | | | | | | | | (207), (208), (211), (237), (239), (240), (241), % 148.67/21.33 | | | | | | | | | (242), (243), (244), (245), (247), (248), (252), % 148.67/21.33 | | | | | | | | | (287), (288), (289), (290), (291), (292), (293), % 148.67/21.33 | | | | | | | | | (294), (295), (296), (297), (320), (321), (322), % 148.67/21.33 | | | | | | | | | (324), (326), (327), (330), (331), (333), (341), % 148.67/21.33 | | | | | | | | | (344), (357), (360), (365), (366), (374), (380), % 148.67/21.33 | | | | | | | | | (381), (386), (389), (402), (407), (419), (431), % 148.67/21.33 | | | | | | | | | (435), (443), (447), (469), (471), (473), (475), % 148.67/21.33 | | | | | | | | | (476), (478), (480), (513), (523), (530), (532), % 148.67/21.33 | | | | | | | | | (535), (540), (541), (542), (543), (544), (545), % 148.67/21.33 | | | | | | | | | (546), (547), (548), (549), (550), (551), (552), % 148.67/21.33 | | | | | | | | | (553), (554), (555), (559), (561), (565), (569), % 148.67/21.33 | | | | | | | | | (570), (571), (573), (575), (577), (579), (580), % 148.67/21.33 | | | | | | | | | (583), (585), (587), (588), (590), (591), (617), % 148.67/21.33 | | | | | | | | | (618), (620), (622), (627), (631), (634), (652), % 148.67/21.33 | | | | | | | | | (657), (665), (740), (752), (762), (764), (767), % 148.67/21.33 | | | | | | | | | (768), (3728), (3730), (4674), (4677), (4680), % 148.67/21.33 | | | | | | | | | (4681), (4682), (4684), (4686), (4688), (4690), % 148.67/21.33 | | | | | | | | | (4691), (4833), (4835), (4838), (function-axioms) % 148.67/21.33 | | | | | | | | | are inconsistent by sub-proof #308. % 148.67/21.33 | | | | | | | | | % 148.67/21.33 | | | | | | | | End of split % 148.67/21.33 | | | | | | | | % 148.67/21.33 | | | | | | | End of split % 148.67/21.33 | | | | | | | % 148.67/21.33 | | | | | | Case 2: % 148.67/21.33 | | | | | | | % 148.67/21.33 | | | | | | | (4839) all_14_0 = e1 % 148.67/21.33 | | | | | | | (4840) ~ (all_14_1 = e3) | ~ (all_14_2 = e0) % 148.67/21.33 | | | | | | | % 148.67/21.33 | | | | | | | COMBINE_EQS: (758), (4839) imply: % 148.67/21.33 | | | | | | | (4841) all_8_0 = e1 % 148.67/21.33 | | | | | | | % 148.67/21.33 | | | | | | | COMBINE_EQS: (763), (4841) imply: % 148.67/21.33 | | | | | | | (4842) all_42_0 = e1 % 148.67/21.33 | | | | | | | % 148.67/21.33 | | | | | | | REDUCE: (47), (4841) imply: % 148.67/21.33 | | | | | | | (4843) op(e2, all_8_1) = e1 % 148.67/21.33 | | | | | | | % 148.67/21.33 | | | | | | | BETA: splitting (99) gives: % 148.67/21.33 | | | | | | | % 148.67/21.33 | | | | | | | Case 1: % 148.67/21.33 | | | | | | | | % 148.67/21.33 | | | | | | | | (4844) ~ (all_28_0 = e2) % 148.67/21.33 | | | | | | | | % 148.67/21.33 | | | | | | | | REDUCE: (740), (4844) imply: % 148.67/21.33 | | | | | | | | (4845) ~ (all_6_0 = e2) % 148.67/21.33 | | | | | | | | % 148.67/21.33 | | | | | | | | BETA: splitting (119) gives: % 148.67/21.33 | | | | | | | | % 148.67/21.33 | | | | | | | | Case 1: % 148.67/21.33 | | | | | | | | | % 148.67/21.33 | | | | | | | | | (4846) ~ (all_36_1 = e3) % 148.67/21.33 | | | | | | | | | % 148.67/21.33 | | | | | | | | | REDUCE: (652), (4846) imply: % 148.67/21.33 | | | | | | | | | (4847) ~ (all_6_1 = e3) % 148.67/21.33 | | | | | | | | | % 148.67/21.33 | | | | | | | | | BETA: splitting (134) gives: % 148.67/21.33 | | | | | | | | | % 148.67/21.33 | | | | | | | | | Case 1: % 148.67/21.33 | | | | | | | | | | % 148.67/21.33 | | | | | | | | | | (4848) ~ (all_42_0 = e1) % 148.67/21.33 | | | | | | | | | | % 148.67/21.33 | | | | | | | | | | REDUCE: (4842), (4848) imply: % 148.67/21.33 | | | | | | | | | | (4849) $false % 148.67/21.33 | | | | | | | | | | % 148.67/21.33 | | | | | | | | | | CLOSE: (4849) is inconsistent. % 148.67/21.33 | | | | | | | | | | % 148.67/21.34 | | | | | | | | | Case 2: % 148.67/21.34 | | | | | | | | | | % 148.67/21.34 | | | | | | | | | | (4850) ~ (all_42_1 = e0) | ~ (all_42_2 = e3) % 148.67/21.34 | | | | | | | | | | % 148.67/21.34 | | | | | | | | | | BETA: splitting (294) gives: % 148.67/21.34 | | | | | | | | | | % 148.67/21.34 | | | | | | | | | | Case 1: % 148.67/21.34 | | | | | | | | | | | % 148.67/21.34 | | | | | | | | | | | (4851) ~ (all_56_11 = e0) % 148.67/21.34 | | | | | | | | | | | % 148.67/21.34 | | | | | | | | | | | REDUCE: (545), (4851) imply: % 148.67/21.34 | | | | | | | | | | | (4852) ~ (all_8_2 = e0) % 148.67/21.34 | | | | | | | | | | | % 148.67/21.34 | | | | | | | | | | | BETA: splitting (288) gives: % 148.67/21.34 | | | | | | | | | | | % 148.67/21.34 | | | | | | | | | | | Case 1: % 148.67/21.34 | | | | | | | | | | | | % 148.67/21.34 | | | | | | | | | | | | (4853) ~ (all_56_31 = e1) % 148.67/21.34 | | | | | | | | | | | | % 148.67/21.34 | | | | | | | | | | | | REDUCE: (544), (4853) imply: % 148.67/21.34 | | | | | | | | | | | | (4854) ~ (all_4_2 = e1) % 148.67/21.34 | | | | | | | | | | | | % 148.67/21.34 | | | | | | | | | | | | BETA: splitting (290) gives: % 148.67/21.34 | | | | | | | | | | | | % 148.67/21.34 | | | | | | | | | | | | Case 1: % 148.67/21.34 | | | | | | | | | | | | | % 148.67/21.34 | | | | | | | | | | | | | (4855) ~ (all_56_31 = e3) % 148.67/21.34 | | | | | | | | | | | | | % 148.67/21.34 | | | | | | | | | | | | | REDUCE: (544), (4855) imply: % 148.67/21.34 | | | | | | | | | | | | | (4856) ~ (all_4_2 = e3) % 148.67/21.34 | | | | | | | | | | | | | % 148.67/21.34 | | | | | | | | | | | | | BETA: splitting (291) gives: % 148.67/21.34 | | | | | | | | | | | | | % 148.67/21.34 | | | | | | | | | | | | | Case 1: % 148.67/21.34 | | | | | | | | | | | | | | % 148.67/21.34 | | | | | | | | | | | | | | (4857) ~ (all_56_21 = e0) % 148.67/21.34 | | | | | | | | | | | | | | % 148.67/21.34 | | | | | | | | | | | | | | REDUCE: (374), (4857) imply: % 148.67/21.34 | | | | | | | | | | | | | | (4858) ~ (all_6_2 = e0) % 148.67/21.34 | | | | | | | | | | | | | | % 148.67/21.34 | | | | | | | | | | | | | | REF_CLOSE: (6), (41), (46), (48), (51), (189), (193), (194), % 148.67/21.34 | | | | | | | | | | | | | | (197), (215), (242), (247), (248), (252), (293), % 148.67/21.34 | | | | | | | | | | | | | | (295), (296), (321), (323), (332), (374), (381), % 148.67/21.34 | | | | | | | | | | | | | | (386), (401), (425), (431), (463), (534), (541), % 148.67/21.34 | | | | | | | | | | | | | | (542), (543), (545), (547), (550), (551), (557), % 148.67/21.34 | | | | | | | | | | | | | | (569), (579), (583), (587), (617), (639), (769), % 148.67/21.34 | | | | | | | | | | | | | | (4843), (4850), (4852), (4854), (4856), (4858), % 148.67/21.34 | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 148.67/21.34 | | | | | | | | | | | | | | #247. % 148.67/21.34 | | | | | | | | | | | | | | % 148.67/21.34 | | | | | | | | | | | | | Case 2: % 148.67/21.34 | | | | | | | | | | | | | | % 148.67/21.34 | | | | | | | | | | | | | | (4859) all_56_23 = e1 % 148.67/21.34 | | | | | | | | | | | | | | (4860) all_56_21 = e0 % 148.67/21.34 | | | | | | | | | | | | | | % 148.67/21.34 | | | | | | | | | | | | | | COMBINE_EQS: (374), (4860) imply: % 148.67/21.34 | | | | | | | | | | | | | | (4861) all_6_2 = e0 % 148.67/21.34 | | | | | | | | | | | | | | % 148.67/21.34 | | | | | | | | | | | | | | SIMP: (4861) implies: % 148.67/21.34 | | | | | | | | | | | | | | (4862) all_6_2 = e0 % 148.67/21.34 | | | | | | | | | | | | | | % 148.67/21.34 | | | | | | | | | | | | | | COMBINE_EQS: (366), (4859) imply: % 148.67/21.34 | | | | | | | | | | | | | | (4863) all_52_14 = e1 % 148.67/21.34 | | | | | | | | | | | | | | % 148.67/21.34 | | | | | | | | | | | | | | SIMP: (4863) implies: % 148.67/21.34 | | | | | | | | | | | | | | (4864) all_52_14 = e1 % 148.67/21.34 | | | | | | | | | | | | | | % 148.67/21.34 | | | | | | | | | | | | | | REDUCE: (569), (4862) imply: % 148.67/21.34 | | | | | | | | | | | | | | (4865) ~ (all_52_2 = e0) % 148.67/21.34 | | | | | | | | | | | | | | % 148.67/21.34 | | | | | | | | | | | | | | REDUCE: (580), (4862) imply: % 148.67/21.34 | | | | | | | | | | | | | | (4866) ~ (all_52_6 = e0) % 148.67/21.34 | | | | | | | | | | | | | | % 148.67/21.34 | | | | | | | | | | | | | | REDUCE: (591), (4864) imply: % 148.67/21.34 | | | | | | | | | | | | | | (4867) ~ (all_4_2 = e1) % 148.67/21.34 | | | | | | | | | | | | | | % 148.67/21.34 | | | | | | | | | | | | | | REDUCE: (43), (4862) imply: % 148.67/21.34 | | | | | | | | | | | | | | (4868) op(e0, e0) = all_6_1 % 148.67/21.34 | | | | | | | | | | | | | | % 148.67/21.34 | | | | | | | | | | | | | | REDUCE: (622), (4862) imply: % 148.67/21.34 | | | | | | | | | | | | | | (4869) op(e1, e0) = all_56_20 % 148.67/21.34 | | | | | | | | | | | | | | % 148.67/21.34 | | | | | | | | | | | | | | REDUCE: (41), (4862) imply: % 148.67/21.34 | | | | | | | | | | | | | | (4870) op(e1, e1) = e0 % 148.67/21.34 | | | | | | | | | | | | | | % 148.67/21.34 | | | | | | | | | | | | | | REDUCE: (208), (4864) imply: % 148.67/21.34 | | | | | | | | | | | | | | (4871) op(e1, e0) = e1 % 148.67/21.34 | | | | | | | | | | | | | | % 148.67/21.34 | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_4_2, % 148.67/21.34 | | | | | | | | | | | | | | all_6_1, e0, e0, simplifying with (36), (4868) % 148.67/21.34 | | | | | | | | | | | | | | gives: % 148.67/21.34 | | | | | | | | | | | | | | (4872) all_6_1 = all_4_2 % 148.67/21.34 | | | | | | | | | | | | | | % 148.67/21.34 | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1, % 148.67/21.34 | | | | | | | | | | | | | | all_56_20, e0, e1, simplifying with (4869), (4871) % 148.67/21.34 | | | | | | | | | | | | | | gives: % 148.67/21.34 | | | | | | | | | | | | | | (4873) all_56_20 = e1 % 148.67/21.34 | | | | | | | | | | | | | | % 148.67/21.34 | | | | | | | | | | | | | | REDUCE: (768), (4872) imply: % 148.67/21.34 | | | | | | | | | | | | | | (4874) ~ (all_4_2 = e2) % 148.67/21.34 | | | | | | | | | | | | | | % 148.67/21.34 | | | | | | | | | | | | | | REDUCE: (42), (4872) imply: % 148.67/21.34 | | | | | | | | | | | | | | (4875) op(e1, all_4_2) = all_6_0 % 148.67/21.34 | | | | | | | | | | | | | | % 148.67/21.34 | | | | | | | | | | | | | | BETA: splitting (237) gives: % 148.67/21.34 | | | | | | | | | | | | | | % 148.67/21.34 | | | | | | | | | | | | | | Case 1: % 148.67/21.34 | | | | | | | | | | | | | | | % 148.67/21.34 | | | | | | | | | | | | | | | (4876) all_54_15 = e3 % 148.67/21.34 | | | | | | | | | | | | | | | % 148.67/21.34 | | | | | | | | | | | | | | | COMBINE_EQS: (540), (4876) imply: % 148.67/21.34 | | | | | | | | | | | | | | | (4877) all_4_2 = e3 % 148.67/21.34 | | | | | | | | | | | | | | | % 148.67/21.34 | | | | | | | | | | | | | | | REDUCE: (4856), (4877) imply: % 148.67/21.34 | | | | | | | | | | | | | | | (4878) $false % 148.67/21.34 | | | | | | | | | | | | | | | % 148.67/21.34 | | | | | | | | | | | | | | | CLOSE: (4878) is inconsistent. % 148.67/21.34 | | | | | | | | | | | | | | | % 148.67/21.34 | | | | | | | | | | | | | | Case 2: % 148.67/21.34 | | | | | | | | | | | | | | | % 148.67/21.34 | | | | | | | | | | | | | | | (4879) all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0 % 148.67/21.34 | | | | | | | | | | | | | | | % 148.67/21.34 | | | | | | | | | | | | | | | BETA: splitting (4879) gives: % 148.67/21.34 | | | | | | | | | | | | | | | % 148.67/21.34 | | | | | | | | | | | | | | | Case 1: % 148.67/21.34 | | | | | | | | | | | | | | | | % 148.67/21.34 | | | | | | | | | | | | | | | | (4880) all_54_15 = e2 % 148.67/21.34 | | | | | | | | | | | | | | | | % 148.67/21.34 | | | | | | | | | | | | | | | | COMBINE_EQS: (540), (4880) imply: % 148.67/21.34 | | | | | | | | | | | | | | | | (4881) all_4_2 = e2 % 148.67/21.34 | | | | | | | | | | | | | | | | % 148.67/21.34 | | | | | | | | | | | | | | | | REDUCE: (4874), (4881) imply: % 148.67/21.34 | | | | | | | | | | | | | | | | (4882) $false % 148.67/21.34 | | | | | | | | | | | | | | | | % 148.67/21.34 | | | | | | | | | | | | | | | | CLOSE: (4882) is inconsistent. % 148.67/21.34 | | | | | | | | | | | | | | | | % 148.67/21.34 | | | | | | | | | | | | | | | Case 2: % 148.67/21.34 | | | | | | | | | | | | | | | | % 148.67/21.34 | | | | | | | | | | | | | | | | (4883) ~ (all_54_15 = e2) % 148.67/21.34 | | | | | | | | | | | | | | | | (4884) all_54_15 = e1 | all_54_15 = e0 % 148.67/21.34 | | | | | | | | | | | | | | | | % 148.67/21.34 | | | | | | | | | | | | | | | | BETA: splitting (4884) gives: % 148.67/21.34 | | | | | | | | | | | | | | | | % 148.67/21.34 | | | | | | | | | | | | | | | | Case 1: % 148.67/21.34 | | | | | | | | | | | | | | | | | % 148.67/21.34 | | | | | | | | | | | | | | | | | (4885) all_54_15 = e1 % 148.67/21.34 | | | | | | | | | | | | | | | | | % 148.67/21.34 | | | | | | | | | | | | | | | | | COMBINE_EQS: (540), (4885) imply: % 148.67/21.34 | | | | | | | | | | | | | | | | | (4886) all_4_2 = e1 % 148.67/21.34 | | | | | | | | | | | | | | | | | % 148.67/21.34 | | | | | | | | | | | | | | | | | REDUCE: (4854), (4886) imply: % 148.67/21.34 | | | | | | | | | | | | | | | | | (4887) $false % 148.67/21.34 | | | | | | | | | | | | | | | | | % 148.67/21.34 | | | | | | | | | | | | | | | | | CLOSE: (4887) is inconsistent. % 148.67/21.34 | | | | | | | | | | | | | | | | | % 148.67/21.34 | | | | | | | | | | | | | | | | Case 2: % 148.67/21.34 | | | | | | | | | | | | | | | | | % 148.67/21.34 | | | | | | | | | | | | | | | | | (4888) all_54_15 = e0 % 148.67/21.34 | | | | | | | | | | | | | | | | | % 148.67/21.34 | | | | | | | | | | | | | | | | | COMBINE_EQS: (540), (4888) imply: % 148.67/21.34 | | | | | | | | | | | | | | | | | (4889) all_4_2 = e0 % 148.67/21.34 | | | | | | | | | | | | | | | | | % 148.67/21.34 | | | | | | | | | | | | | | | | | REDUCE: (570), (4889) imply: % 148.67/21.34 | | | | | | | | | | | | | | | | | (4890) ~ (all_52_3 = e0) % 148.67/21.34 | | | | | | | | | | | | | | | | | % 148.67/21.34 | | | | | | | | | | | | | | | | | REDUCE: (581), (4889) imply: % 148.67/21.34 | | | | | | | | | | | | | | | | | (4891) ~ (all_52_7 = e0) % 148.67/21.34 | | | | | | | | | | | | | | | | | % 148.67/21.34 | | | | | | | | | | | | | | | | | REDUCE: (4874), (4889) imply: % 148.67/21.34 | | | | | | | | | | | | | | | | | (4892) ~ (e2 = e0) % 148.67/21.34 | | | | | | | | | | | | | | | | | % 148.67/21.34 | | | | | | | | | | | | | | | | | REDUCE: (38), (4889) imply: % 148.67/21.34 | | | | | | | | | | | | | | | | | (4893) op(e0, e0) = all_4_1 % 148.67/21.34 | | | | | | | | | | | | | | | | | % 148.67/21.34 | | | | | | | | | | | | | | | | | REDUCE: (4875), (4889) imply: % 148.67/21.34 | | | | | | | | | | | | | | | | | (4894) op(e1, e0) = all_6_0 % 148.67/21.34 | | | | | | | | | | | | | | | | | % 148.67/21.34 | | | | | | | | | | | | | | | | | REDUCE: (627), (4889) imply: % 148.67/21.34 | | | | | | | | | | | | | | | | | (4895) op(e0, e0) = all_56_30 % 148.67/21.34 | | | | | | | | | | | | | | | | | % 148.67/21.34 | | | | | | | | | | | | | | | | | REDUCE: (36), (4889) imply: % 148.67/21.34 | | | | | | | | | | | | | | | | | (4896) op(e0, e0) = e0 % 148.67/21.34 | | | | | | | | | | | | | | | | | % 148.67/21.34 | | | | | | | | | | | | | | | | | BETA: splitting (332) gives: % 148.67/21.34 | | | | | | | | | | | | | | | | | % 148.67/21.34 | | | | | | | | | | | | | | | | | Case 1: % 148.67/21.34 | | | | | | | | | | | | | | | | | | % 148.67/21.34 | | | | | | | | | | | | | | | | | | (4897) all_58_2 = e0 % 148.67/21.34 | | | | | | | | | | | | | | | | | | % 148.67/21.34 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (401), (4897) imply: % 148.67/21.34 | | | | | | | | | | | | | | | | | | (4898) all_52_1 = e0 % 148.67/21.34 | | | | | | | | | | | | | | | | | | % 148.67/21.34 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (425), (4898) imply: % 148.67/21.34 | | | | | | | | | | | | | | | | | | (4899) all_56_9 = e0 % 148.67/21.34 | | | | | | | | | | | | | | | | | | % 148.67/21.34 | | | | | | | | | | | | | | | | | | REDUCE: (568), (4898) imply: % 148.67/21.34 | | | | | | | | | | | | | | | | | | (4900) ~ (all_8_2 = e0) % 148.67/21.34 | | | | | | | | | | | | | | | | | | % 148.67/21.34 | | | | | | | | | | | | | | | | | | BETA: splitting (336) gives: % 148.67/21.34 | | | | | | | | | | | | | | | | | | % 148.67/21.34 | | | | | | | | | | | | | | | | | | Case 1: % 148.67/21.34 | | | | | | | | | | | | | | | | | | | % 148.67/21.34 | | | | | | | | | | | | | | | | | | | (4901) all_58_1 = e0 % 148.67/21.34 | | | | | | | | | | | | | | | | | | | % 148.67/21.34 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (555), (4901) imply: % 148.67/21.34 | | | | | | | | | | | | | | | | | | | (4902) all_52_4 = e0 % 148.67/21.34 | | | | | | | | | | | | | | | | | | | % 148.67/21.34 | | | | | | | | | | | | | | | | | | | REDUCE: (616), (4902) imply: % 148.67/21.34 | | | | | | | | | | | | | | | | | | | (4903) op(e2, e0) = all_56_2 % 148.67/21.34 | | | | | | | | | | | | | | | | | | | % 148.67/21.34 | | | | | | | | | | | | | | | | | | | BETA: splitting (296) gives: % 148.67/21.34 | | | | | | | | | | | | | | | | | | | % 148.67/21.34 | | | | | | | | | | | | | | | | | | | Case 1: % 148.67/21.34 | | | | | | | | | | | | | | | | | | | | % 148.67/21.34 | | | | | | | | | | | | | | | | | | | | (4904) ~ (all_56_11 = e3) % 148.67/21.34 | | | | | | | | | | | | | | | | | | | | % 148.67/21.34 | | | | | | | | | | | | | | | | | | | | REDUCE: (545), (4904) imply: % 148.67/21.34 | | | | | | | | | | | | | | | | | | | | (4905) ~ (all_8_2 = e3) % 148.67/21.34 | | | | | | | | | | | | | | | | | | | | % 148.67/21.34 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_4_1, % 148.67/21.34 | | | | | | | | | | | | | | | | | | | | all_56_30, e0, e0, simplifying with (4893), (4895) % 148.67/21.34 | | | | | | | | | | | | | | | | | | | | gives: % 148.67/21.34 | | | | | | | | | | | | | | | | | | | | (4906) all_56_30 = all_4_1 % 148.67/21.34 | | | | | | | | | | | | | | | | | | | | % 148.67/21.34 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, % 148.67/21.34 | | | | | | | | | | | | | | | | | | | | all_56_30, e0, e0, simplifying with (4895), (4896) % 148.67/21.34 | | | | | | | | | | | | | | | | | | | | gives: % 148.67/21.34 | | | | | | | | | | | | | | | | | | | | (4907) all_56_30 = e0 % 148.67/21.34 | | | | | | | | | | | | | | | | | | | | % 148.67/21.34 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1, all_6_0, % 148.67/21.34 | | | | | | | | | | | | | | | | | | | | e0, e1, simplifying with (4871), (4894) gives: % 148.67/21.34 | | | | | | | | | | | | | | | | | | | | (4908) all_6_0 = e1 % 148.67/21.34 | | | | | | | | | | | | | | | | | | | | % 148.67/21.34 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_13, % 148.67/21.34 | | | | | | | | | | | | | | | | | | | | all_56_2, e0, e2, simplifying with (212), (4903) % 148.67/21.34 | | | | | | | | | | | | | | | | | | | | gives: % 148.67/21.34 | | | | | | | | | | | | | | | | | | | | (4909) all_56_2 = all_52_13 % 148.67/21.34 | | | | | | | | | | | | | | | | | | | | % 148.67/21.34 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4906), (4907) imply: % 148.67/21.34 | | | | | | | | | | | | | | | | | | | | (4910) all_4_1 = e0 % 148.67/21.34 | | | | | | | | | | | | | | | | | | | | % 148.67/21.34 | | | | | | | | | | | | | | | | | | | | SIMP: (4910) implies: % 148.67/21.34 | | | | | | | | | | | | | | | | | | | | (4911) all_4_1 = e0 % 148.67/21.34 | | | | | | | | | | | | | | | | | | | | % 148.67/21.34 | | | | | | | | | | | | | | | | | | | | REDUCE: (4845), (4908) imply: % 148.67/21.34 | | | | | | | | | | | | | | | | | | | | (4912) ~ (e2 = e1) % 148.67/21.34 | | | | | | | | | | | | | | | | | | | | % 148.67/21.34 | | | | | | | | | | | | | | | | | | | | REDUCE: (37), (4911) imply: % 148.67/21.34 | | | | | | | | | | | | | | | | | | | | (4913) op(e0, e0) = all_4_0 % 148.67/21.34 | | | | | | | | | | | | | | | | | | | | % 148.67/21.34 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_4_0, % 148.67/21.34 | | | | | | | | | | | | | | | | | | | | e0, e0, simplifying with (4896), (4913) gives: % 148.67/21.34 | | | | | | | | | | | | | | | | | | | | (4914) all_4_0 = e0 % 148.67/21.34 | | | | | | | | | | | | | | | | | | | | % 148.67/21.34 | | | | | | | | | | | | | | | | | | | | REDUCE: (767), (4914) imply: % 148.67/21.34 | | | | | | | | | | | | | | | | | | | | (4915) ~ (e3 = e0) % 148.67/21.34 | | | | | | | | | | | | | | | | | | | | % 148.67/21.34 | | | | | | | | | | | | | | | | | | | | BETA: splitting (295) gives: % 148.67/21.34 | | | | | | | | | | | | | | | | | | | | % 148.67/21.34 | | | | | | | | | | | | | | | | | | | | Case 1: % 148.67/21.34 | | | | | | | | | | | | | | | | | | | | | % 148.67/21.34 | | | | | | | | | | | | | | | | | | | | | (4916) ~ (all_56_11 = e1) % 148.67/21.34 | | | | | | | | | | | | | | | | | | | | | % 148.67/21.34 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (46), (48), (51), (215), (247), (252), (296), % 148.67/21.34 | | | | | | | | | | | | | | | | | | | | | (425), (534), (542), (543), (545), (557), (617), % 148.67/21.34 | | | | | | | | | | | | | | | | | | | | | (639), (769), (4843), (4850), (4852), (4916), % 148.67/21.34 | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 148.67/21.34 | | | | | | | | | | | | | | | | | | | | | #250. % 148.67/21.34 | | | | | | | | | | | | | | | | | | | | | % 148.67/21.34 | | | | | | | | | | | | | | | | | | | | Case 2: % 148.67/21.34 | | | | | | | | | | | | | | | | | | | | | % 148.67/21.34 | | | | | | | | | | | | | | | | | | | | | (4917) all_56_11 = e1 % 148.67/21.34 | | | | | | | | | | | | | | | | | | | | | % 148.67/21.34 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (545), (4917) imply: % 148.67/21.34 | | | | | | | | | | | | | | | | | | | | | (4918) all_8_2 = e1 % 148.67/21.34 | | | | | | | | | | | | | | | | | | | | | % 148.67/21.34 | | | | | | | | | | | | | | | | | | | | | SIMP: (4918) implies: % 148.67/21.34 | | | | | | | | | | | | | | | | | | | | | (4919) all_8_2 = e1 % 148.67/21.34 | | | | | | | | | | | | | | | | | | | | | % 148.67/21.34 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (554), (4919) imply: % 148.67/21.34 | | | | | | | | | | | | | | | | | | | | | (4920) all_58_3 = e1 % 148.67/21.34 | | | | | | | | | | | | | | | | | | | | | % 148.67/21.34 | | | | | | | | | | | | | | | | | | | | | REDUCE: (579), (4919) imply: % 148.67/21.34 | | | | | | | | | | | | | | | | | | | | | (4921) ~ (all_52_13 = e1) % 148.67/21.34 | | | | | | | | | | | | | | | | | | | | | % 148.67/21.34 | | | | | | | | | | | | | | | | | | | | | REDUCE: (4905), (4919) imply: % 148.67/21.34 | | | | | | | | | | | | | | | | | | | | | (4922) ~ (e3 = e1) % 148.67/21.34 | | | | | | | | | | | | | | | | | | | | | % 148.67/21.34 | | | | | | | | | | | | | | | | | | | | | REDUCE: (48), (4919) imply: % 148.67/21.34 | | | | | | | | | | | | | | | | | | | | | (4923) op(e1, e1) = all_8_1 % 148.67/21.34 | | | | | | | | | | | | | | | | | | | | | % 148.67/21.34 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (335) gives: % 148.67/21.34 | | | | | | | | | | | | | | | | | | | | | % 148.67/21.34 | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.67/21.34 | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.34 | | | | | | | | | | | | | | | | | | | | | | (4924) all_58_2 = e3 % 148.67/21.34 | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.34 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4897), (4924) imply: % 148.67/21.34 | | | | | | | | | | | | | | | | | | | | | | (4925) e3 = e0 % 148.67/21.34 | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.34 | | | | | | | | | | | | | | | | | | | | | | SIMP: (4925) implies: % 148.67/21.34 | | | | | | | | | | | | | | | | | | | | | | (4926) e3 = e0 % 148.67/21.34 | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.34 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7), (4926) imply: % 148.67/21.34 | | | | | | | | | | | | | | | | | | | | | | (4927) $false % 148.67/21.34 | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.34 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (4927) is inconsistent. % 148.67/21.34 | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.34 | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.67/21.34 | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.34 | | | | | | | | | | | | | | | | | | | | | | (4928) all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3 % 148.67/21.34 | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.34 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4928) gives: % 148.67/21.34 | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.34 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.67/21.34 | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.34 | | | | | | | | | | | | | | | | | | | | | | | (4929) all_58_3 = e3 % 148.67/21.34 | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.34 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (4920), (4929) are inconsistent by sub-proof % 148.67/21.34 | | | | | | | | | | | | | | | | | | | | | | | #157. % 148.67/21.34 | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.34 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.67/21.34 | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.34 | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.34 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_8_1, % 148.67/21.34 | | | | | | | | | | | | | | | | | | | | | | | e1, e1, simplifying with (4870), (4923) gives: % 148.67/21.34 | | | | | | | | | | | | | | | | | | | | | | | (4930) all_8_1 = e0 % 148.67/21.34 | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.34 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4843), (4930) imply: % 148.67/21.34 | | | | | | | | | | | | | | | | | | | | | | | (4931) op(e2, e0) = e1 % 148.67/21.34 | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.34 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (212), (4921), (4931), (function-axioms) are % 148.67/21.34 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #258. % 148.67/21.34 | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.34 | | | | | | | | | | | | | | | | | | | | | | End of split % 148.67/21.34 | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.34 | | | | | | | | | | | | | | | | | | | | | End of split % 148.67/21.34 | | | | | | | | | | | | | | | | | | | | | % 148.67/21.34 | | | | | | | | | | | | | | | | | | | | End of split % 148.67/21.34 | | | | | | | | | | | | | | | | | | | | % 148.67/21.34 | | | | | | | | | | | | | | | | | | | Case 2: % 148.67/21.34 | | | | | | | | | | | | | | | | | | | | % 148.67/21.34 | | | | | | | | | | | | | | | | | | | | (4932) all_56_9 = e2 % 148.67/21.34 | | | | | | | | | | | | | | | | | | | | % 148.67/21.34 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (4899), (4932) are inconsistent by sub-proof % 148.67/21.34 | | | | | | | | | | | | | | | | | | | | #486. % 148.67/21.34 | | | | | | | | | | | | | | | | | | | | % 148.67/21.34 | | | | | | | | | | | | | | | | | | | End of split % 148.67/21.34 | | | | | | | | | | | | | | | | | | | % 148.67/21.34 | | | | | | | | | | | | | | | | | | Case 2: % 148.67/21.34 | | | | | | | | | | | | | | | | | | | % 148.67/21.34 | | | | | | | | | | | | | | | | | | | (4933) all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0 % 148.67/21.34 | | | | | | | | | | | | | | | | | | | % 148.67/21.34 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (380), (549), (554), (4852), (4866), (4891), % 148.67/21.34 | | | | | | | | | | | | | | | | | | | (4933) are inconsistent by sub-proof #603. % 148.67/21.34 | | | | | | | | | | | | | | | | | | | % 148.67/21.34 | | | | | | | | | | | | | | | | | | End of split % 148.67/21.34 | | | | | | | | | | | | | | | | | | % 148.67/21.34 | | | | | | | | | | | | | | | | | Case 2: % 148.67/21.34 | | | | | | | | | | | | | | | | | | % 148.67/21.34 | | | | | | | | | | | | | | | | | | (4934) ~ (all_58_2 = e0) % 148.67/21.34 | | | | | | | | | | | | | | | | | | % 148.67/21.34 | | | | | | | | | | | | | | | | | | REF_CLOSE: (336), (340), (365), (380), (401), (419), (549), % 148.67/21.34 | | | | | | | | | | | | | | | | | | (553), (554), (555), (563), (4852), (4865), % 148.67/21.34 | | | | | | | | | | | | | | | | | | (4866), (4890), (4891), (4934) are inconsistent by % 148.67/21.34 | | | | | | | | | | | | | | | | | | sub-proof #602. % 148.67/21.34 | | | | | | | | | | | | | | | | | | % 148.67/21.34 | | | | | | | | | | | | | | | | | End of split % 148.67/21.34 | | | | | | | | | | | | | | | | | % 148.67/21.34 | | | | | | | | | | | | | | | | End of split % 148.67/21.34 | | | | | | | | | | | | | | | | % 148.67/21.34 | | | | | | | | | | | | | | | End of split % 148.67/21.34 | | | | | | | | | | | | | | | % 148.67/21.34 | | | | | | | | | | | | | | End of split % 148.67/21.34 | | | | | | | | | | | | | | % 148.67/21.34 | | | | | | | | | | | | | End of split % 148.67/21.34 | | | | | | | | | | | | | % 148.67/21.34 | | | | | | | | | | | | Case 2: % 148.67/21.34 | | | | | | | | | | | | | % 148.67/21.34 | | | | | | | | | | | | | (4935) all_56_31 = e3 % 148.67/21.34 | | | | | | | | | | | | | (4936) all_56_25 = e0 % 148.67/21.34 | | | | | | | | | | | | | % 148.67/21.34 | | | | | | | | | | | | | REF_CLOSE: (5), (6), (36), (38), (46), (48), (51), (173), % 148.67/21.34 | | | | | | | | | | | | | (188), (194), (196), (215), (239), (247), (248), % 148.67/21.34 | | | | | | | | | | | | | (252), (287), (294), (295), (296), (318), (319), % 148.67/21.34 | | | | | | | | | | | | | (335), (365), (374), (401), (425), (431), (447), % 148.67/21.34 | | | | | | | | | | | | | (463), (480), (528), (534), (542), (543), (544), % 148.67/21.34 | | | | | | | | | | | | | (545), (546), (547), (548), (549), (557), (568), % 148.67/21.34 | | | | | | | | | | | | | (575), (581), (585), (617), (639), (679), (769), % 148.67/21.34 | | | | | | | | | | | | | (4840), (4843), (4850), (4935), (4936), % 148.67/21.34 | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 148.67/21.34 | | | | | | | | | | | | | #243. % 148.67/21.34 | | | | | | | | | | | | | % 148.67/21.34 | | | | | | | | | | | | End of split % 148.67/21.34 | | | | | | | | | | | | % 148.67/21.34 | | | | | | | | | | | Case 2: % 148.67/21.34 | | | | | | | | | | | | % 148.67/21.34 | | | | | | | | | | | | (4937) all_56_31 = e1 % 148.67/21.34 | | | | | | | | | | | | (4938) all_56_29 = e0 % 148.67/21.34 | | | | | | | | | | | | % 148.67/21.34 | | | | | | | | | | | | COMBINE_EQS: (357), (4938) imply: % 148.67/21.34 | | | | | | | | | | | | (4939) all_52_11 = e0 % 148.67/21.34 | | | | | | | | | | | | % 148.67/21.34 | | | | | | | | | | | | SIMP: (4939) implies: % 148.67/21.34 | | | | | | | | | | | | (4940) all_52_11 = e0 % 148.67/21.34 | | | | | | | | | | | | % 148.67/21.34 | | | | | | | | | | | | COMBINE_EQS: (544), (4937) imply: % 148.67/21.34 | | | | | | | | | | | | (4941) all_4_2 = e1 % 148.67/21.34 | | | | | | | | | | | | % 148.67/21.34 | | | | | | | | | | | | REDUCE: (187), (4940) imply: % 148.67/21.34 | | | | | | | | | | | | (4942) ~ (all_52_3 = e0) % 148.67/21.34 | | | | | | | | | | | | % 148.67/21.34 | | | | | | | | | | | | REDUCE: (585), (4940) imply: % 148.67/21.34 | | | | | | | | | | | | (4943) ~ (all_6_2 = e0) % 148.67/21.34 | | | | | | | | | | | | % 148.67/21.34 | | | | | | | | | | | | SIMP: (4943) implies: % 148.67/21.34 | | | | | | | | | | | | (4944) ~ (all_6_2 = e0) % 148.67/21.34 | | | | | | | | | | | | % 148.67/21.34 | | | | | | | | | | | | REDUCE: (590), (4941) imply: % 148.67/21.34 | | | | | | | | | | | | (4945) ~ (all_52_13 = e1) % 148.67/21.34 | | | | | | | | | | | | % 148.67/21.34 | | | | | | | | | | | | REDUCE: (38), (4941) imply: % 148.67/21.34 | | | | | | | | | | | | (4946) op(e1, e1) = all_4_1 % 148.67/21.34 | | | | | | | | | | | | % 148.67/21.34 | | | | | | | | | | | | REF_CLOSE: (36), (37), (41), (42), (43), (46), (48), (51), % 148.67/21.34 | | | | | | | | | | | | (192), (207), (212), (215), (237), (240), (242), % 148.67/21.34 | | | | | | | | | | | | (247), (252), (292), (293), (294), (295), (296), % 148.67/21.34 | | | | | | | | | | | | (374), (381), (425), (435), (443), (478), (528), % 148.67/21.34 | | | | | | | | | | | | (534), (540), (541), (542), (543), (545), (557), % 148.67/21.34 | | | | | | | | | | | | (573), (580), (590), (617), (622), (639), (679), % 148.67/21.34 | | | | | | | | | | | | (767), (768), (769), (3728), (4840), (4843), % 148.67/21.34 | | | | | | | | | | | | (4845), (4847), (4850), (4942), (4944), (4945), % 148.67/21.34 | | | | | | | | | | | | (4946), (function-axioms) are inconsistent by % 148.67/21.34 | | | | | | | | | | | | sub-proof #232. % 148.67/21.34 | | | | | | | | | | | | % 148.67/21.34 | | | | | | | | | | | End of split % 148.67/21.34 | | | | | | | | | | | % 148.67/21.34 | | | | | | | | | | Case 2: % 148.67/21.34 | | | | | | | | | | | % 148.67/21.34 | | | | | | | | | | | (4947) all_56_11 = e0 % 148.67/21.34 | | | | | | | | | | | % 148.67/21.34 | | | | | | | | | | | REF_CLOSE: (6), (36), (48), (212), (237), (294), (443), % 148.67/21.34 | | | | | | | | | | | (528), (540), (545), (590), (617), (679), (769), % 148.67/21.34 | | | | | | | | | | | (4840), (4843), (4947), (function-axioms) are % 148.67/21.34 | | | | | | | | | | | inconsistent by sub-proof #156. % 148.67/21.34 | | | | | | | | | | | % 148.67/21.34 | | | | | | | | | | End of split % 148.67/21.34 | | | | | | | | | | % 148.67/21.34 | | | | | | | | | End of split % 148.67/21.34 | | | | | | | | | % 148.67/21.34 | | | | | | | | Case 2: % 148.67/21.34 | | | | | | | | | % 148.67/21.34 | | | | | | | | | (4948) all_36_1 = e3 % 148.67/21.34 | | | | | | | | | % 148.67/21.34 | | | | | | | | | COMBINE_EQS: (652), (4948) imply: % 148.67/21.34 | | | | | | | | | (4949) all_6_1 = e3 % 148.67/21.34 | | | | | | | | | % 148.67/21.34 | | | | | | | | | REF_CLOSE: (6), (36), (41), (42), (46), (48), (51), (134), % 148.67/21.34 | | | | | | | | | (197), (211), (212), (215), (237), (242), (247), % 148.67/21.34 | | | | | | | | | (252), (293), (294), (295), (296), (374), (381), % 148.67/21.34 | | | | | | | | | (425), (431), (443), (528), (534), (540), (541), % 148.67/21.34 | | | | | | | | | (542), (543), (545), (557), (579), (583), (590), % 148.67/21.34 | | | | | | | | | (617), (639), (679), (769), (4840), (4842), (4843), % 148.67/21.34 | | | | | | | | | (4949), (function-axioms) are inconsistent by % 148.67/21.34 | | | | | | | | | sub-proof #249. % 148.67/21.34 | | | | | | | | | % 148.67/21.34 | | | | | | | | End of split % 148.67/21.34 | | | | | | | | % 148.67/21.34 | | | | | | | Case 2: % 148.67/21.34 | | | | | | | | % 148.67/21.34 | | | | | | | | (4950) all_28_0 = e2 % 148.67/21.34 | | | | | | | | (4951) ~ (all_28_1 = e3) | ~ (all_28_2 = e0) % 148.67/21.34 | | | | | | | | % 148.67/21.34 | | | | | | | | COMBINE_EQS: (740), (4950) imply: % 148.67/21.34 | | | | | | | | (4952) all_6_0 = e2 % 148.67/21.34 | | | | | | | | % 148.67/21.34 | | | | | | | | SIMP: (4952) implies: % 148.67/21.34 | | | | | | | | (4953) all_6_0 = e2 % 148.67/21.34 | | | | | | | | % 148.67/21.34 | | | | | | | | REF_CLOSE: (6), (8), (36), (37), (38), (41), (42), (43), (46), % 148.67/21.34 | | | | | | | | (51), (144), (158), (173), (174), (176), (187), % 148.67/21.34 | | | | | | | | (192), (206), (207), (208), (211), (237), (239), % 148.67/21.34 | | | | | | | | (240), (242), (247), (252), (288), (289), (290), % 148.67/21.34 | | | | | | | | (291), (292), (293), (294), (297), (321), (341), % 148.67/21.34 | | | | | | | | (357), (366), (374), (381), (386), (402), (407), % 148.67/21.34 | | | | | | | | (419), (435), (443), (475), (478), (480), (513), % 148.67/21.34 | | | | | | | | (540), (541), (542), (543), (544), (545), (546), % 148.67/21.34 | | | | | | | | (547), (550), (551), (555), (559), (569), (571), % 148.67/21.34 | | | | | | | | (573), (580), (585), (620), (622), (627), (634), % 148.67/21.34 | | | | | | | | (665), (764), (767), (768), (3728), (4951), (4953), % 148.67/21.34 | | | | | | | | (function-axioms) are inconsistent by sub-proof #364. % 148.67/21.34 | | | | | | | | % 148.67/21.34 | | | | | | | End of split % 148.67/21.34 | | | | | | | % 148.67/21.34 | | | | | | End of split % 148.67/21.34 | | | | | | % 148.67/21.34 | | | | | Case 2: % 148.67/21.34 | | | | | | % 148.67/21.34 | | | | | | (4954) all_12_0 = e2 % 148.67/21.34 | | | | | | (4955) ~ (all_12_1 = e1) | ~ (all_12_2 = e3) % 148.67/21.34 | | | | | | % 148.67/21.34 | | | | | | COMBINE_EQS: (759), (4954) imply: % 148.67/21.34 | | | | | | (4956) all_4_0 = e2 % 148.67/21.34 | | | | | | % 148.67/21.34 | | | | | | COMBINE_EQS: (734), (4956) imply: % 148.67/21.34 | | | | | | (4957) all_34_0 = e2 % 148.67/21.34 | | | | | | % 148.67/21.34 | | | | | | REDUCE: (767), (4956) imply: % 148.67/21.34 | | | | | | (4958) ~ (e3 = e2) % 148.67/21.34 | | | | | | % 148.67/21.34 | | | | | | REDUCE: (37), (4956) imply: % 148.67/21.34 | | | | | | (4959) op(e0, all_4_1) = e2 % 148.67/21.34 | | | | | | % 148.67/21.34 | | | | | | BETA: splitting (64) gives: % 148.67/21.34 | | | | | | % 148.67/21.34 | | | | | | Case 1: % 148.67/21.34 | | | | | | | % 148.67/21.34 | | | | | | | (4960) ~ (all_14_0 = e1) % 148.67/21.34 | | | | | | | % 148.67/21.34 | | | | | | | REDUCE: (758), (4960) imply: % 148.67/21.34 | | | | | | | (4961) ~ (all_8_0 = e1) % 148.67/21.34 | | | | | | | % 148.67/21.34 | | | | | | | BETA: splitting (84) gives: % 148.67/21.34 | | | | | | | % 148.67/21.34 | | | | | | | Case 1: % 148.67/21.34 | | | | | | | | % 148.67/21.34 | | | | | | | | (4962) ~ (all_22_1 = e3) % 148.67/21.34 | | | | | | | | % 148.67/21.34 | | | | | | | | REDUCE: (672), (4962) imply: % 148.67/21.34 | | | | | | | | (4963) ~ (all_8_1 = e3) % 148.67/21.34 | | | | | | | | % 148.67/21.34 | | | | | | | | BETA: splitting (99) gives: % 148.67/21.34 | | | | | | | | % 148.67/21.34 | | | | | | | | Case 1: % 148.67/21.34 | | | | | | | | | % 148.67/21.34 | | | | | | | | | (4964) ~ (all_28_0 = e2) % 148.67/21.34 | | | | | | | | | % 148.67/21.34 | | | | | | | | | REDUCE: (740), (4964) imply: % 148.67/21.34 | | | | | | | | | (4965) ~ (all_6_0 = e2) % 148.67/21.34 | | | | | | | | | % 148.67/21.34 | | | | | | | | | BETA: splitting (114) gives: % 148.67/21.34 | | | | | | | | | % 148.67/21.34 | | | | | | | | | Case 1: % 148.67/21.34 | | | | | | | | | | % 148.67/21.34 | | | | | | | | | | (4966) ~ (all_34_0 = e2) % 148.67/21.34 | | | | | | | | | | % 148.67/21.34 | | | | | | | | | | REDUCE: (4957), (4966) imply: % 148.67/21.34 | | | | | | | | | | (4967) $false % 148.67/21.34 | | | | | | | | | | % 148.67/21.35 | | | | | | | | | | CLOSE: (4967) is inconsistent. % 148.67/21.35 | | | | | | | | | | % 148.67/21.35 | | | | | | | | | Case 2: % 148.67/21.35 | | | | | | | | | | % 148.67/21.35 | | | | | | | | | | (4968) ~ (all_34_1 = e3) | ~ (all_34_2 = e1) % 148.67/21.35 | | | | | | | | | | % 148.67/21.35 | | | | | | | | | | BETA: splitting (119) gives: % 148.67/21.35 | | | | | | | | | | % 148.67/21.35 | | | | | | | | | | Case 1: % 148.67/21.35 | | | | | | | | | | | % 148.67/21.35 | | | | | | | | | | | (4969) ~ (all_36_1 = e3) % 148.67/21.35 | | | | | | | | | | | % 148.67/21.35 | | | | | | | | | | | REDUCE: (652), (4969) imply: % 148.67/21.35 | | | | | | | | | | | (4970) ~ (all_6_1 = e3) % 148.67/21.35 | | | | | | | | | | | % 148.67/21.35 | | | | | | | | | | | BETA: splitting (129) gives: % 148.67/21.35 | | | | | | | | | | | % 148.67/21.35 | | | | | | | | | | | Case 1: % 148.67/21.35 | | | | | | | | | | | | % 148.67/21.35 | | | | | | | | | | | | (4971) ~ (all_40_0 = e3) % 148.67/21.35 | | | | | | | | | | | | % 148.67/21.35 | | | | | | | | | | | | REDUCE: (713), (4971) imply: % 148.67/21.35 | | | | | | | | | | | | (4972) ~ (all_6_0 = e3) % 148.67/21.35 | | | | | | | | | | | | % 148.67/21.35 | | | | | | | | | | | | BETA: splitting (292) gives: % 148.67/21.35 | | | | | | | | | | | | % 148.67/21.35 | | | | | | | | | | | | Case 1: % 148.67/21.35 | | | | | | | | | | | | | % 148.67/21.35 | | | | | | | | | | | | | (4973) ~ (all_56_21 = e2) % 148.67/21.35 | | | | | | | | | | | | | % 148.67/21.35 | | | | | | | | | | | | | REDUCE: (374), (4973) imply: % 148.67/21.35 | | | | | | | | | | | | | (4974) ~ (all_6_2 = e2) % 148.67/21.35 | | | | | | | | | | | | | % 148.67/21.35 | | | | | | | | | | | | | REF_CLOSE: (5), (7), (9), (36), (38), (41), (42), (43), (46), % 148.67/21.35 | | | | | | | | | | | | | (47), (48), (51), (53), (158), (160), (161), % 148.67/21.35 | | | | | | | | | | | | | (165), (166), (168), (169), (171), (173), (174), % 148.67/21.35 | | | | | | | | | | | | | (176), (181), (182), (183), (187), (189), (191), % 148.67/21.35 | | | | | | | | | | | | | (192), (193), (194), (196), (197), (205), (206), % 148.67/21.35 | | | | | | | | | | | | | (208), (212), (217), (218), (237), (238), (239), % 148.67/21.35 | | | | | | | | | | | | | (241), (242), (243), (244), (245), (247), (248), % 148.67/21.35 | | | | | | | | | | | | | (251), (252), (287), (288), (289), (290), (291), % 148.67/21.35 | | | | | | | | | | | | | (293), (294), (295), (296), (297), (298), (299), % 148.67/21.35 | | | | | | | | | | | | | (318), (321), (322), (324), (326), (327), (330), % 148.67/21.35 | | | | | | | | | | | | | (331), (332), (333), (337), (341), (342), (344), % 148.67/21.35 | | | | | | | | | | | | | (346), (357), (360), (365), (366), (374), (380), % 148.67/21.35 | | | | | | | | | | | | | (381), (386), (389), (401), (402), (407), (408), % 148.67/21.35 | | | | | | | | | | | | | (419), (425), (429), (431), (443), (447), (457), % 148.67/21.35 | | | | | | | | | | | | | (463), (469), (471), (473), (476), (480), (482), % 148.67/21.35 | | | | | | | | | | | | | (529), (531), (540), (541), (542), (543), (544), % 148.67/21.35 | | | | | | | | | | | | | (545), (546), (547), (548), (549), (550), (551), % 148.67/21.35 | | | | | | | | | | | | | (552), (553), (554), (555), (557), (559), (561), % 148.67/21.35 | | | | | | | | | | | | | (563), (565), (567), (568), (569), (570), (571), % 148.67/21.35 | | | | | | | | | | | | | (573), (575), (577), (579), (580), (581), (582), % 148.67/21.35 | | | | | | | | | | | | | (583), (585), (587), (588), (590), (591), (612), % 148.67/21.35 | | | | | | | | | | | | | (614), (615), (617), (621), (622), (625), (626), % 148.67/21.35 | | | | | | | | | | | | | (627), (681), (683), (768), (769), (3724), (3726), % 148.67/21.35 | | | | | | | | | | | | | (4955), (4959), (4961), (4963), (4965), (4968), % 148.67/21.35 | | | | | | | | | | | | | (4970), (4974), (function-axioms) are inconsistent % 148.67/21.35 | | | | | | | | | | | | | by sub-proof #150. % 148.67/21.35 | | | | | | | | | | | | | % 148.67/21.35 | | | | | | | | | | | | Case 2: % 148.67/21.35 | | | | | | | | | | | | | % 148.67/21.35 | | | | | | | | | | | | | (4975) all_56_21 = e2 % 148.67/21.35 | | | | | | | | | | | | | (4976) all_56_19 = e1 % 148.67/21.35 | | | | | | | | | | | | | % 148.67/21.35 | | | | | | | | | | | | | COMBINE_EQS: (435), (4976) imply: % 148.67/21.35 | | | | | | | | | | | | | (4977) all_52_6 = e1 % 148.67/21.35 | | | | | | | | | | | | | % 148.67/21.35 | | | | | | | | | | | | | COMBINE_EQS: (374), (4975) imply: % 148.67/21.35 | | | | | | | | | | | | | (4978) all_6_2 = e2 % 148.67/21.35 | | | | | | | | | | | | | % 148.67/21.35 | | | | | | | | | | | | | SIMP: (4978) implies: % 148.67/21.35 | | | | | | | | | | | | | (4979) all_6_2 = e2 % 148.67/21.35 | | | | | | | | | | | | | % 148.67/21.35 | | | | | | | | | | | | | REF_CLOSE: (8), (9), (36), (42), (43), (46), (48), (174), % 148.67/21.35 | | | | | | | | | | | | | (208), (247), (289), (294), (297), (321), (323), % 148.67/21.35 | | | | | | | | | | | | | (341), (360), (386), (402), (407), (419), (443), % 148.67/21.35 | | | | | | | | | | | | | (542), (545), (546), (547), (550), (551), (555), % 148.67/21.35 | | | | | | | | | | | | | (571), (573), (575), (580), (620), (768), (769), % 148.67/21.35 | | | | | | | | | | | | | (4963), (4970), (4972), (4977), (4979), % 148.67/21.35 | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 148.67/21.35 | | | | | | | | | | | | | #209. % 148.67/21.35 | | | | | | | | | | | | | % 148.67/21.35 | | | | | | | | | | | | End of split % 148.67/21.35 | | | | | | | | | | | | % 148.67/21.35 | | | | | | | | | | | Case 2: % 148.67/21.35 | | | | | | | | | | | | % 148.67/21.35 | | | | | | | | | | | | (4980) all_40_0 = e3 % 148.67/21.35 | | | | | | | | | | | | (4981) ~ (all_40_1 = e0) | ~ (all_40_2 = e2) % 148.67/21.35 | | | | | | | | | | | | % 148.67/21.35 | | | | | | | | | | | | COMBINE_EQS: (713), (4980) imply: % 148.67/21.35 | | | | | | | | | | | | (4982) all_6_0 = e3 % 148.67/21.35 | | | | | | | | | | | | % 148.67/21.35 | | | | | | | | | | | | SIMP: (4982) implies: % 148.67/21.35 | | | | | | | | | | | | (4983) all_6_0 = e3 % 148.67/21.35 | | | | | | | | | | | | % 148.67/21.35 | | | | | | | | | | | | BETA: splitting (292) gives: % 148.67/21.35 | | | | | | | | | | | | % 148.67/21.35 | | | | | | | | | | | | Case 1: % 148.67/21.35 | | | | | | | | | | | | | % 148.67/21.35 | | | | | | | | | | | | | (4984) ~ (all_56_21 = e2) % 148.67/21.35 | | | | | | | | | | | | | % 148.67/21.35 | | | | | | | | | | | | | REDUCE: (374), (4984) imply: % 148.67/21.35 | | | | | | | | | | | | | (4985) ~ (all_6_2 = e2) % 148.67/21.35 | | | | | | | | | | | | | % 148.67/21.35 | | | | | | | | | | | | | REF_CLOSE: (5), (7), (9), (36), (38), (41), (42), (43), (46), % 148.67/21.35 | | | | | | | | | | | | | (47), (48), (51), (53), (158), (160), (161), % 148.67/21.35 | | | | | | | | | | | | | (165), (166), (168), (169), (171), (173), (174), % 148.67/21.35 | | | | | | | | | | | | | (176), (181), (182), (183), (187), (189), (191), % 148.67/21.35 | | | | | | | | | | | | | (192), (193), (194), (196), (197), (205), (206), % 148.67/21.35 | | | | | | | | | | | | | (208), (212), (217), (218), (237), (238), (239), % 148.67/21.35 | | | | | | | | | | | | | (241), (242), (243), (244), (245), (247), (248), % 148.67/21.35 | | | | | | | | | | | | | (251), (252), (287), (288), (289), (290), (291), % 148.67/21.35 | | | | | | | | | | | | | (293), (294), (295), (296), (297), (298), (299), % 148.67/21.35 | | | | | | | | | | | | | (318), (321), (322), (324), (326), (327), (330), % 148.67/21.35 | | | | | | | | | | | | | (331), (332), (333), (337), (341), (342), (344), % 148.67/21.35 | | | | | | | | | | | | | (346), (357), (360), (365), (366), (374), (380), % 148.67/21.35 | | | | | | | | | | | | | (381), (386), (389), (401), (402), (407), (408), % 148.67/21.35 | | | | | | | | | | | | | (419), (425), (429), (431), (443), (447), (457), % 148.67/21.35 | | | | | | | | | | | | | (463), (469), (471), (473), (476), (480), (482), % 148.67/21.35 | | | | | | | | | | | | | (529), (531), (540), (541), (542), (543), (544), % 148.67/21.35 | | | | | | | | | | | | | (545), (546), (547), (548), (549), (550), (551), % 148.67/21.35 | | | | | | | | | | | | | (552), (553), (554), (555), (557), (559), (561), % 148.67/21.35 | | | | | | | | | | | | | (563), (565), (567), (568), (569), (570), (571), % 148.67/21.35 | | | | | | | | | | | | | (573), (575), (577), (579), (580), (581), (582), % 148.67/21.35 | | | | | | | | | | | | | (583), (585), (587), (588), (590), (591), (612), % 148.67/21.35 | | | | | | | | | | | | | (614), (615), (617), (621), (622), (625), (626), % 148.67/21.35 | | | | | | | | | | | | | (627), (681), (683), (768), (769), (3724), (3726), % 148.67/21.35 | | | | | | | | | | | | | (4955), (4959), (4961), (4963), (4965), (4968), % 148.67/21.35 | | | | | | | | | | | | | (4970), (4985), (function-axioms) are inconsistent % 148.67/21.35 | | | | | | | | | | | | | by sub-proof #150. % 148.67/21.35 | | | | | | | | | | | | | % 148.67/21.35 | | | | | | | | | | | | Case 2: % 148.67/21.35 | | | | | | | | | | | | | % 148.67/21.35 | | | | | | | | | | | | | (4986) all_56_21 = e2 % 148.67/21.35 | | | | | | | | | | | | | (4987) all_56_19 = e1 % 148.67/21.35 | | | | | | | | | | | | | % 148.67/21.35 | | | | | | | | | | | | | COMBINE_EQS: (435), (4987) imply: % 148.67/21.35 | | | | | | | | | | | | | (4988) all_52_6 = e1 % 148.67/21.35 | | | | | | | | | | | | | % 148.67/21.35 | | | | | | | | | | | | | COMBINE_EQS: (374), (4986) imply: % 148.67/21.35 | | | | | | | | | | | | | (4989) all_6_2 = e2 % 148.67/21.35 | | | | | | | | | | | | | % 148.67/21.35 | | | | | | | | | | | | | REF_CLOSE: (43), (46), (247), (507), (542), (573), (685), % 148.67/21.35 | | | | | | | | | | | | | (768), (4970), (4981), (4988), (4989), % 148.67/21.35 | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 148.67/21.35 | | | | | | | | | | | | | #506. % 148.67/21.35 | | | | | | | | | | | | | % 148.67/21.35 | | | | | | | | | | | | End of split % 148.67/21.35 | | | | | | | | | | | | % 148.67/21.35 | | | | | | | | | | | End of split % 148.67/21.35 | | | | | | | | | | | % 148.67/21.35 | | | | | | | | | | Case 2: % 148.67/21.35 | | | | | | | | | | | % 148.67/21.35 | | | | | | | | | | | (4990) all_36_1 = e3 % 148.67/21.35 | | | | | | | | | | | (4991) ~ (all_36_0 = e0) | ~ (all_36_2 = e2) % 148.67/21.35 | | | | | | | | | | | % 148.67/21.35 | | | | | | | | | | | COMBINE_EQS: (652), (4990) imply: % 148.67/21.35 | | | | | | | | | | | (4992) all_6_1 = e3 % 148.67/21.35 | | | | | | | | | | | % 148.67/21.35 | | | | | | | | | | | SIMP: (4992) implies: % 148.67/21.35 | | | | | | | | | | | (4993) all_6_1 = e3 % 148.67/21.35 | | | | | | | | | | | % 148.67/21.35 | | | | | | | | | | | REDUCE: (43), (4993) imply: % 148.67/21.35 | | | | | | | | | | | (4994) op(all_6_2, all_6_2) = e3 % 148.67/21.35 | | | | | | | | | | | % 148.67/21.35 | | | | | | | | | | | REDUCE: (42), (4993) imply: % 148.67/21.35 | | | | | | | | | | | (4995) op(e1, e3) = all_6_0 % 148.67/21.35 | | | | | | | | | | | % 148.67/21.35 | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_2, % 148.67/21.35 | | | | | | | | | | | all_6_0, e3, e1, simplifying with (211), (4995) % 148.67/21.35 | | | | | | | | | | | gives: % 148.67/21.35 | | | | | | | | | | | (4996) all_52_2 = all_6_0 % 148.67/21.35 | | | | | | | | | | | % 148.67/21.35 | | | | | | | | | | | COMBINE_EQS: (471), (4996) imply: % 148.67/21.35 | | | | | | | | | | | (4997) all_54_8 = all_6_0 % 148.67/21.35 | | | | | | | | | | | % 148.67/21.35 | | | | | | | | | | | COMBINE_EQS: (381), (4996) imply: % 148.67/21.35 | | | | | | | | | | | (4998) all_56_17 = all_6_0 % 148.67/21.35 | | | | | | | | | | | % 148.67/21.35 | | | | | | | | | | | COMBINE_EQS: (553), (4996) imply: % 148.67/21.35 | | | | | | | | | | | (4999) all_58_6 = all_6_0 % 148.67/21.35 | | | | | | | | | | | % 148.67/21.35 | | | | | | | | | | | REDUCE: (192), (4996) imply: % 148.67/21.35 | | | | | | | | | | | (5000) ~ (all_52_3 = all_6_0) % 148.67/21.35 | | | | | | | | | | | % 148.67/21.35 | | | | | | | | | | | SIMP: (5000) implies: % 148.67/21.35 | | | | | | | | | | | (5001) ~ (all_52_3 = all_6_0) % 148.67/21.35 | | | | | | | | | | | % 148.67/21.35 | | | | | | | | | | | REDUCE: (191), (4996) imply: % 148.67/21.35 | | | | | | | | | | | (5002) ~ (all_52_6 = all_6_0) % 148.67/21.35 | | | | | | | | | | | % 148.67/21.35 | | | | | | | | | | | SIMP: (5002) implies: % 148.67/21.35 | | | | | | | | | | | (5003) ~ (all_52_6 = all_6_0) % 148.67/21.35 | | | | | | | | | | | % 148.67/21.35 | | | | | | | | | | | REDUCE: (189), (4996) imply: % 148.67/21.35 | | | | | | | | | | | (5004) ~ (all_52_14 = all_6_0) % 148.67/21.35 | | | | | | | | | | | % 148.67/21.35 | | | | | | | | | | | SIMP: (5004) implies: % 148.67/21.35 | | | | | | | | | | | (5005) ~ (all_52_14 = all_6_0) % 148.67/21.35 | | | | | | | | | | | % 148.67/21.35 | | | | | | | | | | | REDUCE: (559), (4996) imply: % 148.67/21.35 | | | | | | | | | | | (5006) ~ (all_10_2 = all_6_0) % 148.67/21.35 | | | | | | | | | | | % 148.67/21.35 | | | | | | | | | | | SIMP: (5006) implies: % 148.67/21.35 | | | | | | | | | | | (5007) ~ (all_10_2 = all_6_0) % 148.67/21.35 | | | | | | | | | | | % 148.67/21.35 | | | | | | | | | | | REDUCE: (569), (4996) imply: % 148.67/21.35 | | | | | | | | | | | (5008) ~ (all_6_0 = all_6_2) % 148.67/21.35 | | | | | | | | | | | % 148.67/21.35 | | | | | | | | | | | BETA: splitting (292) gives: % 148.67/21.35 | | | | | | | | | | | % 148.67/21.35 | | | | | | | | | | | Case 1: % 148.67/21.35 | | | | | | | | | | | | % 148.67/21.35 | | | | | | | | | | | | (5009) ~ (all_56_21 = e2) % 148.67/21.35 | | | | | | | | | | | | % 148.67/21.35 | | | | | | | | | | | | REDUCE: (374), (5009) imply: % 148.67/21.35 | | | | | | | | | | | | (5010) ~ (all_6_2 = e2) % 148.67/21.35 | | | | | | | | | | | | % 148.67/21.35 | | | | | | | | | | | | BETA: splitting (288) gives: % 148.67/21.35 | | | | | | | | | | | | % 148.67/21.35 | | | | | | | | | | | | Case 1: % 148.67/21.35 | | | | | | | | | | | | | % 148.67/21.35 | | | | | | | | | | | | | (5011) ~ (all_56_31 = e1) % 148.67/21.35 | | | | | | | | | | | | | % 148.67/21.35 | | | | | | | | | | | | | REDUCE: (544), (5011) imply: % 148.67/21.35 | | | | | | | | | | | | | (5012) ~ (all_4_2 = e1) % 148.67/21.35 | | | | | | | | | | | | | % 148.67/21.35 | | | | | | | | | | | | | BETA: splitting (294) gives: % 148.67/21.35 | | | | | | | | | | | | | % 148.67/21.35 | | | | | | | | | | | | | Case 1: % 148.67/21.35 | | | | | | | | | | | | | | % 148.67/21.35 | | | | | | | | | | | | | | (5013) ~ (all_56_11 = e0) % 148.67/21.35 | | | | | | | | | | | | | | % 148.67/21.35 | | | | | | | | | | | | | | REDUCE: (545), (5013) imply: % 148.67/21.35 | | | | | | | | | | | | | | (5014) ~ (all_8_2 = e0) % 148.67/21.35 | | | | | | | | | | | | | | % 148.67/21.35 | | | | | | | | | | | | | | BETA: splitting (290) gives: % 148.67/21.35 | | | | | | | | | | | | | | % 148.67/21.35 | | | | | | | | | | | | | | Case 1: % 148.67/21.35 | | | | | | | | | | | | | | | % 148.67/21.35 | | | | | | | | | | | | | | | (5015) ~ (all_56_31 = e3) % 148.67/21.35 | | | | | | | | | | | | | | | % 148.67/21.35 | | | | | | | | | | | | | | | REDUCE: (544), (5015) imply: % 148.67/21.35 | | | | | | | | | | | | | | | (5016) ~ (all_4_2 = e3) % 148.67/21.35 | | | | | | | | | | | | | | | % 148.67/21.35 | | | | | | | | | | | | | | | REF_CLOSE: (36), (38), (41), (48), (51), (168), (174), (181), % 148.67/21.35 | | | | | | | | | | | | | | | (242), (243), (244), (287), (291), (293), (295), % 148.67/21.35 | | | | | | | | | | | | | | | (320), (321), (323), (329), (337), (365), (366), % 148.67/21.35 | | | | | | | | | | | | | | | (374), (380), (389), (407), (431), (473), (541), % 148.67/21.35 | | | | | | | | | | | | | | | (544), (545), (546), (547), (548), (549), (550), % 148.67/21.35 | | | | | | | | | | | | | | | (551), (552), (554), (555), (561), (567), (573), % 148.67/21.35 | | | | | | | | | | | | | | | (575), (577), (580), (585), (587), (622), (623), % 148.67/21.35 | | | | | | | | | | | | | | | (627), (4963), (4965), (4994), (4997), (4998), % 148.67/21.35 | | | | | | | | | | | | | | | (5003), (5005), (5007), (5008), (5010), (5012), % 148.67/21.35 | | | | | | | | | | | | | | | (5016), (function-axioms) are inconsistent by % 148.67/21.35 | | | | | | | | | | | | | | | sub-proof #275. % 148.67/21.35 | | | | | | | | | | | | | | | % 148.67/21.35 | | | | | | | | | | | | | | Case 2: % 148.67/21.35 | | | | | | | | | | | | | | | % 148.67/21.35 | | | | | | | | | | | | | | | (5017) all_56_31 = e3 % 148.67/21.35 | | | | | | | | | | | | | | | (5018) all_56_25 = e0 % 148.67/21.35 | | | | | | | | | | | | | | | % 148.67/21.35 | | | | | | | | | | | | | | | COMBINE_EQS: (447), (5018) imply: % 148.67/21.35 | | | | | | | | | | | | | | | (5019) all_52_3 = e0 % 148.67/21.35 | | | | | | | | | | | | | | | % 148.67/21.35 | | | | | | | | | | | | | | | SIMP: (5019) implies: % 148.67/21.35 | | | | | | | | | | | | | | | (5020) all_52_3 = e0 % 148.67/21.35 | | | | | | | | | | | | | | | % 148.67/21.35 | | | | | | | | | | | | | | | COMBINE_EQS: (544), (5017) imply: % 148.67/21.35 | | | | | | | | | | | | | | | (5021) all_4_2 = e3 % 148.67/21.35 | | | | | | | | | | | | | | | % 148.67/21.35 | | | | | | | | | | | | | | | COMBINE_EQS: (365), (5020) imply: % 148.67/21.35 | | | | | | | | | | | | | | | (5022) all_58_12 = e0 % 148.67/21.35 | | | | | | | | | | | | | | | % 148.67/21.35 | | | | | | | | | | | | | | | REDUCE: (188), (5020) imply: % 148.67/21.35 | | | | | | | | | | | | | | | (5023) ~ (all_52_7 = e0) % 148.67/21.35 | | | | | | | | | | | | | | | % 148.67/21.35 | | | | | | | | | | | | | | | SIMP: (5023) implies: % 148.67/21.35 | | | | | | | | | | | | | | | (5024) ~ (all_52_7 = e0) % 148.67/21.35 | | | | | | | | | | | | | | | % 148.67/21.35 | | | | | | | | | | | | | | | REDUCE: (561), (5020) imply: % 148.67/21.35 | | | | | | | | | | | | | | | (5025) ~ (all_10_2 = e0) % 148.67/21.35 | | | | | | | | | | | | | | | % 148.67/21.35 | | | | | | | | | | | | | | | SIMP: (5025) implies: % 148.67/21.35 | | | | | | | | | | | | | | | (5026) ~ (all_10_2 = e0) % 148.67/21.35 | | | | | | | | | | | | | | | % 148.67/21.35 | | | | | | | | | | | | | | | REDUCE: (570), (5020), (5021) imply: % 148.67/21.35 | | | | | | | | | | | | | | | (5027) ~ (e3 = e0) % 148.67/21.35 | | | | | | | | | | | | | | | % 148.67/21.35 | | | | | | | | | | | | | | | REDUCE: (588), (5021) imply: % 148.67/21.35 | | | | | | | | | | | | | | | (5028) ~ (all_52_11 = e3) % 148.67/21.35 | | | | | | | | | | | | | | | % 148.67/21.35 | | | | | | | | | | | | | | | REDUCE: (38), (5021) imply: % 148.67/21.35 | | | | | | | | | | | | | | | (5029) op(e3, e3) = all_4_1 % 148.67/21.35 | | | | | | | | | | | | | | | % 148.67/21.35 | | | | | | | | | | | | | | | REDUCE: (627), (5021) imply: % 148.67/21.35 | | | | | | | | | | | | | | | (5030) op(e0, e3) = all_56_30 % 148.67/21.35 | | | | | | | | | | | | | | | % 148.67/21.35 | | | | | | | | | | | | | | | REDUCE: (207), (5020) imply: % 148.67/21.35 | | | | | | | | | | | | | | | (5031) op(e0, e3) = e0 % 148.67/21.35 | | | | | | | | | | | | | | | % 148.67/21.35 | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, % 148.67/21.35 | | | | | | | | | | | | | | | all_56_30, e3, e0, simplifying with (5030), (5031) % 148.67/21.35 | | | | | | | | | | | | | | | gives: % 148.67/21.35 | | | | | | | | | | | | | | | (5032) all_56_30 = e0 % 148.67/21.35 | | | | | | | | | | | | | | | % 148.67/21.35 | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_10_2, % 148.67/21.35 | | | | | | | | | | | | | | | all_4_1, e3, e3, simplifying with (51), (5029) % 148.67/21.35 | | | | | | | | | | | | | | | gives: % 148.67/21.35 | | | | | | | | | | | | | | | (5033) all_10_2 = all_4_1 % 148.67/21.35 | | | | | | | | | | | | | | | % 148.67/21.35 | | | | | | | | | | | | | | | COMBINE_EQS: (546), (5033) imply: % 148.67/21.35 | | | | | | | | | | | | | | | (5034) all_56_1 = all_4_1 % 148.67/21.35 | | | | | | | | | | | | | | | % 148.67/21.35 | | | | | | | | | | | | | | | COMBINE_EQS: (419), (5033) imply: % 148.67/21.35 | | | | | | | | | | | | | | | (5035) all_58_0 = all_4_1 % 148.67/21.35 | | | | | | | | | | | | | | | % 148.67/21.35 | | | | | | | | | | | | | | | REDUCE: (563), (5033) imply: % 148.67/21.35 | | | | | | | | | | | | | | | (5036) ~ (all_52_4 = all_4_1) % 148.67/21.35 | | | | | | | | | | | | | | | % 148.67/21.35 | | | | | | | | | | | | | | | REDUCE: (565), (5033) imply: % 148.67/21.35 | | | | | | | | | | | | | | | (5037) ~ (all_52_8 = all_4_1) % 148.67/21.35 | | | | | | | | | | | | | | | % 148.67/21.35 | | | | | | | | | | | | | | | REDUCE: (5026), (5033) imply: % 148.67/21.35 | | | | | | | | | | | | | | | (5038) ~ (all_4_1 = e0) % 148.67/21.35 | | | | | | | | | | | | | | | % 148.67/21.35 | | | | | | | | | | | | | | | BETA: splitting (295) gives: % 148.67/21.35 | | | | | | | | | | | | | | | % 148.67/21.35 | | | | | | | | | | | | | | | Case 1: % 148.67/21.35 | | | | | | | | | | | | | | | | % 148.67/21.35 | | | | | | | | | | | | | | | | (5039) ~ (all_56_11 = e1) % 148.67/21.35 | | | | | | | | | | | | | | | | % 148.67/21.35 | | | | | | | | | | | | | | | | REDUCE: (545), (5039) imply: % 148.67/21.35 | | | | | | | | | | | | | | | | (5040) ~ (all_8_2 = e1) % 148.67/21.35 | | | | | | | | | | | | | | | | % 148.67/21.35 | | | | | | | | | | | | | | | | BETA: splitting (293) gives: % 148.67/21.35 | | | | | | | | | | | | | | | | % 148.67/21.35 | | | | | | | | | | | | | | | | Case 1: % 148.67/21.35 | | | | | | | | | | | | | | | | | % 148.67/21.35 | | | | | | | | | | | | | | | | | (5041) ~ (all_56_21 = e3) % 148.67/21.35 | | | | | | | | | | | | | | | | | % 148.67/21.35 | | | | | | | | | | | | | | | | | REDUCE: (374), (5041) imply: % 148.67/21.35 | | | | | | | | | | | | | | | | | (5042) ~ (all_6_2 = e3) % 148.67/21.35 | | | | | | | | | | | | | | | | | % 148.67/21.35 | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (41), (242), (247), (287), (296), (299), % 148.67/21.35 | | | | | | | | | | | | | | | | | (331), (336), (344), (374), (380), (389), (401), % 148.67/21.35 | | | | | | | | | | | | | | | | | (407), (408), (425), (541), (542), (545), (548), % 148.67/21.35 | | | | | | | | | | | | | | | | | (549), (552), (554), (555), (568), (577), (580), % 148.67/21.35 | | | | | | | | | | | | | | | | | (622), (4965), (4994), (4999), (5010), (5014), % 148.67/21.35 | | | | | | | | | | | | | | | | | (5017), (5022), (5024), (5028), (5034), (5035), % 148.67/21.35 | | | | | | | | | | | | | | | | | (5036), (5037), (5038), (5040), (5042), % 148.67/21.35 | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 148.67/21.35 | | | | | | | | | | | | | | | | | #148. % 148.67/21.35 | | | | | | | | | | | | | | | | | % 148.67/21.35 | | | | | | | | | | | | | | | | Case 2: % 148.67/21.35 | | | | | | | | | | | | | | | | | % 148.67/21.35 | | | | | | | | | | | | | | | | | (5043) all_56_21 = e3 % 148.67/21.35 | | | | | | | | | | | | | | | | | % 148.67/21.35 | | | | | | | | | | | | | | | | | COMBINE_EQS: (374), (5043) imply: % 148.67/21.35 | | | | | | | | | | | | | | | | | (5044) all_6_2 = e3 % 148.67/21.35 | | | | | | | | | | | | | | | | | % 148.67/21.35 | | | | | | | | | | | | | | | | | SIMP: (5044) implies: % 148.67/21.35 | | | | | | | | | | | | | | | | | (5045) all_6_2 = e3 % 148.67/21.35 | | | | | | | | | | | | | | | | | % 148.67/21.35 | | | | | | | | | | | | | | | | | REDUCE: (4994), (5045) imply: % 148.67/21.35 | | | | | | | | | | | | | | | | | (5046) op(e3, e3) = e3 % 148.67/21.35 | | | | | | | | | | | | | | | | | % 148.67/21.35 | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (4959), (5029), (5030), (5031), (5046), % 148.67/21.35 | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 148.67/21.35 | | | | | | | | | | | | | | | | | #192. % 148.67/21.35 | | | | | | | | | | | | | | | | | % 148.67/21.35 | | | | | | | | | | | | | | | | End of split % 148.67/21.35 | | | | | | | | | | | | | | | | % 148.67/21.35 | | | | | | | | | | | | | | | Case 2: % 148.67/21.35 | | | | | | | | | | | | | | | | % 148.67/21.35 | | | | | | | | | | | | | | | | (5047) all_56_13 = e2 % 148.67/21.35 | | | | | | | | | | | | | | | | (5048) all_56_11 = e1 % 148.67/21.35 | | | | | | | | | | | | | | | | % 148.67/21.35 | | | | | | | | | | | | | | | | COMBINE_EQS: (545), (5048) imply: % 148.67/21.35 | | | | | | | | | | | | | | | | (5049) all_8_2 = e1 % 148.67/21.35 | | | | | | | | | | | | | | | | % 148.67/21.35 | | | | | | | | | | | | | | | | COMBINE_EQS: (431), (5047) imply: % 148.67/21.35 | | | | | | | | | | | | | | | | (5050) all_52_9 = e2 % 148.67/21.35 | | | | | | | | | | | | | | | | % 148.67/21.35 | | | | | | | | | | | | | | | | REDUCE: (194), (5050) imply: % 148.67/21.35 | | | | | | | | | | | | | | | | (5051) ~ (all_52_1 = e2) % 148.67/21.35 | | | | | | | | | | | | | | | | % 148.67/21.35 | | | | | | | | | | | | | | | | REDUCE: (568), (5049) imply: % 148.67/21.35 | | | | | | | | | | | | | | | | (5052) ~ (all_52_1 = e1) % 148.67/21.35 | | | | | | | | | | | | | | | | % 148.67/21.35 | | | | | | | | | | | | | | | | REDUCE: (583), (5050) imply: % 148.67/21.35 | | | | | | | | | | | | | | | | (5053) ~ (all_6_2 = e2) % 148.67/21.35 | | | | | | | | | | | | | | | | % 148.67/21.35 | | | | | | | | | | | | | | | | REDUCE: (48), (5049) imply: % 148.67/21.35 | | | | | | | | | | | | | | | | (5054) op(e1, e1) = all_8_1 % 148.67/21.35 | | | | | | | | | | | | | | | | % 148.67/21.35 | | | | | | | | | | | | | | | | REF_CLOSE: (6), (36), (38), (41), (174), (242), (243), (244), % 148.67/21.35 | | | | | | | | | | | | | | | | (287), (290), (291), (342), (344), (365), (366), % 148.67/21.35 | | | | | | | | | | | | | | | | (374), (401), (447), (473), (541), (544), (545), % 148.67/21.35 | | | | | | | | | | | | | | | | (546), (573), (580), (587), (622), (627), (769), % 148.67/21.35 | | | | | | | | | | | | | | | | (4963), (4965), (4994), (4997), (4999), (5001), % 148.67/21.35 | | | | | | | | | | | | | | | | (5003), (5005), (5007), (5008), (5010), (5051), % 148.67/21.35 | | | | | | | | | | | | | | | | (5052), (5054), (function-axioms) are inconsistent % 148.67/21.35 | | | | | | | | | | | | | | | | by sub-proof #186. % 148.67/21.35 | | | | | | | | | | | | | | | | % 148.67/21.35 | | | | | | | | | | | | | | | End of split % 148.67/21.35 | | | | | | | | | | | | | | | % 148.67/21.35 | | | | | | | | | | | | | | End of split % 148.67/21.35 | | | | | | | | | | | | | | % 148.67/21.35 | | | | | | | | | | | | | Case 2: % 148.67/21.35 | | | | | | | | | | | | | | % 148.67/21.35 | | | | | | | | | | | | | | (5055) all_56_15 = e2 % 148.67/21.35 | | | | | | | | | | | | | | (5056) all_56_11 = e0 % 148.67/21.35 | | | | | | | | | | | | | | % 148.67/21.35 | | | | | | | | | | | | | | REF_CLOSE: (4), (36), (38), (41), (46), (48), (51), (158), % 148.67/21.35 | | | | | | | | | | | | | | (168), (174), (181), (242), (243), (244), (287), % 148.67/21.35 | | | | | | | | | | | | | | (291), (292), (293), (295), (320), (321), (323), % 148.67/21.35 | | | | | | | | | | | | | | (324), (326), (329), (337), (365), (366), (374), % 148.67/21.35 | | | | | | | | | | | | | | (380), (389), (407), (431), (435), (443), (473), % 148.67/21.35 | | | | | | | | | | | | | | (532), (541), (544), (545), (546), (547), (548), % 148.67/21.35 | | | | | | | | | | | | | | (549), (550), (551), (552), (554), (555), (561), % 148.67/21.35 | | | | | | | | | | | | | | (567), (573), (575), (577), (580), (585), (587), % 148.67/21.35 | | | | | | | | | | | | | | (591), (617), (622), (623), (627), (762), (769), % 148.67/21.35 | | | | | | | | | | | | | | (4963), (4965), (4991), (4994), (4997), (4998), % 148.67/21.35 | | | | | | | | | | | | | | (4999), (5003), (5005), (5007), (5008), (5010), % 148.67/21.35 | | | | | | | | | | | | | | (5055), (5056), (function-axioms) are inconsistent % 148.67/21.35 | | | | | | | | | | | | | | by sub-proof #162. % 148.67/21.35 | | | | | | | | | | | | | | % 148.67/21.35 | | | | | | | | | | | | | End of split % 148.67/21.35 | | | | | | | | | | | | | % 148.67/21.35 | | | | | | | | | | | | Case 2: % 148.67/21.35 | | | | | | | | | | | | | % 148.67/21.35 | | | | | | | | | | | | | (5057) all_56_31 = e1 % 148.67/21.35 | | | | | | | | | | | | | (5058) all_56_29 = e0 % 148.67/21.35 | | | | | | | | | | | | | % 148.67/21.35 | | | | | | | | | | | | | REF_CLOSE: (38), (41), (46), (48), (242), (244), (287), % 148.67/21.35 | | | | | | | | | | | | | (292), (324), (357), (374), (380), (435), (531), % 148.67/21.35 | | | | | | | | | | | | | (532), (541), (544), (545), (546), (550), (552), % 148.67/21.35 | | | | | | | | | | | | | (580), (585), (588), (591), (617), (622), (683), % 148.67/21.35 | | | | | | | | | | | | | (762), (4968), (4991), (4994), (4997), (4999), % 148.67/21.35 | | | | | | | | | | | | | (5003), (5005), (5007), (5008), (5057), (5058), % 148.67/21.35 | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 148.67/21.35 | | | | | | | | | | | | | #205. % 148.67/21.35 | | | | | | | | | | | | | % 148.67/21.36 | | | | | | | | | | | | End of split % 148.67/21.36 | | | | | | | | | | | | % 148.67/21.36 | | | | | | | | | | | Case 2: % 148.67/21.36 | | | | | | | | | | | | % 148.67/21.36 | | | | | | | | | | | | (5059) all_56_21 = e2 % 148.67/21.36 | | | | | | | | | | | | (5060) all_56_19 = e1 % 148.67/21.36 | | | | | | | | | | | | % 148.67/21.36 | | | | | | | | | | | | REF_CLOSE: (4), (5), (46), (48), (244), (287), (324), (374), % 148.67/21.36 | | | | | | | | | | | | (380), (435), (532), (544), (545), (546), (550), % 148.67/21.36 | | | | | | | | | | | | (552), (580), (591), (617), (762), (4991), (4994), % 148.67/21.36 | | | | | | | | | | | | (4997), (4999), (5003), (5005), (5007), (5008), % 148.67/21.36 | | | | | | | | | | | | (5059), (5060), (function-axioms) are inconsistent % 148.67/21.36 | | | | | | | | | | | | by sub-proof #412. % 148.67/21.36 | | | | | | | | | | | | % 148.67/21.36 | | | | | | | | | | | End of split % 148.67/21.36 | | | | | | | | | | | % 148.67/21.36 | | | | | | | | | | End of split % 148.67/21.36 | | | | | | | | | | % 148.67/21.36 | | | | | | | | | End of split % 148.67/21.36 | | | | | | | | | % 148.67/21.36 | | | | | | | | Case 2: % 148.67/21.36 | | | | | | | | | % 148.67/21.36 | | | | | | | | | (5061) all_28_0 = e2 % 148.67/21.36 | | | | | | | | | (5062) ~ (all_28_1 = e3) | ~ (all_28_2 = e0) % 148.67/21.36 | | | | | | | | | % 148.67/21.36 | | | | | | | | | COMBINE_EQS: (740), (5061) imply: % 148.67/21.36 | | | | | | | | | (5063) all_6_0 = e2 % 148.67/21.36 | | | | | | | | | % 148.67/21.36 | | | | | | | | | REF_CLOSE: (6), (8), (36), (37), (38), (41), (42), (43), (46), % 148.67/21.36 | | | | | | | | | (48), (51), (144), (158), (169), (171), (174), % 148.67/21.36 | | | | | | | | | (208), (211), (237), (242), (247), (250), (252), % 148.67/21.36 | | | | | | | | | (287), (288), (289), (290), (291), (292), (293), % 148.67/21.36 | | | | | | | | | (294), (297), (321), (332), (333), (341), (357), % 148.67/21.36 | | | | | | | | | (366), (374), (381), (386), (389), (401), (402), % 148.67/21.36 | | | | | | | | | (407), (419), (435), (443), (459), (475), (513), % 148.67/21.36 | | | | | | | | | (540), (541), (542), (543), (544), (545), (546), % 148.67/21.36 | | | | | | | | | (547), (550), (551), (554), (555), (559), (565), % 148.67/21.36 | | | | | | | | | (568), (569), (571), (573), (580), (582), (585), % 148.67/21.36 | | | | | | | | | (588), (590), (620), (622), (627), (634), (665), % 148.67/21.36 | | | | | | | | | (764), (768), (769), (5062), (5063), % 148.67/21.36 | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 148.67/21.36 | | | | | | | | | #200. % 148.67/21.36 | | | | | | | | | % 148.67/21.36 | | | | | | | | End of split % 148.67/21.36 | | | | | | | | % 148.67/21.36 | | | | | | | Case 2: % 148.67/21.36 | | | | | | | | % 148.67/21.36 | | | | | | | | (5064) all_22_1 = e3 % 148.67/21.36 | | | | | | | | (5065) ~ (all_22_0 = e0) | ~ (all_22_2 = e1) % 148.67/21.36 | | | | | | | | % 148.67/21.36 | | | | | | | | REF_CLOSE: (4), (5), (6), (36), (37), (38), (41), (42), (43), % 148.67/21.36 | | | | | | | | (46), (47), (48), (51), (53), (99), (114), (119), % 148.67/21.36 | | | | | | | | (144), (158), (165), (166), (169), (171), (173), % 148.67/21.36 | | | | | | | | (174), (187), (189), (191), (193), (194), (196), % 148.67/21.36 | | | | | | | | (197), (205), (207), (208), (211), (215), (237), % 148.67/21.36 | | | | | | | | (238), (240), (241), (242), (243), (244), (245), % 148.67/21.36 | | | | | | | | (247), (248), (250), (252), (287), (288), (289), % 148.67/21.36 | | | | | | | | (290), (291), (292), (293), (294), (295), (296), % 148.67/21.36 | | | | | | | | (297), (298), (320), (321), (324), (329), (331), % 148.67/21.36 | | | | | | | | (332), (333), (341), (342), (357), (360), (365), % 148.67/21.36 | | | | | | | | (366), (374), (380), (381), (386), (389), (401), % 148.67/21.36 | | | | | | | | (402), (407), (419), (425), (429), (431), (435), % 148.67/21.36 | | | | | | | | (443), (447), (459), (463), (469), (471), (473), % 148.67/21.36 | | | | | | | | (475), (476), (478), (482), (513), (523), (529), % 148.67/21.36 | | | | | | | | (531), (532), (540), (541), (542), (543), (544), % 148.67/21.36 | | | | | | | | (545), (546), (547), (548), (549), (550), (551), % 148.67/21.36 | | | | | | | | (552), (553), (554), (555), (557), (559), (561), % 148.67/21.36 | | | | | | | | (565), (568), (569), (570), (571), (573), (575), % 148.67/21.36 | | | | | | | | (577), (579), (580), (582), (583), (585), (587), % 148.67/21.36 | | | | | | | | (588), (590), (591), (617), (620), (622), (624), % 148.67/21.36 | | | | | | | | (625), (627), (634), (652), (665), (672), (681), % 148.67/21.36 | | | | | | | | (683), (740), (752), (762), (764), (768), (769), % 148.67/21.36 | | | | | | | | (4955), (4957), (4959), (4961), (5064), (5065), % 148.67/21.36 | | | | | | | | (function-axioms) are inconsistent by sub-proof #178. % 148.67/21.36 | | | | | | | | % 148.67/21.36 | | | | | | | End of split % 148.67/21.36 | | | | | | | % 148.67/21.36 | | | | | | Case 2: % 148.67/21.36 | | | | | | | % 148.67/21.36 | | | | | | | (5066) all_14_0 = e1 % 148.67/21.36 | | | | | | | (5067) ~ (all_14_1 = e3) | ~ (all_14_2 = e0) % 148.67/21.36 | | | | | | | % 148.67/21.36 | | | | | | | REF_CLOSE: (5), (6), (36), (38), (41), (42), (43), (46), (47), % 148.67/21.36 | | | | | | | (48), (51), (114), (119), (134), (173), (188), (189), % 148.67/21.36 | | | | | | | (193), (194), (196), (197), (205), (211), (212), (215), % 148.67/21.36 | | | | | | | (237), (239), (242), (247), (248), (252), (287), (288), % 148.67/21.36 | | | | | | | (289), (290), (291), (292), (293), (294), (295), (296), % 148.67/21.36 | | | | | | | (318), (319), (321), (323), (332), (335), (357), (360), % 148.67/21.36 | | | | | | | (365), (374), (381), (386), (401), (425), (431), (435), % 148.67/21.36 | | | | | | | (443), (447), (463), (480), (528), (529), (531), (534), % 148.67/21.36 | | | | | | | (540), (541), (542), (543), (544), (545), (546), (547), % 148.67/21.36 | | | | | | | (548), (549), (550), (551), (557), (568), (569), (573), % 148.67/21.36 | | | | | | | (575), (579), (580), (581), (583), (585), (587), (590), % 148.67/21.36 | | | | | | | (617), (622), (627), (639), (652), (679), (683), (758), % 148.67/21.36 | | | | | | | (763), (768), (769), (4955), (4957), (4959), (5066), % 148.67/21.36 | | | | | | | (5067), (function-axioms) are inconsistent by sub-proof % 148.67/21.36 | | | | | | | #176. % 148.67/21.36 | | | | | | | % 148.67/21.36 | | | | | | End of split % 148.67/21.36 | | | | | | % 148.67/21.36 | | | | | End of split % 148.67/21.36 | | | | | % 148.67/21.36 | | | | End of split % 148.67/21.36 | | | | % 148.67/21.36 | | | Case 2: % 148.67/21.36 | | | | % 148.67/21.36 | | | | (5068) all_8_1 = e1 % 148.67/21.36 | | | | (5069) ~ (all_8_0 = e0) | ~ (all_8_2 = e3) % 148.67/21.36 | | | | % 148.67/21.36 | | | | COMBINE_EQS: (686), (5068) imply: % 148.67/21.36 | | | | (5070) all_48_1 = e1 % 148.67/21.36 | | | | % 148.67/21.36 | | | | REDUCE: (48), (5068) imply: % 148.67/21.36 | | | | (5071) op(all_8_2, all_8_2) = e1 % 148.67/21.36 | | | | % 148.67/21.36 | | | | REDUCE: (47), (5068) imply: % 148.67/21.36 | | | | (5072) op(e2, e1) = all_8_0 % 148.67/21.36 | | | | % 148.67/21.36 | | | | GROUND_INST: instantiating (function-axioms) with all_52_9, all_8_0, e1, % 148.67/21.36 | | | | e2, simplifying with (213), (5072) gives: % 148.67/21.36 | | | | (5073) all_52_9 = all_8_0 % 148.67/21.36 | | | | % 148.67/21.36 | | | | COMBINE_EQS: (467), (5073) imply: % 148.67/21.36 | | | | (5074) all_54_6 = all_8_0 % 148.67/21.36 | | | | % 148.67/21.36 | | | | COMBINE_EQS: (431), (5073) imply: % 148.67/21.36 | | | | (5075) all_56_13 = all_8_0 % 148.67/21.36 | | | | % 148.67/21.36 | | | | COMBINE_EQS: (389), (5073) imply: % 148.67/21.36 | | | | (5076) all_58_5 = all_8_0 % 148.67/21.36 | | | | % 148.67/21.36 | | | | REDUCE: (194), (5073) imply: % 148.67/21.36 | | | | (5077) ~ (all_52_1 = all_8_0) % 148.67/21.36 | | | | % 148.67/21.36 | | | | REDUCE: (171), (5073) imply: % 148.67/21.36 | | | | (5078) ~ (all_52_8 = all_8_0) % 148.67/21.36 | | | | % 148.67/21.36 | | | | REDUCE: (166), (5073) imply: % 148.67/21.36 | | | | (5079) ~ (all_52_11 = all_8_0) % 148.67/21.36 | | | | % 148.67/21.36 | | | | SIMP: (5079) implies: % 148.67/21.36 | | | | (5080) ~ (all_52_11 = all_8_0) % 148.67/21.36 | | | | % 148.67/21.36 | | | | REDUCE: (165), (5073) imply: % 148.67/21.36 | | | | (5081) ~ (all_52_13 = all_8_0) % 148.67/21.36 | | | | % 148.67/21.36 | | | | SIMP: (5081) implies: % 148.67/21.36 | | | | (5082) ~ (all_52_13 = all_8_0) % 148.67/21.36 | | | | % 148.67/21.36 | | | | REDUCE: (577), (5073) imply: % 148.67/21.36 | | | | (5083) ~ (all_8_0 = all_8_2) % 148.67/21.36 | | | | % 148.67/21.36 | | | | REDUCE: (583), (5073) imply: % 148.67/21.36 | | | | (5084) ~ (all_8_0 = all_6_2) % 148.67/21.36 | | | | % 148.67/21.36 | | | | REDUCE: (621), (5073) imply: % 148.67/21.36 | | | | (5085) op(e1, all_8_0) = all_56_12 % 148.67/21.36 | | | | % 148.67/21.36 | | | | BETA: splitting (54) gives: % 148.67/21.36 | | | | % 148.67/21.36 | | | | Case 1: % 148.67/21.36 | | | | | % 148.67/21.36 | | | | | (5086) ~ (all_10_0 = e2) % 148.67/21.36 | | | | | % 148.67/21.36 | | | | | BETA: splitting (59) gives: % 148.67/21.36 | | | | | % 148.67/21.36 | | | | | Case 1: % 148.67/21.36 | | | | | | % 148.67/21.36 | | | | | | (5087) ~ (all_12_0 = e2) % 148.67/21.36 | | | | | | % 148.67/21.36 | | | | | | REDUCE: (759), (5087) imply: % 148.67/21.36 | | | | | | (5088) ~ (all_4_0 = e2) % 148.67/21.36 | | | | | | % 148.67/21.36 | | | | | | BETA: splitting (69) gives: % 148.67/21.36 | | | | | | % 148.67/21.36 | | | | | | Case 1: % 148.67/21.36 | | | | | | | % 148.67/21.36 | | | | | | | (5089) ~ (all_16_0 = e1) % 148.67/21.36 | | | | | | | % 148.67/21.36 | | | | | | | REDUCE: (757), (5089) imply: % 148.67/21.36 | | | | | | | (5090) ~ (all_10_0 = e1) % 148.67/21.36 | | | | | | | % 148.67/21.36 | | | | | | | BETA: splitting (94) gives: % 148.67/21.36 | | | | | | | % 148.67/21.36 | | | | | | | Case 1: % 148.67/21.36 | | | | | | | | % 148.67/21.36 | | | | | | | | (5091) ~ (all_26_0 = e1) % 148.67/21.36 | | | | | | | | % 148.67/21.36 | | | | | | | | REDUCE: (760), (5091) imply: % 148.67/21.36 | | | | | | | | (5092) ~ (all_4_0 = e1) % 148.67/21.36 | | | | | | | | % 148.67/21.36 | | | | | | | | BETA: splitting (99) gives: % 148.67/21.36 | | | | | | | | % 148.67/21.36 | | | | | | | | Case 1: % 148.67/21.36 | | | | | | | | | % 148.67/21.36 | | | | | | | | | (5093) ~ (all_28_0 = e2) % 148.67/21.36 | | | | | | | | | % 148.67/21.36 | | | | | | | | | REDUCE: (740), (5093) imply: % 148.67/21.36 | | | | | | | | | (5094) ~ (all_6_0 = e2) % 148.67/21.36 | | | | | | | | | % 148.67/21.36 | | | | | | | | | BETA: splitting (109) gives: % 148.67/21.36 | | | | | | | | | % 148.67/21.36 | | | | | | | | | Case 1: % 148.67/21.36 | | | | | | | | | | % 148.67/21.36 | | | | | | | | | | (5095) ~ (all_32_1 = e1) % 148.67/21.36 | | | | | | | | | | % 148.67/21.36 | | | | | | | | | | REDUCE: (682), (5095) imply: % 148.67/21.36 | | | | | | | | | | (5096) ~ (all_10_1 = e1) % 148.67/21.36 | | | | | | | | | | % 148.67/21.36 | | | | | | | | | | BETA: splitting (119) gives: % 148.67/21.36 | | | | | | | | | | % 148.67/21.36 | | | | | | | | | | Case 1: % 148.67/21.36 | | | | | | | | | | | % 148.67/21.36 | | | | | | | | | | | (5097) ~ (all_36_1 = e3) % 148.67/21.36 | | | | | | | | | | | % 148.67/21.36 | | | | | | | | | | | REDUCE: (652), (5097) imply: % 148.67/21.36 | | | | | | | | | | | (5098) ~ (all_6_1 = e3) % 148.67/21.36 | | | | | | | | | | | % 148.67/21.36 | | | | | | | | | | | BETA: splitting (149) gives: % 148.67/21.36 | | | | | | | | | | | % 148.67/21.36 | | | | | | | | | | | Case 1: % 148.67/21.36 | | | | | | | | | | | | % 148.67/21.36 | | | | | | | | | | | | (5099) ~ (all_48_0 = e3) % 148.67/21.36 | | | | | | | | | | | | % 148.67/21.36 | | | | | | | | | | | | REDUCE: (765), (5099) imply: % 148.67/21.36 | | | | | | | | | | | | (5100) ~ (all_8_0 = e3) % 148.67/21.36 | | | | | | | | | | | | % 148.67/21.36 | | | | | | | | | | | | BETA: splitting (292) gives: % 148.67/21.36 | | | | | | | | | | | | % 148.67/21.36 | | | | | | | | | | | | Case 1: % 148.67/21.36 | | | | | | | | | | | | | % 148.67/21.36 | | | | | | | | | | | | | (5101) ~ (all_56_21 = e2) % 148.67/21.36 | | | | | | | | | | | | | % 148.67/21.36 | | | | | | | | | | | | | REDUCE: (374), (5101) imply: % 148.67/21.36 | | | | | | | | | | | | | (5102) ~ (all_6_2 = e2) % 148.67/21.36 | | | | | | | | | | | | | % 148.67/21.36 | | | | | | | | | | | | | BETA: splitting (288) gives: % 148.67/21.36 | | | | | | | | | | | | | % 148.67/21.36 | | | | | | | | | | | | | Case 1: % 148.67/21.36 | | | | | | | | | | | | | | % 148.67/21.36 | | | | | | | | | | | | | | (5103) ~ (all_56_31 = e1) % 148.67/21.36 | | | | | | | | | | | | | | % 148.67/21.36 | | | | | | | | | | | | | | REDUCE: (544), (5103) imply: % 148.67/21.36 | | | | | | | | | | | | | | (5104) ~ (all_4_2 = e1) % 148.67/21.36 | | | | | | | | | | | | | | % 148.67/21.36 | | | | | | | | | | | | | | BETA: splitting (290) gives: % 148.67/21.36 | | | | | | | | | | | | | | % 148.67/21.36 | | | | | | | | | | | | | | Case 1: % 148.67/21.36 | | | | | | | | | | | | | | | % 148.67/21.36 | | | | | | | | | | | | | | | (5105) ~ (all_56_31 = e3) % 148.67/21.36 | | | | | | | | | | | | | | | % 148.67/21.36 | | | | | | | | | | | | | | | REDUCE: (544), (5105) imply: % 148.67/21.36 | | | | | | | | | | | | | | | (5106) ~ (all_4_2 = e3) % 148.67/21.36 | | | | | | | | | | | | | | | % 148.67/21.36 | | | | | | | | | | | | | | | BETA: splitting (291) gives: % 148.67/21.36 | | | | | | | | | | | | | | | % 148.67/21.36 | | | | | | | | | | | | | | | Case 1: % 148.67/21.36 | | | | | | | | | | | | | | | | % 148.67/21.36 | | | | | | | | | | | | | | | | (5107) ~ (all_56_21 = e0) % 148.67/21.36 | | | | | | | | | | | | | | | | % 148.67/21.36 | | | | | | | | | | | | | | | | REDUCE: (374), (5107) imply: % 148.67/21.36 | | | | | | | | | | | | | | | | (5108) ~ (all_6_2 = e0) % 148.67/21.36 | | | | | | | | | | | | | | | | % 148.67/21.36 | | | | | | | | | | | | | | | | BETA: splitting (294) gives: % 148.67/21.36 | | | | | | | | | | | | | | | | % 148.67/21.36 | | | | | | | | | | | | | | | | Case 1: % 148.67/21.36 | | | | | | | | | | | | | | | | | % 148.67/21.36 | | | | | | | | | | | | | | | | | (5109) ~ (all_56_11 = e0) % 148.67/21.36 | | | | | | | | | | | | | | | | | % 148.67/21.36 | | | | | | | | | | | | | | | | | REDUCE: (545), (5109) imply: % 148.67/21.36 | | | | | | | | | | | | | | | | | (5110) ~ (all_8_2 = e0) % 148.67/21.36 | | | | | | | | | | | | | | | | | % 148.67/21.36 | | | | | | | | | | | | | | | | | BETA: splitting (289) gives: % 148.67/21.36 | | | | | | | | | | | | | | | | | % 148.67/21.36 | | | | | | | | | | | | | | | | | Case 1: % 148.67/21.36 | | | | | | | | | | | | | | | | | | % 148.67/21.36 | | | | | | | | | | | | | | | | | | (5111) ~ (all_56_31 = e2) % 148.67/21.36 | | | | | | | | | | | | | | | | | | % 148.67/21.36 | | | | | | | | | | | | | | | | | | REDUCE: (544), (5111) imply: % 148.67/21.36 | | | | | | | | | | | | | | | | | | (5112) ~ (all_4_2 = e2) % 148.67/21.36 | | | | | | | | | | | | | | | | | | % 148.67/21.36 | | | | | | | | | | | | | | | | | | BETA: splitting (237) gives: % 148.67/21.36 | | | | | | | | | | | | | | | | | | % 148.67/21.36 | | | | | | | | | | | | | | | | | | Case 1: % 148.67/21.36 | | | | | | | | | | | | | | | | | | | % 148.67/21.36 | | | | | | | | | | | | | | | | | | | (5113) all_54_15 = e3 % 148.67/21.36 | | | | | | | | | | | | | | | | | | | % 148.67/21.36 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (540), (5106), (5113) are inconsistent by % 148.67/21.36 | | | | | | | | | | | | | | | | | | | sub-proof #740. % 148.67/21.36 | | | | | | | | | | | | | | | | | | | % 148.67/21.36 | | | | | | | | | | | | | | | | | | Case 2: % 148.67/21.36 | | | | | | | | | | | | | | | | | | | % 148.67/21.36 | | | | | | | | | | | | | | | | | | | (5114) all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0 % 148.67/21.36 | | | | | | | | | | | | | | | | | | | % 148.67/21.36 | | | | | | | | | | | | | | | | | | | BETA: splitting (5114) gives: % 148.67/21.36 | | | | | | | | | | | | | | | | | | | % 148.67/21.36 | | | | | | | | | | | | | | | | | | | Case 1: % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | (5115) all_54_15 = e2 % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (540), (5112), (5115) are inconsistent by % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | sub-proof #739. % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | % 148.67/21.36 | | | | | | | | | | | | | | | | | | | Case 2: % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | (5116) all_54_15 = e1 | all_54_15 = e0 % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | BETA: splitting (5116) gives: % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | Case 1: % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | | % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | | (5117) all_54_15 = e1 % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | | % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (540), (5104), (5117) are inconsistent by % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | | sub-proof #738. % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | | % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | Case 2: % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | | % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | | (5118) all_54_15 = e0 % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | | % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (540), (5118) imply: % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | | (5119) all_4_2 = e0 % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | | % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | | SIMP: (5119) implies: % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | | (5120) all_4_2 = e0 % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | | % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | | REDUCE: (570), (5120) imply: % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | | (5121) ~ (all_52_3 = e0) % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | | % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | | REDUCE: (581), (5120) imply: % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | | (5122) ~ (all_52_7 = e0) % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | | % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | | REDUCE: (588), (5120) imply: % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | | (5123) ~ (all_52_11 = e0) % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | | % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | | REDUCE: (589), (5120) imply: % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | | (5124) ~ (all_52_12 = e0) % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | | % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | | REDUCE: (590), (5120) imply: % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | | (5125) ~ (all_52_13 = e0) % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | | % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | | REDUCE: (38), (5120) imply: % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | | (5126) op(e0, e0) = all_4_1 % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | | % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | | REDUCE: (627), (5120) imply: % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | | (5127) op(e0, e0) = all_56_30 % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | | % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | | REDUCE: (36), (5120) imply: % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | | (5128) op(e0, e0) = e0 % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | | % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_4_1, % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | | all_56_30, e0, e0, simplifying with (5126), (5127) % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | | gives: % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | | (5129) all_56_30 = all_4_1 % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | | % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | | all_56_30, e0, e0, simplifying with (5127), (5128) % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | | gives: % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | | (5130) all_56_30 = e0 % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | | % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5129), (5130) imply: % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | | (5131) all_4_1 = e0 % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | | % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | | SIMP: (5131) implies: % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | | (5132) all_4_1 = e0 % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | | % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | | REDUCE: (37), (5132) imply: % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | | (5133) op(e0, e0) = all_4_0 % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | | % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_4_0, % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | | e0, e0, simplifying with (5128), (5133) gives: % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | | (5134) all_4_0 = e0 % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | | % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | | REDUCE: (767), (5134) imply: % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | | (5135) ~ (e3 = e0) % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | | % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | | REDUCE: (5088), (5134) imply: % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | | (5136) ~ (e2 = e0) % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | | % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (299) gives: % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | | % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | | | (5137) ~ (all_56_1 = e2) % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (546), (5137) imply: % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | | | (5138) ~ (all_10_2 = e2) % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (41), (46), (51), (158), (160), (161), % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | | | (168), (174), (182), (193), (197), (241), (245), % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | | | (246), (247), (248), (252), (287), (295), (296), % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | | | (298), (321), (324), (327), (328), (329), (332), % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | | | (336), (343), (374), (380), (386), (401), (407), % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | | | (419), (425), (429), (463), (469), (476), (542), % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | | | (543), (544), (545), (546), (547), (548), (549), % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | | | (550), (551), (552), (553), (554), (555), (559), % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | | | (565), (567), (568), (571), (573), (579), (585), % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | | | (590), (617), (623), (5069), (5071), (5074), % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | | | (5075), (5076), (5077), (5082), (5083), (5084), % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | | | (5104), (5108), (5110), (5122), (5123), (5125), % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | | | (5138), (function-axioms) are inconsistent by % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | | | sub-proof #135. % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | | | (5139) all_56_3 = e3 % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | | | (5140) all_56_1 = e2 % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (546), (5140) imply: % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | | | (5141) all_10_2 = e2 % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (408), (5139) imply: % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | | | (5142) all_52_4 = e3 % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (555), (5142) imply: % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | | | (5143) all_58_1 = e3 % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (419), (5141) imply: % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | | | (5144) all_58_0 = e2 % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (557), (5141) imply: % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | | | (5145) ~ (all_52_1 = e2) % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (559), (5141) imply: % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | | | (5146) ~ (all_52_2 = e2) % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (181), (5142) imply: % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | | | (5147) ~ (all_52_12 = e3) % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | | | SIMP: (5147) implies: % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | | | (5148) ~ (all_52_12 = e3) % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (567), (5141) imply: % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | | | (5149) ~ (all_52_12 = e2) % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (53), (5141) imply: % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | | | (5150) op(e2, e2) = all_10_1 % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (249) gives: % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | | | | (5151) all_54_3 = e3 % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (461), (5151) imply: % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | | | | (5152) all_52_12 = e3 % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5148), (5152) imply: % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | | | | (5153) $false % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (5153) is inconsistent. % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | | | | (5154) all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0 % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5154) gives: % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | | | | | (5155) all_54_3 = e2 % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (461), (5155) imply: % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | | | | | (5156) all_52_12 = e2 % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5149), (5156) imply: % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | | | | | (5157) $false % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (5157) is inconsistent. % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | | | | | (5158) all_54_3 = e1 | all_54_3 = e0 % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5158) gives: % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | (5159) all_54_3 = e1 % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (461), (5159) imply: % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | (5160) all_52_12 = e1 % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (161), (5160) imply: % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | (5161) ~ (all_52_13 = e1) % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5161) implies: % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | (5162) ~ (all_52_13 = e1) % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (336) gives: % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | (5163) all_58_1 = e0 % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5143), (5163) imply: % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | (5164) e3 = e0 % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7), (5164) imply: % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | (5165) $false % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (5165) is inconsistent. % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | (5166) all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0 % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (332) gives: % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5167) all_58_2 = e0 % 148.67/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (401), (5167) imply: % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5168) all_52_1 = e0 % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (197), (5168) imply: % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5169) ~ (all_52_2 = e0) % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5169) implies: % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5170) ~ (all_52_2 = e0) % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (193), (5168) imply: % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5171) ~ (all_52_13 = e0) % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (568), (5168) imply: % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5172) ~ (all_8_2 = e0) % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (324) gives: % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5173) all_58_6 = e0 % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (553), (5170), (5173) are inconsistent by % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #273. % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5174) all_58_7 = e0 | all_58_8 = e0 | all_58_11 = e0 % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5174) gives: % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5175) all_58_7 = e0 % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (380), (5175) imply: % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5176) all_52_6 = e0 % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (326) gives: % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5177) all_58_6 = e2 % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (553), (5177) imply: % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5178) all_52_2 = e2 % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5178) implies: % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5179) all_52_2 = e2 % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5146), (5179) imply: % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5180) $false % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (5180) is inconsistent. % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5181) all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2 % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5181) gives: % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5182) all_58_7 = e2 % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5175), (5182) imply: % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5183) e2 = e0 % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5183) implies: % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5184) e2 = e0 % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5), (5184) imply: % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5185) $false % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (5185) is inconsistent. % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5186) all_58_8 = e2 | all_58_11 = e2 % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5186) gives: % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5187) all_58_8 = e2 % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (552), (5187) imply: % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5188) all_6_2 = e2 % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5102), (5188) imply: % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5189) $false % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (5189) is inconsistent. % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5190) all_58_11 = e2 % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (550), (5190) imply: % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5191) all_52_14 = e2 % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (158), (5191) imply: % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5192) ~ (all_52_13 = e2) % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (245) gives: % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5193) all_54_7 = e3 % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (469), (5193) imply: % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5194) all_52_13 = e3 % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5194) implies: % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5195) all_52_13 = e3 % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (579), (5195) imply: % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5196) ~ (all_8_2 = e3) % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5196) implies: % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5197) ~ (all_8_2 = e3) % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_8_2, % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_10_1, e2, e2, simplifying with (46), (5150) % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5198) all_10_1 = all_8_2 % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5096), (5198) imply: % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5199) ~ (all_8_2 = e1) % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (46), (247), (542), (617), (5071), (5110), (5197), % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5199), (function-axioms) are inconsistent by % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #146. % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5200) all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0 % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (469), (5125), (5162), (5192), (5200) are % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #649. % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5201) ~ (all_58_7 = e0) % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (380), (5201) imply: % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5202) ~ (all_52_6 = e0) % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (380), (549), (554), (5110), (5122), (5166), % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5202) are inconsistent by sub-proof #603. % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5203) ~ (all_58_2 = e0) % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (401), (5203) imply: % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5204) ~ (all_52_1 = e0) % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5166) gives: % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5205) all_58_3 = e0 % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (554), (5205) imply: % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5206) all_8_2 = e0 % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5110), (5206) imply: % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5207) $false % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (5207) is inconsistent. % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5208) all_58_7 = e0 | all_58_13 = e0 % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (191), (340), (365), (380), (401), (549), % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (553), (5121), (5122), (5144), (5204), (5208) are % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #174. % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | (5209) all_54_3 = e0 % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (461), (5209) imply: % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | (5210) all_52_12 = e0 % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5124), (5210) imply: % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | (5211) $false % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (5211) is inconsistent. % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | End of split % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | End of split % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | End of split % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | | | | End of split % 148.67/21.37 | | | | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | | | End of split % 148.67/21.37 | | | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | | Case 2: % 148.67/21.37 | | | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | | | (5212) all_56_31 = e2 % 148.67/21.37 | | | | | | | | | | | | | | | | | | (5213) all_56_27 = e0 % 148.67/21.37 | | | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (360), (5213) imply: % 148.67/21.37 | | | | | | | | | | | | | | | | | | (5214) all_52_7 = e0 % 148.67/21.37 | | | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | | | SIMP: (5214) implies: % 148.67/21.37 | | | | | | | | | | | | | | | | | | (5215) all_52_7 = e0 % 148.67/21.37 | | | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (544), (5212) imply: % 148.67/21.37 | | | | | | | | | | | | | | | | | | (5216) all_4_2 = e2 % 148.67/21.37 | | | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (549), (5215) imply: % 148.67/21.37 | | | | | | | | | | | | | | | | | | (5217) all_58_13 = e0 % 148.67/21.37 | | | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | | | REDUCE: (176), (5215) imply: % 148.67/21.37 | | | | | | | | | | | | | | | | | | (5218) ~ (all_52_6 = e0) % 148.67/21.37 | | | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | | | REDUCE: (173), (5215) imply: % 148.67/21.37 | | | | | | | | | | | | | | | | | | (5219) ~ (all_52_11 = e0) % 148.67/21.37 | | | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | | | SIMP: (5219) implies: % 148.67/21.37 | | | | | | | | | | | | | | | | | | (5220) ~ (all_52_11 = e0) % 148.67/21.37 | | | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | | | REDUCE: (575), (5215) imply: % 148.67/21.37 | | | | | | | | | | | | | | | | | | (5221) ~ (all_8_2 = e0) % 148.67/21.37 | | | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | | | REDUCE: (581), (5215), (5216) imply: % 148.67/21.37 | | | | | | | | | | | | | | | | | | (5222) ~ (e2 = e0) % 148.67/21.37 | | | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | | | REDUCE: (588), (5216) imply: % 148.67/21.37 | | | | | | | | | | | | | | | | | | (5223) ~ (all_52_11 = e2) % 148.67/21.37 | | | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | | | REDUCE: (589), (5216) imply: % 148.67/21.37 | | | | | | | | | | | | | | | | | | (5224) ~ (all_52_12 = e2) % 148.67/21.37 | | | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | | | REDUCE: (38), (5216) imply: % 148.67/21.37 | | | | | | | | | | | | | | | | | | (5225) op(e2, e2) = all_4_1 % 148.67/21.37 | | | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_8_2, % 148.67/21.37 | | | | | | | | | | | | | | | | | | all_4_1, e2, e2, simplifying with (46), (5225) % 148.67/21.37 | | | | | | | | | | | | | | | | | | gives: % 148.67/21.37 | | | | | | | | | | | | | | | | | | (5226) all_8_2 = all_4_1 % 148.67/21.37 | | | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (542), (5226) imply: % 148.67/21.37 | | | | | | | | | | | | | | | | | | (5227) all_54_5 = all_4_1 % 148.67/21.37 | | | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (545), (5226) imply: % 148.67/21.37 | | | | | | | | | | | | | | | | | | (5228) all_56_11 = all_4_1 % 148.67/21.37 | | | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (554), (5226) imply: % 148.67/21.37 | | | | | | | | | | | | | | | | | | (5229) all_58_3 = all_4_1 % 148.67/21.37 | | | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | | | REDUCE: (571), (5226) imply: % 148.67/21.37 | | | | | | | | | | | | | | | | | | (5230) ~ (all_52_4 = all_4_1) % 148.67/21.37 | | | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | | | REDUCE: (573), (5226) imply: % 148.67/21.37 | | | | | | | | | | | | | | | | | | (5231) ~ (all_52_6 = all_4_1) % 148.67/21.37 | | | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | | | REDUCE: (579), (5226) imply: % 148.67/21.37 | | | | | | | | | | | | | | | | | | (5232) ~ (all_52_13 = all_4_1) % 148.67/21.37 | | | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | | | BETA: splitting (293) gives: % 148.67/21.37 | | | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | | | Case 1: % 148.67/21.37 | | | | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | | | | (5233) ~ (all_56_21 = e3) % 148.67/21.37 | | | | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | | | | REDUCE: (374), (5233) imply: % 148.67/21.37 | | | | | | | | | | | | | | | | | | | (5234) ~ (all_6_2 = e3) % 148.67/21.37 | | | | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | | | | BETA: splitting (242) gives: % 148.67/21.37 | | | | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | | | | Case 1: % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | (5235) all_54_10 = e3 % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (541), (5234), (5235) are inconsistent by % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | sub-proof #736. % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | | | | Case 2: % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | (5236) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | BETA: splitting (5236) gives: % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | Case 1: % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | (5237) all_54_10 = e2 % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (541), (5102), (5237) are inconsistent by % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | sub-proof #735. % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | Case 2: % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | (5238) all_54_10 = e1 | all_54_10 = e0 % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5238) gives: % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | (5239) all_54_10 = e1 % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (541), (5239) imply: % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | (5240) all_6_2 = e1 % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | SIMP: (5240) implies: % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | (5241) all_6_2 = e1 % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (580), (5241) imply: % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | (5242) ~ (all_52_6 = e1) % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (582), (5241) imply: % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | (5243) ~ (all_52_8 = e1) % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (585), (5241) imply: % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | (5244) ~ (all_52_11 = e1) % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (587), (5241) imply: % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | (5245) ~ (all_52_14 = e1) % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5084), (5241) imply: % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | (5246) ~ (all_8_0 = e1) % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (43), (5241) imply: % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | (5247) op(e1, e1) = all_6_1 % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (622), (5241) imply: % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | (5248) op(e1, e1) = all_56_20 % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (41), (5241) imply: % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | (5249) op(e1, e1) = e1 % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives: % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | (5250) all_54_14 = e3 % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (482), (5250) imply: % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | (5251) all_52_11 = e3 % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5251) implies: % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | (5252) all_52_11 = e3 % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5080), (5252) imply: % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | (5253) ~ (all_8_0 = e3) % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (205), (5252) imply: % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | (5254) op(e0, e1) = e3 % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (318) gives: % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | (5255) all_58_12 = e1 % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (365), (5255) imply: % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | (5256) all_52_3 = e1 % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (196), (5256) imply: % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | (5257) ~ (all_52_1 = e1) % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (561), (5256) imply: % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | (5258) ~ (all_10_2 = e1) % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5258) implies: % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | (5259) ~ (all_10_2 = e1) % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_6_1, % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | all_56_20, e1, e1, simplifying with (5247), (5248) % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | gives: % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | (5260) all_56_20 = all_6_1 % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1, % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | all_56_20, e1, e1, simplifying with (5248), (5249) % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | gives: % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | (5261) all_56_20 = e1 % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5260), (5261) imply: % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | (5262) all_6_1 = e1 % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5262) implies: % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | (5263) all_6_1 = e1 % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (42), (5263) imply: % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | (5264) op(e1, e1) = all_6_0 % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1, all_6_0, % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | e1, e1, simplifying with (5249), (5264) gives: % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | (5265) all_6_0 = e1 % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5094), (5265) imply: % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | (5266) ~ (e2 = e1) % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (299) gives: % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | (5267) ~ (all_56_1 = e2) % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (546), (5267) imply: % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | (5268) ~ (all_10_2 = e2) % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (37), (46), (51), (161), (246), (247), % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | (287), (295), (296), (321), (332), (333), (337), % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | (343), (345), (374), (386), (401), (407), (419), % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | (425), (542), (544), (545), (546), (547), (550), % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | (551), (554), (555), (568), (590), (617), (624), % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | (767), (5069), (5071), (5074), (5075), (5076), % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | (5077), (5078), (5082), (5083), (5084), (5100), % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | (5104), (5110), (5224), (5228), (5229), (5232), % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | (5243), (5245), (5246), (5254), (5257), (5259), % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | (5268), (function-axioms) are inconsistent by % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #133. % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | (5269) all_56_3 = e3 % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | (5270) all_56_1 = e2 % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (546), (5270) imply: % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | (5271) all_10_2 = e2 % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (408), (5269) imply: % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | (5272) all_52_4 = e3 % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5272) implies: % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | (5273) all_52_4 = e3 % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (184), (5273) imply: % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | (5274) ~ (all_52_6 = e3) % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5274) implies: % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | (5275) ~ (all_52_6 = e3) % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5230), (5273) imply: % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | (5276) ~ (all_4_1 = e3) % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5276) implies: % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | (5277) ~ (all_4_1 = e3) % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (53), (5271) imply: % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | (5278) op(e2, e2) = all_10_1 % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (46), (243), (247), (473), (542), (5096), (5110), % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | (5218), (5227), (5231), (5242), (5275), (5277), % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | (5278), (function-axioms) are inconsistent by % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #131. % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | (5279) all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1 % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (547), (548), (5104), (5217), (5244), (5279) % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #575. % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | (5280) all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0 % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (482), (5220), (5223), (5244), (5280) are % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #580. % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | End of split % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | (5281) all_54_10 = e0 % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (541), (5108), (5281) are inconsistent by % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | sub-proof #705. % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | End of split % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | End of split % 148.67/21.37 | | | | | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | | | | End of split % 148.67/21.37 | | | | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | | | Case 2: % 148.67/21.37 | | | | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | | | | (5282) all_56_21 = e3 % 148.67/21.37 | | | | | | | | | | | | | | | | | | | (5283) all_56_17 = e1 % 148.67/21.37 | | | | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (42), (43), (51), (158), (160), (161), (174), % 148.67/21.37 | | | | | | | | | | | | | | | | | | | (189), (191), (208), (241), (243), (252), (287), % 148.67/21.37 | | | | | | | | | | | | | | | | | | | (297), (321), (332), (374), (381), (386), (389), % 148.67/21.37 | | | | | | | | | | | | | | | | | | | (401), (402), (473), (476), (543), (544), (545), % 148.67/21.37 | | | | | | | | | | | | | | | | | | | (546), (547), (550), (551), (554), (557), (559), % 148.67/21.37 | | | | | | | | | | | | | | | | | | | (569), (573), (580), (591), (621), (768), (5094), % 148.67/21.37 | | | | | | | | | | | | | | | | | | | (5098), (5104), (5110), (5282), (5283), % 148.67/21.37 | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 148.67/21.37 | | | | | | | | | | | | | | | | | | | #130. % 148.67/21.37 | | | | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | | | End of split % 148.67/21.37 | | | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | | End of split % 148.67/21.37 | | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | Case 2: % 148.67/21.37 | | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | | (5284) all_56_15 = e2 % 148.67/21.37 | | | | | | | | | | | | | | | | | (5285) all_56_11 = e0 % 148.67/21.37 | | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (8), (9), (36), (38), (246), (287), % 148.67/21.37 | | | | | | | | | | | | | | | | | (333), (335), (374), (386), (401), (443), (544), % 148.67/21.37 | | | | | | | | | | | | | | | | | (545), (546), (554), (557), (579), (627), (5071), % 148.67/21.37 | | | | | | | | | | | | | | | | | (5074), (5076), (5082), (5083), (5084), (5100), % 148.67/21.37 | | | | | | | | | | | | | | | | | (5284), (5285), (function-axioms) are inconsistent % 148.67/21.37 | | | | | | | | | | | | | | | | | by sub-proof #126. % 148.67/21.37 | | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | End of split % 148.67/21.37 | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | Case 2: % 148.67/21.37 | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | (5286) all_56_23 = e1 % 148.67/21.37 | | | | | | | | | | | | | | | | (5287) all_56_21 = e0 % 148.67/21.37 | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | COMBINE_EQS: (374), (5287) imply: % 148.67/21.37 | | | | | | | | | | | | | | | | (5288) all_6_2 = e0 % 148.67/21.37 | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | SIMP: (5288) implies: % 148.67/21.37 | | | | | | | | | | | | | | | | (5289) all_6_2 = e0 % 148.67/21.37 | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | COMBINE_EQS: (366), (5286) imply: % 148.67/21.37 | | | | | | | | | | | | | | | | (5290) all_52_14 = e1 % 148.67/21.37 | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | SIMP: (5290) implies: % 148.67/21.37 | | | | | | | | | | | | | | | | (5291) all_52_14 = e1 % 148.67/21.37 | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | REDUCE: (569), (5289) imply: % 148.67/21.37 | | | | | | | | | | | | | | | | (5292) ~ (all_52_2 = e0) % 148.67/21.37 | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | REDUCE: (580), (5289) imply: % 148.67/21.37 | | | | | | | | | | | | | | | | (5293) ~ (all_52_6 = e0) % 148.67/21.37 | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | REDUCE: (591), (5291) imply: % 148.67/21.37 | | | | | | | | | | | | | | | | (5294) ~ (all_4_2 = e1) % 148.67/21.37 | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | REDUCE: (43), (5289) imply: % 148.67/21.37 | | | | | | | | | | | | | | | | (5295) op(e0, e0) = all_6_1 % 148.67/21.37 | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | REDUCE: (41), (5289) imply: % 148.67/21.37 | | | | | | | | | | | | | | | | (5296) op(e1, e1) = e0 % 148.67/21.37 | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | | REF_CLOSE: (36), (37), (38), (46), (237), (247), (294), % 148.67/21.37 | | | | | | | | | | | | | | | | (295), (296), (332), (336), (340), (365), (380), % 148.67/21.37 | | | | | | | | | | | | | | | | (401), (419), (425), (540), (542), (545), (549), % 148.67/21.37 | | | | | | | | | | | | | | | | (553), (554), (555), (563), (568), (570), (581), % 148.67/21.37 | | | | | | | | | | | | | | | | (617), (627), (768), (5071), (5088), (5092), % 148.67/21.37 | | | | | | | | | | | | | | | | (5098), (5104), (5292), (5293), (5295), (5296), % 148.67/21.37 | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 148.67/21.37 | | | | | | | | | | | | | | | | #125. % 148.67/21.37 | | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | | End of split % 148.67/21.37 | | | | | | | | | | | | | | | % 148.67/21.37 | | | | | | | | | | | | | | Case 2: % 148.67/21.37 | | | | | | | | | | | | | | | % 148.67/21.38 | | | | | | | | | | | | | | | (5297) all_56_31 = e3 % 148.67/21.38 | | | | | | | | | | | | | | | (5298) all_56_25 = e0 % 148.67/21.38 | | | | | | | | | | | | | | | % 148.67/21.38 | | | | | | | | | | | | | | | REF_CLOSE: (5), (36), (38), (43), (46), (51), (182), (187), % 148.67/21.38 | | | | | | | | | | | | | | | (246), (247), (252), (287), (291), (293), (295), % 148.67/21.38 | | | | | | | | | | | | | | | (296), (299), (328), (331), (332), (374), (381), % 148.67/21.38 | | | | | | | | | | | | | | | (386), (401), (407), (408), (425), (447), (542), % 148.67/21.38 | | | | | | | | | | | | | | | (543), (544), (545), (546), (548), (552), (554), % 148.67/21.38 | | | | | | | | | | | | | | | (559), (561), (565), (568), (570), (585), (588), % 148.67/21.38 | | | | | | | | | | | | | | | (590), (617), (768), (5069), (5071), (5074), % 148.67/21.38 | | | | | | | | | | | | | | | (5075), (5076), (5077), (5082), (5083), (5084), % 148.67/21.38 | | | | | | | | | | | | | | | (5098), (5100), (5297), (5298), (function-axioms) % 148.67/21.38 | | | | | | | | | | | | | | | are inconsistent by sub-proof #121. % 148.67/21.38 | | | | | | | | | | | | | | | % 148.67/21.38 | | | | | | | | | | | | | | End of split % 148.67/21.38 | | | | | | | | | | | | | | % 148.67/21.38 | | | | | | | | | | | | | Case 2: % 148.67/21.38 | | | | | | | | | | | | | | % 148.67/21.38 | | | | | | | | | | | | | | (5299) all_56_31 = e1 % 148.67/21.38 | | | | | | | | | | | | | | (5300) all_56_29 = e0 % 148.67/21.38 | | | | | | | | | | | | | | % 148.67/21.38 | | | | | | | | | | | | | | COMBINE_EQS: (357), (5300) imply: % 148.67/21.38 | | | | | | | | | | | | | | (5301) all_52_11 = e0 % 148.67/21.38 | | | | | | | | | | | | | | % 148.67/21.38 | | | | | | | | | | | | | | SIMP: (5301) implies: % 148.67/21.38 | | | | | | | | | | | | | | (5302) all_52_11 = e0 % 148.67/21.38 | | | | | | | | | | | | | | % 148.67/21.38 | | | | | | | | | | | | | | COMBINE_EQS: (544), (5299) imply: % 148.67/21.38 | | | | | | | | | | | | | | (5303) all_4_2 = e1 % 148.67/21.38 | | | | | | | | | | | | | | % 148.67/21.38 | | | | | | | | | | | | | | COMBINE_EQS: (548), (5302) imply: % 148.67/21.38 | | | | | | | | | | | | | | (5304) all_58_14 = e0 % 148.67/21.38 | | | | | | | | | | | | | | % 148.67/21.38 | | | | | | | | | | | | | | REDUCE: (187), (5302) imply: % 148.67/21.38 | | | | | | | | | | | | | | (5305) ~ (all_52_3 = e0) % 148.67/21.38 | | | | | | | | | | | | | | % 148.67/21.38 | | | | | | | | | | | | | | REDUCE: (38), (5303) imply: % 148.67/21.38 | | | | | | | | | | | | | | (5306) op(e1, e1) = all_4_1 % 148.67/21.38 | | | | | | | | | | | | | | % 148.67/21.38 | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_6_2, % 148.67/21.38 | | | | | | | | | | | | | | all_4_1, e1, e1, simplifying with (41), (5306) % 148.67/21.38 | | | | | | | | | | | | | | gives: % 148.67/21.38 | | | | | | | | | | | | | | (5307) all_6_2 = all_4_1 % 148.67/21.38 | | | | | | | | | | | | | | % 148.67/21.38 | | | | | | | | | | | | | | COMBINE_EQS: (374), (5307) imply: % 148.67/21.38 | | | | | | | | | | | | | | (5308) all_56_21 = all_4_1 % 148.67/21.38 | | | | | | | | | | | | | | % 148.67/21.38 | | | | | | | | | | | | | | BETA: splitting (293) gives: % 148.67/21.38 | | | | | | | | | | | | | | % 148.67/21.38 | | | | | | | | | | | | | | Case 1: % 148.67/21.38 | | | | | | | | | | | | | | | % 148.67/21.38 | | | | | | | | | | | | | | | (5309) ~ (all_56_21 = e3) % 148.67/21.38 | | | | | | | | | | | | | | | % 148.67/21.38 | | | | | | | | | | | | | | | REDUCE: (5308), (5309) imply: % 148.67/21.38 | | | | | | | | | | | | | | | (5310) ~ (all_4_1 = e3) % 148.67/21.38 | | | | | | | | | | | | | | | % 148.67/21.38 | | | | | | | | | | | | | | | REF_CLOSE: (7), (41), (46), (53), (168), (182), (252), (287), % 148.67/21.38 | | | | | | | | | | | | | | | (297), (299), (331), (374), (402), (407), (408), % 148.67/21.38 | | | | | | | | | | | | | | | (543), (545), (546), (552), (565), (5071), (5076), % 148.67/21.38 | | | | | | | | | | | | | | | (5096), (5100), (5299), (5304), (5306), (5310), % 148.67/21.38 | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 148.67/21.38 | | | | | | | | | | | | | | | #119. % 148.67/21.38 | | | | | | | | | | | | | | | % 148.67/21.38 | | | | | | | | | | | | | | Case 2: % 148.67/21.38 | | | | | | | | | | | | | | | % 148.67/21.38 | | | | | | | | | | | | | | | (5311) all_56_21 = e3 % 148.67/21.38 | | | | | | | | | | | | | | | (5312) all_56_17 = e1 % 148.67/21.38 | | | | | | | | | | | | | | | % 148.67/21.38 | | | | | | | | | | | | | | | COMBINE_EQS: (381), (5312) imply: % 148.67/21.38 | | | | | | | | | | | | | | | (5313) all_52_2 = e1 % 148.67/21.38 | | | | | | | | | | | | | | | % 148.67/21.38 | | | | | | | | | | | | | | | SIMP: (5313) implies: % 148.67/21.38 | | | | | | | | | | | | | | | (5314) all_52_2 = e1 % 148.67/21.38 | | | | | | | | | | | | | | | % 148.67/21.38 | | | | | | | | | | | | | | | COMBINE_EQS: (5308), (5311) imply: % 148.67/21.38 | | | | | | | | | | | | | | | (5315) all_4_1 = e3 % 148.67/21.38 | | | | | | | | | | | | | | | % 148.67/21.38 | | | | | | | | | | | | | | | SIMP: (5315) implies: % 148.67/21.38 | | | | | | | | | | | | | | | (5316) all_4_1 = e3 % 148.67/21.38 | | | | | | | | | | | | | | | % 148.67/21.38 | | | | | | | | | | | | | | | REDUCE: (192), (5314) imply: % 148.67/21.38 | | | | | | | | | | | | | | | (5317) ~ (all_52_3 = e1) % 148.67/21.38 | | | | | | | | | | | | | | | % 148.67/21.38 | | | | | | | | | | | | | | | SIMP: (5317) implies: % 148.67/21.38 | | | | | | | | | | | | | | | (5318) ~ (all_52_3 = e1) % 148.67/21.38 | | | | | | | | | | | | | | | % 148.67/21.38 | | | | | | | | | | | | | | | REDUCE: (37), (5316) imply: % 148.67/21.38 | | | | | | | | | | | | | | | (5319) op(e0, e3) = all_4_0 % 148.67/21.38 | | | | | | | | | | | | | | | % 148.67/21.38 | | | | | | | | | | | | | | | REF_CLOSE: (207), (240), (478), (767), (5088), (5305), % 148.67/21.38 | | | | | | | | | | | | | | | (5318), (5319), (function-axioms) are inconsistent % 148.67/21.38 | | | | | | | | | | | | | | | by sub-proof #522. % 148.67/21.38 | | | | | | | | | | | | | | | % 148.67/21.38 | | | | | | | | | | | | | | End of split % 148.67/21.38 | | | | | | | | | | | | | | % 148.67/21.38 | | | | | | | | | | | | | End of split % 148.67/21.38 | | | | | | | | | | | | | % 148.67/21.38 | | | | | | | | | | | | Case 2: % 148.67/21.38 | | | | | | | | | | | | | % 148.67/21.38 | | | | | | | | | | | | | (5320) all_56_21 = e2 % 148.67/21.38 | | | | | | | | | | | | | (5321) all_56_19 = e1 % 148.67/21.38 | | | | | | | | | | | | | % 148.67/21.38 | | | | | | | | | | | | | COMBINE_EQS: (435), (5321) imply: % 148.67/21.38 | | | | | | | | | | | | | (5322) all_52_6 = e1 % 148.67/21.38 | | | | | | | | | | | | | % 148.67/21.38 | | | | | | | | | | | | | SIMP: (5322) implies: % 148.67/21.38 | | | | | | | | | | | | | (5323) all_52_6 = e1 % 148.67/21.38 | | | | | | | | | | | | | % 148.67/21.38 | | | | | | | | | | | | | COMBINE_EQS: (374), (5320) imply: % 148.67/21.38 | | | | | | | | | | | | | (5324) all_6_2 = e2 % 148.67/21.38 | | | | | | | | | | | | | % 148.67/21.38 | | | | | | | | | | | | | SIMP: (5324) implies: % 148.67/21.38 | | | | | | | | | | | | | (5325) all_6_2 = e2 % 148.67/21.38 | | | | | | | | | | | | | % 148.67/21.38 | | | | | | | | | | | | | REF_CLOSE: (36), (38), (43), (46), (193), (246), (247), % 148.67/21.38 | | | | | | | | | | | | | (248), (287), (294), (317), (443), (463), (542), % 148.67/21.38 | | | | | | | | | | | | | (544), (545), (546), (547), (557), (568), (573), % 148.67/21.38 | | | | | | | | | | | | | (627), (768), (5071), (5074), (5077), (5082), % 148.67/21.38 | | | | | | | | | | | | | (5083), (5098), (5100), (5320), (5323), (5325), % 148.67/21.38 | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 148.67/21.38 | | | | | | | | | | | | | #117. % 148.67/21.38 | | | | | | | | | | | | | % 148.67/21.38 | | | | | | | | | | | | End of split % 148.67/21.38 | | | | | | | | | | | | % 148.67/21.38 | | | | | | | | | | | Case 2: % 148.67/21.38 | | | | | | | | | | | | % 148.67/21.38 | | | | | | | | | | | | (5326) all_48_0 = e3 % 148.67/21.38 | | | | | | | | | | | | (5327) ~ (all_48_1 = e1) | ~ (all_48_2 = e0) % 148.67/21.38 | | | | | | | | | | | | % 148.67/21.38 | | | | | | | | | | | | COMBINE_EQS: (765), (5326) imply: % 148.67/21.38 | | | | | | | | | | | | (5328) all_8_0 = e3 % 148.67/21.38 | | | | | | | | | | | | % 148.67/21.38 | | | | | | | | | | | | REF_CLOSE: (9), (46), (247), (295), (536), (542), (545), % 148.67/21.38 | | | | | | | | | | | | (617), (5070), (5071), (5075), (5083), (5327), % 148.67/21.38 | | | | | | | | | | | | (5328), (function-axioms) are inconsistent by % 148.67/21.38 | | | | | | | | | | | | sub-proof #115. % 148.67/21.38 | | | | | | | | | | | | % 148.67/21.38 | | | | | | | | | | | End of split % 148.67/21.38 | | | | | | | | | | | % 148.67/21.38 | | | | | | | | | | Case 2: % 148.67/21.38 | | | | | | | | | | | % 148.67/21.38 | | | | | | | | | | | (5329) all_36_1 = e3 % 148.67/21.38 | | | | | | | | | | | % 148.67/21.38 | | | | | | | | | | | COMBINE_EQS: (652), (5329) imply: % 148.67/21.38 | | | | | | | | | | | (5330) all_6_1 = e3 % 148.67/21.38 | | | | | | | | | | | % 148.67/21.38 | | | | | | | | | | | SIMP: (5330) implies: % 148.67/21.38 | | | | | | | | | | | (5331) all_6_1 = e3 % 148.67/21.38 | | | | | | | | | | | % 148.67/21.38 | | | | | | | | | | | REDUCE: (43), (5331) imply: % 148.67/21.38 | | | | | | | | | | | (5332) op(all_6_2, all_6_2) = e3 % 148.67/21.38 | | | | | | | | | | | % 148.67/21.38 | | | | | | | | | | | REDUCE: (42), (5331) imply: % 148.67/21.38 | | | | | | | | | | | (5333) op(e1, e3) = all_6_0 % 148.67/21.38 | | | | | | | | | | | % 148.67/21.38 | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_2, % 148.67/21.38 | | | | | | | | | | | all_6_0, e3, e1, simplifying with (211), (5333) % 148.67/21.38 | | | | | | | | | | | gives: % 148.67/21.38 | | | | | | | | | | | (5334) all_52_2 = all_6_0 % 148.67/21.38 | | | | | | | | | | | % 148.67/21.38 | | | | | | | | | | | COMBINE_EQS: (381), (5334) imply: % 148.67/21.38 | | | | | | | | | | | (5335) all_56_17 = all_6_0 % 148.67/21.38 | | | | | | | | | | | % 148.67/21.38 | | | | | | | | | | | REDUCE: (192), (5334) imply: % 148.67/21.38 | | | | | | | | | | | (5336) ~ (all_52_3 = all_6_0) % 148.67/21.38 | | | | | | | | | | | % 148.67/21.38 | | | | | | | | | | | SIMP: (5336) implies: % 148.67/21.38 | | | | | | | | | | | (5337) ~ (all_52_3 = all_6_0) % 148.67/21.38 | | | | | | | | | | | % 148.67/21.38 | | | | | | | | | | | REDUCE: (189), (5334) imply: % 148.67/21.38 | | | | | | | | | | | (5338) ~ (all_52_14 = all_6_0) % 148.67/21.38 | | | | | | | | | | | % 148.67/21.38 | | | | | | | | | | | SIMP: (5338) implies: % 148.67/21.38 | | | | | | | | | | | (5339) ~ (all_52_14 = all_6_0) % 148.67/21.38 | | | | | | | | | | | % 148.67/21.38 | | | | | | | | | | | BETA: splitting (149) gives: % 148.67/21.38 | | | | | | | | | | | % 148.67/21.38 | | | | | | | | | | | Case 1: % 148.67/21.38 | | | | | | | | | | | | % 148.67/21.38 | | | | | | | | | | | | (5340) ~ (all_48_0 = e3) % 148.67/21.38 | | | | | | | | | | | | % 148.67/21.38 | | | | | | | | | | | | REDUCE: (765), (5340) imply: % 148.67/21.38 | | | | | | | | | | | | (5341) ~ (all_8_0 = e3) % 148.67/21.38 | | | | | | | | | | | | % 148.67/21.38 | | | | | | | | | | | | BETA: splitting (288) gives: % 148.67/21.38 | | | | | | | | | | | | % 148.67/21.38 | | | | | | | | | | | | Case 1: % 148.67/21.38 | | | | | | | | | | | | | % 148.67/21.38 | | | | | | | | | | | | | (5342) ~ (all_56_31 = e1) % 148.67/21.38 | | | | | | | | | | | | | % 148.67/21.38 | | | | | | | | | | | | | REDUCE: (544), (5342) imply: % 148.67/21.38 | | | | | | | | | | | | | (5343) ~ (all_4_2 = e1) % 148.67/21.38 | | | | | | | | | | | | | % 148.67/21.38 | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (38), (41), % 148.67/21.38 | | | | | | | | | | | | | (46), (51), (168), (246), (247), (287), (293), % 148.67/21.38 | | | | | | | | | | | | | (294), (295), (296), (321), (329), (332), (333), % 148.67/21.38 | | | | | | | | | | | | | (335), (374), (386), (401), (407), (425), (443), % 148.67/21.38 | | | | | | | | | | | | | (542), (544), (545), (546), (547), (548), (550), % 148.67/21.38 | | | | | | | | | | | | | (551), (552), (554), (557), (567), (568), (579), % 148.67/21.38 | | | | | | | | | | | | | (585), (590), (617), (622), (623), (627), (5069), % 148.67/21.38 | | | | | | | | | | | | | (5071), (5074), (5075), (5076), (5077), (5082), % 148.67/21.38 | | | | | | | | | | | | | (5083), (5084), (5332), (5335), (5339), (5341), % 148.67/21.38 | | | | | | | | | | | | | (5343), (function-axioms) are inconsistent by % 148.67/21.38 | | | | | | | | | | | | | sub-proof #110. % 148.67/21.38 | | | | | | | | | | | | | % 148.67/21.38 | | | | | | | | | | | | Case 2: % 148.67/21.38 | | | | | | | | | | | | | % 148.67/21.38 | | | | | | | | | | | | | (5344) all_56_31 = e1 % 148.67/21.38 | | | | | | | | | | | | | (5345) all_56_29 = e0 % 148.67/21.38 | | | | | | | | | | | | | % 148.67/21.38 | | | | | | | | | | | | | COMBINE_EQS: (357), (5345) imply: % 148.67/21.38 | | | | | | | | | | | | | (5346) all_52_11 = e0 % 148.67/21.38 | | | | | | | | | | | | | % 148.67/21.38 | | | | | | | | | | | | | COMBINE_EQS: (544), (5344) imply: % 148.67/21.38 | | | | | | | | | | | | | (5347) all_4_2 = e1 % 148.67/21.38 | | | | | | | | | | | | | % 148.67/21.38 | | | | | | | | | | | | | COMBINE_EQS: (548), (5346) imply: % 148.67/21.38 | | | | | | | | | | | | | (5348) all_58_14 = e0 % 148.67/21.38 | | | | | | | | | | | | | % 148.67/21.38 | | | | | | | | | | | | | REDUCE: (187), (5346) imply: % 148.67/21.38 | | | | | | | | | | | | | (5349) ~ (all_52_3 = e0) % 148.67/21.38 | | | | | | | | | | | | | % 148.67/21.38 | | | | | | | | | | | | | REDUCE: (38), (5347) imply: % 148.67/21.38 | | | | | | | | | | | | | (5350) op(e1, e1) = all_4_1 % 148.67/21.38 | | | | | | | | | | | | | % 148.67/21.38 | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_6_2, % 148.67/21.38 | | | | | | | | | | | | | all_4_1, e1, e1, simplifying with (41), (5350) % 148.67/21.38 | | | | | | | | | | | | | gives: % 148.67/21.38 | | | | | | | | | | | | | (5351) all_6_2 = all_4_1 % 148.67/21.38 | | | | | | | | | | | | | % 148.67/21.38 | | | | | | | | | | | | | COMBINE_EQS: (374), (5351) imply: % 148.67/21.38 | | | | | | | | | | | | | (5352) all_56_21 = all_4_1 % 148.67/21.38 | | | | | | | | | | | | | % 148.67/21.38 | | | | | | | | | | | | | REDUCE: (5332), (5351) imply: % 148.67/21.38 | | | | | | | | | | | | | (5353) op(all_4_1, all_4_1) = e3 % 148.67/21.38 | | | | | | | | | | | | | % 148.67/21.38 | | | | | | | | | | | | | BETA: splitting (293) gives: % 148.67/21.38 | | | | | | | | | | | | | % 148.67/21.38 | | | | | | | | | | | | | Case 1: % 148.67/21.38 | | | | | | | | | | | | | | % 148.67/21.38 | | | | | | | | | | | | | | (5354) ~ (all_56_21 = e3) % 148.67/21.38 | | | | | | | | | | | | | | % 148.67/21.38 | | | | | | | | | | | | | | REDUCE: (5352), (5354) imply: % 148.67/21.38 | | | | | | | | | | | | | | (5355) ~ (all_4_1 = e3) % 148.67/21.38 | | | | | | | | | | | | | | % 148.67/21.38 | | | | | | | | | | | | | | REF_CLOSE: (7), (41), (46), (53), (168), (182), (252), (287), % 148.67/21.38 | | | | | | | | | | | | | | (297), (299), (331), (374), (402), (407), (408), % 148.67/21.38 | | | | | | | | | | | | | | (543), (545), (546), (552), (565), (5071), (5076), % 148.67/21.38 | | | | | | | | | | | | | | (5096), (5341), (5344), (5348), (5350), (5355), % 148.67/21.38 | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 148.67/21.38 | | | | | | | | | | | | | | #119. % 148.67/21.38 | | | | | | | | | | | | | | % 148.67/21.38 | | | | | | | | | | | | | Case 2: % 148.67/21.38 | | | | | | | | | | | | | | % 148.67/21.38 | | | | | | | | | | | | | | (5356) all_56_21 = e3 % 148.67/21.38 | | | | | | | | | | | | | | (5357) all_56_17 = e1 % 148.67/21.38 | | | | | | | | | | | | | | % 148.67/21.38 | | | | | | | | | | | | | | COMBINE_EQS: (5335), (5357) imply: % 148.67/21.38 | | | | | | | | | | | | | | (5358) all_6_0 = e1 % 148.67/21.38 | | | | | | | | | | | | | | % 148.67/21.38 | | | | | | | | | | | | | | SIMP: (5358) implies: % 148.67/21.38 | | | | | | | | | | | | | | (5359) all_6_0 = e1 % 148.67/21.38 | | | | | | | | | | | | | | % 148.67/21.38 | | | | | | | | | | | | | | COMBINE_EQS: (5352), (5356) imply: % 148.67/21.38 | | | | | | | | | | | | | | (5360) all_4_1 = e3 % 148.67/21.38 | | | | | | | | | | | | | | % 148.67/21.38 | | | | | | | | | | | | | | SIMP: (5360) implies: % 148.67/21.38 | | | | | | | | | | | | | | (5361) all_4_1 = e3 % 148.67/21.38 | | | | | | | | | | | | | | % 148.67/21.38 | | | | | | | | | | | | | | REDUCE: (5337), (5359) imply: % 148.67/21.38 | | | | | | | | | | | | | | (5362) ~ (all_52_3 = e1) % 148.67/21.38 | | | | | | | | | | | | | | % 148.67/21.38 | | | | | | | | | | | | | | REDUCE: (5353), (5361) imply: % 148.67/21.38 | | | | | | | | | | | | | | (5363) op(e3, e3) = e3 % 148.67/21.38 | | | | | | | | | | | | | | % 148.67/21.38 | | | | | | | | | | | | | | REDUCE: (37), (5361) imply: % 148.67/21.38 | | | | | | | | | | | | | | (5364) op(e0, e3) = all_4_0 % 148.67/21.38 | | | | | | | | | | | | | | % 148.67/21.38 | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_3, % 148.67/21.38 | | | | | | | | | | | | | | all_4_0, e3, e0, simplifying with (207), (5364) % 148.67/21.38 | | | | | | | | | | | | | | gives: % 148.67/21.38 | | | | | | | | | | | | | | (5365) all_52_3 = all_4_0 % 148.67/21.38 | | | | | | | | | | | | | | % 148.67/21.38 | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_10_2, e3, % 148.67/21.38 | | | | | | | | | | | | | | e3, e3, simplifying with (51), (5363) gives: % 148.67/21.38 | | | | | | | | | | | | | | (5366) all_10_2 = e3 % 148.67/21.38 | | | | | | | | | | | | | | % 148.67/21.38 | | | | | | | | | | | | | | COMBINE_EQS: (478), (5365) imply: % 148.67/21.38 | | | | | | | | | | | | | | (5367) all_54_12 = all_4_0 % 148.67/21.38 | | | | | | | | | | | | | | % 148.67/21.38 | | | | | | | | | | | | | | BETA: splitting (240) gives: % 148.67/21.38 | | | | | | | | | | | | | | % 148.67/21.38 | | | | | | | | | | | | | | Case 1: % 148.67/21.38 | | | | | | | | | | | | | | | % 148.67/21.38 | | | | | | | | | | | | | | | (5368) all_54_12 = e3 % 148.67/21.38 | | | | | | | | | | | | | | | % 148.67/21.38 | | | | | | | | | | | | | | | REF_CLOSE: (767), (5367), (5368) are inconsistent by % 148.67/21.38 | | | | | | | | | | | | | | | sub-proof #524. % 148.67/21.38 | | | | | | | | | | | | | | | % 148.67/21.38 | | | | | | | | | | | | | | Case 2: % 148.67/21.38 | | | | | | | | | | | | | | | % 148.67/21.38 | | | | | | | | | | | | | | | (5369) all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0 % 148.67/21.38 | | | | | | | | | | | | | | | % 148.67/21.38 | | | | | | | | | | | | | | | REF_CLOSE: (478), (5088), (5349), (5362), (5367), (5369) are % 148.67/21.38 | | | | | | | | | | | | | | | inconsistent by sub-proof #523. % 148.67/21.38 | | | | | | | | | | | | | | | % 148.67/21.38 | | | | | | | | | | | | | | End of split % 148.67/21.38 | | | | | | | | | | | | | | % 148.67/21.38 | | | | | | | | | | | | | End of split % 148.67/21.38 | | | | | | | | | | | | | % 148.67/21.38 | | | | | | | | | | | | End of split % 148.67/21.38 | | | | | | | | | | | | % 148.67/21.38 | | | | | | | | | | | Case 2: % 148.67/21.38 | | | | | | | | | | | | % 148.67/21.38 | | | | | | | | | | | | (5370) all_48_0 = e3 % 148.67/21.38 | | | | | | | | | | | | (5371) ~ (all_48_1 = e1) | ~ (all_48_2 = e0) % 148.67/21.38 | | | | | | | | | | | | % 148.67/21.38 | | | | | | | | | | | | COMBINE_EQS: (765), (5370) imply: % 148.67/21.38 | | | | | | | | | | | | (5372) all_8_0 = e3 % 148.67/21.38 | | | | | | | | | | | | % 148.67/21.38 | | | | | | | | | | | | SIMP: (5372) implies: % 148.67/21.38 | | | | | | | | | | | | (5373) all_8_0 = e3 % 148.67/21.38 | | | | | | | | | | | | % 148.67/21.38 | | | | | | | | | | | | REF_CLOSE: (9), (46), (247), (295), (536), (542), (545), % 148.67/21.38 | | | | | | | | | | | | (617), (5070), (5071), (5075), (5083), (5371), % 148.67/21.38 | | | | | | | | | | | | (5373), (function-axioms) are inconsistent by % 148.67/21.38 | | | | | | | | | | | | sub-proof #115. % 148.67/21.38 | | | | | | | | | | | | % 148.67/21.38 | | | | | | | | | | | End of split % 148.67/21.38 | | | | | | | | | | | % 148.67/21.38 | | | | | | | | | | End of split % 148.67/21.38 | | | | | | | | | | % 148.67/21.38 | | | | | | | | | Case 2: % 148.67/21.38 | | | | | | | | | | % 148.67/21.38 | | | | | | | | | | (5374) all_32_1 = e1 % 148.67/21.38 | | | | | | | | | | (5375) ~ (all_32_0 = e0) | ~ (all_32_2 = e2) % 148.67/21.38 | | | | | | | | | | % 148.67/21.38 | | | | | | | | | | COMBINE_EQS: (682), (5374) imply: % 148.67/21.38 | | | | | | | | | | (5376) all_10_1 = e1 % 148.67/21.38 | | | | | | | | | | % 148.67/21.38 | | | | | | | | | | REDUCE: (53), (5376) imply: % 148.67/21.38 | | | | | | | | | | (5377) op(all_10_2, all_10_2) = e1 % 148.67/21.38 | | | | | | | | | | % 148.67/21.38 | | | | | | | | | | REDUCE: (52), (5376) imply: % 148.67/21.38 | | | | | | | | | | (5378) op(e3, e1) = all_10_0 % 148.67/21.38 | | | | | | | | | | % 148.67/21.38 | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_8, % 148.67/21.38 | | | | | | | | | | all_10_0, e1, e3, simplifying with (217), (5378) % 148.67/21.38 | | | | | | | | | | gives: % 148.67/21.38 | | | | | | | | | | (5379) all_52_8 = all_10_0 % 148.67/21.38 | | | | | | | | | | % 148.67/21.38 | | | | | | | | | | COMBINE_EQS: (459), (5379) imply: % 148.67/21.38 | | | | | | | | | | (5380) all_54_2 = all_10_0 % 148.67/21.38 | | | | | | | | | | % 148.67/21.38 | | | | | | | | | | COMBINE_EQS: (429), (5379) imply: % 148.67/21.38 | | | | | | | | | | (5381) all_56_5 = all_10_0 % 148.67/21.38 | | | | | | | | | | % 148.67/21.38 | | | | | | | | | | COMBINE_EQS: (407), (5379) imply: % 148.67/21.38 | | | | | | | | | | (5382) all_58_4 = all_10_0 % 148.67/21.38 | | | | | | | | | | % 148.67/21.38 | | | | | | | | | | REDUCE: (182), (5379) imply: % 148.67/21.38 | | | | | | | | | | (5383) ~ (all_52_4 = all_10_0) % 148.67/21.38 | | | | | | | | | | % 148.67/21.38 | | | | | | | | | | REDUCE: (169), (5379) imply: % 148.67/21.38 | | | | | | | | | | (5384) ~ (all_52_11 = all_10_0) % 148.67/21.38 | | | | | | | | | | % 148.67/21.38 | | | | | | | | | | SIMP: (5384) implies: % 148.67/21.38 | | | | | | | | | | (5385) ~ (all_52_11 = all_10_0) % 148.67/21.38 | | | | | | | | | | % 148.67/21.38 | | | | | | | | | | REDUCE: (168), (5379) imply: % 148.67/21.38 | | | | | | | | | | (5386) ~ (all_52_12 = all_10_0) % 148.67/21.38 | | | | | | | | | | % 148.67/21.38 | | | | | | | | | | SIMP: (5386) implies: % 148.67/21.38 | | | | | | | | | | (5387) ~ (all_52_12 = all_10_0) % 148.67/21.38 | | | | | | | | | | % 148.67/21.38 | | | | | | | | | | REDUCE: (565), (5379) imply: % 148.67/21.38 | | | | | | | | | | (5388) ~ (all_10_0 = all_10_2) % 148.67/21.38 | | | | | | | | | | % 148.67/21.38 | | | | | | | | | | REDUCE: (5078), (5379) imply: % 148.67/21.38 | | | | | | | | | | (5389) ~ (all_10_0 = all_8_0) % 148.67/21.38 | | | | | | | | | | % 148.67/21.38 | | | | | | | | | | REDUCE: (582), (5379) imply: % 148.67/21.38 | | | | | | | | | | (5390) ~ (all_10_0 = all_6_2) % 148.67/21.38 | | | | | | | | | | % 148.67/21.38 | | | | | | | | | | REDUCE: (620), (5379) imply: % 148.67/21.38 | | | | | | | | | | (5391) op(e1, all_10_0) = all_56_4 % 148.67/21.38 | | | | | | | | | | % 148.67/21.38 | | | | | | | | | | BETA: splitting (119) gives: % 148.67/21.38 | | | | | | | | | | % 148.67/21.38 | | | | | | | | | | Case 1: % 148.67/21.38 | | | | | | | | | | | % 148.67/21.38 | | | | | | | | | | | (5392) ~ (all_36_1 = e3) % 148.67/21.38 | | | | | | | | | | | % 148.67/21.38 | | | | | | | | | | | REDUCE: (652), (5392) imply: % 148.67/21.38 | | | | | | | | | | | (5393) ~ (all_6_1 = e3) % 148.67/21.38 | | | | | | | | | | | % 148.67/21.38 | | | | | | | | | | | BETA: splitting (129) gives: % 148.67/21.38 | | | | | | | | | | | % 148.67/21.38 | | | | | | | | | | | Case 1: % 148.67/21.38 | | | | | | | | | | | | % 148.67/21.38 | | | | | | | | | | | | (5394) ~ (all_40_0 = e3) % 148.67/21.38 | | | | | | | | | | | | % 148.67/21.38 | | | | | | | | | | | | REDUCE: (713), (5394) imply: % 148.67/21.38 | | | | | | | | | | | | (5395) ~ (all_6_0 = e3) % 148.67/21.38 | | | | | | | | | | | | % 148.67/21.38 | | | | | | | | | | | | BETA: splitting (149) gives: % 148.67/21.38 | | | | | | | | | | | | % 148.67/21.38 | | | | | | | | | | | | Case 1: % 148.67/21.38 | | | | | | | | | | | | | % 148.67/21.38 | | | | | | | | | | | | | (5396) ~ (all_48_0 = e3) % 148.67/21.38 | | | | | | | | | | | | | % 148.67/21.38 | | | | | | | | | | | | | REDUCE: (765), (5396) imply: % 148.67/21.38 | | | | | | | | | | | | | (5397) ~ (all_8_0 = e3) % 148.67/21.38 | | | | | | | | | | | | | % 148.67/21.38 | | | | | | | | | | | | | BETA: splitting (288) gives: % 148.67/21.38 | | | | | | | | | | | | | % 148.67/21.38 | | | | | | | | | | | | | Case 1: % 148.67/21.38 | | | | | | | | | | | | | | % 148.67/21.38 | | | | | | | | | | | | | | (5398) ~ (all_56_31 = e1) % 148.67/21.38 | | | | | | | | | | | | | | % 148.67/21.38 | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (38), (41), % 148.67/21.38 | | | | | | | | | | | | | | (46), (51), (246), (247), (250), (252), (287), % 148.67/21.38 | | | | | | | | | | | | | | (293), (294), (295), (296), (297), (299), (321), % 148.67/21.38 | | | | | | | | | | | | | | (332), (333), (335), (374), (381), (386), (401), % 148.67/21.38 | | | | | | | | | | | | | | (402), (408), (425), (443), (494), (542), (543), % 148.67/21.38 | | | | | | | | | | | | | | (544), (545), (546), (547), (550), (551), (554), % 148.67/21.38 | | | | | | | | | | | | | | (557), (559), (567), (568), (579), (587), (590), % 148.67/21.38 | | | | | | | | | | | | | | (612), (617), (627), (761), (5069), (5071), % 148.67/21.38 | | | | | | | | | | | | | | (5074), (5076), (5077), (5082), (5083), (5084), % 148.67/21.38 | | | | | | | | | | | | | | (5086), (5090), (5375), (5377), (5380), (5383), % 148.67/21.38 | | | | | | | | | | | | | | (5387), (5388), (5390), (5397), (5398), % 148.67/21.38 | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 148.67/21.38 | | | | | | | | | | | | | | #109. % 148.67/21.38 | | | | | | | | | | | | | | % 148.67/21.38 | | | | | | | | | | | | | Case 2: % 148.67/21.38 | | | | | | | | | | | | | | % 148.67/21.38 | | | | | | | | | | | | | | (5399) all_56_31 = e1 % 148.67/21.38 | | | | | | | | | | | | | | (5400) all_56_29 = e0 % 148.67/21.38 | | | | | | | | | | | | | | % 148.67/21.38 | | | | | | | | | | | | | | COMBINE_EQS: (357), (5400) imply: % 148.67/21.38 | | | | | | | | | | | | | | (5401) all_52_11 = e0 % 148.67/21.38 | | | | | | | | | | | | | | % 148.67/21.38 | | | | | | | | | | | | | | COMBINE_EQS: (544), (5399) imply: % 148.67/21.38 | | | | | | | | | | | | | | (5402) all_4_2 = e1 % 148.67/21.38 | | | | | | | | | | | | | | % 148.67/21.38 | | | | | | | | | | | | | | COMBINE_EQS: (547), (5402) imply: % 148.67/21.38 | | | | | | | | | | | | | | (5403) all_58_15 = e1 % 148.67/21.38 | | | | | | | | | | | | | | % 148.67/21.38 | | | | | | | | | | | | | | COMBINE_EQS: (548), (5401) imply: % 148.67/21.38 | | | | | | | | | | | | | | (5404) all_58_14 = e0 % 148.67/21.38 | | | | | | | | | | | | | | % 148.67/21.38 | | | | | | | | | | | | | | REDUCE: (187), (5401) imply: % 148.67/21.38 | | | | | | | | | | | | | | (5405) ~ (all_52_3 = e0) % 148.67/21.38 | | | | | | | | | | | | | | % 148.67/21.38 | | | | | | | | | | | | | | REDUCE: (173), (5401) imply: % 148.67/21.38 | | | | | | | | | | | | | | (5406) ~ (all_52_7 = e0) % 148.67/21.38 | | | | | | | | | | | | | | % 148.67/21.38 | | | | | | | | | | | | | | REDUCE: (5385), (5401) imply: % 148.67/21.38 | | | | | | | | | | | | | | (5407) ~ (all_10_0 = e0) % 148.67/21.38 | | | | | | | | | | | | | | % 148.67/21.38 | | | | | | | | | | | | | | SIMP: (5407) implies: % 148.67/21.38 | | | | | | | | | | | | | | (5408) ~ (all_10_0 = e0) % 148.67/21.38 | | | | | | | | | | | | | | % 148.67/21.38 | | | | | | | | | | | | | | REDUCE: (38), (5402) imply: % 148.67/21.38 | | | | | | | | | | | | | | (5409) op(e1, e1) = all_4_1 % 148.67/21.38 | | | | | | | | | | | | | | % 148.67/21.38 | | | | | | | | | | | | | | REDUCE: (623), (5401) imply: % 148.67/21.38 | | | | | | | | | | | | | | (5410) op(e1, e0) = all_56_28 % 148.67/21.38 | | | | | | | | | | | | | | % 148.67/21.38 | | | | | | | | | | | | | | REDUCE: (627), (5402) imply: % 148.67/21.38 | | | | | | | | | | | | | | (5411) op(e0, e1) = all_56_30 % 148.67/21.38 | | | | | | | | | | | | | | % 148.67/21.38 | | | | | | | | | | | | | | REDUCE: (205), (5401) imply: % 148.67/21.38 | | | | | | | | | | | | | | (5412) op(e0, e1) = e0 % 148.67/21.38 | | | | | | | | | | | | | | % 148.67/21.38 | | | | | | | | | | | | | | BETA: splitting (250) gives: % 148.67/21.38 | | | | | | | | | | | | | | % 148.67/21.38 | | | | | | | | | | | | | | Case 1: % 148.67/21.38 | | | | | | | | | | | | | | | % 148.67/21.38 | | | | | | | | | | | | | | | (5413) all_54_2 = e3 % 148.67/21.38 | | | | | | | | | | | | | | | % 148.67/21.38 | | | | | | | | | | | | | | | COMBINE_EQS: (5380), (5413) imply: % 148.67/21.38 | | | | | | | | | | | | | | | (5414) all_10_0 = e3 % 148.67/21.38 | | | | | | | | | | | | | | | % 148.67/21.38 | | | | | | | | | | | | | | | SIMP: (5414) implies: % 148.67/21.38 | | | | | | | | | | | | | | | (5415) all_10_0 = e3 % 148.67/21.38 | | | | | | | | | | | | | | | % 148.67/21.38 | | | | | | | | | | | | | | | COMBINE_EQS: (5381), (5415) imply: % 148.67/21.38 | | | | | | | | | | | | | | | (5416) all_56_5 = e3 % 148.67/21.38 | | | | | | | | | | | | | | | % 148.67/21.38 | | | | | | | | | | | | | | | COMBINE_EQS: (5382), (5415) imply: % 148.67/21.38 | | | | | | | | | | | | | | | (5417) all_58_4 = e3 % 148.67/21.38 | | | | | | | | | | | | | | | % 148.67/21.38 | | | | | | | | | | | | | | | REDUCE: (5383), (5415) imply: % 148.67/21.38 | | | | | | | | | | | | | | | (5418) ~ (all_52_4 = e3) % 148.67/21.38 | | | | | | | | | | | | | | | % 148.67/21.38 | | | | | | | | | | | | | | | REDUCE: (5387), (5415) imply: % 148.67/21.38 | | | | | | | | | | | | | | | (5419) ~ (all_52_12 = e3) % 148.67/21.38 | | | | | | | | | | | | | | | % 148.67/21.38 | | | | | | | | | | | | | | | REDUCE: (5388), (5415) imply: % 148.67/21.38 | | | | | | | | | | | | | | | (5420) ~ (all_10_2 = e3) % 148.67/21.38 | | | | | | | | | | | | | | | % 148.67/21.38 | | | | | | | | | | | | | | | SIMP: (5420) implies: % 148.67/21.38 | | | | | | | | | | | | | | | (5421) ~ (all_10_2 = e3) % 148.67/21.38 | | | | | | | | | | | | | | | % 148.67/21.38 | | | | | | | | | | | | | | | REDUCE: (5389), (5415) imply: % 148.67/21.38 | | | | | | | | | | | | | | | (5422) ~ (all_8_0 = e3) % 148.67/21.38 | | | | | | | | | | | | | | | % 148.67/21.38 | | | | | | | | | | | | | | | REDUCE: (5391), (5415) imply: % 148.67/21.38 | | | | | | | | | | | | | | | (5423) op(e1, e3) = all_56_4 % 148.67/21.38 | | | | | | | | | | | | | | | % 148.67/21.38 | | | | | | | | | | | | | | | BETA: splitting (297) gives: % 148.67/21.38 | | | | | | | | | | | | | | | % 148.67/21.38 | | | | | | | | | | | | | | | Case 1: % 148.67/21.38 | | | | | | | | | | | | | | | | % 148.67/21.38 | | | | | | | | | | | | | | | | (5424) ~ (all_56_1 = e0) % 148.67/21.38 | | | | | | | | | | | | | | | | % 148.67/21.38 | | | | | | | | | | | | | | | | REDUCE: (546), (5424) imply: % 148.67/21.38 | | | | | | | | | | | | | | | | (5425) ~ (all_10_2 = e0) % 148.67/21.38 | | | | | | | | | | | | | | | | % 148.67/21.38 | | | | | | | | | | | | | | | | BETA: splitting (299) gives: % 148.67/21.38 | | | | | | | | | | | | | | | | % 148.67/21.38 | | | | | | | | | | | | | | | | Case 1: % 148.67/21.38 | | | | | | | | | | | | | | | | | % 148.67/21.38 | | | | | | | | | | | | | | | | | (5426) ~ (all_56_1 = e2) % 148.67/21.38 | | | | | | | | | | | | | | | | | % 148.67/21.38 | | | | | | | | | | | | | | | | | REDUCE: (546), (5426) imply: % 148.67/21.38 | | | | | | | | | | | | | | | | | (5427) ~ (all_10_2 = e2) % 148.67/21.38 | | | | | | | | | | | | | | | | | % 148.67/21.38 | | | | | | | | | | | | | | | | | BETA: splitting (252) gives: % 148.67/21.38 | | | | | | | | | | | | | | | | | % 148.67/21.38 | | | | | | | | | | | | | | | | | Case 1: % 148.67/21.38 | | | | | | | | | | | | | | | | | | % 148.67/21.38 | | | | | | | | | | | | | | | | | | (5428) all_54_0 = e3 % 148.67/21.38 | | | | | | | | | | | | | | | | | | % 148.67/21.38 | | | | | | | | | | | | | | | | | | REF_CLOSE: (543), (5421), (5428) are inconsistent by % 148.67/21.38 | | | | | | | | | | | | | | | | | | sub-proof #709. % 148.67/21.38 | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | Case 2: % 148.67/21.39 | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | (5429) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 148.67/21.39 | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | BETA: splitting (5429) gives: % 148.67/21.39 | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | Case 1: % 148.67/21.39 | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | (5430) all_54_0 = e2 % 148.67/21.39 | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (543), (5427), (5430) are inconsistent by % 148.67/21.39 | | | | | | | | | | | | | | | | | | | sub-proof #734. % 148.67/21.39 | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | Case 2: % 148.67/21.39 | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | (5431) ~ (all_54_0 = e2) % 148.67/21.39 | | | | | | | | | | | | | | | | | | | (5432) all_54_0 = e1 | all_54_0 = e0 % 148.67/21.39 | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | BETA: splitting (5432) gives: % 148.67/21.39 | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | Case 1: % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | (5433) all_54_0 = e1 % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (543), (5433) imply: % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | (5434) all_10_2 = e1 % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | SIMP: (5434) implies: % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | (5435) all_10_2 = e1 % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (419), (5435) imply: % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | (5436) all_58_0 = e1 % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | REDUCE: (561), (5435) imply: % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | (5437) ~ (all_52_3 = e1) % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | REDUCE: (567), (5435) imply: % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | (5438) ~ (all_52_12 = e1) % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | REDUCE: (5427), (5435) imply: % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | (5439) ~ (e2 = e1) % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | REDUCE: (5377), (5435) imply: % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | (5440) op(e1, e1) = e1 % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | all_56_30, e1, e0, simplifying with (5411), (5412) % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | gives: % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | (5441) all_56_30 = e0 % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_14, % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | all_56_28, e0, e1, simplifying with (208), (5410) % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | gives: % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | (5442) all_56_28 = all_52_14 % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_6_2, e1, % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | e1, e1, simplifying with (41), (5440) gives: % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | (5443) all_6_2 = e1 % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_6_2, % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | all_4_1, e1, e1, simplifying with (41), (5409) % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | gives: % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | (5444) all_6_2 = all_4_1 % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_2, % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | all_56_4, e3, e1, simplifying with (211), (5423) % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | gives: % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | (5445) all_56_4 = all_52_2 % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5443), (5444) imply: % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | (5446) all_4_1 = e1 % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | SIMP: (5446) implies: % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | (5447) all_4_1 = e1 % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (374), (5443) imply: % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | (5448) all_56_21 = e1 % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (552), (5443) imply: % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | (5449) all_58_8 = e1 % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | REDUCE: (569), (5443) imply: % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | (5450) ~ (all_52_2 = e1) % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | REDUCE: (587), (5443) imply: % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | (5451) ~ (all_52_14 = e1) % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | REDUCE: (43), (5443) imply: % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | (5452) op(e1, e1) = all_6_1 % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | REDUCE: (622), (5443) imply: % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | (5453) op(e1, e1) = all_56_20 % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | REDUCE: (37), (5447) imply: % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | (5454) op(e0, e1) = all_4_0 % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | BETA: splitting (246) gives: % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | Case 1: % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | (5455) all_54_6 = e3 % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5074), (5397), (5455) are inconsistent by % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | sub-proof #145. % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | Case 2: % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | (5456) all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0 % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5456) gives: % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | (5457) all_54_6 = e2 % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5074), (5457) imply: % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | (5458) all_8_0 = e2 % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | SIMP: (5458) implies: % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | (5459) all_8_0 = e2 % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5075), (5459) imply: % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | (5460) all_56_13 = e2 % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5076), (5459) imply: % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | (5461) all_58_5 = e2 % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5077), (5459) imply: % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | (5462) ~ (all_52_1 = e2) % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5082), (5459) imply: % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | (5463) ~ (all_52_13 = e2) % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5083), (5459) imply: % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | (5464) ~ (all_8_2 = e2) % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | SIMP: (5464) implies: % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | (5465) ~ (all_8_2 = e2) % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5085), (5459) imply: % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | (5466) op(e1, e2) = all_56_12 % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (296) gives: % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | (5467) ~ (all_56_11 = e3) % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (545), (5467) imply: % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | (5468) ~ (all_8_2 = e3) % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (294) gives: % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | (5469) ~ (all_56_11 = e0) % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (545), (5469) imply: % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | (5470) ~ (all_8_2 = e0) % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (247) gives: % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | (5471) all_54_5 = e3 % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (542), (5468), (5471) are inconsistent by % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #737. % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | (5472) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5472) gives: % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | (5473) all_54_5 = e2 % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (542), (5465), (5473) are inconsistent by % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #648. % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | (5474) all_54_5 = e1 | all_54_5 = e0 % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5474) gives: % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5475) all_54_5 = e1 % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (542), (5475) imply: % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5476) all_8_2 = e1 % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5476) implies: % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5477) all_8_2 = e1 % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (554), (5477) imply: % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5478) all_58_3 = e1 % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (568), (5477) imply: % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5479) ~ (all_52_1 = e1) % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (571), (5477) imply: % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5480) ~ (all_52_4 = e1) % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (573), (5477) imply: % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5481) ~ (all_52_6 = e1) % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (575), (5477) imply: % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5482) ~ (all_52_7 = e1) % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_4_0, % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1, e0, simplifying with (5412), (5454) gives: % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5483) all_4_0 = e0 % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1, % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_20, e1, e1, simplifying with (5440), (5453) % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5484) all_56_20 = e1 % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_6_1, % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_20, e1, e1, simplifying with (5452), (5453) % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5485) all_56_20 = all_6_1 % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_6, % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_12, e2, e1, simplifying with (210), (5466) % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5486) all_56_12 = all_52_6 % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5484), (5485) imply: % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5487) all_6_1 = e1 % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (767), (5483) imply: % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5488) ~ (e3 = e0) % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (42), (5487) imply: % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5489) op(e1, e1) = all_6_0 % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1, all_6_0, % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1, e1, simplifying with (5440), (5489) gives: % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5490) all_6_0 = e1 % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5395), (5490) imply: % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5491) ~ (e3 = e1) % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (240) gives: % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5492) all_54_12 = e3 % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (478), (5492) imply: % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5493) all_52_3 = e3 % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5493) implies: % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5494) all_52_3 = e3 % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (188), (5494) imply: % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5495) ~ (all_52_7 = e3) % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5495) implies: % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5496) ~ (all_52_7 = e3) % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (207), (5494) imply: % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5497) op(e0, e3) = e3 % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (239) gives: % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5498) all_54_13 = e3 % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (480), (5498) imply: % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5499) all_52_7 = e3 % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5496), (5499) imply: % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5500) $false % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (5500) is inconsistent. % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5501) all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0 % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5501) gives: % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5502) all_54_13 = e2 % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (480), (5502) imply: % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5503) all_52_7 = e2 % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (183), (5503) imply: % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5504) ~ (all_52_4 = e2) % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (176), (5503) imply: % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5505) ~ (all_52_6 = e2) % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (206), (5503) imply: % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5506) op(e0, e2) = e2 % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (251) gives: % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5507) all_54_1 = e3 % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (457), (5507) imply: % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5508) all_52_4 = e3 % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5418), (5508) imply: % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5509) $false % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (5509) is inconsistent. % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5510) all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0 % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5510) gives: % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5511) all_54_1 = e2 % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (457), (5511) imply: % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5512) all_52_4 = e2 % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5504), (5512) imply: % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5513) $false % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (5513) is inconsistent. % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5514) all_54_1 = e1 | all_54_1 = e0 % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5514) gives: % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5515) all_54_1 = e1 % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (457), (5515) imply: % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5516) all_52_4 = e1 % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5480), (5516) imply: % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5517) $false % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (5517) is inconsistent. % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5518) all_54_1 = e0 % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (457), (5518) imply: % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5519) all_52_4 = e0 % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (184), (5519) imply: % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5520) ~ (all_52_6 = e0) % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5520) implies: % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5521) ~ (all_52_6 = e0) % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (181), (5519) imply: % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5522) ~ (all_52_12 = e0) % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5522) implies: % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5523) ~ (all_52_12 = e0) % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5480), (5519) imply: % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5524) ~ (e1 = e0) % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (243) gives: % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5525) all_54_9 = e3 % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (473), (5525) imply: % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5526) all_52_6 = e3 % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5526) implies: % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5527) all_52_6 = e3 % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (174), (5527) imply: % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5528) ~ (all_52_14 = e3) % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5528) implies: % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5529) ~ (all_52_14 = e3) % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (249) gives: % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5530) all_54_3 = e3 % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (461), (5419), (5530) are inconsistent by % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #659. % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5531) ~ (all_54_3 = e3) % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5532) all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0 % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (323) gives: % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5533) all_58_9 = e3 % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (551), (5533) imply: % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5534) all_52_12 = e3 % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5419), (5534) imply: % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5535) $false % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (5535) is inconsistent. % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5536) all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3 % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5536) gives: % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5537) all_58_10 = e3 % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (386), (5537) imply: % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5538) all_52_13 = e3 % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (443), (5538) imply: % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5539) all_56_15 = e3 % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (625), (5538) imply: % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5540) op(e0, e3) = all_56_14 % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (317) gives: % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5541) all_58_15 = e0 % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5403), (5541) imply: % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5542) e1 = e0 % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4), (5542) imply: % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5543) $false % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (5543) is inconsistent. % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5544) (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5544) implies: % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5545) all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0 % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5532) gives: % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5546) all_54_3 = e2 % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (461), (5546) imply: % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5547) all_52_12 = e2 % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5547) implies: % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5548) all_52_12 = e2 % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (402), (5548) imply: % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5549) all_56_7 = e2 % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (551), (5548) imply: % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5550) all_58_9 = e2 % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (624), (5548) imply: % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5551) op(e0, e2) = all_56_6 % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5545) gives: % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5552) all_58_9 = e0 % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5550), (5552) imply: % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5553) e2 = e0 % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5460), (5553) imply: % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5554) all_56_13 = e0 % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (46), (51), (246), (247), (287), (295), % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (296), (332), (374), (386), (401), (425), (542), % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (544), (545), (546), (554), (568), (590), (617), % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5069), (5071), (5074), (5076), (5077), (5082), % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5083), (5084), (5470), (5554), (function-axioms) % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #134. % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5555) all_58_10 = e0 | all_58_11 = e0 % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5555) gives: % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5556) all_58_10 = e0 % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5537), (5556) imply: % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5557) e3 = e0 % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7), (5557) imply: % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5558) $false % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (5558) is inconsistent. % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5559) all_58_11 = e0 % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (550), (5559) imply: % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5560) all_52_14 = e0 % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5442), (5560) imply: % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5561) all_56_28 = e0 % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, all_56_6, % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2, e0, simplifying with (5506), (5551) gives: % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5562) all_56_6 = e2 % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_14, e3, e0, simplifying with (5497), (5540) % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5563) all_56_14 = e3 % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (286) gives: % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5564) ( ~ (all_56_0 = all_56_1) & ~ (all_56_2 = % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_3) & ~ (all_56_4 = all_56_5) & ~ % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_6 = all_56_7)) | ( ~ (all_56_8 = % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_9) & ~ (all_56_10 = all_56_11) & ~ % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = all_56_13) & ~ (all_56_14 = % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15)) % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5564) gives: % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5565) ~ (all_56_0 = all_56_1) & ~ (all_56_2 = % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_3) & ~ (all_56_4 = all_56_5) & ~ % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_6 = all_56_7) % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5565) implies: % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5566) ~ (all_56_6 = all_56_7) % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5549), (5562), (5566) imply: % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5567) $false % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (5567) is inconsistent. % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5568) ~ (all_56_8 = all_56_9) & ~ (all_56_10 = % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_11) & ~ (all_56_12 = all_56_13) & ~ % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = all_56_15) % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5568) implies: % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5569) ~ (all_56_14 = all_56_15) % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5539), (5563), (5569) imply: % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5570) $false % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (5570) is inconsistent. % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5571) ( ~ (all_56_16 = all_56_17) & ~ (all_56_18 = % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19) & ~ (all_56_20 = all_56_21) & ~ % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_22 = all_56_23)) | ( ~ (all_56_24 = % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_25) & ~ (all_56_26 = all_56_27) & ~ % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_28 = all_56_29) & ~ (all_56_30 = % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31)) % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5571) gives: % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5572) ~ (all_56_16 = all_56_17) & ~ (all_56_18 = % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19) & ~ (all_56_20 = all_56_21) & ~ % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_22 = all_56_23) % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5572) implies: % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5573) ~ (all_56_20 = all_56_21) % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5448), (5484), (5573) imply: % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5574) $false % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (5574) is inconsistent. % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5575) ~ (all_56_24 = all_56_25) & ~ (all_56_26 = % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_27) & ~ (all_56_28 = all_56_29) & ~ % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_30 = all_56_31) % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5575) implies: % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5576) ~ (all_56_28 = all_56_29) % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5400), (5561), (5576) imply: % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5577) $false % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (5577) is inconsistent. % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5578) all_54_3 = e1 | all_54_3 = e0 % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (461), (5438), (5523), (5578) are inconsistent by % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #655. % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5579) all_58_11 = e3 | all_58_15 = e3 % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5579) gives: % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5580) all_58_11 = e3 % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (550), (5580) imply: % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5581) all_52_14 = e3 % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5529), (5581) imply: % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5582) $false % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (5582) is inconsistent. % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5583) all_58_15 = e3 % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (5403), (5583) are inconsistent by sub-proof % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #327. % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.67/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5584) all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0 % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (473), (5481), (5505), (5521), (5584) are % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #677. % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5585) all_54_13 = e1 | all_54_13 = e0 % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (480), (5406), (5482), (5585) are inconsistent by % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #711. % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5586) ~ (all_54_12 = e3) % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (478), (5586) imply: % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5587) ~ (all_52_3 = e3) % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (320) gives: % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5588) all_58_12 = e3 % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (365), (5587), (5588) are inconsistent by % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #449. % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5589) all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3 % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5589) gives: % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5590) all_58_13 = e3 % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (549), (5590) imply: % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5591) all_52_7 = e3 % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5591) implies: % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5592) all_52_7 = e3 % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (360), (5592) imply: % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5593) all_56_27 = e3 % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (176), (5592) imply: % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5594) ~ (all_52_6 = e3) % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (619), (5592) imply: % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5595) op(e2, e3) = all_56_26 % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (319) gives: % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5596) all_58_12 = e2 % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (365), (5596) imply: % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5597) all_52_3 = e2 % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5597) implies: % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5598) all_52_3 = e2 % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (447), (5598) imply: % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5599) all_56_25 = e2 % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (192), (5598) imply: % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5600) ~ (all_52_2 = e2) % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (615), (5598) imply: % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5601) op(e3, e2) = all_56_24 % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_1, % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_26, e3, e2, simplifying with (215), (5595) % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5602) all_56_26 = all_52_1 % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_4, % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_24, e2, e3, simplifying with (218), (5601) % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5603) all_56_24 = all_52_4 % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (248) gives: % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5604) all_54_4 = e3 % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (463), (5604) imply: % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5605) all_52_1 = e3 % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5605) implies: % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5606) all_52_1 = e3 % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5602), (5606) imply: % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5607) all_56_26 = e3 % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (401), (5606) imply: % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5608) all_58_2 = e3 % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (197), (5606) imply: % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5609) ~ (all_52_2 = e3) % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5609) implies: % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5610) ~ (all_52_2 = e3) % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (332) gives: % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5611) all_58_2 = e0 % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5608), (5611) imply: % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5612) e3 = e0 % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7), (5612) imply: % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5613) $false % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (5613) is inconsistent. % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5614) all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0 % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (244) gives: % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5615) all_54_8 = e3 % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (471), (5615) imply: % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5616) all_52_2 = e3 % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5610), (5616) imply: % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5617) $false % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (5617) is inconsistent. % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5618) all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0 % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5618) gives: % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5619) all_54_8 = e2 % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (471), (5619) imply: % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5620) all_52_2 = e2 % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5600), (5620) imply: % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5621) $false % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (5621) is inconsistent. % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5622) all_54_8 = e1 | all_54_8 = e0 % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5622) gives: % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5623) all_54_8 = e1 % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (471), (5623) imply: % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5624) all_52_2 = e1 % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5450), (5624) imply: % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5625) $false % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (5625) is inconsistent. % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5626) all_54_8 = e0 % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (471), (5626) imply: % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5627) all_52_2 = e0 % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (191), (5627) imply: % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5628) ~ (all_52_6 = e0) % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5628) implies: % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5629) ~ (all_52_6 = e0) % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5450), (5627) imply: % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5630) ~ (e1 = e0) % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (243) gives: % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5631) all_54_9 = e3 % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (473), (5594), (5631) are inconsistent by % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #680. % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5632) all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0 % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5632) gives: % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5633) all_54_9 = e2 % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (473), (5633) imply: % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5634) all_52_6 = e2 % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5634) implies: % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5635) all_52_6 = e2 % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5486), (5635) imply: % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5636) all_56_12 = e2 % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5614) gives: % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5637) all_58_3 = e0 % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5478), (5637) imply: % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5638) e1 = e0 % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4), (5638) imply: % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5639) $false % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (5639) is inconsistent. % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5640) all_58_5 = e0 | all_58_10 = e0 % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5640) gives: % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5641) all_58_5 = e0 % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5461), (5641) imply: % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5642) e2 = e0 % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5460), (5642) imply: % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5643) all_56_13 = e0 % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (46), (51), (246), (247), (287), (295), % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (296), (332), (374), (386), (401), (425), (542), % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (544), (545), (546), (554), (568), (590), (617), % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5069), (5071), (5074), (5076), (5077), (5082), % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5083), (5084), (5470), (5643), (function-axioms) % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #134. % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5644) all_58_10 = e0 % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (386), (5644) imply: % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5645) all_52_13 = e0 % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (212), (5645) imply: % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5646) op(e2, e0) = e0 % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (336) gives: % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5647) all_58_1 = e0 % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (555), (5647) imply: % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5648) all_52_4 = e0 % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (408), (5648) imply: % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5649) all_56_3 = e0 % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (616), (5648) imply: % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5650) op(e2, e0) = all_56_2 % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (286) gives: % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5651) ( ~ (all_56_0 = all_56_1) & ~ (all_56_2 = % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_3) & ~ (all_56_4 = all_56_5) & ~ % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_6 = all_56_7)) | ( ~ (all_56_8 = % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_9) & ~ (all_56_10 = all_56_11) & ~ % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = all_56_13) & ~ (all_56_14 = % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15)) % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5651) gives: % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5652) ~ (all_56_0 = all_56_1) & ~ (all_56_2 = % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_3) & ~ (all_56_4 = all_56_5) & ~ % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_6 = all_56_7) % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5652) implies: % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5653) ~ (all_56_2 = all_56_3) % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5649), (5653) imply: % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5654) ~ (all_56_2 = e0) % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_56_2, % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0, e2, simplifying with (5646), (5650) gives: % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5655) all_56_2 = e0 % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5654), (5655) imply: % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5656) $false % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (5656) is inconsistent. % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5657) ~ (all_56_8 = all_56_9) & ~ (all_56_10 = % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_11) & ~ (all_56_12 = all_56_13) & ~ % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = all_56_15) % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5657) implies: % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5658) ~ (all_56_12 = all_56_13) % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5460), (5636), (5658) imply: % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5659) $false % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (5659) is inconsistent. % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5660) ( ~ (all_56_16 = all_56_17) & ~ (all_56_18 = % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19) & ~ (all_56_20 = all_56_21) & ~ % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_22 = all_56_23)) | ( ~ (all_56_24 = % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_25) & ~ (all_56_26 = all_56_27) & ~ % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_28 = all_56_29) & ~ (all_56_30 = % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31)) % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5660) gives: % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5661) ~ (all_56_16 = all_56_17) & ~ (all_56_18 = % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19) & ~ (all_56_20 = all_56_21) & ~ % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_22 = all_56_23) % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5661) implies: % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5662) ~ (all_56_20 = all_56_21) % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5448), (5484), (5662) imply: % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5663) $false % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (5663) is inconsistent. % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5664) ~ (all_56_24 = all_56_25) & ~ (all_56_26 = % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_27) & ~ (all_56_28 = all_56_29) & ~ % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_30 = all_56_31) % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5664) implies: % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5665) ~ (all_56_26 = all_56_27) % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5593), (5607), (5665) imply: % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5666) $false % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (5666) is inconsistent. % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5667) all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0 % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (380), (549), (554), (5406), (5470), (5629), % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5667) are inconsistent by sub-proof #603. % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5668) all_54_9 = e1 | all_54_9 = e0 % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (473), (5481), (5629), (5668) are inconsistent by % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #678. % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5669) ~ (all_54_4 = e3) % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5670) all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0 % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (463), (5669) imply: % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5671) ~ (all_52_1 = e3) % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (335) gives: % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5672) all_58_2 = e3 % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (401), (5672) imply: % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5673) all_52_1 = e3 % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5671), (5673) imply: % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5674) $false % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (5674) is inconsistent. % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5675) ~ (all_58_2 = e3) % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5676) all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3 % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5676) gives: % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5677) all_58_3 = e3 % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (5478), (5677) are inconsistent by sub-proof % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #157. % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5678) all_58_5 = e3 | all_58_10 = e3 % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5670) gives: % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5679) all_54_4 = e2 % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (463), (5462), (5679) are inconsistent by % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #633. % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5680) ~ (all_54_4 = e2) % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5681) all_54_4 = e1 | all_54_4 = e0 % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5681) gives: % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5682) all_54_4 = e1 % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (463), (5479), (5682) are inconsistent by % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #584. % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5683) all_54_4 = e0 % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (463), (5683) imply: % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5684) all_52_1 = e0 % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5684) implies: % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5685) all_52_1 = e0 % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (425), (5685) imply: % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5686) all_56_9 = e0 % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (613), (5685) imply: % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5687) op(e3, e0) = all_56_8 % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (244) gives: % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5688) all_54_8 = e3 % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (471), (5688) imply: % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5689) all_52_2 = e3 % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5445), (5689) imply: % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5690) all_56_4 = e3 % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5678) gives: % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5691) all_58_5 = e3 % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (5461), (5691) are inconsistent by sub-proof % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #457. % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5692) all_58_10 = e3 % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (386), (5692) imply: % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5693) all_52_13 = e3 % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (158), (5693) imply: % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5694) ~ (all_52_14 = e3) % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5694) implies: % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5695) ~ (all_52_14 = e3) % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_12, % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_8, e0, e3, simplifying with (216), (5687) % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5696) all_56_8 = all_52_12 % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (241) gives: % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5697) all_54_11 = e3 % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (476), (5695), (5697) are inconsistent by % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #416. % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5698) all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0 % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (249) gives: % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5699) all_54_3 = e3 % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (461), (5699) imply: % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5700) all_52_12 = e3 % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5419), (5700) imply: % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5701) $false % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (5701) is inconsistent. % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5702) ~ (all_54_3 = e3) % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5703) all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0 % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (322) gives: % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5704) all_58_9 = e2 % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (551), (5704) imply: % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5705) all_52_12 = e2 % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (181), (5705) imply: % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5706) ~ (all_52_4 = e2) % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (160), (5705) imply: % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5707) ~ (all_52_14 = e2) % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5707) implies: % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5708) ~ (all_52_14 = e2) % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5419), (5705) imply: % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5709) ~ (e3 = e2) % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (338) gives: % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5710) all_58_1 = e2 % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (555), (5710) imply: % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5711) all_52_4 = e2 % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5706), (5711) imply: % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5712) $false % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (5712) is inconsistent. % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5713) all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2 % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5713) gives: % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5714) all_58_3 = e2 % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5478), (5714) imply: % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5715) e2 = e1 % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6), (5715) imply: % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5716) $false % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (5716) is inconsistent. % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5717) all_58_7 = e2 | all_58_13 = e2 % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5698) gives: % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5718) all_54_11 = e2 % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (476), (5718) imply: % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5719) all_52_14 = e2 % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5708), (5719) imply: % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5720) $false % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (5720) is inconsistent. % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5721) all_54_11 = e1 | all_54_11 = e0 % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5717) gives: % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5722) all_58_7 = e2 % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (380), (5722) imply: % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5723) all_52_6 = e2 % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5723) implies: % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5724) all_52_6 = e2 % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5486), (5724) imply: % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5725) all_56_12 = e2 % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (286) gives: % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.67/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5726) ( ~ (all_56_0 = all_56_1) & ~ (all_56_2 = % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_3) & ~ (all_56_4 = all_56_5) & ~ % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_6 = all_56_7)) | ( ~ (all_56_8 = % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_9) & ~ (all_56_10 = all_56_11) & ~ % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = all_56_13) & ~ (all_56_14 = % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15)) % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5726) gives: % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5727) ~ (all_56_0 = all_56_1) & ~ (all_56_2 = % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_3) & ~ (all_56_4 = all_56_5) & ~ % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_6 = all_56_7) % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5727) implies: % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5728) ~ (all_56_4 = all_56_5) % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5416), (5690), (5728) imply: % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5729) $false % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (5729) is inconsistent. % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5730) ~ (all_56_8 = all_56_9) & ~ (all_56_10 = % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_11) & ~ (all_56_12 = all_56_13) & ~ % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = all_56_15) % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5730) implies: % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5731) ~ (all_56_12 = all_56_13) % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5460), (5725), (5731) imply: % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5732) $false % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (5732) is inconsistent. % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5733) ( ~ (all_56_16 = all_56_17) & ~ (all_56_18 = % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19) & ~ (all_56_20 = all_56_21) & ~ % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_22 = all_56_23)) | ( ~ (all_56_24 = % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_25) & ~ (all_56_26 = all_56_27) & ~ % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_28 = all_56_29) & ~ (all_56_30 = % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31)) % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5733) gives: % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5734) ~ (all_56_16 = all_56_17) & ~ (all_56_18 = % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19) & ~ (all_56_20 = all_56_21) & ~ % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_22 = all_56_23) % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5734) implies: % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5735) ~ (all_56_20 = all_56_21) % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5448), (5484), (5735) imply: % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5736) $false % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (5736) is inconsistent. % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5737) ~ (all_56_24 = all_56_25) & ~ (all_56_26 = % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_27) & ~ (all_56_28 = all_56_29) & ~ % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_30 = all_56_31) % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5737) implies: % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5738) ~ (all_56_28 = all_56_29) % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5400), (5442), (5738) imply: % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5739) ~ (all_52_14 = e0) % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (476), (5451), (5721), (5739) are inconsistent by % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #688. % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5740) all_58_13 = e2 % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5590), (5740) imply: % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5741) e3 = e2 % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (9), (5741) imply: % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5742) $false % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (5742) is inconsistent. % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5743) ~ (all_58_9 = e2) % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (551), (5743) imply: % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5744) ~ (all_52_12 = e2) % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (345) gives: % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5745) all_58_0 = e2 % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (5436), (5745) are inconsistent by sub-proof % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #187. % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5746) all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2 % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5746) gives: % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5747) all_58_1 = e2 % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (555), (5747) imply: % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5748) all_52_4 = e2 % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5603), (5748) imply: % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5749) all_56_24 = e2 % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (181), (5748) imply: % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5750) ~ (all_52_12 = e2) % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (286) gives: % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5751) ( ~ (all_56_0 = all_56_1) & ~ (all_56_2 = % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_3) & ~ (all_56_4 = all_56_5) & ~ % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_6 = all_56_7)) | ( ~ (all_56_8 = % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_9) & ~ (all_56_10 = all_56_11) & ~ % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = all_56_13) & ~ (all_56_14 = % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15)) % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5751) gives: % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5752) ~ (all_56_0 = all_56_1) & ~ (all_56_2 = % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_3) & ~ (all_56_4 = all_56_5) & ~ % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_6 = all_56_7) % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5752) implies: % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5753) ~ (all_56_4 = all_56_5) % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5416), (5690), (5753) imply: % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5754) $false % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (5754) is inconsistent. % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5755) ~ (all_56_8 = all_56_9) & ~ (all_56_10 = % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_11) & ~ (all_56_12 = all_56_13) & ~ % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = all_56_15) % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5755) implies: % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5756) ~ (all_56_8 = all_56_9) % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5686), (5696), (5756) imply: % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5757) ~ (all_52_12 = e0) % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (461), (5438), (5703), (5744), (5757) are % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #326. % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5758) ( ~ (all_56_16 = all_56_17) & ~ (all_56_18 = % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19) & ~ (all_56_20 = all_56_21) & ~ % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_22 = all_56_23)) | ( ~ (all_56_24 = % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_25) & ~ (all_56_26 = all_56_27) & ~ % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_28 = all_56_29) & ~ (all_56_30 = % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31)) % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5758) gives: % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5759) ~ (all_56_16 = all_56_17) & ~ (all_56_18 = % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19) & ~ (all_56_20 = all_56_21) & ~ % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_22 = all_56_23) % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5759) implies: % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5760) ~ (all_56_20 = all_56_21) % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5448), (5484), (5760) imply: % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5761) $false % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (5761) is inconsistent. % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5762) ~ (all_56_24 = all_56_25) & ~ (all_56_26 = % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_27) & ~ (all_56_28 = all_56_29) & ~ % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_30 = all_56_31) % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5762) implies: % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5763) ~ (all_56_24 = all_56_25) % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5599), (5749), (5763) imply: % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5764) $false % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (5764) is inconsistent. % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5765) all_58_4 = e2 | all_58_9 = e2 % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (551), (5086), (5382), (5744), (5765) are % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #387. % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5766) all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0 % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (197), (248), (463), (471), (5450), (5462), % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5479), (5600), (5671), (5766) are inconsistent by % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #108. % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5767) ~ (all_58_12 = e2) % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (365), (5767) imply: % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5768) ~ (all_52_3 = e2) % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (240), (478), (5405), (5437), (5587), (5768) are % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #300. % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5769) all_58_14 = e3 | all_58_15 = e3 % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5769) gives: % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5770) all_58_14 = e3 % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5404), (5770) imply: % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5771) e3 = e0 % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7), (5771) imply: % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5772) $false % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (5772) is inconsistent. % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5773) all_58_15 = e3 % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (5403), (5773) are inconsistent by sub-proof % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #327. % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5774) all_54_5 = e0 % 148.67/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (542), (5470), (5774) are inconsistent by % 148.93/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #646. % 148.93/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.93/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.93/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.41 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.93/21.41 | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.41 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.93/21.41 | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.41 | | | | | | | | | | | | | | | | | | | | | | | | (5775) all_56_15 = e2 % 148.93/21.41 | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.41 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (443), (5463), (5775) are inconsistent by % 148.93/21.41 | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #352. % 148.93/21.41 | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.41 | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.93/21.41 | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.41 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.93/21.41 | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.41 | | | | | | | | | | | | | | | | | | | | | | | (5776) all_56_9 = e2 % 148.93/21.41 | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.41 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (425), (5776) imply: % 148.93/21.41 | | | | | | | | | | | | | | | | | | | | | | | (5777) all_52_1 = e2 % 148.93/21.41 | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.41 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5462), (5777) imply: % 148.93/21.41 | | | | | | | | | | | | | | | | | | | | | | | (5778) $false % 148.93/21.41 | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.41 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (5778) is inconsistent. % 148.93/21.41 | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.41 | | | | | | | | | | | | | | | | | | | | | | End of split % 148.93/21.41 | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.41 | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.93/21.41 | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.41 | | | | | | | | | | | | | | | | | | | | | | (5779) ~ (all_54_6 = e2) % 148.93/21.41 | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.41 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5074), (5779) imply: % 148.93/21.41 | | | | | | | | | | | | | | | | | | | | | | (5780) ~ (all_8_0 = e2) % 148.93/21.41 | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.41 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (330) gives: % 148.93/21.41 | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.41 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.93/21.41 | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.41 | | | | | | | | | | | | | | | | | | | | | | | (5781) all_58_4 = e2 % 148.93/21.41 | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.41 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5417), (5781) imply: % 148.93/21.41 | | | | | | | | | | | | | | | | | | | | | | | (5782) e3 = e2 % 148.93/21.41 | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.41 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (9), (5782) imply: % 148.93/21.41 | | | | | | | | | | | | | | | | | | | | | | | (5783) $false % 148.93/21.41 | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.41 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (5783) is inconsistent. % 148.93/21.41 | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.41 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.93/21.41 | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.41 | | | | | | | | | | | | | | | | | | | | | | | (5784) all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2 % 148.93/21.41 | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.41 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5784) gives: % 148.93/21.41 | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.41 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.93/21.41 | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.41 | | | | | | | | | | | | | | | | | | | | | | | | (5785) all_58_5 = e2 % 148.93/21.41 | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.41 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5076), (5785) imply: % 148.93/21.41 | | | | | | | | | | | | | | | | | | | | | | | | (5786) all_8_0 = e2 % 148.93/21.41 | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.41 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5780), (5786) imply: % 148.93/21.41 | | | | | | | | | | | | | | | | | | | | | | | | (5787) $false % 148.93/21.41 | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.41 | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (5787) is inconsistent. % 148.93/21.41 | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.41 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.93/21.41 | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.41 | | | | | | | | | | | | | | | | | | | | | | | | (5788) all_58_8 = e2 | all_58_14 = e2 % 148.93/21.41 | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.41 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (5404), (5449), (5788) are inconsistent % 148.93/21.41 | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #214. % 148.93/21.41 | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.41 | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.93/21.41 | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.41 | | | | | | | | | | | | | | | | | | | | | | End of split % 148.93/21.41 | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.41 | | | | | | | | | | | | | | | | | | | | | End of split % 148.93/21.41 | | | | | | | | | | | | | | | | | | | | | % 148.93/21.41 | | | | | | | | | | | | | | | | | | | | End of split % 148.93/21.41 | | | | | | | | | | | | | | | | | | | | % 148.93/21.41 | | | | | | | | | | | | | | | | | | | Case 2: % 148.93/21.41 | | | | | | | | | | | | | | | | | | | | % 148.93/21.41 | | | | | | | | | | | | | | | | | | | | (5789) all_54_0 = e0 % 148.93/21.41 | | | | | | | | | | | | | | | | | | | | % 148.93/21.41 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (543), (5425), (5789) are inconsistent by % 148.93/21.41 | | | | | | | | | | | | | | | | | | | | sub-proof #732. % 148.93/21.41 | | | | | | | | | | | | | | | | | | | | % 148.93/21.41 | | | | | | | | | | | | | | | | | | | End of split % 148.93/21.41 | | | | | | | | | | | | | | | | | | | % 148.93/21.41 | | | | | | | | | | | | | | | | | | End of split % 148.93/21.41 | | | | | | | | | | | | | | | | | | % 148.93/21.41 | | | | | | | | | | | | | | | | | End of split % 148.93/21.41 | | | | | | | | | | | | | | | | | % 148.93/21.41 | | | | | | | | | | | | | | | | Case 2: % 148.93/21.41 | | | | | | | | | | | | | | | | | % 148.93/21.41 | | | | | | | | | | | | | | | | | (5790) all_56_3 = e3 % 148.93/21.41 | | | | | | | | | | | | | | | | | % 148.93/21.41 | | | | | | | | | | | | | | | | | REF_CLOSE: (408), (5418), (5790) are inconsistent by % 148.93/21.41 | | | | | | | | | | | | | | | | | sub-proof #395. % 148.93/21.41 | | | | | | | | | | | | | | | | | % 148.93/21.41 | | | | | | | | | | | | | | | | End of split % 148.93/21.41 | | | | | | | | | | | | | | | | % 148.93/21.41 | | | | | | | | | | | | | | | Case 2: % 148.93/21.41 | | | | | | | | | | | | | | | | % 148.93/21.41 | | | | | | | | | | | | | | | | (5791) all_56_7 = e3 % 148.93/21.41 | | | | | | | | | | | | | | | | % 148.93/21.41 | | | | | | | | | | | | | | | | REF_CLOSE: (402), (5419), (5791) are inconsistent by % 148.93/21.41 | | | | | | | | | | | | | | | | sub-proof #691. % 148.93/21.41 | | | | | | | | | | | | | | | | % 148.93/21.41 | | | | | | | | | | | | | | | End of split % 148.93/21.41 | | | | | | | | | | | | | | | % 148.93/21.41 | | | | | | | | | | | | | | Case 2: % 148.93/21.41 | | | | | | | | | | | | | | | % 148.93/21.41 | | | | | | | | | | | | | | | (5792) all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0 % 148.93/21.41 | | | | | | | | | | | | | | | % 148.93/21.41 | | | | | | | | | | | | | | | REF_CLOSE: (5086), (5090), (5380), (5408), (5792) are % 148.93/21.41 | | | | | | | | | | | | | | | inconsistent by sub-proof #382. % 148.93/21.41 | | | | | | | | | | | | | | | % 148.93/21.41 | | | | | | | | | | | | | | End of split % 148.93/21.41 | | | | | | | | | | | | | | % 148.93/21.41 | | | | | | | | | | | | | End of split % 148.93/21.41 | | | | | | | | | | | | | % 148.93/21.41 | | | | | | | | | | | | Case 2: % 148.93/21.41 | | | | | | | | | | | | | % 148.93/21.41 | | | | | | | | | | | | | (5793) all_48_0 = e3 % 148.93/21.41 | | | | | | | | | | | | | (5794) ~ (all_48_1 = e1) | ~ (all_48_2 = e0) % 148.93/21.41 | | | | | | | | | | | | | % 148.93/21.41 | | | | | | | | | | | | | COMBINE_EQS: (765), (5793) imply: % 148.93/21.41 | | | | | | | | | | | | | (5795) all_8_0 = e3 % 148.93/21.41 | | | | | | | | | | | | | % 148.93/21.41 | | | | | | | | | | | | | SIMP: (5795) implies: % 148.93/21.41 | | | | | | | | | | | | | (5796) all_8_0 = e3 % 148.93/21.41 | | | | | | | | | | | | | % 148.93/21.41 | | | | | | | | | | | | | REF_CLOSE: (9), (46), (247), (295), (536), (542), (545), % 148.93/21.41 | | | | | | | | | | | | | (617), (5070), (5071), (5075), (5083), (5794), % 148.93/21.41 | | | | | | | | | | | | | (5796), (function-axioms) are inconsistent by % 148.93/21.41 | | | | | | | | | | | | | sub-proof #115. % 148.93/21.41 | | | | | | | | | | | | | % 148.93/21.41 | | | | | | | | | | | | End of split % 148.93/21.41 | | | | | | | | | | | | % 148.93/21.41 | | | | | | | | | | | Case 2: % 148.93/21.41 | | | | | | | | | | | | % 148.93/21.41 | | | | | | | | | | | | (5797) all_40_0 = e3 % 148.93/21.41 | | | | | | | | | | | | % 148.93/21.41 | | | | | | | | | | | | COMBINE_EQS: (713), (5797) imply: % 148.93/21.41 | | | | | | | | | | | | (5798) all_6_0 = e3 % 148.93/21.41 | | | | | | | | | | | | % 148.93/21.41 | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (36), (38), (41), (42), % 148.93/21.41 | | | | | | | | | | | | (43), (46), (51), (149), (193), (196), (197), % 148.93/21.41 | | | | | | | | | | | | (246), (247), (287), (294), (295), (296), (332), % 148.93/21.41 | | | | | | | | | | | | (333), (335), (344), (365), (374), (386), (401), % 148.93/21.41 | | | | | | | | | | | | (419), (425), (443), (536), (542), (544), (545), % 148.93/21.41 | | | | | | | | | | | | (546), (553), (554), (557), (568), (579), (590), % 148.93/21.41 | | | | | | | | | | | | (617), (622), (627), (765), (5069), (5070), % 148.93/21.41 | | | | | | | | | | | | (5071), (5074), (5075), (5076), (5077), (5082), % 148.93/21.41 | | | | | | | | | | | | (5083), (5084), (5094), (5393), (5798), % 148.93/21.41 | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 148.93/21.41 | | | | | | | | | | | | #106. % 148.93/21.41 | | | | | | | | | | | | % 148.93/21.41 | | | | | | | | | | | End of split % 148.93/21.41 | | | | | | | | | | | % 148.93/21.41 | | | | | | | | | | Case 2: % 148.93/21.41 | | | | | | | | | | | % 148.93/21.41 | | | | | | | | | | | (5799) all_36_1 = e3 % 148.93/21.41 | | | | | | | | | | | % 148.93/21.41 | | | | | | | | | | | COMBINE_EQS: (652), (5799) imply: % 148.93/21.41 | | | | | | | | | | | (5800) all_6_1 = e3 % 148.93/21.41 | | | | | | | | | | | % 148.93/21.41 | | | | | | | | | | | SIMP: (5800) implies: % 148.93/21.41 | | | | | | | | | | | (5801) all_6_1 = e3 % 148.93/21.41 | | | | | | | | | | | % 148.93/21.41 | | | | | | | | | | | REDUCE: (43), (5801) imply: % 148.93/21.41 | | | | | | | | | | | (5802) op(all_6_2, all_6_2) = e3 % 148.93/21.41 | | | | | | | | | | | % 148.93/21.41 | | | | | | | | | | | REDUCE: (42), (5801) imply: % 148.93/21.41 | | | | | | | | | | | (5803) op(e1, e3) = all_6_0 % 148.93/21.41 | | | | | | | | | | | % 148.93/21.41 | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (38), (41), % 148.93/21.41 | | | | | | | | | | | (46), (51), (149), (211), (246), (247), (250), % 148.93/21.41 | | | | | | | | | | | (252), (287), (293), (294), (295), (296), (332), % 148.93/21.41 | | | | | | | | | | | (333), (335), (374), (381), (386), (401), (425), % 148.93/21.41 | | | | | | | | | | | (443), (494), (536), (542), (543), (544), (545), % 148.93/21.41 | | | | | | | | | | | (546), (554), (557), (559), (568), (579), (590), % 148.93/21.41 | | | | | | | | | | | (612), (617), (622), (627), (761), (765), (5069), % 148.93/21.41 | | | | | | | | | | | (5070), (5071), (5074), (5075), (5076), (5077), % 148.93/21.41 | | | | | | | | | | | (5082), (5083), (5084), (5086), (5090), (5375), % 148.93/21.41 | | | | | | | | | | | (5377), (5380), (5388), (5390), (5802), (5803), % 148.93/21.41 | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 148.93/21.41 | | | | | | | | | | | #105. % 148.93/21.41 | | | | | | | | | | | % 148.93/21.41 | | | | | | | | | | End of split % 148.93/21.41 | | | | | | | | | | % 148.93/21.41 | | | | | | | | | End of split % 148.93/21.41 | | | | | | | | | % 148.93/21.41 | | | | | | | | Case 2: % 148.93/21.41 | | | | | | | | | % 148.93/21.41 | | | | | | | | | (5804) all_28_0 = e2 % 148.93/21.41 | | | | | | | | | % 148.93/21.41 | | | | | | | | | COMBINE_EQS: (740), (5804) imply: % 148.93/21.41 | | | | | | | | | (5805) all_6_0 = e2 % 148.93/21.41 | | | | | | | | | % 148.93/21.41 | | | | | | | | | SIMP: (5805) implies: % 148.93/21.41 | | | | | | | | | (5806) all_6_0 = e2 % 148.93/21.41 | | | | | | | | | % 148.93/21.41 | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (38), (41), % 148.93/21.41 | | | | | | | | | (42), (43), (46), (51), (149), (246), (247), (287), % 148.93/21.41 | | | | | | | | | (294), (295), (296), (332), (333), (335), (374), % 148.93/21.41 | | | | | | | | | (386), (401), (425), (443), (536), (542), (544), % 148.93/21.41 | | | | | | | | | (545), (546), (554), (557), (568), (579), (590), % 148.93/21.41 | | | | | | | | | (617), (622), (627), (765), (768), (5069), (5070), % 148.93/21.41 | | | | | | | | | (5071), (5074), (5075), (5076), (5077), (5082), % 148.93/21.41 | | | | | | | | | (5083), (5084), (5806), (function-axioms) are % 148.93/21.41 | | | | | | | | | inconsistent by sub-proof #104. % 148.93/21.41 | | | | | | | | | % 148.93/21.41 | | | | | | | | End of split % 148.93/21.41 | | | | | | | | % 148.93/21.41 | | | | | | | Case 2: % 148.93/21.41 | | | | | | | | % 148.93/21.41 | | | | | | | | (5807) all_26_0 = e1 % 148.93/21.41 | | | | | | | | (5808) ~ (all_26_1 = e2) | ~ (all_26_2 = e3) % 148.93/21.41 | | | | | | | | % 148.93/21.41 | | | | | | | | COMBINE_EQS: (760), (5807) imply: % 148.93/21.41 | | | | | | | | (5809) all_4_0 = e1 % 148.93/21.41 | | | | | | | | % 148.93/21.41 | | | | | | | | SIMP: (5809) implies: % 148.93/21.41 | | | | | | | | (5810) all_4_0 = e1 % 148.93/21.41 | | | | | | | | % 148.93/21.41 | | | | | | | | COMBINE_EQS: (709), (5810) imply: % 148.93/21.41 | | | | | | | | (5811) all_44_0 = e1 % 148.93/21.41 | | | | | | | | % 148.93/21.41 | | | | | | | | REDUCE: (767), (5810) imply: % 148.93/21.41 | | | | | | | | (5812) ~ (e3 = e1) % 148.93/21.41 | | | | | | | | % 148.93/21.41 | | | | | | | | REDUCE: (5088), (5810) imply: % 148.93/21.41 | | | | | | | | (5813) ~ (e2 = e1) % 148.93/21.41 | | | | | | | | % 148.93/21.41 | | | | | | | | REDUCE: (37), (5810) imply: % 148.93/21.41 | | | | | | | | (5814) op(e0, all_4_1) = e1 % 148.93/21.41 | | | | | | | | % 148.93/21.41 | | | | | | | | BETA: splitting (99) gives: % 148.93/21.41 | | | | | | | | % 148.93/21.41 | | | | | | | | Case 1: % 148.93/21.41 | | | | | | | | | % 148.93/21.41 | | | | | | | | | (5815) ~ (all_28_0 = e2) % 148.93/21.41 | | | | | | | | | % 148.93/21.41 | | | | | | | | | REDUCE: (740), (5815) imply: % 148.93/21.41 | | | | | | | | | (5816) ~ (all_6_0 = e2) % 148.93/21.41 | | | | | | | | | % 148.93/21.41 | | | | | | | | | BETA: splitting (109) gives: % 148.93/21.41 | | | | | | | | | % 148.93/21.41 | | | | | | | | | Case 1: % 148.93/21.41 | | | | | | | | | | % 148.93/21.41 | | | | | | | | | | (5817) ~ (all_32_1 = e1) % 148.93/21.41 | | | | | | | | | | % 148.93/21.41 | | | | | | | | | | REDUCE: (682), (5817) imply: % 148.93/21.41 | | | | | | | | | | (5818) ~ (all_10_1 = e1) % 148.93/21.41 | | | | | | | | | | % 148.93/21.41 | | | | | | | | | | BETA: splitting (119) gives: % 148.93/21.41 | | | | | | | | | | % 148.93/21.41 | | | | | | | | | | Case 1: % 148.93/21.41 | | | | | | | | | | | % 148.93/21.41 | | | | | | | | | | | (5819) ~ (all_36_1 = e3) % 148.93/21.41 | | | | | | | | | | | % 148.93/21.41 | | | | | | | | | | | REDUCE: (652), (5819) imply: % 148.93/21.41 | | | | | | | | | | | (5820) ~ (all_6_1 = e3) % 148.93/21.41 | | | | | | | | | | | % 148.93/21.41 | | | | | | | | | | | BETA: splitting (139) gives: % 148.93/21.41 | | | | | | | | | | | % 148.93/21.41 | | | | | | | | | | | Case 1: % 148.93/21.41 | | | | | | | | | | | | % 148.93/21.41 | | | | | | | | | | | | (5821) ~ (all_44_0 = e1) % 148.93/21.41 | | | | | | | | | | | | % 148.93/21.41 | | | | | | | | | | | | REDUCE: (5811), (5821) imply: % 148.93/21.41 | | | | | | | | | | | | (5822) $false % 148.93/21.41 | | | | | | | | | | | | % 148.93/21.41 | | | | | | | | | | | | CLOSE: (5822) is inconsistent. % 148.93/21.41 | | | | | | | | | | | | % 148.93/21.41 | | | | | | | | | | | Case 2: % 148.93/21.41 | | | | | | | | | | | | % 148.93/21.41 | | | | | | | | | | | | (5823) ~ (all_44_1 = e3) | ~ (all_44_2 = e2) % 148.93/21.41 | | | | | | | | | | | | % 148.93/21.41 | | | | | | | | | | | | BETA: splitting (149) gives: % 148.93/21.41 | | | | | | | | | | | | % 148.93/21.41 | | | | | | | | | | | | Case 1: % 148.93/21.41 | | | | | | | | | | | | | % 148.93/21.41 | | | | | | | | | | | | | (5824) ~ (all_48_0 = e3) % 148.93/21.41 | | | | | | | | | | | | | % 148.93/21.41 | | | | | | | | | | | | | REDUCE: (765), (5824) imply: % 148.93/21.41 | | | | | | | | | | | | | (5825) ~ (all_8_0 = e3) % 148.93/21.41 | | | | | | | | | | | | | % 148.93/21.41 | | | | | | | | | | | | | BETA: splitting (288) gives: % 148.93/21.41 | | | | | | | | | | | | | % 148.93/21.41 | | | | | | | | | | | | | Case 1: % 148.93/21.41 | | | | | | | | | | | | | | % 148.93/21.41 | | | | | | | | | | | | | | (5826) ~ (all_56_31 = e1) % 148.93/21.41 | | | | | | | | | | | | | | % 148.93/21.41 | | | | | | | | | | | | | | REDUCE: (544), (5826) imply: % 148.93/21.41 | | | | | | | | | | | | | | (5827) ~ (all_4_2 = e1) % 148.93/21.41 | | | | | | | | | | | | | | % 148.93/21.41 | | | | | | | | | | | | | | BETA: splitting (290) gives: % 148.93/21.41 | | | | | | | | | | | | | | % 148.93/21.41 | | | | | | | | | | | | | | Case 1: % 148.93/21.41 | | | | | | | | | | | | | | | % 148.93/21.41 | | | | | | | | | | | | | | | (5828) ~ (all_56_31 = e3) % 148.93/21.41 | | | | | | | | | | | | | | | % 148.93/21.41 | | | | | | | | | | | | | | | REDUCE: (544), (5828) imply: % 148.93/21.41 | | | | | | | | | | | | | | | (5829) ~ (all_4_2 = e3) % 148.93/21.41 | | | | | | | | | | | | | | | % 148.93/21.41 | | | | | | | | | | | | | | | BETA: splitting (289) gives: % 148.93/21.41 | | | | | | | | | | | | | | | % 148.93/21.41 | | | | | | | | | | | | | | | Case 1: % 148.93/21.41 | | | | | | | | | | | | | | | | % 148.93/21.41 | | | | | | | | | | | | | | | | (5830) ~ (all_56_31 = e2) % 148.93/21.41 | | | | | | | | | | | | | | | | % 148.93/21.41 | | | | | | | | | | | | | | | | REDUCE: (544), (5830) imply: % 148.93/21.41 | | | | | | | | | | | | | | | | (5831) ~ (all_4_2 = e2) % 148.93/21.41 | | | | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | | | | | REF_CLOSE: (36), (38), (237), (540), (627), (5814), (5827), % 148.93/21.42 | | | | | | | | | | | | | | | | (5829), (5831), (function-axioms) are inconsistent % 148.93/21.42 | | | | | | | | | | | | | | | | by sub-proof #363. % 148.93/21.42 | | | | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | | | | Case 2: % 148.93/21.42 | | | | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | | | | | (5832) all_56_31 = e2 % 148.93/21.42 | | | | | | | | | | | | | | | | (5833) all_56_27 = e0 % 148.93/21.42 | | | | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | | | | | COMBINE_EQS: (360), (5833) imply: % 148.93/21.42 | | | | | | | | | | | | | | | | (5834) all_52_7 = e0 % 148.93/21.42 | | | | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | | | | | SIMP: (5834) implies: % 148.93/21.42 | | | | | | | | | | | | | | | | (5835) all_52_7 = e0 % 148.93/21.42 | | | | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | | | | | COMBINE_EQS: (544), (5832) imply: % 148.93/21.42 | | | | | | | | | | | | | | | | (5836) all_4_2 = e2 % 148.93/21.42 | | | | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | | | | | COMBINE_EQS: (535), (5836) imply: % 148.93/21.42 | | | | | | | | | | | | | | | | (5837) all_44_2 = e2 % 148.93/21.42 | | | | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | | | | | COMBINE_EQS: (549), (5835) imply: % 148.93/21.42 | | | | | | | | | | | | | | | | (5838) all_58_13 = e0 % 148.93/21.42 | | | | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | | | | | REDUCE: (176), (5835) imply: % 148.93/21.42 | | | | | | | | | | | | | | | | (5839) ~ (all_52_6 = e0) % 148.93/21.42 | | | | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | | | | | REDUCE: (173), (5835) imply: % 148.93/21.42 | | | | | | | | | | | | | | | | (5840) ~ (all_52_11 = e0) % 148.93/21.42 | | | | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | | | | | SIMP: (5840) implies: % 148.93/21.42 | | | | | | | | | | | | | | | | (5841) ~ (all_52_11 = e0) % 148.93/21.42 | | | | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | | | | | REDUCE: (575), (5835) imply: % 148.93/21.42 | | | | | | | | | | | | | | | | (5842) ~ (all_8_2 = e0) % 148.93/21.42 | | | | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | | | | | SIMP: (5842) implies: % 148.93/21.42 | | | | | | | | | | | | | | | | (5843) ~ (all_8_2 = e0) % 148.93/21.42 | | | | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | | | | | REDUCE: (581), (5835), (5836) imply: % 148.93/21.42 | | | | | | | | | | | | | | | | (5844) ~ (e2 = e0) % 148.93/21.42 | | | | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | | | | | REDUCE: (588), (5836) imply: % 148.93/21.42 | | | | | | | | | | | | | | | | (5845) ~ (all_52_11 = e2) % 148.93/21.42 | | | | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | | | | | REDUCE: (38), (5836) imply: % 148.93/21.42 | | | | | | | | | | | | | | | | (5846) op(e2, e2) = all_4_1 % 148.93/21.42 | | | | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | | | | | REDUCE: (36), (5836) imply: % 148.93/21.42 | | | | | | | | | | | | | | | | (5847) op(e0, e0) = e2 % 148.93/21.42 | | | | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | | | | | BETA: splitting (5823) gives: % 148.93/21.42 | | | | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | | | | | Case 1: % 148.93/21.42 | | | | | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | | | | | | (5848) ~ (all_44_1 = e3) % 148.93/21.42 | | | | | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | | | | | | REDUCE: (631), (5848) imply: % 148.93/21.42 | | | | | | | | | | | | | | | | | (5849) ~ (all_4_1 = e3) % 148.93/21.42 | | | | | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_8_2, % 148.93/21.42 | | | | | | | | | | | | | | | | | all_4_1, e2, e2, simplifying with (46), (5846) % 148.93/21.42 | | | | | | | | | | | | | | | | | gives: % 148.93/21.42 | | | | | | | | | | | | | | | | | (5850) all_8_2 = all_4_1 % 148.93/21.42 | | | | | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | | | | | | COMBINE_EQS: (542), (5850) imply: % 148.93/21.42 | | | | | | | | | | | | | | | | | (5851) all_54_5 = all_4_1 % 148.93/21.42 | | | | | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | | | | | | COMBINE_EQS: (545), (5850) imply: % 148.93/21.42 | | | | | | | | | | | | | | | | | (5852) all_56_11 = all_4_1 % 148.93/21.42 | | | | | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | | | | | | REDUCE: (571), (5850) imply: % 148.93/21.42 | | | | | | | | | | | | | | | | | (5853) ~ (all_52_4 = all_4_1) % 148.93/21.42 | | | | | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | | | | | | REDUCE: (573), (5850) imply: % 148.93/21.42 | | | | | | | | | | | | | | | | | (5854) ~ (all_52_6 = all_4_1) % 148.93/21.42 | | | | | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | | | | | | REDUCE: (579), (5850) imply: % 148.93/21.42 | | | | | | | | | | | | | | | | | (5855) ~ (all_52_13 = all_4_1) % 148.93/21.42 | | | | | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | | | | | | REDUCE: (5843), (5850) imply: % 148.93/21.42 | | | | | | | | | | | | | | | | | (5856) ~ (all_4_1 = e0) % 148.93/21.42 | | | | | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | | | | | | REDUCE: (5071), (5850) imply: % 148.93/21.42 | | | | | | | | | | | | | | | | | (5857) op(all_4_1, all_4_1) = e1 % 148.93/21.42 | | | | | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | | | | | | BETA: splitting (292) gives: % 148.93/21.42 | | | | | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | | | | | | Case 1: % 148.93/21.42 | | | | | | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | | | | | | | (5858) ~ (all_56_21 = e2) % 148.93/21.42 | | | | | | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | | | | | | | REDUCE: (374), (5858) imply: % 148.93/21.42 | | | | | | | | | | | | | | | | | | (5859) ~ (all_6_2 = e2) % 148.93/21.42 | | | | | | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | | | | | | | BETA: splitting (293) gives: % 148.93/21.42 | | | | | | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | | | | | | | Case 1: % 148.93/21.42 | | | | | | | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | | | | | | | | (5860) ~ (all_56_21 = e3) % 148.93/21.42 | | | | | | | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | | | | | | | | REDUCE: (374), (5860) imply: % 148.93/21.42 | | | | | | | | | | | | | | | | | | | (5861) ~ (all_6_2 = e3) % 148.93/21.42 | | | | | | | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | | | | | | | | BETA: splitting (291) gives: % 148.93/21.42 | | | | | | | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | | | | | | | | Case 1: % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | (5862) ~ (all_56_21 = e0) % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | REDUCE: (374), (5862) imply: % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | (5863) ~ (all_6_2 = e0) % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | BETA: splitting (242) gives: % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | Case 1: % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | (5864) all_54_10 = e3 % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (541), (5864) imply: % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | (5865) all_6_2 = e3 % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | REDUCE: (5861), (5865) imply: % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | (5866) $false % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | CLOSE: (5866) is inconsistent. % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | Case 2: % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | (5867) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5867) gives: % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | (5868) all_54_10 = e2 % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (541), (5868) imply: % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | (5869) all_6_2 = e2 % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5859), (5869) imply: % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | (5870) $false % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (5870) is inconsistent. % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | (5871) all_54_10 = e1 | all_54_10 = e0 % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5871) gives: % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | | (5872) all_54_10 = e1 % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (541), (5872) imply: % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | | (5873) all_6_2 = e1 % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (580), (5873) imply: % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | | (5874) ~ (all_52_6 = e1) % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (585), (5873) imply: % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | | (5875) ~ (all_52_11 = e1) % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (587), (5873) imply: % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | | (5876) ~ (all_52_14 = e1) % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (318) gives: % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | | | (5877) all_58_12 = e1 % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (365), (5877) imply: % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | | | (5878) all_52_3 = e1 % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5878) implies: % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | | | (5879) all_52_3 = e1 % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (187), (5879) imply: % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | | | (5880) ~ (all_52_11 = e1) % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (561), (5879) imply: % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | | | (5881) ~ (all_10_2 = e1) % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5881) implies: % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | | | (5882) ~ (all_10_2 = e1) % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives: % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | | | | (5883) all_54_14 = e3 % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (482), (5883) imply: % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | | | | (5884) all_52_11 = e3 % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5884) implies: % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | | | | (5885) all_52_11 = e3 % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (205), (5885) imply: % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | | | | (5886) op(e0, e1) = e3 % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (299) gives: % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | | | | | (5887) ~ (all_56_1 = e2) % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (546), (5887) imply: % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | | | | | (5888) ~ (all_10_2 = e2) % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (295) gives: % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5889) ~ (all_56_11 = e1) % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5852), (5889) imply: % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5890) ~ (all_4_1 = e1) % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (247), (5846), (5849), (5851), (5856), (5857), % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5890), (function-axioms) are inconsistent by % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #102. % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5891) all_56_13 = e2 % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5892) all_56_11 = e1 % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5852), (5892) imply: % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5893) all_4_1 = e1 % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5075), (5891) imply: % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5894) all_8_0 = e2 % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5076), (5894) imply: % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5895) all_58_5 = e2 % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5855), (5893) imply: % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5896) ~ (all_52_13 = e1) % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5814), (5893) imply: % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5897) op(e0, e1) = e1 % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (328) gives: % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5898) all_58_4 = e0 % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (407), (5898) imply: % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5899) all_52_8 = e0 % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (565), (5899) imply: % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5900) ~ (all_10_2 = e0) % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5900) implies: % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5901) ~ (all_10_2 = e0) % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (252) gives: % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5902) all_54_0 = e3 % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (543), (5902) imply: % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5903) all_10_2 = e3 % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5903) implies: % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5904) all_10_2 = e3 % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (567), (5904) imply: % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5905) ~ (all_52_12 = e3) % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (321), (386), (547), (550), (551), (624), (5827), % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5876), (5886), (5896), (5897), (5905), % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #101. % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5906) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (543), (5882), (5888), (5901), (5906) are % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #731. % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5907) all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0 % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (548), (552), (5841), (5863), (5895), (5907) % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #572. % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | | | | | (5908) all_56_3 = e3 % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | | | | | (5909) all_56_1 = e2 % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (546), (5909) imply: % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | | | | | (5910) all_10_2 = e2 % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (408), (5908) imply: % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | | | | | (5911) all_52_4 = e3 % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (184), (5911) imply: % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | | | | | (5912) ~ (all_52_6 = e3) % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5912) implies: % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | | | | | (5913) ~ (all_52_6 = e3) % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5853), (5911) imply: % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | | | | | (5914) ~ (all_4_1 = e3) % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (53), (5910) imply: % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | | | | | (5915) op(e2, e2) = all_10_1 % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (46), (243), (247), (473), (542), (5818), (5839), % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | | | | | (5843), (5849), (5851), (5854), (5874), (5913), % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | | | | | (5915), (function-axioms) are inconsistent by % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #131. % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | | | | (5916) all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0 % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (482), (5841), (5845), (5875), (5916) are % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #580. % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | | | (5917) all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1 % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (547), (548), (5827), (5838), (5875), (5917) % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #575. % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | | (5918) all_54_10 = e0 % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (541), (5918) imply: % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | | (5919) all_6_2 = e0 % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5863), (5919) imply: % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | | (5920) $false % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (5920) is inconsistent. % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | End of split % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | End of split % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | End of split % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | | | | | | | | Case 2: % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | (5921) all_56_21 = e0 % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (374), (5921) imply: % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | (5922) all_6_2 = e0 % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | SIMP: (5922) implies: % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | (5923) all_6_2 = e0 % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | REDUCE: (43), (5923) imply: % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | (5924) op(e0, e0) = all_6_1 % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, all_6_1, % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | e0, e0, simplifying with (5847), (5924) gives: % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | (5925) all_6_1 = e2 % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | REDUCE: (768), (5925) imply: % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | (5926) $false % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | CLOSE: (5926) is inconsistent. % 148.93/21.42 | | | | | | | | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | | | | | | | | End of split % 148.93/21.42 | | | | | | | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | | | | | | | Case 2: % 148.93/21.42 | | | | | | | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | | | | | | | | (5927) all_56_21 = e3 % 148.93/21.42 | | | | | | | | | | | | | | | | | | | (5928) all_56_17 = e1 % 148.93/21.42 | | | | | | | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (42), (43), (51), (158), (160), (161), (174), % 148.93/21.42 | | | | | | | | | | | | | | | | | | | (189), (191), (208), (241), (243), (252), (287), % 148.93/21.42 | | | | | | | | | | | | | | | | | | | (297), (321), (332), (374), (381), (386), (389), % 148.93/21.42 | | | | | | | | | | | | | | | | | | | (401), (402), (473), (476), (543), (544), (545), % 148.93/21.42 | | | | | | | | | | | | | | | | | | | (546), (547), (550), (551), (554), (557), (559), % 148.93/21.42 | | | | | | | | | | | | | | | | | | | (569), (573), (580), (591), (621), (768), (5816), % 148.93/21.42 | | | | | | | | | | | | | | | | | | | (5820), (5827), (5843), (5927), (5928), % 148.93/21.42 | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 148.93/21.42 | | | | | | | | | | | | | | | | | | | #130. % 148.93/21.42 | | | | | | | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | | | | | | | End of split % 148.93/21.42 | | | | | | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | | | | | | Case 2: % 148.93/21.42 | | | | | | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | | | | | | | (5929) all_56_19 = e1 % 148.93/21.42 | | | | | | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (435), (5929) imply: % 148.93/21.42 | | | | | | | | | | | | | | | | | | (5930) all_52_6 = e1 % 148.93/21.42 | | | | | | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | | | | | | | SIMP: (5930) implies: % 148.93/21.42 | | | | | | | | | | | | | | | | | | (5931) all_52_6 = e1 % 148.93/21.42 | | | | | | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | | | | | | | REDUCE: (5854), (5931) imply: % 148.93/21.42 | | | | | | | | | | | | | | | | | | (5932) ~ (all_4_1 = e1) % 148.93/21.42 | | | | | | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | | | | | | | SIMP: (5932) implies: % 148.93/21.42 | | | | | | | | | | | | | | | | | | (5933) ~ (all_4_1 = e1) % 148.93/21.42 | | | | | | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | | | | | | | REF_CLOSE: (247), (5846), (5849), (5851), (5856), (5857), % 148.93/21.42 | | | | | | | | | | | | | | | | | | (5933), (function-axioms) are inconsistent by % 148.93/21.42 | | | | | | | | | | | | | | | | | | sub-proof #102. % 148.93/21.42 | | | | | | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | | | | | | End of split % 148.93/21.42 | | | | | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | | | | | Case 2: % 148.93/21.42 | | | | | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | | | | | | (5934) ~ (all_44_2 = e2) % 148.93/21.42 | | | | | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | | | | | | REDUCE: (5837), (5934) imply: % 148.93/21.42 | | | | | | | | | | | | | | | | | (5935) $false % 148.93/21.42 | | | | | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | | | | | | CLOSE: (5935) is inconsistent. % 148.93/21.42 | | | | | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | | | | | End of split % 148.93/21.42 | | | | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | | | | End of split % 148.93/21.42 | | | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | | | Case 2: % 148.93/21.42 | | | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | | | | (5936) all_56_31 = e3 % 148.93/21.42 | | | | | | | | | | | | | | | (5937) all_56_25 = e0 % 148.93/21.42 | | | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | | | | COMBINE_EQS: (447), (5937) imply: % 148.93/21.42 | | | | | | | | | | | | | | | (5938) all_52_3 = e0 % 148.93/21.42 | | | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | | | | SIMP: (5938) implies: % 148.93/21.42 | | | | | | | | | | | | | | | (5939) all_52_3 = e0 % 148.93/21.42 | | | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | | | | COMBINE_EQS: (544), (5936) imply: % 148.93/21.42 | | | | | | | | | | | | | | | (5940) all_4_2 = e3 % 148.93/21.42 | | | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | | | | COMBINE_EQS: (530), (5940) imply: % 148.93/21.42 | | | | | | | | | | | | | | | (5941) all_26_2 = e3 % 148.93/21.42 | | | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | | | | REDUCE: (187), (5939) imply: % 148.93/21.42 | | | | | | | | | | | | | | | (5942) ~ (all_52_11 = e0) % 148.93/21.42 | | | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | | | | SIMP: (5942) implies: % 148.93/21.42 | | | | | | | | | | | | | | | (5943) ~ (all_52_11 = e0) % 148.93/21.42 | | | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | | | | REDUCE: (561), (5939) imply: % 148.93/21.42 | | | | | | | | | | | | | | | (5944) ~ (all_10_2 = e0) % 148.93/21.42 | | | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | | | | SIMP: (5944) implies: % 148.93/21.42 | | | | | | | | | | | | | | | (5945) ~ (all_10_2 = e0) % 148.93/21.42 | | | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | | | | REDUCE: (570), (5939), (5940) imply: % 148.93/21.42 | | | | | | | | | | | | | | | (5946) ~ (e3 = e0) % 148.93/21.42 | | | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | | | | REDUCE: (588), (5940) imply: % 148.93/21.42 | | | | | | | | | | | | | | | (5947) ~ (all_52_11 = e3) % 148.93/21.42 | | | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | | | | REDUCE: (38), (5940) imply: % 148.93/21.42 | | | | | | | | | | | | | | | (5948) op(e3, e3) = all_4_1 % 148.93/21.42 | | | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | | | | REDUCE: (36), (5940) imply: % 148.93/21.42 | | | | | | | | | | | | | | | (5949) op(e0, e0) = e3 % 148.93/21.42 | | | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (43), (46), (51), (182), (246), (247), % 148.93/21.42 | | | | | | | | | | | | | | | (252), (287), (291), (293), (295), (296), (299), % 148.93/21.42 | | | | | | | | | | | | | | | (328), (331), (332), (374), (381), (386), (401), % 148.93/21.42 | | | | | | | | | | | | | | | (407), (408), (425), (542), (543), (544), (545), % 148.93/21.42 | | | | | | | | | | | | | | | (546), (548), (552), (554), (559), (565), (568), % 148.93/21.42 | | | | | | | | | | | | | | | (585), (590), (617), (768), (5069), (5071), % 148.93/21.42 | | | | | | | | | | | | | | | (5074), (5075), (5076), (5077), (5082), (5083), % 148.93/21.42 | | | | | | | | | | | | | | | (5084), (5808), (5820), (5825), (5941), (5943), % 148.93/21.42 | | | | | | | | | | | | | | | (5945), (5947), (5948), (5949), (function-axioms) % 148.93/21.42 | | | | | | | | | | | | | | | are inconsistent by sub-proof #100. % 148.93/21.42 | | | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | | | End of split % 148.93/21.42 | | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | | Case 2: % 148.93/21.42 | | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | | | (5950) all_56_31 = e1 % 148.93/21.42 | | | | | | | | | | | | | | (5951) all_56_29 = e0 % 148.93/21.42 | | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | | | COMBINE_EQS: (357), (5951) imply: % 148.93/21.42 | | | | | | | | | | | | | | (5952) all_52_11 = e0 % 148.93/21.42 | | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | | | SIMP: (5952) implies: % 148.93/21.42 | | | | | | | | | | | | | | (5953) all_52_11 = e0 % 148.93/21.42 | | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | | | COMBINE_EQS: (544), (5950) imply: % 148.93/21.42 | | | | | | | | | | | | | | (5954) all_4_2 = e1 % 148.93/21.42 | | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | | | COMBINE_EQS: (548), (5953) imply: % 148.93/21.42 | | | | | | | | | | | | | | (5955) all_58_14 = e0 % 148.93/21.42 | | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | | | REDUCE: (38), (5954) imply: % 148.93/21.42 | | | | | | | | | | | | | | (5956) op(e1, e1) = all_4_1 % 148.93/21.42 | | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_6_2, % 148.93/21.42 | | | | | | | | | | | | | | all_4_1, e1, e1, simplifying with (41), (5956) % 148.93/21.42 | | | | | | | | | | | | | | gives: % 148.93/21.42 | | | | | | | | | | | | | | (5957) all_6_2 = all_4_1 % 148.93/21.42 | | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | | | COMBINE_EQS: (374), (5957) imply: % 148.93/21.42 | | | | | | | | | | | | | | (5958) all_56_21 = all_4_1 % 148.93/21.42 | | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | | | BETA: splitting (293) gives: % 148.93/21.42 | | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | | | Case 1: % 148.93/21.42 | | | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | | | | (5959) ~ (all_56_21 = e3) % 148.93/21.42 | | | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | | | | REDUCE: (5958), (5959) imply: % 148.93/21.42 | | | | | | | | | | | | | | | (5960) ~ (all_4_1 = e3) % 148.93/21.42 | | | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | | | | REF_CLOSE: (7), (41), (46), (53), (168), (182), (252), (287), % 148.93/21.42 | | | | | | | | | | | | | | | (297), (299), (331), (374), (402), (407), (408), % 148.93/21.42 | | | | | | | | | | | | | | | (543), (545), (546), (552), (565), (5071), (5076), % 148.93/21.42 | | | | | | | | | | | | | | | (5818), (5825), (5950), (5955), (5956), (5960), % 148.93/21.42 | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 148.93/21.42 | | | | | | | | | | | | | | | #119. % 148.93/21.42 | | | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | | | Case 2: % 148.93/21.42 | | | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | | | | (5961) all_56_21 = e3 % 148.93/21.42 | | | | | | | | | | | | | | | (5962) all_56_17 = e1 % 148.93/21.42 | | | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | | | | COMBINE_EQS: (381), (5962) imply: % 148.93/21.42 | | | | | | | | | | | | | | | (5963) all_52_2 = e1 % 148.93/21.42 | | | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | | | | SIMP: (5963) implies: % 148.93/21.42 | | | | | | | | | | | | | | | (5964) all_52_2 = e1 % 148.93/21.42 | | | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | | | | COMBINE_EQS: (5958), (5961) imply: % 148.93/21.42 | | | | | | | | | | | | | | | (5965) all_4_1 = e3 % 148.93/21.42 | | | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | | | | SIMP: (5965) implies: % 148.93/21.42 | | | | | | | | | | | | | | | (5966) all_4_1 = e3 % 148.93/21.42 | | | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | | | | REF_CLOSE: (192), (207), (5814), (5964), (5966), % 148.93/21.42 | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 148.93/21.42 | | | | | | | | | | | | | | | #159. % 148.93/21.42 | | | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | | | End of split % 148.93/21.42 | | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | | End of split % 148.93/21.42 | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | Case 2: % 148.93/21.42 | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | | (5967) all_48_0 = e3 % 148.93/21.42 | | | | | | | | | | | | | (5968) ~ (all_48_1 = e1) | ~ (all_48_2 = e0) % 148.93/21.42 | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | | COMBINE_EQS: (765), (5967) imply: % 148.93/21.42 | | | | | | | | | | | | | (5969) all_8_0 = e3 % 148.93/21.42 | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | | SIMP: (5969) implies: % 148.93/21.42 | | | | | | | | | | | | | (5970) all_8_0 = e3 % 148.93/21.42 | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | | REF_CLOSE: (9), (46), (247), (295), (536), (542), (545), % 148.93/21.42 | | | | | | | | | | | | | (617), (5070), (5071), (5075), (5083), (5968), % 148.93/21.42 | | | | | | | | | | | | | (5970), (function-axioms) are inconsistent by % 148.93/21.42 | | | | | | | | | | | | | sub-proof #115. % 148.93/21.42 | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | End of split % 148.93/21.42 | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | End of split % 148.93/21.42 | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | Case 2: % 148.93/21.42 | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | (5971) all_36_1 = e3 % 148.93/21.42 | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | COMBINE_EQS: (652), (5971) imply: % 148.93/21.42 | | | | | | | | | | | (5972) all_6_1 = e3 % 148.93/21.42 | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | SIMP: (5972) implies: % 148.93/21.42 | | | | | | | | | | | (5973) all_6_1 = e3 % 148.93/21.42 | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | REDUCE: (43), (5973) imply: % 148.93/21.42 | | | | | | | | | | | (5974) op(all_6_2, all_6_2) = e3 % 148.93/21.42 | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | REDUCE: (42), (5973) imply: % 148.93/21.42 | | | | | | | | | | | (5975) op(e1, e3) = all_6_0 % 148.93/21.42 | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_2, % 148.93/21.42 | | | | | | | | | | | all_6_0, e3, e1, simplifying with (211), (5975) % 148.93/21.42 | | | | | | | | | | | gives: % 148.93/21.42 | | | | | | | | | | | (5976) all_52_2 = all_6_0 % 148.93/21.42 | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | COMBINE_EQS: (381), (5976) imply: % 148.93/21.42 | | | | | | | | | | | (5977) all_56_17 = all_6_0 % 148.93/21.42 | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | REDUCE: (192), (5976) imply: % 148.93/21.42 | | | | | | | | | | | (5978) ~ (all_52_3 = all_6_0) % 148.93/21.42 | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | SIMP: (5978) implies: % 148.93/21.42 | | | | | | | | | | | (5979) ~ (all_52_3 = all_6_0) % 148.93/21.42 | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | REDUCE: (189), (5976) imply: % 148.93/21.42 | | | | | | | | | | | (5980) ~ (all_52_14 = all_6_0) % 148.93/21.42 | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | SIMP: (5980) implies: % 148.93/21.42 | | | | | | | | | | | (5981) ~ (all_52_14 = all_6_0) % 148.93/21.42 | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | BETA: splitting (149) gives: % 148.93/21.42 | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | Case 1: % 148.93/21.42 | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | (5982) ~ (all_48_0 = e3) % 148.93/21.42 | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | REDUCE: (765), (5982) imply: % 148.93/21.42 | | | | | | | | | | | | (5983) ~ (all_8_0 = e3) % 148.93/21.42 | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | BETA: splitting (288) gives: % 148.93/21.42 | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | Case 1: % 148.93/21.42 | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | | (5984) ~ (all_56_31 = e1) % 148.93/21.42 | | | | | | | | | | | | | % 148.93/21.42 | | | | | | | | | | | | | REDUCE: (544), (5984) imply: % 148.93/21.42 | | | | | | | | | | | | | (5985) ~ (all_4_2 = e1) % 148.93/21.42 | | | | | | | | | | | | | % 148.93/21.43 | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (38), (41), % 148.93/21.43 | | | | | | | | | | | | | (46), (51), (168), (246), (247), (287), (293), % 148.93/21.43 | | | | | | | | | | | | | (294), (295), (296), (321), (329), (332), (333), % 148.93/21.43 | | | | | | | | | | | | | (335), (374), (386), (401), (407), (425), (443), % 148.93/21.43 | | | | | | | | | | | | | (542), (544), (545), (546), (547), (548), (550), % 148.93/21.43 | | | | | | | | | | | | | (551), (552), (554), (557), (567), (568), (579), % 148.93/21.43 | | | | | | | | | | | | | (585), (590), (617), (622), (623), (627), (5069), % 148.93/21.43 | | | | | | | | | | | | | (5071), (5074), (5075), (5076), (5077), (5082), % 148.93/21.43 | | | | | | | | | | | | | (5083), (5084), (5974), (5977), (5981), (5983), % 148.93/21.43 | | | | | | | | | | | | | (5985), (function-axioms) are inconsistent by % 148.93/21.43 | | | | | | | | | | | | | sub-proof #110. % 148.93/21.43 | | | | | | | | | | | | | % 148.93/21.43 | | | | | | | | | | | | Case 2: % 148.93/21.43 | | | | | | | | | | | | | % 148.93/21.43 | | | | | | | | | | | | | (5986) all_56_31 = e1 % 148.93/21.43 | | | | | | | | | | | | | (5987) all_56_29 = e0 % 148.93/21.43 | | | | | | | | | | | | | % 148.93/21.43 | | | | | | | | | | | | | COMBINE_EQS: (357), (5987) imply: % 148.93/21.43 | | | | | | | | | | | | | (5988) all_52_11 = e0 % 148.93/21.43 | | | | | | | | | | | | | % 148.93/21.43 | | | | | | | | | | | | | SIMP: (5988) implies: % 148.93/21.43 | | | | | | | | | | | | | (5989) all_52_11 = e0 % 148.93/21.43 | | | | | | | | | | | | | % 148.93/21.43 | | | | | | | | | | | | | COMBINE_EQS: (544), (5986) imply: % 148.93/21.43 | | | | | | | | | | | | | (5990) all_4_2 = e1 % 148.93/21.43 | | | | | | | | | | | | | % 148.93/21.43 | | | | | | | | | | | | | COMBINE_EQS: (548), (5989) imply: % 148.93/21.43 | | | | | | | | | | | | | (5991) all_58_14 = e0 % 148.93/21.43 | | | | | | | | | | | | | % 148.93/21.43 | | | | | | | | | | | | | REDUCE: (38), (5990) imply: % 148.93/21.43 | | | | | | | | | | | | | (5992) op(e1, e1) = all_4_1 % 148.93/21.43 | | | | | | | | | | | | | % 148.93/21.43 | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_6_2, % 148.93/21.43 | | | | | | | | | | | | | all_4_1, e1, e1, simplifying with (41), (5992) % 148.93/21.43 | | | | | | | | | | | | | gives: % 148.93/21.43 | | | | | | | | | | | | | (5993) all_6_2 = all_4_1 % 148.93/21.43 | | | | | | | | | | | | | % 148.93/21.43 | | | | | | | | | | | | | COMBINE_EQS: (374), (5993) imply: % 148.93/21.43 | | | | | | | | | | | | | (5994) all_56_21 = all_4_1 % 148.93/21.43 | | | | | | | | | | | | | % 148.93/21.43 | | | | | | | | | | | | | BETA: splitting (293) gives: % 148.93/21.43 | | | | | | | | | | | | | % 148.93/21.43 | | | | | | | | | | | | | Case 1: % 148.93/21.43 | | | | | | | | | | | | | | % 148.93/21.43 | | | | | | | | | | | | | | (5995) ~ (all_56_21 = e3) % 148.93/21.43 | | | | | | | | | | | | | | % 148.93/21.43 | | | | | | | | | | | | | | REDUCE: (5994), (5995) imply: % 148.93/21.43 | | | | | | | | | | | | | | (5996) ~ (all_4_1 = e3) % 148.93/21.43 | | | | | | | | | | | | | | % 148.93/21.43 | | | | | | | | | | | | | | REF_CLOSE: (7), (41), (46), (53), (168), (182), (252), (287), % 148.93/21.43 | | | | | | | | | | | | | | (297), (299), (331), (374), (402), (407), (408), % 148.93/21.43 | | | | | | | | | | | | | | (543), (545), (546), (552), (565), (5071), (5076), % 148.93/21.43 | | | | | | | | | | | | | | (5818), (5983), (5986), (5991), (5992), (5996), % 148.93/21.43 | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 148.93/21.43 | | | | | | | | | | | | | | #119. % 148.93/21.43 | | | | | | | | | | | | | | % 148.93/21.43 | | | | | | | | | | | | | Case 2: % 148.93/21.43 | | | | | | | | | | | | | | % 148.93/21.43 | | | | | | | | | | | | | | (5997) all_56_21 = e3 % 148.93/21.43 | | | | | | | | | | | | | | (5998) all_56_17 = e1 % 148.93/21.43 | | | | | | | | | | | | | | % 148.93/21.43 | | | | | | | | | | | | | | COMBINE_EQS: (5977), (5998) imply: % 148.93/21.43 | | | | | | | | | | | | | | (5999) all_6_0 = e1 % 148.93/21.43 | | | | | | | | | | | | | | % 148.93/21.43 | | | | | | | | | | | | | | SIMP: (5999) implies: % 148.93/21.43 | | | | | | | | | | | | | | (6000) all_6_0 = e1 % 148.93/21.43 | | | | | | | | | | | | | | % 148.93/21.43 | | | | | | | | | | | | | | COMBINE_EQS: (5994), (5997) imply: % 148.93/21.43 | | | | | | | | | | | | | | (6001) all_4_1 = e3 % 148.93/21.43 | | | | | | | | | | | | | | % 148.93/21.43 | | | | | | | | | | | | | | SIMP: (6001) implies: % 148.93/21.43 | | | | | | | | | | | | | | (6002) all_4_1 = e3 % 148.93/21.43 | | | | | | | | | | | | | | % 148.93/21.43 | | | | | | | | | | | | | | REDUCE: (5979), (6000) imply: % 148.93/21.43 | | | | | | | | | | | | | | (6003) ~ (all_52_3 = e1) % 148.93/21.43 | | | | | | | | | | | | | | % 148.93/21.43 | | | | | | | | | | | | | | REDUCE: (5814), (6002) imply: % 148.93/21.43 | | | | | | | | | | | | | | (6004) op(e0, e3) = e1 % 148.93/21.43 | | | | | | | | | | | | | | % 148.93/21.43 | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_3, e1, % 148.93/21.43 | | | | | | | | | | | | | | e3, e0, simplifying with (207), (6004) gives: % 148.93/21.43 | | | | | | | | | | | | | | (6005) all_52_3 = e1 % 148.93/21.43 | | | | | | | | | | | | | | % 148.93/21.43 | | | | | | | | | | | | | | REDUCE: (6003), (6005) imply: % 148.93/21.43 | | | | | | | | | | | | | | (6006) $false % 148.93/21.43 | | | | | | | | | | | | | | % 148.93/21.43 | | | | | | | | | | | | | | CLOSE: (6006) is inconsistent. % 148.93/21.43 | | | | | | | | | | | | | | % 148.93/21.43 | | | | | | | | | | | | | End of split % 148.93/21.43 | | | | | | | | | | | | | % 148.93/21.43 | | | | | | | | | | | | End of split % 148.93/21.43 | | | | | | | | | | | | % 148.93/21.43 | | | | | | | | | | | Case 2: % 148.93/21.43 | | | | | | | | | | | | % 148.93/21.43 | | | | | | | | | | | | (6007) all_48_0 = e3 % 148.93/21.43 | | | | | | | | | | | | (6008) ~ (all_48_1 = e1) | ~ (all_48_2 = e0) % 148.93/21.43 | | | | | | | | | | | | % 148.93/21.43 | | | | | | | | | | | | COMBINE_EQS: (765), (6007) imply: % 148.93/21.43 | | | | | | | | | | | | (6009) all_8_0 = e3 % 148.93/21.43 | | | | | | | | | | | | % 148.93/21.43 | | | | | | | | | | | | SIMP: (6009) implies: % 148.93/21.43 | | | | | | | | | | | | (6010) all_8_0 = e3 % 148.93/21.43 | | | | | | | | | | | | % 148.93/21.43 | | | | | | | | | | | | REF_CLOSE: (9), (46), (247), (295), (536), (542), (545), % 148.93/21.43 | | | | | | | | | | | | (617), (5070), (5071), (5075), (5083), (6008), % 148.93/21.43 | | | | | | | | | | | | (6010), (function-axioms) are inconsistent by % 148.93/21.43 | | | | | | | | | | | | sub-proof #115. % 148.93/21.43 | | | | | | | | | | | | % 148.93/21.43 | | | | | | | | | | | End of split % 148.93/21.43 | | | | | | | | | | | % 148.93/21.43 | | | | | | | | | | End of split % 148.93/21.43 | | | | | | | | | | % 148.93/21.43 | | | | | | | | | Case 2: % 148.93/21.43 | | | | | | | | | | % 148.93/21.43 | | | | | | | | | | (6011) all_32_1 = e1 % 148.93/21.43 | | | | | | | | | | (6012) ~ (all_32_0 = e0) | ~ (all_32_2 = e2) % 148.93/21.43 | | | | | | | | | | % 148.93/21.43 | | | | | | | | | | COMBINE_EQS: (682), (6011) imply: % 148.93/21.43 | | | | | | | | | | (6013) all_10_1 = e1 % 148.93/21.43 | | | | | | | | | | % 148.93/21.43 | | | | | | | | | | REDUCE: (53), (6013) imply: % 148.93/21.43 | | | | | | | | | | (6014) op(all_10_2, all_10_2) = e1 % 148.93/21.43 | | | | | | | | | | % 148.93/21.43 | | | | | | | | | | REDUCE: (52), (6013) imply: % 148.93/21.43 | | | | | | | | | | (6015) op(e3, e1) = all_10_0 % 148.93/21.43 | | | | | | | | | | % 148.93/21.43 | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_8, % 148.93/21.43 | | | | | | | | | | all_10_0, e1, e3, simplifying with (217), (6015) % 148.93/21.43 | | | | | | | | | | gives: % 148.93/21.43 | | | | | | | | | | (6016) all_52_8 = all_10_0 % 148.93/21.43 | | | | | | | | | | % 148.93/21.43 | | | | | | | | | | COMBINE_EQS: (459), (6016) imply: % 148.93/21.43 | | | | | | | | | | (6017) all_54_2 = all_10_0 % 148.93/21.43 | | | | | | | | | | % 148.93/21.43 | | | | | | | | | | REDUCE: (182), (6016) imply: % 148.93/21.43 | | | | | | | | | | (6018) ~ (all_52_4 = all_10_0) % 148.93/21.43 | | | | | | | | | | % 148.93/21.43 | | | | | | | | | | REDUCE: (169), (6016) imply: % 148.93/21.43 | | | | | | | | | | (6019) ~ (all_52_11 = all_10_0) % 148.93/21.43 | | | | | | | | | | % 148.93/21.43 | | | | | | | | | | SIMP: (6019) implies: % 148.93/21.43 | | | | | | | | | | (6020) ~ (all_52_11 = all_10_0) % 148.93/21.43 | | | | | | | | | | % 148.93/21.43 | | | | | | | | | | REDUCE: (168), (6016) imply: % 148.93/21.43 | | | | | | | | | | (6021) ~ (all_52_12 = all_10_0) % 148.93/21.43 | | | | | | | | | | % 148.93/21.43 | | | | | | | | | | SIMP: (6021) implies: % 148.93/21.43 | | | | | | | | | | (6022) ~ (all_52_12 = all_10_0) % 148.93/21.43 | | | | | | | | | | % 148.93/21.43 | | | | | | | | | | REDUCE: (565), (6016) imply: % 148.93/21.43 | | | | | | | | | | (6023) ~ (all_10_0 = all_10_2) % 148.93/21.43 | | | | | | | | | | % 148.93/21.43 | | | | | | | | | | REDUCE: (582), (6016) imply: % 148.93/21.43 | | | | | | | | | | (6024) ~ (all_10_0 = all_6_2) % 148.93/21.43 | | | | | | | | | | % 148.93/21.43 | | | | | | | | | | BETA: splitting (149) gives: % 148.93/21.43 | | | | | | | | | | % 148.93/21.43 | | | | | | | | | | Case 1: % 148.93/21.43 | | | | | | | | | | | % 148.93/21.43 | | | | | | | | | | | (6025) ~ (all_48_0 = e3) % 148.93/21.43 | | | | | | | | | | | % 148.93/21.43 | | | | | | | | | | | REDUCE: (765), (6025) imply: % 148.93/21.43 | | | | | | | | | | | (6026) ~ (all_8_0 = e3) % 148.93/21.43 | | | | | | | | | | | % 148.93/21.43 | | | | | | | | | | | BETA: splitting (288) gives: % 148.93/21.43 | | | | | | | | | | | % 148.93/21.43 | | | | | | | | | | | Case 1: % 148.93/21.43 | | | | | | | | | | | | % 148.93/21.43 | | | | | | | | | | | | (6027) ~ (all_56_31 = e1) % 148.93/21.43 | | | | | | | | | | | | % 148.93/21.43 | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (38), (41), % 148.93/21.43 | | | | | | | | | | | | (46), (51), (246), (247), (250), (252), (287), % 148.93/21.43 | | | | | | | | | | | | (293), (294), (295), (296), (297), (299), (321), % 148.93/21.43 | | | | | | | | | | | | (332), (333), (335), (374), (381), (386), (401), % 148.93/21.43 | | | | | | | | | | | | (402), (408), (425), (443), (494), (542), (543), % 148.93/21.43 | | | | | | | | | | | | (544), (545), (546), (547), (550), (551), (554), % 148.93/21.43 | | | | | | | | | | | | (557), (559), (567), (568), (579), (587), (590), % 148.93/21.43 | | | | | | | | | | | | (612), (617), (627), (761), (5069), (5071), % 148.93/21.43 | | | | | | | | | | | | (5074), (5076), (5077), (5082), (5083), (5084), % 148.93/21.43 | | | | | | | | | | | | (5086), (5090), (6012), (6014), (6017), (6018), % 148.93/21.43 | | | | | | | | | | | | (6022), (6023), (6024), (6026), (6027), % 148.93/21.43 | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 148.93/21.43 | | | | | | | | | | | | #109. % 148.93/21.43 | | | | | | | | | | | | % 148.93/21.43 | | | | | | | | | | | Case 2: % 148.93/21.43 | | | | | | | | | | | | % 148.93/21.43 | | | | | | | | | | | | (6028) all_56_31 = e1 % 148.93/21.43 | | | | | | | | | | | | (6029) all_56_29 = e0 % 148.93/21.43 | | | | | | | | | | | | % 148.93/21.43 | | | | | | | | | | | | COMBINE_EQS: (357), (6029) imply: % 148.93/21.43 | | | | | | | | | | | | (6030) all_52_11 = e0 % 148.93/21.43 | | | | | | | | | | | | % 148.93/21.43 | | | | | | | | | | | | SIMP: (6030) implies: % 148.93/21.43 | | | | | | | | | | | | (6031) all_52_11 = e0 % 148.93/21.43 | | | | | | | | | | | | % 148.93/21.43 | | | | | | | | | | | | COMBINE_EQS: (544), (6028) imply: % 148.93/21.43 | | | | | | | | | | | | (6032) all_4_2 = e1 % 148.93/21.43 | | | | | | | | | | | | % 148.93/21.43 | | | | | | | | | | | | REDUCE: (6020), (6031) imply: % 148.93/21.43 | | | | | | | | | | | | (6033) ~ (all_10_0 = e0) % 148.93/21.43 | | | | | | | | | | | | % 148.93/21.43 | | | | | | | | | | | | SIMP: (6033) implies: % 148.93/21.43 | | | | | | | | | | | | (6034) ~ (all_10_0 = e0) % 148.93/21.43 | | | | | | | | | | | | % 148.93/21.43 | | | | | | | | | | | | REDUCE: (585), (6031) imply: % 148.93/21.43 | | | | | | | | | | | | (6035) ~ (all_6_2 = e0) % 148.93/21.43 | | | | | | | | | | | | % 148.93/21.43 | | | | | | | | | | | | SIMP: (6035) implies: % 148.93/21.43 | | | | | | | | | | | | (6036) ~ (all_6_2 = e0) % 148.93/21.43 | | | | | | | | | | | | % 148.93/21.43 | | | | | | | | | | | | REDUCE: (38), (6032) imply: % 148.93/21.43 | | | | | | | | | | | | (6037) op(e1, e1) = all_4_1 % 148.93/21.43 | | | | | | | | | | | | % 148.93/21.43 | | | | | | | | | | | | REDUCE: (627), (6032) imply: % 148.93/21.43 | | | | | | | | | | | | (6038) op(e0, e1) = all_56_30 % 148.93/21.43 | | | | | | | | | | | | % 148.93/21.43 | | | | | | | | | | | | REDUCE: (205), (6031) imply: % 148.93/21.43 | | | | | | | | | | | | (6039) op(e0, e1) = e0 % 148.93/21.43 | | | | | | | | | | | | % 148.93/21.43 | | | | | | | | | | | | REF_CLOSE: (41), (250), (252), (297), (299), (402), (408), % 148.93/21.43 | | | | | | | | | | | | (543), (546), (5086), (5090), (5814), (6014), % 148.93/21.43 | | | | | | | | | | | | (6017), (6018), (6022), (6023), (6034), (6036), % 148.93/21.43 | | | | | | | | | | | | (6037), (6038), (6039), (function-axioms) are % 148.93/21.43 | | | | | | | | | | | | inconsistent by sub-proof #350. % 148.93/21.43 | | | | | | | | | | | | % 148.93/21.43 | | | | | | | | | | | End of split % 148.93/21.43 | | | | | | | | | | | % 148.93/21.43 | | | | | | | | | | Case 2: % 148.93/21.43 | | | | | | | | | | | % 148.93/21.43 | | | | | | | | | | | (6040) all_48_0 = e3 % 148.93/21.43 | | | | | | | | | | | (6041) ~ (all_48_1 = e1) | ~ (all_48_2 = e0) % 148.93/21.43 | | | | | | | | | | | % 148.93/21.43 | | | | | | | | | | | COMBINE_EQS: (765), (6040) imply: % 148.93/21.43 | | | | | | | | | | | (6042) all_8_0 = e3 % 148.93/21.43 | | | | | | | | | | | % 148.93/21.43 | | | | | | | | | | | SIMP: (6042) implies: % 148.93/21.43 | | | | | | | | | | | (6043) all_8_0 = e3 % 148.93/21.43 | | | | | | | | | | | % 148.93/21.43 | | | | | | | | | | | REF_CLOSE: (9), (46), (247), (295), (536), (542), (545), % 148.93/21.43 | | | | | | | | | | | (617), (5070), (5071), (5075), (5083), (6041), % 148.93/21.43 | | | | | | | | | | | (6043), (function-axioms) are inconsistent by % 148.93/21.43 | | | | | | | | | | | sub-proof #115. % 148.93/21.43 | | | | | | | | | | | % 148.93/21.43 | | | | | | | | | | End of split % 148.93/21.43 | | | | | | | | | | % 148.93/21.43 | | | | | | | | | End of split % 148.93/21.43 | | | | | | | | | % 148.93/21.43 | | | | | | | | Case 2: % 148.93/21.43 | | | | | | | | | % 148.93/21.43 | | | | | | | | | (6044) all_28_0 = e2 % 148.93/21.43 | | | | | | | | | % 148.93/21.43 | | | | | | | | | COMBINE_EQS: (740), (6044) imply: % 148.93/21.43 | | | | | | | | | (6045) all_6_0 = e2 % 148.93/21.43 | | | | | | | | | % 148.93/21.43 | | | | | | | | | SIMP: (6045) implies: % 148.93/21.43 | | | | | | | | | (6046) all_6_0 = e2 % 148.93/21.43 | | | | | | | | | % 148.93/21.43 | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (38), (41), % 148.93/21.43 | | | | | | | | | (42), (43), (46), (51), (149), (246), (247), (287), % 148.93/21.43 | | | | | | | | | (294), (295), (296), (332), (333), (335), (374), % 148.93/21.43 | | | | | | | | | (386), (401), (425), (443), (536), (542), (544), % 148.93/21.43 | | | | | | | | | (545), (546), (554), (557), (568), (579), (590), % 148.93/21.43 | | | | | | | | | (617), (622), (627), (765), (768), (5069), (5070), % 148.93/21.43 | | | | | | | | | (5071), (5074), (5075), (5076), (5077), (5082), % 148.93/21.43 | | | | | | | | | (5083), (5084), (6046), (function-axioms) are % 148.93/21.43 | | | | | | | | | inconsistent by sub-proof #104. % 148.93/21.43 | | | | | | | | | % 148.93/21.43 | | | | | | | | End of split % 148.93/21.43 | | | | | | | | % 148.93/21.43 | | | | | | | End of split % 148.93/21.43 | | | | | | | % 148.93/21.43 | | | | | | Case 2: % 148.93/21.43 | | | | | | | % 148.93/21.43 | | | | | | | (6047) all_16_0 = e1 % 148.93/21.43 | | | | | | | % 148.93/21.43 | | | | | | | COMBINE_EQS: (757), (6047) imply: % 148.93/21.43 | | | | | | | (6048) all_10_0 = e1 % 148.93/21.43 | | | | | | | % 148.93/21.43 | | | | | | | COMBINE_EQS: (741), (6048) imply: % 148.93/21.43 | | | | | | | (6049) all_24_0 = e1 % 148.93/21.43 | | | | | | | % 148.93/21.43 | | | | | | | REDUCE: (5086), (6048) imply: % 148.93/21.43 | | | | | | | (6050) ~ (e2 = e1) % 148.93/21.43 | | | | | | | % 148.93/21.43 | | | | | | | REDUCE: (52), (6048) imply: % 148.93/21.43 | | | | | | | (6051) op(e3, all_10_1) = e1 % 148.93/21.43 | | | | | | | % 148.93/21.43 | | | | | | | BETA: splitting (89) gives: % 148.93/21.43 | | | | | | | % 148.93/21.43 | | | | | | | Case 1: % 148.93/21.43 | | | | | | | | % 148.93/21.43 | | | | | | | | (6052) ~ (all_24_0 = e1) % 148.93/21.43 | | | | | | | | % 148.93/21.43 | | | | | | | | REDUCE: (6049), (6052) imply: % 148.93/21.43 | | | | | | | | (6053) $false % 148.93/21.43 | | | | | | | | % 148.93/21.43 | | | | | | | | CLOSE: (6053) is inconsistent. % 148.93/21.43 | | | | | | | | % 148.93/21.43 | | | | | | | Case 2: % 148.93/21.43 | | | | | | | | % 148.93/21.43 | | | | | | | | (6054) ~ (all_24_1 = e0) | ~ (all_24_2 = e2) % 148.93/21.43 | | | | | | | | % 148.93/21.43 | | | | | | | | BETA: splitting (94) gives: % 148.93/21.43 | | | | | | | | % 148.93/21.43 | | | | | | | | Case 1: % 148.93/21.43 | | | | | | | | | % 148.93/21.43 | | | | | | | | | (6055) ~ (all_26_0 = e1) % 148.93/21.43 | | | | | | | | | % 148.93/21.43 | | | | | | | | | REDUCE: (760), (6055) imply: % 148.93/21.43 | | | | | | | | | (6056) ~ (all_4_0 = e1) % 148.93/21.43 | | | | | | | | | % 148.93/21.43 | | | | | | | | | BETA: splitting (99) gives: % 148.93/21.43 | | | | | | | | | % 148.93/21.43 | | | | | | | | | Case 1: % 148.93/21.43 | | | | | | | | | | % 148.93/21.43 | | | | | | | | | | (6057) ~ (all_28_0 = e2) % 148.93/21.43 | | | | | | | | | | % 148.93/21.43 | | | | | | | | | | REDUCE: (740), (6057) imply: % 148.93/21.43 | | | | | | | | | | (6058) ~ (all_6_0 = e2) % 148.93/21.43 | | | | | | | | | | % 148.93/21.43 | | | | | | | | | | BETA: splitting (119) gives: % 148.93/21.43 | | | | | | | | | | % 148.93/21.43 | | | | | | | | | | Case 1: % 148.93/21.43 | | | | | | | | | | | % 148.93/21.43 | | | | | | | | | | | (6059) ~ (all_36_1 = e3) % 148.93/21.43 | | | | | | | | | | | % 148.93/21.43 | | | | | | | | | | | REDUCE: (652), (6059) imply: % 148.93/21.43 | | | | | | | | | | | (6060) ~ (all_6_1 = e3) % 148.93/21.43 | | | | | | | | | | | % 148.93/21.43 | | | | | | | | | | | BETA: splitting (149) gives: % 148.93/21.43 | | | | | | | | | | | % 148.93/21.43 | | | | | | | | | | | Case 1: % 148.93/21.43 | | | | | | | | | | | | % 148.93/21.43 | | | | | | | | | | | | (6061) ~ (all_48_0 = e3) % 148.93/21.43 | | | | | | | | | | | | % 148.93/21.43 | | | | | | | | | | | | REDUCE: (765), (6061) imply: % 148.93/21.43 | | | | | | | | | | | | (6062) ~ (all_8_0 = e3) % 148.93/21.43 | | | | | | | | | | | | % 148.93/21.43 | | | | | | | | | | | | BETA: splitting (292) gives: % 148.93/21.43 | | | | | | | | | | | | % 148.93/21.43 | | | | | | | | | | | | Case 1: % 148.93/21.43 | | | | | | | | | | | | | % 148.93/21.43 | | | | | | | | | | | | | (6063) ~ (all_56_21 = e2) % 148.93/21.43 | | | | | | | | | | | | | % 148.93/21.43 | | | | | | | | | | | | | REDUCE: (374), (6063) imply: % 148.93/21.43 | | | | | | | | | | | | | (6064) ~ (all_6_2 = e2) % 148.93/21.43 | | | | | | | | | | | | | % 148.93/21.43 | | | | | | | | | | | | | BETA: splitting (288) gives: % 148.93/21.43 | | | | | | | | | | | | | % 148.93/21.43 | | | | | | | | | | | | | Case 1: % 148.93/21.43 | | | | | | | | | | | | | | % 148.93/21.43 | | | | | | | | | | | | | | (6065) ~ (all_56_31 = e1) % 148.93/21.43 | | | | | | | | | | | | | | % 148.93/21.43 | | | | | | | | | | | | | | REDUCE: (544), (6065) imply: % 148.93/21.43 | | | | | | | | | | | | | | (6066) ~ (all_4_2 = e1) % 148.93/21.43 | | | | | | | | | | | | | | % 148.93/21.43 | | | | | | | | | | | | | | BETA: splitting (290) gives: % 148.93/21.43 | | | | | | | | | | | | | | % 148.93/21.43 | | | | | | | | | | | | | | Case 1: % 148.93/21.43 | | | | | | | | | | | | | | | % 148.93/21.43 | | | | | | | | | | | | | | | (6067) ~ (all_56_31 = e3) % 148.93/21.43 | | | | | | | | | | | | | | | % 148.93/21.43 | | | | | | | | | | | | | | | REDUCE: (544), (6067) imply: % 148.93/21.43 | | | | | | | | | | | | | | | (6068) ~ (all_4_2 = e3) % 148.93/21.43 | | | | | | | | | | | | | | | % 148.93/21.43 | | | | | | | | | | | | | | | BETA: splitting (291) gives: % 148.93/21.43 | | | | | | | | | | | | | | | % 148.93/21.43 | | | | | | | | | | | | | | | Case 1: % 148.93/21.43 | | | | | | | | | | | | | | | | % 148.93/21.43 | | | | | | | | | | | | | | | | (6069) ~ (all_56_21 = e0) % 148.93/21.43 | | | | | | | | | | | | | | | | % 148.93/21.43 | | | | | | | | | | | | | | | | REDUCE: (374), (6069) imply: % 148.93/21.43 | | | | | | | | | | | | | | | | (6070) ~ (all_6_2 = e0) % 148.93/21.43 | | | | | | | | | | | | | | | | % 148.93/21.43 | | | | | | | | | | | | | | | | BETA: splitting (294) gives: % 148.93/21.43 | | | | | | | | | | | | | | | | % 148.93/21.43 | | | | | | | | | | | | | | | | Case 1: % 148.93/21.43 | | | | | | | | | | | | | | | | | % 148.93/21.43 | | | | | | | | | | | | | | | | | (6071) ~ (all_56_11 = e0) % 148.93/21.43 | | | | | | | | | | | | | | | | | % 148.93/21.43 | | | | | | | | | | | | | | | | | REDUCE: (545), (6071) imply: % 148.93/21.43 | | | | | | | | | | | | | | | | | (6072) ~ (all_8_2 = e0) % 148.93/21.43 | | | | | | | | | | | | | | | | | % 148.93/21.43 | | | | | | | | | | | | | | | | | BETA: splitting (289) gives: % 148.93/21.43 | | | | | | | | | | | | | | | | | % 148.93/21.43 | | | | | | | | | | | | | | | | | Case 1: % 148.93/21.43 | | | | | | | | | | | | | | | | | | % 148.93/21.43 | | | | | | | | | | | | | | | | | | (6073) ~ (all_56_31 = e2) % 148.93/21.43 | | | | | | | | | | | | | | | | | | % 148.93/21.43 | | | | | | | | | | | | | | | | | | REDUCE: (544), (6073) imply: % 148.93/21.43 | | | | | | | | | | | | | | | | | | (6074) ~ (all_4_2 = e2) % 148.93/21.43 | | | | | | | | | | | | | | | | | | % 148.93/21.43 | | | | | | | | | | | | | | | | | | BETA: splitting (237) gives: % 148.93/21.43 | | | | | | | | | | | | | | | | | | % 148.93/21.43 | | | | | | | | | | | | | | | | | | Case 1: % 148.93/21.43 | | | | | | | | | | | | | | | | | | | % 148.93/21.43 | | | | | | | | | | | | | | | | | | | (6075) all_54_15 = e3 % 148.93/21.43 | | | | | | | | | | | | | | | | | | | % 148.93/21.43 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (540), (6068), (6075) are inconsistent by % 148.93/21.43 | | | | | | | | | | | | | | | | | | | sub-proof #740. % 148.93/21.43 | | | | | | | | | | | | | | | | | | | % 148.93/21.43 | | | | | | | | | | | | | | | | | | Case 2: % 148.93/21.43 | | | | | | | | | | | | | | | | | | | % 148.93/21.43 | | | | | | | | | | | | | | | | | | | (6076) all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0 % 148.93/21.43 | | | | | | | | | | | | | | | | | | | % 148.93/21.43 | | | | | | | | | | | | | | | | | | | BETA: splitting (6076) gives: % 148.93/21.43 | | | | | | | | | | | | | | | | | | | % 148.93/21.43 | | | | | | | | | | | | | | | | | | | Case 1: % 148.93/21.43 | | | | | | | | | | | | | | | | | | | | % 148.93/21.43 | | | | | | | | | | | | | | | | | | | | (6077) all_54_15 = e2 % 148.93/21.43 | | | | | | | | | | | | | | | | | | | | % 148.93/21.43 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (540), (6074), (6077) are inconsistent by % 148.93/21.43 | | | | | | | | | | | | | | | | | | | | sub-proof #739. % 148.93/21.43 | | | | | | | | | | | | | | | | | | | | % 148.93/21.43 | | | | | | | | | | | | | | | | | | | Case 2: % 148.93/21.43 | | | | | | | | | | | | | | | | | | | | % 148.93/21.43 | | | | | | | | | | | | | | | | | | | | (6078) all_54_15 = e1 | all_54_15 = e0 % 148.93/21.43 | | | | | | | | | | | | | | | | | | | | % 148.93/21.43 | | | | | | | | | | | | | | | | | | | | BETA: splitting (6078) gives: % 148.93/21.43 | | | | | | | | | | | | | | | | | | | | % 148.93/21.43 | | | | | | | | | | | | | | | | | | | | Case 1: % 148.93/21.43 | | | | | | | | | | | | | | | | | | | | | % 148.93/21.43 | | | | | | | | | | | | | | | | | | | | | (6079) all_54_15 = e1 % 148.93/21.43 | | | | | | | | | | | | | | | | | | | | | % 148.93/21.43 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (540), (6066), (6079) are inconsistent by % 148.93/21.43 | | | | | | | | | | | | | | | | | | | | | sub-proof #738. % 148.93/21.43 | | | | | | | | | | | | | | | | | | | | | % 148.93/21.43 | | | | | | | | | | | | | | | | | | | | Case 2: % 148.93/21.43 | | | | | | | | | | | | | | | | | | | | | % 148.93/21.43 | | | | | | | | | | | | | | | | | | | | | (6080) all_54_15 = e0 % 148.93/21.43 | | | | | | | | | | | | | | | | | | | | | % 148.93/21.43 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (540), (6080) imply: % 148.93/21.43 | | | | | | | | | | | | | | | | | | | | | (6081) all_4_2 = e0 % 148.93/21.43 | | | | | | | | | | | | | | | | | | | | | % 148.93/21.43 | | | | | | | | | | | | | | | | | | | | | SIMP: (6081) implies: % 148.93/21.43 | | | | | | | | | | | | | | | | | | | | | (6082) all_4_2 = e0 % 148.93/21.43 | | | | | | | | | | | | | | | | | | | | | % 148.93/21.43 | | | | | | | | | | | | | | | | | | | | | REDUCE: (581), (6082) imply: % 148.93/21.43 | | | | | | | | | | | | | | | | | | | | | (6083) ~ (all_52_7 = e0) % 148.93/21.43 | | | | | | | | | | | | | | | | | | | | | % 148.93/21.43 | | | | | | | | | | | | | | | | | | | | | REDUCE: (588), (6082) imply: % 148.93/21.43 | | | | | | | | | | | | | | | | | | | | | (6084) ~ (all_52_11 = e0) % 148.93/21.43 | | | | | | | | | | | | | | | | | | | | | % 148.93/21.43 | | | | | | | | | | | | | | | | | | | | | REDUCE: (589), (6082) imply: % 148.93/21.43 | | | | | | | | | | | | | | | | | | | | | (6085) ~ (all_52_12 = e0) % 148.93/21.43 | | | | | | | | | | | | | | | | | | | | | % 148.93/21.43 | | | | | | | | | | | | | | | | | | | | | REDUCE: (590), (6082) imply: % 148.93/21.43 | | | | | | | | | | | | | | | | | | | | | (6086) ~ (all_52_13 = e0) % 148.93/21.43 | | | | | | | | | | | | | | | | | | | | | % 148.93/21.43 | | | | | | | | | | | | | | | | | | | | | REDUCE: (38), (6082) imply: % 148.93/21.43 | | | | | | | | | | | | | | | | | | | | | (6087) op(e0, e0) = all_4_1 % 148.93/21.43 | | | | | | | | | | | | | | | | | | | | | % 148.93/21.43 | | | | | | | | | | | | | | | | | | | | | REDUCE: (627), (6082) imply: % 148.93/21.43 | | | | | | | | | | | | | | | | | | | | | (6088) op(e0, e0) = all_56_30 % 148.93/21.43 | | | | | | | | | | | | | | | | | | | | | % 148.93/21.43 | | | | | | | | | | | | | | | | | | | | | REDUCE: (36), (6082) imply: % 148.93/21.43 | | | | | | | | | | | | | | | | | | | | | (6089) op(e0, e0) = e0 % 148.93/21.43 | | | | | | | | | | | | | | | | | | | | | % 148.93/21.43 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_4_1, % 148.93/21.43 | | | | | | | | | | | | | | | | | | | | | all_56_30, e0, e0, simplifying with (6087), (6088) % 148.93/21.43 | | | | | | | | | | | | | | | | | | | | | gives: % 148.93/21.43 | | | | | | | | | | | | | | | | | | | | | (6090) all_56_30 = all_4_1 % 148.93/21.43 | | | | | | | | | | | | | | | | | | | | | % 148.93/21.43 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, % 148.93/21.43 | | | | | | | | | | | | | | | | | | | | | all_56_30, e0, e0, simplifying with (6088), (6089) % 148.93/21.43 | | | | | | | | | | | | | | | | | | | | | gives: % 148.93/21.43 | | | | | | | | | | | | | | | | | | | | | (6091) all_56_30 = e0 % 148.93/21.43 | | | | | | | | | | | | | | | | | | | | | % 148.93/21.43 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6090), (6091) imply: % 148.93/21.43 | | | | | | | | | | | | | | | | | | | | | (6092) all_4_1 = e0 % 148.93/21.43 | | | | | | | | | | | | | | | | | | | | | % 148.93/21.43 | | | | | | | | | | | | | | | | | | | | | SIMP: (6092) implies: % 148.93/21.43 | | | | | | | | | | | | | | | | | | | | | (6093) all_4_1 = e0 % 148.93/21.43 | | | | | | | | | | | | | | | | | | | | | % 148.93/21.43 | | | | | | | | | | | | | | | | | | | | | REDUCE: (37), (6093) imply: % 148.93/21.43 | | | | | | | | | | | | | | | | | | | | | (6094) op(e0, e0) = all_4_0 % 148.93/21.43 | | | | | | | | | | | | | | | | | | | | | % 148.93/21.43 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_4_0, % 148.93/21.43 | | | | | | | | | | | | | | | | | | | | | e0, e0, simplifying with (6089), (6094) gives: % 148.93/21.43 | | | | | | | | | | | | | | | | | | | | | (6095) all_4_0 = e0 % 148.93/21.43 | | | | | | | | | | | | | | | | | | | | | % 148.93/21.43 | | | | | | | | | | | | | | | | | | | | | REDUCE: (767), (6095) imply: % 148.93/21.43 | | | | | | | | | | | | | | | | | | | | | (6096) ~ (e3 = e0) % 148.93/21.43 | | | | | | | | | | | | | | | | | | | | | % 148.93/21.43 | | | | | | | | | | | | | | | | | | | | | REDUCE: (5088), (6095) imply: % 148.93/21.43 | | | | | | | | | | | | | | | | | | | | | (6097) ~ (e2 = e0) % 148.93/21.43 | | | | | | | | | | | | | | | | | | | | | % 148.93/21.43 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (299) gives: % 148.93/21.43 | | | | | | | | | | | | | | | | | | | | | % 148.93/21.43 | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.93/21.43 | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.43 | | | | | | | | | | | | | | | | | | | | | | (6098) ~ (all_56_1 = e2) % 148.93/21.43 | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.43 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (546), (6098) imply: % 148.93/21.43 | | | | | | | | | | | | | | | | | | | | | | (6099) ~ (all_10_2 = e2) % 148.93/21.43 | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.43 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (41), (46), (51), (158), (160), (161), % 148.93/21.43 | | | | | | | | | | | | | | | | | | | | | | (168), (174), (182), (193), (197), (241), (245), % 148.93/21.43 | | | | | | | | | | | | | | | | | | | | | | (246), (247), (248), (252), (287), (295), (296), % 148.93/21.43 | | | | | | | | | | | | | | | | | | | | | | (298), (321), (324), (327), (328), (329), (332), % 148.93/21.43 | | | | | | | | | | | | | | | | | | | | | | (336), (343), (374), (380), (386), (401), (407), % 148.93/21.43 | | | | | | | | | | | | | | | | | | | | | | (419), (425), (429), (463), (469), (476), (542), % 148.93/21.43 | | | | | | | | | | | | | | | | | | | | | | (543), (544), (545), (546), (547), (548), (549), % 148.93/21.43 | | | | | | | | | | | | | | | | | | | | | | (550), (551), (552), (553), (554), (555), (559), % 148.93/21.43 | | | | | | | | | | | | | | | | | | | | | | (565), (567), (568), (571), (573), (579), (585), % 148.93/21.43 | | | | | | | | | | | | | | | | | | | | | | (590), (617), (623), (5069), (5071), (5074), % 148.93/21.43 | | | | | | | | | | | | | | | | | | | | | | (5075), (5076), (5077), (5082), (5083), (5084), % 148.93/21.43 | | | | | | | | | | | | | | | | | | | | | | (6066), (6070), (6072), (6083), (6084), (6086), % 148.93/21.43 | | | | | | | | | | | | | | | | | | | | | | (6099), (function-axioms) are inconsistent by % 148.93/21.43 | | | | | | | | | | | | | | | | | | | | | | sub-proof #135. % 148.93/21.43 | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.43 | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.93/21.43 | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.43 | | | | | | | | | | | | | | | | | | | | | | (6100) all_56_3 = e3 % 148.93/21.43 | | | | | | | | | | | | | | | | | | | | | | (6101) all_56_1 = e2 % 148.93/21.43 | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.43 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (546), (6101) imply: % 148.93/21.43 | | | | | | | | | | | | | | | | | | | | | | (6102) all_10_2 = e2 % 148.93/21.43 | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.43 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (408), (6100) imply: % 148.93/21.43 | | | | | | | | | | | | | | | | | | | | | | (6103) all_52_4 = e3 % 148.93/21.43 | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.43 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (521), (6102) imply: % 148.93/21.43 | | | | | | | | | | | | | | | | | | | | | | (6104) all_24_2 = e2 % 148.93/21.43 | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.43 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (555), (6103) imply: % 148.93/21.43 | | | | | | | | | | | | | | | | | | | | | | (6105) all_58_1 = e3 % 148.93/21.43 | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.43 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (419), (6102) imply: % 148.93/21.43 | | | | | | | | | | | | | | | | | | | | | | (6106) all_58_0 = e2 % 148.93/21.43 | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.43 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (181), (6103) imply: % 148.93/21.43 | | | | | | | | | | | | | | | | | | | | | | (6107) ~ (all_52_12 = e3) % 148.93/21.43 | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.43 | | | | | | | | | | | | | | | | | | | | | | SIMP: (6107) implies: % 148.93/21.43 | | | | | | | | | | | | | | | | | | | | | | (6108) ~ (all_52_12 = e3) % 148.93/21.43 | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.43 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (565), (6102) imply: % 148.93/21.43 | | | | | | | | | | | | | | | | | | | | | | (6109) ~ (all_52_8 = e2) % 148.93/21.43 | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.43 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (567), (6102) imply: % 148.93/21.43 | | | | | | | | | | | | | | | | | | | | | | (6110) ~ (all_52_12 = e2) % 148.93/21.43 | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.43 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (53), (6102) imply: % 148.93/21.43 | | | | | | | | | | | | | | | | | | | | | | (6111) op(e2, e2) = all_10_1 % 148.93/21.43 | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.43 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (249) gives: % 148.93/21.43 | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.43 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.93/21.43 | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.43 | | | | | | | | | | | | | | | | | | | | | | | (6112) all_54_3 = e3 % 148.93/21.43 | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.43 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (461), (6108), (6112) are inconsistent by % 148.93/21.43 | | | | | | | | | | | | | | | | | | | | | | | sub-proof #659. % 148.93/21.43 | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.43 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.93/21.43 | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.43 | | | | | | | | | | | | | | | | | | | | | | | (6113) all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0 % 148.93/21.43 | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.43 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6113) gives: % 148.93/21.43 | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.43 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.93/21.43 | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.43 | | | | | | | | | | | | | | | | | | | | | | | | (6114) all_54_3 = e2 % 148.93/21.43 | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.43 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (461), (6110), (6114) are inconsistent by % 148.93/21.43 | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #658. % 148.93/21.43 | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.43 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.93/21.43 | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.43 | | | | | | | | | | | | | | | | | | | | | | | | (6115) all_54_3 = e1 | all_54_3 = e0 % 148.93/21.43 | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.43 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6115) gives: % 148.93/21.43 | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.43 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.93/21.43 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.43 | | | | | | | | | | | | | | | | | | | | | | | | | (6116) all_54_3 = e1 % 148.93/21.43 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.43 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (461), (6116) imply: % 148.93/21.43 | | | | | | | | | | | | | | | | | | | | | | | | | (6117) all_52_12 = e1 % 148.93/21.43 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.43 | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6117) implies: % 148.93/21.43 | | | | | | | | | | | | | | | | | | | | | | | | | (6118) all_52_12 = e1 % 148.93/21.43 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.43 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (551), (6118) imply: % 148.93/21.43 | | | | | | | | | | | | | | | | | | | | | | | | | (6119) all_58_9 = e1 % 148.93/21.43 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.43 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6054) gives: % 148.93/21.43 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.43 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.93/21.43 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.43 | | | | | | | | | | | | | | | | | | | | | | | | | | (6120) ~ (all_24_2 = e2) % 148.93/21.43 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.43 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6104), (6120) imply: % 148.93/21.43 | | | | | | | | | | | | | | | | | | | | | | | | | | (6121) $false % 148.93/21.43 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.43 | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (6121) is inconsistent. % 148.93/21.43 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.43 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.93/21.43 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.43 | | | | | | | | | | | | | | | | | | | | | | | | | | (6122) ~ (all_24_1 = e0) % 148.93/21.43 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.43 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (643), (6122) imply: % 148.93/21.43 | | | | | | | | | | | | | | | | | | | | | | | | | | (6123) ~ (all_10_1 = e0) % 148.93/21.43 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.43 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (341) gives: % 148.93/21.43 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.43 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.93/21.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | (6124) all_58_0 = e0 % 148.93/21.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6106), (6124) imply: % 148.93/21.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | (6125) e2 = e0 % 148.93/21.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5), (6125) imply: % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | (6126) $false % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (6126) is inconsistent. % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | (6127) all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0 % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6127) gives: % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6128) all_58_1 = e0 % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6105), (6128) imply: % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6129) e3 = e0 % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7), (6129) imply: % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6130) $false % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (6130) is inconsistent. % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6131) all_58_4 = e0 | all_58_9 = e0 % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6131) gives: % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6132) all_58_4 = e0 % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (407), (6132) imply: % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6133) all_52_8 = e0 % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (217), (6133) imply: % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6134) op(e3, e1) = e0 % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_8_2, % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_10_1, e2, e2, simplifying with (46), (6111) % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6135) all_10_1 = all_8_2 % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6051), (6135) imply: % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6136) op(e3, all_8_2) = e1 % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (295) gives: % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6137) ~ (all_56_11 = e1) % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (545), (6137) imply: % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6138) ~ (all_8_2 = e1) % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (46), (51), (246), (247), (287), (296), % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (332), (374), (386), (401), (425), (542), (544), % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (545), (546), (554), (568), (590), (617), (5069), % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5071), (5074), (5076), (5077), (5082), (5083), % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5084), (6072), (6138), (function-axioms) are % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #141. % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6139) all_56_11 = e1 % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (545), (6139) imply: % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6140) all_8_2 = e1 % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6140) implies: % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6141) all_8_2 = e1 % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6136), (6141) imply: % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6142) op(e3, e1) = e1 % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, e1, e1, % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3, simplifying with (6134), (6142) gives: % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6143) e1 = e0 % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4), (6143) imply: % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6144) $false % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (6144) is inconsistent. % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6145) all_58_9 = e0 % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6119), (6145) imply: % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6146) e1 = e0 % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4), (6146) imply: % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6147) $false % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (6147) is inconsistent. % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | (6148) all_54_3 = e0 % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (461), (6085), (6148) are inconsistent by % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #656. % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | End of split % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | End of split % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | End of split % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | % 148.93/21.44 | | | | | | | | | | | | | | | | | | | End of split % 148.93/21.44 | | | | | | | | | | | | | | | | | | | % 148.93/21.44 | | | | | | | | | | | | | | | | | | End of split % 148.93/21.44 | | | | | | | | | | | | | | | | | | % 148.93/21.44 | | | | | | | | | | | | | | | | | Case 2: % 148.93/21.44 | | | | | | | | | | | | | | | | | | % 148.93/21.44 | | | | | | | | | | | | | | | | | | (6149) all_56_31 = e2 % 148.93/21.44 | | | | | | | | | | | | | | | | | | (6150) all_56_27 = e0 % 148.93/21.44 | | | | | | | | | | | | | | | | | | % 148.93/21.44 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (360), (6150) imply: % 148.93/21.44 | | | | | | | | | | | | | | | | | | (6151) all_52_7 = e0 % 148.93/21.44 | | | | | | | | | | | | | | | | | | % 148.93/21.44 | | | | | | | | | | | | | | | | | | SIMP: (6151) implies: % 148.93/21.44 | | | | | | | | | | | | | | | | | | (6152) all_52_7 = e0 % 148.93/21.44 | | | | | | | | | | | | | | | | | | % 148.93/21.44 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (544), (6149) imply: % 148.93/21.44 | | | | | | | | | | | | | | | | | | (6153) all_4_2 = e2 % 148.93/21.44 | | | | | | | | | | | | | | | | | | % 148.93/21.44 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (549), (6152) imply: % 148.93/21.44 | | | | | | | | | | | | | | | | | | (6154) all_58_13 = e0 % 148.93/21.44 | | | | | | | | | | | | | | | | | | % 148.93/21.44 | | | | | | | | | | | | | | | | | | REDUCE: (176), (6152) imply: % 148.93/21.44 | | | | | | | | | | | | | | | | | | (6155) ~ (all_52_6 = e0) % 148.93/21.44 | | | | | | | | | | | | | | | | | | % 148.93/21.44 | | | | | | | | | | | | | | | | | | REDUCE: (173), (6152) imply: % 148.93/21.44 | | | | | | | | | | | | | | | | | | (6156) ~ (all_52_11 = e0) % 148.93/21.44 | | | | | | | | | | | | | | | | | | % 148.93/21.44 | | | | | | | | | | | | | | | | | | SIMP: (6156) implies: % 148.93/21.44 | | | | | | | | | | | | | | | | | | (6157) ~ (all_52_11 = e0) % 148.93/21.44 | | | | | | | | | | | | | | | | | | % 148.93/21.44 | | | | | | | | | | | | | | | | | | REDUCE: (575), (6152) imply: % 148.93/21.44 | | | | | | | | | | | | | | | | | | (6158) ~ (all_8_2 = e0) % 148.93/21.44 | | | | | | | | | | | | | | | | | | % 148.93/21.44 | | | | | | | | | | | | | | | | | | REDUCE: (581), (6152), (6153) imply: % 148.93/21.44 | | | | | | | | | | | | | | | | | | (6159) ~ (e2 = e0) % 148.93/21.44 | | | | | | | | | | | | | | | | | | % 148.93/21.44 | | | | | | | | | | | | | | | | | | REDUCE: (588), (6153) imply: % 148.93/21.44 | | | | | | | | | | | | | | | | | | (6160) ~ (all_52_11 = e2) % 148.93/21.44 | | | | | | | | | | | | | | | | | | % 148.93/21.44 | | | | | | | | | | | | | | | | | | REDUCE: (589), (6153) imply: % 148.93/21.44 | | | | | | | | | | | | | | | | | | (6161) ~ (all_52_12 = e2) % 148.93/21.44 | | | | | | | | | | | | | | | | | | % 148.93/21.44 | | | | | | | | | | | | | | | | | | REDUCE: (38), (6153) imply: % 148.93/21.44 | | | | | | | | | | | | | | | | | | (6162) op(e2, e2) = all_4_1 % 148.93/21.44 | | | | | | | | | | | | | | | | | | % 148.93/21.44 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_8_2, % 148.93/21.44 | | | | | | | | | | | | | | | | | | all_4_1, e2, e2, simplifying with (46), (6162) % 148.93/21.44 | | | | | | | | | | | | | | | | | | gives: % 148.93/21.44 | | | | | | | | | | | | | | | | | | (6163) all_8_2 = all_4_1 % 148.93/21.44 | | | | | | | | | | | | | | | | | | % 148.93/21.44 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (542), (6163) imply: % 148.93/21.44 | | | | | | | | | | | | | | | | | | (6164) all_54_5 = all_4_1 % 148.93/21.44 | | | | | | | | | | | | | | | | | | % 148.93/21.44 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (545), (6163) imply: % 148.93/21.44 | | | | | | | | | | | | | | | | | | (6165) all_56_11 = all_4_1 % 148.93/21.44 | | | | | | | | | | | | | | | | | | % 148.93/21.44 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (554), (6163) imply: % 148.93/21.44 | | | | | | | | | | | | | | | | | | (6166) all_58_3 = all_4_1 % 148.93/21.44 | | | | | | | | | | | | | | | | | | % 148.93/21.44 | | | | | | | | | | | | | | | | | | REDUCE: (571), (6163) imply: % 148.93/21.44 | | | | | | | | | | | | | | | | | | (6167) ~ (all_52_4 = all_4_1) % 148.93/21.44 | | | | | | | | | | | | | | | | | | % 148.93/21.44 | | | | | | | | | | | | | | | | | | REDUCE: (573), (6163) imply: % 148.93/21.44 | | | | | | | | | | | | | | | | | | (6168) ~ (all_52_6 = all_4_1) % 148.93/21.44 | | | | | | | | | | | | | | | | | | % 148.93/21.44 | | | | | | | | | | | | | | | | | | REDUCE: (579), (6163) imply: % 148.93/21.44 | | | | | | | | | | | | | | | | | | (6169) ~ (all_52_13 = all_4_1) % 148.93/21.44 | | | | | | | | | | | | | | | | | | % 148.93/21.44 | | | | | | | | | | | | | | | | | | REDUCE: (6072), (6163) imply: % 148.93/21.44 | | | | | | | | | | | | | | | | | | (6170) ~ (all_4_1 = e0) % 148.93/21.44 | | | | | | | | | | | | | | | | | | % 148.93/21.44 | | | | | | | | | | | | | | | | | | BETA: splitting (293) gives: % 148.93/21.44 | | | | | | | | | | | | | | | | | | % 148.93/21.44 | | | | | | | | | | | | | | | | | | Case 1: % 148.93/21.44 | | | | | | | | | | | | | | | | | | | % 148.93/21.44 | | | | | | | | | | | | | | | | | | | (6171) ~ (all_56_21 = e3) % 148.93/21.44 | | | | | | | | | | | | | | | | | | | % 148.93/21.44 | | | | | | | | | | | | | | | | | | | REDUCE: (374), (6171) imply: % 148.93/21.44 | | | | | | | | | | | | | | | | | | | (6172) ~ (all_6_2 = e3) % 148.93/21.44 | | | | | | | | | | | | | | | | | | | % 148.93/21.44 | | | | | | | | | | | | | | | | | | | BETA: splitting (242) gives: % 148.93/21.44 | | | | | | | | | | | | | | | | | | | % 148.93/21.44 | | | | | | | | | | | | | | | | | | | Case 1: % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | (6173) all_54_10 = e3 % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (541), (6172), (6173) are inconsistent by % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | sub-proof #736. % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | % 148.93/21.44 | | | | | | | | | | | | | | | | | | | Case 2: % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | (6174) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | BETA: splitting (6174) gives: % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | Case 1: % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | (6175) all_54_10 = e2 % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (541), (6064), (6175) are inconsistent by % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | sub-proof #735. % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | Case 2: % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | (6176) all_54_10 = e1 | all_54_10 = e0 % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6176) gives: % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | (6177) all_54_10 = e1 % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (541), (6177) imply: % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | (6178) all_6_2 = e1 % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | SIMP: (6178) implies: % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | (6179) all_6_2 = e1 % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (580), (6179) imply: % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | (6180) ~ (all_52_6 = e1) % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (582), (6179) imply: % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | (6181) ~ (all_52_8 = e1) % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (585), (6179) imply: % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | (6182) ~ (all_52_11 = e1) % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (587), (6179) imply: % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | (6183) ~ (all_52_14 = e1) % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5084), (6179) imply: % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | (6184) ~ (all_8_0 = e1) % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (43), (6179) imply: % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | (6185) op(e1, e1) = all_6_1 % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (622), (6179) imply: % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | (6186) op(e1, e1) = all_56_20 % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (41), (6179) imply: % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | (6187) op(e1, e1) = e1 % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives: % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | (6188) all_54_14 = e3 % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (482), (6188) imply: % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | (6189) all_52_11 = e3 % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6189) implies: % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | (6190) all_52_11 = e3 % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5080), (6190) imply: % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | (6191) ~ (all_8_0 = e3) % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (205), (6190) imply: % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | (6192) op(e0, e1) = e3 % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (318) gives: % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | (6193) all_58_12 = e1 % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (365), (6193) imply: % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | (6194) all_52_3 = e1 % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (196), (6194) imply: % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | (6195) ~ (all_52_1 = e1) % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (561), (6194) imply: % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | (6196) ~ (all_10_2 = e1) % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6196) implies: % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | (6197) ~ (all_10_2 = e1) % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_6_1, % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | all_56_20, e1, e1, simplifying with (6185), (6186) % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | gives: % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | (6198) all_56_20 = all_6_1 % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1, % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | all_56_20, e1, e1, simplifying with (6186), (6187) % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | gives: % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | (6199) all_56_20 = e1 % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6198), (6199) imply: % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | (6200) all_6_1 = e1 % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6200) implies: % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | (6201) all_6_1 = e1 % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (42), (6201) imply: % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | (6202) op(e1, e1) = all_6_0 % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1, all_6_0, % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | e1, e1, simplifying with (6187), (6202) gives: % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | (6203) all_6_0 = e1 % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (299) gives: % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | (6204) ~ (all_56_1 = e2) % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (546), (6204) imply: % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | (6205) ~ (all_10_2 = e2) % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (37), (46), (51), (161), (246), (247), % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | (287), (295), (296), (321), (332), (333), (337), % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | (343), (345), (374), (386), (401), (407), (419), % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | (425), (542), (544), (545), (546), (547), (550), % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | (551), (554), (555), (568), (590), (617), (624), % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | (767), (5069), (5071), (5074), (5075), (5076), % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | (5077), (5078), (5082), (5083), (5084), (6062), % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | (6066), (6072), (6161), (6165), (6166), (6169), % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | (6181), (6183), (6184), (6192), (6195), (6197), % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | (6205), (function-axioms) are inconsistent by % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #133. % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | (6206) all_56_3 = e3 % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (408), (6206) imply: % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | (6207) all_52_4 = e3 % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6207) implies: % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | (6208) all_52_4 = e3 % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (184), (6208) imply: % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | (6209) ~ (all_52_6 = e3) % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6209) implies: % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | (6210) ~ (all_52_6 = e3) % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6167), (6208) imply: % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | (6211) ~ (all_4_1 = e3) % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6211) implies: % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | (6212) ~ (all_4_1 = e3) % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (243) gives: % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | (6213) all_54_9 = e3 % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (473), (6210), (6213) are inconsistent by % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #680. % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | (6214) all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0 % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6214) gives: % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | (6215) all_54_9 = e2 % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (473), (6215) imply: % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | (6216) all_52_6 = e2 % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6216) implies: % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | (6217) all_52_6 = e2 % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6168), (6217) imply: % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | (6218) ~ (all_4_1 = e2) % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6218) implies: % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | (6219) ~ (all_4_1 = e2) % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (37), (247), (321), (386), (547), (550), (551), % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | (624), (767), (6066), (6164), (6169), (6170), % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | (6183), (6192), (6212), (6219), (function-axioms) % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #167. % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | (6220) all_54_9 = e1 | all_54_9 = e0 % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (473), (6155), (6180), (6220) are inconsistent by % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #678. % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | (6221) all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1 % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (547), (548), (6066), (6154), (6182), (6221) % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #575. % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | (6222) all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0 % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (482), (6157), (6160), (6182), (6222) are % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #580. % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | End of split % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | (6223) all_54_10 = e0 % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (541), (6070), (6223) are inconsistent by % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | sub-proof #705. % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | End of split % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | | % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | End of split % 148.93/21.44 | | | | | | | | | | | | | | | | | | | | % 148.93/21.44 | | | | | | | | | | | | | | | | | | | End of split % 148.93/21.44 | | | | | | | | | | | | | | | | | | | % 148.93/21.44 | | | | | | | | | | | | | | | | | | Case 2: % 148.93/21.44 | | | | | | | | | | | | | | | | | | | % 148.93/21.44 | | | | | | | | | | | | | | | | | | | (6224) all_56_21 = e3 % 148.93/21.44 | | | | | | | | | | | | | | | | | | | (6225) all_56_17 = e1 % 148.93/21.44 | | | | | | | | | | | | | | | | | | | % 148.93/21.44 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (42), (43), (51), (158), (160), (161), (174), % 148.93/21.44 | | | | | | | | | | | | | | | | | | | (189), (191), (208), (241), (243), (252), (287), % 148.93/21.44 | | | | | | | | | | | | | | | | | | | (297), (321), (332), (374), (381), (386), (389), % 148.93/21.44 | | | | | | | | | | | | | | | | | | | (401), (402), (473), (476), (543), (544), (545), % 148.93/21.44 | | | | | | | | | | | | | | | | | | | (546), (547), (550), (551), (554), (557), (559), % 148.93/21.44 | | | | | | | | | | | | | | | | | | | (569), (573), (580), (591), (621), (768), (6058), % 148.93/21.44 | | | | | | | | | | | | | | | | | | | (6060), (6066), (6072), (6224), (6225), % 148.93/21.44 | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 148.93/21.44 | | | | | | | | | | | | | | | | | | | #292. % 148.93/21.44 | | | | | | | | | | | | | | | | | | | % 148.93/21.44 | | | | | | | | | | | | | | | | | | End of split % 148.93/21.44 | | | | | | | | | | | | | | | | | | % 148.93/21.44 | | | | | | | | | | | | | | | | | End of split % 148.93/21.44 | | | | | | | | | | | | | | | | | % 148.93/21.44 | | | | | | | | | | | | | | | | Case 2: % 148.93/21.44 | | | | | | | | | | | | | | | | | % 148.93/21.44 | | | | | | | | | | | | | | | | | (6226) all_56_15 = e2 % 148.93/21.44 | | | | | | | | | | | | | | | | | (6227) all_56_11 = e0 % 148.93/21.44 | | | | | | | | | | | | | | | | | % 148.93/21.44 | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (8), (9), (36), (38), (246), (287), % 148.93/21.44 | | | | | | | | | | | | | | | | | (333), (335), (374), (386), (401), (443), (544), % 148.93/21.44 | | | | | | | | | | | | | | | | | (545), (546), (554), (557), (579), (627), (5071), % 148.93/21.44 | | | | | | | | | | | | | | | | | (5074), (5076), (5082), (5083), (5084), (6062), % 148.93/21.44 | | | | | | | | | | | | | | | | | (6066), (6226), (6227), (function-axioms) are % 148.93/21.44 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #111. % 148.93/21.44 | | | | | | | | | | | | | | | | | % 148.93/21.44 | | | | | | | | | | | | | | | | End of split % 148.93/21.44 | | | | | | | | | | | | | | | | % 148.93/21.44 | | | | | | | | | | | | | | | Case 2: % 148.93/21.44 | | | | | | | | | | | | | | | | % 148.93/21.44 | | | | | | | | | | | | | | | | (6228) all_56_23 = e1 % 148.93/21.44 | | | | | | | | | | | | | | | | (6229) all_56_21 = e0 % 148.93/21.44 | | | | | | | | | | | | | | | | % 148.93/21.44 | | | | | | | | | | | | | | | | COMBINE_EQS: (374), (6229) imply: % 148.93/21.44 | | | | | | | | | | | | | | | | (6230) all_6_2 = e0 % 148.93/21.44 | | | | | | | | | | | | | | | | % 148.93/21.44 | | | | | | | | | | | | | | | | SIMP: (6230) implies: % 148.93/21.44 | | | | | | | | | | | | | | | | (6231) all_6_2 = e0 % 148.93/21.44 | | | | | | | | | | | | | | | | % 148.93/21.44 | | | | | | | | | | | | | | | | COMBINE_EQS: (366), (6228) imply: % 148.93/21.44 | | | | | | | | | | | | | | | | (6232) all_52_14 = e1 % 148.93/21.44 | | | | | | | | | | | | | | | | % 148.93/21.44 | | | | | | | | | | | | | | | | SIMP: (6232) implies: % 148.93/21.44 | | | | | | | | | | | | | | | | (6233) all_52_14 = e1 % 148.93/21.44 | | | | | | | | | | | | | | | | % 148.93/21.44 | | | | | | | | | | | | | | | | REDUCE: (569), (6231) imply: % 148.93/21.44 | | | | | | | | | | | | | | | | (6234) ~ (all_52_2 = e0) % 148.93/21.44 | | | | | | | | | | | | | | | | % 148.93/21.44 | | | | | | | | | | | | | | | | REDUCE: (580), (6231) imply: % 148.93/21.44 | | | | | | | | | | | | | | | | (6235) ~ (all_52_6 = e0) % 148.93/21.44 | | | | | | | | | | | | | | | | % 148.93/21.44 | | | | | | | | | | | | | | | | REDUCE: (591), (6233) imply: % 148.93/21.44 | | | | | | | | | | | | | | | | (6236) ~ (all_4_2 = e1) % 148.93/21.44 | | | | | | | | | | | | | | | | % 148.93/21.44 | | | | | | | | | | | | | | | | REDUCE: (43), (6231) imply: % 148.93/21.44 | | | | | | | | | | | | | | | | (6237) op(e0, e0) = all_6_1 % 148.93/21.44 | | | | | | | | | | | | | | | | % 148.93/21.44 | | | | | | | | | | | | | | | | REDUCE: (41), (6231) imply: % 148.93/21.44 | | | | | | | | | | | | | | | | (6238) op(e1, e1) = e0 % 148.93/21.44 | | | | | | | | | | | | | | | | % 148.93/21.44 | | | | | | | | | | | | | | | | REF_CLOSE: (36), (37), (38), (46), (237), (247), (294), % 148.93/21.44 | | | | | | | | | | | | | | | | (295), (296), (332), (336), (340), (365), (380), % 148.93/21.44 | | | | | | | | | | | | | | | | (401), (419), (425), (540), (542), (545), (549), % 148.93/21.44 | | | | | | | | | | | | | | | | (553), (554), (555), (563), (568), (570), (581), % 148.93/21.44 | | | | | | | | | | | | | | | | (617), (627), (768), (5071), (5088), (6056), % 148.93/21.44 | | | | | | | | | | | | | | | | (6060), (6066), (6234), (6235), (6237), (6238), % 148.93/21.44 | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 148.93/21.44 | | | | | | | | | | | | | | | | #125. % 148.93/21.44 | | | | | | | | | | | | | | | | % 148.93/21.44 | | | | | | | | | | | | | | | End of split % 148.93/21.44 | | | | | | | | | | | | | | | % 148.93/21.44 | | | | | | | | | | | | | | Case 2: % 148.93/21.44 | | | | | | | | | | | | | | | % 148.93/21.44 | | | | | | | | | | | | | | | (6239) all_56_31 = e3 % 148.93/21.44 | | | | | | | | | | | | | | | (6240) all_56_25 = e0 % 148.93/21.44 | | | | | | | | | | | | | | | % 148.93/21.44 | | | | | | | | | | | | | | | REF_CLOSE: (5), (36), (38), (43), (46), (51), (182), (187), % 148.93/21.44 | | | | | | | | | | | | | | | (246), (247), (252), (287), (291), (293), (295), % 148.93/21.44 | | | | | | | | | | | | | | | (296), (299), (328), (331), (332), (374), (381), % 148.93/21.44 | | | | | | | | | | | | | | | (386), (401), (407), (408), (425), (447), (542), % 148.93/21.44 | | | | | | | | | | | | | | | (543), (544), (545), (546), (548), (552), (554), % 148.93/21.44 | | | | | | | | | | | | | | | (559), (561), (565), (568), (570), (585), (588), % 148.93/21.44 | | | | | | | | | | | | | | | (590), (617), (768), (5069), (5071), (5074), % 148.93/21.44 | | | | | | | | | | | | | | | (5075), (5076), (5077), (5082), (5083), (5084), % 148.93/21.44 | | | | | | | | | | | | | | | (6060), (6062), (6239), (6240), (function-axioms) % 148.93/21.44 | | | | | | | | | | | | | | | are inconsistent by sub-proof #121. % 148.93/21.44 | | | | | | | | | | | | | | | % 148.93/21.44 | | | | | | | | | | | | | | End of split % 148.93/21.44 | | | | | | | | | | | | | | % 148.93/21.44 | | | | | | | | | | | | | Case 2: % 148.93/21.44 | | | | | | | | | | | | | | % 148.93/21.44 | | | | | | | | | | | | | | (6241) all_56_31 = e1 % 148.93/21.44 | | | | | | | | | | | | | | (6242) all_56_29 = e0 % 148.93/21.44 | | | | | | | | | | | | | | % 148.93/21.44 | | | | | | | | | | | | | | COMBINE_EQS: (357), (6242) imply: % 148.93/21.44 | | | | | | | | | | | | | | (6243) all_52_11 = e0 % 148.93/21.44 | | | | | | | | | | | | | | % 148.93/21.44 | | | | | | | | | | | | | | SIMP: (6243) implies: % 148.93/21.44 | | | | | | | | | | | | | | (6244) all_52_11 = e0 % 148.93/21.44 | | | | | | | | | | | | | | % 148.93/21.44 | | | | | | | | | | | | | | COMBINE_EQS: (544), (6241) imply: % 148.93/21.44 | | | | | | | | | | | | | | (6245) all_4_2 = e1 % 148.93/21.44 | | | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | | | COMBINE_EQS: (548), (6244) imply: % 148.93/21.45 | | | | | | | | | | | | | | (6246) all_58_14 = e0 % 148.93/21.45 | | | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | | | REDUCE: (187), (6244) imply: % 148.93/21.45 | | | | | | | | | | | | | | (6247) ~ (all_52_3 = e0) % 148.93/21.45 | | | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | | | REDUCE: (585), (6244) imply: % 148.93/21.45 | | | | | | | | | | | | | | (6248) ~ (all_6_2 = e0) % 148.93/21.45 | | | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | | | SIMP: (6248) implies: % 148.93/21.45 | | | | | | | | | | | | | | (6249) ~ (all_6_2 = e0) % 148.93/21.45 | | | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | | | REDUCE: (38), (6245) imply: % 148.93/21.45 | | | | | | | | | | | | | | (6250) op(e1, e1) = all_4_1 % 148.93/21.45 | | | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_6_2, % 148.93/21.45 | | | | | | | | | | | | | | all_4_1, e1, e1, simplifying with (41), (6250) % 148.93/21.45 | | | | | | | | | | | | | | gives: % 148.93/21.45 | | | | | | | | | | | | | | (6251) all_6_2 = all_4_1 % 148.93/21.45 | | | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | | | COMBINE_EQS: (541), (6251) imply: % 148.93/21.45 | | | | | | | | | | | | | | (6252) all_54_10 = all_4_1 % 148.93/21.45 | | | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | | | COMBINE_EQS: (374), (6251) imply: % 148.93/21.45 | | | | | | | | | | | | | | (6253) all_56_21 = all_4_1 % 148.93/21.45 | | | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | | | COMBINE_EQS: (552), (6251) imply: % 148.93/21.45 | | | | | | | | | | | | | | (6254) all_58_8 = all_4_1 % 148.93/21.45 | | | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | | | REDUCE: (582), (6251) imply: % 148.93/21.45 | | | | | | | | | | | | | | (6255) ~ (all_52_8 = all_4_1) % 148.93/21.45 | | | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | | | REDUCE: (6064), (6251) imply: % 148.93/21.45 | | | | | | | | | | | | | | (6256) ~ (all_4_1 = e2) % 148.93/21.45 | | | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | | | REDUCE: (6249), (6251) imply: % 148.93/21.45 | | | | | | | | | | | | | | (6257) ~ (all_4_1 = e0) % 148.93/21.45 | | | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | | | REDUCE: (43), (6251) imply: % 148.93/21.45 | | | | | | | | | | | | | | (6258) op(all_4_1, all_4_1) = all_6_1 % 148.93/21.45 | | | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | | | REDUCE: (622), (6251) imply: % 148.93/21.45 | | | | | | | | | | | | | | (6259) op(e1, all_4_1) = all_56_20 % 148.93/21.45 | | | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | | | BETA: splitting (293) gives: % 148.93/21.45 | | | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | | | Case 1: % 148.93/21.45 | | | | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | | | | (6260) ~ (all_56_21 = e3) % 148.93/21.45 | | | | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | | | | REDUCE: (6253), (6260) imply: % 148.93/21.45 | | | | | | | | | | | | | | | (6261) ~ (all_4_1 = e3) % 148.93/21.45 | | | | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | | | | BETA: splitting (331) gives: % 148.93/21.45 | | | | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | | | | Case 1: % 148.93/21.45 | | | | | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | | | | | (6262) all_58_4 = e3 % 148.93/21.45 | | | | | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | | | | | COMBINE_EQS: (407), (6262) imply: % 148.93/21.45 | | | | | | | | | | | | | | | | (6263) all_52_8 = e3 % 148.93/21.45 | | | | | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | | | | | REDUCE: (182), (6263) imply: % 148.93/21.45 | | | | | | | | | | | | | | | | (6264) ~ (all_52_4 = e3) % 148.93/21.45 | | | | | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | | | | | REDUCE: (168), (6263) imply: % 148.93/21.45 | | | | | | | | | | | | | | | | (6265) ~ (all_52_12 = e3) % 148.93/21.45 | | | | | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | | | | | SIMP: (6265) implies: % 148.93/21.45 | | | | | | | | | | | | | | | | (6266) ~ (all_52_12 = e3) % 148.93/21.45 | | | | | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | | | | | REDUCE: (565), (6263) imply: % 148.93/21.45 | | | | | | | | | | | | | | | | (6267) ~ (all_10_2 = e3) % 148.93/21.45 | | | | | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | | | | | SIMP: (6267) implies: % 148.93/21.45 | | | | | | | | | | | | | | | | (6268) ~ (all_10_2 = e3) % 148.93/21.45 | | | | | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | | | | | REDUCE: (6255), (6263) imply: % 148.93/21.45 | | | | | | | | | | | | | | | | (6269) ~ (all_4_1 = e3) % 148.93/21.45 | | | | | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | | | | | REDUCE: (217), (6263) imply: % 148.93/21.45 | | | | | | | | | | | | | | | | (6270) op(e3, e1) = e3 % 148.93/21.45 | | | | | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | | | | | BETA: splitting (299) gives: % 148.93/21.45 | | | | | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | | | | | Case 1: % 148.93/21.45 | | | | | | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | | | | | | (6271) ~ (all_56_1 = e2) % 148.93/21.45 | | | | | | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | | | | | | REDUCE: (546), (6271) imply: % 148.93/21.45 | | | | | | | | | | | | | | | | | (6272) ~ (all_10_2 = e2) % 148.93/21.45 | | | | | | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | | | | | | BETA: splitting (297) gives: % 148.93/21.45 | | | | | | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | | | | | | Case 1: % 148.93/21.45 | | | | | | | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | | | | | | | (6273) ~ (all_56_1 = e0) % 148.93/21.45 | | | | | | | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | | | | | | | REDUCE: (546), (6273) imply: % 148.93/21.45 | | | | | | | | | | | | | | | | | | (6274) ~ (all_10_2 = e0) % 148.93/21.45 | | | | | | | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | | | | | | | BETA: splitting (242) gives: % 148.93/21.45 | | | | | | | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | | | | | | | Case 1: % 148.93/21.45 | | | | | | | | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | | | | | | | | (6275) all_54_10 = e3 % 148.93/21.45 | | | | | | | | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6252), (6261), (6275) are inconsistent by % 148.93/21.45 | | | | | | | | | | | | | | | | | | | sub-proof #282. % 148.93/21.45 | | | | | | | | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | | | | | | | Case 2: % 148.93/21.45 | | | | | | | | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | | | | | | | | (6276) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 148.93/21.45 | | | | | | | | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | | | | | | | | BETA: splitting (252) gives: % 148.93/21.45 | | | | | | | | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | | | | | | | | Case 1: % 148.93/21.45 | | | | | | | | | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | | | | | | | | | (6277) all_54_0 = e3 % 148.93/21.45 | | | | | | | | | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (543), (6268), (6277) are inconsistent by % 148.93/21.45 | | | | | | | | | | | | | | | | | | | | sub-proof #709. % 148.93/21.45 | | | | | | | | | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | | | | | | | | Case 2: % 148.93/21.45 | | | | | | | | | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | | | | | | | | | (6278) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 148.93/21.45 | | | | | | | | | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | | | | | | | | | BETA: splitting (6276) gives: % 148.93/21.45 | | | | | | | | | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | | | | | | | | | Case 1: % 148.93/21.45 | | | | | | | | | | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | | | | | | | | | | (6279) all_54_10 = e2 % 148.93/21.45 | | | | | | | | | | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6252), (6256), (6279) are inconsistent by % 148.93/21.45 | | | | | | | | | | | | | | | | | | | | | sub-proof #281. % 148.93/21.45 | | | | | | | | | | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | | | | | | | | | Case 2: % 148.93/21.45 | | | | | | | | | | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | | | | | | | | | | (6280) all_54_10 = e1 | all_54_10 = e0 % 148.93/21.45 | | | | | | | | | | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6280) gives: % 148.93/21.45 | | | | | | | | | | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.93/21.45 | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | | | | | | | | | | | (6281) all_54_10 = e1 % 148.93/21.45 | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6252), (6281) imply: % 148.93/21.45 | | | | | | | | | | | | | | | | | | | | | | (6282) all_4_1 = e1 % 148.93/21.45 | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | | | | | | | | | | | SIMP: (6282) implies: % 148.93/21.45 | | | | | | | | | | | | | | | | | | | | | | (6283) all_4_1 = e1 % 148.93/21.45 | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6258), (6283) imply: % 148.93/21.45 | | | | | | | | | | | | | | | | | | | | | | (6284) op(e1, e1) = all_6_1 % 148.93/21.45 | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6259), (6283) imply: % 148.93/21.45 | | | | | | | | | | | | | | | | | | | | | | (6285) op(e1, e1) = all_56_20 % 148.93/21.45 | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6250), (6283) imply: % 148.93/21.45 | | | | | | | | | | | | | | | | | | | | | | (6286) op(e1, e1) = e1 % 148.93/21.45 | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6278) gives: % 148.93/21.45 | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.93/21.45 | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | | | | | | | | | | | | (6287) all_54_0 = e2 % 148.93/21.45 | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (543), (6272), (6287) are inconsistent by % 148.93/21.45 | | | | | | | | | | | | | | | | | | | | | | | sub-proof #734. % 148.93/21.45 | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.93/21.45 | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | | | | | | | | | | | | (6288) all_54_0 = e1 | all_54_0 = e0 % 148.93/21.45 | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6288) gives: % 148.93/21.45 | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.93/21.45 | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | | | | | | | | | | | | | (6289) all_54_0 = e1 % 148.93/21.45 | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (543), (6289) imply: % 148.93/21.45 | | | | | | | | | | | | | | | | | | | | | | | | (6290) all_10_2 = e1 % 148.93/21.45 | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6290) implies: % 148.93/21.45 | | | | | | | | | | | | | | | | | | | | | | | | (6291) all_10_2 = e1 % 148.93/21.45 | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (53), (6291) imply: % 148.93/21.45 | | | | | | | | | | | | | | | | | | | | | | | | (6292) op(e1, e1) = all_10_1 % 148.93/21.45 | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (612), (6291) imply: % 148.93/21.45 | | | | | | | | | | | | | | | | | | | | | | | | (6293) op(e3, e1) = all_56_0 % 148.93/21.45 | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6051), (6060), (6270), (6284), (6285), (6286), % 148.93/21.45 | | | | | | | | | | | | | | | | | | | | | | | | (6292), (6293), (function-axioms) are inconsistent % 148.93/21.45 | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #299. % 148.93/21.45 | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.93/21.45 | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | | | | | | | | | | | | | (6294) all_54_0 = e0 % 148.93/21.45 | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (543), (6274), (6294) are inconsistent by % 148.93/21.45 | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #732. % 148.93/21.45 | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.93/21.45 | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | | | | | | | | | | | End of split % 148.93/21.45 | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.93/21.45 | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | | | | | | | | | | | (6295) all_54_10 = e0 % 148.93/21.45 | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6252), (6257), (6295) are inconsistent by % 148.93/21.45 | | | | | | | | | | | | | | | | | | | | | | sub-proof #277. % 148.93/21.45 | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | | | | | | | | | | End of split % 148.93/21.45 | | | | | | | | | | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | | | | | | | | | End of split % 148.93/21.45 | | | | | | | | | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | | | | | | | | End of split % 148.93/21.45 | | | | | | | | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | | | | | | | End of split % 148.93/21.45 | | | | | | | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | | | | | | Case 2: % 148.93/21.45 | | | | | | | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | | | | | | | (6296) all_56_7 = e3 % 148.93/21.45 | | | | | | | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | | | | | | | REF_CLOSE: (402), (6266), (6296) are inconsistent by % 148.93/21.45 | | | | | | | | | | | | | | | | | | sub-proof #691. % 148.93/21.45 | | | | | | | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | | | | | | End of split % 148.93/21.45 | | | | | | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | | | | | Case 2: % 148.93/21.45 | | | | | | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | | | | | | (6297) all_56_3 = e3 % 148.93/21.45 | | | | | | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | | | | | | REF_CLOSE: (408), (6264), (6297) are inconsistent by % 148.93/21.45 | | | | | | | | | | | | | | | | | sub-proof #395. % 148.93/21.45 | | | | | | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | | | | | End of split % 148.93/21.45 | | | | | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | | | | Case 2: % 148.93/21.45 | | | | | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | | | | | (6298) all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3 % 148.93/21.45 | | | | | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | | | | | REF_CLOSE: (7), (5076), (6062), (6246), (6254), (6261), % 148.93/21.45 | | | | | | | | | | | | | | | | (6298) are inconsistent by sub-proof #120. % 148.93/21.45 | | | | | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | | | | End of split % 148.93/21.45 | | | | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | | | Case 2: % 148.93/21.45 | | | | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | | | | (6299) all_56_21 = e3 % 148.93/21.45 | | | | | | | | | | | | | | | (6300) all_56_17 = e1 % 148.93/21.45 | | | | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | | | | COMBINE_EQS: (381), (6300) imply: % 148.93/21.45 | | | | | | | | | | | | | | | (6301) all_52_2 = e1 % 148.93/21.45 | | | | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | | | | COMBINE_EQS: (6253), (6299) imply: % 148.93/21.45 | | | | | | | | | | | | | | | (6302) all_4_1 = e3 % 148.93/21.45 | | | | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | | | | REF_CLOSE: (37), (192), (207), (240), (478), (767), (5088), % 148.93/21.45 | | | | | | | | | | | | | | | (6247), (6301), (6302), (function-axioms) are % 148.93/21.45 | | | | | | | | | | | | | | | inconsistent by sub-proof #521. % 148.93/21.45 | | | | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | | | End of split % 148.93/21.45 | | | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | | End of split % 148.93/21.45 | | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | Case 2: % 148.93/21.45 | | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | | (6303) all_56_21 = e2 % 148.93/21.45 | | | | | | | | | | | | | (6304) all_56_19 = e1 % 148.93/21.45 | | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | | REF_CLOSE: (36), (38), (43), (46), (193), (246), (247), % 148.93/21.45 | | | | | | | | | | | | | (248), (287), (294), (317), (374), (435), (443), % 148.93/21.45 | | | | | | | | | | | | | (463), (542), (544), (545), (546), (547), (557), % 148.93/21.45 | | | | | | | | | | | | | (568), (573), (627), (768), (5071), (5074), % 148.93/21.45 | | | | | | | | | | | | | (5077), (5082), (5083), (6060), (6062), (6303), % 148.93/21.45 | | | | | | | | | | | | | (6304), (function-axioms) are inconsistent by % 148.93/21.45 | | | | | | | | | | | | | sub-proof #99. % 148.93/21.45 | | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | End of split % 148.93/21.45 | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | Case 2: % 148.93/21.45 | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | (6305) all_48_0 = e3 % 148.93/21.45 | | | | | | | | | | | | (6306) ~ (all_48_1 = e1) | ~ (all_48_2 = e0) % 148.93/21.45 | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | COMBINE_EQS: (765), (6305) imply: % 148.93/21.45 | | | | | | | | | | | | (6307) all_8_0 = e3 % 148.93/21.45 | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | SIMP: (6307) implies: % 148.93/21.45 | | | | | | | | | | | | (6308) all_8_0 = e3 % 148.93/21.45 | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | REF_CLOSE: (9), (46), (247), (295), (536), (542), (545), % 148.93/21.45 | | | | | | | | | | | | (617), (5070), (5071), (5075), (5083), (6306), % 148.93/21.45 | | | | | | | | | | | | (6308), (function-axioms) are inconsistent by % 148.93/21.45 | | | | | | | | | | | | sub-proof #115. % 148.93/21.45 | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | End of split % 148.93/21.45 | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | Case 2: % 148.93/21.45 | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | (6309) all_36_1 = e3 % 148.93/21.45 | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (36), (38), (41), (42), % 148.93/21.45 | | | | | | | | | | | (43), (46), (51), (53), (149), (211), (246), % 148.93/21.45 | | | | | | | | | | | (247), (287), (293), (294), (295), (296), (332), % 148.93/21.45 | | | | | | | | | | | (333), (335), (374), (381), (386), (401), (425), % 148.93/21.45 | | | | | | | | | | | (443), (536), (542), (544), (545), (546), (554), % 148.93/21.45 | | | | | | | | | | | (557), (559), (568), (579), (590), (612), (617), % 148.93/21.45 | | | | | | | | | | | (622), (627), (652), (765), (768), (5069), (5070), % 148.93/21.45 | | | | | | | | | | | (5071), (5074), (5075), (5076), (5077), (5082), % 148.93/21.45 | | | | | | | | | | | (5083), (5084), (6051), (6309), (function-axioms) % 148.93/21.45 | | | | | | | | | | | are inconsistent by sub-proof #97. % 148.93/21.45 | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | End of split % 148.93/21.45 | | | | | | | | | | % 148.93/21.45 | | | | | | | | | Case 2: % 148.93/21.45 | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | (6310) all_28_0 = e2 % 148.93/21.45 | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | COMBINE_EQS: (740), (6310) imply: % 148.93/21.45 | | | | | | | | | | (6311) all_6_0 = e2 % 148.93/21.45 | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (38), (41), % 148.93/21.45 | | | | | | | | | | (42), (43), (46), (51), (149), (246), (247), % 148.93/21.45 | | | | | | | | | | (287), (294), (295), (296), (332), (333), (335), % 148.93/21.45 | | | | | | | | | | (374), (386), (401), (425), (443), (536), (542), % 148.93/21.45 | | | | | | | | | | (544), (545), (546), (554), (557), (568), (579), % 148.93/21.45 | | | | | | | | | | (590), (617), (622), (627), (765), (768), (5069), % 148.93/21.45 | | | | | | | | | | (5070), (5071), (5074), (5075), (5076), (5077), % 148.93/21.45 | | | | | | | | | | (5082), (5083), (5084), (6311), (function-axioms) % 148.93/21.45 | | | | | | | | | | are inconsistent by sub-proof #104. % 148.93/21.45 | | | | | | | | | | % 148.93/21.45 | | | | | | | | | End of split % 148.93/21.45 | | | | | | | | | % 148.93/21.45 | | | | | | | | Case 2: % 148.93/21.45 | | | | | | | | | % 148.93/21.45 | | | | | | | | | (6312) all_26_0 = e1 % 148.93/21.45 | | | | | | | | | (6313) ~ (all_26_1 = e2) | ~ (all_26_2 = e3) % 148.93/21.45 | | | | | | | | | % 148.93/21.45 | | | | | | | | | COMBINE_EQS: (760), (6312) imply: % 148.93/21.45 | | | | | | | | | (6314) all_4_0 = e1 % 148.93/21.45 | | | | | | | | | % 148.93/21.45 | | | | | | | | | COMBINE_EQS: (709), (6314) imply: % 148.93/21.45 | | | | | | | | | (6315) all_44_0 = e1 % 148.93/21.45 | | | | | | | | | % 148.93/21.45 | | | | | | | | | REDUCE: (767), (6314) imply: % 148.93/21.45 | | | | | | | | | (6316) ~ (e3 = e1) % 148.93/21.45 | | | | | | | | | % 148.93/21.45 | | | | | | | | | REDUCE: (37), (6314) imply: % 148.93/21.45 | | | | | | | | | (6317) op(e0, all_4_1) = e1 % 148.93/21.45 | | | | | | | | | % 148.93/21.45 | | | | | | | | | BETA: splitting (99) gives: % 148.93/21.45 | | | | | | | | | % 148.93/21.45 | | | | | | | | | Case 1: % 148.93/21.45 | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | (6318) ~ (all_28_0 = e2) % 148.93/21.45 | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | REDUCE: (740), (6318) imply: % 148.93/21.45 | | | | | | | | | | (6319) ~ (all_6_0 = e2) % 148.93/21.45 | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | BETA: splitting (119) gives: % 148.93/21.45 | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | Case 1: % 148.93/21.45 | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | (6320) ~ (all_36_1 = e3) % 148.93/21.45 | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | REDUCE: (652), (6320) imply: % 148.93/21.45 | | | | | | | | | | | (6321) ~ (all_6_1 = e3) % 148.93/21.45 | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | BETA: splitting (139) gives: % 148.93/21.45 | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | Case 1: % 148.93/21.45 | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | (6322) ~ (all_44_0 = e1) % 148.93/21.45 | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | REDUCE: (6315), (6322) imply: % 148.93/21.45 | | | | | | | | | | | | (6323) $false % 148.93/21.45 | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | CLOSE: (6323) is inconsistent. % 148.93/21.45 | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | Case 2: % 148.93/21.45 | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | (6324) ~ (all_44_1 = e3) | ~ (all_44_2 = e2) % 148.93/21.45 | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | BETA: splitting (149) gives: % 148.93/21.45 | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | Case 1: % 148.93/21.45 | | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | | (6325) ~ (all_48_0 = e3) % 148.93/21.45 | | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | | REDUCE: (765), (6325) imply: % 148.93/21.45 | | | | | | | | | | | | | (6326) ~ (all_8_0 = e3) % 148.93/21.45 | | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | | BETA: splitting (288) gives: % 148.93/21.45 | | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | | Case 1: % 148.93/21.45 | | | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | | | (6327) ~ (all_56_31 = e1) % 148.93/21.45 | | | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | | | REDUCE: (544), (6327) imply: % 148.93/21.45 | | | | | | | | | | | | | | (6328) ~ (all_4_2 = e1) % 148.93/21.45 | | | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | | | BETA: splitting (290) gives: % 148.93/21.45 | | | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | | | Case 1: % 148.93/21.45 | | | | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | | | | (6329) ~ (all_56_31 = e3) % 148.93/21.45 | | | | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | | | | REDUCE: (544), (6329) imply: % 148.93/21.45 | | | | | | | | | | | | | | | (6330) ~ (all_4_2 = e3) % 148.93/21.45 | | | | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | | | | BETA: splitting (289) gives: % 148.93/21.45 | | | | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | | | | Case 1: % 148.93/21.45 | | | | | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | | | | | (6331) ~ (all_56_31 = e2) % 148.93/21.45 | | | | | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | | | | | REDUCE: (544), (6331) imply: % 148.93/21.45 | | | | | | | | | | | | | | | | (6332) ~ (all_4_2 = e2) % 148.93/21.45 | | | | | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | | | | | REF_CLOSE: (36), (38), (237), (540), (627), (6317), (6328), % 148.93/21.45 | | | | | | | | | | | | | | | | (6330), (6332), (function-axioms) are inconsistent % 148.93/21.45 | | | | | | | | | | | | | | | | by sub-proof #363. % 148.93/21.45 | | | | | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | | | | Case 2: % 148.93/21.45 | | | | | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | | | | | (6333) all_56_31 = e2 % 148.93/21.45 | | | | | | | | | | | | | | | | (6334) all_56_27 = e0 % 148.93/21.45 | | | | | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | | | | | COMBINE_EQS: (360), (6334) imply: % 148.93/21.45 | | | | | | | | | | | | | | | | (6335) all_52_7 = e0 % 148.93/21.45 | | | | | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | | | | | SIMP: (6335) implies: % 148.93/21.45 | | | | | | | | | | | | | | | | (6336) all_52_7 = e0 % 148.93/21.45 | | | | | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | | | | | COMBINE_EQS: (544), (6333) imply: % 148.93/21.45 | | | | | | | | | | | | | | | | (6337) all_4_2 = e2 % 148.93/21.45 | | | | | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | | | | | COMBINE_EQS: (535), (6337) imply: % 148.93/21.45 | | | | | | | | | | | | | | | | (6338) all_44_2 = e2 % 148.93/21.45 | | | | | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | | | | | COMBINE_EQS: (549), (6336) imply: % 148.93/21.45 | | | | | | | | | | | | | | | | (6339) all_58_13 = e0 % 148.93/21.45 | | | | | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | | | | | REDUCE: (570), (6337) imply: % 148.93/21.45 | | | | | | | | | | | | | | | | (6340) ~ (all_52_3 = e2) % 148.93/21.45 | | | | | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | | | | | REDUCE: (173), (6336) imply: % 148.93/21.45 | | | | | | | | | | | | | | | | (6341) ~ (all_52_11 = e0) % 148.93/21.45 | | | | | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | | | | | SIMP: (6341) implies: % 148.93/21.45 | | | | | | | | | | | | | | | | (6342) ~ (all_52_11 = e0) % 148.93/21.45 | | | | | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | | | | | REDUCE: (575), (6336) imply: % 148.93/21.45 | | | | | | | | | | | | | | | | (6343) ~ (all_8_2 = e0) % 148.93/21.45 | | | | | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | | | | | SIMP: (6343) implies: % 148.93/21.45 | | | | | | | | | | | | | | | | (6344) ~ (all_8_2 = e0) % 148.93/21.45 | | | | | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | | | | | REDUCE: (581), (6336), (6337) imply: % 148.93/21.45 | | | | | | | | | | | | | | | | (6345) ~ (e2 = e0) % 148.93/21.45 | | | | | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | | | | | REDUCE: (588), (6337) imply: % 148.93/21.45 | | | | | | | | | | | | | | | | (6346) ~ (all_52_11 = e2) % 148.93/21.45 | | | | | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | | | | | REDUCE: (589), (6337) imply: % 148.93/21.45 | | | | | | | | | | | | | | | | (6347) ~ (all_52_12 = e2) % 148.93/21.45 | | | | | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | | | | | REDUCE: (38), (6337) imply: % 148.93/21.45 | | | | | | | | | | | | | | | | (6348) op(e2, e2) = all_4_1 % 148.93/21.45 | | | | | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | | | | | REDUCE: (36), (6337) imply: % 148.93/21.45 | | | | | | | | | | | | | | | | (6349) op(e0, e0) = e2 % 148.93/21.45 | | | | | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | | | | | BETA: splitting (6324) gives: % 148.93/21.45 | | | | | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | | | | | Case 1: % 148.93/21.45 | | | | | | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | | | | | | (6350) ~ (all_44_1 = e3) % 148.93/21.45 | | | | | | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | | | | | | REDUCE: (631), (6350) imply: % 148.93/21.45 | | | | | | | | | | | | | | | | | (6351) ~ (all_4_1 = e3) % 148.93/21.45 | | | | | | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_8_2, % 148.93/21.45 | | | | | | | | | | | | | | | | | all_4_1, e2, e2, simplifying with (46), (6348) % 148.93/21.45 | | | | | | | | | | | | | | | | | gives: % 148.93/21.45 | | | | | | | | | | | | | | | | | (6352) all_8_2 = all_4_1 % 148.93/21.45 | | | | | | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | | | | | | COMBINE_EQS: (542), (6352) imply: % 148.93/21.45 | | | | | | | | | | | | | | | | | (6353) all_54_5 = all_4_1 % 148.93/21.45 | | | | | | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | | | | | | COMBINE_EQS: (545), (6352) imply: % 148.93/21.45 | | | | | | | | | | | | | | | | | (6354) all_56_11 = all_4_1 % 148.93/21.45 | | | | | | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | | | | | | COMBINE_EQS: (554), (6352) imply: % 148.93/21.45 | | | | | | | | | | | | | | | | | (6355) all_58_3 = all_4_1 % 148.93/21.45 | | | | | | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | | | | | | REDUCE: (571), (6352) imply: % 148.93/21.45 | | | | | | | | | | | | | | | | | (6356) ~ (all_52_4 = all_4_1) % 148.93/21.45 | | | | | | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | | | | | | REDUCE: (573), (6352) imply: % 148.93/21.45 | | | | | | | | | | | | | | | | | (6357) ~ (all_52_6 = all_4_1) % 148.93/21.45 | | | | | | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | | | | | | REDUCE: (579), (6352) imply: % 148.93/21.45 | | | | | | | | | | | | | | | | | (6358) ~ (all_52_13 = all_4_1) % 148.93/21.45 | | | | | | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | | | | | | REDUCE: (5083), (6352) imply: % 148.93/21.45 | | | | | | | | | | | | | | | | | (6359) ~ (all_8_0 = all_4_1) % 148.93/21.45 | | | | | | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | | | | | | REDUCE: (6344), (6352) imply: % 148.93/21.45 | | | | | | | | | | | | | | | | | (6360) ~ (all_4_1 = e0) % 148.93/21.45 | | | | | | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | | | | | | REDUCE: (5071), (6352) imply: % 148.93/21.45 | | | | | | | | | | | | | | | | | (6361) op(all_4_1, all_4_1) = e1 % 148.93/21.45 | | | | | | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | | | | | | BETA: splitting (292) gives: % 148.93/21.45 | | | | | | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | | | | | | Case 1: % 148.93/21.45 | | | | | | | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | | | | | | | (6362) ~ (all_56_21 = e2) % 148.93/21.45 | | | | | | | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | | | | | | | REDUCE: (374), (6362) imply: % 148.93/21.45 | | | | | | | | | | | | | | | | | | (6363) ~ (all_6_2 = e2) % 148.93/21.45 | | | | | | | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | | | | | | | BETA: splitting (293) gives: % 148.93/21.45 | | | | | | | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | | | | | | | Case 1: % 148.93/21.45 | | | | | | | | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | | | | | | | | (6364) ~ (all_56_21 = e3) % 148.93/21.45 | | | | | | | | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | | | | | | | | REDUCE: (374), (6364) imply: % 148.93/21.45 | | | | | | | | | | | | | | | | | | | (6365) ~ (all_6_2 = e3) % 148.93/21.45 | | | | | | | | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | | | | | | | | BETA: splitting (299) gives: % 148.93/21.45 | | | | | | | | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | | | | | | | | Case 1: % 148.93/21.45 | | | | | | | | | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | | | | | | | | | (6366) ~ (all_56_1 = e2) % 148.93/21.45 | | | | | | | | | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | | | | | | | | | REDUCE: (546), (6366) imply: % 148.93/21.45 | | | | | | | | | | | | | | | | | | | | (6367) ~ (all_10_2 = e2) % 148.93/21.45 | | | | | | | | | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | | | | | | | | | BETA: splitting (291) gives: % 148.93/21.45 | | | | | | | | | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | | | | | | | | | Case 1: % 148.93/21.45 | | | | | | | | | | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | | | | | | | | | | (6368) ~ (all_56_21 = e0) % 148.93/21.45 | | | | | | | | | | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | | | | | | | | | | REDUCE: (374), (6368) imply: % 148.93/21.45 | | | | | | | | | | | | | | | | | | | | | (6369) ~ (all_6_2 = e0) % 148.93/21.45 | | | | | | | | | | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (242) gives: % 148.93/21.45 | | | | | | | | | | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.93/21.45 | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | | | | | | | | | | | (6370) all_54_10 = e3 % 148.93/21.45 | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (541), (6370) imply: % 148.93/21.45 | | | | | | | | | | | | | | | | | | | | | | (6371) all_6_2 = e3 % 148.93/21.45 | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6365), (6371) imply: % 148.93/21.45 | | | | | | | | | | | | | | | | | | | | | | (6372) $false % 148.93/21.45 | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (6372) is inconsistent. % 148.93/21.45 | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.93/21.45 | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | | | | | | | | | | | (6373) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 148.93/21.45 | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6373) gives: % 148.93/21.45 | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.93/21.45 | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | | | | | | | | | | | | (6374) all_54_10 = e2 % 148.93/21.45 | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (541), (6374) imply: % 148.93/21.45 | | | | | | | | | | | | | | | | | | | | | | | (6375) all_6_2 = e2 % 148.93/21.45 | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6363), (6375) imply: % 148.93/21.45 | | | | | | | | | | | | | | | | | | | | | | | (6376) $false % 148.93/21.45 | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (6376) is inconsistent. % 148.93/21.45 | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.93/21.45 | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | | | | | | | | | | | | (6377) all_54_10 = e1 | all_54_10 = e0 % 148.93/21.45 | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6377) gives: % 148.93/21.45 | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.93/21.45 | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | | | | | | | | | | | | | (6378) all_54_10 = e1 % 148.93/21.45 | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (541), (6378) imply: % 148.93/21.45 | | | | | | | | | | | | | | | | | | | | | | | | (6379) all_6_2 = e1 % 148.93/21.45 | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (582), (6379) imply: % 148.93/21.45 | | | | | | | | | | | | | | | | | | | | | | | | (6380) ~ (all_52_8 = e1) % 148.93/21.45 | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (585), (6379) imply: % 148.93/21.45 | | | | | | | | | | | | | | | | | | | | | | | | (6381) ~ (all_52_11 = e1) % 148.93/21.45 | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (587), (6379) imply: % 148.93/21.45 | | | | | | | | | | | | | | | | | | | | | | | | (6382) ~ (all_52_14 = e1) % 148.93/21.45 | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5084), (6379) imply: % 148.93/21.45 | | | | | | | | | | | | | | | | | | | | | | | | (6383) ~ (all_8_0 = e1) % 148.93/21.45 | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (318) gives: % 148.93/21.45 | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.93/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | (6384) all_58_12 = e1 % 148.93/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (365), (6384) imply: % 148.93/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | (6385) all_52_3 = e1 % 148.93/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (196), (6385) imply: % 148.93/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | (6386) ~ (all_52_1 = e1) % 148.93/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (187), (6385) imply: % 148.93/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | (6387) ~ (all_52_11 = e1) % 148.93/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (561), (6385) imply: % 148.93/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | (6388) ~ (all_10_2 = e1) % 148.93/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6388) implies: % 148.93/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | (6389) ~ (all_10_2 = e1) % 148.93/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives: % 148.93/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.93/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | | (6390) all_54_14 = e3 % 148.93/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (482), (6390) imply: % 148.93/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | | (6391) all_52_11 = e3 % 148.93/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6391) implies: % 148.93/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | | (6392) all_52_11 = e3 % 148.93/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5080), (6392) imply: % 148.93/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | | (6393) ~ (all_8_0 = e3) % 148.93/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (205), (6392) imply: % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | (6394) op(e0, e1) = e3 % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (37), (46), (51), (161), (246), (247), % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | (287), (295), (296), (321), (332), (333), (337), % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | (343), (345), (374), (386), (401), (407), (419), % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | (425), (542), (544), (545), (546), (547), (550), % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | (551), (554), (555), (568), (590), (617), (624), % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | (767), (5069), (5071), (5074), (5075), (5076), % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | (5077), (5078), (5082), (5083), (5084), (6326), % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | (6328), (6344), (6347), (6354), (6355), (6358), % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | (6367), (6380), (6382), (6383), (6386), (6389), % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | (6394), (function-axioms) are inconsistent by % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #133. % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | (6395) all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0 % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (482), (6342), (6346), (6381), (6395) are % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #580. % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | (6396) all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1 % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (547), (548), (6328), (6339), (6381), (6396) % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #575. % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | | | (6397) all_54_10 = e0 % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (541), (6397) imply: % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | | | (6398) all_6_2 = e0 % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6369), (6398) imply: % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | | | (6399) $false % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (6399) is inconsistent. % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | End of split % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | End of split % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | Case 2: % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | (6400) all_56_21 = e0 % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (43), (374), (768), (6349), (6400), % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | #565. % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | End of split % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | | | | | | Case 2: % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | (6401) all_56_3 = e3 % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | (6402) all_56_1 = e2 % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (546), (6402) imply: % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | (6403) all_10_2 = e2 % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (408), (6401) imply: % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | (6404) all_52_4 = e3 % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (555), (6404) imply: % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | (6405) all_58_1 = e3 % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | REDUCE: (181), (6404) imply: % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | (6406) ~ (all_52_12 = e3) % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | SIMP: (6406) implies: % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | (6407) ~ (all_52_12 = e3) % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | REDUCE: (6356), (6404) imply: % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | (6408) ~ (all_4_1 = e3) % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | BETA: splitting (247) gives: % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | Case 1: % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | (6409) all_54_5 = e3 % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6351), (6353), (6409) are inconsistent by % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | sub-proof #199. % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | Case 2: % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | (6410) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (337) gives: % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | (6411) all_58_1 = e1 % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6405), (6411) imply: % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | (6412) e3 = e1 % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8), (6412) imply: % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | (6413) $false % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (6413) is inconsistent. % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | (6414) all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1 % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6414) gives: % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | | (6415) all_58_3 = e1 % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6355), (6415) imply: % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | | (6416) all_4_1 = e1 % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6354), (6416) imply: % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | | (6417) all_56_11 = e1 % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6358), (6416) imply: % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | | (6418) ~ (all_52_13 = e1) % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6359), (6416) imply: % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | | (6419) ~ (all_8_0 = e1) % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6317), (6416) imply: % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | | (6420) op(e0, e1) = e1 % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (295) gives: % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | | | (6421) ~ (all_56_11 = e1) % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6417), (6421) imply: % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | | | (6422) $false % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (6422) is inconsistent. % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | | | (6423) all_56_13 = e2 % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5075), (6423) imply: % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | | | (6424) all_8_0 = e2 % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6326), (6424) imply: % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | | | (6425) ~ (e3 = e2) % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (287) gives: % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | (6426) all_56_1 = e3 % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (6402), (6426) are inconsistent by sub-proof % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | #428. % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | (6427) all_56_11 = e2 | all_56_21 = e1 | all_56_31 = e0 % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6427) gives: % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | (6428) all_56_11 = e2 % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (6417), (6428) are inconsistent by sub-proof % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | #419. % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | (6429) all_56_21 = e1 | all_56_31 = e0 % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6429) gives: % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | (6430) all_56_21 = e1 % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (374), (6430) imply: % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | (6431) all_6_2 = e1 % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (585), (6431) imply: % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | (6432) ~ (all_52_11 = e1) % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (587), (6431) imply: % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | (6433) ~ (all_52_14 = e1) % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives: % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6434) all_54_14 = e3 % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (482), (6434) imply: % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6435) all_52_11 = e3 % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6435) implies: % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6436) all_52_11 = e3 % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (205), (6436) imply: % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6437) op(e0, e1) = e3 % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (321), (386), (547), (550), (551), (624), (6328), % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6407), (6418), (6420), (6433), (6437), % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | #101. % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6438) all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0 % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (482), (6342), (6346), (6432), (6438) are % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #580. % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | (6439) all_56_31 = e0 % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6333), (6439) imply: % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | (6440) e2 = e0 % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6440) implies: % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | (6441) e2 = e0 % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6423), (6441) imply: % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | (6442) all_56_13 = e0 % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (46), (51), (246), (247), (287), (295), % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | (296), (332), (374), (386), (401), (425), (542), % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | (544), (545), (546), (554), (568), (590), (617), % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5069), (5071), (5074), (5076), (5077), (5082), % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5083), (5084), (6344), (6442), (function-axioms) % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #134. % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | | (6443) ~ (all_58_3 = e1) % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6355), (6443) imply: % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | | (6444) ~ (all_4_1 = e1) % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6348), (6353), (6360), (6361), (6410), (6444), % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | | #103. % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | End of split % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | End of split % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | End of split % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | | | | | | End of split % 148.93/21.46 | | | | | | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | | | | | Case 2: % 148.93/21.46 | | | | | | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | | | | | | (6445) all_56_21 = e3 % 148.93/21.46 | | | | | | | | | | | | | | | | | | | (6446) all_56_17 = e1 % 148.93/21.46 | | | | | | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (42), (43), (51), (158), (160), (161), (174), % 148.93/21.46 | | | | | | | | | | | | | | | | | | | (189), (191), (208), (241), (243), (252), (287), % 148.93/21.46 | | | | | | | | | | | | | | | | | | | (297), (321), (332), (374), (381), (386), (389), % 148.93/21.46 | | | | | | | | | | | | | | | | | | | (401), (402), (473), (476), (543), (544), (545), % 148.93/21.46 | | | | | | | | | | | | | | | | | | | (546), (547), (550), (551), (554), (557), (559), % 148.93/21.46 | | | | | | | | | | | | | | | | | | | (569), (573), (580), (591), (621), (768), (6319), % 148.93/21.46 | | | | | | | | | | | | | | | | | | | (6321), (6328), (6344), (6445), (6446), % 148.93/21.46 | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 148.93/21.46 | | | | | | | | | | | | | | | | | | | #292. % 148.93/21.46 | | | | | | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | | | | | End of split % 148.93/21.46 | | | | | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | | | | Case 2: % 148.93/21.46 | | | | | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | | | | | (6447) all_56_19 = e1 % 148.93/21.46 | | | | | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (435), (6447) imply: % 148.93/21.46 | | | | | | | | | | | | | | | | | | (6448) all_52_6 = e1 % 148.93/21.46 | | | | | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | | | | | REDUCE: (6357), (6448) imply: % 148.93/21.46 | | | | | | | | | | | | | | | | | | (6449) ~ (all_4_1 = e1) % 148.93/21.46 | | | | | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | | | | | SIMP: (6449) implies: % 148.93/21.46 | | | | | | | | | | | | | | | | | | (6450) ~ (all_4_1 = e1) % 148.93/21.46 | | | | | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | | | | | REF_CLOSE: (247), (6348), (6351), (6353), (6360), (6361), % 148.93/21.46 | | | | | | | | | | | | | | | | | | (6450), (function-axioms) are inconsistent by % 148.93/21.46 | | | | | | | | | | | | | | | | | | sub-proof #102. % 148.93/21.46 | | | | | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | | | | End of split % 148.93/21.46 | | | | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | | | Case 2: % 148.93/21.46 | | | | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | | | | (6451) ~ (all_44_2 = e2) % 148.93/21.46 | | | | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | | | | REDUCE: (6338), (6451) imply: % 148.93/21.46 | | | | | | | | | | | | | | | | | (6452) $false % 148.93/21.46 | | | | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | | | | CLOSE: (6452) is inconsistent. % 148.93/21.46 | | | | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | | | End of split % 148.93/21.46 | | | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | | End of split % 148.93/21.46 | | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | Case 2: % 148.93/21.46 | | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | | (6453) all_56_31 = e3 % 148.93/21.46 | | | | | | | | | | | | | | | (6454) all_56_25 = e0 % 148.93/21.46 | | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | | COMBINE_EQS: (447), (6454) imply: % 148.93/21.46 | | | | | | | | | | | | | | | (6455) all_52_3 = e0 % 148.93/21.46 | | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | | SIMP: (6455) implies: % 148.93/21.46 | | | | | | | | | | | | | | | (6456) all_52_3 = e0 % 148.93/21.46 | | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | | COMBINE_EQS: (544), (6453) imply: % 148.93/21.46 | | | | | | | | | | | | | | | (6457) all_4_2 = e3 % 148.93/21.46 | | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | | COMBINE_EQS: (530), (6457) imply: % 148.93/21.46 | | | | | | | | | | | | | | | (6458) all_26_2 = e3 % 148.93/21.46 | | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | | REDUCE: (187), (6456) imply: % 148.93/21.46 | | | | | | | | | | | | | | | (6459) ~ (all_52_11 = e0) % 148.93/21.46 | | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | | SIMP: (6459) implies: % 148.93/21.46 | | | | | | | | | | | | | | | (6460) ~ (all_52_11 = e0) % 148.93/21.46 | | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | | REDUCE: (561), (6456) imply: % 148.93/21.46 | | | | | | | | | | | | | | | (6461) ~ (all_10_2 = e0) % 148.93/21.46 | | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | | SIMP: (6461) implies: % 148.93/21.46 | | | | | | | | | | | | | | | (6462) ~ (all_10_2 = e0) % 148.93/21.46 | | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | | REDUCE: (570), (6456), (6457) imply: % 148.93/21.46 | | | | | | | | | | | | | | | (6463) ~ (e3 = e0) % 148.93/21.46 | | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | | REDUCE: (588), (6457) imply: % 148.93/21.46 | | | | | | | | | | | | | | | (6464) ~ (all_52_11 = e3) % 148.93/21.46 | | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | | REDUCE: (38), (6457) imply: % 148.93/21.46 | | | | | | | | | | | | | | | (6465) op(e3, e3) = all_4_1 % 148.93/21.46 | | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | | REDUCE: (36), (6457) imply: % 148.93/21.46 | | | | | | | | | | | | | | | (6466) op(e0, e0) = e3 % 148.93/21.46 | | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (43), (46), (51), (182), (246), (247), % 148.93/21.46 | | | | | | | | | | | | | | | (252), (287), (291), (293), (295), (296), (299), % 148.93/21.46 | | | | | | | | | | | | | | | (328), (331), (332), (374), (381), (386), (401), % 148.93/21.46 | | | | | | | | | | | | | | | (407), (408), (425), (542), (543), (544), (545), % 148.93/21.46 | | | | | | | | | | | | | | | (546), (548), (552), (554), (559), (565), (568), % 148.93/21.46 | | | | | | | | | | | | | | | (585), (590), (617), (768), (5069), (5071), % 148.93/21.46 | | | | | | | | | | | | | | | (5074), (5075), (5076), (5077), (5082), (5083), % 148.93/21.46 | | | | | | | | | | | | | | | (5084), (6313), (6321), (6326), (6458), (6460), % 148.93/21.46 | | | | | | | | | | | | | | | (6462), (6464), (6465), (6466), (function-axioms) % 148.93/21.46 | | | | | | | | | | | | | | | are inconsistent by sub-proof #100. % 148.93/21.46 | | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | End of split % 148.93/21.46 | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | Case 2: % 148.93/21.46 | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | (6467) all_56_31 = e1 % 148.93/21.46 | | | | | | | | | | | | | | (6468) all_56_29 = e0 % 148.93/21.46 | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | COMBINE_EQS: (357), (6468) imply: % 148.93/21.46 | | | | | | | | | | | | | | (6469) all_52_11 = e0 % 148.93/21.46 | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | SIMP: (6469) implies: % 148.93/21.46 | | | | | | | | | | | | | | (6470) all_52_11 = e0 % 148.93/21.46 | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | COMBINE_EQS: (544), (6467) imply: % 148.93/21.46 | | | | | | | | | | | | | | (6471) all_4_2 = e1 % 148.93/21.46 | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | COMBINE_EQS: (548), (6470) imply: % 148.93/21.46 | | | | | | | | | | | | | | (6472) all_58_14 = e0 % 148.93/21.46 | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | REDUCE: (585), (6470) imply: % 148.93/21.46 | | | | | | | | | | | | | | (6473) ~ (all_6_2 = e0) % 148.93/21.46 | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | SIMP: (6473) implies: % 148.93/21.46 | | | | | | | | | | | | | | (6474) ~ (all_6_2 = e0) % 148.93/21.46 | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | REDUCE: (588), (6470), (6471) imply: % 148.93/21.46 | | | | | | | | | | | | | | (6475) ~ (e1 = e0) % 148.93/21.46 | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | REDUCE: (38), (6471) imply: % 148.93/21.46 | | | | | | | | | | | | | | (6476) op(e1, e1) = all_4_1 % 148.93/21.46 | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | REDUCE: (627), (6471) imply: % 148.93/21.46 | | | | | | | | | | | | | | (6477) op(e0, e1) = all_56_30 % 148.93/21.46 | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | REDUCE: (205), (6470) imply: % 148.93/21.46 | | | | | | | | | | | | | | (6478) op(e0, e1) = e0 % 148.93/21.46 | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, % 148.93/21.46 | | | | | | | | | | | | | | all_56_30, e1, e0, simplifying with (6477), (6478) % 148.93/21.46 | | | | | | | | | | | | | | gives: % 148.93/21.46 | | | | | | | | | | | | | | (6479) all_56_30 = e0 % 148.93/21.46 | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_6_2, % 148.93/21.46 | | | | | | | | | | | | | | all_4_1, e1, e1, simplifying with (41), (6476) % 148.93/21.46 | | | | | | | | | | | | | | gives: % 148.93/21.46 | | | | | | | | | | | | | | (6480) all_6_2 = all_4_1 % 148.93/21.46 | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | COMBINE_EQS: (374), (6480) imply: % 148.93/21.46 | | | | | | | | | | | | | | (6481) all_56_21 = all_4_1 % 148.93/21.46 | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | COMBINE_EQS: (552), (6480) imply: % 148.93/21.46 | | | | | | | | | | | | | | (6482) all_58_8 = all_4_1 % 148.93/21.46 | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | REDUCE: (6474), (6480) imply: % 148.93/21.46 | | | | | | | | | | | | | | (6483) ~ (all_4_1 = e0) % 148.93/21.46 | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | REDUCE: (43), (6480) imply: % 148.93/21.46 | | | | | | | | | | | | | | (6484) op(all_4_1, all_4_1) = all_6_1 % 148.93/21.46 | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | BETA: splitting (292) gives: % 148.93/21.46 | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | Case 1: % 148.93/21.46 | | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | | (6485) ~ (all_56_21 = e2) % 148.93/21.46 | | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | | REDUCE: (6481), (6485) imply: % 148.93/21.46 | | | | | | | | | | | | | | | (6486) ~ (all_4_1 = e2) % 148.93/21.46 | | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | | BETA: splitting (293) gives: % 148.93/21.46 | | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | | Case 1: % 148.93/21.46 | | | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | | | (6487) ~ (all_56_21 = e3) % 148.93/21.46 | | | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | | | REDUCE: (6481), (6487) imply: % 148.93/21.46 | | | | | | | | | | | | | | | | (6488) ~ (all_4_1 = e3) % 148.93/21.46 | | | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | | | BETA: splitting (331) gives: % 148.93/21.46 | | | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | | | Case 1: % 148.93/21.46 | | | | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | | | | (6489) all_58_4 = e3 % 148.93/21.46 | | | | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | | | | COMBINE_EQS: (407), (6489) imply: % 148.93/21.46 | | | | | | | | | | | | | | | | | (6490) all_52_8 = e3 % 148.93/21.46 | | | | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | | | | REDUCE: (565), (6490) imply: % 148.93/21.46 | | | | | | | | | | | | | | | | | (6491) ~ (all_10_2 = e3) % 148.93/21.46 | | | | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | | | | SIMP: (6491) implies: % 148.93/21.46 | | | | | | | | | | | | | | | | | (6492) ~ (all_10_2 = e3) % 148.93/21.46 | | | | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | | | | BETA: splitting (330) gives: % 148.93/21.46 | | | | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | | | | Case 1: % 148.93/21.46 | | | | | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | | | | | (6493) all_58_4 = e2 % 148.93/21.46 | | | | | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6489), (6493) imply: % 148.93/21.46 | | | | | | | | | | | | | | | | | | (6494) e3 = e2 % 148.93/21.46 | | | | | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | | | | | REDUCE: (9), (6494) imply: % 148.93/21.46 | | | | | | | | | | | | | | | | | | (6495) $false % 148.93/21.46 | | | | | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | | | | | CLOSE: (6495) is inconsistent. % 148.93/21.46 | | | | | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | | | | Case 2: % 148.93/21.46 | | | | | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | | | | | (6496) all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2 % 148.93/21.46 | | | | | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | | | | | BETA: splitting (6496) gives: % 148.93/21.46 | | | | | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | | | | | Case 1: % 148.93/21.46 | | | | | | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | | | | | | (6497) all_58_5 = e2 % 148.93/21.46 | | | | | | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5076), (6497) imply: % 148.93/21.46 | | | | | | | | | | | | | | | | | | | (6498) all_8_0 = e2 % 148.93/21.46 | | | | | | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | | | | | | REDUCE: (5083), (6498) imply: % 148.93/21.46 | | | | | | | | | | | | | | | | | | | (6499) ~ (all_8_2 = e2) % 148.93/21.46 | | | | | | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | | | | | | SIMP: (6499) implies: % 148.93/21.46 | | | | | | | | | | | | | | | | | | | (6500) ~ (all_8_2 = e2) % 148.93/21.46 | | | | | | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | | | | | | BETA: splitting (287) gives: % 148.93/21.46 | | | | | | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | | | | | | Case 1: % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | (6501) all_56_1 = e3 % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (546), (6501) imply: % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | (6502) all_10_2 = e3 % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | REDUCE: (6492), (6502) imply: % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | (6503) $false % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | CLOSE: (6503) is inconsistent. % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | | | | | | Case 2: % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | (6504) all_56_11 = e2 | all_56_21 = e1 | all_56_31 = e0 % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | BETA: splitting (6504) gives: % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | Case 1: % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | (6505) all_56_11 = e2 % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (545), (6505) imply: % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | (6506) all_8_2 = e2 % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | REDUCE: (6500), (6506) imply: % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | (6507) $false % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | CLOSE: (6507) is inconsistent. % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | Case 2: % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | (6508) all_56_21 = e1 | all_56_31 = e0 % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6508) gives: % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | (6509) all_56_21 = e1 % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6481), (6509) imply: % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | (6510) all_4_1 = e1 % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | SIMP: (6510) implies: % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | (6511) all_4_1 = e1 % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6317), (6511) imply: % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | (6512) op(e0, e1) = e1 % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6478), (6512), (function-axioms) are % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #351. % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | (6513) all_56_31 = e0 % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6467), (6513) are inconsistent by sub-proof % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | #201. % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | End of split % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | End of split % 148.93/21.46 | | | | | | | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | | | | | | End of split % 148.93/21.46 | | | | | | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | | | | | Case 2: % 148.93/21.46 | | | | | | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | | | | | | (6514) all_58_8 = e2 | all_58_14 = e2 % 148.93/21.46 | | | | | | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6472), (6482), (6486), (6514) are % 148.93/21.46 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #537. % 148.93/21.46 | | | | | | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | | | | | End of split % 148.93/21.46 | | | | | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | | | | End of split % 148.93/21.46 | | | | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | | | Case 2: % 148.93/21.46 | | | | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | | | | (6515) all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3 % 148.93/21.46 | | | | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (5076), (6326), (6472), (6482), (6488), % 148.93/21.46 | | | | | | | | | | | | | | | | | (6515) are inconsistent by sub-proof #120. % 148.93/21.46 | | | | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | | | End of split % 148.93/21.46 | | | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | | Case 2: % 148.93/21.46 | | | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | | | (6516) all_56_21 = e3 % 148.93/21.46 | | | | | | | | | | | | | | | | (6517) all_56_17 = e1 % 148.93/21.46 | | | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | | | COMBINE_EQS: (381), (6517) imply: % 148.93/21.46 | | | | | | | | | | | | | | | | (6518) all_52_2 = e1 % 148.93/21.46 | | | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | | | COMBINE_EQS: (6481), (6516) imply: % 148.93/21.46 | | | | | | | | | | | | | | | | (6519) all_4_1 = e3 % 148.93/21.46 | | | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | | | REF_CLOSE: (192), (207), (6317), (6518), (6519), % 148.93/21.46 | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 148.93/21.46 | | | | | | | | | | | | | | | | #159. % 148.93/21.46 | | | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | | End of split % 148.93/21.46 | | | | | | | | | | | | | | | % 148.93/21.46 | | | | | | | | | | | | | | Case 2: % 148.93/21.46 | | | | | | | | | | | | | | | % 148.93/21.47 | | | | | | | | | | | | | | | (6520) all_56_21 = e2 % 148.93/21.47 | | | | | | | | | | | | | | | (6521) all_56_19 = e1 % 148.93/21.47 | | | | | | | | | | | | | | | % 148.93/21.47 | | | | | | | | | | | | | | | COMBINE_EQS: (435), (6521) imply: % 148.93/21.47 | | | | | | | | | | | | | | | (6522) all_52_6 = e1 % 148.93/21.47 | | | | | | | | | | | | | | | % 148.93/21.47 | | | | | | | | | | | | | | | COMBINE_EQS: (6481), (6520) imply: % 148.93/21.47 | | | | | | | | | | | | | | | (6523) all_4_1 = e2 % 148.93/21.47 | | | | | | | | | | | | | | | % 148.93/21.47 | | | | | | | | | | | | | | | REDUCE: (573), (6522) imply: % 148.93/21.47 | | | | | | | | | | | | | | | (6524) ~ (all_8_2 = e1) % 148.93/21.47 | | | | | | | | | | | | | | | % 148.93/21.47 | | | | | | | | | | | | | | | SIMP: (6524) implies: % 148.93/21.47 | | | | | | | | | | | | | | | (6525) ~ (all_8_2 = e1) % 148.93/21.47 | | | | | | | | | | | | | | | % 148.93/21.47 | | | | | | | | | | | | | | | REDUCE: (6484), (6523) imply: % 148.93/21.47 | | | | | | | | | | | | | | | (6526) op(e2, e2) = all_6_1 % 148.93/21.47 | | | | | | | | | | | | | | | % 148.93/21.47 | | | | | | | | | | | | | | | REF_CLOSE: (36), (38), (46), (193), (246), (247), (248), % 148.93/21.47 | | | | | | | | | | | | | | | (287), (294), (317), (443), (463), (542), (544), % 148.93/21.47 | | | | | | | | | | | | | | | (545), (546), (547), (557), (568), (627), (768), % 148.93/21.47 | | | | | | | | | | | | | | | (5071), (5074), (5077), (5082), (5083), (6321), % 148.93/21.47 | | | | | | | | | | | | | | | (6326), (6520), (6525), (6526), (function-axioms) % 148.93/21.47 | | | | | | | | | | | | | | | are inconsistent by sub-proof #118. % 148.93/21.47 | | | | | | | | | | | | | | | % 148.93/21.47 | | | | | | | | | | | | | | End of split % 148.93/21.47 | | | | | | | | | | | | | | % 148.93/21.47 | | | | | | | | | | | | | End of split % 148.93/21.47 | | | | | | | | | | | | | % 148.93/21.47 | | | | | | | | | | | | Case 2: % 148.93/21.47 | | | | | | | | | | | | | % 148.93/21.47 | | | | | | | | | | | | | (6527) all_48_0 = e3 % 148.93/21.47 | | | | | | | | | | | | | (6528) ~ (all_48_1 = e1) | ~ (all_48_2 = e0) % 148.93/21.47 | | | | | | | | | | | | | % 148.93/21.47 | | | | | | | | | | | | | COMBINE_EQS: (765), (6527) imply: % 148.93/21.47 | | | | | | | | | | | | | (6529) all_8_0 = e3 % 148.93/21.47 | | | | | | | | | | | | | % 148.93/21.47 | | | | | | | | | | | | | SIMP: (6529) implies: % 148.93/21.47 | | | | | | | | | | | | | (6530) all_8_0 = e3 % 148.93/21.47 | | | | | | | | | | | | | % 148.93/21.47 | | | | | | | | | | | | | REF_CLOSE: (9), (46), (247), (295), (536), (542), (545), % 148.93/21.47 | | | | | | | | | | | | | (617), (5070), (5071), (5075), (5083), (6528), % 148.93/21.47 | | | | | | | | | | | | | (6530), (function-axioms) are inconsistent by % 148.93/21.47 | | | | | | | | | | | | | sub-proof #115. % 148.93/21.47 | | | | | | | | | | | | | % 148.93/21.47 | | | | | | | | | | | | End of split % 148.93/21.47 | | | | | | | | | | | | % 148.93/21.47 | | | | | | | | | | | End of split % 148.93/21.47 | | | | | | | | | | | % 148.93/21.47 | | | | | | | | | | Case 2: % 148.93/21.47 | | | | | | | | | | | % 148.93/21.47 | | | | | | | | | | | (6531) all_36_1 = e3 % 148.93/21.47 | | | | | | | | | | | % 148.93/21.47 | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (36), (38), (41), (42), % 148.93/21.47 | | | | | | | | | | | (43), (46), (51), (53), (149), (211), (246), % 148.93/21.47 | | | | | | | | | | | (247), (287), (293), (294), (295), (296), (332), % 148.93/21.47 | | | | | | | | | | | (333), (335), (374), (381), (386), (401), (425), % 148.93/21.47 | | | | | | | | | | | (443), (536), (542), (544), (545), (546), (554), % 148.93/21.47 | | | | | | | | | | | (557), (559), (568), (579), (590), (612), (617), % 148.93/21.47 | | | | | | | | | | | (622), (627), (652), (765), (768), (5069), (5070), % 148.93/21.47 | | | | | | | | | | | (5071), (5074), (5075), (5076), (5077), (5082), % 148.93/21.47 | | | | | | | | | | | (5083), (5084), (6051), (6531), (function-axioms) % 148.93/21.47 | | | | | | | | | | | are inconsistent by sub-proof #97. % 148.93/21.47 | | | | | | | | | | | % 148.93/21.47 | | | | | | | | | | End of split % 148.93/21.47 | | | | | | | | | | % 148.93/21.47 | | | | | | | | | Case 2: % 148.93/21.47 | | | | | | | | | | % 148.93/21.47 | | | | | | | | | | (6532) all_28_0 = e2 % 148.93/21.47 | | | | | | | | | | % 148.93/21.47 | | | | | | | | | | COMBINE_EQS: (740), (6532) imply: % 148.93/21.47 | | | | | | | | | | (6533) all_6_0 = e2 % 148.93/21.47 | | | | | | | | | | % 148.93/21.47 | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (38), (41), % 148.93/21.47 | | | | | | | | | | (42), (43), (46), (51), (149), (246), (247), % 148.93/21.47 | | | | | | | | | | (287), (294), (295), (296), (332), (333), (335), % 148.93/21.47 | | | | | | | | | | (374), (386), (401), (425), (443), (536), (542), % 148.93/21.47 | | | | | | | | | | (544), (545), (546), (554), (557), (568), (579), % 148.93/21.47 | | | | | | | | | | (590), (617), (622), (627), (765), (768), (5069), % 148.93/21.47 | | | | | | | | | | (5070), (5071), (5074), (5075), (5076), (5077), % 148.93/21.47 | | | | | | | | | | (5082), (5083), (5084), (6533), (function-axioms) % 148.93/21.47 | | | | | | | | | | are inconsistent by sub-proof #104. % 148.93/21.47 | | | | | | | | | | % 148.93/21.47 | | | | | | | | | End of split % 148.93/21.47 | | | | | | | | | % 148.93/21.47 | | | | | | | | End of split % 148.93/21.47 | | | | | | | | % 148.93/21.47 | | | | | | | End of split % 148.93/21.47 | | | | | | | % 148.93/21.47 | | | | | | End of split % 148.93/21.47 | | | | | | % 148.93/21.47 | | | | | Case 2: % 148.93/21.47 | | | | | | % 148.93/21.47 | | | | | | (6534) all_12_0 = e2 % 148.93/21.47 | | | | | | (6535) ~ (all_12_1 = e1) | ~ (all_12_2 = e3) % 148.93/21.47 | | | | | | % 148.93/21.47 | | | | | | COMBINE_EQS: (759), (6534) imply: % 148.93/21.47 | | | | | | (6536) all_4_0 = e2 % 148.93/21.47 | | | | | | % 148.93/21.47 | | | | | | COMBINE_EQS: (734), (6536) imply: % 148.93/21.47 | | | | | | (6537) all_34_0 = e2 % 148.93/21.47 | | | | | | % 148.93/21.47 | | | | | | REDUCE: (767), (6536) imply: % 148.93/21.47 | | | | | | (6538) ~ (e3 = e2) % 148.93/21.47 | | | | | | % 148.93/21.47 | | | | | | REDUCE: (37), (6536) imply: % 148.93/21.47 | | | | | | (6539) op(e0, all_4_1) = e2 % 148.93/21.47 | | | | | | % 148.93/21.47 | | | | | | BETA: splitting (69) gives: % 148.93/21.47 | | | | | | % 148.93/21.47 | | | | | | Case 1: % 148.93/21.47 | | | | | | | % 148.93/21.47 | | | | | | | (6540) ~ (all_16_0 = e1) % 148.93/21.47 | | | | | | | % 148.93/21.47 | | | | | | | REDUCE: (757), (6540) imply: % 148.93/21.47 | | | | | | | (6541) ~ (all_10_0 = e1) % 148.93/21.47 | | | | | | | % 148.93/21.47 | | | | | | | BETA: splitting (99) gives: % 148.93/21.47 | | | | | | | % 148.93/21.47 | | | | | | | Case 1: % 148.93/21.47 | | | | | | | | % 148.93/21.47 | | | | | | | | (6542) ~ (all_28_0 = e2) % 148.93/21.47 | | | | | | | | % 148.93/21.47 | | | | | | | | REDUCE: (740), (6542) imply: % 148.93/21.47 | | | | | | | | (6543) ~ (all_6_0 = e2) % 148.93/21.47 | | | | | | | | % 148.93/21.47 | | | | | | | | BETA: splitting (109) gives: % 148.93/21.47 | | | | | | | | % 148.93/21.47 | | | | | | | | Case 1: % 148.93/21.47 | | | | | | | | | % 148.93/21.47 | | | | | | | | | (6544) ~ (all_32_1 = e1) % 148.93/21.47 | | | | | | | | | % 148.93/21.47 | | | | | | | | | REDUCE: (682), (6544) imply: % 148.93/21.47 | | | | | | | | | (6545) ~ (all_10_1 = e1) % 148.93/21.47 | | | | | | | | | % 148.93/21.47 | | | | | | | | | BETA: splitting (114) gives: % 148.93/21.47 | | | | | | | | | % 148.93/21.47 | | | | | | | | | Case 1: % 148.93/21.47 | | | | | | | | | | % 148.93/21.47 | | | | | | | | | | (6546) ~ (all_34_0 = e2) % 148.93/21.47 | | | | | | | | | | % 148.93/21.47 | | | | | | | | | | REDUCE: (6537), (6546) imply: % 148.93/21.47 | | | | | | | | | | (6547) $false % 148.93/21.47 | | | | | | | | | | % 148.93/21.47 | | | | | | | | | | CLOSE: (6547) is inconsistent. % 148.93/21.47 | | | | | | | | | | % 148.93/21.47 | | | | | | | | | Case 2: % 148.93/21.47 | | | | | | | | | | % 148.93/21.47 | | | | | | | | | | (6548) ~ (all_34_1 = e3) | ~ (all_34_2 = e1) % 148.93/21.47 | | | | | | | | | | % 148.93/21.47 | | | | | | | | | | BETA: splitting (119) gives: % 148.93/21.47 | | | | | | | | | | % 148.93/21.47 | | | | | | | | | | Case 1: % 148.93/21.47 | | | | | | | | | | | % 148.93/21.47 | | | | | | | | | | | (6549) ~ (all_36_1 = e3) % 148.93/21.47 | | | | | | | | | | | % 148.93/21.47 | | | | | | | | | | | REDUCE: (652), (6549) imply: % 148.93/21.47 | | | | | | | | | | | (6550) ~ (all_6_1 = e3) % 148.93/21.47 | | | | | | | | | | | % 148.93/21.47 | | | | | | | | | | | BETA: splitting (124) gives: % 148.93/21.47 | | | | | | | | | | | % 148.93/21.47 | | | | | | | | | | | Case 1: % 148.93/21.47 | | | | | | | | | | | | % 148.93/21.47 | | | | | | | | | | | | (6551) ~ (all_38_1 = e2) % 148.93/21.47 | | | | | | | | | | | | % 148.93/21.47 | | | | | | | | | | | | REDUCE: (684), (6551) imply: % 148.93/21.47 | | | | | | | | | | | | (6552) ~ (all_10_1 = e2) % 148.93/21.47 | | | | | | | | | | | | % 148.93/21.47 | | | | | | | | | | | | BETA: splitting (149) gives: % 148.93/21.47 | | | | | | | | | | | | % 148.93/21.47 | | | | | | | | | | | | Case 1: % 148.93/21.47 | | | | | | | | | | | | | % 148.93/21.47 | | | | | | | | | | | | | (6553) ~ (all_48_0 = e3) % 148.93/21.47 | | | | | | | | | | | | | % 148.93/21.47 | | | | | | | | | | | | | REDUCE: (765), (6553) imply: % 148.93/21.47 | | | | | | | | | | | | | (6554) ~ (all_8_0 = e3) % 148.93/21.47 | | | | | | | | | | | | | % 148.93/21.47 | | | | | | | | | | | | | BETA: splitting (292) gives: % 148.93/21.47 | | | | | | | | | | | | | % 148.93/21.47 | | | | | | | | | | | | | Case 1: % 148.93/21.47 | | | | | | | | | | | | | | % 148.93/21.47 | | | | | | | | | | | | | | (6555) ~ (all_56_21 = e2) % 148.93/21.47 | | | | | | | | | | | | | | % 148.93/21.47 | | | | | | | | | | | | | | REDUCE: (374), (6555) imply: % 148.93/21.47 | | | | | | | | | | | | | | (6556) ~ (all_6_2 = e2) % 148.93/21.47 | | | | | | | | | | | | | | % 148.93/21.47 | | | | | | | | | | | | | | BETA: splitting (294) gives: % 148.93/21.47 | | | | | | | | | | | | | | % 148.93/21.47 | | | | | | | | | | | | | | Case 1: % 148.93/21.47 | | | | | | | | | | | | | | | % 148.93/21.47 | | | | | | | | | | | | | | | (6557) ~ (all_56_11 = e0) % 148.93/21.47 | | | | | | | | | | | | | | | % 148.93/21.47 | | | | | | | | | | | | | | | REDUCE: (545), (6557) imply: % 148.93/21.47 | | | | | | | | | | | | | | | (6558) ~ (all_8_2 = e0) % 148.93/21.47 | | | | | | | | | | | | | | | % 148.93/21.47 | | | | | | | | | | | | | | | BETA: splitting (288) gives: % 148.93/21.47 | | | | | | | | | | | | | | | % 148.93/21.47 | | | | | | | | | | | | | | | Case 1: % 148.93/21.47 | | | | | | | | | | | | | | | | % 148.93/21.47 | | | | | | | | | | | | | | | | (6559) ~ (all_56_31 = e1) % 148.93/21.47 | | | | | | | | | | | | | | | | % 148.93/21.47 | | | | | | | | | | | | | | | | REDUCE: (544), (6559) imply: % 148.93/21.47 | | | | | | | | | | | | | | | | (6560) ~ (all_4_2 = e1) % 148.93/21.47 | | | | | | | | | | | | | | | | % 148.93/21.47 | | | | | | | | | | | | | | | | BETA: splitting (293) gives: % 148.93/21.47 | | | | | | | | | | | | | | | | % 148.93/21.47 | | | | | | | | | | | | | | | | Case 1: % 148.93/21.47 | | | | | | | | | | | | | | | | | % 148.93/21.47 | | | | | | | | | | | | | | | | | (6561) ~ (all_56_21 = e3) % 148.93/21.47 | | | | | | | | | | | | | | | | | % 148.93/21.47 | | | | | | | | | | | | | | | | | REDUCE: (374), (6561) imply: % 148.93/21.47 | | | | | | | | | | | | | | | | | (6562) ~ (all_6_2 = e3) % 148.93/21.47 | | | | | | | | | | | | | | | | | % 148.93/21.47 | | | | | | | | | | | | | | | | | BETA: splitting (296) gives: % 148.93/21.47 | | | | | | | | | | | | | | | | | % 148.93/21.47 | | | | | | | | | | | | | | | | | Case 1: % 148.93/21.47 | | | | | | | | | | | | | | | | | | % 148.93/21.47 | | | | | | | | | | | | | | | | | | (6563) ~ (all_56_11 = e3) % 148.93/21.47 | | | | | | | | | | | | | | | | | | % 148.93/21.47 | | | | | | | | | | | | | | | | | | REDUCE: (545), (6563) imply: % 148.93/21.47 | | | | | | | | | | | | | | | | | | (6564) ~ (all_8_2 = e3) % 148.93/21.47 | | | | | | | | | | | | | | | | | | % 148.93/21.47 | | | | | | | | | | | | | | | | | | BETA: splitting (299) gives: % 148.93/21.47 | | | | | | | | | | | | | | | | | | % 148.93/21.47 | | | | | | | | | | | | | | | | | | Case 1: % 148.93/21.47 | | | | | | | | | | | | | | | | | | | % 148.93/21.47 | | | | | | | | | | | | | | | | | | | (6565) ~ (all_56_1 = e2) % 148.93/21.47 | | | | | | | | | | | | | | | | | | | % 148.93/21.47 | | | | | | | | | | | | | | | | | | | REDUCE: (546), (6565) imply: % 148.93/21.47 | | | | | | | | | | | | | | | | | | | (6566) ~ (all_10_2 = e2) % 148.93/21.47 | | | | | | | | | | | | | | | | | | | % 148.93/21.47 | | | | | | | | | | | | | | | | | | | BETA: splitting (295) gives: % 148.93/21.47 | | | | | | | | | | | | | | | | | | | % 148.93/21.47 | | | | | | | | | | | | | | | | | | | Case 1: % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | (6567) ~ (all_56_11 = e1) % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | REDUCE: (545), (6567) imply: % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | (6568) ~ (all_8_2 = e1) % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (46), (247), (542), (617), (5071), (6558), (6564), % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | (6568), (function-axioms) are inconsistent by % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | sub-proof #146. % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | % 148.93/21.47 | | | | | | | | | | | | | | | | | | | Case 2: % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | (6569) all_56_13 = e2 % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | (6570) all_56_11 = e1 % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (545), (6570) imply: % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | (6571) all_8_2 = e1 % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5075), (6569) imply: % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | (6572) all_8_0 = e2 % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5076), (6572) imply: % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | (6573) all_58_5 = e2 % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | REDUCE: (5077), (6572) imply: % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | (6574) ~ (all_52_1 = e2) % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | REDUCE: (568), (6571) imply: % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | (6575) ~ (all_52_1 = e1) % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | REDUCE: (5078), (6572) imply: % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | (6576) ~ (all_52_8 = e2) % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | REDUCE: (5082), (6572) imply: % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | (6577) ~ (all_52_13 = e2) % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | REDUCE: (579), (6571) imply: % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | (6578) ~ (all_52_13 = e1) % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | REDUCE: (5084), (6572) imply: % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | (6579) ~ (all_6_2 = e2) % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | REDUCE: (5071), (6571) imply: % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | (6580) op(e1, e1) = e1 % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | REDUCE: (46), (6571) imply: % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | (6581) op(e2, e2) = e1 % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_6_2, e1, % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | e1, e1, simplifying with (41), (6580) gives: % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | (6582) all_6_2 = e1 % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (552), (6582) imply: % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | (6583) all_58_8 = e1 % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | REDUCE: (580), (6582) imply: % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | (6584) ~ (all_52_6 = e1) % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | REDUCE: (587), (6582) imply: % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | (6585) ~ (all_52_14 = e1) % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | REDUCE: (6562), (6582) imply: % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | (6586) ~ (e3 = e1) % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | REDUCE: (6556), (6582) imply: % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | (6587) ~ (e2 = e1) % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | BETA: splitting (321) gives: % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | Case 1: % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | | % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | | (6588) all_58_9 = e1 % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | | % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (551), (6588) imply: % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | | (6589) all_52_12 = e1 % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | | % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (402), (6589) imply: % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | | (6590) all_56_7 = e1 % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | | % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | | REDUCE: (161), (6589) imply: % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | | (6591) ~ (all_52_13 = e1) % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | | % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | | REDUCE: (567), (6589) imply: % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | | (6592) ~ (all_10_2 = e1) % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | | % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | | SIMP: (6592) implies: % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | | (6593) ~ (all_10_2 = e1) % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | | % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | | REDUCE: (589), (6589) imply: % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | | (6594) ~ (all_4_2 = e1) % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | | % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | | REDUCE: (624), (6589) imply: % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | | (6595) op(e0, e1) = all_56_6 % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | | % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (297) gives: % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | | % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | | | (6596) ~ (all_56_1 = e0) % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (546), (6596) imply: % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | | | (6597) ~ (all_10_2 = e0) % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (345) gives: % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | | | | (6598) all_58_0 = e2 % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (419), (6598) imply: % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | | | | (6599) all_10_2 = e2 % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6566), (6599) imply: % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | | | | (6600) $false % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (6600) is inconsistent. % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | | | | (6601) ~ (all_58_0 = e2) % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | | | | (6602) all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2 % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (252) gives: % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | | | | | (6603) all_54_0 = e3 % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (543), (6603) imply: % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | | | | | (6604) all_10_2 = e3 % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6604) implies: % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | | | | | (6605) all_10_2 = e3 % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (557), (6605) imply: % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | | | | | (6606) ~ (all_52_1 = e3) % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (559), (6605) imply: % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | | | | | (6607) ~ (all_52_2 = e3) % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (565), (6605) imply: % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | | | | | (6608) ~ (all_52_8 = e3) % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (53), (6605) imply: % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | | | | | (6609) op(e3, e3) = all_10_1 % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (612), (6605) imply: % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | | | | | (6610) op(e3, e3) = all_56_0 % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (51), (6605) imply: % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | | | | | (6611) op(e3, e3) = e3 % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (331) gives: % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | (6612) all_58_4 = e3 % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (407), (6612) imply: % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | (6613) all_52_8 = e3 % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6608), (6613) imply: % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | (6614) $false % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (6614) is inconsistent. % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | (6615) all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3 % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (248) gives: % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | (6616) all_54_4 = e3 % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (463), (6606), (6616) are inconsistent by % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #634. % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | (6617) all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0 % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6617) gives: % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | (6618) all_54_4 = e2 % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (463), (6574), (6618) are inconsistent by % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #633. % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | (6619) all_54_4 = e1 | all_54_4 = e0 % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6615) gives: % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6620) all_58_5 = e3 % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (6573), (6620) are inconsistent by sub-proof % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | #457. % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6621) all_58_8 = e3 | all_58_14 = e3 % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6619) gives: % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6622) all_54_4 = e1 % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (463), (6575), (6622) are inconsistent by % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #584. % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6623) all_54_4 = e0 % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (463), (6623) imply: % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6624) all_52_1 = e0 % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6624) implies: % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6625) all_52_1 = e0 % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (197), (6625) imply: % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6626) ~ (all_52_2 = e0) % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6626) implies: % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6627) ~ (all_52_2 = e0) % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (193), (6625) imply: % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6628) ~ (all_52_13 = e0) % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6628) implies: % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6629) ~ (all_52_13 = e0) % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6575), (6625) imply: % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6630) ~ (e1 = e0) % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (245) gives: % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6631) all_54_7 = e3 % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (469), (6631) imply: % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6632) all_52_13 = e3 % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6632) implies: % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6633) all_52_13 = e3 % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (158), (6633) imply: % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6634) ~ (all_52_14 = e3) % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6634) implies: % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6635) ~ (all_52_14 = e3) % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (327) gives: % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6636) all_58_6 = e3 % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (553), (6636) imply: % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6637) all_52_2 = e3 % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6607), (6637) imply: % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6638) $false % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (6638) is inconsistent. % 148.93/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.07/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6639) all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3 % 149.07/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6639) gives: % 149.07/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.07/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6640) all_58_7 = e3 % 149.07/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (380), (6640) imply: % 149.07/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6641) all_52_6 = e3 % 149.07/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6621) gives: % 149.07/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.07/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6642) all_58_8 = e3 % 149.07/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (6583), (6642) are inconsistent by sub-proof % 149.07/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #161. % 149.07/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.07/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6643) all_58_14 = e3 % 149.07/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (548), (6643) imply: % 149.07/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6644) all_52_11 = e3 % 149.07/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (588), (6644) imply: % 149.07/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6645) ~ (all_4_2 = e3) % 149.07/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6645) implies: % 149.07/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6646) ~ (all_4_2 = e3) % 149.07/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (205), (6644) imply: % 149.07/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6647) op(e0, e1) = e3 % 149.07/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (324) gives: % 149.07/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.07/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6648) all_58_6 = e0 % 149.07/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (553), (6648) imply: % 149.07/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6649) all_52_2 = e0 % 149.07/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6627), (6649) imply: % 149.07/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6650) $false % 149.07/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (6650) is inconsistent. % 149.07/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.07/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6651) all_58_7 = e0 | all_58_8 = e0 | all_58_11 = e0 % 149.07/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6651) gives: % 149.07/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.07/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6652) all_58_7 = e0 % 149.07/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6640), (6652) imply: % 149.07/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6653) e3 = e0 % 149.07/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7), (6653) imply: % 149.07/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6654) $false % 149.07/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (6654) is inconsistent. % 149.07/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.07/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6655) all_58_8 = e0 | all_58_11 = e0 % 149.07/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6655) gives: % 149.07/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.07/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6656) all_58_8 = e0 % 149.07/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6583), (6656) imply: % 149.07/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6657) e1 = e0 % 149.07/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4), (6657) imply: % 149.07/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6658) $false % 149.07/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (6658) is inconsistent. % 149.07/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.07/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6659) all_58_11 = e0 % 149.07/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (550), (6659) imply: % 149.07/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6660) all_52_14 = e0 % 149.07/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (591), (6660) imply: % 149.07/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6661) ~ (all_4_2 = e0) % 149.07/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6661) implies: % 149.07/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6662) ~ (all_4_2 = e0) % 149.07/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (237) gives: % 149.07/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.07/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6663) all_54_15 = e3 % 149.07/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (540), (6646), (6663) are inconsistent by % 149.07/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #740. % 149.07/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.07/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6664) all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0 % 149.07/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6602) gives: % 149.07/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.07/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6665) all_58_1 = e2 % 149.07/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (555), (6665) imply: % 149.07/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6666) all_52_4 = e2 % 149.07/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (616), (6666) imply: % 149.07/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6667) op(e2, e2) = all_56_2 % 149.07/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6664) gives: % 149.07/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.07/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6668) all_54_15 = e2 % 149.07/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (540), (6668) imply: % 149.07/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6669) all_4_2 = e2 % 149.07/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6669) implies: % 149.07/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6670) all_4_2 = e2 % 149.07/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (544), (6670) imply: % 149.07/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6671) all_56_31 = e2 % 149.07/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (38), (6670) imply: % 149.07/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6672) op(e2, e2) = all_4_1 % 149.07/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (289) gives: % 149.07/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.07/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6673) ~ (all_56_31 = e2) % 149.07/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6671), (6673) imply: % 149.07/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6674) $false % 149.07/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (6674) is inconsistent. % 149.07/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.07/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_56_6, % 149.07/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1, e0, simplifying with (6595), (6647) gives: % 149.07/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6675) all_56_6 = e3 % 149.07/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1, all_56_2, % 149.07/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2, e2, simplifying with (6581), (6667) gives: % 149.07/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6676) all_56_2 = e1 % 149.07/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_4_1, % 149.07/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_2, e2, e2, simplifying with (6667), (6672) % 149.07/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 149.07/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6677) all_56_2 = all_4_1 % 149.07/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_10_1, % 149.07/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_0, e3, e3, simplifying with (6609), (6610) % 149.07/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 149.07/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6678) all_56_0 = all_10_1 % 149.07/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_56_0, % 149.07/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3, e3, simplifying with (6610), (6611) gives: % 149.07/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6679) all_56_0 = e3 % 149.07/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6678), (6679) imply: % 149.07/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6680) all_10_1 = e3 % 149.07/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6680) implies: % 149.07/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6681) all_10_1 = e3 % 149.07/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6676), (6677) imply: % 149.07/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6682) all_4_1 = e1 % 149.07/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6539), (6682) imply: % 149.07/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6683) op(e0, e1) = e2 % 149.07/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, e2, e1, % 149.07/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0, simplifying with (6647), (6683) gives: % 149.07/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6684) e3 = e2 % 149.07/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6643), (6684) imply: % 149.07/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6685) all_58_14 = e2 % 149.07/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (552), (6562), (6621), (6685) are % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #591. % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6686) all_54_15 = e1 | all_54_15 = e0 % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (540), (6560), (6662), (6686) are inconsistent by % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #96. % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6687) all_58_4 = e2 | all_58_9 = e2 % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (407), (6576), (6588), (6687) are % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #562. % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6688) all_58_8 = e3 | all_58_11 = e3 % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (550), (6583), (6635), (6688) are % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #160. % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6689) all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0 % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (469), (6577), (6578), (6629), (6689) are % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #649. % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | | | | | (6690) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (543), (6566), (6593), (6597), (6690) are % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #731. % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | | | | End of split % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | | | End of split % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | | | (6691) all_56_7 = e3 % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (6590), (6691) are inconsistent by sub-proof % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | | | #497. % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | | End of split % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | Case 2: % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | | (6692) all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1 % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (386), (547), (550), (6560), (6578), (6585), % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | | (6692) are inconsistent by sub-proof #587. % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | End of split % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | | | | | | End of split % 149.07/21.48 | | | | | | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | | | | | Case 2: % 149.07/21.48 | | | | | | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | | | | | | (6693) all_56_3 = e3 % 149.07/21.48 | | | | | | | | | | | | | | | | | | | (6694) all_56_1 = e2 % 149.07/21.48 | | | | | | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (546), (6694) imply: % 149.07/21.48 | | | | | | | | | | | | | | | | | | | (6695) all_10_2 = e2 % 149.07/21.48 | | | | | | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (408), (6693) imply: % 149.07/21.48 | | | | | | | | | | | | | | | | | | | (6696) all_52_4 = e3 % 149.07/21.48 | | | | | | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | | | | | | REDUCE: (182), (6696) imply: % 149.07/21.48 | | | | | | | | | | | | | | | | | | | (6697) ~ (all_52_8 = e3) % 149.07/21.48 | | | | | | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | | | | | | SIMP: (6697) implies: % 149.07/21.48 | | | | | | | | | | | | | | | | | | | (6698) ~ (all_52_8 = e3) % 149.07/21.48 | | | | | | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | | | | | | REDUCE: (571), (6696) imply: % 149.07/21.48 | | | | | | | | | | | | | | | | | | | (6699) ~ (all_8_2 = e3) % 149.07/21.48 | | | | | | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | | | | | | REDUCE: (565), (6695) imply: % 149.07/21.48 | | | | | | | | | | | | | | | | | | | (6700) ~ (all_52_8 = e2) % 149.07/21.48 | | | | | | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | | | | | | REDUCE: (53), (6695) imply: % 149.07/21.48 | | | | | | | | | | | | | | | | | | | (6701) op(e2, e2) = all_10_1 % 149.07/21.48 | | | | | | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | | | | | | BETA: splitting (331) gives: % 149.07/21.48 | | | | | | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | | | | | | Case 1: % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | (6702) all_58_4 = e3 % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (407), (6702) imply: % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | (6703) all_52_8 = e3 % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | REDUCE: (6698), (6703) imply: % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | (6704) $false % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | CLOSE: (6704) is inconsistent. % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | | | | | | Case 2: % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | (6705) all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3 % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | BETA: splitting (6705) gives: % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | Case 1: % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | | (6706) all_58_5 = e3 % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5076), (6706) imply: % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | | (6707) all_8_0 = e3 % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | | REDUCE: (6554), (6707) imply: % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | | (6708) $false % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | | CLOSE: (6708) is inconsistent. % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | Case 2: % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | | (6709) all_58_8 = e3 | all_58_14 = e3 % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (330) gives: % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | | | (6710) all_58_4 = e2 % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (407), (6710) imply: % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | | | (6711) all_52_8 = e2 % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6700), (6711) imply: % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | | | (6712) $false % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (6712) is inconsistent. % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | | | (6713) all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2 % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6713) gives: % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | | | | (6714) all_58_5 = e2 % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5076), (6714) imply: % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | | | | (6715) all_8_0 = e2 % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5083), (6715) imply: % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | | | | (6716) ~ (all_8_2 = e2) % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6716) implies: % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | | | | (6717) ~ (all_8_2 = e2) % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (247) gives: % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | | | | | (6718) all_54_5 = e3 % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (542), (6564), (6718) are inconsistent by % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #737. % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | | | | | (6719) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6719) gives: % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | | | | | | (6720) all_54_5 = e2 % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (542), (6717), (6720) are inconsistent by % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #648. % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | | | | | | (6721) all_54_5 = e1 | all_54_5 = e0 % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (46), (542), (6545), (6558), (6701), (6721), % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | | | | | | #132. % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | | | | End of split % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | | | | (6722) all_58_8 = e2 | all_58_14 = e2 % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (552), (6556), (6562), (6709), (6722) are % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #590. % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | | | End of split % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | | End of split % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | End of split % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | | | | | | End of split % 149.07/21.48 | | | | | | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | | | | | End of split % 149.07/21.48 | | | | | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | | | | Case 2: % 149.07/21.48 | | | | | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | | | | | (6723) all_56_11 = e3 % 149.07/21.48 | | | | | | | | | | | | | | | | | | (6724) all_56_9 = e2 % 149.07/21.48 | | | | | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (425), (6724) imply: % 149.07/21.48 | | | | | | | | | | | | | | | | | | (6725) all_52_1 = e2 % 149.07/21.48 | | | | | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (545), (6723) imply: % 149.07/21.48 | | | | | | | | | | | | | | | | | | (6726) all_8_2 = e3 % 149.07/21.48 | | | | | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (554), (6726) imply: % 149.07/21.48 | | | | | | | | | | | | | | | | | | (6727) all_58_3 = e3 % 149.07/21.48 | | | | | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (401), (6725) imply: % 149.07/21.48 | | | | | | | | | | | | | | | | | | (6728) all_58_2 = e2 % 149.07/21.48 | | | | | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | | | | | REDUCE: (197), (6725) imply: % 149.07/21.48 | | | | | | | | | | | | | | | | | | (6729) ~ (all_52_2 = e2) % 149.07/21.48 | | | | | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | | | | | SIMP: (6729) implies: % 149.07/21.48 | | | | | | | | | | | | | | | | | | (6730) ~ (all_52_2 = e2) % 149.07/21.48 | | | | | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | | | | | REDUCE: (196), (6725) imply: % 149.07/21.48 | | | | | | | | | | | | | | | | | | (6731) ~ (all_52_3 = e2) % 149.07/21.48 | | | | | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | | | | | SIMP: (6731) implies: % 149.07/21.48 | | | | | | | | | | | | | | | | | | (6732) ~ (all_52_3 = e2) % 149.07/21.48 | | | | | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | | | | | REDUCE: (557), (6725) imply: % 149.07/21.48 | | | | | | | | | | | | | | | | | | (6733) ~ (all_10_2 = e2) % 149.07/21.48 | | | | | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | | | | | SIMP: (6733) implies: % 149.07/21.48 | | | | | | | | | | | | | | | | | | (6734) ~ (all_10_2 = e2) % 149.07/21.48 | | | | | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | | | | | REDUCE: (5077), (6725) imply: % 149.07/21.48 | | | | | | | | | | | | | | | | | | (6735) ~ (all_8_0 = e2) % 149.07/21.48 | | | | | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | | | | | SIMP: (6735) implies: % 149.07/21.48 | | | | | | | | | | | | | | | | | | (6736) ~ (all_8_0 = e2) % 149.07/21.48 | | | | | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | | | | | REDUCE: (5071), (6726) imply: % 149.07/21.48 | | | | | | | | | | | | | | | | | | (6737) op(e3, e3) = e1 % 149.07/21.48 | | | | | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (9), (51), (193), (246), (287), (294), (332), % 149.07/21.48 | | | | | | | | | | | | | | | | | | (344), (365), (374), (386), (401), (419), (443), % 149.07/21.48 | | | | | | | | | | | | | | | | | | (544), (546), (553), (590), (5069), (5074), % 149.07/21.48 | | | | | | | | | | | | | | | | | | (5076), (5082), (5084), (6554), (6723), (6726), % 149.07/21.48 | | | | | | | | | | | | | | | | | | (6727), (6728), (6730), (6732), (6734), (6736), % 149.07/21.48 | | | | | | | | | | | | | | | | | | (6737), (function-axioms) are inconsistent by % 149.07/21.48 | | | | | | | | | | | | | | | | | | sub-proof #107. % 149.07/21.48 | | | | | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | | | | End of split % 149.07/21.48 | | | | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | | | Case 2: % 149.07/21.48 | | | | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | | | | (6738) all_56_21 = e3 % 149.07/21.48 | | | | | | | | | | | | | | | | | (6739) all_56_17 = e1 % 149.07/21.48 | | | | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | | | | REF_CLOSE: (42), (43), (51), (158), (160), (161), (174), % 149.07/21.48 | | | | | | | | | | | | | | | | | (189), (191), (208), (241), (243), (252), (287), % 149.07/21.48 | | | | | | | | | | | | | | | | | (297), (321), (332), (374), (381), (386), (389), % 149.07/21.48 | | | | | | | | | | | | | | | | | (401), (402), (473), (476), (543), (544), (545), % 149.07/21.48 | | | | | | | | | | | | | | | | | (546), (547), (550), (551), (554), (557), (559), % 149.07/21.48 | | | | | | | | | | | | | | | | | (569), (573), (580), (591), (621), (768), (6543), % 149.07/21.48 | | | | | | | | | | | | | | | | | (6550), (6558), (6560), (6738), (6739), % 149.07/21.48 | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 149.07/21.48 | | | | | | | | | | | | | | | | | #130. % 149.07/21.48 | | | | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | | | End of split % 149.07/21.48 | | | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | | Case 2: % 149.07/21.48 | | | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | | | (6740) all_56_31 = e1 % 149.07/21.48 | | | | | | | | | | | | | | | | (6741) all_56_29 = e0 % 149.07/21.48 | | | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | | | REF_CLOSE: (7), (38), (41), (46), (53), (168), (182), (252), % 149.07/21.48 | | | | | | | | | | | | | | | | (287), (297), (299), (331), (357), (374), (402), % 149.07/21.48 | | | | | | | | | | | | | | | | (407), (408), (531), (543), (544), (545), (546), % 149.07/21.48 | | | | | | | | | | | | | | | | (548), (552), (565), (683), (5071), (5076), % 149.07/21.48 | | | | | | | | | | | | | | | | (6545), (6548), (6554), (6740), (6741), % 149.07/21.48 | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 149.07/21.48 | | | | | | | | | | | | | | | | #95. % 149.07/21.48 | | | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | | End of split % 149.07/21.48 | | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | Case 2: % 149.07/21.48 | | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | | (6742) all_56_15 = e2 % 149.07/21.48 | | | | | | | | | | | | | | | (6743) all_56_11 = e0 % 149.07/21.48 | | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | | COMBINE_EQS: (545), (6743) imply: % 149.07/21.48 | | | | | | | | | | | | | | | (6744) all_8_2 = e0 % 149.07/21.48 | | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | | COMBINE_EQS: (443), (6742) imply: % 149.07/21.48 | | | | | | | | | | | | | | | (6745) all_52_13 = e2 % 149.07/21.48 | | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | | COMBINE_EQS: (386), (6745) imply: % 149.07/21.48 | | | | | | | | | | | | | | | (6746) all_58_10 = e2 % 149.07/21.48 | | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | | COMBINE_EQS: (554), (6744) imply: % 149.07/21.48 | | | | | | | | | | | | | | | (6747) all_58_3 = e0 % 149.07/21.48 | | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | | REDUCE: (5082), (6745) imply: % 149.07/21.48 | | | | | | | | | | | | | | | (6748) ~ (all_8_0 = e2) % 149.07/21.48 | | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | | SIMP: (6748) implies: % 149.07/21.48 | | | | | | | | | | | | | | | (6749) ~ (all_8_0 = e2) % 149.07/21.48 | | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | | REDUCE: (5083), (6744) imply: % 149.07/21.48 | | | | | | | | | | | | | | | (6750) ~ (all_8_0 = e0) % 149.07/21.48 | | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | | REDUCE: (5071), (6744) imply: % 149.07/21.48 | | | | | | | | | | | | | | | (6751) op(e0, e0) = e1 % 149.07/21.48 | | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (38), (246), % 149.07/21.48 | | | | | | | | | | | | | | | (287), (333), (335), (374), (401), (544), (546), % 149.07/21.48 | | | | | | | | | | | | | | | (557), (627), (5074), (5076), (5084), (6554), % 149.07/21.48 | | | | | | | | | | | | | | | (6743), (6746), (6747), (6749), (6750), (6751), % 149.07/21.48 | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 149.07/21.48 | | | | | | | | | | | | | | | #128. % 149.07/21.48 | | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | End of split % 149.07/21.48 | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | Case 2: % 149.07/21.48 | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | (6752) all_56_21 = e2 % 149.07/21.48 | | | | | | | | | | | | | | (6753) all_56_19 = e1 % 149.07/21.48 | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | COMBINE_EQS: (435), (6753) imply: % 149.07/21.48 | | | | | | | | | | | | | | (6754) all_52_6 = e1 % 149.07/21.48 | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | COMBINE_EQS: (374), (6752) imply: % 149.07/21.48 | | | | | | | | | | | | | | (6755) all_6_2 = e2 % 149.07/21.48 | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | REDUCE: (573), (6754) imply: % 149.07/21.48 | | | | | | | | | | | | | | (6756) ~ (all_8_2 = e1) % 149.07/21.48 | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | SIMP: (6756) implies: % 149.07/21.48 | | | | | | | | | | | | | | (6757) ~ (all_8_2 = e1) % 149.07/21.48 | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | REDUCE: (43), (6755) imply: % 149.07/21.48 | | | | | | | | | | | | | | (6758) op(e2, e2) = all_6_1 % 149.07/21.48 | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | REF_CLOSE: (36), (38), (46), (193), (246), (247), (248), % 149.07/21.48 | | | | | | | | | | | | | | (287), (294), (317), (443), (463), (542), (544), % 149.07/21.48 | | | | | | | | | | | | | | (545), (546), (547), (557), (568), (627), (768), % 149.07/21.48 | | | | | | | | | | | | | | (5071), (5074), (5077), (5082), (5083), (6550), % 149.07/21.48 | | | | | | | | | | | | | | (6554), (6752), (6757), (6758), (function-axioms) % 149.07/21.48 | | | | | | | | | | | | | | are inconsistent by sub-proof #118. % 149.07/21.48 | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | End of split % 149.07/21.48 | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | Case 2: % 149.07/21.48 | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | (6759) all_48_0 = e3 % 149.07/21.48 | | | | | | | | | | | | | (6760) ~ (all_48_1 = e1) | ~ (all_48_2 = e0) % 149.07/21.48 | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | COMBINE_EQS: (765), (6759) imply: % 149.07/21.48 | | | | | | | | | | | | | (6761) all_8_0 = e3 % 149.07/21.48 | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | SIMP: (6761) implies: % 149.07/21.48 | | | | | | | | | | | | | (6762) all_8_0 = e3 % 149.07/21.48 | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | REF_CLOSE: (9), (46), (247), (295), (536), (542), (545), % 149.07/21.48 | | | | | | | | | | | | | (617), (5070), (5071), (5075), (5083), (6760), % 149.07/21.48 | | | | | | | | | | | | | (6762), (function-axioms) are inconsistent by % 149.07/21.48 | | | | | | | | | | | | | sub-proof #115. % 149.07/21.48 | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | End of split % 149.07/21.48 | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | Case 2: % 149.07/21.48 | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | (6763) all_38_1 = e2 % 149.07/21.48 | | | | | | | | | | | | (6764) ~ (all_38_0 = e0) | ~ (all_38_2 = e1) % 149.07/21.48 | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | COMBINE_EQS: (684), (6763) imply: % 149.07/21.48 | | | | | | | | | | | | (6765) all_10_1 = e2 % 149.07/21.48 | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | SIMP: (6765) implies: % 149.07/21.48 | | | | | | | | | | | | (6766) all_10_1 = e2 % 149.07/21.48 | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | REDUCE: (53), (6766) imply: % 149.07/21.48 | | | | | | | | | | | | (6767) op(all_10_2, all_10_2) = e2 % 149.07/21.48 | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | REDUCE: (52), (6766) imply: % 149.07/21.48 | | | | | | | | | | | | (6768) op(e3, e2) = all_10_0 % 149.07/21.48 | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_4, % 149.07/21.48 | | | | | | | | | | | | all_10_0, e2, e3, simplifying with (218), (6768) % 149.07/21.48 | | | | | | | | | | | | gives: % 149.07/21.48 | | | | | | | | | | | | (6769) all_52_4 = all_10_0 % 149.07/21.48 | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | COMBINE_EQS: (457), (6769) imply: % 149.07/21.48 | | | | | | | | | | | | (6770) all_54_1 = all_10_0 % 149.07/21.48 | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | COMBINE_EQS: (555), (6769) imply: % 149.07/21.48 | | | | | | | | | | | | (6771) all_58_1 = all_10_0 % 149.07/21.48 | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | REDUCE: (182), (6769) imply: % 149.07/21.48 | | | | | | | | | | | | (6772) ~ (all_52_8 = all_10_0) % 149.07/21.48 | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | SIMP: (6772) implies: % 149.07/21.48 | | | | | | | | | | | | (6773) ~ (all_52_8 = all_10_0) % 149.07/21.48 | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | REDUCE: (181), (6769) imply: % 149.07/21.48 | | | | | | | | | | | | (6774) ~ (all_52_12 = all_10_0) % 149.07/21.48 | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | SIMP: (6774) implies: % 149.07/21.48 | | | | | | | | | | | | (6775) ~ (all_52_12 = all_10_0) % 149.07/21.48 | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | REDUCE: (563), (6769) imply: % 149.07/21.48 | | | | | | | | | | | | (6776) ~ (all_10_0 = all_10_2) % 149.07/21.48 | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | REDUCE: (571), (6769) imply: % 149.07/21.48 | | | | | | | | | | | | (6777) ~ (all_10_0 = all_8_2) % 149.07/21.48 | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | BETA: splitting (149) gives: % 149.07/21.48 | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | Case 1: % 149.07/21.48 | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | (6778) ~ (all_48_0 = e3) % 149.07/21.48 | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | REDUCE: (765), (6778) imply: % 149.07/21.48 | | | | | | | | | | | | | (6779) ~ (all_8_0 = e3) % 149.07/21.48 | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | BETA: splitting (294) gives: % 149.07/21.48 | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | Case 1: % 149.07/21.48 | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | (6780) ~ (all_56_11 = e0) % 149.07/21.48 | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | REDUCE: (545), (6780) imply: % 149.07/21.48 | | | | | | | | | | | | | | (6781) ~ (all_8_2 = e0) % 149.07/21.48 | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | BETA: splitting (295) gives: % 149.07/21.48 | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | Case 1: % 149.07/21.48 | | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | | (6782) ~ (all_56_11 = e1) % 149.07/21.48 | | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | | REDUCE: (545), (6782) imply: % 149.07/21.48 | | | | | | | | | | | | | | | (6783) ~ (all_8_2 = e1) % 149.07/21.48 | | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | | BETA: splitting (296) gives: % 149.07/21.48 | | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | | Case 1: % 149.07/21.48 | | | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | | | (6784) ~ (all_56_11 = e3) % 149.07/21.48 | | | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | | | REDUCE: (545), (6784) imply: % 149.07/21.48 | | | | | | | | | | | | | | | | (6785) ~ (all_8_2 = e3) % 149.07/21.48 | | | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | | | REF_CLOSE: (46), (247), (542), (617), (5071), (6781), (6783), % 149.07/21.48 | | | | | | | | | | | | | | | | (6785), (function-axioms) are inconsistent by % 149.07/21.48 | | | | | | | | | | | | | | | | sub-proof #146. % 149.07/21.48 | | | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | | Case 2: % 149.07/21.48 | | | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | | | (6786) all_56_11 = e3 % 149.07/21.48 | | | | | | | | | | | | | | | | (6787) all_56_9 = e2 % 149.07/21.48 | | | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | | | COMBINE_EQS: (425), (6787) imply: % 149.07/21.48 | | | | | | | | | | | | | | | | (6788) all_52_1 = e2 % 149.07/21.48 | | | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | | | COMBINE_EQS: (545), (6786) imply: % 149.07/21.48 | | | | | | | | | | | | | | | | (6789) all_8_2 = e3 % 149.07/21.48 | | | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | | | REDUCE: (557), (6788) imply: % 149.07/21.48 | | | | | | | | | | | | | | | | (6790) ~ (all_10_2 = e2) % 149.07/21.48 | | | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | | | SIMP: (6790) implies: % 149.07/21.48 | | | | | | | | | | | | | | | | (6791) ~ (all_10_2 = e2) % 149.07/21.48 | | | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | | | REDUCE: (6777), (6789) imply: % 149.07/21.48 | | | | | | | | | | | | | | | | (6792) ~ (all_10_0 = e3) % 149.07/21.48 | | | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | | | REDUCE: (5071), (6789) imply: % 149.07/21.48 | | | | | | | | | | | | | | | | (6793) op(e3, e3) = e1 % 149.07/21.48 | | | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | | | BETA: splitting (251) gives: % 149.07/21.48 | | | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | | | Case 1: % 149.07/21.48 | | | | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | | | | (6794) all_54_1 = e3 % 149.07/21.48 | | | | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | | | | REF_CLOSE: (6770), (6792), (6794) are inconsistent by % 149.07/21.48 | | | | | | | | | | | | | | | | | sub-proof #493. % 149.07/21.48 | | | | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | | | Case 2: % 149.07/21.48 | | | | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | | | | (6795) all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0 % 149.07/21.48 | | | | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | | | | BETA: splitting (6795) gives: % 149.07/21.48 | | | | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | | | | Case 1: % 149.07/21.48 | | | | | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | | | | | (6796) all_54_1 = e2 % 149.07/21.48 | | | | | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | | | | | REF_CLOSE: (5086), (6770), (6796) are inconsistent by % 149.07/21.48 | | | | | | | | | | | | | | | | | | sub-proof #492. % 149.07/21.48 | | | | | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | | | | Case 2: % 149.07/21.48 | | | | | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | | | | | (6797) all_54_1 = e1 | all_54_1 = e0 % 149.07/21.48 | | | | | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | | | | | BETA: splitting (6797) gives: % 149.07/21.48 | | | | | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | | | | | Case 1: % 149.07/21.48 | | | | | | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | | | | | | (6798) all_54_1 = e1 % 149.07/21.48 | | | | | | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6541), (6770), (6798) are inconsistent by % 149.07/21.48 | | | | | | | | | | | | | | | | | | | sub-proof #491. % 149.07/21.48 | | | | | | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | | | | | Case 2: % 149.07/21.48 | | | | | | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | | | | | | (6799) all_54_1 = e0 % 149.07/21.48 | | | | | | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6770), (6799) imply: % 149.07/21.48 | | | | | | | | | | | | | | | | | | | (6800) all_10_0 = e0 % 149.07/21.48 | | | | | | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | | | | | | SIMP: (6800) implies: % 149.07/21.48 | | | | | | | | | | | | | | | | | | | (6801) all_10_0 = e0 % 149.07/21.48 | | | | | | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (723), (6801) imply: % 149.07/21.48 | | | | | | | | | | | | | | | | | | | (6802) all_38_0 = e0 % 149.07/21.48 | | | | | | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | | | | | | REDUCE: (6776), (6801) imply: % 149.07/21.48 | | | | | | | | | | | | | | | | | | | (6803) ~ (all_10_2 = e0) % 149.07/21.48 | | | | | | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | | | | | | SIMP: (6803) implies: % 149.07/21.48 | | | | | | | | | | | | | | | | | | | (6804) ~ (all_10_2 = e0) % 149.07/21.48 | | | | | | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | | | | | | BETA: splitting (6764) gives: % 149.07/21.48 | | | | | | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | | | | | | Case 1: % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | (6805) ~ (all_38_2 = e1) % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | REDUCE: (533), (6805) imply: % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | (6806) ~ (all_10_2 = e1) % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (51), (252), (543), (6791), (6793), (6804), % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | (6806), (function-axioms) are inconsistent by % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | sub-proof #305. % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | | | | | | Case 2: % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | (6807) all_38_2 = e1 % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6764), (6802), (6807) are inconsistent by % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | sub-proof #487. % 149.07/21.48 | | | | | | | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | | | | | | End of split % 149.07/21.48 | | | | | | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | | | | | End of split % 149.07/21.48 | | | | | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | | | | End of split % 149.07/21.48 | | | | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | | | End of split % 149.07/21.48 | | | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | | End of split % 149.07/21.48 | | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | Case 2: % 149.07/21.48 | | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | | (6808) all_56_13 = e2 % 149.07/21.48 | | | | | | | | | | | | | | | (6809) all_56_11 = e1 % 149.07/21.48 | | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | | COMBINE_EQS: (545), (6809) imply: % 149.07/21.48 | | | | | | | | | | | | | | | (6810) all_8_2 = e1 % 149.07/21.48 | | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | | COMBINE_EQS: (5075), (6808) imply: % 149.07/21.48 | | | | | | | | | | | | | | | (6811) all_8_0 = e2 % 149.07/21.48 | | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | | REDUCE: (5078), (6811) imply: % 149.07/21.48 | | | | | | | | | | | | | | | (6812) ~ (all_52_8 = e2) % 149.07/21.48 | | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | | REDUCE: (579), (6810) imply: % 149.07/21.48 | | | | | | | | | | | | | | | (6813) ~ (all_52_13 = e1) % 149.07/21.48 | | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | | REDUCE: (5071), (6810) imply: % 149.07/21.48 | | | | | | | | | | | | | | | (6814) op(e1, e1) = e1 % 149.07/21.48 | | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | | REDUCE: (46), (6810) imply: % 149.07/21.48 | | | | | | | | | | | | | | | (6815) op(e2, e2) = e1 % 149.07/21.48 | | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_6_2, e1, % 149.07/21.48 | | | | | | | | | | | | | | | e1, e1, simplifying with (41), (6814) gives: % 149.07/21.48 | | | | | | | | | | | | | | | (6816) all_6_2 = e1 % 149.07/21.48 | | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | | REDUCE: (582), (6816) imply: % 149.07/21.48 | | | | | | | | | | | | | | | (6817) ~ (all_52_8 = e1) % 149.07/21.48 | | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | | REDUCE: (587), (6816) imply: % 149.07/21.48 | | | | | | | | | | | | | | | (6818) ~ (all_52_14 = e1) % 149.07/21.48 | | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | | REDUCE: (43), (6816) imply: % 149.07/21.48 | | | | | | | | | | | | | | | (6819) op(e1, e1) = all_6_1 % 149.07/21.48 | | | | | | | | | | | | | | | % 149.07/21.48 | | | | | | | | | | | | | | | REDUCE: (622), (6816) imply: % 149.07/21.48 | | | | | | | | | | | | | | | (6820) op(e1, e1) = all_56_20 % 149.07/21.49 | | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1, % 149.07/21.49 | | | | | | | | | | | | | | | all_56_20, e1, e1, simplifying with (6814), (6820) % 149.07/21.49 | | | | | | | | | | | | | | | gives: % 149.07/21.49 | | | | | | | | | | | | | | | (6821) all_56_20 = e1 % 149.07/21.49 | | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_6_1, % 149.07/21.49 | | | | | | | | | | | | | | | all_56_20, e1, e1, simplifying with (6819), (6820) % 149.07/21.49 | | | | | | | | | | | | | | | gives: % 149.07/21.49 | | | | | | | | | | | | | | | (6822) all_56_20 = all_6_1 % 149.07/21.49 | | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | | COMBINE_EQS: (6821), (6822) imply: % 149.07/21.49 | | | | | | | | | | | | | | | (6823) all_6_1 = e1 % 149.07/21.49 | | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | | SIMP: (6823) implies: % 149.07/21.49 | | | | | | | | | | | | | | | (6824) all_6_1 = e1 % 149.07/21.49 | | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | | REDUCE: (42), (6824) imply: % 149.07/21.49 | | | | | | | | | | | | | | | (6825) op(e1, e1) = all_6_0 % 149.07/21.49 | | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1, all_6_0, % 149.07/21.49 | | | | | | | | | | | | | | | e1, e1, simplifying with (6814), (6825) gives: % 149.07/21.49 | | | | | | | | | | | | | | | (6826) all_6_0 = e1 % 149.07/21.49 | | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | | REDUCE: (6543), (6826) imply: % 149.07/21.49 | | | | | | | | | | | | | | | (6827) ~ (e2 = e1) % 149.07/21.49 | | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | | BETA: splitting (288) gives: % 149.07/21.49 | | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | | Case 1: % 149.07/21.49 | | | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | | | (6828) ~ (all_56_31 = e1) % 149.07/21.49 | | | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | | | REDUCE: (544), (6828) imply: % 149.07/21.49 | | | | | | | | | | | | | | | | (6829) ~ (all_4_2 = e1) % 149.07/21.49 | | | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | | | BETA: splitting (321) gives: % 149.07/21.49 | | | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | | | Case 1: % 149.07/21.49 | | | | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | | | | (6830) all_58_9 = e1 % 149.07/21.49 | | | | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | | | | COMBINE_EQS: (551), (6830) imply: % 149.07/21.49 | | | | | | | | | | | | | | | | | (6831) all_52_12 = e1 % 149.07/21.49 | | | | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | | | | REDUCE: (567), (6831) imply: % 149.07/21.49 | | | | | | | | | | | | | | | | | (6832) ~ (all_10_2 = e1) % 149.07/21.49 | | | | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | | | | SIMP: (6832) implies: % 149.07/21.49 | | | | | | | | | | | | | | | | | (6833) ~ (all_10_2 = e1) % 149.07/21.49 | | | | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | | | | BETA: splitting (345) gives: % 149.07/21.49 | | | | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | | | | Case 1: % 149.07/21.49 | | | | | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | | | | | (6834) all_58_0 = e2 % 149.07/21.49 | | | | | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (419), (6834) imply: % 149.07/21.49 | | | | | | | | | | | | | | | | | | (6835) all_10_2 = e2 % 149.07/21.49 | | | | | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | | | | | REDUCE: (6767), (6835) imply: % 149.07/21.49 | | | | | | | | | | | | | | | | | | (6836) op(e2, e2) = e2 % 149.07/21.49 | | | | | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (6815), (6836), (function-axioms) are % 149.07/21.49 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #479. % 149.07/21.49 | | | | | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | | | | Case 2: % 149.07/21.49 | | | | | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | | | | | (6837) all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2 % 149.07/21.49 | | | | | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (407), (5086), (6771), (6812), (6830), (6837) % 149.07/21.49 | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #473. % 149.07/21.49 | | | | | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | | | | End of split % 149.07/21.49 | | | | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | | | Case 2: % 149.07/21.49 | | | | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | | | | (6838) all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1 % 149.07/21.49 | | | | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | | | | REF_CLOSE: (386), (547), (550), (6813), (6818), (6829), % 149.07/21.49 | | | | | | | | | | | | | | | | | (6838) are inconsistent by sub-proof #587. % 149.07/21.49 | | | | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | | | End of split % 149.07/21.49 | | | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | | Case 2: % 149.07/21.49 | | | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | | | (6839) all_56_31 = e1 % 149.07/21.49 | | | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | | | COMBINE_EQS: (544), (6839) imply: % 149.07/21.49 | | | | | | | | | | | | | | | | (6840) all_4_2 = e1 % 149.07/21.49 | | | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | | | REDUCE: (589), (6840) imply: % 149.07/21.49 | | | | | | | | | | | | | | | | (6841) ~ (all_52_12 = e1) % 149.07/21.49 | | | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | | | BETA: splitting (342) gives: % 149.07/21.49 | | | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | | | Case 1: % 149.07/21.49 | | | | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | | | | (6842) all_58_0 = e1 % 149.07/21.49 | | | | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | | | | COMBINE_EQS: (419), (6842) imply: % 149.07/21.49 | | | | | | | | | | | | | | | | | (6843) all_10_2 = e1 % 149.07/21.49 | | | | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | | | | REDUCE: (6767), (6843) imply: % 149.07/21.49 | | | | | | | | | | | | | | | | | (6844) op(e1, e1) = e2 % 149.07/21.49 | | | | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (6814), (6820), (6844), (function-axioms) are % 149.07/21.49 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #494. % 149.07/21.49 | | | | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | | | Case 2: % 149.07/21.49 | | | | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | | | | (6845) ~ (all_58_0 = e1) % 149.07/21.49 | | | | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | | | | REDUCE: (419), (6845) imply: % 149.07/21.49 | | | | | | | | | | | | | | | | | (6846) ~ (all_10_2 = e1) % 149.07/21.49 | | | | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | | | | BETA: splitting (343) gives: % 149.07/21.49 | | | | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | | | | Case 1: % 149.07/21.49 | | | | | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | | | | | (6847) all_58_0 = e1 % 149.07/21.49 | | | | | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (419), (6847) imply: % 149.07/21.49 | | | | | | | | | | | | | | | | | | (6848) all_10_2 = e1 % 149.07/21.49 | | | | | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | | | | | REDUCE: (6846), (6848) imply: % 149.07/21.49 | | | | | | | | | | | | | | | | | | (6849) $false % 149.07/21.49 | | | | | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | | | | | CLOSE: (6849) is inconsistent. % 149.07/21.49 | | | | | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | | | | Case 2: % 149.07/21.49 | | | | | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | | | | | (6850) all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1 % 149.07/21.49 | | | | | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | | | | | BETA: splitting (6850) gives: % 149.07/21.49 | | | | | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | | | | | Case 1: % 149.07/21.49 | | | | | | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | | | | | | (6851) all_58_1 = e1 % 149.07/21.49 | | | | | | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6771), (6851) imply: % 149.07/21.49 | | | | | | | | | | | | | | | | | | | (6852) all_10_0 = e1 % 149.07/21.49 | | | | | | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | | | | | | REDUCE: (6541), (6852) imply: % 149.07/21.49 | | | | | | | | | | | | | | | | | | | (6853) $false % 149.07/21.49 | | | | | | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | | | | | | CLOSE: (6853) is inconsistent. % 149.07/21.49 | | | | | | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | | | | | Case 2: % 149.07/21.49 | | | | | | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | | | | | | (6854) all_58_4 = e1 | all_58_9 = e1 % 149.07/21.49 | | | | | | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (407), (551), (6817), (6841), (6854) are % 149.07/21.49 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #578. % 149.07/21.49 | | | | | | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | | | | | End of split % 149.07/21.49 | | | | | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | | | | End of split % 149.07/21.49 | | | | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | | | End of split % 149.07/21.49 | | | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | | End of split % 149.07/21.49 | | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | End of split % 149.07/21.49 | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | Case 2: % 149.07/21.49 | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | (6855) all_56_15 = e2 % 149.07/21.49 | | | | | | | | | | | | | | (6856) all_56_11 = e0 % 149.07/21.49 | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | COMBINE_EQS: (545), (6856) imply: % 149.07/21.49 | | | | | | | | | | | | | | (6857) all_8_2 = e0 % 149.07/21.49 | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | COMBINE_EQS: (443), (6855) imply: % 149.07/21.49 | | | | | | | | | | | | | | (6858) all_52_13 = e2 % 149.07/21.49 | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | REDUCE: (5082), (6858) imply: % 149.07/21.49 | | | | | | | | | | | | | | (6859) ~ (all_8_0 = e2) % 149.07/21.49 | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | SIMP: (6859) implies: % 149.07/21.49 | | | | | | | | | | | | | | (6860) ~ (all_8_0 = e2) % 149.07/21.49 | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | REDUCE: (6777), (6857) imply: % 149.07/21.49 | | | | | | | | | | | | | | (6861) ~ (all_10_0 = e0) % 149.07/21.49 | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | REDUCE: (5083), (6857) imply: % 149.07/21.49 | | | | | | | | | | | | | | (6862) ~ (all_8_0 = e0) % 149.07/21.49 | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | REDUCE: (5071), (6857) imply: % 149.07/21.49 | | | | | | | | | | | | | | (6863) op(e0, e0) = e1 % 149.07/21.49 | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | BETA: splitting (251) gives: % 149.07/21.49 | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | Case 1: % 149.07/21.49 | | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | | (6864) all_54_1 = e3 % 149.07/21.49 | | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | | COMBINE_EQS: (6770), (6864) imply: % 149.07/21.49 | | | | | | | | | | | | | | | (6865) all_10_0 = e3 % 149.07/21.49 | | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | | SIMP: (6865) implies: % 149.07/21.49 | | | | | | | | | | | | | | | (6866) all_10_0 = e3 % 149.07/21.49 | | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | | COMBINE_EQS: (6771), (6866) imply: % 149.07/21.49 | | | | | | | | | | | | | | | (6867) all_58_1 = e3 % 149.07/21.49 | | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | | REDUCE: (6773), (6866) imply: % 149.07/21.49 | | | | | | | | | | | | | | | (6868) ~ (all_52_8 = e3) % 149.07/21.49 | | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | | REDUCE: (6775), (6866) imply: % 149.07/21.49 | | | | | | | | | | | | | | | (6869) ~ (all_52_12 = e3) % 149.07/21.49 | | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | | REDUCE: (6776), (6866) imply: % 149.07/21.49 | | | | | | | | | | | | | | | (6870) ~ (all_10_2 = e3) % 149.07/21.49 | | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | | SIMP: (6870) implies: % 149.07/21.49 | | | | | | | | | | | | | | | (6871) ~ (all_10_2 = e3) % 149.07/21.49 | | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | | BETA: splitting (298) gives: % 149.07/21.49 | | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | | Case 1: % 149.07/21.49 | | | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | | | (6872) ~ (all_56_1 = e1) % 149.07/21.49 | | | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | | | REDUCE: (546), (6872) imply: % 149.07/21.49 | | | | | | | | | | | | | | | | (6873) ~ (all_10_2 = e1) % 149.07/21.49 | | | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | | | BETA: splitting (297) gives: % 149.07/21.49 | | | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | | | Case 1: % 149.07/21.49 | | | | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | | | | (6874) ~ (all_56_1 = e0) % 149.07/21.49 | | | | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | | | | REDUCE: (546), (6874) imply: % 149.07/21.49 | | | | | | | | | | | | | | | | | (6875) ~ (all_10_2 = e0) % 149.07/21.49 | | | | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | | | | BETA: splitting (246) gives: % 149.07/21.49 | | | | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | | | | Case 1: % 149.07/21.49 | | | | | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | | | | | (6876) all_54_6 = e3 % 149.07/21.49 | | | | | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | | | | | REF_CLOSE: (5074), (6779), (6876) are inconsistent by % 149.07/21.49 | | | | | | | | | | | | | | | | | | sub-proof #145. % 149.07/21.49 | | | | | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | | | | Case 2: % 149.07/21.49 | | | | | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | | | | | (6877) ~ (all_54_6 = e3) % 149.07/21.49 | | | | | | | | | | | | | | | | | | (6878) all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0 % 149.07/21.49 | | | | | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | | | | | BETA: splitting (6878) gives: % 149.07/21.49 | | | | | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | | | | | Case 1: % 149.07/21.49 | | | | | | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | | | | | | (6879) all_54_6 = e2 % 149.07/21.49 | | | | | | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5074), (6860), (6879) are inconsistent by % 149.07/21.49 | | | | | | | | | | | | | | | | | | | sub-proof #144. % 149.07/21.49 | | | | | | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | | | | | Case 2: % 149.07/21.49 | | | | | | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | | | | | | (6880) all_54_6 = e1 | all_54_6 = e0 % 149.07/21.49 | | | | | | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | | | | | | BETA: splitting (6880) gives: % 149.07/21.49 | | | | | | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | | | | | | Case 1: % 149.07/21.49 | | | | | | | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | | | | | | | (6881) all_54_6 = e1 % 149.07/21.49 | | | | | | | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5074), (6881) imply: % 149.07/21.49 | | | | | | | | | | | | | | | | | | | | (6882) all_8_0 = e1 % 149.07/21.49 | | | | | | | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | | | | | | | SIMP: (6882) implies: % 149.07/21.49 | | | | | | | | | | | | | | | | | | | | (6883) all_8_0 = e1 % 149.07/21.49 | | | | | | | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | | | | | | | REDUCE: (5078), (6883) imply: % 149.07/21.49 | | | | | | | | | | | | | | | | | | | | (6884) ~ (all_52_8 = e1) % 149.07/21.49 | | | | | | | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | | | | | | | REDUCE: (5084), (6883) imply: % 149.07/21.49 | | | | | | | | | | | | | | | | | | | | (6885) ~ (all_6_2 = e1) % 149.07/21.49 | | | | | | | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | | | | | | | SIMP: (6885) implies: % 149.07/21.49 | | | | | | | | | | | | | | | | | | | | (6886) ~ (all_6_2 = e1) % 149.07/21.49 | | | | | | | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | | | | | | | REDUCE: (6779), (6883) imply: % 149.07/21.49 | | | | | | | | | | | | | | | | | | | | (6887) ~ (e3 = e1) % 149.07/21.49 | | | | | | | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | | | | | | | BETA: splitting (252) gives: % 149.07/21.49 | | | | | | | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | | | | | | | Case 1: % 149.07/21.49 | | | | | | | | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | | | | | | | | (6888) all_54_0 = e3 % 149.07/21.49 | | | | | | | | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (543), (6871), (6888) are inconsistent by % 149.07/21.49 | | | | | | | | | | | | | | | | | | | | | sub-proof #709. % 149.07/21.49 | | | | | | | | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | | | | | | | Case 2: % 149.07/21.49 | | | | | | | | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | | | | | | | | (6889) ~ (all_54_0 = e3) % 149.07/21.49 | | | | | | | | | | | | | | | | | | | | | (6890) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 149.07/21.49 | | | | | | | | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6890) gives: % 149.07/21.49 | | | | | | | | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.07/21.49 | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | | | | | | | | | (6891) all_54_0 = e2 % 149.07/21.49 | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (543), (6891) imply: % 149.07/21.49 | | | | | | | | | | | | | | | | | | | | | | (6892) all_10_2 = e2 % 149.07/21.49 | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | | | | | | | | | SIMP: (6892) implies: % 149.07/21.49 | | | | | | | | | | | | | | | | | | | | | | (6893) all_10_2 = e2 % 149.07/21.49 | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (546), (6893) imply: % 149.07/21.49 | | | | | | | | | | | | | | | | | | | | | | (6894) all_56_1 = e2 % 149.07/21.49 | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (419), (6893) imply: % 149.07/21.49 | | | | | | | | | | | | | | | | | | | | | | (6895) all_58_0 = e2 % 149.07/21.49 | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (287) gives: % 149.07/21.49 | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.07/21.49 | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | | | | | | | | | | (6896) all_56_1 = e3 % 149.07/21.49 | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (6894), (6896) are inconsistent by sub-proof % 149.07/21.49 | | | | | | | | | | | | | | | | | | | | | | | #428. % 149.07/21.49 | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.07/21.49 | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | | | | | | | | | | (6897) all_56_11 = e2 | all_56_21 = e1 | all_56_31 = e0 % 149.07/21.49 | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6897) gives: % 149.07/21.49 | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.07/21.49 | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | | | | | | | | | | | (6898) all_56_11 = e2 % 149.07/21.49 | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6856), (6898) are inconsistent by sub-proof % 149.07/21.49 | | | | | | | | | | | | | | | | | | | | | | | | #427. % 149.07/21.49 | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.07/21.49 | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | | | | | | | | | | | (6899) all_56_21 = e1 | all_56_31 = e0 % 149.07/21.49 | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (343) gives: % 149.07/21.49 | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.07/21.49 | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | | | | | | | | | | | | (6900) all_58_0 = e1 % 149.07/21.49 | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6895), (6900) imply: % 149.07/21.49 | | | | | | | | | | | | | | | | | | | | | | | | | (6901) e2 = e1 % 149.07/21.49 | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6), (6901) imply: % 149.07/21.49 | | | | | | | | | | | | | | | | | | | | | | | | | (6902) $false % 149.07/21.49 | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (6902) is inconsistent. % 149.07/21.49 | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.07/21.49 | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | | | | | | | | | | | | (6903) all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1 % 149.07/21.49 | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6903) gives: % 149.07/21.49 | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.07/21.49 | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | | | | | | | | | | | | | (6904) all_58_1 = e1 % 149.07/21.49 | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6867), (6904) imply: % 149.07/21.49 | | | | | | | | | | | | | | | | | | | | | | | | | | (6905) e3 = e1 % 149.07/21.49 | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8), (6905) imply: % 149.07/21.49 | | | | | | | | | | | | | | | | | | | | | | | | | | (6906) $false % 149.07/21.49 | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (6906) is inconsistent. % 149.07/21.49 | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.07/21.49 | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | | | | | | | | | | | | | (6907) all_58_4 = e1 | all_58_9 = e1 % 149.07/21.49 | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6907) gives: % 149.07/21.49 | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.07/21.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | (6908) all_58_4 = e1 % 149.07/21.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (407), (6908) imply: % 149.07/21.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | (6909) all_52_8 = e1 % 149.07/21.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6884), (6909) imply: % 149.07/21.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | (6910) $false % 149.07/21.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (6910) is inconsistent. % 149.07/21.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.07/21.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | (6911) all_58_9 = e1 % 149.07/21.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (551), (6911) imply: % 149.07/21.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | (6912) all_52_12 = e1 % 149.07/21.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (589), (6912) imply: % 149.07/21.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | (6913) ~ (all_4_2 = e1) % 149.07/21.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6913) implies: % 149.07/21.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | (6914) ~ (all_4_2 = e1) % 149.07/21.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (38), (374), (544), (627), (6863), (6886), % 149.07/21.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | (6899), (6914), (function-axioms) are inconsistent % 149.07/21.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #113. % 149.07/21.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 149.07/21.49 | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 149.07/21.49 | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 149.07/21.49 | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | | | | | | | | | | End of split % 149.07/21.49 | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | | | | | | | | | End of split % 149.07/21.49 | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.07/21.49 | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | | | | | | | | | (6915) all_54_0 = e1 | all_54_0 = e0 % 149.07/21.49 | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (543), (6873), (6875), (6915) are inconsistent by % 149.07/21.49 | | | | | | | | | | | | | | | | | | | | | | sub-proof #483. % 149.07/21.49 | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | | | | | | | | End of split % 149.07/21.49 | | | | | | | | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | | | | | | | End of split % 149.07/21.49 | | | | | | | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | | | | | | Case 2: % 149.07/21.49 | | | | | | | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | | | | | | | (6916) all_54_6 = e0 % 149.07/21.49 | | | | | | | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5074), (6862), (6916) are inconsistent by % 149.07/21.49 | | | | | | | | | | | | | | | | | | | | sub-proof #143. % 149.07/21.49 | | | | | | | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | | | | | | End of split % 149.07/21.49 | | | | | | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | | | | | End of split % 149.07/21.49 | | | | | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | | | | End of split % 149.07/21.49 | | | | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | | | Case 2: % 149.07/21.49 | | | | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | | | | (6917) all_56_7 = e3 % 149.07/21.49 | | | | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | | | | COMBINE_EQS: (402), (6917) imply: % 149.07/21.49 | | | | | | | | | | | | | | | | | (6918) all_52_12 = e3 % 149.07/21.49 | | | | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | | | | REDUCE: (6869), (6918) imply: % 149.07/21.49 | | | | | | | | | | | | | | | | | (6919) $false % 149.07/21.49 | | | | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | | | | CLOSE: (6919) is inconsistent. % 149.07/21.49 | | | | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | | | End of split % 149.07/21.49 | | | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | | Case 2: % 149.07/21.49 | | | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | | | (6920) all_56_5 = e3 % 149.07/21.49 | | | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | | | COMBINE_EQS: (429), (6920) imply: % 149.07/21.49 | | | | | | | | | | | | | | | | (6921) all_52_8 = e3 % 149.07/21.49 | | | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | | | REDUCE: (6868), (6921) imply: % 149.07/21.49 | | | | | | | | | | | | | | | | (6922) $false % 149.07/21.49 | | | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | | | CLOSE: (6922) is inconsistent. % 149.07/21.49 | | | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | | End of split % 149.07/21.49 | | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | Case 2: % 149.07/21.49 | | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | | (6923) all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0 % 149.07/21.49 | | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | | REF_CLOSE: (5086), (6541), (6770), (6861), (6923) are % 149.07/21.49 | | | | | | | | | | | | | | | inconsistent by sub-proof #490. % 149.07/21.49 | | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | End of split % 149.07/21.49 | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | End of split % 149.07/21.49 | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | Case 2: % 149.07/21.49 | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | (6924) all_48_0 = e3 % 149.07/21.49 | | | | | | | | | | | | | (6925) ~ (all_48_1 = e1) | ~ (all_48_2 = e0) % 149.07/21.49 | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | COMBINE_EQS: (765), (6924) imply: % 149.07/21.49 | | | | | | | | | | | | | (6926) all_8_0 = e3 % 149.07/21.49 | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | SIMP: (6926) implies: % 149.07/21.49 | | | | | | | | | | | | | (6927) all_8_0 = e3 % 149.07/21.49 | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | REF_CLOSE: (9), (46), (247), (295), (536), (542), (545), % 149.07/21.49 | | | | | | | | | | | | | (617), (5070), (5071), (5075), (5083), (6925), % 149.07/21.49 | | | | | | | | | | | | | (6927), (function-axioms) are inconsistent by % 149.07/21.49 | | | | | | | | | | | | | sub-proof #115. % 149.07/21.49 | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | End of split % 149.07/21.49 | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | End of split % 149.07/21.49 | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | Case 2: % 149.07/21.49 | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | (6928) all_36_1 = e3 % 149.07/21.49 | | | | | | | | | | | (6929) ~ (all_36_0 = e0) | ~ (all_36_2 = e2) % 149.07/21.49 | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | COMBINE_EQS: (652), (6928) imply: % 149.07/21.49 | | | | | | | | | | | (6930) all_6_1 = e3 % 149.07/21.49 | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | REDUCE: (43), (6930) imply: % 149.07/21.49 | | | | | | | | | | | (6931) op(all_6_2, all_6_2) = e3 % 149.07/21.49 | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | REDUCE: (42), (6930) imply: % 149.07/21.49 | | | | | | | | | | | (6932) op(e1, e3) = all_6_0 % 149.07/21.49 | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_2, % 149.07/21.49 | | | | | | | | | | | all_6_0, e3, e1, simplifying with (211), (6932) % 149.07/21.49 | | | | | | | | | | | gives: % 149.07/21.49 | | | | | | | | | | | (6933) all_52_2 = all_6_0 % 149.07/21.49 | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | COMBINE_EQS: (471), (6933) imply: % 149.07/21.49 | | | | | | | | | | | (6934) all_54_8 = all_6_0 % 149.07/21.49 | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | COMBINE_EQS: (381), (6933) imply: % 149.07/21.49 | | | | | | | | | | | (6935) all_56_17 = all_6_0 % 149.07/21.49 | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | COMBINE_EQS: (553), (6933) imply: % 149.07/21.49 | | | | | | | | | | | (6936) all_58_6 = all_6_0 % 149.07/21.49 | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | REDUCE: (197), (6933) imply: % 149.07/21.49 | | | | | | | | | | | (6937) ~ (all_52_1 = all_6_0) % 149.07/21.49 | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | REDUCE: (192), (6933) imply: % 149.07/21.49 | | | | | | | | | | | (6938) ~ (all_52_3 = all_6_0) % 149.07/21.49 | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | SIMP: (6938) implies: % 149.07/21.49 | | | | | | | | | | | (6939) ~ (all_52_3 = all_6_0) % 149.07/21.49 | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | REDUCE: (191), (6933) imply: % 149.07/21.49 | | | | | | | | | | | (6940) ~ (all_52_6 = all_6_0) % 149.07/21.49 | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | SIMP: (6940) implies: % 149.07/21.49 | | | | | | | | | | | (6941) ~ (all_52_6 = all_6_0) % 149.07/21.49 | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | REDUCE: (189), (6933) imply: % 149.07/21.49 | | | | | | | | | | | (6942) ~ (all_52_14 = all_6_0) % 149.07/21.49 | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | SIMP: (6942) implies: % 149.07/21.49 | | | | | | | | | | | (6943) ~ (all_52_14 = all_6_0) % 149.07/21.49 | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | REDUCE: (559), (6933) imply: % 149.07/21.49 | | | | | | | | | | | (6944) ~ (all_10_2 = all_6_0) % 149.07/21.49 | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | SIMP: (6944) implies: % 149.07/21.49 | | | | | | | | | | | (6945) ~ (all_10_2 = all_6_0) % 149.07/21.49 | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | REDUCE: (569), (6933) imply: % 149.07/21.49 | | | | | | | | | | | (6946) ~ (all_6_0 = all_6_2) % 149.07/21.49 | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | BETA: splitting (149) gives: % 149.07/21.49 | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | Case 1: % 149.07/21.49 | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | (6947) ~ (all_48_0 = e3) % 149.07/21.49 | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | REDUCE: (765), (6947) imply: % 149.07/21.49 | | | | | | | | | | | | (6948) ~ (all_8_0 = e3) % 149.07/21.49 | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | BETA: splitting (288) gives: % 149.07/21.49 | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | Case 1: % 149.07/21.49 | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | (6949) ~ (all_56_31 = e1) % 149.07/21.49 | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | REDUCE: (544), (6949) imply: % 149.07/21.49 | | | | | | | | | | | | | (6950) ~ (all_4_2 = e1) % 149.07/21.49 | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | BETA: splitting (290) gives: % 149.07/21.49 | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | Case 1: % 149.07/21.49 | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | (6951) ~ (all_56_31 = e3) % 149.07/21.49 | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | REDUCE: (544), (6951) imply: % 149.07/21.49 | | | | | | | | | | | | | | (6952) ~ (all_4_2 = e3) % 149.07/21.49 | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | REF_CLOSE: (36), (38), (41), (46), (48), (51), (174), (176), % 149.07/21.49 | | | | | | | | | | | | | | (188), (207), (237), (240), (242), (243), (244), % 149.07/21.49 | | | | | | | | | | | | | | (287), (289), (291), (292), (293), (324), (360), % 149.07/21.49 | | | | | | | | | | | | | | (366), (374), (380), (435), (473), (478), (532), % 149.07/21.49 | | | | | | | | | | | | | | (540), (541), (544), (545), (546), (550), (552), % 149.07/21.49 | | | | | | | | | | | | | | (561), (570), (573), (580), (587), (591), (617), % 149.07/21.49 | | | | | | | | | | | | | | (622), (627), (762), (6539), (6543), (6929), % 149.07/21.49 | | | | | | | | | | | | | | (6931), (6934), (6935), (6936), (6939), (6941), % 149.07/21.49 | | | | | | | | | | | | | | (6943), (6945), (6946), (6950), (6952), % 149.07/21.49 | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 149.07/21.49 | | | | | | | | | | | | | | #208. % 149.07/21.49 | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | Case 2: % 149.07/21.49 | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | (6953) all_56_31 = e3 % 149.07/21.49 | | | | | | | | | | | | | | (6954) all_56_25 = e0 % 149.07/21.49 | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | COMBINE_EQS: (447), (6954) imply: % 149.07/21.49 | | | | | | | | | | | | | | (6955) all_52_3 = e0 % 149.07/21.49 | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | SIMP: (6955) implies: % 149.07/21.49 | | | | | | | | | | | | | | (6956) all_52_3 = e0 % 149.07/21.49 | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | COMBINE_EQS: (544), (6953) imply: % 149.07/21.49 | | | | | | | | | | | | | | (6957) all_4_2 = e3 % 149.07/21.49 | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | REDUCE: (196), (6956) imply: % 149.07/21.49 | | | | | | | | | | | | | | (6958) ~ (all_52_1 = e0) % 149.07/21.49 | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | REDUCE: (6939), (6956) imply: % 149.07/21.49 | | | | | | | | | | | | | | (6959) ~ (all_6_0 = e0) % 149.07/21.49 | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | SIMP: (6959) implies: % 149.07/21.49 | | | | | | | | | | | | | | (6960) ~ (all_6_0 = e0) % 149.07/21.49 | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | REDUCE: (570), (6956), (6957) imply: % 149.07/21.49 | | | | | | | | | | | | | | (6961) ~ (e3 = e0) % 149.07/21.49 | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | REDUCE: (590), (6957) imply: % 149.07/21.49 | | | | | | | | | | | | | | (6962) ~ (all_52_13 = e3) % 149.07/21.49 | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | REDUCE: (38), (6957) imply: % 149.07/21.49 | | | | | | | | | | | | | | (6963) op(e3, e3) = all_4_1 % 149.07/21.49 | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_10_2, % 149.07/21.49 | | | | | | | | | | | | | | all_4_1, e3, e3, simplifying with (51), (6963) % 149.07/21.49 | | | | | | | | | | | | | | gives: % 149.07/21.49 | | | | | | | | | | | | | | (6964) all_10_2 = all_4_1 % 149.07/21.49 | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | COMBINE_EQS: (546), (6964) imply: % 149.07/21.49 | | | | | | | | | | | | | | (6965) all_56_1 = all_4_1 % 149.07/21.49 | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | REDUCE: (557), (6964) imply: % 149.07/21.49 | | | | | | | | | | | | | | (6966) ~ (all_52_1 = all_4_1) % 149.07/21.49 | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | REDUCE: (6945), (6964) imply: % 149.07/21.49 | | | | | | | | | | | | | | (6967) ~ (all_6_0 = all_4_1) % 149.07/21.49 | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | SIMP: (6967) implies: % 149.07/21.49 | | | | | | | | | | | | | | (6968) ~ (all_6_0 = all_4_1) % 149.07/21.49 | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | REDUCE: (612), (6964) imply: % 149.07/21.49 | | | | | | | | | | | | | | (6969) op(e3, all_4_1) = all_56_0 % 149.07/21.49 | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | BETA: splitting (291) gives: % 149.07/21.49 | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | Case 1: % 149.07/21.49 | | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | | (6970) ~ (all_56_21 = e0) % 149.07/21.49 | | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | | REDUCE: (374), (6970) imply: % 149.07/21.49 | | | | | | | | | | | | | | | (6971) ~ (all_6_2 = e0) % 149.07/21.49 | | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | | BETA: splitting (292) gives: % 149.07/21.49 | | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | | Case 1: % 149.07/21.49 | | | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | | | (6972) ~ (all_56_21 = e2) % 149.07/21.49 | | | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | | | REDUCE: (374), (6972) imply: % 149.07/21.49 | | | | | | | | | | | | | | | | (6973) ~ (all_6_2 = e2) % 149.07/21.49 | | | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | | | BETA: splitting (294) gives: % 149.07/21.49 | | | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | | | Case 1: % 149.07/21.49 | | | | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | | | | (6974) ~ (all_56_11 = e0) % 149.07/21.49 | | | | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | | | | REDUCE: (545), (6974) imply: % 149.07/21.49 | | | | | | | | | | | | | | | | | (6975) ~ (all_8_2 = e0) % 149.07/21.49 | | | | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | | | | BETA: splitting (293) gives: % 149.07/21.49 | | | | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | | | | Case 1: % 149.07/21.49 | | | | | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | | | | | (6976) ~ (all_56_21 = e3) % 149.07/21.49 | | | | | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | | | | | REDUCE: (374), (6976) imply: % 149.07/21.49 | | | | | | | | | | | | | | | | | | (6977) ~ (all_6_2 = e3) % 149.07/21.49 | | | | | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | | | | | REF_CLOSE: (41), (242), (541), (622), (6931), (6971), (6973), % 149.07/21.49 | | | | | | | | | | | | | | | | | | (6977), (function-axioms) are inconsistent by % 149.07/21.49 | | | | | | | | | | | | | | | | | | sub-proof #459. % 149.07/21.49 | | | | | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | | | | Case 2: % 149.07/21.49 | | | | | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | | | | | (6978) all_56_21 = e3 % 149.07/21.49 | | | | | | | | | | | | | | | | | | (6979) all_56_17 = e1 % 149.07/21.49 | | | | | | | | | | | | | | | | | | % 149.07/21.49 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6935), (6979) imply: % 149.07/21.49 | | | | | | | | | | | | | | | | | | (6980) all_6_0 = e1 % 149.07/21.49 | | | | | | | | | | | | | | | | | | % 149.07/21.50 | | | | | | | | | | | | | | | | | | SIMP: (6980) implies: % 149.07/21.50 | | | | | | | | | | | | | | | | | | (6981) all_6_0 = e1 % 149.07/21.50 | | | | | | | | | | | | | | | | | | % 149.07/21.50 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (374), (6978) imply: % 149.07/21.50 | | | | | | | | | | | | | | | | | | (6982) all_6_2 = e3 % 149.07/21.50 | | | | | | | | | | | | | | | | | | % 149.07/21.50 | | | | | | | | | | | | | | | | | | SIMP: (6982) implies: % 149.07/21.50 | | | | | | | | | | | | | | | | | | (6983) all_6_2 = e3 % 149.07/21.50 | | | | | | | | | | | | | | | | | | % 149.07/21.50 | | | | | | | | | | | | | | | | | | REDUCE: (6937), (6981) imply: % 149.07/21.50 | | | | | | | | | | | | | | | | | | (6984) ~ (all_52_1 = e1) % 149.07/21.50 | | | | | | | | | | | | | | | | | | % 149.07/21.50 | | | | | | | | | | | | | | | | | | REDUCE: (6968), (6981) imply: % 149.07/21.50 | | | | | | | | | | | | | | | | | | (6985) ~ (all_4_1 = e1) % 149.07/21.50 | | | | | | | | | | | | | | | | | | % 149.07/21.50 | | | | | | | | | | | | | | | | | | SIMP: (6985) implies: % 149.07/21.50 | | | | | | | | | | | | | | | | | | (6986) ~ (all_4_1 = e1) % 149.07/21.50 | | | | | | | | | | | | | | | | | | % 149.07/21.50 | | | | | | | | | | | | | | | | | | REDUCE: (6931), (6983) imply: % 149.07/21.50 | | | | | | | | | | | | | | | | | | (6987) op(e3, e3) = e3 % 149.07/21.50 | | | | | | | | | | | | | | | | | | % 149.07/21.50 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_4_1, e3, % 149.07/21.50 | | | | | | | | | | | | | | | | | | e3, e3, simplifying with (6963), (6987) gives: % 149.07/21.50 | | | | | | | | | | | | | | | | | | (6988) all_4_1 = e3 % 149.07/21.50 | | | | | | | | | | | | | | | | | | % 149.07/21.50 | | | | | | | | | | | | | | | | | | REDUCE: (6966), (6988) imply: % 149.07/21.50 | | | | | | | | | | | | | | | | | | (6989) ~ (all_52_1 = e3) % 149.07/21.50 | | | | | | | | | | | | | | | | | | % 149.07/21.50 | | | | | | | | | | | | | | | | | | REDUCE: (6969), (6988) imply: % 149.07/21.50 | | | | | | | | | | | | | | | | | | (6990) op(e3, e3) = all_56_0 % 149.07/21.50 | | | | | | | | | | | | | | | | | | % 149.07/21.50 | | | | | | | | | | | | | | | | | | BETA: splitting (335) gives: % 149.07/21.50 | | | | | | | | | | | | | | | | | | % 149.07/21.50 | | | | | | | | | | | | | | | | | | Case 1: % 149.07/21.50 | | | | | | | | | | | | | | | | | | | % 149.07/21.50 | | | | | | | | | | | | | | | | | | | (6991) all_58_2 = e3 % 149.07/21.50 | | | | | | | | | | | | | | | | | | | % 149.07/21.50 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (401), (6991) imply: % 149.07/21.50 | | | | | | | | | | | | | | | | | | | (6992) all_52_1 = e3 % 149.07/21.50 | | | | | | | | | | | | | | | | | | | % 149.07/21.50 | | | | | | | | | | | | | | | | | | | REDUCE: (6989), (6992) imply: % 149.07/21.50 | | | | | | | | | | | | | | | | | | | (6993) $false % 149.07/21.50 | | | | | | | | | | | | | | | | | | | % 149.07/21.50 | | | | | | | | | | | | | | | | | | | CLOSE: (6993) is inconsistent. % 149.07/21.50 | | | | | | | | | | | | | | | | | | | % 149.07/21.50 | | | | | | | | | | | | | | | | | | Case 2: % 149.07/21.50 | | | | | | | | | | | | | | | | | | | % 149.07/21.50 | | | | | | | | | | | | | | | | | | | (6994) ~ (all_58_2 = e3) % 149.07/21.50 | | | | | | | | | | | | | | | | | | | (6995) all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3 % 149.07/21.50 | | | | | | | | | | | | | | | | | | | % 149.07/21.50 | | | | | | | | | | | | | | | | | | | BETA: splitting (6995) gives: % 149.07/21.50 | | | | | | | | | | | | | | | | | | | % 149.07/21.50 | | | | | | | | | | | | | | | | | | | Case 1: % 149.07/21.50 | | | | | | | | | | | | | | | | | | | | % 149.07/21.50 | | | | | | | | | | | | | | | | | | | | (6996) all_58_3 = e3 % 149.07/21.50 | | | | | | | | | | | | | | | | | | | | % 149.07/21.50 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (554), (6996) imply: % 149.07/21.50 | | | | | | | | | | | | | | | | | | | | (6997) all_8_2 = e3 % 149.07/21.50 | | | | | | | | | | | | | | | | | | | | % 149.07/21.50 | | | | | | | | | | | | | | | | | | | | REDUCE: (5071), (6997) imply: % 149.07/21.50 | | | | | | | | | | | | | | | | | | | | (6998) op(e3, e3) = e1 % 149.07/21.50 | | | | | | | | | | | | | | | | | | | | % 149.07/21.50 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (6987), (6990), (6998), (function-axioms) are % 149.07/21.50 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #410. % 149.07/21.50 | | | | | | | | | | | | | | | | | | | | % 149.07/21.50 | | | | | | | | | | | | | | | | | | | Case 2: % 149.07/21.50 | | | | | | | | | | | | | | | | | | | | % 149.07/21.50 | | | | | | | | | | | | | | | | | | | | (6999) ~ (all_58_3 = e3) % 149.07/21.50 | | | | | | | | | | | | | | | | | | | | % 149.07/21.50 | | | | | | | | | | | | | | | | | | | | REDUCE: (554), (6999) imply: % 149.07/21.50 | | | | | | | | | | | | | | | | | | | | (7000) ~ (all_8_2 = e3) % 149.07/21.50 | | | | | | | | | | | | | | | | | | | | % 149.07/21.50 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (247), (248), (295), (463), (542), (545), (568), % 149.07/21.50 | | | | | | | | | | | | | | | | | | | | (5075), (5077), (6958), (6975), (6984), (6989), % 149.07/21.50 | | | | | | | | | | | | | | | | | | | | (7000) are inconsistent by sub-proof #137. % 149.07/21.50 | | | | | | | | | | | | | | | | | | | | % 149.07/21.50 | | | | | | | | | | | | | | | | | | | End of split % 149.07/21.50 | | | | | | | | | | | | | | | | | | | % 149.07/21.50 | | | | | | | | | | | | | | | | | | End of split % 149.07/21.50 | | | | | | | | | | | | | | | | | | % 149.07/21.50 | | | | | | | | | | | | | | | | | End of split % 149.07/21.50 | | | | | | | | | | | | | | | | | % 149.07/21.50 | | | | | | | | | | | | | | | | Case 2: % 149.07/21.50 | | | | | | | | | | | | | | | | | % 149.07/21.50 | | | | | | | | | | | | | | | | | (7001) all_56_15 = e2 % 149.07/21.50 | | | | | | | | | | | | | | | | | (7002) all_56_11 = e0 % 149.07/21.50 | | | | | | | | | | | | | | | | | % 149.07/21.50 | | | | | | | | | | | | | | | | | COMBINE_EQS: (545), (7002) imply: % 149.07/21.50 | | | | | | | | | | | | | | | | | (7003) all_8_2 = e0 % 149.07/21.50 | | | | | | | | | | | | | | | | | % 149.07/21.50 | | | | | | | | | | | | | | | | | COMBINE_EQS: (443), (7001) imply: % 149.07/21.50 | | | | | | | | | | | | | | | | | (7004) all_52_13 = e2 % 149.07/21.50 | | | | | | | | | | | | | | | | | % 149.07/21.50 | | | | | | | | | | | | | | | | | COMBINE_EQS: (386), (7004) imply: % 149.07/21.50 | | | | | | | | | | | | | | | | | (7005) all_58_10 = e2 % 149.07/21.50 | | | | | | | | | | | | | | | | | % 149.07/21.50 | | | | | | | | | | | | | | | | | COMBINE_EQS: (554), (7003) imply: % 149.07/21.50 | | | | | | | | | | | | | | | | | (7006) all_58_3 = e0 % 149.07/21.50 | | | | | | | | | | | | | | | | | % 149.07/21.50 | | | | | | | | | | | | | | | | | REDUCE: (5082), (7004) imply: % 149.07/21.50 | | | | | | | | | | | | | | | | | (7007) ~ (all_8_0 = e2) % 149.07/21.50 | | | | | | | | | | | | | | | | | % 149.07/21.50 | | | | | | | | | | | | | | | | | SIMP: (7007) implies: % 149.07/21.50 | | | | | | | | | | | | | | | | | (7008) ~ (all_8_0 = e2) % 149.07/21.50 | | | | | | | | | | | | | | | | | % 149.07/21.50 | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (38), (246), % 149.07/21.50 | | | | | | | | | | | | | | | | | (287), (333), (335), (374), (401), (544), (546), % 149.07/21.50 | | | | | | | | | | | | | | | | | (557), (627), (5071), (5074), (5076), (5083), % 149.07/21.50 | | | | | | | | | | | | | | | | | (5084), (6948), (7002), (7003), (7005), (7006), % 149.07/21.50 | | | | | | | | | | | | | | | | | (7008), (function-axioms) are inconsistent by % 149.07/21.50 | | | | | | | | | | | | | | | | | sub-proof #127. % 149.07/21.50 | | | | | | | | | | | | | | | | | % 149.07/21.50 | | | | | | | | | | | | | | | | End of split % 149.07/21.50 | | | | | | | | | | | | | | | | % 149.07/21.50 | | | | | | | | | | | | | | | Case 2: % 149.07/21.50 | | | | | | | | | | | | | | | | % 149.07/21.50 | | | | | | | | | | | | | | | | (7009) all_56_21 = e2 % 149.07/21.50 | | | | | | | | | | | | | | | | (7010) all_56_19 = e1 % 149.07/21.50 | | | | | | | | | | | | | | | | % 149.07/21.50 | | | | | | | | | | | | | | | | REF_CLOSE: (4), (46), (48), (244), (287), (324), (374), % 149.07/21.50 | | | | | | | | | | | | | | | | (380), (435), (544), (545), (546), (550), (552), % 149.07/21.50 | | | | | | | | | | | | | | | | (580), (591), (617), (6931), (6934), (6936), % 149.07/21.50 | | | | | | | | | | | | | | | | (6941), (6943), (6945), (6946), (6960), (6971), % 149.07/21.50 | | | | | | | | | | | | | | | | (7009), (7010), (function-axioms) are inconsistent % 149.07/21.50 | | | | | | | | | | | | | | | | by sub-proof #207. % 149.07/21.50 | | | | | | | | | | | | | | | | % 149.07/21.50 | | | | | | | | | | | | | | | End of split % 149.07/21.50 | | | | | | | | | | | | | | | % 149.07/21.50 | | | | | | | | | | | | | | Case 2: % 149.07/21.50 | | | | | | | | | | | | | | | % 149.07/21.50 | | | | | | | | | | | | | | | (7011) all_56_23 = e1 % 149.07/21.50 | | | | | | | | | | | | | | | (7012) all_56_21 = e0 % 149.07/21.50 | | | | | | | | | | | | | | | % 149.07/21.50 | | | | | | | | | | | | | | | REF_CLOSE: (174), (243), (244), (287), (366), (374), (473), % 149.07/21.50 | | | | | | | | | | | | | | | (545), (573), (580), (587), (6543), (6934), % 149.07/21.50 | | | | | | | | | | | | | | | (6941), (6943), (6946), (6953), (6965), (6968), % 149.07/21.50 | | | | | | | | | | | | | | | (7011), (7012) are inconsistent by sub-proof #320. % 149.07/21.50 | | | | | | | | | | | | | | | % 149.07/21.50 | | | | | | | | | | | | | | End of split % 149.07/21.50 | | | | | | | | | | | | | | % 149.07/21.50 | | | | | | | | | | | | | End of split % 149.07/21.50 | | | | | | | | | | | | | % 149.07/21.50 | | | | | | | | | | | | Case 2: % 149.07/21.50 | | | | | | | | | | | | | % 149.07/21.50 | | | | | | | | | | | | | (7013) all_56_31 = e1 % 149.07/21.50 | | | | | | | | | | | | | (7014) all_56_29 = e0 % 149.07/21.50 | | | | | | | | | | | | | % 149.07/21.50 | | | | | | | | | | | | | REF_CLOSE: (7), (38), (41), (46), (53), (168), (182), (252), % 149.07/21.50 | | | | | | | | | | | | | (287), (297), (299), (331), (357), (374), (402), % 149.07/21.50 | | | | | | | | | | | | | (407), (408), (531), (543), (544), (545), (546), % 149.07/21.50 | | | | | | | | | | | | | (548), (552), (565), (683), (5071), (5076), % 149.07/21.50 | | | | | | | | | | | | | (6545), (6548), (6948), (7013), (7014), % 149.07/21.50 | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 149.07/21.50 | | | | | | | | | | | | | #95. % 149.07/21.50 | | | | | | | | | | | | | % 149.07/21.50 | | | | | | | | | | | | End of split % 149.07/21.50 | | | | | | | | | | | | % 149.07/21.50 | | | | | | | | | | | Case 2: % 149.07/21.50 | | | | | | | | | | | | % 149.07/21.50 | | | | | | | | | | | | (7015) all_48_0 = e3 % 149.07/21.50 | | | | | | | | | | | | (7016) ~ (all_48_1 = e1) | ~ (all_48_2 = e0) % 149.07/21.50 | | | | | | | | | | | | % 149.07/21.50 | | | | | | | | | | | | COMBINE_EQS: (765), (7015) imply: % 149.07/21.50 | | | | | | | | | | | | (7017) all_8_0 = e3 % 149.07/21.50 | | | | | | | | | | | | % 149.07/21.50 | | | | | | | | | | | | SIMP: (7017) implies: % 149.07/21.50 | | | | | | | | | | | | (7018) all_8_0 = e3 % 149.07/21.50 | | | | | | | | | | | | % 149.07/21.50 | | | | | | | | | | | | REF_CLOSE: (9), (46), (247), (295), (536), (542), (545), % 149.07/21.50 | | | | | | | | | | | | (617), (5070), (5071), (5075), (5083), (7016), % 149.07/21.50 | | | | | | | | | | | | (7018), (function-axioms) are inconsistent by % 149.07/21.50 | | | | | | | | | | | | sub-proof #115. % 149.07/21.50 | | | | | | | | | | | | % 149.07/21.50 | | | | | | | | | | | End of split % 149.07/21.50 | | | | | | | | | | | % 149.07/21.50 | | | | | | | | | | End of split % 149.07/21.50 | | | | | | | | | | % 149.07/21.50 | | | | | | | | | End of split % 149.07/21.50 | | | | | | | | | % 149.07/21.50 | | | | | | | | Case 2: % 149.07/21.50 | | | | | | | | | % 149.07/21.50 | | | | | | | | | (7019) all_32_1 = e1 % 149.07/21.50 | | | | | | | | | (7020) ~ (all_32_0 = e0) | ~ (all_32_2 = e2) % 149.07/21.50 | | | | | | | | | % 149.07/21.50 | | | | | | | | | COMBINE_EQS: (682), (7019) imply: % 149.07/21.50 | | | | | | | | | (7021) all_10_1 = e1 % 149.07/21.50 | | | | | | | | | % 149.07/21.50 | | | | | | | | | REDUCE: (53), (7021) imply: % 149.07/21.50 | | | | | | | | | (7022) op(all_10_2, all_10_2) = e1 % 149.07/21.50 | | | | | | | | | % 149.07/21.50 | | | | | | | | | REDUCE: (52), (7021) imply: % 149.07/21.50 | | | | | | | | | (7023) op(e3, e1) = all_10_0 % 149.07/21.50 | | | | | | | | | % 149.07/21.50 | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_8, % 149.07/21.50 | | | | | | | | | all_10_0, e1, e3, simplifying with (217), (7023) % 149.07/21.50 | | | | | | | | | gives: % 149.07/21.50 | | | | | | | | | (7024) all_52_8 = all_10_0 % 149.07/21.50 | | | | | | | | | % 149.07/21.50 | | | | | | | | | COMBINE_EQS: (459), (7024) imply: % 149.07/21.50 | | | | | | | | | (7025) all_54_2 = all_10_0 % 149.07/21.50 | | | | | | | | | % 149.07/21.50 | | | | | | | | | COMBINE_EQS: (429), (7024) imply: % 149.07/21.50 | | | | | | | | | (7026) all_56_5 = all_10_0 % 149.07/21.50 | | | | | | | | | % 149.07/21.50 | | | | | | | | | COMBINE_EQS: (407), (7024) imply: % 149.07/21.50 | | | | | | | | | (7027) all_58_4 = all_10_0 % 149.07/21.50 | | | | | | | | | % 149.07/21.50 | | | | | | | | | REDUCE: (182), (7024) imply: % 149.07/21.50 | | | | | | | | | (7028) ~ (all_52_4 = all_10_0) % 149.07/21.50 | | | | | | | | | % 149.07/21.50 | | | | | | | | | REDUCE: (169), (7024) imply: % 149.07/21.50 | | | | | | | | | (7029) ~ (all_52_11 = all_10_0) % 149.07/21.50 | | | | | | | | | % 149.07/21.50 | | | | | | | | | SIMP: (7029) implies: % 149.07/21.50 | | | | | | | | | (7030) ~ (all_52_11 = all_10_0) % 149.07/21.50 | | | | | | | | | % 149.07/21.50 | | | | | | | | | REDUCE: (168), (7024) imply: % 149.07/21.50 | | | | | | | | | (7031) ~ (all_52_12 = all_10_0) % 149.07/21.50 | | | | | | | | | % 149.07/21.50 | | | | | | | | | SIMP: (7031) implies: % 149.07/21.50 | | | | | | | | | (7032) ~ (all_52_12 = all_10_0) % 149.07/21.50 | | | | | | | | | % 149.07/21.50 | | | | | | | | | REDUCE: (565), (7024) imply: % 149.07/21.50 | | | | | | | | | (7033) ~ (all_10_0 = all_10_2) % 149.07/21.50 | | | | | | | | | % 149.07/21.50 | | | | | | | | | REDUCE: (582), (7024) imply: % 149.07/21.50 | | | | | | | | | (7034) ~ (all_10_0 = all_6_2) % 149.07/21.50 | | | | | | | | | % 149.07/21.50 | | | | | | | | | BETA: splitting (119) gives: % 149.07/21.50 | | | | | | | | | % 149.07/21.50 | | | | | | | | | Case 1: % 149.07/21.50 | | | | | | | | | | % 149.07/21.50 | | | | | | | | | | (7035) ~ (all_36_1 = e3) % 149.07/21.50 | | | | | | | | | | % 149.07/21.50 | | | | | | | | | | REDUCE: (652), (7035) imply: % 149.07/21.50 | | | | | | | | | | (7036) ~ (all_6_1 = e3) % 149.07/21.50 | | | | | | | | | | % 149.07/21.50 | | | | | | | | | | BETA: splitting (149) gives: % 149.07/21.50 | | | | | | | | | | % 149.07/21.50 | | | | | | | | | | Case 1: % 149.07/21.50 | | | | | | | | | | | % 149.07/21.50 | | | | | | | | | | | (7037) ~ (all_48_0 = e3) % 149.07/21.50 | | | | | | | | | | | % 149.07/21.50 | | | | | | | | | | | REDUCE: (765), (7037) imply: % 149.07/21.50 | | | | | | | | | | | (7038) ~ (all_8_0 = e3) % 149.07/21.50 | | | | | | | | | | | % 149.07/21.50 | | | | | | | | | | | BETA: splitting (292) gives: % 149.07/21.50 | | | | | | | | | | | % 149.07/21.50 | | | | | | | | | | | Case 1: % 149.07/21.50 | | | | | | | | | | | | % 149.07/21.50 | | | | | | | | | | | | (7039) ~ (all_56_21 = e2) % 149.07/21.50 | | | | | | | | | | | | % 149.07/21.50 | | | | | | | | | | | | REDUCE: (374), (7039) imply: % 149.07/21.50 | | | | | | | | | | | | (7040) ~ (all_6_2 = e2) % 149.07/21.50 | | | | | | | | | | | | % 149.07/21.50 | | | | | | | | | | | | BETA: splitting (288) gives: % 149.07/21.50 | | | | | | | | | | | | % 149.07/21.50 | | | | | | | | | | | | Case 1: % 149.07/21.50 | | | | | | | | | | | | | % 149.07/21.50 | | | | | | | | | | | | | (7041) ~ (all_56_31 = e1) % 149.07/21.50 | | | | | | | | | | | | | % 149.07/21.50 | | | | | | | | | | | | | REDUCE: (544), (7041) imply: % 149.07/21.50 | | | | | | | | | | | | | (7042) ~ (all_4_2 = e1) % 149.07/21.50 | | | | | | | | | | | | | % 149.07/21.50 | | | | | | | | | | | | | REF_CLOSE: (7), (36), (38), (41), (51), (173), (237), (250), % 149.07/21.50 | | | | | | | | | | | | | (252), (289), (290), (291), (297), (298), (299), % 149.07/21.50 | | | | | | | | | | | | | (328), (330), (331), (360), (374), (389), (402), % 149.07/21.50 | | | | | | | | | | | | | (408), (447), (494), (529), (540), (543), (544), % 149.07/21.50 | | | | | | | | | | | | | (546), (548), (552), (561), (570), (581), (588), % 149.07/21.50 | | | | | | | | | | | | | (612), (627), (681), (761), (5086), (6535), % 149.07/21.50 | | | | | | | | | | | | | (6539), (6541), (7020), (7022), (7025), (7026), % 149.07/21.50 | | | | | | | | | | | | | (7027), (7028), (7032), (7033), (7034), (7040), % 149.07/21.50 | | | | | | | | | | | | | (7042), (function-axioms) are inconsistent by % 149.07/21.50 | | | | | | | | | | | | | sub-proof #204. % 149.07/21.50 | | | | | | | | | | | | | % 149.07/21.50 | | | | | | | | | | | | Case 2: % 149.07/21.50 | | | | | | | | | | | | | % 149.07/21.50 | | | | | | | | | | | | | (7043) all_56_31 = e1 % 149.07/21.50 | | | | | | | | | | | | | (7044) all_56_29 = e0 % 149.07/21.50 | | | | | | | | | | | | | % 149.07/21.50 | | | | | | | | | | | | | COMBINE_EQS: (357), (7044) imply: % 149.07/21.50 | | | | | | | | | | | | | (7045) all_52_11 = e0 % 149.07/21.50 | | | | | | | | | | | | | % 149.07/21.50 | | | | | | | | | | | | | SIMP: (7045) implies: % 149.07/21.50 | | | | | | | | | | | | | (7046) all_52_11 = e0 % 149.07/21.50 | | | | | | | | | | | | | % 149.07/21.50 | | | | | | | | | | | | | COMBINE_EQS: (544), (7043) imply: % 149.07/21.50 | | | | | | | | | | | | | (7047) all_4_2 = e1 % 149.07/21.50 | | | | | | | | | | | | | % 149.07/21.50 | | | | | | | | | | | | | COMBINE_EQS: (548), (7046) imply: % 149.07/21.50 | | | | | | | | | | | | | (7048) all_58_14 = e0 % 149.07/21.50 | | | | | | | | | | | | | % 149.07/21.50 | | | | | | | | | | | | | REDUCE: (7030), (7046) imply: % 149.07/21.50 | | | | | | | | | | | | | (7049) ~ (all_10_0 = e0) % 149.07/21.50 | | | | | | | | | | | | | % 149.07/21.50 | | | | | | | | | | | | | SIMP: (7049) implies: % 149.07/21.50 | | | | | | | | | | | | | (7050) ~ (all_10_0 = e0) % 149.07/21.50 | | | | | | | | | | | | | % 149.07/21.50 | | | | | | | | | | | | | REDUCE: (5080), (7046) imply: % 149.07/21.50 | | | | | | | | | | | | | (7051) ~ (all_8_0 = e0) % 149.07/21.50 | | | | | | | | | | | | | % 149.07/21.50 | | | | | | | | | | | | | SIMP: (7051) implies: % 149.07/21.50 | | | | | | | | | | | | | (7052) ~ (all_8_0 = e0) % 149.07/21.50 | | | | | | | | | | | | | % 149.07/21.50 | | | | | | | | | | | | | REDUCE: (585), (7046) imply: % 149.07/21.50 | | | | | | | | | | | | | (7053) ~ (all_6_2 = e0) % 149.07/21.50 | | | | | | | | | | | | | % 149.07/21.50 | | | | | | | | | | | | | SIMP: (7053) implies: % 149.07/21.50 | | | | | | | | | | | | | (7054) ~ (all_6_2 = e0) % 149.07/21.50 | | | | | | | | | | | | | % 149.07/21.50 | | | | | | | | | | | | | REDUCE: (588), (7046), (7047) imply: % 149.07/21.50 | | | | | | | | | | | | | (7055) ~ (e1 = e0) % 149.07/21.50 | | | | | | | | | | | | | % 149.07/21.50 | | | | | | | | | | | | | REDUCE: (38), (7047) imply: % 149.07/21.50 | | | | | | | | | | | | | (7056) op(e1, e1) = all_4_1 % 149.07/21.50 | | | | | | | | | | | | | % 149.07/21.50 | | | | | | | | | | | | | REDUCE: (627), (7047) imply: % 149.07/21.50 | | | | | | | | | | | | | (7057) op(e0, e1) = all_56_30 % 149.07/21.50 | | | | | | | | | | | | | % 149.07/21.50 | | | | | | | | | | | | | REDUCE: (205), (7046) imply: % 149.07/21.50 | | | | | | | | | | | | | (7058) op(e0, e1) = e0 % 149.07/21.50 | | | | | | | | | | | | | % 149.07/21.50 | | | | | | | | | | | | | BETA: splitting (330) gives: % 149.07/21.50 | | | | | | | | | | | | | % 149.07/21.50 | | | | | | | | | | | | | Case 1: % 149.07/21.50 | | | | | | | | | | | | | | % 149.07/21.50 | | | | | | | | | | | | | | (7059) all_58_4 = e2 % 149.07/21.50 | | | | | | | | | | | | | | % 149.07/21.50 | | | | | | | | | | | | | | COMBINE_EQS: (7027), (7059) imply: % 149.07/21.50 | | | | | | | | | | | | | | (7060) all_10_0 = e2 % 149.07/21.50 | | | | | | | | | | | | | | % 149.07/21.50 | | | | | | | | | | | | | | REDUCE: (5086), (7060) imply: % 149.07/21.50 | | | | | | | | | | | | | | (7061) $false % 149.07/21.50 | | | | | | | | | | | | | | % 149.07/21.50 | | | | | | | | | | | | | | CLOSE: (7061) is inconsistent. % 149.07/21.50 | | | | | | | | | | | | | | % 149.07/21.50 | | | | | | | | | | | | | Case 2: % 149.07/21.50 | | | | | | | | | | | | | | % 149.07/21.50 | | | | | | | | | | | | | | (7062) ~ (all_58_4 = e2) % 149.07/21.50 | | | | | | | | | | | | | | (7063) all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2 % 149.07/21.50 | | | | | | | | | | | | | | % 149.07/21.50 | | | | | | | | | | | | | | BETA: splitting (250) gives: % 149.07/21.50 | | | | | | | | | | | | | | % 149.07/21.50 | | | | | | | | | | | | | | Case 1: % 149.07/21.50 | | | | | | | | | | | | | | | % 149.07/21.50 | | | | | | | | | | | | | | | (7064) all_54_2 = e3 % 149.07/21.50 | | | | | | | | | | | | | | | % 149.07/21.50 | | | | | | | | | | | | | | | COMBINE_EQS: (7025), (7064) imply: % 149.07/21.50 | | | | | | | | | | | | | | | (7065) all_10_0 = e3 % 149.07/21.50 | | | | | | | | | | | | | | | % 149.07/21.50 | | | | | | | | | | | | | | | SIMP: (7065) implies: % 149.07/21.50 | | | | | | | | | | | | | | | (7066) all_10_0 = e3 % 149.07/21.50 | | | | | | | | | | | | | | | % 149.07/21.50 | | | | | | | | | | | | | | | COMBINE_EQS: (7027), (7066) imply: % 149.07/21.50 | | | | | | | | | | | | | | | (7067) all_58_4 = e3 % 149.07/21.50 | | | | | | | | | | | | | | | % 149.07/21.50 | | | | | | | | | | | | | | | REDUCE: (7034), (7066) imply: % 149.07/21.50 | | | | | | | | | | | | | | | (7068) ~ (all_6_2 = e3) % 149.07/21.50 | | | | | | | | | | | | | | | % 149.07/21.50 | | | | | | | | | | | | | | | SIMP: (7068) implies: % 149.07/21.50 | | | | | | | | | | | | | | | (7069) ~ (all_6_2 = e3) % 149.07/21.50 | | | | | | | | | | | | | | | % 149.07/21.50 | | | | | | | | | | | | | | | BETA: splitting (242) gives: % 149.07/21.50 | | | | | | | | | | | | | | | % 149.07/21.50 | | | | | | | | | | | | | | | Case 1: % 149.07/21.50 | | | | | | | | | | | | | | | | % 149.07/21.50 | | | | | | | | | | | | | | | | (7070) all_54_10 = e3 % 149.07/21.50 | | | | | | | | | | | | | | | | % 149.07/21.50 | | | | | | | | | | | | | | | | REF_CLOSE: (541), (7069), (7070) are inconsistent by % 149.07/21.50 | | | | | | | | | | | | | | | | sub-proof #736. % 149.07/21.50 | | | | | | | | | | | | | | | | % 149.07/21.50 | | | | | | | | | | | | | | | Case 2: % 149.07/21.50 | | | | | | | | | | | | | | | | % 149.07/21.50 | | | | | | | | | | | | | | | | (7071) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 149.07/21.50 | | | | | | | | | | | | | | | | % 149.07/21.50 | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (41), (43), (329), (541), % 149.07/21.50 | | | | | | | | | | | | | | | | (552), (622), (5076), (6539), (7040), (7048), % 149.07/21.50 | | | | | | | | | | | | | | | | (7052), (7054), (7056), (7057), (7058), (7063), % 149.07/21.50 | | | | | | | | | | | | | | | | (7067), (7071), (function-axioms) are inconsistent % 149.07/21.50 | | | | | | | | | | | | | | | | by sub-proof #94. % 149.07/21.50 | | | | | | | | | | | | | | | | % 149.07/21.50 | | | | | | | | | | | | | | | End of split % 149.07/21.50 | | | | | | | | | | | | | | | % 149.07/21.50 | | | | | | | | | | | | | | Case 2: % 149.07/21.50 | | | | | | | | | | | | | | | % 149.07/21.50 | | | | | | | | | | | | | | | (7072) all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0 % 149.07/21.50 | | | | | | | | | | | | | | | % 149.07/21.50 | | | | | | | | | | | | | | | REF_CLOSE: (5086), (6541), (7025), (7050), (7072) are % 149.07/21.50 | | | | | | | | | | | | | | | inconsistent by sub-proof #382. % 149.07/21.50 | | | | | | | | | | | | | | | % 149.07/21.50 | | | | | | | | | | | | | | End of split % 149.07/21.50 | | | | | | | | | | | | | | % 149.07/21.50 | | | | | | | | | | | | | End of split % 149.07/21.50 | | | | | | | | | | | | | % 149.07/21.50 | | | | | | | | | | | | End of split % 149.07/21.50 | | | | | | | | | | | | % 149.07/21.50 | | | | | | | | | | | Case 2: % 149.07/21.50 | | | | | | | | | | | | % 149.07/21.50 | | | | | | | | | | | | (7073) all_56_21 = e2 % 149.07/21.50 | | | | | | | | | | | | (7074) all_56_19 = e1 % 149.07/21.50 | | | | | | | | | | | | % 149.07/21.50 | | | | | | | | | | | | COMBINE_EQS: (435), (7074) imply: % 149.07/21.50 | | | | | | | | | | | | (7075) all_52_6 = e1 % 149.07/21.50 | | | | | | | | | | | | % 149.07/21.50 | | | | | | | | | | | | COMBINE_EQS: (374), (7073) imply: % 149.07/21.50 | | | | | | | | | | | | (7076) all_6_2 = e2 % 149.07/21.50 | | | | | | | | | | | | % 149.07/21.50 | | | | | | | | | | | | SIMP: (7076) implies: % 149.07/21.50 | | | | | | | | | | | | (7077) all_6_2 = e2 % 149.07/21.50 | | | | | | | | | | | | % 149.07/21.50 | | | | | | | | | | | | REF_CLOSE: (36), (38), (43), (46), (193), (246), (247), % 149.07/21.50 | | | | | | | | | | | | (248), (287), (294), (317), (443), (463), (542), % 149.07/21.50 | | | | | | | | | | | | (544), (545), (546), (547), (557), (568), (573), % 149.07/21.50 | | | | | | | | | | | | (627), (768), (5071), (5074), (5077), (5082), % 149.07/21.50 | | | | | | | | | | | | (5083), (7036), (7038), (7073), (7075), (7077), % 149.07/21.50 | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 149.07/21.50 | | | | | | | | | | | | #117. % 149.07/21.50 | | | | | | | | | | | | % 149.07/21.50 | | | | | | | | | | | End of split % 149.07/21.50 | | | | | | | | | | | % 149.07/21.50 | | | | | | | | | | Case 2: % 149.07/21.50 | | | | | | | | | | | % 149.07/21.50 | | | | | | | | | | | (7078) all_48_0 = e3 % 149.07/21.50 | | | | | | | | | | | (7079) ~ (all_48_1 = e1) | ~ (all_48_2 = e0) % 149.07/21.50 | | | | | | | | | | | % 149.07/21.50 | | | | | | | | | | | COMBINE_EQS: (765), (7078) imply: % 149.07/21.50 | | | | | | | | | | | (7080) all_8_0 = e3 % 149.07/21.50 | | | | | | | | | | | % 149.07/21.50 | | | | | | | | | | | SIMP: (7080) implies: % 149.07/21.50 | | | | | | | | | | | (7081) all_8_0 = e3 % 149.07/21.50 | | | | | | | | | | | % 149.07/21.50 | | | | | | | | | | | REF_CLOSE: (9), (46), (247), (295), (536), (542), (545), % 149.07/21.50 | | | | | | | | | | | (617), (5070), (5071), (5075), (5083), (7079), % 149.07/21.50 | | | | | | | | | | | (7081), (function-axioms) are inconsistent by % 149.07/21.50 | | | | | | | | | | | sub-proof #115. % 149.07/21.50 | | | | | | | | | | | % 149.07/21.50 | | | | | | | | | | End of split % 149.07/21.50 | | | | | | | | | | % 149.07/21.50 | | | | | | | | | Case 2: % 149.07/21.50 | | | | | | | | | | % 149.07/21.50 | | | | | | | | | | (7082) all_36_1 = e3 % 149.07/21.50 | | | | | | | | | | % 149.07/21.50 | | | | | | | | | | COMBINE_EQS: (652), (7082) imply: % 149.07/21.50 | | | | | | | | | | (7083) all_6_1 = e3 % 149.07/21.50 | | | | | | | | | | % 149.07/21.50 | | | | | | | | | | SIMP: (7083) implies: % 149.07/21.50 | | | | | | | | | | (7084) all_6_1 = e3 % 149.07/21.50 | | | | | | | | | | % 149.07/21.50 | | | | | | | | | | REDUCE: (43), (7084) imply: % 149.07/21.50 | | | | | | | | | | (7085) op(all_6_2, all_6_2) = e3 % 149.07/21.50 | | | | | | | | | | % 149.07/21.50 | | | | | | | | | | REDUCE: (42), (7084) imply: % 149.07/21.50 | | | | | | | | | | (7086) op(e1, e3) = all_6_0 % 149.07/21.50 | | | | | | | | | | % 149.07/21.50 | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (38), (41), % 149.07/21.50 | | | | | | | | | | (46), (51), (149), (211), (246), (247), (250), % 149.07/21.50 | | | | | | | | | | (252), (287), (293), (294), (295), (296), (332), % 149.07/21.50 | | | | | | | | | | (333), (335), (374), (381), (386), (401), (425), % 149.07/21.50 | | | | | | | | | | (443), (494), (536), (542), (543), (544), (545), % 149.07/21.50 | | | | | | | | | | (546), (554), (557), (559), (568), (579), (590), % 149.07/21.50 | | | | | | | | | | (612), (617), (622), (627), (761), (765), (5069), % 149.07/21.50 | | | | | | | | | | (5070), (5071), (5074), (5075), (5076), (5077), % 149.07/21.50 | | | | | | | | | | (5082), (5083), (5084), (5086), (6541), (7020), % 149.07/21.50 | | | | | | | | | | (7022), (7025), (7033), (7034), (7085), (7086), % 149.07/21.50 | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 149.07/21.50 | | | | | | | | | | #105. % 149.07/21.50 | | | | | | | | | | % 149.07/21.50 | | | | | | | | | End of split % 149.07/21.50 | | | | | | | | | % 149.07/21.50 | | | | | | | | End of split % 149.07/21.50 | | | | | | | | % 149.07/21.50 | | | | | | | Case 2: % 149.07/21.50 | | | | | | | | % 149.07/21.50 | | | | | | | | (7087) all_28_0 = e2 % 149.07/21.50 | | | | | | | | % 149.07/21.50 | | | | | | | | COMBINE_EQS: (740), (7087) imply: % 149.07/21.50 | | | | | | | | (7088) all_6_0 = e2 % 149.07/21.50 | | | | | | | | % 149.07/21.50 | | | | | | | | SIMP: (7088) implies: % 149.07/21.50 | | | | | | | | (7089) all_6_0 = e2 % 149.07/21.50 | | | | | | | | % 149.07/21.50 | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (38), (41), (42), % 149.07/21.50 | | | | | | | | (43), (46), (51), (149), (246), (247), (287), (294), % 149.07/21.50 | | | | | | | | (295), (296), (332), (333), (335), (374), (386), % 149.07/21.50 | | | | | | | | (401), (425), (443), (536), (542), (544), (545), % 149.07/21.50 | | | | | | | | (546), (554), (557), (568), (579), (590), (617), % 149.07/21.50 | | | | | | | | (622), (627), (765), (768), (5069), (5070), (5071), % 149.07/21.50 | | | | | | | | (5074), (5075), (5076), (5077), (5082), (5083), % 149.07/21.50 | | | | | | | | (5084), (7089), (function-axioms) are inconsistent by % 149.07/21.50 | | | | | | | | sub-proof #104. % 149.07/21.50 | | | | | | | | % 149.07/21.50 | | | | | | | End of split % 149.07/21.50 | | | | | | | % 149.07/21.50 | | | | | | Case 2: % 149.07/21.50 | | | | | | | % 149.07/21.50 | | | | | | | (7090) all_16_0 = e1 % 149.07/21.50 | | | | | | | % 149.07/21.50 | | | | | | | COMBINE_EQS: (757), (7090) imply: % 149.07/21.50 | | | | | | | (7091) all_10_0 = e1 % 149.07/21.50 | | | | | | | % 149.07/21.50 | | | | | | | SIMP: (7091) implies: % 149.07/21.50 | | | | | | | (7092) all_10_0 = e1 % 149.07/21.50 | | | | | | | % 149.07/21.50 | | | | | | | REDUCE: (5086), (7092) imply: % 149.07/21.50 | | | | | | | (7093) ~ (e2 = e1) % 149.07/21.50 | | | | | | | % 149.07/21.50 | | | | | | | REDUCE: (52), (7092) imply: % 149.07/21.50 | | | | | | | (7094) op(e3, all_10_1) = e1 % 149.07/21.50 | | | | | | | % 149.07/21.50 | | | | | | | BETA: splitting (99) gives: % 149.07/21.50 | | | | | | | % 149.07/21.50 | | | | | | | Case 1: % 149.07/21.50 | | | | | | | | % 149.07/21.50 | | | | | | | | (7095) ~ (all_28_0 = e2) % 149.07/21.50 | | | | | | | | % 149.07/21.50 | | | | | | | | REDUCE: (740), (7095) imply: % 149.07/21.50 | | | | | | | | (7096) ~ (all_6_0 = e2) % 149.07/21.50 | | | | | | | | % 149.07/21.50 | | | | | | | | BETA: splitting (114) gives: % 149.07/21.50 | | | | | | | | % 149.07/21.50 | | | | | | | | Case 1: % 149.07/21.50 | | | | | | | | | % 149.07/21.50 | | | | | | | | | (7097) ~ (all_34_0 = e2) % 149.07/21.50 | | | | | | | | | % 149.07/21.50 | | | | | | | | | REDUCE: (6537), (7097) imply: % 149.07/21.50 | | | | | | | | | (7098) $false % 149.07/21.50 | | | | | | | | | % 149.07/21.50 | | | | | | | | | CLOSE: (7098) is inconsistent. % 149.07/21.50 | | | | | | | | | % 149.07/21.50 | | | | | | | | Case 2: % 149.07/21.50 | | | | | | | | | % 149.07/21.50 | | | | | | | | | (7099) ~ (all_34_1 = e3) | ~ (all_34_2 = e1) % 149.07/21.50 | | | | | | | | | % 149.07/21.50 | | | | | | | | | BETA: splitting (119) gives: % 149.07/21.50 | | | | | | | | | % 149.07/21.50 | | | | | | | | | Case 1: % 149.07/21.50 | | | | | | | | | | % 149.07/21.50 | | | | | | | | | | (7100) ~ (all_36_1 = e3) % 149.07/21.50 | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | REF_CLOSE: (5), (6), (7), (8), (9), (36), (38), (41), (42), % 149.07/21.51 | | | | | | | | | | (43), (46), (51), (149), (158), (160), (161), % 149.07/21.51 | | | | | | | | | | (173), (174), (182), (189), (191), (193), (197), % 149.07/21.51 | | | | | | | | | | (205), (208), (237), (238), (241), (242), (243), % 149.07/21.51 | | | | | | | | | | (246), (247), (248), (252), (287), (288), (289), % 149.07/21.51 | | | | | | | | | | (290), (291), (292), (293), (294), (295), (296), % 149.07/21.51 | | | | | | | | | | (297), (299), (317), (321), (329), (330), (331), % 149.07/21.51 | | | | | | | | | | (332), (344), (357), (360), (365), (366), (374), % 149.07/21.51 | | | | | | | | | | (381), (386), (389), (401), (402), (407), (408), % 149.07/21.51 | | | | | | | | | | (419), (425), (435), (443), (447), (463), (473), % 149.07/21.51 | | | | | | | | | | (476), (482), (529), (531), (536), (540), (541), % 149.07/21.51 | | | | | | | | | | (542), (543), (544), (545), (546), (547), (548), % 149.07/21.51 | | | | | | | | | | (550), (551), (552), (553), (554), (557), (559), % 149.07/21.51 | | | | | | | | | | (561), (565), (568), (569), (570), (573), (575), % 149.07/21.51 | | | | | | | | | | (580), (581), (585), (587), (588), (590), (591), % 149.07/21.51 | | | | | | | | | | (617), (621), (622), (624), (625), (627), (652), % 149.07/21.51 | | | | | | | | | | (681), (683), (765), (768), (5069), (5070), % 149.07/21.51 | | | | | | | | | | (5071), (5074), (5075), (5076), (5077), (5080), % 149.07/21.51 | | | | | | | | | | (5082), (5083), (5084), (6535), (6539), (7096), % 149.07/21.51 | | | | | | | | | | (7099), (7100), (function-axioms) are inconsistent % 149.07/21.51 | | | | | | | | | | by sub-proof #92. % 149.07/21.51 | | | | | | | | | | % 149.07/21.51 | | | | | | | | | Case 2: % 149.07/21.51 | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | (7101) all_36_1 = e3 % 149.07/21.51 | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | COMBINE_EQS: (652), (7101) imply: % 149.07/21.51 | | | | | | | | | | (7102) all_6_1 = e3 % 149.07/21.51 | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | SIMP: (7102) implies: % 149.07/21.51 | | | | | | | | | | (7103) all_6_1 = e3 % 149.07/21.51 | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | REDUCE: (43), (7103) imply: % 149.07/21.51 | | | | | | | | | | (7104) op(all_6_2, all_6_2) = e3 % 149.07/21.51 | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | REDUCE: (42), (7103) imply: % 149.07/21.51 | | | | | | | | | | (7105) op(e1, e3) = all_6_0 % 149.07/21.51 | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (38), (41), % 149.07/21.51 | | | | | | | | | | (46), (51), (53), (149), (211), (246), (247), % 149.07/21.51 | | | | | | | | | | (287), (293), (294), (295), (296), (332), (333), % 149.07/21.51 | | | | | | | | | | (335), (374), (381), (386), (401), (425), (443), % 149.07/21.51 | | | | | | | | | | (536), (542), (544), (545), (546), (554), (557), % 149.07/21.51 | | | | | | | | | | (559), (568), (579), (590), (612), (617), (622), % 149.07/21.51 | | | | | | | | | | (627), (765), (5069), (5070), (5071), (5074), % 149.07/21.51 | | | | | | | | | | (5075), (5076), (5077), (5082), (5083), (5084), % 149.07/21.51 | | | | | | | | | | (7094), (7104), (7105), (function-axioms) are % 149.07/21.51 | | | | | | | | | | inconsistent by sub-proof #98. % 149.07/21.51 | | | | | | | | | | % 149.07/21.51 | | | | | | | | | End of split % 149.07/21.51 | | | | | | | | | % 149.07/21.51 | | | | | | | | End of split % 149.07/21.51 | | | | | | | | % 149.07/21.51 | | | | | | | Case 2: % 149.07/21.51 | | | | | | | | % 149.07/21.51 | | | | | | | | (7106) all_28_0 = e2 % 149.07/21.51 | | | | | | | | % 149.07/21.51 | | | | | | | | COMBINE_EQS: (740), (7106) imply: % 149.07/21.51 | | | | | | | | (7107) all_6_0 = e2 % 149.07/21.51 | | | | | | | | % 149.07/21.51 | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (38), (41), (42), % 149.07/21.51 | | | | | | | | (43), (46), (51), (149), (246), (247), (287), (294), % 149.07/21.51 | | | | | | | | (295), (296), (332), (333), (335), (374), (386), % 149.07/21.51 | | | | | | | | (401), (425), (443), (536), (542), (544), (545), % 149.07/21.51 | | | | | | | | (546), (554), (557), (568), (579), (590), (617), % 149.07/21.51 | | | | | | | | (622), (627), (765), (768), (5069), (5070), (5071), % 149.07/21.51 | | | | | | | | (5074), (5075), (5076), (5077), (5082), (5083), % 149.07/21.51 | | | | | | | | (5084), (7107), (function-axioms) are inconsistent by % 149.07/21.51 | | | | | | | | sub-proof #104. % 149.07/21.51 | | | | | | | | % 149.07/21.51 | | | | | | | End of split % 149.07/21.51 | | | | | | | % 149.07/21.51 | | | | | | End of split % 149.07/21.51 | | | | | | % 149.07/21.51 | | | | | End of split % 149.07/21.51 | | | | | % 149.07/21.51 | | | | Case 2: % 149.07/21.51 | | | | | % 149.07/21.51 | | | | | (7108) all_10_0 = e2 % 149.07/21.51 | | | | | % 149.07/21.51 | | | | | REDUCE: (52), (7108) imply: % 149.07/21.51 | | | | | (7109) op(e3, all_10_1) = e2 % 149.07/21.51 | | | | | % 149.07/21.51 | | | | | BETA: splitting (59) gives: % 149.07/21.51 | | | | | % 149.07/21.51 | | | | | Case 1: % 149.07/21.51 | | | | | | % 149.07/21.51 | | | | | | (7110) ~ (all_12_0 = e2) % 149.07/21.51 | | | | | | % 149.07/21.51 | | | | | | REDUCE: (759), (7110) imply: % 149.07/21.51 | | | | | | (7111) ~ (all_4_0 = e2) % 149.07/21.51 | | | | | | % 149.07/21.51 | | | | | | BETA: splitting (99) gives: % 149.07/21.51 | | | | | | % 149.07/21.51 | | | | | | Case 1: % 149.07/21.51 | | | | | | | % 149.07/21.51 | | | | | | | (7112) ~ (all_28_0 = e2) % 149.07/21.51 | | | | | | | % 149.07/21.51 | | | | | | | REDUCE: (740), (7112) imply: % 149.07/21.51 | | | | | | | (7113) ~ (all_6_0 = e2) % 149.07/21.51 | | | | | | | % 149.07/21.51 | | | | | | | BETA: splitting (119) gives: % 149.07/21.51 | | | | | | | % 149.07/21.51 | | | | | | | Case 1: % 149.07/21.51 | | | | | | | | % 149.07/21.51 | | | | | | | | (7114) ~ (all_36_1 = e3) % 149.07/21.51 | | | | | | | | % 149.07/21.51 | | | | | | | | REDUCE: (652), (7114) imply: % 149.07/21.51 | | | | | | | | (7115) ~ (all_6_1 = e3) % 149.07/21.51 | | | | | | | | % 149.07/21.51 | | | | | | | | BETA: splitting (129) gives: % 149.07/21.51 | | | | | | | | % 149.07/21.51 | | | | | | | | Case 1: % 149.07/21.51 | | | | | | | | | % 149.07/21.51 | | | | | | | | | (7116) ~ (all_40_0 = e3) % 149.07/21.51 | | | | | | | | | % 149.07/21.51 | | | | | | | | | REDUCE: (713), (7116) imply: % 149.07/21.51 | | | | | | | | | (7117) ~ (all_6_0 = e3) % 149.07/21.51 | | | | | | | | | % 149.07/21.51 | | | | | | | | | BETA: splitting (149) gives: % 149.07/21.51 | | | | | | | | | % 149.07/21.51 | | | | | | | | | Case 1: % 149.07/21.51 | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | (7118) ~ (all_48_0 = e3) % 149.07/21.51 | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | REDUCE: (765), (7118) imply: % 149.07/21.51 | | | | | | | | | | (7119) ~ (all_8_0 = e3) % 149.07/21.51 | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | BETA: splitting (294) gives: % 149.07/21.51 | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | Case 1: % 149.07/21.51 | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | (7120) ~ (all_56_11 = e0) % 149.07/21.51 | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | REDUCE: (545), (7120) imply: % 149.07/21.51 | | | | | | | | | | | (7121) ~ (all_8_2 = e0) % 149.07/21.51 | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | BETA: splitting (295) gives: % 149.07/21.51 | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | Case 1: % 149.07/21.51 | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | (7122) ~ (all_56_11 = e1) % 149.07/21.51 | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | REDUCE: (545), (7122) imply: % 149.07/21.51 | | | | | | | | | | | | (7123) ~ (all_8_2 = e1) % 149.07/21.51 | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | REF_CLOSE: (5), (46), (51), (246), (247), (287), (296), % 149.07/21.51 | | | | | | | | | | | | (332), (374), (386), (401), (425), (542), (544), % 149.07/21.51 | | | | | | | | | | | | (545), (546), (554), (568), (590), (617), (5069), % 149.07/21.51 | | | | | | | | | | | | (5071), (5074), (5076), (5077), (5082), (5083), % 149.07/21.51 | | | | | | | | | | | | (5084), (7121), (7123), (function-axioms) are % 149.07/21.51 | | | | | | | | | | | | inconsistent by sub-proof #141. % 149.07/21.51 | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | Case 2: % 149.07/21.51 | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | (7124) all_56_13 = e2 % 149.07/21.51 | | | | | | | | | | | | (7125) all_56_11 = e1 % 149.07/21.51 | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | COMBINE_EQS: (545), (7125) imply: % 149.07/21.51 | | | | | | | | | | | | (7126) all_8_2 = e1 % 149.07/21.51 | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | COMBINE_EQS: (5075), (7124) imply: % 149.07/21.51 | | | | | | | | | | | | (7127) all_8_0 = e2 % 149.07/21.51 | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | COMBINE_EQS: (5076), (7127) imply: % 149.07/21.51 | | | | | | | | | | | | (7128) all_58_5 = e2 % 149.07/21.51 | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | COMBINE_EQS: (554), (7126) imply: % 149.07/21.51 | | | | | | | | | | | | (7129) all_58_3 = e1 % 149.07/21.51 | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | REDUCE: (568), (7126) imply: % 149.07/21.51 | | | | | | | | | | | | (7130) ~ (all_52_1 = e1) % 149.07/21.51 | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | REDUCE: (5078), (7127) imply: % 149.07/21.51 | | | | | | | | | | | | (7131) ~ (all_52_8 = e2) % 149.07/21.51 | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | REDUCE: (5080), (7127) imply: % 149.07/21.51 | | | | | | | | | | | | (7132) ~ (all_52_11 = e2) % 149.07/21.51 | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | REDUCE: (579), (7126) imply: % 149.07/21.51 | | | | | | | | | | | | (7133) ~ (all_52_13 = e1) % 149.07/21.51 | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | REDUCE: (5071), (7126) imply: % 149.07/21.51 | | | | | | | | | | | | (7134) op(e1, e1) = e1 % 149.07/21.51 | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | REDUCE: (46), (7126) imply: % 149.07/21.51 | | | | | | | | | | | | (7135) op(e2, e2) = e1 % 149.07/21.51 | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_6_2, e1, % 149.07/21.51 | | | | | | | | | | | | e1, e1, simplifying with (41), (7134) gives: % 149.07/21.51 | | | | | | | | | | | | (7136) all_6_2 = e1 % 149.07/21.51 | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | REDUCE: (569), (7136) imply: % 149.07/21.51 | | | | | | | | | | | | (7137) ~ (all_52_2 = e1) % 149.07/21.51 | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | REDUCE: (587), (7136) imply: % 149.07/21.51 | | | | | | | | | | | | (7138) ~ (all_52_14 = e1) % 149.07/21.51 | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | REDUCE: (43), (7136) imply: % 149.07/21.51 | | | | | | | | | | | | (7139) op(e1, e1) = all_6_1 % 149.07/21.51 | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | REDUCE: (622), (7136) imply: % 149.07/21.51 | | | | | | | | | | | | (7140) op(e1, e1) = all_56_20 % 149.07/21.51 | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1, % 149.07/21.51 | | | | | | | | | | | | all_56_20, e1, e1, simplifying with (7134), (7140) % 149.07/21.51 | | | | | | | | | | | | gives: % 149.07/21.51 | | | | | | | | | | | | (7141) all_56_20 = e1 % 149.07/21.51 | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_6_1, % 149.07/21.51 | | | | | | | | | | | | all_56_20, e1, e1, simplifying with (7139), (7140) % 149.07/21.51 | | | | | | | | | | | | gives: % 149.07/21.51 | | | | | | | | | | | | (7142) all_56_20 = all_6_1 % 149.07/21.51 | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | COMBINE_EQS: (7141), (7142) imply: % 149.07/21.51 | | | | | | | | | | | | (7143) all_6_1 = e1 % 149.07/21.51 | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | REDUCE: (42), (7143) imply: % 149.07/21.51 | | | | | | | | | | | | (7144) op(e1, e1) = all_6_0 % 149.07/21.51 | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1, all_6_0, % 149.07/21.51 | | | | | | | | | | | | e1, e1, simplifying with (7134), (7144) gives: % 149.07/21.51 | | | | | | | | | | | | (7145) all_6_0 = e1 % 149.07/21.51 | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | REDUCE: (7117), (7145) imply: % 149.07/21.51 | | | | | | | | | | | | (7146) ~ (e3 = e1) % 149.07/21.51 | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | REDUCE: (7113), (7145) imply: % 149.07/21.51 | | | | | | | | | | | | (7147) ~ (e2 = e1) % 149.07/21.51 | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | BETA: splitting (298) gives: % 149.07/21.51 | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | Case 1: % 149.07/21.51 | | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | | (7148) ~ (all_56_1 = e1) % 149.07/21.51 | | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | | REDUCE: (546), (7148) imply: % 149.07/21.51 | | | | | | | | | | | | | (7149) ~ (all_10_2 = e1) % 149.07/21.51 | | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | | BETA: splitting (342) gives: % 149.07/21.51 | | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | | Case 1: % 149.07/21.51 | | | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | | | (7150) all_58_0 = e1 % 149.07/21.51 | | | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | | | COMBINE_EQS: (419), (7150) imply: % 149.07/21.51 | | | | | | | | | | | | | | (7151) all_10_2 = e1 % 149.07/21.51 | | | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | | | REDUCE: (7149), (7151) imply: % 149.07/21.51 | | | | | | | | | | | | | | (7152) $false % 149.07/21.51 | | | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | | | CLOSE: (7152) is inconsistent. % 149.07/21.51 | | | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | | Case 2: % 149.07/21.51 | | | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | | | (7153) all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1 % 149.07/21.51 | | | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | | | BETA: splitting (7153) gives: % 149.07/21.51 | | | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | | | Case 1: % 149.07/21.51 | | | | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | | | | (7154) all_58_2 = e1 % 149.07/21.51 | | | | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | | | | COMBINE_EQS: (401), (7154) imply: % 149.07/21.51 | | | | | | | | | | | | | | | (7155) all_52_1 = e1 % 149.07/21.51 | | | | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | | | | REDUCE: (7130), (7155) imply: % 149.07/21.51 | | | | | | | | | | | | | | | (7156) $false % 149.07/21.51 | | | | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | | | | CLOSE: (7156) is inconsistent. % 149.07/21.51 | | | | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | | | Case 2: % 149.07/21.51 | | | | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | | | | (7157) all_58_6 = e1 | all_58_12 = e1 % 149.07/21.51 | | | | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | | | | BETA: splitting (7157) gives: % 149.07/21.51 | | | | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | | | | Case 1: % 149.07/21.51 | | | | | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | | | | | (7158) all_58_6 = e1 % 149.07/21.51 | | | | | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | | | | | REF_CLOSE: (553), (7137), (7158) are inconsistent by % 149.07/21.51 | | | | | | | | | | | | | | | | sub-proof #472. % 149.07/21.51 | | | | | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | | | | Case 2: % 149.07/21.51 | | | | | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | | | | | (7159) all_58_12 = e1 % 149.07/21.51 | | | | | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | | | | | COMBINE_EQS: (365), (7159) imply: % 149.07/21.51 | | | | | | | | | | | | | | | | (7160) all_52_3 = e1 % 149.07/21.51 | | | | | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | | | | | SIMP: (7160) implies: % 149.07/21.51 | | | | | | | | | | | | | | | | (7161) all_52_3 = e1 % 149.07/21.51 | | | | | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | | | | | REDUCE: (187), (7161) imply: % 149.07/21.51 | | | | | | | | | | | | | | | | (7162) ~ (all_52_11 = e1) % 149.07/21.51 | | | | | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | | | | | SIMP: (7162) implies: % 149.07/21.51 | | | | | | | | | | | | | | | | (7163) ~ (all_52_11 = e1) % 149.07/21.51 | | | | | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | | | | | REDUCE: (570), (7161) imply: % 149.07/21.51 | | | | | | | | | | | | | | | | (7164) ~ (all_4_2 = e1) % 149.07/21.51 | | | | | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | | | | | SIMP: (7164) implies: % 149.07/21.51 | | | | | | | | | | | | | | | | (7165) ~ (all_4_2 = e1) % 149.07/21.51 | | | | | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | | | | | REDUCE: (615), (7161) imply: % 149.07/21.51 | | | | | | | | | | | | | | | | (7166) op(e3, e1) = all_56_24 % 149.07/21.51 | | | | | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | | | | | BETA: splitting (321) gives: % 149.07/21.51 | | | | | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | | | | | Case 1: % 149.07/21.51 | | | | | | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | | | | | | (7167) all_58_9 = e1 % 149.07/21.51 | | | | | | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | | | | | | COMBINE_EQS: (551), (7167) imply: % 149.07/21.51 | | | | | | | | | | | | | | | | | (7168) all_52_12 = e1 % 149.07/21.51 | | | | | | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | | | | | | COMBINE_EQS: (402), (7168) imply: % 149.07/21.51 | | | | | | | | | | | | | | | | | (7169) all_56_7 = e1 % 149.07/21.51 | | | | | | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | | | | | | REDUCE: (181), (7168) imply: % 149.07/21.51 | | | | | | | | | | | | | | | | | (7170) ~ (all_52_4 = e1) % 149.07/21.51 | | | | | | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | | | | | | REDUCE: (168), (7168) imply: % 149.07/21.51 | | | | | | | | | | | | | | | | | (7171) ~ (all_52_8 = e1) % 149.07/21.51 | | | | | | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | | | | | | REDUCE: (161), (7168) imply: % 149.07/21.51 | | | | | | | | | | | | | | | | | (7172) ~ (all_52_13 = e1) % 149.07/21.51 | | | | | | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | | | | | | REDUCE: (160), (7168) imply: % 149.07/21.51 | | | | | | | | | | | | | | | | | (7173) ~ (all_52_14 = e1) % 149.07/21.51 | | | | | | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | | | | | | REDUCE: (567), (7168) imply: % 149.07/21.51 | | | | | | | | | | | | | | | | | (7174) ~ (all_10_2 = e1) % 149.07/21.51 | | | | | | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | | | | | | REDUCE: (624), (7168) imply: % 149.07/21.51 | | | | | | | | | | | | | | | | | (7175) op(e0, e1) = all_56_6 % 149.07/21.51 | | | | | | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | | | | | | BETA: splitting (297) gives: % 149.07/21.51 | | | | | | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | | | | | | Case 1: % 149.07/21.51 | | | | | | | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | | | | | | | (7176) ~ (all_56_1 = e0) % 149.07/21.51 | | | | | | | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | | | | | | | REDUCE: (546), (7176) imply: % 149.07/21.51 | | | | | | | | | | | | | | | | | | (7177) ~ (all_10_2 = e0) % 149.07/21.51 | | | | | | | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_11, % 149.07/21.51 | | | | | | | | | | | | | | | | | | all_56_6, e1, e0, simplifying with (205), (7175) % 149.07/21.51 | | | | | | | | | | | | | | | | | | gives: % 149.07/21.51 | | | | | | | | | | | | | | | | | | (7178) all_56_6 = all_52_11 % 149.07/21.51 | | | | | | | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_8, % 149.07/21.51 | | | | | | | | | | | | | | | | | | all_56_24, e1, e3, simplifying with (217), (7166) % 149.07/21.51 | | | | | | | | | | | | | | | | | | gives: % 149.07/21.51 | | | | | | | | | | | | | | | | | | (7179) all_56_24 = all_52_8 % 149.07/21.51 | | | | | | | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | | | | | | | BETA: splitting (299) gives: % 149.07/21.51 | | | | | | | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | | | | | | | Case 1: % 149.07/21.51 | | | | | | | | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | | | | | | | | (7180) ~ (all_56_1 = e2) % 149.07/21.51 | | | | | | | | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | | | | | | | | REDUCE: (546), (7180) imply: % 149.07/21.51 | | | | | | | | | | | | | | | | | | | (7181) ~ (all_10_2 = e2) % 149.07/21.51 | | | | | | | | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | | | | | | | | BETA: splitting (252) gives: % 149.07/21.51 | | | | | | | | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | | | | | | | | Case 1: % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | (7182) all_54_0 = e3 % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (543), (7182) imply: % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | (7183) all_10_2 = e3 % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | SIMP: (7183) implies: % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | (7184) all_10_2 = e3 % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (419), (7184) imply: % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | (7185) all_58_0 = e3 % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | REDUCE: (557), (7184) imply: % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | (7186) ~ (all_52_1 = e3) % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | REDUCE: (565), (7184) imply: % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | (7187) ~ (all_52_8 = e3) % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | REDUCE: (53), (7184) imply: % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | (7188) op(e3, e3) = all_10_1 % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | REDUCE: (612), (7184) imply: % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | (7189) op(e3, e3) = all_56_0 % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | REDUCE: (51), (7184) imply: % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | (7190) op(e3, e3) = e3 % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | BETA: splitting (345) gives: % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | Case 1: % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | (7191) all_58_0 = e2 % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (7185), (7191) imply: % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | (7192) e3 = e2 % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | REDUCE: (9), (7192) imply: % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | (7193) $false % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | CLOSE: (7193) is inconsistent. % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | Case 2: % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | (7194) all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2 % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7194) gives: % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | (7195) all_58_1 = e2 % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (555), (7195) imply: % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | (7196) all_52_4 = e2 % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (183), (7196) imply: % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | (7197) ~ (all_52_7 = e2) % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | SIMP: (7197) implies: % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | (7198) ~ (all_52_7 = e2) % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (182), (7196) imply: % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | (7199) ~ (all_52_8 = e2) % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (616), (7196) imply: % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | (7200) op(e2, e2) = all_56_2 % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (250) gives: % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | (7201) all_54_2 = e3 % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (459), (7187), (7201) are inconsistent by % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | sub-proof #728. % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | (7202) all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0 % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7202) gives: % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | (7203) all_54_2 = e2 % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (459), (7131), (7203) are inconsistent by % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #727. % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | (7204) ~ (all_54_2 = e2) % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | (7205) all_54_2 = e1 | all_54_2 = e0 % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (335) gives: % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | (7206) all_58_2 = e3 % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (401), (7206) imply: % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | (7207) all_52_1 = e3 % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7186), (7207) imply: % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | (7208) $false % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (7208) is inconsistent. % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | (7209) all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3 % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7209) gives: % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | (7210) all_58_3 = e3 % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (7129), (7210) are inconsistent by sub-proof % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | #157. % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | (7211) all_58_5 = e3 | all_58_10 = e3 % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7205) gives: % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | (7212) all_54_2 = e1 % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (459), (7171), (7212) are inconsistent by % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #726. % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | (7213) all_54_2 = e0 % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (459), (7213) imply: % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | (7214) all_52_8 = e0 % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (7214) implies: % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | (7215) all_52_8 = e0 % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (169), (7215) imply: % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | (7216) ~ (all_52_11 = e0) % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (7216) implies: % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | (7217) ~ (all_52_11 = e0) % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7131), (7215) imply: % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | (7218) ~ (e2 = e0) % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7171), (7215) imply: % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | (7219) ~ (e1 = e0) % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (319) gives: % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7220) all_58_12 = e2 % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7159), (7220) are inconsistent by sub-proof % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | #622. % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7221) all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2 % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7221) gives: % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7222) all_58_13 = e2 % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (549), (7198), (7222) are inconsistent by % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #91. % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7223) all_58_14 = e2 | all_58_15 = e2 % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7223) gives: % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7224) all_58_14 = e2 % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (548), (7132), (7224) are inconsistent by % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #629. % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7225) all_58_15 = e2 % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (547), (7225) imply: % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7226) all_4_2 = e2 % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (590), (7226) imply: % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7227) ~ (all_52_13 = e2) % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (38), (7226) imply: % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7228) op(e2, e2) = all_4_1 % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives: % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7229) all_54_14 = e3 % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (482), (7229) imply: % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7230) all_52_11 = e3 % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (205), (7230) imply: % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7231) op(e0, e1) = e3 % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7211) gives: % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7232) all_58_5 = e3 % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (7128), (7232) are inconsistent by sub-proof % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #457. % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7233) all_58_10 = e3 % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (386), (7233) imply: % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7234) all_52_13 = e3 % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (317) gives: % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7235) all_58_15 = e0 % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (7225), (7235) imply: % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7236) e2 = e0 % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (7124), (7236) imply: % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7237) all_56_13 = e0 % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (46), (51), (246), (247), (287), (295), % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (296), (332), (374), (386), (401), (425), (542), % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (544), (545), (546), (554), (568), (590), (617), % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5069), (5071), (5074), (5076), (5077), (5082), % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5083), (5084), (7121), (7237), (function-axioms) % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #134. % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7238) (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7238) implies: % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7239) all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0 % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7239) gives: % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7240) all_58_9 = e0 % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (9), (321), (7109), (7188), (7189), (7190), % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7240), (function-axioms) are inconsistent by % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #158. % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7241) all_58_10 = e0 | all_58_11 = e0 % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7241) gives: % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7242) all_58_10 = e0 % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (7233), (7242) imply: % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7243) e3 = e0 % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7), (7243) imply: % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7244) $false % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (7244) is inconsistent. % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1, all_56_2, % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2, e2, simplifying with (7135), (7200) gives: % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7245) all_56_2 = e1 % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_4_1, % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_2, e2, e2, simplifying with (7200), (7228) % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7246) all_56_2 = all_4_1 % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (7245), (7246) imply: % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7247) all_4_1 = e1 % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (37), (321), (386), (547), (550), (551), (624), % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (767), (7133), (7138), (7165), (7231), (7247), % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #586. % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7248) all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0 % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (482), (7132), (7163), (7217), (7248) are % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #580. % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | End of split % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | End of split % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | (7249) all_58_4 = e2 | all_58_9 = e2 % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (407), (7131), (7167), (7249) are % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #562. % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | End of split % 149.07/21.51 | | | | | | | | | | | | | | | | | | | | | % 149.07/21.52 | | | | | | | | | | | | | | | | | | | | End of split % 149.07/21.52 | | | | | | | | | | | | | | | | | | | | % 149.07/21.52 | | | | | | | | | | | | | | | | | | | Case 2: % 149.07/21.52 | | | | | | | | | | | | | | | | | | | | % 149.07/21.52 | | | | | | | | | | | | | | | | | | | | (7250) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 149.07/21.52 | | | | | | | | | | | | | | | | | | | | % 149.07/21.52 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (543), (7149), (7177), (7181), (7250) are % 149.07/21.52 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #731. % 149.07/21.52 | | | | | | | | | | | | | | | | | | | | % 149.07/21.52 | | | | | | | | | | | | | | | | | | | End of split % 149.07/21.52 | | | | | | | | | | | | | | | | | | | % 149.07/21.52 | | | | | | | | | | | | | | | | | | Case 2: % 149.07/21.52 | | | | | | | | | | | | | | | | | | | % 149.07/21.52 | | | | | | | | | | | | | | | | | | | (7251) all_56_3 = e3 % 149.07/21.52 | | | | | | | | | | | | | | | | | | | (7252) all_56_1 = e2 % 149.07/21.52 | | | | | | | | | | | | | | | | | | | % 149.07/21.52 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (546), (7252) imply: % 149.07/21.52 | | | | | | | | | | | | | | | | | | | (7253) all_10_2 = e2 % 149.07/21.52 | | | | | | | | | | | | | | | | | | | % 149.07/21.52 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (408), (7251) imply: % 149.07/21.52 | | | | | | | | | | | | | | | | | | | (7254) all_52_4 = e3 % 149.07/21.52 | | | | | | | | | | | | | | | | | | | % 149.07/21.52 | | | | | | | | | | | | | | | | | | | REDUCE: (182), (7254) imply: % 149.07/21.52 | | | | | | | | | | | | | | | | | | | (7255) ~ (all_52_8 = e3) % 149.07/21.52 | | | | | | | | | | | | | | | | | | | % 149.07/21.52 | | | | | | | | | | | | | | | | | | | SIMP: (7255) implies: % 149.07/21.52 | | | | | | | | | | | | | | | | | | | (7256) ~ (all_52_8 = e3) % 149.07/21.52 | | | | | | | | | | | | | | | | | | | % 149.07/21.52 | | | | | | | | | | | | | | | | | | | REDUCE: (53), (7253) imply: % 149.07/21.52 | | | | | | | | | | | | | | | | | | | (7257) op(e2, e2) = all_10_1 % 149.07/21.52 | | | | | | | | | | | | | | | | | | | % 149.07/21.52 | | | | | | | | | | | | | | | | | | | BETA: splitting (250) gives: % 149.07/21.52 | | | | | | | | | | | | | | | | | | | % 149.07/21.52 | | | | | | | | | | | | | | | | | | | Case 1: % 149.07/21.52 | | | | | | | | | | | | | | | | | | | | % 149.07/21.52 | | | | | | | | | | | | | | | | | | | | (7258) all_54_2 = e3 % 149.07/21.52 | | | | | | | | | | | | | | | | | | | | % 149.07/21.52 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (459), (7258) imply: % 149.07/21.52 | | | | | | | | | | | | | | | | | | | | (7259) all_52_8 = e3 % 149.07/21.52 | | | | | | | | | | | | | | | | | | | | % 149.07/21.52 | | | | | | | | | | | | | | | | | | | | REDUCE: (7256), (7259) imply: % 149.07/21.52 | | | | | | | | | | | | | | | | | | | | (7260) $false % 149.07/21.52 | | | | | | | | | | | | | | | | | | | | % 149.07/21.52 | | | | | | | | | | | | | | | | | | | | CLOSE: (7260) is inconsistent. % 149.07/21.52 | | | | | | | | | | | | | | | | | | | | % 149.07/21.52 | | | | | | | | | | | | | | | | | | | Case 2: % 149.07/21.52 | | | | | | | | | | | | | | | | | | | | % 149.07/21.52 | | | | | | | | | | | | | | | | | | | | (7261) all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0 % 149.07/21.52 | | | | | | | | | | | | | | | | | | | | % 149.07/21.52 | | | | | | | | | | | | | | | | | | | | BETA: splitting (7261) gives: % 149.07/21.52 | | | | | | | | | | | | | | | | | | | | % 149.07/21.52 | | | | | | | | | | | | | | | | | | | | Case 1: % 149.07/21.52 | | | | | | | | | | | | | | | | | | | | | % 149.07/21.52 | | | | | | | | | | | | | | | | | | | | | (7262) all_54_2 = e2 % 149.07/21.52 | | | | | | | | | | | | | | | | | | | | | % 149.07/21.52 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (459), (7262) imply: % 149.07/21.52 | | | | | | | | | | | | | | | | | | | | | (7263) all_52_8 = e2 % 149.07/21.52 | | | | | | | | | | | | | | | | | | | | | % 149.07/21.52 | | | | | | | | | | | | | | | | | | | | | REDUCE: (7131), (7263) imply: % 149.07/21.52 | | | | | | | | | | | | | | | | | | | | | (7264) $false % 149.07/21.52 | | | | | | | | | | | | | | | | | | | | | % 149.07/21.52 | | | | | | | | | | | | | | | | | | | | | CLOSE: (7264) is inconsistent. % 149.07/21.52 | | | | | | | | | | | | | | | | | | | | | % 149.07/21.52 | | | | | | | | | | | | | | | | | | | | Case 2: % 149.07/21.52 | | | | | | | | | | | | | | | | | | | | | % 149.07/21.52 | | | | | | | | | | | | | | | | | | | | | (7265) ~ (all_54_2 = e2) % 149.07/21.52 | | | | | | | | | | | | | | | | | | | | | (7266) all_54_2 = e1 | all_54_2 = e0 % 149.07/21.52 | | | | | | | | | | | | | | | | | | | | | % 149.07/21.52 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (328) gives: % 149.07/21.52 | | | | | | | | | | | | | | | | | | | | | % 149.07/21.52 | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.07/21.52 | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.52 | | | | | | | | | | | | | | | | | | | | | | (7267) all_58_4 = e0 % 149.07/21.52 | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.52 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (407), (7267) imply: % 149.07/21.52 | | | | | | | | | | | | | | | | | | | | | | (7268) all_52_8 = e0 % 149.07/21.52 | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.52 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7131), (7268) imply: % 149.07/21.52 | | | | | | | | | | | | | | | | | | | | | | (7269) ~ (e2 = e0) % 149.07/21.52 | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.52 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (217), (7268) imply: % 149.07/21.52 | | | | | | | | | | | | | | | | | | | | | | (7270) op(e3, e1) = e0 % 149.07/21.52 | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.52 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1, all_10_1, % 149.07/21.52 | | | | | | | | | | | | | | | | | | | | | | e2, e2, simplifying with (7135), (7257) gives: % 149.07/21.52 | | | | | | | | | | | | | | | | | | | | | | (7271) all_10_1 = e1 % 149.07/21.52 | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.52 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7109), (7271) imply: % 149.07/21.52 | | | | | | | | | | | | | | | | | | | | | | (7272) op(e3, e1) = e2 % 149.07/21.52 | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.52 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, e2, e1, % 149.07/21.52 | | | | | | | | | | | | | | | | | | | | | | e3, simplifying with (7270), (7272) gives: % 149.07/21.52 | | | | | | | | | | | | | | | | | | | | | | (7273) e2 = e0 % 149.07/21.52 | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.52 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (7124), (7273) imply: % 149.07/21.52 | | | | | | | | | | | | | | | | | | | | | | (7274) all_56_13 = e0 % 149.07/21.52 | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.52 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (46), (51), (246), (247), (287), (295), % 149.07/21.52 | | | | | | | | | | | | | | | | | | | | | | (296), (332), (374), (386), (401), (425), (542), % 149.07/21.52 | | | | | | | | | | | | | | | | | | | | | | (544), (545), (546), (554), (568), (590), (617), % 149.07/21.52 | | | | | | | | | | | | | | | | | | | | | | (5069), (5071), (5074), (5076), (5077), (5082), % 149.07/21.52 | | | | | | | | | | | | | | | | | | | | | | (5083), (5084), (7121), (7274), (function-axioms) % 149.07/21.52 | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #134. % 149.07/21.52 | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.52 | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.07/21.52 | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.52 | | | | | | | | | | | | | | | | | | | | | | (7275) ~ (all_58_4 = e0) % 149.07/21.52 | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.52 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (407), (7275) imply: % 149.07/21.52 | | | | | | | | | | | | | | | | | | | | | | (7276) ~ (all_52_8 = e0) % 149.07/21.52 | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.52 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7266) gives: % 149.07/21.52 | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.52 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.07/21.52 | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.52 | | | | | | | | | | | | | | | | | | | | | | | (7277) all_54_2 = e1 % 149.07/21.52 | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.52 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (459), (7171), (7277) are inconsistent by % 149.07/21.52 | | | | | | | | | | | | | | | | | | | | | | | sub-proof #726. % 149.07/21.52 | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.52 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.07/21.52 | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.52 | | | | | | | | | | | | | | | | | | | | | | | (7278) all_54_2 = e0 % 149.07/21.52 | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.52 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (459), (7276), (7278) are inconsistent by % 149.07/21.52 | | | | | | | | | | | | | | | | | | | | | | | sub-proof #725. % 149.07/21.52 | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.52 | | | | | | | | | | | | | | | | | | | | | | End of split % 149.07/21.52 | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.52 | | | | | | | | | | | | | | | | | | | | | End of split % 149.07/21.52 | | | | | | | | | | | | | | | | | | | | | % 149.07/21.52 | | | | | | | | | | | | | | | | | | | | End of split % 149.07/21.52 | | | | | | | | | | | | | | | | | | | | % 149.07/21.52 | | | | | | | | | | | | | | | | | | | End of split % 149.07/21.52 | | | | | | | | | | | | | | | | | | | % 149.07/21.52 | | | | | | | | | | | | | | | | | | End of split % 149.07/21.52 | | | | | | | | | | | | | | | | | | % 149.07/21.52 | | | | | | | | | | | | | | | | | Case 2: % 149.07/21.52 | | | | | | | | | | | | | | | | | | % 149.07/21.52 | | | | | | | | | | | | | | | | | | (7279) all_56_7 = e3 % 149.07/21.52 | | | | | | | | | | | | | | | | | | % 149.07/21.52 | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (7169), (7279) are inconsistent by sub-proof % 149.07/21.52 | | | | | | | | | | | | | | | | | | #497. % 149.07/21.52 | | | | | | | | | | | | | | | | | | % 149.07/21.52 | | | | | | | | | | | | | | | | | End of split % 149.07/21.52 | | | | | | | | | | | | | | | | | % 149.07/21.52 | | | | | | | | | | | | | | | | Case 2: % 149.07/21.52 | | | | | | | | | | | | | | | | | % 149.07/21.52 | | | | | | | | | | | | | | | | | (7280) all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1 % 149.07/21.52 | | | | | | | | | | | | | | | | | % 149.07/21.52 | | | | | | | | | | | | | | | | | REF_CLOSE: (386), (547), (550), (7133), (7138), (7165), % 149.07/21.52 | | | | | | | | | | | | | | | | | (7280) are inconsistent by sub-proof #587. % 149.07/21.52 | | | | | | | | | | | | | | | | | % 149.07/21.52 | | | | | | | | | | | | | | | | End of split % 149.07/21.52 | | | | | | | | | | | | | | | | % 149.07/21.52 | | | | | | | | | | | | | | | End of split % 149.07/21.52 | | | | | | | | | | | | | | | % 149.07/21.52 | | | | | | | | | | | | | | End of split % 149.07/21.52 | | | | | | | | | | | | | | % 149.07/21.52 | | | | | | | | | | | | | End of split % 149.07/21.52 | | | | | | | | | | | | | % 149.07/21.52 | | | | | | | | | | | | Case 2: % 149.07/21.52 | | | | | | | | | | | | | % 149.07/21.52 | | | | | | | | | | | | | (7281) all_56_5 = e3 % 149.07/21.52 | | | | | | | | | | | | | (7282) all_56_1 = e1 % 149.07/21.52 | | | | | | | | | | | | | % 149.07/21.52 | | | | | | | | | | | | | COMBINE_EQS: (546), (7282) imply: % 149.07/21.52 | | | | | | | | | | | | | (7283) all_10_2 = e1 % 149.07/21.52 | | | | | | | | | | | | | % 149.07/21.52 | | | | | | | | | | | | | COMBINE_EQS: (429), (7281) imply: % 149.07/21.52 | | | | | | | | | | | | | (7284) all_52_8 = e3 % 149.07/21.52 | | | | | | | | | | | | | % 149.07/21.52 | | | | | | | | | | | | | REDUCE: (53), (7283) imply: % 149.07/21.52 | | | | | | | | | | | | | (7285) op(e1, e1) = all_10_1 % 149.07/21.52 | | | | | | | | | | | | | % 149.07/21.52 | | | | | | | | | | | | | REDUCE: (612), (7283) imply: % 149.07/21.52 | | | | | | | | | | | | | (7286) op(e3, e1) = all_56_0 % 149.07/21.52 | | | | | | | | | | | | | % 149.07/21.52 | | | | | | | | | | | | | REDUCE: (217), (7284) imply: % 149.07/21.52 | | | | | | | | | | | | | (7287) op(e3, e1) = e3 % 149.07/21.52 | | | | | | | | | | | | | % 149.07/21.52 | | | | | | | | | | | | | REF_CLOSE: (9), (7109), (7134), (7285), (7286), (7287), % 149.07/21.52 | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 149.07/21.52 | | | | | | | | | | | | | #171. % 149.07/21.52 | | | | | | | | | | | | | % 149.07/21.52 | | | | | | | | | | | | End of split % 149.07/21.52 | | | | | | | | | | | | % 149.07/21.52 | | | | | | | | | | | End of split % 149.07/21.52 | | | | | | | | | | | % 149.07/21.52 | | | | | | | | | | Case 2: % 149.07/21.52 | | | | | | | | | | | % 149.07/21.52 | | | | | | | | | | | (7288) all_56_15 = e2 % 149.07/21.52 | | | | | | | | | | | (7289) all_56_11 = e0 % 149.07/21.52 | | | | | | | | | | | % 149.07/21.52 | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (8), (9), (36), (38), (246), (287), % 149.07/21.52 | | | | | | | | | | | (333), (335), (374), (386), (401), (443), (544), % 149.07/21.52 | | | | | | | | | | | (545), (546), (554), (557), (579), (627), (5071), % 149.07/21.52 | | | | | | | | | | | (5074), (5076), (5082), (5083), (5084), (7119), % 149.07/21.52 | | | | | | | | | | | (7288), (7289), (function-axioms) are inconsistent % 149.07/21.52 | | | | | | | | | | | by sub-proof #126. % 149.07/21.52 | | | | | | | | | | | % 149.07/21.52 | | | | | | | | | | End of split % 149.07/21.52 | | | | | | | | | | % 149.07/21.52 | | | | | | | | | Case 2: % 149.07/21.52 | | | | | | | | | | % 149.07/21.52 | | | | | | | | | | (7290) all_48_0 = e3 % 149.07/21.52 | | | | | | | | | | (7291) ~ (all_48_1 = e1) | ~ (all_48_2 = e0) % 149.07/21.52 | | | | | | | | | | % 149.07/21.52 | | | | | | | | | | COMBINE_EQS: (765), (7290) imply: % 149.07/21.52 | | | | | | | | | | (7292) all_8_0 = e3 % 149.07/21.52 | | | | | | | | | | % 149.07/21.52 | | | | | | | | | | REF_CLOSE: (9), (46), (247), (295), (536), (542), (545), % 149.07/21.52 | | | | | | | | | | (617), (5070), (5071), (5075), (5083), (7291), % 149.07/21.52 | | | | | | | | | | (7292), (function-axioms) are inconsistent by % 149.07/21.52 | | | | | | | | | | sub-proof #115. % 149.07/21.52 | | | | | | | | | | % 149.07/21.52 | | | | | | | | | End of split % 149.07/21.52 | | | | | | | | | % 149.07/21.52 | | | | | | | | Case 2: % 149.07/21.52 | | | | | | | | | % 149.07/21.52 | | | | | | | | | (7293) all_40_0 = e3 % 149.07/21.52 | | | | | | | | | % 149.07/21.52 | | | | | | | | | COMBINE_EQS: (713), (7293) imply: % 149.07/21.52 | | | | | | | | | (7294) all_6_0 = e3 % 149.07/21.52 | | | | | | | | | % 149.07/21.52 | | | | | | | | | SIMP: (7294) implies: % 149.07/21.52 | | | | | | | | | (7295) all_6_0 = e3 % 149.07/21.52 | | | | | | | | | % 149.07/21.52 | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (36), (38), (41), (42), % 149.07/21.52 | | | | | | | | | (43), (46), (51), (149), (193), (196), (197), % 149.07/21.52 | | | | | | | | | (246), (247), (287), (294), (295), (296), (332), % 149.07/21.52 | | | | | | | | | (333), (335), (344), (365), (374), (386), (401), % 149.07/21.52 | | | | | | | | | (419), (425), (443), (536), (542), (544), (545), % 149.07/21.52 | | | | | | | | | (546), (553), (554), (557), (568), (579), (590), % 149.07/21.52 | | | | | | | | | (617), (622), (627), (765), (5069), (5070), (5071), % 149.07/21.52 | | | | | | | | | (5074), (5075), (5076), (5077), (5082), (5083), % 149.07/21.52 | | | | | | | | | (5084), (7113), (7115), (7295), (function-axioms) % 149.07/21.52 | | | | | | | | | are inconsistent by sub-proof #106. % 149.07/21.52 | | | | | | | | | % 149.07/21.52 | | | | | | | | End of split % 149.07/21.52 | | | | | | | | % 149.07/21.52 | | | | | | | Case 2: % 149.07/21.52 | | | | | | | | % 149.07/21.52 | | | | | | | | (7296) all_36_1 = e3 % 149.07/21.52 | | | | | | | | (7297) ~ (all_36_0 = e0) | ~ (all_36_2 = e2) % 149.07/21.52 | | | | | | | | % 149.07/21.52 | | | | | | | | COMBINE_EQS: (652), (7296) imply: % 149.07/21.52 | | | | | | | | (7298) all_6_1 = e3 % 149.07/21.52 | | | | | | | | % 149.07/21.52 | | | | | | | | SIMP: (7298) implies: % 149.07/21.52 | | | | | | | | (7299) all_6_1 = e3 % 149.07/21.52 | | | | | | | | % 149.07/21.52 | | | | | | | | REDUCE: (43), (7299) imply: % 149.07/21.52 | | | | | | | | (7300) op(all_6_2, all_6_2) = e3 % 149.07/21.52 | | | | | | | | % 149.07/21.52 | | | | | | | | REDUCE: (42), (7299) imply: % 149.07/21.52 | | | | | | | | (7301) op(e1, e3) = all_6_0 % 149.07/21.52 | | | | | | | | % 149.07/21.52 | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_2, % 149.07/21.52 | | | | | | | | all_6_0, e3, e1, simplifying with (211), (7301) % 149.07/21.52 | | | | | | | | gives: % 149.07/21.52 | | | | | | | | (7302) all_52_2 = all_6_0 % 149.07/21.52 | | | | | | | | % 149.07/21.52 | | | | | | | | COMBINE_EQS: (471), (7302) imply: % 149.07/21.52 | | | | | | | | (7303) all_54_8 = all_6_0 % 149.07/21.52 | | | | | | | | % 149.07/21.52 | | | | | | | | COMBINE_EQS: (381), (7302) imply: % 149.07/21.52 | | | | | | | | (7304) all_56_17 = all_6_0 % 149.07/21.52 | | | | | | | | % 149.07/21.52 | | | | | | | | COMBINE_EQS: (553), (7302) imply: % 149.07/21.52 | | | | | | | | (7305) all_58_6 = all_6_0 % 149.07/21.52 | | | | | | | | % 149.07/21.52 | | | | | | | | REDUCE: (192), (7302) imply: % 149.07/21.52 | | | | | | | | (7306) ~ (all_52_3 = all_6_0) % 149.07/21.52 | | | | | | | | % 149.07/21.52 | | | | | | | | SIMP: (7306) implies: % 149.07/21.52 | | | | | | | | (7307) ~ (all_52_3 = all_6_0) % 149.07/21.52 | | | | | | | | % 149.07/21.52 | | | | | | | | REDUCE: (191), (7302) imply: % 149.07/21.52 | | | | | | | | (7308) ~ (all_52_6 = all_6_0) % 149.07/21.52 | | | | | | | | % 149.07/21.52 | | | | | | | | SIMP: (7308) implies: % 149.07/21.52 | | | | | | | | (7309) ~ (all_52_6 = all_6_0) % 149.07/21.52 | | | | | | | | % 149.07/21.52 | | | | | | | | REDUCE: (189), (7302) imply: % 149.07/21.52 | | | | | | | | (7310) ~ (all_52_14 = all_6_0) % 149.07/21.52 | | | | | | | | % 149.07/21.52 | | | | | | | | SIMP: (7310) implies: % 149.07/21.52 | | | | | | | | (7311) ~ (all_52_14 = all_6_0) % 149.07/21.52 | | | | | | | | % 149.07/21.52 | | | | | | | | REDUCE: (559), (7302) imply: % 149.07/21.52 | | | | | | | | (7312) ~ (all_10_2 = all_6_0) % 149.07/21.52 | | | | | | | | % 149.07/21.52 | | | | | | | | SIMP: (7312) implies: % 149.07/21.52 | | | | | | | | (7313) ~ (all_10_2 = all_6_0) % 149.07/21.52 | | | | | | | | % 149.07/21.52 | | | | | | | | REDUCE: (569), (7302) imply: % 149.07/21.52 | | | | | | | | (7314) ~ (all_6_0 = all_6_2) % 149.07/21.52 | | | | | | | | % 149.07/21.52 | | | | | | | | BETA: splitting (149) gives: % 149.07/21.52 | | | | | | | | % 149.07/21.52 | | | | | | | | Case 1: % 149.07/21.52 | | | | | | | | | % 149.07/21.52 | | | | | | | | | (7315) ~ (all_48_0 = e3) % 149.07/21.52 | | | | | | | | | % 149.07/21.52 | | | | | | | | | REDUCE: (765), (7315) imply: % 149.07/21.52 | | | | | | | | | (7316) ~ (all_8_0 = e3) % 149.07/21.52 | | | | | | | | | % 149.07/21.52 | | | | | | | | | BETA: splitting (292) gives: % 149.07/21.52 | | | | | | | | | % 149.07/21.52 | | | | | | | | | Case 1: % 149.07/21.52 | | | | | | | | | | % 149.07/21.52 | | | | | | | | | | (7317) ~ (all_56_21 = e2) % 149.07/21.52 | | | | | | | | | | % 149.07/21.52 | | | | | | | | | | REDUCE: (374), (7317) imply: % 149.07/21.52 | | | | | | | | | | (7318) ~ (all_6_2 = e2) % 149.07/21.52 | | | | | | | | | | % 149.07/21.52 | | | | | | | | | | BETA: splitting (288) gives: % 149.07/21.52 | | | | | | | | | | % 149.07/21.52 | | | | | | | | | | Case 1: % 149.07/21.52 | | | | | | | | | | | % 149.07/21.52 | | | | | | | | | | | (7319) ~ (all_56_31 = e1) % 149.07/21.52 | | | | | | | | | | | % 149.07/21.52 | | | | | | | | | | | REDUCE: (544), (7319) imply: % 149.07/21.52 | | | | | | | | | | | (7320) ~ (all_4_2 = e1) % 149.07/21.52 | | | | | | | | | | | % 149.07/21.54 | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (38), (41), % 149.07/21.54 | | | | | | | | | | | (46), (51), (168), (246), (247), (287), (293), % 149.07/21.54 | | | | | | | | | | | (294), (295), (296), (321), (329), (332), (333), % 149.07/21.54 | | | | | | | | | | | (335), (374), (386), (401), (407), (425), (443), % 149.07/21.54 | | | | | | | | | | | (542), (544), (545), (546), (547), (548), (550), % 149.07/21.54 | | | | | | | | | | | (551), (552), (554), (557), (567), (568), (579), % 149.07/21.54 | | | | | | | | | | | (585), (590), (617), (622), (623), (627), (5069), % 149.07/21.54 | | | | | | | | | | | (5071), (5074), (5075), (5076), (5077), (5082), % 149.07/21.54 | | | | | | | | | | | (5083), (5084), (7300), (7304), (7311), (7316), % 149.07/21.54 | | | | | | | | | | | (7320), (function-axioms) are inconsistent by % 149.07/21.54 | | | | | | | | | | | sub-proof #110. % 149.07/21.54 | | | | | | | | | | | % 149.07/21.54 | | | | | | | | | | Case 2: % 149.07/21.54 | | | | | | | | | | | % 149.07/21.54 | | | | | | | | | | | (7321) all_56_31 = e1 % 149.07/21.54 | | | | | | | | | | | (7322) all_56_29 = e0 % 149.07/21.54 | | | | | | | | | | | % 149.07/21.54 | | | | | | | | | | | COMBINE_EQS: (357), (7322) imply: % 149.07/21.54 | | | | | | | | | | | (7323) all_52_11 = e0 % 149.07/21.54 | | | | | | | | | | | % 149.07/21.54 | | | | | | | | | | | COMBINE_EQS: (544), (7321) imply: % 149.07/21.54 | | | | | | | | | | | (7324) all_4_2 = e1 % 149.07/21.54 | | | | | | | | | | | % 149.07/21.54 | | | | | | | | | | | COMBINE_EQS: (548), (7323) imply: % 149.07/21.54 | | | | | | | | | | | (7325) all_58_14 = e0 % 149.07/21.54 | | | | | | | | | | | % 149.07/21.54 | | | | | | | | | | | REDUCE: (187), (7323) imply: % 149.07/21.54 | | | | | | | | | | | (7326) ~ (all_52_3 = e0) % 149.07/21.54 | | | | | | | | | | | % 149.07/21.54 | | | | | | | | | | | REDUCE: (588), (7323), (7324) imply: % 149.07/21.54 | | | | | | | | | | | (7327) ~ (e1 = e0) % 149.07/21.54 | | | | | | | | | | | % 149.07/21.54 | | | | | | | | | | | REDUCE: (38), (7324) imply: % 149.07/21.54 | | | | | | | | | | | (7328) op(e1, e1) = all_4_1 % 149.07/21.54 | | | | | | | | | | | % 149.07/21.54 | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_6_2, % 149.07/21.54 | | | | | | | | | | | all_4_1, e1, e1, simplifying with (41), (7328) % 149.07/21.54 | | | | | | | | | | | gives: % 149.07/21.54 | | | | | | | | | | | (7329) all_6_2 = all_4_1 % 149.07/21.54 | | | | | | | | | | | % 149.07/21.54 | | | | | | | | | | | COMBINE_EQS: (374), (7329) imply: % 149.07/21.54 | | | | | | | | | | | (7330) all_56_21 = all_4_1 % 149.07/21.54 | | | | | | | | | | | % 149.07/21.54 | | | | | | | | | | | COMBINE_EQS: (552), (7329) imply: % 149.07/21.54 | | | | | | | | | | | (7331) all_58_8 = all_4_1 % 149.07/21.54 | | | | | | | | | | | % 149.07/21.54 | | | | | | | | | | | REDUCE: (582), (7329) imply: % 149.07/21.54 | | | | | | | | | | | (7332) ~ (all_52_8 = all_4_1) % 149.07/21.54 | | | | | | | | | | | % 149.07/21.54 | | | | | | | | | | | REDUCE: (7318), (7329) imply: % 149.07/21.54 | | | | | | | | | | | (7333) ~ (all_4_1 = e2) % 149.07/21.54 | | | | | | | | | | | % 149.07/21.54 | | | | | | | | | | | REDUCE: (7300), (7329) imply: % 149.07/21.54 | | | | | | | | | | | (7334) op(all_4_1, all_4_1) = e3 % 149.07/21.54 | | | | | | | | | | | % 149.07/21.54 | | | | | | | | | | | REDUCE: (622), (7329) imply: % 149.07/21.54 | | | | | | | | | | | (7335) op(e1, all_4_1) = all_56_20 % 149.07/21.54 | | | | | | | | | | | % 149.07/21.54 | | | | | | | | | | | BETA: splitting (293) gives: % 149.07/21.54 | | | | | | | | | | | % 149.07/21.54 | | | | | | | | | | | Case 1: % 149.07/21.54 | | | | | | | | | | | | % 149.07/21.54 | | | | | | | | | | | | (7336) ~ (all_56_21 = e3) % 149.07/21.54 | | | | | | | | | | | | % 149.07/21.54 | | | | | | | | | | | | REDUCE: (7330), (7336) imply: % 149.07/21.54 | | | | | | | | | | | | (7337) ~ (all_4_1 = e3) % 149.07/21.54 | | | | | | | | | | | | % 149.07/21.54 | | | | | | | | | | | | BETA: splitting (331) gives: % 149.07/21.54 | | | | | | | | | | | | % 149.07/21.54 | | | | | | | | | | | | Case 1: % 149.07/21.54 | | | | | | | | | | | | | % 149.07/21.54 | | | | | | | | | | | | | (7338) all_58_4 = e3 % 149.07/21.54 | | | | | | | | | | | | | % 149.07/21.54 | | | | | | | | | | | | | COMBINE_EQS: (407), (7338) imply: % 149.07/21.54 | | | | | | | | | | | | | (7339) all_52_8 = e3 % 149.07/21.54 | | | | | | | | | | | | | % 149.07/21.54 | | | | | | | | | | | | | REDUCE: (7332), (7339) imply: % 149.07/21.54 | | | | | | | | | | | | | (7340) ~ (all_4_1 = e3) % 149.07/21.54 | | | | | | | | | | | | | % 149.07/21.54 | | | | | | | | | | | | | BETA: splitting (330) gives: % 149.07/21.54 | | | | | | | | | | | | | % 149.07/21.54 | | | | | | | | | | | | | Case 1: % 149.07/21.54 | | | | | | | | | | | | | | % 149.07/21.54 | | | | | | | | | | | | | | (7341) all_58_4 = e2 % 149.07/21.54 | | | | | | | | | | | | | | % 149.07/21.54 | | | | | | | | | | | | | | COMBINE_EQS: (7338), (7341) imply: % 149.07/21.54 | | | | | | | | | | | | | | (7342) e3 = e2 % 149.07/21.54 | | | | | | | | | | | | | | % 149.07/21.54 | | | | | | | | | | | | | | REDUCE: (9), (7342) imply: % 149.07/21.54 | | | | | | | | | | | | | | (7343) $false % 149.07/21.54 | | | | | | | | | | | | | | % 149.07/21.54 | | | | | | | | | | | | | | CLOSE: (7343) is inconsistent. % 149.07/21.54 | | | | | | | | | | | | | | % 149.07/21.54 | | | | | | | | | | | | | Case 2: % 149.07/21.54 | | | | | | | | | | | | | | % 149.07/21.54 | | | | | | | | | | | | | | (7344) all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2 % 149.07/21.54 | | | | | | | | | | | | | | % 149.07/21.54 | | | | | | | | | | | | | | BETA: splitting (7344) gives: % 149.07/21.54 | | | | | | | | | | | | | | % 149.07/21.54 | | | | | | | | | | | | | | Case 1: % 149.07/21.54 | | | | | | | | | | | | | | | % 149.07/21.54 | | | | | | | | | | | | | | | (7345) all_58_5 = e2 % 149.07/21.54 | | | | | | | | | | | | | | | % 149.07/21.54 | | | | | | | | | | | | | | | COMBINE_EQS: (5076), (7345) imply: % 149.07/21.54 | | | | | | | | | | | | | | | (7346) all_8_0 = e2 % 149.07/21.54 | | | | | | | | | | | | | | | % 149.07/21.54 | | | | | | | | | | | | | | | BETA: splitting (329) gives: % 149.07/21.54 | | | | | | | | | | | | | | | % 149.07/21.54 | | | | | | | | | | | | | | | Case 1: % 149.07/21.54 | | | | | | | | | | | | | | | | % 149.07/21.54 | | | | | | | | | | | | | | | | (7347) all_58_4 = e1 % 149.07/21.54 | | | | | | | | | | | | | | | | % 149.07/21.54 | | | | | | | | | | | | | | | | COMBINE_EQS: (7338), (7347) imply: % 149.07/21.54 | | | | | | | | | | | | | | | | (7348) e3 = e1 % 149.07/21.54 | | | | | | | | | | | | | | | | % 149.07/21.54 | | | | | | | | | | | | | | | | REDUCE: (8), (7348) imply: % 149.07/21.54 | | | | | | | | | | | | | | | | (7349) $false % 149.07/21.54 | | | | | | | | | | | | | | | | % 149.07/21.54 | | | | | | | | | | | | | | | | CLOSE: (7349) is inconsistent. % 149.07/21.54 | | | | | | | | | | | | | | | | % 149.07/21.54 | | | | | | | | | | | | | | | Case 2: % 149.07/21.54 | | | | | | | | | | | | | | | | % 149.07/21.54 | | | | | | | | | | | | | | | | (7350) all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1 % 149.07/21.54 | | | | | | | | | | | | | | | | % 149.07/21.54 | | | | | | | | | | | | | | | | BETA: splitting (7350) gives: % 149.07/21.54 | | | | | | | | | | | | | | | | % 149.07/21.54 | | | | | | | | | | | | | | | | Case 1: % 149.07/21.54 | | | | | | | | | | | | | | | | | % 149.07/21.54 | | | | | | | | | | | | | | | | | (7351) all_58_5 = e1 % 149.07/21.54 | | | | | | | | | | | | | | | | | % 149.07/21.54 | | | | | | | | | | | | | | | | | COMBINE_EQS: (7345), (7351) imply: % 149.07/21.54 | | | | | | | | | | | | | | | | | (7352) e2 = e1 % 149.07/21.54 | | | | | | | | | | | | | | | | | % 149.07/21.54 | | | | | | | | | | | | | | | | | REDUCE: (6), (7352) imply: % 149.07/21.54 | | | | | | | | | | | | | | | | | (7353) $false % 149.07/21.54 | | | | | | | | | | | | | | | | | % 149.07/21.54 | | | | | | | | | | | | | | | | | CLOSE: (7353) is inconsistent. % 149.07/21.54 | | | | | | | | | | | | | | | | | % 149.07/21.54 | | | | | | | | | | | | | | | | Case 2: % 149.07/21.54 | | | | | | | | | | | | | | | | | % 149.07/21.54 | | | | | | | | | | | | | | | | | (7354) all_58_8 = e1 | all_58_14 = e1 % 149.07/21.54 | | | | | | | | | | | | | | | | | % 149.07/21.54 | | | | | | | | | | | | | | | | | BETA: splitting (7354) gives: % 149.07/21.54 | | | | | | | | | | | | | | | | | % 149.07/21.54 | | | | | | | | | | | | | | | | | Case 1: % 149.07/21.54 | | | | | | | | | | | | | | | | | | % 149.07/21.54 | | | | | | | | | | | | | | | | | | (7355) all_58_8 = e1 % 149.07/21.54 | | | | | | | | | | | | | | | | | | % 149.07/21.54 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (7331), (7355) imply: % 149.07/21.54 | | | | | | | | | | | | | | | | | | (7356) all_4_1 = e1 % 149.07/21.54 | | | | | | | | | | | | | | | | | | % 149.07/21.54 | | | | | | | | | | | | | | | | | | REF_CLOSE: (7328), (7334), (7335), (7337), (7356), % 149.07/21.54 | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 149.07/21.54 | | | | | | | | | | | | | | | | | | #440. % 149.07/21.54 | | | | | | | | | | | | | | | | | | % 149.07/21.54 | | | | | | | | | | | | | | | | | Case 2: % 149.07/21.54 | | | | | | | | | | | | | | | | | | % 149.07/21.54 | | | | | | | | | | | | | | | | | | (7357) all_58_14 = e1 % 149.07/21.54 | | | | | | | | | | | | | | | | | | % 149.07/21.54 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (7325), (7357) imply: % 149.07/21.54 | | | | | | | | | | | | | | | | | | (7358) e1 = e0 % 149.07/21.54 | | | | | | | | | | | | | | | | | | % 149.07/21.54 | | | | | | | | | | | | | | | | | | REDUCE: (4), (7358) imply: % 149.07/21.54 | | | | | | | | | | | | | | | | | | (7359) $false % 149.07/21.54 | | | | | | | | | | | | | | | | | | % 149.07/21.54 | | | | | | | | | | | | | | | | | | CLOSE: (7359) is inconsistent. % 149.07/21.54 | | | | | | | | | | | | | | | | | | % 149.07/21.54 | | | | | | | | | | | | | | | | | End of split % 149.07/21.54 | | | | | | | | | | | | | | | | | % 149.07/21.54 | | | | | | | | | | | | | | | | End of split % 149.07/21.54 | | | | | | | | | | | | | | | | % 149.07/21.54 | | | | | | | | | | | | | | | End of split % 149.07/21.54 | | | | | | | | | | | | | | | % 149.07/21.54 | | | | | | | | | | | | | | Case 2: % 149.07/21.54 | | | | | | | | | | | | | | | % 149.07/21.54 | | | | | | | | | | | | | | | (7360) all_58_8 = e2 | all_58_14 = e2 % 149.07/21.54 | | | | | | | | | | | | | | | % 149.07/21.54 | | | | | | | | | | | | | | | REF_CLOSE: (5), (7325), (7331), (7333), (7360) are % 149.07/21.54 | | | | | | | | | | | | | | | inconsistent by sub-proof #537. % 149.07/21.54 | | | | | | | | | | | | | | | % 149.07/21.54 | | | | | | | | | | | | | | End of split % 149.07/21.54 | | | | | | | | | | | | | | % 149.07/21.54 | | | | | | | | | | | | | End of split % 149.07/21.54 | | | | | | | | | | | | | % 149.07/21.54 | | | | | | | | | | | | Case 2: % 149.07/21.54 | | | | | | | | | | | | | % 149.07/21.54 | | | | | | | | | | | | | (7361) all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3 % 149.07/21.54 | | | | | | | | | | | | | % 149.07/21.54 | | | | | | | | | | | | | REF_CLOSE: (7), (5076), (7316), (7325), (7331), (7337), % 149.07/21.54 | | | | | | | | | | | | | (7361) are inconsistent by sub-proof #120. % 149.07/21.54 | | | | | | | | | | | | | % 149.07/21.54 | | | | | | | | | | | | End of split % 149.07/21.54 | | | | | | | | | | | | % 149.07/21.54 | | | | | | | | | | | Case 2: % 149.07/21.54 | | | | | | | | | | | | % 149.07/21.54 | | | | | | | | | | | | (7362) all_56_21 = e3 % 149.07/21.54 | | | | | | | | | | | | (7363) all_56_17 = e1 % 149.07/21.54 | | | | | | | | | | | | % 149.07/21.54 | | | | | | | | | | | | COMBINE_EQS: (7304), (7363) imply: % 149.07/21.54 | | | | | | | | | | | | (7364) all_6_0 = e1 % 149.07/21.54 | | | | | | | | | | | | % 149.07/21.54 | | | | | | | | | | | | REF_CLOSE: (37), (207), (240), (478), (767), (7111), (7307), % 149.07/21.54 | | | | | | | | | | | | (7326), (7330), (7362), (7364), (function-axioms) % 149.07/21.54 | | | | | | | | | | | | are inconsistent by sub-proof #438. % 149.07/21.54 | | | | | | | | | | | | % 149.07/21.54 | | | | | | | | | | | End of split % 149.07/21.54 | | | | | | | | | | | % 149.07/21.54 | | | | | | | | | | End of split % 149.07/21.54 | | | | | | | | | | % 149.07/21.54 | | | | | | | | | Case 2: % 149.07/21.54 | | | | | | | | | | % 149.07/21.54 | | | | | | | | | | (7365) all_56_21 = e2 % 149.07/21.54 | | | | | | | | | | (7366) all_56_19 = e1 % 149.07/21.54 | | | | | | | | | | % 149.07/21.55 | | | | | | | | | | REF_CLOSE: (4), (5), (46), (48), (244), (287), (324), (374), % 149.07/21.55 | | | | | | | | | | (380), (435), (532), (544), (545), (546), (550), % 149.07/21.55 | | | | | | | | | | (552), (580), (591), (617), (762), (7297), (7300), % 149.07/21.55 | | | | | | | | | | (7303), (7305), (7309), (7311), (7313), (7314), % 149.07/21.55 | | | | | | | | | | (7365), (7366), (function-axioms) are inconsistent % 149.07/21.55 | | | | | | | | | | by sub-proof #412. % 149.07/21.55 | | | | | | | | | | % 149.07/21.55 | | | | | | | | | End of split % 149.07/21.55 | | | | | | | | | % 149.07/21.55 | | | | | | | | Case 2: % 149.07/21.55 | | | | | | | | | % 149.07/21.55 | | | | | | | | | (7367) all_48_0 = e3 % 149.07/21.55 | | | | | | | | | (7368) ~ (all_48_1 = e1) | ~ (all_48_2 = e0) % 149.07/21.55 | | | | | | | | | % 149.07/21.55 | | | | | | | | | COMBINE_EQS: (765), (7367) imply: % 149.07/21.55 | | | | | | | | | (7369) all_8_0 = e3 % 149.07/21.55 | | | | | | | | | % 149.07/21.55 | | | | | | | | | REF_CLOSE: (9), (46), (247), (295), (536), (542), (545), % 149.07/21.55 | | | | | | | | | (617), (5070), (5071), (5075), (5083), (7368), % 149.07/21.55 | | | | | | | | | (7369), (function-axioms) are inconsistent by % 149.07/21.55 | | | | | | | | | sub-proof #115. % 149.07/21.55 | | | | | | | | | % 149.07/21.55 | | | | | | | | End of split % 149.07/21.55 | | | | | | | | % 149.07/21.55 | | | | | | | End of split % 149.07/21.55 | | | | | | | % 149.07/21.55 | | | | | | Case 2: % 149.07/21.55 | | | | | | | % 149.07/21.55 | | | | | | | (7370) all_28_0 = e2 % 149.07/21.55 | | | | | | | % 149.07/21.55 | | | | | | | COMBINE_EQS: (740), (7370) imply: % 149.07/21.55 | | | | | | | (7371) all_6_0 = e2 % 149.07/21.55 | | | | | | | % 149.07/21.55 | | | | | | | SIMP: (7371) implies: % 149.07/21.55 | | | | | | | (7372) all_6_0 = e2 % 149.07/21.55 | | | | | | | % 149.07/21.55 | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (38), (41), (42), % 149.07/21.55 | | | | | | | (43), (46), (51), (149), (246), (247), (287), (294), % 149.07/21.55 | | | | | | | (295), (296), (332), (333), (335), (374), (386), (401), % 149.07/21.55 | | | | | | | (425), (443), (536), (542), (544), (545), (546), (554), % 149.07/21.55 | | | | | | | (557), (568), (579), (590), (617), (622), (627), (765), % 149.07/21.55 | | | | | | | (768), (5069), (5070), (5071), (5074), (5075), (5076), % 149.07/21.55 | | | | | | | (5077), (5082), (5083), (5084), (7372), % 149.07/21.55 | | | | | | | (function-axioms) are inconsistent by sub-proof #104. % 149.07/21.55 | | | | | | | % 149.07/21.55 | | | | | | End of split % 149.07/21.55 | | | | | | % 149.07/21.55 | | | | | Case 2: % 149.07/21.55 | | | | | | % 149.07/21.55 | | | | | | (7373) all_12_0 = e2 % 149.07/21.55 | | | | | | (7374) ~ (all_12_1 = e1) | ~ (all_12_2 = e3) % 149.07/21.55 | | | | | | % 149.07/21.55 | | | | | | COMBINE_EQS: (759), (7373) imply: % 149.07/21.55 | | | | | | (7375) all_4_0 = e2 % 149.07/21.55 | | | | | | % 149.07/21.55 | | | | | | SIMP: (7375) implies: % 149.07/21.55 | | | | | | (7376) all_4_0 = e2 % 149.07/21.55 | | | | | | % 149.07/21.55 | | | | | | COMBINE_EQS: (734), (7376) imply: % 149.07/21.55 | | | | | | (7377) all_34_0 = e2 % 149.07/21.55 | | | | | | % 149.07/21.55 | | | | | | REDUCE: (767), (7376) imply: % 149.07/21.55 | | | | | | (7378) ~ (e3 = e2) % 149.07/21.55 | | | | | | % 149.07/21.55 | | | | | | REDUCE: (37), (7376) imply: % 149.07/21.55 | | | | | | (7379) op(e0, all_4_1) = e2 % 149.07/21.55 | | | | | | % 149.07/21.55 | | | | | | BETA: splitting (99) gives: % 149.07/21.55 | | | | | | % 149.07/21.55 | | | | | | Case 1: % 149.07/21.55 | | | | | | | % 149.07/21.55 | | | | | | | (7380) ~ (all_28_0 = e2) % 149.07/21.55 | | | | | | | % 149.07/21.55 | | | | | | | REDUCE: (740), (7380) imply: % 149.07/21.55 | | | | | | | (7381) ~ (all_6_0 = e2) % 149.07/21.55 | | | | | | | % 149.07/21.55 | | | | | | | BETA: splitting (114) gives: % 149.07/21.55 | | | | | | | % 149.07/21.55 | | | | | | | Case 1: % 149.07/21.55 | | | | | | | | % 149.07/21.55 | | | | | | | | (7382) ~ (all_34_0 = e2) % 149.07/21.55 | | | | | | | | % 149.07/21.55 | | | | | | | | REDUCE: (7377), (7382) imply: % 149.07/21.55 | | | | | | | | (7383) $false % 149.07/21.55 | | | | | | | | % 149.07/21.55 | | | | | | | | CLOSE: (7383) is inconsistent. % 149.07/21.55 | | | | | | | | % 149.07/21.55 | | | | | | | Case 2: % 149.07/21.55 | | | | | | | | % 149.07/21.55 | | | | | | | | (7384) ~ (all_34_1 = e3) | ~ (all_34_2 = e1) % 149.07/21.55 | | | | | | | | % 149.07/21.55 | | | | | | | | BETA: splitting (119) gives: % 149.07/21.55 | | | | | | | | % 149.07/21.55 | | | | | | | | Case 1: % 149.07/21.55 | | | | | | | | | % 149.07/21.55 | | | | | | | | | (7385) ~ (all_36_1 = e3) % 149.07/21.55 | | | | | | | | | % 149.07/21.55 | | | | | | | | | REF_CLOSE: (5), (6), (7), (8), (9), (36), (38), (41), (42), % 149.07/21.55 | | | | | | | | | (43), (46), (51), (149), (158), (160), (161), % 149.07/21.55 | | | | | | | | | (173), (174), (182), (189), (191), (193), (197), % 149.07/21.55 | | | | | | | | | (205), (208), (237), (238), (241), (242), (243), % 149.07/21.55 | | | | | | | | | (246), (247), (248), (252), (287), (288), (289), % 149.07/21.55 | | | | | | | | | (290), (291), (292), (293), (294), (295), (296), % 149.07/21.55 | | | | | | | | | (297), (299), (317), (321), (329), (330), (331), % 149.07/21.55 | | | | | | | | | (332), (344), (357), (360), (365), (366), (374), % 149.07/21.55 | | | | | | | | | (381), (386), (389), (401), (402), (407), (408), % 149.07/21.55 | | | | | | | | | (419), (425), (435), (443), (447), (463), (473), % 149.07/21.55 | | | | | | | | | (476), (482), (529), (531), (536), (540), (541), % 149.07/21.55 | | | | | | | | | (542), (543), (544), (545), (546), (547), (548), % 149.07/21.55 | | | | | | | | | (550), (551), (552), (553), (554), (557), (559), % 149.07/21.55 | | | | | | | | | (561), (565), (568), (569), (570), (573), (575), % 149.07/21.55 | | | | | | | | | (580), (581), (585), (587), (588), (590), (591), % 149.07/21.55 | | | | | | | | | (617), (621), (622), (624), (625), (627), (652), % 149.07/21.55 | | | | | | | | | (681), (683), (765), (768), (5069), (5070), (5071), % 149.07/21.55 | | | | | | | | | (5074), (5075), (5076), (5077), (5080), (5082), % 149.07/21.55 | | | | | | | | | (5083), (5084), (7374), (7379), (7381), (7384), % 149.07/21.55 | | | | | | | | | (7385), (function-axioms) are inconsistent by % 149.07/21.55 | | | | | | | | | sub-proof #92. % 149.07/21.55 | | | | | | | | | % 149.07/21.55 | | | | | | | | Case 2: % 149.07/21.55 | | | | | | | | | % 149.07/21.55 | | | | | | | | | (7386) all_36_1 = e3 % 149.07/21.55 | | | | | | | | | (7387) ~ (all_36_0 = e0) | ~ (all_36_2 = e2) % 149.07/21.55 | | | | | | | | | % 149.07/21.55 | | | | | | | | | COMBINE_EQS: (652), (7386) imply: % 149.07/21.55 | | | | | | | | | (7388) all_6_1 = e3 % 149.07/21.55 | | | | | | | | | % 149.07/21.55 | | | | | | | | | REDUCE: (43), (7388) imply: % 149.07/21.55 | | | | | | | | | (7389) op(all_6_2, all_6_2) = e3 % 149.07/21.55 | | | | | | | | | % 149.07/21.55 | | | | | | | | | REDUCE: (42), (7388) imply: % 149.07/21.55 | | | | | | | | | (7390) op(e1, e3) = all_6_0 % 149.07/21.55 | | | | | | | | | % 149.07/21.55 | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_2, % 149.07/21.55 | | | | | | | | | all_6_0, e3, e1, simplifying with (211), (7390) % 149.07/21.55 | | | | | | | | | gives: % 149.07/21.55 | | | | | | | | | (7391) all_52_2 = all_6_0 % 149.07/21.55 | | | | | | | | | % 149.07/21.55 | | | | | | | | | COMBINE_EQS: (471), (7391) imply: % 149.07/21.55 | | | | | | | | | (7392) all_54_8 = all_6_0 % 149.07/21.55 | | | | | | | | | % 149.07/21.55 | | | | | | | | | COMBINE_EQS: (381), (7391) imply: % 149.07/21.55 | | | | | | | | | (7393) all_56_17 = all_6_0 % 149.07/21.55 | | | | | | | | | % 149.07/21.55 | | | | | | | | | COMBINE_EQS: (553), (7391) imply: % 149.07/21.55 | | | | | | | | | (7394) all_58_6 = all_6_0 % 149.07/21.55 | | | | | | | | | % 149.07/21.55 | | | | | | | | | REDUCE: (191), (7391) imply: % 149.07/21.55 | | | | | | | | | (7395) ~ (all_52_6 = all_6_0) % 149.07/21.55 | | | | | | | | | % 149.07/21.55 | | | | | | | | | SIMP: (7395) implies: % 149.07/21.55 | | | | | | | | | (7396) ~ (all_52_6 = all_6_0) % 149.07/21.55 | | | | | | | | | % 149.07/21.55 | | | | | | | | | REDUCE: (189), (7391) imply: % 149.07/21.55 | | | | | | | | | (7397) ~ (all_52_14 = all_6_0) % 149.07/21.55 | | | | | | | | | % 149.07/21.55 | | | | | | | | | SIMP: (7397) implies: % 149.07/21.55 | | | | | | | | | (7398) ~ (all_52_14 = all_6_0) % 149.07/21.55 | | | | | | | | | % 149.07/21.55 | | | | | | | | | REDUCE: (559), (7391) imply: % 149.07/21.55 | | | | | | | | | (7399) ~ (all_10_2 = all_6_0) % 149.07/21.55 | | | | | | | | | % 149.07/21.55 | | | | | | | | | SIMP: (7399) implies: % 149.07/21.55 | | | | | | | | | (7400) ~ (all_10_2 = all_6_0) % 149.07/21.55 | | | | | | | | | % 149.07/21.55 | | | | | | | | | REDUCE: (569), (7391) imply: % 149.07/21.55 | | | | | | | | | (7401) ~ (all_6_0 = all_6_2) % 149.07/21.55 | | | | | | | | | % 149.07/21.55 | | | | | | | | | BETA: splitting (149) gives: % 149.07/21.55 | | | | | | | | | % 149.07/21.55 | | | | | | | | | Case 1: % 149.07/21.55 | | | | | | | | | | % 149.07/21.55 | | | | | | | | | | (7402) ~ (all_48_0 = e3) % 149.07/21.55 | | | | | | | | | | % 149.07/21.55 | | | | | | | | | | REDUCE: (765), (7402) imply: % 149.07/21.55 | | | | | | | | | | (7403) ~ (all_8_0 = e3) % 149.07/21.55 | | | | | | | | | | % 149.07/21.55 | | | | | | | | | | BETA: splitting (292) gives: % 149.07/21.55 | | | | | | | | | | % 149.07/21.55 | | | | | | | | | | Case 1: % 149.07/21.55 | | | | | | | | | | | % 149.07/21.55 | | | | | | | | | | | (7404) ~ (all_56_21 = e2) % 149.07/21.55 | | | | | | | | | | | % 149.07/21.55 | | | | | | | | | | | REDUCE: (374), (7404) imply: % 149.07/21.55 | | | | | | | | | | | (7405) ~ (all_6_2 = e2) % 149.07/21.55 | | | | | | | | | | | % 149.07/21.55 | | | | | | | | | | | BETA: splitting (288) gives: % 149.07/21.55 | | | | | | | | | | | % 149.07/21.55 | | | | | | | | | | | Case 1: % 149.07/21.55 | | | | | | | | | | | | % 149.07/21.55 | | | | | | | | | | | | (7406) ~ (all_56_31 = e1) % 149.07/21.55 | | | | | | | | | | | | % 149.07/21.55 | | | | | | | | | | | | REDUCE: (544), (7406) imply: % 149.07/21.55 | | | | | | | | | | | | (7407) ~ (all_4_2 = e1) % 149.07/21.55 | | | | | | | | | | | | % 149.07/21.55 | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (38), (41), % 149.07/21.55 | | | | | | | | | | | | (46), (51), (168), (246), (247), (287), (293), % 149.07/21.55 | | | | | | | | | | | | (294), (295), (296), (321), (329), (332), (333), % 149.07/21.55 | | | | | | | | | | | | (335), (374), (386), (401), (407), (425), (443), % 149.07/21.55 | | | | | | | | | | | | (542), (544), (545), (546), (547), (548), (550), % 149.07/21.55 | | | | | | | | | | | | (551), (552), (554), (557), (567), (568), (579), % 149.07/21.55 | | | | | | | | | | | | (585), (590), (617), (622), (623), (627), (5069), % 149.07/21.55 | | | | | | | | | | | | (5071), (5074), (5075), (5076), (5077), (5082), % 149.07/21.55 | | | | | | | | | | | | (5083), (5084), (7389), (7393), (7398), (7403), % 149.07/21.55 | | | | | | | | | | | | (7407), (function-axioms) are inconsistent by % 149.07/21.55 | | | | | | | | | | | | sub-proof #110. % 149.07/21.55 | | | | | | | | | | | | % 149.07/21.55 | | | | | | | | | | | Case 2: % 149.07/21.55 | | | | | | | | | | | | % 149.07/21.55 | | | | | | | | | | | | (7408) all_56_31 = e1 % 149.07/21.55 | | | | | | | | | | | | (7409) all_56_29 = e0 % 149.07/21.55 | | | | | | | | | | | | % 149.07/21.55 | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (8), (9), (38), (41), (43), (205), % 149.07/21.55 | | | | | | | | | | | | (242), (329), (330), (331), (357), (407), (531), % 149.07/21.55 | | | | | | | | | | | | (541), (544), (548), (552), (585), (588), (622), % 149.07/21.55 | | | | | | | | | | | | (627), (683), (5076), (5080), (7379), (7384), % 149.07/21.55 | | | | | | | | | | | | (7403), (7405), (7408), (7409), (function-axioms) % 149.07/21.55 | | | | | | | | | | | | are inconsistent by sub-proof #93. % 149.07/21.55 | | | | | | | | | | | | % 149.07/21.55 | | | | | | | | | | | End of split % 149.07/21.55 | | | | | | | | | | | % 149.07/21.55 | | | | | | | | | | Case 2: % 149.07/21.55 | | | | | | | | | | | % 149.07/21.55 | | | | | | | | | | | (7410) all_56_21 = e2 % 149.07/21.55 | | | | | | | | | | | (7411) all_56_19 = e1 % 149.07/21.55 | | | | | | | | | | | % 149.07/21.55 | | | | | | | | | | | REF_CLOSE: (4), (5), (46), (48), (244), (287), (324), (374), % 149.07/21.55 | | | | | | | | | | | (380), (435), (532), (544), (545), (546), (550), % 149.07/21.55 | | | | | | | | | | | (552), (580), (591), (617), (762), (7387), (7389), % 149.07/21.55 | | | | | | | | | | | (7392), (7394), (7396), (7398), (7400), (7401), % 149.07/21.55 | | | | | | | | | | | (7410), (7411), (function-axioms) are inconsistent % 149.07/21.55 | | | | | | | | | | | by sub-proof #412. % 149.07/21.55 | | | | | | | | | | | % 149.07/21.55 | | | | | | | | | | End of split % 149.07/21.55 | | | | | | | | | | % 149.07/21.55 | | | | | | | | | Case 2: % 149.07/21.55 | | | | | | | | | | % 149.07/21.55 | | | | | | | | | | (7412) all_48_0 = e3 % 149.07/21.55 | | | | | | | | | | (7413) ~ (all_48_1 = e1) | ~ (all_48_2 = e0) % 149.07/21.55 | | | | | | | | | | % 149.07/21.55 | | | | | | | | | | COMBINE_EQS: (765), (7412) imply: % 149.07/21.55 | | | | | | | | | | (7414) all_8_0 = e3 % 149.07/21.55 | | | | | | | | | | % 149.07/21.55 | | | | | | | | | | REF_CLOSE: (9), (46), (247), (295), (536), (542), (545), % 149.07/21.55 | | | | | | | | | | (617), (5070), (5071), (5075), (5083), (7413), % 149.07/21.55 | | | | | | | | | | (7414), (function-axioms) are inconsistent by % 149.07/21.55 | | | | | | | | | | sub-proof #115. % 149.07/21.55 | | | | | | | | | | % 149.07/21.55 | | | | | | | | | End of split % 149.07/21.55 | | | | | | | | | % 149.07/21.55 | | | | | | | | End of split % 149.07/21.55 | | | | | | | | % 149.07/21.55 | | | | | | | End of split % 149.07/21.55 | | | | | | | % 149.07/21.55 | | | | | | Case 2: % 149.07/21.55 | | | | | | | % 149.07/21.55 | | | | | | | (7415) all_28_0 = e2 % 149.07/21.55 | | | | | | | % 149.07/21.55 | | | | | | | COMBINE_EQS: (740), (7415) imply: % 149.07/21.55 | | | | | | | (7416) all_6_0 = e2 % 149.07/21.55 | | | | | | | % 149.07/21.55 | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (38), (41), (42), % 149.07/21.55 | | | | | | | (43), (46), (51), (149), (246), (247), (287), (294), % 149.07/21.55 | | | | | | | (295), (296), (332), (333), (335), (374), (386), (401), % 149.07/21.55 | | | | | | | (425), (443), (536), (542), (544), (545), (546), (554), % 149.07/21.55 | | | | | | | (557), (568), (579), (590), (617), (622), (627), (765), % 149.07/21.55 | | | | | | | (768), (5069), (5070), (5071), (5074), (5075), (5076), % 149.07/21.55 | | | | | | | (5077), (5082), (5083), (5084), (7416), % 149.07/21.55 | | | | | | | (function-axioms) are inconsistent by sub-proof #104. % 149.07/21.55 | | | | | | | % 149.07/21.55 | | | | | | End of split % 149.07/21.55 | | | | | | % 149.07/21.55 | | | | | End of split % 149.07/21.55 | | | | | % 149.07/21.55 | | | | End of split % 149.07/21.55 | | | | % 149.07/21.55 | | | End of split % 149.07/21.55 | | | % 149.07/21.55 | | Case 2: % 149.07/21.55 | | | % 149.07/21.55 | | | (7417) all_6_1 = e2 % 149.07/21.55 | | | (7418) ~ (all_6_0 = e0) | ~ (all_6_2 = e3) % 149.07/21.55 | | | % 149.07/21.55 | | | COMBINE_EQS: (674), (7417) imply: % 149.07/21.55 | | | (7419) all_18_1 = e2 % 149.07/21.55 | | | % 149.07/21.55 | | | REDUCE: (43), (7417) imply: % 149.07/21.55 | | | (7420) op(all_6_2, all_6_2) = e2 % 149.07/21.55 | | | % 149.07/21.55 | | | REDUCE: (42), (7417) imply: % 149.07/21.55 | | | (7421) op(e1, e2) = all_6_0 % 149.07/21.55 | | | % 149.07/21.55 | | | GROUND_INST: instantiating (function-axioms) with all_52_6, all_6_0, e2, % 149.07/21.55 | | | e1, simplifying with (210), (7421) gives: % 149.07/21.55 | | | (7422) all_52_6 = all_6_0 % 149.07/21.55 | | | % 149.07/21.55 | | | COMBINE_EQS: (473), (7422) imply: % 149.07/21.55 | | | (7423) all_54_9 = all_6_0 % 149.07/21.55 | | | % 149.07/21.55 | | | COMBINE_EQS: (435), (7422) imply: % 149.07/21.55 | | | (7424) all_56_19 = all_6_0 % 149.07/21.55 | | | % 149.07/21.55 | | | COMBINE_EQS: (380), (7422) imply: % 149.07/21.55 | | | (7425) all_58_7 = all_6_0 % 149.07/21.55 | | | % 149.07/21.55 | | | REDUCE: (191), (7422) imply: % 149.07/21.55 | | | (7426) ~ (all_52_2 = all_6_0) % 149.07/21.55 | | | % 149.07/21.55 | | | REDUCE: (184), (7422) imply: % 149.07/21.55 | | | (7427) ~ (all_52_4 = all_6_0) % 149.07/21.55 | | | % 149.07/21.55 | | | REDUCE: (176), (7422) imply: % 149.07/21.55 | | | (7428) ~ (all_52_7 = all_6_0) % 149.07/21.55 | | | % 149.07/21.55 | | | SIMP: (7428) implies: % 149.07/21.55 | | | (7429) ~ (all_52_7 = all_6_0) % 149.07/21.55 | | | % 149.07/21.55 | | | REDUCE: (174), (7422) imply: % 149.07/21.55 | | | (7430) ~ (all_52_14 = all_6_0) % 149.07/21.55 | | | % 149.07/21.55 | | | SIMP: (7430) implies: % 149.07/21.55 | | | (7431) ~ (all_52_14 = all_6_0) % 149.07/21.55 | | | % 149.07/21.55 | | | REDUCE: (573), (7422) imply: % 149.07/21.55 | | | (7432) ~ (all_8_2 = all_6_0) % 149.07/21.55 | | | % 149.07/21.55 | | | SIMP: (7432) implies: % 149.07/21.55 | | | (7433) ~ (all_8_2 = all_6_0) % 149.07/21.55 | | | % 149.07/21.55 | | | REDUCE: (580), (7422) imply: % 149.07/21.55 | | | (7434) ~ (all_6_0 = all_6_2) % 149.07/21.55 | | | % 149.07/21.55 | | | REDUCE: (618), (7422) imply: % 149.07/21.55 | | | (7435) op(e2, all_6_0) = all_56_18 % 149.07/21.55 | | | % 149.07/21.55 | | | BETA: splitting (49) gives: % 149.07/21.55 | | | % 149.07/21.55 | | | Case 1: % 149.07/21.55 | | | | % 149.07/21.55 | | | | (7436) ~ (all_8_1 = e1) % 149.07/21.55 | | | | % 149.07/21.55 | | | | BETA: splitting (54) gives: % 149.07/21.55 | | | | % 149.07/21.55 | | | | Case 1: % 149.07/21.55 | | | | | % 149.07/21.55 | | | | | (7437) ~ (all_10_0 = e2) % 149.07/21.55 | | | | | % 149.07/21.55 | | | | | BETA: splitting (59) gives: % 149.07/21.55 | | | | | % 149.07/21.55 | | | | | Case 1: % 149.07/21.55 | | | | | | % 149.07/21.55 | | | | | | (7438) ~ (all_12_0 = e2) % 149.07/21.55 | | | | | | % 149.07/21.55 | | | | | | REDUCE: (759), (7438) imply: % 149.07/21.55 | | | | | | (7439) ~ (all_4_0 = e2) % 149.07/21.55 | | | | | | % 149.07/21.55 | | | | | | BETA: splitting (64) gives: % 149.07/21.55 | | | | | | % 149.07/21.55 | | | | | | Case 1: % 149.07/21.55 | | | | | | | % 149.07/21.55 | | | | | | | (7440) ~ (all_14_0 = e1) % 149.07/21.55 | | | | | | | % 149.07/21.55 | | | | | | | REDUCE: (758), (7440) imply: % 149.07/21.55 | | | | | | | (7441) ~ (all_8_0 = e1) % 149.07/21.55 | | | | | | | % 149.07/21.55 | | | | | | | BETA: splitting (69) gives: % 149.07/21.55 | | | | | | | % 149.07/21.55 | | | | | | | Case 1: % 149.07/21.55 | | | | | | | | % 149.07/21.55 | | | | | | | | (7442) ~ (all_16_0 = e1) % 149.07/21.55 | | | | | | | | % 149.07/21.55 | | | | | | | | REDUCE: (757), (7442) imply: % 149.07/21.55 | | | | | | | | (7443) ~ (all_10_0 = e1) % 149.07/21.55 | | | | | | | | % 149.07/21.55 | | | | | | | | BETA: splitting (74) gives: % 149.07/21.55 | | | | | | | | % 149.07/21.55 | | | | | | | | Case 1: % 149.07/21.55 | | | | | | | | | % 149.07/21.55 | | | | | | | | | (7444) ~ (all_18_0 = e3) % 149.07/21.55 | | | | | | | | | % 149.07/21.55 | | | | | | | | | REDUCE: (753), (7444) imply: % 149.07/21.55 | | | | | | | | | (7445) ~ (all_6_0 = e3) % 149.07/21.55 | | | | | | | | | % 149.07/21.55 | | | | | | | | | BETA: splitting (84) gives: % 149.07/21.55 | | | | | | | | | % 149.07/21.55 | | | | | | | | | Case 1: % 149.07/21.55 | | | | | | | | | | % 149.07/21.55 | | | | | | | | | | (7446) ~ (all_22_1 = e3) % 149.07/21.55 | | | | | | | | | | % 149.07/21.55 | | | | | | | | | | REDUCE: (672), (7446) imply: % 149.07/21.55 | | | | | | | | | | (7447) ~ (all_8_1 = e3) % 149.07/21.55 | | | | | | | | | | % 149.07/21.55 | | | | | | | | | | BETA: splitting (94) gives: % 149.07/21.55 | | | | | | | | | | % 149.07/21.55 | | | | | | | | | | Case 1: % 149.07/21.55 | | | | | | | | | | | % 149.07/21.55 | | | | | | | | | | | (7448) ~ (all_26_0 = e1) % 149.07/21.55 | | | | | | | | | | | % 149.07/21.55 | | | | | | | | | | | REDUCE: (760), (7448) imply: % 149.07/21.55 | | | | | | | | | | | (7449) ~ (all_4_0 = e1) % 149.07/21.55 | | | | | | | | | | | % 149.07/21.55 | | | | | | | | | | | BETA: splitting (104) gives: % 149.07/21.55 | | | | | | | | | | | % 149.07/21.55 | | | | | | | | | | | Case 1: % 149.07/21.55 | | | | | | | | | | | | % 149.07/21.55 | | | | | | | | | | | | (7450) ~ (all_30_0 = e3) % 149.07/21.55 | | | | | | | | | | | | % 149.07/21.55 | | | | | | | | | | | | REDUCE: (718), (7450) imply: % 149.07/21.55 | | | | | | | | | | | | (7451) ~ (all_8_0 = e3) % 149.07/21.55 | | | | | | | | | | | | % 149.07/21.55 | | | | | | | | | | | | BETA: splitting (109) gives: % 149.07/21.55 | | | | | | | | | | | | % 149.07/21.55 | | | | | | | | | | | | Case 1: % 149.07/21.55 | | | | | | | | | | | | | % 149.07/21.55 | | | | | | | | | | | | | (7452) ~ (all_32_1 = e1) % 149.07/21.55 | | | | | | | | | | | | | % 149.07/21.55 | | | | | | | | | | | | | REDUCE: (682), (7452) imply: % 149.07/21.55 | | | | | | | | | | | | | (7453) ~ (all_10_1 = e1) % 149.07/21.55 | | | | | | | | | | | | | % 149.07/21.55 | | | | | | | | | | | | | BETA: splitting (124) gives: % 149.07/21.55 | | | | | | | | | | | | | % 149.07/21.55 | | | | | | | | | | | | | Case 1: % 149.07/21.55 | | | | | | | | | | | | | | % 149.07/21.55 | | | | | | | | | | | | | | (7454) ~ (all_38_1 = e2) % 149.07/21.55 | | | | | | | | | | | | | | % 149.07/21.55 | | | | | | | | | | | | | | REDUCE: (684), (7454) imply: % 149.07/21.55 | | | | | | | | | | | | | | (7455) ~ (all_10_1 = e2) % 149.07/21.55 | | | | | | | | | | | | | | % 149.07/21.55 | | | | | | | | | | | | | | BETA: splitting (292) gives: % 149.07/21.55 | | | | | | | | | | | | | | % 149.07/21.55 | | | | | | | | | | | | | | Case 1: % 149.07/21.55 | | | | | | | | | | | | | | | % 149.07/21.55 | | | | | | | | | | | | | | | (7456) ~ (all_56_21 = e2) % 149.07/21.55 | | | | | | | | | | | | | | | % 149.07/21.55 | | | | | | | | | | | | | | | REDUCE: (374), (7456) imply: % 149.07/21.55 | | | | | | | | | | | | | | | (7457) ~ (all_6_2 = e2) % 149.07/21.55 | | | | | | | | | | | | | | | % 149.07/21.55 | | | | | | | | | | | | | | | BETA: splitting (294) gives: % 149.07/21.55 | | | | | | | | | | | | | | | % 149.07/21.55 | | | | | | | | | | | | | | | Case 1: % 149.07/21.55 | | | | | | | | | | | | | | | | % 149.07/21.55 | | | | | | | | | | | | | | | | (7458) ~ (all_56_11 = e0) % 149.07/21.55 | | | | | | | | | | | | | | | | % 149.07/21.55 | | | | | | | | | | | | | | | | REF_CLOSE: (8), (36), (38), (41), (47), (48), (51), (53), % 149.07/21.55 | | | | | | | | | | | | | | | | (161), (168), (169), (181), (182), (188), (189), % 149.07/21.55 | | | | | | | | | | | | | | | | (192), (193), (194), (196), (212), (237), (240), % 149.07/21.55 | | | | | | | | | | | | | | | | (241), (242), (243), (245), (247), (250), (251), % 149.07/21.55 | | | | | | | | | | | | | | | | (252), (287), (291), (293), (295), (296), (297), % 149.07/21.55 | | | | | | | | | | | | | | | | (327), (330), (331), (337), (343), (366), (374), % 149.07/21.55 | | | | | | | | | | | | | | | | (381), (389), (402), (407), (419), (425), (431), % 149.07/21.55 | | | | | | | | | | | | | | | | (457), (459), (469), (476), (478), (540), (541), % 149.07/21.55 | | | | | | | | | | | | | | | | (542), (543), (544), (545), (546), (548), (549), % 149.07/21.55 | | | | | | | | | | | | | | | | (550), (552), (553), (554), (555), (557), (559), % 149.07/21.55 | | | | | | | | | | | | | | | | (561), (563), (565), (567), (569), (577), (583), % 149.07/21.55 | | | | | | | | | | | | | | | | (585), (587), (588), (590), (591), (612), (622), % 149.07/21.55 | | | | | | | | | | | | | | | | (627), (7418), (7420), (7423), (7425), (7426), % 149.07/21.55 | | | | | | | | | | | | | | | | (7431), (7433), (7434), (7436), (7441), (7445), % 149.07/21.55 | | | | | | | | | | | | | | | | (7447), (7453), (7455), (7457), (7458), % 149.07/21.55 | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 149.07/21.55 | | | | | | | | | | | | | | | | #78. % 149.07/21.55 | | | | | | | | | | | | | | | | % 149.07/21.55 | | | | | | | | | | | | | | | Case 2: % 149.07/21.55 | | | | | | | | | | | | | | | | % 149.07/21.55 | | | | | | | | | | | | | | | | (7459) all_56_11 = e0 % 149.07/21.55 | | | | | | | | | | | | | | | | % 149.07/21.55 | | | | | | | | | | | | | | | | COMBINE_EQS: (545), (7459) imply: % 149.07/21.55 | | | | | | | | | | | | | | | | (7460) all_8_2 = e0 % 149.07/21.55 | | | | | | | | | | | | | | | | % 149.07/21.55 | | | | | | | | | | | | | | | | REDUCE: (48), (7460) imply: % 149.07/21.55 | | | | | | | | | | | | | | | | (7461) op(e0, e0) = all_8_1 % 149.07/21.55 | | | | | | | | | | | | | | | | % 149.07/21.55 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_4_2, % 149.07/21.55 | | | | | | | | | | | | | | | | all_8_1, e0, e0, simplifying with (36), (7461) % 149.07/21.55 | | | | | | | | | | | | | | | | gives: % 149.07/21.55 | | | | | | | | | | | | | | | | (7462) all_8_1 = all_4_2 % 149.07/21.55 | | | | | | | | | | | | | | | | % 149.07/21.55 | | | | | | | | | | | | | | | | REDUCE: (7447), (7462) imply: % 149.07/21.55 | | | | | | | | | | | | | | | | (7463) ~ (all_4_2 = e3) % 149.07/21.55 | | | | | | | | | | | | | | | | % 149.07/21.55 | | | | | | | | | | | | | | | | REDUCE: (7436), (7462) imply: % 149.07/21.55 | | | | | | | | | | | | | | | | (7464) ~ (all_4_2 = e1) % 149.07/21.55 | | | | | | | | | | | | | | | | % 149.07/21.55 | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (8), (36), (38), (41), (188), (192), % 149.07/21.55 | | | | | | | | | | | | | | | | (237), (240), (242), (243), (287), (289), (291), % 149.07/21.55 | | | | | | | | | | | | | | | | (293), (324), (326), (327), (360), (366), (374), % 149.07/21.55 | | | | | | | | | | | | | | | | (381), (478), (540), (541), (544), (545), (546), % 149.07/21.55 | | | | | | | | | | | | | | | | (550), (552), (553), (559), (561), (569), (570), % 149.07/21.55 | | | | | | | | | | | | | | | | (587), (591), (622), (627), (7418), (7420), % 149.07/21.55 | | | | | | | | | | | | | | | | (7423), (7425), (7429), (7431), (7433), (7434), % 149.07/21.55 | | | | | | | | | | | | | | | | (7445), (7457), (7463), (7464), (function-axioms) % 149.07/21.55 | | | | | | | | | | | | | | | | are inconsistent by sub-proof #74. % 149.07/21.55 | | | | | | | | | | | | | | | | % 149.07/21.55 | | | | | | | | | | | | | | | End of split % 149.07/21.55 | | | | | | | | | | | | | | | % 149.07/21.55 | | | | | | | | | | | | | | Case 2: % 149.07/21.55 | | | | | | | | | | | | | | | % 149.07/21.55 | | | | | | | | | | | | | | | (7465) all_56_21 = e2 % 149.07/21.55 | | | | | | | | | | | | | | | (7466) all_56_19 = e1 % 149.07/21.55 | | | | | | | | | | | | | | | % 149.07/21.55 | | | | | | | | | | | | | | | COMBINE_EQS: (7424), (7466) imply: % 149.07/21.55 | | | | | | | | | | | | | | | (7467) all_6_0 = e1 % 149.07/21.55 | | | | | | | | | | | | | | | % 149.07/21.55 | | | | | | | | | | | | | | | SIMP: (7467) implies: % 149.07/21.56 | | | | | | | | | | | | | | | (7468) all_6_0 = e1 % 149.07/21.56 | | | | | | | | | | | | | | | % 149.07/21.56 | | | | | | | | | | | | | | | COMBINE_EQS: (374), (7465) imply: % 149.07/21.56 | | | | | | | | | | | | | | | (7469) all_6_2 = e2 % 149.07/21.56 | | | | | | | | | | | | | | | % 149.07/21.56 | | | | | | | | | | | | | | | SIMP: (7469) implies: % 149.07/21.56 | | | | | | | | | | | | | | | (7470) all_6_2 = e2 % 149.07/21.56 | | | | | | | | | | | | | | | % 149.07/21.56 | | | | | | | | | | | | | | | REDUCE: (7426), (7468) imply: % 149.07/21.56 | | | | | | | | | | | | | | | (7471) ~ (all_52_2 = e1) % 149.07/21.56 | | | | | | | | | | | | | | | % 149.07/21.56 | | | | | | | | | | | | | | | REDUCE: (569), (7470) imply: % 149.07/21.56 | | | | | | | | | | | | | | | (7472) ~ (all_52_2 = e2) % 149.07/21.56 | | | | | | | | | | | | | | | % 149.07/21.56 | | | | | | | | | | | | | | | REDUCE: (7427), (7468) imply: % 149.07/21.56 | | | | | | | | | | | | | | | (7473) ~ (all_52_4 = e1) % 149.07/21.56 | | | | | | | | | | | | | | | % 149.07/21.56 | | | | | | | | | | | | | | | REDUCE: (7429), (7468) imply: % 149.07/21.56 | | | | | | | | | | | | | | | (7474) ~ (all_52_7 = e1) % 149.07/21.56 | | | | | | | | | | | | | | | % 149.07/21.56 | | | | | | | | | | | | | | | REDUCE: (7431), (7468) imply: % 149.07/21.56 | | | | | | | | | | | | | | | (7475) ~ (all_52_14 = e1) % 149.07/21.56 | | | | | | | | | | | | | | | % 149.07/21.56 | | | | | | | | | | | | | | | REDUCE: (587), (7470) imply: % 149.07/21.56 | | | | | | | | | | | | | | | (7476) ~ (all_52_14 = e2) % 149.07/21.56 | | | | | | | | | | | | | | | % 149.07/21.56 | | | | | | | | | | | | | | | REDUCE: (7420), (7470) imply: % 149.07/21.56 | | | | | | | | | | | | | | | (7477) op(e2, e2) = e2 % 149.07/21.56 | | | | | | | | | | | | | | | % 149.07/21.56 | | | | | | | | | | | | | | | REDUCE: (41), (7470) imply: % 149.07/21.56 | | | | | | | | | | | | | | | (7478) op(e1, e1) = e2 % 149.07/21.56 | | | | | | | | | | | | | | | % 149.07/21.56 | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_8_2, e2, % 149.07/21.56 | | | | | | | | | | | | | | | e2, e2, simplifying with (46), (7477) gives: % 149.07/21.56 | | | | | | | | | | | | | | | (7479) all_8_2 = e2 % 149.07/21.56 | | | | | | | | | | | | | | | % 149.07/21.56 | | | | | | | | | | | | | | | REDUCE: (568), (7479) imply: % 149.07/21.56 | | | | | | | | | | | | | | | (7480) ~ (all_52_1 = e2) % 149.07/21.56 | | | | | | | | | | | | | | | % 149.07/21.56 | | | | | | | | | | | | | | | REDUCE: (571), (7479) imply: % 149.07/21.56 | | | | | | | | | | | | | | | (7481) ~ (all_52_4 = e2) % 149.07/21.56 | | | | | | | | | | | | | | | % 149.07/21.56 | | | | | | | | | | | | | | | REDUCE: (575), (7479) imply: % 149.07/21.56 | | | | | | | | | | | | | | | (7482) ~ (all_52_7 = e2) % 149.07/21.56 | | | | | | | | | | | | | | | % 149.07/21.56 | | | | | | | | | | | | | | | REDUCE: (579), (7479) imply: % 149.07/21.56 | | | | | | | | | | | | | | | (7483) ~ (all_52_13 = e2) % 149.07/21.56 | | | | | | | | | | | | | | | % 149.07/21.56 | | | | | | | | | | | | | | | REDUCE: (48), (7479) imply: % 149.07/21.56 | | | | | | | | | | | | | | | (7484) op(e2, e2) = all_8_1 % 149.07/21.56 | | | | | | | | | | | | | | | % 149.07/21.56 | | | | | | | | | | | | | | | REDUCE: (617), (7479) imply: % 149.07/21.56 | | | | | | | | | | | | | | | (7485) op(e2, e2) = all_56_10 % 149.07/21.56 | | | | | | | | | | | | | | | % 149.07/21.56 | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, % 149.07/21.56 | | | | | | | | | | | | | | | all_56_10, e2, e2, simplifying with (7477), (7485) % 149.07/21.56 | | | | | | | | | | | | | | | gives: % 149.07/21.56 | | | | | | | | | | | | | | | (7486) all_56_10 = e2 % 149.07/21.56 | | | | | | | | | | | | | | | % 149.07/21.56 | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_8_1, % 149.07/21.56 | | | | | | | | | | | | | | | all_56_10, e2, e2, simplifying with (7484), (7485) % 149.07/21.56 | | | | | | | | | | | | | | | gives: % 149.07/21.56 | | | | | | | | | | | | | | | (7487) all_56_10 = all_8_1 % 149.07/21.56 | | | | | | | | | | | | | | | % 149.07/21.56 | | | | | | | | | | | | | | | COMBINE_EQS: (7486), (7487) imply: % 149.07/21.56 | | | | | | | | | | | | | | | (7488) all_8_1 = e2 % 149.07/21.56 | | | | | | | | | | | | | | | % 149.07/21.56 | | | | | | | | | | | | | | | SIMP: (7488) implies: % 149.07/21.56 | | | | | | | | | | | | | | | (7489) all_8_1 = e2 % 149.07/21.56 | | | | | | | | | | | | | | | % 149.07/21.56 | | | | | | | | | | | | | | | REDUCE: (47), (7489) imply: % 149.07/21.56 | | | | | | | | | | | | | | | (7490) op(e2, e2) = all_8_0 % 149.07/21.56 | | | | | | | | | | | | | | | % 149.07/21.56 | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, all_8_0, % 149.07/21.56 | | | | | | | | | | | | | | | e2, e2, simplifying with (7477), (7490) gives: % 149.07/21.56 | | | | | | | | | | | | | | | (7491) all_8_0 = e2 % 149.07/21.56 | | | | | | | | | | | | | | | % 149.07/21.56 | | | | | | | | | | | | | | | REDUCE: (7451), (7491) imply: % 149.07/21.56 | | | | | | | | | | | | | | | (7492) ~ (e3 = e2) % 149.07/21.56 | | | | | | | | | | | | | | | % 149.07/21.56 | | | | | | | | | | | | | | | BETA: splitting (288) gives: % 149.07/21.56 | | | | | | | | | | | | | | | % 149.07/21.56 | | | | | | | | | | | | | | | Case 1: % 149.07/21.56 | | | | | | | | | | | | | | | | % 149.07/21.56 | | | | | | | | | | | | | | | | (7493) ~ (all_56_31 = e1) % 149.07/21.56 | | | | | | | | | | | | | | | | % 149.07/21.56 | | | | | | | | | | | | | | | | REDUCE: (544), (7493) imply: % 149.07/21.56 | | | | | | | | | | | | | | | | (7494) ~ (all_4_2 = e1) % 149.07/21.56 | | | | | | | | | | | | | | | | % 149.07/21.56 | | | | | | | | | | | | | | | | BETA: splitting (290) gives: % 149.07/21.56 | | | | | | | | | | | | | | | | % 149.07/21.56 | | | | | | | | | | | | | | | | Case 1: % 149.07/21.56 | | | | | | | | | | | | | | | | | % 149.07/21.56 | | | | | | | | | | | | | | | | | (7495) ~ (all_56_31 = e3) % 149.07/21.56 | | | | | | | | | | | | | | | | | % 149.07/21.56 | | | | | | | | | | | | | | | | | REDUCE: (544), (7495) imply: % 149.07/21.56 | | | | | | | | | | | | | | | | | (7496) ~ (all_4_2 = e3) % 149.07/21.56 | | | | | | | | | | | | | | | | | % 149.07/21.56 | | | | | | | | | | | | | | | | | BETA: splitting (289) gives: % 149.07/21.56 | | | | | | | | | | | | | | | | | % 149.07/21.56 | | | | | | | | | | | | | | | | | Case 1: % 149.07/21.56 | | | | | | | | | | | | | | | | | | % 149.07/21.56 | | | | | | | | | | | | | | | | | | (7497) ~ (all_56_31 = e2) % 149.07/21.56 | | | | | | | | | | | | | | | | | | % 149.07/21.56 | | | | | | | | | | | | | | | | | | REDUCE: (544), (7497) imply: % 149.07/21.56 | | | | | | | | | | | | | | | | | | (7498) ~ (all_4_2 = e2) % 149.07/21.56 | | | | | | | | | | | | | | | | | | % 149.07/21.56 | | | | | | | | | | | | | | | | | | BETA: splitting (322) gives: % 149.07/21.56 | | | | | | | | | | | | | | | | | | % 149.07/21.56 | | | | | | | | | | | | | | | | | | Case 1: % 149.07/21.56 | | | | | | | | | | | | | | | | | | | % 149.07/21.56 | | | | | | | | | | | | | | | | | | | (7499) all_58_9 = e2 % 149.07/21.56 | | | | | | | | | | | | | | | | | | | % 149.07/21.56 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (551), (7499) imply: % 149.07/21.56 | | | | | | | | | | | | | | | | | | | (7500) all_52_12 = e2 % 149.07/21.56 | | | | | | | | | | | | | | | | | | | % 149.07/21.56 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (402), (7500) imply: % 149.07/21.56 | | | | | | | | | | | | | | | | | | | (7501) all_56_7 = e2 % 149.07/21.56 | | | | | | | | | | | | | | | | | | | % 149.07/21.56 | | | | | | | | | | | | | | | | | | | REDUCE: (567), (7500) imply: % 149.07/21.56 | | | | | | | | | | | | | | | | | | | (7502) ~ (all_10_2 = e2) % 149.07/21.56 | | | | | | | | | | | | | | | | | | | % 149.07/21.56 | | | | | | | | | | | | | | | | | | | SIMP: (7502) implies: % 149.07/21.56 | | | | | | | | | | | | | | | | | | | (7503) ~ (all_10_2 = e2) % 149.07/21.56 | | | | | | | | | | | | | | | | | | | % 149.07/21.56 | | | | | | | | | | | | | | | | | | | BETA: splitting (297) gives: % 149.07/21.56 | | | | | | | | | | | | | | | | | | | % 149.07/21.56 | | | | | | | | | | | | | | | | | | | Case 1: % 149.07/21.56 | | | | | | | | | | | | | | | | | | | | % 149.07/21.56 | | | | | | | | | | | | | | | | | | | | (7504) ~ (all_56_1 = e0) % 149.07/21.56 | | | | | | | | | | | | | | | | | | | | % 149.07/21.56 | | | | | | | | | | | | | | | | | | | | REDUCE: (546), (7504) imply: % 149.07/21.56 | | | | | | | | | | | | | | | | | | | | (7505) ~ (all_10_2 = e0) % 149.07/21.56 | | | | | | | | | | | | | | | | | | | | % 149.07/21.56 | | | | | | | | | | | | | | | | | | | | BETA: splitting (321) gives: % 149.07/21.56 | | | | | | | | | | | | | | | | | | | | % 149.07/21.56 | | | | | | | | | | | | | | | | | | | | Case 1: % 149.07/21.56 | | | | | | | | | | | | | | | | | | | | | % 149.07/21.56 | | | | | | | | | | | | | | | | | | | | | (7506) all_58_9 = e1 % 149.07/21.56 | | | | | | | | | | | | | | | | | | | | | % 149.07/21.56 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (7499), (7506) imply: % 149.07/21.56 | | | | | | | | | | | | | | | | | | | | | (7507) e2 = e1 % 149.07/21.56 | | | | | | | | | | | | | | | | | | | | | % 149.07/21.56 | | | | | | | | | | | | | | | | | | | | | REDUCE: (6), (7507) imply: % 149.07/21.56 | | | | | | | | | | | | | | | | | | | | | (7508) $false % 149.07/21.56 | | | | | | | | | | | | | | | | | | | | | % 149.07/21.56 | | | | | | | | | | | | | | | | | | | | | CLOSE: (7508) is inconsistent. % 149.07/21.56 | | | | | | | | | | | | | | | | | | | | | % 149.07/21.56 | | | | | | | | | | | | | | | | | | | | Case 2: % 149.07/21.56 | | | | | | | | | | | | | | | | | | | | | % 149.07/21.56 | | | | | | | | | | | | | | | | | | | | | (7509) all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1 % 149.07/21.56 | | | | | | | | | | | | | | | | | | | | | % 149.07/21.56 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7509) gives: % 149.07/21.56 | | | | | | | | | | | | | | | | | | | | | % 149.07/21.56 | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.07/21.56 | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.56 | | | | | | | | | | | | | | | | | | | | | | (7510) all_58_10 = e1 % 149.07/21.56 | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.56 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (386), (7510) imply: % 149.07/21.56 | | | | | | | | | | | | | | | | | | | | | | (7511) all_52_13 = e1 % 149.07/21.56 | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.56 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (193), (7511) imply: % 149.07/21.56 | | | | | | | | | | | | | | | | | | | | | | (7512) ~ (all_52_1 = e1) % 149.07/21.56 | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.56 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (342) gives: % 149.07/21.56 | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.56 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.07/21.56 | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.56 | | | | | | | | | | | | | | | | | | | | | | | (7513) all_58_0 = e1 % 149.07/21.56 | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.56 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (419), (7513) imply: % 149.07/21.56 | | | | | | | | | | | | | | | | | | | | | | | (7514) all_10_2 = e1 % 149.07/21.56 | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.56 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (53), (7514) imply: % 149.07/21.56 | | | | | | | | | | | | | | | | | | | | | | | (7515) op(e1, e1) = all_10_1 % 149.07/21.56 | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.56 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, all_10_1, % 149.07/21.56 | | | | | | | | | | | | | | | | | | | | | | | e1, e1, simplifying with (7478), (7515) gives: % 149.07/21.56 | | | | | | | | | | | | | | | | | | | | | | | (7516) all_10_1 = e2 % 149.07/21.56 | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.56 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7455), (7516) imply: % 149.07/21.56 | | | | | | | | | | | | | | | | | | | | | | | (7517) $false % 149.07/21.56 | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.56 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (7517) is inconsistent. % 149.07/21.56 | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.56 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.07/21.56 | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.56 | | | | | | | | | | | | | | | | | | | | | | | (7518) ~ (all_58_0 = e1) % 149.07/21.56 | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.56 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (197), (244), (248), (252), (419), (463), (471), % 149.07/21.56 | | | | | | | | | | | | | | | | | | | | | | | (543), (557), (559), (7471), (7472), (7480), % 149.07/21.56 | | | | | | | | | | | | | | | | | | | | | | | (7503), (7505), (7512), (7518) are inconsistent by % 149.07/21.56 | | | | | | | | | | | | | | | | | | | | | | | sub-proof #73. % 149.07/21.56 | | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.56 | | | | | | | | | | | | | | | | | | | | | | End of split % 149.07/21.56 | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.56 | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.07/21.56 | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.56 | | | | | | | | | | | | | | | | | | | | | | (7519) all_58_11 = e1 | all_58_15 = e1 % 149.07/21.56 | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.56 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (547), (550), (7475), (7494), (7519) are % 149.07/21.56 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #672. % 149.07/21.56 | | | | | | | | | | | | | | | | | | | | | | % 149.07/21.56 | | | | | | | | | | | | | | | | | | | | | End of split % 149.07/21.56 | | | | | | | | | | | | | | | | | | | | | % 149.07/21.56 | | | | | | | | | | | | | | | | | | | | End of split % 149.07/21.56 | | | | | | | | | | | | | | | | | | | | % 149.07/21.56 | | | | | | | | | | | | | | | | | | | Case 2: % 149.07/21.56 | | | | | | | | | | | | | | | | | | | | % 149.07/21.56 | | | | | | | | | | | | | | | | | | | | (7520) all_56_7 = e3 % 149.07/21.56 | | | | | | | | | | | | | | | | | | | | % 149.07/21.56 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (7501), (7520) imply: % 149.07/21.56 | | | | | | | | | | | | | | | | | | | | (7521) e3 = e2 % 149.07/21.56 | | | | | | | | | | | | | | | | | | | | % 149.07/21.56 | | | | | | | | | | | | | | | | | | | | REDUCE: (9), (7521) imply: % 149.07/21.56 | | | | | | | | | | | | | | | | | | | | (7522) $false % 149.07/21.56 | | | | | | | | | | | | | | | | | | | | % 149.07/21.56 | | | | | | | | | | | | | | | | | | | | CLOSE: (7522) is inconsistent. % 149.07/21.56 | | | | | | | | | | | | | | | | | | | | % 149.07/21.56 | | | | | | | | | | | | | | | | | | | End of split % 149.07/21.56 | | | | | | | | | | | | | | | | | | | % 149.07/21.56 | | | | | | | | | | | | | | | | | | Case 2: % 149.07/21.56 | | | | | | | | | | | | | | | | | | | % 149.07/21.56 | | | | | | | | | | | | | | | | | | | (7523) all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2 % 149.07/21.56 | | | | | | | | | | | | | | | | | | | % 149.07/21.56 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (386), (547), (550), (7476), (7483), (7498), % 149.07/21.56 | | | | | | | | | | | | | | | | | | | (7523) are inconsistent by sub-proof #693. % 149.07/21.56 | | | | | | | | | | | | | | | | | | | % 149.07/21.56 | | | | | | | | | | | | | | | | | | End of split % 149.07/21.56 | | | | | | | | | | | | | | | | | | % 149.07/21.56 | | | | | | | | | | | | | | | | | Case 2: % 149.07/21.56 | | | | | | | | | | | | | | | | | | % 149.07/21.56 | | | | | | | | | | | | | | | | | | (7524) all_56_31 = e2 % 149.07/21.56 | | | | | | | | | | | | | | | | | | (7525) all_56_27 = e0 % 149.07/21.56 | | | | | | | | | | | | | | | | | | % 149.07/21.56 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (360), (7525) imply: % 149.07/21.56 | | | | | | | | | | | | | | | | | | (7526) all_52_7 = e0 % 149.07/21.56 | | | | | | | | | | | | | | | | | | % 149.07/21.56 | | | | | | | | | | | | | | | | | | SIMP: (7526) implies: % 149.07/21.56 | | | | | | | | | | | | | | | | | | (7527) all_52_7 = e0 % 149.07/21.56 | | | | | | | | | | | | | | | | | | % 149.07/21.56 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (544), (7524) imply: % 149.07/21.56 | | | | | | | | | | | | | | | | | | (7528) all_4_2 = e2 % 149.07/21.56 | | | | | | | | | | | | | | | | | | % 149.07/21.56 | | | | | | | | | | | | | | | | | | REDUCE: (183), (7527) imply: % 149.07/21.56 | | | | | | | | | | | | | | | | | | (7529) ~ (all_52_4 = e0) % 149.07/21.56 | | | | | | | | | | | | | | | | | | % 149.07/21.56 | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (53), (168), (169), (181), (182), (183), % 149.07/21.56 | | | | | | | | | | | | | | | | | | (237), (250), (251), (252), (289), (297), (298), % 149.07/21.56 | | | | | | | | | | | | | | | | | | (318), (319), (322), (339), (343), (344), (360), % 149.07/21.56 | | | | | | | | | | | | | | | | | | (365), (386), (401), (402), (407), (419), (429), % 149.07/21.56 | | | | | | | | | | | | | | | | | | (457), (459), (540), (543), (544), (546), (547), % 149.07/21.56 | | | | | | | | | | | | | | | | | | (548), (549), (550), (551), (553), (555), (563), % 149.07/21.56 | | | | | | | | | | | | | | | | | | (567), (589), (7455), (7472), (7473), (7474), % 149.07/21.56 | | | | | | | | | | | | | | | | | | (7476), (7477), (7480), (7481), (7483), (7494), % 149.07/21.56 | | | | | | | | | | | | | | | | | | (7496), (7529), (function-axioms) are inconsistent % 149.07/21.56 | | | | | | | | | | | | | | | | | | by sub-proof #72. % 149.07/21.56 | | | | | | | | | | | | | | | | | | % 149.07/21.56 | | | | | | | | | | | | | | | | | End of split % 149.07/21.56 | | | | | | | | | | | | | | | | | % 149.07/21.56 | | | | | | | | | | | | | | | | Case 2: % 149.07/21.56 | | | | | | | | | | | | | | | | | % 149.07/21.56 | | | | | | | | | | | | | | | | | (7530) all_56_31 = e3 % 149.07/21.56 | | | | | | | | | | | | | | | | | (7531) all_56_25 = e0 % 149.07/21.56 | | | | | | | | | | | | | | | | | % 149.07/21.56 | | | | | | | | | | | | | | | | | REF_CLOSE: (188), (239), (447), (480), (544), (581), (7474), % 149.07/21.56 | | | | | | | | | | | | | | | | | (7482), (7530), (7531) are inconsistent by % 149.07/21.56 | | | | | | | | | | | | | | | | | sub-proof #71. % 149.07/21.56 | | | | | | | | | | | | | | | | | % 149.07/21.56 | | | | | | | | | | | | | | | | End of split % 149.07/21.56 | | | | | | | | | | | | | | | | % 149.07/21.56 | | | | | | | | | | | | | | | Case 2: % 149.07/21.56 | | | | | | | | | | | | | | | | % 149.07/21.56 | | | | | | | | | | | | | | | | (7532) all_56_31 = e1 % 149.07/21.56 | | | | | | | | | | | | | | | | (7533) all_56_29 = e0 % 149.07/21.56 | | | | | | | | | | | | | | | | % 149.07/21.56 | | | | | | | | | | | | | | | | COMBINE_EQS: (357), (7533) imply: % 149.07/21.56 | | | | | | | | | | | | | | | | (7534) all_52_11 = e0 % 149.07/21.56 | | | | | | | | | | | | | | | | % 149.07/21.56 | | | | | | | | | | | | | | | | SIMP: (7534) implies: % 149.07/21.56 | | | | | | | | | | | | | | | | (7535) all_52_11 = e0 % 149.07/21.56 | | | | | | | | | | | | | | | | % 149.07/21.56 | | | | | | | | | | | | | | | | COMBINE_EQS: (544), (7532) imply: % 149.07/21.56 | | | | | | | | | | | | | | | | (7536) all_4_2 = e1 % 149.07/21.56 | | | | | | | | | | | | | | | | % 149.07/21.56 | | | | | | | | | | | | | | | | COMBINE_EQS: (547), (7536) imply: % 149.07/21.56 | | | | | | | | | | | | | | | | (7537) all_58_15 = e1 % 149.07/21.56 | | | | | | | | | | | | | | | | % 149.07/21.56 | | | | | | | | | | | | | | | | REDUCE: (173), (7535) imply: % 149.07/21.56 | | | | | | | | | | | | | | | | (7538) ~ (all_52_7 = e0) % 149.07/21.56 | | | | | | | | | | | | | | | | % 149.07/21.56 | | | | | | | | | | | | | | | | REDUCE: (38), (7536) imply: % 149.07/21.56 | | | | | | | | | | | | | | | | (7539) op(e1, e1) = all_4_1 % 149.07/21.56 | | | | | | | | | | | | | | | | % 149.33/21.56 | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9), (37), (206), (239), (297), (322), (386), % 149.33/21.56 | | | | | | | | | | | | | | | | (402), (480), (550), (551), (767), (7439), (7474), % 149.33/21.56 | | | | | | | | | | | | | | | | (7476), (7478), (7483), (7537), (7538), (7539), % 149.33/21.56 | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 149.33/21.56 | | | | | | | | | | | | | | | | #68. % 149.33/21.56 | | | | | | | | | | | | | | | | % 149.33/21.56 | | | | | | | | | | | | | | | End of split % 149.33/21.56 | | | | | | | | | | | | | | | % 149.33/21.56 | | | | | | | | | | | | | | End of split % 149.33/21.56 | | | | | | | | | | | | | | % 149.33/21.56 | | | | | | | | | | | | | Case 2: % 149.33/21.56 | | | | | | | | | | | | | | % 149.33/21.56 | | | | | | | | | | | | | | (7540) all_38_1 = e2 % 149.33/21.56 | | | | | | | | | | | | | | (7541) ~ (all_38_0 = e0) | ~ (all_38_2 = e1) % 149.33/21.56 | | | | | | | | | | | | | | % 149.33/21.56 | | | | | | | | | | | | | | COMBINE_EQS: (684), (7540) imply: % 149.33/21.56 | | | | | | | | | | | | | | (7542) all_10_1 = e2 % 149.33/21.56 | | | | | | | | | | | | | | % 149.33/21.56 | | | | | | | | | | | | | | SIMP: (7542) implies: % 149.33/21.56 | | | | | | | | | | | | | | (7543) all_10_1 = e2 % 149.33/21.56 | | | | | | | | | | | | | | % 149.33/21.56 | | | | | | | | | | | | | | REDUCE: (53), (7543) imply: % 149.33/21.56 | | | | | | | | | | | | | | (7544) op(all_10_2, all_10_2) = e2 % 149.33/21.56 | | | | | | | | | | | | | | % 149.33/21.56 | | | | | | | | | | | | | | REDUCE: (52), (7543) imply: % 149.33/21.56 | | | | | | | | | | | | | | (7545) op(e3, e2) = all_10_0 % 149.33/21.56 | | | | | | | | | | | | | | % 149.33/21.56 | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_4, % 149.33/21.56 | | | | | | | | | | | | | | all_10_0, e2, e3, simplifying with (218), (7545) % 149.33/21.56 | | | | | | | | | | | | | | gives: % 149.33/21.56 | | | | | | | | | | | | | | (7546) all_52_4 = all_10_0 % 149.33/21.56 | | | | | | | | | | | | | | % 149.33/21.56 | | | | | | | | | | | | | | COMBINE_EQS: (457), (7546) imply: % 149.33/21.56 | | | | | | | | | | | | | | (7547) all_54_1 = all_10_0 % 149.33/21.56 | | | | | | | | | | | | | | % 149.33/21.56 | | | | | | | | | | | | | | COMBINE_EQS: (408), (7546) imply: % 149.33/21.56 | | | | | | | | | | | | | | (7548) all_56_3 = all_10_0 % 149.33/21.56 | | | | | | | | | | | | | | % 149.33/21.56 | | | | | | | | | | | | | | REDUCE: (183), (7546) imply: % 149.33/21.56 | | | | | | | | | | | | | | (7549) ~ (all_52_7 = all_10_0) % 149.33/21.56 | | | | | | | | | | | | | | % 149.33/21.56 | | | | | | | | | | | | | | SIMP: (7549) implies: % 149.33/21.56 | | | | | | | | | | | | | | (7550) ~ (all_52_7 = all_10_0) % 149.33/21.56 | | | | | | | | | | | | | | % 149.33/21.56 | | | | | | | | | | | | | | REDUCE: (182), (7546) imply: % 149.33/21.56 | | | | | | | | | | | | | | (7551) ~ (all_52_8 = all_10_0) % 149.33/21.56 | | | | | | | | | | | | | | % 149.33/21.56 | | | | | | | | | | | | | | SIMP: (7551) implies: % 149.33/21.56 | | | | | | | | | | | | | | (7552) ~ (all_52_8 = all_10_0) % 149.33/21.56 | | | | | | | | | | | | | | % 149.33/21.56 | | | | | | | | | | | | | | REDUCE: (181), (7546) imply: % 149.33/21.56 | | | | | | | | | | | | | | (7553) ~ (all_52_12 = all_10_0) % 149.33/21.56 | | | | | | | | | | | | | | % 149.33/21.56 | | | | | | | | | | | | | | SIMP: (7553) implies: % 149.33/21.56 | | | | | | | | | | | | | | (7554) ~ (all_52_12 = all_10_0) % 149.33/21.56 | | | | | | | | | | | | | | % 149.33/21.56 | | | | | | | | | | | | | | REDUCE: (563), (7546) imply: % 149.33/21.56 | | | | | | | | | | | | | | (7555) ~ (all_10_0 = all_10_2) % 149.33/21.56 | | | | | | | | | | | | | | % 149.33/21.56 | | | | | | | | | | | | | | REDUCE: (571), (7546) imply: % 149.33/21.56 | | | | | | | | | | | | | | (7556) ~ (all_10_0 = all_8_2) % 149.33/21.56 | | | | | | | | | | | | | | % 149.33/21.56 | | | | | | | | | | | | | | REDUCE: (7427), (7546) imply: % 149.33/21.56 | | | | | | | | | | | | | | (7557) ~ (all_10_0 = all_6_0) % 149.33/21.56 | | | | | | | | | | | | | | % 149.33/21.56 | | | | | | | | | | | | | | REDUCE: (616), (7546) imply: % 149.33/21.56 | | | | | | | | | | | | | | (7558) op(e2, all_10_0) = all_56_2 % 149.33/21.56 | | | | | | | | | | | | | | % 149.33/21.56 | | | | | | | | | | | | | | BETA: splitting (292) gives: % 149.33/21.56 | | | | | | | | | | | | | | % 149.33/21.56 | | | | | | | | | | | | | | Case 1: % 149.33/21.56 | | | | | | | | | | | | | | | % 149.33/21.56 | | | | | | | | | | | | | | | (7559) ~ (all_56_21 = e2) % 149.33/21.56 | | | | | | | | | | | | | | | % 149.33/21.56 | | | | | | | | | | | | | | | REF_CLOSE: (36), (38), (41), (46), (48), (51), (53), (158), % 149.33/21.56 | | | | | | | | | | | | | | | (189), (241), (242), (243), (247), (251), (252), % 149.33/21.56 | | | | | | | | | | | | | | | (287), (291), (293), (294), (295), (296), (297), % 149.33/21.56 | | | | | | | | | | | | | | | (298), (326), (327), (366), (374), (381), (402), % 149.33/21.56 | | | | | | | | | | | | | | | (425), (429), (431), (443), (476), (533), (541), % 149.33/21.56 | | | | | | | | | | | | | | | (542), (543), (544), (545), (546), (550), (552), % 149.33/21.56 | | | | | | | | | | | | | | | (553), (557), (559), (569), (577), (583), (587), % 149.33/21.56 | | | | | | | | | | | | | | | (591), (612), (622), (627), (723), (7418), (7420), % 149.33/21.56 | | | | | | | | | | | | | | | (7423), (7425), (7426), (7431), (7433), (7434), % 149.33/21.56 | | | | | | | | | | | | | | | (7435), (7436), (7437), (7443), (7445), (7447), % 149.33/21.56 | | | | | | | | | | | | | | | (7541), (7544), (7547), (7552), (7554), (7555), % 149.33/21.56 | | | | | | | | | | | | | | | (7556), (7559), (function-axioms) are inconsistent % 149.33/21.56 | | | | | | | | | | | | | | | by sub-proof #65. % 149.33/21.56 | | | | | | | | | | | | | | | % 149.33/21.56 | | | | | | | | | | | | | | Case 2: % 149.33/21.56 | | | | | | | | | | | | | | | % 149.33/21.56 | | | | | | | | | | | | | | | (7560) all_56_21 = e2 % 149.33/21.56 | | | | | | | | | | | | | | | (7561) all_56_19 = e1 % 149.33/21.56 | | | | | | | | | | | | | | | % 149.33/21.56 | | | | | | | | | | | | | | | COMBINE_EQS: (7424), (7561) imply: % 149.33/21.56 | | | | | | | | | | | | | | | (7562) all_6_0 = e1 % 149.33/21.56 | | | | | | | | | | | | | | | % 149.33/21.56 | | | | | | | | | | | | | | | SIMP: (7562) implies: % 149.33/21.56 | | | | | | | | | | | | | | | (7563) all_6_0 = e1 % 149.33/21.56 | | | | | | | | | | | | | | | % 149.33/21.56 | | | | | | | | | | | | | | | COMBINE_EQS: (374), (7560) imply: % 149.33/21.56 | | | | | | | | | | | | | | | (7564) all_6_2 = e2 % 149.33/21.56 | | | | | | | | | | | | | | | % 149.33/21.56 | | | | | | | | | | | | | | | SIMP: (7564) implies: % 149.33/21.56 | | | | | | | | | | | | | | | (7565) all_6_2 = e2 % 149.33/21.56 | | | | | | | | | | | | | | | % 149.33/21.56 | | | | | | | | | | | | | | | COMBINE_EQS: (552), (7565) imply: % 149.33/21.56 | | | | | | | | | | | | | | | (7566) all_58_8 = e2 % 149.33/21.56 | | | | | | | | | | | | | | | % 149.33/21.56 | | | | | | | | | | | | | | | COMBINE_EQS: (7425), (7563) imply: % 149.33/21.56 | | | | | | | | | | | | | | | (7567) all_58_7 = e1 % 149.33/21.56 | | | | | | | | | | | | | | | % 149.33/21.56 | | | | | | | | | | | | | | | REDUCE: (7426), (7563) imply: % 149.33/21.56 | | | | | | | | | | | | | | | (7568) ~ (all_52_2 = e1) % 149.33/21.56 | | | | | | | | | | | | | | | % 149.33/21.56 | | | | | | | | | | | | | | | REDUCE: (569), (7565) imply: % 149.33/21.56 | | | | | | | | | | | | | | | (7569) ~ (all_52_2 = e2) % 149.33/21.56 | | | | | | | | | | | | | | | % 149.33/21.56 | | | | | | | | | | | | | | | REDUCE: (7429), (7563) imply: % 149.33/21.56 | | | | | | | | | | | | | | | (7570) ~ (all_52_7 = e1) % 149.33/21.56 | | | | | | | | | | | | | | | % 149.33/21.56 | | | | | | | | | | | | | | | REDUCE: (582), (7565) imply: % 149.33/21.56 | | | | | | | | | | | | | | | (7571) ~ (all_52_8 = e2) % 149.33/21.56 | | | | | | | | | | | | | | | % 149.33/21.56 | | | | | | | | | | | | | | | REDUCE: (7431), (7563) imply: % 149.33/21.56 | | | | | | | | | | | | | | | (7572) ~ (all_52_14 = e1) % 149.33/21.56 | | | | | | | | | | | | | | | % 149.33/21.56 | | | | | | | | | | | | | | | REDUCE: (587), (7565) imply: % 149.33/21.56 | | | | | | | | | | | | | | | (7573) ~ (all_52_14 = e2) % 149.33/21.56 | | | | | | | | | | | | | | | % 149.33/21.56 | | | | | | | | | | | | | | | REDUCE: (7420), (7565) imply: % 149.33/21.56 | | | | | | | | | | | | | | | (7574) op(e2, e2) = e2 % 149.33/21.56 | | | | | | | | | | | | | | | % 149.33/21.56 | | | | | | | | | | | | | | | REDUCE: (7435), (7563) imply: % 149.33/21.56 | | | | | | | | | | | | | | | (7575) op(e2, e1) = all_56_18 % 149.33/21.56 | | | | | | | | | | | | | | | % 149.33/21.56 | | | | | | | | | | | | | | | REDUCE: (41), (7565) imply: % 149.33/21.56 | | | | | | | | | | | | | | | (7576) op(e1, e1) = e2 % 149.33/21.56 | | | | | | | | | | | | | | | % 149.33/21.56 | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_9, % 149.33/21.56 | | | | | | | | | | | | | | | all_56_18, e1, e2, simplifying with (213), (7575) % 149.33/21.56 | | | | | | | | | | | | | | | gives: % 149.33/21.56 | | | | | | | | | | | | | | | (7577) all_56_18 = all_52_9 % 149.33/21.56 | | | | | | | | | | | | | | | % 149.33/21.56 | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_8_2, e2, % 149.33/21.56 | | | | | | | | | | | | | | | e2, e2, simplifying with (46), (7574) gives: % 149.33/21.56 | | | | | | | | | | | | | | | (7578) all_8_2 = e2 % 149.33/21.56 | | | | | | | | | | | | | | | % 149.33/21.56 | | | | | | | | | | | | | | | COMBINE_EQS: (545), (7578) imply: % 149.33/21.56 | | | | | | | | | | | | | | | (7579) all_56_11 = e2 % 149.33/21.56 | | | | | | | | | | | | | | | % 149.33/21.56 | | | | | | | | | | | | | | | COMBINE_EQS: (554), (7578) imply: % 149.33/21.56 | | | | | | | | | | | | | | | (7580) all_58_3 = e2 % 149.33/21.56 | | | | | | | | | | | | | | | % 149.33/21.56 | | | | | | | | | | | | | | | REDUCE: (568), (7578) imply: % 149.33/21.56 | | | | | | | | | | | | | | | (7581) ~ (all_52_1 = e2) % 149.33/21.56 | | | | | | | | | | | | | | | % 149.33/21.56 | | | | | | | | | | | | | | | REDUCE: (575), (7578) imply: % 149.33/21.56 | | | | | | | | | | | | | | | (7582) ~ (all_52_7 = e2) % 149.33/21.56 | | | | | | | | | | | | | | | % 149.33/21.56 | | | | | | | | | | | | | | | REDUCE: (577), (7578) imply: % 149.33/21.56 | | | | | | | | | | | | | | | (7583) ~ (all_52_9 = e2) % 149.33/21.56 | | | | | | | | | | | | | | | % 149.33/21.56 | | | | | | | | | | | | | | | REDUCE: (579), (7578) imply: % 149.33/21.56 | | | | | | | | | | | | | | | (7584) ~ (all_52_13 = e2) % 149.33/21.56 | | | | | | | | | | | | | | | % 149.33/21.56 | | | | | | | | | | | | | | | REDUCE: (48), (7578) imply: % 149.33/21.56 | | | | | | | | | | | | | | | (7585) op(e2, e2) = all_8_1 % 149.33/21.56 | | | | | | | | | | | | | | | % 149.33/21.56 | | | | | | | | | | | | | | | REDUCE: (617), (7578) imply: % 149.33/21.56 | | | | | | | | | | | | | | | (7586) op(e2, e2) = all_56_10 % 149.33/21.56 | | | | | | | | | | | | | | | % 149.33/21.56 | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, % 149.33/21.56 | | | | | | | | | | | | | | | all_56_10, e2, e2, simplifying with (7574), (7586) % 149.33/21.56 | | | | | | | | | | | | | | | gives: % 149.33/21.56 | | | | | | | | | | | | | | | (7587) all_56_10 = e2 % 149.33/21.56 | | | | | | | | | | | | | | | % 149.33/21.56 | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_8_1, % 149.33/21.56 | | | | | | | | | | | | | | | all_56_10, e2, e2, simplifying with (7585), (7586) % 149.33/21.56 | | | | | | | | | | | | | | | gives: % 149.33/21.56 | | | | | | | | | | | | | | | (7588) all_56_10 = all_8_1 % 149.33/21.56 | | | | | | | | | | | | | | | % 149.33/21.56 | | | | | | | | | | | | | | | COMBINE_EQS: (7587), (7588) imply: % 149.33/21.56 | | | | | | | | | | | | | | | (7589) all_8_1 = e2 % 149.33/21.56 | | | | | | | | | | | | | | | % 149.33/21.56 | | | | | | | | | | | | | | | SIMP: (7589) implies: % 149.33/21.56 | | | | | | | | | | | | | | | (7590) all_8_1 = e2 % 149.33/21.56 | | | | | | | | | | | | | | | % 149.33/21.56 | | | | | | | | | | | | | | | REDUCE: (47), (7590) imply: % 149.33/21.56 | | | | | | | | | | | | | | | (7591) op(e2, e2) = all_8_0 % 149.33/21.56 | | | | | | | | | | | | | | | % 149.33/21.56 | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, all_8_0, % 149.33/21.56 | | | | | | | | | | | | | | | e2, e2, simplifying with (7574), (7591) gives: % 149.33/21.56 | | | | | | | | | | | | | | | (7592) all_8_0 = e2 % 149.33/21.56 | | | | | | | | | | | | | | | % 149.33/21.56 | | | | | | | | | | | | | | | REDUCE: (7451), (7592) imply: % 149.33/21.56 | | | | | | | | | | | | | | | (7593) ~ (e3 = e2) % 149.33/21.56 | | | | | | | | | | | | | | | % 149.33/21.56 | | | | | | | | | | | | | | | BETA: splitting (288) gives: % 149.33/21.56 | | | | | | | | | | | | | | | % 149.33/21.56 | | | | | | | | | | | | | | | Case 1: % 149.33/21.56 | | | | | | | | | | | | | | | | % 149.33/21.56 | | | | | | | | | | | | | | | | (7594) ~ (all_56_31 = e1) % 149.33/21.56 | | | | | | | | | | | | | | | | % 149.33/21.56 | | | | | | | | | | | | | | | | REDUCE: (544), (7594) imply: % 149.33/21.56 | | | | | | | | | | | | | | | | (7595) ~ (all_4_2 = e1) % 149.33/21.56 | | | | | | | | | | | | | | | | % 149.33/21.56 | | | | | | | | | | | | | | | | BETA: splitting (298) gives: % 149.33/21.56 | | | | | | | | | | | | | | | | % 149.33/21.56 | | | | | | | | | | | | | | | | Case 1: % 149.33/21.56 | | | | | | | | | | | | | | | | | % 149.33/21.56 | | | | | | | | | | | | | | | | | (7596) ~ (all_56_1 = e1) % 149.33/21.56 | | | | | | | | | | | | | | | | | % 149.33/21.56 | | | | | | | | | | | | | | | | | REDUCE: (546), (7596) imply: % 149.33/21.56 | | | | | | | | | | | | | | | | | (7597) ~ (all_10_2 = e1) % 149.33/21.56 | | | | | | | | | | | | | | | | | % 149.33/21.56 | | | | | | | | | | | | | | | | | BETA: splitting (290) gives: % 149.33/21.56 | | | | | | | | | | | | | | | | | % 149.33/21.56 | | | | | | | | | | | | | | | | | Case 1: % 149.33/21.56 | | | | | | | | | | | | | | | | | | % 149.33/21.56 | | | | | | | | | | | | | | | | | | (7598) ~ (all_56_31 = e3) % 149.33/21.56 | | | | | | | | | | | | | | | | | | % 149.33/21.56 | | | | | | | | | | | | | | | | | | REDUCE: (544), (7598) imply: % 149.33/21.56 | | | | | | | | | | | | | | | | | | (7599) ~ (all_4_2 = e3) % 149.33/21.56 | | | | | | | | | | | | | | | | | | % 149.33/21.56 | | | | | | | | | | | | | | | | | | BETA: splitting (289) gives: % 149.33/21.56 | | | | | | | | | | | | | | | | | | % 149.33/21.56 | | | | | | | | | | | | | | | | | | Case 1: % 149.33/21.56 | | | | | | | | | | | | | | | | | | | % 149.33/21.56 | | | | | | | | | | | | | | | | | | | (7600) ~ (all_56_31 = e2) % 149.33/21.56 | | | | | | | | | | | | | | | | | | | % 149.33/21.56 | | | | | | | | | | | | | | | | | | | REDUCE: (544), (7600) imply: % 149.33/21.56 | | | | | | | | | | | | | | | | | | | (7601) ~ (all_4_2 = e2) % 149.33/21.56 | | | | | | | | | | | | | | | | | | | % 149.33/21.56 | | | | | | | | | | | | | | | | | | | BETA: splitting (322) gives: % 149.33/21.56 | | | | | | | | | | | | | | | | | | | % 149.33/21.56 | | | | | | | | | | | | | | | | | | | Case 1: % 149.33/21.56 | | | | | | | | | | | | | | | | | | | | % 149.33/21.56 | | | | | | | | | | | | | | | | | | | | (7602) all_58_9 = e2 % 149.33/21.56 | | | | | | | | | | | | | | | | | | | | % 149.33/21.56 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (551), (7602) imply: % 149.33/21.56 | | | | | | | | | | | | | | | | | | | | (7603) all_52_12 = e2 % 149.33/21.56 | | | | | | | | | | | | | | | | | | | | % 149.33/21.56 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (402), (7603) imply: % 149.33/21.56 | | | | | | | | | | | | | | | | | | | | (7604) all_56_7 = e2 % 149.33/21.56 | | | | | | | | | | | | | | | | | | | | % 149.33/21.56 | | | | | | | | | | | | | | | | | | | | REDUCE: (7554), (7603) imply: % 149.33/21.56 | | | | | | | | | | | | | | | | | | | | (7605) ~ (all_10_0 = e2) % 149.33/21.56 | | | | | | | | | | | | | | | | | | | | % 149.33/21.56 | | | | | | | | | | | | | | | | | | | | REDUCE: (567), (7603) imply: % 149.33/21.56 | | | | | | | | | | | | | | | | | | | | (7606) ~ (all_10_2 = e2) % 149.33/21.56 | | | | | | | | | | | | | | | | | | | | % 149.33/21.56 | | | | | | | | | | | | | | | | | | | | SIMP: (7606) implies: % 149.33/21.56 | | | | | | | | | | | | | | | | | | | | (7607) ~ (all_10_2 = e2) % 149.33/21.56 | | | | | | | | | | | | | | | | | | | | % 149.33/21.56 | | | | | | | | | | | | | | | | | | | | BETA: splitting (297) gives: % 149.33/21.56 | | | | | | | | | | | | | | | | | | | | % 149.33/21.56 | | | | | | | | | | | | | | | | | | | | Case 1: % 149.33/21.56 | | | | | | | | | | | | | | | | | | | | | % 149.33/21.56 | | | | | | | | | | | | | | | | | | | | | (7608) ~ (all_56_1 = e0) % 149.33/21.56 | | | | | | | | | | | | | | | | | | | | | % 149.33/21.56 | | | | | | | | | | | | | | | | | | | | | REDUCE: (546), (7608) imply: % 149.33/21.56 | | | | | | | | | | | | | | | | | | | | | (7609) ~ (all_10_2 = e0) % 149.33/21.56 | | | | | | | | | | | | | | | | | | | | | % 149.33/21.56 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (169), (237), (239), (250), (251), (252), % 149.33/21.56 | | | | | | | | | | | | | | | | | | | | | (290), (318), (319), (336), (339), (344), (365), % 149.33/21.56 | | | | | | | | | | | | | | | | | | | | | (401), (419), (447), (459), (480), (540), (543), % 149.33/21.56 | | | | | | | | | | | | | | | | | | | | | (544), (547), (548), (549), (553), (561), (565), % 149.33/21.56 | | | | | | | | | | | | | | | | | | | | | (570), (7437), (7443), (7547), (7550), (7552), % 149.33/21.56 | | | | | | | | | | | | | | | | | | | | | (7555), (7567), (7569), (7570), (7571), (7580), % 149.33/21.56 | | | | | | | | | | | | | | | | | | | | | (7581), (7595), (7597), (7607), (7609) are % 149.33/21.56 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #64. % 149.33/21.56 | | | | | | | | | | | | | | | | | | | | | % 149.33/21.56 | | | | | | | | | | | | | | | | | | | | Case 2: % 149.33/21.56 | | | | | | | | | | | | | | | | | | | | | % 149.33/21.56 | | | | | | | | | | | | | | | | | | | | | (7610) all_56_7 = e3 % 149.33/21.56 | | | | | | | | | | | | | | | | | | | | | % 149.33/21.56 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (7604), (7610) imply: % 149.33/21.56 | | | | | | | | | | | | | | | | | | | | | (7611) e3 = e2 % 149.33/21.56 | | | | | | | | | | | | | | | | | | | | | % 149.33/21.56 | | | | | | | | | | | | | | | | | | | | | REDUCE: (9), (7611) imply: % 149.33/21.56 | | | | | | | | | | | | | | | | | | | | | (7612) $false % 149.33/21.56 | | | | | | | | | | | | | | | | | | | | | % 149.33/21.56 | | | | | | | | | | | | | | | | | | | | | CLOSE: (7612) is inconsistent. % 149.33/21.56 | | | | | | | | | | | | | | | | | | | | | % 149.33/21.56 | | | | | | | | | | | | | | | | | | | | End of split % 149.33/21.56 | | | | | | | | | | | | | | | | | | | | % 149.33/21.56 | | | | | | | | | | | | | | | | | | | Case 2: % 149.33/21.56 | | | | | | | | | | | | | | | | | | | | % 149.33/21.56 | | | | | | | | | | | | | | | | | | | | (7613) all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2 % 149.33/21.56 | | | | | | | | | | | | | | | | | | | | % 149.33/21.56 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (386), (547), (550), (7573), (7584), (7601), % 149.33/21.56 | | | | | | | | | | | | | | | | | | | | (7613) are inconsistent by sub-proof #693. % 149.33/21.56 | | | | | | | | | | | | | | | | | | | | % 149.33/21.56 | | | | | | | | | | | | | | | | | | | End of split % 149.33/21.56 | | | | | | | | | | | | | | | | | | | % 149.33/21.56 | | | | | | | | | | | | | | | | | | Case 2: % 149.33/21.56 | | | | | | | | | | | | | | | | | | | % 149.33/21.56 | | | | | | | | | | | | | | | | | | | (7614) all_56_31 = e2 % 149.33/21.56 | | | | | | | | | | | | | | | | | | | (7615) all_56_27 = e0 % 149.33/21.56 | | | | | | | | | | | | | | | | | | | % 149.33/21.56 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (360), (7615) imply: % 149.33/21.56 | | | | | | | | | | | | | | | | | | | (7616) all_52_7 = e0 % 149.33/21.56 | | | | | | | | | | | | | | | | | | | % 149.33/21.56 | | | | | | | | | | | | | | | | | | | SIMP: (7616) implies: % 149.33/21.56 | | | | | | | | | | | | | | | | | | | (7617) all_52_7 = e0 % 149.33/21.56 | | | | | | | | | | | | | | | | | | | % 149.33/21.56 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (544), (7614) imply: % 149.33/21.56 | | | | | | | | | | | | | | | | | | | (7618) all_4_2 = e2 % 149.33/21.56 | | | | | | | | | | | | | | | | | | | % 149.33/21.56 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (547), (7618) imply: % 149.33/21.56 | | | | | | | | | | | | | | | | | | | (7619) all_58_15 = e2 % 149.33/21.56 | | | | | | | | | | | | | | | | | | | % 149.33/21.56 | | | | | | | | | | | | | | | | | | | REDUCE: (188), (7617) imply: % 149.33/21.56 | | | | | | | | | | | | | | | | | | | (7620) ~ (all_52_3 = e0) % 149.33/21.56 | | | | | | | | | | | | | | | | | | | % 149.33/21.56 | | | | | | | | | | | | | | | | | | | REDUCE: (173), (7617) imply: % 149.33/21.57 | | | | | | | | | | | | | | | | | | | (7621) ~ (all_52_11 = e0) % 149.33/21.57 | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | SIMP: (7621) implies: % 149.33/21.57 | | | | | | | | | | | | | | | | | | | (7622) ~ (all_52_11 = e0) % 149.33/21.57 | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | REDUCE: (7550), (7617) imply: % 149.33/21.57 | | | | | | | | | | | | | | | | | | | (7623) ~ (all_10_0 = e0) % 149.33/21.57 | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | SIMP: (7623) implies: % 149.33/21.57 | | | | | | | | | | | | | | | | | | | (7624) ~ (all_10_0 = e0) % 149.33/21.57 | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | REDUCE: (588), (7618) imply: % 149.33/21.57 | | | | | | | | | | | | | | | | | | | (7625) ~ (all_52_11 = e2) % 149.33/21.57 | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | REDUCE: (619), (7617) imply: % 149.33/21.57 | | | | | | | | | | | | | | | | | | | (7626) op(e2, e0) = all_56_26 % 149.33/21.57 | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | BETA: splitting (251) gives: % 149.33/21.57 | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | Case 1: % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | (7627) all_54_1 = e3 % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (7547), (7627) imply: % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | (7628) all_10_0 = e3 % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (7548), (7628) imply: % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | (7629) all_56_3 = e3 % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | REDUCE: (7552), (7628) imply: % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | (7630) ~ (all_52_8 = e3) % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | REDUCE: (7554), (7628) imply: % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | (7631) ~ (all_52_12 = e3) % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | REDUCE: (7558), (7628) imply: % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | (7632) op(e2, e3) = all_56_2 % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | BETA: splitting (297) gives: % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | Case 1: % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | (7633) ~ (all_56_1 = e0) % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | REDUCE: (546), (7633) imply: % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | (7634) ~ (all_10_2 = e0) % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (345) gives: % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | (7635) all_58_0 = e2 % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (419), (7635) imply: % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | (7636) all_10_2 = e2 % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (546), (7636) imply: % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | (7637) all_56_1 = e2 % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (561), (7636) imply: % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | (7638) ~ (all_52_3 = e2) % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (567), (7636) imply: % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | (7639) ~ (all_52_12 = e2) % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_13, % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | all_56_26, e0, e2, simplifying with (212), (7626) % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | gives: % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | (7640) all_56_26 = all_52_13 % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_1, % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | all_56_2, e3, e2, simplifying with (215), (7632) % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | gives: % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | (7641) all_56_2 = all_52_1 % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (241) gives: % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | (7642) all_54_11 = e3 % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (476), (7642) imply: % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | (7643) all_52_14 = e3 % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (7643) implies: % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | (7644) all_52_14 = e3 % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (366), (7644) imply: % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | (7645) all_56_23 = e3 % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (550), (7644) imply: % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | (7646) all_58_11 = e3 % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (189), (7644) imply: % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | (7647) ~ (all_52_2 = e3) % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (626), (7644) imply: % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | (7648) op(e0, e3) = all_56_22 % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (244) gives: % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | (7649) all_54_8 = e3 % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (471), (7647), (7649) are inconsistent by % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #345. % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | (7650) all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0 % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (324) gives: % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | (7651) all_58_6 = e0 % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (553), (7651) imply: % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | (7652) all_52_2 = e0 % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (7652) implies: % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | (7653) all_52_2 = e0 % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (381), (7653) imply: % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | (7654) all_56_17 = e0 % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (197), (7653) imply: % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | (7655) ~ (all_52_1 = e0) % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (192), (7653) imply: % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | (7656) ~ (all_52_3 = e0) % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (614), (7653) imply: % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | (7657) op(e3, e0) = all_56_16 % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_3, % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_22, e3, e0, simplifying with (207), (7648) % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | (7658) all_56_22 = all_52_3 % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_12, % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_16, e0, e3, simplifying with (216), (7657) % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | (7659) all_56_16 = all_52_12 % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (240) gives: % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | (7660) all_54_12 = e3 % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (478), (7660) imply: % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | (7661) all_52_3 = e3 % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (7658), (7661) imply: % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | (7662) all_56_22 = e3 % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (196), (7661) imply: % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | (7663) ~ (all_52_1 = e3) % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (187), (7661) imply: % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | (7664) ~ (all_52_11 = e3) % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (7664) implies: % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | (7665) ~ (all_52_11 = e3) % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (248) gives: % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | (7666) all_54_4 = e3 % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (463), (7663), (7666) are inconsistent by % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #634. % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | (7667) all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0 % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives: % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7668) all_54_14 = e3 % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (482), (7665), (7668) are inconsistent by % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #729. % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7669) all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0 % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7669) gives: % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7670) all_54_14 = e2 % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (482), (7625), (7670) are inconsistent by % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #581. % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7671) all_54_14 = e1 | all_54_14 = e0 % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7667) gives: % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7672) all_54_4 = e2 % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (463), (7581), (7672) are inconsistent by % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #633. % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7673) all_54_4 = e1 | all_54_4 = e0 % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7673) gives: % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7674) all_54_4 = e1 % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (463), (7674) imply: % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7675) all_52_1 = e1 % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (7675) implies: % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7676) all_52_1 = e1 % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (193), (7676) imply: % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7677) ~ (all_52_13 = e1) % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (7677) implies: % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7678) ~ (all_52_13 = e1) % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (321) gives: % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7679) all_58_9 = e1 % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (551), (7679) imply: % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7680) all_52_12 = e1 % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (402), (7680) imply: % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7681) all_56_7 = e1 % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (624), (7680) imply: % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7682) op(e0, e1) = all_56_6 % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (317) gives: % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7683) all_58_15 = e0 % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (7619), (7683) imply: % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7684) e2 = e0 % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (7684) implies: % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7685) e2 = e0 % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (7637), (7685) imply: % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7686) all_56_1 = e0 % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (251), (297), (402), (7437), (7443), (7547), % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7554), (7624), (7686) are inconsistent by % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #489. % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7687) (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7687) implies: % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7688) all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0 % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7671) gives: % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7689) all_54_14 = e1 % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (482), (7689) imply: % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7690) all_52_11 = e1 % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (7690) implies: % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7691) all_52_11 = e1 % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (205), (7691) imply: % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7692) op(e0, e1) = e1 % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7688) gives: % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7693) all_58_9 = e0 % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (7679), (7693) imply: % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7694) e1 = e0 % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4), (7694) imply: % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7695) $false % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (7695) is inconsistent. % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7696) all_58_10 = e0 | all_58_11 = e0 % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7696) gives: % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7697) all_58_10 = e0 % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (386), (7697) imply: % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7698) all_52_13 = e0 % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (7640), (7698) imply: % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7699) all_56_26 = e0 % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (286) gives: % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7700) ( ~ (all_56_0 = all_56_1) & ~ (all_56_2 = % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_3) & ~ (all_56_4 = all_56_5) & ~ % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_6 = all_56_7)) | ( ~ (all_56_8 = % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_9) & ~ (all_56_10 = all_56_11) & ~ % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = all_56_13) & ~ (all_56_14 = % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15)) % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7700) gives: % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7701) ~ (all_56_0 = all_56_1) & ~ (all_56_2 = % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_3) & ~ (all_56_4 = all_56_5) & ~ % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_6 = all_56_7) % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7701) implies: % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7702) ~ (all_56_6 = all_56_7) % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7681), (7702) imply: % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7703) ~ (all_56_6 = e1) % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1, all_56_6, % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1, e0, simplifying with (7682), (7692) gives: % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7704) all_56_6 = e1 % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7703), (7704) imply: % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7705) $false % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (7705) is inconsistent. % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7706) ~ (all_56_8 = all_56_9) & ~ (all_56_10 = % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_11) & ~ (all_56_12 = all_56_13) & ~ % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = all_56_15) % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7706) implies: % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7707) ~ (all_56_10 = all_56_11) % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7579), (7587), (7707) imply: % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7708) $false % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (7708) is inconsistent. % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7709) ( ~ (all_56_16 = all_56_17) & ~ (all_56_18 = % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19) & ~ (all_56_20 = all_56_21) & ~ % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_22 = all_56_23)) | ( ~ (all_56_24 = % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_25) & ~ (all_56_26 = all_56_27) & ~ % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_28 = all_56_29) & ~ (all_56_30 = % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31)) % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7709) gives: % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7710) ~ (all_56_16 = all_56_17) & ~ (all_56_18 = % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19) & ~ (all_56_20 = all_56_21) & ~ % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_22 = all_56_23) % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7710) implies: % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7711) ~ (all_56_22 = all_56_23) % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7645), (7662), (7711) imply: % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7712) $false % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (7712) is inconsistent. % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7713) ~ (all_56_24 = all_56_25) & ~ (all_56_26 = % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_27) & ~ (all_56_28 = all_56_29) & ~ % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_30 = all_56_31) % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7713) implies: % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7714) ~ (all_56_26 = all_56_27) % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7615), (7699), (7714) imply: % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7715) $false % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (7715) is inconsistent. % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7716) all_58_11 = e0 % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (7646), (7716) imply: % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7717) e3 = e0 % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7), (7717) imply: % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7718) $false % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (7718) is inconsistent. % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7719) all_54_14 = e0 % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (482), (7622), (7719) are inconsistent by % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #715. % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7720) all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1 % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (386), (547), (550), (7572), (7595), (7678), % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7720) are inconsistent by sub-proof #587. % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7721) all_54_4 = e0 % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (463), (7655), (7721) are inconsistent by % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #614. % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | (7722) all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0 % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7722) gives: % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | (7723) all_54_12 = e2 % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (478), (7723) imply: % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | (7724) all_52_3 = e2 % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7638), (7724) imply: % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | (7725) $false % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (7725) is inconsistent. % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | (7726) ~ (all_54_12 = e2) % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | (7727) all_54_12 = e1 | all_54_12 = e0 % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (346) gives: % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7728) all_58_0 = e3 % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (344), (365), (401), (553), (7569), (7581), % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7638), (7728) are inconsistent by sub-proof #694. % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7729) all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3 % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7729) gives: % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7730) all_58_2 = e3 % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (401), (7730) imply: % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7731) all_52_1 = e3 % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (7641), (7731) imply: % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7732) all_56_2 = e3 % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (194), (7731) imply: % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7733) ~ (all_52_9 = e3) % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (7733) implies: % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7734) ~ (all_52_9 = e3) % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (193), (7731) imply: % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7735) ~ (all_52_13 = e3) % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (7735) implies: % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7736) ~ (all_52_13 = e3) % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7727) gives: % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7737) all_54_12 = e1 % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (478), (7737) imply: % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7738) all_52_3 = e1 % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (7738) implies: % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7739) all_52_3 = e1 % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (447), (7739) imply: % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7740) all_56_25 = e1 % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (615), (7739) imply: % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7741) op(e3, e1) = all_56_24 % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_8, % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_24, e1, e3, simplifying with (217), (7741) % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7742) all_56_24 = all_52_8 % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (246) gives: % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7743) all_54_6 = e3 % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (467), (7734), (7743) are inconsistent by % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #402. % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7744) all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0 % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (249) gives: % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7745) all_54_3 = e3 % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (461), (7745) imply: % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7746) all_52_12 = e3 % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7631), (7746) imply: % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7747) $false % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (7747) is inconsistent. % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7748) all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0 % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (245) gives: % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7749) all_54_7 = e3 % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (469), (7736), (7749) are inconsistent by % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #601. % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7750) all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0 % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (329) gives: % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7751) all_58_4 = e1 % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (407), (7751) imply: % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7752) all_52_8 = e1 % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (7742), (7752) imply: % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7753) all_56_24 = e1 % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (168), (7752) imply: % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7754) ~ (all_52_12 = e1) % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (7754) implies: % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7755) ~ (all_52_12 = e1) % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (286) gives: % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7756) ( ~ (all_56_0 = all_56_1) & ~ (all_56_2 = % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_3) & ~ (all_56_4 = all_56_5) & ~ % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_6 = all_56_7)) | ( ~ (all_56_8 = % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_9) & ~ (all_56_10 = all_56_11) & ~ % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = all_56_13) & ~ (all_56_14 = % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15)) % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7579), (7587), (7629), (7732), (7756) are % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #63. % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7757) ( ~ (all_56_16 = all_56_17) & ~ (all_56_18 = % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19) & ~ (all_56_20 = all_56_21) & ~ % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_22 = all_56_23)) | ( ~ (all_56_24 = % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_25) & ~ (all_56_26 = all_56_27) & ~ % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_28 = all_56_29) & ~ (all_56_30 = % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31)) % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7757) gives: % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7758) ~ (all_56_16 = all_56_17) & ~ (all_56_18 = % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19) & ~ (all_56_20 = all_56_21) & ~ % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_22 = all_56_23) % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7758) implies: % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7759) ~ (all_56_16 = all_56_17) % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7654), (7659), (7759) imply: % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7760) ~ (all_52_12 = e0) % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (461), (7639), (7748), (7755), (7760) are % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #326. % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7761) ~ (all_56_24 = all_56_25) & ~ (all_56_26 = % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_27) & ~ (all_56_28 = all_56_29) & ~ % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_30 = all_56_31) % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7761) implies: % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7762) ~ (all_56_24 = all_56_25) % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7740), (7753), (7762) imply: % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7763) $false % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (7763) is inconsistent. % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7764) ~ (all_58_4 = e1) % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7765) all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1 % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (407), (7764) imply: % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7766) ~ (all_52_8 = e1) % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7765) gives: % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7767) all_58_5 = e1 % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (389), (7767) imply: % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7768) all_52_9 = e1 % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (7768) implies: % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7769) all_52_9 = e1 % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (7577), (7769) imply: % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7770) all_56_18 = e1 % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (165), (7769) imply: % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7771) ~ (all_52_13 = e1) % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (7771) implies: % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7772) ~ (all_52_13 = e1) % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (286) gives: % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7773) ( ~ (all_56_0 = all_56_1) & ~ (all_56_2 = % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_3) & ~ (all_56_4 = all_56_5) & ~ % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_6 = all_56_7)) | ( ~ (all_56_8 = % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_9) & ~ (all_56_10 = all_56_11) & ~ % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = all_56_13) & ~ (all_56_14 = % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15)) % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7579), (7587), (7629), (7732), (7773) are % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #63. % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7774) ( ~ (all_56_16 = all_56_17) & ~ (all_56_18 = % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19) & ~ (all_56_20 = all_56_21) & ~ % 149.33/21.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_22 = all_56_23)) | ( ~ (all_56_24 = % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_25) & ~ (all_56_26 = all_56_27) & ~ % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_28 = all_56_29) & ~ (all_56_30 = % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31)) % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7774) gives: % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7775) ~ (all_56_16 = all_56_17) & ~ (all_56_18 = % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19) & ~ (all_56_20 = all_56_21) & ~ % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_22 = all_56_23) % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7775) implies: % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7776) ~ (all_56_18 = all_56_19) % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7561), (7770), (7776) imply: % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7777) $false % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (7777) is inconsistent. % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7778) ~ (all_56_24 = all_56_25) & ~ (all_56_26 = % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_27) & ~ (all_56_28 = all_56_29) & ~ % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_30 = all_56_31) % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7778) implies: % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7779) ~ (all_56_26 = all_56_27) % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7615), (7640), (7779) imply: % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7780) ~ (all_52_13 = e0) % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (469), (7584), (7750), (7772), (7780) are % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #649. % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7781) ~ (all_58_5 = e1) % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (389), (7781) imply: % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7782) ~ (all_52_9 = e1) % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (250) gives: % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7783) all_54_2 = e3 % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (459), (7630), (7783) are inconsistent by % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #728. % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7784) all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0 % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (171), (459), (467), (7571), (7583), (7744), % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7766), (7782), (7784) are inconsistent by % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #329. % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7785) all_54_12 = e0 % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (478), (7620), (7785) are inconsistent by % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #617. % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7786) ~ (all_58_2 = e3) % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (401), (7786) imply: % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7787) ~ (all_52_1 = e3) % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (248) gives: % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7788) all_54_4 = e3 % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (463), (7787), (7788) are inconsistent by % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #634. % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7789) all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0 % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7727) gives: % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7790) all_54_12 = e1 % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (478), (7790) imply: % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7791) all_52_3 = e1 % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (196), (7791) imply: % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7792) ~ (all_52_1 = e1) % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7789) gives: % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7793) all_54_4 = e2 % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (463), (7581), (7793) are inconsistent by % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #633. % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7794) all_54_4 = e1 | all_54_4 = e0 % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (463), (7655), (7792), (7794) are inconsistent by % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #583. % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7795) all_54_12 = e0 % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (478), (7795) imply: % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7796) all_52_3 = e0 % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7620), (7796) imply: % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7797) $false % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (7797) is inconsistent. % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | (7798) ~ (all_58_6 = e0) % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (553), (7798) imply: % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | (7799) ~ (all_52_2 = e0) % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (471), (7568), (7569), (7650), (7799) are % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #270. % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | End of split % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | (7800) all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0 % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (327) gives: % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | (7801) all_58_6 = e3 % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (553), (7801) imply: % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | (7802) all_52_2 = e3 % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (7802) implies: % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | (7803) all_52_2 = e3 % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (197), (7803) imply: % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | (7804) ~ (all_52_1 = e3) % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (192), (7803) imply: % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | (7805) ~ (all_52_3 = e3) % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (7805) implies: % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | (7806) ~ (all_52_3 = e3) % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (189), (7803) imply: % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | (7807) ~ (all_52_14 = e3) % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (7807) implies: % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | (7808) ~ (all_52_14 = e3) % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (211), (7803) imply: % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | (7809) op(e1, e3) = e3 % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (240) gives: % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | (7810) all_54_12 = e3 % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (478), (7810) imply: % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | (7811) all_52_3 = e3 % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7806), (7811) imply: % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | (7812) $false % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (7812) is inconsistent. % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | (7813) all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0 % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7813) gives: % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | (7814) all_54_12 = e2 % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (478), (7814) imply: % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | (7815) all_52_3 = e2 % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7638), (7815) imply: % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | (7816) $false % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (7816) is inconsistent. % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | (7817) ~ (all_54_12 = e2) % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | (7818) all_54_12 = e1 | all_54_12 = e0 % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7818) gives: % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | (7819) all_54_12 = e1 % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (478), (7819) imply: % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | (7820) all_52_3 = e1 % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (196), (7820) imply: % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | (7821) ~ (all_52_1 = e1) % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (187), (7820) imply: % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | (7822) ~ (all_52_11 = e1) % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (7822) implies: % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | (7823) ~ (all_52_11 = e1) % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7638), (7820) imply: % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | (7824) ~ (e2 = e1) % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives: % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7825) all_54_14 = e3 % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (482), (7825) imply: % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7826) all_52_11 = e3 % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (7826) implies: % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7827) all_52_11 = e3 % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (357), (7827) imply: % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7828) all_56_29 = e3 % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (623), (7827) imply: % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7829) op(e1, e3) = all_56_28 % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (340) gives: % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7830) all_58_0 = e0 % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (7635), (7830) imply: % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7831) e2 = e0 % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (7637), (7831) imply: % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7832) all_56_1 = e0 % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (251), (297), (402), (7437), (7443), (7547), % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7554), (7624), (7832) are inconsistent by % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #489. % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7833) all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0 % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (323) gives: % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7834) all_58_9 = e3 % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (551), (7834) imply: % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7835) all_52_12 = e3 % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7631), (7835) imply: % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7836) $false % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (7836) is inconsistent. % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7837) all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3 % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (324) gives: % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7838) all_58_6 = e0 % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (7801), (7838) imply: % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7839) e3 = e0 % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (7839) implies: % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7840) e3 = e0 % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7), (7840) imply: % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7841) $false % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (7841) is inconsistent. % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7842) all_58_7 = e0 | all_58_8 = e0 | all_58_11 = e0 % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7833) gives: % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7843) all_58_2 = e0 % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (401), (7843) imply: % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7844) all_52_1 = e0 % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7821), (7844) imply: % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7845) ~ (e1 = e0) % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7842) gives: % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7846) all_58_7 = e0 % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (7567), (7846) imply: % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7847) e1 = e0 % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4), (7847) imply: % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7848) $false % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (7848) is inconsistent. % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7849) ~ (all_58_7 = e0) % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7850) all_58_8 = e0 | all_58_11 = e0 % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (328) gives: % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7851) all_58_4 = e0 % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (407), (7851) imply: % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7852) all_52_8 = e0 % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (429), (7852) imply: % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7853) all_56_5 = e0 % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (620), (7852) imply: % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7854) op(e1, e0) = all_56_4 % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7837) gives: % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7855) all_58_10 = e3 % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (386), (7855) imply: % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7856) all_52_13 = e3 % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (333) gives: % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7857) all_58_2 = e1 % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7843), (7857) are inconsistent by sub-proof % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #241. % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7858) all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1 % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7858) gives: % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7859) all_58_3 = e1 % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (7580), (7859) imply: % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7860) e2 = e1 % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6), (7860) imply: % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7861) $false % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (7861) is inconsistent. % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7862) all_58_5 = e1 | all_58_10 = e1 % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7850) gives: % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7863) all_58_8 = e0 % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (7566), (7863) imply: % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7864) e2 = e0 % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (7637), (7864) imply: % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7865) all_56_1 = e0 % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (251), (297), (402), (7437), (7443), (7547), % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7554), (7624), (7865) are inconsistent by % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #489. % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7866) all_58_11 = e0 % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (550), (7866) imply: % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7867) all_52_14 = e0 % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (208), (7867) imply: % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7868) op(e1, e0) = e0 % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7862) gives: % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7869) all_58_5 = e1 % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (389), (7869) imply: % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7870) all_52_9 = e1 % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (7577), (7870) imply: % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7871) all_56_18 = e1 % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_56_4, % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0, e1, simplifying with (7854), (7868) gives: % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7872) all_56_4 = e0 % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_28, e3, e1, simplifying with (7809), (7829) % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7873) all_56_28 = e3 % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (286) gives: % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7874) ( ~ (all_56_0 = all_56_1) & ~ (all_56_2 = % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_3) & ~ (all_56_4 = all_56_5) & ~ % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_6 = all_56_7)) | ( ~ (all_56_8 = % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_9) & ~ (all_56_10 = all_56_11) & ~ % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = all_56_13) & ~ (all_56_14 = % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15)) % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7874) gives: % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7875) ~ (all_56_0 = all_56_1) & ~ (all_56_2 = % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_3) & ~ (all_56_4 = all_56_5) & ~ % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_6 = all_56_7) % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7875) implies: % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7876) ~ (all_56_4 = all_56_5) % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7853), (7872), (7876) imply: % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7877) $false % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (7877) is inconsistent. % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7878) ~ (all_56_8 = all_56_9) & ~ (all_56_10 = % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_11) & ~ (all_56_12 = all_56_13) & ~ % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = all_56_15) % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7878) implies: % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7879) ~ (all_56_10 = all_56_11) % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7579), (7587), (7879) imply: % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7880) $false % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (7880) is inconsistent. % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7881) ( ~ (all_56_16 = all_56_17) & ~ (all_56_18 = % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19) & ~ (all_56_20 = all_56_21) & ~ % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_22 = all_56_23)) | ( ~ (all_56_24 = % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_25) & ~ (all_56_26 = all_56_27) & ~ % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_28 = all_56_29) & ~ (all_56_30 = % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31)) % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7881) gives: % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7882) ~ (all_56_16 = all_56_17) & ~ (all_56_18 = % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19) & ~ (all_56_20 = all_56_21) & ~ % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_22 = all_56_23) % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7882) implies: % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7883) ~ (all_56_18 = all_56_19) % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7561), (7871), (7883) imply: % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7884) $false % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (7884) is inconsistent. % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7885) ~ (all_56_24 = all_56_25) & ~ (all_56_26 = % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_27) & ~ (all_56_28 = all_56_29) & ~ % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_30 = all_56_31) % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7885) implies: % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7886) ~ (all_56_28 = all_56_29) % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7828), (7873), (7886) imply: % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7887) $false % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (7887) is inconsistent. % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7888) all_58_10 = e1 % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (7855), (7888) imply: % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7889) e3 = e1 % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8), (7889) imply: % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7890) $false % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (7890) is inconsistent. % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7891) all_58_11 = e3 | all_58_15 = e3 % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (547), (550), (7599), (7808), (7891) are % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #331. % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 149.33/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.39/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.39/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.39/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7892) ~ (all_58_4 = e0) % 149.39/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.39/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (407), (7892) imply: % 149.39/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7893) ~ (all_52_8 = e0) % 149.39/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.39/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (250) gives: % 149.39/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.39/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.39/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.39/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7894) all_54_2 = e3 % 149.39/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.39/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (459), (7630), (7894) are inconsistent by % 149.39/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #728. % 149.39/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.39/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.39/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.39/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7895) all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0 % 149.39/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.39/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7837) gives: % 149.39/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.39/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.39/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.39/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7896) all_58_10 = e3 % 149.39/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.39/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (386), (7896) imply: % 149.39/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7897) all_52_13 = e3 % 149.39/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.39/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (321) gives: % 149.39/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.39/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.39/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.39/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7898) all_58_9 = e1 % 149.39/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.39/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (551), (7898) imply: % 149.39/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7899) all_52_12 = e1 % 149.39/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.39/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (168), (7899) imply: % 149.39/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7900) ~ (all_52_8 = e1) % 149.39/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.39/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (459), (7571), (7893), (7895), (7900) are % 149.39/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #723. % 149.39/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.39/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.39/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.39/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7901) all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1 % 149.39/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.39/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (547), (550), (7572), (7595), (7896), (7901) % 149.39/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #446. % 149.39/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.39/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 149.39/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.39/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.39/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.39/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7902) all_58_11 = e3 | all_58_15 = e3 % 149.39/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.39/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (547), (550), (7599), (7808), (7902) are % 149.39/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #331. % 149.39/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.39/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 149.39/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.39/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 149.39/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.39/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 149.39/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.39/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 149.39/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.39/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.39/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.39/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7903) ~ (all_58_2 = e0) % 149.39/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.39/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (401), (7903) imply: % 149.39/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7904) ~ (all_52_1 = e0) % 149.39/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.39/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (248), (463), (7581), (7804), (7821), (7904) are % 149.39/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #559. % 149.39/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.39/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 149.39/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.39/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 149.39/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.39/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 149.39/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.39/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 149.39/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.39/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.39/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.39/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7905) all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0 % 149.39/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.39/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (482), (7622), (7625), (7823), (7905) are % 149.39/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #580. % 149.39/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.39/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 149.39/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.39/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.39/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.39/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | (7906) all_54_12 = e0 % 149.39/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.39/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (478), (7906) imply: % 149.39/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | (7907) all_52_3 = e0 % 149.39/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.39/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7620), (7907) imply: % 149.39/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | (7908) $false % 149.39/21.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.39/21.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (7908) is inconsistent. % 149.39/21.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.39/21.59 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 149.39/21.59 | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.39/21.59 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 149.39/21.59 | | | | | | | | | | | | | | | | | | | | | | | | | % 149.39/21.59 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 149.39/21.59 | | | | | | | | | | | | | | | | | | | | | | | | % 149.39/21.59 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.39/21.59 | | | | | | | | | | | | | | | | | | | | | | | | % 149.39/21.59 | | | | | | | | | | | | | | | | | | | | | | | | (7909) ~ (all_58_6 = e3) % 149.39/21.59 | | | | | | | | | | | | | | | | | | | | | | | | % 149.39/21.59 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (553), (7909) imply: % 149.39/21.59 | | | | | | | | | | | | | | | | | | | | | | | | (7910) ~ (all_52_2 = e3) % 149.39/21.59 | | | | | | | | | | | | | | | | | | | | | | | | % 149.39/21.59 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (244) gives: % 149.39/21.59 | | | | | | | | | | | | | | | | | | | | | | | | % 149.39/21.59 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.39/21.59 | | | | | | | | | | | | | | | | | | | | | | | | | % 149.39/21.59 | | | | | | | | | | | | | | | | | | | | | | | | | (7911) all_54_8 = e3 % 149.39/21.59 | | | | | | | | | | | | | | | | | | | | | | | | | % 149.39/21.59 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (471), (7911) imply: % 149.39/21.59 | | | | | | | | | | | | | | | | | | | | | | | | | (7912) all_52_2 = e3 % 149.39/21.59 | | | | | | | | | | | | | | | | | | | | | | | | | % 149.39/21.59 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7910), (7912) imply: % 149.39/21.59 | | | | | | | | | | | | | | | | | | | | | | | | | (7913) $false % 149.39/21.59 | | | | | | | | | | | | | | | | | | | | | | | | | % 149.39/21.59 | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (7913) is inconsistent. % 149.39/21.59 | | | | | | | | | | | | | | | | | | | | | | | | | % 149.39/21.59 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.39/21.59 | | | | | | | | | | | | | | | | | | | | | | | | | % 149.39/21.59 | | | | | | | | | | | | | | | | | | | | | | | | | (7914) all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0 % 149.39/21.59 | | | | | | | | | | | | | | | | | | | | | | | | | % 149.39/21.59 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7914) gives: % 149.39/21.59 | | | | | | | | | | | | | | | | | | | | | | | | | % 149.39/21.59 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.39/21.59 | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.39/21.59 | | | | | | | | | | | | | | | | | | | | | | | | | | (7915) all_54_8 = e2 % 149.39/21.59 | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.39/21.59 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (471), (7915) imply: % 149.39/21.59 | | | | | | | | | | | | | | | | | | | | | | | | | | (7916) all_52_2 = e2 % 149.39/21.59 | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.39/21.59 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7569), (7916) imply: % 149.39/21.59 | | | | | | | | | | | | | | | | | | | | | | | | | | (7917) $false % 149.39/21.59 | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.39/21.59 | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (7917) is inconsistent. % 149.39/21.59 | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.39/21.59 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.39/21.59 | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.39/21.59 | | | | | | | | | | | | | | | | | | | | | | | | | | (7918) all_54_8 = e1 | all_54_8 = e0 % 149.39/21.59 | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.39/21.59 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7918) gives: % 149.39/21.59 | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.39/21.59 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.39/21.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.39/21.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | (7919) all_54_8 = e1 % 149.39/21.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.39/21.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (471), (7919) imply: % 149.39/21.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | (7920) all_52_2 = e1 % 149.39/21.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.39/21.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7568), (7920) imply: % 149.39/21.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | (7921) $false % 149.39/21.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.39/21.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (7921) is inconsistent. % 149.39/21.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.39/21.59 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.39/21.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.39/21.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | (7922) all_54_8 = e0 % 149.39/21.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.39/21.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (471), (7922) imply: % 149.39/21.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | (7923) all_52_2 = e0 % 149.39/21.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.39/21.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (189), (7923) imply: % 149.39/21.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | (7924) ~ (all_52_14 = e0) % 149.39/21.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.39/21.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (7924) implies: % 149.39/21.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | (7925) ~ (all_52_14 = e0) % 149.39/21.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.39/21.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7800) gives: % 149.39/21.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.39/21.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.39/21.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.39/21.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7926) all_54_11 = e2 % 149.39/21.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.39/21.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (476), (7573), (7926) are inconsistent by % 149.39/21.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #690. % 149.39/21.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.39/21.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.39/21.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.39/21.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7927) all_54_11 = e1 | all_54_11 = e0 % 149.39/21.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.39/21.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (476), (7572), (7925), (7927) are inconsistent by % 149.39/21.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #688. % 149.39/21.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.39/21.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 149.39/21.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.39/21.59 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 149.39/21.59 | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.39/21.59 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 149.39/21.59 | | | | | | | | | | | | | | | | | | | | | | | | | % 149.39/21.59 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 149.39/21.59 | | | | | | | | | | | | | | | | | | | | | | | | % 149.39/21.59 | | | | | | | | | | | | | | | | | | | | | | | End of split % 149.39/21.59 | | | | | | | | | | | | | | | | | | | | | | | % 149.39/21.59 | | | | | | | | | | | | | | | | | | | | | | End of split % 149.39/21.59 | | | | | | | | | | | | | | | | | | | | | | % 149.39/21.59 | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.39/21.59 | | | | | | | | | | | | | | | | | | | | | | % 149.39/21.59 | | | | | | | | | | | | | | | | | | | | | | (7928) ~ (all_58_0 = e2) % 149.39/21.59 | | | | | | | | | | | | | | | | | | | | | | % 149.39/21.59 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (419), (7928) imply: % 149.39/21.59 | | | | | | | | | | | | | | | | | | | | | | (7929) ~ (all_10_2 = e2) % 149.39/21.59 | | | | | | | | | | | | | | | | | | | | | | % 149.39/21.59 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (169), (237), (239), (250), (251), (252), % 149.39/21.59 | | | | | | | | | | | | | | | | | | | | | | (290), (318), (319), (336), (339), (344), (365), % 149.39/21.59 | | | | | | | | | | | | | | | | | | | | | | (401), (419), (447), (459), (480), (540), (543), % 149.39/21.59 | | | | | | | | | | | | | | | | | | | | | | (544), (547), (548), (549), (553), (561), (565), % 149.39/21.59 | | | | | | | | | | | | | | | | | | | | | | (570), (7437), (7443), (7547), (7550), (7552), % 149.39/21.59 | | | | | | | | | | | | | | | | | | | | | | (7555), (7567), (7569), (7570), (7571), (7580), % 149.39/21.59 | | | | | | | | | | | | | | | | | | | | | | (7581), (7595), (7597), (7634), (7929) are % 149.39/21.59 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #64. % 149.39/21.59 | | | | | | | | | | | | | | | | | | | | | | % 149.39/21.59 | | | | | | | | | | | | | | | | | | | | | End of split % 149.39/21.59 | | | | | | | | | | | | | | | | | | | | | % 149.39/21.59 | | | | | | | | | | | | | | | | | | | | Case 2: % 149.39/21.59 | | | | | | | | | | | | | | | | | | | | | % 149.39/21.59 | | | | | | | | | | | | | | | | | | | | | (7930) all_56_1 = e0 % 149.39/21.59 | | | | | | | | | | | | | | | | | | | | | % 149.39/21.59 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (251), (297), (402), (7437), (7443), (7547), % 149.39/21.59 | | | | | | | | | | | | | | | | | | | | | (7554), (7624), (7930) are inconsistent by % 149.39/21.59 | | | | | | | | | | | | | | | | | | | | | sub-proof #489. % 149.39/21.59 | | | | | | | | | | | | | | | | | | | | | % 149.39/21.59 | | | | | | | | | | | | | | | | | | | | End of split % 149.39/21.59 | | | | | | | | | | | | | | | | | | | | % 149.39/21.59 | | | | | | | | | | | | | | | | | | | Case 2: % 149.39/21.59 | | | | | | | | | | | | | | | | | | | | % 149.39/21.59 | | | | | | | | | | | | | | | | | | | | (7931) all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0 % 149.39/21.59 | | | | | | | | | | | | | | | | | | | | % 149.39/21.59 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7437), (7443), (7547), (7624), (7931) are % 149.39/21.59 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #490. % 149.39/21.59 | | | | | | | | | | | | | | | | | | | | % 149.39/21.59 | | | | | | | | | | | | | | | | | | | End of split % 149.39/21.59 | | | | | | | | | | | | | | | | | | | % 149.39/21.59 | | | | | | | | | | | | | | | | | | End of split % 149.39/21.59 | | | | | | | | | | | | | | | | | | % 149.39/21.59 | | | | | | | | | | | | | | | | | Case 2: % 149.39/21.59 | | | | | | | | | | | | | | | | | | % 149.39/21.59 | | | | | | | | | | | | | | | | | | (7932) all_56_31 = e3 % 149.39/21.59 | | | | | | | | | | | | | | | | | | (7933) all_56_25 = e0 % 149.39/21.59 | | | | | | | | | | | | | | | | | | % 149.39/21.59 | | | | | | | | | | | | | | | | | | REF_CLOSE: (188), (239), (447), (480), (544), (581), (7570), % 149.39/21.59 | | | | | | | | | | | | | | | | | | (7582), (7932), (7933) are inconsistent by % 149.39/21.59 | | | | | | | | | | | | | | | | | | sub-proof #71. % 149.39/21.59 | | | | | | | | | | | | | | | | | | % 149.39/21.59 | | | | | | | | | | | | | | | | | End of split % 149.39/21.59 | | | | | | | | | | | | | | | | | % 149.39/21.59 | | | | | | | | | | | | | | | | Case 2: % 149.39/21.59 | | | | | | | | | | | | | | | | | % 149.39/21.59 | | | | | | | | | | | | | | | | | (7934) all_56_5 = e3 % 149.39/21.59 | | | | | | | | | | | | | | | | | (7935) all_56_1 = e1 % 149.39/21.59 | | | | | | | | | | | | | | | | | % 149.39/21.59 | | | | | | | | | | | | | | | | | REF_CLOSE: (251), (429), (533), (546), (723), (7437), (7541), % 149.39/21.59 | | | | | | | | | | | | | | | | | (7547), (7552), (7555), (7934), (7935) are % 149.39/21.59 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #211. % 149.39/21.59 | | | | | | | | | | | | | | | | | % 149.39/21.59 | | | | | | | | | | | | | | | | End of split % 149.39/21.59 | | | | | | | | | | | | | | | | % 149.39/21.59 | | | | | | | | | | | | | | | Case 2: % 149.39/21.59 | | | | | | | | | | | | | | | | % 149.39/21.59 | | | | | | | | | | | | | | | | (7936) all_56_31 = e1 % 149.39/21.59 | | | | | | | | | | | | | | | | (7937) all_56_29 = e0 % 149.39/21.59 | | | | | | | | | | | | | | | | % 149.39/21.59 | | | | | | | | | | | | | | | | COMBINE_EQS: (357), (7937) imply: % 149.39/21.59 | | | | | | | | | | | | | | | | (7938) all_52_11 = e0 % 149.39/21.59 | | | | | | | | | | | | | | | | % 149.39/21.59 | | | | | | | | | | | | | | | | SIMP: (7938) implies: % 149.39/21.59 | | | | | | | | | | | | | | | | (7939) all_52_11 = e0 % 149.39/21.59 | | | | | | | | | | | | | | | | % 149.39/21.59 | | | | | | | | | | | | | | | | COMBINE_EQS: (544), (7936) imply: % 149.39/21.59 | | | | | | | | | | | | | | | | (7940) all_4_2 = e1 % 149.39/21.59 | | | | | | | | | | | | | | | | % 149.39/21.59 | | | | | | | | | | | | | | | | COMBINE_EQS: (547), (7940) imply: % 149.39/21.59 | | | | | | | | | | | | | | | | (7941) all_58_15 = e1 % 149.39/21.59 | | | | | | | | | | | | | | | | % 149.39/21.59 | | | | | | | | | | | | | | | | REDUCE: (173), (7939) imply: % 149.39/21.59 | | | | | | | | | | | | | | | | (7942) ~ (all_52_7 = e0) % 149.39/21.59 | | | | | | | | | | | | | | | | % 149.39/21.59 | | | | | | | | | | | | | | | | REDUCE: (38), (7940) imply: % 149.39/21.59 | | | | | | | | | | | | | | | | (7943) op(e1, e1) = all_4_1 % 149.39/21.59 | | | | | | | | | | | | | | | | % 149.39/21.59 | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9), (37), (206), (239), (297), (322), (386), % 149.39/21.59 | | | | | | | | | | | | | | | | (402), (480), (550), (551), (767), (7439), (7570), % 149.39/21.59 | | | | | | | | | | | | | | | | (7573), (7576), (7584), (7941), (7942), (7943), % 149.39/21.59 | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 149.39/21.59 | | | | | | | | | | | | | | | | #68. % 149.39/21.59 | | | | | | | | | | | | | | | | % 149.39/21.59 | | | | | | | | | | | | | | | End of split % 149.39/21.59 | | | | | | | | | | | | | | | % 149.39/21.59 | | | | | | | | | | | | | | End of split % 149.39/21.59 | | | | | | | | | | | | | | % 149.39/21.59 | | | | | | | | | | | | | End of split % 149.39/21.59 | | | | | | | | | | | | | % 149.39/21.59 | | | | | | | | | | | | Case 2: % 149.39/21.59 | | | | | | | | | | | | | % 149.39/21.59 | | | | | | | | | | | | | (7944) all_32_1 = e1 % 149.39/21.59 | | | | | | | | | | | | | (7945) ~ (all_32_0 = e0) | ~ (all_32_2 = e2) % 149.39/21.59 | | | | | | | | | | | | | % 149.39/21.59 | | | | | | | | | | | | | COMBINE_EQS: (682), (7944) imply: % 149.39/21.59 | | | | | | | | | | | | | (7946) all_10_1 = e1 % 149.39/21.59 | | | | | | | | | | | | | % 149.39/21.59 | | | | | | | | | | | | | SIMP: (7946) implies: % 149.39/21.59 | | | | | | | | | | | | | (7947) all_10_1 = e1 % 149.39/21.59 | | | | | | | | | | | | | % 149.39/21.59 | | | | | | | | | | | | | REDUCE: (53), (7947) imply: % 149.39/21.59 | | | | | | | | | | | | | (7948) op(all_10_2, all_10_2) = e1 % 149.39/21.59 | | | | | | | | | | | | | % 149.39/21.59 | | | | | | | | | | | | | REDUCE: (52), (7947) imply: % 149.39/21.59 | | | | | | | | | | | | | (7949) op(e3, e1) = all_10_0 % 149.39/21.59 | | | | | | | | | | | | | % 149.39/21.59 | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_8, % 149.39/21.59 | | | | | | | | | | | | | all_10_0, e1, e3, simplifying with (217), (7949) % 149.39/21.59 | | | | | | | | | | | | | gives: % 149.39/21.59 | | | | | | | | | | | | | (7950) all_52_8 = all_10_0 % 149.39/21.59 | | | | | | | | | | | | | % 149.39/21.59 | | | | | | | | | | | | | COMBINE_EQS: (459), (7950) imply: % 149.39/21.59 | | | | | | | | | | | | | (7951) all_54_2 = all_10_0 % 149.39/21.59 | | | | | | | | | | | | | % 149.39/21.59 | | | | | | | | | | | | | COMBINE_EQS: (429), (7950) imply: % 149.39/21.59 | | | | | | | | | | | | | (7952) all_56_5 = all_10_0 % 149.39/21.59 | | | | | | | | | | | | | % 149.39/21.59 | | | | | | | | | | | | | COMBINE_EQS: (407), (7950) imply: % 149.39/21.59 | | | | | | | | | | | | | (7953) all_58_4 = all_10_0 % 149.39/21.59 | | | | | | | | | | | | | % 149.39/21.59 | | | | | | | | | | | | | REDUCE: (182), (7950) imply: % 149.39/21.59 | | | | | | | | | | | | | (7954) ~ (all_52_4 = all_10_0) % 149.39/21.59 | | | | | | | | | | | | | % 149.39/21.59 | | | | | | | | | | | | | REDUCE: (171), (7950) imply: % 149.39/21.59 | | | | | | | | | | | | | (7955) ~ (all_52_9 = all_10_0) % 149.39/21.59 | | | | | | | | | | | | | % 149.39/21.59 | | | | | | | | | | | | | SIMP: (7955) implies: % 149.39/21.59 | | | | | | | | | | | | | (7956) ~ (all_52_9 = all_10_0) % 149.39/21.59 | | | | | | | | | | | | | % 149.39/21.59 | | | | | | | | | | | | | REDUCE: (169), (7950) imply: % 149.39/21.59 | | | | | | | | | | | | | (7957) ~ (all_52_11 = all_10_0) % 149.39/21.59 | | | | | | | | | | | | | % 149.39/21.59 | | | | | | | | | | | | | SIMP: (7957) implies: % 149.39/21.59 | | | | | | | | | | | | | (7958) ~ (all_52_11 = all_10_0) % 149.39/21.59 | | | | | | | | | | | | | % 149.39/21.59 | | | | | | | | | | | | | REDUCE: (168), (7950) imply: % 149.39/21.59 | | | | | | | | | | | | | (7959) ~ (all_52_12 = all_10_0) % 149.39/21.59 | | | | | | | | | | | | | % 149.39/21.59 | | | | | | | | | | | | | SIMP: (7959) implies: % 149.39/21.59 | | | | | | | | | | | | | (7960) ~ (all_52_12 = all_10_0) % 149.39/21.59 | | | | | | | | | | | | | % 149.39/21.59 | | | | | | | | | | | | | REDUCE: (565), (7950) imply: % 149.39/21.59 | | | | | | | | | | | | | (7961) ~ (all_10_0 = all_10_2) % 149.39/21.59 | | | | | | | | | | | | | % 149.39/21.59 | | | | | | | | | | | | | REDUCE: (582), (7950) imply: % 149.39/21.59 | | | | | | | | | | | | | (7962) ~ (all_10_0 = all_6_2) % 149.39/21.59 | | | | | | | | | | | | | % 149.39/21.59 | | | | | | | | | | | | | BETA: splitting (288) gives: % 149.39/21.59 | | | | | | | | | | | | | % 149.39/21.59 | | | | | | | | | | | | | Case 1: % 149.39/21.59 | | | | | | | | | | | | | | % 149.39/21.59 | | | | | | | | | | | | | | (7963) ~ (all_56_31 = e1) % 149.39/21.59 | | | | | | | | | | | | | | % 149.39/21.59 | | | | | | | | | | | | | | REDUCE: (544), (7963) imply: % 149.39/21.59 | | | | | | | | | | | | | | (7964) ~ (all_4_2 = e1) % 149.39/21.59 | | | | | | | | | | | | | | % 149.39/21.59 | | | | | | | | | | | | | | BETA: splitting (292) gives: % 149.39/21.59 | | | | | | | | | | | | | | % 149.39/21.59 | | | | | | | | | | | | | | Case 1: % 149.39/21.59 | | | | | | | | | | | | | | | % 149.39/21.59 | | | | | | | | | | | | | | | (7965) ~ (all_56_21 = e2) % 149.39/21.59 | | | | | | | | | | | | | | | % 149.39/21.59 | | | | | | | | | | | | | | | REDUCE: (374), (7965) imply: % 149.39/21.59 | | | | | | | | | | | | | | | (7966) ~ (all_6_2 = e2) % 149.39/21.59 | | | | | | | | | | | | | | | % 149.39/21.59 | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (36), (37), (38), (41), (46), (47), % 149.39/21.59 | | | | | | | | | | | | | | | (48), (51), (161), (165), (166), (193), (194), % 149.39/21.59 | | | | | | | | | | | | | | | (196), (205), (237), (246), (247), (248), (250), % 149.39/21.59 | | | | | | | | | | | | | | | (252), (293), (294), (295), (296), (297), (298), % 149.39/21.59 | | | | | | | | | | | | | | | (299), (318), (320), (321), (328), (329), (330), % 149.39/21.59 | | | | | | | | | | | | | | | (331), (335), (340), (341), (345), (365), (374), % 149.39/21.59 | | | | | | | | | | | | | | | (386), (389), (401), (402), (408), (419), (425), % 149.39/21.59 | | | | | | | | | | | | | | | (431), (443), (463), (467), (494), (540), (542), % 149.39/21.59 | | | | | | | | | | | | | | | (543), (545), (546), (547), (548), (549), (550), % 149.39/21.59 | | | | | | | | | | | | | | | (551), (552), (555), (557), (561), (563), (567), % 149.39/21.59 | | | | | | | | | | | | | | | (568), (571), (577), (581), (585), (587), (589), % 149.39/21.59 | | | | | | | | | | | | | | | (590), (612), (613), (617), (625), (627), (761), % 149.39/21.59 | | | | | | | | | | | | | | | (767), (7436), (7437), (7439), (7441), (7443), % 149.39/21.59 | | | | | | | | | | | | | | | (7447), (7449), (7451), (7945), (7948), (7951), % 149.39/21.59 | | | | | | | | | | | | | | | (7952), (7953), (7954), (7956), (7958), (7960), % 149.39/21.59 | | | | | | | | | | | | | | | (7961), (7962), (7964), (7966), (function-axioms) % 149.39/21.59 | | | | | | | | | | | | | | | are inconsistent by sub-proof #383. % 149.39/21.59 | | | | | | | | | | | | | | | % 149.39/21.59 | | | | | | | | | | | | | | Case 2: % 149.39/21.59 | | | | | | | | | | | | | | | % 149.39/21.59 | | | | | | | | | | | | | | | (7967) all_56_21 = e2 % 149.39/21.59 | | | | | | | | | | | | | | | (7968) all_56_19 = e1 % 149.39/21.59 | | | | | | | | | | | | | | | % 149.39/21.59 | | | | | | | | | | | | | | | COMBINE_EQS: (7424), (7968) imply: % 149.39/21.59 | | | | | | | | | | | | | | | (7969) all_6_0 = e1 % 149.39/21.59 | | | | | | | | | | | | | | | % 149.39/21.59 | | | | | | | | | | | | | | | SIMP: (7969) implies: % 149.39/21.59 | | | | | | | | | | | | | | | (7970) all_6_0 = e1 % 149.39/21.59 | | | | | | | | | | | | | | | % 149.39/21.59 | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (38), (41), (46), (47), (48), (173), % 149.39/21.59 | | | | | | | | | | | | | | | (181), (183), (188), (237), (238), (239), (250), % 149.39/21.59 | | | | | | | | | | | | | | | (251), (288), (289), (290), (298), (322), (329), % 149.39/21.59 | | | | | | | | | | | | | | | (333), (336), (339), (343), (345), (357), (360), % 149.39/21.59 | | | | | | | | | | | | | | | (374), (386), (389), (401), (419), (447), (457), % 149.39/21.59 | | | | | | | | | | | | | | | (480), (482), (494), (540), (544), (546), (547), % 149.39/21.59 | | | | | | | | | | | | | | | (549), (550), (551), (554), (555), (557), (570), % 149.39/21.59 | | | | | | | | | | | | | | | (571), (577), (579), (581), (585), (587), (588), % 149.39/21.59 | | | | | | | | | | | | | | | (589), (590), (617), (621), (623), (761), (7420), % 149.39/21.59 | | | | | | | | | | | | | | | (7425), (7427), (7441), (7443), (7445), (7451), % 149.39/21.59 | | | | | | | | | | | | | | | (7945), (7948), (7951), (7952), (7953), (7954), % 149.39/21.59 | | | | | | | | | | | | | | | (7958), (7960), (7961), (7962), (7967), (7970), % 149.39/21.59 | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 149.39/21.59 | | | | | | | | | | | | | | | #60. % 149.39/21.59 | | | | | | | | | | | | | | | % 149.39/21.59 | | | | | | | | | | | | | | End of split % 149.39/21.59 | | | | | | | | | | | | | | % 149.39/21.59 | | | | | | | | | | | | | Case 2: % 149.39/21.59 | | | | | | | | | | | | | | % 149.39/21.59 | | | | | | | | | | | | | | (7971) all_56_31 = e1 % 149.39/21.59 | | | | | | | | | | | | | | (7972) all_56_29 = e0 % 149.39/21.59 | | | | | | | | | | | | | | % 149.39/21.59 | | | | | | | | | | | | | | COMBINE_EQS: (357), (7972) imply: % 149.39/21.59 | | | | | | | | | | | | | | (7973) all_52_11 = e0 % 149.39/21.59 | | | | | | | | | | | | | | % 149.39/21.59 | | | | | | | | | | | | | | REF_CLOSE: (38), (41), (48), (250), (252), (297), (299), % 149.39/21.59 | | | | | | | | | | | | | | (337), (380), (402), (408), (543), (544), (546), % 149.39/21.59 | | | | | | | | | | | | | | (549), (554), (555), (563), (580), (581), (622), % 149.39/21.59 | | | | | | | | | | | | | | (7436), (7437), (7443), (7948), (7951), (7954), % 149.39/21.59 | | | | | | | | | | | | | | (7958), (7960), (7961), (7971), (7973), % 149.39/21.59 | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 149.39/21.59 | | | | | | | | | | | | | | #381. % 149.39/21.59 | | | | | | | | | | | | | | % 149.39/21.59 | | | | | | | | | | | | | End of split % 149.39/21.59 | | | | | | | | | | | | | % 149.39/21.59 | | | | | | | | | | | | End of split % 149.39/21.59 | | | | | | | | | | | | % 149.39/21.59 | | | | | | | | | | | Case 2: % 149.39/21.59 | | | | | | | | | | | | % 149.39/21.59 | | | | | | | | | | | | (7974) all_30_0 = e3 % 149.39/21.59 | | | | | | | | | | | | (7975) ~ (all_30_1 = e0) | ~ (all_30_2 = e1) % 149.39/21.59 | | | | | | | | | | | | % 149.39/21.59 | | | | | | | | | | | | COMBINE_EQS: (718), (7974) imply: % 149.39/21.59 | | | | | | | | | | | | (7976) all_8_0 = e3 % 149.39/21.59 | | | | | | | | | | | | % 149.39/21.59 | | | | | | | | | | | | SIMP: (7976) implies: % 149.39/21.59 | | | | | | | | | | | | (7977) all_8_0 = e3 % 149.39/21.59 | | | | | | | | | | | | % 149.39/21.59 | | | | | | | | | | | | REF_CLOSE: (9), (36), (41), (46), (47), (48), (51), (212), % 149.39/21.59 | | | | | | | | | | | | (237), (242), (247), (252), (294), (295), (296), % 149.39/21.59 | | | | | | | | | | | | (390), (425), (431), (443), (540), (541), (542), % 149.39/21.59 | | | | | | | | | | | | (543), (545), (557), (579), (583), (590), (617), % 149.39/21.59 | | | | | | | | | | | | (658), (7436), (7447), (7975), (7977), % 149.39/21.59 | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 149.39/21.59 | | | | | | | | | | | | #379. % 149.39/21.59 | | | | | | | | | | | | % 149.39/21.59 | | | | | | | | | | | End of split % 149.39/21.59 | | | | | | | | | | | % 149.39/21.59 | | | | | | | | | | Case 2: % 149.39/21.59 | | | | | | | | | | | % 149.39/21.59 | | | | | | | | | | | (7978) all_26_0 = e1 % 149.39/21.59 | | | | | | | | | | | % 149.39/21.59 | | | | | | | | | | | COMBINE_EQS: (760), (7978) imply: % 149.39/21.59 | | | | | | | | | | | (7979) all_4_0 = e1 % 149.39/21.59 | | | | | | | | | | | % 149.39/21.59 | | | | | | | | | | | REF_CLOSE: (4), (9), (36), (37), (38), (41), (46), (47), % 149.39/21.59 | | | | | | | | | | | (48), (51), (53), (168), (173), (181), (182), % 149.39/21.59 | | | | | | | | | | | (188), (189), (192), (193), (194), (196), (197), % 149.39/21.59 | | | | | | | | | | | (206), (212), (237), (239), (241), (242), (243), % 149.39/21.59 | | | | | | | | | | | (244), (247), (251), (252), (287), (288), (289), % 149.39/21.59 | | | | | | | | | | | (290), (291), (292), (293), (294), (295), (296), % 149.39/21.59 | | | | | | | | | | | (297), (327), (330), (331), (332), (333), (336), % 149.39/21.59 | | | | | | | | | | | (339), (344), (357), (360), (365), (366), (374), % 149.39/21.59 | | | | | | | | | | | (381), (386), (389), (401), (402), (407), (419), % 149.39/21.59 | | | | | | | | | | | (425), (431), (443), (447), (457), (471), (476), % 149.39/21.59 | | | | | | | | | | | (480), (540), (541), (542), (543), (544), (545), % 149.39/21.59 | | | | | | | | | | | (546), (549), (550), (552), (553), (554), (557), % 149.39/21.59 | | | | | | | | | | | (559), (563), (565), (568), (569), (570), (577), % 149.39/21.59 | | | | | | | | | | | (581), (583), (585), (587), (590), (591), (612), % 149.39/21.59 | | | | | | | | | | | (622), (627), (767), (7418), (7420), (7423), % 149.39/21.59 | | | | | | | | | | | (7424), (7425), (7426), (7429), (7431), (7433), % 149.39/21.59 | | | | | | | | | | | (7434), (7436), (7439), (7441), (7445), (7447), % 149.39/21.59 | | | | | | | | | | | (7979), (function-axioms) are inconsistent by % 149.39/21.59 | | | | | | | | | | | sub-proof #49. % 149.39/21.59 | | | | | | | | | | | % 149.39/21.59 | | | | | | | | | | End of split % 149.39/21.59 | | | | | | | | | | % 149.39/21.59 | | | | | | | | | Case 2: % 149.39/21.59 | | | | | | | | | | % 149.39/21.59 | | | | | | | | | | (7980) all_22_1 = e3 % 149.39/21.59 | | | | | | | | | | % 149.39/21.59 | | | | | | | | | | COMBINE_EQS: (672), (7980) imply: % 149.39/21.59 | | | | | | | | | | (7981) all_8_1 = e3 % 149.39/21.59 | | | | | | | | | | % 149.39/21.59 | | | | | | | | | | SIMP: (7981) implies: % 149.39/21.59 | | | | | | | | | | (7982) all_8_1 = e3 % 149.39/21.59 | | | | | | | | | | % 149.39/21.59 | | | | | | | | | | REF_CLOSE: (4), (7), (9), (36), (38), (41), (46), (47), (48), % 149.39/21.59 | | | | | | | | | | (51), (53), (182), (183), (188), (189), (192), % 149.39/21.59 | | | | | | | | | | (215), (237), (239), (240), (241), (242), (243), % 149.39/21.59 | | | | | | | | | | (244), (247), (252), (287), (288), (289), (290), % 149.39/21.59 | | | | | | | | | | (291), (292), (293), (294), (298), (299), (324), % 149.39/21.59 | | | | | | | | | | (326), (327), (336), (339), (342), (343), (357), % 149.39/21.59 | | | | | | | | | | (360), (365), (366), (374), (381), (401), (408), % 149.39/21.59 | | | | | | | | | | (419), (429), (447), (471), (476), (478), (480), % 149.39/21.59 | | | | | | | | | | (540), (541), (542), (543), (544), (545), (546), % 149.39/21.59 | | | | | | | | | | (549), (550), (552), (553), (554), (555), (559), % 149.39/21.59 | | | | | | | | | | (561), (563), (569), (570), (571), (575), (581), % 149.39/21.59 | | | | | | | | | | (585), (587), (591), (612), (617), (622), (627), % 149.39/21.59 | | | | | | | | | | (7418), (7420), (7423), (7425), (7426), (7429), % 149.39/21.59 | | | | | | | | | | (7431), (7433), (7434), (7436), (7441), (7445), % 149.39/21.59 | | | | | | | | | | (7982), (function-axioms) are inconsistent by % 149.39/21.59 | | | | | | | | | | sub-proof #42. % 149.39/21.59 | | | | | | | | | | % 149.39/21.59 | | | | | | | | | End of split % 149.39/21.59 | | | | | | | | | % 149.39/21.59 | | | | | | | | Case 2: % 149.39/21.59 | | | | | | | | | % 149.39/21.59 | | | | | | | | | (7983) all_18_0 = e3 % 149.39/21.59 | | | | | | | | | (7984) ~ (all_18_1 = e2) | ~ (all_18_2 = e0) % 149.39/21.59 | | | | | | | | | % 149.39/21.59 | | | | | | | | | COMBINE_EQS: (753), (7983) imply: % 149.39/21.59 | | | | | | | | | (7985) all_6_0 = e3 % 149.39/21.59 | | | | | | | | | % 149.39/21.59 | | | | | | | | | SIMP: (7985) implies: % 149.39/21.59 | | | | | | | | | (7986) all_6_0 = e3 % 149.39/21.59 | | | | | | | | | % 149.39/21.59 | | | | | | | | | REF_CLOSE: (8), (41), (242), (292), (374), (524), (541), % 149.39/21.59 | | | | | | | | | (622), (7419), (7420), (7424), (7434), (7984), % 149.39/21.59 | | | | | | | | | (7986), (function-axioms) are inconsistent by % 149.39/21.59 | | | | | | | | | sub-proof #40. % 149.39/21.59 | | | | | | | | | % 149.39/21.59 | | | | | | | | End of split % 149.39/21.59 | | | | | | | | % 149.39/21.59 | | | | | | | Case 2: % 149.39/21.59 | | | | | | | | % 149.39/21.59 | | | | | | | | (7987) all_16_0 = e1 % 149.39/21.59 | | | | | | | | % 149.39/21.59 | | | | | | | | COMBINE_EQS: (757), (7987) imply: % 149.39/21.59 | | | | | | | | (7988) all_10_0 = e1 % 149.39/21.59 | | | | | | | | % 149.39/21.59 | | | | | | | | SIMP: (7988) implies: % 149.39/21.59 | | | | | | | | (7989) all_10_0 = e1 % 149.39/21.59 | | | | | | | | % 149.39/21.59 | | | | | | | | COMBINE_EQS: (741), (7989) imply: % 149.39/21.59 | | | | | | | | (7990) all_24_0 = e1 % 149.39/21.59 | | | | | | | | % 149.39/21.59 | | | | | | | | REDUCE: (52), (7989) imply: % 149.39/21.59 | | | | | | | | (7991) op(e3, all_10_1) = e1 % 149.39/21.59 | | | | | | | | % 149.39/21.59 | | | | | | | | BETA: splitting (74) gives: % 149.39/21.59 | | | | | | | | % 149.39/21.59 | | | | | | | | Case 1: % 149.39/21.59 | | | | | | | | | % 149.39/21.59 | | | | | | | | | (7992) ~ (all_18_0 = e3) % 149.39/21.59 | | | | | | | | | % 149.39/21.59 | | | | | | | | | REDUCE: (753), (7992) imply: % 149.39/21.59 | | | | | | | | | (7993) ~ (all_6_0 = e3) % 149.39/21.59 | | | | | | | | | % 149.39/21.59 | | | | | | | | | BETA: splitting (84) gives: % 149.39/21.59 | | | | | | | | | % 149.39/21.59 | | | | | | | | | Case 1: % 149.39/21.59 | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | (7994) ~ (all_22_1 = e3) % 149.39/21.60 | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | REDUCE: (672), (7994) imply: % 149.39/21.60 | | | | | | | | | | (7995) ~ (all_8_1 = e3) % 149.39/21.60 | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | BETA: splitting (89) gives: % 149.39/21.60 | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | Case 1: % 149.39/21.60 | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | | (7996) ~ (all_24_0 = e1) % 149.39/21.60 | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | | REDUCE: (7990), (7996) imply: % 149.39/21.60 | | | | | | | | | | | (7997) $false % 149.39/21.60 | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | | CLOSE: (7997) is inconsistent. % 149.39/21.60 | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | Case 2: % 149.39/21.60 | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | | (7998) ~ (all_24_1 = e0) | ~ (all_24_2 = e2) % 149.39/21.60 | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | | BETA: splitting (94) gives: % 149.39/21.60 | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | | Case 1: % 149.39/21.60 | | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | | | (7999) ~ (all_26_0 = e1) % 149.39/21.60 | | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | | | REDUCE: (760), (7999) imply: % 149.39/21.60 | | | | | | | | | | | | (8000) ~ (all_4_0 = e1) % 149.39/21.60 | | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | | | BETA: splitting (288) gives: % 149.39/21.60 | | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | | | Case 1: % 149.39/21.60 | | | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | | | | (8001) ~ (all_56_31 = e1) % 149.39/21.60 | | | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | | | | REDUCE: (544), (8001) imply: % 149.39/21.60 | | | | | | | | | | | | | (8002) ~ (all_4_2 = e1) % 149.39/21.60 | | | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | | | | BETA: splitting (292) gives: % 149.39/21.60 | | | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | | | | Case 1: % 149.39/21.60 | | | | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | | | | | (8003) ~ (all_56_21 = e2) % 149.39/21.60 | | | | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | | | | | REDUCE: (374), (8003) imply: % 149.39/21.60 | | | | | | | | | | | | | | (8004) ~ (all_6_2 = e2) % 149.39/21.60 | | | | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | | | | | BETA: splitting (294) gives: % 149.39/21.60 | | | | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | | | | | Case 1: % 149.39/21.60 | | | | | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | | | | | | (8005) ~ (all_56_11 = e0) % 149.39/21.60 | | | | | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | | | | | | REDUCE: (545), (8005) imply: % 149.39/21.60 | | | | | | | | | | | | | | | (8006) ~ (all_8_2 = e0) % 149.39/21.60 | | | | | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | | | | | | REF_CLOSE: (36), (38), (41), (47), (48), (51), (53), (168), % 149.39/21.60 | | | | | | | | | | | | | | | (181), (182), (189), (193), (194), (196), (197), % 149.39/21.60 | | | | | | | | | | | | | | | (212), (241), (242), (243), (247), (251), (252), % 149.39/21.60 | | | | | | | | | | | | | | | (287), (291), (293), (294), (295), (296), (297), % 149.39/21.60 | | | | | | | | | | | | | | | (327), (330), (331), (332), (333), (344), (365), % 149.39/21.60 | | | | | | | | | | | | | | | (366), (374), (381), (386), (389), (401), (402), % 149.39/21.60 | | | | | | | | | | | | | | | (407), (419), (425), (431), (443), (457), (476), % 149.39/21.60 | | | | | | | | | | | | | | | (541), (542), (543), (544), (545), (546), (550), % 149.39/21.60 | | | | | | | | | | | | | | | (552), (553), (554), (557), (559), (563), (565), % 149.39/21.60 | | | | | | | | | | | | | | | (568), (569), (577), (583), (587), (590), (591), % 149.39/21.60 | | | | | | | | | | | | | | | (612), (622), (627), (7418), (7420), (7423), % 149.39/21.60 | | | | | | | | | | | | | | | (7425), (7426), (7431), (7433), (7434), (7436), % 149.39/21.60 | | | | | | | | | | | | | | | (7441), (7993), (7995), (8004), (8006), % 149.39/21.60 | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 149.39/21.60 | | | | | | | | | | | | | | | #59. % 149.39/21.60 | | | | | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | | | | | Case 2: % 149.39/21.60 | | | | | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | | | | | | (8007) all_56_15 = e2 % 149.39/21.60 | | | | | | | | | | | | | | | (8008) all_56_11 = e0 % 149.39/21.60 | | | | | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | | | | | | COMBINE_EQS: (545), (8008) imply: % 149.39/21.60 | | | | | | | | | | | | | | | (8009) all_8_2 = e0 % 149.39/21.60 | | | | | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | | | | | | COMBINE_EQS: (443), (8007) imply: % 149.39/21.60 | | | | | | | | | | | | | | | (8010) all_52_13 = e2 % 149.39/21.60 | | | | | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | | | | | | COMBINE_EQS: (386), (8010) imply: % 149.39/21.60 | | | | | | | | | | | | | | | (8011) all_58_10 = e2 % 149.39/21.60 | | | | | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | | | | | | COMBINE_EQS: (554), (8009) imply: % 149.39/21.60 | | | | | | | | | | | | | | | (8012) all_58_3 = e0 % 149.39/21.60 | | | | | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | | | | | | REDUCE: (193), (8010) imply: % 149.39/21.60 | | | | | | | | | | | | | | | (8013) ~ (all_52_1 = e2) % 149.39/21.60 | | | | | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | | | | | | REDUCE: (568), (8009) imply: % 149.39/21.60 | | | | | | | | | | | | | | | (8014) ~ (all_52_1 = e0) % 149.39/21.60 | | | | | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | | | | | | REDUCE: (571), (8009) imply: % 149.39/21.60 | | | | | | | | | | | | | | | (8015) ~ (all_52_4 = e0) % 149.39/21.60 | | | | | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | | | | | | REDUCE: (165), (8010) imply: % 149.39/21.60 | | | | | | | | | | | | | | | (8016) ~ (all_52_9 = e2) % 149.39/21.60 | | | | | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | | | | | | REDUCE: (577), (8009) imply: % 149.39/21.60 | | | | | | | | | | | | | | | (8017) ~ (all_52_9 = e0) % 149.39/21.60 | | | | | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | | | | | | REDUCE: (161), (8010) imply: % 149.39/21.60 | | | | | | | | | | | | | | | (8018) ~ (all_52_12 = e2) % 149.39/21.60 | | | | | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | | | | | | REDUCE: (158), (8010) imply: % 149.39/21.60 | | | | | | | | | | | | | | | (8019) ~ (all_52_14 = e2) % 149.39/21.60 | | | | | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | | | | | | SIMP: (8019) implies: % 149.39/21.60 | | | | | | | | | | | | | | | (8020) ~ (all_52_14 = e2) % 149.39/21.60 | | | | | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | | | | | | REDUCE: (590), (8010) imply: % 149.39/21.60 | | | | | | | | | | | | | | | (8021) ~ (all_4_2 = e2) % 149.39/21.60 | | | | | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | | | | | | SIMP: (8021) implies: % 149.39/21.60 | | | | | | | | | | | | | | | (8022) ~ (all_4_2 = e2) % 149.39/21.60 | | | | | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | | | | | | REDUCE: (48), (8009) imply: % 149.39/21.60 | | | | | | | | | | | | | | | (8023) op(e0, e0) = all_8_1 % 149.39/21.60 | | | | | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | | | | | | REDUCE: (46), (8009) imply: % 149.39/21.60 | | | | | | | | | | | | | | | (8024) op(e2, e2) = e0 % 149.39/21.60 | | | | | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | | | | | | REDUCE: (625), (8010) imply: % 149.39/21.60 | | | | | | | | | | | | | | | (8025) op(e0, e2) = all_56_14 % 149.39/21.60 | | | | | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | | | | | | REF_CLOSE: (36), (37), (38), (53), (160), (168), (171), % 149.39/21.60 | | | | | | | | | | | | | | | (174), (176), (181), (182), (183), (184), (187), % 149.39/21.60 | | | | | | | | | | | | | | | (188), (189), (191), (192), (194), (196), (197), % 149.39/21.60 | | | | | | | | | | | | | | | (205), (206), (207), (210), (211), (213), (215), % 149.39/21.60 | | | | | | | | | | | | | | | (217), (218), (237), (239), (240), (242), (243), % 149.39/21.60 | | | | | | | | | | | | | | | (244), (246), (248), (249), (250), (251), (252), % 149.39/21.60 | | | | | | | | | | | | | | | (286), (291), (293), (318), (319), (321), (324), % 149.39/21.60 | | | | | | | | | | | | | | | (326), (328), (329), (330), (335), (337), (338), % 149.39/21.60 | | | | | | | | | | | | | | | (340), (345), (365), (366), (374), (380), (381), % 149.39/21.60 | | | | | | | | | | | | | | | (389), (401), (402), (407), (408), (419), (425), % 149.39/21.60 | | | | | | | | | | | | | | | (429), (431), (435), (457), (459), (461), (463), % 149.39/21.60 | | | | | | | | | | | | | | | (467), (471), (473), (478), (480), (521), (540), % 149.39/21.60 | | | | | | | | | | | | | | | (541), (543), (544), (547), (548), (549), (550), % 149.39/21.60 | | | | | | | | | | | | | | | (551), (552), (553), (555), (559), (563), (565), % 149.39/21.60 | | | | | | | | | | | | | | | (567), (569), (570), (580), (581), (582), (583), % 149.39/21.60 | | | | | | | | | | | | | | | (587), (588), (589), (613), (614), (616), (618), % 149.39/21.60 | | | | | | | | | | | | | | | (620), (621), (624), (626), (627), (643), (7436), % 149.39/21.60 | | | | | | | | | | | | | | | (7439), (7995), (7998), (8000), (8004), (8007), % 149.39/21.60 | | | | | | | | | | | | | | | (8011), (8012), (8013), (8014), (8015), (8016), % 149.39/21.60 | | | | | | | | | | | | | | | (8017), (8018), (8020), (8022), (8023), (8024), % 149.39/21.60 | | | | | | | | | | | | | | | (8025), (function-axioms) are inconsistent by % 149.39/21.60 | | | | | | | | | | | | | | | sub-proof #286. % 149.39/21.60 | | | | | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | | | | | End of split % 149.39/21.60 | | | | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | | | | Case 2: % 149.39/21.60 | | | | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | | | | | (8026) all_56_21 = e2 % 149.39/21.60 | | | | | | | | | | | | | | (8027) all_56_19 = e1 % 149.39/21.60 | | | | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | | | | | COMBINE_EQS: (7424), (8027) imply: % 149.39/21.60 | | | | | | | | | | | | | | (8028) all_6_0 = e1 % 149.39/21.60 | | | | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | | | | | COMBINE_EQS: (374), (8026) imply: % 149.39/21.60 | | | | | | | | | | | | | | (8029) all_6_2 = e2 % 149.39/21.60 | | | | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | | | | | COMBINE_EQS: (7425), (8028) imply: % 149.39/21.60 | | | | | | | | | | | | | | (8030) all_58_7 = e1 % 149.39/21.60 | | | | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | | | | | REDUCE: (569), (8029) imply: % 149.39/21.60 | | | | | | | | | | | | | | (8031) ~ (all_52_2 = e2) % 149.39/21.60 | | | | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | | | | | REDUCE: (7427), (8028) imply: % 149.39/21.60 | | | | | | | | | | | | | | (8032) ~ (all_52_4 = e1) % 149.39/21.60 | | | | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | | | | | REDUCE: (7429), (8028) imply: % 149.39/21.60 | | | | | | | | | | | | | | (8033) ~ (all_52_7 = e1) % 149.39/21.60 | | | | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | | | | | REDUCE: (587), (8029) imply: % 149.39/21.60 | | | | | | | | | | | | | | (8034) ~ (all_52_14 = e2) % 149.39/21.60 | | | | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | | | | | REDUCE: (7420), (8029) imply: % 149.39/21.60 | | | | | | | | | | | | | | (8035) op(e2, e2) = e2 % 149.39/21.60 | | | | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | | | | | REDUCE: (41), (8029) imply: % 149.39/21.60 | | | | | | | | | | | | | | (8036) op(e1, e1) = e2 % 149.39/21.60 | | | | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_8_2, e2, % 149.39/21.60 | | | | | | | | | | | | | | e2, e2, simplifying with (46), (8035) gives: % 149.39/21.60 | | | | | | | | | | | | | | (8037) all_8_2 = e2 % 149.39/21.60 | | | | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | | | | | COMBINE_EQS: (554), (8037) imply: % 149.39/21.60 | | | | | | | | | | | | | | (8038) all_58_3 = e2 % 149.39/21.60 | | | | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | | | | | REDUCE: (568), (8037) imply: % 149.39/21.60 | | | | | | | | | | | | | | (8039) ~ (all_52_1 = e2) % 149.39/21.60 | | | | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | | | | | REDUCE: (571), (8037) imply: % 149.39/21.60 | | | | | | | | | | | | | | (8040) ~ (all_52_4 = e2) % 149.39/21.60 | | | | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | | | | | REDUCE: (575), (8037) imply: % 149.39/21.60 | | | | | | | | | | | | | | (8041) ~ (all_52_7 = e2) % 149.39/21.60 | | | | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | | | | | REDUCE: (579), (8037) imply: % 149.39/21.60 | | | | | | | | | | | | | | (8042) ~ (all_52_13 = e2) % 149.39/21.60 | | | | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | | | | | REDUCE: (48), (8037) imply: % 149.39/21.60 | | | | | | | | | | | | | | (8043) op(e2, e2) = all_8_1 % 149.39/21.60 | | | | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | | | | | REDUCE: (617), (8037) imply: % 149.39/21.60 | | | | | | | | | | | | | | (8044) op(e2, e2) = all_56_10 % 149.39/21.60 | | | | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, % 149.39/21.60 | | | | | | | | | | | | | | all_56_10, e2, e2, simplifying with (8035), (8044) % 149.39/21.60 | | | | | | | | | | | | | | gives: % 149.39/21.60 | | | | | | | | | | | | | | (8045) all_56_10 = e2 % 149.39/21.60 | | | | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_8_1, % 149.39/21.60 | | | | | | | | | | | | | | all_56_10, e2, e2, simplifying with (8043), (8044) % 149.39/21.60 | | | | | | | | | | | | | | gives: % 149.39/21.60 | | | | | | | | | | | | | | (8046) all_56_10 = all_8_1 % 149.39/21.60 | | | | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | | | | | COMBINE_EQS: (8045), (8046) imply: % 149.39/21.60 | | | | | | | | | | | | | | (8047) all_8_1 = e2 % 149.39/21.60 | | | | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | | | | | SIMP: (8047) implies: % 149.39/21.60 | | | | | | | | | | | | | | (8048) all_8_1 = e2 % 149.39/21.60 | | | | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | | | | | REDUCE: (47), (8048) imply: % 149.39/21.60 | | | | | | | | | | | | | | (8049) op(e2, e2) = all_8_0 % 149.39/21.60 | | | | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, all_8_0, % 149.39/21.60 | | | | | | | | | | | | | | e2, e2, simplifying with (8035), (8049) gives: % 149.39/21.60 | | | | | | | | | | | | | | (8050) all_8_0 = e2 % 149.39/21.60 | | | | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | | | | | BETA: splitting (290) gives: % 149.39/21.60 | | | | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | | | | | Case 1: % 149.39/21.60 | | | | | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | | | | | | (8051) ~ (all_56_31 = e3) % 149.39/21.60 | | | | | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | | | | | | REDUCE: (544), (8051) imply: % 149.39/21.60 | | | | | | | | | | | | | | | (8052) ~ (all_4_2 = e3) % 149.39/21.60 | | | | | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | | | | | | BETA: splitting (289) gives: % 149.39/21.60 | | | | | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | | | | | | Case 1: % 149.39/21.60 | | | | | | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | | | | | | | (8053) ~ (all_56_31 = e2) % 149.39/21.60 | | | | | | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | | | | | | | REDUCE: (544), (8053) imply: % 149.39/21.60 | | | | | | | | | | | | | | | | (8054) ~ (all_4_2 = e2) % 149.39/21.60 | | | | | | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | | | | | | | BETA: splitting (237) gives: % 149.39/21.60 | | | | | | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | | | | | | | Case 1: % 149.39/21.60 | | | | | | | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | | | | | | | | (8055) all_54_15 = e3 % 149.39/21.60 | | | | | | | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | | | | | | | | REF_CLOSE: (540), (8052), (8055) are inconsistent by % 149.39/21.60 | | | | | | | | | | | | | | | | | sub-proof #740. % 149.39/21.60 | | | | | | | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | | | | | | | Case 2: % 149.39/21.60 | | | | | | | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | | | | | | | | (8056) all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0 % 149.39/21.60 | | | | | | | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | | | | | | | | BETA: splitting (319) gives: % 149.39/21.60 | | | | | | | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | | | | | | | | Case 1: % 149.39/21.60 | | | | | | | | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | | | | | | | | | (8057) all_58_12 = e2 % 149.39/21.60 | | | | | | | | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (365), (8057) imply: % 149.39/21.60 | | | | | | | | | | | | | | | | | | (8058) all_52_3 = e2 % 149.39/21.60 | | | | | | | | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | | | | | | | | | REDUCE: (188), (8058) imply: % 149.39/21.60 | | | | | | | | | | | | | | | | | | (8059) ~ (all_52_7 = e2) % 149.39/21.60 | | | | | | | | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | | | | | | | | | REDUCE: (187), (8058) imply: % 149.39/21.60 | | | | | | | | | | | | | | | | | | (8060) ~ (all_52_11 = e2) % 149.39/21.60 | | | | | | | | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | | | | | | | | | SIMP: (8060) implies: % 149.39/21.60 | | | | | | | | | | | | | | | | | | (8061) ~ (all_52_11 = e2) % 149.39/21.60 | | | | | | | | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | | | | | | | | | REDUCE: (570), (8058) imply: % 149.39/21.60 | | | | | | | | | | | | | | | | | | (8062) ~ (all_4_2 = e2) % 149.39/21.60 | | | | | | | | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | | | | | | | | | REDUCE: (615), (8058) imply: % 149.39/21.60 | | | | | | | | | | | | | | | | | | (8063) op(e3, e2) = all_56_24 % 149.39/21.60 | | | | | | | | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | | | | | | | | | BETA: splitting (318) gives: % 149.39/21.60 | | | | | | | | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | | | | | | | | | Case 1: % 149.39/21.60 | | | | | | | | | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | | | | | | | | | | (8064) all_58_12 = e1 % 149.39/21.60 | | | | | | | | | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (8057), (8064) imply: % 149.39/21.60 | | | | | | | | | | | | | | | | | | | (8065) e2 = e1 % 149.39/21.60 | | | | | | | | | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | | | | | | | | | | REDUCE: (6), (8065) imply: % 149.39/21.60 | | | | | | | | | | | | | | | | | | | (8066) $false % 149.39/21.60 | | | | | | | | | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | | | | | | | | | | CLOSE: (8066) is inconsistent. % 149.39/21.60 | | | | | | | | | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | | | | | | | | | Case 2: % 149.39/21.60 | | | | | | | | | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | | | | | | | | | | (8067) all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1 % 149.39/21.60 | | | | | | | | | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | | | | | | | | | | BETA: splitting (8056) gives: % 149.39/21.60 | | | | | | | | | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | | | | | | | | | | Case 1: % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | (8068) all_54_15 = e2 % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (540), (8068) imply: % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | (8069) all_4_2 = e2 % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | REDUCE: (8054), (8069) imply: % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | (8070) $false % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | CLOSE: (8070) is inconsistent. % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | | | | | | | | | | Case 2: % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | (8071) ~ (all_54_15 = e2) % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | (8072) all_54_15 = e1 | all_54_15 = e0 % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | BETA: splitting (322) gives: % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | Case 1: % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | (8073) all_58_9 = e2 % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (551), (8073) imply: % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | (8074) all_52_12 = e2 % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | REDUCE: (168), (8074) imply: % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | (8075) ~ (all_52_8 = e2) % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8072) gives: % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | | (8076) all_54_15 = e1 % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (540), (8002), (8076) are inconsistent by % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | | sub-proof #738. % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | | (8077) all_54_15 = e0 % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (540), (8077) imply: % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | | (8078) all_4_2 = e0 % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | | SIMP: (8078) implies: % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | | (8079) all_4_2 = e0 % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (547), (8079) imply: % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | | (8080) all_58_15 = e0 % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (581), (8079) imply: % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | | (8081) ~ (all_52_7 = e0) % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (588), (8079) imply: % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | | (8082) ~ (all_52_11 = e0) % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8054), (8079) imply: % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | | (8083) ~ (e2 = e0) % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8002), (8079) imply: % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | | (8084) ~ (e1 = e0) % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (336) gives: % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | | | (8085) all_58_1 = e0 % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (555), (8085) imply: % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | | | (8086) all_52_4 = e0 % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (183), (8086) imply: % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | | | (8087) ~ (all_52_7 = e0) % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (182), (8086) imply: % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | | | (8088) ~ (all_52_8 = e0) % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (8088) implies: % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | | | (8089) ~ (all_52_8 = e0) % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (563), (8086) imply: % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | | | (8090) ~ (all_10_2 = e0) % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (8090) implies: % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | | | (8091) ~ (all_10_2 = e0) % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (218), (8086) imply: % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | | | (8092) op(e3, e2) = e0 % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (239) gives: % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | | | | (8093) all_54_13 = e3 % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (480), (8093) imply: % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | | | | (8094) all_52_7 = e3 % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (8094) implies: % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | | | | (8095) all_52_7 = e3 % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (549), (8095) imply: % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | | | | (8096) all_58_13 = e3 % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8067) gives: % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | | | | | (8097) all_58_13 = e1 % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (8096), (8097) imply: % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | | | | | (8098) e3 = e1 % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8), (8098) imply: % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | | | | | (8099) $false % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (8099) is inconsistent. % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | | | | | (8100) all_58_14 = e1 | all_58_15 = e1 % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8100) gives: % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | | | | | | (8101) all_58_14 = e1 % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (548), (8101) imply: % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | | | | | | (8102) all_52_11 = e1 % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (169), (8102) imply: % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | | | | | | (8103) ~ (all_52_8 = e1) % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8061), (8102) imply: % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | | | | | | (8104) ~ (e2 = e1) % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (623), (8102) imply: % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | | | | | | (8105) op(e1, e1) = all_56_28 % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (250) gives: % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | (8106) all_54_2 = e3 % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (459), (8106) imply: % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | (8107) all_52_8 = e3 % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (8107) implies: % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | (8108) all_52_8 = e3 % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (407), (8108) imply: % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | (8109) all_58_4 = e3 % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (343) gives: % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8110) all_58_0 = e1 % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (419), (8110) imply: % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8111) all_10_2 = e1 % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (53), (8111) imply: % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8112) op(e1, e1) = all_10_1 % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_28, e1, e1, simplifying with (8036), (8105) % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8113) all_56_28 = e2 % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_10_1, % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_28, e1, e1, simplifying with (8105), (8112) % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8114) all_56_28 = all_10_1 % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_24, e2, e3, simplifying with (8063), (8092) % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8115) all_56_24 = e0 % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (8113), (8114) imply: % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8116) all_10_1 = e2 % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7991), (8116) imply: % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8117) op(e3, e2) = e1 % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, e1, e2, % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3, simplifying with (8092), (8117) gives: % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8118) e1 = e0 % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4), (8118) imply: % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8119) $false % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (8119) is inconsistent. % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8120) all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1 % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (8073), (8085), (8109), (8120) are % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #702. % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | (8121) all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0 % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (459), (540), (547), (548), (8002), (8072), % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | (8075), (8089), (8100), (8121) are inconsistent by % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #697. % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | | | | | | (8122) all_58_15 = e1 % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8080), (8122) are inconsistent by sub-proof % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | | | | | | #698. % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | | | | (8123) all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0 % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (480), (8033), (8041), (8081), (8123) are % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #710. % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | | | End of split % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | | | (8124) all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0 % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (549), (8030), (8038), (8081), (8124) % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #545. % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | | End of split % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | End of split % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | Case 2: % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | (8125) all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2 % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (386), (547), (550), (8034), (8042), (8054), % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | (8125) are inconsistent by sub-proof #693. % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | End of split % 149.39/21.60 | | | | | | | | | | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | | | | | | | | | | End of split % 149.39/21.60 | | | | | | | | | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | | | | | | | | | End of split % 149.39/21.60 | | | | | | | | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | | | | | | | | Case 2: % 149.39/21.60 | | | | | | | | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | | | | | | | | | (8126) ~ (all_58_12 = e2) % 149.39/21.60 | | | | | | | | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | | | | | | | | | REF_CLOSE: (322), (344), (365), (386), (401), (419), (547), % 149.39/21.60 | | | | | | | | | | | | | | | | | | (550), (551), (553), (567), (8031), (8034), % 149.39/21.60 | | | | | | | | | | | | | | | | | | (8039), (8042), (8054), (8126) are inconsistent by % 149.39/21.60 | | | | | | | | | | | | | | | | | | sub-proof #39. % 149.39/21.60 | | | | | | | | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | | | | | | | | End of split % 149.39/21.60 | | | | | | | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | | | | | | | End of split % 149.39/21.60 | | | | | | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | | | | | | Case 2: % 149.39/21.60 | | | | | | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | | | | | | | (8127) all_56_31 = e2 % 149.39/21.60 | | | | | | | | | | | | | | | | (8128) all_56_27 = e0 % 149.39/21.60 | | | | | | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | | | | | | | COMBINE_EQS: (360), (8128) imply: % 149.39/21.60 | | | | | | | | | | | | | | | | (8129) all_52_7 = e0 % 149.39/21.60 | | | | | | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | | | | | | | SIMP: (8129) implies: % 149.39/21.60 | | | | | | | | | | | | | | | | (8130) all_52_7 = e0 % 149.39/21.60 | | | | | | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | | | | | | | COMBINE_EQS: (544), (8127) imply: % 149.39/21.60 | | | | | | | | | | | | | | | | (8131) all_4_2 = e2 % 149.39/21.60 | | | | | | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | | | | | | | REDUCE: (570), (8131) imply: % 149.39/21.60 | | | | | | | | | | | | | | | | (8132) ~ (all_52_3 = e2) % 149.39/21.60 | | | | | | | | | | | | | | | | % 149.39/21.60 | | | | | | | | | | | | | | | | REDUCE: (183), (8130) imply: % 149.39/21.60 | | | | | | | | | | | | | | | | (8133) ~ (all_52_4 = e0) % 149.39/21.60 | | | | | | | | | | | | | | | | % 149.39/21.61 | | | | | | | | | | | | | | | | REF_CLOSE: (53), (218), (251), (344), (365), (401), (419), % 149.39/21.61 | | | | | | | | | | | | | | | | (457), (521), (553), (612), (7991), (7998), % 149.39/21.61 | | | | | | | | | | | | | | | | (8031), (8032), (8035), (8039), (8040), (8132), % 149.39/21.61 | | | | | | | | | | | | | | | | (8133), (function-axioms) are inconsistent by % 149.39/21.61 | | | | | | | | | | | | | | | | sub-proof #38. % 149.39/21.61 | | | | | | | | | | | | | | | | % 149.39/21.61 | | | | | | | | | | | | | | | End of split % 149.39/21.61 | | | | | | | | | | | | | | | % 149.39/21.61 | | | | | | | | | | | | | | Case 2: % 149.39/21.61 | | | | | | | | | | | | | | | % 149.39/21.61 | | | | | | | | | | | | | | | (8134) all_56_31 = e3 % 149.39/21.61 | | | | | | | | | | | | | | | (8135) all_56_25 = e0 % 149.39/21.61 | | | | | | | | | | | | | | | % 149.39/21.61 | | | | | | | | | | | | | | | REF_CLOSE: (188), (239), (447), (480), (544), (581), (8033), % 149.39/21.61 | | | | | | | | | | | | | | | (8041), (8134), (8135) are inconsistent by % 149.39/21.61 | | | | | | | | | | | | | | | sub-proof #71. % 149.39/21.61 | | | | | | | | | | | | | | | % 149.39/21.61 | | | | | | | | | | | | | | End of split % 149.39/21.61 | | | | | | | | | | | | | | % 149.39/21.61 | | | | | | | | | | | | | End of split % 149.39/21.61 | | | | | | | | | | | | | % 149.39/21.61 | | | | | | | | | | | | Case 2: % 149.39/21.61 | | | | | | | | | | | | | % 149.39/21.61 | | | | | | | | | | | | | (8136) all_56_31 = e1 % 149.39/21.61 | | | | | | | | | | | | | (8137) all_56_29 = e0 % 149.39/21.61 | | | | | | | | | | | | | % 149.39/21.61 | | | | | | | | | | | | | COMBINE_EQS: (357), (8137) imply: % 149.39/21.61 | | | | | | | | | | | | | (8138) all_52_11 = e0 % 149.39/21.61 | | | | | | | | | | | | | % 149.39/21.61 | | | | | | | | | | | | | SIMP: (8138) implies: % 149.39/21.61 | | | | | | | | | | | | | (8139) all_52_11 = e0 % 149.39/21.61 | | | | | | | | | | | | | % 149.39/21.61 | | | | | | | | | | | | | REF_CLOSE: (37), (38), (41), (51), (53), (173), (189), (206), % 149.39/21.61 | | | | | | | | | | | | | (239), (241), (242), (243), (287), (292), (293), % 149.39/21.61 | | | | | | | | | | | | | (374), (381), (476), (480), (541), (544), (545), % 149.39/21.61 | | | | | | | | | | | | | (546), (569), (585), (587), (591), (612), (622), % 149.39/21.61 | | | | | | | | | | | | | (767), (7418), (7420), (7423), (7424), (7426), % 149.39/21.61 | | | | | | | | | | | | | (7429), (7431), (7433), (7434), (7439), (8136), % 149.39/21.61 | | | | | | | | | | | | | (8139), (function-axioms) are inconsistent by % 149.39/21.61 | | | | | | | | | | | | | sub-proof #50. % 149.39/21.61 | | | | | | | | | | | | | % 149.39/21.61 | | | | | | | | | | | | End of split % 149.39/21.61 | | | | | | | | | | | | % 149.39/21.61 | | | | | | | | | | | Case 2: % 149.39/21.61 | | | | | | | | | | | | % 149.39/21.61 | | | | | | | | | | | | (8140) all_26_0 = e1 % 149.39/21.61 | | | | | | | | | | | | % 149.39/21.61 | | | | | | | | | | | | COMBINE_EQS: (760), (8140) imply: % 149.39/21.61 | | | | | | | | | | | | (8141) all_4_0 = e1 % 149.39/21.61 | | | | | | | | | | | | % 149.39/21.61 | | | | | | | | | | | | SIMP: (8141) implies: % 149.39/21.61 | | | | | | | | | | | | (8142) all_4_0 = e1 % 149.39/21.61 | | | | | | | | | | | | % 149.39/21.61 | | | | | | | | | | | | REF_CLOSE: (4), (9), (36), (37), (38), (41), (46), (47), % 149.39/21.61 | | | | | | | | | | | | (48), (51), (53), (168), (173), (181), (182), % 149.39/21.61 | | | | | | | | | | | | (188), (189), (192), (193), (194), (196), (197), % 149.39/21.61 | | | | | | | | | | | | (206), (212), (237), (239), (241), (242), (243), % 149.39/21.61 | | | | | | | | | | | | (244), (247), (251), (252), (287), (288), (289), % 149.39/21.61 | | | | | | | | | | | | (290), (291), (292), (293), (294), (295), (296), % 149.39/21.61 | | | | | | | | | | | | (297), (327), (330), (331), (332), (333), (336), % 149.39/21.61 | | | | | | | | | | | | (339), (344), (357), (360), (365), (366), (374), % 149.39/21.61 | | | | | | | | | | | | (381), (386), (389), (401), (402), (407), (419), % 149.39/21.61 | | | | | | | | | | | | (425), (431), (443), (447), (457), (471), (476), % 149.39/21.61 | | | | | | | | | | | | (480), (540), (541), (542), (543), (544), (545), % 149.39/21.61 | | | | | | | | | | | | (546), (549), (550), (552), (553), (554), (557), % 149.39/21.61 | | | | | | | | | | | | (559), (563), (565), (568), (569), (570), (577), % 149.39/21.61 | | | | | | | | | | | | (581), (583), (585), (587), (590), (591), (612), % 149.39/21.61 | | | | | | | | | | | | (622), (627), (767), (7418), (7420), (7423), % 149.39/21.61 | | | | | | | | | | | | (7424), (7425), (7426), (7429), (7431), (7433), % 149.39/21.61 | | | | | | | | | | | | (7434), (7436), (7439), (7441), (7993), (7995), % 149.39/21.61 | | | | | | | | | | | | (8142), (function-axioms) are inconsistent by % 149.39/21.61 | | | | | | | | | | | | sub-proof #49. % 149.39/21.61 | | | | | | | | | | | | % 149.39/21.61 | | | | | | | | | | | End of split % 149.39/21.61 | | | | | | | | | | | % 149.39/21.61 | | | | | | | | | | End of split % 149.39/21.61 | | | | | | | | | | % 149.39/21.61 | | | | | | | | | Case 2: % 149.39/21.61 | | | | | | | | | | % 149.39/21.61 | | | | | | | | | | (8143) all_22_1 = e3 % 149.39/21.61 | | | | | | | | | | % 149.39/21.61 | | | | | | | | | | COMBINE_EQS: (672), (8143) imply: % 149.39/21.61 | | | | | | | | | | (8144) all_8_1 = e3 % 149.39/21.61 | | | | | | | | | | % 149.39/21.61 | | | | | | | | | | SIMP: (8144) implies: % 149.39/21.61 | | | | | | | | | | (8145) all_8_1 = e3 % 149.39/21.61 | | | | | | | | | | % 149.39/21.61 | | | | | | | | | | REF_CLOSE: (4), (7), (9), (36), (38), (41), (46), (47), (48), % 149.39/21.61 | | | | | | | | | | (51), (53), (182), (183), (188), (189), (192), % 149.39/21.61 | | | | | | | | | | (215), (237), (239), (240), (241), (242), (243), % 149.39/21.61 | | | | | | | | | | (244), (247), (252), (287), (288), (289), (290), % 149.39/21.61 | | | | | | | | | | (291), (292), (293), (294), (298), (299), (324), % 149.39/21.61 | | | | | | | | | | (326), (327), (336), (339), (342), (343), (357), % 149.39/21.61 | | | | | | | | | | (360), (365), (366), (374), (381), (401), (408), % 149.39/21.61 | | | | | | | | | | (419), (429), (447), (471), (476), (478), (480), % 149.39/21.61 | | | | | | | | | | (540), (541), (542), (543), (544), (545), (546), % 149.39/21.61 | | | | | | | | | | (549), (550), (552), (553), (554), (555), (559), % 149.39/21.61 | | | | | | | | | | (561), (563), (569), (570), (571), (575), (581), % 149.39/21.61 | | | | | | | | | | (585), (587), (591), (612), (617), (622), (627), % 149.39/21.61 | | | | | | | | | | (7418), (7420), (7423), (7425), (7426), (7429), % 149.39/21.61 | | | | | | | | | | (7431), (7433), (7434), (7436), (7441), (7993), % 149.39/21.61 | | | | | | | | | | (8145), (function-axioms) are inconsistent by % 149.39/21.61 | | | | | | | | | | sub-proof #42. % 149.39/21.61 | | | | | | | | | | % 149.39/21.61 | | | | | | | | | End of split % 149.39/21.61 | | | | | | | | | % 149.39/21.61 | | | | | | | | Case 2: % 149.39/21.61 | | | | | | | | | % 149.39/21.61 | | | | | | | | | (8146) all_18_0 = e3 % 149.39/21.61 | | | | | | | | | (8147) ~ (all_18_1 = e2) | ~ (all_18_2 = e0) % 149.39/21.61 | | | | | | | | | % 149.39/21.61 | | | | | | | | | COMBINE_EQS: (753), (8146) imply: % 149.39/21.61 | | | | | | | | | (8148) all_6_0 = e3 % 149.39/21.61 | | | | | | | | | % 149.39/21.61 | | | | | | | | | SIMP: (8148) implies: % 149.39/21.61 | | | | | | | | | (8149) all_6_0 = e3 % 149.39/21.61 | | | | | | | | | % 149.39/21.61 | | | | | | | | | REF_CLOSE: (8), (41), (242), (292), (374), (524), (541), % 149.39/21.61 | | | | | | | | | (622), (7419), (7420), (7424), (7434), (8147), % 149.39/21.61 | | | | | | | | | (8149), (function-axioms) are inconsistent by % 149.39/21.61 | | | | | | | | | sub-proof #40. % 149.39/21.61 | | | | | | | | | % 149.39/21.61 | | | | | | | | End of split % 149.39/21.61 | | | | | | | | % 149.39/21.61 | | | | | | | End of split % 149.39/21.61 | | | | | | | % 149.39/21.61 | | | | | | Case 2: % 149.39/21.61 | | | | | | | % 149.39/21.61 | | | | | | | (8150) all_14_0 = e1 % 149.39/21.61 | | | | | | | % 149.39/21.61 | | | | | | | COMBINE_EQS: (758), (8150) imply: % 149.39/21.61 | | | | | | | (8151) all_8_0 = e1 % 149.39/21.61 | | | | | | | % 149.39/21.61 | | | | | | | REDUCE: (47), (8151) imply: % 149.39/21.61 | | | | | | | (8152) op(e2, all_8_1) = e1 % 149.39/21.61 | | | | | | | % 149.39/21.61 | | | | | | | REF_CLOSE: (4), (7), (8), (9), (36), (37), (38), (41), (46), (48), % 149.39/21.61 | | | | | | | (51), (53), (74), (173), (188), (189), (192), (206), % 149.39/21.61 | | | | | | | (237), (239), (240), (241), (242), (243), (244), (287), % 149.39/21.61 | | | | | | | (288), (289), (290), (291), (292), (293), (324), (326), % 149.39/21.61 | | | | | | | (327), (336), (339), (357), (360), (366), (374), (381), % 149.39/21.61 | | | | | | | (447), (471), (476), (478), (480), (524), (540), (541), % 149.39/21.61 | | | | | | | (544), (545), (546), (549), (550), (552), (553), (554), % 149.39/21.61 | | | | | | | (559), (561), (569), (570), (581), (585), (587), (591), % 149.39/21.61 | | | | | | | (612), (617), (622), (627), (753), (767), (7418), % 149.39/21.61 | | | | | | | (7419), (7420), (7423), (7424), (7425), (7426), (7429), % 149.39/21.61 | | | | | | | (7431), (7433), (7434), (7436), (7439), (8152), % 149.39/21.61 | | | | | | | (function-axioms) are inconsistent by sub-proof #37. % 149.39/21.61 | | | | | | | % 149.39/21.61 | | | | | | End of split % 149.39/21.61 | | | | | | % 149.39/21.61 | | | | | Case 2: % 149.39/21.61 | | | | | | % 149.39/21.61 | | | | | | (8153) all_12_0 = e2 % 149.39/21.61 | | | | | | (8154) ~ (all_12_1 = e1) | ~ (all_12_2 = e3) % 149.39/21.61 | | | | | | % 149.39/21.61 | | | | | | COMBINE_EQS: (759), (8153) imply: % 149.39/21.61 | | | | | | (8155) all_4_0 = e2 % 149.39/21.61 | | | | | | % 149.39/21.61 | | | | | | COMBINE_EQS: (734), (8155) imply: % 149.39/21.61 | | | | | | (8156) all_34_0 = e2 % 149.39/21.61 | | | | | | % 149.39/21.61 | | | | | | REDUCE: (767), (8155) imply: % 149.39/21.61 | | | | | | (8157) ~ (e3 = e2) % 149.39/21.61 | | | | | | % 149.39/21.61 | | | | | | REDUCE: (37), (8155) imply: % 149.39/21.61 | | | | | | (8158) op(e0, all_4_1) = e2 % 149.39/21.61 | | | | | | % 149.39/21.61 | | | | | | BETA: splitting (64) gives: % 149.39/21.61 | | | | | | % 149.39/21.61 | | | | | | Case 1: % 149.39/21.61 | | | | | | | % 149.39/21.61 | | | | | | | (8159) ~ (all_14_0 = e1) % 149.39/21.61 | | | | | | | % 149.39/21.61 | | | | | | | REDUCE: (758), (8159) imply: % 149.39/21.61 | | | | | | | (8160) ~ (all_8_0 = e1) % 149.39/21.61 | | | | | | | % 149.39/21.61 | | | | | | | BETA: splitting (69) gives: % 149.39/21.61 | | | | | | | % 149.39/21.61 | | | | | | | Case 1: % 149.39/21.61 | | | | | | | | % 149.39/21.61 | | | | | | | | (8161) ~ (all_16_0 = e1) % 149.39/21.61 | | | | | | | | % 149.39/21.61 | | | | | | | | REDUCE: (757), (8161) imply: % 149.39/21.61 | | | | | | | | (8162) ~ (all_10_0 = e1) % 149.39/21.61 | | | | | | | | % 149.39/21.61 | | | | | | | | BETA: splitting (74) gives: % 149.39/21.61 | | | | | | | | % 149.39/21.61 | | | | | | | | Case 1: % 149.39/21.61 | | | | | | | | | % 149.39/21.61 | | | | | | | | | (8163) ~ (all_18_0 = e3) % 149.39/21.61 | | | | | | | | | % 149.39/21.61 | | | | | | | | | REDUCE: (753), (8163) imply: % 149.39/21.61 | | | | | | | | | (8164) ~ (all_6_0 = e3) % 149.39/21.61 | | | | | | | | | % 149.39/21.61 | | | | | | | | | BETA: splitting (84) gives: % 149.39/21.61 | | | | | | | | | % 149.39/21.61 | | | | | | | | | Case 1: % 149.39/21.61 | | | | | | | | | | % 149.39/21.61 | | | | | | | | | | (8165) ~ (all_22_1 = e3) % 149.39/21.61 | | | | | | | | | | % 149.39/21.61 | | | | | | | | | | REDUCE: (672), (8165) imply: % 149.39/21.61 | | | | | | | | | | (8166) ~ (all_8_1 = e3) % 149.39/21.61 | | | | | | | | | | % 149.39/21.61 | | | | | | | | | | BETA: splitting (104) gives: % 149.39/21.61 | | | | | | | | | | % 149.39/21.61 | | | | | | | | | | Case 1: % 149.39/21.61 | | | | | | | | | | | % 149.39/21.61 | | | | | | | | | | | (8167) ~ (all_30_0 = e3) % 149.39/21.61 | | | | | | | | | | | % 149.39/21.61 | | | | | | | | | | | REDUCE: (718), (8167) imply: % 149.39/21.61 | | | | | | | | | | | (8168) ~ (all_8_0 = e3) % 149.39/21.61 | | | | | | | | | | | % 149.39/21.61 | | | | | | | | | | | BETA: splitting (109) gives: % 149.39/21.61 | | | | | | | | | | | % 149.39/21.61 | | | | | | | | | | | Case 1: % 149.39/21.61 | | | | | | | | | | | | % 149.39/21.61 | | | | | | | | | | | | (8169) ~ (all_32_1 = e1) % 149.39/21.61 | | | | | | | | | | | | % 149.39/21.61 | | | | | | | | | | | | REDUCE: (682), (8169) imply: % 149.39/21.61 | | | | | | | | | | | | (8170) ~ (all_10_1 = e1) % 149.39/21.61 | | | | | | | | | | | | % 149.39/21.61 | | | | | | | | | | | | BETA: splitting (114) gives: % 149.39/21.61 | | | | | | | | | | | | % 149.39/21.61 | | | | | | | | | | | | Case 1: % 149.39/21.61 | | | | | | | | | | | | | % 149.39/21.61 | | | | | | | | | | | | | (8171) ~ (all_34_0 = e2) % 149.39/21.61 | | | | | | | | | | | | | % 149.39/21.61 | | | | | | | | | | | | | REDUCE: (8156), (8171) imply: % 149.39/21.61 | | | | | | | | | | | | | (8172) $false % 149.39/21.61 | | | | | | | | | | | | | % 149.39/21.61 | | | | | | | | | | | | | CLOSE: (8172) is inconsistent. % 149.39/21.61 | | | | | | | | | | | | | % 149.39/21.61 | | | | | | | | | | | | Case 2: % 149.39/21.61 | | | | | | | | | | | | | % 149.39/21.61 | | | | | | | | | | | | | (8173) ~ (all_34_1 = e3) | ~ (all_34_2 = e1) % 149.39/21.61 | | | | | | | | | | | | | % 149.39/21.61 | | | | | | | | | | | | | BETA: splitting (124) gives: % 149.39/21.61 | | | | | | | | | | | | | % 149.39/21.61 | | | | | | | | | | | | | Case 1: % 149.39/21.61 | | | | | | | | | | | | | | % 149.39/21.61 | | | | | | | | | | | | | | (8174) ~ (all_38_1 = e2) % 149.39/21.61 | | | | | | | | | | | | | | % 149.39/21.61 | | | | | | | | | | | | | | REDUCE: (684), (8174) imply: % 149.39/21.61 | | | | | | | | | | | | | | (8175) ~ (all_10_1 = e2) % 149.39/21.61 | | | | | | | | | | | | | | % 149.39/21.61 | | | | | | | | | | | | | | BETA: splitting (292) gives: % 149.39/21.61 | | | | | | | | | | | | | | % 149.39/21.61 | | | | | | | | | | | | | | Case 1: % 149.39/21.61 | | | | | | | | | | | | | | | % 149.39/21.61 | | | | | | | | | | | | | | | (8176) ~ (all_56_21 = e2) % 149.39/21.61 | | | | | | | | | | | | | | | % 149.39/21.61 | | | | | | | | | | | | | | | REDUCE: (374), (8176) imply: % 149.39/21.61 | | | | | | | | | | | | | | | (8177) ~ (all_6_2 = e2) % 149.39/21.61 | | | | | | | | | | | | | | | % 149.39/21.61 | | | | | | | | | | | | | | | BETA: splitting (294) gives: % 149.39/21.61 | | | | | | | | | | | | | | | % 149.39/21.61 | | | | | | | | | | | | | | | Case 1: % 149.39/21.61 | | | | | | | | | | | | | | | | % 149.39/21.61 | | | | | | | | | | | | | | | | (8178) ~ (all_56_11 = e0) % 149.39/21.61 | | | | | | | | | | | | | | | | % 149.39/21.61 | | | | | | | | | | | | | | | | REF_CLOSE: (8), (36), (38), (41), (47), (48), (51), (53), % 149.39/21.61 | | | | | | | | | | | | | | | | (161), (168), (169), (181), (182), (188), (189), % 149.39/21.61 | | | | | | | | | | | | | | | | (192), (193), (194), (196), (212), (237), (240), % 149.39/21.61 | | | | | | | | | | | | | | | | (241), (242), (243), (245), (247), (250), (251), % 149.39/21.61 | | | | | | | | | | | | | | | | (252), (287), (291), (293), (295), (296), (297), % 149.39/21.61 | | | | | | | | | | | | | | | | (327), (330), (331), (337), (343), (366), (374), % 149.39/21.61 | | | | | | | | | | | | | | | | (381), (389), (402), (407), (419), (425), (431), % 149.39/21.61 | | | | | | | | | | | | | | | | (457), (459), (469), (476), (478), (540), (541), % 149.39/21.61 | | | | | | | | | | | | | | | | (542), (543), (544), (545), (546), (548), (549), % 149.39/21.61 | | | | | | | | | | | | | | | | (550), (552), (553), (554), (555), (557), (559), % 149.39/21.61 | | | | | | | | | | | | | | | | (561), (563), (565), (567), (569), (577), (583), % 149.39/21.61 | | | | | | | | | | | | | | | | (585), (587), (588), (590), (591), (612), (622), % 149.39/21.61 | | | | | | | | | | | | | | | | (627), (7418), (7420), (7423), (7425), (7426), % 149.39/21.61 | | | | | | | | | | | | | | | | (7431), (7433), (7434), (7436), (8160), (8164), % 149.39/21.61 | | | | | | | | | | | | | | | | (8166), (8170), (8175), (8177), (8178), % 149.39/21.61 | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 149.39/21.61 | | | | | | | | | | | | | | | | #78. % 149.39/21.61 | | | | | | | | | | | | | | | | % 149.39/21.61 | | | | | | | | | | | | | | | Case 2: % 149.39/21.61 | | | | | | | | | | | | | | | | % 149.39/21.61 | | | | | | | | | | | | | | | | (8179) all_56_15 = e2 % 149.39/21.61 | | | | | | | | | | | | | | | | (8180) all_56_11 = e0 % 149.39/21.61 | | | | | | | | | | | | | | | | % 149.39/21.61 | | | | | | | | | | | | | | | | REF_CLOSE: (36), (38), (48), (237), (443), (540), (545), % 149.39/21.61 | | | | | | | | | | | | | | | | (590), (627), (7436), (8158), (8166), (8179), % 149.39/21.61 | | | | | | | | | | | | | | | | (8180), (function-axioms) are inconsistent by % 149.39/21.61 | | | | | | | | | | | | | | | | sub-proof #224. % 149.39/21.61 | | | | | | | | | | | | | | | | % 149.39/21.61 | | | | | | | | | | | | | | | End of split % 149.39/21.61 | | | | | | | | | | | | | | | % 149.39/21.61 | | | | | | | | | | | | | | Case 2: % 149.39/21.61 | | | | | | | | | | | | | | | % 149.39/21.61 | | | | | | | | | | | | | | | (8181) all_56_21 = e2 % 149.39/21.61 | | | | | | | | | | | | | | | (8182) all_56_19 = e1 % 149.39/21.61 | | | | | | | | | | | | | | | % 149.39/21.61 | | | | | | | | | | | | | | | COMBINE_EQS: (7424), (8182) imply: % 149.39/21.61 | | | | | | | | | | | | | | | (8183) all_6_0 = e1 % 149.39/21.61 | | | | | | | | | | | | | | | % 149.39/21.61 | | | | | | | | | | | | | | | COMBINE_EQS: (374), (8181) imply: % 149.39/21.61 | | | | | | | | | | | | | | | (8184) all_6_2 = e2 % 149.39/21.61 | | | | | | | | | | | | | | | % 149.39/21.61 | | | | | | | | | | | | | | | REDUCE: (569), (8184) imply: % 149.39/21.61 | | | | | | | | | | | | | | | (8185) ~ (all_52_2 = e2) % 149.39/21.61 | | | | | | | | | | | | | | | % 149.39/21.61 | | | | | | | | | | | | | | | REDUCE: (7427), (8183) imply: % 149.39/21.61 | | | | | | | | | | | | | | | (8186) ~ (all_52_4 = e1) % 149.39/21.61 | | | | | | | | | | | | | | | % 149.39/21.61 | | | | | | | | | | | | | | | REDUCE: (7429), (8183) imply: % 149.39/21.61 | | | | | | | | | | | | | | | (8187) ~ (all_52_7 = e1) % 149.39/21.61 | | | | | | | | | | | | | | | % 149.39/21.61 | | | | | | | | | | | | | | | REDUCE: (585), (8184) imply: % 149.39/21.61 | | | | | | | | | | | | | | | (8188) ~ (all_52_11 = e2) % 149.39/21.61 | | | | | | | | | | | | | | | % 149.39/21.61 | | | | | | | | | | | | | | | REDUCE: (587), (8184) imply: % 149.39/21.61 | | | | | | | | | | | | | | | (8189) ~ (all_52_14 = e2) % 149.39/21.61 | | | | | | | | | | | | | | | % 149.39/21.61 | | | | | | | | | | | | | | | REDUCE: (7420), (8184) imply: % 149.39/21.61 | | | | | | | | | | | | | | | (8190) op(e2, e2) = e2 % 149.39/21.61 | | | | | | | | | | | | | | | % 149.39/21.61 | | | | | | | | | | | | | | | REDUCE: (41), (8184) imply: % 149.39/21.61 | | | | | | | | | | | | | | | (8191) op(e1, e1) = e2 % 149.39/21.61 | | | | | | | | | | | | | | | % 149.39/21.61 | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_8_2, e2, % 149.39/21.61 | | | | | | | | | | | | | | | e2, e2, simplifying with (46), (8190) gives: % 149.39/21.61 | | | | | | | | | | | | | | | (8192) all_8_2 = e2 % 149.39/21.61 | | | | | | | | | | | | | | | % 149.39/21.61 | | | | | | | | | | | | | | | REDUCE: (568), (8192) imply: % 149.39/21.61 | | | | | | | | | | | | | | | (8193) ~ (all_52_1 = e2) % 149.39/21.61 | | | | | | | | | | | | | | | % 149.39/21.61 | | | | | | | | | | | | | | | REDUCE: (571), (8192) imply: % 149.39/21.61 | | | | | | | | | | | | | | | (8194) ~ (all_52_4 = e2) % 149.39/21.61 | | | | | | | | | | | | | | | % 149.39/21.61 | | | | | | | | | | | | | | | REDUCE: (575), (8192) imply: % 149.39/21.61 | | | | | | | | | | | | | | | (8195) ~ (all_52_7 = e2) % 149.39/21.61 | | | | | | | | | | | | | | | % 149.39/21.61 | | | | | | | | | | | | | | | REDUCE: (579), (8192) imply: % 149.39/21.61 | | | | | | | | | | | | | | | (8196) ~ (all_52_13 = e2) % 149.39/21.61 | | | | | | | | | | | | | | | % 149.39/21.61 | | | | | | | | | | | | | | | REDUCE: (48), (8192) imply: % 149.39/21.61 | | | | | | | | | | | | | | | (8197) op(e2, e2) = all_8_1 % 149.39/21.61 | | | | | | | | | | | | | | | % 149.39/21.61 | | | | | | | | | | | | | | | REDUCE: (617), (8192) imply: % 149.39/21.61 | | | | | | | | | | | | | | | (8198) op(e2, e2) = all_56_10 % 149.39/21.61 | | | | | | | | | | | | | | | % 149.39/21.61 | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, % 149.39/21.61 | | | | | | | | | | | | | | | all_56_10, e2, e2, simplifying with (8190), (8198) % 149.39/21.61 | | | | | | | | | | | | | | | gives: % 149.39/21.61 | | | | | | | | | | | | | | | (8199) all_56_10 = e2 % 149.39/21.61 | | | | | | | | | | | | | | | % 149.39/21.61 | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_8_1, % 149.39/21.61 | | | | | | | | | | | | | | | all_56_10, e2, e2, simplifying with (8197), (8198) % 149.39/21.61 | | | | | | | | | | | | | | | gives: % 149.39/21.61 | | | | | | | | | | | | | | | (8200) all_56_10 = all_8_1 % 149.39/21.61 | | | | | | | | | | | | | | | % 149.39/21.61 | | | | | | | | | | | | | | | COMBINE_EQS: (8199), (8200) imply: % 149.39/21.61 | | | | | | | | | | | | | | | (8201) all_8_1 = e2 % 149.39/21.61 | | | | | | | | | | | | | | | % 149.39/21.61 | | | | | | | | | | | | | | | SIMP: (8201) implies: % 149.39/21.61 | | | | | | | | | | | | | | | (8202) all_8_1 = e2 % 149.39/21.61 | | | | | | | | | | | | | | | % 149.39/21.61 | | | | | | | | | | | | | | | REDUCE: (47), (8202) imply: % 149.39/21.61 | | | | | | | | | | | | | | | (8203) op(e2, e2) = all_8_0 % 149.39/21.61 | | | | | | | | | | | | | | | % 149.39/21.61 | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, all_8_0, % 149.39/21.61 | | | | | | | | | | | | | | | e2, e2, simplifying with (8190), (8203) gives: % 149.39/21.61 | | | | | | | | | | | | | | | (8204) all_8_0 = e2 % 149.39/21.61 | | | | | | | | | | | | | | | % 149.39/21.61 | | | | | | | | | | | | | | | BETA: splitting (288) gives: % 149.39/21.61 | | | | | | | | | | | | | | | % 149.39/21.61 | | | | | | | | | | | | | | | Case 1: % 149.39/21.61 | | | | | | | | | | | | | | | | % 149.39/21.61 | | | | | | | | | | | | | | | | (8205) ~ (all_56_31 = e1) % 149.39/21.61 | | | | | | | | | | | | | | | | % 149.39/21.61 | | | | | | | | | | | | | | | | REDUCE: (544), (8205) imply: % 149.39/21.61 | | | | | | | | | | | | | | | | (8206) ~ (all_4_2 = e1) % 149.39/21.61 | | | | | | | | | | | | | | | | % 149.39/21.61 | | | | | | | | | | | | | | | | BETA: splitting (290) gives: % 149.39/21.61 | | | | | | | | | | | | | | | | % 149.39/21.61 | | | | | | | | | | | | | | | | Case 1: % 149.39/21.61 | | | | | | | | | | | | | | | | | % 149.39/21.61 | | | | | | | | | | | | | | | | | (8207) ~ (all_56_31 = e3) % 149.39/21.61 | | | | | | | | | | | | | | | | | % 149.39/21.61 | | | | | | | | | | | | | | | | | REDUCE: (544), (8207) imply: % 149.39/21.61 | | | | | | | | | | | | | | | | | (8208) ~ (all_4_2 = e3) % 149.39/21.61 | | | | | | | | | | | | | | | | | % 149.39/21.61 | | | | | | | | | | | | | | | | | BETA: splitting (289) gives: % 149.39/21.61 | | | | | | | | | | | | | | | | | % 149.39/21.61 | | | | | | | | | | | | | | | | | Case 1: % 149.39/21.61 | | | | | | | | | | | | | | | | | | % 149.39/21.61 | | | | | | | | | | | | | | | | | | (8209) ~ (all_56_31 = e2) % 149.39/21.61 | | | | | | | | | | | | | | | | | | % 149.39/21.61 | | | | | | | | | | | | | | | | | | REDUCE: (544), (8209) imply: % 149.39/21.61 | | | | | | | | | | | | | | | | | | (8210) ~ (all_4_2 = e2) % 149.39/21.61 | | | | | | | | | | | | | | | | | | % 149.39/21.61 | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (38), (237), (540), (627), (8158), (8206), % 149.39/21.61 | | | | | | | | | | | | | | | | | | (8208), (8210), (function-axioms) are inconsistent % 149.39/21.61 | | | | | | | | | | | | | | | | | | by sub-proof #229. % 149.39/21.61 | | | | | | | | | | | | | | | | | | % 149.39/21.61 | | | | | | | | | | | | | | | | | Case 2: % 149.39/21.61 | | | | | | | | | | | | | | | | | | % 149.39/21.61 | | | | | | | | | | | | | | | | | | (8211) all_56_31 = e2 % 149.39/21.61 | | | | | | | | | | | | | | | | | | (8212) all_56_27 = e0 % 149.39/21.61 | | | | | | | | | | | | | | | | | | % 149.39/21.61 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (360), (8212) imply: % 149.39/21.61 | | | | | | | | | | | | | | | | | | (8213) all_52_7 = e0 % 149.39/21.61 | | | | | | | | | | | | | | | | | | % 149.39/21.61 | | | | | | | | | | | | | | | | | | SIMP: (8213) implies: % 149.39/21.61 | | | | | | | | | | | | | | | | | | (8214) all_52_7 = e0 % 149.39/21.61 | | | | | | | | | | | | | | | | | | % 149.39/21.61 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (544), (8211) imply: % 149.39/21.61 | | | | | | | | | | | | | | | | | | (8215) all_4_2 = e2 % 149.39/21.61 | | | | | | | | | | | | | | | | | | % 149.39/21.61 | | | | | | | | | | | | | | | | | | REDUCE: (183), (8214) imply: % 149.39/21.61 | | | | | | | | | | | | | | | | | | (8216) ~ (all_52_4 = e0) % 149.39/21.61 | | | | | | | | | | | | | | | | | | % 149.39/21.61 | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (53), (168), (169), (181), (182), (183), % 149.39/21.61 | | | | | | | | | | | | | | | | | | (237), (250), (251), (252), (289), (297), (298), % 149.39/21.61 | | | | | | | | | | | | | | | | | | (318), (319), (322), (339), (343), (344), (360), % 149.39/21.61 | | | | | | | | | | | | | | | | | | (365), (386), (401), (402), (407), (419), (429), % 149.39/21.61 | | | | | | | | | | | | | | | | | | (457), (459), (540), (543), (544), (546), (547), % 149.39/21.61 | | | | | | | | | | | | | | | | | | (548), (549), (550), (551), (553), (555), (563), % 149.39/21.61 | | | | | | | | | | | | | | | | | | (567), (589), (8175), (8185), (8186), (8187), % 149.39/21.61 | | | | | | | | | | | | | | | | | | (8189), (8190), (8193), (8194), (8196), (8206), % 149.39/21.61 | | | | | | | | | | | | | | | | | | (8208), (8216), (function-axioms) are inconsistent % 149.39/21.61 | | | | | | | | | | | | | | | | | | by sub-proof #72. % 149.39/21.61 | | | | | | | | | | | | | | | | | | % 149.39/21.61 | | | | | | | | | | | | | | | | | End of split % 149.39/21.61 | | | | | | | | | | | | | | | | | % 149.39/21.61 | | | | | | | | | | | | | | | | Case 2: % 149.39/21.61 | | | | | | | | | | | | | | | | | % 149.39/21.61 | | | | | | | | | | | | | | | | | (8217) all_56_31 = e3 % 149.39/21.61 | | | | | | | | | | | | | | | | | (8218) all_56_25 = e0 % 149.39/21.61 | | | | | | | | | | | | | | | | | % 149.39/21.61 | | | | | | | | | | | | | | | | | REF_CLOSE: (188), (239), (447), (480), (544), (581), (8187), % 149.39/21.61 | | | | | | | | | | | | | | | | | (8195), (8217), (8218) are inconsistent by % 149.39/21.61 | | | | | | | | | | | | | | | | | sub-proof #71. % 149.39/21.61 | | | | | | | | | | | | | | | | | % 149.39/21.61 | | | | | | | | | | | | | | | | End of split % 149.39/21.61 | | | | | | | | | | | | | | | | % 149.39/21.61 | | | | | | | | | | | | | | | Case 2: % 149.39/21.61 | | | | | | | | | | | | | | | | % 149.39/21.61 | | | | | | | | | | | | | | | | (8219) all_56_31 = e1 % 149.39/21.62 | | | | | | | | | | | | | | | | (8220) all_56_29 = e0 % 149.39/21.62 | | | | | | | | | | | | | | | | % 149.39/21.62 | | | | | | | | | | | | | | | | COMBINE_EQS: (357), (8220) imply: % 149.39/21.62 | | | | | | | | | | | | | | | | (8221) all_52_11 = e0 % 149.39/21.62 | | | | | | | | | | | | | | | | % 149.39/21.62 | | | | | | | | | | | | | | | | SIMP: (8221) implies: % 149.39/21.62 | | | | | | | | | | | | | | | | (8222) all_52_11 = e0 % 149.39/21.62 | | | | | | | | | | | | | | | | % 149.39/21.62 | | | | | | | | | | | | | | | | COMBINE_EQS: (544), (8219) imply: % 149.39/21.62 | | | | | | | | | | | | | | | | (8223) all_4_2 = e1 % 149.39/21.62 | | | | | | | | | | | | | | | | % 149.39/21.62 | | | | | | | | | | | | | | | | COMBINE_EQS: (531), (8223) imply: % 149.39/21.62 | | | | | | | | | | | | | | | | (8224) all_34_2 = e1 % 149.39/21.62 | | | | | | | | | | | | | | | | % 149.39/21.62 | | | | | | | | | | | | | | | | COMBINE_EQS: (547), (8223) imply: % 149.39/21.62 | | | | | | | | | | | | | | | | (8225) all_58_15 = e1 % 149.39/21.62 | | | | | | | | | | | | | | | | % 149.39/21.62 | | | | | | | | | | | | | | | | COMBINE_EQS: (548), (8222) imply: % 149.39/21.62 | | | | | | | | | | | | | | | | (8226) all_58_14 = e0 % 149.39/21.62 | | | | | | | | | | | | | | | | % 149.39/21.62 | | | | | | | | | | | | | | | | REDUCE: (173), (8222) imply: % 149.39/21.62 | | | | | | | | | | | | | | | | (8227) ~ (all_52_7 = e0) % 149.39/21.62 | | | | | | | | | | | | | | | | % 149.39/21.62 | | | | | | | | | | | | | | | | REDUCE: (8188), (8222) imply: % 149.39/21.62 | | | | | | | | | | | | | | | | (8228) ~ (e2 = e0) % 149.39/21.62 | | | | | | | | | | | | | | | | % 149.39/21.62 | | | | | | | | | | | | | | | | REDUCE: (589), (8223) imply: % 149.39/21.62 | | | | | | | | | | | | | | | | (8229) ~ (all_52_12 = e1) % 149.39/21.62 | | | | | | | | | | | | | | | | % 149.39/21.62 | | | | | | | | | | | | | | | | REDUCE: (38), (8223) imply: % 149.39/21.62 | | | | | | | | | | | | | | | | (8230) op(e1, e1) = all_4_1 % 149.39/21.62 | | | | | | | | | | | | | | | | % 149.39/21.62 | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (206), (239), (319), (322), (386), % 149.39/21.62 | | | | | | | | | | | | | | | | (480), (549), (550), (551), (624), (683), (8158), % 149.39/21.62 | | | | | | | | | | | | | | | | (8173), (8187), (8189), (8191), (8195), (8196), % 149.39/21.62 | | | | | | | | | | | | | | | | (8224), (8225), (8226), (8227), (8229), (8230), % 149.39/21.62 | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 149.39/21.62 | | | | | | | | | | | | | | | | #34. % 149.39/21.62 | | | | | | | | | | | | | | | | % 149.39/21.62 | | | | | | | | | | | | | | | End of split % 149.39/21.62 | | | | | | | | | | | | | | | % 149.39/21.62 | | | | | | | | | | | | | | End of split % 149.39/21.62 | | | | | | | | | | | | | | % 149.39/21.62 | | | | | | | | | | | | | Case 2: % 149.39/21.62 | | | | | | | | | | | | | | % 149.39/21.62 | | | | | | | | | | | | | | (8231) all_38_1 = e2 % 149.39/21.62 | | | | | | | | | | | | | | (8232) ~ (all_38_0 = e0) | ~ (all_38_2 = e1) % 149.39/21.62 | | | | | | | | | | | | | | % 149.39/21.62 | | | | | | | | | | | | | | COMBINE_EQS: (684), (8231) imply: % 149.39/21.62 | | | | | | | | | | | | | | (8233) all_10_1 = e2 % 149.39/21.62 | | | | | | | | | | | | | | % 149.39/21.62 | | | | | | | | | | | | | | SIMP: (8233) implies: % 149.39/21.62 | | | | | | | | | | | | | | (8234) all_10_1 = e2 % 149.39/21.62 | | | | | | | | | | | | | | % 149.39/21.62 | | | | | | | | | | | | | | REDUCE: (53), (8234) imply: % 149.39/21.62 | | | | | | | | | | | | | | (8235) op(all_10_2, all_10_2) = e2 % 149.39/21.62 | | | | | | | | | | | | | | % 149.39/21.62 | | | | | | | | | | | | | | REDUCE: (52), (8234) imply: % 149.39/21.62 | | | | | | | | | | | | | | (8236) op(e3, e2) = all_10_0 % 149.39/21.62 | | | | | | | | | | | | | | % 149.39/21.62 | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_4, % 149.39/21.62 | | | | | | | | | | | | | | all_10_0, e2, e3, simplifying with (218), (8236) % 149.39/21.62 | | | | | | | | | | | | | | gives: % 149.39/21.62 | | | | | | | | | | | | | | (8237) all_52_4 = all_10_0 % 149.39/21.62 | | | | | | | | | | | | | | % 149.39/21.62 | | | | | | | | | | | | | | COMBINE_EQS: (457), (8237) imply: % 149.39/21.62 | | | | | | | | | | | | | | (8238) all_54_1 = all_10_0 % 149.39/21.62 | | | | | | | | | | | | | | % 149.39/21.62 | | | | | | | | | | | | | | REDUCE: (183), (8237) imply: % 149.39/21.62 | | | | | | | | | | | | | | (8239) ~ (all_52_7 = all_10_0) % 149.39/21.62 | | | | | | | | | | | | | | % 149.39/21.62 | | | | | | | | | | | | | | SIMP: (8239) implies: % 149.39/21.62 | | | | | | | | | | | | | | (8240) ~ (all_52_7 = all_10_0) % 149.39/21.62 | | | | | | | | | | | | | | % 149.39/21.62 | | | | | | | | | | | | | | REDUCE: (182), (8237) imply: % 149.39/21.62 | | | | | | | | | | | | | | (8241) ~ (all_52_8 = all_10_0) % 149.39/21.62 | | | | | | | | | | | | | | % 149.39/21.62 | | | | | | | | | | | | | | SIMP: (8241) implies: % 149.39/21.62 | | | | | | | | | | | | | | (8242) ~ (all_52_8 = all_10_0) % 149.39/21.62 | | | | | | | | | | | | | | % 149.39/21.62 | | | | | | | | | | | | | | REDUCE: (181), (8237) imply: % 149.39/21.62 | | | | | | | | | | | | | | (8243) ~ (all_52_12 = all_10_0) % 149.39/21.62 | | | | | | | | | | | | | | % 149.39/21.62 | | | | | | | | | | | | | | SIMP: (8243) implies: % 149.39/21.62 | | | | | | | | | | | | | | (8244) ~ (all_52_12 = all_10_0) % 149.39/21.62 | | | | | | | | | | | | | | % 149.39/21.62 | | | | | | | | | | | | | | REDUCE: (563), (8237) imply: % 149.39/21.62 | | | | | | | | | | | | | | (8245) ~ (all_10_0 = all_10_2) % 149.39/21.62 | | | | | | | | | | | | | | % 149.39/21.62 | | | | | | | | | | | | | | REDUCE: (571), (8237) imply: % 149.39/21.62 | | | | | | | | | | | | | | (8246) ~ (all_10_0 = all_8_2) % 149.39/21.62 | | | | | | | | | | | | | | % 149.39/21.62 | | | | | | | | | | | | | | REDUCE: (7427), (8237) imply: % 149.39/21.62 | | | | | | | | | | | | | | (8247) ~ (all_10_0 = all_6_0) % 149.39/21.62 | | | | | | | | | | | | | | % 149.39/21.62 | | | | | | | | | | | | | | BETA: splitting (292) gives: % 149.39/21.62 | | | | | | | | | | | | | | % 149.39/21.62 | | | | | | | | | | | | | | Case 1: % 149.39/21.62 | | | | | | | | | | | | | | | % 149.39/21.62 | | | | | | | | | | | | | | | (8248) ~ (all_56_21 = e2) % 149.39/21.62 | | | | | | | | | | | | | | | % 149.39/21.62 | | | | | | | | | | | | | | | REF_CLOSE: (36), (38), (41), (46), (48), (51), (53), (158), % 149.39/21.62 | | | | | | | | | | | | | | | (189), (241), (242), (243), (247), (251), (252), % 149.39/21.62 | | | | | | | | | | | | | | | (287), (291), (293), (294), (295), (296), (297), % 149.39/21.62 | | | | | | | | | | | | | | | (298), (326), (327), (366), (374), (381), (402), % 149.39/21.62 | | | | | | | | | | | | | | | (425), (429), (431), (443), (476), (533), (541), % 149.39/21.62 | | | | | | | | | | | | | | | (542), (543), (544), (545), (546), (550), (552), % 149.39/21.62 | | | | | | | | | | | | | | | (553), (557), (559), (569), (577), (583), (587), % 149.39/21.62 | | | | | | | | | | | | | | | (591), (612), (622), (627), (723), (7418), (7420), % 149.39/21.62 | | | | | | | | | | | | | | | (7423), (7425), (7426), (7431), (7433), (7434), % 149.39/21.62 | | | | | | | | | | | | | | | (7435), (7436), (7437), (8162), (8164), (8166), % 149.39/21.62 | | | | | | | | | | | | | | | (8232), (8235), (8238), (8242), (8244), (8245), % 149.39/21.62 | | | | | | | | | | | | | | | (8246), (8248), (function-axioms) are inconsistent % 149.39/21.62 | | | | | | | | | | | | | | | by sub-proof #65. % 149.39/21.62 | | | | | | | | | | | | | | | % 149.39/21.62 | | | | | | | | | | | | | | Case 2: % 149.39/21.62 | | | | | | | | | | | | | | | % 149.39/21.62 | | | | | | | | | | | | | | | (8249) all_56_21 = e2 % 149.39/21.62 | | | | | | | | | | | | | | | (8250) all_56_19 = e1 % 149.39/21.62 | | | | | | | | | | | | | | | % 149.39/21.62 | | | | | | | | | | | | | | | COMBINE_EQS: (7424), (8250) imply: % 149.39/21.62 | | | | | | | | | | | | | | | (8251) all_6_0 = e1 % 149.39/21.62 | | | | | | | | | | | | | | | % 149.39/21.62 | | | | | | | | | | | | | | | COMBINE_EQS: (374), (8249) imply: % 149.39/21.62 | | | | | | | | | | | | | | | (8252) all_6_2 = e2 % 149.39/21.62 | | | | | | | | | | | | | | | % 149.39/21.62 | | | | | | | | | | | | | | | SIMP: (8252) implies: % 149.39/21.62 | | | | | | | | | | | | | | | (8253) all_6_2 = e2 % 149.39/21.62 | | | | | | | | | | | | | | | % 149.39/21.62 | | | | | | | | | | | | | | | REDUCE: (569), (8253) imply: % 149.39/21.62 | | | | | | | | | | | | | | | (8254) ~ (all_52_2 = e2) % 149.39/21.62 | | | | | | | | | | | | | | | % 149.39/21.62 | | | | | | | | | | | | | | | REDUCE: (7429), (8251) imply: % 149.39/21.62 | | | | | | | | | | | | | | | (8255) ~ (all_52_7 = e1) % 149.39/21.62 | | | | | | | | | | | | | | | % 149.39/21.62 | | | | | | | | | | | | | | | REDUCE: (585), (8253) imply: % 149.39/21.62 | | | | | | | | | | | | | | | (8256) ~ (all_52_11 = e2) % 149.39/21.62 | | | | | | | | | | | | | | | % 149.39/21.62 | | | | | | | | | | | | | | | REDUCE: (587), (8253) imply: % 149.39/21.62 | | | | | | | | | | | | | | | (8257) ~ (all_52_14 = e2) % 149.39/21.62 | | | | | | | | | | | | | | | % 149.39/21.62 | | | | | | | | | | | | | | | REDUCE: (7420), (8253) imply: % 149.39/21.62 | | | | | | | | | | | | | | | (8258) op(e2, e2) = e2 % 149.39/21.62 | | | | | | | | | | | | | | | % 149.39/21.62 | | | | | | | | | | | | | | | REDUCE: (41), (8253) imply: % 149.39/21.62 | | | | | | | | | | | | | | | (8259) op(e1, e1) = e2 % 149.39/21.62 | | | | | | | | | | | | | | | % 149.39/21.62 | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_8_2, e2, % 149.39/21.62 | | | | | | | | | | | | | | | e2, e2, simplifying with (46), (8258) gives: % 149.39/21.62 | | | | | | | | | | | | | | | (8260) all_8_2 = e2 % 149.39/21.62 | | | | | | | | | | | | | | | % 149.39/21.62 | | | | | | | | | | | | | | | REDUCE: (568), (8260) imply: % 149.39/21.62 | | | | | | | | | | | | | | | (8261) ~ (all_52_1 = e2) % 149.39/21.62 | | | | | | | | | | | | | | | % 149.39/21.62 | | | | | | | | | | | | | | | REDUCE: (575), (8260) imply: % 149.39/21.62 | | | | | | | | | | | | | | | (8262) ~ (all_52_7 = e2) % 149.39/21.62 | | | | | | | | | | | | | | | % 149.39/21.62 | | | | | | | | | | | | | | | REDUCE: (579), (8260) imply: % 149.39/21.62 | | | | | | | | | | | | | | | (8263) ~ (all_52_13 = e2) % 149.39/21.62 | | | | | | | | | | | | | | | % 149.39/21.62 | | | | | | | | | | | | | | | REDUCE: (48), (8260) imply: % 149.39/21.62 | | | | | | | | | | | | | | | (8264) op(e2, e2) = all_8_1 % 149.39/21.62 | | | | | | | | | | | | | | | % 149.39/21.62 | | | | | | | | | | | | | | | REDUCE: (617), (8260) imply: % 149.39/21.62 | | | | | | | | | | | | | | | (8265) op(e2, e2) = all_56_10 % 149.39/21.62 | | | | | | | | | | | | | | | % 149.39/21.62 | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, % 149.39/21.62 | | | | | | | | | | | | | | | all_56_10, e2, e2, simplifying with (8258), (8265) % 149.39/21.62 | | | | | | | | | | | | | | | gives: % 149.39/21.62 | | | | | | | | | | | | | | | (8266) all_56_10 = e2 % 149.39/21.62 | | | | | | | | | | | | | | | % 149.39/21.62 | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_8_1, % 149.39/21.62 | | | | | | | | | | | | | | | all_56_10, e2, e2, simplifying with (8264), (8265) % 149.39/21.62 | | | | | | | | | | | | | | | gives: % 149.39/21.62 | | | | | | | | | | | | | | | (8267) all_56_10 = all_8_1 % 149.39/21.62 | | | | | | | | | | | | | | | % 149.39/21.62 | | | | | | | | | | | | | | | COMBINE_EQS: (8266), (8267) imply: % 149.39/21.62 | | | | | | | | | | | | | | | (8268) all_8_1 = e2 % 149.39/21.62 | | | | | | | | | | | | | | | % 149.39/21.62 | | | | | | | | | | | | | | | SIMP: (8268) implies: % 149.39/21.62 | | | | | | | | | | | | | | | (8269) all_8_1 = e2 % 149.39/21.62 | | | | | | | | | | | | | | | % 149.39/21.62 | | | | | | | | | | | | | | | REDUCE: (47), (8269) imply: % 149.39/21.62 | | | | | | | | | | | | | | | (8270) op(e2, e2) = all_8_0 % 149.39/21.62 | | | | | | | | | | | | | | | % 149.39/21.62 | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, all_8_0, % 149.39/21.62 | | | | | | | | | | | | | | | e2, e2, simplifying with (8258), (8270) gives: % 149.39/21.62 | | | | | | | | | | | | | | | (8271) all_8_0 = e2 % 149.39/21.62 | | | | | | | | | | | | | | | % 149.39/21.62 | | | | | | | | | | | | | | | BETA: splitting (288) gives: % 149.39/21.62 | | | | | | | | | | | | | | | % 149.39/21.62 | | | | | | | | | | | | | | | Case 1: % 149.39/21.62 | | | | | | | | | | | | | | | | % 149.39/21.62 | | | | | | | | | | | | | | | | (8272) ~ (all_56_31 = e1) % 149.39/21.62 | | | | | | | | | | | | | | | | % 149.39/21.62 | | | | | | | | | | | | | | | | REDUCE: (544), (8272) imply: % 149.39/21.62 | | | | | | | | | | | | | | | | (8273) ~ (all_4_2 = e1) % 149.39/21.62 | | | | | | | | | | | | | | | | % 149.39/21.62 | | | | | | | | | | | | | | | | BETA: splitting (290) gives: % 149.39/21.62 | | | | | | | | | | | | | | | | % 149.39/21.62 | | | | | | | | | | | | | | | | Case 1: % 149.39/21.62 | | | | | | | | | | | | | | | | | % 149.39/21.62 | | | | | | | | | | | | | | | | | (8274) ~ (all_56_31 = e3) % 149.39/21.62 | | | | | | | | | | | | | | | | | % 149.39/21.62 | | | | | | | | | | | | | | | | | REDUCE: (544), (8274) imply: % 149.39/21.62 | | | | | | | | | | | | | | | | | (8275) ~ (all_4_2 = e3) % 149.39/21.62 | | | | | | | | | | | | | | | | | % 149.39/21.62 | | | | | | | | | | | | | | | | | BETA: splitting (289) gives: % 149.39/21.62 | | | | | | | | | | | | | | | | | % 149.39/21.62 | | | | | | | | | | | | | | | | | Case 1: % 149.39/21.62 | | | | | | | | | | | | | | | | | | % 149.39/21.62 | | | | | | | | | | | | | | | | | | (8276) ~ (all_56_31 = e2) % 149.39/21.62 | | | | | | | | | | | | | | | | | | % 149.39/21.62 | | | | | | | | | | | | | | | | | | REDUCE: (544), (8276) imply: % 149.39/21.62 | | | | | | | | | | | | | | | | | | (8277) ~ (all_4_2 = e2) % 149.39/21.62 | | | | | | | | | | | | | | | | | | % 149.39/21.62 | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (38), (237), (540), (627), (8158), (8273), % 149.39/21.62 | | | | | | | | | | | | | | | | | | (8275), (8277), (function-axioms) are inconsistent % 149.39/21.62 | | | | | | | | | | | | | | | | | | by sub-proof #229. % 149.39/21.62 | | | | | | | | | | | | | | | | | | % 149.39/21.62 | | | | | | | | | | | | | | | | | Case 2: % 149.39/21.62 | | | | | | | | | | | | | | | | | | % 149.39/21.62 | | | | | | | | | | | | | | | | | | (8278) all_56_31 = e2 % 149.39/21.62 | | | | | | | | | | | | | | | | | | (8279) all_56_27 = e0 % 149.39/21.62 | | | | | | | | | | | | | | | | | | % 149.39/21.62 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (360), (8279) imply: % 149.39/21.62 | | | | | | | | | | | | | | | | | | (8280) all_52_7 = e0 % 149.39/21.62 | | | | | | | | | | | | | | | | | | % 149.39/21.62 | | | | | | | | | | | | | | | | | | SIMP: (8280) implies: % 149.39/21.62 | | | | | | | | | | | | | | | | | | (8281) all_52_7 = e0 % 149.39/21.62 | | | | | | | | | | | | | | | | | | % 149.39/21.62 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (544), (8278) imply: % 149.39/21.62 | | | | | | | | | | | | | | | | | | (8282) all_4_2 = e2 % 149.39/21.62 | | | | | | | | | | | | | | | | | | % 149.39/21.62 | | | | | | | | | | | | | | | | | | REDUCE: (570), (8282) imply: % 149.39/21.62 | | | | | | | | | | | | | | | | | | (8283) ~ (all_52_3 = e2) % 149.39/21.62 | | | | | | | | | | | | | | | | | | % 149.39/21.62 | | | | | | | | | | | | | | | | | | REDUCE: (8240), (8281) imply: % 149.39/21.62 | | | | | | | | | | | | | | | | | | (8284) ~ (all_10_0 = e0) % 149.39/21.62 | | | | | | | | | | | | | | | | | | % 149.39/21.62 | | | | | | | | | | | | | | | | | | SIMP: (8284) implies: % 149.39/21.62 | | | | | | | | | | | | | | | | | | (8285) ~ (all_10_0 = e0) % 149.39/21.62 | | | | | | | | | | | | | | | | | | % 149.39/21.62 | | | | | | | | | | | | | | | | | | REDUCE: (38), (8282) imply: % 149.39/21.62 | | | | | | | | | | | | | | | | | | (8286) op(e2, e2) = all_4_1 % 149.39/21.62 | | | | | | | | | | | | | | | | | | % 149.39/21.62 | | | | | | | | | | | | | | | | | | REDUCE: (627), (8282) imply: % 149.39/21.62 | | | | | | | | | | | | | | | | | | (8287) op(e0, e2) = all_56_30 % 149.39/21.62 | | | | | | | | | | | | | | | | | | % 149.39/21.62 | | | | | | | | | | | | | | | | | | REDUCE: (206), (8281) imply: % 149.39/21.62 | | | | | | | | | | | | | | | | | | (8288) op(e0, e2) = e0 % 149.39/21.62 | | | | | | | | | | | | | | | | | | % 149.39/21.62 | | | | | | | | | | | | | | | | | | BETA: splitting (345) gives: % 149.39/21.62 | | | | | | | | | | | | | | | | | | % 149.39/21.62 | | | | | | | | | | | | | | | | | | Case 1: % 149.39/21.62 | | | | | | | | | | | | | | | | | | | % 149.39/21.62 | | | | | | | | | | | | | | | | | | | (8289) all_58_0 = e2 % 149.39/21.62 | | | | | | | | | | | | | | | | | | | % 149.39/21.62 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (419), (8289) imply: % 149.39/21.62 | | | | | | | | | | | | | | | | | | | (8290) all_10_2 = e2 % 149.39/21.62 | | | | | | | | | | | | | | | | | | | % 149.39/21.62 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (546), (8290) imply: % 149.39/21.62 | | | | | | | | | | | | | | | | | | | (8291) all_56_1 = e2 % 149.39/21.62 | | | | | | | | | | | | | | | | | | | % 149.39/21.62 | | | | | | | | | | | | | | | | | | | BETA: splitting (251) gives: % 149.39/21.62 | | | | | | | | | | | | | | | | | | | % 149.39/21.62 | | | | | | | | | | | | | | | | | | | Case 1: % 149.39/21.62 | | | | | | | | | | | | | | | | | | | | % 149.39/21.62 | | | | | | | | | | | | | | | | | | | | % 149.39/21.62 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, % 149.39/21.62 | | | | | | | | | | | | | | | | | | | | all_56_30, e2, e0, simplifying with (8287), (8288) % 149.39/21.62 | | | | | | | | | | | | | | | | | | | | gives: % 149.39/21.62 | | | | | | | | | | | | | | | | | | | | (8292) all_56_30 = e0 % 149.39/21.62 | | | | | | | | | | | | | | | | | | | | % 149.39/21.62 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, all_4_1, % 149.39/21.62 | | | | | | | | | | | | | | | | | | | | e2, e2, simplifying with (8258), (8286) gives: % 149.39/21.62 | | | | | | | | | | | | | | | | | | | | (8293) all_4_1 = e2 % 149.39/21.62 | | | | | | | | | | | | | | | | | | | | % 149.39/21.62 | | | | | | | | | | | | | | | | | | | | REDUCE: (8158), (8293) imply: % 149.39/21.62 | | | | | | | | | | | | | | | | | | | | (8294) op(e0, e2) = e2 % 149.39/21.62 | | | | | | | | | | | | | | | | | | | | % 149.39/21.62 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, e2, e2, % 149.39/21.62 | | | | | | | | | | | | | | | | | | | | e0, simplifying with (8288), (8294) gives: % 149.39/21.62 | | | | | | | | | | | | | | | | | | | | (8295) e2 = e0 % 149.39/21.62 | | | | | | | | | | | | | | | | | | | | % 149.39/21.62 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (8291), (8295) imply: % 149.39/21.62 | | | | | | | | | | | | | | | | | | | | (8296) all_56_1 = e0 % 149.39/21.62 | | | | | | | | | | | | | | | | | | | | % 149.39/21.62 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (251), (297), (402), (7437), (8162), (8238), % 149.39/21.62 | | | | | | | | | | | | | | | | | | | | (8244), (8285), (8296) are inconsistent by % 149.39/21.62 | | | | | | | | | | | | | | | | | | | | sub-proof #489. % 149.39/21.62 | | | | | | | | | | | | | | | | | | | | % 149.39/21.62 | | | | | | | | | | | | | | | | | | | Case 2: % 149.39/21.62 | | | | | | | | | | | | | | | | | | | | % 149.39/21.62 | | | | | | | | | | | | | | | | | | | | (8297) all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0 % 149.39/21.62 | | | | | | | | | | | | | | | | | | | | % 149.39/21.62 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7437), (8162), (8238), (8285), (8297) are % 149.39/21.62 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #490. % 149.39/21.62 | | | | | | | | | | | | | | | | | | | | % 149.39/21.62 | | | | | | | | | | | | | | | | | | | End of split % 149.39/21.62 | | | | | | | | | | | | | | | | | | | % 149.39/21.62 | | | | | | | | | | | | | | | | | | Case 2: % 149.39/21.62 | | | | | | | | | | | | | | | | | | | % 149.39/21.62 | | | | | | | | | | | | | | | | | | | (8298) ~ (all_58_0 = e2) % 149.39/21.62 | | | | | | | | | | | | | | | | | | | % 149.39/21.62 | | | | | | | | | | | | | | | | | | | REDUCE: (419), (8298) imply: % 149.39/21.62 | | | | | | | | | | | | | | | | | | | (8299) ~ (all_10_2 = e2) % 149.39/21.62 | | | | | | | | | | | | | | | | | | | % 149.39/21.62 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (344), (365), (401), (419), (553), (8254), (8261), % 149.39/21.62 | | | | | | | | | | | | | | | | | | | (8283), (8299) are inconsistent by sub-proof #597. % 149.39/21.62 | | | | | | | | | | | | | | | | | | | % 149.39/21.62 | | | | | | | | | | | | | | | | | | End of split % 149.39/21.62 | | | | | | | | | | | | | | | | | | % 149.48/21.62 | | | | | | | | | | | | | | | | | End of split % 149.48/21.62 | | | | | | | | | | | | | | | | | % 149.48/21.62 | | | | | | | | | | | | | | | | Case 2: % 149.48/21.62 | | | | | | | | | | | | | | | | | % 149.48/21.62 | | | | | | | | | | | | | | | | | (8300) all_56_31 = e3 % 149.48/21.62 | | | | | | | | | | | | | | | | | (8301) all_56_25 = e0 % 149.48/21.62 | | | | | | | | | | | | | | | | | % 149.48/21.62 | | | | | | | | | | | | | | | | | REF_CLOSE: (188), (239), (447), (480), (544), (581), (8255), % 149.48/21.62 | | | | | | | | | | | | | | | | | (8262), (8300), (8301) are inconsistent by % 149.48/21.62 | | | | | | | | | | | | | | | | | sub-proof #71. % 149.48/21.62 | | | | | | | | | | | | | | | | | % 149.48/21.62 | | | | | | | | | | | | | | | | End of split % 149.48/21.62 | | | | | | | | | | | | | | | | % 149.48/21.62 | | | | | | | | | | | | | | | Case 2: % 149.48/21.62 | | | | | | | | | | | | | | | | % 149.48/21.62 | | | | | | | | | | | | | | | | (8302) all_56_31 = e1 % 149.48/21.62 | | | | | | | | | | | | | | | | (8303) all_56_29 = e0 % 149.48/21.62 | | | | | | | | | | | | | | | | % 149.48/21.62 | | | | | | | | | | | | | | | | COMBINE_EQS: (357), (8303) imply: % 149.48/21.62 | | | | | | | | | | | | | | | | (8304) all_52_11 = e0 % 149.48/21.62 | | | | | | | | | | | | | | | | % 149.48/21.62 | | | | | | | | | | | | | | | | SIMP: (8304) implies: % 149.48/21.62 | | | | | | | | | | | | | | | | (8305) all_52_11 = e0 % 149.48/21.62 | | | | | | | | | | | | | | | | % 149.48/21.62 | | | | | | | | | | | | | | | | COMBINE_EQS: (544), (8302) imply: % 149.48/21.62 | | | | | | | | | | | | | | | | (8306) all_4_2 = e1 % 149.48/21.62 | | | | | | | | | | | | | | | | % 149.48/21.62 | | | | | | | | | | | | | | | | COMBINE_EQS: (531), (8306) imply: % 149.48/21.62 | | | | | | | | | | | | | | | | (8307) all_34_2 = e1 % 149.48/21.62 | | | | | | | | | | | | | | | | % 149.48/21.62 | | | | | | | | | | | | | | | | COMBINE_EQS: (547), (8306) imply: % 149.48/21.62 | | | | | | | | | | | | | | | | (8308) all_58_15 = e1 % 149.48/21.62 | | | | | | | | | | | | | | | | % 149.48/21.62 | | | | | | | | | | | | | | | | COMBINE_EQS: (548), (8305) imply: % 149.48/21.62 | | | | | | | | | | | | | | | | (8309) all_58_14 = e0 % 149.48/21.62 | | | | | | | | | | | | | | | | % 149.48/21.62 | | | | | | | | | | | | | | | | REDUCE: (173), (8305) imply: % 149.48/21.62 | | | | | | | | | | | | | | | | (8310) ~ (all_52_7 = e0) % 149.48/21.62 | | | | | | | | | | | | | | | | % 149.48/21.62 | | | | | | | | | | | | | | | | REDUCE: (8256), (8305) imply: % 149.48/21.62 | | | | | | | | | | | | | | | | (8311) ~ (e2 = e0) % 149.48/21.62 | | | | | | | | | | | | | | | | % 149.48/21.62 | | | | | | | | | | | | | | | | REDUCE: (589), (8306) imply: % 149.48/21.62 | | | | | | | | | | | | | | | | (8312) ~ (all_52_12 = e1) % 149.48/21.62 | | | | | | | | | | | | | | | | % 149.48/21.62 | | | | | | | | | | | | | | | | REDUCE: (38), (8306) imply: % 149.48/21.62 | | | | | | | | | | | | | | | | (8313) op(e1, e1) = all_4_1 % 149.48/21.62 | | | | | | | | | | | | | | | | % 149.48/21.62 | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (206), (239), (319), (322), (386), % 149.48/21.62 | | | | | | | | | | | | | | | | (480), (549), (550), (551), (624), (683), (8158), % 149.48/21.62 | | | | | | | | | | | | | | | | (8173), (8255), (8257), (8259), (8262), (8263), % 149.48/21.62 | | | | | | | | | | | | | | | | (8307), (8308), (8309), (8310), (8312), (8313), % 149.48/21.62 | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 149.48/21.62 | | | | | | | | | | | | | | | | #34. % 149.48/21.62 | | | | | | | | | | | | | | | | % 149.48/21.62 | | | | | | | | | | | | | | | End of split % 149.48/21.62 | | | | | | | | | | | | | | | % 149.48/21.62 | | | | | | | | | | | | | | End of split % 149.48/21.62 | | | | | | | | | | | | | | % 149.48/21.62 | | | | | | | | | | | | | End of split % 149.48/21.62 | | | | | | | | | | | | | % 149.48/21.62 | | | | | | | | | | | | End of split % 149.48/21.62 | | | | | | | | | | | | % 149.48/21.62 | | | | | | | | | | | Case 2: % 149.48/21.62 | | | | | | | | | | | | % 149.48/21.62 | | | | | | | | | | | | (8314) all_32_1 = e1 % 149.48/21.62 | | | | | | | | | | | | (8315) ~ (all_32_0 = e0) | ~ (all_32_2 = e2) % 149.48/21.62 | | | | | | | | | | | | % 149.48/21.62 | | | | | | | | | | | | COMBINE_EQS: (682), (8314) imply: % 149.48/21.62 | | | | | | | | | | | | (8316) all_10_1 = e1 % 149.48/21.62 | | | | | | | | | | | | % 149.48/21.62 | | | | | | | | | | | | SIMP: (8316) implies: % 149.48/21.62 | | | | | | | | | | | | (8317) all_10_1 = e1 % 149.48/21.62 | | | | | | | | | | | | % 149.48/21.62 | | | | | | | | | | | | REDUCE: (53), (8317) imply: % 149.48/21.62 | | | | | | | | | | | | (8318) op(all_10_2, all_10_2) = e1 % 149.48/21.62 | | | | | | | | | | | | % 149.48/21.62 | | | | | | | | | | | | REDUCE: (52), (8317) imply: % 149.48/21.62 | | | | | | | | | | | | (8319) op(e3, e1) = all_10_0 % 149.48/21.62 | | | | | | | | | | | | % 149.48/21.62 | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_8, % 149.48/21.62 | | | | | | | | | | | | all_10_0, e1, e3, simplifying with (217), (8319) % 149.48/21.62 | | | | | | | | | | | | gives: % 149.48/21.62 | | | | | | | | | | | | (8320) all_52_8 = all_10_0 % 149.48/21.62 | | | | | | | | | | | | % 149.48/21.62 | | | | | | | | | | | | COMBINE_EQS: (459), (8320) imply: % 149.48/21.62 | | | | | | | | | | | | (8321) all_54_2 = all_10_0 % 149.48/21.62 | | | | | | | | | | | | % 149.48/21.62 | | | | | | | | | | | | COMBINE_EQS: (429), (8320) imply: % 149.48/21.62 | | | | | | | | | | | | (8322) all_56_5 = all_10_0 % 149.48/21.62 | | | | | | | | | | | | % 149.48/21.62 | | | | | | | | | | | | COMBINE_EQS: (407), (8320) imply: % 149.48/21.62 | | | | | | | | | | | | (8323) all_58_4 = all_10_0 % 149.48/21.62 | | | | | | | | | | | | % 149.48/21.62 | | | | | | | | | | | | REDUCE: (182), (8320) imply: % 149.48/21.62 | | | | | | | | | | | | (8324) ~ (all_52_4 = all_10_0) % 149.48/21.62 | | | | | | | | | | | | % 149.48/21.62 | | | | | | | | | | | | REDUCE: (169), (8320) imply: % 149.48/21.62 | | | | | | | | | | | | (8325) ~ (all_52_11 = all_10_0) % 149.48/21.62 | | | | | | | | | | | | % 149.48/21.62 | | | | | | | | | | | | SIMP: (8325) implies: % 149.48/21.62 | | | | | | | | | | | | (8326) ~ (all_52_11 = all_10_0) % 149.48/21.62 | | | | | | | | | | | | % 149.48/21.62 | | | | | | | | | | | | REDUCE: (168), (8320) imply: % 149.48/21.62 | | | | | | | | | | | | (8327) ~ (all_52_12 = all_10_0) % 149.48/21.62 | | | | | | | | | | | | % 149.48/21.62 | | | | | | | | | | | | SIMP: (8327) implies: % 149.48/21.62 | | | | | | | | | | | | (8328) ~ (all_52_12 = all_10_0) % 149.48/21.62 | | | | | | | | | | | | % 149.48/21.62 | | | | | | | | | | | | REDUCE: (565), (8320) imply: % 149.48/21.62 | | | | | | | | | | | | (8329) ~ (all_10_0 = all_10_2) % 149.48/21.62 | | | | | | | | | | | | % 149.48/21.62 | | | | | | | | | | | | REDUCE: (582), (8320) imply: % 149.48/21.62 | | | | | | | | | | | | (8330) ~ (all_10_0 = all_6_2) % 149.48/21.62 | | | | | | | | | | | | % 149.48/21.62 | | | | | | | | | | | | BETA: splitting (292) gives: % 149.48/21.62 | | | | | | | | | | | | % 149.48/21.62 | | | | | | | | | | | | Case 1: % 149.48/21.62 | | | | | | | | | | | | | % 149.48/21.62 | | | | | | | | | | | | | (8331) ~ (all_56_21 = e2) % 149.48/21.62 | | | | | | | | | | | | | % 149.48/21.62 | | | | | | | | | | | | | REDUCE: (374), (8331) imply: % 149.48/21.62 | | | | | | | | | | | | | (8332) ~ (all_6_2 = e2) % 149.48/21.62 | | | | | | | | | | | | | % 149.48/21.62 | | | | | | | | | | | | | REF_CLOSE: (7), (36), (38), (41), (48), (51), (173), (237), % 149.48/21.62 | | | | | | | | | | | | | (250), (252), (288), (289), (290), (291), (297), % 149.48/21.62 | | | | | | | | | | | | | (298), (299), (328), (330), (331), (337), (357), % 149.48/21.62 | | | | | | | | | | | | | (360), (374), (380), (389), (402), (408), (447), % 149.48/21.62 | | | | | | | | | | | | | (494), (529), (540), (543), (544), (546), (548), % 149.48/21.62 | | | | | | | | | | | | | (549), (552), (554), (555), (561), (563), (570), % 149.48/21.62 | | | | | | | | | | | | | (580), (581), (588), (612), (622), (627), (681), % 149.48/21.62 | | | | | | | | | | | | | (761), (7436), (7437), (8154), (8158), (8162), % 149.48/21.62 | | | | | | | | | | | | | (8315), (8318), (8321), (8322), (8323), (8324), % 149.48/21.62 | | | | | | | | | | | | | (8326), (8328), (8329), (8330), (8332), % 149.48/21.62 | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 149.48/21.62 | | | | | | | | | | | | | #203. % 149.48/21.62 | | | | | | | | | | | | | % 149.48/21.62 | | | | | | | | | | | | Case 2: % 149.48/21.62 | | | | | | | | | | | | | % 149.48/21.62 | | | | | | | | | | | | | (8333) all_56_21 = e2 % 149.48/21.62 | | | | | | | | | | | | | (8334) all_56_19 = e1 % 149.48/21.62 | | | | | | | | | | | | | % 149.48/21.62 | | | | | | | | | | | | | COMBINE_EQS: (7424), (8334) imply: % 149.48/21.62 | | | | | | | | | | | | | (8335) all_6_0 = e1 % 149.48/21.62 | | | | | | | | | | | | | % 149.48/21.62 | | | | | | | | | | | | | REF_CLOSE: (4), (5), (38), (41), (46), (47), (48), (173), % 149.48/21.62 | | | | | | | | | | | | | (181), (183), (188), (237), (238), (239), (250), % 149.48/21.62 | | | | | | | | | | | | | (251), (288), (289), (290), (298), (322), (329), % 149.48/21.62 | | | | | | | | | | | | | (333), (336), (339), (343), (345), (357), (360), % 149.48/21.62 | | | | | | | | | | | | | (374), (386), (389), (401), (419), (447), (457), % 149.48/21.62 | | | | | | | | | | | | | (480), (482), (494), (540), (544), (546), (547), % 149.48/21.62 | | | | | | | | | | | | | (549), (550), (551), (554), (555), (557), (570), % 149.48/21.62 | | | | | | | | | | | | | (571), (577), (579), (581), (585), (587), (588), % 149.48/21.62 | | | | | | | | | | | | | (589), (590), (617), (621), (623), (761), (7420), % 149.48/21.62 | | | | | | | | | | | | | (7425), (7427), (8160), (8162), (8164), (8168), % 149.48/21.62 | | | | | | | | | | | | | (8315), (8318), (8321), (8322), (8323), (8324), % 149.48/21.62 | | | | | | | | | | | | | (8326), (8328), (8329), (8330), (8333), (8335), % 149.48/21.62 | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 149.48/21.62 | | | | | | | | | | | | | #60. % 149.48/21.62 | | | | | | | | | | | | | % 149.48/21.62 | | | | | | | | | | | | End of split % 149.48/21.62 | | | | | | | | | | | | % 149.48/21.62 | | | | | | | | | | | End of split % 149.48/21.62 | | | | | | | | | | | % 149.48/21.62 | | | | | | | | | | Case 2: % 149.48/21.62 | | | | | | | | | | | % 149.48/21.62 | | | | | | | | | | | (8336) all_30_0 = e3 % 149.48/21.62 | | | | | | | | | | | (8337) ~ (all_30_1 = e0) | ~ (all_30_2 = e1) % 149.48/21.62 | | | | | | | | | | | % 149.48/21.62 | | | | | | | | | | | COMBINE_EQS: (718), (8336) imply: % 149.48/21.62 | | | | | | | | | | | (8338) all_8_0 = e3 % 149.48/21.62 | | | | | | | | | | | % 149.48/21.62 | | | | | | | | | | | REF_CLOSE: (9), (36), (41), (46), (47), (48), (51), (212), % 149.48/21.62 | | | | | | | | | | | (237), (242), (247), (252), (294), (295), (296), % 149.48/21.62 | | | | | | | | | | | (390), (425), (431), (443), (540), (541), (542), % 149.48/21.62 | | | | | | | | | | | (543), (545), (557), (579), (583), (590), (617), % 149.48/21.62 | | | | | | | | | | | (658), (7436), (8166), (8337), (8338), % 149.48/21.62 | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 149.48/21.62 | | | | | | | | | | | #379. % 149.48/21.62 | | | | | | | | | | | % 149.48/21.62 | | | | | | | | | | End of split % 149.48/21.62 | | | | | | | | | | % 149.48/21.62 | | | | | | | | | Case 2: % 149.48/21.62 | | | | | | | | | | % 149.48/21.62 | | | | | | | | | | (8339) all_22_1 = e3 % 149.48/21.62 | | | | | | | | | | % 149.48/21.62 | | | | | | | | | | COMBINE_EQS: (672), (8339) imply: % 149.48/21.62 | | | | | | | | | | (8340) all_8_1 = e3 % 149.48/21.62 | | | | | | | | | | % 149.48/21.62 | | | | | | | | | | SIMP: (8340) implies: % 149.48/21.62 | | | | | | | | | | (8341) all_8_1 = e3 % 149.48/21.62 | | | | | | | | | | % 149.48/21.63 | | | | | | | | | | REF_CLOSE: (4), (7), (9), (36), (38), (41), (46), (47), (48), % 149.48/21.63 | | | | | | | | | | (51), (53), (182), (183), (188), (189), (192), % 149.48/21.63 | | | | | | | | | | (215), (237), (239), (240), (241), (242), (243), % 149.48/21.63 | | | | | | | | | | (244), (247), (252), (287), (288), (289), (290), % 149.48/21.63 | | | | | | | | | | (291), (292), (293), (294), (298), (299), (324), % 149.48/21.63 | | | | | | | | | | (326), (327), (336), (339), (342), (343), (357), % 149.48/21.63 | | | | | | | | | | (360), (365), (366), (374), (381), (401), (408), % 149.48/21.63 | | | | | | | | | | (419), (429), (447), (471), (476), (478), (480), % 149.48/21.63 | | | | | | | | | | (540), (541), (542), (543), (544), (545), (546), % 149.48/21.63 | | | | | | | | | | (549), (550), (552), (553), (554), (555), (559), % 149.48/21.63 | | | | | | | | | | (561), (563), (569), (570), (571), (575), (581), % 149.48/21.63 | | | | | | | | | | (585), (587), (591), (612), (617), (622), (627), % 149.48/21.63 | | | | | | | | | | (7418), (7420), (7423), (7425), (7426), (7429), % 149.48/21.63 | | | | | | | | | | (7431), (7433), (7434), (7436), (8160), (8164), % 149.48/21.63 | | | | | | | | | | (8341), (function-axioms) are inconsistent by % 149.48/21.63 | | | | | | | | | | sub-proof #42. % 149.48/21.63 | | | | | | | | | | % 149.48/21.63 | | | | | | | | | End of split % 149.48/21.63 | | | | | | | | | % 149.48/21.63 | | | | | | | | Case 2: % 149.48/21.63 | | | | | | | | | % 149.48/21.63 | | | | | | | | | (8342) all_18_0 = e3 % 149.48/21.63 | | | | | | | | | (8343) ~ (all_18_1 = e2) | ~ (all_18_2 = e0) % 149.48/21.63 | | | | | | | | | % 149.48/21.63 | | | | | | | | | COMBINE_EQS: (753), (8342) imply: % 149.48/21.63 | | | | | | | | | (8344) all_6_0 = e3 % 149.48/21.63 | | | | | | | | | % 149.48/21.63 | | | | | | | | | SIMP: (8344) implies: % 149.48/21.63 | | | | | | | | | (8345) all_6_0 = e3 % 149.48/21.63 | | | | | | | | | % 149.48/21.63 | | | | | | | | | REF_CLOSE: (8), (41), (242), (292), (374), (524), (541), % 149.48/21.63 | | | | | | | | | (622), (7419), (7420), (7424), (7434), (8343), % 149.48/21.63 | | | | | | | | | (8345), (function-axioms) are inconsistent by % 149.48/21.63 | | | | | | | | | sub-proof #40. % 149.48/21.63 | | | | | | | | | % 149.48/21.63 | | | | | | | | End of split % 149.48/21.63 | | | | | | | | % 149.48/21.63 | | | | | | | Case 2: % 149.48/21.63 | | | | | | | | % 149.48/21.63 | | | | | | | | (8346) all_16_0 = e1 % 149.48/21.63 | | | | | | | | % 149.48/21.63 | | | | | | | | COMBINE_EQS: (757), (8346) imply: % 149.48/21.63 | | | | | | | | (8347) all_10_0 = e1 % 149.48/21.63 | | | | | | | | % 149.48/21.63 | | | | | | | | SIMP: (8347) implies: % 149.48/21.63 | | | | | | | | (8348) all_10_0 = e1 % 149.48/21.63 | | | | | | | | % 149.48/21.63 | | | | | | | | COMBINE_EQS: (741), (8348) imply: % 149.48/21.63 | | | | | | | | (8349) all_24_0 = e1 % 149.48/21.63 | | | | | | | | % 149.48/21.63 | | | | | | | | REDUCE: (7437), (8348) imply: % 149.48/21.63 | | | | | | | | (8350) ~ (e2 = e1) % 149.48/21.63 | | | | | | | | % 149.48/21.63 | | | | | | | | REDUCE: (52), (8348) imply: % 149.48/21.63 | | | | | | | | (8351) op(e3, all_10_1) = e1 % 149.48/21.63 | | | | | | | | % 149.48/21.63 | | | | | | | | BETA: splitting (74) gives: % 149.48/21.63 | | | | | | | | % 149.48/21.63 | | | | | | | | Case 1: % 149.48/21.63 | | | | | | | | | % 149.48/21.63 | | | | | | | | | (8352) ~ (all_18_0 = e3) % 149.48/21.63 | | | | | | | | | % 149.48/21.63 | | | | | | | | | REDUCE: (753), (8352) imply: % 149.48/21.63 | | | | | | | | | (8353) ~ (all_6_0 = e3) % 149.48/21.63 | | | | | | | | | % 149.48/21.63 | | | | | | | | | BETA: splitting (89) gives: % 149.48/21.63 | | | | | | | | | % 149.48/21.63 | | | | | | | | | Case 1: % 149.48/21.63 | | | | | | | | | | % 149.48/21.63 | | | | | | | | | | (8354) ~ (all_24_0 = e1) % 149.48/21.63 | | | | | | | | | | % 149.48/21.63 | | | | | | | | | | REDUCE: (8349), (8354) imply: % 149.48/21.63 | | | | | | | | | | (8355) $false % 149.48/21.63 | | | | | | | | | | % 149.48/21.63 | | | | | | | | | | CLOSE: (8355) is inconsistent. % 149.48/21.63 | | | | | | | | | | % 149.48/21.63 | | | | | | | | | Case 2: % 149.48/21.63 | | | | | | | | | | % 149.48/21.63 | | | | | | | | | | (8356) ~ (all_24_1 = e0) | ~ (all_24_2 = e2) % 149.48/21.63 | | | | | | | | | | % 149.48/21.63 | | | | | | | | | | BETA: splitting (114) gives: % 149.48/21.63 | | | | | | | | | | % 149.48/21.63 | | | | | | | | | | Case 1: % 149.48/21.63 | | | | | | | | | | | % 149.48/21.63 | | | | | | | | | | | (8357) ~ (all_34_0 = e2) % 149.48/21.63 | | | | | | | | | | | % 149.48/21.63 | | | | | | | | | | | REDUCE: (8156), (8357) imply: % 149.48/21.63 | | | | | | | | | | | (8358) $false % 149.48/21.63 | | | | | | | | | | | % 149.48/21.63 | | | | | | | | | | | CLOSE: (8358) is inconsistent. % 149.48/21.63 | | | | | | | | | | | % 149.48/21.63 | | | | | | | | | | Case 2: % 149.48/21.63 | | | | | | | | | | | % 149.48/21.63 | | | | | | | | | | | (8359) ~ (all_34_1 = e3) | ~ (all_34_2 = e1) % 149.48/21.63 | | | | | | | | | | | % 149.48/21.63 | | | | | | | | | | | BETA: splitting (288) gives: % 149.48/21.63 | | | | | | | | | | | % 149.48/21.63 | | | | | | | | | | | Case 1: % 149.48/21.63 | | | | | | | | | | | | % 149.48/21.63 | | | | | | | | | | | | (8360) ~ (all_56_31 = e1) % 149.48/21.63 | | | | | | | | | | | | % 149.48/21.63 | | | | | | | | | | | | REDUCE: (544), (8360) imply: % 149.48/21.63 | | | | | | | | | | | | (8361) ~ (all_4_2 = e1) % 149.48/21.63 | | | | | | | | | | | | % 149.48/21.63 | | | | | | | | | | | | BETA: splitting (290) gives: % 149.48/21.63 | | | | | | | | | | | | % 149.48/21.63 | | | | | | | | | | | | Case 1: % 149.48/21.63 | | | | | | | | | | | | | % 149.48/21.63 | | | | | | | | | | | | | (8362) ~ (all_56_31 = e3) % 149.48/21.63 | | | | | | | | | | | | | % 149.48/21.63 | | | | | | | | | | | | | REDUCE: (544), (8362) imply: % 149.48/21.63 | | | | | | | | | | | | | (8363) ~ (all_4_2 = e3) % 149.48/21.63 | | | | | | | | | | | | | % 149.48/21.63 | | | | | | | | | | | | | BETA: splitting (292) gives: % 149.48/21.63 | | | | | | | | | | | | | % 149.48/21.63 | | | | | | | | | | | | | Case 1: % 149.48/21.63 | | | | | | | | | | | | | | % 149.48/21.63 | | | | | | | | | | | | | | (8364) ~ (all_56_21 = e2) % 149.48/21.63 | | | | | | | | | | | | | | % 149.48/21.63 | | | | | | | | | | | | | | REDUCE: (374), (8364) imply: % 149.48/21.63 | | | | | | | | | | | | | | (8365) ~ (all_6_2 = e2) % 149.48/21.63 | | | | | | | | | | | | | | % 149.48/21.63 | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (8), (36), (38), (41), (188), (192), % 149.48/21.63 | | | | | | | | | | | | | | (237), (240), (242), (243), (287), (289), (291), % 149.48/21.63 | | | | | | | | | | | | | | (293), (324), (326), (327), (360), (366), (374), % 149.48/21.63 | | | | | | | | | | | | | | (381), (478), (540), (541), (544), (545), (546), % 149.48/21.63 | | | | | | | | | | | | | | (550), (552), (553), (559), (561), (569), (570), % 149.48/21.63 | | | | | | | | | | | | | | (587), (591), (622), (627), (7418), (7420), % 149.48/21.63 | | | | | | | | | | | | | | (7423), (7425), (7429), (7431), (7433), (7434), % 149.48/21.63 | | | | | | | | | | | | | | (8353), (8361), (8363), (8365), (function-axioms) % 149.48/21.63 | | | | | | | | | | | | | | are inconsistent by sub-proof #74. % 149.48/21.63 | | | | | | | | | | | | | | % 149.48/21.63 | | | | | | | | | | | | | Case 2: % 149.48/21.63 | | | | | | | | | | | | | | % 149.48/21.63 | | | | | | | | | | | | | | (8366) all_56_21 = e2 % 149.48/21.63 | | | | | | | | | | | | | | (8367) all_56_19 = e1 % 149.48/21.63 | | | | | | | | | | | | | | % 149.48/21.63 | | | | | | | | | | | | | | COMBINE_EQS: (7424), (8367) imply: % 149.48/21.63 | | | | | | | | | | | | | | (8368) all_6_0 = e1 % 149.48/21.63 | | | | | | | | | | | | | | % 149.48/21.63 | | | | | | | | | | | | | | COMBINE_EQS: (374), (8366) imply: % 149.48/21.63 | | | | | | | | | | | | | | (8369) all_6_2 = e2 % 149.48/21.63 | | | | | | | | | | | | | | % 149.48/21.63 | | | | | | | | | | | | | | REDUCE: (569), (8369) imply: % 149.48/21.63 | | | | | | | | | | | | | | (8370) ~ (all_52_2 = e2) % 149.48/21.63 | | | | | | | | | | | | | | % 149.48/21.63 | | | | | | | | | | | | | | REDUCE: (7427), (8368) imply: % 149.48/21.63 | | | | | | | | | | | | | | (8371) ~ (all_52_4 = e1) % 149.48/21.63 | | | | | | | | | | | | | | % 149.48/21.63 | | | | | | | | | | | | | | REDUCE: (7420), (8369) imply: % 149.48/21.63 | | | | | | | | | | | | | | (8372) op(e2, e2) = e2 % 149.48/21.63 | | | | | | | | | | | | | | % 149.48/21.63 | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_8_2, e2, % 149.48/21.63 | | | | | | | | | | | | | | e2, e2, simplifying with (46), (8372) gives: % 149.48/21.63 | | | | | | | | | | | | | | (8373) all_8_2 = e2 % 149.48/21.63 | | | | | | | | | | | | | | % 149.48/21.63 | | | | | | | | | | | | | | REDUCE: (568), (8373) imply: % 149.48/21.63 | | | | | | | | | | | | | | (8374) ~ (all_52_1 = e2) % 149.48/21.63 | | | | | | | | | | | | | | % 149.48/21.63 | | | | | | | | | | | | | | REDUCE: (571), (8373) imply: % 149.48/21.63 | | | | | | | | | | | | | | (8375) ~ (all_52_4 = e2) % 149.48/21.63 | | | | | | | | | | | | | | % 149.48/21.63 | | | | | | | | | | | | | | REDUCE: (48), (8373) imply: % 149.48/21.63 | | | | | | | | | | | | | | (8376) op(e2, e2) = all_8_1 % 149.48/21.63 | | | | | | | | | | | | | | % 149.48/21.63 | | | | | | | | | | | | | | REDUCE: (617), (8373) imply: % 149.48/21.63 | | | | | | | | | | | | | | (8377) op(e2, e2) = all_56_10 % 149.48/21.63 | | | | | | | | | | | | | | % 149.48/21.63 | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, % 149.48/21.63 | | | | | | | | | | | | | | all_56_10, e2, e2, simplifying with (8372), (8377) % 149.48/21.63 | | | | | | | | | | | | | | gives: % 149.48/21.63 | | | | | | | | | | | | | | (8378) all_56_10 = e2 % 149.48/21.63 | | | | | | | | | | | | | | % 149.48/21.63 | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_8_1, % 149.48/21.63 | | | | | | | | | | | | | | all_56_10, e2, e2, simplifying with (8376), (8377) % 149.48/21.63 | | | | | | | | | | | | | | gives: % 149.48/21.63 | | | | | | | | | | | | | | (8379) all_56_10 = all_8_1 % 149.48/21.63 | | | | | | | | | | | | | | % 149.48/21.63 | | | | | | | | | | | | | | COMBINE_EQS: (8378), (8379) imply: % 149.48/21.63 | | | | | | | | | | | | | | (8380) all_8_1 = e2 % 149.48/21.63 | | | | | | | | | | | | | | % 149.48/21.63 | | | | | | | | | | | | | | SIMP: (8380) implies: % 149.48/21.63 | | | | | | | | | | | | | | (8381) all_8_1 = e2 % 149.48/21.63 | | | | | | | | | | | | | | % 149.48/21.63 | | | | | | | | | | | | | | REDUCE: (47), (8381) imply: % 149.48/21.63 | | | | | | | | | | | | | | (8382) op(e2, e2) = all_8_0 % 149.48/21.63 | | | | | | | | | | | | | | % 149.48/21.63 | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, all_8_0, % 149.48/21.63 | | | | | | | | | | | | | | e2, e2, simplifying with (8372), (8382) gives: % 149.48/21.63 | | | | | | | | | | | | | | (8383) all_8_0 = e2 % 149.48/21.63 | | | | | | | | | | | | | | % 149.48/21.63 | | | | | | | | | | | | | | BETA: splitting (289) gives: % 149.48/21.63 | | | | | | | | | | | | | | % 149.48/21.63 | | | | | | | | | | | | | | Case 1: % 149.48/21.63 | | | | | | | | | | | | | | | % 149.48/21.63 | | | | | | | | | | | | | | | (8384) ~ (all_56_31 = e2) % 149.48/21.63 | | | | | | | | | | | | | | | % 149.48/21.63 | | | | | | | | | | | | | | | REDUCE: (544), (8384) imply: % 149.48/21.63 | | | | | | | | | | | | | | | (8385) ~ (all_4_2 = e2) % 149.48/21.63 | | | | | | | | | | | | | | | % 149.48/21.63 | | | | | | | | | | | | | | | REF_CLOSE: (36), (38), (237), (540), (627), (8158), (8361), % 149.48/21.63 | | | | | | | | | | | | | | | (8363), (8385), (function-axioms) are inconsistent % 149.48/21.63 | | | | | | | | | | | | | | | by sub-proof #229. % 149.48/21.63 | | | | | | | | | | | | | | | % 149.48/21.63 | | | | | | | | | | | | | | Case 2: % 149.48/21.63 | | | | | | | | | | | | | | | % 149.48/21.63 | | | | | | | | | | | | | | | (8386) all_56_31 = e2 % 149.48/21.63 | | | | | | | | | | | | | | | (8387) all_56_27 = e0 % 149.48/21.63 | | | | | | | | | | | | | | | % 149.48/21.63 | | | | | | | | | | | | | | | COMBINE_EQS: (360), (8387) imply: % 149.48/21.63 | | | | | | | | | | | | | | | (8388) all_52_7 = e0 % 149.48/21.63 | | | | | | | | | | | | | | | % 149.48/21.63 | | | | | | | | | | | | | | | SIMP: (8388) implies: % 149.48/21.63 | | | | | | | | | | | | | | | (8389) all_52_7 = e0 % 149.48/21.63 | | | | | | | | | | | | | | | % 149.48/21.63 | | | | | | | | | | | | | | | COMBINE_EQS: (544), (8386) imply: % 149.48/21.63 | | | | | | | | | | | | | | | (8390) all_4_2 = e2 % 149.48/21.63 | | | | | | | | | | | | | | | % 149.48/21.63 | | | | | | | | | | | | | | | REDUCE: (570), (8390) imply: % 149.48/21.63 | | | | | | | | | | | | | | | (8391) ~ (all_52_3 = e2) % 149.48/21.63 | | | | | | | | | | | | | | | % 149.48/21.63 | | | | | | | | | | | | | | | REDUCE: (183), (8389) imply: % 149.48/21.63 | | | | | | | | | | | | | | | (8392) ~ (all_52_4 = e0) % 149.48/21.63 | | | | | | | | | | | | | | | % 149.48/21.63 | | | | | | | | | | | | | | | REF_CLOSE: (53), (218), (251), (344), (365), (401), (419), % 149.48/21.63 | | | | | | | | | | | | | | | (457), (521), (553), (612), (8351), (8356), % 149.48/21.63 | | | | | | | | | | | | | | | (8370), (8371), (8372), (8374), (8375), (8391), % 149.48/21.63 | | | | | | | | | | | | | | | (8392), (function-axioms) are inconsistent by % 149.48/21.63 | | | | | | | | | | | | | | | sub-proof #38. % 149.48/21.63 | | | | | | | | | | | | | | | % 149.48/21.63 | | | | | | | | | | | | | | End of split % 149.48/21.63 | | | | | | | | | | | | | | % 149.48/21.63 | | | | | | | | | | | | | End of split % 149.48/21.63 | | | | | | | | | | | | | % 149.48/21.63 | | | | | | | | | | | | Case 2: % 149.48/21.63 | | | | | | | | | | | | | % 149.48/21.63 | | | | | | | | | | | | | (8393) all_56_31 = e3 % 149.48/21.63 | | | | | | | | | | | | | (8394) all_56_25 = e0 % 149.48/21.63 | | | | | | | | | | | | | % 149.48/21.63 | | | | | | | | | | | | | REF_CLOSE: (4), (9), (36), (38), (41), (51), (53), (188), % 149.48/21.63 | | | | | | | | | | | | | (189), (192), (241), (242), (243), (244), (287), % 149.48/21.63 | | | | | | | | | | | | | (291), (292), (293), (327), (336), (339), (366), % 149.48/21.63 | | | | | | | | | | | | | (374), (381), (447), (471), (476), (541), (544), % 149.48/21.63 | | | | | | | | | | | | | (545), (546), (549), (550), (552), (553), (554), % 149.48/21.63 | | | | | | | | | | | | | (559), (569), (570), (581), (587), (591), (612), % 149.48/21.63 | | | | | | | | | | | | | (622), (627), (7418), (7420), (7423), (7424), % 149.48/21.63 | | | | | | | | | | | | | (7425), (7426), (7431), (7433), (7434), (8353), % 149.48/21.63 | | | | | | | | | | | | | (8393), (8394), (function-axioms) are inconsistent % 149.48/21.63 | | | | | | | | | | | | | by sub-proof #55. % 149.48/21.63 | | | | | | | | | | | | | % 149.48/21.63 | | | | | | | | | | | | End of split % 149.48/21.63 | | | | | | | | | | | | % 149.48/21.63 | | | | | | | | | | | Case 2: % 149.48/21.63 | | | | | | | | | | | | % 149.48/21.63 | | | | | | | | | | | | (8395) all_56_31 = e1 % 149.48/21.63 | | | | | | | | | | | | (8396) all_56_29 = e0 % 149.48/21.63 | | | | | | | | | | | | % 149.48/21.63 | | | | | | | | | | | | COMBINE_EQS: (357), (8396) imply: % 149.48/21.63 | | | | | | | | | | | | (8397) all_52_11 = e0 % 149.48/21.63 | | | | | | | | | | | | % 149.48/21.63 | | | | | | | | | | | | SIMP: (8397) implies: % 149.48/21.63 | | | | | | | | | | | | (8398) all_52_11 = e0 % 149.48/21.63 | | | | | | | | | | | | % 149.48/21.63 | | | | | | | | | | | | COMBINE_EQS: (544), (8395) imply: % 149.48/21.63 | | | | | | | | | | | | (8399) all_4_2 = e1 % 149.48/21.63 | | | | | | | | | | | | % 149.48/21.63 | | | | | | | | | | | | COMBINE_EQS: (531), (8399) imply: % 149.48/21.63 | | | | | | | | | | | | (8400) all_34_2 = e1 % 149.48/21.63 | | | | | | | | | | | | % 149.48/21.63 | | | | | | | | | | | | COMBINE_EQS: (547), (8399) imply: % 149.48/21.63 | | | | | | | | | | | | (8401) all_58_15 = e1 % 149.48/21.63 | | | | | | | | | | | | % 149.48/21.63 | | | | | | | | | | | | COMBINE_EQS: (548), (8398) imply: % 149.48/21.63 | | | | | | | | | | | | (8402) all_58_14 = e0 % 149.48/21.63 | | | | | | | | | | | | % 149.48/21.63 | | | | | | | | | | | | REDUCE: (187), (8398) imply: % 149.48/21.63 | | | | | | | | | | | | (8403) ~ (all_52_3 = e0) % 149.48/21.63 | | | | | | | | | | | | % 149.48/21.63 | | | | | | | | | | | | REDUCE: (570), (8399) imply: % 149.48/21.63 | | | | | | | | | | | | (8404) ~ (all_52_3 = e1) % 149.48/21.63 | | | | | | | | | | | | % 149.48/21.63 | | | | | | | | | | | | REDUCE: (173), (8398) imply: % 149.48/21.63 | | | | | | | | | | | | (8405) ~ (all_52_7 = e0) % 149.48/21.63 | | | | | | | | | | | | % 149.48/21.63 | | | | | | | | | | | | REDUCE: (585), (8398) imply: % 149.48/21.63 | | | | | | | | | | | | (8406) ~ (all_6_2 = e0) % 149.48/21.63 | | | | | | | | | | | | % 149.48/21.63 | | | | | | | | | | | | SIMP: (8406) implies: % 149.48/21.63 | | | | | | | | | | | | (8407) ~ (all_6_2 = e0) % 149.48/21.63 | | | | | | | | | | | | % 149.48/21.63 | | | | | | | | | | | | REDUCE: (588), (8398), (8399) imply: % 149.48/21.63 | | | | | | | | | | | | (8408) ~ (e1 = e0) % 149.48/21.63 | | | | | | | | | | | | % 149.48/21.63 | | | | | | | | | | | | REDUCE: (38), (8399) imply: % 149.48/21.63 | | | | | | | | | | | | (8409) op(e1, e1) = all_4_1 % 149.48/21.63 | | | | | | | | | | | | % 149.48/21.63 | | | | | | | | | | | | REDUCE: (36), (8399) imply: % 149.48/21.63 | | | | | | | | | | | | (8410) op(e0, e0) = e1 % 149.48/21.63 | | | | | | | | | | | | % 149.48/21.63 | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (41), (48), (51), (168), (183), % 149.48/21.63 | | | | | | | | | | | | (196), (206), (239), (240), (242), (247), (251), % 149.48/21.63 | | | | | | | | | | | | (252), (292), (294), (296), (297), (298), (299), % 149.48/21.63 | | | | | | | | | | | | (319), (331), (336), (345), (365), (374), (402), % 149.48/21.63 | | | | | | | | | | | | (407), (408), (419), (425), (429), (457), (478), % 149.48/21.63 | | | | | | | | | | | | (480), (541), (542), (543), (545), (546), (549), % 149.48/21.63 | | | | | | | | | | | | (551), (554), (555), (557), (561), (563), (565), % 149.48/21.63 | | | | | | | | | | | | (571), (575), (582), (622), (624), (683), (7420), % 149.48/21.63 | | | | | | | | | | | | (7424), (7425), (7427), (7429), (7433), (7436), % 149.48/21.63 | | | | | | | | | | | | (8158), (8359), (8400), (8401), (8402), (8403), % 149.48/21.63 | | | | | | | | | | | | (8404), (8405), (8407), (8409), (8410), % 149.48/21.63 | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 149.48/21.63 | | | | | | | | | | | | #33. % 149.48/21.63 | | | | | | | | | | | | % 149.48/21.63 | | | | | | | | | | | End of split % 149.48/21.63 | | | | | | | | | | | % 149.48/21.63 | | | | | | | | | | End of split % 149.48/21.63 | | | | | | | | | | % 149.48/21.63 | | | | | | | | | End of split % 149.48/21.63 | | | | | | | | | % 149.48/21.63 | | | | | | | | Case 2: % 149.48/21.63 | | | | | | | | | % 149.48/21.63 | | | | | | | | | (8411) all_18_0 = e3 % 149.48/21.63 | | | | | | | | | (8412) ~ (all_18_1 = e2) | ~ (all_18_2 = e0) % 149.48/21.63 | | | | | | | | | % 149.48/21.63 | | | | | | | | | COMBINE_EQS: (753), (8411) imply: % 149.48/21.63 | | | | | | | | | (8413) all_6_0 = e3 % 149.48/21.63 | | | | | | | | | % 149.48/21.63 | | | | | | | | | REF_CLOSE: (8), (41), (242), (292), (374), (524), (541), % 149.48/21.63 | | | | | | | | | (622), (7419), (7420), (7424), (7434), (8412), % 149.48/21.63 | | | | | | | | | (8413), (function-axioms) are inconsistent by % 149.48/21.63 | | | | | | | | | sub-proof #40. % 149.48/21.63 | | | | | | | | | % 149.48/21.63 | | | | | | | | End of split % 149.48/21.63 | | | | | | | | % 149.48/21.63 | | | | | | | End of split % 149.48/21.63 | | | | | | | % 149.48/21.63 | | | | | | Case 2: % 149.48/21.63 | | | | | | | % 149.48/21.63 | | | | | | | (8414) all_14_0 = e1 % 149.48/21.63 | | | | | | | (8415) ~ (all_14_1 = e3) | ~ (all_14_2 = e0) % 149.48/21.63 | | | | | | | % 149.48/21.63 | | | | | | | COMBINE_EQS: (758), (8414) imply: % 149.48/21.63 | | | | | | | (8416) all_8_0 = e1 % 149.48/21.63 | | | | | | | % 149.48/21.63 | | | | | | | SIMP: (8416) implies: % 149.48/21.63 | | | | | | | (8417) all_8_0 = e1 % 149.48/21.63 | | | | | | | % 149.48/21.63 | | | | | | | REF_CLOSE: (6), (36), (41), (46), (47), (48), (51), (53), (134), % 149.48/21.63 | | | | | | | (189), (212), (215), (237), (241), (242), (243), (247), % 149.48/21.63 | | | | | | | (252), (287), (291), (292), (293), (294), (295), (296), % 149.48/21.63 | | | | | | | (366), (374), (381), (425), (431), (443), (476), (528), % 149.48/21.63 | | | | | | | (534), (540), (541), (542), (543), (544), (545), (546), % 149.48/21.63 | | | | | | | (557), (569), (579), (583), (587), (590), (591), (612), % 149.48/21.63 | | | | | | | (617), (622), (639), (679), (763), (7418), (7420), % 149.48/21.63 | | | | | | | (7423), (7426), (7431), (7433), (7434), (7436), (8415), % 149.48/21.63 | | | | | | | (8417), (function-axioms) are inconsistent by sub-proof % 149.48/21.63 | | | | | | | #32. % 149.48/21.63 | | | | | | | % 149.48/21.63 | | | | | | End of split % 149.48/21.63 | | | | | | % 149.48/21.63 | | | | | End of split % 149.48/21.63 | | | | | % 149.48/21.63 | | | | Case 2: % 149.48/21.63 | | | | | % 149.48/21.63 | | | | | (8418) all_10_0 = e2 % 149.48/21.63 | | | | | (8419) ~ (all_10_1 = e0) | ~ (all_10_2 = e1) % 149.48/21.63 | | | | | % 149.48/21.63 | | | | | REDUCE: (52), (8418) imply: % 149.48/21.63 | | | | | (8420) op(e3, all_10_1) = e2 % 149.48/21.63 | | | | | % 149.48/21.63 | | | | | BETA: splitting (59) gives: % 149.48/21.63 | | | | | % 149.48/21.63 | | | | | Case 1: % 149.48/21.63 | | | | | | % 149.48/21.63 | | | | | | (8421) ~ (all_12_0 = e2) % 149.48/21.63 | | | | | | % 149.48/21.63 | | | | | | REDUCE: (759), (8421) imply: % 149.48/21.63 | | | | | | (8422) ~ (all_4_0 = e2) % 149.48/21.63 | | | | | | % 149.48/21.63 | | | | | | BETA: splitting (64) gives: % 149.48/21.63 | | | | | | % 149.48/21.63 | | | | | | Case 1: % 149.48/21.63 | | | | | | | % 149.48/21.63 | | | | | | | (8423) ~ (all_14_0 = e1) % 149.48/21.63 | | | | | | | % 149.48/21.63 | | | | | | | REDUCE: (758), (8423) imply: % 149.48/21.63 | | | | | | | (8424) ~ (all_8_0 = e1) % 149.48/21.63 | | | | | | | % 149.48/21.63 | | | | | | | BETA: splitting (74) gives: % 149.48/21.63 | | | | | | | % 149.48/21.63 | | | | | | | Case 1: % 149.48/21.63 | | | | | | | | % 149.48/21.63 | | | | | | | | (8425) ~ (all_18_0 = e3) % 149.48/21.63 | | | | | | | | % 149.48/21.63 | | | | | | | | REDUCE: (753), (8425) imply: % 149.48/21.63 | | | | | | | | (8426) ~ (all_6_0 = e3) % 149.48/21.63 | | | | | | | | % 149.48/21.63 | | | | | | | | BETA: splitting (84) gives: % 149.48/21.63 | | | | | | | | % 149.48/21.63 | | | | | | | | Case 1: % 149.48/21.63 | | | | | | | | | % 149.48/21.63 | | | | | | | | | (8427) ~ (all_22_1 = e3) % 149.48/21.63 | | | | | | | | | % 149.48/21.63 | | | | | | | | | REDUCE: (672), (8427) imply: % 149.48/21.63 | | | | | | | | | (8428) ~ (all_8_1 = e3) % 149.48/21.63 | | | | | | | | | % 149.48/21.63 | | | | | | | | | BETA: splitting (104) gives: % 149.48/21.63 | | | | | | | | | % 149.48/21.63 | | | | | | | | | Case 1: % 149.48/21.63 | | | | | | | | | | % 149.48/21.63 | | | | | | | | | | (8429) ~ (all_30_0 = e3) % 149.48/21.63 | | | | | | | | | | % 149.48/21.63 | | | | | | | | | | REDUCE: (718), (8429) imply: % 149.48/21.63 | | | | | | | | | | (8430) ~ (all_8_0 = e3) % 149.48/21.63 | | | | | | | | | | % 149.48/21.63 | | | | | | | | | | BETA: splitting (288) gives: % 149.48/21.63 | | | | | | | | | | % 149.48/21.63 | | | | | | | | | | Case 1: % 149.48/21.63 | | | | | | | | | | | % 149.48/21.63 | | | | | | | | | | | (8431) ~ (all_56_31 = e1) % 149.48/21.63 | | | | | | | | | | | % 149.48/21.63 | | | | | | | | | | | REDUCE: (544), (8431) imply: % 149.48/21.63 | | | | | | | | | | | (8432) ~ (all_4_2 = e1) % 149.48/21.63 | | | | | | | | | | | % 149.51/21.63 | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (9), (36), (38), (41), (46), % 149.51/21.63 | | | | | | | | | | | (47), (48), (51), (53), (183), (188), (189), % 149.51/21.63 | | | | | | | | | | | (192), (193), (196), (197), (218), (237), (240), % 149.51/21.63 | | | | | | | | | | | (241), (242), (243), (244), (248), (251), (252), % 149.51/21.63 | | | | | | | | | | | (287), (289), (290), (291), (292), (293), (318), % 149.51/21.63 | | | | | | | | | | | (319), (320), (321), (322), (324), (326), (327), % 149.51/21.63 | | | | | | | | | | | (336), (339), (342), (344), (360), (365), (366), % 149.51/21.63 | | | | | | | | | | | (374), (381), (386), (401), (419), (447), (457), % 149.51/21.63 | | | | | | | | | | | (463), (471), (476), (478), (540), (541), (543), % 149.51/21.63 | | | | | | | | | | | (544), (545), (546), (547), (549), (550), (551), % 149.51/21.63 | | | | | | | | | | | (552), (553), (554), (555), (557), (559), (561), % 149.51/21.63 | | | | | | | | | | | (563), (567), (568), (569), (570), (571), (579), % 149.51/21.63 | | | | | | | | | | | (581), (587), (590), (591), (612), (615), (617), % 149.51/21.63 | | | | | | | | | | | (622), (627), (7418), (7420), (7423), (7424), % 149.51/21.63 | | | | | | | | | | | (7425), (7426), (7427), (7429), (7431), (7433), % 149.51/21.63 | | | | | | | | | | | (7434), (8419), (8420), (8424), (8426), (8430), % 149.51/21.63 | | | | | | | | | | | (8432), (function-axioms) are inconsistent by % 149.51/21.63 | | | | | | | | | | | sub-proof #31. % 149.51/21.63 | | | | | | | | | | | % 149.51/21.63 | | | | | | | | | | Case 2: % 149.51/21.63 | | | | | | | | | | | % 149.51/21.63 | | | | | | | | | | | (8433) all_56_31 = e1 % 149.51/21.63 | | | | | | | | | | | (8434) all_56_29 = e0 % 149.51/21.63 | | | | | | | | | | | % 149.51/21.63 | | | | | | | | | | | COMBINE_EQS: (357), (8434) imply: % 149.51/21.63 | | | | | | | | | | | (8435) all_52_11 = e0 % 149.51/21.63 | | | | | | | | | | | % 149.51/21.63 | | | | | | | | | | | REF_CLOSE: (37), (38), (41), (51), (53), (173), (189), (206), % 149.51/21.63 | | | | | | | | | | | (239), (241), (242), (243), (287), (292), (293), % 149.51/21.63 | | | | | | | | | | | (374), (381), (476), (480), (541), (544), (545), % 149.51/21.63 | | | | | | | | | | | (546), (569), (585), (587), (591), (612), (622), % 149.51/21.63 | | | | | | | | | | | (767), (7418), (7420), (7423), (7424), (7426), % 149.51/21.63 | | | | | | | | | | | (7429), (7431), (7433), (7434), (8422), (8433), % 149.51/21.63 | | | | | | | | | | | (8435), (function-axioms) are inconsistent by % 149.51/21.63 | | | | | | | | | | | sub-proof #50. % 149.51/21.63 | | | | | | | | | | | % 149.51/21.63 | | | | | | | | | | End of split % 149.51/21.63 | | | | | | | | | | % 149.51/21.63 | | | | | | | | | Case 2: % 149.51/21.63 | | | | | | | | | | % 149.51/21.63 | | | | | | | | | | (8436) all_30_0 = e3 % 149.51/21.63 | | | | | | | | | | (8437) ~ (all_30_1 = e0) | ~ (all_30_2 = e1) % 149.51/21.63 | | | | | | | | | | % 149.51/21.63 | | | | | | | | | | COMBINE_EQS: (718), (8436) imply: % 149.51/21.63 | | | | | | | | | | (8438) all_8_0 = e3 % 149.51/21.63 | | | | | | | | | | % 149.51/21.64 | | | | | | | | | | REF_CLOSE: (9), (36), (41), (46), (47), (48), (51), (212), % 149.51/21.64 | | | | | | | | | | (237), (242), (247), (252), (294), (295), (296), % 149.51/21.64 | | | | | | | | | | (390), (425), (431), (443), (540), (541), (542), % 149.51/21.64 | | | | | | | | | | (543), (545), (557), (579), (583), (590), (617), % 149.51/21.64 | | | | | | | | | | (658), (7436), (8428), (8437), (8438), % 149.51/21.64 | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 149.51/21.64 | | | | | | | | | | #379. % 149.51/21.64 | | | | | | | | | | % 149.51/21.64 | | | | | | | | | End of split % 149.51/21.64 | | | | | | | | | % 149.51/21.64 | | | | | | | | Case 2: % 149.51/21.64 | | | | | | | | | % 149.51/21.64 | | | | | | | | | (8439) all_22_1 = e3 % 149.51/21.64 | | | | | | | | | % 149.51/21.64 | | | | | | | | | COMBINE_EQS: (672), (8439) imply: % 149.51/21.64 | | | | | | | | | (8440) all_8_1 = e3 % 149.51/21.64 | | | | | | | | | % 149.51/21.64 | | | | | | | | | REF_CLOSE: (4), (7), (9), (36), (38), (41), (46), (47), (48), % 149.51/21.64 | | | | | | | | | (51), (53), (182), (183), (188), (189), (192), % 149.51/21.64 | | | | | | | | | (215), (237), (239), (240), (241), (242), (243), % 149.51/21.64 | | | | | | | | | (244), (247), (252), (287), (288), (289), (290), % 149.51/21.64 | | | | | | | | | (291), (292), (293), (294), (298), (299), (324), % 149.51/21.64 | | | | | | | | | (326), (327), (336), (339), (342), (343), (357), % 149.51/21.64 | | | | | | | | | (360), (365), (366), (374), (381), (401), (408), % 149.51/21.64 | | | | | | | | | (419), (429), (447), (471), (476), (478), (480), % 149.51/21.64 | | | | | | | | | (540), (541), (542), (543), (544), (545), (546), % 149.51/21.64 | | | | | | | | | (549), (550), (552), (553), (554), (555), (559), % 149.51/21.64 | | | | | | | | | (561), (563), (569), (570), (571), (575), (581), % 149.51/21.64 | | | | | | | | | (585), (587), (591), (612), (617), (622), (627), % 149.51/21.64 | | | | | | | | | (7418), (7420), (7423), (7425), (7426), (7429), % 149.51/21.64 | | | | | | | | | (7431), (7433), (7434), (7436), (8424), (8426), % 149.51/21.64 | | | | | | | | | (8440), (function-axioms) are inconsistent by % 149.51/21.64 | | | | | | | | | sub-proof #42. % 149.51/21.64 | | | | | | | | | % 149.51/21.64 | | | | | | | | End of split % 149.51/21.64 | | | | | | | | % 149.51/21.64 | | | | | | | Case 2: % 149.51/21.64 | | | | | | | | % 149.51/21.64 | | | | | | | | (8441) all_18_0 = e3 % 149.51/21.64 | | | | | | | | (8442) ~ (all_18_1 = e2) | ~ (all_18_2 = e0) % 149.51/21.64 | | | | | | | | % 149.51/21.64 | | | | | | | | COMBINE_EQS: (753), (8441) imply: % 149.51/21.64 | | | | | | | | (8443) all_6_0 = e3 % 149.51/21.64 | | | | | | | | % 149.51/21.64 | | | | | | | | SIMP: (8443) implies: % 149.51/21.64 | | | | | | | | (8444) all_6_0 = e3 % 149.51/21.64 | | | | | | | | % 149.51/21.64 | | | | | | | | REF_CLOSE: (8), (41), (242), (292), (374), (524), (541), (622), % 149.51/21.64 | | | | | | | | (7419), (7420), (7424), (7434), (8442), (8444), % 149.51/21.64 | | | | | | | | (function-axioms) are inconsistent by sub-proof #40. % 149.51/21.64 | | | | | | | | % 149.51/21.64 | | | | | | | End of split % 149.51/21.64 | | | | | | | % 149.51/21.64 | | | | | | Case 2: % 149.51/21.64 | | | | | | | % 149.51/21.64 | | | | | | | (8445) all_14_0 = e1 % 149.51/21.64 | | | | | | | % 149.51/21.64 | | | | | | | COMBINE_EQS: (758), (8445) imply: % 149.51/21.64 | | | | | | | (8446) all_8_0 = e1 % 149.51/21.64 | | | | | | | % 149.51/21.64 | | | | | | | REDUCE: (47), (8446) imply: % 149.51/21.64 | | | | | | | (8447) op(e2, all_8_1) = e1 % 149.51/21.64 | | | | | | | % 149.51/21.64 | | | | | | | REF_CLOSE: (4), (7), (8), (9), (36), (37), (38), (41), (46), (48), % 149.51/21.64 | | | | | | | (51), (53), (74), (173), (188), (189), (192), (206), % 149.51/21.64 | | | | | | | (237), (239), (240), (241), (242), (243), (244), (287), % 149.51/21.64 | | | | | | | (288), (289), (290), (291), (292), (293), (324), (326), % 149.51/21.64 | | | | | | | (327), (336), (339), (357), (360), (366), (374), (381), % 149.51/21.64 | | | | | | | (447), (471), (476), (478), (480), (524), (540), (541), % 149.51/21.64 | | | | | | | (544), (545), (546), (549), (550), (552), (553), (554), % 149.51/21.64 | | | | | | | (559), (561), (569), (570), (581), (585), (587), (591), % 149.51/21.64 | | | | | | | (612), (617), (622), (627), (753), (767), (7418), % 149.51/21.64 | | | | | | | (7419), (7420), (7423), (7424), (7425), (7426), (7429), % 149.51/21.64 | | | | | | | (7431), (7433), (7434), (7436), (8422), (8447), % 149.51/21.64 | | | | | | | (function-axioms) are inconsistent by sub-proof #37. % 149.51/21.64 | | | | | | | % 149.51/21.64 | | | | | | End of split % 149.51/21.64 | | | | | | % 149.51/21.64 | | | | | Case 2: % 149.51/21.64 | | | | | | % 149.51/21.64 | | | | | | (8448) all_12_0 = e2 % 149.51/21.64 | | | | | | % 149.51/21.64 | | | | | | COMBINE_EQS: (759), (8448) imply: % 149.51/21.64 | | | | | | (8449) all_4_0 = e2 % 149.51/21.64 | | | | | | % 149.51/21.64 | | | | | | SIMP: (8449) implies: % 149.51/21.64 | | | | | | (8450) all_4_0 = e2 % 149.51/21.64 | | | | | | % 149.51/21.64 | | | | | | COMBINE_EQS: (734), (8450) imply: % 149.51/21.64 | | | | | | (8451) all_34_0 = e2 % 149.51/21.64 | | | | | | % 149.51/21.64 | | | | | | REDUCE: (767), (8450) imply: % 149.51/21.64 | | | | | | (8452) ~ (e3 = e2) % 149.51/21.64 | | | | | | % 149.51/21.64 | | | | | | REDUCE: (37), (8450) imply: % 149.51/21.64 | | | | | | (8453) op(e0, all_4_1) = e2 % 149.51/21.64 | | | | | | % 149.51/21.64 | | | | | | BETA: splitting (64) gives: % 149.51/21.64 | | | | | | % 149.51/21.64 | | | | | | Case 1: % 149.51/21.64 | | | | | | | % 149.51/21.64 | | | | | | | (8454) ~ (all_14_0 = e1) % 149.51/21.64 | | | | | | | % 149.51/21.64 | | | | | | | REDUCE: (758), (8454) imply: % 149.51/21.64 | | | | | | | (8455) ~ (all_8_0 = e1) % 149.51/21.64 | | | | | | | % 149.51/21.64 | | | | | | | BETA: splitting (74) gives: % 149.51/21.64 | | | | | | | % 149.51/21.64 | | | | | | | Case 1: % 149.51/21.64 | | | | | | | | % 149.51/21.64 | | | | | | | | (8456) ~ (all_18_0 = e3) % 149.51/21.64 | | | | | | | | % 149.51/21.64 | | | | | | | | REDUCE: (753), (8456) imply: % 149.51/21.64 | | | | | | | | (8457) ~ (all_6_0 = e3) % 149.51/21.64 | | | | | | | | % 149.51/21.64 | | | | | | | | BETA: splitting (84) gives: % 149.51/21.64 | | | | | | | | % 149.51/21.64 | | | | | | | | Case 1: % 149.51/21.64 | | | | | | | | | % 149.51/21.64 | | | | | | | | | (8458) ~ (all_22_1 = e3) % 149.51/21.64 | | | | | | | | | % 149.51/21.64 | | | | | | | | | REDUCE: (672), (8458) imply: % 149.51/21.64 | | | | | | | | | (8459) ~ (all_8_1 = e3) % 149.51/21.64 | | | | | | | | | % 149.51/21.64 | | | | | | | | | BETA: splitting (104) gives: % 149.51/21.64 | | | | | | | | | % 149.51/21.64 | | | | | | | | | Case 1: % 149.51/21.64 | | | | | | | | | | % 149.51/21.64 | | | | | | | | | | (8460) ~ (all_30_0 = e3) % 149.51/21.64 | | | | | | | | | | % 149.51/21.64 | | | | | | | | | | REDUCE: (718), (8460) imply: % 149.51/21.64 | | | | | | | | | | (8461) ~ (all_8_0 = e3) % 149.51/21.64 | | | | | | | | | | % 149.51/21.64 | | | | | | | | | | BETA: splitting (114) gives: % 149.51/21.64 | | | | | | | | | | % 149.51/21.64 | | | | | | | | | | Case 1: % 149.51/21.64 | | | | | | | | | | | % 149.51/21.64 | | | | | | | | | | | (8462) ~ (all_34_0 = e2) % 149.51/21.64 | | | | | | | | | | | % 149.51/21.64 | | | | | | | | | | | REDUCE: (8451), (8462) imply: % 149.51/21.64 | | | | | | | | | | | (8463) $false % 149.51/21.64 | | | | | | | | | | | % 149.51/21.64 | | | | | | | | | | | CLOSE: (8463) is inconsistent. % 149.51/21.64 | | | | | | | | | | | % 149.51/21.64 | | | | | | | | | | Case 2: % 149.51/21.64 | | | | | | | | | | | % 149.51/21.64 | | | | | | | | | | | (8464) ~ (all_34_1 = e3) | ~ (all_34_2 = e1) % 149.51/21.64 | | | | | | | | | | | % 149.51/21.64 | | | | | | | | | | | BETA: splitting (288) gives: % 149.51/21.64 | | | | | | | | | | | % 149.51/21.64 | | | | | | | | | | | Case 1: % 149.51/21.64 | | | | | | | | | | | | % 149.51/21.64 | | | | | | | | | | | | (8465) ~ (all_56_31 = e1) % 149.51/21.64 | | | | | | | | | | | | % 149.51/21.64 | | | | | | | | | | | | REDUCE: (544), (8465) imply: % 149.51/21.64 | | | | | | | | | | | | (8466) ~ (all_4_2 = e1) % 149.51/21.64 | | | | | | | | | | | | % 149.51/21.64 | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (9), (36), (38), (41), (46), % 149.51/21.64 | | | | | | | | | | | | (47), (48), (51), (53), (183), (188), (189), % 149.51/21.64 | | | | | | | | | | | | (192), (193), (196), (197), (218), (237), (240), % 149.51/21.64 | | | | | | | | | | | | (241), (242), (243), (244), (248), (251), (252), % 149.51/21.64 | | | | | | | | | | | | (287), (289), (290), (291), (292), (293), (318), % 149.51/21.64 | | | | | | | | | | | | (319), (320), (321), (322), (324), (326), (327), % 149.51/21.64 | | | | | | | | | | | | (336), (339), (342), (344), (360), (365), (366), % 149.51/21.64 | | | | | | | | | | | | (374), (381), (386), (401), (419), (447), (457), % 149.51/21.64 | | | | | | | | | | | | (463), (471), (476), (478), (540), (541), (543), % 149.51/21.64 | | | | | | | | | | | | (544), (545), (546), (547), (549), (550), (551), % 149.51/21.64 | | | | | | | | | | | | (552), (553), (554), (555), (557), (559), (561), % 149.51/21.64 | | | | | | | | | | | | (563), (567), (568), (569), (570), (571), (579), % 149.51/21.64 | | | | | | | | | | | | (581), (587), (590), (591), (612), (615), (617), % 149.51/21.64 | | | | | | | | | | | | (622), (627), (7418), (7420), (7423), (7424), % 149.51/21.64 | | | | | | | | | | | | (7425), (7426), (7427), (7429), (7431), (7433), % 149.51/21.64 | | | | | | | | | | | | (7434), (8419), (8420), (8455), (8457), (8461), % 149.51/21.64 | | | | | | | | | | | | (8466), (function-axioms) are inconsistent by % 149.51/21.64 | | | | | | | | | | | | sub-proof #31. % 149.51/21.64 | | | | | | | | | | | | % 149.51/21.64 | | | | | | | | | | | Case 2: % 149.51/21.64 | | | | | | | | | | | | % 149.51/21.64 | | | | | | | | | | | | (8467) all_56_31 = e1 % 149.51/21.64 | | | | | | | | | | | | (8468) all_56_29 = e0 % 149.51/21.64 | | | | | | | | | | | | % 149.51/21.64 | | | | | | | | | | | | COMBINE_EQS: (357), (8468) imply: % 149.51/21.64 | | | | | | | | | | | | (8469) all_52_11 = e0 % 149.51/21.64 | | | | | | | | | | | | % 149.51/21.64 | | | | | | | | | | | | SIMP: (8469) implies: % 149.51/21.64 | | | | | | | | | | | | (8470) all_52_11 = e0 % 149.51/21.64 | | | | | | | | | | | | % 149.51/21.64 | | | | | | | | | | | | COMBINE_EQS: (544), (8467) imply: % 149.51/21.64 | | | | | | | | | | | | (8471) all_4_2 = e1 % 149.51/21.64 | | | | | | | | | | | | % 149.51/21.64 | | | | | | | | | | | | COMBINE_EQS: (531), (8471) imply: % 149.51/21.64 | | | | | | | | | | | | (8472) all_34_2 = e1 % 149.51/21.64 | | | | | | | | | | | | % 149.51/21.64 | | | | | | | | | | | | COMBINE_EQS: (547), (8471) imply: % 149.51/21.64 | | | | | | | | | | | | (8473) all_58_15 = e1 % 149.51/21.64 | | | | | | | | | | | | % 149.51/21.64 | | | | | | | | | | | | COMBINE_EQS: (548), (8470) imply: % 149.51/21.64 | | | | | | | | | | | | (8474) all_58_14 = e0 % 149.51/21.64 | | | | | | | | | | | | % 149.51/21.64 | | | | | | | | | | | | REDUCE: (187), (8470) imply: % 149.51/21.64 | | | | | | | | | | | | (8475) ~ (all_52_3 = e0) % 149.51/21.64 | | | | | | | | | | | | % 149.51/21.64 | | | | | | | | | | | | REDUCE: (570), (8471) imply: % 149.51/21.64 | | | | | | | | | | | | (8476) ~ (all_52_3 = e1) % 149.51/21.64 | | | | | | | | | | | | % 149.51/21.64 | | | | | | | | | | | | REDUCE: (173), (8470) imply: % 149.51/21.64 | | | | | | | | | | | | (8477) ~ (all_52_7 = e0) % 149.51/21.64 | | | | | | | | | | | | % 149.51/21.64 | | | | | | | | | | | | REDUCE: (585), (8470) imply: % 149.51/21.64 | | | | | | | | | | | | (8478) ~ (all_6_2 = e0) % 149.51/21.64 | | | | | | | | | | | | % 149.51/21.64 | | | | | | | | | | | | SIMP: (8478) implies: % 149.51/21.64 | | | | | | | | | | | | (8479) ~ (all_6_2 = e0) % 149.51/21.64 | | | | | | | | | | | | % 149.51/21.64 | | | | | | | | | | | | REDUCE: (588), (8470), (8471) imply: % 149.51/21.64 | | | | | | | | | | | | (8480) ~ (e1 = e0) % 149.51/21.64 | | | | | | | | | | | | % 149.51/21.64 | | | | | | | | | | | | REDUCE: (38), (8471) imply: % 149.51/21.64 | | | | | | | | | | | | (8481) op(e1, e1) = all_4_1 % 149.51/21.64 | | | | | | | | | | | | % 149.51/21.64 | | | | | | | | | | | | REDUCE: (36), (8471) imply: % 149.51/21.64 | | | | | | | | | | | | (8482) op(e0, e0) = e1 % 149.51/21.64 | | | | | | | | | | | | % 149.51/21.64 | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (41), (48), (51), (168), (183), % 149.51/21.64 | | | | | | | | | | | | (196), (206), (239), (240), (242), (247), (251), % 149.51/21.64 | | | | | | | | | | | | (252), (292), (294), (296), (297), (298), (299), % 149.51/21.64 | | | | | | | | | | | | (319), (331), (336), (345), (365), (374), (402), % 149.51/21.64 | | | | | | | | | | | | (407), (408), (419), (425), (429), (457), (478), % 149.51/21.64 | | | | | | | | | | | | (480), (541), (542), (543), (545), (546), (549), % 149.51/21.64 | | | | | | | | | | | | (551), (554), (555), (557), (561), (563), (565), % 149.51/21.64 | | | | | | | | | | | | (571), (575), (582), (622), (624), (683), (7420), % 149.51/21.64 | | | | | | | | | | | | (7424), (7425), (7427), (7429), (7433), (7436), % 149.51/21.64 | | | | | | | | | | | | (8453), (8464), (8472), (8473), (8474), (8475), % 149.51/21.64 | | | | | | | | | | | | (8476), (8477), (8479), (8481), (8482), % 149.51/21.64 | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 149.51/21.64 | | | | | | | | | | | | #33. % 149.51/21.64 | | | | | | | | | | | | % 149.51/21.64 | | | | | | | | | | | End of split % 149.51/21.64 | | | | | | | | | | | % 149.51/21.64 | | | | | | | | | | End of split % 149.51/21.64 | | | | | | | | | | % 149.51/21.64 | | | | | | | | | Case 2: % 149.51/21.64 | | | | | | | | | | % 149.51/21.64 | | | | | | | | | | (8483) all_30_0 = e3 % 149.51/21.64 | | | | | | | | | | (8484) ~ (all_30_1 = e0) | ~ (all_30_2 = e1) % 149.51/21.64 | | | | | | | | | | % 149.51/21.64 | | | | | | | | | | COMBINE_EQS: (718), (8483) imply: % 149.51/21.64 | | | | | | | | | | (8485) all_8_0 = e3 % 149.51/21.64 | | | | | | | | | | % 149.51/21.64 | | | | | | | | | | SIMP: (8485) implies: % 149.51/21.64 | | | | | | | | | | (8486) all_8_0 = e3 % 149.51/21.64 | | | | | | | | | | % 149.51/21.64 | | | | | | | | | | REF_CLOSE: (9), (36), (41), (46), (47), (48), (51), (212), % 149.51/21.64 | | | | | | | | | | (237), (242), (247), (252), (294), (295), (296), % 149.51/21.64 | | | | | | | | | | (390), (425), (431), (443), (540), (541), (542), % 149.51/21.64 | | | | | | | | | | (543), (545), (557), (579), (583), (590), (617), % 149.51/21.64 | | | | | | | | | | (658), (7436), (8459), (8484), (8486), % 149.51/21.64 | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 149.51/21.64 | | | | | | | | | | #379. % 149.51/21.64 | | | | | | | | | | % 149.51/21.64 | | | | | | | | | End of split % 149.51/21.64 | | | | | | | | | % 149.51/21.64 | | | | | | | | Case 2: % 149.51/21.64 | | | | | | | | | % 149.51/21.64 | | | | | | | | | (8487) all_22_1 = e3 % 149.51/21.64 | | | | | | | | | % 149.51/21.64 | | | | | | | | | COMBINE_EQS: (672), (8487) imply: % 149.51/21.64 | | | | | | | | | (8488) all_8_1 = e3 % 149.51/21.64 | | | | | | | | | % 149.51/21.64 | | | | | | | | | REF_CLOSE: (4), (7), (9), (36), (38), (41), (46), (47), (48), % 149.51/21.64 | | | | | | | | | (51), (53), (182), (183), (188), (189), (192), % 149.51/21.64 | | | | | | | | | (215), (237), (239), (240), (241), (242), (243), % 149.51/21.64 | | | | | | | | | (244), (247), (252), (287), (288), (289), (290), % 149.51/21.64 | | | | | | | | | (291), (292), (293), (294), (298), (299), (324), % 149.51/21.64 | | | | | | | | | (326), (327), (336), (339), (342), (343), (357), % 149.51/21.64 | | | | | | | | | (360), (365), (366), (374), (381), (401), (408), % 149.51/21.64 | | | | | | | | | (419), (429), (447), (471), (476), (478), (480), % 149.51/21.64 | | | | | | | | | (540), (541), (542), (543), (544), (545), (546), % 149.51/21.64 | | | | | | | | | (549), (550), (552), (553), (554), (555), (559), % 149.51/21.64 | | | | | | | | | (561), (563), (569), (570), (571), (575), (581), % 149.51/21.64 | | | | | | | | | (585), (587), (591), (612), (617), (622), (627), % 149.51/21.64 | | | | | | | | | (7418), (7420), (7423), (7425), (7426), (7429), % 149.51/21.64 | | | | | | | | | (7431), (7433), (7434), (7436), (8455), (8457), % 149.51/21.64 | | | | | | | | | (8488), (function-axioms) are inconsistent by % 149.51/21.64 | | | | | | | | | sub-proof #42. % 149.51/21.64 | | | | | | | | | % 149.51/21.64 | | | | | | | | End of split % 149.51/21.64 | | | | | | | | % 149.51/21.64 | | | | | | | Case 2: % 149.51/21.64 | | | | | | | | % 149.51/21.64 | | | | | | | | (8489) all_18_0 = e3 % 149.51/21.64 | | | | | | | | (8490) ~ (all_18_1 = e2) | ~ (all_18_2 = e0) % 149.51/21.64 | | | | | | | | % 149.51/21.64 | | | | | | | | COMBINE_EQS: (753), (8489) imply: % 149.51/21.64 | | | | | | | | (8491) all_6_0 = e3 % 149.51/21.64 | | | | | | | | % 149.51/21.64 | | | | | | | | SIMP: (8491) implies: % 149.51/21.64 | | | | | | | | (8492) all_6_0 = e3 % 149.51/21.64 | | | | | | | | % 149.51/21.64 | | | | | | | | REF_CLOSE: (8), (41), (242), (292), (374), (524), (541), (622), % 149.51/21.64 | | | | | | | | (7419), (7420), (7424), (7434), (8490), (8492), % 149.51/21.64 | | | | | | | | (function-axioms) are inconsistent by sub-proof #40. % 149.51/21.64 | | | | | | | | % 149.51/21.64 | | | | | | | End of split % 149.51/21.64 | | | | | | | % 149.51/21.64 | | | | | | Case 2: % 149.51/21.64 | | | | | | | % 149.51/21.64 | | | | | | | (8493) all_14_0 = e1 % 149.51/21.64 | | | | | | | (8494) ~ (all_14_1 = e3) | ~ (all_14_2 = e0) % 149.51/21.64 | | | | | | | % 149.51/21.64 | | | | | | | COMBINE_EQS: (758), (8493) imply: % 149.51/21.64 | | | | | | | (8495) all_8_0 = e1 % 149.51/21.64 | | | | | | | % 149.51/21.64 | | | | | | | REF_CLOSE: (6), (36), (41), (46), (47), (48), (51), (53), (134), % 149.51/21.64 | | | | | | | (189), (212), (215), (237), (241), (242), (243), (247), % 149.51/21.64 | | | | | | | (252), (287), (291), (292), (293), (294), (295), (296), % 149.51/21.64 | | | | | | | (366), (374), (381), (425), (431), (443), (476), (528), % 149.51/21.64 | | | | | | | (534), (540), (541), (542), (543), (544), (545), (546), % 149.51/21.64 | | | | | | | (557), (569), (579), (583), (587), (590), (591), (612), % 149.51/21.64 | | | | | | | (617), (622), (639), (679), (763), (7418), (7420), % 149.51/21.64 | | | | | | | (7423), (7426), (7431), (7433), (7434), (7436), (8494), % 149.51/21.64 | | | | | | | (8495), (function-axioms) are inconsistent by sub-proof % 149.51/21.64 | | | | | | | #32. % 149.51/21.64 | | | | | | | % 149.51/21.64 | | | | | | End of split % 149.51/21.64 | | | | | | % 149.51/21.64 | | | | | End of split % 149.51/21.64 | | | | | % 149.51/21.64 | | | | End of split % 149.51/21.64 | | | | % 149.51/21.64 | | | Case 2: % 149.51/21.64 | | | | % 149.51/21.64 | | | | (8496) all_8_1 = e1 % 149.51/21.64 | | | | (8497) ~ (all_8_0 = e0) | ~ (all_8_2 = e3) % 149.51/21.64 | | | | % 149.51/21.64 | | | | COMBINE_EQS: (686), (8496) imply: % 149.51/21.64 | | | | (8498) all_48_1 = e1 % 149.51/21.64 | | | | % 149.51/21.64 | | | | REDUCE: (48), (8496) imply: % 149.51/21.64 | | | | (8499) op(all_8_2, all_8_2) = e1 % 149.51/21.64 | | | | % 149.51/21.64 | | | | REDUCE: (47), (8496) imply: % 149.51/21.64 | | | | (8500) op(e2, e1) = all_8_0 % 149.51/21.64 | | | | % 149.51/21.64 | | | | GROUND_INST: instantiating (function-axioms) with all_52_9, all_8_0, e1, % 149.51/21.64 | | | | e2, simplifying with (213), (8500) gives: % 149.51/21.64 | | | | (8501) all_52_9 = all_8_0 % 149.51/21.64 | | | | % 149.51/21.64 | | | | COMBINE_EQS: (467), (8501) imply: % 149.51/21.64 | | | | (8502) all_54_6 = all_8_0 % 149.51/21.64 | | | | % 149.51/21.64 | | | | COMBINE_EQS: (431), (8501) imply: % 149.51/21.64 | | | | (8503) all_56_13 = all_8_0 % 149.51/21.64 | | | | % 149.51/21.64 | | | | COMBINE_EQS: (389), (8501) imply: % 149.51/21.64 | | | | (8504) all_58_5 = all_8_0 % 149.51/21.64 | | | | % 149.51/21.64 | | | | REDUCE: (194), (8501) imply: % 149.51/21.64 | | | | (8505) ~ (all_52_1 = all_8_0) % 149.51/21.64 | | | | % 149.51/21.64 | | | | REDUCE: (166), (8501) imply: % 149.51/21.64 | | | | (8506) ~ (all_52_11 = all_8_0) % 149.51/21.64 | | | | % 149.51/21.64 | | | | SIMP: (8506) implies: % 149.51/21.64 | | | | (8507) ~ (all_52_11 = all_8_0) % 149.51/21.64 | | | | % 149.51/21.64 | | | | REDUCE: (165), (8501) imply: % 149.51/21.64 | | | | (8508) ~ (all_52_13 = all_8_0) % 149.51/21.64 | | | | % 149.51/21.64 | | | | SIMP: (8508) implies: % 149.51/21.64 | | | | (8509) ~ (all_52_13 = all_8_0) % 149.51/21.64 | | | | % 149.51/21.64 | | | | REDUCE: (577), (8501) imply: % 149.51/21.64 | | | | (8510) ~ (all_8_0 = all_8_2) % 149.51/21.64 | | | | % 149.51/21.64 | | | | REDUCE: (583), (8501) imply: % 149.51/21.64 | | | | (8511) ~ (all_8_0 = all_6_2) % 149.51/21.64 | | | | % 149.51/21.64 | | | | BETA: splitting (74) gives: % 149.51/21.64 | | | | % 149.51/21.64 | | | | Case 1: % 149.51/21.64 | | | | | % 149.51/21.64 | | | | | (8512) ~ (all_18_0 = e3) % 149.51/21.64 | | | | | % 149.51/21.64 | | | | | REDUCE: (753), (8512) imply: % 149.51/21.64 | | | | | (8513) ~ (all_6_0 = e3) % 149.51/21.64 | | | | | % 149.51/21.64 | | | | | BETA: splitting (149) gives: % 149.51/21.64 | | | | | % 149.51/21.64 | | | | | Case 1: % 149.51/21.64 | | | | | | % 149.51/21.64 | | | | | | (8514) ~ (all_48_0 = e3) % 149.51/21.64 | | | | | | % 149.51/21.64 | | | | | | REDUCE: (765), (8514) imply: % 149.51/21.64 | | | | | | (8515) ~ (all_8_0 = e3) % 149.51/21.64 | | | | | | % 149.51/21.64 | | | | | | BETA: splitting (292) gives: % 149.51/21.64 | | | | | | % 149.51/21.64 | | | | | | Case 1: % 149.51/21.64 | | | | | | | % 149.51/21.64 | | | | | | | (8516) ~ (all_56_21 = e2) % 149.51/21.64 | | | | | | | % 149.51/21.64 | | | | | | | REDUCE: (374), (8516) imply: % 149.51/21.64 | | | | | | | (8517) ~ (all_6_2 = e2) % 149.51/21.64 | | | | | | | % 149.51/21.64 | | | | | | | BETA: splitting (288) gives: % 149.51/21.64 | | | | | | | % 149.51/21.64 | | | | | | | Case 1: % 149.51/21.64 | | | | | | | | % 149.51/21.64 | | | | | | | | (8518) ~ (all_56_31 = e1) % 149.51/21.64 | | | | | | | | % 149.51/21.64 | | | | | | | | REDUCE: (544), (8518) imply: % 149.51/21.64 | | | | | | | | (8519) ~ (all_4_2 = e1) % 149.51/21.64 | | | | | | | | % 149.51/21.64 | | | | | | | | BETA: splitting (294) gives: % 149.51/21.64 | | | | | | | | % 149.51/21.64 | | | | | | | | Case 1: % 149.51/21.64 | | | | | | | | | % 149.51/21.64 | | | | | | | | | (8520) ~ (all_56_11 = e0) % 149.51/21.64 | | | | | | | | | % 149.51/21.64 | | | | | | | | | REDUCE: (545), (8520) imply: % 149.51/21.64 | | | | | | | | | (8521) ~ (all_8_2 = e0) % 149.51/21.64 | | | | | | | | | % 149.51/21.64 | | | | | | | | | BETA: splitting (290) gives: % 149.51/21.64 | | | | | | | | | % 149.51/21.64 | | | | | | | | | Case 1: % 149.51/21.64 | | | | | | | | | | % 149.51/21.64 | | | | | | | | | | (8522) ~ (all_56_31 = e3) % 149.51/21.64 | | | | | | | | | | % 149.51/21.64 | | | | | | | | | | REDUCE: (544), (8522) imply: % 149.51/21.64 | | | | | | | | | | (8523) ~ (all_4_2 = e3) % 149.51/21.64 | | | | | | | | | | % 149.51/21.64 | | | | | | | | | | BETA: splitting (291) gives: % 149.51/21.64 | | | | | | | | | | % 149.51/21.64 | | | | | | | | | | Case 1: % 149.51/21.64 | | | | | | | | | | | % 149.51/21.64 | | | | | | | | | | | (8524) ~ (all_56_21 = e0) % 149.51/21.64 | | | | | | | | | | | % 149.51/21.64 | | | | | | | | | | | REDUCE: (374), (8524) imply: % 149.51/21.64 | | | | | | | | | | | (8525) ~ (all_6_2 = e0) % 149.51/21.64 | | | | | | | | | | | % 149.51/21.64 | | | | | | | | | | | REF_CLOSE: (4), (41), (188), (192), (237), (240), (242), % 149.51/21.64 | | | | | | | | | | | (287), (289), (293), (324), (326), (360), (374), % 149.51/21.64 | | | | | | | | | | | (381), (478), (540), (541), (544), (545), (546), % 149.51/21.64 | | | | | | | | | | | (550), (552), (553), (561), (569), (570), (591), % 149.51/21.64 | | | | | | | | | | | (622), (7418), (7420), (7425), (7429), (7433), % 149.51/21.64 | | | | | | | | | | | (8517), (8519), (8523), (8525), (function-axioms) % 149.51/21.64 | | | | | | | | | | | are inconsistent by sub-proof #76. % 149.51/21.64 | | | | | | | | | | | % 149.51/21.64 | | | | | | | | | | Case 2: % 149.51/21.64 | | | | | | | | | | | % 149.51/21.64 | | | | | | | | | | | (8526) all_56_23 = e1 % 149.51/21.64 | | | | | | | | | | | (8527) all_56_21 = e0 % 149.51/21.64 | | | | | | | | | | | % 149.51/21.64 | | | | | | | | | | | COMBINE_EQS: (374), (8527) imply: % 149.51/21.64 | | | | | | | | | | | (8528) all_6_2 = e0 % 149.51/21.64 | | | | | | | | | | | % 149.51/21.64 | | | | | | | | | | | SIMP: (8528) implies: % 149.51/21.64 | | | | | | | | | | | (8529) all_6_2 = e0 % 149.51/21.64 | | | | | | | | | | | % 149.51/21.64 | | | | | | | | | | | COMBINE_EQS: (366), (8526) imply: % 149.51/21.64 | | | | | | | | | | | (8530) all_52_14 = e1 % 149.51/21.64 | | | | | | | | | | | % 149.51/21.64 | | | | | | | | | | | SIMP: (8530) implies: % 149.51/21.64 | | | | | | | | | | | (8531) all_52_14 = e1 % 149.51/21.64 | | | | | | | | | | | % 149.51/21.64 | | | | | | | | | | | COMBINE_EQS: (550), (8531) imply: % 149.51/21.64 | | | | | | | | | | | (8532) all_58_11 = e1 % 149.51/21.64 | | | | | | | | | | | % 149.51/21.64 | | | | | | | | | | | COMBINE_EQS: (552), (8529) imply: % 149.51/21.64 | | | | | | | | | | | (8533) all_58_8 = e0 % 149.51/21.64 | | | | | | | | | | | % 149.51/21.64 | | | | | | | | | | | REDUCE: (158), (8531) imply: % 149.51/21.64 | | | | | | | | | | | (8534) ~ (all_52_13 = e1) % 149.51/21.64 | | | | | | | | | | | % 149.51/21.64 | | | | | | | | | | | REDUCE: (7431), (8531) imply: % 149.51/21.64 | | | | | | | | | | | (8535) ~ (all_6_0 = e1) % 149.51/21.64 | | | | | | | | | | | % 149.51/21.64 | | | | | | | | | | | SIMP: (8535) implies: % 149.51/21.64 | | | | | | | | | | | (8536) ~ (all_6_0 = e1) % 149.51/21.64 | | | | | | | | | | | % 149.51/21.64 | | | | | | | | | | | REDUCE: (7434), (8529) imply: % 149.51/21.64 | | | | | | | | | | | (8537) ~ (all_6_0 = e0) % 149.51/21.64 | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | REDUCE: (41), (8529) imply: % 149.51/21.65 | | | | | | | | | | | (8538) op(e1, e1) = e0 % 149.51/21.65 | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | BETA: splitting (327) gives: % 149.51/21.65 | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | Case 1: % 149.51/21.65 | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | (8539) all_58_6 = e3 % 149.51/21.65 | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | COMBINE_EQS: (553), (8539) imply: % 149.51/21.65 | | | | | | | | | | | | (8540) all_52_2 = e3 % 149.51/21.65 | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | SIMP: (8540) implies: % 149.51/21.65 | | | | | | | | | | | | (8541) all_52_2 = e3 % 149.51/21.65 | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | REDUCE: (197), (8541) imply: % 149.51/21.65 | | | | | | | | | | | | (8542) ~ (all_52_1 = e3) % 149.51/21.65 | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | REDUCE: (192), (8541) imply: % 149.51/21.65 | | | | | | | | | | | | (8543) ~ (all_52_3 = e3) % 149.51/21.65 | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | SIMP: (8543) implies: % 149.51/21.65 | | | | | | | | | | | | (8544) ~ (all_52_3 = e3) % 149.51/21.65 | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | REDUCE: (559), (8541) imply: % 149.51/21.65 | | | | | | | | | | | | (8545) ~ (all_10_2 = e3) % 149.51/21.65 | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | SIMP: (8545) implies: % 149.51/21.65 | | | | | | | | | | | | (8546) ~ (all_10_2 = e3) % 149.51/21.65 | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | REDUCE: (7426), (8541) imply: % 149.51/21.65 | | | | | | | | | | | | (8547) ~ (all_6_0 = e3) % 149.51/21.65 | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | BETA: splitting (243) gives: % 149.51/21.65 | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | Case 1: % 149.51/21.65 | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | (8548) all_54_9 = e3 % 149.51/21.65 | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | REF_CLOSE: (7423), (8513), (8548) are inconsistent by % 149.51/21.65 | | | | | | | | | | | | | sub-proof #88. % 149.51/21.65 | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | Case 2: % 149.51/21.65 | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | (8549) all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0 % 149.51/21.65 | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | BETA: splitting (8549) gives: % 149.51/21.65 | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | Case 1: % 149.51/21.65 | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | (8550) all_54_9 = e2 % 149.51/21.65 | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | COMBINE_EQS: (7423), (8550) imply: % 149.51/21.65 | | | | | | | | | | | | | | (8551) all_6_0 = e2 % 149.51/21.65 | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | SIMP: (8551) implies: % 149.51/21.65 | | | | | | | | | | | | | | (8552) all_6_0 = e2 % 149.51/21.65 | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | REDUCE: (7427), (8552) imply: % 149.51/21.65 | | | | | | | | | | | | | | (8553) ~ (all_52_4 = e2) % 149.51/21.65 | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | REDUCE: (7433), (8552) imply: % 149.51/21.65 | | | | | | | | | | | | | | (8554) ~ (all_8_2 = e2) % 149.51/21.65 | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | BETA: splitting (287) gives: % 149.51/21.65 | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | Case 1: % 149.51/21.65 | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | (8555) all_56_1 = e3 % 149.51/21.65 | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | COMBINE_EQS: (546), (8555) imply: % 149.51/21.65 | | | | | | | | | | | | | | | (8556) all_10_2 = e3 % 149.51/21.65 | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | REDUCE: (8546), (8556) imply: % 149.51/21.65 | | | | | | | | | | | | | | | (8557) $false % 149.51/21.65 | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | CLOSE: (8557) is inconsistent. % 149.51/21.65 | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | Case 2: % 149.51/21.65 | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | (8558) ~ (all_56_1 = e3) % 149.51/21.65 | | | | | | | | | | | | | | | (8559) all_56_11 = e2 | all_56_21 = e1 | all_56_31 = e0 % 149.51/21.65 | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | BETA: splitting (8559) gives: % 149.51/21.65 | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | Case 1: % 149.51/21.65 | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | (8560) all_56_11 = e2 % 149.51/21.65 | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | COMBINE_EQS: (545), (8560) imply: % 149.51/21.65 | | | | | | | | | | | | | | | | (8561) all_8_2 = e2 % 149.51/21.65 | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | REDUCE: (8554), (8561) imply: % 149.51/21.65 | | | | | | | | | | | | | | | | (8562) $false % 149.51/21.65 | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | CLOSE: (8562) is inconsistent. % 149.51/21.65 | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | Case 2: % 149.51/21.65 | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | (8563) ~ (all_56_11 = e2) % 149.51/21.65 | | | | | | | | | | | | | | | | (8564) all_56_21 = e1 | all_56_31 = e0 % 149.51/21.65 | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | BETA: splitting (8564) gives: % 149.51/21.65 | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | Case 1: % 149.51/21.65 | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | (8565) all_56_21 = e1 % 149.51/21.65 | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | COMBINE_EQS: (8527), (8565) imply: % 149.51/21.65 | | | | | | | | | | | | | | | | | (8566) e1 = e0 % 149.51/21.65 | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | REDUCE: (4), (8566) imply: % 149.51/21.65 | | | | | | | | | | | | | | | | | (8567) $false % 149.51/21.65 | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | CLOSE: (8567) is inconsistent. % 149.51/21.65 | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | Case 2: % 149.51/21.65 | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | (8568) all_56_31 = e0 % 149.51/21.65 | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | COMBINE_EQS: (544), (8568) imply: % 149.51/21.65 | | | | | | | | | | | | | | | | | (8569) all_4_2 = e0 % 149.51/21.65 | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | SIMP: (8569) implies: % 149.51/21.65 | | | | | | | | | | | | | | | | | (8570) all_4_2 = e0 % 149.51/21.65 | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | REDUCE: (581), (8570) imply: % 149.51/21.65 | | | | | | | | | | | | | | | | | (8571) ~ (all_52_7 = e0) % 149.51/21.65 | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | REDUCE: (588), (8570) imply: % 149.51/21.65 | | | | | | | | | | | | | | | | | (8572) ~ (all_52_11 = e0) % 149.51/21.65 | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | REDUCE: (590), (8570) imply: % 149.51/21.65 | | | | | | | | | | | | | | | | | (8573) ~ (all_52_13 = e0) % 149.51/21.65 | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | REDUCE: (8523), (8570) imply: % 149.51/21.65 | | | | | | | | | | | | | | | | | (8574) ~ (e3 = e0) % 149.51/21.65 | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | BETA: splitting (336) gives: % 149.51/21.65 | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | Case 1: % 149.51/21.65 | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | (8575) all_58_1 = e0 % 149.51/21.65 | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (555), (8575) imply: % 149.51/21.65 | | | | | | | | | | | | | | | | | | (8576) all_52_4 = e0 % 149.51/21.65 | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (408), (8576) imply: % 149.51/21.65 | | | | | | | | | | | | | | | | | | (8577) all_56_3 = e0 % 149.51/21.65 | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | REDUCE: (181), (8576) imply: % 149.51/21.65 | | | | | | | | | | | | | | | | | | (8578) ~ (all_52_12 = e0) % 149.51/21.65 | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | SIMP: (8578) implies: % 149.51/21.65 | | | | | | | | | | | | | | | | | | (8579) ~ (all_52_12 = e0) % 149.51/21.65 | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | REDUCE: (563), (8576) imply: % 149.51/21.65 | | | | | | | | | | | | | | | | | | (8580) ~ (all_10_2 = e0) % 149.51/21.65 | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | SIMP: (8580) implies: % 149.51/21.65 | | | | | | | | | | | | | | | | | | (8581) ~ (all_10_2 = e0) % 149.51/21.65 | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | REDUCE: (571), (8576) imply: % 149.51/21.65 | | | | | | | | | | | | | | | | | | (8582) ~ (all_8_2 = e0) % 149.51/21.65 | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | REDUCE: (8553), (8576) imply: % 149.51/21.65 | | | | | | | | | | | | | | | | | | (8583) ~ (e2 = e0) % 149.51/21.65 | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | BETA: splitting (340) gives: % 149.51/21.65 | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | Case 1: % 149.51/21.65 | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | (8584) all_58_0 = e0 % 149.51/21.65 | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (419), (8584) imply: % 149.51/21.65 | | | | | | | | | | | | | | | | | | | (8585) all_10_2 = e0 % 149.51/21.65 | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | REDUCE: (8581), (8585) imply: % 149.51/21.65 | | | | | | | | | | | | | | | | | | | (8586) $false % 149.51/21.65 | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | CLOSE: (8586) is inconsistent. % 149.51/21.65 | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | Case 2: % 149.51/21.65 | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | (8587) ~ (all_58_0 = e0) % 149.51/21.65 | | | | | | | | | | | | | | | | | | | (8588) all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0 % 149.51/21.65 | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | BETA: splitting (8588) gives: % 149.51/21.65 | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | Case 1: % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | (8589) all_58_2 = e0 % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (401), (8589) imply: % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | (8590) all_52_1 = e0 % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (425), (8590) imply: % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | (8591) all_56_9 = e0 % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | REDUCE: (196), (8590) imply: % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | (8592) ~ (all_52_3 = e0) % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | SIMP: (8592) implies: % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | (8593) ~ (all_52_3 = e0) % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | BETA: splitting (299) gives: % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | Case 1: % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | (8594) ~ (all_56_1 = e2) % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | REDUCE: (546), (8594) imply: % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | (8595) ~ (all_10_2 = e2) % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (252) gives: % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | (8596) all_54_0 = e3 % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (543), (8546), (8596) are inconsistent by % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | sub-proof #709. % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | (8597) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8597) gives: % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | (8598) all_54_0 = e2 % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (543), (8595), (8598) are inconsistent by % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | sub-proof #734. % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | (8599) all_54_0 = e1 | all_54_0 = e0 % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (296) gives: % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | (8600) ~ (all_56_11 = e3) % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (545), (8600) imply: % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | (8601) ~ (all_8_2 = e3) % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (247) gives: % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | (8602) all_54_5 = e3 % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (542), (8601), (8602) are inconsistent by % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #737. % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | (8603) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8603) gives: % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | (8604) all_54_5 = e2 % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (542), (8554), (8604) are inconsistent by % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #648. % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | (8605) all_54_5 = e1 | all_54_5 = e0 % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8599) gives: % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | (8606) all_54_0 = e1 % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (543), (8606) imply: % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | (8607) all_10_2 = e1 % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (8607) implies: % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | (8608) all_10_2 = e1 % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (546), (8608) imply: % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | (8609) all_56_1 = e1 % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (561), (8608) imply: % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | (8610) ~ (all_52_3 = e1) % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (53), (8608) imply: % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | (8611) op(e1, e1) = all_10_1 % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (298) gives: % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8612) ~ (all_56_1 = e1) % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8609), (8612) imply: % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8613) $false % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (8613) is inconsistent. % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8614) all_56_5 = e3 % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (429), (8614) imply: % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8615) all_52_8 = e3 % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (169), (8615) imply: % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8616) ~ (all_52_11 = e3) % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (8616) implies: % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8617) ~ (all_52_11 = e3) % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (240) gives: % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8618) all_54_12 = e3 % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (478), (8544), (8618) are inconsistent by % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #667. % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8619) all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0 % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8619) gives: % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8620) all_54_12 = e2 % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (478), (8620) imply: % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8621) all_52_3 = e2 % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (8621) implies: % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8622) all_52_3 = e2 % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (187), (8622) imply: % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8623) ~ (all_52_11 = e2) % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (8623) implies: % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8624) ~ (all_52_11 = e2) % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives: % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8625) all_54_14 = e3 % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (482), (8625) imply: % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8626) all_52_11 = e3 % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8617), (8626) imply: % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8627) $false % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (8627) is inconsistent. % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8628) all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0 % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8628) gives: % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8629) all_54_14 = e2 % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (482), (8629) imply: % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8630) all_52_11 = e2 % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8624), (8630) imply: % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8631) $false % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (8631) is inconsistent. % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8632) all_54_14 = e1 | all_54_14 = e0 % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8632) gives: % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8633) all_54_14 = e1 % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (482), (8633) imply: % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8634) all_52_11 = e1 % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (623), (8634) imply: % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8635) op(e1, e1) = all_56_28 % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (333) gives: % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8636) all_58_2 = e1 % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8589), (8636) are inconsistent by sub-proof % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #241. % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8637) all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1 % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8637) gives: % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8638) all_58_3 = e1 % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (554), (8638) imply: % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8639) all_8_2 = e1 % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8499), (8639) imply: % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8640) op(e1, e1) = e1 % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_10_1, % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_28, e1, e1, simplifying with (8611), (8635) % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8641) all_56_28 = all_10_1 % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1, % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_28, e1, e1, simplifying with (8635), (8640) % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8642) all_56_28 = e1 % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_28, e1, e1, simplifying with (8538), (8635) % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8643) all_56_28 = e0 % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (8641), (8643) imply: % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8644) all_10_1 = e0 % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (8641), (8642) imply: % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8645) all_10_1 = e1 % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (8644), (8645) imply: % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8646) e1 = e0 % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (8646) implies: % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8647) e1 = e0 % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4), (8647) imply: % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8648) $false % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (8648) is inconsistent. % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8649) ~ (all_58_3 = e1) % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (554), (8649) imply: % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8650) ~ (all_8_2 = e1) % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8605) gives: % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8651) all_54_5 = e1 % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (542), (8650), (8651) are inconsistent by % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #647. % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8652) all_54_5 = e0 % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (542), (8521), (8652) are inconsistent by % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #646. % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8653) all_54_14 = e0 % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (482), (8653) imply: % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8654) all_52_11 = e0 % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8572), (8654) imply: % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8655) $false % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (8655) is inconsistent. % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8656) all_54_12 = e1 | all_54_12 = e0 % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (478), (8593), (8610), (8656) are inconsistent by % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #616. % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | (8657) all_54_0 = e0 % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (543), (8581), (8657) are inconsistent by % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #732. % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | (8658) all_56_9 = e2 % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (8591), (8658) are inconsistent by sub-proof % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | #486. % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | End of split % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | End of split % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | End of split % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | Case 2: % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | (8659) all_56_3 = e3 % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (8577), (8659) imply: % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | (8660) e3 = e0 % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | REDUCE: (7), (8660) imply: % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | (8661) $false % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | CLOSE: (8661) is inconsistent. % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | End of split % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | Case 2: % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | (8662) ~ (all_58_2 = e0) % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | REDUCE: (401), (8662) imply: % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | (8663) ~ (all_52_1 = e0) % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | BETA: splitting (299) gives: % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | Case 1: % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | (8664) ~ (all_56_1 = e2) % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | REDUCE: (546), (8664) imply: % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | (8665) ~ (all_10_2 = e2) % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (252) gives: % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | (8666) all_54_0 = e3 % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (543), (8546), (8666) are inconsistent by % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | sub-proof #709. % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | (8667) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8667) gives: % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | (8668) all_54_0 = e2 % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (543), (8665), (8668) are inconsistent by % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | sub-proof #734. % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | (8669) all_54_0 = e1 | all_54_0 = e0 % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8669) gives: % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | (8670) all_54_0 = e1 % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (543), (8670) imply: % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | (8671) all_10_2 = e1 % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (8671) implies: % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | (8672) all_10_2 = e1 % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (546), (8672) imply: % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | (8673) all_56_1 = e1 % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (557), (8672) imply: % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | (8674) ~ (all_52_1 = e1) % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (567), (8672) imply: % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | (8675) ~ (all_52_12 = e1) % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (298) gives: % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | (8676) ~ (all_56_1 = e1) % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8673), (8676) imply: % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | (8677) $false % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (8677) is inconsistent. % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | (8678) all_56_5 = e3 % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (429), (8678) imply: % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | (8679) all_52_8 = e3 % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (8679) implies: % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | (8680) all_52_8 = e3 % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (168), (8680) imply: % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | (8681) ~ (all_52_12 = e3) % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (8681) implies: % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | (8682) ~ (all_52_12 = e3) % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (249) gives: % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | (8683) all_54_3 = e3 % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (461), (8682), (8683) are inconsistent by % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #659. % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | (8684) all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0 % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8684) gives: % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | (8685) all_54_3 = e2 % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (461), (8685) imply: % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | (8686) all_52_12 = e2 % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (8686) implies: % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | (8687) all_52_12 = e2 % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (161), (8687) imply: % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | (8688) ~ (all_52_13 = e2) % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (8688) implies: % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | (8689) ~ (all_52_13 = e2) % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (193), (245), (247), (248), (295), (463), (469), % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | (542), (545), (568), (579), (8503), (8505), % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | (8521), (8534), (8573), (8663), (8674), (8689) are % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #136. % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | (8690) all_54_3 = e1 | all_54_3 = e0 % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (461), (8579), (8675), (8690) are inconsistent by % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #655. % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | (8691) all_54_0 = e0 % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (543), (8581), (8691) are inconsistent by % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #732. % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | End of split % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | End of split % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | End of split % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | Case 2: % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | (8692) all_56_3 = e3 % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8577), (8692) are inconsistent by sub-proof % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | #47. % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | End of split % 149.51/21.65 | | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | | End of split % 149.51/21.65 | | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | End of split % 149.51/21.65 | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | Case 2: % 149.51/21.65 | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | (8693) all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0 % 149.51/21.65 | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | | REF_CLOSE: (549), (554), (7425), (8521), (8537), (8571), % 149.51/21.65 | | | | | | | | | | | | | | | | | | (8693) are inconsistent by sub-proof #45. % 149.51/21.65 | | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | | End of split % 149.51/21.65 | | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | | End of split % 149.51/21.65 | | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | | End of split % 149.51/21.65 | | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | End of split % 149.51/21.65 | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | Case 2: % 149.51/21.65 | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | (8694) all_54_9 = e1 | all_54_9 = e0 % 149.51/21.65 | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | | REF_CLOSE: (7423), (8536), (8537), (8694) are inconsistent by % 149.51/21.65 | | | | | | | | | | | | | | sub-proof #81. % 149.51/21.65 | | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | | End of split % 149.51/21.65 | | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | End of split % 149.51/21.65 | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | Case 2: % 149.51/21.65 | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | (8695) all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3 % 149.51/21.65 | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | | REF_CLOSE: (7), (8), (7425), (8513), (8532), (8533), (8695) % 149.51/21.65 | | | | | | | | | | | | are inconsistent by sub-proof #85. % 149.51/21.65 | | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | | End of split % 149.51/21.65 | | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | End of split % 149.51/21.65 | | | | | | | | | | % 149.51/21.65 | | | | | | | | | Case 2: % 149.51/21.65 | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | (8696) all_56_31 = e3 % 149.51/21.65 | | | | | | | | | | (8697) all_56_25 = e0 % 149.51/21.65 | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | COMBINE_EQS: (447), (8697) imply: % 149.51/21.65 | | | | | | | | | | (8698) all_52_3 = e0 % 149.51/21.65 | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | SIMP: (8698) implies: % 149.51/21.65 | | | | | | | | | | (8699) all_52_3 = e0 % 149.51/21.65 | | | | | | | | | | % 149.51/21.65 | | | | | | | | | | COMBINE_EQS: (544), (8696) imply: % 149.51/21.66 | | | | | | | | | | (8700) all_4_2 = e3 % 149.51/21.66 | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | COMBINE_EQS: (547), (8700) imply: % 149.51/21.66 | | | | | | | | | | (8701) all_58_15 = e3 % 149.51/21.66 | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | COMBINE_EQS: (365), (8699) imply: % 149.51/21.66 | | | | | | | | | | (8702) all_58_12 = e0 % 149.51/21.66 | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | REDUCE: (188), (8699) imply: % 149.51/21.66 | | | | | | | | | | (8703) ~ (all_52_7 = e0) % 149.51/21.66 | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | SIMP: (8703) implies: % 149.51/21.66 | | | | | | | | | | (8704) ~ (all_52_7 = e0) % 149.51/21.66 | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | REDUCE: (187), (8699) imply: % 149.51/21.66 | | | | | | | | | | (8705) ~ (all_52_11 = e0) % 149.51/21.66 | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | SIMP: (8705) implies: % 149.51/21.66 | | | | | | | | | | (8706) ~ (all_52_11 = e0) % 149.51/21.66 | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | REDUCE: (561), (8699) imply: % 149.51/21.66 | | | | | | | | | | (8707) ~ (all_10_2 = e0) % 149.51/21.66 | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | SIMP: (8707) implies: % 149.51/21.66 | | | | | | | | | | (8708) ~ (all_10_2 = e0) % 149.51/21.66 | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | REDUCE: (581), (8700) imply: % 149.51/21.66 | | | | | | | | | | (8709) ~ (all_52_7 = e3) % 149.51/21.66 | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | REDUCE: (38), (8700) imply: % 149.51/21.66 | | | | | | | | | | (8710) op(e3, e3) = all_4_1 % 149.51/21.66 | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_10_2, % 149.51/21.66 | | | | | | | | | | all_4_1, e3, e3, simplifying with (51), (8710) % 149.51/21.66 | | | | | | | | | | gives: % 149.51/21.66 | | | | | | | | | | (8711) all_10_2 = all_4_1 % 149.51/21.66 | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | COMBINE_EQS: (543), (8711) imply: % 149.51/21.66 | | | | | | | | | | (8712) all_54_0 = all_4_1 % 149.51/21.66 | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | COMBINE_EQS: (546), (8711) imply: % 149.51/21.66 | | | | | | | | | | (8713) all_56_1 = all_4_1 % 149.51/21.66 | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | COMBINE_EQS: (419), (8711) imply: % 149.51/21.66 | | | | | | | | | | (8714) all_58_0 = all_4_1 % 149.51/21.66 | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | REDUCE: (557), (8711) imply: % 149.51/21.66 | | | | | | | | | | (8715) ~ (all_52_1 = all_4_1) % 149.51/21.66 | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | REDUCE: (559), (8711) imply: % 149.51/21.66 | | | | | | | | | | (8716) ~ (all_52_2 = all_4_1) % 149.51/21.66 | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | REDUCE: (563), (8711) imply: % 149.51/21.66 | | | | | | | | | | (8717) ~ (all_52_4 = all_4_1) % 149.51/21.66 | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | REDUCE: (8708), (8711) imply: % 149.51/21.66 | | | | | | | | | | (8718) ~ (all_4_1 = e0) % 149.51/21.66 | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | BETA: splitting (291) gives: % 149.51/21.66 | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | Case 1: % 149.51/21.66 | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | (8719) ~ (all_56_21 = e0) % 149.51/21.66 | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | REDUCE: (374), (8719) imply: % 149.51/21.66 | | | | | | | | | | | (8720) ~ (all_6_2 = e0) % 149.51/21.66 | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | BETA: splitting (293) gives: % 149.51/21.66 | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | Case 1: % 149.51/21.66 | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | (8721) ~ (all_56_21 = e3) % 149.51/21.66 | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | REDUCE: (374), (8721) imply: % 149.51/21.66 | | | | | | | | | | | | (8722) ~ (all_6_2 = e3) % 149.51/21.66 | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | REF_CLOSE: (41), (242), (541), (622), (7420), (8517), (8720), % 149.51/21.66 | | | | | | | | | | | | (8722), (function-axioms) are inconsistent by % 149.51/21.66 | | | | | | | | | | | | sub-proof #89. % 149.51/21.66 | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | Case 2: % 149.51/21.66 | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | (8723) all_56_21 = e3 % 149.51/21.66 | | | | | | | | | | | | (8724) all_56_17 = e1 % 149.51/21.66 | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | COMBINE_EQS: (381), (8724) imply: % 149.51/21.66 | | | | | | | | | | | | (8725) all_52_2 = e1 % 149.51/21.66 | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | SIMP: (8725) implies: % 149.51/21.66 | | | | | | | | | | | | (8726) all_52_2 = e1 % 149.51/21.66 | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | COMBINE_EQS: (374), (8723) imply: % 149.51/21.66 | | | | | | | | | | | | (8727) all_6_2 = e3 % 149.51/21.66 | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | SIMP: (8727) implies: % 149.51/21.66 | | | | | | | | | | | | (8728) all_6_2 = e3 % 149.51/21.66 | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | COMBINE_EQS: (552), (8728) imply: % 149.51/21.66 | | | | | | | | | | | | (8729) all_58_8 = e3 % 149.51/21.66 | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | REDUCE: (7426), (8726) imply: % 149.51/21.66 | | | | | | | | | | | | (8730) ~ (all_6_0 = e1) % 149.51/21.66 | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | SIMP: (8730) implies: % 149.51/21.66 | | | | | | | | | | | | (8731) ~ (all_6_0 = e1) % 149.51/21.66 | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | REDUCE: (8716), (8726) imply: % 149.51/21.66 | | | | | | | | | | | | (8732) ~ (all_4_1 = e1) % 149.51/21.66 | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | SIMP: (8732) implies: % 149.51/21.66 | | | | | | | | | | | | (8733) ~ (all_4_1 = e1) % 149.51/21.66 | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | BETA: splitting (7418) gives: % 149.51/21.66 | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | Case 1: % 149.51/21.66 | | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | | (8734) ~ (all_6_2 = e3) % 149.51/21.66 | | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | | REF_CLOSE: (41), (242), (541), (622), (7420), (8517), (8720), % 149.51/21.66 | | | | | | | | | | | | | (8734), (function-axioms) are inconsistent by % 149.51/21.66 | | | | | | | | | | | | | sub-proof #77. % 149.51/21.66 | | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | Case 2: % 149.51/21.66 | | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | | (8735) ~ (all_6_0 = e0) % 149.51/21.66 | | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | | BETA: splitting (243) gives: % 149.51/21.66 | | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | | Case 1: % 149.51/21.66 | | | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | | | (8736) all_54_9 = e3 % 149.51/21.66 | | | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | | | COMBINE_EQS: (7423), (8736) imply: % 149.51/21.66 | | | | | | | | | | | | | | (8737) all_6_0 = e3 % 149.51/21.66 | | | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | | | REDUCE: (8513), (8737) imply: % 149.51/21.66 | | | | | | | | | | | | | | (8738) $false % 149.51/21.66 | | | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | | | CLOSE: (8738) is inconsistent. % 149.51/21.66 | | | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | | Case 2: % 149.51/21.66 | | | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | | | (8739) ~ (all_54_9 = e3) % 149.51/21.66 | | | | | | | | | | | | | | (8740) all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0 % 149.51/21.66 | | | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | | | BETA: splitting (8740) gives: % 149.51/21.66 | | | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | | | Case 1: % 149.51/21.66 | | | | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | | | | (8741) all_54_9 = e2 % 149.51/21.66 | | | | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | | | | COMBINE_EQS: (7423), (8741) imply: % 149.51/21.66 | | | | | | | | | | | | | | | (8742) all_6_0 = e2 % 149.51/21.66 | | | | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | | | | REDUCE: (7429), (8742) imply: % 149.51/21.66 | | | | | | | | | | | | | | | (8743) ~ (all_52_7 = e2) % 149.51/21.66 | | | | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | | | | REDUCE: (7433), (8742) imply: % 149.51/21.66 | | | | | | | | | | | | | | | (8744) ~ (all_8_2 = e2) % 149.51/21.66 | | | | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | | | | REDUCE: (8513), (8742) imply: % 149.51/21.66 | | | | | | | | | | | | | | | (8745) ~ (e3 = e2) % 149.51/21.66 | | | | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | | | | BETA: splitting (319) gives: % 149.51/21.66 | | | | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | | | | Case 1: % 149.51/21.66 | | | | | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | | | | | (8746) all_58_12 = e2 % 149.51/21.66 | | | | | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | | | | | REF_CLOSE: (5), (8702), (8746) are inconsistent by sub-proof % 149.51/21.66 | | | | | | | | | | | | | | | | #423. % 149.51/21.66 | | | | | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | | | | Case 2: % 149.51/21.66 | | | | | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | | | | | (8747) all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2 % 149.51/21.66 | | | | | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | | | | | BETA: splitting (287) gives: % 149.51/21.66 | | | | | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | | | | | Case 1: % 149.51/21.66 | | | | | | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | | | | | | (8748) all_56_1 = e3 % 149.51/21.66 | | | | | | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | | | | | | COMBINE_EQS: (8713), (8748) imply: % 149.51/21.66 | | | | | | | | | | | | | | | | | (8749) all_4_1 = e3 % 149.51/21.66 | | | | | | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | | | | | | REDUCE: (8715), (8749) imply: % 149.51/21.66 | | | | | | | | | | | | | | | | | (8750) ~ (all_52_1 = e3) % 149.51/21.66 | | | | | | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | | | | | | BETA: splitting (248) gives: % 149.51/21.66 | | | | | | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | | | | | | Case 1: % 149.51/21.66 | | | | | | | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | | | | | | | (8751) all_54_4 = e3 % 149.51/21.66 | | | | | | | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | | | | | | | REF_CLOSE: (463), (8750), (8751) are inconsistent by % 149.51/21.66 | | | | | | | | | | | | | | | | | | sub-proof #634. % 149.51/21.66 | | | | | | | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | | | | | | Case 2: % 149.51/21.66 | | | | | | | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | | | | | | | (8752) ~ (all_54_4 = e3) % 149.51/21.66 | | | | | | | | | | | | | | | | | | (8753) all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0 % 149.51/21.66 | | | | | | | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | | | | | | | BETA: splitting (8747) gives: % 149.51/21.66 | | | | | | | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | | | | | | | Case 1: % 149.51/21.66 | | | | | | | | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | | | | | | | | (8754) all_58_13 = e2 % 149.51/21.66 | | | | | | | | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (549), (8743), (8754) are inconsistent by % 149.51/21.66 | | | | | | | | | | | | | | | | | | | sub-proof #91. % 149.51/21.66 | | | | | | | | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | | | | | | | Case 2: % 149.51/21.66 | | | | | | | | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | | | | | | | | (8755) all_58_14 = e2 | all_58_15 = e2 % 149.51/21.66 | | | | | | | | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | | | | | | | | BETA: splitting (8753) gives: % 149.51/21.66 | | | | | | | | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | | | | | | | | Case 1: % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | (8756) all_54_4 = e2 % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (463), (8756) imply: % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | (8757) all_52_1 = e2 % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | REDUCE: (8505), (8757) imply: % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | (8758) ~ (all_8_0 = e2) % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | SIMP: (8758) implies: % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | (8759) ~ (all_8_0 = e2) % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | REDUCE: (568), (8757) imply: % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | (8760) ~ (all_8_2 = e2) % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | BETA: splitting (295) gives: % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | Case 1: % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | (8761) ~ (all_56_11 = e1) % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | REDUCE: (545), (8761) imply: % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | (8762) ~ (all_8_2 = e1) % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8755) gives: % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | | (8763) all_58_14 = e2 % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (548), (8763) imply: % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | | (8764) all_52_11 = e2 % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | | SIMP: (8764) implies: % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | | (8765) all_52_11 = e2 % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8497) gives: % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | | | (8766) ~ (all_8_2 = e3) % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (247) gives: % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | | | | (8767) all_54_5 = e3 % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (542), (8766), (8767) are inconsistent by % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #737. % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | | | | (8768) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (542), (8521), (8744), (8762), (8768) are % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #644. % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | | | End of split % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | | | (8769) ~ (all_8_0 = e0) % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (328) gives: % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | | | | (8770) all_58_4 = e0 % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (407), (8770) imply: % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | | | | (8771) all_52_8 = e0 % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (182), (8771) imply: % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | | | | (8772) ~ (all_52_4 = e0) % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (336) gives: % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | | | | | (8773) all_58_1 = e0 % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (555), (8773) imply: % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | | | | | (8774) all_52_4 = e0 % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8772), (8774) imply: % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | | | | | (8775) $false % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (8775) is inconsistent. % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | | | | | (8776) all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0 % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (549), (554), (7425), (8521), (8704), (8735), % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | | | | | (8776) are inconsistent by sub-proof #45. % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | | | | (8777) all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0 % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8777) gives: % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | | | | | (8778) all_58_5 = e0 % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (8504), (8778) imply: % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | | | | | (8779) all_8_0 = e0 % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8769), (8779) imply: % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | | | | | (8780) $false % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (8780) is inconsistent. % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | | | | | (8781) all_58_8 = e0 | all_58_14 = e0 % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8781) gives: % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | | | | | | (8782) all_58_8 = e0 % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (8729), (8782) imply: % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | | | | | | (8783) e3 = e0 % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7), (8783) imply: % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | | | | | | (8784) $false % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (8784) is inconsistent. % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | | | | | | (8785) all_58_14 = e0 % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (8763), (8785) imply: % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | | | | | | (8786) e2 = e0 % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5), (8786) imply: % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | | | | | | (8787) $false % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (8787) is inconsistent. % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | | | End of split % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | | End of split % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | | (8788) all_58_15 = e2 % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (8701), (8788) imply: % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | | (8789) e3 = e2 % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (9), (8789) imply: % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | | (8790) $false % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (8790) is inconsistent. % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | End of split % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | Case 2: % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | (8791) all_56_13 = e2 % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8503), (8759), (8791) are inconsistent by % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | sub-proof #139. % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | End of split % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | | | | | | | | Case 2: % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | (8792) ~ (all_54_4 = e2) % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | REDUCE: (463), (8792) imply: % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | (8793) ~ (all_52_1 = e2) % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | BETA: splitting (296) gives: % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | Case 1: % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | (8794) ~ (all_56_11 = e3) % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | REDUCE: (545), (8794) imply: % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | (8795) ~ (all_8_2 = e3) % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8755) gives: % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | | (8796) all_58_14 = e2 % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (548), (8796) imply: % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | | (8797) all_52_11 = e2 % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | | SIMP: (8797) implies: % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | | (8798) all_52_11 = e2 % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8507), (8798) imply: % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | | (8799) ~ (all_8_0 = e2) % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | | SIMP: (8799) implies: % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | | (8800) ~ (all_8_0 = e2) % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (247), (295), (542), (545), (8503), (8521), % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | | (8744), (8795), (8800) are inconsistent by % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | | sub-proof #138. % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | | (8801) all_58_15 = e2 % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (8701), (8801) imply: % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | | (8802) e3 = e2 % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (9), (8802) imply: % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | | (8803) $false % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (8803) is inconsistent. % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | End of split % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | Case 2: % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | (8804) all_56_9 = e2 % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (425), (8804) imply: % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | (8805) all_52_1 = e2 % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | REDUCE: (8793), (8805) imply: % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | (8806) $false % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | CLOSE: (8806) is inconsistent. % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | End of split % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | | | | | | | | End of split % 149.51/21.66 | | | | | | | | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | | | | | | | End of split % 149.51/21.66 | | | | | | | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | | | | | | End of split % 149.51/21.66 | | | | | | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | | | | | Case 2: % 149.51/21.66 | | | | | | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | | | | | | (8807) ~ (all_56_1 = e3) % 149.51/21.66 | | | | | | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | | | | | | REDUCE: (8713), (8807) imply: % 149.51/21.66 | | | | | | | | | | | | | | | | | (8808) ~ (all_4_1 = e3) % 149.51/21.66 | | | | | | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | | | | | | BETA: splitting (239) gives: % 149.51/21.66 | | | | | | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | | | | | | Case 1: % 149.51/21.66 | | | | | | | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | | | | | | | (8809) all_54_13 = e3 % 149.51/21.66 | | | | | | | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | | | | | | | REF_CLOSE: (480), (8709), (8809) are inconsistent by % 149.51/21.66 | | | | | | | | | | | | | | | | | | sub-proof #668. % 149.51/21.66 | | | | | | | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | | | | | | Case 2: % 149.51/21.66 | | | | | | | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | | | | | | | (8810) all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0 % 149.51/21.66 | | | | | | | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | | | | | | | BETA: splitting (252) gives: % 149.51/21.66 | | | | | | | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | | | | | | | Case 1: % 149.51/21.66 | | | | | | | | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | | | | | | | | (8811) all_54_0 = e3 % 149.51/21.66 | | | | | | | | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8712), (8808), (8811) are inconsistent by % 149.51/21.66 | | | | | | | | | | | | | | | | | | | sub-proof #554. % 149.51/21.66 | | | | | | | | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | | | | | | | Case 2: % 149.51/21.66 | | | | | | | | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | | | | | | | | (8812) ~ (all_54_0 = e3) % 149.51/21.66 | | | | | | | | | | | | | | | | | | | (8813) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 149.51/21.66 | | | | | | | | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | | | | | | | | BETA: splitting (8813) gives: % 149.51/21.66 | | | | | | | | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | | | | | | | | Case 1: % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | (8814) all_54_0 = e2 % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (8712), (8814) imply: % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | (8815) all_4_1 = e2 % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | SIMP: (8815) implies: % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | (8816) all_4_1 = e2 % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (8713), (8816) imply: % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | (8817) all_56_1 = e2 % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | BETA: splitting (299) gives: % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | Case 1: % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | (8818) ~ (all_56_1 = e2) % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | REDUCE: (8817), (8818) imply: % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | (8819) $false % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | CLOSE: (8819) is inconsistent. % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | Case 2: % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | (8820) all_56_3 = e3 % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (408), (8820) imply: % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | (8821) all_52_4 = e3 % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | SIMP: (8821) implies: % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | (8822) all_52_4 = e3 % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (555), (8822) imply: % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | (8823) all_58_1 = e3 % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (336) gives: % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | | (8824) all_58_1 = e0 % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (8823), (8824) imply: % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | | (8825) e3 = e0 % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (8723), (8825) imply: % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | | (8826) all_56_21 = e0 % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (8820), (8825) imply: % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | | (8827) all_56_3 = e0 % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (247), (252), (287), (299), (343), (480), % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | | (542), (545), (575), (8521), (8696), (8704), % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | | (8712), (8713), (8714), (8718), (8743), (8744), % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | | (8808), (8810), (8826), (8827) are inconsistent by % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | | sub-proof #46. % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | | (8828) all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0 % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (549), (554), (7425), (8521), (8704), (8735), % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | | (8828) are inconsistent by sub-proof #45. % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | End of split % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | End of split % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | | | | | | | | Case 2: % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | (8829) all_54_0 = e1 | all_54_0 = e0 % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8712), (8718), (8733), (8829) are inconsistent by % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | sub-proof #550. % 149.51/21.66 | | | | | | | | | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | | | | | | | | End of split % 149.51/21.66 | | | | | | | | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | | | | | | | End of split % 149.51/21.66 | | | | | | | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | | | | | | End of split % 149.51/21.66 | | | | | | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | | | | | End of split % 149.51/21.66 | | | | | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | | | | End of split % 149.51/21.66 | | | | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | | | Case 2: % 149.51/21.66 | | | | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | | | | (8830) all_54_9 = e1 | all_54_9 = e0 % 149.51/21.66 | | | | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | | | | REF_CLOSE: (7423), (8731), (8735), (8830) are inconsistent by % 149.51/21.66 | | | | | | | | | | | | | | | sub-proof #81. % 149.51/21.66 | | | | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | | | End of split % 149.51/21.66 | | | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | | End of split % 149.51/21.66 | | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | | End of split % 149.51/21.66 | | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | End of split % 149.51/21.66 | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | Case 2: % 149.51/21.66 | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | (8831) all_56_23 = e1 % 149.51/21.66 | | | | | | | | | | | (8832) all_56_21 = e0 % 149.51/21.66 | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | COMBINE_EQS: (374), (8832) imply: % 149.51/21.66 | | | | | | | | | | | (8833) all_6_2 = e0 % 149.51/21.66 | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | SIMP: (8833) implies: % 149.51/21.66 | | | | | | | | | | | (8834) all_6_2 = e0 % 149.51/21.66 | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | COMBINE_EQS: (366), (8831) imply: % 149.51/21.66 | | | | | | | | | | | (8835) all_52_14 = e1 % 149.51/21.66 | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | SIMP: (8835) implies: % 149.51/21.66 | | | | | | | | | | | (8836) all_52_14 = e1 % 149.51/21.66 | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | REDUCE: (189), (8836) imply: % 149.51/21.66 | | | | | | | | | | | (8837) ~ (all_52_2 = e1) % 149.51/21.66 | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | REDUCE: (569), (8834) imply: % 149.51/21.66 | | | | | | | | | | | (8838) ~ (all_52_2 = e0) % 149.51/21.66 | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | REDUCE: (7431), (8836) imply: % 149.51/21.66 | | | | | | | | | | | (8839) ~ (all_6_0 = e1) % 149.51/21.66 | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | SIMP: (8839) implies: % 149.51/21.66 | | | | | | | | | | | (8840) ~ (all_6_0 = e1) % 149.51/21.66 | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | REDUCE: (7434), (8834) imply: % 149.51/21.66 | | | | | | | | | | | (8841) ~ (all_6_0 = e0) % 149.51/21.66 | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | | REF_CLOSE: (183), (239), (243), (244), (247), (252), (287), % 149.51/21.66 | | | | | | | | | | | (299), (336), (343), (408), (471), (480), (542), % 149.51/21.66 | | | | | | | | | | | (545), (549), (554), (555), (571), (575), (7423), % 149.51/21.66 | | | | | | | | | | | (7425), (7426), (7429), (7433), (8513), (8521), % 149.51/21.66 | | | | | | | | | | | (8696), (8704), (8709), (8712), (8713), (8714), % 149.51/21.66 | | | | | | | | | | | (8716), (8717), (8832), (8837), (8838), (8840), % 149.51/21.66 | | | | | | | | | | | (8841) are inconsistent by sub-proof #44. % 149.51/21.66 | | | | | | | | | | | % 149.51/21.66 | | | | | | | | | | End of split % 149.51/21.66 | | | | | | | | | | % 149.51/21.66 | | | | | | | | | End of split % 149.51/21.66 | | | | | | | | | % 149.51/21.66 | | | | | | | | Case 2: % 149.51/21.66 | | | | | | | | | % 149.51/21.66 | | | | | | | | | (8842) all_56_15 = e2 % 149.51/21.66 | | | | | | | | | (8843) all_56_11 = e0 % 149.51/21.66 | | | | | | | | | % 149.51/21.66 | | | | | | | | | COMBINE_EQS: (545), (8843) imply: % 149.51/21.66 | | | | | | | | | (8844) all_8_2 = e0 % 149.51/21.66 | | | | | | | | | % 149.51/21.66 | | | | | | | | | COMBINE_EQS: (443), (8842) imply: % 149.51/21.66 | | | | | | | | | (8845) all_52_13 = e2 % 149.51/21.66 | | | | | | | | | % 149.51/21.66 | | | | | | | | | COMBINE_EQS: (386), (8845) imply: % 149.51/21.66 | | | | | | | | | (8846) all_58_10 = e2 % 149.51/21.66 | | | | | | | | | % 149.51/21.66 | | | | | | | | | COMBINE_EQS: (554), (8844) imply: % 149.51/21.66 | | | | | | | | | (8847) all_58_3 = e0 % 149.51/21.66 | | | | | | | | | % 149.51/21.66 | | | | | | | | | REDUCE: (8509), (8845) imply: % 149.51/21.66 | | | | | | | | | (8848) ~ (all_8_0 = e2) % 149.51/21.66 | | | | | | | | | % 149.51/21.66 | | | | | | | | | SIMP: (8848) implies: % 149.51/21.66 | | | | | | | | | (8849) ~ (all_8_0 = e2) % 149.51/21.66 | | | | | | | | | % 149.51/21.66 | | | | | | | | | REDUCE: (8510), (8844) imply: % 149.51/21.66 | | | | | | | | | (8850) ~ (all_8_0 = e0) % 149.51/21.66 | | | | | | | | | % 149.51/21.66 | | | | | | | | | REDUCE: (8499), (8844) imply: % 149.51/21.66 | | | | | | | | | (8851) op(e0, e0) = e1 % 149.51/21.66 | | | | | | | | | % 149.51/21.66 | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (38), (246), % 149.51/21.66 | | | | | | | | | (287), (333), (335), (374), (401), (544), (546), % 149.51/21.66 | | | | | | | | | (557), (627), (8502), (8504), (8511), (8515), % 149.51/21.66 | | | | | | | | | (8519), (8843), (8846), (8847), (8849), (8850), % 149.51/21.66 | | | | | | | | | (8851), (function-axioms) are inconsistent by % 149.51/21.66 | | | | | | | | | sub-proof #112. % 149.51/21.66 | | | | | | | | | % 149.51/21.66 | | | | | | | | End of split % 149.51/21.66 | | | | | | | | % 149.51/21.66 | | | | | | | Case 2: % 149.51/21.66 | | | | | | | | % 149.51/21.66 | | | | | | | | (8852) all_56_31 = e1 % 149.51/21.66 | | | | | | | | (8853) all_56_29 = e0 % 149.51/21.66 | | | | | | | | % 149.51/21.66 | | | | | | | | COMBINE_EQS: (357), (8853) imply: % 149.51/21.66 | | | | | | | | (8854) all_52_11 = e0 % 149.51/21.66 | | | | | | | | % 149.51/21.66 | | | | | | | | SIMP: (8854) implies: % 149.51/21.66 | | | | | | | | (8855) all_52_11 = e0 % 149.51/21.66 | | | | | | | | % 149.51/21.66 | | | | | | | | COMBINE_EQS: (544), (8852) imply: % 149.51/21.66 | | | | | | | | (8856) all_4_2 = e1 % 149.51/21.66 | | | | | | | | % 149.51/21.66 | | | | | | | | REDUCE: (173), (8855) imply: % 149.51/21.66 | | | | | | | | (8857) ~ (all_52_7 = e0) % 149.51/21.66 | | | | | | | | % 149.51/21.66 | | | | | | | | REDUCE: (581), (8856) imply: % 149.51/21.66 | | | | | | | | (8858) ~ (all_52_7 = e1) % 149.51/21.66 | | | | | | | | % 149.51/21.66 | | | | | | | | REDUCE: (585), (8855) imply: % 149.51/21.66 | | | | | | | | (8859) ~ (all_6_2 = e0) % 149.51/21.66 | | | | | | | | % 149.51/21.66 | | | | | | | | SIMP: (8859) implies: % 149.51/21.66 | | | | | | | | (8860) ~ (all_6_2 = e0) % 149.51/21.66 | | | | | | | | % 149.51/21.66 | | | | | | | | REDUCE: (588), (8855), (8856) imply: % 149.51/21.66 | | | | | | | | (8861) ~ (e1 = e0) % 149.51/21.66 | | | | | | | | % 149.51/21.66 | | | | | | | | REDUCE: (38), (8856) imply: % 149.51/21.66 | | | | | | | | (8862) op(e1, e1) = all_4_1 % 149.51/21.66 | | | | | | | | % 149.51/21.66 | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_6_2, % 149.51/21.66 | | | | | | | | all_4_1, e1, e1, simplifying with (41), (8862) % 149.51/21.66 | | | | | | | | gives: % 149.51/21.66 | | | | | | | | (8863) all_6_2 = all_4_1 % 149.51/21.66 | | | | | | | | % 149.51/21.66 | | | | | | | | COMBINE_EQS: (541), (8863) imply: % 149.51/21.66 | | | | | | | | (8864) all_54_10 = all_4_1 % 149.51/21.66 | | | | | | | | % 149.51/21.66 | | | | | | | | COMBINE_EQS: (374), (8863) imply: % 149.51/21.66 | | | | | | | | (8865) all_56_21 = all_4_1 % 149.51/21.66 | | | | | | | | % 149.51/21.66 | | | | | | | | REDUCE: (8511), (8863) imply: % 149.51/21.66 | | | | | | | | (8866) ~ (all_8_0 = all_4_1) % 149.51/21.66 | | | | | | | | % 149.51/21.66 | | | | | | | | REDUCE: (7434), (8863) imply: % 149.51/21.66 | | | | | | | | (8867) ~ (all_6_0 = all_4_1) % 149.51/21.66 | | | | | | | | % 149.51/21.66 | | | | | | | | REDUCE: (8517), (8863) imply: % 149.51/21.66 | | | | | | | | (8868) ~ (all_4_1 = e2) % 149.51/21.66 | | | | | | | | % 149.51/21.66 | | | | | | | | REDUCE: (8860), (8863) imply: % 149.51/21.66 | | | | | | | | (8869) ~ (all_4_1 = e0) % 149.51/21.66 | | | | | | | | % 149.51/21.66 | | | | | | | | REDUCE: (7420), (8863) imply: % 149.51/21.66 | | | | | | | | (8870) op(all_4_1, all_4_1) = e2 % 149.51/21.66 | | | | | | | | % 149.51/21.66 | | | | | | | | REDUCE: (622), (8863) imply: % 149.51/21.66 | | | | | | | | (8871) op(e1, all_4_1) = all_56_20 % 149.51/21.66 | | | | | | | | % 149.51/21.66 | | | | | | | | BETA: splitting (295) gives: % 149.51/21.66 | | | | | | | | % 149.51/21.66 | | | | | | | | Case 1: % 149.51/21.66 | | | | | | | | | % 149.51/21.66 | | | | | | | | | (8872) ~ (all_56_11 = e1) % 149.51/21.66 | | | | | | | | | % 149.51/21.66 | | | | | | | | | REDUCE: (545), (8872) imply: % 149.51/21.67 | | | | | | | | | (8873) ~ (all_8_2 = e1) % 149.51/21.67 | | | | | | | | | % 149.51/21.67 | | | | | | | | | BETA: splitting (294) gives: % 149.51/21.67 | | | | | | | | | % 149.51/21.67 | | | | | | | | | Case 1: % 149.51/21.67 | | | | | | | | | | % 149.51/21.67 | | | | | | | | | | (8874) ~ (all_56_11 = e0) % 149.51/21.67 | | | | | | | | | | % 149.51/21.67 | | | | | | | | | | REDUCE: (545), (8874) imply: % 149.51/21.67 | | | | | | | | | | (8875) ~ (all_8_2 = e0) % 149.51/21.67 | | | | | | | | | | % 149.51/21.67 | | | | | | | | | | BETA: splitting (293) gives: % 149.51/21.67 | | | | | | | | | | % 149.51/21.67 | | | | | | | | | | Case 1: % 149.51/21.67 | | | | | | | | | | | % 149.51/21.67 | | | | | | | | | | | (8876) ~ (all_56_21 = e3) % 149.51/21.67 | | | | | | | | | | | % 149.51/21.67 | | | | | | | | | | | REDUCE: (8865), (8876) imply: % 149.51/21.67 | | | | | | | | | | | (8877) ~ (all_4_1 = e3) % 149.51/21.67 | | | | | | | | | | | % 149.51/21.67 | | | | | | | | | | | REF_CLOSE: (41), (242), (541), (622), (7420), (8517), (8860), % 149.51/21.67 | | | | | | | | | | | (8864), (8877), (function-axioms) are inconsistent % 149.51/21.67 | | | | | | | | | | | by sub-proof #43. % 149.51/21.67 | | | | | | | | | | | % 149.51/21.67 | | | | | | | | | | Case 2: % 149.51/21.67 | | | | | | | | | | | % 149.51/21.67 | | | | | | | | | | | (8878) all_56_21 = e3 % 149.51/21.67 | | | | | | | | | | | (8879) all_56_17 = e1 % 149.51/21.67 | | | | | | | | | | | % 149.51/21.67 | | | | | | | | | | | COMBINE_EQS: (381), (8879) imply: % 149.51/21.67 | | | | | | | | | | | (8880) all_52_2 = e1 % 149.51/21.67 | | | | | | | | | | | % 149.51/21.67 | | | | | | | | | | | COMBINE_EQS: (8865), (8878) imply: % 149.51/21.67 | | | | | | | | | | | (8881) all_4_1 = e3 % 149.51/21.67 | | | | | | | | | | | % 149.51/21.67 | | | | | | | | | | | SIMP: (8881) implies: % 149.51/21.67 | | | | | | | | | | | (8882) all_4_1 = e3 % 149.51/21.67 | | | | | | | | | | | % 149.51/21.67 | | | | | | | | | | | REDUCE: (7426), (8880) imply: % 149.51/21.67 | | | | | | | | | | | (8883) ~ (all_6_0 = e1) % 149.51/21.67 | | | | | | | | | | | % 149.51/21.67 | | | | | | | | | | | SIMP: (8883) implies: % 149.51/21.67 | | | | | | | | | | | (8884) ~ (all_6_0 = e1) % 149.51/21.67 | | | | | | | | | | | % 149.51/21.67 | | | | | | | | | | | BETA: splitting (337) gives: % 149.51/21.67 | | | | | | | | | | | % 149.51/21.67 | | | | | | | | | | | Case 1: % 149.51/21.67 | | | | | | | | | | | | % 149.51/21.67 | | | | | | | | | | | | (8885) all_58_1 = e1 % 149.51/21.67 | | | | | | | | | | | | % 149.51/21.67 | | | | | | | | | | | | COMBINE_EQS: (555), (8885) imply: % 149.51/21.67 | | | | | | | | | | | | (8886) all_52_4 = e1 % 149.51/21.67 | | | | | | | | | | | | % 149.51/21.67 | | | | | | | | | | | | BETA: splitting (7418) gives: % 149.51/21.67 | | | | | | | | | | | | % 149.51/21.67 | | | | | | | | | | | | Case 1: % 149.51/21.67 | | | | | | | | | | | | | % 149.51/21.67 | | | | | | | | | | | | | (8887) ~ (all_6_2 = e3) % 149.51/21.67 | | | | | | | | | | | | | % 149.51/21.67 | | | | | | | | | | | | | REF_CLOSE: (41), (242), (541), (622), (7420), (8517), (8860), % 149.51/21.67 | | | | | | | | | | | | | (8887), (function-axioms) are inconsistent by % 149.51/21.67 | | | | | | | | | | | | | sub-proof #77. % 149.51/21.67 | | | | | | | | | | | | | % 149.51/21.67 | | | | | | | | | | | | Case 2: % 149.51/21.67 | | | | | | | | | | | | | % 149.51/21.67 | | | | | | | | | | | | | (8888) ~ (all_6_0 = e0) % 149.51/21.67 | | | | | | | | | | | | | % 149.51/21.67 | | | | | | | | | | | | | BETA: splitting (336) gives: % 149.51/21.67 | | | | | | | | | | | | | % 149.51/21.67 | | | | | | | | | | | | | Case 1: % 149.51/21.67 | | | | | | | | | | | | | | % 149.51/21.67 | | | | | | | | | | | | | | (8889) all_58_1 = e0 % 149.51/21.67 | | | | | | | | | | | | | | % 149.51/21.67 | | | | | | | | | | | | | | COMBINE_EQS: (8885), (8889) imply: % 149.51/21.67 | | | | | | | | | | | | | | (8890) e1 = e0 % 149.51/21.67 | | | | | | | | | | | | | | % 149.51/21.67 | | | | | | | | | | | | | | REDUCE: (4), (8890) imply: % 149.51/21.67 | | | | | | | | | | | | | | (8891) $false % 149.51/21.67 | | | | | | | | | | | | | | % 149.51/21.67 | | | | | | | | | | | | | | CLOSE: (8891) is inconsistent. % 149.51/21.67 | | | | | | | | | | | | | | % 149.51/21.67 | | | | | | | | | | | | | Case 2: % 149.51/21.67 | | | | | | | | | | | | | | % 149.51/21.67 | | | | | | | | | | | | | | (8892) all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0 % 149.51/21.67 | | | | | | | | | | | | | | % 149.51/21.67 | | | | | | | | | | | | | | REF_CLOSE: (549), (554), (7425), (8857), (8875), (8888), % 149.51/21.67 | | | | | | | | | | | | | | (8892) are inconsistent by sub-proof #45. % 149.51/21.67 | | | | | | | | | | | | | | % 149.51/21.67 | | | | | | | | | | | | | End of split % 149.51/21.67 | | | | | | | | | | | | | % 149.51/21.67 | | | | | | | | | | | | End of split % 149.51/21.67 | | | | | | | | | | | | % 149.51/21.67 | | | | | | | | | | | Case 2: % 149.51/21.67 | | | | | | | | | | | | % 149.51/21.67 | | | | | | | | | | | | (8893) all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1 % 149.51/21.67 | | | | | | | | | | | | % 149.51/21.67 | | | | | | | | | | | | BETA: splitting (8893) gives: % 149.51/21.67 | | | | | | | | | | | | % 149.51/21.67 | | | | | | | | | | | | Case 1: % 149.51/21.67 | | | | | | | | | | | | | % 149.51/21.67 | | | | | | | | | | | | | (8894) all_58_3 = e1 % 149.51/21.67 | | | | | | | | | | | | | % 149.51/21.67 | | | | | | | | | | | | | COMBINE_EQS: (554), (8894) imply: % 149.51/21.67 | | | | | | | | | | | | | (8895) all_8_2 = e1 % 149.51/21.67 | | | | | | | | | | | | | % 149.51/21.67 | | | | | | | | | | | | | REDUCE: (8873), (8895) imply: % 149.51/21.67 | | | | | | | | | | | | | (8896) $false % 149.51/21.67 | | | | | | | | | | | | | % 149.51/21.67 | | | | | | | | | | | | | CLOSE: (8896) is inconsistent. % 149.51/21.67 | | | | | | | | | | | | | % 149.51/21.67 | | | | | | | | | | | | Case 2: % 149.51/21.67 | | | | | | | | | | | | | % 149.51/21.67 | | | | | | | | | | | | | (8897) all_58_7 = e1 | all_58_13 = e1 % 149.51/21.67 | | | | | | | | | | | | | % 149.51/21.67 | | | | | | | | | | | | | BETA: splitting (7418) gives: % 149.51/21.67 | | | | | | | | | | | | | % 149.51/21.67 | | | | | | | | | | | | | Case 1: % 149.51/21.67 | | | | | | | | | | | | | | % 149.51/21.67 | | | | | | | | | | | | | | (8898) ~ (all_6_2 = e3) % 149.51/21.67 | | | | | | | | | | | | | | % 149.51/21.67 | | | | | | | | | | | | | | REF_CLOSE: (41), (242), (541), (622), (7420), (8517), (8860), % 149.51/21.67 | | | | | | | | | | | | | | (8898), (function-axioms) are inconsistent by % 149.51/21.67 | | | | | | | | | | | | | | sub-proof #77. % 149.51/21.67 | | | | | | | | | | | | | | % 149.51/21.67 | | | | | | | | | | | | | Case 2: % 149.51/21.67 | | | | | | | | | | | | | | % 149.51/21.67 | | | | | | | | | | | | | | (8899) ~ (all_6_0 = e0) % 149.51/21.67 | | | | | | | | | | | | | | % 149.51/21.67 | | | | | | | | | | | | | | BETA: splitting (243) gives: % 149.51/21.67 | | | | | | | | | | | | | | % 149.51/21.67 | | | | | | | | | | | | | | Case 1: % 149.51/21.67 | | | | | | | | | | | | | | | % 149.51/21.67 | | | | | | | | | | | | | | | (8900) all_54_9 = e3 % 149.51/21.67 | | | | | | | | | | | | | | | % 149.51/21.67 | | | | | | | | | | | | | | | COMBINE_EQS: (7423), (8900) imply: % 149.51/21.67 | | | | | | | | | | | | | | | (8901) all_6_0 = e3 % 149.51/21.67 | | | | | | | | | | | | | | | % 149.51/21.67 | | | | | | | | | | | | | | | REDUCE: (8513), (8901) imply: % 149.51/21.67 | | | | | | | | | | | | | | | (8902) $false % 149.51/21.67 | | | | | | | | | | | | | | | % 149.51/21.67 | | | | | | | | | | | | | | | CLOSE: (8902) is inconsistent. % 149.51/21.67 | | | | | | | | | | | | | | | % 149.51/21.67 | | | | | | | | | | | | | | Case 2: % 149.51/21.67 | | | | | | | | | | | | | | | % 149.51/21.67 | | | | | | | | | | | | | | | (8903) all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0 % 149.51/21.67 | | | | | | | | | | | | | | | % 149.51/21.67 | | | | | | | | | | | | | | | BETA: splitting (8903) gives: % 149.51/21.67 | | | | | | | | | | | | | | | % 149.51/21.67 | | | | | | | | | | | | | | | Case 1: % 149.51/21.67 | | | | | | | | | | | | | | | | % 149.51/21.67 | | | | | | | | | | | | | | | | (8904) all_54_9 = e2 % 149.51/21.67 | | | | | | | | | | | | | | | | % 149.51/21.67 | | | | | | | | | | | | | | | | COMBINE_EQS: (7423), (8904) imply: % 149.51/21.67 | | | | | | | | | | | | | | | | (8905) all_6_0 = e2 % 149.51/21.67 | | | | | | | | | | | | | | | | % 149.51/21.67 | | | | | | | | | | | | | | | | SIMP: (8905) implies: % 149.51/21.67 | | | | | | | | | | | | | | | | (8906) all_6_0 = e2 % 149.51/21.67 | | | | | | | | | | | | | | | | % 149.51/21.67 | | | | | | | | | | | | | | | | COMBINE_EQS: (7425), (8906) imply: % 149.51/21.67 | | | | | | | | | | | | | | | | (8907) all_58_7 = e2 % 149.51/21.67 | | | | | | | | | | | | | | | | % 149.51/21.67 | | | | | | | | | | | | | | | | BETA: splitting (8897) gives: % 149.51/21.67 | | | | | | | | | | | | | | | | % 149.51/21.67 | | | | | | | | | | | | | | | | Case 1: % 149.51/21.67 | | | | | | | | | | | | | | | | | % 149.51/21.67 | | | | | | | | | | | | | | | | | (8908) all_58_7 = e1 % 149.51/21.67 | | | | | | | | | | | | | | | | | % 149.51/21.67 | | | | | | | | | | | | | | | | | COMBINE_EQS: (8907), (8908) imply: % 149.51/21.67 | | | | | | | | | | | | | | | | | (8909) e2 = e1 % 149.51/21.67 | | | | | | | | | | | | | | | | | % 149.51/21.67 | | | | | | | | | | | | | | | | | REDUCE: (6), (8909) imply: % 149.51/21.67 | | | | | | | | | | | | | | | | | (8910) $false % 149.51/21.67 | | | | | | | | | | | | | | | | | % 149.51/21.67 | | | | | | | | | | | | | | | | | CLOSE: (8910) is inconsistent. % 149.51/21.67 | | | | | | | | | | | | | | | | | % 149.51/21.67 | | | | | | | | | | | | | | | | Case 2: % 149.51/21.67 | | | | | | | | | | | | | | | | | % 149.51/21.67 | | | | | | | | | | | | | | | | | (8911) all_58_13 = e1 % 149.51/21.67 | | | | | | | | | | | | | | | | | % 149.51/21.67 | | | | | | | | | | | | | | | | | COMBINE_EQS: (549), (8911) imply: % 149.51/21.67 | | | | | | | | | | | | | | | | | (8912) all_52_7 = e1 % 149.51/21.67 | | | | | | | | | | | | | | | | | % 149.51/21.67 | | | | | | | | | | | | | | | | | REDUCE: (8858), (8912) imply: % 149.51/21.67 | | | | | | | | | | | | | | | | | (8913) $false % 149.51/21.67 | | | | | | | | | | | | | | | | | % 149.51/21.67 | | | | | | | | | | | | | | | | | CLOSE: (8913) is inconsistent. % 149.51/21.67 | | | | | | | | | | | | | | | | | % 149.51/21.67 | | | | | | | | | | | | | | | | End of split % 149.51/21.67 | | | | | | | | | | | | | | | | % 149.51/21.67 | | | | | | | | | | | | | | | Case 2: % 149.51/21.67 | | | | | | | | | | | | | | | | % 149.51/21.67 | | | | | | | | | | | | | | | | (8914) all_54_9 = e1 | all_54_9 = e0 % 149.51/21.67 | | | | | | | | | | | | | | | | % 149.51/21.67 | | | | | | | | | | | | | | | | REF_CLOSE: (7423), (8884), (8899), (8914) are inconsistent by % 149.51/21.67 | | | | | | | | | | | | | | | | sub-proof #81. % 149.51/21.67 | | | | | | | | | | | | | | | | % 149.51/21.67 | | | | | | | | | | | | | | | End of split % 149.51/21.67 | | | | | | | | | | | | | | | % 149.51/21.67 | | | | | | | | | | | | | | End of split % 149.51/21.67 | | | | | | | | | | | | | | % 149.51/21.67 | | | | | | | | | | | | | End of split % 149.51/21.67 | | | | | | | | | | | | | % 149.51/21.67 | | | | | | | | | | | | End of split % 149.51/21.67 | | | | | | | | | | | | % 149.51/21.67 | | | | | | | | | | | End of split % 149.51/21.67 | | | | | | | | | | | % 149.51/21.67 | | | | | | | | | | End of split % 149.51/21.67 | | | | | | | | | | % 149.51/21.67 | | | | | | | | | Case 2: % 149.51/21.67 | | | | | | | | | | % 149.51/21.67 | | | | | | | | | | (8915) all_56_15 = e2 % 149.51/21.67 | | | | | | | | | | (8916) all_56_11 = e0 % 149.51/21.67 | | | | | | | | | | % 149.51/21.67 | | | | | | | | | | COMBINE_EQS: (545), (8916) imply: % 149.51/21.67 | | | | | | | | | | (8917) all_8_2 = e0 % 149.51/21.67 | | | | | | | | | | % 149.51/21.67 | | | | | | | | | | COMBINE_EQS: (443), (8915) imply: % 149.51/21.67 | | | | | | | | | | (8918) all_52_13 = e2 % 149.51/21.67 | | | | | | | | | | % 149.51/21.67 | | | | | | | | | | SIMP: (8918) implies: % 149.51/21.67 | | | | | | | | | | (8919) all_52_13 = e2 % 149.51/21.67 | | | | | | | | | | % 149.51/21.67 | | | | | | | | | | COMBINE_EQS: (386), (8919) imply: % 149.51/21.67 | | | | | | | | | | (8920) all_58_10 = e2 % 149.51/21.67 | | | | | | | | | | % 149.51/21.67 | | | | | | | | | | COMBINE_EQS: (554), (8917) imply: % 149.51/21.67 | | | | | | | | | | (8921) all_58_3 = e0 % 149.51/21.67 | | | | | | | | | | % 149.51/21.67 | | | | | | | | | | REDUCE: (8509), (8919) imply: % 149.51/21.67 | | | | | | | | | | (8922) ~ (all_8_0 = e2) % 149.51/21.67 | | | | | | | | | | % 149.51/21.67 | | | | | | | | | | SIMP: (8922) implies: % 149.51/21.67 | | | | | | | | | | (8923) ~ (all_8_0 = e2) % 149.51/21.67 | | | | | | | | | | % 149.51/21.67 | | | | | | | | | | REDUCE: (8510), (8917) imply: % 149.51/21.67 | | | | | | | | | | (8924) ~ (all_8_0 = e0) % 149.51/21.67 | | | | | | | | | | % 149.51/21.67 | | | | | | | | | | BETA: splitting (246) gives: % 149.51/21.67 | | | | | | | | | | % 149.51/21.67 | | | | | | | | | | Case 1: % 149.51/21.67 | | | | | | | | | | | % 149.51/21.67 | | | | | | | | | | | (8925) all_54_6 = e3 % 149.51/21.67 | | | | | | | | | | | % 149.51/21.67 | | | | | | | | | | | REF_CLOSE: (8502), (8515), (8925) are inconsistent by % 149.51/21.67 | | | | | | | | | | | sub-proof #145. % 149.51/21.67 | | | | | | | | | | | % 149.51/21.67 | | | | | | | | | | Case 2: % 149.51/21.67 | | | | | | | | | | | % 149.51/21.67 | | | | | | | | | | | (8926) all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0 % 149.51/21.67 | | | | | | | | | | | % 149.51/21.67 | | | | | | | | | | | BETA: splitting (8926) gives: % 149.51/21.67 | | | | | | | | | | | % 149.51/21.67 | | | | | | | | | | | Case 1: % 149.51/21.67 | | | | | | | | | | | | % 149.51/21.67 | | | | | | | | | | | | (8927) all_54_6 = e2 % 149.51/21.67 | | | | | | | | | | | | % 149.51/21.67 | | | | | | | | | | | | REF_CLOSE: (8502), (8923), (8927) are inconsistent by % 149.51/21.67 | | | | | | | | | | | | sub-proof #144. % 149.51/21.67 | | | | | | | | | | | | % 149.51/21.67 | | | | | | | | | | | Case 2: % 149.51/21.67 | | | | | | | | | | | | % 149.51/21.67 | | | | | | | | | | | | (8928) all_54_6 = e1 | all_54_6 = e0 % 149.51/21.67 | | | | | | | | | | | | % 149.51/21.67 | | | | | | | | | | | | BETA: splitting (8928) gives: % 149.51/21.67 | | | | | | | | | | | | % 149.51/21.67 | | | | | | | | | | | | Case 1: % 149.51/21.67 | | | | | | | | | | | | | % 149.51/21.67 | | | | | | | | | | | | | (8929) all_54_6 = e1 % 149.51/21.67 | | | | | | | | | | | | | % 149.51/21.67 | | | | | | | | | | | | | COMBINE_EQS: (8502), (8929) imply: % 149.51/21.67 | | | | | | | | | | | | | (8930) all_8_0 = e1 % 149.51/21.67 | | | | | | | | | | | | | % 149.51/21.67 | | | | | | | | | | | | | SIMP: (8930) implies: % 149.51/21.67 | | | | | | | | | | | | | (8931) all_8_0 = e1 % 149.51/21.67 | | | | | | | | | | | | | % 149.51/21.67 | | | | | | | | | | | | | COMBINE_EQS: (8504), (8931) imply: % 149.51/21.67 | | | | | | | | | | | | | (8932) all_58_5 = e1 % 149.51/21.67 | | | | | | | | | | | | | % 149.51/21.67 | | | | | | | | | | | | | REDUCE: (8505), (8931) imply: % 149.51/21.67 | | | | | | | | | | | | | (8933) ~ (all_52_1 = e1) % 149.51/21.67 | | | | | | | | | | | | | % 149.51/21.67 | | | | | | | | | | | | | REDUCE: (8866), (8931) imply: % 149.51/21.67 | | | | | | | | | | | | | (8934) ~ (all_4_1 = e1) % 149.51/21.67 | | | | | | | | | | | | | % 149.51/21.67 | | | | | | | | | | | | | SIMP: (8934) implies: % 149.51/21.67 | | | | | | | | | | | | | (8935) ~ (all_4_1 = e1) % 149.51/21.67 | | | | | | | | | | | | | % 149.51/21.67 | | | | | | | | | | | | | BETA: splitting (242) gives: % 149.51/21.67 | | | | | | | | | | | | | % 149.51/21.67 | | | | | | | | | | | | | Case 1: % 149.51/21.67 | | | | | | | | | | | | | | % 149.51/21.67 | | | | | | | | | | | | | | (8936) all_54_10 = e3 % 149.51/21.67 | | | | | | | | | | | | | | % 149.51/21.67 | | | | | | | | | | | | | | COMBINE_EQS: (8864), (8936) imply: % 149.51/21.67 | | | | | | | | | | | | | | (8937) all_4_1 = e3 % 149.51/21.67 | | | | | | | | | | | | | | % 149.51/21.67 | | | | | | | | | | | | | | COMBINE_EQS: (8865), (8937) imply: % 149.51/21.67 | | | | | | | | | | | | | | (8938) all_56_21 = e3 % 149.51/21.67 | | | | | | | | | | | | | | % 149.51/21.67 | | | | | | | | | | | | | | BETA: splitting (335) gives: % 149.51/21.67 | | | | | | | | | | | | | | % 149.51/21.67 | | | | | | | | | | | | | | Case 1: % 149.51/21.67 | | | | | | | | | | | | | | | % 149.51/21.67 | | | | | | | | | | | | | | | (8939) all_58_2 = e3 % 149.51/21.67 | | | | | | | | | | | | | | | % 149.51/21.67 | | | | | | | | | | | | | | | COMBINE_EQS: (401), (8939) imply: % 149.51/21.67 | | | | | | | | | | | | | | | (8940) all_52_1 = e3 % 149.51/21.67 | | | | | | | | | | | | | | | % 149.51/21.67 | | | | | | | | | | | | | | | REDUCE: (557), (8940) imply: % 149.51/21.67 | | | | | | | | | | | | | | | (8941) ~ (all_10_2 = e3) % 149.51/21.67 | | | | | | | | | | | | | | | % 149.51/21.67 | | | | | | | | | | | | | | | SIMP: (8941) implies: % 149.51/21.67 | | | | | | | | | | | | | | | (8942) ~ (all_10_2 = e3) % 149.51/21.67 | | | | | | | | | | | | | | | % 149.51/21.67 | | | | | | | | | | | | | | | BETA: splitting (287) gives: % 149.51/21.67 | | | | | | | | | | | | | | | % 149.51/21.67 | | | | | | | | | | | | | | | Case 1: % 149.51/21.67 | | | | | | | | | | | | | | | | % 149.51/21.67 | | | | | | | | | | | | | | | | (8943) all_56_1 = e3 % 149.51/21.67 | | | | | | | | | | | | | | | | % 149.51/21.67 | | | | | | | | | | | | | | | | COMBINE_EQS: (546), (8943) imply: % 149.51/21.67 | | | | | | | | | | | | | | | | (8944) all_10_2 = e3 % 149.51/21.67 | | | | | | | | | | | | | | | | % 149.51/21.67 | | | | | | | | | | | | | | | | REDUCE: (8942), (8944) imply: % 149.51/21.67 | | | | | | | | | | | | | | | | (8945) $false % 149.51/21.67 | | | | | | | | | | | | | | | | % 149.51/21.67 | | | | | | | | | | | | | | | | CLOSE: (8945) is inconsistent. % 149.51/21.67 | | | | | | | | | | | | | | | | % 149.51/21.67 | | | | | | | | | | | | | | | Case 2: % 149.51/21.67 | | | | | | | | | | | | | | | | % 149.51/21.67 | | | | | | | | | | | | | | | | (8946) all_56_11 = e2 | all_56_21 = e1 | all_56_31 = e0 % 149.51/21.67 | | | | | | | | | | | | | | | | % 149.51/21.67 | | | | | | | | | | | | | | | | BETA: splitting (8946) gives: % 149.51/21.67 | | | | | | | | | | | | | | | | % 149.51/21.67 | | | | | | | | | | | | | | | | Case 1: % 149.51/21.67 | | | | | | | | | | | | | | | | | % 149.51/21.67 | | | | | | | | | | | | | | | | | (8947) all_56_11 = e2 % 149.51/21.67 | | | | | | | | | | | | | | | | | % 149.51/21.67 | | | | | | | | | | | | | | | | | COMBINE_EQS: (8916), (8947) imply: % 149.51/21.67 | | | | | | | | | | | | | | | | | (8948) e2 = e0 % 149.51/21.67 | | | | | | | | | | | | | | | | | % 149.51/21.67 | | | | | | | | | | | | | | | | | REDUCE: (5), (8948) imply: % 149.51/21.67 | | | | | | | | | | | | | | | | | (8949) $false % 149.51/21.67 | | | | | | | | | | | | | | | | | % 149.51/21.67 | | | | | | | | | | | | | | | | | CLOSE: (8949) is inconsistent. % 149.51/21.67 | | | | | | | | | | | | | | | | | % 149.51/21.67 | | | | | | | | | | | | | | | | Case 2: % 149.51/21.67 | | | | | | | | | | | | | | | | | % 149.51/21.67 | | | | | | | | | | | | | | | | | (8950) all_56_21 = e1 | all_56_31 = e0 % 149.51/21.67 | | | | | | | | | | | | | | | | | % 149.51/21.67 | | | | | | | | | | | | | | | | | BETA: splitting (8950) gives: % 149.51/21.67 | | | | | | | | | | | | | | | | | % 149.51/21.67 | | | | | | | | | | | | | | | | | Case 1: % 149.51/21.67 | | | | | | | | | | | | | | | | | | % 149.51/21.67 | | | | | | | | | | | | | | | | | | (8951) all_56_21 = e1 % 149.51/21.67 | | | | | | | | | | | | | | | | | | % 149.51/21.67 | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (8938), (8951) are inconsistent by sub-proof % 149.51/21.67 | | | | | | | | | | | | | | | | | | #676. % 149.51/21.67 | | | | | | | | | | | | | | | | | | % 149.51/21.67 | | | | | | | | | | | | | | | | | Case 2: % 149.51/21.67 | | | | | | | | | | | | | | | | | | % 149.51/21.67 | | | | | | | | | | | | | | | | | | (8952) all_56_31 = e0 % 149.51/21.67 | | | | | | | | | | | | | | | | | | % 149.51/21.67 | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8852), (8952) are inconsistent by sub-proof % 149.51/21.67 | | | | | | | | | | | | | | | | | | #201. % 149.51/21.67 | | | | | | | | | | | | | | | | | | % 149.51/21.67 | | | | | | | | | | | | | | | | | End of split % 149.51/21.67 | | | | | | | | | | | | | | | | | % 149.51/21.67 | | | | | | | | | | | | | | | | End of split % 149.51/21.67 | | | | | | | | | | | | | | | | % 149.51/21.67 | | | | | | | | | | | | | | | End of split % 149.51/21.67 | | | | | | | | | | | | | | | % 149.51/21.67 | | | | | | | | | | | | | | Case 2: % 149.51/21.67 | | | | | | | | | | | | | | | % 149.51/21.67 | | | | | | | | | | | | | | | (8953) all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3 % 149.51/21.67 | | | | | | | | | | | | | | | % 149.51/21.67 | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (9), (8920), (8921), (8932), (8953) are % 149.51/21.67 | | | | | | | | | | | | | | | inconsistent by sub-proof #611. % 149.51/21.67 | | | | | | | | | | | | | | | % 149.51/21.67 | | | | | | | | | | | | | | End of split % 149.51/21.67 | | | | | | | | | | | | | | % 149.51/21.67 | | | | | | | | | | | | | Case 2: % 149.51/21.67 | | | | | | | | | | | | | | % 149.51/21.67 | | | | | | | | | | | | | | (8954) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 149.51/21.67 | | | | | | | | | | | | | | % 149.51/21.67 | | | | | | | | | | | | | | REF_CLOSE: (41), (541), (622), (7420), (8517), (8860), % 149.51/21.67 | | | | | | | | | | | | | | (8954), (function-axioms) are inconsistent by % 149.51/21.67 | | | | | | | | | | | | | | sub-proof #90. % 149.51/21.67 | | | | | | | | | | | | | | % 149.51/21.67 | | | | | | | | | | | | | End of split % 149.51/21.67 | | | | | | | | | | | | | % 149.51/21.67 | | | | | | | | | | | | Case 2: % 149.51/21.67 | | | | | | | | | | | | | % 149.51/21.67 | | | | | | | | | | | | | (8955) all_54_6 = e0 % 149.51/21.67 | | | | | | | | | | | | | % 149.51/21.67 | | | | | | | | | | | | | REF_CLOSE: (8502), (8924), (8955) are inconsistent by % 149.51/21.67 | | | | | | | | | | | | | sub-proof #143. % 149.51/21.67 | | | | | | | | | | | | | % 149.51/21.67 | | | | | | | | | | | | End of split % 149.51/21.67 | | | | | | | | | | | | % 149.51/21.67 | | | | | | | | | | | End of split % 149.51/21.67 | | | | | | | | | | | % 149.51/21.67 | | | | | | | | | | End of split % 149.51/21.67 | | | | | | | | | | % 149.51/21.67 | | | | | | | | | End of split % 149.51/21.67 | | | | | | | | | % 149.51/21.67 | | | | | | | | Case 2: % 149.51/21.67 | | | | | | | | | % 149.51/21.67 | | | | | | | | | (8956) all_56_13 = e2 % 149.51/21.67 | | | | | | | | | (8957) all_56_11 = e1 % 149.51/21.67 | | | | | | | | | % 149.51/21.67 | | | | | | | | | COMBINE_EQS: (545), (8957) imply: % 149.51/21.67 | | | | | | | | | (8958) all_8_2 = e1 % 149.51/21.67 | | | | | | | | | % 149.51/21.67 | | | | | | | | | COMBINE_EQS: (8503), (8956) imply: % 149.51/21.67 | | | | | | | | | (8959) all_8_0 = e2 % 149.51/21.67 | | | | | | | | | % 149.51/21.67 | | | | | | | | | SIMP: (8959) implies: % 149.51/21.67 | | | | | | | | | (8960) all_8_0 = e2 % 149.51/21.67 | | | | | | | | | % 149.51/21.67 | | | | | | | | | REDUCE: (8866), (8960) imply: % 149.51/21.67 | | | | | | | | | (8961) ~ (all_4_1 = e2) % 149.51/21.67 | | | | | | | | | % 149.51/21.67 | | | | | | | | | REDUCE: (8499), (8958) imply: % 149.51/21.67 | | | | | | | | | (8962) op(e1, e1) = e1 % 149.51/21.67 | | | | | | | | | % 149.51/21.67 | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_4_1, e1, % 149.51/21.67 | | | | | | | | | e1, e1, simplifying with (8862), (8962) gives: % 149.51/21.67 | | | | | | | | | (8963) all_4_1 = e1 % 149.51/21.67 | | | | | | | | | % 149.51/21.67 | | | | | | | | | REF_CLOSE: (8862), (8868), (8870), (8871), (8963), % 149.51/21.67 | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 149.51/21.67 | | | | | | | | | #54. % 149.51/21.67 | | | | | | | | | % 149.51/21.67 | | | | | | | | End of split % 149.51/21.67 | | | | | | | | % 149.51/21.67 | | | | | | | End of split % 149.51/21.67 | | | | | | | % 149.51/21.67 | | | | | | Case 2: % 149.51/21.67 | | | | | | | % 149.51/21.67 | | | | | | | (8964) all_56_21 = e2 % 149.51/21.67 | | | | | | | (8965) all_56_19 = e1 % 149.51/21.67 | | | | | | | % 149.51/21.67 | | | | | | | COMBINE_EQS: (7424), (8965) imply: % 149.51/21.67 | | | | | | | (8966) all_6_0 = e1 % 149.51/21.67 | | | | | | | % 149.51/21.67 | | | | | | | COMBINE_EQS: (374), (8964) imply: % 149.51/21.67 | | | | | | | (8967) all_6_2 = e2 % 149.51/21.67 | | | | | | | % 149.51/21.67 | | | | | | | REDUCE: (7433), (8966) imply: % 149.51/21.67 | | | | | | | (8968) ~ (all_8_2 = e1) % 149.51/21.67 | | | | | | | % 149.51/21.67 | | | | | | | REDUCE: (7420), (8967) imply: % 149.51/21.67 | | | | | | | (8969) op(e2, e2) = e2 % 149.51/21.67 | | | | | | | % 149.51/21.67 | | | | | | | REF_CLOSE: (46), (617), (8499), (8968), (8969), (function-axioms) % 149.51/21.67 | | | | | | | are inconsistent by sub-proof #147. % 149.51/21.67 | | | | | | | % 149.51/21.67 | | | | | | End of split % 149.51/21.67 | | | | | | % 149.51/21.67 | | | | | Case 2: % 149.51/21.67 | | | | | | % 149.51/21.67 | | | | | | (8970) all_48_0 = e3 % 149.51/21.67 | | | | | | (8971) ~ (all_48_1 = e1) | ~ (all_48_2 = e0) % 149.51/21.67 | | | | | | % 149.51/21.67 | | | | | | COMBINE_EQS: (765), (8970) imply: % 149.51/21.67 | | | | | | (8972) all_8_0 = e3 % 149.51/21.67 | | | | | | % 149.51/21.67 | | | | | | COMBINE_EQS: (8503), (8972) imply: % 149.51/21.67 | | | | | | (8973) all_56_13 = e3 % 149.51/21.67 | | | | | | % 149.51/21.67 | | | | | | REDUCE: (8510), (8972) imply: % 149.51/21.67 | | | | | | (8974) ~ (all_8_2 = e3) % 149.51/21.67 | | | | | | % 149.51/21.67 | | | | | | SIMP: (8974) implies: % 149.51/21.67 | | | | | | (8975) ~ (all_8_2 = e3) % 149.51/21.67 | | | | | | % 149.51/21.67 | | | | | | REF_CLOSE: (9), (46), (247), (295), (536), (542), (545), (617), % 149.51/21.67 | | | | | | (8498), (8499), (8971), (8973), (8975), (function-axioms) % 149.51/21.67 | | | | | | are inconsistent by sub-proof #116. % 149.51/21.67 | | | | | | % 149.51/21.67 | | | | | End of split % 149.51/21.67 | | | | | % 149.51/21.67 | | | | Case 2: % 149.51/21.67 | | | | | % 149.51/21.67 | | | | | (8976) all_18_0 = e3 % 149.51/21.67 | | | | | (8977) ~ (all_18_1 = e2) | ~ (all_18_2 = e0) % 149.51/21.67 | | | | | % 149.51/21.67 | | | | | COMBINE_EQS: (753), (8976) imply: % 149.51/21.67 | | | | | (8978) all_6_0 = e3 % 149.51/21.67 | | | | | % 149.51/21.67 | | | | | COMBINE_EQS: (7424), (8978) imply: % 149.51/21.67 | | | | | (8979) all_56_19 = e3 % 149.51/21.67 | | | | | % 149.51/21.67 | | | | | REDUCE: (7434), (8978) imply: % 149.51/21.67 | | | | | (8980) ~ (all_6_2 = e3) % 149.51/21.67 | | | | | % 149.51/21.67 | | | | | SIMP: (8980) implies: % 149.51/21.67 | | | | | (8981) ~ (all_6_2 = e3) % 149.51/21.67 | | | | | % 149.51/21.67 | | | | | REF_CLOSE: (8), (41), (242), (292), (374), (524), (541), (622), % 149.51/21.67 | | | | | (7419), (7420), (8977), (8979), (8981), (function-axioms) % 149.51/21.67 | | | | | are inconsistent by sub-proof #41. % 149.51/21.67 | | | | | % 149.51/21.67 | | | | End of split % 149.51/21.67 | | | | % 149.51/21.67 | | | End of split % 149.51/21.67 | | | % 149.51/21.67 | | End of split % 149.51/21.67 | | % 149.51/21.67 | Case 2: % 149.51/21.67 | | % 149.51/21.67 | | (8982) all_4_0 = e3 % 149.51/21.67 | | (8983) ~ (all_4_1 = e1) | ~ (all_4_2 = e2) % 149.51/21.67 | | % 149.51/21.67 | | COMBINE_EQS: (746), (8982) imply: % 149.51/21.67 | | (8984) all_20_0 = e3 % 149.51/21.67 | | % 149.51/21.67 | | REDUCE: (37), (8982) imply: % 149.51/21.67 | | (8985) op(e0, all_4_1) = e3 % 149.51/21.67 | | % 149.51/21.67 | | BETA: splitting (44) gives: % 149.51/21.67 | | % 149.51/21.67 | | Case 1: % 149.51/21.67 | | | % 149.51/21.67 | | | (8986) ~ (all_6_1 = e2) % 149.51/21.67 | | | % 149.51/21.67 | | | BETA: splitting (49) gives: % 149.51/21.67 | | | % 149.51/21.67 | | | Case 1: % 149.51/21.67 | | | | % 149.51/21.67 | | | | (8987) ~ (all_8_1 = e1) % 149.51/21.67 | | | | % 149.51/21.67 | | | | BETA: splitting (64) gives: % 149.51/21.67 | | | | % 149.51/21.67 | | | | Case 1: % 149.51/21.67 | | | | | % 149.51/21.67 | | | | | (8988) ~ (all_14_0 = e1) % 149.51/21.67 | | | | | % 149.51/21.67 | | | | | REDUCE: (758), (8988) imply: % 149.51/21.67 | | | | | (8989) ~ (all_8_0 = e1) % 149.51/21.67 | | | | | % 149.51/21.67 | | | | | BETA: splitting (79) gives: % 149.51/21.67 | | | | | % 149.51/21.67 | | | | | Case 1: % 149.51/21.67 | | | | | | % 149.51/21.67 | | | | | | (8990) ~ (all_20_0 = e3) % 149.51/21.67 | | | | | | % 149.51/21.67 | | | | | | REDUCE: (8984), (8990) imply: % 149.51/21.67 | | | | | | (8991) $false % 149.51/21.67 | | | | | | % 149.51/21.67 | | | | | | CLOSE: (8991) is inconsistent. % 149.51/21.67 | | | | | | % 149.51/21.67 | | | | | Case 2: % 149.51/21.67 | | | | | | % 149.51/21.67 | | | | | | (8992) ~ (all_20_1 = e2) | ~ (all_20_2 = e1) % 149.51/21.67 | | | | | | % 149.51/21.67 | | | | | | BETA: splitting (84) gives: % 149.51/21.67 | | | | | | % 149.51/21.67 | | | | | | Case 1: % 149.51/21.67 | | | | | | | % 149.51/21.67 | | | | | | | (8993) ~ (all_22_1 = e3) % 149.51/21.67 | | | | | | | % 149.51/21.67 | | | | | | | REDUCE: (672), (8993) imply: % 149.51/21.67 | | | | | | | (8994) ~ (all_8_1 = e3) % 149.51/21.67 | | | | | | | % 149.51/21.67 | | | | | | | BETA: splitting (99) gives: % 149.51/21.67 | | | | | | | % 149.51/21.67 | | | | | | | Case 1: % 149.51/21.67 | | | | | | | | % 149.51/21.67 | | | | | | | | (8995) ~ (all_28_0 = e2) % 149.51/21.67 | | | | | | | | % 149.51/21.67 | | | | | | | | REDUCE: (740), (8995) imply: % 149.51/21.67 | | | | | | | | (8996) ~ (all_6_0 = e2) % 149.51/21.67 | | | | | | | | % 149.51/21.67 | | | | | | | | BETA: splitting (119) gives: % 149.51/21.67 | | | | | | | | % 149.51/21.67 | | | | | | | | Case 1: % 149.51/21.67 | | | | | | | | | % 149.51/21.67 | | | | | | | | | (8997) ~ (all_36_1 = e3) % 149.51/21.67 | | | | | | | | | % 149.51/21.67 | | | | | | | | | REDUCE: (652), (8997) imply: % 149.51/21.67 | | | | | | | | | (8998) ~ (all_6_1 = e3) % 149.51/21.67 | | | | | | | | | % 149.51/21.67 | | | | | | | | | BETA: splitting (288) gives: % 149.51/21.67 | | | | | | | | | % 149.51/21.67 | | | | | | | | | Case 1: % 149.51/21.67 | | | | | | | | | | % 149.51/21.67 | | | | | | | | | | (8999) ~ (all_56_31 = e1) % 149.51/21.67 | | | | | | | | | | % 149.51/21.67 | | | | | | | | | | REDUCE: (544), (8999) imply: % 149.51/21.67 | | | | | | | | | | (9000) ~ (all_4_2 = e1) % 149.51/21.67 | | | | | | | | | | % 149.51/21.67 | | | | | | | | | | BETA: splitting (292) gives: % 149.51/21.67 | | | | | | | | | | % 149.51/21.67 | | | | | | | | | | Case 1: % 149.51/21.67 | | | | | | | | | | | % 149.51/21.67 | | | | | | | | | | | (9001) ~ (all_56_21 = e2) % 149.51/21.67 | | | | | | | | | | | % 149.51/21.67 | | | | | | | | | | | REDUCE: (374), (9001) imply: % 149.51/21.67 | | | | | | | | | | | (9002) ~ (all_6_2 = e2) % 149.51/21.67 | | | | | | | | | | | % 149.51/21.67 | | | | | | | | | | | BETA: splitting (294) gives: % 149.51/21.67 | | | | | | | | | | | % 149.51/21.67 | | | | | | | | | | | Case 1: % 149.51/21.67 | | | | | | | | | | | | % 149.51/21.67 | | | | | | | | | | | | (9003) ~ (all_56_11 = e0) % 149.51/21.67 | | | | | | | | | | | | % 149.51/21.67 | | | | | | | | | | | | REDUCE: (545), (9003) imply: % 149.51/21.67 | | | | | | | | | | | | (9004) ~ (all_8_2 = e0) % 149.51/21.67 | | | | | | | | | | | | % 149.51/21.67 | | | | | | | | | | | | BETA: splitting (295) gives: % 149.51/21.67 | | | | | | | | | | | | % 149.51/21.67 | | | | | | | | | | | | Case 1: % 149.51/21.67 | | | | | | | | | | | | | % 149.51/21.67 | | | | | | | | | | | | | (9005) ~ (all_56_11 = e1) % 149.51/21.67 | | | | | | | | | | | | | % 149.51/21.67 | | | | | | | | | | | | | REDUCE: (545), (9005) imply: % 149.51/21.67 | | | | | | | | | | | | | (9006) ~ (all_8_2 = e1) % 149.51/21.67 | | | | | | | | | | | | | % 149.51/21.67 | | | | | | | | | | | | | BETA: splitting (293) gives: % 149.51/21.67 | | | | | | | | | | | | | % 149.51/21.67 | | | | | | | | | | | | | Case 1: % 149.51/21.67 | | | | | | | | | | | | | | % 149.51/21.67 | | | | | | | | | | | | | | (9007) ~ (all_56_21 = e3) % 149.51/21.67 | | | | | | | | | | | | | | % 149.51/21.67 | | | | | | | | | | | | | | REDUCE: (374), (9007) imply: % 149.51/21.67 | | | | | | | | | | | | | | (9008) ~ (all_6_2 = e3) % 149.51/21.67 | | | | | | | | | | | | | | % 149.51/21.67 | | | | | | | | | | | | | | REF_CLOSE: (7), (36), (38), (43), (46), (51), (166), (168), % 149.51/21.67 | | | | | | | | | | | | | | (169), (171), (173), (174), (181), (182), (183), % 149.51/21.67 | | | | | | | | | | | | | | (187), (188), (194), (196), (205), (206), (207), % 149.51/21.67 | | | | | | | | | | | | | | (237), (238), (240), (241), (242), (246), (247), % 149.51/21.67 | | | | | | | | | | | | | | (250), (251), (252), (289), (290), (291), (296), % 149.51/21.67 | | | | | | | | | | | | | | (298), (299), (318), (321), (328), (330), (331), % 149.51/21.67 | | | | | | | | | | | | | | (333), (336), (343), (345), (360), (365), (366), % 149.51/21.67 | | | | | | | | | | | | | | (374), (380), (386), (389), (401), (407), (408), % 149.51/21.67 | | | | | | | | | | | | | | (419), (425), (429), (447), (457), (459), (467), % 149.51/21.67 | | | | | | | | | | | | | | (476), (478), (482), (540), (541), (542), (543), % 149.51/21.67 | | | | | | | | | | | | | | (544), (545), (546), (547), (548), (549), (550), % 149.51/21.67 | | | | | | | | | | | | | | (551), (552), (554), (555), (557), (561), (563), % 149.51/21.67 | | | | | | | | | | | | | | (565), (567), (568), (570), (571), (575), (577), % 149.51/21.67 | | | | | | | | | | | | | | (582), (583), (585), (587), (588), (591), (625), % 149.51/21.67 | | | | | | | | | | | | | | (626), (627), (8985), (8986), (8998), (9000), % 149.51/21.67 | | | | | | | | | | | | | | (9002), (9004), (9006), (9008), (function-axioms) % 149.51/21.67 | | | | | | | | | | | | | | are inconsistent by sub-proof #20. % 149.51/21.67 | | | | | | | | | | | | | | % 149.51/21.67 | | | | | | | | | | | | | Case 2: % 149.51/21.67 | | | | | | | | | | | | | | % 149.51/21.67 | | | | | | | | | | | | | | (9009) all_56_21 = e3 % 149.51/21.67 | | | | | | | | | | | | | | (9010) all_56_17 = e1 % 149.51/21.67 | | | | | | | | | | | | | | % 149.51/21.67 | | | | | | | | | | | | | | COMBINE_EQS: (381), (9010) imply: % 149.51/21.67 | | | | | | | | | | | | | | (9011) all_52_2 = e1 % 149.51/21.67 | | | | | | | | | | | | | | % 149.51/21.67 | | | | | | | | | | | | | | COMBINE_EQS: (374), (9009) imply: % 149.51/21.67 | | | | | | | | | | | | | | (9012) all_6_2 = e3 % 149.51/21.67 | | | | | | | | | | | | | | % 149.51/21.67 | | | | | | | | | | | | | | SIMP: (9012) implies: % 149.51/21.67 | | | | | | | | | | | | | | (9013) all_6_2 = e3 % 149.51/21.67 | | | | | | | | | | | | | | % 149.51/21.67 | | | | | | | | | | | | | | REDUCE: (191), (9011) imply: % 149.51/21.67 | | | | | | | | | | | | | | (9014) ~ (all_52_6 = e1) % 149.51/21.67 | | | | | | | | | | | | | | % 149.51/21.67 | | | | | | | | | | | | | | SIMP: (9014) implies: % 149.51/21.67 | | | | | | | | | | | | | | (9015) ~ (all_52_6 = e1) % 149.51/21.67 | | | | | | | | | | | | | | % 149.51/21.67 | | | | | | | | | | | | | | REDUCE: (189), (9011) imply: % 149.51/21.67 | | | | | | | | | | | | | | (9016) ~ (all_52_14 = e1) % 149.51/21.67 | | | | | | | | | | | | | | % 149.51/21.67 | | | | | | | | | | | | | | SIMP: (9016) implies: % 149.51/21.67 | | | | | | | | | | | | | | (9017) ~ (all_52_14 = e1) % 149.51/21.67 | | | | | | | | | | | | | | % 149.51/21.67 | | | | | | | | | | | | | | REDUCE: (559), (9011) imply: % 149.51/21.67 | | | | | | | | | | | | | | (9018) ~ (all_10_2 = e1) % 149.51/21.67 | | | | | | | | | | | | | | % 149.51/21.67 | | | | | | | | | | | | | | SIMP: (9018) implies: % 149.51/21.67 | | | | | | | | | | | | | | (9019) ~ (all_10_2 = e1) % 149.51/21.67 | | | | | | | | | | | | | | % 149.51/21.67 | | | | | | | | | | | | | | REDUCE: (569), (9011), (9013) imply: % 149.51/21.67 | | | | | | | | | | | | | | (9020) ~ (e3 = e1) % 149.51/21.67 | | | | | | | | | | | | | | % 149.51/21.67 | | | | | | | | | | | | | | REDUCE: (580), (9013) imply: % 149.51/21.67 | | | | | | | | | | | | | | (9021) ~ (all_52_6 = e3) % 149.51/21.67 | | | | | | | | | | | | | | % 149.51/21.67 | | | | | | | | | | | | | | REDUCE: (43), (9013) imply: % 149.51/21.67 | | | | | | | | | | | | | | (9022) op(e3, e3) = all_6_1 % 149.51/21.67 | | | | | | | | | | | | | | % 149.51/21.67 | | | | | | | | | | | | | | REF_CLOSE: (8), (42), (51), (158), (160), (161), (174), % 149.51/21.67 | | | | | | | | | | | | | | (208), (241), (243), (252), (287), (297), (321), % 149.51/21.67 | | | | | | | | | | | | | | (332), (386), (389), (401), (402), (473), (476), % 149.51/21.67 | | | | | | | | | | | | | | (543), (544), (545), (546), (547), (550), (551), % 149.51/21.67 | | | | | | | | | | | | | | (554), (557), (573), (591), (621), (8986), (8996), % 149.51/21.67 | | | | | | | | | | | | | | (8998), (9000), (9004), (9009), (9015), (9017), % 149.51/21.67 | | | | | | | | | | | | | | (9019), (9021), (9022), (function-axioms) are % 149.51/21.67 | | | | | | | | | | | | | | inconsistent by sub-proof #294. % 149.51/21.67 | | | | | | | | | | | | | | % 149.51/21.67 | | | | | | | | | | | | | End of split % 149.51/21.67 | | | | | | | | | | | | | % 149.51/21.67 | | | | | | | | | | | | Case 2: % 149.51/21.67 | | | | | | | | | | | | | % 149.51/21.67 | | | | | | | | | | | | | (9023) all_56_13 = e2 % 149.51/21.67 | | | | | | | | | | | | | (9024) all_56_11 = e1 % 149.51/21.67 | | | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | | | | COMBINE_EQS: (545), (9024) imply: % 149.51/21.68 | | | | | | | | | | | | | (9025) all_8_2 = e1 % 149.51/21.68 | | | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | | | | COMBINE_EQS: (431), (9023) imply: % 149.51/21.68 | | | | | | | | | | | | | (9026) all_52_9 = e2 % 149.51/21.68 | | | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | | | | REDUCE: (583), (9026) imply: % 149.51/21.68 | | | | | | | | | | | | | (9027) ~ (all_6_2 = e2) % 149.51/21.68 | | | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | | | | REDUCE: (48), (9025) imply: % 149.51/21.68 | | | | | | | | | | | | | (9028) op(e1, e1) = all_8_1 % 149.51/21.68 | | | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_6_2, % 149.51/21.68 | | | | | | | | | | | | | all_8_1, e1, e1, simplifying with (41), (9028) % 149.51/21.68 | | | | | | | | | | | | | gives: % 149.51/21.68 | | | | | | | | | | | | | (9029) all_8_1 = all_6_2 % 149.51/21.68 | | | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | | | | REDUCE: (8994), (9029) imply: % 149.51/21.68 | | | | | | | | | | | | | (9030) ~ (all_6_2 = e3) % 149.51/21.68 | | | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | | | | REDUCE: (8987), (9029) imply: % 149.51/21.68 | | | | | | | | | | | | | (9031) ~ (all_6_2 = e1) % 149.51/21.68 | | | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | | | | BETA: splitting (242) gives: % 149.51/21.68 | | | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | | | | Case 1: % 149.51/21.68 | | | | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | | | | | (9032) all_54_10 = e3 % 149.51/21.68 | | | | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | | | | | REF_CLOSE: (541), (9030), (9032) are inconsistent by % 149.51/21.68 | | | | | | | | | | | | | | sub-proof #736. % 149.51/21.68 | | | | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | | | | Case 2: % 149.51/21.68 | | | | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | | | | | (9033) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 149.51/21.68 | | | | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | | | | | REF_CLOSE: (36), (38), (43), (237), (291), (366), (374), % 149.51/21.68 | | | | | | | | | | | | | | (540), (541), (591), (627), (8985), (8986), % 149.51/21.68 | | | | | | | | | | | | | | (8998), (9002), (9031), (9033), (function-axioms) % 149.51/21.68 | | | | | | | | | | | | | | are inconsistent by sub-proof #19. % 149.51/21.68 | | | | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | | | | End of split % 149.51/21.68 | | | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | | | End of split % 149.51/21.68 | | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | | Case 2: % 149.51/21.68 | | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | | | (9034) all_56_15 = e2 % 149.51/21.68 | | | | | | | | | | | | (9035) all_56_11 = e0 % 149.51/21.68 | | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | | | COMBINE_EQS: (545), (9035) imply: % 149.51/21.68 | | | | | | | | | | | | (9036) all_8_2 = e0 % 149.51/21.68 | | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | | | COMBINE_EQS: (443), (9034) imply: % 149.51/21.68 | | | | | | | | | | | | (9037) all_52_13 = e2 % 149.51/21.68 | | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | | | REDUCE: (590), (9037) imply: % 149.51/21.68 | | | | | | | | | | | | (9038) ~ (all_4_2 = e2) % 149.51/21.68 | | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | | | SIMP: (9038) implies: % 149.51/21.68 | | | | | | | | | | | | (9039) ~ (all_4_2 = e2) % 149.51/21.68 | | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | | | REDUCE: (48), (9036) imply: % 149.51/21.68 | | | | | | | | | | | | (9040) op(e0, e0) = all_8_1 % 149.51/21.68 | | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_4_2, % 149.51/21.68 | | | | | | | | | | | | all_8_1, e0, e0, simplifying with (36), (9040) % 149.51/21.68 | | | | | | | | | | | | gives: % 149.51/21.68 | | | | | | | | | | | | (9041) all_8_1 = all_4_2 % 149.51/21.68 | | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | | | REF_CLOSE: (38), (237), (540), (627), (8985), (8987), (8994), % 149.51/21.68 | | | | | | | | | | | | (9039), (9040), (9041), (function-axioms) are % 149.51/21.68 | | | | | | | | | | | | inconsistent by sub-proof #18. % 149.51/21.68 | | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | | End of split % 149.51/21.68 | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | Case 2: % 149.51/21.68 | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | | (9042) all_56_21 = e2 % 149.51/21.68 | | | | | | | | | | | (9043) all_56_19 = e1 % 149.51/21.68 | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | | COMBINE_EQS: (435), (9043) imply: % 149.51/21.68 | | | | | | | | | | | (9044) all_52_6 = e1 % 149.51/21.68 | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | | SIMP: (9044) implies: % 149.51/21.68 | | | | | | | | | | | (9045) all_52_6 = e1 % 149.51/21.68 | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | | COMBINE_EQS: (374), (9042) imply: % 149.51/21.68 | | | | | | | | | | | (9046) all_6_2 = e2 % 149.51/21.68 | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | | SIMP: (9046) implies: % 149.51/21.68 | | | | | | | | | | | (9047) all_6_2 = e2 % 149.51/21.68 | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | | REDUCE: (174), (9045) imply: % 149.51/21.68 | | | | | | | | | | | (9048) ~ (all_52_14 = e1) % 149.51/21.68 | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | | SIMP: (9048) implies: % 149.51/21.68 | | | | | | | | | | | (9049) ~ (all_52_14 = e1) % 149.51/21.68 | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | | REDUCE: (573), (9045) imply: % 149.51/21.68 | | | | | | | | | | | (9050) ~ (all_8_2 = e1) % 149.51/21.68 | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | | SIMP: (9050) implies: % 149.51/21.68 | | | | | | | | | | | (9051) ~ (all_8_2 = e1) % 149.51/21.68 | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | | REDUCE: (580), (9045), (9047) imply: % 149.51/21.68 | | | | | | | | | | | (9052) ~ (e2 = e1) % 149.51/21.68 | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | | REDUCE: (43), (9047) imply: % 149.51/21.68 | | | | | | | | | | | (9053) op(e2, e2) = all_6_1 % 149.51/21.68 | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_8_2, % 149.51/21.68 | | | | | | | | | | | all_6_1, e2, e2, simplifying with (46), (9053) % 149.51/21.68 | | | | | | | | | | | gives: % 149.51/21.68 | | | | | | | | | | | (9054) all_8_2 = all_6_1 % 149.51/21.68 | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | | COMBINE_EQS: (542), (9054) imply: % 149.51/21.68 | | | | | | | | | | | (9055) all_54_5 = all_6_1 % 149.51/21.68 | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | | COMBINE_EQS: (545), (9054) imply: % 149.51/21.68 | | | | | | | | | | | (9056) all_56_11 = all_6_1 % 149.51/21.68 | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | | REDUCE: (571), (9054) imply: % 149.51/21.68 | | | | | | | | | | | (9057) ~ (all_52_4 = all_6_1) % 149.51/21.68 | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | | REDUCE: (9051), (9054) imply: % 149.51/21.68 | | | | | | | | | | | (9058) ~ (all_6_1 = e1) % 149.51/21.68 | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | | REDUCE: (48), (9054) imply: % 149.51/21.68 | | | | | | | | | | | (9059) op(all_6_1, all_6_1) = all_8_1 % 149.51/21.68 | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | | BETA: splitting (247) gives: % 149.51/21.68 | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | | Case 1: % 149.51/21.68 | | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | | | (9060) all_54_5 = e3 % 149.51/21.68 | | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | | | REF_CLOSE: (8998), (9055), (9060) are inconsistent by % 149.51/21.68 | | | | | | | | | | | | sub-proof #509. % 149.51/21.68 | | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | | Case 2: % 149.51/21.68 | | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | | | (9061) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 149.51/21.68 | | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | | | BETA: splitting (9061) gives: % 149.51/21.68 | | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | | | Case 1: % 149.51/21.68 | | | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | | | | (9062) all_54_5 = e2 % 149.51/21.68 | | | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | | | | REF_CLOSE: (8986), (9055), (9062) are inconsistent by % 149.51/21.68 | | | | | | | | | | | | | sub-proof #466. % 149.51/21.68 | | | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | | | Case 2: % 149.51/21.68 | | | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | | | | (9063) all_54_5 = e1 | all_54_5 = e0 % 149.51/21.68 | | | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | | | | BETA: splitting (9063) gives: % 149.51/21.68 | | | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | | | | Case 1: % 149.51/21.68 | | | | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | | | | | (9064) all_54_5 = e1 % 149.51/21.68 | | | | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | | | | | REF_CLOSE: (9055), (9058), (9064) are inconsistent by % 149.51/21.68 | | | | | | | | | | | | | | sub-proof #465. % 149.51/21.68 | | | | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | | | | Case 2: % 149.51/21.68 | | | | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | | | | | (9065) all_54_5 = e0 % 149.51/21.68 | | | | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | | | | | COMBINE_EQS: (9055), (9065) imply: % 149.51/21.68 | | | | | | | | | | | | | | (9066) all_6_1 = e0 % 149.51/21.68 | | | | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | | | | | SIMP: (9066) implies: % 149.51/21.68 | | | | | | | | | | | | | | (9067) all_6_1 = e0 % 149.51/21.68 | | | | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | | | | | COMBINE_EQS: (9056), (9067) imply: % 149.51/21.68 | | | | | | | | | | | | | | (9068) all_56_11 = e0 % 149.51/21.68 | | | | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | | | | | REDUCE: (9057), (9067) imply: % 149.51/21.68 | | | | | | | | | | | | | | (9069) ~ (all_52_4 = e0) % 149.51/21.68 | | | | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | | | | | REDUCE: (9058), (9067) imply: % 149.51/21.68 | | | | | | | | | | | | | | (9070) ~ (e1 = e0) % 149.51/21.68 | | | | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | | | | | REDUCE: (9059), (9067) imply: % 149.51/21.68 | | | | | | | | | | | | | | (9071) op(e0, e0) = all_8_1 % 149.51/21.68 | | | | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | | | | | BETA: splitting (294) gives: % 149.51/21.68 | | | | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | | | | | Case 1: % 149.51/21.68 | | | | | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | | | | | | (9072) ~ (all_56_11 = e0) % 149.51/21.68 | | | | | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | | | | | | REDUCE: (9068), (9072) imply: % 149.51/21.68 | | | | | | | | | | | | | | | (9073) $false % 149.51/21.68 | | | | | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | | | | | | CLOSE: (9073) is inconsistent. % 149.51/21.68 | | | | | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | | | | | Case 2: % 149.51/21.68 | | | | | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | | | | | | (9074) all_56_15 = e2 % 149.51/21.68 | | | | | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | | | | | | COMBINE_EQS: (443), (9074) imply: % 149.51/21.68 | | | | | | | | | | | | | | | (9075) all_52_13 = e2 % 149.51/21.68 | | | | | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | | | | | | COMBINE_EQS: (386), (9075) imply: % 149.51/21.68 | | | | | | | | | | | | | | | (9076) all_58_10 = e2 % 149.51/21.68 | | | | | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | | | | | | REDUCE: (590), (9075) imply: % 149.51/21.68 | | | | | | | | | | | | | | | (9077) ~ (all_4_2 = e2) % 149.51/21.68 | | | | | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | | | | | | SIMP: (9077) implies: % 149.51/21.68 | | | | | | | | | | | | | | | (9078) ~ (all_4_2 = e2) % 149.51/21.68 | | | | | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | | | | | | BETA: splitting (321) gives: % 149.51/21.68 | | | | | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | | | | | | Case 1: % 149.51/21.68 | | | | | | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | | | | | | | (9079) all_58_9 = e1 % 149.51/21.68 | | | | | | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | | | | | | | COMBINE_EQS: (551), (9079) imply: % 149.51/21.68 | | | | | | | | | | | | | | | | (9080) all_52_12 = e1 % 149.51/21.68 | | | | | | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | | | | | | | COMBINE_EQS: (402), (9080) imply: % 149.51/21.68 | | | | | | | | | | | | | | | | (9081) all_56_7 = e1 % 149.51/21.68 | | | | | | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | | | | | | | BETA: splitting (297) gives: % 149.51/21.68 | | | | | | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | | | | | | | Case 1: % 149.51/21.68 | | | | | | | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | | | | | | | | (9082) ~ (all_56_1 = e0) % 149.51/21.68 | | | | | | | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | | | | | | | | REDUCE: (546), (9082) imply: % 149.51/21.68 | | | | | | | | | | | | | | | | | (9083) ~ (all_10_2 = e0) % 149.51/21.68 | | | | | | | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | | | | | | | | BETA: splitting (341) gives: % 149.51/21.68 | | | | | | | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | | | | | | | | Case 1: % 149.51/21.68 | | | | | | | | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | | | | | | | | | (9084) all_58_0 = e0 % 149.51/21.68 | | | | | | | | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (419), (9084) imply: % 149.51/21.68 | | | | | | | | | | | | | | | | | | (9085) all_10_2 = e0 % 149.51/21.68 | | | | | | | | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | | | | | | | | | REDUCE: (9083), (9085) imply: % 149.51/21.68 | | | | | | | | | | | | | | | | | | (9086) $false % 149.51/21.68 | | | | | | | | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | | | | | | | | | CLOSE: (9086) is inconsistent. % 149.51/21.68 | | | | | | | | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | | | | | | | | Case 2: % 149.51/21.68 | | | | | | | | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | | | | | | | | | (9087) all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0 % 149.51/21.68 | | | | | | | | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | | | | | | | | | BETA: splitting (9087) gives: % 149.51/21.68 | | | | | | | | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | | | | | | | | | Case 1: % 149.51/21.68 | | | | | | | | | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | | | | | | | | | | (9088) all_58_1 = e0 % 149.51/21.68 | | | | | | | | | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (555), (9088) imply: % 149.51/21.68 | | | | | | | | | | | | | | | | | | | (9089) all_52_4 = e0 % 149.51/21.68 | | | | | | | | | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | | | | | | | | | | REDUCE: (9069), (9089) imply: % 149.51/21.68 | | | | | | | | | | | | | | | | | | | (9090) $false % 149.51/21.68 | | | | | | | | | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | | | | | | | | | | CLOSE: (9090) is inconsistent. % 149.51/21.68 | | | | | | | | | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | | | | | | | | | Case 2: % 149.51/21.68 | | | | | | | | | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | | | | | | | | | | (9091) all_58_4 = e0 | all_58_9 = e0 % 149.51/21.68 | | | | | | | | | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | | | | | | | | | | BETA: splitting (9091) gives: % 149.51/21.68 | | | | | | | | | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | | | | | | | | | | Case 1: % 149.51/21.68 | | | | | | | | | | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_4_2, % 149.51/21.68 | | | | | | | | | | | | | | | | | | | | all_8_1, e0, e0, simplifying with (36), (9071) % 149.51/21.68 | | | | | | | | | | | | | | | | | | | | gives: % 149.51/21.68 | | | | | | | | | | | | | | | | | | | | (9092) all_8_1 = all_4_2 % 149.51/21.68 | | | | | | | | | | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (38), (237), (540), (627), (8985), (8987), (8994), % 149.51/21.68 | | | | | | | | | | | | | | | | | | | | (9071), (9078), (9092), (function-axioms) are % 149.51/21.68 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #18. % 149.51/21.68 | | | | | | | | | | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | | | | | | | | | | Case 2: % 149.51/21.68 | | | | | | | | | | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | | | | | | | | | | | (9093) all_58_9 = e0 % 149.51/21.68 | | | | | | | | | | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (9079), (9093) imply: % 149.51/21.68 | | | | | | | | | | | | | | | | | | | | (9094) e1 = e0 % 149.51/21.68 | | | | | | | | | | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | | | | | | | | | | | REDUCE: (4), (9094) imply: % 149.51/21.68 | | | | | | | | | | | | | | | | | | | | (9095) $false % 149.51/21.68 | | | | | | | | | | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | | | | | | | | | | | CLOSE: (9095) is inconsistent. % 149.51/21.68 | | | | | | | | | | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | | | | | | | | | | End of split % 149.51/21.68 | | | | | | | | | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | | | | | | | | | End of split % 149.51/21.68 | | | | | | | | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | | | | | | | | End of split % 149.51/21.68 | | | | | | | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | | | | | | | Case 2: % 149.51/21.68 | | | | | | | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | | | | | | | | (9096) all_56_7 = e3 % 149.51/21.68 | | | | | | | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9081), (9096) are inconsistent by sub-proof % 149.51/21.68 | | | | | | | | | | | | | | | | | #497. % 149.51/21.68 | | | | | | | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | | | | | | | End of split % 149.51/21.68 | | | | | | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | | | | | | Case 2: % 149.51/21.68 | | | | | | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | | | | | | | (9097) all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1 % 149.51/21.68 | | | | | | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | | | | | | | REF_CLOSE: (6), (547), (550), (9000), (9049), (9076), (9097) % 149.51/21.68 | | | | | | | | | | | | | | | | are inconsistent by sub-proof #370. % 149.51/21.68 | | | | | | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | | | | | | End of split % 149.51/21.68 | | | | | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | | | | | End of split % 149.51/21.68 | | | | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | | | | End of split % 149.51/21.68 | | | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | | | End of split % 149.51/21.68 | | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | | End of split % 149.51/21.68 | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | End of split % 149.51/21.68 | | | | | | | | | | % 149.51/21.68 | | | | | | | | | Case 2: % 149.51/21.68 | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | (9098) all_56_31 = e1 % 149.51/21.68 | | | | | | | | | | (9099) all_56_29 = e0 % 149.51/21.68 | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | REF_CLOSE: (6), (7), (36), (38), (41), (43), (48), (51), % 149.51/21.68 | | | | | | | | | | (192), (205), (207), (242), (287), (293), (294), % 149.51/21.68 | | | | | | | | | | (319), (357), (365), (374), (381), (499), (541), % 149.51/21.68 | | | | | | | | | | (544), (545), (546), (547), (548), (549), (561), % 149.51/21.68 | | | | | | | | | | (575), (585), (588), (627), (676), (8985), (8987), % 149.51/21.68 | | | | | | | | | | (8992), (9098), (9099), (function-axioms) are % 149.51/21.68 | | | | | | | | | | inconsistent by sub-proof #13. % 149.51/21.68 | | | | | | | | | | % 149.51/21.68 | | | | | | | | | End of split % 149.51/21.68 | | | | | | | | | % 149.51/21.68 | | | | | | | | Case 2: % 149.51/21.68 | | | | | | | | | % 149.51/21.68 | | | | | | | | | (9100) all_36_1 = e3 % 149.51/21.68 | | | | | | | | | (9101) ~ (all_36_0 = e0) | ~ (all_36_2 = e2) % 149.51/21.68 | | | | | | | | | % 149.51/21.68 | | | | | | | | | COMBINE_EQS: (652), (9100) imply: % 149.51/21.68 | | | | | | | | | (9102) all_6_1 = e3 % 149.51/21.68 | | | | | | | | | % 149.51/21.68 | | | | | | | | | SIMP: (9102) implies: % 149.51/21.68 | | | | | | | | | (9103) all_6_1 = e3 % 149.51/21.68 | | | | | | | | | % 149.51/21.68 | | | | | | | | | REDUCE: (43), (9103) imply: % 149.51/21.68 | | | | | | | | | (9104) op(all_6_2, all_6_2) = e3 % 149.51/21.68 | | | | | | | | | % 149.51/21.68 | | | | | | | | | REDUCE: (42), (9103) imply: % 149.51/21.68 | | | | | | | | | (9105) op(e1, e3) = all_6_0 % 149.51/21.68 | | | | | | | | | % 149.51/21.68 | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_2, % 149.51/21.68 | | | | | | | | | all_6_0, e3, e1, simplifying with (211), (9105) % 149.51/21.68 | | | | | | | | | gives: % 149.51/21.68 | | | | | | | | | (9106) all_52_2 = all_6_0 % 149.51/21.68 | | | | | | | | | % 149.51/21.68 | | | | | | | | | COMBINE_EQS: (471), (9106) imply: % 149.51/21.68 | | | | | | | | | (9107) all_54_8 = all_6_0 % 149.51/21.68 | | | | | | | | | % 149.51/21.68 | | | | | | | | | COMBINE_EQS: (553), (9106) imply: % 149.51/21.68 | | | | | | | | | (9108) all_58_6 = all_6_0 % 149.51/21.68 | | | | | | | | | % 149.51/21.68 | | | | | | | | | REDUCE: (192), (9106) imply: % 149.51/21.68 | | | | | | | | | (9109) ~ (all_52_3 = all_6_0) % 149.51/21.68 | | | | | | | | | % 149.51/21.68 | | | | | | | | | SIMP: (9109) implies: % 149.51/21.68 | | | | | | | | | (9110) ~ (all_52_3 = all_6_0) % 149.51/21.68 | | | | | | | | | % 149.51/21.68 | | | | | | | | | REDUCE: (191), (9106) imply: % 149.51/21.68 | | | | | | | | | (9111) ~ (all_52_6 = all_6_0) % 149.51/21.68 | | | | | | | | | % 149.51/21.68 | | | | | | | | | SIMP: (9111) implies: % 149.51/21.68 | | | | | | | | | (9112) ~ (all_52_6 = all_6_0) % 149.51/21.68 | | | | | | | | | % 149.51/21.68 | | | | | | | | | REDUCE: (189), (9106) imply: % 149.51/21.68 | | | | | | | | | (9113) ~ (all_52_14 = all_6_0) % 149.51/21.68 | | | | | | | | | % 149.51/21.68 | | | | | | | | | SIMP: (9113) implies: % 149.51/21.68 | | | | | | | | | (9114) ~ (all_52_14 = all_6_0) % 149.51/21.68 | | | | | | | | | % 149.51/21.68 | | | | | | | | | REDUCE: (559), (9106) imply: % 149.51/21.68 | | | | | | | | | (9115) ~ (all_10_2 = all_6_0) % 149.51/21.68 | | | | | | | | | % 149.51/21.68 | | | | | | | | | SIMP: (9115) implies: % 149.51/21.68 | | | | | | | | | (9116) ~ (all_10_2 = all_6_0) % 149.51/21.68 | | | | | | | | | % 149.51/21.68 | | | | | | | | | REDUCE: (569), (9106) imply: % 149.51/21.68 | | | | | | | | | (9117) ~ (all_6_0 = all_6_2) % 149.51/21.68 | | | | | | | | | % 149.51/21.68 | | | | | | | | | BETA: splitting (288) gives: % 149.51/21.68 | | | | | | | | | % 149.51/21.68 | | | | | | | | | Case 1: % 149.51/21.68 | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | (9118) ~ (all_56_31 = e1) % 149.51/21.68 | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | REDUCE: (544), (9118) imply: % 149.51/21.68 | | | | | | | | | | (9119) ~ (all_4_2 = e1) % 149.51/21.68 | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | BETA: splitting (290) gives: % 149.51/21.68 | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | Case 1: % 149.51/21.68 | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | | (9120) ~ (all_56_31 = e3) % 149.51/21.68 | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | | REDUCE: (544), (9120) imply: % 149.51/21.68 | | | | | | | | | | | (9121) ~ (all_4_2 = e3) % 149.51/21.68 | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | | REF_CLOSE: (36), (38), (41), (46), (48), (51), (171), (173), % 149.51/21.68 | | | | | | | | | | | (174), (176), (182), (183), (184), (194), (196), % 149.51/21.68 | | | | | | | | | | | (207), (237), (243), (244), (247), (251), (287), % 149.51/21.68 | | | | | | | | | | | (289), (291), (292), (296), (324), (326), (327), % 149.51/21.68 | | | | | | | | | | | (328), (330), (333), (337), (360), (366), (374), % 149.51/21.68 | | | | | | | | | | | (380), (386), (389), (401), (407), (425), (435), % 149.51/21.68 | | | | | | | | | | | (457), (473), (532), (540), (542), (544), (545), % 149.51/21.68 | | | | | | | | | | | (546), (548), (550), (552), (554), (555), (561), % 149.51/21.68 | | | | | | | | | | | (571), (573), (575), (579), (580), (587), (588), % 149.51/21.68 | | | | | | | | | | | (591), (617), (622), (627), (762), (8983), (8985), % 149.51/21.68 | | | | | | | | | | | (8996), (9101), (9104), (9107), (9108), (9112), % 149.51/21.68 | | | | | | | | | | | (9114), (9116), (9117), (9119), (9121), % 149.51/21.68 | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 149.51/21.68 | | | | | | | | | | | #10. % 149.51/21.68 | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | Case 2: % 149.51/21.68 | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | | (9122) all_56_31 = e3 % 149.51/21.68 | | | | | | | | | | | (9123) all_56_25 = e0 % 149.51/21.68 | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | | COMBINE_EQS: (447), (9123) imply: % 149.51/21.68 | | | | | | | | | | | (9124) all_52_3 = e0 % 149.51/21.68 | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | | SIMP: (9124) implies: % 149.51/21.68 | | | | | | | | | | | (9125) all_52_3 = e0 % 149.51/21.68 | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | | COMBINE_EQS: (544), (9122) imply: % 149.51/21.68 | | | | | | | | | | | (9126) all_4_2 = e3 % 149.51/21.68 | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | | COMBINE_EQS: (365), (9125) imply: % 149.51/21.68 | | | | | | | | | | | (9127) all_58_12 = e0 % 149.51/21.68 | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | | REDUCE: (188), (9125) imply: % 149.51/21.68 | | | | | | | | | | | (9128) ~ (all_52_7 = e0) % 149.51/21.68 | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | | SIMP: (9128) implies: % 149.51/21.68 | | | | | | | | | | | (9129) ~ (all_52_7 = e0) % 149.51/21.68 | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | | REDUCE: (561), (9125) imply: % 149.51/21.68 | | | | | | | | | | | (9130) ~ (all_10_2 = e0) % 149.51/21.68 | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | | SIMP: (9130) implies: % 149.51/21.68 | | | | | | | | | | | (9131) ~ (all_10_2 = e0) % 149.51/21.68 | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | | REDUCE: (9110), (9125) imply: % 149.51/21.68 | | | | | | | | | | | (9132) ~ (all_6_0 = e0) % 149.51/21.68 | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | | SIMP: (9132) implies: % 149.51/21.68 | | | | | | | | | | | (9133) ~ (all_6_0 = e0) % 149.51/21.68 | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | | REDUCE: (570), (9125), (9126) imply: % 149.51/21.68 | | | | | | | | | | | (9134) ~ (e3 = e0) % 149.51/21.68 | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | | REDUCE: (588), (9126) imply: % 149.51/21.68 | | | | | | | | | | | (9135) ~ (all_52_11 = e3) % 149.51/21.68 | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | | REDUCE: (590), (9126) imply: % 149.51/21.68 | | | | | | | | | | | (9136) ~ (all_52_13 = e3) % 149.51/21.68 | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | | REDUCE: (38), (9126) imply: % 149.51/21.68 | | | | | | | | | | | (9137) op(e3, e3) = all_4_1 % 149.51/21.68 | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | | REDUCE: (627), (9126) imply: % 149.51/21.68 | | | | | | | | | | | (9138) op(e0, e3) = all_56_30 % 149.51/21.68 | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | | REDUCE: (207), (9125) imply: % 149.51/21.68 | | | | | | | | | | | (9139) op(e0, e3) = e0 % 149.51/21.68 | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, % 149.51/21.68 | | | | | | | | | | | all_56_30, e3, e0, simplifying with (9138), (9139) % 149.51/21.68 | | | | | | | | | | | gives: % 149.51/21.68 | | | | | | | | | | | (9140) all_56_30 = e0 % 149.51/21.68 | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_10_2, % 149.51/21.68 | | | | | | | | | | | all_4_1, e3, e3, simplifying with (51), (9137) % 149.51/21.68 | | | | | | | | | | | gives: % 149.51/21.68 | | | | | | | | | | | (9141) all_10_2 = all_4_1 % 149.51/21.68 | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | | COMBINE_EQS: (546), (9141) imply: % 149.51/21.68 | | | | | | | | | | | (9142) all_56_1 = all_4_1 % 149.51/21.68 | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | | COMBINE_EQS: (419), (9141) imply: % 149.51/21.68 | | | | | | | | | | | (9143) all_58_0 = all_4_1 % 149.51/21.68 | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | | REDUCE: (563), (9141) imply: % 149.51/21.68 | | | | | | | | | | | (9144) ~ (all_52_4 = all_4_1) % 149.51/21.68 | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | | REDUCE: (565), (9141) imply: % 149.51/21.68 | | | | | | | | | | | (9145) ~ (all_52_8 = all_4_1) % 149.51/21.68 | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | | REDUCE: (9131), (9141) imply: % 149.51/21.68 | | | | | | | | | | | (9146) ~ (all_4_1 = e0) % 149.51/21.68 | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | | BETA: splitting (292) gives: % 149.51/21.68 | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | | Case 1: % 149.51/21.68 | | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | | | (9147) ~ (all_56_21 = e2) % 149.51/21.68 | | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | | | REDUCE: (374), (9147) imply: % 149.51/21.68 | | | | | | | | | | | | (9148) ~ (all_6_2 = e2) % 149.51/21.68 | | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | | | BETA: splitting (294) gives: % 149.51/21.68 | | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | | | Case 1: % 149.51/21.68 | | | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | | | | (9149) ~ (all_56_11 = e0) % 149.51/21.68 | | | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | | | | REDUCE: (545), (9149) imply: % 149.51/21.68 | | | | | | | | | | | | | (9150) ~ (all_8_2 = e0) % 149.51/21.68 | | | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | | | | BETA: splitting (295) gives: % 149.51/21.68 | | | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | | | | Case 1: % 149.51/21.68 | | | | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | | | | | (9151) ~ (all_56_11 = e1) % 149.51/21.68 | | | | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | | | | | REDUCE: (545), (9151) imply: % 149.51/21.68 | | | | | | | | | | | | | | (9152) ~ (all_8_2 = e1) % 149.51/21.68 | | | | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | | | | | BETA: splitting (293) gives: % 149.51/21.68 | | | | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | | | | | Case 1: % 149.51/21.68 | | | | | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | | | | | | (9153) ~ (all_56_21 = e3) % 149.51/21.68 | | | | | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | | | | | | REDUCE: (374), (9153) imply: % 149.51/21.68 | | | | | | | | | | | | | | | (9154) ~ (all_6_2 = e3) % 149.51/21.68 | | | | | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (41), (242), (247), (287), (296), (299), % 149.51/21.68 | | | | | | | | | | | | | | | (331), (336), (344), (374), (380), (389), (401), % 149.51/21.68 | | | | | | | | | | | | | | | (407), (408), (425), (541), (542), (545), (548), % 149.51/21.68 | | | | | | | | | | | | | | | (549), (552), (554), (555), (568), (577), (580), % 149.51/21.68 | | | | | | | | | | | | | | | (622), (8996), (9104), (9108), (9122), (9127), % 149.51/21.68 | | | | | | | | | | | | | | | (9129), (9135), (9142), (9143), (9144), (9145), % 149.51/21.68 | | | | | | | | | | | | | | | (9146), (9148), (9150), (9152), (9154), % 149.51/21.68 | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 149.51/21.68 | | | | | | | | | | | | | | | #148. % 149.51/21.68 | | | | | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | | | | | Case 2: % 149.51/21.68 | | | | | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | | | | | | (9155) all_56_21 = e3 % 149.51/21.68 | | | | | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | | | | | | REF_CLOSE: (374), (8985), (9104), (9137), (9139), (9146), % 149.51/21.68 | | | | | | | | | | | | | | | (9155), (function-axioms) are inconsistent by % 149.51/21.68 | | | | | | | | | | | | | | | sub-proof #9. % 149.51/21.68 | | | | | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | | | | | End of split % 149.51/21.68 | | | | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | | | | Case 2: % 149.51/21.68 | | | | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | | | | | (9156) all_56_13 = e2 % 149.51/21.68 | | | | | | | | | | | | | | (9157) all_56_11 = e1 % 149.51/21.68 | | | | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | | | | | COMBINE_EQS: (545), (9157) imply: % 149.51/21.68 | | | | | | | | | | | | | | (9158) all_8_2 = e1 % 149.51/21.68 | | | | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | | | | | COMBINE_EQS: (431), (9156) imply: % 149.51/21.68 | | | | | | | | | | | | | | (9159) all_52_9 = e2 % 149.51/21.68 | | | | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | | | | | REDUCE: (583), (9159) imply: % 149.51/21.68 | | | | | | | | | | | | | | (9160) ~ (all_6_2 = e2) % 149.51/21.68 | | | | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | | | | | REDUCE: (48), (9158) imply: % 149.51/21.68 | | | | | | | | | | | | | | (9161) op(e1, e1) = all_8_1 % 149.51/21.68 | | | | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_6_2, % 149.51/21.68 | | | | | | | | | | | | | | all_8_1, e1, e1, simplifying with (41), (9161) % 149.51/21.68 | | | | | | | | | | | | | | gives: % 149.51/21.68 | | | | | | | | | | | | | | (9162) all_8_1 = all_6_2 % 149.51/21.68 | | | | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | | | | | REDUCE: (8994), (9162) imply: % 149.51/21.68 | | | | | | | | | | | | | | (9163) ~ (all_6_2 = e3) % 149.51/21.68 | | | | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | | | | | REDUCE: (8987), (9162) imply: % 149.51/21.68 | | | | | | | | | | | | | | (9164) ~ (all_6_2 = e1) % 149.51/21.68 | | | | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | | | | | BETA: splitting (242) gives: % 149.51/21.68 | | | | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | | | | | Case 1: % 149.51/21.68 | | | | | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | | | | | | (9165) all_54_10 = e3 % 149.51/21.68 | | | | | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | | | | | | REF_CLOSE: (541), (9163), (9165) are inconsistent by % 149.51/21.68 | | | | | | | | | | | | | | | sub-proof #736. % 149.51/21.68 | | | | | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | | | | | Case 2: % 149.51/21.68 | | | | | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | | | | | | (9166) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 149.51/21.68 | | | | | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | | | | | | BETA: splitting (9166) gives: % 149.51/21.68 | | | | | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | | | | | | Case 1: % 149.51/21.68 | | | | | | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | | | | | | | (9167) all_54_10 = e2 % 149.51/21.68 | | | | | | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | | | | | | | REF_CLOSE: (541), (9148), (9167) are inconsistent by % 149.51/21.68 | | | | | | | | | | | | | | | | sub-proof #735. % 149.51/21.68 | | | | | | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | | | | | | Case 2: % 149.51/21.68 | | | | | | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | | | | | | | (9168) all_54_10 = e1 | all_54_10 = e0 % 149.51/21.68 | | | | | | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | | | | | | | BETA: splitting (9168) gives: % 149.51/21.68 | | | | | | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | | | | | | | Case 1: % 149.51/21.68 | | | | | | | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | | | | | | | | (9169) all_54_10 = e1 % 149.51/21.68 | | | | | | | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | | | | | | | | REF_CLOSE: (541), (9164), (9169) are inconsistent by % 149.51/21.68 | | | | | | | | | | | | | | | | | sub-proof #606. % 149.51/21.68 | | | | | | | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | | | | | | | Case 2: % 149.51/21.68 | | | | | | | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | | | | | | | | (9170) all_54_10 = e0 % 149.51/21.68 | | | | | | | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | | | | | | | | COMBINE_EQS: (541), (9170) imply: % 149.51/21.68 | | | | | | | | | | | | | | | | | (9171) all_6_2 = e0 % 149.51/21.68 | | | | | | | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | | | | | | | | SIMP: (9171) implies: % 149.51/21.68 | | | | | | | | | | | | | | | | | (9172) all_6_2 = e0 % 149.51/21.68 | | | | | | | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | | | | | | | | COMBINE_EQS: (374), (9172) imply: % 149.51/21.68 | | | | | | | | | | | | | | | | | (9173) all_56_21 = e0 % 149.51/21.68 | | | | | | | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | | | | | | | | BETA: splitting (291) gives: % 149.51/21.68 | | | | | | | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | | | | | | | | Case 1: % 149.51/21.68 | | | | | | | | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | | | | | | | | | (9174) ~ (all_56_21 = e0) % 149.51/21.68 | | | | | | | | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | | | | | | | | | REDUCE: (9173), (9174) imply: % 149.51/21.68 | | | | | | | | | | | | | | | | | | (9175) $false % 149.51/21.68 | | | | | | | | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | | | | | | | | | CLOSE: (9175) is inconsistent. % 149.51/21.68 | | | | | | | | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | | | | | | | | Case 2: % 149.51/21.68 | | | | | | | | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | | | | | | | | | (9176) all_56_23 = e1 % 149.51/21.68 | | | | | | | | | | | | | | | | | | % 149.51/21.68 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (366), (9176) imply: % 149.51/21.69 | | | | | | | | | | | | | | | | | | (9177) all_52_14 = e1 % 149.51/21.69 | | | | | | | | | | | | | | | | | | % 149.51/21.69 | | | | | | | | | | | | | | | | | | SIMP: (9177) implies: % 149.51/21.69 | | | | | | | | | | | | | | | | | | (9178) all_52_14 = e1 % 149.51/21.69 | | | | | | | | | | | | | | | | | | % 149.51/21.69 | | | | | | | | | | | | | | | | | | REDUCE: (9114), (9178) imply: % 149.51/21.69 | | | | | | | | | | | | | | | | | | (9179) ~ (all_6_0 = e1) % 149.51/21.69 | | | | | | | | | | | | | | | | | | % 149.51/21.69 | | | | | | | | | | | | | | | | | | SIMP: (9179) implies: % 149.51/21.69 | | | | | | | | | | | | | | | | | | (9180) ~ (all_6_0 = e1) % 149.51/21.69 | | | | | | | | | | | | | | | | | | % 149.51/21.69 | | | | | | | | | | | | | | | | | | BETA: splitting (327) gives: % 149.51/21.69 | | | | | | | | | | | | | | | | | | % 149.51/21.69 | | | | | | | | | | | | | | | | | | Case 1: % 149.51/21.69 | | | | | | | | | | | | | | | | | | | % 149.51/21.69 | | | | | | | | | | | | | | | | | | | (9181) all_58_6 = e3 % 149.51/21.69 | | | | | | | | | | | | | | | | | | | % 149.51/21.69 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (9108), (9181) imply: % 149.51/21.69 | | | | | | | | | | | | | | | | | | | (9182) all_6_0 = e3 % 149.51/21.69 | | | | | | | | | | | | | | | | | | | % 149.51/21.69 | | | | | | | | | | | | | | | | | | | REDUCE: (9116), (9182) imply: % 149.51/21.69 | | | | | | | | | | | | | | | | | | | (9183) ~ (all_10_2 = e3) % 149.51/21.69 | | | | | | | | | | | | | | | | | | | % 149.51/21.69 | | | | | | | | | | | | | | | | | | | BETA: splitting (287) gives: % 149.51/21.69 | | | | | | | | | | | | | | | | | | | % 149.51/21.69 | | | | | | | | | | | | | | | | | | | Case 1: % 149.51/21.69 | | | | | | | | | | | | | | | | | | | | % 149.51/21.69 | | | | | | | | | | | | | | | | | | | | (9184) all_56_1 = e3 % 149.51/21.69 | | | | | | | | | | | | | | | | | | | | % 149.51/21.69 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (546), (9184) imply: % 149.51/21.69 | | | | | | | | | | | | | | | | | | | | (9185) all_10_2 = e3 % 149.51/21.69 | | | | | | | | | | | | | | | | | | | | % 149.51/21.69 | | | | | | | | | | | | | | | | | | | | REDUCE: (9183), (9185) imply: % 149.51/21.69 | | | | | | | | | | | | | | | | | | | | (9186) $false % 149.51/21.69 | | | | | | | | | | | | | | | | | | | | % 149.51/21.69 | | | | | | | | | | | | | | | | | | | | CLOSE: (9186) is inconsistent. % 149.51/21.69 | | | | | | | | | | | | | | | | | | | | % 149.51/21.69 | | | | | | | | | | | | | | | | | | | Case 2: % 149.51/21.69 | | | | | | | | | | | | | | | | | | | | % 149.51/21.69 | | | | | | | | | | | | | | | | | | | | (9187) all_56_11 = e2 | all_56_21 = e1 | all_56_31 = e0 % 149.51/21.69 | | | | | | | | | | | | | | | | | | | | % 149.51/21.69 | | | | | | | | | | | | | | | | | | | | BETA: splitting (9187) gives: % 149.51/21.69 | | | | | | | | | | | | | | | | | | | | % 149.51/21.69 | | | | | | | | | | | | | | | | | | | | Case 1: % 149.51/21.69 | | | | | | | | | | | | | | | | | | | | | % 149.51/21.69 | | | | | | | | | | | | | | | | | | | | | (9188) all_56_11 = e2 % 149.51/21.69 | | | | | | | | | | | | | | | | | | | | | % 149.51/21.69 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9157), (9188) are inconsistent by sub-proof % 149.51/21.69 | | | | | | | | | | | | | | | | | | | | | #419. % 149.51/21.69 | | | | | | | | | | | | | | | | | | | | | % 149.51/21.69 | | | | | | | | | | | | | | | | | | | | Case 2: % 149.51/21.69 | | | | | | | | | | | | | | | | | | | | | % 149.51/21.69 | | | | | | | | | | | | | | | | | | | | | (9189) all_56_21 = e1 | all_56_31 = e0 % 149.51/21.69 | | | | | | | | | | | | | | | | | | | | | % 149.51/21.69 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (36), (38), (374), (544), (627), (8985), % 149.51/21.69 | | | | | | | | | | | | | | | | | | | | | (9164), (9189), (function-axioms) are inconsistent % 149.51/21.69 | | | | | | | | | | | | | | | | | | | | | by sub-proof #8. % 149.51/21.69 | | | | | | | | | | | | | | | | | | | | | % 149.51/21.69 | | | | | | | | | | | | | | | | | | | | End of split % 149.51/21.69 | | | | | | | | | | | | | | | | | | | | % 149.51/21.69 | | | | | | | | | | | | | | | | | | | End of split % 149.51/21.69 | | | | | | | | | | | | | | | | | | | % 149.51/21.69 | | | | | | | | | | | | | | | | | | Case 2: % 149.51/21.69 | | | | | | | | | | | | | | | | | | | % 149.51/21.69 | | | | | | | | | | | | | | | | | | | (9190) ~ (all_58_6 = e3) % 149.51/21.69 | | | | | | | | | | | | | | | | | | | % 149.51/21.69 | | | | | | | | | | | | | | | | | | | REDUCE: (9108), (9190) imply: % 149.51/21.69 | | | | | | | | | | | | | | | | | | | (9191) ~ (all_6_0 = e3) % 149.51/21.69 | | | | | | | | | | | | | | | | | | | % 149.51/21.69 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (244), (8996), (9107), (9133), (9180), (9191) are % 149.51/21.69 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #11. % 149.51/21.69 | | | | | | | | | | | | | | | | | | | % 149.51/21.69 | | | | | | | | | | | | | | | | | | End of split % 149.51/21.69 | | | | | | | | | | | | | | | | | | % 149.51/21.69 | | | | | | | | | | | | | | | | | End of split % 149.51/21.69 | | | | | | | | | | | | | | | | | % 149.51/21.69 | | | | | | | | | | | | | | | | End of split % 149.51/21.69 | | | | | | | | | | | | | | | | % 149.51/21.69 | | | | | | | | | | | | | | | End of split % 149.51/21.69 | | | | | | | | | | | | | | | % 149.51/21.69 | | | | | | | | | | | | | | End of split % 149.51/21.69 | | | | | | | | | | | | | | % 149.51/21.69 | | | | | | | | | | | | | End of split % 149.51/21.69 | | | | | | | | | | | | | % 149.51/21.69 | | | | | | | | | | | | Case 2: % 149.51/21.69 | | | | | | | | | | | | | % 149.51/21.69 | | | | | | | | | | | | | (9192) all_56_15 = e2 % 149.51/21.69 | | | | | | | | | | | | | (9193) all_56_11 = e0 % 149.51/21.69 | | | | | | | | | | | | | % 149.51/21.69 | | | | | | | | | | | | | COMBINE_EQS: (545), (9193) imply: % 149.51/21.69 | | | | | | | | | | | | | (9194) all_8_2 = e0 % 149.51/21.69 | | | | | | | | | | | | | % 149.51/21.69 | | | | | | | | | | | | | COMBINE_EQS: (443), (9192) imply: % 149.51/21.69 | | | | | | | | | | | | | (9195) all_52_13 = e2 % 149.51/21.69 | | | | | | | | | | | | | % 149.51/21.69 | | | | | | | | | | | | | REDUCE: (193), (9195) imply: % 149.51/21.69 | | | | | | | | | | | | | (9196) ~ (all_52_1 = e2) % 149.51/21.69 | | | | | | | | | | | | | % 149.51/21.69 | | | | | | | | | | | | | REDUCE: (9136), (9195) imply: % 149.51/21.69 | | | | | | | | | | | | | (9197) ~ (e3 = e2) % 149.51/21.69 | | | | | | | | | | | | | % 149.51/21.69 | | | | | | | | | | | | | REF_CLOSE: (5), (7), (8), (9), (41), (287), (344), (374), % 149.51/21.69 | | | | | | | | | | | | | (401), (622), (8996), (9104), (9108), (9122), % 149.51/21.69 | | | | | | | | | | | | | (9127), (9142), (9143), (9146), (9193), (9196), % 149.51/21.69 | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 149.51/21.69 | | | | | | | | | | | | | #7. % 149.51/21.69 | | | | | | | | | | | | | % 149.51/21.69 | | | | | | | | | | | | End of split % 149.51/21.69 | | | | | | | | | | | | % 149.51/21.69 | | | | | | | | | | | Case 2: % 149.51/21.69 | | | | | | | | | | | | % 149.51/21.69 | | | | | | | | | | | | (9198) all_56_21 = e2 % 149.51/21.69 | | | | | | | | | | | | (9199) all_56_19 = e1 % 149.51/21.69 | | | | | | | | | | | | % 149.51/21.69 | | | | | | | | | | | | REF_CLOSE: (4), (5), (46), (48), (244), (287), (324), (374), % 149.51/21.69 | | | | | | | | | | | | (380), (435), (544), (545), (546), (550), (552), % 149.51/21.69 | | | | | | | | | | | | (580), (591), (617), (9104), (9107), (9108), % 149.51/21.69 | | | | | | | | | | | | (9112), (9114), (9116), (9117), (9133), (9198), % 149.51/21.69 | | | | | | | | | | | | (9199), (function-axioms) are inconsistent by % 149.51/21.69 | | | | | | | | | | | | sub-proof #319. % 149.51/21.69 | | | | | | | | | | | | % 149.51/21.69 | | | | | | | | | | | End of split % 149.51/21.69 | | | | | | | | | | | % 149.51/21.69 | | | | | | | | | | End of split % 149.51/21.69 | | | | | | | | | | % 149.51/21.69 | | | | | | | | | Case 2: % 149.51/21.69 | | | | | | | | | | % 149.51/21.69 | | | | | | | | | | (9200) all_56_31 = e1 % 149.51/21.69 | | | | | | | | | | (9201) all_56_29 = e0 % 149.51/21.69 | | | | | | | | | | % 149.51/21.69 | | | | | | | | | | REF_CLOSE: (6), (7), (36), (38), (41), (43), (48), (51), % 149.51/21.69 | | | | | | | | | | (192), (205), (207), (242), (287), (293), (294), % 149.51/21.69 | | | | | | | | | | (319), (357), (365), (374), (381), (499), (541), % 149.51/21.69 | | | | | | | | | | (544), (545), (546), (547), (548), (549), (561), % 149.51/21.69 | | | | | | | | | | (575), (585), (588), (627), (676), (8985), (8987), % 149.51/21.69 | | | | | | | | | | (8992), (9200), (9201), (function-axioms) are % 149.51/21.69 | | | | | | | | | | inconsistent by sub-proof #13. % 149.51/21.69 | | | | | | | | | | % 149.51/21.69 | | | | | | | | | End of split % 149.51/21.69 | | | | | | | | | % 149.51/21.69 | | | | | | | | End of split % 149.51/21.69 | | | | | | | | % 149.51/21.69 | | | | | | | Case 2: % 149.51/21.69 | | | | | | | | % 149.51/21.69 | | | | | | | | (9202) all_28_0 = e2 % 149.51/21.69 | | | | | | | | (9203) ~ (all_28_1 = e3) | ~ (all_28_2 = e0) % 149.51/21.69 | | | | | | | | % 149.51/21.69 | | | | | | | | REF_CLOSE: (6), (7), (8), (36), (38), (41), (42), (43), (46), % 149.51/21.69 | | | | | | | | (48), (51), (144), (158), (174), (192), (205), (207), % 149.51/21.69 | | | | | | | | (208), (211), (237), (242), (247), (252), (287), % 149.51/21.69 | | | | | | | | (288), (291), (292), (293), (294), (297), (319), % 149.51/21.69 | | | | | | | | (321), (341), (357), (365), (366), (374), (381), % 149.51/21.69 | | | | | | | | (386), (402), (407), (419), (435), (443), (475), % 149.51/21.69 | | | | | | | | (499), (513), (540), (541), (542), (543), (544), % 149.51/21.69 | | | | | | | | (545), (546), (547), (548), (549), (550), (551), % 149.51/21.69 | | | | | | | | (555), (559), (561), (569), (571), (573), (575), % 149.51/21.69 | | | | | | | | (580), (585), (588), (591), (620), (622), (627), % 149.51/21.69 | | | | | | | | (634), (665), (676), (740), (764), (8985), (8986), % 149.51/21.69 | | | | | | | | (8987), (8992), (9202), (9203), (function-axioms) are % 149.51/21.69 | | | | | | | | inconsistent by sub-proof #5. % 149.51/21.69 | | | | | | | | % 149.51/21.69 | | | | | | | End of split % 149.51/21.69 | | | | | | | % 149.51/21.69 | | | | | | Case 2: % 149.51/21.69 | | | | | | | % 149.51/21.69 | | | | | | | (9204) all_22_1 = e3 % 149.51/21.69 | | | | | | | (9205) ~ (all_22_0 = e0) | ~ (all_22_2 = e1) % 149.51/21.69 | | | | | | | % 149.51/21.69 | | | | | | | COMBINE_EQS: (672), (9204) imply: % 149.51/21.69 | | | | | | | (9206) all_8_1 = e3 % 149.51/21.69 | | | | | | | % 149.51/21.69 | | | | | | | SIMP: (9206) implies: % 149.51/21.69 | | | | | | | (9207) all_8_1 = e3 % 149.51/21.69 | | | | | | | % 149.51/21.69 | | | | | | | REDUCE: (48), (9207) imply: % 149.51/21.69 | | | | | | | (9208) op(all_8_2, all_8_2) = e3 % 149.51/21.69 | | | | | | | % 149.51/21.69 | | | | | | | REDUCE: (47), (9207) imply: % 149.51/21.69 | | | | | | | (9209) op(e2, e3) = all_8_0 % 149.51/21.69 | | | | | | | % 149.51/21.69 | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_1, % 149.51/21.69 | | | | | | | all_8_0, e3, e2, simplifying with (215), (9209) % 149.51/21.69 | | | | | | | gives: % 149.51/21.69 | | | | | | | (9210) all_52_1 = all_8_0 % 149.51/21.69 | | | | | | | % 149.51/21.69 | | | | | | | COMBINE_EQS: (463), (9210) imply: % 149.51/21.69 | | | | | | | (9211) all_54_4 = all_8_0 % 149.51/21.69 | | | | | | | % 149.51/21.69 | | | | | | | COMBINE_EQS: (401), (9210) imply: % 149.51/21.69 | | | | | | | (9212) all_58_2 = all_8_0 % 149.51/21.69 | | | | | | | % 149.51/21.69 | | | | | | | REDUCE: (194), (9210) imply: % 149.51/21.69 | | | | | | | (9213) ~ (all_52_9 = all_8_0) % 149.51/21.69 | | | | | | | % 149.51/21.69 | | | | | | | SIMP: (9213) implies: % 149.51/21.69 | | | | | | | (9214) ~ (all_52_9 = all_8_0) % 149.51/21.69 | | | | | | | % 149.51/21.69 | | | | | | | REDUCE: (193), (9210) imply: % 149.51/21.69 | | | | | | | (9215) ~ (all_52_13 = all_8_0) % 149.51/21.69 | | | | | | | % 149.51/21.69 | | | | | | | SIMP: (9215) implies: % 149.51/21.69 | | | | | | | (9216) ~ (all_52_13 = all_8_0) % 149.51/21.69 | | | | | | | % 149.51/21.69 | | | | | | | REDUCE: (557), (9210) imply: % 149.51/21.69 | | | | | | | (9217) ~ (all_10_2 = all_8_0) % 149.51/21.69 | | | | | | | % 149.51/21.69 | | | | | | | SIMP: (9217) implies: % 149.51/21.69 | | | | | | | (9218) ~ (all_10_2 = all_8_0) % 149.51/21.69 | | | | | | | % 149.51/21.69 | | | | | | | REDUCE: (568), (9210) imply: % 149.51/21.69 | | | | | | | (9219) ~ (all_8_0 = all_8_2) % 149.51/21.69 | | | | | | | % 149.51/21.69 | | | | | | | BETA: splitting (99) gives: % 149.51/21.69 | | | | | | | % 149.51/21.69 | | | | | | | Case 1: % 149.51/21.69 | | | | | | | | % 149.51/21.69 | | | | | | | | (9220) ~ (all_28_0 = e2) % 149.51/21.69 | | | | | | | | % 149.51/21.69 | | | | | | | | REDUCE: (740), (9220) imply: % 149.51/21.69 | | | | | | | | (9221) ~ (all_6_0 = e2) % 149.51/21.69 | | | | | | | | % 149.51/21.69 | | | | | | | | BETA: splitting (119) gives: % 149.51/21.69 | | | | | | | | % 149.51/21.69 | | | | | | | | Case 1: % 149.51/21.69 | | | | | | | | | % 149.51/21.69 | | | | | | | | | (9222) ~ (all_36_1 = e3) % 149.51/21.69 | | | | | | | | | % 149.51/21.69 | | | | | | | | | REDUCE: (652), (9222) imply: % 149.51/21.69 | | | | | | | | | (9223) ~ (all_6_1 = e3) % 149.51/21.69 | | | | | | | | | % 149.51/21.69 | | | | | | | | | BETA: splitting (292) gives: % 149.51/21.69 | | | | | | | | | % 149.51/21.69 | | | | | | | | | Case 1: % 149.51/21.69 | | | | | | | | | | % 149.51/21.69 | | | | | | | | | | (9224) ~ (all_56_21 = e2) % 149.51/21.69 | | | | | | | | | | % 149.51/21.69 | | | | | | | | | | REDUCE: (374), (9224) imply: % 149.51/21.69 | | | | | | | | | | (9225) ~ (all_6_2 = e2) % 149.51/21.69 | | | | | | | | | | % 149.51/21.69 | | | | | | | | | | BETA: splitting (294) gives: % 149.51/21.69 | | | | | | | | | | % 149.51/21.69 | | | | | | | | | | Case 1: % 149.51/21.69 | | | | | | | | | | | % 149.51/21.69 | | | | | | | | | | | (9226) ~ (all_56_11 = e0) % 149.51/21.69 | | | | | | | | | | | % 149.51/21.69 | | | | | | | | | | | REDUCE: (545), (9226) imply: % 149.51/21.69 | | | | | | | | | | | (9227) ~ (all_8_2 = e0) % 149.51/21.69 | | | | | | | | | | | % 149.51/21.69 | | | | | | | | | | | BETA: splitting (293) gives: % 149.51/21.69 | | | | | | | | | | | % 149.51/21.69 | | | | | | | | | | | Case 1: % 149.51/21.69 | | | | | | | | | | | | % 149.51/21.69 | | | | | | | | | | | | (9228) ~ (all_56_21 = e3) % 149.51/21.69 | | | | | | | | | | | | % 149.51/21.69 | | | | | | | | | | | | REDUCE: (374), (9228) imply: % 149.51/21.69 | | | | | | | | | | | | (9229) ~ (all_6_2 = e3) % 149.51/21.69 | | | | | | | | | | | | % 149.51/21.69 | | | | | | | | | | | | BETA: splitting (288) gives: % 149.51/21.69 | | | | | | | | | | | | % 149.51/21.69 | | | | | | | | | | | | Case 1: % 149.51/21.69 | | | | | | | | | | | | | % 149.51/21.69 | | | | | | | | | | | | | (9230) ~ (all_56_31 = e1) % 149.51/21.69 | | | | | | | | | | | | | % 149.51/21.69 | | | | | | | | | | | | | REDUCE: (544), (9230) imply: % 149.51/21.69 | | | | | | | | | | | | | (9231) ~ (all_4_2 = e1) % 149.51/21.69 | | | | | | | | | | | | | % 149.51/21.69 | | | | | | | | | | | | | BETA: splitting (295) gives: % 149.51/21.69 | | | | | | | | | | | | | % 149.51/21.69 | | | | | | | | | | | | | Case 1: % 149.51/21.69 | | | | | | | | | | | | | | % 149.51/21.69 | | | | | | | | | | | | | | (9232) ~ (all_56_11 = e1) % 149.51/21.69 | | | | | | | | | | | | | | % 149.51/21.69 | | | | | | | | | | | | | | REDUCE: (545), (9232) imply: % 149.51/21.69 | | | | | | | | | | | | | | (9233) ~ (all_8_2 = e1) % 149.51/21.69 | | | | | | | | | | | | | | % 149.51/21.69 | | | | | | | | | | | | | | REF_CLOSE: (7), (36), (38), (43), (46), (51), (166), (168), % 149.51/21.69 | | | | | | | | | | | | | | (169), (171), (173), (174), (181), (182), (183), % 149.51/21.69 | | | | | | | | | | | | | | (187), (188), (194), (196), (205), (206), (207), % 149.51/21.69 | | | | | | | | | | | | | | (237), (238), (240), (241), (242), (246), (247), % 149.51/21.69 | | | | | | | | | | | | | | (250), (251), (252), (289), (290), (291), (296), % 149.51/21.69 | | | | | | | | | | | | | | (298), (299), (318), (321), (328), (330), (331), % 149.51/21.69 | | | | | | | | | | | | | | (333), (336), (343), (345), (360), (365), (366), % 149.51/21.69 | | | | | | | | | | | | | | (374), (380), (386), (389), (401), (407), (408), % 149.51/21.69 | | | | | | | | | | | | | | (419), (425), (429), (447), (457), (459), (467), % 149.51/21.69 | | | | | | | | | | | | | | (476), (478), (482), (540), (541), (542), (543), % 149.51/21.69 | | | | | | | | | | | | | | (544), (545), (546), (547), (548), (549), (550), % 149.51/21.69 | | | | | | | | | | | | | | (551), (552), (554), (555), (557), (561), (563), % 149.51/21.69 | | | | | | | | | | | | | | (565), (567), (568), (570), (571), (575), (577), % 149.51/21.69 | | | | | | | | | | | | | | (582), (583), (585), (587), (588), (591), (625), % 149.51/21.69 | | | | | | | | | | | | | | (626), (627), (8985), (8986), (9223), (9225), % 149.51/21.69 | | | | | | | | | | | | | | (9227), (9229), (9231), (9233), (function-axioms) % 149.51/21.69 | | | | | | | | | | | | | | are inconsistent by sub-proof #20. % 149.51/21.69 | | | | | | | | | | | | | | % 149.51/21.69 | | | | | | | | | | | | | Case 2: % 149.51/21.69 | | | | | | | | | | | | | | % 149.51/21.69 | | | | | | | | | | | | | | (9234) all_56_13 = e2 % 149.51/21.69 | | | | | | | | | | | | | | (9235) all_56_11 = e1 % 149.51/21.69 | | | | | | | | | | | | | | % 149.51/21.69 | | | | | | | | | | | | | | REF_CLOSE: (41), (165), (245), (248), (287), (374), (431), % 149.51/21.69 | | | | | | | | | | | | | | (469), (523), (544), (545), (546), (577), (579), % 149.51/21.69 | | | | | | | | | | | | | | (590), (622), (752), (9205), (9208), (9211), % 149.51/21.69 | | | | | | | | | | | | | | (9214), (9216), (9218), (9219), (9229), (9234), % 149.51/21.69 | | | | | | | | | | | | | | (9235), (function-axioms) are inconsistent by % 149.51/21.69 | | | | | | | | | | | | | | sub-proof #340. % 149.51/21.69 | | | | | | | | | | | | | | % 149.51/21.69 | | | | | | | | | | | | | End of split % 149.51/21.69 | | | | | | | | | | | | | % 149.51/21.69 | | | | | | | | | | | | Case 2: % 149.51/21.69 | | | | | | | | | | | | | % 149.51/21.69 | | | | | | | | | | | | | (9236) all_56_31 = e1 % 149.51/21.69 | | | | | | | | | | | | | (9237) all_56_29 = e0 % 149.51/21.69 | | | | | | | | | | | | | % 149.51/21.69 | | | | | | | | | | | | | REF_CLOSE: (6), (7), (36), (38), (41), (43), (48), (51), % 149.51/21.69 | | | | | | | | | | | | | (192), (205), (207), (242), (287), (293), (294), % 149.51/21.69 | | | | | | | | | | | | | (319), (357), (365), (374), (381), (499), (541), % 149.51/21.69 | | | | | | | | | | | | | (544), (545), (546), (547), (548), (549), (561), % 149.51/21.69 | | | | | | | | | | | | | (575), (585), (588), (627), (676), (8985), (8987), % 149.51/21.69 | | | | | | | | | | | | | (8992), (9236), (9237), (function-axioms) are % 149.51/21.69 | | | | | | | | | | | | | inconsistent by sub-proof #13. % 149.51/21.69 | | | | | | | | | | | | | % 149.51/21.69 | | | | | | | | | | | | End of split % 149.51/21.69 | | | | | | | | | | | | % 149.51/21.69 | | | | | | | | | | | Case 2: % 149.51/21.69 | | | | | | | | | | | | % 149.51/21.69 | | | | | | | | | | | | (9238) all_56_21 = e3 % 149.51/21.69 | | | | | | | | | | | | (9239) all_56_17 = e1 % 149.51/21.69 | | | | | | | | | | | | % 149.51/21.69 | | | | | | | | | | | | REF_CLOSE: (42), (43), (46), (51), (189), (208), (241), % 149.51/21.69 | | | | | | | | | | | | (252), (287), (374), (381), (476), (543), (544), % 149.51/21.69 | | | | | | | | | | | | (545), (546), (559), (569), (587), (591), (617), % 149.51/21.69 | | | | | | | | | | | | (8986), (9208), (9221), (9223), (9225), (9238), % 149.51/21.69 | | | | | | | | | | | | (9239), (function-axioms) are inconsistent by % 149.51/21.69 | | | | | | | | | | | | sub-proof #339. % 149.51/21.69 | | | | | | | | | | | | % 149.51/21.69 | | | | | | | | | | | End of split % 149.51/21.69 | | | | | | | | | | | % 149.51/21.69 | | | | | | | | | | Case 2: % 149.51/21.69 | | | | | | | | | | | % 149.51/21.69 | | | | | | | | | | | (9240) all_56_15 = e2 % 149.51/21.69 | | | | | | | | | | | (9241) all_56_11 = e0 % 149.51/21.69 | | | | | | | | | | | % 149.51/21.69 | | | | | | | | | | | COMBINE_EQS: (545), (9241) imply: % 149.51/21.69 | | | | | | | | | | | (9242) all_8_2 = e0 % 149.51/21.69 | | | | | | | | | | | % 149.51/21.69 | | | | | | | | | | | COMBINE_EQS: (443), (9240) imply: % 149.51/21.69 | | | | | | | | | | | (9243) all_52_13 = e2 % 149.51/21.69 | | | | | | | | | | | % 149.51/21.69 | | | | | | | | | | | COMBINE_EQS: (386), (9243) imply: % 149.51/21.69 | | | | | | | | | | | (9244) all_58_10 = e2 % 149.51/21.69 | | | | | | | | | | | % 149.51/21.69 | | | | | | | | | | | COMBINE_EQS: (554), (9242) imply: % 149.51/21.69 | | | | | | | | | | | (9245) all_58_3 = e0 % 149.51/21.69 | | | | | | | | | | | % 149.51/21.69 | | | | | | | | | | | REDUCE: (9216), (9243) imply: % 149.51/21.69 | | | | | | | | | | | (9246) ~ (all_8_0 = e2) % 149.51/21.69 | | | | | | | | | | | % 149.51/21.69 | | | | | | | | | | | SIMP: (9246) implies: % 149.51/21.69 | | | | | | | | | | | (9247) ~ (all_8_0 = e2) % 149.51/21.69 | | | | | | | | | | | % 149.51/21.69 | | | | | | | | | | | REDUCE: (9219), (9242) imply: % 149.51/21.69 | | | | | | | | | | | (9248) ~ (all_8_0 = e0) % 149.51/21.69 | | | | | | | | | | | % 149.51/21.69 | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (36), (38), (248), (287), (333), % 149.51/21.69 | | | | | | | | | | | (374), (389), (544), (546), (583), (627), (8985), % 149.51/21.69 | | | | | | | | | | | (8989), (9211), (9212), (9218), (9241), (9244), % 149.51/21.69 | | | | | | | | | | | (9245), (9247), (9248), (function-axioms) are % 149.51/21.69 | | | | | | | | | | | inconsistent by sub-proof #3. % 149.51/21.69 | | | | | | | | | | | % 149.51/21.69 | | | | | | | | | | End of split % 149.51/21.69 | | | | | | | | | | % 149.51/21.69 | | | | | | | | | Case 2: % 149.51/21.69 | | | | | | | | | | % 149.51/21.69 | | | | | | | | | | (9249) all_56_21 = e2 % 149.51/21.69 | | | | | | | | | | (9250) all_56_19 = e1 % 149.51/21.69 | | | | | | | | | | % 149.51/21.69 | | | | | | | | | | COMBINE_EQS: (435), (9250) imply: % 149.51/21.69 | | | | | | | | | | (9251) all_52_6 = e1 % 149.51/21.69 | | | | | | | | | | % 149.51/21.69 | | | | | | | | | | COMBINE_EQS: (374), (9249) imply: % 149.51/21.69 | | | | | | | | | | (9252) all_6_2 = e2 % 149.51/21.69 | | | | | | | | | | % 149.51/21.69 | | | | | | | | | | SIMP: (9252) implies: % 149.51/21.69 | | | | | | | | | | (9253) all_6_2 = e2 % 149.51/21.69 | | | | | | | | | | % 149.51/21.69 | | | | | | | | | | REDUCE: (573), (9251) imply: % 149.51/21.69 | | | | | | | | | | (9254) ~ (all_8_2 = e1) % 149.51/21.69 | | | | | | | | | | % 149.51/21.69 | | | | | | | | | | SIMP: (9254) implies: % 149.51/21.69 | | | | | | | | | | (9255) ~ (all_8_2 = e1) % 149.51/21.69 | | | | | | | | | | % 149.51/21.69 | | | | | | | | | | REDUCE: (580), (9251), (9253) imply: % 149.51/21.69 | | | | | | | | | | (9256) ~ (e2 = e1) % 149.51/21.69 | | | | | | | | | | % 149.51/21.69 | | | | | | | | | | REDUCE: (43), (9253) imply: % 149.51/21.69 | | | | | | | | | | (9257) op(e2, e2) = all_6_1 % 149.51/21.69 | | | | | | | | | | % 149.51/21.69 | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_8_2, % 149.51/21.69 | | | | | | | | | | all_6_1, e2, e2, simplifying with (46), (9257) % 149.51/21.69 | | | | | | | | | | gives: % 149.51/21.69 | | | | | | | | | | (9258) all_8_2 = all_6_1 % 149.51/21.69 | | | | | | | | | | % 149.51/21.69 | | | | | | | | | | COMBINE_EQS: (542), (9258) imply: % 149.51/21.69 | | | | | | | | | | (9259) all_54_5 = all_6_1 % 149.51/21.69 | | | | | | | | | | % 149.51/21.69 | | | | | | | | | | COMBINE_EQS: (545), (9258) imply: % 149.51/21.69 | | | | | | | | | | (9260) all_56_11 = all_6_1 % 149.51/21.69 | | | | | | | | | | % 149.51/21.69 | | | | | | | | | | COMBINE_EQS: (554), (9258) imply: % 149.51/21.69 | | | | | | | | | | (9261) all_58_3 = all_6_1 % 149.51/21.69 | | | | | | | | | | % 149.51/21.69 | | | | | | | | | | REDUCE: (579), (9258) imply: % 149.51/21.69 | | | | | | | | | | (9262) ~ (all_52_13 = all_6_1) % 149.51/21.69 | | | | | | | | | | % 149.51/21.69 | | | | | | | | | | REDUCE: (9219), (9258) imply: % 149.51/21.69 | | | | | | | | | | (9263) ~ (all_8_0 = all_6_1) % 149.51/21.69 | | | | | | | | | | % 149.51/21.69 | | | | | | | | | | REDUCE: (9255), (9258) imply: % 149.51/21.69 | | | | | | | | | | (9264) ~ (all_6_1 = e1) % 149.51/21.69 | | | | | | | | | | % 149.51/21.69 | | | | | | | | | | BETA: splitting (247) gives: % 149.51/21.69 | | | | | | | | | | % 149.51/21.69 | | | | | | | | | | Case 1: % 149.51/21.69 | | | | | | | | | | | % 149.51/21.69 | | | | | | | | | | | (9265) all_54_5 = e3 % 149.51/21.69 | | | | | | | | | | | % 149.51/21.69 | | | | | | | | | | | REF_CLOSE: (9223), (9259), (9265) are inconsistent by % 149.51/21.69 | | | | | | | | | | | sub-proof #509. % 149.51/21.69 | | | | | | | | | | | % 149.51/21.69 | | | | | | | | | | Case 2: % 149.51/21.69 | | | | | | | | | | | % 149.51/21.69 | | | | | | | | | | | (9266) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 149.51/21.69 | | | | | | | | | | | % 149.51/21.69 | | | | | | | | | | | BETA: splitting (9266) gives: % 149.51/21.69 | | | | | | | | | | | % 149.51/21.69 | | | | | | | | | | | Case 1: % 149.51/21.69 | | | | | | | | | | | | % 149.51/21.69 | | | | | | | | | | | | (9267) all_54_5 = e2 % 149.51/21.69 | | | | | | | | | | | | % 149.51/21.69 | | | | | | | | | | | | REF_CLOSE: (8986), (9259), (9267) are inconsistent by % 149.51/21.69 | | | | | | | | | | | | sub-proof #466. % 149.51/21.69 | | | | | | | | | | | | % 149.51/21.69 | | | | | | | | | | | Case 2: % 149.51/21.69 | | | | | | | | | | | | % 149.51/21.69 | | | | | | | | | | | | (9268) all_54_5 = e1 | all_54_5 = e0 % 149.51/21.69 | | | | | | | | | | | | % 149.51/21.69 | | | | | | | | | | | | BETA: splitting (9268) gives: % 149.51/21.69 | | | | | | | | | | | | % 149.51/21.69 | | | | | | | | | | | | Case 1: % 149.51/21.69 | | | | | | | | | | | | | % 149.51/21.69 | | | | | | | | | | | | | (9269) all_54_5 = e1 % 149.51/21.69 | | | | | | | | | | | | | % 149.51/21.69 | | | | | | | | | | | | | REF_CLOSE: (9259), (9264), (9269) are inconsistent by % 149.51/21.69 | | | | | | | | | | | | | sub-proof #465. % 149.51/21.69 | | | | | | | | | | | | | % 149.51/21.69 | | | | | | | | | | | | Case 2: % 149.51/21.69 | | | | | | | | | | | | | % 149.51/21.69 | | | | | | | | | | | | | (9270) all_54_5 = e0 % 149.51/21.69 | | | | | | | | | | | | | % 149.51/21.69 | | | | | | | | | | | | | COMBINE_EQS: (9259), (9270) imply: % 149.51/21.69 | | | | | | | | | | | | | (9271) all_6_1 = e0 % 149.51/21.69 | | | | | | | | | | | | | % 149.51/21.69 | | | | | | | | | | | | | SIMP: (9271) implies: % 149.51/21.69 | | | | | | | | | | | | | (9272) all_6_1 = e0 % 149.51/21.69 | | | | | | | | | | | | | % 149.51/21.69 | | | | | | | | | | | | | COMBINE_EQS: (9260), (9272) imply: % 149.51/21.69 | | | | | | | | | | | | | (9273) all_56_11 = e0 % 149.51/21.69 | | | | | | | | | | | | | % 149.51/21.69 | | | | | | | | | | | | | COMBINE_EQS: (9261), (9272) imply: % 149.51/21.69 | | | | | | | | | | | | | (9274) all_58_3 = e0 % 149.51/21.69 | | | | | | | | | | | | | % 149.51/21.69 | | | | | | | | | | | | | REDUCE: (9262), (9272) imply: % 149.51/21.69 | | | | | | | | | | | | | (9275) ~ (all_52_13 = e0) % 149.51/21.69 | | | | | | | | | | | | | % 149.51/21.69 | | | | | | | | | | | | | REDUCE: (9263), (9272) imply: % 149.51/21.69 | | | | | | | | | | | | | (9276) ~ (all_8_0 = e0) % 149.51/21.69 | | | | | | | | | | | | | % 149.51/21.69 | | | | | | | | | | | | | REDUCE: (9264), (9272) imply: % 149.51/21.69 | | | | | | | | | | | | | (9277) ~ (e1 = e0) % 149.51/21.69 | | | | | | | | | | | | | % 149.51/21.69 | | | | | | | | | | | | | BETA: splitting (294) gives: % 149.51/21.69 | | | | | | | | | | | | | % 149.51/21.69 | | | | | | | | | | | | | Case 1: % 149.51/21.69 | | | | | | | | | | | | | | % 149.51/21.69 | | | | | | | | | | | | | | (9278) ~ (all_56_11 = e0) % 149.51/21.69 | | | | | | | | | | | | | | % 149.51/21.69 | | | | | | | | | | | | | | REDUCE: (9273), (9278) imply: % 149.51/21.69 | | | | | | | | | | | | | | (9279) $false % 149.51/21.69 | | | | | | | | | | | | | | % 149.51/21.69 | | | | | | | | | | | | | | CLOSE: (9279) is inconsistent. % 149.51/21.69 | | | | | | | | | | | | | | % 149.51/21.69 | | | | | | | | | | | | | Case 2: % 149.51/21.69 | | | | | | | | | | | | | | % 149.51/21.69 | | | | | | | | | | | | | | (9280) all_56_15 = e2 % 149.51/21.69 | | | | | | | | | | | | | | % 149.51/21.69 | | | | | | | | | | | | | | COMBINE_EQS: (443), (9280) imply: % 149.51/21.69 | | | | | | | | | | | | | | (9281) all_52_13 = e2 % 149.51/21.69 | | | | | | | | | | | | | | % 149.51/21.69 | | | | | | | | | | | | | | COMBINE_EQS: (386), (9281) imply: % 149.51/21.69 | | | | | | | | | | | | | | (9282) all_58_10 = e2 % 149.51/21.69 | | | | | | | | | | | | | | % 149.51/21.69 | | | | | | | | | | | | | | REDUCE: (9216), (9281) imply: % 149.51/21.69 | | | | | | | | | | | | | | (9283) ~ (all_8_0 = e2) % 149.51/21.69 | | | | | | | | | | | | | | % 149.51/21.69 | | | | | | | | | | | | | | SIMP: (9283) implies: % 149.51/21.69 | | | | | | | | | | | | | | (9284) ~ (all_8_0 = e2) % 149.51/21.69 | | | | | | | | | | | | | | % 149.51/21.69 | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (36), (38), (248), (287), (333), % 149.51/21.69 | | | | | | | | | | | | | | (374), (389), (544), (546), (583), (627), (8985), % 149.51/21.69 | | | | | | | | | | | | | | (8989), (9211), (9212), (9218), (9273), (9274), % 149.51/21.69 | | | | | | | | | | | | | | (9276), (9282), (9284), (function-axioms) are % 149.51/21.69 | | | | | | | | | | | | | | inconsistent by sub-proof #3. % 149.51/21.69 | | | | | | | | | | | | | | % 149.51/21.69 | | | | | | | | | | | | | End of split % 149.51/21.69 | | | | | | | | | | | | | % 149.51/21.69 | | | | | | | | | | | | End of split % 149.51/21.69 | | | | | | | | | | | | % 149.51/21.69 | | | | | | | | | | | End of split % 149.51/21.69 | | | | | | | | | | | % 149.51/21.69 | | | | | | | | | | End of split % 149.51/21.69 | | | | | | | | | | % 149.51/21.69 | | | | | | | | | End of split % 149.51/21.69 | | | | | | | | | % 149.51/21.69 | | | | | | | | Case 2: % 149.51/21.69 | | | | | | | | | % 149.51/21.69 | | | | | | | | | (9285) all_36_1 = e3 % 149.51/21.69 | | | | | | | | | (9286) ~ (all_36_0 = e0) | ~ (all_36_2 = e2) % 149.51/21.69 | | | | | | | | | % 149.51/21.69 | | | | | | | | | COMBINE_EQS: (652), (9285) imply: % 149.51/21.69 | | | | | | | | | (9287) all_6_1 = e3 % 149.51/21.69 | | | | | | | | | % 149.51/21.69 | | | | | | | | | SIMP: (9287) implies: % 149.51/21.69 | | | | | | | | | (9288) all_6_1 = e3 % 149.51/21.69 | | | | | | | | | % 149.51/21.69 | | | | | | | | | REDUCE: (43), (9288) imply: % 149.51/21.69 | | | | | | | | | (9289) op(all_6_2, all_6_2) = e3 % 149.51/21.69 | | | | | | | | | % 149.51/21.69 | | | | | | | | | REDUCE: (42), (9288) imply: % 149.51/21.69 | | | | | | | | | (9290) op(e1, e3) = all_6_0 % 149.51/21.69 | | | | | | | | | % 149.51/21.69 | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_2, % 149.51/21.69 | | | | | | | | | all_6_0, e3, e1, simplifying with (211), (9290) % 149.51/21.69 | | | | | | | | | gives: % 149.51/21.69 | | | | | | | | | (9291) all_52_2 = all_6_0 % 149.51/21.69 | | | | | | | | | % 149.51/21.69 | | | | | | | | | COMBINE_EQS: (471), (9291) imply: % 149.51/21.69 | | | | | | | | | (9292) all_54_8 = all_6_0 % 149.51/21.69 | | | | | | | | | % 149.51/21.69 | | | | | | | | | COMBINE_EQS: (553), (9291) imply: % 149.51/21.69 | | | | | | | | | (9293) all_58_6 = all_6_0 % 149.51/21.69 | | | | | | | | | % 149.51/21.69 | | | | | | | | | REDUCE: (192), (9291) imply: % 149.51/21.69 | | | | | | | | | (9294) ~ (all_52_3 = all_6_0) % 149.51/21.69 | | | | | | | | | % 149.51/21.69 | | | | | | | | | SIMP: (9294) implies: % 149.51/21.69 | | | | | | | | | (9295) ~ (all_52_3 = all_6_0) % 149.51/21.69 | | | | | | | | | % 149.51/21.69 | | | | | | | | | REDUCE: (191), (9291) imply: % 149.51/21.69 | | | | | | | | | (9296) ~ (all_52_6 = all_6_0) % 149.51/21.69 | | | | | | | | | % 149.51/21.69 | | | | | | | | | SIMP: (9296) implies: % 149.51/21.69 | | | | | | | | | (9297) ~ (all_52_6 = all_6_0) % 149.51/21.69 | | | | | | | | | % 149.51/21.69 | | | | | | | | | REDUCE: (189), (9291) imply: % 149.51/21.69 | | | | | | | | | (9298) ~ (all_52_14 = all_6_0) % 149.51/21.69 | | | | | | | | | % 149.51/21.69 | | | | | | | | | SIMP: (9298) implies: % 149.51/21.69 | | | | | | | | | (9299) ~ (all_52_14 = all_6_0) % 149.51/21.69 | | | | | | | | | % 149.51/21.69 | | | | | | | | | REDUCE: (559), (9291) imply: % 149.51/21.69 | | | | | | | | | (9300) ~ (all_10_2 = all_6_0) % 149.51/21.69 | | | | | | | | | % 149.51/21.69 | | | | | | | | | SIMP: (9300) implies: % 149.51/21.70 | | | | | | | | | (9301) ~ (all_10_2 = all_6_0) % 149.51/21.70 | | | | | | | | | % 149.51/21.70 | | | | | | | | | REDUCE: (569), (9291) imply: % 149.51/21.70 | | | | | | | | | (9302) ~ (all_6_0 = all_6_2) % 149.51/21.70 | | | | | | | | | % 149.51/21.70 | | | | | | | | | BETA: splitting (288) gives: % 149.51/21.70 | | | | | | | | | % 149.51/21.70 | | | | | | | | | Case 1: % 149.51/21.70 | | | | | | | | | | % 149.51/21.70 | | | | | | | | | | (9303) ~ (all_56_31 = e1) % 149.51/21.70 | | | | | | | | | | % 149.51/21.70 | | | | | | | | | | REDUCE: (544), (9303) imply: % 149.51/21.70 | | | | | | | | | | (9304) ~ (all_4_2 = e1) % 149.51/21.70 | | | | | | | | | | % 149.51/21.70 | | | | | | | | | | REF_CLOSE: (4), (5), (36), (38), (41), (46), (48), (51), % 149.51/21.70 | | | | | | | | | | (171), (173), (174), (176), (182), (183), (184), % 149.51/21.70 | | | | | | | | | | (194), (196), (207), (237), (242), (243), (244), % 149.51/21.70 | | | | | | | | | | (247), (251), (287), (289), (290), (291), (292), % 149.51/21.70 | | | | | | | | | | (293), (296), (324), (326), (327), (328), (330), % 149.51/21.70 | | | | | | | | | | (333), (337), (360), (366), (374), (380), (386), % 149.51/21.70 | | | | | | | | | | (389), (401), (407), (425), (435), (447), (457), % 149.51/21.70 | | | | | | | | | | (473), (532), (540), (541), (542), (544), (545), % 149.51/21.70 | | | | | | | | | | (546), (548), (550), (552), (554), (555), (561), % 149.51/21.70 | | | | | | | | | | (571), (573), (575), (579), (580), (587), (588), % 149.51/21.70 | | | | | | | | | | (591), (617), (622), (627), (762), (8983), (8985), % 149.51/21.70 | | | | | | | | | | (9221), (9286), (9289), (9292), (9293), (9295), % 149.51/21.70 | | | | | | | | | | (9297), (9299), (9301), (9302), (9304), % 149.51/21.70 | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 149.51/21.70 | | | | | | | | | | #2. % 149.51/21.70 | | | | | | | | | | % 149.51/21.70 | | | | | | | | | Case 2: % 149.51/21.70 | | | | | | | | | | % 149.51/21.70 | | | | | | | | | | (9305) all_56_31 = e1 % 149.51/21.70 | | | | | | | | | | (9306) all_56_29 = e0 % 149.51/21.70 | | | | | | | | | | % 149.51/21.70 | | | | | | | | | | REF_CLOSE: (6), (7), (36), (38), (41), (43), (48), (51), % 149.51/21.70 | | | | | | | | | | (192), (205), (207), (242), (287), (293), (294), % 149.51/21.70 | | | | | | | | | | (319), (357), (365), (374), (381), (499), (541), % 149.51/21.70 | | | | | | | | | | (544), (545), (546), (547), (548), (549), (561), % 149.51/21.70 | | | | | | | | | | (575), (585), (588), (627), (676), (8985), (8987), % 149.51/21.70 | | | | | | | | | | (8992), (9305), (9306), (function-axioms) are % 149.51/21.70 | | | | | | | | | | inconsistent by sub-proof #13. % 149.51/21.70 | | | | | | | | | | % 149.51/21.70 | | | | | | | | | End of split % 149.51/21.70 | | | | | | | | | % 149.51/21.70 | | | | | | | | End of split % 149.51/21.70 | | | | | | | | % 149.51/21.70 | | | | | | | Case 2: % 149.51/21.70 | | | | | | | | % 149.51/21.70 | | | | | | | | (9307) all_28_0 = e2 % 149.51/21.70 | | | | | | | | (9308) ~ (all_28_1 = e3) | ~ (all_28_2 = e0) % 149.51/21.70 | | | | | | | | % 149.51/21.70 | | | | | | | | REF_CLOSE: (6), (7), (8), (36), (38), (41), (42), (43), (46), % 149.51/21.70 | | | | | | | | (48), (51), (144), (158), (174), (192), (205), (207), % 149.51/21.70 | | | | | | | | (208), (211), (237), (242), (247), (252), (287), % 149.51/21.70 | | | | | | | | (288), (291), (292), (293), (294), (297), (319), % 149.51/21.70 | | | | | | | | (321), (341), (357), (365), (366), (374), (381), % 149.51/21.70 | | | | | | | | (386), (402), (407), (419), (435), (443), (475), % 149.51/21.70 | | | | | | | | (499), (513), (540), (541), (542), (543), (544), % 149.51/21.70 | | | | | | | | (545), (546), (547), (548), (549), (550), (551), % 149.51/21.70 | | | | | | | | (555), (559), (561), (569), (571), (573), (575), % 149.51/21.70 | | | | | | | | (580), (585), (588), (591), (620), (622), (627), % 149.51/21.70 | | | | | | | | (634), (665), (676), (740), (764), (8985), (8986), % 149.51/21.70 | | | | | | | | (8987), (8992), (9307), (9308), (function-axioms) are % 149.51/21.70 | | | | | | | | inconsistent by sub-proof #5. % 149.51/21.70 | | | | | | | | % 149.51/21.70 | | | | | | | End of split % 149.51/21.70 | | | | | | | % 149.51/21.70 | | | | | | End of split % 149.51/21.70 | | | | | | % 149.51/21.70 | | | | | End of split % 149.51/21.70 | | | | | % 149.51/21.70 | | | | Case 2: % 149.51/21.70 | | | | | % 149.51/21.70 | | | | | (9309) all_14_0 = e1 % 149.51/21.70 | | | | | (9310) ~ (all_14_1 = e3) | ~ (all_14_2 = e0) % 149.51/21.70 | | | | | % 149.51/21.70 | | | | | COMBINE_EQS: (758), (9309) imply: % 149.51/21.70 | | | | | (9311) all_8_0 = e1 % 149.51/21.70 | | | | | % 149.51/21.70 | | | | | COMBINE_EQS: (763), (9311) imply: % 149.51/21.70 | | | | | (9312) all_42_0 = e1 % 149.51/21.70 | | | | | % 149.51/21.70 | | | | | REDUCE: (47), (9311) imply: % 149.51/21.70 | | | | | (9313) op(e2, all_8_1) = e1 % 149.51/21.70 | | | | | % 149.51/21.70 | | | | | BETA: splitting (79) gives: % 149.51/21.70 | | | | | % 149.51/21.70 | | | | | Case 1: % 149.51/21.70 | | | | | | % 149.51/21.70 | | | | | | (9314) ~ (all_20_0 = e3) % 149.51/21.70 | | | | | | % 149.51/21.70 | | | | | | REDUCE: (8984), (9314) imply: % 149.51/21.70 | | | | | | (9315) $false % 149.51/21.70 | | | | | | % 149.51/21.70 | | | | | | CLOSE: (9315) is inconsistent. % 149.51/21.70 | | | | | | % 149.51/21.70 | | | | | Case 2: % 149.51/21.70 | | | | | | % 149.51/21.70 | | | | | | (9316) ~ (all_20_1 = e2) | ~ (all_20_2 = e1) % 149.51/21.70 | | | | | | % 149.51/21.70 | | | | | | BETA: splitting (99) gives: % 149.51/21.70 | | | | | | % 149.51/21.70 | | | | | | Case 1: % 149.51/21.70 | | | | | | | % 149.51/21.70 | | | | | | | (9317) ~ (all_28_0 = e2) % 149.51/21.70 | | | | | | | % 149.51/21.70 | | | | | | | REDUCE: (740), (9317) imply: % 149.51/21.70 | | | | | | | (9318) ~ (all_6_0 = e2) % 149.51/21.70 | | | | | | | % 149.51/21.70 | | | | | | | BETA: splitting (119) gives: % 149.51/21.70 | | | | | | | % 149.51/21.70 | | | | | | | Case 1: % 149.51/21.70 | | | | | | | | % 149.51/21.70 | | | | | | | | (9319) ~ (all_36_1 = e3) % 149.51/21.70 | | | | | | | | % 149.51/21.70 | | | | | | | | REDUCE: (652), (9319) imply: % 149.51/21.70 | | | | | | | | (9320) ~ (all_6_1 = e3) % 149.51/21.70 | | | | | | | | % 149.51/21.70 | | | | | | | | BETA: splitting (134) gives: % 149.51/21.70 | | | | | | | | % 149.51/21.70 | | | | | | | | Case 1: % 149.51/21.70 | | | | | | | | | % 149.51/21.70 | | | | | | | | | (9321) ~ (all_42_0 = e1) % 149.51/21.70 | | | | | | | | | % 149.51/21.70 | | | | | | | | | REDUCE: (9312), (9321) imply: % 149.51/21.70 | | | | | | | | | (9322) $false % 149.51/21.70 | | | | | | | | | % 149.51/21.70 | | | | | | | | | CLOSE: (9322) is inconsistent. % 149.51/21.70 | | | | | | | | | % 149.51/21.70 | | | | | | | | Case 2: % 149.51/21.70 | | | | | | | | | % 149.51/21.70 | | | | | | | | | (9323) ~ (all_42_1 = e0) | ~ (all_42_2 = e3) % 149.51/21.70 | | | | | | | | | % 149.51/21.70 | | | | | | | | | BETA: splitting (288) gives: % 149.51/21.70 | | | | | | | | | % 149.51/21.70 | | | | | | | | | Case 1: % 149.51/21.70 | | | | | | | | | | % 149.51/21.70 | | | | | | | | | | (9324) ~ (all_56_31 = e1) % 149.51/21.70 | | | | | | | | | | % 149.51/21.70 | | | | | | | | | | REDUCE: (544), (9324) imply: % 149.51/21.70 | | | | | | | | | | (9325) ~ (all_4_2 = e1) % 149.51/21.70 | | | | | | | | | | % 149.51/21.70 | | | | | | | | | | BETA: splitting (290) gives: % 149.51/21.70 | | | | | | | | | | % 149.51/21.70 | | | | | | | | | | Case 1: % 149.51/21.70 | | | | | | | | | | | % 149.51/21.70 | | | | | | | | | | | (9326) ~ (all_56_31 = e3) % 149.51/21.70 | | | | | | | | | | | % 149.51/21.70 | | | | | | | | | | | REDUCE: (544), (9326) imply: % 149.51/21.70 | | | | | | | | | | | (9327) ~ (all_4_2 = e3) % 149.51/21.70 | | | | | | | | | | | % 149.51/21.70 | | | | | | | | | | | BETA: splitting (291) gives: % 149.51/21.70 | | | | | | | | | | | % 149.51/21.70 | | | | | | | | | | | Case 1: % 149.51/21.70 | | | | | | | | | | | | % 149.51/21.70 | | | | | | | | | | | | (9328) ~ (all_56_21 = e0) % 149.51/21.70 | | | | | | | | | | | | % 149.51/21.70 | | | | | | | | | | | | REDUCE: (374), (9328) imply: % 149.51/21.70 | | | | | | | | | | | | (9329) ~ (all_6_2 = e0) % 149.51/21.70 | | | | | | | | | | | | % 149.51/21.70 | | | | | | | | | | | | BETA: splitting (295) gives: % 149.51/21.70 | | | | | | | | | | | | % 149.51/21.70 | | | | | | | | | | | | Case 1: % 149.51/21.70 | | | | | | | | | | | | | % 149.51/21.70 | | | | | | | | | | | | | (9330) ~ (all_56_11 = e1) % 149.51/21.70 | | | | | | | | | | | | | % 149.51/21.70 | | | | | | | | | | | | | REDUCE: (545), (9330) imply: % 149.51/21.70 | | | | | | | | | | | | | (9331) ~ (all_8_2 = e1) % 149.51/21.70 | | | | | | | | | | | | | % 149.51/21.70 | | | | | | | | | | | | | BETA: splitting (289) gives: % 149.51/21.70 | | | | | | | | | | | | | % 149.51/21.70 | | | | | | | | | | | | | Case 1: % 149.51/21.70 | | | | | | | | | | | | | | % 149.51/21.70 | | | | | | | | | | | | | | (9332) ~ (all_56_31 = e2) % 149.51/21.70 | | | | | | | | | | | | | | % 149.51/21.70 | | | | | | | | | | | | | | REDUCE: (544), (9332) imply: % 149.51/21.70 | | | | | | | | | | | | | | (9333) ~ (all_4_2 = e2) % 149.51/21.70 | | | | | | | | | | | | | | % 149.51/21.70 | | | | | | | | | | | | | | REF_CLOSE: (36), (38), (237), (540), (627), (8985), (9325), % 149.51/21.70 | | | | | | | | | | | | | | (9327), (9333), (function-axioms) are inconsistent % 149.51/21.70 | | | | | | | | | | | | | | by sub-proof #29. % 149.51/21.70 | | | | | | | | | | | | | | % 149.51/21.70 | | | | | | | | | | | | | Case 2: % 149.51/21.70 | | | | | | | | | | | | | | % 149.51/21.70 | | | | | | | | | | | | | | (9334) all_56_31 = e2 % 149.51/21.70 | | | | | | | | | | | | | | (9335) all_56_27 = e0 % 149.51/21.70 | | | | | | | | | | | | | | % 149.51/21.70 | | | | | | | | | | | | | | COMBINE_EQS: (360), (9335) imply: % 149.51/21.70 | | | | | | | | | | | | | | (9336) all_52_7 = e0 % 149.51/21.70 | | | | | | | | | | | | | | % 149.51/21.70 | | | | | | | | | | | | | | SIMP: (9336) implies: % 149.51/21.70 | | | | | | | | | | | | | | (9337) all_52_7 = e0 % 149.51/21.70 | | | | | | | | | | | | | | % 149.51/21.70 | | | | | | | | | | | | | | COMBINE_EQS: (544), (9334) imply: % 149.51/21.70 | | | | | | | | | | | | | | (9338) all_4_2 = e2 % 149.51/21.70 | | | | | | | | | | | | | | % 149.51/21.70 | | | | | | | | | | | | | | REDUCE: (575), (9337) imply: % 149.51/21.70 | | | | | | | | | | | | | | (9339) ~ (all_8_2 = e0) % 149.51/21.70 | | | | | | | | | | | | | | % 149.51/21.70 | | | | | | | | | | | | | | SIMP: (9339) implies: % 149.51/21.70 | | | | | | | | | | | | | | (9340) ~ (all_8_2 = e0) % 149.51/21.70 | | | | | | | | | | | | | | % 149.51/21.70 | | | | | | | | | | | | | | REDUCE: (38), (9338) imply: % 149.51/21.70 | | | | | | | | | | | | | | (9341) op(e2, e2) = all_4_1 % 149.51/21.70 | | | | | | | | | | | | | | % 149.51/21.70 | | | | | | | | | | | | | | REDUCE: (627), (9338) imply: % 149.51/21.70 | | | | | | | | | | | | | | (9342) op(e0, e2) = all_56_30 % 149.51/21.70 | | | | | | | | | | | | | | % 149.51/21.70 | | | | | | | | | | | | | | REDUCE: (206), (9337) imply: % 149.51/21.70 | | | | | | | | | | | | | | (9343) op(e0, e2) = e0 % 149.51/21.70 | | | | | | | | | | | | | | % 149.51/21.70 | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, % 149.51/21.70 | | | | | | | | | | | | | | all_56_30, e2, e0, simplifying with (9342), (9343) % 149.51/21.70 | | | | | | | | | | | | | | gives: % 149.51/21.70 | | | | | | | | | | | | | | (9344) all_56_30 = e0 % 149.51/21.70 | | | | | | | | | | | | | | % 149.51/21.70 | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_8_2, % 149.51/21.70 | | | | | | | | | | | | | | all_4_1, e2, e2, simplifying with (46), (9341) % 149.51/21.70 | | | | | | | | | | | | | | gives: % 149.51/21.70 | | | | | | | | | | | | | | (9345) all_8_2 = all_4_1 % 149.51/21.70 | | | | | | | | | | | | | | % 149.51/21.70 | | | | | | | | | | | | | | COMBINE_EQS: (534), (9345) imply: % 149.51/21.70 | | | | | | | | | | | | | | (9346) all_42_2 = all_4_1 % 149.51/21.70 | | | | | | | | | | | | | | % 149.51/21.70 | | | | | | | | | | | | | | COMBINE_EQS: (542), (9345) imply: % 149.51/21.70 | | | | | | | | | | | | | | (9347) all_54_5 = all_4_1 % 149.51/21.70 | | | | | | | | | | | | | | % 149.51/21.70 | | | | | | | | | | | | | | COMBINE_EQS: (545), (9345) imply: % 149.51/21.70 | | | | | | | | | | | | | | (9348) all_56_11 = all_4_1 % 149.51/21.70 | | | | | | | | | | | | | | % 149.51/21.70 | | | | | | | | | | | | | | REDUCE: (48), (9345) imply: % 149.51/21.70 | | | | | | | | | | | | | | (9349) op(all_4_1, all_4_1) = all_8_1 % 149.51/21.70 | | | | | | | | | | | | | | % 149.51/21.70 | | | | | | | | | | | | | | REDUCE: (617), (9345) imply: % 149.51/21.70 | | | | | | | | | | | | | | (9350) op(e2, all_4_1) = all_56_10 % 149.51/21.70 | | | | | | | | | | | | | | % 149.51/21.70 | | | | | | | | | | | | | | BETA: splitting (296) gives: % 149.51/21.70 | | | | | | | | | | | | | | % 149.51/21.70 | | | | | | | | | | | | | | Case 1: % 149.51/21.70 | | | | | | | | | | | | | | | % 149.51/21.70 | | | | | | | | | | | | | | | (9351) ~ (all_56_11 = e3) % 149.51/21.70 | | | | | | | | | | | | | | | % 149.51/21.70 | | | | | | | | | | | | | | | REDUCE: (9348), (9351) imply: % 149.51/21.70 | | | | | | | | | | | | | | | (9352) ~ (all_4_1 = e3) % 149.51/21.70 | | | | | | | | | | | | | | | % 149.51/21.70 | | | | | | | | | | | | | | | REF_CLOSE: (7), (247), (542), (8985), (9331), (9340), (9343), % 149.51/21.70 | | | | | | | | | | | | | | | (9347), (9352), (function-axioms) are inconsistent % 149.51/21.70 | | | | | | | | | | | | | | | by sub-proof #27. % 149.51/21.70 | | | | | | | | | | | | | | | % 149.51/21.70 | | | | | | | | | | | | | | Case 2: % 149.51/21.70 | | | | | | | | | | | | | | | % 149.51/21.70 | | | | | | | | | | | | | | | (9353) all_56_11 = e3 % 149.51/21.70 | | | | | | | | | | | | | | | % 149.51/21.70 | | | | | | | | | | | | | | | COMBINE_EQS: (9348), (9353) imply: % 149.51/21.70 | | | | | | | | | | | | | | | (9354) all_4_1 = e3 % 149.51/21.70 | | | | | | | | | | | | | | | % 149.51/21.70 | | | | | | | | | | | | | | | REF_CLOSE: (6), (51), (215), (252), (296), (425), (543), % 149.51/21.70 | | | | | | | | | | | | | | | (557), (639), (8987), (9313), (9323), (9346), % 149.51/21.70 | | | | | | | | | | | | | | | (9348), (9349), (9350), (9354), (function-axioms) % 149.51/21.70 | | | | | | | | | | | | | | | are inconsistent by sub-proof #1. % 149.51/21.70 | | | | | | | | | | | | | | | % 149.51/21.70 | | | | | | | | | | | | | | End of split % 149.51/21.70 | | | | | | | | | | | | | | % 149.51/21.70 | | | | | | | | | | | | | End of split % 149.51/21.70 | | | | | | | | | | | | | % 149.51/21.70 | | | | | | | | | | | | Case 2: % 149.51/21.70 | | | | | | | | | | | | | % 149.51/21.70 | | | | | | | | | | | | | (9355) all_56_13 = e2 % 149.51/21.70 | | | | | | | | | | | | | (9356) all_56_11 = e1 % 149.51/21.70 | | | | | | | | | | | | | % 149.51/21.70 | | | | | | | | | | | | | COMBINE_EQS: (545), (9356) imply: % 149.51/21.70 | | | | | | | | | | | | | (9357) all_8_2 = e1 % 149.51/21.70 | | | | | | | | | | | | | % 149.51/21.70 | | | | | | | | | | | | | COMBINE_EQS: (431), (9355) imply: % 149.51/21.70 | | | | | | | | | | | | | (9358) all_52_9 = e2 % 149.51/21.70 | | | | | | | | | | | | | % 149.51/21.70 | | | | | | | | | | | | | REDUCE: (194), (9358) imply: % 149.51/21.70 | | | | | | | | | | | | | (9359) ~ (all_52_1 = e2) % 149.51/21.70 | | | | | | | | | | | | | % 149.51/21.70 | | | | | | | | | | | | | REDUCE: (583), (9358) imply: % 149.51/21.70 | | | | | | | | | | | | | (9360) ~ (all_6_2 = e2) % 149.51/21.70 | | | | | | | | | | | | | % 149.51/21.70 | | | | | | | | | | | | | SIMP: (9360) implies: % 149.51/21.70 | | | | | | | | | | | | | (9361) ~ (all_6_2 = e2) % 149.51/21.70 | | | | | | | | | | | | | % 149.51/21.70 | | | | | | | | | | | | | REDUCE: (579), (9357) imply: % 149.51/21.70 | | | | | | | | | | | | | (9362) ~ (all_52_13 = e1) % 149.51/21.70 | | | | | | | | | | | | | % 149.51/21.70 | | | | | | | | | | | | | REDUCE: (48), (9357) imply: % 149.51/21.70 | | | | | | | | | | | | | (9363) op(e1, e1) = all_8_1 % 149.51/21.70 | | | | | | | | | | | | | % 149.51/21.70 | | | | | | | | | | | | | REF_CLOSE: (41), (189), (193), (197), (215), (242), (248), % 149.51/21.70 | | | | | | | | | | | | | (293), (321), (323), (332), (374), (381), (386), % 149.51/21.70 | | | | | | | | | | | | | (401), (463), (541), (547), (550), (551), (569), % 149.51/21.70 | | | | | | | | | | | | | (587), (8987), (9313), (9325), (9327), (9329), % 149.51/21.70 | | | | | | | | | | | | | (9359), (9361), (9362), (9363), (function-axioms) % 149.51/21.70 | | | | | | | | | | | | | are inconsistent by sub-proof #248. % 149.51/21.70 | | | | | | | | | | | | | % 149.51/21.70 | | | | | | | | | | | | End of split % 149.51/21.70 | | | | | | | | | | | | % 149.51/21.70 | | | | | | | | | | | Case 2: % 149.51/21.70 | | | | | | | | | | | | % 149.51/21.70 | | | | | | | | | | | | (9364) all_56_23 = e1 % 149.51/21.70 | | | | | | | | | | | | (9365) all_56_21 = e0 % 149.51/21.70 | | | | | | | | | | | | % 149.51/21.70 | | | | | | | | | | | | COMBINE_EQS: (374), (9365) imply: % 149.51/21.70 | | | | | | | | | | | | (9366) all_6_2 = e0 % 149.51/21.70 | | | | | | | | | | | | % 149.51/21.70 | | | | | | | | | | | | SIMP: (9366) implies: % 149.51/21.70 | | | | | | | | | | | | (9367) all_6_2 = e0 % 149.51/21.70 | | | | | | | | | | | | % 149.51/21.70 | | | | | | | | | | | | COMBINE_EQS: (366), (9364) imply: % 149.51/21.70 | | | | | | | | | | | | (9368) all_52_14 = e1 % 149.51/21.70 | | | | | | | | | | | | % 149.51/21.70 | | | | | | | | | | | | SIMP: (9368) implies: % 149.51/21.70 | | | | | | | | | | | | (9369) all_52_14 = e1 % 149.51/21.70 | | | | | | | | | | | | % 149.51/21.70 | | | | | | | | | | | | REDUCE: (591), (9369) imply: % 149.51/21.70 | | | | | | | | | | | | (9370) ~ (all_4_2 = e1) % 149.51/21.70 | | | | | | | | | | | | % 149.51/21.70 | | | | | | | | | | | | REDUCE: (43), (9367) imply: % 149.51/21.70 | | | | | | | | | | | | (9371) op(e0, e0) = all_6_1 % 149.51/21.70 | | | | | | | | | | | | % 149.51/21.70 | | | | | | | | | | | | REF_CLOSE: (36), (38), (237), (540), (627), (8985), (8986), % 149.51/21.70 | | | | | | | | | | | | (9320), (9325), (9371), (function-axioms) are % 149.51/21.70 | | | | | | | | | | | | inconsistent by sub-proof #23. % 149.51/21.70 | | | | | | | | | | | | % 149.51/21.70 | | | | | | | | | | | End of split % 149.51/21.70 | | | | | | | | | | | % 149.51/21.70 | | | | | | | | | | Case 2: % 149.51/21.70 | | | | | | | | | | | % 149.51/21.70 | | | | | | | | | | | (9372) all_56_31 = e3 % 149.51/21.70 | | | | | | | | | | | (9373) all_56_25 = e0 % 149.51/21.70 | | | | | | | | | | | % 149.51/21.70 | | | | | | | | | | | COMBINE_EQS: (447), (9373) imply: % 149.51/21.70 | | | | | | | | | | | (9374) all_52_3 = e0 % 149.51/21.70 | | | | | | | | | | | % 149.51/21.70 | | | | | | | | | | | SIMP: (9374) implies: % 149.51/21.70 | | | | | | | | | | | (9375) all_52_3 = e0 % 149.51/21.70 | | | | | | | | | | | % 149.51/21.70 | | | | | | | | | | | COMBINE_EQS: (544), (9372) imply: % 149.51/21.70 | | | | | | | | | | | (9376) all_4_2 = e3 % 149.51/21.70 | | | | | | | | | | | % 149.51/21.70 | | | | | | | | | | | COMBINE_EQS: (547), (9376) imply: % 149.51/21.70 | | | | | | | | | | | (9377) all_58_15 = e3 % 149.51/21.70 | | | | | | | | | | | % 149.51/21.70 | | | | | | | | | | | COMBINE_EQS: (365), (9375) imply: % 149.51/21.70 | | | | | | | | | | | (9378) all_58_12 = e0 % 149.51/21.70 | | | | | | | | | | | % 149.51/21.70 | | | | | | | | | | | REDUCE: (192), (9375) imply: % 149.51/21.70 | | | | | | | | | | | (9379) ~ (all_52_2 = e0) % 149.51/21.70 | | | | | | | | | | | % 149.51/21.70 | | | | | | | | | | | REDUCE: (188), (9375) imply: % 149.51/21.70 | | | | | | | | | | | (9380) ~ (all_52_7 = e0) % 149.51/21.70 | | | | | | | | | | | % 149.51/21.70 | | | | | | | | | | | SIMP: (9380) implies: % 149.51/21.70 | | | | | | | | | | | (9381) ~ (all_52_7 = e0) % 149.51/21.70 | | | | | | | | | | | % 149.51/21.70 | | | | | | | | | | | REDUCE: (187), (9375) imply: % 149.51/21.70 | | | | | | | | | | | (9382) ~ (all_52_11 = e0) % 149.51/21.70 | | | | | | | | | | | % 149.51/21.70 | | | | | | | | | | | SIMP: (9382) implies: % 149.51/21.70 | | | | | | | | | | | (9383) ~ (all_52_11 = e0) % 149.51/21.70 | | | | | | | | | | | % 149.51/21.70 | | | | | | | | | | | REDUCE: (561), (9375) imply: % 149.51/21.70 | | | | | | | | | | | (9384) ~ (all_10_2 = e0) % 149.51/21.70 | | | | | | | | | | | % 149.51/21.70 | | | | | | | | | | | SIMP: (9384) implies: % 149.51/21.70 | | | | | | | | | | | (9385) ~ (all_10_2 = e0) % 149.51/21.70 | | | | | | | | | | | % 149.51/21.70 | | | | | | | | | | | REDUCE: (570), (9375), (9376) imply: % 149.51/21.70 | | | | | | | | | | | (9386) ~ (e3 = e0) % 149.51/21.70 | | | | | | | | | | | % 149.51/21.70 | | | | | | | | | | | REDUCE: (581), (9376) imply: % 149.51/21.70 | | | | | | | | | | | (9387) ~ (all_52_7 = e3) % 149.51/21.70 | | | | | | | | | | | % 149.51/21.70 | | | | | | | | | | | REDUCE: (588), (9376) imply: % 149.51/21.70 | | | | | | | | | | | (9388) ~ (all_52_11 = e3) % 149.51/21.70 | | | | | | | | | | | % 149.51/21.70 | | | | | | | | | | | REDUCE: (591), (9376) imply: % 149.51/21.70 | | | | | | | | | | | (9389) ~ (all_52_14 = e3) % 149.51/21.70 | | | | | | | | | | | % 149.51/21.70 | | | | | | | | | | | REDUCE: (38), (9376) imply: % 149.51/21.70 | | | | | | | | | | | (9390) op(e3, e3) = all_4_1 % 149.51/21.70 | | | | | | | | | | | % 149.51/21.70 | | | | | | | | | | | REDUCE: (36), (9376) imply: % 149.51/21.70 | | | | | | | | | | | (9391) op(e0, e0) = e3 % 149.51/21.70 | | | | | | | | | | | % 149.51/21.70 | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_10_2, % 149.51/21.70 | | | | | | | | | | | all_4_1, e3, e3, simplifying with (51), (9390) % 149.51/21.70 | | | | | | | | | | | gives: % 149.51/21.70 | | | | | | | | | | | (9392) all_10_2 = all_4_1 % 149.51/21.70 | | | | | | | | | | | % 149.51/21.70 | | | | | | | | | | | COMBINE_EQS: (543), (9392) imply: % 149.51/21.70 | | | | | | | | | | | (9393) all_54_0 = all_4_1 % 149.51/21.70 | | | | | | | | | | | % 149.51/21.70 | | | | | | | | | | | COMBINE_EQS: (546), (9392) imply: % 149.51/21.70 | | | | | | | | | | | (9394) all_56_1 = all_4_1 % 149.51/21.70 | | | | | | | | | | | % 149.51/21.70 | | | | | | | | | | | COMBINE_EQS: (419), (9392) imply: % 149.51/21.70 | | | | | | | | | | | (9395) all_58_0 = all_4_1 % 149.51/21.70 | | | | | | | | | | | % 149.51/21.70 | | | | | | | | | | | REDUCE: (557), (9392) imply: % 149.51/21.70 | | | | | | | | | | | (9396) ~ (all_52_1 = all_4_1) % 149.51/21.70 | | | | | | | | | | | % 149.51/21.70 | | | | | | | | | | | REDUCE: (559), (9392) imply: % 149.51/21.70 | | | | | | | | | | | (9397) ~ (all_52_2 = all_4_1) % 149.51/21.70 | | | | | | | | | | | % 149.51/21.70 | | | | | | | | | | | REDUCE: (563), (9392) imply: % 149.51/21.70 | | | | | | | | | | | (9398) ~ (all_52_4 = all_4_1) % 149.51/21.70 | | | | | | | | | | | % 149.51/21.70 | | | | | | | | | | | REDUCE: (567), (9392) imply: % 149.51/21.70 | | | | | | | | | | | (9399) ~ (all_52_12 = all_4_1) % 149.51/21.70 | | | | | | | | | | | % 149.51/21.70 | | | | | | | | | | | REDUCE: (9385), (9392) imply: % 149.51/21.70 | | | | | | | | | | | (9400) ~ (all_4_1 = e0) % 149.51/21.70 | | | | | | | | | | | % 149.51/21.70 | | | | | | | | | | | BETA: splitting (291) gives: % 149.51/21.70 | | | | | | | | | | | % 149.51/21.70 | | | | | | | | | | | Case 1: % 149.51/21.70 | | | | | | | | | | | | % 149.51/21.70 | | | | | | | | | | | | (9401) ~ (all_56_21 = e0) % 149.51/21.70 | | | | | | | | | | | | % 149.51/21.70 | | | | | | | | | | | | REDUCE: (374), (9401) imply: % 149.51/21.70 | | | | | | | | | | | | (9402) ~ (all_6_2 = e0) % 149.51/21.70 | | | | | | | | | | | | % 149.51/21.70 | | | | | | | | | | | | BETA: splitting (292) gives: % 149.51/21.70 | | | | | | | | | | | | % 149.51/21.70 | | | | | | | | | | | | Case 1: % 149.51/21.70 | | | | | | | | | | | | | % 149.51/21.70 | | | | | | | | | | | | | (9403) ~ (all_56_21 = e2) % 149.51/21.70 | | | | | | | | | | | | | % 149.51/21.70 | | | | | | | | | | | | | REDUCE: (374), (9403) imply: % 149.51/21.70 | | | | | | | | | | | | | (9404) ~ (all_6_2 = e2) % 149.51/21.70 | | | | | | | | | | | | | % 149.51/21.70 | | | | | | | | | | | | | BETA: splitting (294) gives: % 149.51/21.70 | | | | | | | | | | | | | % 149.51/21.70 | | | | | | | | | | | | | Case 1: % 149.51/21.70 | | | | | | | | | | | | | | % 149.51/21.70 | | | | | | | | | | | | | | (9405) ~ (all_56_11 = e0) % 149.51/21.70 | | | | | | | | | | | | | | % 149.51/21.70 | | | | | | | | | | | | | | REDUCE: (545), (9405) imply: % 149.51/21.70 | | | | | | | | | | | | | | (9406) ~ (all_8_2 = e0) % 149.51/21.70 | | | | | | | | | | | | | | % 149.51/21.70 | | | | | | | | | | | | | | BETA: splitting (293) gives: % 149.51/21.70 | | | | | | | | | | | | | | % 149.51/21.70 | | | | | | | | | | | | | | Case 1: % 149.51/21.70 | | | | | | | | | | | | | | | % 149.51/21.70 | | | | | | | | | | | | | | | (9407) ~ (all_56_21 = e3) % 149.51/21.70 | | | | | | | | | | | | | | | % 149.51/21.70 | | | | | | | | | | | | | | | REDUCE: (374), (9407) imply: % 149.51/21.70 | | | | | | | | | | | | | | | (9408) ~ (all_6_2 = e3) % 149.51/21.70 | | | | | | | | | | | | | | | % 149.51/21.70 | | | | | | | | | | | | | | | BETA: splitting (242) gives: % 149.51/21.70 | | | | | | | | | | | | | | | % 149.51/21.70 | | | | | | | | | | | | | | | Case 1: % 149.51/21.70 | | | | | | | | | | | | | | | | % 149.51/21.70 | | | | | | | | | | | | | | | | (9409) all_54_10 = e3 % 149.51/21.70 | | | | | | | | | | | | | | | | % 149.51/21.70 | | | | | | | | | | | | | | | | REF_CLOSE: (541), (9408), (9409) are inconsistent by % 149.51/21.70 | | | | | | | | | | | | | | | | sub-proof #736. % 149.51/21.70 | | | | | | | | | | | | | | | | % 149.51/21.70 | | | | | | | | | | | | | | | Case 2: % 149.51/21.70 | | | | | | | | | | | | | | | | % 149.51/21.70 | | | | | | | | | | | | | | | | (9410) ~ (all_54_10 = e3) % 149.51/21.70 | | | | | | | | | | | | | | | | (9411) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 149.51/21.70 | | | | | | | | | | | | | | | | % 149.51/21.70 | | | | | | | | | | | | | | | | BETA: splitting (9411) gives: % 149.51/21.70 | | | | | | | | | | | | | | | | % 149.51/21.70 | | | | | | | | | | | | | | | | Case 1: % 149.51/21.70 | | | | | | | | | | | | | | | | | % 149.51/21.70 | | | | | | | | | | | | | | | | | (9412) all_54_10 = e2 % 149.51/21.70 | | | | | | | | | | | | | | | | | % 149.51/21.70 | | | | | | | | | | | | | | | | | REF_CLOSE: (541), (9404), (9412) are inconsistent by % 149.51/21.70 | | | | | | | | | | | | | | | | | sub-proof #735. % 149.51/21.70 | | | | | | | | | | | | | | | | | % 149.51/21.70 | | | | | | | | | | | | | | | | Case 2: % 149.51/21.70 | | | | | | | | | | | | | | | | | % 149.51/21.70 | | | | | | | | | | | | | | | | | (9413) all_54_10 = e1 | all_54_10 = e0 % 149.51/21.70 | | | | | | | | | | | | | | | | | % 149.51/21.70 | | | | | | | | | | | | | | | | | BETA: splitting (9413) gives: % 149.51/21.70 | | | | | | | | | | | | | | | | | % 149.51/21.70 | | | | | | | | | | | | | | | | | Case 1: % 149.51/21.70 | | | | | | | | | | | | | | | | | | % 149.51/21.70 | | | | | | | | | | | | | | | | | | (9414) all_54_10 = e1 % 149.51/21.70 | | | | | | | | | | | | | | | | | | % 149.51/21.70 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (541), (9414) imply: % 149.51/21.70 | | | | | | | | | | | | | | | | | | (9415) all_6_2 = e1 % 149.51/21.70 | | | | | | | | | | | | | | | | | | % 149.51/21.70 | | | | | | | | | | | | | | | | | | SIMP: (9415) implies: % 149.51/21.70 | | | | | | | | | | | | | | | | | | (9416) all_6_2 = e1 % 149.51/21.70 | | | | | | | | | | | | | | | | | | % 149.51/21.70 | | | | | | | | | | | | | | | | | | REDUCE: (582), (9416) imply: % 149.51/21.70 | | | | | | | | | | | | | | | | | | (9417) ~ (all_52_8 = e1) % 149.51/21.70 | | | | | | | | | | | | | | | | | | % 149.51/21.70 | | | | | | | | | | | | | | | | | | REDUCE: (583), (9416) imply: % 149.51/21.70 | | | | | | | | | | | | | | | | | | (9418) ~ (all_52_9 = e1) % 149.51/21.70 | | | | | | | | | | | | | | | | | | % 149.51/21.70 | | | | | | | | | | | | | | | | | | REDUCE: (585), (9416) imply: % 149.51/21.70 | | | | | | | | | | | | | | | | | | (9419) ~ (all_52_11 = e1) % 149.51/21.70 | | | | | | | | | | | | | | | | | | % 149.51/21.70 | | | | | | | | | | | | | | | | | | REDUCE: (587), (9416) imply: % 149.51/21.70 | | | | | | | | | | | | | | | | | | (9420) ~ (all_52_14 = e1) % 149.51/21.70 | | | | | | | | | | | | | | | | | | % 149.51/21.70 | | | | | | | | | | | | | | | | | | REDUCE: (9408), (9416) imply: % 149.51/21.70 | | | | | | | | | | | | | | | | | | (9421) ~ (e3 = e1) % 149.51/21.70 | | | | | | | | | | | | | | | | | | % 149.51/21.70 | | | | | | | | | | | | | | | | | | REDUCE: (43), (9416) imply: % 149.51/21.70 | | | | | | | | | | | | | | | | | | (9422) op(e1, e1) = all_6_1 % 149.51/21.70 | | | | | | | | | | | | | | | | | | % 149.51/21.70 | | | | | | | | | | | | | | | | | | REDUCE: (622), (9416) imply: % 149.51/21.70 | | | | | | | | | | | | | | | | | | (9423) op(e1, e1) = all_56_20 % 149.51/21.70 | | | | | | | | | | | | | | | | | | % 149.51/21.70 | | | | | | | | | | | | | | | | | | REDUCE: (41), (9416) imply: % 149.51/21.70 | | | | | | | | | | | | | | | | | | (9424) op(e1, e1) = e1 % 149.51/21.70 | | | | | | | | | | | | | | | | | | % 149.51/21.70 | | | | | | | | | | | | | | | | | | BETA: splitting (318) gives: % 149.51/21.70 | | | | | | | | | | | | | | | | | | % 149.51/21.70 | | | | | | | | | | | | | | | | | | Case 1: % 149.51/21.70 | | | | | | | | | | | | | | | | | | | % 149.51/21.70 | | | | | | | | | | | | | | | | | | | (9425) all_58_12 = e1 % 149.51/21.70 | | | | | | | | | | | | | | | | | | | % 149.51/21.70 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (9378), (9425) are inconsistent by sub-proof % 149.51/21.70 | | | | | | | | | | | | | | | | | | | #475. % 149.51/21.70 | | | | | | | | | | | | | | | | | | | % 149.51/21.70 | | | | | | | | | | | | | | | | | | Case 2: % 149.51/21.70 | | | | | | | | | | | | | | | | | | | % 149.51/21.70 | | | | | | | | | | | | | | | | | | | (9426) all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1 % 149.51/21.70 | | | | | | | | | | | | | | | | | | | % 149.51/21.70 | | | | | | | | | | | | | | | | | | | BETA: splitting (9426) gives: % 149.51/21.70 | | | | | | | | | | | | | | | | | | | % 149.51/21.70 | | | | | | | | | | | | | | | | | | | Case 1: % 149.51/21.70 | | | | | | | | | | | | | | | | | | | | % 149.51/21.70 | | | | | | | | | | | | | | | | | | | | (9427) all_58_13 = e1 % 149.51/21.70 | | | | | | | | | | | | | | | | | | | | % 149.51/21.70 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (549), (9427) imply: % 149.51/21.70 | | | | | | | | | | | | | | | | | | | | (9428) all_52_7 = e1 % 149.51/21.70 | | | | | | | | | | | | | | | | | | | | % 149.51/21.70 | | | | | | | | | | | | | | | | | | | | SIMP: (9428) implies: % 149.51/21.70 | | | | | | | | | | | | | | | | | | | | (9429) all_52_7 = e1 % 149.51/21.70 | | | | | | | | | | | | | | | | | | | | % 149.51/21.70 | | | | | | | | | | | | | | | | | | | | REDUCE: (183), (9429) imply: % 149.51/21.70 | | | | | | | | | | | | | | | | | | | | (9430) ~ (all_52_4 = e1) % 149.51/21.70 | | | | | | | | | | | | | | | | | | | | % 149.51/21.70 | | | | | | | | | | | | | | | | | | | | REDUCE: (173), (9429) imply: % 149.51/21.70 | | | | | | | | | | | | | | | | | | | | (9431) ~ (all_52_11 = e1) % 149.51/21.70 | | | | | | | | | | | | | | | | | | | | % 149.51/21.70 | | | | | | | | | | | | | | | | | | | | REDUCE: (575), (9429) imply: % 149.51/21.70 | | | | | | | | | | | | | | | | | | | | (9432) ~ (all_8_2 = e1) % 149.51/21.70 | | | | | | | | | | | | | | | | | | | | % 149.51/21.70 | | | | | | | | | | | | | | | | | | | | SIMP: (9432) implies: % 149.51/21.70 | | | | | | | | | | | | | | | | | | | | (9433) ~ (all_8_2 = e1) % 149.51/21.70 | | | | | | | | | | | | | | | | | | | | % 149.51/21.70 | | | | | | | | | | | | | | | | | | | | REDUCE: (206), (9429) imply: % 149.51/21.70 | | | | | | | | | | | | | | | | | | | | (9434) op(e0, e2) = e1 % 149.51/21.70 | | | | | | | | | | | | | | | | | | | | % 149.51/21.70 | | | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives: % 149.51/21.70 | | | | | | | | | | | | | | | | | | | | % 149.51/21.70 | | | | | | | | | | | | | | | | | | | | Case 1: % 149.51/21.70 | | | | | | | | | | | | | | | | | | | | | % 149.51/21.70 | | | | | | | | | | | | | | | | | | | | | (9435) all_54_14 = e3 % 149.51/21.70 | | | | | | | | | | | | | | | | | | | | | % 149.51/21.70 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (482), (9435) imply: % 149.51/21.70 | | | | | | | | | | | | | | | | | | | | | (9436) all_52_11 = e3 % 149.51/21.70 | | | | | | | | | | | | | | | | | | | | | % 149.51/21.70 | | | | | | | | | | | | | | | | | | | | | REDUCE: (9388), (9436) imply: % 149.51/21.70 | | | | | | | | | | | | | | | | | | | | | (9437) $false % 149.51/21.70 | | | | | | | | | | | | | | | | | | | | | % 149.51/21.70 | | | | | | | | | | | | | | | | | | | | | CLOSE: (9437) is inconsistent. % 149.51/21.70 | | | | | | | | | | | | | | | | | | | | | % 149.51/21.70 | | | | | | | | | | | | | | | | | | | | Case 2: % 149.51/21.70 | | | | | | | | | | | | | | | | | | | | | % 149.51/21.70 | | | | | | | | | | | | | | | | | | | | | (9438) all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0 % 149.51/21.70 | | | | | | | | | | | | | | | | | | | | | % 149.51/21.70 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9438) gives: % 149.51/21.70 | | | | | | | | | | | | | | | | | | | | | % 149.51/21.70 | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.51/21.70 | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.70 | | | | | | | | | | | | | | | | | | | | | | (9439) all_54_14 = e2 % 149.51/21.70 | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.70 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (482), (9439) imply: % 149.51/21.70 | | | | | | | | | | | | | | | | | | | | | | (9440) all_52_11 = e2 % 149.51/21.70 | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.70 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (169), (9440) imply: % 149.51/21.70 | | | | | | | | | | | | | | | | | | | | | | (9441) ~ (all_52_8 = e2) % 149.51/21.70 | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.70 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (205), (9440) imply: % 149.51/21.70 | | | | | | | | | | | | | | | | | | | | | | (9442) op(e0, e1) = e2 % 149.51/21.70 | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.70 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_6_1, % 149.51/21.70 | | | | | | | | | | | | | | | | | | | | | | all_56_20, e1, e1, simplifying with (9422), (9423) % 149.51/21.70 | | | | | | | | | | | | | | | | | | | | | | gives: % 149.51/21.70 | | | | | | | | | | | | | | | | | | | | | | (9443) all_56_20 = all_6_1 % 149.51/21.70 | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.70 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1, % 149.51/21.70 | | | | | | | | | | | | | | | | | | | | | | all_56_20, e1, e1, simplifying with (9423), (9424) % 149.51/21.70 | | | | | | | | | | | | | | | | | | | | | | gives: % 149.51/21.70 | | | | | | | | | | | | | | | | | | | | | | (9444) all_56_20 = e1 % 149.51/21.70 | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.70 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (9443), (9444) imply: % 149.51/21.70 | | | | | | | | | | | | | | | | | | | | | | (9445) all_6_1 = e1 % 149.51/21.70 | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.70 | | | | | | | | | | | | | | | | | | | | | | SIMP: (9445) implies: % 149.51/21.70 | | | | | | | | | | | | | | | | | | | | | | (9446) all_6_1 = e1 % 149.51/21.70 | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.70 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (42), (9446) imply: % 149.51/21.70 | | | | | | | | | | | | | | | | | | | | | | (9447) op(e1, e1) = all_6_0 % 149.51/21.70 | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.70 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1, all_6_0, % 149.51/21.70 | | | | | | | | | | | | | | | | | | | | | | e1, e1, simplifying with (9424), (9447) gives: % 149.51/21.70 | | | | | | | | | | | | | | | | | | | | | | (9448) all_6_0 = e1 % 149.51/21.70 | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.70 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (9318), (9448) imply: % 149.51/21.70 | | | | | | | | | | | | | | | | | | | | | | (9449) ~ (e2 = e1) % 149.51/21.70 | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.70 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (299) gives: % 149.51/21.70 | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.70 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.51/21.70 | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.70 | | | | | | | | | | | | | | | | | | | | | | | (9450) ~ (all_56_1 = e2) % 149.51/21.70 | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.70 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (9394), (9450) imply: % 149.51/21.71 | | | | | | | | | | | | | | | | | | | | | | | (9451) ~ (all_4_1 = e2) % 149.51/21.71 | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.71 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (296) gives: % 149.51/21.71 | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.71 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.51/21.71 | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.71 | | | | | | | | | | | | | | | | | | | | | | | | (9452) ~ (all_56_11 = e3) % 149.51/21.71 | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.71 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (545), (9452) imply: % 149.51/21.71 | | | | | | | | | | | | | | | | | | | | | | | | (9453) ~ (all_8_2 = e3) % 149.51/21.71 | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.71 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (168), (181), (182), (247), (250), (251), % 149.51/21.71 | | | | | | | | | | | | | | | | | | | | | | | | (252), (298), (328), (333), (343), (345), (386), % 149.51/21.71 | | | | | | | | | | | | | | | | | | | | | | | | (389), (401), (407), (429), (457), (459), (542), % 149.51/21.71 | | | | | | | | | | | | | | | | | | | | | | | | (548), (551), (552), (554), (555), (571), (625), % 149.51/21.71 | | | | | | | | | | | | | | | | | | | | | | | | (8985), (9383), (9393), (9394), (9395), (9396), % 149.51/21.71 | | | | | | | | | | | | | | | | | | | | | | | | (9398), (9399), (9400), (9402), (9406), (9417), % 149.51/21.71 | | | | | | | | | | | | | | | | | | | | | | | | (9418), (9430), (9433), (9441), (9442), (9451), % 149.51/21.71 | | | | | | | | | | | | | | | | | | | | | | | | (9453), (function-axioms) are inconsistent by % 149.51/21.71 | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #25. % 149.51/21.71 | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.71 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.51/21.71 | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.71 | | | | | | | | | | | | | | | | | | | | | | | | (9454) all_56_11 = e3 % 149.51/21.71 | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.71 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (545), (9454) imply: % 149.51/21.71 | | | | | | | | | | | | | | | | | | | | | | | | (9455) all_8_2 = e3 % 149.51/21.71 | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.71 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (9455) implies: % 149.51/21.71 | | | | | | | | | | | | | | | | | | | | | | | | (9456) all_8_2 = e3 % 149.51/21.71 | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.71 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (534), (9456) imply: % 149.51/21.71 | | | | | | | | | | | | | | | | | | | | | | | | (9457) all_42_2 = e3 % 149.51/21.71 | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.71 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (48), (9456) imply: % 149.51/21.71 | | | | | | | | | | | | | | | | | | | | | | | | (9458) op(e3, e3) = all_8_1 % 149.51/21.71 | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.71 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (617), (9456) imply: % 149.51/21.71 | | | | | | | | | | | | | | | | | | | | | | | | (9459) op(e2, e3) = all_56_10 % 149.51/21.71 | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.71 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (51), (215), (252), (296), (425), (543), % 149.51/21.71 | | | | | | | | | | | | | | | | | | | | | | | | (557), (639), (8987), (9313), (9323), (9454), % 149.51/21.71 | | | | | | | | | | | | | | | | | | | | | | | | (9457), (9458), (9459), (function-axioms) are % 149.51/21.71 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #256. % 149.51/21.71 | | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.71 | | | | | | | | | | | | | | | | | | | | | | | End of split % 149.51/21.71 | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.71 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.51/21.71 | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.71 | | | | | | | | | | | | | | | | | | | | | | | (9460) all_56_3 = e3 % 149.51/21.71 | | | | | | | | | | | | | | | | | | | | | | | (9461) all_56_1 = e2 % 149.51/21.71 | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.71 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (9394), (9461) imply: % 149.51/21.71 | | | | | | | | | | | | | | | | | | | | | | | (9462) all_4_1 = e2 % 149.51/21.71 | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.71 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (408), (9460) imply: % 149.51/21.71 | | | | | | | | | | | | | | | | | | | | | | | (9463) all_52_4 = e3 % 149.51/21.71 | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.71 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (9463) implies: % 149.51/21.71 | | | | | | | | | | | | | | | | | | | | | | | (9464) all_52_4 = e3 % 149.51/21.71 | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.71 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (555), (9464) imply: % 149.51/21.71 | | | | | | | | | | | | | | | | | | | | | | | (9465) all_58_1 = e3 % 149.51/21.71 | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.71 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (571), (9464) imply: % 149.51/21.71 | | | | | | | | | | | | | | | | | | | | | | | (9466) ~ (all_8_2 = e3) % 149.51/21.71 | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.71 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (9466) implies: % 149.51/21.71 | | | | | | | | | | | | | | | | | | | | | | | (9467) ~ (all_8_2 = e3) % 149.51/21.71 | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.71 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8985), (9462) imply: % 149.51/21.71 | | | | | | | | | | | | | | | | | | | | | | | (9468) op(e0, e2) = e3 % 149.51/21.71 | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.71 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (8), (174), (241), (247), (336), (380), % 149.51/21.71 | | | | | | | | | | | | | | | | | | | | | | | (476), (542), (554), (626), (9389), (9406), % 149.51/21.71 | | | | | | | | | | | | | | | | | | | | | | | (9420), (9427), (9433), (9434), (9465), (9467), % 149.51/21.71 | | | | | | | | | | | | | | | | | | | | | | | (9468), (function-axioms) are inconsistent by % 149.51/21.71 | | | | | | | | | | | | | | | | | | | | | | | sub-proof #24. % 149.51/21.71 | | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.71 | | | | | | | | | | | | | | | | | | | | | | End of split % 149.51/21.71 | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.71 | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.51/21.71 | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.71 | | | | | | | | | | | | | | | | | | | | | | (9469) all_54_14 = e1 | all_54_14 = e0 % 149.51/21.71 | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.71 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (482), (9383), (9419), (9469) are inconsistent by % 149.51/21.71 | | | | | | | | | | | | | | | | | | | | | | sub-proof #714. % 149.51/21.71 | | | | | | | | | | | | | | | | | | | | | | % 149.51/21.71 | | | | | | | | | | | | | | | | | | | | | End of split % 149.51/21.71 | | | | | | | | | | | | | | | | | | | | | % 149.51/21.71 | | | | | | | | | | | | | | | | | | | | End of split % 149.51/21.71 | | | | | | | | | | | | | | | | | | | | % 149.51/21.71 | | | | | | | | | | | | | | | | | | | Case 2: % 149.51/21.71 | | | | | | | | | | | | | | | | | | | | % 149.51/21.71 | | | | | | | | | | | | | | | | | | | | (9470) all_58_14 = e1 | all_58_15 = e1 % 149.51/21.71 | | | | | | | | | | | | | | | | | | | | % 149.51/21.71 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (548), (9377), (9419), (9470) are % 149.51/21.71 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #226. % 149.51/21.71 | | | | | | | | | | | | | | | | | | | | % 149.51/21.71 | | | | | | | | | | | | | | | | | | | End of split % 149.51/21.71 | | | | | | | | | | | | | | | | | | | % 149.51/21.71 | | | | | | | | | | | | | | | | | | End of split % 149.51/21.71 | | | | | | | | | | | | | | | | | | % 149.51/21.71 | | | | | | | | | | | | | | | | | Case 2: % 149.51/21.71 | | | | | | | | | | | | | | | | | | % 149.51/21.71 | | | | | | | | | | | | | | | | | | (9471) all_54_10 = e0 % 149.51/21.71 | | | | | | | | | | | | | | | | | | % 149.51/21.71 | | | | | | | | | | | | | | | | | | REF_CLOSE: (541), (9402), (9471) are inconsistent by % 149.51/21.71 | | | | | | | | | | | | | | | | | | sub-proof #705. % 149.51/21.71 | | | | | | | | | | | | | | | | | | % 149.51/21.71 | | | | | | | | | | | | | | | | | End of split % 149.51/21.71 | | | | | | | | | | | | | | | | | % 149.51/21.71 | | | | | | | | | | | | | | | | End of split % 149.51/21.71 | | | | | | | | | | | | | | | | % 149.51/21.71 | | | | | | | | | | | | | | | End of split % 149.51/21.71 | | | | | | | | | | | | | | | % 149.51/21.71 | | | | | | | | | | | | | | Case 2: % 149.51/21.71 | | | | | | | | | | | | | | | % 149.51/21.71 | | | | | | | | | | | | | | | (9472) all_56_21 = e3 % 149.51/21.71 | | | | | | | | | | | | | | | (9473) all_56_17 = e1 % 149.51/21.71 | | | | | | | | | | | | | | | % 149.51/21.71 | | | | | | | | | | | | | | | COMBINE_EQS: (381), (9473) imply: % 149.51/21.71 | | | | | | | | | | | | | | | (9474) all_52_2 = e1 % 149.51/21.71 | | | | | | | | | | | | | | | % 149.51/21.71 | | | | | | | | | | | | | | | REF_CLOSE: (43), (252), (374), (8986), (9320), (9390), % 149.51/21.71 | | | | | | | | | | | | | | | (9393), (9397), (9400), (9472), (9474), % 149.51/21.71 | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 149.51/21.71 | | | | | | | | | | | | | | | #547. % 149.51/21.71 | | | | | | | | | | | | | | | % 149.51/21.71 | | | | | | | | | | | | | | End of split % 149.51/21.71 | | | | | | | | | | | | | | % 149.51/21.71 | | | | | | | | | | | | | Case 2: % 149.51/21.71 | | | | | | | | | | | | | | % 149.51/21.71 | | | | | | | | | | | | | | (9475) all_56_11 = e0 % 149.51/21.71 | | | | | | | | | | | | | | % 149.51/21.71 | | | | | | | | | | | | | | COMBINE_EQS: (545), (9475) imply: % 149.51/21.71 | | | | | | | | | | | | | | (9476) all_8_2 = e0 % 149.51/21.71 | | | | | | | | | | | | | | % 149.51/21.71 | | | | | | | | | | | | | | COMBINE_EQS: (528), (9476) imply: % 149.51/21.71 | | | | | | | | | | | | | | (9477) all_14_2 = e0 % 149.51/21.71 | | | | | | | | | | | | | | % 149.51/21.71 | | | | | | | | | | | | | | REDUCE: (573), (9476) imply: % 149.51/21.71 | | | | | | | | | | | | | | (9478) ~ (all_52_6 = e0) % 149.51/21.71 | | | | | | | | | | | | | | % 149.51/21.71 | | | | | | | | | | | | | | REDUCE: (48), (9476) imply: % 149.51/21.71 | | | | | | | | | | | | | | (9479) op(e0, e0) = all_8_1 % 149.51/21.71 | | | | | | | | | | | | | | % 149.51/21.71 | | | | | | | | | | | | | | BETA: splitting (324) gives: % 149.51/21.71 | | | | | | | | | | | | | | % 149.51/21.71 | | | | | | | | | | | | | | Case 1: % 149.51/21.71 | | | | | | | | | | | | | | | % 149.51/21.71 | | | | | | | | | | | | | | | (9480) all_58_6 = e0 % 149.51/21.71 | | | | | | | | | | | | | | | % 149.51/21.71 | | | | | | | | | | | | | | | COMBINE_EQS: (553), (9480) imply: % 149.51/21.71 | | | | | | | | | | | | | | | (9481) all_52_2 = e0 % 149.51/21.71 | | | | | | | | | | | | | | | % 149.51/21.71 | | | | | | | | | | | | | | | REDUCE: (9379), (9481) imply: % 149.51/21.71 | | | | | | | | | | | | | | | (9482) $false % 149.51/21.71 | | | | | | | | | | | | | | | % 149.51/21.71 | | | | | | | | | | | | | | | CLOSE: (9482) is inconsistent. % 149.51/21.71 | | | | | | | | | | | | | | | % 149.51/21.71 | | | | | | | | | | | | | | Case 2: % 149.51/21.71 | | | | | | | | | | | | | | | % 149.51/21.71 | | | | | | | | | | | | | | | (9483) all_58_7 = e0 | all_58_8 = e0 | all_58_11 = e0 % 149.51/21.71 | | | | | | | | | | | | | | | % 149.51/21.71 | | | | | | | | | | | | | | | BETA: splitting (9483) gives: % 149.51/21.71 | | | | | | | | | | | | | | | % 149.51/21.71 | | | | | | | | | | | | | | | Case 1: % 149.51/21.71 | | | | | | | | | | | | | | | | % 149.51/21.71 | | | | | | | | | | | | | | | | (9484) all_58_7 = e0 % 149.51/21.71 | | | | | | | | | | | | | | | | % 149.51/21.71 | | | | | | | | | | | | | | | | COMBINE_EQS: (380), (9484) imply: % 149.51/21.71 | | | | | | | | | | | | | | | | (9485) all_52_6 = e0 % 149.51/21.71 | | | | | | | | | | | | | | | | % 149.51/21.71 | | | | | | | | | | | | | | | | REDUCE: (9478), (9485) imply: % 149.51/21.71 | | | | | | | | | | | | | | | | (9486) $false % 149.51/21.71 | | | | | | | | | | | | | | | | % 149.51/21.71 | | | | | | | | | | | | | | | | CLOSE: (9486) is inconsistent. % 149.51/21.71 | | | | | | | | | | | | | | | | % 149.51/21.71 | | | | | | | | | | | | | | | Case 2: % 149.51/21.71 | | | | | | | | | | | | | | | | % 149.51/21.71 | | | | | | | | | | | | | | | | (9487) all_58_8 = e0 | all_58_11 = e0 % 149.51/21.71 | | | | | | | | | | | | | | | | % 149.51/21.71 | | | | | | | | | | | | | | | | BETA: splitting (9487) gives: % 149.51/21.71 | | | | | | | | | | | | | | | | % 149.51/21.71 | | | | | | | | | | | | | | | | Case 1: % 149.51/21.71 | | | | | | | | | | | | | | | | | % 149.51/21.71 | | | | | | | | | | | | | | | | | (9488) all_58_8 = e0 % 149.51/21.71 | | | | | | | | | | | | | | | | | % 149.51/21.71 | | | | | | | | | | | | | | | | | COMBINE_EQS: (552), (9488) imply: % 149.51/21.71 | | | | | | | | | | | | | | | | | (9489) all_6_2 = e0 % 149.51/21.71 | | | | | | | | | | | | | | | | | % 149.51/21.71 | | | | | | | | | | | | | | | | | REDUCE: (9402), (9489) imply: % 149.51/21.71 | | | | | | | | | | | | | | | | | (9490) $false % 149.51/21.71 | | | | | | | | | | | | | | | | | % 149.51/21.71 | | | | | | | | | | | | | | | | | CLOSE: (9490) is inconsistent. % 149.51/21.71 | | | | | | | | | | | | | | | | | % 149.51/21.71 | | | | | | | | | | | | | | | | Case 2: % 149.51/21.71 | | | | | | | | | | | | | | | | | % 149.51/21.71 | | | | | | | | | | | | | | | | | (9491) all_58_11 = e0 % 149.51/21.71 | | | | | | | | | | | | | | | | | % 149.51/21.71 | | | | | | | | | | | | | | | | | COMBINE_EQS: (550), (9491) imply: % 149.51/21.71 | | | | | | | | | | | | | | | | | (9492) all_52_14 = e0 % 149.51/21.71 | | | | | | | | | | | | | | | | | % 149.51/21.71 | | | | | | | | | | | | | | | | | REDUCE: (626), (9492) imply: % 149.51/21.71 | | | | | | | | | | | | | | | | | (9493) op(e0, e0) = all_56_22 % 149.51/21.71 | | | | | | | | | | | | | | | | | % 149.51/21.71 | | | | | | | | | | | | | | | | | BETA: splitting (9310) gives: % 149.51/21.71 | | | | | | | | | | | | | | | | | % 149.51/21.71 | | | | | | | | | | | | | | | | | Case 1: % 149.51/21.71 | | | | | | | | | | | | | | | | | | % 149.51/21.71 | | | | | | | | | | | | | | | | | | (9494) ~ (all_14_1 = e3) % 149.51/21.71 | | | | | | | | | | | | | | | | | | % 149.51/21.71 | | | | | | | | | | | | | | | | | | REDUCE: (679), (9494) imply: % 149.51/21.71 | | | | | | | | | | | | | | | | | | (9495) ~ (all_8_1 = e3) % 149.51/21.71 | | | | | | | | | | | | | | | | | | % 149.51/21.71 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, % 149.51/21.71 | | | | | | | | | | | | | | | | | | all_56_22, e0, e0, simplifying with (9391), (9493) % 149.51/21.71 | | | | | | | | | | | | | | | | | | gives: % 149.51/21.71 | | | | | | | | | | | | | | | | | | (9496) all_56_22 = e3 % 149.51/21.71 | | | | | | | | | | | | | | | | | | % 149.51/21.71 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_8_1, % 149.51/21.71 | | | | | | | | | | | | | | | | | | all_56_22, e0, e0, simplifying with (9479), (9493) % 149.51/21.71 | | | | | | | | | | | | | | | | | | gives: % 149.51/21.71 | | | | | | | | | | | | | | | | | | (9497) all_56_22 = all_8_1 % 149.51/21.71 | | | | | | | | | | | | | | | | | | % 149.51/21.71 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (9496), (9497) imply: % 149.51/21.71 | | | | | | | | | | | | | | | | | | (9498) all_8_1 = e3 % 149.51/21.71 | | | | | | | | | | | | | | | | | | % 149.51/21.71 | | | | | | | | | | | | | | | | | | REDUCE: (9495), (9498) imply: % 149.51/21.71 | | | | | | | | | | | | | | | | | | (9499) $false % 149.51/21.71 | | | | | | | | | | | | | | | | | | % 149.51/21.71 | | | | | | | | | | | | | | | | | | CLOSE: (9499) is inconsistent. % 149.51/21.71 | | | | | | | | | | | | | | | | | | % 149.51/21.71 | | | | | | | | | | | | | | | | | Case 2: % 149.51/21.71 | | | | | | | | | | | | | | | | | | % 149.51/21.71 | | | | | | | | | | | | | | | | | | (9500) ~ (all_14_2 = e0) % 149.51/21.71 | | | | | | | | | | | | | | | | | | % 149.51/21.71 | | | | | | | | | | | | | | | | | | REDUCE: (9477), (9500) imply: % 149.51/21.71 | | | | | | | | | | | | | | | | | | (9501) $false % 149.51/21.71 | | | | | | | | | | | | | | | | | | % 149.51/21.71 | | | | | | | | | | | | | | | | | | CLOSE: (9501) is inconsistent. % 149.51/21.71 | | | | | | | | | | | | | | | | | | % 149.51/21.71 | | | | | | | | | | | | | | | | | End of split % 149.51/21.71 | | | | | | | | | | | | | | | | | % 149.51/21.71 | | | | | | | | | | | | | | | | End of split % 149.51/21.71 | | | | | | | | | | | | | | | | % 149.51/21.71 | | | | | | | | | | | | | | | End of split % 149.51/21.71 | | | | | | | | | | | | | | | % 149.51/21.71 | | | | | | | | | | | | | | End of split % 149.51/21.71 | | | | | | | | | | | | | | % 149.51/21.71 | | | | | | | | | | | | | End of split % 149.51/21.71 | | | | | | | | | | | | | % 149.51/21.71 | | | | | | | | | | | | Case 2: % 149.51/21.71 | | | | | | | | | | | | | % 149.51/21.71 | | | | | | | | | | | | | (9502) all_56_21 = e2 % 149.51/21.71 | | | | | | | | | | | | | (9503) all_56_19 = e1 % 149.51/21.71 | | | | | | | | | | | | | % 149.51/21.71 | | | | | | | | | | | | | COMBINE_EQS: (435), (9503) imply: % 149.51/21.71 | | | | | | | | | | | | | (9504) all_52_6 = e1 % 149.51/21.71 | | | | | | | | | | | | | % 149.51/21.71 | | | | | | | | | | | | | COMBINE_EQS: (374), (9502) imply: % 149.51/21.71 | | | | | | | | | | | | | (9505) all_6_2 = e2 % 149.51/21.71 | | | | | | | | | | | | | % 149.51/21.71 | | | | | | | | | | | | | REF_CLOSE: (4), (7), (8), (9), (191), (244), (287), (336), % 149.51/21.71 | | | | | | | | | | | | | (339), (380), (471), (545), (549), (554), (569), % 149.51/21.71 | | | | | | | | | | | | | (580), (9372), (9379), (9381), (9387), (9394), % 149.51/21.71 | | | | | | | | | | | | | (9397), (9402), (9502), (9504), (9505) are % 149.51/21.71 | | | | | | | | | | | | | inconsistent by sub-proof #541. % 149.51/21.71 | | | | | | | | | | | | | % 149.51/21.71 | | | | | | | | | | | | End of split % 149.51/21.71 | | | | | | | | | | | | % 149.51/21.71 | | | | | | | | | | | Case 2: % 149.51/21.71 | | | | | | | | | | | | % 149.51/21.71 | | | | | | | | | | | | (9506) all_56_21 = e0 % 149.51/21.71 | | | | | | | | | | | | % 149.51/21.71 | | | | | | | | | | | | COMBINE_EQS: (374), (9506) imply: % 149.51/21.71 | | | | | | | | | | | | (9507) all_6_2 = e0 % 149.51/21.71 | | | | | | | | | | | | % 149.51/21.71 | | | | | | | | | | | | SIMP: (9507) implies: % 149.51/21.71 | | | | | | | | | | | | (9508) all_6_2 = e0 % 149.51/21.71 | | | | | | | | | | | | % 149.51/21.71 | | | | | | | | | | | | REDUCE: (43), (9508) imply: % 149.51/21.71 | | | | | | | | | | | | (9509) op(e0, e0) = all_6_1 % 149.51/21.71 | | | | | | | | | | | | % 149.51/21.71 | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_6_1, % 149.51/21.71 | | | | | | | | | | | | e0, e0, simplifying with (9391), (9509) gives: % 149.51/21.71 | | | | | | | | | | | | (9510) all_6_1 = e3 % 149.51/21.71 | | | | | | | | | | | | % 149.51/21.71 | | | | | | | | | | | | REDUCE: (9320), (9510) imply: % 149.51/21.71 | | | | | | | | | | | | (9511) $false % 149.51/21.71 | | | | | | | | | | | | % 149.51/21.71 | | | | | | | | | | | | CLOSE: (9511) is inconsistent. % 149.51/21.71 | | | | | | | | | | | | % 149.51/21.71 | | | | | | | | | | | End of split % 149.51/21.71 | | | | | | | | | | | % 149.51/21.71 | | | | | | | | | | End of split % 149.51/21.71 | | | | | | | | | | % 149.51/21.71 | | | | | | | | | Case 2: % 149.51/21.71 | | | | | | | | | | % 149.51/21.71 | | | | | | | | | | (9512) all_56_31 = e1 % 149.51/21.71 | | | | | | | | | | (9513) all_56_29 = e0 % 149.51/21.71 | | | | | | | | | | % 149.66/21.71 | | | | | | | | | | REF_CLOSE: (6), (7), (36), (38), (41), (43), (48), (51), % 149.66/21.71 | | | | | | | | | | (192), (205), (207), (242), (287), (293), (294), % 149.66/21.71 | | | | | | | | | | (319), (357), (365), (374), (381), (499), (541), % 149.66/21.71 | | | | | | | | | | (544), (545), (546), (547), (548), (549), (561), % 149.66/21.71 | | | | | | | | | | (575), (585), (588), (627), (676), (8985), (8987), % 149.66/21.71 | | | | | | | | | | (9316), (9512), (9513), (function-axioms) are % 149.66/21.71 | | | | | | | | | | inconsistent by sub-proof #13. % 149.66/21.71 | | | | | | | | | | % 149.66/21.71 | | | | | | | | | End of split % 149.66/21.71 | | | | | | | | | % 149.66/21.71 | | | | | | | | End of split % 149.66/21.71 | | | | | | | | % 149.66/21.71 | | | | | | | Case 2: % 149.66/21.71 | | | | | | | | % 149.66/21.71 | | | | | | | | (9514) all_36_1 = e3 % 149.66/21.71 | | | | | | | | (9515) ~ (all_36_0 = e0) | ~ (all_36_2 = e2) % 149.66/21.71 | | | | | | | | % 149.66/21.71 | | | | | | | | COMBINE_EQS: (652), (9514) imply: % 149.66/21.71 | | | | | | | | (9516) all_6_1 = e3 % 149.66/21.71 | | | | | | | | % 149.66/21.71 | | | | | | | | REDUCE: (43), (9516) imply: % 149.66/21.71 | | | | | | | | (9517) op(all_6_2, all_6_2) = e3 % 149.66/21.71 | | | | | | | | % 149.66/21.71 | | | | | | | | REDUCE: (42), (9516) imply: % 149.66/21.71 | | | | | | | | (9518) op(e1, e3) = all_6_0 % 149.66/21.71 | | | | | | | | % 149.66/21.71 | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_2, % 149.66/21.71 | | | | | | | | all_6_0, e3, e1, simplifying with (211), (9518) % 149.66/21.71 | | | | | | | | gives: % 149.66/21.71 | | | | | | | | (9519) all_52_2 = all_6_0 % 149.66/21.71 | | | | | | | | % 149.66/21.71 | | | | | | | | COMBINE_EQS: (471), (9519) imply: % 149.66/21.71 | | | | | | | | (9520) all_54_8 = all_6_0 % 149.66/21.71 | | | | | | | | % 149.66/21.71 | | | | | | | | COMBINE_EQS: (381), (9519) imply: % 149.66/21.71 | | | | | | | | (9521) all_56_17 = all_6_0 % 149.66/21.71 | | | | | | | | % 149.66/21.71 | | | | | | | | COMBINE_EQS: (553), (9519) imply: % 149.66/21.71 | | | | | | | | (9522) all_58_6 = all_6_0 % 149.66/21.71 | | | | | | | | % 149.66/21.71 | | | | | | | | REDUCE: (197), (9519) imply: % 149.66/21.71 | | | | | | | | (9523) ~ (all_52_1 = all_6_0) % 149.66/21.71 | | | | | | | | % 149.66/21.71 | | | | | | | | REDUCE: (192), (9519) imply: % 149.66/21.71 | | | | | | | | (9524) ~ (all_52_3 = all_6_0) % 149.66/21.71 | | | | | | | | % 149.66/21.71 | | | | | | | | SIMP: (9524) implies: % 149.66/21.71 | | | | | | | | (9525) ~ (all_52_3 = all_6_0) % 149.66/21.71 | | | | | | | | % 149.66/21.71 | | | | | | | | REDUCE: (191), (9519) imply: % 149.66/21.71 | | | | | | | | (9526) ~ (all_52_6 = all_6_0) % 149.66/21.71 | | | | | | | | % 149.66/21.71 | | | | | | | | SIMP: (9526) implies: % 149.66/21.71 | | | | | | | | (9527) ~ (all_52_6 = all_6_0) % 149.66/21.71 | | | | | | | | % 149.66/21.71 | | | | | | | | REDUCE: (189), (9519) imply: % 149.66/21.71 | | | | | | | | (9528) ~ (all_52_14 = all_6_0) % 149.66/21.71 | | | | | | | | % 149.66/21.71 | | | | | | | | SIMP: (9528) implies: % 149.66/21.71 | | | | | | | | (9529) ~ (all_52_14 = all_6_0) % 149.66/21.71 | | | | | | | | % 149.66/21.71 | | | | | | | | REDUCE: (559), (9519) imply: % 149.66/21.71 | | | | | | | | (9530) ~ (all_10_2 = all_6_0) % 149.66/21.71 | | | | | | | | % 149.66/21.71 | | | | | | | | SIMP: (9530) implies: % 149.66/21.71 | | | | | | | | (9531) ~ (all_10_2 = all_6_0) % 149.66/21.71 | | | | | | | | % 149.66/21.71 | | | | | | | | REDUCE: (569), (9519) imply: % 149.66/21.71 | | | | | | | | (9532) ~ (all_6_0 = all_6_2) % 149.66/21.71 | | | | | | | | % 149.66/21.71 | | | | | | | | BETA: splitting (134) gives: % 149.66/21.71 | | | | | | | | % 149.66/21.71 | | | | | | | | Case 1: % 149.66/21.71 | | | | | | | | | % 149.66/21.71 | | | | | | | | | (9533) ~ (all_42_0 = e1) % 149.66/21.71 | | | | | | | | | % 149.66/21.71 | | | | | | | | | REDUCE: (9312), (9533) imply: % 149.66/21.71 | | | | | | | | | (9534) $false % 149.66/21.71 | | | | | | | | | % 149.66/21.71 | | | | | | | | | CLOSE: (9534) is inconsistent. % 149.66/21.71 | | | | | | | | | % 149.66/21.71 | | | | | | | | Case 2: % 149.66/21.71 | | | | | | | | | % 149.66/21.71 | | | | | | | | | (9535) ~ (all_42_1 = e0) | ~ (all_42_2 = e3) % 149.66/21.71 | | | | | | | | | % 149.66/21.71 | | | | | | | | | BETA: splitting (292) gives: % 149.66/21.71 | | | | | | | | | % 149.66/21.71 | | | | | | | | | Case 1: % 149.66/21.71 | | | | | | | | | | % 149.66/21.71 | | | | | | | | | | (9536) ~ (all_56_21 = e2) % 149.66/21.71 | | | | | | | | | | % 149.66/21.71 | | | | | | | | | | REDUCE: (374), (9536) imply: % 149.66/21.71 | | | | | | | | | | (9537) ~ (all_6_2 = e2) % 149.66/21.71 | | | | | | | | | | % 149.66/21.71 | | | | | | | | | | BETA: splitting (288) gives: % 149.66/21.71 | | | | | | | | | | % 149.66/21.71 | | | | | | | | | | Case 1: % 149.66/21.71 | | | | | | | | | | | % 149.66/21.71 | | | | | | | | | | | (9538) ~ (all_56_31 = e1) % 149.66/21.71 | | | | | | | | | | | % 149.66/21.71 | | | | | | | | | | | REDUCE: (544), (9538) imply: % 149.66/21.71 | | | | | | | | | | | (9539) ~ (all_4_2 = e1) % 149.66/21.71 | | | | | | | | | | | % 149.66/21.71 | | | | | | | | | | | BETA: splitting (290) gives: % 149.66/21.71 | | | | | | | | | | | % 149.66/21.71 | | | | | | | | | | | Case 1: % 149.66/21.71 | | | | | | | | | | | | % 149.66/21.71 | | | | | | | | | | | | (9540) ~ (all_56_31 = e3) % 149.66/21.71 | | | | | | | | | | | | % 149.66/21.71 | | | | | | | | | | | | REDUCE: (544), (9540) imply: % 149.66/21.71 | | | | | | | | | | | | (9541) ~ (all_4_2 = e3) % 149.66/21.71 | | | | | | | | | | | | % 149.66/21.71 | | | | | | | | | | | | BETA: splitting (289) gives: % 149.66/21.71 | | | | | | | | | | | | % 149.66/21.71 | | | | | | | | | | | | Case 1: % 149.66/21.71 | | | | | | | | | | | | | % 149.66/21.71 | | | | | | | | | | | | | (9542) ~ (all_56_31 = e2) % 149.66/21.71 | | | | | | | | | | | | | % 149.66/21.71 | | | | | | | | | | | | | REDUCE: (544), (9542) imply: % 149.66/21.71 | | | | | | | | | | | | | (9543) ~ (all_4_2 = e2) % 149.66/21.71 | | | | | | | | | | | | | % 149.66/21.71 | | | | | | | | | | | | | REF_CLOSE: (36), (38), (237), (540), (627), (8985), (9539), % 149.66/21.71 | | | | | | | | | | | | | (9541), (9543), (function-axioms) are inconsistent % 149.66/21.71 | | | | | | | | | | | | | by sub-proof #29. % 149.66/21.71 | | | | | | | | | | | | | % 149.66/21.71 | | | | | | | | | | | | Case 2: % 149.66/21.71 | | | | | | | | | | | | | % 149.66/21.71 | | | | | | | | | | | | | (9544) all_56_31 = e2 % 149.66/21.71 | | | | | | | | | | | | | (9545) all_56_27 = e0 % 149.66/21.71 | | | | | | | | | | | | | % 149.66/21.71 | | | | | | | | | | | | | COMBINE_EQS: (360), (9545) imply: % 149.66/21.71 | | | | | | | | | | | | | (9546) all_52_7 = e0 % 149.66/21.71 | | | | | | | | | | | | | % 149.66/21.71 | | | | | | | | | | | | | SIMP: (9546) implies: % 149.66/21.71 | | | | | | | | | | | | | (9547) all_52_7 = e0 % 149.66/21.71 | | | | | | | | | | | | | % 149.66/21.71 | | | | | | | | | | | | | COMBINE_EQS: (544), (9544) imply: % 149.66/21.71 | | | | | | | | | | | | | (9548) all_4_2 = e2 % 149.66/21.71 | | | | | | | | | | | | | % 149.66/21.71 | | | | | | | | | | | | | REDUCE: (575), (9547) imply: % 149.66/21.71 | | | | | | | | | | | | | (9549) ~ (all_8_2 = e0) % 149.66/21.71 | | | | | | | | | | | | | % 149.66/21.71 | | | | | | | | | | | | | SIMP: (9549) implies: % 149.66/21.71 | | | | | | | | | | | | | (9550) ~ (all_8_2 = e0) % 149.66/21.71 | | | | | | | | | | | | | % 149.66/21.71 | | | | | | | | | | | | | REDUCE: (591), (9548) imply: % 149.66/21.71 | | | | | | | | | | | | | (9551) ~ (all_52_14 = e2) % 149.66/21.71 | | | | | | | | | | | | | % 149.66/21.71 | | | | | | | | | | | | | REDUCE: (38), (9548) imply: % 149.66/21.71 | | | | | | | | | | | | | (9552) op(e2, e2) = all_4_1 % 149.66/21.71 | | | | | | | | | | | | | % 149.66/21.71 | | | | | | | | | | | | | BETA: splitting (326) gives: % 149.66/21.71 | | | | | | | | | | | | | % 149.66/21.71 | | | | | | | | | | | | | Case 1: % 149.66/21.71 | | | | | | | | | | | | | | % 149.66/21.71 | | | | | | | | | | | | | | (9553) all_58_6 = e2 % 149.66/21.71 | | | | | | | | | | | | | | % 149.66/21.71 | | | | | | | | | | | | | | REF_CLOSE: (9318), (9522), (9553) are inconsistent by % 149.66/21.71 | | | | | | | | | | | | | | sub-proof #461. % 149.66/21.71 | | | | | | | | | | | | | | % 149.66/21.71 | | | | | | | | | | | | | Case 2: % 149.66/21.71 | | | | | | | | | | | | | | % 149.66/21.71 | | | | | | | | | | | | | | (9554) all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2 % 149.66/21.71 | | | | | | | | | | | | | | % 149.66/21.71 | | | | | | | | | | | | | | BETA: splitting (9554) gives: % 149.66/21.71 | | | | | | | | | | | | | | % 149.66/21.71 | | | | | | | | | | | | | | Case 1: % 149.66/21.71 | | | | | | | | | | | | | | | % 149.66/21.71 | | | | | | | | | | | | | | | (9555) all_58_7 = e2 % 149.66/21.71 | | | | | | | | | | | | | | | % 149.66/21.71 | | | | | | | | | | | | | | | COMBINE_EQS: (380), (9555) imply: % 149.66/21.71 | | | | | | | | | | | | | | | (9556) all_52_6 = e2 % 149.66/21.71 | | | | | | | | | | | | | | | % 149.66/21.71 | | | | | | | | | | | | | | | REDUCE: (573), (9556) imply: % 149.66/21.71 | | | | | | | | | | | | | | | (9557) ~ (all_8_2 = e2) % 149.66/21.71 | | | | | | | | | | | | | | | % 149.66/21.71 | | | | | | | | | | | | | | | SIMP: (9557) implies: % 149.66/21.71 | | | | | | | | | | | | | | | (9558) ~ (all_8_2 = e2) % 149.66/21.71 | | | | | | | | | | | | | | | % 149.66/21.71 | | | | | | | | | | | | | | | REDUCE: (618), (9556) imply: % 149.66/21.71 | | | | | | | | | | | | | | | (9559) op(e2, e2) = all_56_18 % 149.66/21.71 | | | | | | | | | | | | | | | % 149.66/21.71 | | | | | | | | | | | | | | | BETA: splitting (8983) gives: % 149.66/21.71 | | | | | | | | | | | | | | | % 149.66/21.71 | | | | | | | | | | | | | | | Case 1: % 149.66/21.71 | | | | | | | | | | | | | | | | % 149.66/21.71 | | | | | | | | | | | | | | | | (9560) ~ (all_4_1 = e1) % 149.66/21.71 | | | | | | | | | | | | | | | | % 149.66/21.71 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_8_2, % 149.66/21.71 | | | | | | | | | | | | | | | | all_56_18, e2, e2, simplifying with (46), (9559) % 149.66/21.71 | | | | | | | | | | | | | | | | gives: % 149.66/21.71 | | | | | | | | | | | | | | | | (9561) all_56_18 = all_8_2 % 149.66/21.71 | | | | | | | | | | | | | | | | % 149.66/21.71 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_4_1, % 149.66/21.71 | | | | | | | | | | | | | | | | all_56_18, e2, e2, simplifying with (9552), (9559) % 149.66/21.71 | | | | | | | | | | | | | | | | gives: % 149.66/21.71 | | | | | | | | | | | | | | | | (9562) all_56_18 = all_4_1 % 149.66/21.71 | | | | | | | | | | | | | | | | % 149.66/21.71 | | | | | | | | | | | | | | | | COMBINE_EQS: (9561), (9562) imply: % 149.66/21.71 | | | | | | | | | | | | | | | | (9563) all_8_2 = all_4_1 % 149.66/21.71 | | | | | | | | | | | | | | | | % 149.66/21.71 | | | | | | | | | | | | | | | | COMBINE_EQS: (534), (9563) imply: % 149.66/21.71 | | | | | | | | | | | | | | | | (9564) all_42_2 = all_4_1 % 149.66/21.71 | | | | | | | | | | | | | | | | % 149.66/21.71 | | | | | | | | | | | | | | | | COMBINE_EQS: (542), (9563) imply: % 149.66/21.71 | | | | | | | | | | | | | | | | (9565) all_54_5 = all_4_1 % 149.66/21.71 | | | | | | | | | | | | | | | | % 149.66/21.71 | | | | | | | | | | | | | | | | COMBINE_EQS: (545), (9563) imply: % 149.66/21.71 | | | | | | | | | | | | | | | | (9566) all_56_11 = all_4_1 % 149.66/21.71 | | | | | | | | | | | | | | | | % 149.66/21.71 | | | | | | | | | | | | | | | | REDUCE: (9558), (9563) imply: % 149.66/21.71 | | | | | | | | | | | | | | | | (9567) ~ (all_4_1 = e2) % 149.66/21.71 | | | | | | | | | | | | | | | | % 149.66/21.71 | | | | | | | | | | | | | | | | REDUCE: (9550), (9563) imply: % 149.66/21.71 | | | | | | | | | | | | | | | | (9568) ~ (all_4_1 = e0) % 149.66/21.71 | | | | | | | | | | | | | | | | % 149.66/21.71 | | | | | | | | | | | | | | | | REDUCE: (48), (9563) imply: % 149.66/21.71 | | | | | | | | | | | | | | | | (9569) op(all_4_1, all_4_1) = all_8_1 % 149.66/21.71 | | | | | | | | | | | | | | | | % 149.66/21.71 | | | | | | | | | | | | | | | | REDUCE: (617), (9563) imply: % 149.66/21.71 | | | | | | | | | | | | | | | | (9570) op(e2, all_4_1) = all_56_10 % 149.66/21.71 | | | | | | | | | | | | | | | | % 149.66/21.71 | | | | | | | | | | | | | | | | BETA: splitting (247) gives: % 149.66/21.71 | | | | | | | | | | | | | | | | % 149.66/21.71 | | | | | | | | | | | | | | | | Case 1: % 149.66/21.71 | | | | | | | | | | | | | | | | | % 149.66/21.71 | | | | | | | | | | | | | | | | | (9571) all_54_5 = e3 % 149.66/21.71 | | | | | | | | | | | | | | | | | % 149.66/21.71 | | | | | | | | | | | | | | | | | COMBINE_EQS: (9565), (9571) imply: % 149.66/21.71 | | | | | | | | | | | | | | | | | (9572) all_4_1 = e3 % 149.66/21.71 | | | | | | | | | | | | | | | | | % 149.66/21.71 | | | | | | | | | | | | | | | | | SIMP: (9572) implies: % 149.66/21.71 | | | | | | | | | | | | | | | | | (9573) all_4_1 = e3 % 149.66/21.71 | | | | | | | | | | | | | | | | | % 149.66/21.71 | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (51), (215), (252), (296), (425), (543), % 149.66/21.71 | | | | | | | | | | | | | | | | | (557), (639), (8987), (9313), (9535), (9564), % 149.66/21.71 | | | | | | | | | | | | | | | | | (9566), (9569), (9570), (9573), (function-axioms) % 149.66/21.71 | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #1. % 149.66/21.71 | | | | | | | | | | | | | | | | | % 149.66/21.71 | | | | | | | | | | | | | | | | Case 2: % 149.66/21.71 | | | | | | | | | | | | | | | | | % 149.66/21.71 | | | | | | | | | | | | | | | | | (9574) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 149.66/21.71 | | | | | | | | | | | | | | | | | % 149.66/21.71 | | | | | | | | | | | | | | | | | REF_CLOSE: (9560), (9565), (9567), (9568), (9574) are % 149.66/21.71 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #568. % 149.66/21.71 | | | | | | | | | | | | | | | | | % 149.66/21.71 | | | | | | | | | | | | | | | | End of split % 149.66/21.71 | | | | | | | | | | | | | | | | % 149.66/21.71 | | | | | | | | | | | | | | | Case 2: % 149.66/21.71 | | | | | | | | | | | | | | | | % 149.66/21.71 | | | | | | | | | | | | | | | | (9575) ~ (all_4_2 = e2) % 149.66/21.71 | | | | | | | | | | | | | | | | % 149.66/21.71 | | | | | | | | | | | | | | | | REF_CLOSE: (36), (38), (237), (540), (627), (8985), (9539), % 149.66/21.71 | | | | | | | | | | | | | | | | (9541), (9575), (function-axioms) are inconsistent % 149.66/21.71 | | | | | | | | | | | | | | | | by sub-proof #29. % 149.66/21.71 | | | | | | | | | | | | | | | | % 149.66/21.71 | | | | | | | | | | | | | | | End of split % 149.66/21.71 | | | | | | | | | | | | | | | % 149.66/21.71 | | | | | | | | | | | | | | Case 2: % 149.66/21.71 | | | | | | | | | | | | | | | % 149.66/21.71 | | | | | | | | | | | | | | | (9576) all_58_8 = e2 | all_58_11 = e2 % 149.66/21.71 | | | | | | | | | | | | | | | % 149.66/21.71 | | | | | | | | | | | | | | | REF_CLOSE: (550), (552), (9537), (9551), (9576) are % 149.66/21.71 | | | | | | | | | | | | | | | inconsistent by sub-proof #511. % 149.66/21.71 | | | | | | | | | | | | | | | % 149.66/21.71 | | | | | | | | | | | | | | End of split % 149.66/21.71 | | | | | | | | | | | | | | % 149.66/21.71 | | | | | | | | | | | | | End of split % 149.66/21.71 | | | | | | | | | | | | | % 149.66/21.71 | | | | | | | | | | | | End of split % 149.66/21.71 | | | | | | | | | | | | % 149.66/21.71 | | | | | | | | | | | Case 2: % 149.66/21.71 | | | | | | | | | | | | % 149.66/21.71 | | | | | | | | | | | | (9577) all_56_31 = e3 % 149.66/21.71 | | | | | | | | | | | | (9578) all_56_25 = e0 % 149.66/21.71 | | | | | | | | | | | | % 149.66/21.71 | | | | | | | | | | | | COMBINE_EQS: (447), (9578) imply: % 149.66/21.71 | | | | | | | | | | | | (9579) all_52_3 = e0 % 149.66/21.71 | | | | | | | | | | | | % 149.66/21.71 | | | | | | | | | | | | SIMP: (9579) implies: % 149.66/21.71 | | | | | | | | | | | | (9580) all_52_3 = e0 % 149.66/21.71 | | | | | | | | | | | | % 149.66/21.71 | | | | | | | | | | | | COMBINE_EQS: (544), (9577) imply: % 149.66/21.71 | | | | | | | | | | | | (9581) all_4_2 = e3 % 149.66/21.71 | | | | | | | | | | | | % 149.66/21.71 | | | | | | | | | | | | COMBINE_EQS: (365), (9580) imply: % 149.66/21.71 | | | | | | | | | | | | (9582) all_58_12 = e0 % 149.66/21.71 | | | | | | | | | | | | % 149.66/21.71 | | | | | | | | | | | | REDUCE: (196), (9580) imply: % 149.66/21.71 | | | | | | | | | | | | (9583) ~ (all_52_1 = e0) % 149.66/21.71 | | | | | | | | | | | | % 149.66/21.71 | | | | | | | | | | | | REDUCE: (187), (9580) imply: % 149.66/21.71 | | | | | | | | | | | | (9584) ~ (all_52_11 = e0) % 149.66/21.71 | | | | | | | | | | | | % 149.66/21.71 | | | | | | | | | | | | SIMP: (9584) implies: % 149.66/21.71 | | | | | | | | | | | | (9585) ~ (all_52_11 = e0) % 149.66/21.71 | | | | | | | | | | | | % 149.66/21.71 | | | | | | | | | | | | REDUCE: (561), (9580) imply: % 149.66/21.71 | | | | | | | | | | | | (9586) ~ (all_10_2 = e0) % 149.66/21.71 | | | | | | | | | | | | % 149.66/21.71 | | | | | | | | | | | | SIMP: (9586) implies: % 149.66/21.71 | | | | | | | | | | | | (9587) ~ (all_10_2 = e0) % 149.66/21.71 | | | | | | | | | | | | % 149.66/21.71 | | | | | | | | | | | | REDUCE: (9525), (9580) imply: % 149.66/21.72 | | | | | | | | | | | | (9588) ~ (all_6_0 = e0) % 149.66/21.72 | | | | | | | | | | | | % 149.66/21.72 | | | | | | | | | | | | SIMP: (9588) implies: % 149.66/21.72 | | | | | | | | | | | | (9589) ~ (all_6_0 = e0) % 149.66/21.72 | | | | | | | | | | | | % 149.66/21.72 | | | | | | | | | | | | REDUCE: (570), (9580), (9581) imply: % 149.66/21.72 | | | | | | | | | | | | (9590) ~ (e3 = e0) % 149.66/21.72 | | | | | | | | | | | | % 149.66/21.72 | | | | | | | | | | | | REDUCE: (588), (9581) imply: % 149.66/21.72 | | | | | | | | | | | | (9591) ~ (all_52_11 = e3) % 149.66/21.72 | | | | | | | | | | | | % 149.66/21.72 | | | | | | | | | | | | REDUCE: (590), (9581) imply: % 149.66/21.72 | | | | | | | | | | | | (9592) ~ (all_52_13 = e3) % 149.66/21.72 | | | | | | | | | | | | % 149.66/21.72 | | | | | | | | | | | | REDUCE: (38), (9581) imply: % 149.66/21.72 | | | | | | | | | | | | (9593) op(e3, e3) = all_4_1 % 149.66/21.72 | | | | | | | | | | | | % 149.66/21.72 | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_10_2, % 149.66/21.72 | | | | | | | | | | | | all_4_1, e3, e3, simplifying with (51), (9593) % 149.66/21.72 | | | | | | | | | | | | gives: % 149.66/21.72 | | | | | | | | | | | | (9594) all_10_2 = all_4_1 % 149.66/21.72 | | | | | | | | | | | | % 149.66/21.72 | | | | | | | | | | | | COMBINE_EQS: (543), (9594) imply: % 149.66/21.72 | | | | | | | | | | | | (9595) all_54_0 = all_4_1 % 149.66/21.72 | | | | | | | | | | | | % 149.66/21.72 | | | | | | | | | | | | COMBINE_EQS: (546), (9594) imply: % 149.66/21.72 | | | | | | | | | | | | (9596) all_56_1 = all_4_1 % 149.66/21.72 | | | | | | | | | | | | % 149.66/21.72 | | | | | | | | | | | | COMBINE_EQS: (419), (9594) imply: % 149.66/21.72 | | | | | | | | | | | | (9597) all_58_0 = all_4_1 % 149.66/21.72 | | | | | | | | | | | | % 149.66/21.72 | | | | | | | | | | | | REDUCE: (557), (9594) imply: % 149.66/21.72 | | | | | | | | | | | | (9598) ~ (all_52_1 = all_4_1) % 149.66/21.72 | | | | | | | | | | | | % 149.66/21.72 | | | | | | | | | | | | REDUCE: (9531), (9594) imply: % 149.66/21.72 | | | | | | | | | | | | (9599) ~ (all_6_0 = all_4_1) % 149.66/21.72 | | | | | | | | | | | | % 149.66/21.72 | | | | | | | | | | | | SIMP: (9599) implies: % 149.66/21.72 | | | | | | | | | | | | (9600) ~ (all_6_0 = all_4_1) % 149.66/21.72 | | | | | | | | | | | | % 149.66/21.72 | | | | | | | | | | | | REDUCE: (9587), (9594) imply: % 149.66/21.72 | | | | | | | | | | | | (9601) ~ (all_4_1 = e0) % 149.66/21.72 | | | | | | | | | | | | % 149.66/21.72 | | | | | | | | | | | | BETA: splitting (291) gives: % 149.66/21.72 | | | | | | | | | | | | % 149.66/21.72 | | | | | | | | | | | | Case 1: % 149.66/21.72 | | | | | | | | | | | | | % 149.66/21.72 | | | | | | | | | | | | | (9602) ~ (all_56_21 = e0) % 149.66/21.72 | | | | | | | | | | | | | % 149.66/21.72 | | | | | | | | | | | | | REDUCE: (374), (9602) imply: % 149.66/21.72 | | | | | | | | | | | | | (9603) ~ (all_6_2 = e0) % 149.66/21.72 | | | | | | | | | | | | | % 149.66/21.72 | | | | | | | | | | | | | BETA: splitting (294) gives: % 149.66/21.72 | | | | | | | | | | | | | % 149.66/21.72 | | | | | | | | | | | | | Case 1: % 149.66/21.72 | | | | | | | | | | | | | | % 149.66/21.72 | | | | | | | | | | | | | | (9604) ~ (all_56_11 = e0) % 149.66/21.72 | | | | | | | | | | | | | | % 149.66/21.72 | | | | | | | | | | | | | | REDUCE: (545), (9604) imply: % 149.66/21.72 | | | | | | | | | | | | | | (9605) ~ (all_8_2 = e0) % 149.66/21.72 | | | | | | | | | | | | | | % 149.66/21.72 | | | | | | | | | | | | | | BETA: splitting (295) gives: % 149.66/21.72 | | | | | | | | | | | | | | % 149.66/21.72 | | | | | | | | | | | | | | Case 1: % 149.66/21.72 | | | | | | | | | | | | | | | % 149.66/21.72 | | | | | | | | | | | | | | | (9606) ~ (all_56_11 = e1) % 149.66/21.72 | | | | | | | | | | | | | | | % 149.66/21.72 | | | | | | | | | | | | | | | REDUCE: (545), (9606) imply: % 149.66/21.72 | | | | | | | | | | | | | | | (9607) ~ (all_8_2 = e1) % 149.66/21.72 | | | | | | | | | | | | | | | % 149.66/21.72 | | | | | | | | | | | | | | | BETA: splitting (293) gives: % 149.66/21.72 | | | | | | | | | | | | | | | % 149.66/21.72 | | | | | | | | | | | | | | | Case 1: % 149.66/21.72 | | | | | | | | | | | | | | | | % 149.66/21.72 | | | | | | | | | | | | | | | | (9608) ~ (all_56_21 = e3) % 149.66/21.72 | | | | | | | | | | | | | | | | % 149.66/21.72 | | | | | | | | | | | | | | | | REDUCE: (374), (9608) imply: % 149.66/21.72 | | | | | | | | | | | | | | | | (9609) ~ (all_6_2 = e3) % 149.66/21.72 | | | | | | | | | | | | | | | | % 149.66/21.72 | | | | | | | | | | | | | | | | REF_CLOSE: (41), (242), (541), (622), (9517), (9537), (9603), % 149.66/21.72 | | | | | | | | | | | | | | | | (9609), (function-axioms) are inconsistent by % 149.66/21.72 | | | | | | | | | | | | | | | | sub-proof #459. % 149.66/21.72 | | | | | | | | | | | | | | | | % 149.66/21.72 | | | | | | | | | | | | | | | Case 2: % 149.66/21.72 | | | | | | | | | | | | | | | | % 149.66/21.72 | | | | | | | | | | | | | | | | (9610) all_56_21 = e3 % 149.66/21.72 | | | | | | | | | | | | | | | | (9611) all_56_17 = e1 % 149.66/21.72 | | | | | | | | | | | | | | | | % 149.66/21.72 | | | | | | | | | | | | | | | | COMBINE_EQS: (9521), (9611) imply: % 149.66/21.72 | | | | | | | | | | | | | | | | (9612) all_6_0 = e1 % 149.66/21.72 | | | | | | | | | | | | | | | | % 149.66/21.72 | | | | | | | | | | | | | | | | COMBINE_EQS: (374), (9610) imply: % 149.66/21.72 | | | | | | | | | | | | | | | | (9613) all_6_2 = e3 % 149.66/21.72 | | | | | | | | | | | | | | | | % 149.66/21.72 | | | | | | | | | | | | | | | | SIMP: (9613) implies: % 149.66/21.72 | | | | | | | | | | | | | | | | (9614) all_6_2 = e3 % 149.66/21.72 | | | | | | | | | | | | | | | | % 149.66/21.72 | | | | | | | | | | | | | | | | REDUCE: (9523), (9612) imply: % 149.66/21.72 | | | | | | | | | | | | | | | | (9615) ~ (all_52_1 = e1) % 149.66/21.72 | | | | | | | | | | | | | | | | % 149.66/21.72 | | | | | | | | | | | | | | | | REDUCE: (9517), (9614) imply: % 149.66/21.72 | | | | | | | | | | | | | | | | (9616) op(e3, e3) = e3 % 149.66/21.72 | | | | | | | | | | | | | | | | % 149.66/21.72 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_4_1, e3, % 149.66/21.72 | | | | | | | | | | | | | | | | e3, e3, simplifying with (9593), (9616) gives: % 149.66/21.72 | | | | | | | | | | | | | | | | (9617) all_4_1 = e3 % 149.66/21.72 | | | | | | | | | | | | | | | | % 149.66/21.72 | | | | | | | | | | | | | | | | REDUCE: (9598), (9617) imply: % 149.66/21.72 | | | | | | | | | | | | | | | | (9618) ~ (all_52_1 = e3) % 149.66/21.72 | | | | | | | | | | | | | | | | % 149.66/21.72 | | | | | | | | | | | | | | | | BETA: splitting (248) gives: % 149.66/21.72 | | | | | | | | | | | | | | | | % 149.66/21.72 | | | | | | | | | | | | | | | | Case 1: % 149.66/21.72 | | | | | | | | | | | | | | | | | % 149.66/21.72 | | | | | | | | | | | | | | | | | (9619) all_54_4 = e3 % 149.66/21.72 | | | | | | | | | | | | | | | | | % 149.66/21.72 | | | | | | | | | | | | | | | | | COMBINE_EQS: (463), (9619) imply: % 149.66/21.72 | | | | | | | | | | | | | | | | | (9620) all_52_1 = e3 % 149.66/21.72 | | | | | | | | | | | | | | | | | % 149.66/21.72 | | | | | | | | | | | | | | | | | REDUCE: (9618), (9620) imply: % 149.66/21.72 | | | | | | | | | | | | | | | | | (9621) $false % 149.66/21.72 | | | | | | | | | | | | | | | | | % 149.66/21.72 | | | | | | | | | | | | | | | | | CLOSE: (9621) is inconsistent. % 149.66/21.72 | | | | | | | | | | | | | | | | | % 149.66/21.72 | | | | | | | | | | | | | | | | Case 2: % 149.66/21.72 | | | | | | | | | | | | | | | | | % 149.66/21.72 | | | | | | | | | | | | | | | | | (9622) all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0 % 149.66/21.72 | | | | | | | | | | | | | | | | | % 149.66/21.72 | | | | | | | | | | | | | | | | | BETA: splitting (9622) gives: % 149.66/21.72 | | | | | | | | | | | | | | | | | % 149.66/21.72 | | | | | | | | | | | | | | | | | Case 1: % 149.66/21.72 | | | | | | | | | | | | | | | | | | % 149.66/21.72 | | | | | | | | | | | | | | | | | | (9623) all_54_4 = e2 % 149.66/21.72 | | | | | | | | | | | | | | | | | | % 149.66/21.72 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (463), (9623) imply: % 149.66/21.72 | | | | | | | | | | | | | | | | | | (9624) all_52_1 = e2 % 149.66/21.72 | | | | | | | | | | | | | | | | | | % 149.66/21.72 | | | | | | | | | | | | | | | | | | REDUCE: (568), (9624) imply: % 149.66/21.72 | | | | | | | | | | | | | | | | | | (9625) ~ (all_8_2 = e2) % 149.66/21.72 | | | | | | | | | | | | | | | | | | % 149.66/21.72 | | | | | | | | | | | | | | | | | | SIMP: (9625) implies: % 149.66/21.72 | | | | | | | | | | | | | | | | | | (9626) ~ (all_8_2 = e2) % 149.66/21.72 | | | | | | | | | | | | | | | | | | % 149.66/21.72 | | | | | | | | | | | | | | | | | | BETA: splitting (247) gives: % 149.66/21.72 | | | | | | | | | | | | | | | | | | % 149.66/21.72 | | | | | | | | | | | | | | | | | | Case 1: % 149.66/21.72 | | | | | | | | | | | | | | | | | | | % 149.66/21.72 | | | | | | | | | | | | | | | | | | | (9627) all_54_5 = e3 % 149.66/21.72 | | | | | | | | | | | | | | | | | | | % 149.66/21.72 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (542), (9627) imply: % 149.66/21.72 | | | | | | | | | | | | | | | | | | | (9628) all_8_2 = e3 % 149.66/21.72 | | | | | | | | | | | | | | | | | | | % 149.66/21.72 | | | | | | | | | | | | | | | | | | | SIMP: (9628) implies: % 149.66/21.72 | | | | | | | | | | | | | | | | | | | (9629) all_8_2 = e3 % 149.66/21.72 | | | | | | | | | | | | | | | | | | | % 149.66/21.72 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (48), (51), (215), (252), (296), (425), % 149.66/21.72 | | | | | | | | | | | | | | | | | | | (534), (543), (545), (557), (617), (639), (8987), % 149.66/21.72 | | | | | | | | | | | | | | | | | | | (9313), (9535), (9629), (function-axioms) are % 149.66/21.72 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #255. % 149.66/21.72 | | | | | | | | | | | | | | | | | | | % 149.66/21.72 | | | | | | | | | | | | | | | | | | Case 2: % 149.66/21.72 | | | | | | | | | | | | | | | | | | | % 149.66/21.72 | | | | | | | | | | | | | | | | | | | (9630) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 149.66/21.72 | | | | | | | | | | | | | | | | | | | % 149.66/21.72 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (542), (9605), (9607), (9626), (9630) are % 149.66/21.72 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #644. % 149.66/21.72 | | | | | | | | | | | | | | | | | | | % 149.66/21.72 | | | | | | | | | | | | | | | | | | End of split % 149.66/21.72 | | | | | | | | | | | | | | | | | | % 149.66/21.72 | | | | | | | | | | | | | | | | | Case 2: % 149.66/21.72 | | | | | | | | | | | | | | | | | | % 149.66/21.72 | | | | | | | | | | | | | | | | | | (9631) all_54_4 = e1 | all_54_4 = e0 % 149.66/21.72 | | | | | | | | | | | | | | | | | | % 149.66/21.72 | | | | | | | | | | | | | | | | | | REF_CLOSE: (463), (9583), (9615), (9631) are inconsistent by % 149.66/21.72 | | | | | | | | | | | | | | | | | | sub-proof #583. % 149.66/21.72 | | | | | | | | | | | | | | | | | | % 149.66/21.72 | | | | | | | | | | | | | | | | | End of split % 149.66/21.72 | | | | | | | | | | | | | | | | | % 149.66/21.72 | | | | | | | | | | | | | | | | End of split % 149.66/21.72 | | | | | | | | | | | | | | | | % 149.66/21.72 | | | | | | | | | | | | | | | End of split % 149.66/21.72 | | | | | | | | | | | | | | | % 149.66/21.72 | | | | | | | | | | | | | | Case 2: % 149.66/21.72 | | | | | | | | | | | | | | | % 149.66/21.72 | | | | | | | | | | | | | | | (9632) all_56_13 = e2 % 149.66/21.72 | | | | | | | | | | | | | | | (9633) all_56_11 = e1 % 149.66/21.72 | | | | | | | | | | | | | | | % 149.66/21.72 | | | | | | | | | | | | | | | COMBINE_EQS: (545), (9633) imply: % 149.66/21.72 | | | | | | | | | | | | | | | (9634) all_8_2 = e1 % 149.66/21.72 | | | | | | | | | | | | | | | % 149.66/21.72 | | | | | | | | | | | | | | | COMBINE_EQS: (431), (9632) imply: % 149.66/21.72 | | | | | | | | | | | | | | | (9635) all_52_9 = e2 % 149.66/21.72 | | | | | | | | | | | | | | | % 149.66/21.72 | | | | | | | | | | | | | | | SIMP: (9635) implies: % 149.66/21.72 | | | | | | | | | | | | | | | (9636) all_52_9 = e2 % 149.66/21.72 | | | | | | | | | | | | | | | % 149.66/21.72 | | | | | | | | | | | | | | | REF_CLOSE: (166), (194), (238), (244), (248), (252), (287), % 149.66/21.72 | | | | | | | | | | | | | | | (344), (374), (463), (482), (545), (568), (585), % 149.66/21.72 | | | | | | | | | | | | | | | (9318), (9520), (9523), (9577), (9583), (9585), % 149.66/21.72 | | | | | | | | | | | | | | | (9589), (9591), (9595), (9596), (9597), (9598), % 149.66/21.72 | | | | | | | | | | | | | | | (9600), (9601), (9634), (9636) are inconsistent by % 149.66/21.72 | | | | | | | | | | | | | | | sub-proof #417. % 149.66/21.72 | | | | | | | | | | | | | | | % 149.66/21.72 | | | | | | | | | | | | | | End of split % 149.66/21.72 | | | | | | | | | | | | | | % 149.66/21.72 | | | | | | | | | | | | | Case 2: % 149.66/21.72 | | | | | | | | | | | | | | % 149.66/21.72 | | | | | | | | | | | | | | (9637) all_56_15 = e2 % 149.66/21.72 | | | | | | | | | | | | | | (9638) all_56_11 = e0 % 149.66/21.72 | | | | | | | | | | | | | | % 149.66/21.72 | | | | | | | | | | | | | | COMBINE_EQS: (545), (9638) imply: % 149.66/21.72 | | | | | | | | | | | | | | (9639) all_8_2 = e0 % 149.66/21.72 | | | | | | | | | | | | | | % 149.66/21.72 | | | | | | | | | | | | | | COMBINE_EQS: (443), (9637) imply: % 149.66/21.72 | | | | | | | | | | | | | | (9640) all_52_13 = e2 % 149.66/21.72 | | | | | | | | | | | | | | % 149.66/21.72 | | | | | | | | | | | | | | SIMP: (9640) implies: % 149.66/21.72 | | | | | | | | | | | | | | (9641) all_52_13 = e2 % 149.66/21.72 | | | | | | | | | | | | | | % 149.66/21.72 | | | | | | | | | | | | | | REDUCE: (193), (9641) imply: % 149.66/21.72 | | | | | | | | | | | | | | (9642) ~ (all_52_1 = e2) % 149.66/21.72 | | | | | | | | | | | | | | % 149.66/21.72 | | | | | | | | | | | | | | REDUCE: (9592), (9641) imply: % 149.66/21.72 | | | | | | | | | | | | | | (9643) ~ (e3 = e2) % 149.66/21.72 | | | | | | | | | | | | | | % 149.66/21.72 | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (8), (9), (41), (287), (344), (374), % 149.66/21.72 | | | | | | | | | | | | | | (401), (622), (9318), (9517), (9522), (9577), % 149.66/21.72 | | | | | | | | | | | | | | (9582), (9596), (9597), (9601), (9638), (9642), % 149.66/21.72 | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 149.66/21.72 | | | | | | | | | | | | | | #7. % 149.66/21.72 | | | | | | | | | | | | | | % 149.66/21.72 | | | | | | | | | | | | | End of split % 149.66/21.72 | | | | | | | | | | | | | % 149.66/21.72 | | | | | | | | | | | | Case 2: % 149.66/21.72 | | | | | | | | | | | | | % 149.66/21.72 | | | | | | | | | | | | | (9644) all_56_23 = e1 % 149.66/21.72 | | | | | | | | | | | | | (9645) all_56_21 = e0 % 149.66/21.72 | | | | | | | | | | | | | % 149.66/21.72 | | | | | | | | | | | | | COMBINE_EQS: (374), (9645) imply: % 149.66/21.72 | | | | | | | | | | | | | (9646) all_6_2 = e0 % 149.66/21.72 | | | | | | | | | | | | | % 149.66/21.72 | | | | | | | | | | | | | SIMP: (9646) implies: % 149.66/21.72 | | | | | | | | | | | | | (9647) all_6_2 = e0 % 149.66/21.72 | | | | | | | | | | | | | % 149.66/21.72 | | | | | | | | | | | | | COMBINE_EQS: (366), (9644) imply: % 149.66/21.72 | | | | | | | | | | | | | (9648) all_52_14 = e1 % 149.66/21.72 | | | | | | | | | | | | | % 149.66/21.72 | | | | | | | | | | | | | SIMP: (9648) implies: % 149.66/21.72 | | | | | | | | | | | | | (9649) all_52_14 = e1 % 149.66/21.72 | | | | | | | | | | | | | % 149.66/21.72 | | | | | | | | | | | | | REDUCE: (174), (9649) imply: % 149.66/21.72 | | | | | | | | | | | | | (9650) ~ (all_52_6 = e1) % 149.66/21.72 | | | | | | | | | | | | | % 149.66/21.72 | | | | | | | | | | | | | REDUCE: (580), (9647) imply: % 149.66/21.72 | | | | | | | | | | | | | (9651) ~ (all_52_6 = e0) % 149.66/21.72 | | | | | | | | | | | | | % 149.66/21.72 | | | | | | | | | | | | | REDUCE: (9529), (9649) imply: % 149.66/21.72 | | | | | | | | | | | | | (9652) ~ (all_6_0 = e1) % 149.66/21.72 | | | | | | | | | | | | | % 149.66/21.72 | | | | | | | | | | | | | SIMP: (9652) implies: % 149.66/21.72 | | | | | | | | | | | | | (9653) ~ (all_6_0 = e1) % 149.66/21.72 | | | | | | | | | | | | | % 149.66/21.72 | | | | | | | | | | | | | REF_CLOSE: (4), (243), (244), (287), (473), (545), (573), % 149.66/21.72 | | | | | | | | | | | | | (9318), (9520), (9527), (9577), (9589), (9596), % 149.66/21.72 | | | | | | | | | | | | | (9600), (9645), (9650), (9651), (9653) are % 149.66/21.72 | | | | | | | | | | | | | inconsistent by sub-proof #321. % 149.66/21.72 | | | | | | | | | | | | | % 149.66/21.72 | | | | | | | | | | | | End of split % 149.66/21.72 | | | | | | | | | | | | % 149.66/21.72 | | | | | | | | | | | End of split % 149.66/21.72 | | | | | | | | | | | % 149.66/21.72 | | | | | | | | | | Case 2: % 149.66/21.72 | | | | | | | | | | | % 149.66/21.72 | | | | | | | | | | | (9654) all_56_31 = e1 % 149.66/21.72 | | | | | | | | | | | (9655) all_56_29 = e0 % 149.66/21.72 | | | | | | | | | | | % 149.66/21.72 | | | | | | | | | | | REF_CLOSE: (6), (7), (36), (38), (41), (43), (48), (51), % 149.66/21.72 | | | | | | | | | | | (192), (205), (207), (242), (287), (293), (294), % 149.66/21.72 | | | | | | | | | | | (319), (357), (365), (374), (381), (499), (541), % 149.66/21.72 | | | | | | | | | | | (544), (545), (546), (547), (548), (549), (561), % 149.66/21.72 | | | | | | | | | | | (575), (585), (588), (627), (676), (8985), (8987), % 149.66/21.72 | | | | | | | | | | | (9316), (9654), (9655), (function-axioms) are % 149.66/21.72 | | | | | | | | | | | inconsistent by sub-proof #13. % 149.66/21.72 | | | | | | | | | | | % 149.66/21.72 | | | | | | | | | | End of split % 149.66/21.72 | | | | | | | | | | % 149.66/21.72 | | | | | | | | | Case 2: % 149.66/21.72 | | | | | | | | | | % 149.66/21.72 | | | | | | | | | | (9656) all_56_21 = e2 % 149.66/21.72 | | | | | | | | | | (9657) all_56_19 = e1 % 149.66/21.72 | | | | | | | | | | % 149.66/21.72 | | | | | | | | | | COMBINE_EQS: (435), (9657) imply: % 149.66/21.72 | | | | | | | | | | (9658) all_52_6 = e1 % 149.66/21.72 | | | | | | | | | | % 149.66/21.72 | | | | | | | | | | COMBINE_EQS: (374), (9656) imply: % 149.66/21.72 | | | | | | | | | | (9659) all_6_2 = e2 % 149.66/21.72 | | | | | | | | | | % 149.66/21.72 | | | | | | | | | | COMBINE_EQS: (532), (9659) imply: % 149.66/21.72 | | | | | | | | | | (9660) all_36_2 = e2 % 149.66/21.72 | | | | | | | | | | % 149.66/21.72 | | | | | | | | | | COMBINE_EQS: (552), (9659) imply: % 149.66/21.72 | | | | | | | | | | (9661) all_58_8 = e2 % 149.66/21.72 | | | | | | | | | | % 149.66/21.72 | | | | | | | | | | COMBINE_EQS: (380), (9658) imply: % 149.66/21.72 | | | | | | | | | | (9662) all_58_7 = e1 % 149.66/21.72 | | | | | | | | | | % 149.66/21.72 | | | | | | | | | | REDUCE: (9527), (9658) imply: % 149.66/21.72 | | | | | | | | | | (9663) ~ (all_6_0 = e1) % 149.66/21.72 | | | | | | | | | | % 149.66/21.72 | | | | | | | | | | SIMP: (9663) implies: % 149.66/21.72 | | | | | | | | | | (9664) ~ (all_6_0 = e1) % 149.66/21.72 | | | | | | | | | | % 149.66/21.72 | | | | | | | | | | REDUCE: (580), (9658), (9659) imply: % 149.66/21.72 | | | | | | | | | | (9665) ~ (e2 = e1) % 149.66/21.72 | | | | | | | | | | % 149.66/21.72 | | | | | | | | | | REDUCE: (9517), (9659) imply: % 149.66/21.72 | | | | | | | | | | (9666) op(e2, e2) = e3 % 149.66/21.72 | | | | | | | | | | % 149.66/21.72 | | | | | | | | | | REF_CLOSE: (4), (5), (6), (46), (48), (244), (287), (324), % 149.66/21.72 | | | | | | | | | | (544), (545), (546), (550), (591), (617), (762), % 149.66/21.72 | | | | | | | | | | (9318), (9515), (9520), (9522), (9529), (9531), % 149.66/21.72 | | | | | | | | | | (9656), (9660), (9661), (9662), (9664), (9666), % 149.66/21.72 | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 149.66/21.72 | | | | | | | | | | #433. % 149.66/21.72 | | | | | | | | | | % 149.66/21.72 | | | | | | | | | End of split % 149.66/21.72 | | | | | | | | | % 149.66/21.72 | | | | | | | | End of split % 149.66/21.72 | | | | | | | | % 149.66/21.72 | | | | | | | End of split % 149.66/21.72 | | | | | | | % 149.66/21.72 | | | | | | Case 2: % 149.66/21.72 | | | | | | | % 149.66/21.72 | | | | | | | (9667) all_28_0 = e2 % 149.66/21.72 | | | | | | | (9668) ~ (all_28_1 = e3) | ~ (all_28_2 = e0) % 149.66/21.72 | | | | | | | % 149.66/21.72 | | | | | | | REF_CLOSE: (6), (7), (8), (36), (38), (41), (42), (43), (46), % 149.66/21.72 | | | | | | | (48), (51), (144), (158), (174), (192), (205), (207), % 149.66/21.72 | | | | | | | (208), (211), (237), (242), (247), (252), (287), (288), % 149.66/21.72 | | | | | | | (291), (292), (293), (294), (297), (319), (321), (341), % 149.66/21.72 | | | | | | | (357), (365), (366), (374), (381), (386), (402), (407), % 149.66/21.72 | | | | | | | (419), (435), (443), (475), (499), (513), (540), (541), % 149.66/21.72 | | | | | | | (542), (543), (544), (545), (546), (547), (548), (549), % 149.66/21.72 | | | | | | | (550), (551), (555), (559), (561), (569), (571), (573), % 149.66/21.72 | | | | | | | (575), (580), (585), (588), (591), (620), (622), (627), % 149.66/21.72 | | | | | | | (634), (665), (676), (740), (764), (8985), (8986), % 149.66/21.72 | | | | | | | (8987), (9316), (9667), (9668), (function-axioms) are % 149.66/21.72 | | | | | | | inconsistent by sub-proof #5. % 149.66/21.72 | | | | | | | % 149.66/21.72 | | | | | | End of split % 149.66/21.72 | | | | | | % 149.66/21.72 | | | | | End of split % 149.66/21.72 | | | | | % 149.66/21.72 | | | | End of split % 149.66/21.72 | | | | % 149.66/21.72 | | | Case 2: % 149.66/21.72 | | | | % 149.66/21.72 | | | | (9669) all_8_1 = e1 % 149.66/21.72 | | | | (9670) ~ (all_8_0 = e0) | ~ (all_8_2 = e3) % 149.66/21.72 | | | | % 149.66/21.72 | | | | COMBINE_EQS: (686), (9669) imply: % 149.66/21.72 | | | | (9671) all_48_1 = e1 % 149.66/21.72 | | | | % 149.66/21.72 | | | | REDUCE: (48), (9669) imply: % 149.66/21.72 | | | | (9672) op(all_8_2, all_8_2) = e1 % 149.66/21.72 | | | | % 149.66/21.72 | | | | REDUCE: (47), (9669) imply: % 149.66/21.72 | | | | (9673) op(e2, e1) = all_8_0 % 149.66/21.72 | | | | % 149.66/21.72 | | | | GROUND_INST: instantiating (function-axioms) with all_52_9, all_8_0, e1, % 149.66/21.72 | | | | e2, simplifying with (213), (9673) gives: % 149.66/21.72 | | | | (9674) all_52_9 = all_8_0 % 149.66/21.72 | | | | % 149.66/21.72 | | | | COMBINE_EQS: (467), (9674) imply: % 149.66/21.72 | | | | (9675) all_54_6 = all_8_0 % 149.66/21.72 | | | | % 149.66/21.72 | | | | COMBINE_EQS: (431), (9674) imply: % 149.66/21.72 | | | | (9676) all_56_13 = all_8_0 % 149.66/21.72 | | | | % 149.66/21.72 | | | | COMBINE_EQS: (389), (9674) imply: % 149.66/21.72 | | | | (9677) all_58_5 = all_8_0 % 149.66/21.72 | | | | % 149.66/21.72 | | | | REDUCE: (165), (9674) imply: % 149.66/21.72 | | | | (9678) ~ (all_52_13 = all_8_0) % 149.66/21.72 | | | | % 149.66/21.72 | | | | SIMP: (9678) implies: % 149.66/21.72 | | | | (9679) ~ (all_52_13 = all_8_0) % 149.66/21.72 | | | | % 149.66/21.72 | | | | REDUCE: (577), (9674) imply: % 149.66/21.72 | | | | (9680) ~ (all_8_0 = all_8_2) % 149.66/21.72 | | | | % 149.66/21.72 | | | | REDUCE: (583), (9674) imply: % 149.66/21.72 | | | | (9681) ~ (all_8_0 = all_6_2) % 149.66/21.72 | | | | % 149.66/21.72 | | | | BETA: splitting (79) gives: % 149.66/21.72 | | | | % 149.66/21.72 | | | | Case 1: % 149.66/21.72 | | | | | % 149.66/21.72 | | | | | (9682) ~ (all_20_0 = e3) % 149.66/21.72 | | | | | % 149.66/21.72 | | | | | REDUCE: (8984), (9682) imply: % 149.66/21.72 | | | | | (9683) $false % 149.66/21.72 | | | | | % 149.66/21.72 | | | | | CLOSE: (9683) is inconsistent. % 149.66/21.72 | | | | | % 149.66/21.72 | | | | Case 2: % 149.66/21.72 | | | | | % 149.66/21.72 | | | | | (9684) ~ (all_20_1 = e2) | ~ (all_20_2 = e1) % 149.66/21.72 | | | | | % 149.66/21.72 | | | | | BETA: splitting (99) gives: % 149.66/21.72 | | | | | % 149.66/21.72 | | | | | Case 1: % 149.66/21.72 | | | | | | % 149.66/21.72 | | | | | | (9685) ~ (all_28_0 = e2) % 149.66/21.72 | | | | | | % 149.66/21.72 | | | | | | REDUCE: (740), (9685) imply: % 149.66/21.72 | | | | | | (9686) ~ (all_6_0 = e2) % 149.66/21.72 | | | | | | % 149.66/21.72 | | | | | | BETA: splitting (119) gives: % 149.66/21.72 | | | | | | % 149.66/21.72 | | | | | | Case 1: % 149.66/21.72 | | | | | | | % 149.66/21.72 | | | | | | | (9687) ~ (all_36_1 = e3) % 149.66/21.72 | | | | | | | % 149.66/21.72 | | | | | | | REDUCE: (652), (9687) imply: % 149.66/21.72 | | | | | | | (9688) ~ (all_6_1 = e3) % 149.66/21.72 | | | | | | | % 149.66/21.72 | | | | | | | BETA: splitting (149) gives: % 149.66/21.72 | | | | | | | % 149.66/21.72 | | | | | | | Case 1: % 149.66/21.72 | | | | | | | | % 149.66/21.72 | | | | | | | | (9689) ~ (all_48_0 = e3) % 149.66/21.72 | | | | | | | | % 149.66/21.72 | | | | | | | | REDUCE: (765), (9689) imply: % 149.66/21.72 | | | | | | | | (9690) ~ (all_8_0 = e3) % 149.66/21.72 | | | | | | | | % 149.66/21.72 | | | | | | | | BETA: splitting (288) gives: % 149.66/21.72 | | | | | | | | % 149.66/21.72 | | | | | | | | Case 1: % 149.66/21.72 | | | | | | | | | % 149.66/21.72 | | | | | | | | | (9691) ~ (all_56_31 = e1) % 149.66/21.72 | | | | | | | | | % 149.66/21.72 | | | | | | | | | REDUCE: (544), (9691) imply: % 149.66/21.72 | | | | | | | | | (9692) ~ (all_4_2 = e1) % 149.66/21.72 | | | | | | | | | % 149.66/21.72 | | | | | | | | | BETA: splitting (292) gives: % 149.66/21.72 | | | | | | | | | % 149.66/21.72 | | | | | | | | | Case 1: % 149.66/21.72 | | | | | | | | | | % 149.66/21.72 | | | | | | | | | | (9693) ~ (all_56_21 = e2) % 149.66/21.72 | | | | | | | | | | % 149.66/21.72 | | | | | | | | | | REDUCE: (374), (9693) imply: % 149.66/21.72 | | | | | | | | | | (9694) ~ (all_6_2 = e2) % 149.66/21.72 | | | | | | | | | | % 149.66/21.72 | | | | | | | | | | BETA: splitting (294) gives: % 149.66/21.72 | | | | | | | | | | % 149.66/21.72 | | | | | | | | | | Case 1: % 149.66/21.72 | | | | | | | | | | | % 149.66/21.72 | | | | | | | | | | | (9695) ~ (all_56_11 = e0) % 149.66/21.72 | | | | | | | | | | | % 149.66/21.72 | | | | | | | | | | | REDUCE: (545), (9695) imply: % 149.66/21.72 | | | | | | | | | | | (9696) ~ (all_8_2 = e0) % 149.66/21.72 | | | | | | | | | | | % 149.66/21.72 | | | | | | | | | | | BETA: splitting (293) gives: % 149.66/21.72 | | | | | | | | | | | % 149.66/21.72 | | | | | | | | | | | Case 1: % 149.66/21.72 | | | | | | | | | | | | % 149.66/21.72 | | | | | | | | | | | | (9697) ~ (all_56_21 = e3) % 149.66/21.72 | | | | | | | | | | | | % 149.66/21.72 | | | | | | | | | | | | REDUCE: (374), (9697) imply: % 149.66/21.72 | | | | | | | | | | | | (9698) ~ (all_6_2 = e3) % 149.66/21.72 | | | | | | | | | | | | % 149.66/21.72 | | | | | | | | | | | | BETA: splitting (296) gives: % 149.66/21.72 | | | | | | | | | | | | % 149.66/21.72 | | | | | | | | | | | | Case 1: % 149.66/21.72 | | | | | | | | | | | | | % 149.66/21.72 | | | | | | | | | | | | | (9699) ~ (all_56_11 = e3) % 149.66/21.72 | | | | | | | | | | | | | % 149.66/21.72 | | | | | | | | | | | | | REDUCE: (545), (9699) imply: % 149.66/21.72 | | | | | | | | | | | | | (9700) ~ (all_8_2 = e3) % 149.66/21.72 | | | | | | | | | | | | | % 149.66/21.72 | | | | | | | | | | | | | BETA: splitting (290) gives: % 149.66/21.72 | | | | | | | | | | | | | % 149.66/21.72 | | | | | | | | | | | | | Case 1: % 149.66/21.72 | | | | | | | | | | | | | | % 149.66/21.72 | | | | | | | | | | | | | | (9701) ~ (all_56_31 = e3) % 149.66/21.72 | | | | | | | | | | | | | | % 149.66/21.72 | | | | | | | | | | | | | | REDUCE: (544), (9701) imply: % 149.66/21.72 | | | | | | | | | | | | | | (9702) ~ (all_4_2 = e3) % 149.66/21.72 | | | | | | | | | | | | | | % 149.66/21.72 | | | | | | | | | | | | | | BETA: splitting (289) gives: % 149.66/21.72 | | | | | | | | | | | | | | % 149.66/21.72 | | | | | | | | | | | | | | Case 1: % 149.66/21.72 | | | | | | | | | | | | | | | % 149.66/21.72 | | | | | | | | | | | | | | | (9703) ~ (all_56_31 = e2) % 149.66/21.72 | | | | | | | | | | | | | | | % 149.66/21.72 | | | | | | | | | | | | | | | REDUCE: (544), (9703) imply: % 149.66/21.72 | | | | | | | | | | | | | | | (9704) ~ (all_4_2 = e2) % 149.66/21.72 | | | | | | | | | | | | | | | % 149.66/21.72 | | | | | | | | | | | | | | | REF_CLOSE: (36), (38), (237), (540), (627), (8985), (9692), % 149.66/21.72 | | | | | | | | | | | | | | | (9702), (9704), (function-axioms) are inconsistent % 149.66/21.72 | | | | | | | | | | | | | | | by sub-proof #29. % 149.66/21.72 | | | | | | | | | | | | | | | % 149.66/21.72 | | | | | | | | | | | | | | Case 2: % 149.66/21.72 | | | | | | | | | | | | | | | % 149.66/21.72 | | | | | | | | | | | | | | | (9705) all_56_31 = e2 % 149.66/21.72 | | | | | | | | | | | | | | | (9706) all_56_27 = e0 % 149.66/21.72 | | | | | | | | | | | | | | | % 149.66/21.72 | | | | | | | | | | | | | | | COMBINE_EQS: (360), (9706) imply: % 149.66/21.72 | | | | | | | | | | | | | | | (9707) all_52_7 = e0 % 149.66/21.72 | | | | | | | | | | | | | | | % 149.66/21.72 | | | | | | | | | | | | | | | SIMP: (9707) implies: % 149.66/21.72 | | | | | | | | | | | | | | | (9708) all_52_7 = e0 % 149.66/21.72 | | | | | | | | | | | | | | | % 149.66/21.72 | | | | | | | | | | | | | | | COMBINE_EQS: (544), (9705) imply: % 149.66/21.72 | | | | | | | | | | | | | | | (9709) all_4_2 = e2 % 149.66/21.72 | | | | | | | | | | | | | | | % 149.66/21.72 | | | | | | | | | | | | | | | REDUCE: (575), (9708) imply: % 149.66/21.72 | | | | | | | | | | | | | | | (9710) ~ (all_8_2 = e0) % 149.66/21.72 | | | | | | | | | | | | | | | % 149.66/21.72 | | | | | | | | | | | | | | | REDUCE: (38), (9709) imply: % 149.66/21.72 | | | | | | | | | | | | | | | (9711) op(e2, e2) = all_4_1 % 149.66/21.72 | | | | | | | | | | | | | | | % 149.66/21.72 | | | | | | | | | | | | | | | REDUCE: (627), (9709) imply: % 149.66/21.72 | | | | | | | | | | | | | | | (9712) op(e0, e2) = all_56_30 % 149.66/21.72 | | | | | | | | | | | | | | | % 149.66/21.72 | | | | | | | | | | | | | | | REDUCE: (206), (9708) imply: % 149.66/21.72 | | | | | | | | | | | | | | | (9713) op(e0, e2) = e0 % 149.66/21.72 | | | | | | | | | | | | | | | % 149.66/21.72 | | | | | | | | | | | | | | | BETA: splitting (8983) gives: % 149.66/21.72 | | | | | | | | | | | | | | | % 149.66/21.72 | | | | | | | | | | | | | | | Case 1: % 149.66/21.72 | | | | | | | | | | | | | | | | % 149.66/21.72 | | | | | | | | | | | | | | | | (9714) ~ (all_4_1 = e1) % 149.66/21.72 | | | | | | | | | | | | | | | | % 149.66/21.72 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, % 149.66/21.72 | | | | | | | | | | | | | | | | all_56_30, e2, e0, simplifying with (9712), (9713) % 149.66/21.72 | | | | | | | | | | | | | | | | gives: % 149.66/21.72 | | | | | | | | | | | | | | | | (9715) all_56_30 = e0 % 149.66/21.72 | | | | | | | | | | | | | | | | % 149.66/21.72 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_8_2, % 149.66/21.72 | | | | | | | | | | | | | | | | all_4_1, e2, e2, simplifying with (46), (9711) % 149.66/21.72 | | | | | | | | | | | | | | | | gives: % 149.66/21.72 | | | | | | | | | | | | | | | | (9716) all_8_2 = all_4_1 % 149.66/21.72 | | | | | | | | | | | | | | | | % 149.66/21.72 | | | | | | | | | | | | | | | | COMBINE_EQS: (542), (9716) imply: % 149.66/21.72 | | | | | | | | | | | | | | | | (9717) all_54_5 = all_4_1 % 149.66/21.72 | | | | | | | | | | | | | | | | % 149.66/21.72 | | | | | | | | | | | | | | | | REDUCE: (9700), (9716) imply: % 149.66/21.72 | | | | | | | | | | | | | | | | (9718) ~ (all_4_1 = e3) % 149.66/21.72 | | | | | | | | | | | | | | | | % 149.66/21.72 | | | | | | | | | | | | | | | | REDUCE: (9696), (9716) imply: % 149.66/21.72 | | | | | | | | | | | | | | | | (9719) ~ (all_4_1 = e0) % 149.66/21.72 | | | | | | | | | | | | | | | | % 149.66/21.72 | | | | | | | | | | | | | | | | BETA: splitting (247) gives: % 149.66/21.72 | | | | | | | | | | | | | | | | % 149.66/21.72 | | | | | | | | | | | | | | | | Case 1: % 149.66/21.72 | | | | | | | | | | | | | | | | | % 149.66/21.72 | | | | | | | | | | | | | | | | | (9720) all_54_5 = e3 % 149.66/21.72 | | | | | | | | | | | | | | | | | % 149.66/21.72 | | | | | | | | | | | | | | | | | REF_CLOSE: (9717), (9718), (9720) are inconsistent by % 149.66/21.72 | | | | | | | | | | | | | | | | | sub-proof #199. % 149.66/21.72 | | | | | | | | | | | | | | | | | % 149.66/21.72 | | | | | | | | | | | | | | | | Case 2: % 149.66/21.72 | | | | | | | | | | | | | | | | | % 149.66/21.72 | | | | | | | | | | | | | | | | | (9721) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 149.66/21.72 | | | | | | | | | | | | | | | | | % 149.66/21.72 | | | | | | | | | | | | | | | | | BETA: splitting (9721) gives: % 149.66/21.72 | | | | | | | | | | | | | | | | | % 149.66/21.72 | | | | | | | | | | | | | | | | | Case 1: % 149.66/21.72 | | | | | | | | | | | | | | | | | | % 149.66/21.72 | | | | | | | | | | | | | | | | | | (9722) all_54_5 = e2 % 149.66/21.72 | | | | | | | | | | | | | | | | | | % 149.66/21.72 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (9717), (9722) imply: % 149.66/21.72 | | | | | | | | | | | | | | | | | | (9723) all_4_1 = e2 % 149.66/21.72 | | | | | | | | | | | | | | | | | | % 149.66/21.72 | | | | | | | | | | | | | | | | | | SIMP: (9723) implies: % 149.66/21.72 | | | | | | | | | | | | | | | | | | (9724) all_4_1 = e2 % 149.66/21.72 | | | | | | | | | | | | | | | | | | % 149.66/21.72 | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8985), (9713), (9724), (function-axioms) are % 149.66/21.72 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #28. % 149.66/21.72 | | | | | | | | | | | | | | | | | | % 149.66/21.72 | | | | | | | | | | | | | | | | | Case 2: % 149.66/21.72 | | | | | | | | | | | | | | | | | | % 149.66/21.72 | | | | | | | | | | | | | | | | | | (9725) all_54_5 = e1 | all_54_5 = e0 % 149.66/21.72 | | | | | | | | | | | | | | | | | | % 149.66/21.72 | | | | | | | | | | | | | | | | | | REF_CLOSE: (9714), (9717), (9719), (9725) are inconsistent by % 149.66/21.72 | | | | | | | | | | | | | | | | | | sub-proof #569. % 149.66/21.72 | | | | | | | | | | | | | | | | | | % 149.66/21.72 | | | | | | | | | | | | | | | | | End of split % 149.66/21.72 | | | | | | | | | | | | | | | | | % 149.66/21.72 | | | | | | | | | | | | | | | | End of split % 149.66/21.72 | | | | | | | | | | | | | | | | % 149.66/21.72 | | | | | | | | | | | | | | | Case 2: % 149.66/21.72 | | | | | | | | | | | | | | | | % 149.66/21.72 | | | | | | | | | | | | | | | | (9726) ~ (all_4_2 = e2) % 149.66/21.72 | | | | | | | | | | | | | | | | % 149.66/21.72 | | | | | | | | | | | | | | | | REF_CLOSE: (36), (38), (237), (540), (627), (8985), (9692), % 149.66/21.72 | | | | | | | | | | | | | | | | (9702), (9726), (function-axioms) are inconsistent % 149.66/21.73 | | | | | | | | | | | | | | | | by sub-proof #29. % 149.66/21.73 | | | | | | | | | | | | | | | | % 149.66/21.73 | | | | | | | | | | | | | | | End of split % 149.66/21.73 | | | | | | | | | | | | | | | % 149.66/21.73 | | | | | | | | | | | | | | End of split % 149.66/21.73 | | | | | | | | | | | | | | % 149.66/21.73 | | | | | | | | | | | | | Case 2: % 149.66/21.73 | | | | | | | | | | | | | | % 149.66/21.73 | | | | | | | | | | | | | | (9727) all_56_31 = e3 % 149.66/21.73 | | | | | | | | | | | | | | (9728) all_56_25 = e0 % 149.66/21.73 | | | | | | | | | | | | | | % 149.66/21.73 | | | | | | | | | | | | | | COMBINE_EQS: (447), (9728) imply: % 149.66/21.73 | | | | | | | | | | | | | | (9729) all_52_3 = e0 % 149.66/21.73 | | | | | | | | | | | | | | % 149.66/21.73 | | | | | | | | | | | | | | SIMP: (9729) implies: % 149.66/21.73 | | | | | | | | | | | | | | (9730) all_52_3 = e0 % 149.66/21.73 | | | | | | | | | | | | | | % 149.66/21.73 | | | | | | | | | | | | | | COMBINE_EQS: (544), (9727) imply: % 149.66/21.73 | | | | | | | | | | | | | | (9731) all_4_2 = e3 % 149.66/21.73 | | | | | | | | | | | | | | % 149.66/21.73 | | | | | | | | | | | | | | COMBINE_EQS: (547), (9731) imply: % 149.66/21.73 | | | | | | | | | | | | | | (9732) all_58_15 = e3 % 149.66/21.73 | | | | | | | | | | | | | | % 149.66/21.73 | | | | | | | | | | | | | | COMBINE_EQS: (365), (9730) imply: % 149.66/21.73 | | | | | | | | | | | | | | (9733) all_58_12 = e0 % 149.66/21.73 | | | | | | | | | | | | | | % 149.66/21.73 | | | | | | | | | | | | | | REDUCE: (188), (9730) imply: % 149.66/21.73 | | | | | | | | | | | | | | (9734) ~ (all_52_7 = e0) % 149.66/21.73 | | | | | | | | | | | | | | % 149.66/21.73 | | | | | | | | | | | | | | SIMP: (9734) implies: % 149.66/21.73 | | | | | | | | | | | | | | (9735) ~ (all_52_7 = e0) % 149.66/21.73 | | | | | | | | | | | | | | % 149.66/21.73 | | | | | | | | | | | | | | REDUCE: (187), (9730) imply: % 149.66/21.73 | | | | | | | | | | | | | | (9736) ~ (all_52_11 = e0) % 149.66/21.73 | | | | | | | | | | | | | | % 149.66/21.73 | | | | | | | | | | | | | | SIMP: (9736) implies: % 149.66/21.73 | | | | | | | | | | | | | | (9737) ~ (all_52_11 = e0) % 149.66/21.73 | | | | | | | | | | | | | | % 149.66/21.73 | | | | | | | | | | | | | | REDUCE: (561), (9730) imply: % 149.66/21.73 | | | | | | | | | | | | | | (9738) ~ (all_10_2 = e0) % 149.66/21.73 | | | | | | | | | | | | | | % 149.66/21.73 | | | | | | | | | | | | | | SIMP: (9738) implies: % 149.66/21.73 | | | | | | | | | | | | | | (9739) ~ (all_10_2 = e0) % 149.66/21.73 | | | | | | | | | | | | | | % 149.66/21.73 | | | | | | | | | | | | | | REDUCE: (570), (9730), (9731) imply: % 149.66/21.73 | | | | | | | | | | | | | | (9740) ~ (e3 = e0) % 149.66/21.73 | | | | | | | | | | | | | | % 149.66/21.73 | | | | | | | | | | | | | | REDUCE: (588), (9731) imply: % 149.66/21.73 | | | | | | | | | | | | | | (9741) ~ (all_52_11 = e3) % 149.66/21.73 | | | | | | | | | | | | | | % 149.66/21.73 | | | | | | | | | | | | | | REDUCE: (591), (9731) imply: % 149.66/21.73 | | | | | | | | | | | | | | (9742) ~ (all_52_14 = e3) % 149.66/21.73 | | | | | | | | | | | | | | % 149.66/21.73 | | | | | | | | | | | | | | REDUCE: (38), (9731) imply: % 149.66/21.73 | | | | | | | | | | | | | | (9743) op(e3, e3) = all_4_1 % 149.66/21.73 | | | | | | | | | | | | | | % 149.66/21.73 | | | | | | | | | | | | | | REF_CLOSE: (7), (36), (38), (43), (51), (166), (168), (169), % 149.66/21.73 | | | | | | | | | | | | | | (171), (173), (174), (181), (182), (183), (205), % 149.66/21.73 | | | | | | | | | | | | | | (206), (237), (238), (241), (242), (246), (247), % 149.66/21.73 | | | | | | | | | | | | | | (250), (251), (252), (291), (298), (299), (318), % 149.66/21.73 | | | | | | | | | | | | | | (321), (328), (333), (336), (343), (345), (366), % 149.66/21.73 | | | | | | | | | | | | | | (374), (380), (386), (389), (401), (407), (408), % 149.66/21.73 | | | | | | | | | | | | | | (419), (429), (457), (459), (467), (476), (482), % 149.66/21.73 | | | | | | | | | | | | | | (540), (541), (542), (543), (546), (547), (548), % 149.66/21.73 | | | | | | | | | | | | | | (549), (550), (551), (552), (554), (555), (557), % 149.66/21.73 | | | | | | | | | | | | | | (563), (565), (567), (571), (575), (577), (582), % 149.66/21.73 | | | | | | | | | | | | | | (583), (585), (587), (591), (625), (626), (627), % 149.66/21.73 | | | | | | | | | | | | | | (8985), (8986), (9688), (9692), (9694), (9696), % 149.66/21.73 | | | | | | | | | | | | | | (9698), (9732), (9733), (9735), (9737), (9739), % 149.66/21.73 | | | | | | | | | | | | | | (9741), (9742), (9743), (function-axioms) are % 149.66/21.73 | | | | | | | | | | | | | | inconsistent by sub-proof #21. % 149.66/21.73 | | | | | | | | | | | | | | % 149.66/21.73 | | | | | | | | | | | | | End of split % 149.66/21.73 | | | | | | | | | | | | | % 149.66/21.73 | | | | | | | | | | | | Case 2: % 149.66/21.73 | | | | | | | | | | | | | % 149.66/21.73 | | | | | | | | | | | | | (9744) all_56_11 = e3 % 149.66/21.73 | | | | | | | | | | | | | (9745) all_56_9 = e2 % 149.66/21.73 | | | | | | | | | | | | | % 149.66/21.73 | | | | | | | | | | | | | COMBINE_EQS: (425), (9745) imply: % 149.66/21.73 | | | | | | | | | | | | | (9746) all_52_1 = e2 % 149.66/21.73 | | | | | | | | | | | | | % 149.66/21.73 | | | | | | | | | | | | | COMBINE_EQS: (545), (9744) imply: % 149.66/21.73 | | | | | | | | | | | | | (9747) all_8_2 = e3 % 149.66/21.73 | | | | | | | | | | | | | % 149.66/21.73 | | | | | | | | | | | | | COMBINE_EQS: (554), (9747) imply: % 149.66/21.73 | | | | | | | | | | | | | (9748) all_58_3 = e3 % 149.66/21.73 | | | | | | | | | | | | | % 149.66/21.73 | | | | | | | | | | | | | COMBINE_EQS: (401), (9746) imply: % 149.66/21.73 | | | | | | | | | | | | | (9749) all_58_2 = e2 % 149.66/21.73 | | | | | | | | | | | | | % 149.66/21.73 | | | | | | | | | | | | | BETA: splitting (9670) gives: % 149.66/21.73 | | | | | | | | | | | | | % 149.66/21.73 | | | | | | | | | | | | | Case 1: % 149.66/21.73 | | | | | | | | | | | | | | % 149.66/21.73 | | | | | | | | | | | | | | (9750) ~ (all_8_2 = e3) % 149.66/21.73 | | | | | | | | | | | | | | % 149.66/21.73 | | | | | | | | | | | | | | REDUCE: (9747), (9750) imply: % 149.66/21.73 | | | | | | | | | | | | | | (9751) $false % 149.66/21.73 | | | | | | | | | | | | | | % 149.66/21.73 | | | | | | | | | | | | | | CLOSE: (9751) is inconsistent. % 149.66/21.73 | | | | | | | | | | | | | | % 149.66/21.73 | | | | | | | | | | | | | Case 2: % 149.66/21.73 | | | | | | | | | | | | | | % 149.66/21.73 | | | | | | | | | | | | | | (9752) ~ (all_8_0 = e0) % 149.66/21.73 | | | | | | | | | | | | | | % 149.66/21.73 | | | | | | | | | | | | | | BETA: splitting (332) gives: % 149.66/21.73 | | | | | | | | | | | | | | % 149.66/21.73 | | | | | | | | | | | | | | Case 1: % 149.66/21.73 | | | | | | | | | | | | | | | % 149.66/21.73 | | | | | | | | | | | | | | | (9753) all_58_2 = e0 % 149.66/21.73 | | | | | | | | | | | | | | | % 149.66/21.73 | | | | | | | | | | | | | | | COMBINE_EQS: (9749), (9753) imply: % 149.66/21.73 | | | | | | | | | | | | | | | (9754) e2 = e0 % 149.66/21.73 | | | | | | | | | | | | | | | % 149.66/21.73 | | | | | | | | | | | | | | | REDUCE: (5), (9754) imply: % 149.66/21.73 | | | | | | | | | | | | | | | (9755) $false % 149.66/21.73 | | | | | | | | | | | | | | | % 149.66/21.73 | | | | | | | | | | | | | | | CLOSE: (9755) is inconsistent. % 149.66/21.73 | | | | | | | | | | | | | | | % 149.66/21.73 | | | | | | | | | | | | | | Case 2: % 149.66/21.73 | | | | | | | | | | | | | | | % 149.66/21.73 | | | | | | | | | | | | | | | (9756) all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0 % 149.66/21.73 | | | | | | | | | | | | | | | % 149.66/21.73 | | | | | | | | | | | | | | | BETA: splitting (9756) gives: % 149.66/21.73 | | | | | | | | | | | | | | | % 149.66/21.73 | | | | | | | | | | | | | | | Case 1: % 149.66/21.73 | | | | | | | | | | | | | | | | % 149.66/21.73 | | | | | | | | | | | | | | | | (9757) all_58_3 = e0 % 149.66/21.73 | | | | | | | | | | | | | | | | % 149.66/21.73 | | | | | | | | | | | | | | | | COMBINE_EQS: (9748), (9757) imply: % 149.66/21.73 | | | | | | | | | | | | | | | | (9758) e3 = e0 % 149.66/21.73 | | | | | | | | | | | | | | | | % 149.66/21.73 | | | | | | | | | | | | | | | | REDUCE: (7), (9758) imply: % 149.66/21.73 | | | | | | | | | | | | | | | | (9759) $false % 149.66/21.73 | | | | | | | | | | | | | | | | % 149.66/21.73 | | | | | | | | | | | | | | | | CLOSE: (9759) is inconsistent. % 149.66/21.73 | | | | | | | | | | | | | | | | % 149.66/21.73 | | | | | | | | | | | | | | | Case 2: % 149.66/21.73 | | | | | | | | | | | | | | | | % 149.66/21.73 | | | | | | | | | | | | | | | | (9760) all_58_5 = e0 | all_58_10 = e0 % 149.66/21.73 | | | | | | | | | | | | | | | | % 149.66/21.73 | | | | | | | | | | | | | | | | BETA: splitting (9760) gives: % 149.66/21.73 | | | | | | | | | | | | | | | | % 149.66/21.73 | | | | | | | | | | | | | | | | Case 1: % 149.66/21.73 | | | | | | | | | | | | | | | | | % 149.66/21.73 | | | | | | | | | | | | | | | | | (9761) all_58_5 = e0 % 149.66/21.73 | | | | | | | | | | | | | | | | | % 149.66/21.73 | | | | | | | | | | | | | | | | | COMBINE_EQS: (9677), (9761) imply: % 149.66/21.73 | | | | | | | | | | | | | | | | | (9762) all_8_0 = e0 % 149.66/21.73 | | | | | | | | | | | | | | | | | % 149.66/21.73 | | | | | | | | | | | | | | | | | REDUCE: (9752), (9762) imply: % 149.66/21.73 | | | | | | | | | | | | | | | | | (9763) $false % 149.66/21.73 | | | | | | | | | | | | | | | | | % 149.66/21.73 | | | | | | | | | | | | | | | | | CLOSE: (9763) is inconsistent. % 149.66/21.73 | | | | | | | | | | | | | | | | | % 149.66/21.73 | | | | | | | | | | | | | | | | Case 2: % 149.66/21.73 | | | | | | | | | | | | | | | | | % 149.66/21.73 | | | | | | | | | | | | | | | | | (9764) all_58_10 = e0 % 149.66/21.73 | | | | | | | | | | | | | | | | | % 149.66/21.73 | | | | | | | | | | | | | | | | | COMBINE_EQS: (386), (9764) imply: % 149.66/21.73 | | | | | | | | | | | | | | | | | (9765) all_52_13 = e0 % 149.66/21.73 | | | | | | | | | | | | | | | | | % 149.66/21.73 | | | | | | | | | | | | | | | | | BETA: splitting (333) gives: % 149.66/21.73 | | | | | | | | | | | | | | | | | % 149.66/21.73 | | | | | | | | | | | | | | | | | Case 1: % 149.66/21.73 | | | | | | | | | | | | | | | | | | % 149.66/21.73 | | | | | | | | | | | | | | | | | | (9766) all_58_2 = e1 % 149.66/21.73 | | | | | | | | | | | | | | | | | | % 149.66/21.73 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (9749), (9766) imply: % 149.66/21.73 | | | | | | | | | | | | | | | | | | (9767) e2 = e1 % 149.66/21.73 | | | | | | | | | | | | | | | | | | % 149.66/21.73 | | | | | | | | | | | | | | | | | | REDUCE: (6), (9767) imply: % 149.66/21.73 | | | | | | | | | | | | | | | | | | (9768) $false % 149.66/21.73 | | | | | | | | | | | | | | | | | | % 149.66/21.73 | | | | | | | | | | | | | | | | | | CLOSE: (9768) is inconsistent. % 149.66/21.73 | | | | | | | | | | | | | | | | | | % 149.66/21.73 | | | | | | | | | | | | | | | | | Case 2: % 149.66/21.73 | | | | | | | | | | | | | | | | | | % 149.66/21.73 | | | | | | | | | | | | | | | | | | (9769) all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1 % 149.66/21.73 | | | | | | | | | | | | | | | | | | % 149.66/21.73 | | | | | | | | | | | | | | | | | | BETA: splitting (9769) gives: % 149.66/21.73 | | | | | | | | | | | | | | | | | | % 149.66/21.73 | | | | | | | | | | | | | | | | | | Case 1: % 149.66/21.73 | | | | | | | | | | | | | | | | | | | % 149.66/21.73 | | | | | | | | | | | | | | | | | | | (9770) all_58_3 = e1 % 149.66/21.73 | | | | | | | | | | | | | | | | | | | % 149.66/21.73 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (9748), (9770) imply: % 149.66/21.73 | | | | | | | | | | | | | | | | | | | (9771) e3 = e1 % 149.66/21.73 | | | | | | | | | | | | | | | | | | | % 149.66/21.73 | | | | | | | | | | | | | | | | | | | REDUCE: (8), (9771) imply: % 149.66/21.73 | | | | | | | | | | | | | | | | | | | (9772) $false % 149.66/21.73 | | | | | | | | | | | | | | | | | | | % 149.66/21.73 | | | | | | | | | | | | | | | | | | | CLOSE: (9772) is inconsistent. % 149.66/21.73 | | | | | | | | | | | | | | | | | | | % 149.66/21.73 | | | | | | | | | | | | | | | | | | Case 2: % 149.66/21.73 | | | | | | | | | | | | | | | | | | | % 149.66/21.73 | | | | | | | | | | | | | | | | | | | (9773) all_58_5 = e1 | all_58_10 = e1 % 149.66/21.73 | | | | | | | | | | | | | | | | | | | % 149.66/21.73 | | | | | | | | | | | | | | | | | | | BETA: splitting (9773) gives: % 149.66/21.73 | | | | | | | | | | | | | | | | | | | % 149.66/21.73 | | | | | | | | | | | | | | | | | | | Case 1: % 149.66/21.73 | | | | | | | | | | | | | | | | | | | | % 149.66/21.73 | | | | | | | | | | | | | | | | | | | | (9774) all_58_5 = e1 % 149.66/21.73 | | | | | | | | | | | | | | | | | | | | % 149.66/21.73 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (9677), (9774) imply: % 149.66/21.73 | | | | | | | | | | | | | | | | | | | | (9775) all_8_0 = e1 % 149.66/21.73 | | | | | | | | | | | | | | | | | | | | % 149.66/21.73 | | | | | | | | | | | | | | | | | | | | REDUCE: (9681), (9775) imply: % 149.66/21.73 | | | | | | | | | | | | | | | | | | | | (9776) ~ (all_6_2 = e1) % 149.66/21.73 | | | | | | | | | | | | | | | | | | | | % 149.66/21.73 | | | | | | | | | | | | | | | | | | | | SIMP: (9776) implies: % 149.66/21.73 | | | | | | | | | | | | | | | | | | | | (9777) ~ (all_6_2 = e1) % 149.66/21.73 | | | | | | | | | | | | | | | | | | | | % 149.66/21.73 | | | | | | | | | | | | | | | | | | | | BETA: splitting (242) gives: % 149.66/21.73 | | | | | | | | | | | | | | | | | | | | % 149.66/21.73 | | | | | | | | | | | | | | | | | | | | Case 1: % 149.66/21.73 | | | | | | | | | | | | | | | | | | | | | % 149.66/21.73 | | | | | | | | | | | | | | | | | | | | | (9778) all_54_10 = e3 % 149.66/21.73 | | | | | | | | | | | | | | | | | | | | | % 149.66/21.73 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (541), (9698), (9778) are inconsistent by % 149.66/21.73 | | | | | | | | | | | | | | | | | | | | | sub-proof #736. % 149.66/21.73 | | | | | | | | | | | | | | | | | | | | | % 149.66/21.73 | | | | | | | | | | | | | | | | | | | | Case 2: % 149.66/21.73 | | | | | | | | | | | | | | | | | | | | | % 149.66/21.73 | | | | | | | | | | | | | | | | | | | | | (9779) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 149.66/21.73 | | | | | | | | | | | | | | | | | | | | | % 149.66/21.73 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (38), (43), (237), (291), (366), (374), % 149.66/21.73 | | | | | | | | | | | | | | | | | | | | | (540), (541), (591), (627), (8985), (8986), % 149.66/21.73 | | | | | | | | | | | | | | | | | | | | | (9688), (9694), (9777), (9779), (function-axioms) % 149.66/21.73 | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #19. % 149.66/21.73 | | | | | | | | | | | | | | | | | | | | | % 149.66/21.73 | | | | | | | | | | | | | | | | | | | | End of split % 149.66/21.73 | | | | | | | | | | | | | | | | | | | | % 149.66/21.73 | | | | | | | | | | | | | | | | | | | Case 2: % 149.66/21.73 | | | | | | | | | | | | | | | | | | | | % 149.66/21.73 | | | | | | | | | | | | | | | | | | | | (9780) all_58_10 = e1 % 149.66/21.73 | | | | | | | | | | | | | | | | | | | | % 149.66/21.73 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (9764), (9780) imply: % 149.66/21.73 | | | | | | | | | | | | | | | | | | | | (9781) e1 = e0 % 149.66/21.73 | | | | | | | | | | | | | | | | | | | | % 149.66/21.73 | | | | | | | | | | | | | | | | | | | | SIMP: (9781) implies: % 149.66/21.73 | | | | | | | | | | | | | | | | | | | | (9782) e1 = e0 % 149.66/21.73 | | | | | | | | | | | | | | | | | | | | % 149.66/21.73 | | | | | | | | | | | | | | | | | | | | REDUCE: (4), (9782) imply: % 149.66/21.73 | | | | | | | | | | | | | | | | | | | | (9783) $false % 149.66/21.73 | | | | | | | | | | | | | | | | | | | | % 149.66/21.73 | | | | | | | | | | | | | | | | | | | | CLOSE: (9783) is inconsistent. % 149.66/21.73 | | | | | | | | | | | | | | | | | | | | % 149.66/21.73 | | | | | | | | | | | | | | | | | | | End of split % 149.66/21.73 | | | | | | | | | | | | | | | | | | | % 149.66/21.73 | | | | | | | | | | | | | | | | | | End of split % 149.66/21.73 | | | | | | | | | | | | | | | | | | % 149.66/21.73 | | | | | | | | | | | | | | | | | End of split % 149.66/21.73 | | | | | | | | | | | | | | | | | % 149.66/21.73 | | | | | | | | | | | | | | | | End of split % 149.66/21.73 | | | | | | | | | | | | | | | | % 149.66/21.73 | | | | | | | | | | | | | | | End of split % 149.66/21.73 | | | | | | | | | | | | | | | % 149.66/21.73 | | | | | | | | | | | | | | End of split % 149.66/21.73 | | | | | | | | | | | | | | % 149.66/21.73 | | | | | | | | | | | | | End of split % 149.66/21.73 | | | | | | | | | | | | | % 149.66/21.73 | | | | | | | | | | | | End of split % 149.66/21.73 | | | | | | | | | | | | % 149.66/21.73 | | | | | | | | | | | Case 2: % 149.66/21.73 | | | | | | | | | | | | % 149.66/21.73 | | | | | | | | | | | | (9784) all_56_21 = e3 % 149.66/21.73 | | | | | | | | | | | | (9785) all_56_17 = e1 % 149.66/21.73 | | | | | | | | | | | | % 149.66/21.73 | | | | | | | | | | | | REF_CLOSE: (42), (43), (51), (158), (160), (161), (174), % 149.66/21.73 | | | | | | | | | | | | (189), (191), (208), (241), (243), (252), (287), % 149.66/21.73 | | | | | | | | | | | | (297), (321), (332), (374), (381), (386), (389), % 149.66/21.73 | | | | | | | | | | | | (401), (402), (473), (476), (543), (544), (545), % 149.66/21.73 | | | | | | | | | | | | (546), (547), (550), (551), (554), (557), (559), % 149.66/21.73 | | | | | | | | | | | | (569), (573), (580), (591), (621), (8986), (9686), % 149.66/21.73 | | | | | | | | | | | | (9688), (9692), (9696), (9784), (9785), % 149.66/21.73 | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 149.66/21.73 | | | | | | | | | | | | #130. % 149.66/21.73 | | | | | | | | | | | | % 149.66/21.73 | | | | | | | | | | | End of split % 149.66/21.73 | | | | | | | | | | | % 149.66/21.73 | | | | | | | | | | Case 2: % 149.66/21.73 | | | | | | | | | | | % 149.66/21.73 | | | | | | | | | | | (9786) all_56_15 = e2 % 149.66/21.73 | | | | | | | | | | | (9787) all_56_11 = e0 % 149.66/21.73 | | | | | | | | | | | % 149.66/21.73 | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (8), (9), (36), (38), (246), (287), % 149.66/21.73 | | | | | | | | | | | (333), (335), (374), (386), (401), (443), (544), % 149.66/21.73 | | | | | | | | | | | (545), (546), (554), (557), (579), (627), (9672), % 149.66/21.73 | | | | | | | | | | | (9675), (9677), (9679), (9680), (9681), (9690), % 149.66/21.73 | | | | | | | | | | | (9692), (9786), (9787), (function-axioms) are % 149.66/21.73 | | | | | | | | | | | inconsistent by sub-proof #111. % 149.66/21.73 | | | | | | | | | | | % 149.66/21.73 | | | | | | | | | | End of split % 149.66/21.73 | | | | | | | | | | % 149.66/21.73 | | | | | | | | | Case 2: % 149.66/21.73 | | | | | | | | | | % 149.66/21.73 | | | | | | | | | | (9788) all_56_21 = e2 % 149.66/21.73 | | | | | | | | | | (9789) all_56_19 = e1 % 149.66/21.73 | | | | | | | | | | % 149.66/21.73 | | | | | | | | | | COMBINE_EQS: (435), (9789) imply: % 149.66/21.73 | | | | | | | | | | (9790) all_52_6 = e1 % 149.66/21.73 | | | | | | | | | | % 149.66/21.73 | | | | | | | | | | SIMP: (9790) implies: % 149.66/21.73 | | | | | | | | | | (9791) all_52_6 = e1 % 149.66/21.73 | | | | | | | | | | % 149.66/21.73 | | | | | | | | | | COMBINE_EQS: (374), (9788) imply: % 149.66/21.73 | | | | | | | | | | (9792) all_6_2 = e2 % 149.66/21.73 | | | | | | | | | | % 149.66/21.73 | | | | | | | | | | SIMP: (9792) implies: % 149.66/21.73 | | | | | | | | | | (9793) all_6_2 = e2 % 149.66/21.73 | | | | | | | | | | % 149.66/21.73 | | | | | | | | | | REDUCE: (573), (9791) imply: % 149.66/21.73 | | | | | | | | | | (9794) ~ (all_8_2 = e1) % 149.66/21.73 | | | | | | | | | | % 149.66/21.73 | | | | | | | | | | SIMP: (9794) implies: % 149.66/21.73 | | | | | | | | | | (9795) ~ (all_8_2 = e1) % 149.66/21.73 | | | | | | | | | | % 149.66/21.73 | | | | | | | | | | REDUCE: (580), (9791), (9793) imply: % 149.66/21.73 | | | | | | | | | | (9796) ~ (e2 = e1) % 149.66/21.73 | | | | | | | | | | % 149.66/21.73 | | | | | | | | | | REDUCE: (9681), (9793) imply: % 149.66/21.73 | | | | | | | | | | (9797) ~ (all_8_0 = e2) % 149.66/21.73 | | | | | | | | | | % 149.66/21.73 | | | | | | | | | | REDUCE: (43), (9793) imply: % 149.66/21.73 | | | | | | | | | | (9798) op(e2, e2) = all_6_1 % 149.66/21.73 | | | | | | | | | | % 149.66/21.73 | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_8_2, % 149.66/21.73 | | | | | | | | | | all_6_1, e2, e2, simplifying with (46), (9798) % 149.66/21.73 | | | | | | | | | | gives: % 149.66/21.73 | | | | | | | | | | (9799) all_8_2 = all_6_1 % 149.66/21.73 | | | | | | | | | | % 149.66/21.73 | | | | | | | | | | COMBINE_EQS: (542), (9799) imply: % 149.66/21.73 | | | | | | | | | | (9800) all_54_5 = all_6_1 % 149.66/21.73 | | | | | | | | | | % 149.66/21.73 | | | | | | | | | | COMBINE_EQS: (545), (9799) imply: % 149.66/21.73 | | | | | | | | | | (9801) all_56_11 = all_6_1 % 149.66/21.73 | | | | | | | | | | % 149.66/21.73 | | | | | | | | | | COMBINE_EQS: (554), (9799) imply: % 149.66/21.73 | | | | | | | | | | (9802) all_58_3 = all_6_1 % 149.66/21.73 | | | | | | | | | | % 149.66/21.73 | | | | | | | | | | REDUCE: (568), (9799) imply: % 149.66/21.73 | | | | | | | | | | (9803) ~ (all_52_1 = all_6_1) % 149.66/21.73 | | | | | | | | | | % 149.66/21.73 | | | | | | | | | | REDUCE: (9680), (9799) imply: % 149.66/21.73 | | | | | | | | | | (9804) ~ (all_8_0 = all_6_1) % 149.66/21.73 | | | | | | | | | | % 149.66/21.73 | | | | | | | | | | REDUCE: (9795), (9799) imply: % 149.66/21.73 | | | | | | | | | | (9805) ~ (all_6_1 = e1) % 149.66/21.73 | | | | | | | | | | % 149.66/21.73 | | | | | | | | | | BETA: splitting (247) gives: % 149.66/21.73 | | | | | | | | | | % 149.66/21.73 | | | | | | | | | | Case 1: % 149.66/21.73 | | | | | | | | | | | % 149.66/21.73 | | | | | | | | | | | (9806) all_54_5 = e3 % 149.66/21.73 | | | | | | | | | | | % 149.66/21.73 | | | | | | | | | | | REF_CLOSE: (9688), (9800), (9806) are inconsistent by % 149.66/21.73 | | | | | | | | | | | sub-proof #509. % 149.66/21.73 | | | | | | | | | | | % 149.66/21.73 | | | | | | | | | | Case 2: % 149.66/21.73 | | | | | | | | | | | % 149.66/21.73 | | | | | | | | | | | (9807) ~ (all_54_5 = e3) % 149.66/21.73 | | | | | | | | | | | (9808) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 149.66/21.73 | | | | | | | | | | | % 149.66/21.73 | | | | | | | | | | | BETA: splitting (9808) gives: % 149.66/21.73 | | | | | | | | | | | % 149.66/21.73 | | | | | | | | | | | Case 1: % 149.66/21.73 | | | | | | | | | | | | % 149.66/21.73 | | | | | | | | | | | | (9809) all_54_5 = e2 % 149.66/21.73 | | | | | | | | | | | | % 149.66/21.73 | | | | | | | | | | | | REF_CLOSE: (8986), (9800), (9809) are inconsistent by % 149.66/21.73 | | | | | | | | | | | | sub-proof #466. % 149.66/21.73 | | | | | | | | | | | | % 149.66/21.73 | | | | | | | | | | | Case 2: % 149.66/21.73 | | | | | | | | | | | | % 149.66/21.73 | | | | | | | | | | | | (9810) ~ (all_54_5 = e2) % 149.66/21.73 | | | | | | | | | | | | (9811) all_54_5 = e1 | all_54_5 = e0 % 149.66/21.73 | | | | | | | | | | | | % 149.66/21.73 | | | | | | | | | | | | BETA: splitting (9811) gives: % 149.66/21.73 | | | | | | | | | | | | % 149.66/21.73 | | | | | | | | | | | | Case 1: % 149.66/21.73 | | | | | | | | | | | | | % 149.66/21.73 | | | | | | | | | | | | | (9812) all_54_5 = e1 % 149.66/21.73 | | | | | | | | | | | | | % 149.66/21.73 | | | | | | | | | | | | | REF_CLOSE: (9800), (9805), (9812) are inconsistent by % 149.66/21.73 | | | | | | | | | | | | | sub-proof #465. % 149.66/21.73 | | | | | | | | | | | | | % 149.66/21.73 | | | | | | | | | | | | Case 2: % 149.66/21.73 | | | | | | | | | | | | | % 149.66/21.73 | | | | | | | | | | | | | (9813) all_54_5 = e0 % 149.66/21.73 | | | | | | | | | | | | | % 149.66/21.73 | | | | | | | | | | | | | COMBINE_EQS: (9800), (9813) imply: % 149.66/21.73 | | | | | | | | | | | | | (9814) all_6_1 = e0 % 149.66/21.73 | | | | | | | | | | | | | % 149.66/21.73 | | | | | | | | | | | | | SIMP: (9814) implies: % 149.66/21.73 | | | | | | | | | | | | | (9815) all_6_1 = e0 % 149.66/21.73 | | | | | | | | | | | | | % 149.66/21.73 | | | | | | | | | | | | | COMBINE_EQS: (9801), (9815) imply: % 149.66/21.73 | | | | | | | | | | | | | (9816) all_56_11 = e0 % 149.66/21.73 | | | | | | | | | | | | | % 149.66/21.73 | | | | | | | | | | | | | COMBINE_EQS: (9802), (9815) imply: % 149.66/21.73 | | | | | | | | | | | | | (9817) all_58_3 = e0 % 149.66/21.73 | | | | | | | | | | | | | % 149.66/21.73 | | | | | | | | | | | | | REDUCE: (9803), (9815) imply: % 149.66/21.73 | | | | | | | | | | | | | (9818) ~ (all_52_1 = e0) % 149.66/21.73 | | | | | | | | | | | | | % 149.66/21.73 | | | | | | | | | | | | | REDUCE: (9804), (9815) imply: % 149.66/21.73 | | | | | | | | | | | | | (9819) ~ (all_8_0 = e0) % 149.66/21.73 | | | | | | | | | | | | | % 149.66/21.73 | | | | | | | | | | | | | REDUCE: (9688), (9815) imply: % 149.66/21.73 | | | | | | | | | | | | | (9820) ~ (e3 = e0) % 149.66/21.73 | | | | | | | | | | | | | % 149.66/21.73 | | | | | | | | | | | | | REDUCE: (8986), (9815) imply: % 149.66/21.73 | | | | | | | | | | | | | (9821) ~ (e2 = e0) % 149.66/21.73 | | | | | | | | | | | | | % 149.66/21.73 | | | | | | | | | | | | | REDUCE: (9805), (9815) imply: % 149.66/21.73 | | | | | | | | | | | | | (9822) ~ (e1 = e0) % 149.66/21.73 | | | | | | | | | | | | | % 149.66/21.73 | | | | | | | | | | | | | BETA: splitting (294) gives: % 149.66/21.73 | | | | | | | | | | | | | % 149.66/21.73 | | | | | | | | | | | | | Case 1: % 149.66/21.73 | | | | | | | | | | | | | | % 149.66/21.73 | | | | | | | | | | | | | | (9823) ~ (all_56_11 = e0) % 149.66/21.73 | | | | | | | | | | | | | | % 149.66/21.73 | | | | | | | | | | | | | | REDUCE: (9816), (9823) imply: % 149.66/21.73 | | | | | | | | | | | | | | (9824) $false % 149.66/21.73 | | | | | | | | | | | | | | % 149.66/21.73 | | | | | | | | | | | | | | CLOSE: (9824) is inconsistent. % 149.66/21.73 | | | | | | | | | | | | | | % 149.66/21.73 | | | | | | | | | | | | | Case 2: % 149.66/21.73 | | | | | | | | | | | | | | % 149.66/21.73 | | | | | | | | | | | | | | (9825) all_56_15 = e2 % 149.66/21.73 | | | | | | | | | | | | | | % 149.66/21.73 | | | | | | | | | | | | | | COMBINE_EQS: (443), (9825) imply: % 149.66/21.73 | | | | | | | | | | | | | | (9826) all_52_13 = e2 % 149.66/21.73 | | | | | | | | | | | | | | % 149.66/21.73 | | | | | | | | | | | | | | COMBINE_EQS: (386), (9826) imply: % 149.66/21.73 | | | | | | | | | | | | | | (9827) all_58_10 = e2 % 149.66/21.73 | | | | | | | | | | | | | | % 149.66/21.73 | | | | | | | | | | | | | | BETA: splitting (335) gives: % 149.66/21.73 | | | | | | | | | | | | | | % 149.66/21.73 | | | | | | | | | | | | | | Case 1: % 149.66/21.73 | | | | | | | | | | | | | | | % 149.66/21.73 | | | | | | | | | | | | | | | (9828) all_58_2 = e3 % 149.66/21.73 | | | | | | | | | | | | | | | % 149.66/21.73 | | | | | | | | | | | | | | | COMBINE_EQS: (401), (9828) imply: % 149.66/21.73 | | | | | | | | | | | | | | | (9829) all_52_1 = e3 % 149.66/21.73 | | | | | | | | | | | | | | | % 149.66/21.73 | | | | | | | | | | | | | | | REDUCE: (557), (9829) imply: % 149.66/21.73 | | | | | | | | | | | | | | | (9830) ~ (all_10_2 = e3) % 149.66/21.73 | | | | | | | | | | | | | | | % 149.66/21.73 | | | | | | | | | | | | | | | SIMP: (9830) implies: % 149.66/21.73 | | | | | | | | | | | | | | | (9831) ~ (all_10_2 = e3) % 149.66/21.73 | | | | | | | | | | | | | | | % 149.66/21.73 | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (36), (38), (287), (333), % 149.66/21.73 | | | | | | | | | | | | | | | (374), (389), (544), (546), (583), (627), (8985), % 149.66/21.73 | | | | | | | | | | | | | | | (9816), (9817), (9827), (9828), (9831), % 149.66/21.73 | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 149.66/21.73 | | | | | | | | | | | | | | | #4. % 149.66/21.73 | | | | | | | | | | | | | | | % 149.66/21.73 | | | | | | | | | | | | | | Case 2: % 149.66/21.73 | | | | | | | | | | | | | | | % 149.66/21.73 | | | | | | | | | | | | | | | (9832) all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3 % 149.66/21.73 | | | | | | | | | | | | | | | % 149.66/21.73 | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (9), (246), (9675), (9677), (9690), % 149.66/21.73 | | | | | | | | | | | | | | | (9797), (9817), (9819), (9827), (9832) are % 149.66/21.73 | | | | | | | | | | | | | | | inconsistent by sub-proof #129. % 149.66/21.73 | | | | | | | | | | | | | | | % 149.66/21.73 | | | | | | | | | | | | | | End of split % 149.66/21.73 | | | | | | | | | | | | | | % 149.66/21.73 | | | | | | | | | | | | | End of split % 149.66/21.73 | | | | | | | | | | | | | % 149.66/21.73 | | | | | | | | | | | | End of split % 149.66/21.73 | | | | | | | | | | | | % 149.66/21.73 | | | | | | | | | | | End of split % 149.66/21.73 | | | | | | | | | | | % 149.66/21.73 | | | | | | | | | | End of split % 149.66/21.73 | | | | | | | | | | % 149.66/21.73 | | | | | | | | | End of split % 149.66/21.73 | | | | | | | | | % 149.66/21.73 | | | | | | | | Case 2: % 149.66/21.73 | | | | | | | | | % 149.66/21.73 | | | | | | | | | (9833) all_56_31 = e1 % 149.66/21.73 | | | | | | | | | (9834) all_56_29 = e0 % 149.66/21.73 | | | | | | | | | % 149.66/21.73 | | | | | | | | | COMBINE_EQS: (357), (9834) imply: % 149.66/21.73 | | | | | | | | | (9835) all_52_11 = e0 % 149.66/21.73 | | | | | | | | | % 149.66/21.73 | | | | | | | | | COMBINE_EQS: (544), (9833) imply: % 149.66/21.73 | | | | | | | | | (9836) all_4_2 = e1 % 149.66/21.73 | | | | | | | | | % 149.66/21.73 | | | | | | | | | COMBINE_EQS: (499), (9836) imply: % 149.66/21.73 | | | | | | | | | (9837) all_20_2 = e1 % 149.66/21.73 | | | | | | | | | % 149.66/21.73 | | | | | | | | | COMBINE_EQS: (547), (9836) imply: % 149.66/21.73 | | | | | | | | | (9838) all_58_15 = e1 % 149.66/21.73 | | | | | | | | | % 149.66/21.73 | | | | | | | | | COMBINE_EQS: (548), (9835) imply: % 149.66/21.73 | | | | | | | | | (9839) all_58_14 = e0 % 149.66/21.73 | | | | | | | | | % 149.66/21.73 | | | | | | | | | REDUCE: (585), (9835) imply: % 149.66/21.73 | | | | | | | | | (9840) ~ (all_6_2 = e0) % 149.66/21.73 | | | | | | | | | % 149.66/21.73 | | | | | | | | | SIMP: (9840) implies: % 149.66/21.73 | | | | | | | | | (9841) ~ (all_6_2 = e0) % 149.66/21.73 | | | | | | | | | % 149.66/21.73 | | | | | | | | | REDUCE: (588), (9835), (9836) imply: % 149.66/21.73 | | | | | | | | | (9842) ~ (e1 = e0) % 149.66/21.73 | | | | | | | | | % 149.66/21.73 | | | | | | | | | REDUCE: (38), (9836) imply: % 149.66/21.73 | | | | | | | | | (9843) op(e1, e1) = all_4_1 % 149.66/21.73 | | | | | | | | | % 149.66/21.73 | | | | | | | | | REDUCE: (627), (9836) imply: % 149.66/21.73 | | | | | | | | | (9844) op(e0, e1) = all_56_30 % 149.66/21.73 | | | | | | | | | % 149.66/21.73 | | | | | | | | | REDUCE: (205), (9835) imply: % 149.66/21.73 | | | | | | | | | (9845) op(e0, e1) = e0 % 149.66/21.73 | | | | | | | | | % 149.66/21.73 | | | | | | | | | BETA: splitting (9684) gives: % 149.66/21.73 | | | | | | | | | % 149.66/21.73 | | | | | | | | | Case 1: % 149.66/21.73 | | | | | | | | | | % 149.66/21.73 | | | | | | | | | | (9846) ~ (all_20_1 = e2) % 149.66/21.73 | | | | | | | | | | % 149.66/21.73 | | | | | | | | | | REDUCE: (676), (9846) imply: % 149.66/21.73 | | | | | | | | | | (9847) ~ (all_4_1 = e2) % 149.66/21.73 | | | | | | | | | | % 149.66/21.73 | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, % 149.66/21.73 | | | | | | | | | | all_56_30, e1, e0, simplifying with (9844), (9845) % 149.66/21.73 | | | | | | | | | | gives: % 149.66/21.73 | | | | | | | | | | (9848) all_56_30 = e0 % 149.66/21.73 | | | | | | | | | | % 149.66/21.73 | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_6_2, % 149.66/21.73 | | | | | | | | | | all_4_1, e1, e1, simplifying with (41), (9843) % 149.66/21.73 | | | | | | | | | | gives: % 149.66/21.73 | | | | | | | | | | (9849) all_6_2 = all_4_1 % 149.66/21.73 | | | | | | | | | | % 149.66/21.73 | | | | | | | | | | COMBINE_EQS: (541), (9849) imply: % 149.66/21.73 | | | | | | | | | | (9850) all_54_10 = all_4_1 % 149.66/21.73 | | | | | | | | | | % 149.66/21.73 | | | | | | | | | | COMBINE_EQS: (374), (9849) imply: % 149.66/21.73 | | | | | | | | | | (9851) all_56_21 = all_4_1 % 149.66/21.73 | | | | | | | | | | % 149.66/21.73 | | | | | | | | | | REDUCE: (9841), (9849) imply: % 149.66/21.73 | | | | | | | | | | (9852) ~ (all_4_1 = e0) % 149.66/21.73 | | | | | | | | | | % 149.66/21.73 | | | | | | | | | | REDUCE: (43), (9849) imply: % 149.66/21.73 | | | | | | | | | | (9853) op(all_4_1, all_4_1) = all_6_1 % 149.66/21.73 | | | | | | | | | | % 149.66/21.73 | | | | | | | | | | BETA: splitting (293) gives: % 149.66/21.73 | | | | | | | | | | % 149.66/21.73 | | | | | | | | | | Case 1: % 149.66/21.73 | | | | | | | | | | | % 149.66/21.73 | | | | | | | | | | | (9854) ~ (all_56_21 = e3) % 149.66/21.73 | | | | | | | | | | | % 149.66/21.73 | | | | | | | | | | | REDUCE: (9851), (9854) imply: % 149.66/21.73 | | | | | | | | | | | (9855) ~ (all_4_1 = e3) % 149.66/21.73 | | | | | | | | | | | % 149.66/21.73 | | | | | | | | | | | REF_CLOSE: (7), (242), (8985), (9845), (9847), (9850), % 149.66/21.73 | | | | | | | | | | | (9852), (9855), (function-axioms) are inconsistent % 149.66/21.73 | | | | | | | | | | | by sub-proof #17. % 149.66/21.73 | | | | | | | | | | | % 149.66/21.73 | | | | | | | | | | Case 2: % 149.66/21.73 | | | | | | | | | | | % 149.66/21.73 | | | | | | | | | | | (9856) all_56_21 = e3 % 149.66/21.73 | | | | | | | | | | | (9857) all_56_17 = e1 % 149.66/21.73 | | | | | | | | | | | % 149.66/21.73 | | | | | | | | | | | COMBINE_EQS: (381), (9857) imply: % 149.66/21.73 | | | | | | | | | | | (9858) all_52_2 = e1 % 149.66/21.73 | | | | | | | | | | | % 149.66/21.73 | | | | | | | | | | | SIMP: (9858) implies: % 149.66/21.73 | | | | | | | | | | | (9859) all_52_2 = e1 % 149.66/21.73 | | | | | | | | | | | % 149.66/21.73 | | | | | | | | | | | COMBINE_EQS: (9851), (9856) imply: % 149.66/21.73 | | | | | | | | | | | (9860) all_4_1 = e3 % 149.66/21.73 | | | | | | | | | | | % 149.66/21.73 | | | | | | | | | | | SIMP: (9860) implies: % 149.66/21.73 | | | | | | | | | | | (9861) all_4_1 = e3 % 149.66/21.73 | | | | | | | | | | | % 149.66/21.73 | | | | | | | | | | | REDUCE: (192), (9859) imply: % 149.66/21.73 | | | | | | | | | | | (9862) ~ (all_52_3 = e1) % 149.66/21.73 | | | | | | | | | | | % 149.66/21.73 | | | | | | | | | | | SIMP: (9862) implies: % 149.66/21.73 | | | | | | | | | | | (9863) ~ (all_52_3 = e1) % 149.66/21.73 | | | | | | | | | | | % 149.66/21.73 | | | | | | | | | | | REDUCE: (9853), (9861) imply: % 149.66/21.73 | | | | | | | | | | | (9864) op(e3, e3) = all_6_1 % 149.66/21.73 | | | | | | | | | | | % 149.66/21.73 | | | | | | | | | | | REDUCE: (8985), (9861) imply: % 149.66/21.73 | | | | | | | | | | | (9865) op(e0, e3) = e3 % 149.66/21.73 | | | | | | | | | | | % 149.66/21.73 | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_3, e3, % 149.66/21.73 | | | | | | | | | | | e3, e0, simplifying with (207), (9865) gives: % 149.66/21.73 | | | | | | | | | | | (9866) all_52_3 = e3 % 149.66/21.73 | | | | | | | | | | | % 149.66/21.73 | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_10_2, % 149.66/21.73 | | | | | | | | | | | all_6_1, e3, e3, simplifying with (51), (9864) % 149.66/21.73 | | | | | | | | | | | gives: % 149.66/21.73 | | | | | | | | | | | (9867) all_10_2 = all_6_1 % 149.66/21.73 | | | | | | | | | | | % 149.66/21.73 | | | | | | | | | | | COMBINE_EQS: (546), (9867) imply: % 149.66/21.73 | | | | | | | | | | | (9868) all_56_1 = all_6_1 % 149.66/21.73 | | | | | | | | | | | % 149.66/21.73 | | | | | | | | | | | COMBINE_EQS: (365), (9866) imply: % 149.66/21.73 | | | | | | | | | | | (9869) all_58_12 = e3 % 149.66/21.73 | | | | | | | | | | | % 149.66/21.74 | | | | | | | | | | | REDUCE: (561), (9866), (9867) imply: % 149.66/21.74 | | | | | | | | | | | (9870) ~ (all_6_1 = e3) % 149.66/21.74 | | | | | | | | | | | % 149.66/21.74 | | | | | | | | | | | BETA: splitting (287) gives: % 149.66/21.74 | | | | | | | | | | | % 149.66/21.74 | | | | | | | | | | | Case 1: % 149.66/21.74 | | | | | | | | | | | | % 149.66/21.74 | | | | | | | | | | | | (9871) all_56_1 = e3 % 149.66/21.74 | | | | | | | | | | | | % 149.66/21.74 | | | | | | | | | | | | COMBINE_EQS: (9868), (9871) imply: % 149.66/21.74 | | | | | | | | | | | | (9872) all_6_1 = e3 % 149.66/21.74 | | | | | | | | | | | | % 149.66/21.74 | | | | | | | | | | | | REDUCE: (9688), (9872) imply: % 149.66/21.74 | | | | | | | | | | | | (9873) $false % 149.66/21.74 | | | | | | | | | | | | % 149.66/21.74 | | | | | | | | | | | | CLOSE: (9873) is inconsistent. % 149.66/21.74 | | | | | | | | | | | | % 149.66/21.74 | | | | | | | | | | | Case 2: % 149.66/21.74 | | | | | | | | | | | | % 149.66/21.74 | | | | | | | | | | | | (9874) all_56_11 = e2 | all_56_21 = e1 | all_56_31 = e0 % 149.66/21.74 | | | | | | | | | | | | % 149.66/21.74 | | | | | | | | | | | | BETA: splitting (319) gives: % 149.66/21.74 | | | | | | | | | | | | % 149.66/21.74 | | | | | | | | | | | | Case 1: % 149.66/21.74 | | | | | | | | | | | | | % 149.66/21.74 | | | | | | | | | | | | | (9875) all_58_12 = e2 % 149.66/21.74 | | | | | | | | | | | | | % 149.66/21.74 | | | | | | | | | | | | | COMBINE_EQS: (9869), (9875) imply: % 149.66/21.74 | | | | | | | | | | | | | (9876) e3 = e2 % 149.66/21.74 | | | | | | | | | | | | | % 149.66/21.74 | | | | | | | | | | | | | REDUCE: (9), (9876) imply: % 149.66/21.74 | | | | | | | | | | | | | (9877) $false % 149.66/21.74 | | | | | | | | | | | | | % 149.66/21.74 | | | | | | | | | | | | | CLOSE: (9877) is inconsistent. % 149.66/21.74 | | | | | | | | | | | | | % 149.66/21.74 | | | | | | | | | | | | Case 2: % 149.66/21.74 | | | | | | | | | | | | | % 149.66/21.74 | | | | | | | | | | | | | (9878) all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2 % 149.66/21.74 | | | | | | | | | | | | | % 149.66/21.74 | | | | | | | | | | | | | BETA: splitting (9878) gives: % 149.66/21.74 | | | | | | | | | | | | | % 149.66/21.74 | | | | | | | | | | | | | Case 1: % 149.66/21.74 | | | | | | | | | | | | | | % 149.66/21.74 | | | | | | | | | | | | | | (9879) all_58_13 = e2 % 149.66/21.74 | | | | | | | | | | | | | | % 149.66/21.74 | | | | | | | | | | | | | | COMBINE_EQS: (549), (9879) imply: % 149.66/21.74 | | | | | | | | | | | | | | (9880) all_52_7 = e2 % 149.66/21.74 | | | | | | | | | | | | | | % 149.66/21.74 | | | | | | | | | | | | | | SIMP: (9880) implies: % 149.66/21.74 | | | | | | | | | | | | | | (9881) all_52_7 = e2 % 149.66/21.74 | | | | | | | | | | | | | | % 149.66/21.74 | | | | | | | | | | | | | | REDUCE: (575), (9881) imply: % 149.66/21.74 | | | | | | | | | | | | | | (9882) ~ (all_8_2 = e2) % 149.66/21.74 | | | | | | | | | | | | | | % 149.66/21.74 | | | | | | | | | | | | | | SIMP: (9882) implies: % 149.66/21.74 | | | | | | | | | | | | | | (9883) ~ (all_8_2 = e2) % 149.66/21.74 | | | | | | | | | | | | | | % 149.66/21.74 | | | | | | | | | | | | | | BETA: splitting (9874) gives: % 149.66/21.74 | | | | | | | | | | | | | | % 149.66/21.74 | | | | | | | | | | | | | | Case 1: % 149.66/21.74 | | | | | | | | | | | | | | | % 149.66/21.74 | | | | | | | | | | | | | | | (9884) all_56_11 = e2 % 149.66/21.74 | | | | | | | | | | | | | | | % 149.66/21.74 | | | | | | | | | | | | | | | COMBINE_EQS: (545), (9884) imply: % 149.66/21.74 | | | | | | | | | | | | | | | (9885) all_8_2 = e2 % 149.66/21.74 | | | | | | | | | | | | | | | % 149.66/21.74 | | | | | | | | | | | | | | | REDUCE: (9883), (9885) imply: % 149.66/21.74 | | | | | | | | | | | | | | | (9886) $false % 149.66/21.74 | | | | | | | | | | | | | | | % 149.66/21.74 | | | | | | | | | | | | | | | CLOSE: (9886) is inconsistent. % 149.66/21.74 | | | | | | | | | | | | | | | % 149.66/21.74 | | | | | | | | | | | | | | Case 2: % 149.66/21.74 | | | | | | | | | | | | | | | % 149.66/21.74 | | | | | | | | | | | | | | | (9887) all_56_21 = e1 | all_56_31 = e0 % 149.66/21.74 | | | | | | | | | | | | | | | % 149.66/21.74 | | | | | | | | | | | | | | | REF_CLOSE: (4), (8), (9833), (9856), (9887) are inconsistent % 149.66/21.74 | | | | | | | | | | | | | | | by sub-proof #16. % 149.66/21.74 | | | | | | | | | | | | | | | % 149.66/21.74 | | | | | | | | | | | | | | End of split % 149.66/21.74 | | | | | | | | | | | | | | % 149.66/21.74 | | | | | | | | | | | | | Case 2: % 149.66/21.74 | | | | | | | | | | | | | | % 149.66/21.74 | | | | | | | | | | | | | | (9888) all_58_14 = e2 | all_58_15 = e2 % 149.66/21.74 | | | | | | | | | | | | | | % 149.66/21.74 | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (9838), (9839), (9888) are inconsistent % 149.66/21.74 | | | | | | | | | | | | | | by sub-proof #36. % 149.66/21.74 | | | | | | | | | | | | | | % 149.66/21.74 | | | | | | | | | | | | | End of split % 149.66/21.74 | | | | | | | | | | | | | % 149.66/21.74 | | | | | | | | | | | | End of split % 149.66/21.74 | | | | | | | | | | | | % 149.66/21.74 | | | | | | | | | | | End of split % 149.66/21.74 | | | | | | | | | | | % 149.66/21.74 | | | | | | | | | | End of split % 149.66/21.74 | | | | | | | | | | % 149.66/21.74 | | | | | | | | | Case 2: % 149.66/21.74 | | | | | | | | | | % 149.66/21.74 | | | | | | | | | | (9889) ~ (all_20_2 = e1) % 149.66/21.74 | | | | | | | | | | % 149.66/21.74 | | | | | | | | | | REDUCE: (9837), (9889) imply: % 149.66/21.74 | | | | | | | | | | (9890) $false % 149.66/21.74 | | | | | | | | | | % 149.66/21.74 | | | | | | | | | | CLOSE: (9890) is inconsistent. % 149.66/21.74 | | | | | | | | | | % 149.66/21.74 | | | | | | | | | End of split % 149.66/21.74 | | | | | | | | | % 149.66/21.74 | | | | | | | | End of split % 149.66/21.74 | | | | | | | | % 149.66/21.74 | | | | | | | Case 2: % 149.66/21.74 | | | | | | | | % 149.66/21.74 | | | | | | | | (9891) all_48_0 = e3 % 149.66/21.74 | | | | | | | | (9892) ~ (all_48_1 = e1) | ~ (all_48_2 = e0) % 149.66/21.74 | | | | | | | | % 149.66/21.74 | | | | | | | | COMBINE_EQS: (765), (9891) imply: % 149.66/21.74 | | | | | | | | (9893) all_8_0 = e3 % 149.66/21.74 | | | | | | | | % 149.66/21.74 | | | | | | | | SIMP: (9893) implies: % 149.66/21.74 | | | | | | | | (9894) all_8_0 = e3 % 149.66/21.74 | | | | | | | | % 149.66/21.74 | | | | | | | | REF_CLOSE: (9), (46), (247), (295), (536), (542), (545), (617), % 149.66/21.74 | | | | | | | | (9671), (9672), (9676), (9680), (9892), (9894), % 149.66/21.74 | | | | | | | | (function-axioms) are inconsistent by sub-proof #115. % 149.66/21.74 | | | | | | | | % 149.66/21.74 | | | | | | | End of split % 149.66/21.74 | | | | | | | % 149.66/21.74 | | | | | | Case 2: % 149.66/21.74 | | | | | | | % 149.66/21.74 | | | | | | | (9895) all_36_1 = e3 % 149.66/21.74 | | | | | | | (9896) ~ (all_36_0 = e0) | ~ (all_36_2 = e2) % 149.66/21.74 | | | | | | | % 149.66/21.74 | | | | | | | COMBINE_EQS: (652), (9895) imply: % 149.66/21.74 | | | | | | | (9897) all_6_1 = e3 % 149.66/21.74 | | | | | | | % 149.66/21.74 | | | | | | | REDUCE: (43), (9897) imply: % 149.66/21.74 | | | | | | | (9898) op(all_6_2, all_6_2) = e3 % 149.66/21.74 | | | | | | | % 149.66/21.74 | | | | | | | REDUCE: (42), (9897) imply: % 149.66/21.74 | | | | | | | (9899) op(e1, e3) = all_6_0 % 149.66/21.74 | | | | | | | % 149.66/21.74 | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_2, % 149.66/21.74 | | | | | | | all_6_0, e3, e1, simplifying with (211), (9899) % 149.66/21.74 | | | | | | | gives: % 149.66/21.74 | | | | | | | (9900) all_52_2 = all_6_0 % 149.66/21.74 | | | | | | | % 149.66/21.74 | | | | | | | COMBINE_EQS: (471), (9900) imply: % 149.66/21.74 | | | | | | | (9901) all_54_8 = all_6_0 % 149.66/21.74 | | | | | | | % 149.66/21.74 | | | | | | | COMBINE_EQS: (553), (9900) imply: % 149.66/21.74 | | | | | | | (9902) all_58_6 = all_6_0 % 149.66/21.74 | | | | | | | % 149.66/21.74 | | | | | | | REDUCE: (192), (9900) imply: % 149.66/21.74 | | | | | | | (9903) ~ (all_52_3 = all_6_0) % 149.66/21.74 | | | | | | | % 149.66/21.74 | | | | | | | SIMP: (9903) implies: % 149.66/21.74 | | | | | | | (9904) ~ (all_52_3 = all_6_0) % 149.66/21.74 | | | | | | | % 149.66/21.74 | | | | | | | REDUCE: (191), (9900) imply: % 149.66/21.74 | | | | | | | (9905) ~ (all_52_6 = all_6_0) % 149.66/21.74 | | | | | | | % 149.66/21.74 | | | | | | | SIMP: (9905) implies: % 149.66/21.74 | | | | | | | (9906) ~ (all_52_6 = all_6_0) % 149.66/21.74 | | | | | | | % 149.66/21.74 | | | | | | | REDUCE: (189), (9900) imply: % 149.66/21.74 | | | | | | | (9907) ~ (all_52_14 = all_6_0) % 149.66/21.74 | | | | | | | % 149.66/21.74 | | | | | | | SIMP: (9907) implies: % 149.66/21.74 | | | | | | | (9908) ~ (all_52_14 = all_6_0) % 149.66/21.74 | | | | | | | % 149.66/21.74 | | | | | | | REDUCE: (559), (9900) imply: % 149.66/21.74 | | | | | | | (9909) ~ (all_10_2 = all_6_0) % 149.66/21.74 | | | | | | | % 149.66/21.74 | | | | | | | SIMP: (9909) implies: % 149.66/21.74 | | | | | | | (9910) ~ (all_10_2 = all_6_0) % 149.66/21.74 | | | | | | | % 149.66/21.74 | | | | | | | REDUCE: (569), (9900) imply: % 149.66/21.74 | | | | | | | (9911) ~ (all_6_0 = all_6_2) % 149.66/21.74 | | | | | | | % 149.66/21.74 | | | | | | | BETA: splitting (288) gives: % 149.66/21.74 | | | | | | | % 149.66/21.74 | | | | | | | Case 1: % 149.66/21.74 | | | | | | | | % 149.66/21.74 | | | | | | | | (9912) ~ (all_56_31 = e1) % 149.66/21.74 | | | | | | | | % 149.66/21.74 | | | | | | | | REDUCE: (544), (9912) imply: % 149.66/21.74 | | | | | | | | (9913) ~ (all_4_2 = e1) % 149.66/21.74 | | | | | | | | % 149.66/21.74 | | | | | | | | REF_CLOSE: (4), (5), (36), (38), (41), (46), (48), (51), (171), % 149.66/21.74 | | | | | | | | (173), (174), (176), (182), (183), (184), (194), % 149.66/21.74 | | | | | | | | (196), (207), (237), (242), (243), (244), (247), % 149.66/21.74 | | | | | | | | (251), (287), (289), (290), (291), (292), (293), % 149.66/21.74 | | | | | | | | (296), (324), (326), (327), (328), (330), (333), % 149.66/21.74 | | | | | | | | (337), (360), (366), (374), (380), (386), (389), % 149.66/21.74 | | | | | | | | (401), (407), (425), (435), (447), (457), (473), % 149.66/21.74 | | | | | | | | (532), (540), (541), (542), (544), (545), (546), % 149.66/21.74 | | | | | | | | (548), (550), (552), (554), (555), (561), (571), % 149.66/21.74 | | | | | | | | (573), (575), (579), (580), (587), (588), (591), % 149.66/21.74 | | | | | | | | (617), (622), (627), (762), (8983), (8985), (9686), % 149.66/21.74 | | | | | | | | (9896), (9898), (9901), (9902), (9904), (9906), % 149.66/21.74 | | | | | | | | (9908), (9910), (9911), (9913), (function-axioms) are % 149.66/21.74 | | | | | | | | inconsistent by sub-proof #2. % 149.66/21.74 | | | | | | | | % 149.66/21.74 | | | | | | | Case 2: % 149.66/21.74 | | | | | | | | % 149.66/21.74 | | | | | | | | (9914) all_56_31 = e1 % 149.66/21.74 | | | | | | | | (9915) all_56_29 = e0 % 149.66/21.74 | | | | | | | | % 149.66/21.74 | | | | | | | | COMBINE_EQS: (357), (9915) imply: % 149.66/21.74 | | | | | | | | (9916) all_52_11 = e0 % 149.66/21.74 | | | | | | | | % 149.66/21.74 | | | | | | | | SIMP: (9916) implies: % 149.66/21.74 | | | | | | | | (9917) all_52_11 = e0 % 149.66/21.74 | | | | | | | | % 149.66/21.74 | | | | | | | | COMBINE_EQS: (544), (9914) imply: % 149.66/21.74 | | | | | | | | (9918) all_4_2 = e1 % 149.66/21.74 | | | | | | | | % 149.66/21.74 | | | | | | | | COMBINE_EQS: (499), (9918) imply: % 149.66/21.74 | | | | | | | | (9919) all_20_2 = e1 % 149.66/21.74 | | | | | | | | % 149.66/21.74 | | | | | | | | REDUCE: (585), (9917) imply: % 149.66/21.74 | | | | | | | | (9920) ~ (all_6_2 = e0) % 149.66/21.74 | | | | | | | | % 149.66/21.74 | | | | | | | | SIMP: (9920) implies: % 149.66/21.74 | | | | | | | | (9921) ~ (all_6_2 = e0) % 149.66/21.74 | | | | | | | | % 149.66/21.74 | | | | | | | | REDUCE: (38), (9918) imply: % 149.66/21.74 | | | | | | | | (9922) op(e1, e1) = all_4_1 % 149.66/21.74 | | | | | | | | % 149.66/21.74 | | | | | | | | REDUCE: (627), (9918) imply: % 149.66/21.74 | | | | | | | | (9923) op(e0, e1) = all_56_30 % 149.66/21.74 | | | | | | | | % 149.66/21.74 | | | | | | | | REDUCE: (205), (9917) imply: % 149.66/21.74 | | | | | | | | (9924) op(e0, e1) = e0 % 149.66/21.74 | | | | | | | | % 149.66/21.74 | | | | | | | | BETA: splitting (9684) gives: % 149.66/21.74 | | | | | | | | % 149.66/21.74 | | | | | | | | Case 1: % 149.66/21.74 | | | | | | | | | % 149.66/21.74 | | | | | | | | | (9925) ~ (all_20_1 = e2) % 149.66/21.74 | | | | | | | | | % 149.66/21.74 | | | | | | | | | REDUCE: (676), (9925) imply: % 149.66/21.74 | | | | | | | | | (9926) ~ (all_4_1 = e2) % 149.66/21.74 | | | | | | | | | % 149.66/21.74 | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, % 149.66/21.74 | | | | | | | | | all_56_30, e1, e0, simplifying with (9923), (9924) % 149.66/21.74 | | | | | | | | | gives: % 149.66/21.74 | | | | | | | | | (9927) all_56_30 = e0 % 149.66/21.74 | | | | | | | | | % 149.66/21.74 | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_6_2, % 149.66/21.74 | | | | | | | | | all_4_1, e1, e1, simplifying with (41), (9922) % 149.66/21.74 | | | | | | | | | gives: % 149.66/21.74 | | | | | | | | | (9928) all_6_2 = all_4_1 % 149.66/21.74 | | | | | | | | | % 149.66/21.74 | | | | | | | | | COMBINE_EQS: (541), (9928) imply: % 149.66/21.74 | | | | | | | | | (9929) all_54_10 = all_4_1 % 149.66/21.74 | | | | | | | | | % 149.66/21.74 | | | | | | | | | COMBINE_EQS: (374), (9928) imply: % 149.66/21.74 | | | | | | | | | (9930) all_56_21 = all_4_1 % 149.66/21.74 | | | | | | | | | % 149.66/21.74 | | | | | | | | | REDUCE: (9921), (9928) imply: % 149.66/21.74 | | | | | | | | | (9931) ~ (all_4_1 = e0) % 149.66/21.74 | | | | | | | | | % 149.66/21.74 | | | | | | | | | REDUCE: (9898), (9928) imply: % 149.66/21.74 | | | | | | | | | (9932) op(all_4_1, all_4_1) = e3 % 149.66/21.74 | | | | | | | | | % 149.66/21.74 | | | | | | | | | BETA: splitting (293) gives: % 149.66/21.74 | | | | | | | | | % 149.66/21.74 | | | | | | | | | Case 1: % 149.66/21.74 | | | | | | | | | | % 149.66/21.74 | | | | | | | | | | (9933) ~ (all_56_21 = e3) % 149.66/21.74 | | | | | | | | | | % 149.66/21.74 | | | | | | | | | | REDUCE: (9930), (9933) imply: % 149.66/21.74 | | | | | | | | | | (9934) ~ (all_4_1 = e3) % 149.66/21.74 | | | | | | | | | | % 149.66/21.74 | | | | | | | | | | REF_CLOSE: (7), (242), (8985), (9924), (9926), (9929), % 149.66/21.74 | | | | | | | | | | (9931), (9934), (function-axioms) are inconsistent % 149.66/21.74 | | | | | | | | | | by sub-proof #17. % 149.66/21.74 | | | | | | | | | | % 149.66/21.74 | | | | | | | | | Case 2: % 149.66/21.74 | | | | | | | | | | % 149.66/21.74 | | | | | | | | | | (9935) all_56_21 = e3 % 149.66/21.74 | | | | | | | | | | % 149.66/21.74 | | | | | | | | | | COMBINE_EQS: (9930), (9935) imply: % 149.66/21.74 | | | | | | | | | | (9936) all_4_1 = e3 % 149.66/21.74 | | | | | | | | | | % 149.66/21.74 | | | | | | | | | | SIMP: (9936) implies: % 149.66/21.74 | | | | | | | | | | (9937) all_4_1 = e3 % 149.66/21.74 | | | | | | | | | | % 149.66/21.74 | | | | | | | | | | REDUCE: (9932), (9937) imply: % 149.66/21.74 | | | | | | | | | | (9938) op(e3, e3) = e3 % 149.66/21.74 | | | | | | | | | | % 149.66/21.74 | | | | | | | | | | REDUCE: (8985), (9937) imply: % 149.66/21.74 | | | | | | | | | | (9939) op(e0, e3) = e3 % 149.66/21.74 | | | | | | | | | | % 149.66/21.74 | | | | | | | | | | REF_CLOSE: (51), (207), (561), (9938), (9939), % 149.66/21.74 | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 149.66/21.74 | | | | | | | | | | #314. % 149.66/21.74 | | | | | | | | | | % 149.66/21.74 | | | | | | | | | End of split % 149.66/21.74 | | | | | | | | | % 149.66/21.74 | | | | | | | | Case 2: % 149.66/21.74 | | | | | | | | | % 149.66/21.74 | | | | | | | | | (9940) ~ (all_20_2 = e1) % 149.66/21.74 | | | | | | | | | % 149.66/21.74 | | | | | | | | | REDUCE: (9919), (9940) imply: % 149.66/21.74 | | | | | | | | | (9941) $false % 149.66/21.74 | | | | | | | | | % 149.66/21.74 | | | | | | | | | CLOSE: (9941) is inconsistent. % 149.66/21.74 | | | | | | | | | % 149.66/21.74 | | | | | | | | End of split % 149.66/21.74 | | | | | | | | % 149.66/21.74 | | | | | | | End of split % 149.66/21.74 | | | | | | | % 149.66/21.74 | | | | | | End of split % 149.66/21.74 | | | | | | % 149.66/21.74 | | | | | Case 2: % 149.66/21.74 | | | | | | % 149.66/21.74 | | | | | | (9942) all_28_0 = e2 % 149.66/21.74 | | | | | | (9943) ~ (all_28_1 = e3) | ~ (all_28_2 = e0) % 149.66/21.74 | | | | | | % 149.66/21.74 | | | | | | COMBINE_EQS: (740), (9942) imply: % 149.66/21.74 | | | | | | (9944) all_6_0 = e2 % 149.66/21.74 | | | | | | % 149.66/21.74 | | | | | | COMBINE_EQS: (764), (9944) imply: % 149.66/21.74 | | | | | | (9945) all_46_0 = e2 % 149.66/21.74 | | | | | | % 149.66/21.74 | | | | | | REDUCE: (42), (9944) imply: % 149.66/21.74 | | | | | | (9946) op(e1, all_6_1) = e2 % 149.66/21.74 | | | | | | % 149.66/21.74 | | | | | | BETA: splitting (144) gives: % 149.66/21.74 | | | | | | % 149.66/21.74 | | | | | | Case 1: % 149.66/21.74 | | | | | | | % 149.66/21.74 | | | | | | | (9947) ~ (all_46_0 = e2) % 149.66/21.74 | | | | | | | % 149.66/21.74 | | | | | | | REDUCE: (9945), (9947) imply: % 149.66/21.74 | | | | | | | (9948) $false % 149.66/21.74 | | | | | | | % 149.66/21.74 | | | | | | | CLOSE: (9948) is inconsistent. % 149.66/21.74 | | | | | | | % 149.66/21.74 | | | | | | Case 2: % 149.66/21.74 | | | | | | | % 149.66/21.74 | | | | | | | (9949) ~ (all_46_1 = e0) | ~ (all_46_2 = e3) % 149.66/21.74 | | | | | | | % 149.66/21.74 | | | | | | | BETA: splitting (149) gives: % 149.66/21.74 | | | | | | | % 149.66/21.74 | | | | | | | Case 1: % 149.66/21.74 | | | | | | | | % 149.66/21.74 | | | | | | | | (9950) ~ (all_48_0 = e3) % 149.66/21.74 | | | | | | | | % 149.66/21.74 | | | | | | | | REDUCE: (765), (9950) imply: % 149.66/21.74 | | | | | | | | (9951) ~ (all_8_0 = e3) % 149.66/21.74 | | | | | | | | % 149.66/21.74 | | | | | | | | BETA: splitting (288) gives: % 149.66/21.74 | | | | | | | | % 149.66/21.74 | | | | | | | | Case 1: % 149.66/21.74 | | | | | | | | | % 149.66/21.74 | | | | | | | | | (9952) ~ (all_56_31 = e1) % 149.66/21.74 | | | | | | | | | % 149.66/21.74 | | | | | | | | | REDUCE: (544), (9952) imply: % 149.66/21.74 | | | | | | | | | (9953) ~ (all_4_2 = e1) % 149.66/21.74 | | | | | | | | | % 149.66/21.74 | | | | | | | | | REF_CLOSE: (6), (8), (36), (38), (41), (43), (46), (51), % 149.66/21.74 | | | | | | | | | (158), (174), (208), (211), (237), (242), (247), % 149.66/21.74 | | | | | | | | | (252), (291), (292), (293), (294), (297), (321), % 149.66/21.74 | | | | | | | | | (341), (366), (374), (381), (386), (402), (407), % 149.66/21.74 | | | | | | | | | (419), (435), (443), (475), (513), (540), (541), % 149.66/21.74 | | | | | | | | | (542), (543), (545), (546), (547), (550), (551), % 149.66/21.74 | | | | | | | | | (555), (559), (569), (571), (573), (580), (591), % 149.66/21.74 | | | | | | | | | (620), (622), (627), (634), (665), (8985), (8986), % 149.66/21.74 | | | | | | | | | (9943), (9946), (9949), (9953), (function-axioms) % 149.66/21.74 | | | | | | | | | are inconsistent by sub-proof #6. % 149.66/21.74 | | | | | | | | | % 149.66/21.74 | | | | | | | | Case 2: % 149.66/21.74 | | | | | | | | | % 149.66/21.74 | | | | | | | | | (9954) all_56_31 = e1 % 149.66/21.74 | | | | | | | | | (9955) all_56_29 = e0 % 149.66/21.74 | | | | | | | | | % 149.66/21.74 | | | | | | | | | COMBINE_EQS: (357), (9955) imply: % 149.66/21.74 | | | | | | | | | (9956) all_52_11 = e0 % 149.66/21.74 | | | | | | | | | % 149.66/21.74 | | | | | | | | | SIMP: (9956) implies: % 149.66/21.74 | | | | | | | | | (9957) all_52_11 = e0 % 149.66/21.74 | | | | | | | | | % 149.66/21.74 | | | | | | | | | COMBINE_EQS: (544), (9954) imply: % 149.66/21.74 | | | | | | | | | (9958) all_4_2 = e1 % 149.66/21.74 | | | | | | | | | % 149.66/21.74 | | | | | | | | | COMBINE_EQS: (499), (9958) imply: % 149.66/21.74 | | | | | | | | | (9959) all_20_2 = e1 % 149.66/21.74 | | | | | | | | | % 149.66/21.74 | | | | | | | | | COMBINE_EQS: (547), (9958) imply: % 149.66/21.74 | | | | | | | | | (9960) all_58_15 = e1 % 149.66/21.74 | | | | | | | | | % 149.66/21.74 | | | | | | | | | COMBINE_EQS: (548), (9957) imply: % 149.66/21.74 | | | | | | | | | (9961) all_58_14 = e0 % 149.66/21.74 | | | | | | | | | % 149.66/21.74 | | | | | | | | | REDUCE: (585), (9957) imply: % 149.66/21.74 | | | | | | | | | (9962) ~ (all_6_2 = e0) % 149.66/21.74 | | | | | | | | | % 149.66/21.74 | | | | | | | | | SIMP: (9962) implies: % 149.66/21.74 | | | | | | | | | (9963) ~ (all_6_2 = e0) % 149.66/21.74 | | | | | | | | | % 149.66/21.74 | | | | | | | | | REDUCE: (588), (9957), (9958) imply: % 149.66/21.74 | | | | | | | | | (9964) ~ (e1 = e0) % 149.66/21.74 | | | | | | | | | % 149.66/21.74 | | | | | | | | | REDUCE: (590), (9958) imply: % 149.66/21.74 | | | | | | | | | (9965) ~ (all_52_13 = e1) % 149.66/21.74 | | | | | | | | | % 149.66/21.74 | | | | | | | | | REDUCE: (38), (9958) imply: % 149.66/21.74 | | | | | | | | | (9966) op(e1, e1) = all_4_1 % 149.66/21.74 | | | | | | | | | % 149.66/21.74 | | | | | | | | | REDUCE: (627), (9958) imply: % 149.66/21.74 | | | | | | | | | (9967) op(e0, e1) = all_56_30 % 149.66/21.74 | | | | | | | | | % 149.66/21.74 | | | | | | | | | REDUCE: (205), (9957) imply: % 149.66/21.74 | | | | | | | | | (9968) op(e0, e1) = e0 % 149.66/21.74 | | | | | | | | | % 149.66/21.74 | | | | | | | | | BETA: splitting (9684) gives: % 149.66/21.74 | | | | | | | | | % 149.66/21.74 | | | | | | | | | Case 1: % 149.66/21.74 | | | | | | | | | | % 149.66/21.74 | | | | | | | | | | (9969) ~ (all_20_1 = e2) % 149.66/21.74 | | | | | | | | | | % 149.66/21.74 | | | | | | | | | | REDUCE: (676), (9969) imply: % 149.66/21.74 | | | | | | | | | | (9970) ~ (all_4_1 = e2) % 149.66/21.74 | | | | | | | | | | % 149.66/21.74 | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, % 149.66/21.74 | | | | | | | | | | all_56_30, e1, e0, simplifying with (9967), (9968) % 149.66/21.74 | | | | | | | | | | gives: % 149.66/21.74 | | | | | | | | | | (9971) all_56_30 = e0 % 149.66/21.74 | | | | | | | | | | % 149.66/21.74 | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_6_2, % 149.66/21.74 | | | | | | | | | | all_4_1, e1, e1, simplifying with (41), (9966) % 149.66/21.74 | | | | | | | | | | gives: % 149.66/21.74 | | | | | | | | | | (9972) all_6_2 = all_4_1 % 149.66/21.74 | | | | | | | | | | % 149.66/21.74 | | | | | | | | | | COMBINE_EQS: (475), (9972) imply: % 149.66/21.74 | | | | | | | | | | (9973) all_46_2 = all_4_1 % 149.66/21.74 | | | | | | | | | | % 149.66/21.74 | | | | | | | | | | COMBINE_EQS: (541), (9972) imply: % 149.66/21.74 | | | | | | | | | | (9974) all_54_10 = all_4_1 % 149.66/21.74 | | | | | | | | | | % 149.66/21.74 | | | | | | | | | | COMBINE_EQS: (374), (9972) imply: % 149.66/21.74 | | | | | | | | | | (9975) all_56_21 = all_4_1 % 149.66/21.74 | | | | | | | | | | % 149.66/21.74 | | | | | | | | | | COMBINE_EQS: (552), (9972) imply: % 149.66/21.74 | | | | | | | | | | (9976) all_58_8 = all_4_1 % 149.66/21.74 | | | | | | | | | | % 149.66/21.74 | | | | | | | | | | REDUCE: (9963), (9972) imply: % 149.66/21.74 | | | | | | | | | | (9977) ~ (all_4_1 = e0) % 149.66/21.74 | | | | | | | | | | % 149.66/21.74 | | | | | | | | | | REDUCE: (43), (9972) imply: % 149.66/21.74 | | | | | | | | | | (9978) op(all_4_1, all_4_1) = all_6_1 % 149.66/21.74 | | | | | | | | | | % 149.66/21.74 | | | | | | | | | | REDUCE: (622), (9972) imply: % 149.66/21.74 | | | | | | | | | | (9979) op(e1, all_4_1) = all_56_20 % 149.66/21.74 | | | | | | | | | | % 149.66/21.74 | | | | | | | | | | BETA: splitting (294) gives: % 149.66/21.74 | | | | | | | | | | % 149.66/21.74 | | | | | | | | | | Case 1: % 149.66/21.74 | | | | | | | | | | | % 149.66/21.74 | | | | | | | | | | | (9980) ~ (all_56_11 = e0) % 149.66/21.74 | | | | | | | | | | | % 149.66/21.74 | | | | | | | | | | | REDUCE: (545), (9980) imply: % 149.66/21.74 | | | | | | | | | | | (9981) ~ (all_8_2 = e0) % 149.66/21.74 | | | | | | | | | | | % 149.66/21.74 | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (51), (192), (207), (242), (287), % 149.66/21.74 | | | | | | | | | | | (293), (319), (365), (381), (545), (546), (549), % 149.66/21.74 | | | | | | | | | | | (561), (575), (8985), (9954), (9960), (9961), % 149.66/21.74 | | | | | | | | | | | (9968), (9970), (9974), (9975), (9977), (9978), % 149.66/21.74 | | | | | | | | | | | (9981), (function-axioms) are inconsistent by % 149.66/21.74 | | | | | | | | | | | sub-proof #15. % 149.66/21.74 | | | | | | | | | | | % 149.66/21.74 | | | | | | | | | | Case 2: % 149.66/21.74 | | | | | | | | | | | % 149.66/21.74 | | | | | | | | | | | (9982) all_56_15 = e2 % 149.66/21.74 | | | | | | | | | | | (9983) all_56_11 = e0 % 149.66/21.74 | | | | | | | | | | | % 149.66/21.74 | | | | | | | | | | | COMBINE_EQS: (545), (9983) imply: % 149.66/21.74 | | | | | | | | | | | (9984) all_8_2 = e0 % 149.66/21.74 | | | | | | | | | | | % 149.66/21.74 | | | | | | | | | | | COMBINE_EQS: (443), (9982) imply: % 149.66/21.74 | | | | | | | | | | | (9985) all_52_13 = e2 % 149.66/21.74 | | | | | | | | | | | % 149.66/21.74 | | | | | | | | | | | REDUCE: (9679), (9985) imply: % 149.66/21.74 | | | | | | | | | | | (9986) ~ (all_8_0 = e2) % 149.66/21.74 | | | | | | | | | | | % 149.66/21.74 | | | | | | | | | | | SIMP: (9986) implies: % 149.66/21.74 | | | | | | | | | | | (9987) ~ (all_8_0 = e2) % 149.66/21.74 | | | | | | | | | | | % 149.66/21.74 | | | | | | | | | | | BETA: splitting (330) gives: % 149.66/21.74 | | | | | | | | | | | % 149.66/21.74 | | | | | | | | | | | Case 1: % 149.66/21.74 | | | | | | | | | | | | % 149.66/21.74 | | | | | | | | | | | | (9988) all_58_4 = e2 % 149.66/21.74 | | | | | | | | | | | | % 149.66/21.74 | | | | | | | | | | | | COMBINE_EQS: (407), (9988) imply: % 149.66/21.74 | | | | | | | | | | | | (9989) all_52_8 = e2 % 149.66/21.74 | | | | | | | | | | | | % 149.66/21.74 | | | | | | | | | | | | BETA: splitting (331) gives: % 149.66/21.74 | | | | | | | | | | | | % 149.66/21.74 | | | | | | | | | | | | Case 1: % 149.66/21.74 | | | | | | | | | | | | | % 149.66/21.74 | | | | | | | | | | | | | (9990) all_58_4 = e3 % 149.66/21.74 | | | | | | | | | | | | | % 149.66/21.74 | | | | | | | | | | | | | REF_CLOSE: (9), (9988), (9990) are inconsistent by sub-proof % 149.66/21.74 | | | | | | | | | | | | | #296. % 149.66/21.74 | | | | | | | | | | | | | % 149.66/21.74 | | | | | | | | | | | | Case 2: % 149.66/21.74 | | | | | | | | | | | | | % 149.66/21.74 | | | | | | | | | | | | | (9991) all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3 % 149.66/21.74 | | | | | | | | | | | | | % 149.66/21.74 | | | | | | | | | | | | | BETA: splitting (9991) gives: % 149.66/21.74 | | | | | | | | | | | | | % 149.66/21.74 | | | | | | | | | | | | | Case 1: % 149.66/21.74 | | | | | | | | | | | | | | % 149.66/21.74 | | | | | | | | | | | | | | (9992) all_58_5 = e3 % 149.66/21.74 | | | | | | | | | | | | | | % 149.66/21.74 | | | | | | | | | | | | | | COMBINE_EQS: (9677), (9992) imply: % 149.66/21.74 | | | | | | | | | | | | | | (9993) all_8_0 = e3 % 149.66/21.74 | | | | | | | | | | | | | | % 149.66/21.74 | | | | | | | | | | | | | | REDUCE: (9951), (9993) imply: % 149.66/21.74 | | | | | | | | | | | | | | (9994) $false % 149.66/21.74 | | | | | | | | | | | | | | % 149.66/21.74 | | | | | | | | | | | | | | CLOSE: (9994) is inconsistent. % 149.66/21.74 | | | | | | | | | | | | | | % 149.66/21.74 | | | | | | | | | | | | | Case 2: % 149.66/21.74 | | | | | | | | | | | | | | % 149.66/21.74 | | | | | | | | | | | | | | (9995) all_58_8 = e3 | all_58_14 = e3 % 149.66/21.74 | | | | | | | | | | | | | | % 149.66/21.74 | | | | | | | | | | | | | | BETA: splitting (9995) gives: % 149.66/21.74 | | | | | | | | | | | | | | % 149.66/21.74 | | | | | | | | | | | | | | Case 1: % 149.66/21.74 | | | | | | | | | | | | | | | % 149.66/21.74 | | | | | | | | | | | | | | | (9996) all_58_8 = e3 % 149.66/21.74 | | | | | | | | | | | | | | | % 149.66/21.74 | | | | | | | | | | | | | | | COMBINE_EQS: (9976), (9996) imply: % 149.66/21.74 | | | | | | | | | | | | | | | (9997) all_4_1 = e3 % 149.66/21.74 | | | | | | | | | | | | | | | % 149.66/21.74 | | | | | | | | | | | | | | | COMBINE_EQS: (9973), (9997) imply: % 149.66/21.74 | | | | | | | | | | | | | | | (9998) all_46_2 = e3 % 149.66/21.74 | | | | | | | | | | | | | | | % 149.66/21.74 | | | | | | | | | | | | | | | COMBINE_EQS: (9975), (9997) imply: % 149.66/21.74 | | | | | | | | | | | | | | | (9999) all_56_21 = e3 % 149.66/21.74 | | | | | | | | | | | | | | | % 149.66/21.74 | | | | | | | | | | | | | | | REDUCE: (9978), (9997) imply: % 149.66/21.74 | | | | | | | | | | | | | | | (10000) op(e3, e3) = all_6_1 % 149.66/21.74 | | | | | | | | | | | | | | | % 149.66/21.74 | | | | | | | | | | | | | | | REDUCE: (9979), (9997) imply: % 149.66/21.74 | | | | | | | | | | | | | | | (10001) op(e1, e3) = all_56_20 % 149.66/21.74 | | | | | | | | | | | | | | | % 149.66/21.74 | | | | | | | | | | | | | | | REF_CLOSE: (6), (51), (211), (252), (293), (381), (543), % 149.66/21.74 | | | | | | | | | | | | | | | (559), (634), (8986), (9946), (9949), (9998), % 149.66/21.74 | | | | | | | | | | | | | | | (9999), (10000), (10001), (function-axioms) are % 149.66/21.74 | | | | | | | | | | | | | | | inconsistent by sub-proof #374. % 149.66/21.74 | | | | | | | | | | | | | | | % 149.66/21.74 | | | | | | | | | | | | | | Case 2: % 149.66/21.74 | | | | | | | | | | | | | | | % 149.66/21.74 | | | | | | | | | | | | | | | (10002) all_58_14 = e3 % 149.66/21.74 | | | | | | | | | | | | | | | % 149.66/21.74 | | | | | | | | | | | | | | | COMBINE_EQS: (9961), (10002) imply: % 149.66/21.74 | | | | | | | | | | | | | | | (10003) e3 = e0 % 149.66/21.74 | | | | | | | | | | | | | | | % 149.66/21.74 | | | | | | | | | | | | | | | REDUCE: (7), (10003) imply: % 149.66/21.74 | | | | | | | | | | | | | | | (10004) $false % 149.66/21.74 | | | | | | | | | | | | | | | % 149.66/21.74 | | | | | | | | | | | | | | | CLOSE: (10004) is inconsistent. % 149.66/21.74 | | | | | | | | | | | | | | | % 149.66/21.74 | | | | | | | | | | | | | | End of split % 149.66/21.74 | | | | | | | | | | | | | | % 149.66/21.74 | | | | | | | | | | | | | End of split % 149.66/21.74 | | | | | | | | | | | | | % 149.66/21.74 | | | | | | | | | | | | End of split % 149.66/21.74 | | | | | | | | | | | | % 149.66/21.74 | | | | | | | | | | | Case 2: % 149.66/21.74 | | | | | | | | | | | | % 149.66/21.74 | | | | | | | | | | | | (10005) all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2 % 149.66/21.74 | | | | | | | | | | | | % 149.66/21.74 | | | | | | | | | | | | BETA: splitting (10005) gives: % 149.66/21.74 | | | | | | | | | | | | % 149.66/21.74 | | | | | | | | | | | | Case 1: % 149.66/21.74 | | | | | | | | | | | | | % 149.66/21.74 | | | | | | | | | | | | | (10006) all_58_5 = e2 % 149.66/21.74 | | | | | | | | | | | | | % 149.66/21.74 | | | | | | | | | | | | | COMBINE_EQS: (9677), (10006) imply: % 149.66/21.74 | | | | | | | | | | | | | (10007) all_8_0 = e2 % 149.66/21.74 | | | | | | | | | | | | | % 149.66/21.74 | | | | | | | | | | | | | REDUCE: (9987), (10007) imply: % 149.66/21.74 | | | | | | | | | | | | | (10008) $false % 149.66/21.74 | | | | | | | | | | | | | % 149.66/21.74 | | | | | | | | | | | | | CLOSE: (10008) is inconsistent. % 149.66/21.74 | | | | | | | | | | | | | % 149.66/21.74 | | | | | | | | | | | | Case 2: % 149.66/21.74 | | | | | | | | | | | | | % 149.66/21.74 | | | | | | | | | | | | | (10009) all_58_8 = e2 | all_58_14 = e2 % 149.66/21.74 | | | | | | | | | | | | | % 149.66/21.74 | | | | | | | | | | | | | REF_CLOSE: (5), (9961), (9970), (9976), (10009) are % 149.66/21.74 | | | | | | | | | | | | | inconsistent by sub-proof #537. % 149.66/21.74 | | | | | | | | | | | | | % 149.66/21.74 | | | | | | | | | | | | End of split % 149.66/21.74 | | | | | | | | | | | | % 149.66/21.74 | | | | | | | | | | | End of split % 149.66/21.74 | | | | | | | | | | | % 149.66/21.74 | | | | | | | | | | End of split % 149.66/21.74 | | | | | | | | | | % 149.66/21.74 | | | | | | | | | Case 2: % 149.66/21.74 | | | | | | | | | | % 149.66/21.74 | | | | | | | | | | (10010) ~ (all_20_2 = e1) % 149.66/21.74 | | | | | | | | | | % 149.66/21.74 | | | | | | | | | | REDUCE: (9959), (10010) imply: % 149.66/21.74 | | | | | | | | | | (10011) $false % 149.66/21.74 | | | | | | | | | | % 149.66/21.74 | | | | | | | | | | CLOSE: (10011) is inconsistent. % 149.66/21.74 | | | | | | | | | | % 149.66/21.74 | | | | | | | | | End of split % 149.66/21.74 | | | | | | | | | % 149.66/21.74 | | | | | | | | End of split % 149.66/21.74 | | | | | | | | % 149.66/21.74 | | | | | | | Case 2: % 149.66/21.74 | | | | | | | | % 149.66/21.74 | | | | | | | | (10012) all_48_0 = e3 % 149.66/21.74 | | | | | | | | (10013) ~ (all_48_1 = e1) | ~ (all_48_2 = e0) % 149.66/21.74 | | | | | | | | % 149.66/21.74 | | | | | | | | COMBINE_EQS: (765), (10012) imply: % 149.66/21.74 | | | | | | | | (10014) all_8_0 = e3 % 149.66/21.74 | | | | | | | | % 149.66/21.74 | | | | | | | | SIMP: (10014) implies: % 149.66/21.74 | | | | | | | | (10015) all_8_0 = e3 % 149.66/21.74 | | | | | | | | % 149.66/21.75 | | | | | | | | REF_CLOSE: (9), (46), (247), (295), (536), (542), (545), (617), % 149.66/21.75 | | | | | | | | (9671), (9672), (9676), (9680), (10013), (10015), % 149.66/21.75 | | | | | | | | (function-axioms) are inconsistent by sub-proof #115. % 149.66/21.75 | | | | | | | | % 149.66/21.75 | | | | | | | End of split % 149.66/21.75 | | | | | | | % 149.66/21.75 | | | | | | End of split % 149.66/21.75 | | | | | | % 149.66/21.75 | | | | | End of split % 149.66/21.75 | | | | | % 149.66/21.75 | | | | End of split % 149.66/21.75 | | | | % 149.66/21.75 | | | End of split % 149.66/21.75 | | | % 149.66/21.75 | | Case 2: % 149.66/21.75 | | | % 149.66/21.75 | | | (10016) all_6_1 = e2 % 149.66/21.75 | | | (10017) ~ (all_6_0 = e0) | ~ (all_6_2 = e3) % 149.66/21.75 | | | % 149.66/21.75 | | | COMBINE_EQS: (674), (10016) imply: % 149.66/21.75 | | | (10018) all_18_1 = e2 % 149.66/21.75 | | | % 149.66/21.75 | | | REDUCE: (43), (10016) imply: % 149.66/21.75 | | | (10019) op(all_6_2, all_6_2) = e2 % 149.66/21.75 | | | % 149.66/21.75 | | | REDUCE: (42), (10016) imply: % 149.66/21.75 | | | (10020) op(e1, e2) = all_6_0 % 149.66/21.75 | | | % 149.66/21.75 | | | GROUND_INST: instantiating (function-axioms) with all_52_6, all_6_0, e2, % 149.66/21.75 | | | e1, simplifying with (210), (10020) gives: % 149.66/21.75 | | | (10021) all_52_6 = all_6_0 % 149.66/21.75 | | | % 149.66/21.75 | | | COMBINE_EQS: (473), (10021) imply: % 149.66/21.75 | | | (10022) all_54_9 = all_6_0 % 149.66/21.75 | | | % 149.66/21.75 | | | COMBINE_EQS: (435), (10021) imply: % 149.66/21.75 | | | (10023) all_56_19 = all_6_0 % 149.66/21.75 | | | % 149.66/21.75 | | | COMBINE_EQS: (380), (10021) imply: % 149.66/21.75 | | | (10024) all_58_7 = all_6_0 % 149.66/21.75 | | | % 149.66/21.75 | | | REDUCE: (191), (10021) imply: % 149.66/21.75 | | | (10025) ~ (all_52_2 = all_6_0) % 149.66/21.75 | | | % 149.66/21.75 | | | REDUCE: (176), (10021) imply: % 149.66/21.75 | | | (10026) ~ (all_52_7 = all_6_0) % 149.66/21.75 | | | % 149.66/21.75 | | | SIMP: (10026) implies: % 149.66/21.75 | | | (10027) ~ (all_52_7 = all_6_0) % 149.66/21.75 | | | % 149.66/21.75 | | | REDUCE: (174), (10021) imply: % 149.66/21.75 | | | (10028) ~ (all_52_14 = all_6_0) % 149.66/21.75 | | | % 149.66/21.75 | | | SIMP: (10028) implies: % 149.66/21.75 | | | (10029) ~ (all_52_14 = all_6_0) % 149.66/21.75 | | | % 149.66/21.75 | | | REDUCE: (573), (10021) imply: % 149.66/21.75 | | | (10030) ~ (all_8_2 = all_6_0) % 149.66/21.75 | | | % 149.66/21.75 | | | SIMP: (10030) implies: % 149.66/21.75 | | | (10031) ~ (all_8_2 = all_6_0) % 149.66/21.75 | | | % 149.66/21.75 | | | REDUCE: (580), (10021) imply: % 149.66/21.75 | | | (10032) ~ (all_6_0 = all_6_2) % 149.66/21.75 | | | % 149.66/21.75 | | | BETA: splitting (74) gives: % 149.66/21.75 | | | % 149.66/21.75 | | | Case 1: % 149.66/21.75 | | | | % 149.66/21.75 | | | | (10033) ~ (all_18_0 = e3) % 149.66/21.75 | | | | % 149.66/21.75 | | | | REDUCE: (753), (10033) imply: % 149.66/21.75 | | | | (10034) ~ (all_6_0 = e3) % 149.66/21.75 | | | | % 149.66/21.75 | | | | BETA: splitting (79) gives: % 149.66/21.75 | | | | % 149.66/21.75 | | | | Case 1: % 149.66/21.75 | | | | | % 149.66/21.75 | | | | | (10035) ~ (all_20_0 = e3) % 149.66/21.75 | | | | | % 149.66/21.75 | | | | | REDUCE: (8984), (10035) imply: % 149.66/21.75 | | | | | (10036) $false % 149.66/21.75 | | | | | % 149.66/21.75 | | | | | CLOSE: (10036) is inconsistent. % 149.66/21.75 | | | | | % 149.66/21.75 | | | | Case 2: % 149.66/21.75 | | | | | % 149.66/21.75 | | | | | (10037) ~ (all_20_1 = e2) | ~ (all_20_2 = e1) % 149.66/21.75 | | | | | % 149.66/21.75 | | | | | BETA: splitting (288) gives: % 149.66/21.75 | | | | | % 149.66/21.75 | | | | | Case 1: % 149.66/21.75 | | | | | | % 149.66/21.75 | | | | | | (10038) ~ (all_56_31 = e1) % 149.66/21.75 | | | | | | % 149.66/21.75 | | | | | | REDUCE: (544), (10038) imply: % 149.66/21.75 | | | | | | (10039) ~ (all_4_2 = e1) % 149.66/21.75 | | | | | | % 149.66/21.75 | | | | | | BETA: splitting (290) gives: % 149.66/21.75 | | | | | | % 149.66/21.75 | | | | | | Case 1: % 149.66/21.75 | | | | | | | % 149.66/21.75 | | | | | | | (10040) ~ (all_56_31 = e3) % 149.66/21.75 | | | | | | | % 149.66/21.75 | | | | | | | REDUCE: (544), (10040) imply: % 149.66/21.75 | | | | | | | (10041) ~ (all_4_2 = e3) % 149.66/21.75 | | | | | | | % 149.66/21.75 | | | | | | | BETA: splitting (291) gives: % 149.66/21.75 | | | | | | | % 149.66/21.75 | | | | | | | Case 1: % 149.66/21.75 | | | | | | | | % 149.66/21.75 | | | | | | | | (10042) ~ (all_56_21 = e0) % 149.66/21.75 | | | | | | | | % 149.66/21.75 | | | | | | | | REDUCE: (374), (10042) imply: % 149.66/21.75 | | | | | | | | (10043) ~ (all_6_2 = e0) % 149.66/21.75 | | | | | | | | % 149.66/21.75 | | | | | | | | BETA: splitting (289) gives: % 149.66/21.75 | | | | | | | | % 149.66/21.75 | | | | | | | | Case 1: % 149.66/21.75 | | | | | | | | | % 149.66/21.75 | | | | | | | | | (10044) ~ (all_56_31 = e2) % 149.66/21.75 | | | | | | | | | % 149.66/21.75 | | | | | | | | | REDUCE: (544), (10044) imply: % 149.66/21.75 | | | | | | | | | (10045) ~ (all_4_2 = e2) % 149.66/21.75 | | | | | | | | | % 149.66/21.75 | | | | | | | | | REF_CLOSE: (36), (38), (237), (540), (627), (8985), (10039), % 149.66/21.75 | | | | | | | | | (10041), (10045), (function-axioms) are % 149.66/21.75 | | | | | | | | | inconsistent by sub-proof #29. % 149.66/21.75 | | | | | | | | | % 149.66/21.75 | | | | | | | | Case 2: % 149.66/21.75 | | | | | | | | | % 149.66/21.75 | | | | | | | | | (10046) all_56_31 = e2 % 149.66/21.75 | | | | | | | | | (10047) all_56_27 = e0 % 149.66/21.75 | | | | | | | | | % 149.66/21.75 | | | | | | | | | COMBINE_EQS: (360), (10047) imply: % 149.66/21.75 | | | | | | | | | (10048) all_52_7 = e0 % 149.66/21.75 | | | | | | | | | % 149.66/21.75 | | | | | | | | | SIMP: (10048) implies: % 149.66/21.75 | | | | | | | | | (10049) all_52_7 = e0 % 149.66/21.75 | | | | | | | | | % 149.66/21.75 | | | | | | | | | COMBINE_EQS: (544), (10046) imply: % 149.66/21.75 | | | | | | | | | (10050) all_4_2 = e2 % 149.66/21.75 | | | | | | | | | % 149.66/21.75 | | | | | | | | | REDUCE: (10027), (10049) imply: % 149.66/21.75 | | | | | | | | | (10051) ~ (all_6_0 = e0) % 149.66/21.75 | | | | | | | | | % 149.66/21.75 | | | | | | | | | SIMP: (10051) implies: % 149.66/21.75 | | | | | | | | | (10052) ~ (all_6_0 = e0) % 149.66/21.75 | | | | | | | | | % 149.66/21.75 | | | | | | | | | REDUCE: (38), (10050) imply: % 149.66/21.75 | | | | | | | | | (10053) op(e2, e2) = all_4_1 % 149.66/21.75 | | | | | | | | | % 149.66/21.75 | | | | | | | | | REDUCE: (627), (10050) imply: % 149.66/21.75 | | | | | | | | | (10054) op(e0, e2) = all_56_30 % 149.66/21.75 | | | | | | | | | % 149.66/21.75 | | | | | | | | | REDUCE: (206), (10049) imply: % 149.66/21.75 | | | | | | | | | (10055) op(e0, e2) = e0 % 149.66/21.75 | | | | | | | | | % 149.66/21.75 | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, % 149.66/21.75 | | | | | | | | | all_56_30, e2, e0, simplifying with (10054), % 149.66/21.75 | | | | | | | | | (10055) gives: % 149.66/21.75 | | | | | | | | | (10056) all_56_30 = e0 % 149.66/21.75 | | | | | | | | | % 149.66/21.75 | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_8_2, % 149.66/21.75 | | | | | | | | | all_4_1, e2, e2, simplifying with (46), (10053) % 149.66/21.75 | | | | | | | | | gives: % 149.66/21.75 | | | | | | | | | (10057) all_8_2 = all_4_1 % 149.66/21.75 | | | | | | | | | % 149.66/21.75 | | | | | | | | | BETA: splitting (293) gives: % 149.66/21.75 | | | | | | | | | % 149.66/21.75 | | | | | | | | | Case 1: % 149.66/21.75 | | | | | | | | | | % 149.66/21.75 | | | | | | | | | | (10058) ~ (all_56_21 = e3) % 149.66/21.75 | | | | | | | | | | % 149.66/21.75 | | | | | | | | | | REDUCE: (374), (10058) imply: % 149.66/21.75 | | | | | | | | | | (10059) ~ (all_6_2 = e3) % 149.66/21.75 | | | | | | | | | | % 149.66/21.75 | | | | | | | | | | BETA: splitting (292) gives: % 149.66/21.75 | | | | | | | | | | % 149.66/21.75 | | | | | | | | | | Case 1: % 149.66/21.75 | | | | | | | | | | | % 149.66/21.75 | | | | | | | | | | | (10060) ~ (all_56_21 = e2) % 149.66/21.75 | | | | | | | | | | | % 149.66/21.75 | | | | | | | | | | | REDUCE: (374), (10060) imply: % 149.66/21.75 | | | | | | | | | | | (10061) ~ (all_6_2 = e2) % 149.66/21.75 | | | | | | | | | | | % 149.66/21.75 | | | | | | | | | | | REF_CLOSE: (41), (242), (541), (622), (10019), (10043), % 149.66/21.75 | | | | | | | | | | | (10059), (10061), (function-axioms) are % 149.66/21.75 | | | | | | | | | | | inconsistent by sub-proof #89. % 149.66/21.75 | | | | | | | | | | | % 149.66/21.75 | | | | | | | | | | Case 2: % 149.66/21.75 | | | | | | | | | | | % 149.66/21.75 | | | | | | | | | | | (10062) all_56_21 = e2 % 149.66/21.75 | | | | | | | | | | | % 149.66/21.75 | | | | | | | | | | | COMBINE_EQS: (374), (10062) imply: % 149.66/21.75 | | | | | | | | | | | (10063) all_6_2 = e2 % 149.66/21.75 | | | | | | | | | | | % 149.66/21.75 | | | | | | | | | | | REDUCE: (10019), (10063) imply: % 149.66/21.75 | | | | | | | | | | | (10064) op(e2, e2) = e2 % 149.66/21.75 | | | | | | | | | | | % 149.66/21.75 | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_4_1, e2, % 149.66/21.75 | | | | | | | | | | | e2, e2, simplifying with (10053), (10064) gives: % 149.66/21.75 | | | | | | | | | | | (10065) all_4_1 = e2 % 149.66/21.75 | | | | | | | | | | | % 149.66/21.75 | | | | | | | | | | | REF_CLOSE: (7), (8985), (10055), (10065), (function-axioms) % 149.66/21.75 | | | | | | | | | | | are inconsistent by sub-proof #28. % 149.66/21.75 | | | | | | | | | | | % 149.66/21.75 | | | | | | | | | | End of split % 149.66/21.75 | | | | | | | | | | % 149.66/21.75 | | | | | | | | | Case 2: % 149.66/21.75 | | | | | | | | | | % 149.66/21.75 | | | | | | | | | | (10066) all_56_21 = e3 % 149.66/21.75 | | | | | | | | | | (10067) all_56_17 = e1 % 149.66/21.75 | | | | | | | | | | % 149.66/21.75 | | | | | | | | | | COMBINE_EQS: (381), (10067) imply: % 149.66/21.75 | | | | | | | | | | (10068) all_52_2 = e1 % 149.66/21.75 | | | | | | | | | | % 149.66/21.75 | | | | | | | | | | COMBINE_EQS: (374), (10066) imply: % 149.66/21.75 | | | | | | | | | | (10069) all_6_2 = e3 % 149.66/21.75 | | | | | | | | | | % 149.66/21.75 | | | | | | | | | | REDUCE: (189), (10068) imply: % 149.66/21.75 | | | | | | | | | | (10070) ~ (all_52_14 = e1) % 149.66/21.75 | | | | | | | | | | % 149.66/21.75 | | | | | | | | | | SIMP: (10070) implies: % 149.66/21.75 | | | | | | | | | | (10071) ~ (all_52_14 = e1) % 149.66/21.75 | | | | | | | | | | % 149.66/21.75 | | | | | | | | | | REDUCE: (10025), (10068) imply: % 149.66/21.75 | | | | | | | | | | (10072) ~ (all_6_0 = e1) % 149.66/21.75 | | | | | | | | | | % 149.66/21.75 | | | | | | | | | | SIMP: (10072) implies: % 149.66/21.75 | | | | | | | | | | (10073) ~ (all_6_0 = e1) % 149.66/21.75 | | | | | | | | | | % 149.66/21.75 | | | | | | | | | | REDUCE: (569), (10068), (10069) imply: % 149.66/21.75 | | | | | | | | | | (10074) ~ (e3 = e1) % 149.66/21.75 | | | | | | | | | | % 149.66/21.75 | | | | | | | | | | REDUCE: (587), (10069) imply: % 149.66/21.75 | | | | | | | | | | (10075) ~ (all_52_14 = e3) % 149.66/21.75 | | | | | | | | | | % 149.66/21.75 | | | | | | | | | | REDUCE: (10019), (10069) imply: % 149.66/21.75 | | | | | | | | | | (10076) op(e3, e3) = e2 % 149.66/21.75 | | | | | | | | | | % 149.66/21.75 | | | | | | | | | | REF_CLOSE: (8), (51), (53), (241), (243), (287), (476), % 149.66/21.75 | | | | | | | | | | (544), (545), (546), (591), (612), (10022), % 149.66/21.75 | | | | | | | | | | (10029), (10031), (10034), (10052), (10066), % 149.66/21.75 | | | | | | | | | | (10071), (10073), (10075), (10076), % 149.66/21.75 | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 149.66/21.75 | | | | | | | | | | #80. % 149.66/21.75 | | | | | | | | | | % 149.66/21.75 | | | | | | | | | End of split % 149.66/21.75 | | | | | | | | | % 149.66/21.75 | | | | | | | | End of split % 149.66/21.75 | | | | | | | | % 149.66/21.75 | | | | | | | Case 2: % 149.66/21.75 | | | | | | | | % 149.66/21.75 | | | | | | | | (10077) all_56_23 = e1 % 149.66/21.75 | | | | | | | | (10078) all_56_21 = e0 % 149.66/21.75 | | | | | | | | % 149.66/21.75 | | | | | | | | COMBINE_EQS: (374), (10078) imply: % 149.66/21.75 | | | | | | | | (10079) all_6_2 = e0 % 149.66/21.75 | | | | | | | | % 149.66/21.75 | | | | | | | | SIMP: (10079) implies: % 149.66/21.75 | | | | | | | | (10080) all_6_2 = e0 % 149.66/21.75 | | | | | | | | % 149.66/21.75 | | | | | | | | COMBINE_EQS: (366), (10077) imply: % 149.66/21.75 | | | | | | | | (10081) all_52_14 = e1 % 149.66/21.75 | | | | | | | | % 149.66/21.75 | | | | | | | | SIMP: (10081) implies: % 149.66/21.75 | | | | | | | | (10082) all_52_14 = e1 % 149.66/21.75 | | | | | | | | % 149.66/21.75 | | | | | | | | COMBINE_EQS: (550), (10082) imply: % 149.66/21.75 | | | | | | | | (10083) all_58_11 = e1 % 149.66/21.75 | | | | | | | | % 149.66/21.75 | | | | | | | | COMBINE_EQS: (552), (10080) imply: % 149.66/21.75 | | | | | | | | (10084) all_58_8 = e0 % 149.66/21.75 | | | | | | | | % 149.66/21.75 | | | | | | | | REDUCE: (10029), (10082) imply: % 149.66/21.75 | | | | | | | | (10085) ~ (all_6_0 = e1) % 149.66/21.75 | | | | | | | | % 149.66/21.75 | | | | | | | | SIMP: (10085) implies: % 149.66/21.75 | | | | | | | | (10086) ~ (all_6_0 = e1) % 149.66/21.75 | | | | | | | | % 149.66/21.75 | | | | | | | | REF_CLOSE: (4), (7), (8), (36), (38), (243), (287), (327), % 149.66/21.75 | | | | | | | | (544), (545), (546), (553), (559), (627), (10019), % 149.66/21.75 | | | | | | | | (10022), (10024), (10031), (10032), (10034), (10078), % 149.66/21.75 | | | | | | | | (10080), (10083), (10084), (10086), (function-axioms) % 149.66/21.75 | | | | | | | | are inconsistent by sub-proof #57. % 149.66/21.75 | | | | | | | | % 149.66/21.75 | | | | | | | End of split % 149.66/21.75 | | | | | | | % 149.66/21.75 | | | | | | Case 2: % 149.66/21.75 | | | | | | | % 149.66/21.75 | | | | | | | (10087) all_56_31 = e3 % 149.66/21.75 | | | | | | | (10088) all_56_25 = e0 % 149.66/21.75 | | | | | | | % 149.66/21.75 | | | | | | | COMBINE_EQS: (447), (10088) imply: % 149.66/21.75 | | | | | | | (10089) all_52_3 = e0 % 149.66/21.75 | | | | | | | % 149.66/21.75 | | | | | | | SIMP: (10089) implies: % 149.66/21.75 | | | | | | | (10090) all_52_3 = e0 % 149.66/21.75 | | | | | | | % 149.66/21.75 | | | | | | | COMBINE_EQS: (544), (10087) imply: % 149.66/21.75 | | | | | | | (10091) all_4_2 = e3 % 149.66/21.75 | | | | | | | % 149.66/21.75 | | | | | | | REDUCE: (192), (10090) imply: % 149.66/21.75 | | | | | | | (10092) ~ (all_52_2 = e0) % 149.66/21.75 | | | | | | | % 149.66/21.75 | | | | | | | REDUCE: (188), (10090) imply: % 149.66/21.75 | | | | | | | (10093) ~ (all_52_7 = e0) % 149.66/21.75 | | | | | | | % 149.66/21.75 | | | | | | | SIMP: (10093) implies: % 149.66/21.75 | | | | | | | (10094) ~ (all_52_7 = e0) % 149.66/21.75 | | | | | | | % 149.66/21.75 | | | | | | | REDUCE: (570), (10090), (10091) imply: % 149.66/21.75 | | | | | | | (10095) ~ (e3 = e0) % 149.66/21.75 | | | | | | | % 149.66/21.75 | | | | | | | REDUCE: (581), (10091) imply: % 149.66/21.75 | | | | | | | (10096) ~ (all_52_7 = e3) % 149.66/21.75 | | | | | | | % 149.66/21.75 | | | | | | | REDUCE: (591), (10091) imply: % 149.66/21.75 | | | | | | | (10097) ~ (all_52_14 = e3) % 149.66/21.75 | | | | | | | % 149.66/21.75 | | | | | | | REDUCE: (38), (10091) imply: % 149.66/21.75 | | | | | | | (10098) op(e3, e3) = all_4_1 % 149.66/21.75 | | | | | | | % 149.66/21.75 | | | | | | | REF_CLOSE: (4), (7), (9), (36), (38), (41), (51), (53), (189), % 149.66/21.75 | | | | | | | (241), (242), (243), (244), (287), (291), (292), (293), % 149.66/21.75 | | | | | | | (327), (336), (339), (366), (374), (381), (471), (476), % 149.66/21.75 | | | | | | | (541), (544), (545), (546), (549), (550), (552), (553), % 149.66/21.75 | | | | | | | (554), (559), (569), (587), (591), (612), (622), (627), % 149.66/21.75 | | | | | | | (10017), (10019), (10022), (10023), (10024), (10025), % 149.66/21.75 | | | | | | | (10029), (10031), (10032), (10034), (10087), (10092), % 149.66/21.75 | | | | | | | (10094), (10096), (10097), (10098), (function-axioms) % 149.66/21.75 | | | | | | | are inconsistent by sub-proof #56. % 149.66/21.75 | | | | | | | % 149.66/21.75 | | | | | | End of split % 149.66/21.75 | | | | | | % 149.66/21.75 | | | | | Case 2: % 149.66/21.75 | | | | | | % 149.66/21.75 | | | | | | (10099) all_56_31 = e1 % 149.66/21.75 | | | | | | (10100) all_56_29 = e0 % 149.66/21.75 | | | | | | % 149.66/21.75 | | | | | | COMBINE_EQS: (357), (10100) imply: % 149.66/21.75 | | | | | | (10101) all_52_11 = e0 % 149.66/21.75 | | | | | | % 149.66/21.75 | | | | | | SIMP: (10101) implies: % 149.66/21.75 | | | | | | (10102) all_52_11 = e0 % 149.66/21.75 | | | | | | % 149.66/21.75 | | | | | | COMBINE_EQS: (544), (10099) imply: % 149.66/21.75 | | | | | | (10103) all_4_2 = e1 % 149.66/21.75 | | | | | | % 149.66/21.75 | | | | | | COMBINE_EQS: (499), (10103) imply: % 149.66/21.75 | | | | | | (10104) all_20_2 = e1 % 149.66/21.75 | | | | | | % 149.66/21.75 | | | | | | REDUCE: (585), (10102) imply: % 149.66/21.75 | | | | | | (10105) ~ (all_6_2 = e0) % 149.66/21.75 | | | | | | % 149.66/21.75 | | | | | | SIMP: (10105) implies: % 149.66/21.75 | | | | | | (10106) ~ (all_6_2 = e0) % 149.66/21.75 | | | | | | % 149.66/21.75 | | | | | | REDUCE: (38), (10103) imply: % 149.66/21.75 | | | | | | (10107) op(e1, e1) = all_4_1 % 149.66/21.75 | | | | | | % 149.66/21.75 | | | | | | BETA: splitting (10037) gives: % 149.66/21.75 | | | | | | % 149.66/21.75 | | | | | | Case 1: % 149.66/21.75 | | | | | | | % 149.66/21.75 | | | | | | | (10108) ~ (all_20_1 = e2) % 149.66/21.75 | | | | | | | % 149.66/21.75 | | | | | | | REDUCE: (676), (10108) imply: % 149.66/21.75 | | | | | | | (10109) ~ (all_4_1 = e2) % 149.66/21.75 | | | | | | | % 149.66/21.75 | | | | | | | GROUND_INST: instantiating (function-axioms) with all_6_2, % 149.66/21.75 | | | | | | | all_4_1, e1, e1, simplifying with (41), (10107) % 149.66/21.75 | | | | | | | gives: % 149.66/21.75 | | | | | | | (10110) all_6_2 = all_4_1 % 149.66/21.75 | | | | | | | % 149.66/21.75 | | | | | | | COMBINE_EQS: (541), (10110) imply: % 149.66/21.75 | | | | | | | (10111) all_54_10 = all_4_1 % 149.66/21.75 | | | | | | | % 149.66/21.75 | | | | | | | COMBINE_EQS: (374), (10110) imply: % 149.66/21.75 | | | | | | | (10112) all_56_21 = all_4_1 % 149.66/21.75 | | | | | | | % 149.66/21.75 | | | | | | | REDUCE: (569), (10110) imply: % 149.66/21.75 | | | | | | | (10113) ~ (all_52_2 = all_4_1) % 149.66/21.75 | | | | | | | % 149.66/21.75 | | | | | | | REDUCE: (587), (10110) imply: % 149.66/21.75 | | | | | | | (10114) ~ (all_52_14 = all_4_1) % 149.66/21.75 | | | | | | | % 149.66/21.75 | | | | | | | REDUCE: (10032), (10110) imply: % 149.66/21.75 | | | | | | | (10115) ~ (all_6_0 = all_4_1) % 149.66/21.75 | | | | | | | % 149.66/21.75 | | | | | | | REDUCE: (10106), (10110) imply: % 149.66/21.75 | | | | | | | (10116) ~ (all_4_1 = e0) % 149.66/21.75 | | | | | | | % 149.66/21.75 | | | | | | | REDUCE: (10019), (10110) imply: % 149.66/21.75 | | | | | | | (10117) op(all_4_1, all_4_1) = e2 % 149.66/21.75 | | | | | | | % 149.66/21.75 | | | | | | | REDUCE: (622), (10110) imply: % 149.66/21.75 | | | | | | | (10118) op(e1, all_4_1) = all_56_20 % 149.66/21.75 | | | | | | | % 149.66/21.75 | | | | | | | REF_CLOSE: (51), (53), (189), (241), (242), (243), (287), (293), % 149.66/21.75 | | | | | | | (381), (476), (544), (545), (546), (591), (612), % 149.66/21.75 | | | | | | | (10017), (10022), (10025), (10029), (10031), (10107), % 149.66/21.75 | | | | | | | (10109), (10110), (10111), (10112), (10113), (10114), % 149.66/21.75 | | | | | | | (10115), (10116), (10117), (10118), (function-axioms) % 149.66/21.75 | | | | | | | are inconsistent by sub-proof #52. % 149.66/21.75 | | | | | | | % 149.66/21.75 | | | | | | Case 2: % 149.66/21.75 | | | | | | | % 149.66/21.75 | | | | | | | (10119) ~ (all_20_2 = e1) % 149.66/21.75 | | | | | | | % 149.66/21.75 | | | | | | | REDUCE: (10104), (10119) imply: % 149.66/21.75 | | | | | | | (10120) $false % 149.66/21.75 | | | | | | | % 149.66/21.75 | | | | | | | CLOSE: (10120) is inconsistent. % 149.66/21.75 | | | | | | | % 149.66/21.75 | | | | | | End of split % 149.66/21.75 | | | | | | % 149.66/21.75 | | | | | End of split % 149.66/21.75 | | | | | % 149.66/21.75 | | | | End of split % 149.66/21.75 | | | | % 149.66/21.75 | | | Case 2: % 149.66/21.75 | | | | % 149.66/21.75 | | | | (10121) all_18_0 = e3 % 149.66/21.75 | | | | (10122) ~ (all_18_1 = e2) | ~ (all_18_2 = e0) % 149.66/21.75 | | | | % 149.66/21.75 | | | | COMBINE_EQS: (753), (10121) imply: % 149.66/21.75 | | | | (10123) all_6_0 = e3 % 149.66/21.75 | | | | % 149.66/21.75 | | | | SIMP: (10123) implies: % 149.66/21.75 | | | | (10124) all_6_0 = e3 % 149.66/21.75 | | | | % 149.66/21.75 | | | | REF_CLOSE: (8), (41), (242), (292), (374), (524), (541), (622), (10018), % 149.66/21.75 | | | | (10019), (10023), (10032), (10122), (10124), % 149.66/21.75 | | | | (function-axioms) are inconsistent by sub-proof #40. % 149.66/21.75 | | | | % 149.66/21.75 | | | End of split % 149.66/21.75 | | | % 149.66/21.75 | | End of split % 149.66/21.75 | | % 149.66/21.75 | End of split % 149.66/21.75 | % 149.66/21.75 End of proof % 149.66/21.75 % 149.66/21.75 Sub-proof #1 shows that the following formulas are inconsistent: % 149.66/21.75 ---------------------------------------------------------------- % 149.66/21.75 (1) ~ (all_8_1 = e1) % 149.66/21.75 (2) op(e2, all_4_1) = all_56_10 % 149.66/21.75 (3) all_4_1 = e3 % 149.66/21.75 (4) all_54_0 = all_10_2 % 149.66/21.75 (5) all_42_2 = all_4_1 % 149.66/21.75 (6) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 149.66/21.75 (7) all_42_1 = all_8_1 % 149.66/21.75 (8) op(all_4_1, all_4_1) = all_8_1 % 149.66/21.75 (9) op(e3, e3) = all_10_2 % 149.66/21.75 (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 149.66/21.75 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 149.66/21.75 (11) all_56_11 = all_4_1 % 149.66/21.75 (12) ~ (all_56_11 = e3) | all_56_9 = e2 % 149.66/21.75 (13) op(e2, all_8_1) = e1 % 149.66/21.75 (14) ~ (e2 = e1) % 149.66/21.75 (15) ~ (all_42_1 = e0) | ~ (all_42_2 = e3) % 149.66/21.75 (16) op(e2, e3) = all_52_1 % 149.66/21.75 (17) all_56_9 = all_52_1 % 149.66/21.75 (18) ~ (all_52_1 = all_10_2) % 149.66/21.75 % 149.66/21.75 Begin of proof % 149.66/21.75 | % 149.66/21.75 | COMBINE_EQS: (3), (5) imply: % 149.66/21.75 | (19) all_42_2 = e3 % 149.66/21.75 | % 149.66/21.75 | COMBINE_EQS: (3), (11) imply: % 149.66/21.75 | (20) all_56_11 = e3 % 149.66/21.75 | % 149.66/21.75 | REDUCE: (3), (8) imply: % 149.66/21.75 | (21) op(e3, e3) = all_8_1 % 149.66/21.75 | % 149.66/21.75 | REDUCE: (2), (3) imply: % 149.66/21.75 | (22) op(e2, e3) = all_56_10 % 149.66/21.75 | % 149.66/21.75 | REF_CLOSE: (1), (4), (6), (7), (9), (10), (12), (13), (14), (15), (16), (17), % 149.66/21.75 | (18), (19), (20), (21), (22) are inconsistent by sub-proof #256. % 149.66/21.75 | % 149.66/21.75 End of proof % 149.66/21.75 % 149.66/21.75 Sub-proof #2 shows that the following formulas are inconsistent: % 149.66/21.75 ---------------------------------------------------------------- % 149.66/21.75 (1) all_56_11 = all_8_2 % 149.66/21.75 (2) ~ (all_52_3 = all_6_0) % 149.66/21.75 (3) ~ (all_52_4 = all_52_8) % 149.66/21.75 (4) all_56_25 = all_52_3 % 149.66/21.75 (5) ~ (all_52_7 = all_52_11) % 149.66/21.75 (6) ~ (all_52_8 = all_52_9) % 149.66/21.75 (7) all_54_9 = all_52_6 % 149.66/21.75 (8) ~ (all_52_1 = all_52_9) % 149.66/21.75 (9) all_54_10 = all_6_2 % 149.66/21.75 (10) op(e0, all_4_1) = e3 % 149.66/21.75 (11) ~ (all_52_13 = all_8_2) % 149.66/21.75 (12) ~ (all_56_21 = e2) | all_56_19 = e1 % 149.66/21.76 (13) ~ (all_52_14 = all_4_2) % 149.66/21.76 (14) all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2 % 149.66/21.76 (15) ~ (all_52_4 = all_52_7) % 149.66/21.76 (16) op(e0, e0) = all_4_2 % 149.66/21.76 (17) all_58_6 = e0 | all_58_7 = e0 | all_58_8 = e0 | all_58_11 = e0 % 149.66/21.76 (18) all_58_4 = all_52_8 % 149.66/21.76 (19) all_54_5 = all_8_2 % 149.66/21.76 (20) ~ (all_52_6 = all_52_14) % 149.66/21.76 (21) ~ (all_6_0 = e2) % 149.66/21.76 (22) all_54_15 = all_4_2 % 149.66/21.76 (23) all_56_21 = all_6_2 % 149.66/21.76 (24) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 149.66/21.76 (25) ~ (all_52_7 = all_8_2) % 149.66/21.76 (26) ~ (all_4_1 = e1) | ~ (all_4_2 = e2) % 149.66/21.76 (27) all_56_1 = all_10_2 % 149.66/21.76 (28) all_56_27 = all_52_7 % 149.66/21.76 (29) all_58_5 = all_52_9 % 149.66/21.76 (30) all_54_1 = all_52_4 % 149.66/21.76 (31) all_58_1 = all_52_4 % 149.66/21.76 (32) all_58_4 = e0 | all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0 % 149.66/21.76 (33) op(e2, all_8_2) = all_56_10 % 149.66/21.76 (34) op(e3, e3) = all_10_2 % 149.66/21.76 (35) ~ (all_52_6 = all_6_0) % 149.66/21.76 (36) ~ (all_56_21 = e3) | all_56_17 = e1 % 149.66/21.76 (37) ~ (e1 = e0) % 149.66/21.76 (38) all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1 % 149.66/21.76 (39) all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2 % 149.66/21.76 (40) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 149.66/21.76 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 149.66/21.76 (41) ~ (all_52_3 = all_10_2) % 149.66/21.76 (42) ~ (all_56_11 = e3) | all_56_9 = e2 % 149.66/21.76 (43) all_36_0 = all_6_0 % 149.66/21.76 (44) ~ (all_6_0 = all_6_2) % 149.66/21.76 (45) ~ (all_4_2 = e1) % 149.66/21.76 (46) all_54_8 = all_6_0 % 149.66/21.76 (47) all_58_8 = all_6_2 % 149.66/21.76 (48) all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3 % 149.66/21.76 (49) ~ (all_52_14 = all_6_0) % 149.66/21.76 (50) op(all_4_2, all_4_2) = all_4_1 % 149.66/21.76 (51) all_58_3 = all_8_2 % 149.66/21.76 (52) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0 % 149.66/21.76 (53) ~ (all_52_11 = all_4_2) % 149.66/21.76 (54) ~ (all_52_1 = all_52_3) % 149.66/21.76 (55) all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1 % 149.66/21.76 (56) ~ (all_52_6 = all_52_7) % 149.66/21.76 (57) all_56_31 = all_4_2 % 149.66/21.76 (58) all_58_11 = all_52_14 % 149.66/21.76 (59) all_36_2 = all_6_2 % 149.66/21.76 (60) all_56_1 = e3 | all_56_11 = e2 | all_56_21 = e1 | all_56_31 = e0 % 149.66/21.76 (61) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0 % 149.66/21.76 (62) all_56_23 = all_52_14 % 149.66/21.76 (63) all_58_6 = all_6_0 % 149.66/21.76 (64) op(e1, e1) = all_6_2 % 149.66/21.76 (65) ~ (all_52_6 = all_8_2) % 149.66/21.76 (66) op(e0, e3) = all_52_3 % 149.66/21.76 (67) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0 % 149.66/21.76 (68) all_58_2 = all_52_1 % 149.66/21.76 (69) all_58_7 = all_52_6 % 149.66/21.76 (70) all_58_10 = all_52_13 % 149.66/21.76 (71) op(e1, all_6_2) = all_56_20 % 149.66/21.76 (72) ~ (all_56_31 = e2) | all_56_27 = e0 % 149.66/21.76 (73) op(e2, e2) = all_8_2 % 149.66/21.76 (74) ~ (all_36_0 = e0) | ~ (all_36_2 = e2) % 149.66/21.76 (75) ~ (all_56_21 = e0) | all_56_23 = e1 % 149.66/21.76 (76) op(e0, all_4_2) = all_56_30 % 149.66/21.76 (77) ~ (all_52_6 = all_6_2) % 149.66/21.76 (78) op(all_6_2, all_6_2) = e3 % 149.66/21.76 (79) ~ (all_52_14 = all_6_2) % 149.66/21.76 (80) ~ (e2 = e0) % 149.66/21.76 (81) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0 % 149.66/21.76 (82) ~ (all_10_2 = all_6_0) % 149.66/21.76 (83) ~ (all_52_4 = all_8_2) % 149.66/21.76 (84) op(all_8_2, all_8_2) = all_8_1 % 149.66/21.76 (85) ~ (all_52_4 = all_52_6) % 149.66/21.76 (86) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 149.66/21.76 (87) all_58_14 = all_52_11 % 149.66/21.76 (88) all_56_19 = all_52_6 % 149.66/21.76 (89) all_56_9 = all_52_1 % 149.66/21.76 (90) ~ (all_56_31 = e3) | all_56_25 = e0 % 149.66/21.76 % 149.66/21.76 Begin of proof % 149.66/21.76 | % 149.66/21.76 | BETA: splitting (90) gives: % 149.66/21.76 | % 149.66/21.76 | Case 1: % 149.66/21.76 | | % 149.66/21.76 | | (91) ~ (all_56_31 = e3) % 149.66/21.76 | | % 149.66/21.76 | | REDUCE: (57), (91) imply: % 149.66/21.76 | | (92) ~ (all_4_2 = e3) % 149.66/21.76 | | % 149.66/21.76 | | REF_CLOSE: (1), (3), (5), (6), (7), (8), (10), (11), (12), (13), (14), (15), % 149.66/21.76 | | (16), (17), (18), (19), (20), (21), (22), (23), (25), (26), (27), % 149.66/21.76 | | (28), (29), (30), (31), (32), (33), (34), (35), (38), (39), (40), % 149.66/21.76 | | (41), (42), (43), (44), (45), (46), (47), (48), (49), (50), (51), % 149.66/21.76 | | (52), (53), (54), (55), (56), (57), (58), (59), (60), (61), (62), % 149.66/21.76 | | (63), (64), (65), (66), (67), (68), (69), (70), (71), (72), (73), % 149.66/21.76 | | (74), (75), (76), (77), (78), (79), (81), (82), (83), (84), (85), % 149.66/21.76 | | (86), (87), (88), (89), (92) are inconsistent by sub-proof #10. % 149.66/21.76 | | % 149.66/21.76 | Case 2: % 149.66/21.76 | | % 149.66/21.76 | | (93) all_56_31 = e3 % 149.66/21.76 | | (94) all_56_25 = e0 % 149.66/21.76 | | % 149.66/21.76 | | COMBINE_EQS: (4), (94) imply: % 149.66/21.76 | | (95) all_52_3 = e0 % 149.66/21.76 | | % 149.66/21.76 | | SIMP: (95) implies: % 149.66/21.76 | | (96) all_52_3 = e0 % 149.66/21.76 | | % 149.66/21.76 | | COMBINE_EQS: (57), (93) imply: % 149.66/21.76 | | (97) all_4_2 = e3 % 149.66/21.76 | | % 149.66/21.76 | | REDUCE: (41), (96) imply: % 149.66/21.76 | | (98) ~ (all_10_2 = e0) % 149.66/21.76 | | % 149.66/21.76 | | SIMP: (98) implies: % 149.66/21.76 | | (99) ~ (all_10_2 = e0) % 149.66/21.76 | | % 149.66/21.76 | | REDUCE: (2), (96) imply: % 149.66/21.76 | | (100) ~ (all_6_0 = e0) % 149.66/21.76 | | % 149.66/21.76 | | SIMP: (100) implies: % 149.66/21.76 | | (101) ~ (all_6_0 = e0) % 149.66/21.76 | | % 149.66/21.76 | | REDUCE: (50), (97) imply: % 149.66/21.76 | | (102) op(e3, e3) = all_4_1 % 149.66/21.76 | | % 149.66/21.76 | | REDUCE: (76), (97) imply: % 149.66/21.76 | | (103) op(e0, e3) = all_56_30 % 149.66/21.76 | | % 149.66/21.76 | | REDUCE: (66), (96) imply: % 149.66/21.76 | | (104) op(e0, e3) = e0 % 149.66/21.76 | | % 149.66/21.76 | | GROUND_INST: instantiating (40) with e0, all_56_30, e3, e0, simplifying with % 149.66/21.76 | | (103), (104) gives: % 149.66/21.76 | | (105) all_56_30 = e0 % 149.66/21.76 | | % 149.66/21.76 | | GROUND_INST: instantiating (40) with all_10_2, all_4_1, e3, e3, simplifying % 149.66/21.76 | | with (34), (102) gives: % 149.66/21.76 | | (106) all_10_2 = all_4_1 % 149.66/21.76 | | % 149.66/21.76 | | COMBINE_EQS: (27), (106) imply: % 149.66/21.76 | | (107) all_56_1 = all_4_1 % 149.66/21.76 | | % 149.66/21.76 | | REDUCE: (82), (106) imply: % 149.66/21.76 | | (108) ~ (all_6_0 = all_4_1) % 149.66/21.76 | | % 149.66/21.76 | | SIMP: (108) implies: % 149.66/21.76 | | (109) ~ (all_6_0 = all_4_1) % 149.66/21.76 | | % 149.66/21.76 | | REDUCE: (99), (106) imply: % 149.66/21.76 | | (110) ~ (all_4_1 = e0) % 149.66/21.76 | | % 149.66/21.76 | | BETA: splitting (12) gives: % 149.66/21.76 | | % 149.66/21.76 | | Case 1: % 149.66/21.76 | | | % 149.66/21.76 | | | (111) ~ (all_56_21 = e2) % 149.66/21.76 | | | % 149.66/21.76 | | | REDUCE: (23), (111) imply: % 149.66/21.76 | | | (112) ~ (all_6_2 = e2) % 149.66/21.76 | | | % 149.66/21.76 | | | BETA: splitting (75) gives: % 149.66/21.76 | | | % 149.66/21.76 | | | Case 1: % 149.66/21.76 | | | | % 149.66/21.76 | | | | (113) ~ (all_56_21 = e0) % 149.66/21.76 | | | | % 149.66/21.76 | | | | REDUCE: (23), (113) imply: % 149.66/21.76 | | | | (114) ~ (all_6_2 = e0) % 149.66/21.76 | | | | % 149.66/21.76 | | | | BETA: splitting (36) gives: % 149.66/21.76 | | | | % 149.66/21.76 | | | | Case 1: % 149.66/21.76 | | | | | % 149.66/21.76 | | | | | (115) ~ (all_56_21 = e3) % 149.66/21.76 | | | | | % 149.66/21.76 | | | | | REDUCE: (23), (115) imply: % 149.66/21.76 | | | | | (116) ~ (all_6_2 = e3) % 149.66/21.76 | | | | | % 149.66/21.76 | | | | | REF_CLOSE: (9), (24), (40), (64), (71), (78), (112), (114), (116) are % 149.66/21.76 | | | | | inconsistent by sub-proof #459. % 149.66/21.76 | | | | | % 149.66/21.76 | | | | Case 2: % 149.66/21.76 | | | | | % 149.66/21.76 | | | | | (117) all_56_21 = e3 % 149.66/21.76 | | | | | % 149.66/21.76 | | | | | REF_CLOSE: (10), (23), (40), (78), (102), (104), (110), (117) are % 149.66/21.76 | | | | | inconsistent by sub-proof #9. % 149.66/21.76 | | | | | % 149.66/21.76 | | | | End of split % 149.66/21.76 | | | | % 149.66/21.76 | | | Case 2: % 149.66/21.76 | | | | % 149.66/21.76 | | | | (118) all_56_23 = e1 % 149.66/21.76 | | | | (119) all_56_21 = e0 % 149.66/21.76 | | | | % 149.66/21.76 | | | | REF_CLOSE: (1), (7), (20), (21), (23), (35), (44), (46), (49), (52), % 149.66/21.76 | | | | (60), (62), (65), (77), (79), (81), (93), (107), (109), % 149.66/21.76 | | | | (118), (119) are inconsistent by sub-proof #320. % 149.66/21.76 | | | | % 149.66/21.76 | | | End of split % 149.66/21.76 | | | % 149.66/21.76 | | Case 2: % 149.66/21.76 | | | % 149.66/21.76 | | | (120) all_56_21 = e2 % 149.66/21.76 | | | (121) all_56_19 = e1 % 149.66/21.76 | | | % 149.66/21.76 | | | REF_CLOSE: (1), (13), (17), (23), (27), (33), (35), (37), (40), (44), % 149.66/21.76 | | | (46), (47), (49), (57), (58), (60), (63), (69), (73), (77), % 149.66/21.76 | | | (78), (80), (81), (82), (84), (88), (101), (120), (121) are % 149.66/21.76 | | | inconsistent by sub-proof #319. % 149.66/21.76 | | | % 149.66/21.76 | | End of split % 149.66/21.76 | | % 149.66/21.76 | End of split % 149.66/21.76 | % 149.66/21.76 End of proof % 149.66/21.76 % 149.66/21.76 Sub-proof #3 shows that the following formulas are inconsistent: % 149.66/21.76 ---------------------------------------------------------------- % 149.66/21.76 (1) op(e0, all_4_1) = e3 % 149.66/21.76 (2) ~ (all_8_0 = e1) % 149.66/21.76 (3) op(e0, e0) = all_4_2 % 149.66/21.76 (4) all_58_10 = e2 % 149.66/21.76 (5) all_56_21 = all_6_2 % 149.66/21.76 (6) all_56_1 = all_10_2 % 149.66/21.76 (7) all_58_5 = all_52_9 % 149.66/21.76 (8) ~ (e1 = e0) % 149.66/21.76 (9) all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1 % 149.66/21.76 (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 149.66/21.76 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 149.66/21.76 (11) ~ (all_10_2 = all_8_0) % 149.66/21.76 (12) ~ (all_8_0 = e0) % 149.66/21.76 (13) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0 % 149.66/21.76 (14) all_58_3 = e0 % 149.66/21.76 (15) ~ (e2 = e1) % 149.66/21.76 (16) op(all_4_2, all_4_2) = all_4_1 % 149.66/21.76 (17) all_56_31 = all_4_2 % 149.66/21.76 (18) all_56_1 = e3 | all_56_11 = e2 | all_56_21 = e1 | all_56_31 = e0 % 149.66/21.76 (19) ~ (all_8_0 = e2) % 149.66/21.76 (20) all_56_11 = e0 % 149.66/21.76 (21) ~ (all_52_9 = all_6_2) % 149.66/21.76 (22) all_58_2 = all_8_0 % 149.66/21.76 (23) all_54_4 = all_8_0 % 149.66/21.76 (24) op(e0, all_4_2) = all_56_30 % 149.66/21.76 (25) ~ (e2 = e0) % 149.66/21.76 % 149.66/21.76 Begin of proof % 149.66/21.76 | % 149.66/21.76 | BETA: splitting (13) gives: % 149.66/21.76 | % 149.66/21.76 | Case 1: % 149.66/21.76 | | % 149.66/21.76 | | (26) all_54_4 = e3 % 149.66/21.76 | | % 149.66/21.76 | | COMBINE_EQS: (23), (26) imply: % 149.66/21.76 | | (27) all_8_0 = e3 % 149.66/21.76 | | % 149.66/21.76 | | SIMP: (27) implies: % 149.66/21.76 | | (28) all_8_0 = e3 % 149.66/21.76 | | % 149.66/21.76 | | COMBINE_EQS: (22), (28) imply: % 149.66/21.76 | | (29) all_58_2 = e3 % 149.66/21.76 | | % 149.66/21.76 | | REDUCE: (11), (28) imply: % 149.66/21.76 | | (30) ~ (all_10_2 = e3) % 149.66/21.76 | | % 149.66/21.76 | | REDUCE: (2), (28) imply: % 149.66/21.76 | | (31) ~ (e3 = e1) % 149.66/21.76 | | % 149.66/21.76 | | REDUCE: (12), (28) imply: % 149.66/21.76 | | (32) ~ (e3 = e0) % 149.66/21.76 | | % 149.66/21.76 | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (10), (14), (15), (16), % 149.66/21.76 | | (17), (18), (20), (21), (24), (25), (29), (30), (31), (32) are % 149.66/21.76 | | inconsistent by sub-proof #4. % 149.66/21.76 | | % 149.66/21.76 | Case 2: % 149.66/21.76 | | % 149.66/21.76 | | (33) all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0 % 149.66/21.76 | | % 149.66/21.76 | | REF_CLOSE: (2), (12), (19), (23), (33) are inconsistent by sub-proof #342. % 149.66/21.76 | | % 149.66/21.76 | End of split % 149.66/21.76 | % 149.66/21.76 End of proof % 149.66/21.76 % 149.66/21.76 Sub-proof #4 shows that the following formulas are inconsistent: % 149.66/21.76 ---------------------------------------------------------------- % 149.66/21.76 (1) ~ (e3 = e0) % 149.66/21.76 (2) op(e0, all_4_1) = e3 % 149.66/21.76 (3) op(e0, e0) = all_4_2 % 149.66/21.76 (4) all_58_10 = e2 % 149.66/21.76 (5) all_56_21 = all_6_2 % 149.66/21.76 (6) all_56_1 = all_10_2 % 149.66/21.76 (7) all_58_5 = all_52_9 % 149.66/21.76 (8) all_58_2 = e3 % 149.66/21.76 (9) ~ (e1 = e0) % 149.66/21.76 (10) all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1 % 149.66/21.76 (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 149.66/21.76 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 149.66/21.76 (12) all_58_3 = e0 % 149.66/21.76 (13) ~ (e2 = e1) % 149.66/21.76 (14) op(all_4_2, all_4_2) = all_4_1 % 149.66/21.76 (15) all_56_31 = all_4_2 % 149.66/21.76 (16) all_56_1 = e3 | all_56_11 = e2 | all_56_21 = e1 | all_56_31 = e0 % 149.66/21.76 (17) all_56_11 = e0 % 149.66/21.76 (18) ~ (all_52_9 = all_6_2) % 149.66/21.76 (19) ~ (e3 = e1) % 149.66/21.76 (20) op(e0, all_4_2) = all_56_30 % 149.66/21.76 (21) ~ (e2 = e0) % 149.66/21.76 (22) ~ (all_10_2 = e3) % 149.66/21.76 % 149.66/21.76 Begin of proof % 149.66/21.76 | % 149.66/21.76 | BETA: splitting (10) gives: % 149.66/21.76 | % 149.66/21.76 | Case 1: % 149.66/21.76 | | % 149.66/21.76 | | (23) all_58_2 = e1 % 149.66/21.76 | | % 149.66/21.76 | | COMBINE_EQS: (8), (23) imply: % 149.66/21.76 | | (24) e3 = e1 % 149.66/21.76 | | % 149.66/21.76 | | REDUCE: (19), (24) imply: % 149.66/21.76 | | (25) $false % 149.66/21.76 | | % 149.66/21.76 | | CLOSE: (25) is inconsistent. % 149.66/21.76 | | % 149.66/21.76 | Case 2: % 149.66/21.76 | | % 149.66/21.76 | | (26) all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1 % 149.66/21.76 | | % 149.66/21.76 | | BETA: splitting (26) gives: % 149.66/21.76 | | % 149.66/21.76 | | Case 1: % 149.66/21.76 | | | % 149.66/21.76 | | | (27) all_58_3 = e1 % 149.66/21.76 | | | % 149.66/21.76 | | | REF_CLOSE: (9), (12), (27) are inconsistent by sub-proof #338. % 149.66/21.76 | | | % 149.66/21.76 | | Case 2: % 149.66/21.76 | | | % 149.66/21.76 | | | (28) all_58_5 = e1 | all_58_10 = e1 % 149.66/21.76 | | | % 149.66/21.76 | | | BETA: splitting (28) gives: % 149.66/21.76 | | | % 149.66/21.76 | | | Case 1: % 149.66/21.76 | | | | % 149.66/21.76 | | | | (29) all_58_5 = e1 % 149.66/21.76 | | | | % 149.66/21.76 | | | | COMBINE_EQS: (7), (29) imply: % 149.66/21.76 | | | | (30) all_52_9 = e1 % 149.66/21.76 | | | | % 149.66/21.76 | | | | REDUCE: (18), (30) imply: % 149.66/21.76 | | | | (31) ~ (all_6_2 = e1) % 149.66/21.76 | | | | % 149.66/21.76 | | | | SIMP: (31) implies: % 149.66/21.76 | | | | (32) ~ (all_6_2 = e1) % 149.66/21.76 | | | | % 149.66/21.76 | | | | BETA: splitting (16) gives: % 149.66/21.76 | | | | % 149.66/21.76 | | | | Case 1: % 149.66/21.76 | | | | | % 149.66/21.76 | | | | | (33) all_56_1 = e3 % 149.66/21.76 | | | | | % 149.66/21.76 | | | | | COMBINE_EQS: (6), (33) imply: % 149.66/21.76 | | | | | (34) all_10_2 = e3 % 149.66/21.76 | | | | | % 149.66/21.76 | | | | | REDUCE: (22), (34) imply: % 149.66/21.76 | | | | | (35) $false % 149.66/21.76 | | | | | % 149.66/21.76 | | | | | CLOSE: (35) is inconsistent. % 149.66/21.76 | | | | | % 149.66/21.76 | | | | Case 2: % 149.66/21.76 | | | | | % 149.66/21.76 | | | | | (36) all_56_11 = e2 | all_56_21 = e1 | all_56_31 = e0 % 149.66/21.76 | | | | | % 149.66/21.76 | | | | | BETA: splitting (36) gives: % 149.66/21.76 | | | | | % 149.66/21.76 | | | | | Case 1: % 149.66/21.76 | | | | | | % 149.66/21.76 | | | | | | (37) all_56_11 = e2 % 149.66/21.76 | | | | | | % 149.66/21.76 | | | | | | REF_CLOSE: (17), (21), (37) are inconsistent by sub-proof #427. % 149.66/21.76 | | | | | | % 149.66/21.76 | | | | | Case 2: % 149.66/21.76 | | | | | | % 149.66/21.76 | | | | | | (38) all_56_21 = e1 | all_56_31 = e0 % 149.66/21.76 | | | | | | % 149.66/21.76 | | | | | | REF_CLOSE: (1), (2), (3), (5), (11), (14), (15), (20), (32), (38) % 149.66/21.76 | | | | | | are inconsistent by sub-proof #8. % 149.66/21.76 | | | | | | % 149.66/21.76 | | | | | End of split % 149.66/21.76 | | | | | % 149.66/21.76 | | | | End of split % 149.66/21.76 | | | | % 149.66/21.76 | | | Case 2: % 149.66/21.76 | | | | % 149.66/21.76 | | | | (39) all_58_10 = e1 % 149.66/21.76 | | | | % 149.66/21.76 | | | | COMBINE_EQS: (4), (39) imply: % 149.66/21.76 | | | | (40) e2 = e1 % 149.66/21.76 | | | | % 149.66/21.76 | | | | REDUCE: (13), (40) imply: % 149.66/21.76 | | | | (41) $false % 149.66/21.76 | | | | % 149.66/21.76 | | | | CLOSE: (41) is inconsistent. % 149.66/21.76 | | | | % 149.66/21.76 | | | End of split % 149.66/21.76 | | | % 149.66/21.76 | | End of split % 149.66/21.76 | | % 149.66/21.76 | End of split % 149.66/21.76 | % 149.66/21.76 End of proof % 149.66/21.76 % 149.66/21.76 Sub-proof #5 shows that the following formulas are inconsistent: % 149.66/21.76 ---------------------------------------------------------------- % 149.66/21.76 (1) all_56_11 = all_8_2 % 149.66/21.76 (2) ~ (all_52_11 = all_6_2) % 149.66/21.76 (3) ~ (all_8_1 = e1) % 149.66/21.76 (4) ~ (e3 = e0) % 149.66/21.76 (5) ~ (all_56_31 = e1) | all_56_29 = e0 % 149.66/21.76 (6) all_54_10 = all_6_2 % 149.66/21.76 (7) ~ (all_6_1 = e2) % 149.66/21.76 (8) op(e0, all_4_1) = e3 % 149.66/21.76 (9) ~ (all_56_21 = e2) | all_56_19 = e1 % 149.66/21.76 (10) all_54_0 = all_10_2 % 149.66/21.76 (11) ~ (all_52_14 = all_4_2) % 149.66/21.76 (12) op(e0, e0) = all_4_2 % 149.66/21.76 (13) all_58_4 = all_52_8 % 149.66/21.76 (14) all_54_5 = all_8_2 % 149.66/21.76 (15) ~ (all_52_6 = all_52_14) % 149.66/21.76 (16) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 149.66/21.76 (17) all_54_15 = all_4_2 % 149.66/21.76 (18) all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1 % 149.66/21.76 (19) all_56_21 = all_6_2 % 149.66/21.76 (20) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 149.66/21.76 (21) ~ (all_52_7 = all_8_2) % 149.66/21.76 (22) all_56_1 = all_10_2 % 149.66/21.76 (23) all_56_17 = all_52_2 % 149.66/21.76 (24) all_58_9 = all_52_12 % 149.66/21.76 (25) all_20_1 = all_4_1 % 149.66/21.76 (26) op(e1, e0) = all_52_14 % 149.66/21.76 (27) all_28_1 = all_6_1 % 149.66/21.76 (28) all_58_1 = all_52_4 % 149.66/21.76 (29) all_58_13 = all_52_7 % 149.66/21.76 (30) op(e3, e3) = all_10_2 % 149.66/21.76 (31) ~ (all_56_21 = e3) | all_56_17 = e1 % 149.66/21.76 (32) ~ (all_20_1 = e2) | ~ (all_20_2 = e1) % 149.66/21.76 (33) all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0 % 149.66/21.76 (34) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 149.66/21.76 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 149.66/21.76 (35) ~ (all_52_3 = all_10_2) % 149.66/21.76 (36) all_28_0 = all_6_0 % 149.66/21.76 (37) all_56_7 = all_52_12 % 149.66/21.76 (38) all_46_2 = all_6_2 % 149.66/21.76 (39) all_28_2 = all_6_2 % 149.66/21.76 (40) op(e0, e1) = all_52_11 % 149.66/21.76 (41) op(e1, e3) = all_52_2 % 149.66/21.76 (42) ~ (all_56_1 = e0) | all_56_7 = e3 % 149.66/21.76 (43) all_46_0 = all_6_0 % 149.66/21.76 (44) ~ (e2 = e1) % 149.66/21.76 (45) ~ (all_52_2 = all_52_3) % 149.66/21.76 (46) op(e1, all_6_1) = all_6_0 % 149.66/21.76 (47) op(all_4_2, all_4_2) = all_4_1 % 149.66/21.76 (48) ~ (all_52_11 = all_4_2) % 149.66/21.76 (49) op(e1, all_52_8) = all_56_4 % 149.66/21.76 (50) all_56_31 = all_4_2 % 149.66/21.76 (51) all_58_11 = all_52_14 % 149.66/21.76 (52) op(all_6_2, all_6_2) = all_6_1 % 149.66/21.76 (53) all_56_1 = e3 | all_56_11 = e2 | all_56_21 = e1 | all_56_31 = e0 % 149.66/21.76 (54) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0 % 149.66/21.76 (55) ~ (all_52_13 = all_52_14) % 149.66/21.76 (56) ~ (all_28_1 = e3) | ~ (all_28_2 = e0) % 149.66/21.76 (57) all_56_23 = all_52_14 % 149.66/21.76 (58) all_46_1 = all_6_1 % 149.66/21.76 (59) op(e1, e1) = all_6_2 % 149.66/21.76 (60) ~ (all_52_6 = all_8_2) % 149.66/21.76 (61) op(e0, e3) = all_52_3 % 149.66/21.76 (62) all_58_15 = all_4_2 % 149.66/21.76 (63) all_56_29 = all_52_11 % 149.66/21.76 (64) all_28_0 = e2 % 149.66/21.76 (65) all_58_10 = all_52_13 % 149.66/21.76 (66) ~ (all_56_11 = e0) | all_56_15 = e2 % 149.66/21.76 (67) all_58_0 = all_10_2 % 149.66/21.76 (68) op(e1, all_6_2) = all_56_20 % 149.66/21.77 (69) all_20_2 = all_4_2 % 149.66/21.77 (70) ~ (e3 = e1) % 149.66/21.77 (71) op(e2, e2) = all_8_2 % 149.66/21.77 (72) ~ (all_52_2 = all_6_2) % 149.66/21.77 (73) ~ (all_56_21 = e0) | all_56_23 = e1 % 149.66/21.77 (74) op(e0, all_4_2) = all_56_30 % 149.66/21.77 (75) ~ (all_52_6 = all_6_2) % 149.66/21.77 (76) ~ (all_52_2 = all_10_2) % 149.66/21.77 (77) ~ (all_46_0 = e2) | ~ (all_46_1 = e0) | ~ (all_46_2 = e3) % 149.66/21.77 (78) ~ (all_52_4 = all_8_2) % 149.66/21.77 (79) op(all_8_2, all_8_2) = all_8_1 % 149.66/21.77 (80) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 149.66/21.77 (81) all_58_14 = all_52_11 % 149.66/21.77 (82) all_56_19 = all_52_6 % 149.66/21.77 (83) all_56_15 = all_52_13 % 149.66/21.77 (84) all_58_12 = all_52_3 % 149.66/21.77 (85) all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2 % 149.66/21.77 % 149.66/21.77 Begin of proof % 149.66/21.77 | % 149.66/21.77 | COMBINE_EQS: (36), (64) imply: % 149.66/21.77 | (86) all_6_0 = e2 % 149.66/21.77 | % 149.66/21.77 | COMBINE_EQS: (43), (86) imply: % 149.66/21.77 | (87) all_46_0 = e2 % 149.66/21.77 | % 149.66/21.77 | REDUCE: (46), (86) imply: % 149.66/21.77 | (88) op(e1, all_6_1) = e2 % 149.66/21.77 | % 149.66/21.77 | BETA: splitting (77) gives: % 149.66/21.77 | % 149.66/21.77 | Case 1: % 149.66/21.77 | | % 149.66/21.77 | | (89) ~ (all_46_0 = e2) % 149.66/21.77 | | % 149.66/21.77 | | REDUCE: (87), (89) imply: % 149.66/21.77 | | (90) $false % 149.66/21.77 | | % 149.66/21.77 | | CLOSE: (90) is inconsistent. % 149.66/21.77 | | % 149.66/21.77 | Case 2: % 149.66/21.77 | | % 149.66/21.77 | | (91) ~ (all_46_1 = e0) | ~ (all_46_2 = e3) % 149.66/21.77 | | % 149.66/21.77 | | BETA: splitting (5) gives: % 149.66/21.77 | | % 149.66/21.77 | | Case 1: % 149.66/21.77 | | | % 149.66/21.77 | | | (92) ~ (all_56_31 = e1) % 149.66/21.77 | | | % 149.66/21.77 | | | REDUCE: (50), (92) imply: % 149.66/21.77 | | | (93) ~ (all_4_2 = e1) % 149.66/21.77 | | | % 149.66/21.77 | | | REF_CLOSE: (1), (6), (7), (8), (9), (10), (11), (12), (13), (14), (15), % 149.66/21.77 | | | (16), (17), (18), (19), (20), (22), (23), (24), (26), (27), % 149.66/21.77 | | | (28), (30), (31), (33), (34), (37), (38), (39), (41), (42), % 149.66/21.77 | | | (44), (47), (49), (51), (52), (54), (55), (56), (57), (58), % 149.66/21.77 | | | (59), (60), (62), (65), (66), (67), (68), (70), (71), (72), % 149.66/21.77 | | | (73), (74), (75), (76), (78), (80), (82), (83), (88), (91), % 149.66/21.77 | | | (93) are inconsistent by sub-proof #6. % 149.66/21.77 | | | % 149.66/21.77 | | Case 2: % 149.66/21.77 | | | % 149.66/21.77 | | | (94) all_56_31 = e1 % 149.66/21.77 | | | (95) all_56_29 = e0 % 149.66/21.77 | | | % 149.66/21.77 | | | COMBINE_EQS: (63), (95) imply: % 149.66/21.77 | | | (96) all_52_11 = e0 % 149.66/21.77 | | | % 149.66/21.77 | | | SIMP: (96) implies: % 149.66/21.77 | | | (97) all_52_11 = e0 % 149.66/21.77 | | | % 149.66/21.77 | | | COMBINE_EQS: (50), (94) imply: % 149.66/21.77 | | | (98) all_4_2 = e1 % 149.66/21.77 | | | % 149.66/21.77 | | | COMBINE_EQS: (69), (98) imply: % 149.66/21.77 | | | (99) all_20_2 = e1 % 149.66/21.77 | | | % 149.66/21.77 | | | COMBINE_EQS: (62), (98) imply: % 149.66/21.77 | | | (100) all_58_15 = e1 % 149.66/21.77 | | | % 149.66/21.77 | | | COMBINE_EQS: (81), (97) imply: % 149.66/21.77 | | | (101) all_58_14 = e0 % 149.66/21.77 | | | % 149.66/21.77 | | | REDUCE: (2), (97) imply: % 149.66/21.77 | | | (102) ~ (all_6_2 = e0) % 149.66/21.77 | | | % 149.66/21.77 | | | SIMP: (102) implies: % 149.66/21.77 | | | (103) ~ (all_6_2 = e0) % 149.66/21.77 | | | % 149.66/21.77 | | | REDUCE: (48), (97), (98) imply: % 149.66/21.77 | | | (104) ~ (e1 = e0) % 149.66/21.77 | | | % 149.66/21.77 | | | SIMP: (104) implies: % 149.66/21.77 | | | (105) ~ (e1 = e0) % 149.66/21.77 | | | % 149.66/21.77 | | | REDUCE: (47), (98) imply: % 149.66/21.77 | | | (106) op(e1, e1) = all_4_1 % 149.66/21.77 | | | % 149.66/21.77 | | | REDUCE: (74), (98) imply: % 149.66/21.77 | | | (107) op(e0, e1) = all_56_30 % 149.66/21.77 | | | % 149.66/21.77 | | | REDUCE: (40), (97) imply: % 149.66/21.77 | | | (108) op(e0, e1) = e0 % 149.66/21.77 | | | % 149.66/21.77 | | | REDUCE: (12), (98) imply: % 149.66/21.77 | | | (109) op(e0, e0) = e1 % 149.66/21.77 | | | % 149.66/21.77 | | | REF_CLOSE: (1), (3), (4), (6), (8), (19), (20), (21), (22), (23), (25), % 149.66/21.77 | | | (29), (30), (31), (32), (34), (35), (44), (45), (52), (53), % 149.66/21.77 | | | (59), (61), (66), (79), (84), (85), (94), (99), (100), (101), % 149.66/21.77 | | | (103), (105), (106), (107), (108), (109) are inconsistent by % 149.66/21.77 | | | sub-proof #14. % 149.66/21.77 | | | % 149.66/21.77 | | End of split % 149.66/21.77 | | % 149.66/21.77 | End of split % 149.66/21.77 | % 149.66/21.77 End of proof % 149.66/21.77 % 149.66/21.77 Sub-proof #6 shows that the following formulas are inconsistent: % 149.66/21.77 ---------------------------------------------------------------- % 149.66/21.77 (1) all_56_11 = all_8_2 % 149.66/21.77 (2) all_54_10 = all_6_2 % 149.66/21.77 (3) ~ (all_6_1 = e2) % 149.66/21.77 (4) op(e0, all_4_1) = e3 % 149.66/21.77 (5) ~ (all_56_21 = e2) | all_56_19 = e1 % 149.66/21.77 (6) all_54_0 = all_10_2 % 149.66/21.77 (7) ~ (all_52_14 = all_4_2) % 149.66/21.77 (8) op(e0, e0) = all_4_2 % 149.66/21.77 (9) all_58_4 = all_52_8 % 149.66/21.77 (10) all_54_5 = all_8_2 % 149.66/21.77 (11) ~ (all_52_6 = all_52_14) % 149.66/21.77 (12) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 149.66/21.77 (13) all_54_15 = all_4_2 % 149.66/21.77 (14) all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1 % 149.66/21.77 (15) all_56_21 = all_6_2 % 149.66/21.77 (16) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 149.66/21.77 (17) all_56_1 = all_10_2 % 149.66/21.77 (18) all_56_17 = all_52_2 % 149.66/21.77 (19) all_58_9 = all_52_12 % 149.66/21.77 (20) op(e1, e0) = all_52_14 % 149.66/21.77 (21) all_28_1 = all_6_1 % 149.66/21.77 (22) all_58_1 = all_52_4 % 149.66/21.77 (23) op(e3, e3) = all_10_2 % 149.66/21.77 (24) ~ (all_56_21 = e3) | all_56_17 = e1 % 149.66/21.77 (25) all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0 % 149.66/21.77 (26) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 149.66/21.77 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 149.66/21.77 (27) all_56_7 = all_52_12 % 149.66/21.77 (28) all_46_2 = all_6_2 % 149.66/21.77 (29) all_28_2 = all_6_2 % 149.66/21.77 (30) op(e1, e3) = all_52_2 % 149.66/21.77 (31) ~ (all_4_2 = e1) % 149.66/21.77 (32) ~ (all_46_1 = e0) | ~ (all_46_2 = e3) % 149.66/21.77 (33) ~ (all_56_1 = e0) | all_56_7 = e3 % 149.66/21.77 (34) ~ (e2 = e1) % 149.66/21.77 (35) op(all_4_2, all_4_2) = all_4_1 % 149.66/21.77 (36) op(e1, all_52_8) = all_56_4 % 149.66/21.77 (37) all_58_11 = all_52_14 % 149.66/21.77 (38) op(e1, all_6_1) = e2 % 149.66/21.77 (39) op(all_6_2, all_6_2) = all_6_1 % 149.66/21.77 (40) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0 % 149.66/21.77 (41) ~ (all_52_13 = all_52_14) % 149.66/21.77 (42) ~ (all_28_1 = e3) | ~ (all_28_2 = e0) % 149.66/21.77 (43) all_56_23 = all_52_14 % 149.66/21.77 (44) all_46_1 = all_6_1 % 149.66/21.77 (45) op(e1, e1) = all_6_2 % 149.66/21.77 (46) ~ (all_52_6 = all_8_2) % 149.66/21.77 (47) all_58_15 = all_4_2 % 149.66/21.77 (48) all_58_10 = all_52_13 % 149.66/21.77 (49) ~ (all_56_11 = e0) | all_56_15 = e2 % 149.66/21.77 (50) all_58_0 = all_10_2 % 149.66/21.77 (51) op(e1, all_6_2) = all_56_20 % 149.66/21.77 (52) ~ (e3 = e1) % 149.66/21.77 (53) op(e2, e2) = all_8_2 % 149.66/21.77 (54) ~ (all_52_2 = all_6_2) % 149.66/21.77 (55) ~ (all_56_21 = e0) | all_56_23 = e1 % 149.66/21.77 (56) op(e0, all_4_2) = all_56_30 % 149.66/21.77 (57) ~ (all_52_6 = all_6_2) % 149.66/21.77 (58) ~ (all_52_2 = all_10_2) % 149.66/21.77 (59) ~ (all_52_4 = all_8_2) % 149.66/21.77 (60) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 149.66/21.77 (61) all_56_19 = all_52_6 % 149.66/21.77 (62) all_56_15 = all_52_13 % 149.66/21.77 % 149.66/21.77 Begin of proof % 149.66/21.77 | % 149.66/21.77 | BETA: splitting (5) gives: % 149.66/21.77 | % 149.66/21.77 | Case 1: % 149.66/21.77 | | % 149.66/21.77 | | (63) ~ (all_56_21 = e2) % 149.66/21.77 | | % 149.66/21.77 | | REDUCE: (15), (63) imply: % 149.66/21.77 | | (64) ~ (all_6_2 = e2) % 149.66/21.77 | | % 149.66/21.77 | | BETA: splitting (24) gives: % 149.66/21.77 | | % 149.66/21.77 | | Case 1: % 149.66/21.77 | | | % 149.66/21.77 | | | (65) ~ (all_56_21 = e3) % 149.66/21.77 | | | % 149.66/21.77 | | | REDUCE: (15), (65) imply: % 149.66/21.77 | | | (66) ~ (all_6_2 = e3) % 149.66/21.77 | | | % 149.66/21.77 | | | BETA: splitting (55) gives: % 149.66/21.77 | | | % 149.66/21.77 | | | Case 1: % 149.66/21.77 | | | | % 149.66/21.77 | | | | (67) ~ (all_56_21 = e0) % 149.66/21.77 | | | | % 149.66/21.77 | | | | REDUCE: (15), (67) imply: % 149.66/21.77 | | | | (68) ~ (all_6_2 = e0) % 149.66/21.77 | | | | % 149.66/21.77 | | | | REF_CLOSE: (2), (3), (16), (26), (38), (39), (45), (51), (64), (66), % 149.66/21.77 | | | | (68) are inconsistent by sub-proof #376. % 149.66/21.77 | | | | % 149.66/21.77 | | | Case 2: % 149.66/21.77 | | | | % 149.66/21.77 | | | | (69) all_56_23 = e1 % 149.66/21.77 | | | | (70) all_56_21 = e0 % 149.66/21.77 | | | | % 149.66/21.77 | | | | COMBINE_EQS: (15), (70) imply: % 149.66/21.77 | | | | (71) all_6_2 = e0 % 149.66/21.77 | | | | % 149.66/21.77 | | | | SIMP: (71) implies: % 149.66/21.77 | | | | (72) all_6_2 = e0 % 149.66/21.77 | | | | % 149.66/21.77 | | | | COMBINE_EQS: (43), (69) imply: % 149.66/21.77 | | | | (73) all_52_14 = e1 % 149.66/21.77 | | | | % 149.66/21.77 | | | | SIMP: (73) implies: % 149.66/21.77 | | | | (74) all_52_14 = e1 % 149.66/21.77 | | | | % 149.66/21.77 | | | | COMBINE_EQS: (29), (72) imply: % 149.66/21.77 | | | | (75) all_28_2 = e0 % 149.66/21.77 | | | | % 149.66/21.77 | | | | REDUCE: (7), (74) imply: % 149.66/21.77 | | | | (76) ~ (all_4_2 = e1) % 149.66/21.77 | | | | % 149.66/21.77 | | | | REDUCE: (39), (72) imply: % 149.66/21.77 | | | | (77) op(e0, e0) = all_6_1 % 149.66/21.77 | | | | % 149.66/21.77 | | | | BETA: splitting (42) gives: % 149.66/21.77 | | | | % 149.66/21.77 | | | | Case 1: % 149.66/21.77 | | | | | % 149.66/21.77 | | | | | (78) ~ (all_28_1 = e3) % 149.66/21.77 | | | | | % 149.66/21.77 | | | | | REDUCE: (21), (78) imply: % 149.66/21.77 | | | | | (79) ~ (all_6_1 = e3) % 149.66/21.77 | | | | | % 149.66/21.77 | | | | | REF_CLOSE: (3), (4), (8), (13), (26), (31), (35), (40), (56), (77), % 149.66/21.77 | | | | | (79) are inconsistent by sub-proof #23. % 149.66/21.77 | | | | | % 149.66/21.77 | | | | Case 2: % 149.66/21.77 | | | | | % 149.66/21.77 | | | | | (80) ~ (all_28_2 = e0) % 149.66/21.77 | | | | | % 149.66/21.77 | | | | | REDUCE: (75), (80) imply: % 149.66/21.77 | | | | | (81) $false % 149.66/21.77 | | | | | % 149.66/21.77 | | | | | CLOSE: (81) is inconsistent. % 149.66/21.77 | | | | | % 149.66/21.77 | | | | End of split % 149.66/21.77 | | | | % 149.66/21.77 | | | End of split % 149.66/21.77 | | | % 149.66/21.77 | | Case 2: % 149.66/21.77 | | | % 149.66/21.77 | | | (82) all_56_21 = e3 % 149.66/21.77 | | | (83) all_56_17 = e1 % 149.66/21.77 | | | % 149.66/21.77 | | | COMBINE_EQS: (18), (83) imply: % 149.66/21.77 | | | (84) all_52_2 = e1 % 149.66/21.77 | | | % 149.66/21.77 | | | COMBINE_EQS: (15), (82) imply: % 149.66/21.77 | | | (85) all_6_2 = e3 % 149.66/21.77 | | | % 149.66/21.77 | | | COMBINE_EQS: (28), (85) imply: % 149.66/21.77 | | | (86) all_46_2 = e3 % 149.66/21.77 | | | % 149.66/21.77 | | | REDUCE: (58), (84) imply: % 149.66/21.77 | | | (87) ~ (all_10_2 = e1) % 149.66/21.77 | | | % 149.66/21.77 | | | SIMP: (87) implies: % 149.66/21.77 | | | (88) ~ (all_10_2 = e1) % 149.66/21.77 | | | % 149.66/21.77 | | | REDUCE: (39), (85) imply: % 149.66/21.77 | | | (89) op(e3, e3) = all_6_1 % 149.66/21.77 | | | % 149.66/21.77 | | | REDUCE: (51), (85) imply: % 149.66/21.77 | | | (90) op(e1, e3) = all_56_20 % 149.66/21.77 | | | % 149.66/21.77 | | | REDUCE: (30), (84) imply: % 149.66/21.77 | | | (91) op(e1, e3) = e1 % 149.66/21.77 | | | % 149.66/21.77 | | | REF_CLOSE: (3), (6), (12), (23), (26), (32), (34), (38), (44), (86), (88), % 149.66/21.77 | | | (89), (90), (91) are inconsistent by sub-proof #375. % 149.66/21.77 | | | % 149.66/21.77 | | End of split % 149.66/21.77 | | % 149.66/21.77 | Case 2: % 149.66/21.77 | | % 149.66/21.77 | | (92) all_56_21 = e2 % 149.66/21.77 | | (93) all_56_19 = e1 % 149.66/21.77 | | % 149.66/21.77 | | COMBINE_EQS: (61), (93) imply: % 149.66/21.77 | | (94) all_52_6 = e1 % 149.66/21.77 | | % 149.66/21.77 | | COMBINE_EQS: (15), (92) imply: % 149.66/21.77 | | (95) all_6_2 = e2 % 149.66/21.77 | | % 149.66/21.77 | | REDUCE: (54), (95) imply: % 149.66/21.77 | | (96) ~ (all_52_2 = e2) % 149.66/21.77 | | % 149.66/21.77 | | REDUCE: (11), (94) imply: % 149.66/21.77 | | (97) ~ (all_52_14 = e1) % 149.66/21.77 | | % 149.66/21.77 | | SIMP: (97) implies: % 149.66/21.77 | | (98) ~ (all_52_14 = e1) % 149.66/21.77 | | % 149.66/21.77 | | REDUCE: (46), (94) imply: % 149.66/21.77 | | (99) ~ (all_8_2 = e1) % 149.66/21.77 | | % 149.66/21.77 | | SIMP: (99) implies: % 149.66/21.77 | | (100) ~ (all_8_2 = e1) % 149.66/21.77 | | % 149.66/21.77 | | REDUCE: (57), (94), (95) imply: % 149.66/21.77 | | (101) ~ (e2 = e1) % 149.66/21.77 | | % 149.66/21.77 | | REDUCE: (39), (95) imply: % 149.66/21.77 | | (102) op(e2, e2) = all_6_1 % 149.66/21.77 | | % 149.66/21.77 | | REF_CLOSE: (1), (3), (9), (10), (14), (17), (19), (20), (22), (25), (26), % 149.66/21.77 | | (27), (30), (31), (33), (34), (36), (37), (38), (41), (47), (48), % 149.66/21.77 | | (49), (50), (52), (53), (59), (60), (62), (96), (98), (100), % 149.66/21.77 | | (102) are inconsistent by sub-proof #369. % 149.66/21.77 | | % 149.66/21.77 | End of split % 149.66/21.77 | % 149.66/21.77 End of proof % 149.66/21.77 % 149.66/21.77 Sub-proof #7 shows that the following formulas are inconsistent: % 149.66/21.77 ---------------------------------------------------------------- % 149.66/21.77 (1) ~ (e3 = e0) % 149.66/21.77 (2) ~ (all_4_1 = e0) % 149.66/21.77 (3) all_56_31 = e3 % 149.66/21.77 (4) ~ (e3 = e2) % 149.66/21.77 (5) ~ (all_6_0 = e2) % 149.66/21.77 (6) all_56_21 = all_6_2 % 149.66/21.77 (7) all_56_1 = all_4_1 % 149.66/21.77 (8) all_58_12 = e0 % 149.66/21.77 (9) all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2 % 149.66/21.77 (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 149.66/21.77 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 149.66/21.77 (11) all_58_0 = all_4_1 % 149.66/21.77 (12) all_56_1 = e3 | all_56_11 = e2 | all_56_21 = e1 | all_56_31 = e0 % 149.66/21.77 (13) all_56_11 = e0 % 149.66/21.77 (14) all_58_6 = all_6_0 % 149.66/21.77 (15) op(e1, e1) = all_6_2 % 149.66/21.77 (16) all_58_2 = all_52_1 % 149.66/21.77 (17) op(e1, all_6_2) = all_56_20 % 149.66/21.77 (18) ~ (e3 = e1) % 149.66/21.77 (19) op(all_6_2, all_6_2) = e3 % 149.66/21.77 (20) ~ (e2 = e0) % 149.66/21.77 (21) ~ (all_52_1 = e2) % 149.66/21.77 % 149.66/21.77 Begin of proof % 149.66/21.77 | % 149.66/21.77 | BETA: splitting (9) gives: % 149.66/21.77 | % 149.66/21.77 | Case 1: % 149.66/21.77 | | % 149.66/21.77 | | (22) all_58_0 = e2 % 149.66/21.77 | | % 149.66/21.77 | | COMBINE_EQS: (11), (22) imply: % 149.66/21.77 | | (23) all_4_1 = e2 % 149.66/21.77 | | % 149.66/21.77 | | COMBINE_EQS: (7), (23) imply: % 149.66/21.77 | | (24) all_56_1 = e2 % 149.66/21.77 | | % 149.66/21.77 | | REF_CLOSE: (1), (3), (4), (6), (10), (12), (13), (15), (17), (18), (19), % 149.66/21.77 | | (20), (24) are inconsistent by sub-proof #425. % 149.66/21.77 | | % 149.66/21.77 | Case 2: % 149.66/21.77 | | % 149.66/21.77 | | (25) all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2 % 149.66/21.77 | | % 149.66/21.77 | | REF_CLOSE: (5), (8), (14), (16), (20), (21), (25) are inconsistent by % 149.66/21.77 | | sub-proof #421. % 149.66/21.77 | | % 149.66/21.77 | End of split % 149.66/21.77 | % 149.66/21.77 End of proof % 149.66/21.77 % 149.66/21.77 Sub-proof #8 shows that the following formulas are inconsistent: % 149.66/21.77 ---------------------------------------------------------------- % 149.66/21.77 (1) ~ (e3 = e0) % 149.90/21.77 (2) op(e0, all_4_1) = e3 % 149.90/21.77 (3) op(e0, e0) = all_4_2 % 149.90/21.77 (4) all_56_21 = all_6_2 % 149.90/21.77 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 149.90/21.77 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 149.90/21.77 (6) op(all_4_2, all_4_2) = all_4_1 % 149.90/21.77 (7) all_56_31 = all_4_2 % 149.90/21.77 (8) ~ (all_6_2 = e1) % 149.90/21.77 (9) all_56_21 = e1 | all_56_31 = e0 % 149.90/21.77 (10) op(e0, all_4_2) = all_56_30 % 149.90/21.77 % 149.90/21.77 Begin of proof % 149.90/21.77 | % 149.90/21.77 | BETA: splitting (9) gives: % 149.90/21.77 | % 149.90/21.77 | Case 1: % 149.90/21.77 | | % 149.90/21.77 | | (11) all_56_21 = e1 % 149.90/21.77 | | % 149.90/21.77 | | COMBINE_EQS: (4), (11) imply: % 149.90/21.77 | | (12) all_6_2 = e1 % 149.90/21.77 | | % 149.90/21.77 | | REDUCE: (8), (12) imply: % 149.90/21.77 | | (13) $false % 149.90/21.77 | | % 149.90/21.77 | | CLOSE: (13) is inconsistent. % 149.90/21.77 | | % 149.90/21.77 | Case 2: % 149.90/21.77 | | % 149.90/21.77 | | (14) all_56_31 = e0 % 149.90/21.77 | | % 149.90/21.77 | | COMBINE_EQS: (7), (14) imply: % 149.90/21.77 | | (15) all_4_2 = e0 % 149.90/21.77 | | % 149.90/21.77 | | SIMP: (15) implies: % 149.90/21.77 | | (16) all_4_2 = e0 % 149.90/21.77 | | % 149.90/21.77 | | REF_CLOSE: (1), (2), (3), (5), (6), (10), (16) are inconsistent by sub-proof % 149.90/21.77 | | #12. % 149.90/21.77 | | % 149.90/21.77 | End of split % 149.90/21.77 | % 149.90/21.77 End of proof % 149.90/21.77 % 149.90/21.77 Sub-proof #9 shows that the following formulas are inconsistent: % 149.90/21.77 ---------------------------------------------------------------- % 149.90/21.77 (1) ~ (all_4_1 = e0) % 149.90/21.77 (2) op(e0, all_4_1) = e3 % 149.90/21.77 (3) all_56_21 = e3 % 149.90/21.77 (4) all_56_21 = all_6_2 % 149.90/21.77 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 149.90/21.77 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 149.90/21.77 (6) op(all_6_2, all_6_2) = e3 % 149.90/21.77 (7) op(e3, e3) = all_4_1 % 149.90/21.77 (8) op(e0, e3) = e0 % 149.90/21.77 % 149.90/21.77 Begin of proof % 149.90/21.77 | % 149.90/21.77 | COMBINE_EQS: (3), (4) imply: % 149.90/21.77 | (9) all_6_2 = e3 % 149.90/21.77 | % 149.90/21.77 | SIMP: (9) implies: % 149.90/21.77 | (10) all_6_2 = e3 % 149.90/21.77 | % 149.90/21.77 | REDUCE: (6), (10) imply: % 149.90/21.77 | (11) op(e3, e3) = e3 % 149.90/21.77 | % 149.90/21.77 | GROUND_INST: instantiating (5) with all_4_1, e3, e3, e3, simplifying with (7), % 149.90/21.77 | (11) gives: % 149.90/21.77 | (12) all_4_1 = e3 % 149.90/21.77 | % 149.90/21.77 | REDUCE: (1), (12) imply: % 149.90/21.77 | (13) ~ (e3 = e0) % 149.90/21.77 | % 149.90/21.77 | REDUCE: (2), (12) imply: % 149.90/21.77 | (14) op(e0, e3) = e3 % 149.90/21.77 | % 149.90/21.77 | GROUND_INST: instantiating (5) with e0, e3, e3, e0, simplifying with (8), (14) % 149.90/21.77 | gives: % 149.90/21.77 | (15) e3 = e0 % 149.90/21.77 | % 149.90/21.77 | REDUCE: (13), (15) imply: % 149.90/21.77 | (16) $false % 149.90/21.77 | % 149.90/21.77 | CLOSE: (16) is inconsistent. % 149.90/21.77 | % 149.90/21.78 End of proof % 149.90/21.78 % 149.90/21.78 Sub-proof #10 shows that the following formulas are inconsistent: % 149.90/21.78 ---------------------------------------------------------------- % 149.90/21.78 (1) all_56_11 = all_8_2 % 149.90/21.78 (2) ~ (all_52_4 = all_52_8) % 149.90/21.78 (3) ~ (all_52_7 = all_52_11) % 149.90/21.78 (4) ~ (all_52_8 = all_52_9) % 149.90/21.78 (5) all_54_9 = all_52_6 % 149.90/21.78 (6) ~ (all_52_1 = all_52_9) % 149.90/21.78 (7) op(e0, all_4_1) = e3 % 149.90/21.78 (8) ~ (all_52_13 = all_8_2) % 149.90/21.78 (9) ~ (all_56_21 = e2) | all_56_19 = e1 % 149.90/21.78 (10) ~ (all_52_14 = all_4_2) % 149.90/21.78 (11) all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2 % 149.90/21.78 (12) ~ (all_52_4 = all_52_7) % 149.90/21.78 (13) op(e0, e0) = all_4_2 % 149.90/21.78 (14) all_58_6 = e0 | all_58_7 = e0 | all_58_8 = e0 | all_58_11 = e0 % 149.90/21.78 (15) all_58_4 = all_52_8 % 149.90/21.78 (16) all_54_5 = all_8_2 % 149.90/21.78 (17) ~ (all_52_6 = all_52_14) % 149.90/21.78 (18) ~ (all_6_0 = e2) % 149.90/21.78 (19) all_54_15 = all_4_2 % 149.90/21.78 (20) all_56_21 = all_6_2 % 149.90/21.78 (21) ~ (all_52_7 = all_8_2) % 149.90/21.78 (22) ~ (all_4_1 = e1) | ~ (all_4_2 = e2) % 149.90/21.78 (23) all_56_1 = all_10_2 % 149.90/21.78 (24) all_56_27 = all_52_7 % 149.90/21.78 (25) all_58_5 = all_52_9 % 149.90/21.78 (26) all_54_1 = all_52_4 % 149.90/21.78 (27) all_58_1 = all_52_4 % 149.90/21.78 (28) all_58_4 = e0 | all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0 % 149.90/21.78 (29) op(e2, all_8_2) = all_56_10 % 149.90/21.78 (30) op(e3, e3) = all_10_2 % 149.90/21.78 (31) ~ (all_52_6 = all_6_0) % 149.90/21.78 (32) all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1 % 149.90/21.78 (33) all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2 % 149.90/21.78 (34) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 149.90/21.78 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 149.90/21.78 (35) ~ (all_52_3 = all_10_2) % 149.90/21.78 (36) ~ (all_56_11 = e3) | all_56_9 = e2 % 149.90/21.78 (37) all_36_0 = all_6_0 % 149.90/21.78 (38) ~ (all_6_0 = all_6_2) % 149.90/21.78 (39) ~ (all_4_2 = e1) % 149.90/21.78 (40) all_54_8 = all_6_0 % 149.90/21.78 (41) all_58_8 = all_6_2 % 149.90/21.78 (42) all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3 % 149.90/21.78 (43) ~ (all_52_14 = all_6_0) % 149.90/21.78 (44) op(all_4_2, all_4_2) = all_4_1 % 149.90/21.78 (45) all_58_3 = all_8_2 % 149.90/21.78 (46) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0 % 149.90/21.78 (47) ~ (all_52_11 = all_4_2) % 149.90/21.78 (48) ~ (all_52_1 = all_52_3) % 149.90/21.78 (49) all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1 % 149.90/21.78 (50) ~ (all_52_6 = all_52_7) % 149.90/21.78 (51) all_56_31 = all_4_2 % 149.90/21.78 (52) all_58_11 = all_52_14 % 149.90/21.78 (53) all_36_2 = all_6_2 % 149.90/21.78 (54) all_56_1 = e3 | all_56_11 = e2 | all_56_21 = e1 | all_56_31 = e0 % 149.90/21.78 (55) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0 % 149.90/21.78 (56) all_56_23 = all_52_14 % 149.90/21.78 (57) all_58_6 = all_6_0 % 149.90/21.78 (58) op(e1, e1) = all_6_2 % 149.90/21.78 (59) ~ (all_52_6 = all_8_2) % 149.90/21.78 (60) op(e0, e3) = all_52_3 % 149.90/21.78 (61) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0 % 149.90/21.78 (62) all_58_2 = all_52_1 % 149.90/21.78 (63) ~ (all_4_2 = e3) % 149.90/21.78 (64) all_58_7 = all_52_6 % 149.90/21.78 (65) all_58_10 = all_52_13 % 149.90/21.78 (66) op(e1, all_6_2) = all_56_20 % 149.90/21.78 (67) ~ (all_56_31 = e2) | all_56_27 = e0 % 149.90/21.78 (68) op(e2, e2) = all_8_2 % 149.90/21.78 (69) ~ (all_36_0 = e0) | ~ (all_36_2 = e2) % 149.90/21.78 (70) ~ (all_56_21 = e0) | all_56_23 = e1 % 149.90/21.78 (71) op(e0, all_4_2) = all_56_30 % 149.90/21.78 (72) ~ (all_52_6 = all_6_2) % 149.90/21.78 (73) op(all_6_2, all_6_2) = e3 % 149.90/21.78 (74) ~ (all_52_14 = all_6_2) % 149.90/21.78 (75) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0 % 149.90/21.78 (76) ~ (all_10_2 = all_6_0) % 149.90/21.78 (77) ~ (all_52_4 = all_8_2) % 149.90/21.78 (78) op(all_8_2, all_8_2) = all_8_1 % 149.90/21.78 (79) ~ (all_52_4 = all_52_6) % 149.90/21.78 (80) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 149.90/21.78 (81) all_58_14 = all_52_11 % 149.90/21.78 (82) all_56_19 = all_52_6 % 149.90/21.78 (83) all_56_9 = all_52_1 % 149.90/21.78 % 149.90/21.78 Begin of proof % 149.90/21.78 | % 149.90/21.78 | BETA: splitting (67) gives: % 149.90/21.78 | % 149.90/21.78 | Case 1: % 149.90/21.78 | | % 149.90/21.78 | | (84) ~ (all_56_31 = e2) % 149.90/21.78 | | % 149.90/21.78 | | REDUCE: (51), (84) imply: % 149.90/21.78 | | (85) ~ (all_4_2 = e2) % 149.90/21.78 | | % 149.90/21.78 | | REF_CLOSE: (7), (13), (19), (34), (39), (44), (55), (63), (71), (85) are % 149.90/21.78 | | inconsistent by sub-proof #29. % 149.90/21.78 | | % 149.90/21.78 | Case 2: % 149.90/21.78 | | % 149.90/21.78 | | (86) all_56_31 = e2 % 149.90/21.78 | | (87) all_56_27 = e0 % 149.90/21.78 | | % 149.90/21.78 | | COMBINE_EQS: (24), (87) imply: % 149.90/21.78 | | (88) all_52_7 = e0 % 149.90/21.78 | | % 149.90/21.78 | | SIMP: (88) implies: % 149.90/21.78 | | (89) all_52_7 = e0 % 149.90/21.78 | | % 149.90/21.78 | | COMBINE_EQS: (51), (86) imply: % 149.90/21.78 | | (90) all_4_2 = e2 % 149.90/21.78 | | % 149.90/21.78 | | REDUCE: (12), (89) imply: % 149.90/21.78 | | (91) ~ (all_52_4 = e0) % 149.90/21.78 | | % 149.90/21.78 | | REDUCE: (50), (89) imply: % 149.90/21.78 | | (92) ~ (all_52_6 = e0) % 149.90/21.78 | | % 149.90/21.78 | | REDUCE: (3), (89) imply: % 149.90/21.78 | | (93) ~ (all_52_11 = e0) % 149.90/21.78 | | % 149.90/21.78 | | SIMP: (93) implies: % 149.90/21.78 | | (94) ~ (all_52_11 = e0) % 149.90/21.78 | | % 149.90/21.78 | | REDUCE: (21), (89) imply: % 149.90/21.78 | | (95) ~ (all_8_2 = e0) % 149.90/21.78 | | % 149.90/21.78 | | SIMP: (95) implies: % 149.90/21.78 | | (96) ~ (all_8_2 = e0) % 149.90/21.78 | | % 149.90/21.78 | | REDUCE: (47), (90) imply: % 149.90/21.78 | | (97) ~ (all_52_11 = e2) % 149.90/21.78 | | % 149.90/21.78 | | REDUCE: (10), (90) imply: % 149.90/21.78 | | (98) ~ (all_52_14 = e2) % 149.90/21.78 | | % 149.90/21.78 | | REDUCE: (44), (90) imply: % 149.90/21.78 | | (99) op(e2, e2) = all_4_1 % 149.90/21.78 | | % 149.90/21.78 | | BETA: splitting (22) gives: % 149.90/21.78 | | % 149.90/21.78 | | Case 1: % 149.90/21.78 | | | % 149.90/21.78 | | | (100) ~ (all_4_1 = e1) % 149.90/21.78 | | | % 149.90/21.78 | | | GROUND_INST: instantiating (34) with all_8_2, all_4_1, e2, e2, simplifying % 149.90/21.78 | | | with (68), (99) gives: % 149.90/21.78 | | | (101) all_8_2 = all_4_1 % 149.90/21.78 | | | % 149.90/21.78 | | | COMBINE_EQS: (16), (101) imply: % 149.90/21.78 | | | (102) all_54_5 = all_4_1 % 149.90/21.78 | | | % 149.90/21.78 | | | COMBINE_EQS: (1), (101) imply: % 149.90/21.78 | | | (103) all_56_11 = all_4_1 % 149.90/21.78 | | | % 149.90/21.78 | | | COMBINE_EQS: (45), (101) imply: % 149.90/21.78 | | | (104) all_58_3 = all_4_1 % 149.90/21.78 | | | % 149.90/21.78 | | | REDUCE: (77), (101) imply: % 149.90/21.78 | | | (105) ~ (all_52_4 = all_4_1) % 149.90/21.78 | | | % 149.90/21.78 | | | REDUCE: (59), (101) imply: % 149.90/21.78 | | | (106) ~ (all_52_6 = all_4_1) % 149.90/21.78 | | | % 149.90/21.78 | | | REDUCE: (8), (101) imply: % 149.90/21.78 | | | (107) ~ (all_52_13 = all_4_1) % 149.90/21.78 | | | % 149.90/21.78 | | | REDUCE: (96), (101) imply: % 149.90/21.78 | | | (108) ~ (all_4_1 = e0) % 149.90/21.78 | | | % 149.90/21.78 | | | REDUCE: (78), (101) imply: % 149.90/21.78 | | | (109) op(all_4_1, all_4_1) = all_8_1 % 149.90/21.78 | | | % 149.90/21.78 | | | BETA: splitting (70) gives: % 149.90/21.78 | | | % 149.90/21.78 | | | Case 1: % 149.90/21.78 | | | | % 149.90/21.78 | | | | (110) ~ (all_56_21 = e0) % 149.90/21.78 | | | | % 149.90/21.78 | | | | REDUCE: (20), (110) imply: % 149.90/21.78 | | | | (111) ~ (all_6_2 = e0) % 149.90/21.78 | | | | % 149.90/21.78 | | | | BETA: splitting (9) gives: % 149.90/21.78 | | | | % 149.90/21.78 | | | | Case 1: % 149.90/21.78 | | | | | % 149.90/21.78 | | | | | (112) ~ (all_56_21 = e2) % 149.90/21.78 | | | | | % 149.90/21.78 | | | | | REDUCE: (20), (112) imply: % 149.90/21.78 | | | | | (113) ~ (all_6_2 = e2) % 149.90/21.78 | | | | | % 149.90/21.78 | | | | | BETA: splitting (33) gives: % 149.90/21.78 | | | | | % 149.90/21.78 | | | | | Case 1: % 149.90/21.78 | | | | | | % 149.90/21.78 | | | | | | (114) all_58_6 = e2 % 149.90/21.78 | | | | | | % 149.90/21.78 | | | | | | REF_CLOSE: (18), (57), (114) are inconsistent by sub-proof #461. % 149.90/21.78 | | | | | | % 149.90/21.78 | | | | | Case 2: % 149.90/21.78 | | | | | | % 149.90/21.78 | | | | | | (115) all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2 % 149.90/21.78 | | | | | | % 149.90/21.78 | | | | | | BETA: splitting (115) gives: % 149.90/21.78 | | | | | | % 149.90/21.78 | | | | | | Case 1: % 149.90/21.78 | | | | | | | % 149.90/21.78 | | | | | | | (116) all_58_7 = e2 % 149.90/21.78 | | | | | | | % 149.90/21.78 | | | | | | | COMBINE_EQS: (64), (116) imply: % 149.90/21.78 | | | | | | | (117) all_52_6 = e2 % 149.90/21.78 | | | | | | | % 149.90/21.78 | | | | | | | REDUCE: (79), (117) imply: % 149.90/21.78 | | | | | | | (118) ~ (all_52_4 = e2) % 149.90/21.78 | | | | | | | % 149.90/21.78 | | | | | | | REDUCE: (72), (117) imply: % 149.90/21.78 | | | | | | | (119) ~ (all_6_2 = e2) % 149.90/21.78 | | | | | | | % 149.90/21.78 | | | | | | | REDUCE: (106), (117) imply: % 149.90/21.78 | | | | | | | (120) ~ (all_4_1 = e2) % 149.90/21.78 | | | | | | | % 149.90/21.78 | | | | | | | SIMP: (120) implies: % 149.90/21.78 | | | | | | | (121) ~ (all_4_1 = e2) % 149.90/21.78 | | | | | | | % 149.90/21.78 | | | | | | | REDUCE: (92), (117) imply: % 149.90/21.78 | | | | | | | (122) ~ (e2 = e0) % 149.90/21.78 | | | | | | | % 149.90/21.78 | | | | | | | BETA: splitting (80) gives: % 149.90/21.78 | | | | | | | % 149.90/21.78 | | | | | | | Case 1: % 149.90/21.78 | | | | | | | | % 149.90/21.78 | | | | | | | | (123) all_54_5 = e3 % 149.90/21.78 | | | | | | | | % 149.90/21.78 | | | | | | | | COMBINE_EQS: (102), (123) imply: % 149.90/21.78 | | | | | | | | (124) all_4_1 = e3 % 149.90/21.78 | | | | | | | | % 149.90/21.78 | | | | | | | | SIMP: (124) implies: % 149.90/21.78 | | | | | | | | (125) all_4_1 = e3 % 149.90/21.78 | | | | | | | | % 149.90/21.78 | | | | | | | | COMBINE_EQS: (103), (125) imply: % 149.90/21.78 | | | | | | | | (126) all_56_11 = e3 % 149.90/21.78 | | | | | | | | % 149.90/21.78 | | | | | | | | COMBINE_EQS: (104), (125) imply: % 149.90/21.78 | | | | | | | | (127) all_58_3 = e3 % 149.90/21.78 | | | | | | | | % 149.90/21.78 | | | | | | | | REDUCE: (105), (125) imply: % 149.90/21.78 | | | | | | | | (128) ~ (all_52_4 = e3) % 149.90/21.78 | | | | | | | | % 149.90/21.78 | | | | | | | | REDUCE: (107), (125) imply: % 149.90/21.78 | | | | | | | | (129) ~ (all_52_13 = e3) % 149.90/21.78 | | | | | | | | % 149.90/21.78 | | | | | | | | REDUCE: (109), (125) imply: % 149.90/21.78 | | | | | | | | (130) op(e3, e3) = all_8_1 % 149.90/21.78 | | | | | | | | % 149.90/21.78 | | | | | | | | REDUCE: (7), (125) imply: % 149.90/21.78 | | | | | | | | (131) op(e0, e3) = e3 % 149.90/21.78 | | | | | | | | % 149.90/21.78 | | | | | | | | BETA: splitting (61) gives: % 149.90/21.78 | | | | | | | | % 149.90/21.78 | | | | | | | | Case 1: % 149.90/21.78 | | | | | | | | | % 149.90/21.78 | | | | | | | | | (132) all_54_1 = e3 % 149.90/21.78 | | | | | | | | | % 149.90/21.78 | | | | | | | | | REF_CLOSE: (26), (128), (132) are inconsistent by sub-proof % 149.90/21.78 | | | | | | | | | #722. % 149.90/21.78 | | | | | | | | | % 149.90/21.78 | | | | | | | | Case 2: % 149.90/21.78 | | | | | | | | | % 149.90/21.78 | | | | | | | | | (133) ~ (all_54_1 = e3) % 149.90/21.78 | | | | | | | | | (134) all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0 % 149.90/21.78 | | | | | | | | | % 149.90/21.78 | | | | | | | | | BETA: splitting (49) gives: % 149.90/21.78 | | | | | | | | | % 149.90/21.78 | | | | | | | | | Case 1: % 149.90/21.78 | | | | | | | | | | % 149.90/21.78 | | | | | | | | | | (135) all_58_1 = e1 % 149.90/21.78 | | | | | | | | | | % 149.90/21.78 | | | | | | | | | | COMBINE_EQS: (27), (135) imply: % 149.90/21.78 | | | | | | | | | | (136) all_52_4 = e1 % 149.90/21.78 | | | | | | | | | | % 149.90/21.78 | | | | | | | | | | REDUCE: (2), (136) imply: % 149.90/21.78 | | | | | | | | | | (137) ~ (all_52_8 = e1) % 149.90/21.78 | | | | | | | | | | % 149.90/21.78 | | | | | | | | | | SIMP: (137) implies: % 149.90/21.78 | | | | | | | | | | (138) ~ (all_52_8 = e1) % 149.90/21.78 | | | | | | | | | | % 149.90/21.78 | | | | | | | | | | REDUCE: (128), (136) imply: % 149.90/21.78 | | | | | | | | | | (139) ~ (e3 = e1) % 149.90/21.78 | | | | | | | | | | % 149.90/21.78 | | | | | | | | | | SIMP: (139) implies: % 149.90/21.78 | | | | | | | | | | (140) ~ (e3 = e1) % 149.90/21.78 | | | | | | | | | | % 149.90/21.78 | | | | | | | | | | REDUCE: (91), (136) imply: % 149.90/21.78 | | | | | | | | | | (141) ~ (e1 = e0) % 149.90/21.78 | | | | | | | | | | % 149.90/21.78 | | | | | | | | | | BETA: splitting (36) gives: % 149.90/21.78 | | | | | | | | | | % 149.90/21.78 | | | | | | | | | | Case 1: % 149.90/21.78 | | | | | | | | | | | % 149.90/21.78 | | | | | | | | | | | (142) ~ (all_56_11 = e3) % 149.90/21.78 | | | | | | | | | | | % 149.90/21.78 | | | | | | | | | | | REDUCE: (126), (142) imply: % 149.90/21.78 | | | | | | | | | | | (143) $false % 149.90/21.78 | | | | | | | | | | | % 149.90/21.78 | | | | | | | | | | | CLOSE: (143) is inconsistent. % 149.90/21.78 | | | | | | | | | | | % 149.90/21.78 | | | | | | | | | | Case 2: % 149.90/21.78 | | | | | | | | | | | % 149.90/21.78 | | | | | | | | | | | (144) all_56_9 = e2 % 149.90/21.78 | | | | | | | | | | | % 149.90/21.78 | | | | | | | | | | | COMBINE_EQS: (83), (144) imply: % 149.90/21.78 | | | | | | | | | | | (145) all_52_1 = e2 % 149.90/21.78 | | | | | | | | | | | % 149.90/21.78 | | | | | | | | | | | COMBINE_EQS: (62), (145) imply: % 149.90/21.78 | | | | | | | | | | | (146) all_58_2 = e2 % 149.90/21.78 | | | | | | | | | | | % 149.90/21.78 | | | | | | | | | | | REDUCE: (48), (145) imply: % 149.90/21.78 | | | | | | | | | | | (147) ~ (all_52_3 = e2) % 149.90/21.78 | | | | | | | | | | | % 149.90/21.78 | | | | | | | | | | | SIMP: (147) implies: % 149.90/21.78 | | | | | | | | | | | (148) ~ (all_52_3 = e2) % 149.90/21.78 | | | | | | | | | | | % 149.90/21.78 | | | | | | | | | | | REDUCE: (6), (145) imply: % 149.90/21.78 | | | | | | | | | | | (149) ~ (all_52_9 = e2) % 149.90/21.78 | | | | | | | | | | | % 149.90/21.78 | | | | | | | | | | | SIMP: (149) implies: % 149.90/21.78 | | | | | | | | | | | (150) ~ (all_52_9 = e2) % 149.90/21.78 | | | | | | | | | | | % 149.90/21.78 | | | | | | | | | | | BETA: splitting (11) gives: % 149.90/21.78 | | | | | | | | | | | % 149.90/21.78 | | | | | | | | | | | Case 1: % 149.90/21.78 | | | | | | | | | | | | % 149.90/21.78 | | | | | | | | | | | | (151) all_58_4 = e2 % 149.90/21.78 | | | | | | | | | | | | % 149.90/21.78 | | | | | | | | | | | | COMBINE_EQS: (15), (151) imply: % 149.90/21.78 | | | | | | | | | | | | (152) all_52_8 = e2 % 149.90/21.78 | | | | | | | | | | | | % 149.90/21.78 | | | | | | | | | | | | REDUCE: (138), (152) imply: % 149.90/21.78 | | | | | | | | | | | | (153) ~ (e2 = e1) % 149.90/21.78 | | | | | | | | | | | | % 149.90/21.78 | | | | | | | | | | | | BETA: splitting (28) gives: % 149.90/21.78 | | | | | | | | | | | | % 149.90/21.78 | | | | | | | | | | | | Case 1: % 149.90/21.78 | | | | | | | | | | | | | % 149.90/21.78 | | | | | | | | | | | | | (154) all_58_4 = e0 % 149.90/21.78 | | | | | | | | | | | | | % 149.90/21.78 | | | | | | | | | | | | | COMBINE_EQS: (151), (154) imply: % 149.90/21.78 | | | | | | | | | | | | | (155) e2 = e0 % 149.90/21.78 | | | | | | | | | | | | | % 149.90/21.78 | | | | | | | | | | | | | REDUCE: (122), (155) imply: % 149.90/21.78 | | | | | | | | | | | | | (156) $false % 149.90/21.78 | | | | | | | | | | | | | % 149.90/21.78 | | | | | | | | | | | | | CLOSE: (156) is inconsistent. % 149.90/21.78 | | | | | | | | | | | | | % 149.90/21.78 | | | | | | | | | | | | Case 2: % 149.90/21.78 | | | | | | | | | | | | | % 149.90/21.78 | | | | | | | | | | | | | (157) all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0 % 149.90/21.78 | | | | | | | | | | | | | % 149.90/21.78 | | | | | | | | | | | | | BETA: splitting (157) gives: % 149.90/21.78 | | | | | | | | | | | | | % 149.90/21.78 | | | | | | | | | | | | | Case 1: % 149.90/21.78 | | | | | | | | | | | | | | % 149.90/21.78 | | | | | | | | | | | | | | (158) all_58_5 = e0 % 149.90/21.78 | | | | | | | | | | | | | | % 149.90/21.78 | | | | | | | | | | | | | | COMBINE_EQS: (25), (158) imply: % 149.90/21.78 | | | | | | | | | | | | | | (159) all_52_9 = e0 % 149.90/21.78 | | | | | | | | | | | | | | % 149.90/21.78 | | | | | | | | | | | | | | REDUCE: (150), (159) imply: % 149.90/21.78 | | | | | | | | | | | | | | (160) ~ (e2 = e0) % 149.90/21.78 | | | | | | | | | | | | | | % 149.90/21.78 | | | | | | | | | | | | | | BETA: splitting (32) gives: % 149.90/21.78 | | | | | | | | | | | | | | % 149.90/21.78 | | | | | | | | | | | | | | Case 1: % 149.90/21.78 | | | | | | | | | | | | | | | % 149.90/21.78 | | | | | | | | | | | | | | | (161) all_58_2 = e1 % 149.90/21.78 | | | | | | | | | | | | | | | % 149.90/21.78 | | | | | | | | | | | | | | | COMBINE_EQS: (146), (161) imply: % 149.90/21.78 | | | | | | | | | | | | | | | (162) e2 = e1 % 149.90/21.78 | | | | | | | | | | | | | | | % 149.90/21.78 | | | | | | | | | | | | | | | REDUCE: (153), (162) imply: % 149.90/21.78 | | | | | | | | | | | | | | | (163) $false % 149.90/21.78 | | | | | | | | | | | | | | | % 149.90/21.78 | | | | | | | | | | | | | | | CLOSE: (163) is inconsistent. % 149.90/21.78 | | | | | | | | | | | | | | | % 149.90/21.78 | | | | | | | | | | | | | | Case 2: % 149.90/21.78 | | | | | | | | | | | | | | | % 149.90/21.78 | | | | | | | | | | | | | | | (164) all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1 % 149.90/21.78 | | | | | | | | | | | | | | | % 149.90/21.78 | | | | | | | | | | | | | | | BETA: splitting (164) gives: % 149.90/21.78 | | | | | | | | | | | | | | | % 149.90/21.78 | | | | | | | | | | | | | | | Case 1: % 149.90/21.78 | | | | | | | | | | | | | | | | % 149.90/21.78 | | | | | | | | | | | | | | | | (165) all_58_3 = e1 % 149.90/21.78 | | | | | | | | | | | | | | | | % 149.90/21.78 | | | | | | | | | | | | | | | | COMBINE_EQS: (127), (165) imply: % 149.90/21.78 | | | | | | | | | | | | | | | | (166) e3 = e1 % 149.90/21.78 | | | | | | | | | | | | | | | | % 149.90/21.78 | | | | | | | | | | | | | | | | REDUCE: (140), (166) imply: % 149.90/21.78 | | | | | | | | | | | | | | | | (167) $false % 149.90/21.78 | | | | | | | | | | | | | | | | % 149.90/21.78 | | | | | | | | | | | | | | | | CLOSE: (167) is inconsistent. % 149.90/21.78 | | | | | | | | | | | | | | | | % 149.90/21.78 | | | | | | | | | | | | | | | Case 2: % 149.90/21.78 | | | | | | | | | | | | | | | | % 149.90/21.78 | | | | | | | | | | | | | | | | (168) all_58_5 = e1 | all_58_10 = e1 % 149.90/21.78 | | | | | | | | | | | | | | | | % 149.90/21.78 | | | | | | | | | | | | | | | | BETA: splitting (168) gives: % 149.90/21.78 | | | | | | | | | | | | | | | | % 149.90/21.78 | | | | | | | | | | | | | | | | Case 1: % 149.90/21.78 | | | | | | | | | | | | | | | | | % 149.90/21.78 | | | | | | | | | | | | | | | | | (169) all_58_5 = e1 % 149.90/21.78 | | | | | | | | | | | | | | | | | % 149.90/21.78 | | | | | | | | | | | | | | | | | REF_CLOSE: (141), (158), (169) are inconsistent by sub-proof % 149.90/21.78 | | | | | | | | | | | | | | | | | #172. % 149.90/21.78 | | | | | | | | | | | | | | | | | % 149.90/21.78 | | | | | | | | | | | | | | | | Case 2: % 149.90/21.78 | | | | | | | | | | | | | | | | | % 149.90/21.78 | | | | | | | | | | | | | | | | | (170) all_58_10 = e1 % 149.90/21.78 | | | | | | | | | | | | | | | | | % 149.90/21.78 | | | | | | | | | | | | | | | | | COMBINE_EQS: (65), (170) imply: % 149.90/21.78 | | | | | | | | | | | | | | | | | (171) all_52_13 = e1 % 149.90/21.78 | | | | | | | | | | | | | | | | | % 149.90/21.78 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (34) with all_52_3, e3, e3, e0, % 149.90/21.78 | | | | | | | | | | | | | | | | | simplifying with (60), (131) gives: % 149.90/21.78 | | | | | | | | | | | | | | | | | (172) all_52_3 = e3 % 149.90/21.78 | | | | | | | | | | | | | | | | | % 149.90/21.78 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (34) with all_10_2, all_8_1, e3, e3, % 149.90/21.78 | | | | | | | | | | | | | | | | | simplifying with (30), (130) gives: % 149.90/21.78 | | | | | | | | | | | | | | | | | (173) all_10_2 = all_8_1 % 149.90/21.78 | | | | | | | | | | | | | | | | | % 149.90/21.78 | | | | | | | | | | | | | | | | | COMBINE_EQS: (23), (173) imply: % 149.90/21.78 | | | | | | | | | | | | | | | | | (174) all_56_1 = all_8_1 % 149.90/21.78 | | | | | | | | | | | | | | | | | % 149.90/21.78 | | | | | | | | | | | | | | | | | REDUCE: (35), (172), (173) imply: % 149.90/21.78 | | | | | | | | | | | | | | | | | (175) ~ (all_8_1 = e3) % 149.90/21.78 | | | | | | | | | | | | | | | | | % 149.90/21.78 | | | | | | | | | | | | | | | | | SIMP: (175) implies: % 149.90/21.78 | | | | | | | | | | | | | | | | | (176) ~ (all_8_1 = e3) % 149.90/21.78 | | | | | | | | | | | | | | | | | % 149.90/21.78 | | | | | | | | | | | | | | | | | REDUCE: (148), (172) imply: % 149.90/21.78 | | | | | | | | | | | | | | | | | (177) ~ (e3 = e2) % 149.90/21.78 | | | | | | | | | | | | | | | | | % 149.90/21.78 | | | | | | | | | | | | | | | | | BETA: splitting (54) gives: % 149.90/21.78 | | | | | | | | | | | | | | | | | % 149.90/21.78 | | | | | | | | | | | | | | | | | Case 1: % 149.90/21.78 | | | | | | | | | | | | | | | | | | % 149.90/21.78 | | | | | | | | | | | | | | | | | | (178) all_56_1 = e3 % 149.90/21.78 | | | | | | | | | | | | | | | | | | % 149.90/21.78 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (174), (178) imply: % 149.90/21.78 | | | | | | | | | | | | | | | | | | (179) all_8_1 = e3 % 149.90/21.78 | | | | | | | | | | | | | | | | | | % 149.90/21.78 | | | | | | | | | | | | | | | | | | SIMP: (179) implies: % 149.90/21.78 | | | | | | | | | | | | | | | | | | (180) all_8_1 = e3 % 149.90/21.78 | | | | | | | | | | | | | | | | | | % 149.90/21.78 | | | | | | | | | | | | | | | | | | REDUCE: (176), (180) imply: % 149.90/21.78 | | | | | | | | | | | | | | | | | | (181) $false % 149.90/21.78 | | | | | | | | | | | | | | | | | | % 149.90/21.78 | | | | | | | | | | | | | | | | | | CLOSE: (181) is inconsistent. % 149.90/21.78 | | | | | | | | | | | | | | | | | | % 149.90/21.78 | | | | | | | | | | | | | | | | | Case 2: % 149.90/21.78 | | | | | | | | | | | | | | | | | | % 149.90/21.78 | | | | | | | | | | | | | | | | | | (182) all_56_11 = e2 | all_56_21 = e1 | all_56_31 = e0 % 149.90/21.78 | | | | | | | | | | | | | | | | | | % 149.90/21.78 | | | | | | | | | | | | | | | | | | BETA: splitting (182) gives: % 149.90/21.78 | | | | | | | | | | | | | | | | | | % 149.90/21.78 | | | | | | | | | | | | | | | | | | Case 1: % 149.90/21.78 | | | | | | | | | | | | | | | | | | | % 149.90/21.78 | | | | | | | | | | | | | | | | | | | (183) all_56_11 = e2 % 149.90/21.78 | | | | | | | | | | | | | | | | | | | % 149.90/21.78 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (126), (177), (183) are inconsistent by sub-proof % 149.90/21.78 | | | | | | | | | | | | | | | | | | | #48. % 149.90/21.78 | | | | | | | | | | | | | | | | | | | % 149.90/21.78 | | | | | | | | | | | | | | | | | | Case 2: % 149.90/21.78 | | | | | | | | | | | | | | | | | | | % 149.90/21.78 | | | | | | | | | | | | | | | | | | | (184) all_56_21 = e1 | all_56_31 = e0 % 149.90/21.78 | | | | | | | | | | | | | | | | | | | % 149.90/21.78 | | | | | | | | | | | | | | | | | | | BETA: splitting (184) gives: % 149.90/21.78 | | | | | | | | | | | | | | | | | | | % 149.90/21.78 | | | | | | | | | | | | | | | | | | | Case 1: % 149.90/21.78 | | | | | | | | | | | | | | | | | | | | % 149.90/21.78 | | | | | | | | | | | | | | | | | | | | (185) all_56_21 = e1 % 149.90/21.78 | | | | | | | | | | | | | | | | | | | | % 149.90/21.78 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (20), (185) imply: % 149.90/21.78 | | | | | | | | | | | | | | | | | | | | (186) all_6_2 = e1 % 149.90/21.78 | | | | | | | | | | | | | | | | | | | | % 149.90/21.78 | | | | | | | | | | | | | | | | | | | | SIMP: (186) implies: % 149.90/21.78 | | | | | | | | | | | | | | | | | | | | (187) all_6_2 = e1 % 149.90/21.78 | | | | | | | | | | | | | | | | | | | | % 149.90/21.78 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (34), (58), (66), (73), (140), (187) are % 149.90/21.78 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #460. % 149.90/21.78 | | | | | | | | | | | | | | | | | | | | % 149.90/21.78 | | | | | | | | | | | | | | | | | | | Case 2: % 149.90/21.78 | | | | | | | | | | | | | | | | | | | | % 149.90/21.78 | | | | | | | | | | | | | | | | | | | | (188) all_56_31 = e0 % 149.90/21.78 | | | | | | | | | | | | | | | | | | | | % 149.90/21.78 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (86), (122), (188) are inconsistent by sub-proof % 149.90/21.78 | | | | | | | | | | | | | | | | | | | | #166. % 149.90/21.78 | | | | | | | | | | | | | | | | | | | | % 149.90/21.78 | | | | | | | | | | | | | | | | | | | End of split % 149.90/21.78 | | | | | | | | | | | | | | | | | | | % 149.90/21.78 | | | | | | | | | | | | | | | | | | End of split % 149.90/21.78 | | | | | | | | | | | | | | | | | | % 149.90/21.78 | | | | | | | | | | | | | | | | | End of split % 149.90/21.78 | | | | | | | | | | | | | | | | | % 149.90/21.78 | | | | | | | | | | | | | | | | End of split % 149.90/21.78 | | | | | | | | | | | | | | | | % 149.90/21.78 | | | | | | | | | | | | | | | End of split % 149.90/21.78 | | | | | | | | | | | | | | | % 149.90/21.78 | | | | | | | | | | | | | | End of split % 149.90/21.78 | | | | | | | | | | | | | | % 149.90/21.78 | | | | | | | | | | | | | Case 2: % 149.90/21.78 | | | | | | | | | | | | | | % 149.90/21.78 | | | | | | | | | | | | | | (189) all_58_8 = e0 | all_58_14 = e0 % 149.90/21.78 | | | | | | | | | | | | | | % 149.90/21.78 | | | | | | | | | | | | | | REF_CLOSE: (41), (81), (94), (111), (189) are inconsistent by % 149.90/21.78 | | | | | | | | | | | | | | sub-proof #627. % 149.90/21.78 | | | | | | | | | | | | | | % 149.90/21.78 | | | | | | | | | | | | | End of split % 149.90/21.78 | | | | | | | | | | | | | % 149.90/21.78 | | | | | | | | | | | | End of split % 149.90/21.78 | | | | | | | | | | | | % 149.90/21.78 | | | | | | | | | | | Case 2: % 149.90/21.78 | | | | | | | | | | | | % 149.90/21.78 | | | | | | | | | | | | (190) all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2 % 149.90/21.78 | | | | | | | | | | | | % 149.90/21.78 | | | | | | | | | | | | REF_CLOSE: (25), (41), (81), (97), (113), (150), (190) are % 149.90/21.78 | | | | | | | | | | | | inconsistent by sub-proof #26. % 149.90/21.78 | | | | | | | | | | | | % 149.90/21.78 | | | | | | | | | | | End of split % 149.90/21.78 | | | | | | | | | | | % 149.90/21.78 | | | | | | | | | | End of split % 149.90/21.78 | | | | | | | | | | % 149.90/21.78 | | | | | | | | | Case 2: % 149.90/21.78 | | | | | | | | | | % 149.90/21.78 | | | | | | | | | | (191) ~ (all_58_1 = e1) % 149.90/21.78 | | | | | | | | | | % 149.90/21.78 | | | | | | | | | | REDUCE: (27), (191) imply: % 149.90/21.78 | | | | | | | | | | (192) ~ (all_52_4 = e1) % 149.90/21.78 | | | | | | | | | | % 149.90/21.78 | | | | | | | | | | REF_CLOSE: (26), (91), (118), (134), (192) are inconsistent % 149.90/21.78 | | | | | | | | | | by sub-proof #718. % 149.90/21.78 | | | | | | | | | | % 149.90/21.78 | | | | | | | | | End of split % 149.90/21.78 | | | | | | | | | % 149.90/21.78 | | | | | | | | End of split % 149.90/21.78 | | | | | | | | % 149.90/21.78 | | | | | | | Case 2: % 149.90/21.78 | | | | | | | | % 149.90/21.78 | | | | | | | | (193) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 149.90/21.78 | | | | | | | | % 149.90/21.78 | | | | | | | | REF_CLOSE: (100), (102), (108), (121), (193) are inconsistent by % 149.90/21.78 | | | | | | | | sub-proof #568. % 149.90/21.78 | | | | | | | | % 149.90/21.78 | | | | | | | End of split % 149.90/21.78 | | | | | | | % 149.90/21.78 | | | | | | Case 2: % 149.90/21.78 | | | | | | | % 149.90/21.78 | | | | | | | (194) all_58_8 = e2 | all_58_11 = e2 % 149.90/21.78 | | | | | | | % 149.90/21.78 | | | | | | | REF_CLOSE: (41), (52), (98), (113), (194) are inconsistent by % 149.90/21.78 | | | | | | | sub-proof #511. % 149.90/21.78 | | | | | | | % 149.90/21.78 | | | | | | End of split % 149.90/21.78 | | | | | | % 149.90/21.78 | | | | | End of split % 149.90/21.78 | | | | | % 149.90/21.78 | | | | Case 2: % 149.90/21.78 | | | | | % 149.90/21.78 | | | | | (195) all_56_21 = e2 % 149.90/21.78 | | | | | (196) all_56_19 = e1 % 149.90/21.78 | | | | | % 149.90/21.78 | | | | | REF_CLOSE: (1), (10), (14), (20), (23), (29), (31), (34), (37), (38), % 149.90/21.78 | | | | | (40), (41), (43), (51), (52), (53), (54), (57), (64), (68), % 149.90/21.78 | | | | | (69), (72), (73), (75), (76), (78), (82), (92), (111), % 149.90/21.78 | | | | | (195), (196) are inconsistent by sub-proof #312. % 149.90/21.78 | | | | | % 149.90/21.78 | | | | End of split % 149.90/21.78 | | | | % 149.90/21.78 | | | Case 2: % 149.90/21.78 | | | | % 149.90/21.78 | | | | (197) all_56_23 = e1 % 149.90/21.78 | | | | (198) all_56_21 = e0 % 149.90/21.78 | | | | % 149.90/21.78 | | | | COMBINE_EQS: (20), (198) imply: % 149.90/21.78 | | | | (199) all_6_2 = e0 % 149.90/21.78 | | | | % 149.90/21.78 | | | | SIMP: (199) implies: % 149.90/21.78 | | | | (200) all_6_2 = e0 % 149.90/21.78 | | | | % 149.90/21.78 | | | | COMBINE_EQS: (56), (197) imply: % 149.90/21.78 | | | | (201) all_52_14 = e1 % 149.90/21.78 | | | | % 149.90/21.78 | | | | SIMP: (201) implies: % 149.90/21.78 | | | | (202) all_52_14 = e1 % 149.90/21.78 | | | | % 149.90/21.78 | | | | REDUCE: (17), (202) imply: % 149.90/21.78 | | | | (203) ~ (all_52_6 = e1) % 149.90/21.78 | | | | % 149.90/21.78 | | | | REDUCE: (43), (202) imply: % 149.90/21.78 | | | | (204) ~ (all_6_0 = e1) % 149.90/21.78 | | | | % 149.90/21.78 | | | | SIMP: (204) implies: % 149.90/21.78 | | | | (205) ~ (all_6_0 = e1) % 149.90/21.78 | | | | % 149.90/21.78 | | | | REDUCE: (74), (200), (202) imply: % 149.90/21.78 | | | | (206) ~ (e1 = e0) % 149.90/21.78 | | | | % 149.90/21.78 | | | | REDUCE: (38), (200) imply: % 149.90/21.78 | | | | (207) ~ (all_6_0 = e0) % 149.90/21.78 | | | | % 149.90/21.78 | | | | BETA: splitting (33) gives: % 149.90/21.78 | | | | % 149.90/21.78 | | | | Case 1: % 149.90/21.78 | | | | | % 149.90/21.78 | | | | | (208) all_58_6 = e2 % 149.90/21.78 | | | | | % 149.90/21.78 | | | | | COMBINE_EQS: (57), (208) imply: % 149.90/21.78 | | | | | (209) all_6_0 = e2 % 149.90/21.78 | | | | | % 149.90/21.78 | | | | | REDUCE: (18), (209) imply: % 149.90/21.78 | | | | | (210) $false % 149.90/21.78 | | | | | % 149.90/21.78 | | | | | CLOSE: (210) is inconsistent. % 149.90/21.78 | | | | | % 149.90/21.78 | | | | Case 2: % 149.90/21.78 | | | | | % 149.90/21.78 | | | | | (211) ~ (all_58_6 = e2) % 149.90/21.78 | | | | | (212) all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2 % 149.90/21.78 | | | | | % 149.90/21.78 | | | | | BETA: splitting (212) gives: % 149.90/21.78 | | | | | % 149.90/21.78 | | | | | Case 1: % 149.90/21.78 | | | | | | % 149.90/21.78 | | | | | | (213) all_58_7 = e2 % 149.90/21.78 | | | | | | % 149.90/21.78 | | | | | | COMBINE_EQS: (64), (213) imply: % 149.90/21.78 | | | | | | (214) all_52_6 = e2 % 149.90/21.78 | | | | | | % 149.90/21.78 | | | | | | REDUCE: (59), (214) imply: % 149.90/21.78 | | | | | | (215) ~ (all_8_2 = e2) % 149.90/21.78 | | | | | | % 149.90/21.78 | | | | | | SIMP: (215) implies: % 149.90/21.78 | | | | | | (216) ~ (all_8_2 = e2) % 149.90/21.78 | | | | | | % 149.90/21.78 | | | | | | REDUCE: (31), (214) imply: % 149.90/21.78 | | | | | | (217) ~ (all_6_0 = e2) % 149.90/21.78 | | | | | | % 149.90/21.78 | | | | | | BETA: splitting (42) gives: % 149.90/21.78 | | | | | | % 149.90/21.78 | | | | | | Case 1: % 149.90/21.78 | | | | | | | % 149.90/21.78 | | | | | | | (218) all_58_6 = e3 % 149.90/21.78 | | | | | | | % 149.90/21.78 | | | | | | | COMBINE_EQS: (57), (218) imply: % 149.90/21.78 | | | | | | | (219) all_6_0 = e3 % 149.90/21.78 | | | | | | | % 149.90/21.78 | | | | | | | REDUCE: (76), (219) imply: % 149.90/21.78 | | | | | | | (220) ~ (all_10_2 = e3) % 149.90/21.78 | | | | | | | % 149.90/21.78 | | | | | | | BETA: splitting (54) gives: % 149.90/21.78 | | | | | | | % 149.90/21.78 | | | | | | | Case 1: % 149.90/21.78 | | | | | | | | % 149.90/21.78 | | | | | | | | (221) all_56_1 = e3 % 149.90/21.78 | | | | | | | | % 149.90/21.78 | | | | | | | | COMBINE_EQS: (23), (221) imply: % 149.90/21.78 | | | | | | | | (222) all_10_2 = e3 % 149.90/21.78 | | | | | | | | % 149.90/21.78 | | | | | | | | REDUCE: (220), (222) imply: % 149.90/21.78 | | | | | | | | (223) $false % 149.90/21.78 | | | | | | | | % 149.90/21.78 | | | | | | | | CLOSE: (223) is inconsistent. % 149.90/21.78 | | | | | | | | % 149.90/21.78 | | | | | | | Case 2: % 149.90/21.78 | | | | | | | | % 149.90/21.78 | | | | | | | | (224) all_56_11 = e2 | all_56_21 = e1 | all_56_31 = e0 % 149.90/21.78 | | | | | | | | % 149.90/21.78 | | | | | | | | BETA: splitting (224) gives: % 149.90/21.78 | | | | | | | | % 149.90/21.78 | | | | | | | | Case 1: % 149.90/21.78 | | | | | | | | | % 149.90/21.78 | | | | | | | | | (225) all_56_11 = e2 % 149.90/21.78 | | | | | | | | | % 149.90/21.78 | | | | | | | | | COMBINE_EQS: (1), (225) imply: % 149.90/21.78 | | | | | | | | | (226) all_8_2 = e2 % 149.90/21.78 | | | | | | | | | % 149.90/21.78 | | | | | | | | | REDUCE: (216), (226) imply: % 149.90/21.78 | | | | | | | | | (227) $false % 149.90/21.78 | | | | | | | | | % 149.90/21.79 | | | | | | | | | CLOSE: (227) is inconsistent. % 149.90/21.79 | | | | | | | | | % 149.90/21.79 | | | | | | | | Case 2: % 149.90/21.79 | | | | | | | | | % 149.90/21.79 | | | | | | | | | (228) all_56_21 = e1 | all_56_31 = e0 % 149.90/21.79 | | | | | | | | | % 149.90/21.79 | | | | | | | | | BETA: splitting (228) gives: % 149.90/21.79 | | | | | | | | | % 149.90/21.79 | | | | | | | | | Case 1: % 149.90/21.79 | | | | | | | | | | % 149.90/21.79 | | | | | | | | | | (229) all_56_21 = e1 % 149.90/21.79 | | | | | | | | | | % 149.90/21.79 | | | | | | | | | | COMBINE_EQS: (198), (229) imply: % 149.90/21.79 | | | | | | | | | | (230) e1 = e0 % 149.90/21.79 | | | | | | | | | | % 149.90/21.79 | | | | | | | | | | SIMP: (230) implies: % 149.90/21.79 | | | | | | | | | | (231) e1 = e0 % 149.90/21.79 | | | | | | | | | | % 149.90/21.79 | | | | | | | | | | REDUCE: (206), (231) imply: % 149.90/21.79 | | | | | | | | | | (232) $false % 149.90/21.79 | | | | | | | | | | % 149.90/21.79 | | | | | | | | | | CLOSE: (232) is inconsistent. % 149.90/21.79 | | | | | | | | | | % 149.90/21.79 | | | | | | | | | Case 2: % 149.90/21.79 | | | | | | | | | | % 149.90/21.79 | | | | | | | | | | (233) all_56_31 = e0 % 149.90/21.79 | | | | | | | | | | % 149.90/21.79 | | | | | | | | | | COMBINE_EQS: (51), (233) imply: % 149.90/21.79 | | | | | | | | | | (234) all_4_2 = e0 % 149.90/21.79 | | | | | | | | | | % 149.90/21.79 | | | | | | | | | | SIMP: (234) implies: % 149.90/21.79 | | | | | | | | | | (235) all_4_2 = e0 % 149.90/21.79 | | | | | | | | | | % 149.90/21.79 | | | | | | | | | | REDUCE: (63), (235) imply: % 149.90/21.79 | | | | | | | | | | (236) ~ (e3 = e0) % 149.90/21.79 | | | | | | | | | | % 149.90/21.79 | | | | | | | | | | SIMP: (236) implies: % 149.90/21.79 | | | | | | | | | | (237) ~ (e3 = e0) % 149.90/21.79 | | | | | | | | | | % 149.90/21.79 | | | | | | | | | | REF_CLOSE: (7), (13), (34), (44), (71), (235), (237) are % 149.90/21.79 | | | | | | | | | | inconsistent by sub-proof #12. % 149.90/21.79 | | | | | | | | | | % 149.90/21.79 | | | | | | | | | End of split % 149.90/21.79 | | | | | | | | | % 149.90/21.79 | | | | | | | | End of split % 149.90/21.79 | | | | | | | | % 149.90/21.79 | | | | | | | End of split % 149.90/21.79 | | | | | | | % 149.90/21.79 | | | | | | Case 2: % 149.90/21.79 | | | | | | | % 149.90/21.79 | | | | | | | (238) ~ (all_58_6 = e3) % 149.90/21.79 | | | | | | | % 149.90/21.79 | | | | | | | REDUCE: (57), (238) imply: % 149.90/21.79 | | | | | | | (239) ~ (all_6_0 = e3) % 149.90/21.79 | | | | | | | % 149.90/21.79 | | | | | | | BETA: splitting (75) gives: % 149.90/21.79 | | | | | | | % 149.90/21.79 | | | | | | | Case 1: % 149.90/21.79 | | | | | | | | % 149.90/21.79 | | | | | | | | (240) all_54_8 = e3 % 149.90/21.79 | | | | | | | | % 149.90/21.79 | | | | | | | | REF_CLOSE: (40), (239), (240) are inconsistent by sub-proof % 149.90/21.79 | | | | | | | | #420. % 149.90/21.79 | | | | | | | | % 149.90/21.79 | | | | | | | Case 2: % 149.90/21.79 | | | | | | | | % 149.90/21.79 | | | | | | | | (241) all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0 % 149.90/21.79 | | | | | | | | % 149.90/21.79 | | | | | | | | REF_CLOSE: (18), (40), (205), (207), (241) are inconsistent by % 149.90/21.79 | | | | | | | | sub-proof #451. % 149.90/21.79 | | | | | | | | % 149.90/21.79 | | | | | | | End of split % 149.90/21.79 | | | | | | | % 149.90/21.79 | | | | | | End of split % 149.90/21.79 | | | | | | % 149.90/21.79 | | | | | Case 2: % 149.90/21.79 | | | | | | % 149.90/21.79 | | | | | | (242) ~ (all_58_7 = e2) % 149.90/21.79 | | | | | | % 149.90/21.79 | | | | | | REDUCE: (64), (242) imply: % 149.90/21.79 | | | | | | (243) ~ (all_52_6 = e2) % 149.90/21.79 | | | | | | % 149.90/21.79 | | | | | | BETA: splitting (46) gives: % 149.90/21.79 | | | | | | % 149.90/21.79 | | | | | | Case 1: % 149.90/21.79 | | | | | | | % 149.90/21.79 | | | | | | | (244) all_54_9 = e3 % 149.90/21.79 | | | | | | | % 149.90/21.79 | | | | | | | COMBINE_EQS: (5), (244) imply: % 149.90/21.79 | | | | | | | (245) all_52_6 = e3 % 149.90/21.79 | | | | | | | % 149.90/21.79 | | | | | | | REDUCE: (31), (245) imply: % 149.90/21.79 | | | | | | | (246) ~ (all_6_0 = e3) % 149.90/21.79 | | | | | | | % 149.90/21.79 | | | | | | | SIMP: (246) implies: % 149.90/21.79 | | | | | | | (247) ~ (all_6_0 = e3) % 149.90/21.79 | | | | | | | % 149.90/21.79 | | | | | | | REF_CLOSE: (18), (40), (75), (205), (207), (247) are inconsistent % 149.90/21.79 | | | | | | | by sub-proof #11. % 149.90/21.79 | | | | | | | % 149.90/21.79 | | | | | | Case 2: % 149.90/21.79 | | | | | | | % 149.90/21.79 | | | | | | | (248) all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0 % 149.90/21.79 | | | | | | | % 149.90/21.79 | | | | | | | REF_CLOSE: (5), (92), (203), (243), (248) are inconsistent by % 149.90/21.79 | | | | | | | sub-proof #677. % 149.90/21.79 | | | | | | | % 149.90/21.79 | | | | | | End of split % 149.90/21.79 | | | | | | % 149.90/21.79 | | | | | End of split % 149.90/21.79 | | | | | % 149.90/21.79 | | | | End of split % 149.90/21.79 | | | | % 149.90/21.79 | | | End of split % 149.90/21.79 | | | % 149.90/21.79 | | Case 2: % 149.90/21.79 | | | % 149.90/21.79 | | | (249) ~ (all_4_2 = e2) % 149.90/21.79 | | | % 149.90/21.79 | | | REF_CLOSE: (7), (13), (19), (34), (39), (44), (55), (63), (71), (249) are % 149.90/21.79 | | | inconsistent by sub-proof #29. % 149.90/21.79 | | | % 149.90/21.79 | | End of split % 149.90/21.79 | | % 149.90/21.79 | End of split % 149.90/21.79 | % 149.90/21.79 End of proof % 149.90/21.79 % 149.90/21.79 Sub-proof #11 shows that the following formulas are inconsistent: % 149.90/21.79 ---------------------------------------------------------------- % 149.90/21.79 (1) ~ (all_6_0 = e2) % 149.90/21.79 (2) ~ (all_6_0 = e1) % 149.90/21.79 (3) all_54_8 = all_6_0 % 149.90/21.79 (4) ~ (all_6_0 = e3) % 149.90/21.79 (5) ~ (all_6_0 = e0) % 149.90/21.79 (6) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0 % 149.90/21.79 % 149.90/21.79 Begin of proof % 149.90/21.79 | % 149.90/21.79 | BETA: splitting (6) gives: % 149.90/21.79 | % 149.90/21.79 | Case 1: % 149.90/21.79 | | % 149.90/21.79 | | (7) all_54_8 = e3 % 149.90/21.79 | | % 149.90/21.79 | | REF_CLOSE: (3), (4), (7) are inconsistent by sub-proof #420. % 149.90/21.79 | | % 149.90/21.79 | Case 2: % 149.90/21.79 | | % 149.90/21.79 | | (8) all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0 % 149.90/21.79 | | % 149.90/21.79 | | REF_CLOSE: (1), (2), (3), (5), (8) are inconsistent by sub-proof #451. % 149.90/21.79 | | % 149.90/21.79 | End of split % 149.90/21.79 | % 149.90/21.79 End of proof % 149.90/21.79 % 149.90/21.79 Sub-proof #12 shows that the following formulas are inconsistent: % 149.90/21.79 ---------------------------------------------------------------- % 149.90/21.79 (1) ~ (e3 = e0) % 149.90/21.79 (2) op(e0, all_4_1) = e3 % 149.90/21.79 (3) op(e0, e0) = all_4_2 % 149.90/21.79 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 149.90/21.79 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 149.90/21.79 (5) op(all_4_2, all_4_2) = all_4_1 % 149.90/21.79 (6) all_4_2 = e0 % 149.90/21.79 (7) op(e0, all_4_2) = all_56_30 % 149.90/21.79 % 149.90/21.79 Begin of proof % 149.90/21.79 | % 149.90/21.79 | REDUCE: (5), (6) imply: % 149.90/21.79 | (8) op(e0, e0) = all_4_1 % 149.90/21.79 | % 149.90/21.79 | REDUCE: (6), (7) imply: % 149.90/21.79 | (9) op(e0, e0) = all_56_30 % 149.90/21.79 | % 149.90/21.79 | REDUCE: (3), (6) imply: % 149.90/21.79 | (10) op(e0, e0) = e0 % 149.90/21.79 | % 149.90/21.79 | REF_CLOSE: (1), (2), (4), (8), (9), (10) are inconsistent by sub-proof #30. % 149.90/21.79 | % 149.90/21.79 End of proof % 149.90/21.79 % 149.90/21.79 Sub-proof #13 shows that the following formulas are inconsistent: % 149.90/21.79 ---------------------------------------------------------------- % 149.90/21.79 (1) all_56_11 = all_8_2 % 149.90/21.79 (2) ~ (all_52_11 = all_6_2) % 149.90/21.79 (3) all_56_31 = e1 % 149.90/21.79 (4) ~ (all_8_1 = e1) % 149.90/21.79 (5) ~ (e3 = e0) % 149.90/21.79 (6) all_54_10 = all_6_2 % 149.90/21.79 (7) op(e0, all_4_1) = e3 % 149.90/21.79 (8) op(e0, e0) = all_4_2 % 149.90/21.79 (9) all_56_21 = all_6_2 % 149.90/21.79 (10) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 149.90/21.79 (11) ~ (all_52_7 = all_8_2) % 149.90/21.79 (12) all_56_1 = all_10_2 % 149.90/21.79 (13) all_56_17 = all_52_2 % 149.90/21.79 (14) all_20_1 = all_4_1 % 149.90/21.79 (15) all_58_13 = all_52_7 % 149.90/21.79 (16) op(e3, e3) = all_10_2 % 149.90/21.79 (17) ~ (all_56_21 = e3) | all_56_17 = e1 % 149.90/21.79 (18) ~ (all_20_1 = e2) | ~ (all_20_2 = e1) % 149.90/21.79 (19) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 149.90/21.79 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 149.90/21.79 (20) ~ (all_52_3 = all_10_2) % 149.90/21.79 (21) op(e0, e1) = all_52_11 % 149.90/21.79 (22) ~ (e2 = e1) % 149.90/21.79 (23) ~ (all_52_2 = all_52_3) % 149.90/21.79 (24) op(all_4_2, all_4_2) = all_4_1 % 149.90/21.79 (25) all_56_29 = e0 % 149.90/21.79 (26) ~ (all_52_11 = all_4_2) % 149.90/21.79 (27) all_56_31 = all_4_2 % 149.90/21.79 (28) op(all_6_2, all_6_2) = all_6_1 % 149.90/21.79 (29) all_56_1 = e3 | all_56_11 = e2 | all_56_21 = e1 | all_56_31 = e0 % 149.90/21.79 (30) op(e1, e1) = all_6_2 % 149.90/21.79 (31) op(e0, e3) = all_52_3 % 149.90/21.79 (32) all_58_15 = all_4_2 % 149.90/21.79 (33) all_56_29 = all_52_11 % 149.90/21.79 (34) ~ (all_56_11 = e0) | all_56_15 = e2 % 149.90/21.79 (35) all_20_2 = all_4_2 % 149.90/21.79 (36) op(e0, all_4_2) = all_56_30 % 149.90/21.79 (37) op(all_8_2, all_8_2) = all_8_1 % 149.90/21.79 (38) all_58_14 = all_52_11 % 149.90/21.79 (39) all_58_12 = all_52_3 % 149.90/21.79 (40) all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2 % 149.90/21.79 % 149.90/21.79 Begin of proof % 149.90/21.79 | % 149.90/21.79 | COMBINE_EQS: (25), (33) imply: % 149.90/21.79 | (41) all_52_11 = e0 % 149.90/21.79 | % 149.90/21.79 | SIMP: (41) implies: % 149.90/21.79 | (42) all_52_11 = e0 % 149.90/21.79 | % 149.90/21.79 | COMBINE_EQS: (3), (27) imply: % 149.90/21.79 | (43) all_4_2 = e1 % 149.90/21.79 | % 149.90/21.79 | COMBINE_EQS: (35), (43) imply: % 149.90/21.79 | (44) all_20_2 = e1 % 149.90/21.79 | % 149.90/21.79 | COMBINE_EQS: (32), (43) imply: % 149.90/21.79 | (45) all_58_15 = e1 % 149.90/21.79 | % 149.90/21.79 | COMBINE_EQS: (38), (42) imply: % 149.90/21.79 | (46) all_58_14 = e0 % 149.90/21.79 | % 149.90/21.79 | REDUCE: (2), (42) imply: % 149.90/21.79 | (47) ~ (all_6_2 = e0) % 149.90/21.79 | % 149.90/21.79 | SIMP: (47) implies: % 149.90/21.79 | (48) ~ (all_6_2 = e0) % 149.90/21.79 | % 149.90/21.79 | REDUCE: (26), (42), (43) imply: % 149.90/21.79 | (49) ~ (e1 = e0) % 149.90/21.79 | % 149.90/21.79 | SIMP: (49) implies: % 149.90/21.79 | (50) ~ (e1 = e0) % 149.90/21.79 | % 149.90/21.79 | REDUCE: (24), (43) imply: % 149.90/21.79 | (51) op(e1, e1) = all_4_1 % 149.90/21.79 | % 149.90/21.79 | REDUCE: (36), (43) imply: % 149.90/21.79 | (52) op(e0, e1) = all_56_30 % 149.90/21.79 | % 149.90/21.79 | REDUCE: (21), (42) imply: % 149.90/21.79 | (53) op(e0, e1) = e0 % 149.90/21.79 | % 149.90/21.79 | REDUCE: (8), (43) imply: % 149.90/21.79 | (54) op(e0, e0) = e1 % 149.90/21.79 | % 149.90/21.79 | REF_CLOSE: (1), (3), (4), (5), (6), (7), (9), (10), (11), (12), (13), (14), % 149.90/21.79 | (15), (16), (17), (18), (19), (20), (22), (23), (28), (29), (30), % 149.90/21.79 | (31), (34), (37), (39), (40), (44), (45), (46), (48), (50), (51), % 149.90/21.79 | (52), (53), (54) are inconsistent by sub-proof #14. % 149.90/21.79 | % 149.90/21.79 End of proof % 149.90/21.79 % 149.90/21.79 Sub-proof #14 shows that the following formulas are inconsistent: % 149.90/21.79 ---------------------------------------------------------------- % 149.90/21.79 (1) all_56_11 = all_8_2 % 149.90/21.79 (2) all_56_31 = e1 % 149.90/21.79 (3) op(e0, e1) = all_56_30 % 149.90/21.79 (4) op(e0, e0) = e1 % 149.90/21.79 (5) ~ (all_8_1 = e1) % 149.90/21.79 (6) ~ (e3 = e0) % 149.90/21.79 (7) all_20_2 = e1 % 149.90/21.79 (8) all_54_10 = all_6_2 % 149.90/21.79 (9) op(e0, all_4_1) = e3 % 149.90/21.79 (10) all_56_21 = all_6_2 % 149.90/21.79 (11) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 149.90/21.79 (12) ~ (all_52_7 = all_8_2) % 149.90/21.79 (13) all_56_1 = all_10_2 % 149.90/21.79 (14) all_56_17 = all_52_2 % 149.90/21.79 (15) all_20_1 = all_4_1 % 149.90/21.79 (16) all_58_13 = all_52_7 % 149.90/21.79 (17) op(e3, e3) = all_10_2 % 149.90/21.79 (18) ~ (all_56_21 = e3) | all_56_17 = e1 % 149.90/21.79 (19) ~ (all_20_1 = e2) | ~ (all_20_2 = e1) % 149.90/21.79 (20) ~ (e1 = e0) % 149.90/21.79 (21) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 149.90/21.79 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 149.90/21.79 (22) ~ (all_52_3 = all_10_2) % 149.90/21.79 (23) ~ (all_6_2 = e0) % 149.90/21.79 (24) ~ (e2 = e1) % 149.90/21.79 (25) ~ (all_52_2 = all_52_3) % 149.90/21.79 (26) op(e0, e1) = e0 % 149.90/21.79 (27) op(all_6_2, all_6_2) = all_6_1 % 149.90/21.79 (28) all_56_1 = e3 | all_56_11 = e2 | all_56_21 = e1 | all_56_31 = e0 % 149.90/21.79 (29) all_58_14 = e0 % 149.90/21.79 (30) op(e1, e1) = all_6_2 % 149.90/21.79 (31) op(e0, e3) = all_52_3 % 149.90/21.79 (32) all_58_15 = e1 % 149.90/21.79 (33) ~ (all_56_11 = e0) | all_56_15 = e2 % 149.90/21.79 (34) op(e1, e1) = all_4_1 % 149.90/21.79 (35) op(all_8_2, all_8_2) = all_8_1 % 149.90/21.79 (36) all_58_12 = all_52_3 % 149.90/21.79 (37) all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2 % 149.90/21.79 % 149.90/21.79 Begin of proof % 149.90/21.79 | % 149.90/21.79 | BETA: splitting (19) gives: % 149.90/21.79 | % 149.90/21.79 | Case 1: % 149.90/21.79 | | % 149.90/21.79 | | (38) ~ (all_20_1 = e2) % 149.90/21.79 | | % 149.90/21.79 | | REDUCE: (15), (38) imply: % 149.90/21.79 | | (39) ~ (all_4_1 = e2) % 149.90/21.79 | | % 149.90/21.79 | | GROUND_INST: instantiating (21) with e0, all_56_30, e1, e0, simplifying with % 149.90/21.79 | | (3), (26) gives: % 149.90/21.79 | | (40) all_56_30 = e0 % 149.90/21.79 | | % 149.90/21.79 | | GROUND_INST: instantiating (21) with all_6_2, all_4_1, e1, e1, simplifying % 149.90/21.79 | | with (30), (34) gives: % 149.90/21.79 | | (41) all_6_2 = all_4_1 % 149.90/21.79 | | % 149.90/21.79 | | COMBINE_EQS: (8), (41) imply: % 149.90/21.79 | | (42) all_54_10 = all_4_1 % 149.90/21.79 | | % 149.90/21.79 | | COMBINE_EQS: (10), (41) imply: % 149.90/21.79 | | (43) all_56_21 = all_4_1 % 149.90/21.79 | | % 149.90/21.79 | | REDUCE: (23), (41) imply: % 149.90/21.79 | | (44) ~ (all_4_1 = e0) % 149.90/21.79 | | % 149.90/21.79 | | REDUCE: (27), (41) imply: % 149.90/21.79 | | (45) op(all_4_1, all_4_1) = all_6_1 % 149.90/21.79 | | % 149.90/21.79 | | BETA: splitting (33) gives: % 149.90/21.79 | | % 149.90/21.79 | | Case 1: % 149.90/21.79 | | | % 149.90/21.79 | | | (46) ~ (all_56_11 = e0) % 149.90/21.79 | | | % 149.90/21.79 | | | REDUCE: (1), (46) imply: % 149.90/21.79 | | | (47) ~ (all_8_2 = e0) % 149.90/21.79 | | | % 149.90/21.79 | | | REF_CLOSE: (1), (2), (6), (9), (11), (12), (13), (14), (16), (17), (18), % 149.90/21.79 | | | (20), (21), (22), (24), (25), (26), (28), (29), (31), (32), % 149.90/21.79 | | | (36), (37), (39), (42), (43), (44), (45), (47) are inconsistent % 149.90/21.79 | | | by sub-proof #15. % 149.90/21.79 | | | % 149.90/21.79 | | Case 2: % 149.90/21.79 | | | % 149.90/21.79 | | | (48) all_56_11 = e0 % 149.90/21.79 | | | % 149.90/21.79 | | | COMBINE_EQS: (1), (48) imply: % 149.90/21.79 | | | (49) all_8_2 = e0 % 149.90/21.79 | | | % 149.90/21.79 | | | REDUCE: (35), (49) imply: % 149.90/21.79 | | | (50) op(e0, e0) = all_8_1 % 149.90/21.79 | | | % 149.90/21.79 | | | REF_CLOSE: (4), (5), (21), (50) are inconsistent by sub-proof #519. % 149.90/21.79 | | | % 149.90/21.79 | | End of split % 149.90/21.79 | | % 149.90/21.79 | Case 2: % 149.90/21.79 | | % 149.90/21.79 | | (51) ~ (all_20_2 = e1) % 149.90/21.79 | | % 149.90/21.79 | | REDUCE: (7), (51) imply: % 149.90/21.79 | | (52) $false % 149.90/21.79 | | % 149.90/21.79 | | CLOSE: (52) is inconsistent. % 149.90/21.79 | | % 149.90/21.79 | End of split % 149.90/21.79 | % 149.90/21.79 End of proof % 149.90/21.79 % 149.90/21.79 Sub-proof #15 shows that the following formulas are inconsistent: % 149.90/21.79 ---------------------------------------------------------------- % 149.90/21.79 (1) all_56_11 = all_8_2 % 149.90/21.79 (2) all_56_31 = e1 % 149.90/21.79 (3) ~ (e3 = e0) % 149.90/21.79 (4) ~ (all_4_1 = e0) % 149.90/21.79 (5) op(e0, all_4_1) = e3 % 149.90/21.79 (6) ~ (all_4_1 = e2) % 149.90/21.79 (7) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 149.90/21.79 (8) ~ (all_52_7 = all_8_2) % 149.90/21.79 (9) all_56_1 = all_10_2 % 149.90/21.79 (10) all_56_17 = all_52_2 % 149.90/21.79 (11) all_58_13 = all_52_7 % 149.90/21.79 (12) op(e3, e3) = all_10_2 % 149.90/21.79 (13) ~ (all_56_21 = e3) | all_56_17 = e1 % 149.90/21.79 (14) ~ (e1 = e0) % 149.90/21.79 (15) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 149.90/21.79 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 149.90/21.79 (16) ~ (all_52_3 = all_10_2) % 149.90/21.79 (17) all_56_21 = all_4_1 % 149.90/21.79 (18) ~ (e2 = e1) % 149.90/21.79 (19) op(all_4_1, all_4_1) = all_6_1 % 149.90/21.79 (20) ~ (all_52_2 = all_52_3) % 149.90/21.79 (21) op(e0, e1) = e0 % 149.90/21.79 (22) all_56_1 = e3 | all_56_11 = e2 | all_56_21 = e1 | all_56_31 = e0 % 149.90/21.79 (23) all_58_14 = e0 % 149.90/21.79 (24) all_54_10 = all_4_1 % 149.90/21.79 (25) op(e0, e3) = all_52_3 % 149.90/21.79 (26) all_58_15 = e1 % 149.90/21.79 (27) ~ (all_8_2 = e0) % 149.90/21.79 (28) all_58_12 = all_52_3 % 149.90/21.79 (29) all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2 % 149.90/21.79 % 149.90/21.79 Begin of proof % 149.90/21.79 | % 149.90/21.79 | BETA: splitting (13) gives: % 149.90/21.79 | % 149.90/21.79 | Case 1: % 149.90/21.79 | | % 149.90/21.79 | | (30) ~ (all_56_21 = e3) % 149.90/21.79 | | % 149.90/21.79 | | REDUCE: (17), (30) imply: % 149.90/21.79 | | (31) ~ (all_4_1 = e3) % 149.90/21.79 | | % 149.90/21.79 | | REF_CLOSE: (3), (4), (5), (6), (7), (15), (21), (24), (31) are inconsistent % 149.90/21.79 | | by sub-proof #17. % 149.90/21.79 | | % 149.90/21.79 | Case 2: % 149.90/21.79 | | % 149.90/21.79 | | (32) all_56_21 = e3 % 149.90/21.79 | | (33) all_56_17 = e1 % 149.90/21.79 | | % 149.90/21.79 | | COMBINE_EQS: (10), (33) imply: % 149.90/21.79 | | (34) all_52_2 = e1 % 149.90/21.79 | | % 149.90/21.79 | | COMBINE_EQS: (17), (32) imply: % 149.90/21.79 | | (35) all_4_1 = e3 % 149.90/21.79 | | % 149.90/21.79 | | SIMP: (35) implies: % 149.90/21.79 | | (36) all_4_1 = e3 % 149.90/21.79 | | % 149.90/21.79 | | REDUCE: (20), (34) imply: % 149.90/21.79 | | (37) ~ (all_52_3 = e1) % 149.90/21.79 | | % 149.90/21.79 | | SIMP: (37) implies: % 149.90/21.79 | | (38) ~ (all_52_3 = e1) % 149.90/21.79 | | % 149.90/21.79 | | REDUCE: (6), (36) imply: % 149.90/21.79 | | (39) ~ (e3 = e2) % 149.90/21.79 | | % 149.90/21.79 | | REDUCE: (19), (36) imply: % 149.90/21.79 | | (40) op(e3, e3) = all_6_1 % 149.90/21.79 | | % 149.90/21.79 | | REDUCE: (5), (36) imply: % 149.90/21.79 | | (41) op(e0, e3) = e3 % 149.90/21.79 | | % 149.90/21.79 | | GROUND_INST: instantiating (15) with all_52_3, e3, e3, e0, simplifying with % 149.90/21.79 | | (25), (41) gives: % 149.90/21.79 | | (42) all_52_3 = e3 % 149.90/21.79 | | % 149.90/21.79 | | GROUND_INST: instantiating (15) with all_10_2, all_6_1, e3, e3, simplifying % 149.90/21.79 | | with (12), (40) gives: % 149.90/21.79 | | (43) all_10_2 = all_6_1 % 149.90/21.79 | | % 149.90/21.79 | | COMBINE_EQS: (9), (43) imply: % 149.90/21.79 | | (44) all_56_1 = all_6_1 % 149.90/21.79 | | % 149.90/21.79 | | COMBINE_EQS: (28), (42) imply: % 149.90/21.79 | | (45) all_58_12 = e3 % 149.90/21.79 | | % 149.90/21.79 | | REDUCE: (16), (42), (43) imply: % 149.90/21.79 | | (46) ~ (all_6_1 = e3) % 149.90/21.79 | | % 149.90/21.79 | | SIMP: (46) implies: % 149.90/21.79 | | (47) ~ (all_6_1 = e3) % 149.90/21.79 | | % 149.90/21.79 | | REDUCE: (38), (42) imply: % 149.90/21.79 | | (48) ~ (e3 = e1) % 149.90/21.79 | | % 149.90/21.79 | | BETA: splitting (22) gives: % 149.90/21.79 | | % 149.90/21.79 | | Case 1: % 149.90/21.79 | | | % 149.90/21.79 | | | (49) all_56_1 = e3 % 149.90/21.79 | | | % 149.90/21.79 | | | COMBINE_EQS: (44), (49) imply: % 149.90/21.79 | | | (50) all_6_1 = e3 % 149.90/21.79 | | | % 149.90/21.79 | | | REDUCE: (47), (50) imply: % 149.90/21.79 | | | (51) $false % 149.90/21.79 | | | % 149.90/21.79 | | | CLOSE: (51) is inconsistent. % 149.90/21.79 | | | % 149.90/21.79 | | Case 2: % 149.90/21.79 | | | % 149.90/21.79 | | | (52) all_56_11 = e2 | all_56_21 = e1 | all_56_31 = e0 % 149.90/21.79 | | | % 149.90/21.79 | | | BETA: splitting (29) gives: % 149.90/21.79 | | | % 149.90/21.79 | | | Case 1: % 149.90/21.79 | | | | % 149.90/21.79 | | | | (53) all_58_12 = e2 % 149.90/21.79 | | | | % 149.90/21.79 | | | | COMBINE_EQS: (45), (53) imply: % 149.90/21.79 | | | | (54) e3 = e2 % 149.90/21.79 | | | | % 149.90/21.79 | | | | REDUCE: (39), (54) imply: % 149.90/21.79 | | | | (55) $false % 149.90/21.79 | | | | % 149.90/21.79 | | | | CLOSE: (55) is inconsistent. % 149.90/21.79 | | | | % 149.90/21.79 | | | Case 2: % 149.90/21.79 | | | | % 149.90/21.79 | | | | (56) all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2 % 149.90/21.79 | | | | % 149.90/21.79 | | | | BETA: splitting (52) gives: % 149.90/21.79 | | | | % 149.90/21.79 | | | | Case 1: % 149.90/21.79 | | | | | % 149.90/21.79 | | | | | (57) all_56_11 = e2 % 149.90/21.79 | | | | | % 149.90/21.79 | | | | | COMBINE_EQS: (1), (57) imply: % 149.90/21.79 | | | | | (58) all_8_2 = e2 % 149.90/21.79 | | | | | % 149.90/21.79 | | | | | REDUCE: (8), (58) imply: % 149.90/21.79 | | | | | (59) ~ (all_52_7 = e2) % 149.90/21.79 | | | | | % 149.90/21.79 | | | | | REDUCE: (27), (58) imply: % 149.90/21.79 | | | | | (60) ~ (e2 = e0) % 149.90/21.79 | | | | | % 149.90/21.79 | | | | | REF_CLOSE: (11), (18), (23), (26), (56), (59), (60) are inconsistent % 149.90/21.79 | | | | | by sub-proof #35. % 149.90/21.79 | | | | | % 149.90/21.79 | | | | Case 2: % 149.90/21.79 | | | | | % 149.90/21.79 | | | | | (61) all_56_21 = e1 | all_56_31 = e0 % 149.90/21.79 | | | | | % 149.90/21.79 | | | | | REF_CLOSE: (2), (14), (32), (48), (61) are inconsistent by sub-proof % 149.90/21.79 | | | | | #16. % 149.90/21.79 | | | | | % 149.90/21.79 | | | | End of split % 149.90/21.79 | | | | % 149.90/21.79 | | | End of split % 149.90/21.79 | | | % 149.90/21.79 | | End of split % 149.90/21.79 | | % 149.90/21.79 | End of split % 149.90/21.79 | % 149.90/21.79 End of proof % 149.90/21.79 % 149.90/21.79 Sub-proof #16 shows that the following formulas are inconsistent: % 149.90/21.79 ---------------------------------------------------------------- % 149.90/21.79 (1) all_56_31 = e1 % 149.90/21.79 (2) all_56_21 = e3 % 149.90/21.79 (3) ~ (e1 = e0) % 149.90/21.79 (4) all_56_21 = e1 | all_56_31 = e0 % 149.90/21.79 (5) ~ (e3 = e1) % 149.90/21.79 % 149.90/21.79 Begin of proof % 149.90/21.79 | % 149.90/21.79 | BETA: splitting (4) gives: % 149.90/21.79 | % 149.90/21.79 | Case 1: % 149.90/21.79 | | % 149.90/21.79 | | (6) all_56_21 = e1 % 149.90/21.79 | | % 149.90/21.79 | | REF_CLOSE: (2), (5), (6) are inconsistent by sub-proof #676. % 149.90/21.79 | | % 149.90/21.79 | Case 2: % 149.90/21.79 | | % 149.90/21.79 | | (7) all_56_31 = e0 % 149.90/21.79 | | % 149.90/21.79 | | REF_CLOSE: (1), (3), (7) are inconsistent by sub-proof #201. % 149.90/21.79 | | % 149.90/21.79 | End of split % 149.90/21.79 | % 149.90/21.80 End of proof % 149.90/21.80 % 149.90/21.80 Sub-proof #17 shows that the following formulas are inconsistent: % 149.90/21.80 ---------------------------------------------------------------- % 149.90/21.80 (1) ~ (e3 = e0) % 149.90/21.80 (2) ~ (all_4_1 = e0) % 149.90/21.80 (3) ~ (all_4_1 = e3) % 149.90/21.80 (4) op(e0, all_4_1) = e3 % 149.90/21.80 (5) ~ (all_4_1 = e2) % 149.90/21.80 (6) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 149.90/21.80 (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 149.90/21.80 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 149.90/21.80 (8) op(e0, e1) = e0 % 149.90/21.80 (9) all_54_10 = all_4_1 % 149.90/21.80 % 149.90/21.80 Begin of proof % 149.90/21.80 | % 149.90/21.80 | BETA: splitting (6) gives: % 149.90/21.80 | % 149.90/21.80 | Case 1: % 149.90/21.80 | | % 149.90/21.80 | | (10) all_54_10 = e3 % 149.90/21.80 | | % 149.90/21.80 | | COMBINE_EQS: (9), (10) imply: % 149.90/21.80 | | (11) all_4_1 = e3 % 149.90/21.80 | | % 149.90/21.80 | | REDUCE: (3), (11) imply: % 149.90/21.80 | | (12) $false % 149.90/21.80 | | % 149.90/21.80 | | CLOSE: (12) is inconsistent. % 149.90/21.80 | | % 149.90/21.80 | Case 2: % 149.90/21.80 | | % 149.90/21.80 | | (13) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 149.90/21.80 | | % 149.90/21.80 | | BETA: splitting (13) gives: % 149.90/21.80 | | % 149.90/21.80 | | Case 1: % 149.90/21.80 | | | % 149.90/21.80 | | | (14) all_54_10 = e2 % 149.90/21.80 | | | % 149.90/21.80 | | | COMBINE_EQS: (9), (14) imply: % 149.90/21.80 | | | (15) all_4_1 = e2 % 149.90/21.80 | | | % 149.90/21.80 | | | REDUCE: (5), (15) imply: % 149.90/21.80 | | | (16) $false % 149.90/21.80 | | | % 149.90/21.80 | | | CLOSE: (16) is inconsistent. % 149.90/21.80 | | | % 149.90/21.80 | | Case 2: % 149.90/21.80 | | | % 149.90/21.80 | | | (17) all_54_10 = e1 | all_54_10 = e0 % 149.90/21.80 | | | % 149.90/21.80 | | | BETA: splitting (17) gives: % 149.90/21.80 | | | % 149.90/21.80 | | | Case 1: % 149.90/21.80 | | | | % 149.90/21.80 | | | | (18) all_54_10 = e1 % 149.90/21.80 | | | | % 149.90/21.80 | | | | COMBINE_EQS: (9), (18) imply: % 149.90/21.80 | | | | (19) all_4_1 = e1 % 149.90/21.80 | | | | % 149.90/21.80 | | | | REDUCE: (4), (19) imply: % 149.90/21.80 | | | | (20) op(e0, e1) = e3 % 149.90/21.80 | | | | % 149.90/21.80 | | | | GROUND_INST: instantiating (7) with e0, e3, e1, e0, simplifying with % 149.90/21.80 | | | | (8), (20) gives: % 149.90/21.80 | | | | (21) e3 = e0 % 149.90/21.80 | | | | % 149.90/21.80 | | | | REDUCE: (1), (21) imply: % 149.90/21.80 | | | | (22) $false % 149.90/21.80 | | | | % 149.90/21.80 | | | | CLOSE: (22) is inconsistent. % 149.90/21.80 | | | | % 149.90/21.80 | | | Case 2: % 149.90/21.80 | | | | % 149.90/21.80 | | | | (23) all_54_10 = e0 % 149.90/21.80 | | | | % 149.90/21.80 | | | | COMBINE_EQS: (9), (23) imply: % 149.90/21.80 | | | | (24) all_4_1 = e0 % 149.90/21.80 | | | | % 149.90/21.80 | | | | REDUCE: (2), (24) imply: % 149.90/21.80 | | | | (25) $false % 149.90/21.80 | | | | % 149.90/21.80 | | | | CLOSE: (25) is inconsistent. % 149.90/21.80 | | | | % 149.90/21.80 | | | End of split % 149.90/21.80 | | | % 149.90/21.80 | | End of split % 149.90/21.80 | | % 149.90/21.80 | End of split % 149.90/21.80 | % 149.90/21.80 End of proof % 149.90/21.80 % 149.90/21.80 Sub-proof #18 shows that the following formulas are inconsistent: % 149.90/21.80 ---------------------------------------------------------------- % 149.90/21.80 (1) ~ (all_8_1 = e1) % 149.90/21.80 (2) op(e0, all_4_1) = e3 % 149.90/21.80 (3) all_8_1 = all_4_2 % 149.90/21.80 (4) ~ (all_8_1 = e3) % 149.90/21.80 (5) all_54_15 = all_4_2 % 149.90/21.80 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 149.90/21.80 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 149.90/21.80 (7) op(e0, e0) = all_8_1 % 149.90/21.80 (8) ~ (all_4_2 = e2) % 149.90/21.80 (9) op(all_4_2, all_4_2) = all_4_1 % 149.90/21.80 (10) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0 % 149.90/21.80 (11) op(e0, all_4_2) = all_56_30 % 149.90/21.80 % 149.90/21.80 Begin of proof % 149.90/21.80 | % 149.90/21.80 | REDUCE: (3), (4) imply: % 149.90/21.80 | (12) ~ (all_4_2 = e3) % 149.90/21.80 | % 149.90/21.80 | REDUCE: (1), (3) imply: % 149.90/21.80 | (13) ~ (all_4_2 = e1) % 149.90/21.80 | % 149.90/21.80 | REDUCE: (3), (7) imply: % 149.90/21.80 | (14) op(e0, e0) = all_4_2 % 149.90/21.80 | % 149.90/21.80 | REF_CLOSE: (2), (5), (6), (8), (9), (10), (11), (12), (13), (14) are % 149.90/21.80 | inconsistent by sub-proof #29. % 149.90/21.80 | % 149.90/21.80 End of proof % 149.90/21.80 % 149.90/21.80 Sub-proof #19 shows that the following formulas are inconsistent: % 149.90/21.80 ---------------------------------------------------------------- % 149.90/21.80 (1) all_54_10 = all_6_2 % 149.90/21.80 (2) ~ (all_6_1 = e2) % 149.90/21.80 (3) op(e0, all_4_1) = e3 % 149.90/21.80 (4) ~ (all_52_14 = all_4_2) % 149.90/21.80 (5) op(e0, e0) = all_4_2 % 149.90/21.80 (6) ~ (all_6_1 = e3) % 149.90/21.80 (7) all_54_15 = all_4_2 % 149.90/21.80 (8) all_56_21 = all_6_2 % 149.90/21.80 (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 149.90/21.80 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 149.90/21.80 (10) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 149.90/21.80 (11) op(all_4_2, all_4_2) = all_4_1 % 149.90/21.80 (12) op(all_6_2, all_6_2) = all_6_1 % 149.90/21.80 (13) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0 % 149.90/21.80 (14) all_56_23 = all_52_14 % 149.90/21.80 (15) ~ (all_6_2 = e1) % 149.90/21.80 (16) ~ (all_6_2 = e2) % 149.90/21.80 (17) ~ (all_56_21 = e0) | all_56_23 = e1 % 149.90/21.80 (18) op(e0, all_4_2) = all_56_30 % 149.90/21.80 % 149.90/21.80 Begin of proof % 149.90/21.80 | % 149.90/21.80 | BETA: splitting (10) gives: % 149.90/21.80 | % 149.90/21.80 | Case 1: % 149.90/21.80 | | % 149.90/21.80 | | (19) all_54_10 = e2 % 149.90/21.80 | | % 149.90/21.80 | | REF_CLOSE: (1), (16), (19) are inconsistent by sub-proof #735. % 149.90/21.80 | | % 149.90/21.80 | Case 2: % 149.90/21.80 | | % 149.90/21.80 | | (20) all_54_10 = e1 | all_54_10 = e0 % 149.90/21.80 | | % 149.90/21.80 | | BETA: splitting (20) gives: % 149.90/21.80 | | % 149.90/21.80 | | Case 1: % 149.90/21.80 | | | % 149.90/21.80 | | | (21) all_54_10 = e1 % 149.90/21.80 | | | % 149.90/21.80 | | | REF_CLOSE: (1), (15), (21) are inconsistent by sub-proof #606. % 149.90/21.80 | | | % 149.90/21.80 | | Case 2: % 149.90/21.80 | | | % 149.90/21.80 | | | (22) all_54_10 = e0 % 149.90/21.80 | | | % 149.90/21.80 | | | COMBINE_EQS: (1), (22) imply: % 149.90/21.80 | | | (23) all_6_2 = e0 % 149.90/21.80 | | | % 149.90/21.80 | | | SIMP: (23) implies: % 149.90/21.80 | | | (24) all_6_2 = e0 % 149.90/21.80 | | | % 149.90/21.80 | | | COMBINE_EQS: (8), (24) imply: % 149.90/21.80 | | | (25) all_56_21 = e0 % 149.90/21.80 | | | % 149.90/21.80 | | | REDUCE: (12), (24) imply: % 149.90/21.80 | | | (26) op(e0, e0) = all_6_1 % 149.90/21.80 | | | % 149.90/21.80 | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (9), (11), (13), (14), (17), % 149.90/21.80 | | | (18), (25), (26) are inconsistent by sub-proof #22. % 149.90/21.80 | | | % 149.90/21.80 | | End of split % 149.90/21.80 | | % 149.90/21.80 | End of split % 149.90/21.80 | % 149.90/21.80 End of proof % 149.90/21.80 % 149.90/21.80 Sub-proof #20 shows that the following formulas are inconsistent: % 149.90/21.80 ---------------------------------------------------------------- % 149.90/21.80 (1) all_56_11 = all_8_2 % 149.90/21.80 (2) op(e0, all_52_13) = all_56_14 % 149.90/21.80 (3) ~ (all_52_11 = all_6_2) % 149.90/21.80 (4) ~ (all_52_4 = all_52_8) % 149.90/21.80 (5) all_56_25 = all_52_3 % 149.90/21.80 (6) ~ (all_52_7 = all_52_11) % 149.90/21.80 (7) ~ (all_52_8 = all_52_9) % 149.90/21.80 (8) ~ (all_52_1 = all_52_9) % 149.90/21.80 (9) ~ (e3 = e0) % 149.90/21.80 (10) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0 % 149.90/21.80 (11) all_54_10 = all_6_2 % 149.90/21.80 (12) ~ (all_6_1 = e2) % 149.90/21.80 (13) op(e0, all_4_1) = e3 % 149.90/21.80 (14) ~ (all_8_2 = e1) % 149.90/21.80 (15) all_54_0 = all_10_2 % 149.90/21.80 (16) ~ (all_52_14 = all_4_2) % 149.90/21.80 (17) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0 % 149.90/21.80 (18) all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2 % 149.90/21.80 (19) all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2 % 149.90/21.80 (20) ~ (all_52_9 = all_8_2) % 149.90/21.80 (21) all_54_12 = all_52_3 % 149.90/21.80 (22) ~ (all_52_4 = all_52_7) % 149.90/21.80 (23) ~ (all_6_2 = e3) % 149.90/21.80 (24) op(e0, e0) = all_4_2 % 149.90/21.80 (25) all_58_4 = all_52_8 % 149.90/21.80 (26) all_54_5 = all_8_2 % 149.90/21.80 (27) ~ (all_6_1 = e3) % 149.90/21.80 (28) ~ (all_52_6 = all_52_14) % 149.90/21.80 (29) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 149.90/21.80 (30) all_54_15 = all_4_2 % 149.90/21.80 (31) all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1 % 149.90/21.80 (32) all_56_21 = all_6_2 % 149.90/21.80 (33) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 149.90/21.80 (34) ~ (all_52_7 = all_8_2) % 149.90/21.80 (35) all_56_1 = all_10_2 % 149.90/21.80 (36) all_56_27 = all_52_7 % 149.90/21.80 (37) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0 % 149.90/21.80 (38) all_58_5 = all_52_9 % 149.90/21.80 (39) all_54_1 = all_52_4 % 149.90/21.80 (40) all_58_9 = all_52_12 % 149.90/21.80 (41) op(e0, all_52_14) = all_56_22 % 149.90/21.80 (42) op(e0, e2) = all_52_7 % 149.90/21.80 (43) ~ (all_56_1 = e1) | all_56_5 = e3 % 149.90/21.80 (44) all_54_14 = all_52_11 % 149.90/21.80 (45) all_58_1 = all_52_4 % 149.90/21.80 (46) all_58_13 = all_52_7 % 149.90/21.80 (47) all_58_4 = e0 | all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0 % 149.90/21.80 (48) op(e3, e3) = all_10_2 % 149.90/21.80 (49) ~ (all_52_8 = all_6_2) % 149.90/21.80 (50) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0 % 149.90/21.80 (51) all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1 % 149.90/21.80 (52) all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1 % 149.90/21.80 (53) ~ (all_52_1 = all_8_2) % 149.90/21.80 (54) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 149.90/21.80 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 149.90/21.80 (55) ~ (all_52_3 = all_10_2) % 149.90/21.80 (56) ~ (all_52_3 = all_52_7) % 149.90/21.80 (57) ~ (all_56_11 = e3) | all_56_9 = e2 % 149.90/21.80 (58) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0 % 149.90/21.80 (59) op(e0, e1) = all_52_11 % 149.90/21.80 (60) ~ (all_4_2 = e1) % 149.90/21.80 (61) all_58_8 = all_6_2 % 149.90/21.80 (62) all_54_6 = all_52_9 % 149.90/21.80 (63) ~ (all_52_3 = all_4_2) % 149.90/21.80 (64) ~ (all_52_8 = all_10_2) % 149.90/21.80 (65) ~ (all_56_1 = e2) | all_56_3 = e3 % 149.90/21.80 (66) all_56_5 = all_52_8 % 149.90/21.80 (67) op(all_4_2, all_4_2) = all_4_1 % 149.90/21.80 (68) all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3 % 149.90/21.80 (69) ~ (all_52_3 = all_52_11) % 149.90/21.80 (70) all_58_3 = all_8_2 % 149.90/21.80 (71) all_56_3 = all_52_4 % 149.90/21.80 (72) ~ (all_52_11 = all_4_2) % 149.90/21.80 (73) ~ (all_52_1 = all_52_3) % 149.90/21.80 (74) all_56_31 = all_4_2 % 149.90/21.80 (75) all_58_11 = all_52_14 % 149.90/21.80 (76) ~ (all_52_9 = all_52_11) % 149.90/21.80 (77) op(all_6_2, all_6_2) = all_6_1 % 149.90/21.80 (78) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0 % 149.90/21.80 (79) ~ (all_52_8 = all_52_11) % 149.90/21.80 (80) all_54_2 = all_52_8 % 149.90/21.80 (81) all_56_23 = all_52_14 % 149.90/21.80 (82) op(e0, e3) = all_52_3 % 149.90/21.80 (83) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0 % 149.90/21.80 (84) all_58_15 = all_4_2 % 149.90/21.80 (85) ~ (all_6_2 = e2) % 149.90/21.80 (86) all_58_2 = all_52_1 % 149.90/21.80 (87) ~ (all_52_9 = all_6_2) % 149.90/21.80 (88) all_58_7 = all_52_6 % 149.90/21.80 (89) all_58_10 = all_52_13 % 149.90/21.80 (90) all_58_0 = all_10_2 % 149.90/21.80 (91) all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1 % 149.90/21.80 (92) all_58_1 = e0 | all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0 % 149.90/21.80 (93) ~ (all_56_31 = e2) | all_56_27 = e0 % 149.90/21.80 (94) op(e2, e2) = all_8_2 % 149.90/21.80 (95) ~ (all_52_4 = all_52_12) % 149.90/21.80 (96) ~ (all_52_8 = all_52_12) % 149.90/21.80 (97) ~ (all_56_21 = e0) | all_56_23 = e1 % 149.90/21.80 (98) op(e0, all_4_2) = all_56_30 % 149.90/21.80 (99) ~ (all_8_2 = e0) % 149.90/21.80 (100) ~ (all_52_14 = all_6_2) % 149.90/21.80 (101) ~ (all_52_4 = all_10_2) % 149.90/21.80 (102) ~ (all_52_4 = all_8_2) % 149.90/21.80 (103) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 149.90/21.80 (104) all_58_14 = all_52_11 % 149.90/21.80 (105) ~ (all_52_12 = all_10_2) % 149.90/21.80 (106) all_56_9 = all_52_1 % 149.90/21.80 (107) ~ (all_52_1 = all_10_2) % 149.90/21.80 (108) all_58_12 = all_52_3 % 149.90/21.80 (109) all_54_11 = all_52_14 % 149.90/21.80 (110) ~ (all_56_31 = e3) | all_56_25 = e0 % 149.90/21.80 % 149.90/21.80 Begin of proof % 149.90/21.80 | % 149.90/21.80 | BETA: splitting (110) gives: % 149.90/21.80 | % 149.90/21.80 | Case 1: % 149.90/21.80 | | % 149.90/21.80 | | (111) ~ (all_56_31 = e3) % 149.90/21.80 | | % 149.90/21.80 | | REDUCE: (74), (111) imply: % 149.90/21.80 | | (112) ~ (all_4_2 = e3) % 149.90/21.80 | | % 149.90/21.80 | | BETA: splitting (93) gives: % 149.90/21.80 | | % 149.90/21.80 | | Case 1: % 149.90/21.80 | | | % 149.90/21.80 | | | (113) ~ (all_56_31 = e2) % 149.90/21.80 | | | % 149.90/21.80 | | | REDUCE: (74), (113) imply: % 149.90/21.80 | | | (114) ~ (all_4_2 = e2) % 149.90/21.80 | | | % 149.90/21.80 | | | REF_CLOSE: (13), (24), (30), (54), (60), (67), (78), (98), (112), (114) % 149.90/21.80 | | | are inconsistent by sub-proof #29. % 149.90/21.80 | | | % 149.90/21.80 | | Case 2: % 149.90/21.80 | | | % 149.90/21.80 | | | (115) all_56_31 = e2 % 149.90/21.80 | | | (116) all_56_27 = e0 % 149.90/21.80 | | | % 149.90/21.80 | | | COMBINE_EQS: (36), (116) imply: % 149.90/21.80 | | | (117) all_52_7 = e0 % 149.90/21.80 | | | % 149.90/21.80 | | | SIMP: (117) implies: % 149.90/21.80 | | | (118) all_52_7 = e0 % 149.90/21.80 | | | % 149.90/21.80 | | | COMBINE_EQS: (74), (115) imply: % 149.90/21.80 | | | (119) all_4_2 = e2 % 149.90/21.80 | | | % 149.90/21.80 | | | REDUCE: (56), (118) imply: % 149.90/21.80 | | | (120) ~ (all_52_3 = e0) % 149.90/21.80 | | | % 149.90/21.80 | | | REDUCE: (34), (118) imply: % 149.90/21.80 | | | (121) ~ (all_8_2 = e0) % 149.90/21.80 | | | % 149.90/21.80 | | | REDUCE: (72), (119) imply: % 149.90/21.80 | | | (122) ~ (all_52_11 = e2) % 149.90/21.80 | | | % 149.90/21.80 | | | REDUCE: (67), (119) imply: % 149.90/21.80 | | | (123) op(e2, e2) = all_4_1 % 149.90/21.80 | | | % 149.90/21.80 | | | REDUCE: (98), (119) imply: % 149.90/21.80 | | | (124) op(e0, e2) = all_56_30 % 149.90/21.80 | | | % 149.90/21.80 | | | REDUCE: (42), (118) imply: % 149.90/21.80 | | | (125) op(e0, e2) = e0 % 149.90/21.80 | | | % 149.90/21.80 | | | GROUND_INST: instantiating (54) with e0, all_56_30, e2, e0, simplifying % 149.90/21.80 | | | with (124), (125) gives: % 149.90/21.80 | | | (126) all_56_30 = e0 % 149.90/21.80 | | | % 149.90/21.80 | | | GROUND_INST: instantiating (54) with all_8_2, all_4_1, e2, e2, simplifying % 149.90/21.80 | | | with (94), (123) gives: % 149.90/21.80 | | | (127) all_8_2 = all_4_1 % 149.90/21.80 | | | % 149.90/21.80 | | | COMBINE_EQS: (26), (127) imply: % 149.90/21.80 | | | (128) all_54_5 = all_4_1 % 149.90/21.80 | | | % 149.90/21.80 | | | COMBINE_EQS: (1), (127) imply: % 149.90/21.80 | | | (129) all_56_11 = all_4_1 % 149.90/21.80 | | | % 149.90/21.80 | | | REDUCE: (53), (127) imply: % 149.90/21.80 | | | (130) ~ (all_52_1 = all_4_1) % 149.90/21.80 | | | % 149.90/21.80 | | | REDUCE: (20), (127) imply: % 149.90/21.80 | | | (131) ~ (all_52_9 = all_4_1) % 149.90/21.80 | | | % 149.90/21.80 | | | BETA: splitting (57) gives: % 149.90/21.80 | | | % 149.90/21.80 | | | Case 1: % 149.90/21.80 | | | | % 149.90/21.80 | | | | (132) ~ (all_56_11 = e3) % 149.90/21.80 | | | | % 149.90/21.80 | | | | REDUCE: (129), (132) imply: % 149.90/21.80 | | | | (133) ~ (all_4_1 = e3) % 149.90/21.80 | | | | % 149.90/21.80 | | | | REF_CLOSE: (9), (13), (14), (26), (54), (99), (103), (125), (128), (133) % 149.90/21.80 | | | | are inconsistent by sub-proof #27. % 149.90/21.80 | | | | % 149.90/21.80 | | | Case 2: % 149.90/21.80 | | | | % 149.90/21.80 | | | | (134) all_56_11 = e3 % 149.90/21.80 | | | | (135) all_56_9 = e2 % 149.90/21.80 | | | | % 149.90/21.80 | | | | COMBINE_EQS: (106), (135) imply: % 149.90/21.80 | | | | (136) all_52_1 = e2 % 149.90/21.80 | | | | % 149.90/21.80 | | | | COMBINE_EQS: (129), (134) imply: % 149.90/21.80 | | | | (137) all_4_1 = e3 % 149.90/21.80 | | | | % 149.90/21.80 | | | | REDUCE: (73), (136) imply: % 149.90/21.80 | | | | (138) ~ (all_52_3 = e2) % 149.90/21.80 | | | | % 149.90/21.80 | | | | SIMP: (138) implies: % 149.90/21.80 | | | | (139) ~ (all_52_3 = e2) % 149.90/21.80 | | | | % 149.90/21.80 | | | | REDUCE: (8), (136) imply: % 149.90/21.80 | | | | (140) ~ (all_52_9 = e2) % 149.90/21.80 | | | | % 149.90/21.80 | | | | SIMP: (140) implies: % 149.90/21.80 | | | | (141) ~ (all_52_9 = e2) % 149.90/21.80 | | | | % 149.90/21.80 | | | | REDUCE: (130), (136), (137) imply: % 149.90/21.80 | | | | (142) ~ (e3 = e2) % 149.90/21.80 | | | | % 149.90/21.80 | | | | SIMP: (142) implies: % 149.90/21.80 | | | | (143) ~ (e3 = e2) % 149.90/21.80 | | | | % 149.90/21.80 | | | | REDUCE: (131), (137) imply: % 149.90/21.80 | | | | (144) ~ (all_52_9 = e3) % 149.90/21.80 | | | | % 149.90/21.80 | | | | REDUCE: (13), (137) imply: % 149.90/21.80 | | | | (145) op(e0, e3) = e3 % 149.90/21.80 | | | | % 149.90/21.80 | | | | BETA: splitting (18) gives: % 149.90/21.80 | | | | % 149.90/21.80 | | | | Case 1: % 149.90/21.80 | | | | | % 149.90/21.80 | | | | | (146) all_58_4 = e2 % 149.90/21.80 | | | | | % 149.90/21.80 | | | | | COMBINE_EQS: (25), (146) imply: % 149.90/21.80 | | | | | (147) all_52_8 = e2 % 149.90/21.80 | | | | | % 149.90/21.80 | | | | | BETA: splitting (68) gives: % 149.90/21.80 | | | | | % 149.90/21.80 | | | | | Case 1: % 149.90/21.80 | | | | | | % 149.90/21.80 | | | | | | (148) all_58_4 = e3 % 149.90/21.80 | | | | | | % 149.90/21.80 | | | | | | REF_CLOSE: (143), (146), (148) are inconsistent by sub-proof #296. % 149.90/21.80 | | | | | | % 149.90/21.80 | | | | | Case 2: % 149.90/21.80 | | | | | | % 149.90/21.80 | | | | | | (149) all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3 % 149.90/21.80 | | | | | | % 149.90/21.80 | | | | | | BETA: splitting (149) gives: % 149.90/21.80 | | | | | | % 149.90/21.80 | | | | | | Case 1: % 149.90/21.80 | | | | | | | % 149.90/21.80 | | | | | | | (150) all_58_5 = e3 % 149.90/21.80 | | | | | | | % 149.90/21.80 | | | | | | | COMBINE_EQS: (38), (150) imply: % 149.90/21.80 | | | | | | | (151) all_52_9 = e3 % 149.90/21.80 | | | | | | | % 149.90/21.80 | | | | | | | REDUCE: (144), (151) imply: % 149.90/21.80 | | | | | | | (152) $false % 149.90/21.80 | | | | | | | % 149.90/21.80 | | | | | | | CLOSE: (152) is inconsistent. % 149.90/21.80 | | | | | | | % 149.90/21.80 | | | | | | Case 2: % 149.90/21.80 | | | | | | | % 149.90/21.80 | | | | | | | (153) all_58_8 = e3 | all_58_14 = e3 % 149.90/21.80 | | | | | | | % 149.90/21.80 | | | | | | | BETA: splitting (153) gives: % 149.90/21.80 | | | | | | | % 149.90/21.80 | | | | | | | Case 1: % 149.90/21.80 | | | | | | | | % 149.90/21.80 | | | | | | | | (154) all_58_8 = e3 % 149.90/21.80 | | | | | | | | % 149.90/21.80 | | | | | | | | COMBINE_EQS: (61), (154) imply: % 149.90/21.80 | | | | | | | | (155) all_6_2 = e3 % 149.90/21.80 | | | | | | | | % 149.90/21.80 | | | | | | | | REDUCE: (23), (155) imply: % 149.90/21.80 | | | | | | | | (156) $false % 149.90/21.80 | | | | | | | | % 149.90/21.80 | | | | | | | | CLOSE: (156) is inconsistent. % 149.90/21.80 | | | | | | | | % 149.90/21.80 | | | | | | | Case 2: % 149.90/21.80 | | | | | | | | % 149.90/21.80 | | | | | | | | (157) all_58_14 = e3 % 149.90/21.80 | | | | | | | | % 149.90/21.80 | | | | | | | | COMBINE_EQS: (104), (157) imply: % 149.90/21.80 | | | | | | | | (158) all_52_11 = e3 % 149.90/21.80 | | | | | | | | % 149.90/21.80 | | | | | | | | SIMP: (158) implies: % 149.90/21.80 | | | | | | | | (159) all_52_11 = e3 % 149.90/21.80 | | | | | | | | % 149.90/21.80 | | | | | | | | REDUCE: (69), (159) imply: % 149.90/21.80 | | | | | | | | (160) ~ (all_52_3 = e3) % 149.90/21.80 | | | | | | | | % 149.90/21.80 | | | | | | | | BETA: splitting (58) gives: % 149.90/21.80 | | | | | | | | % 149.90/21.80 | | | | | | | | Case 1: % 149.90/21.80 | | | | | | | | | % 149.90/21.80 | | | | | | | | | (161) all_54_12 = e3 % 149.90/21.80 | | | | | | | | | % 149.90/21.80 | | | | | | | | | COMBINE_EQS: (21), (161) imply: % 149.90/21.80 | | | | | | | | | (162) all_52_3 = e3 % 149.90/21.80 | | | | | | | | | % 149.90/21.80 | | | | | | | | | REDUCE: (160), (162) imply: % 149.90/21.80 | | | | | | | | | (163) $false % 149.90/21.80 | | | | | | | | | % 149.90/21.80 | | | | | | | | | CLOSE: (163) is inconsistent. % 149.90/21.80 | | | | | | | | | % 149.90/21.80 | | | | | | | | Case 2: % 149.90/21.80 | | | | | | | | | % 149.90/21.80 | | | | | | | | | (164) ~ (all_54_12 = e3) % 149.90/21.80 | | | | | | | | | (165) all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0 % 149.90/21.80 | | | | | | | | | % 149.90/21.80 | | | | | | | | | BETA: splitting (165) gives: % 149.90/21.80 | | | | | | | | | % 149.90/21.80 | | | | | | | | | Case 1: % 149.90/21.80 | | | | | | | | | | % 149.90/21.80 | | | | | | | | | | (166) all_54_12 = e2 % 149.90/21.80 | | | | | | | | | | % 149.90/21.80 | | | | | | | | | | COMBINE_EQS: (21), (166) imply: % 149.90/21.80 | | | | | | | | | | (167) all_52_3 = e2 % 149.90/21.80 | | | | | | | | | | % 149.90/21.80 | | | | | | | | | | REDUCE: (139), (167) imply: % 149.90/21.80 | | | | | | | | | | (168) $false % 149.90/21.80 | | | | | | | | | | % 149.90/21.80 | | | | | | | | | | CLOSE: (168) is inconsistent. % 149.90/21.80 | | | | | | | | | | % 149.90/21.80 | | | | | | | | | Case 2: % 149.90/21.80 | | | | | | | | | | % 149.90/21.80 | | | | | | | | | | (169) all_54_12 = e1 | all_54_12 = e0 % 149.90/21.80 | | | | | | | | | | % 149.90/21.80 | | | | | | | | | | BETA: splitting (91) gives: % 149.90/21.80 | | | | | | | | | | % 149.90/21.80 | | | | | | | | | | Case 1: % 149.90/21.80 | | | | | | | | | | | % 149.90/21.80 | | | | | | | | | | | (170) all_58_12 = e1 % 149.90/21.80 | | | | | | | | | | | % 149.90/21.80 | | | | | | | | | | | COMBINE_EQS: (108), (170) imply: % 149.90/21.80 | | | | | | | | | | | (171) all_52_3 = e1 % 149.90/21.80 | | | | | | | | | | | % 149.90/21.80 | | | | | | | | | | | REDUCE: (160), (171) imply: % 149.90/21.80 | | | | | | | | | | | (172) ~ (e3 = e1) % 149.90/21.80 | | | | | | | | | | | % 149.90/21.80 | | | | | | | | | | | SIMP: (172) implies: % 149.90/21.80 | | | | | | | | | | | (173) ~ (e3 = e1) % 149.90/21.80 | | | | | | | | | | | % 149.90/21.80 | | | | | | | | | | | REDUCE: (82), (171) imply: % 149.90/21.80 | | | | | | | | | | | (174) op(e0, e3) = e1 % 149.90/21.80 | | | | | | | | | | | % 149.90/21.80 | | | | | | | | | | | GROUND_INST: instantiating (54) with e1, e3, e3, e0, % 149.90/21.80 | | | | | | | | | | | simplifying with (145), (174) gives: % 149.90/21.80 | | | | | | | | | | | (175) e3 = e1 % 149.90/21.80 | | | | | | | | | | | % 149.90/21.80 | | | | | | | | | | | REDUCE: (173), (175) imply: % 149.90/21.80 | | | | | | | | | | | (176) $false % 149.90/21.80 | | | | | | | | | | | % 149.90/21.80 | | | | | | | | | | | CLOSE: (176) is inconsistent. % 149.90/21.80 | | | | | | | | | | | % 149.90/21.80 | | | | | | | | | | Case 2: % 149.90/21.80 | | | | | | | | | | | % 149.90/21.80 | | | | | | | | | | | (177) ~ (all_58_12 = e1) % 149.90/21.80 | | | | | | | | | | | % 149.90/21.80 | | | | | | | | | | | REDUCE: (108), (177) imply: % 149.90/21.80 | | | | | | | | | | | (178) ~ (all_52_3 = e1) % 149.90/21.80 | | | | | | | | | | | % 149.90/21.80 | | | | | | | | | | | REF_CLOSE: (21), (120), (169), (178) are inconsistent by % 149.90/21.80 | | | | | | | | | | | sub-proof #616. % 149.90/21.80 | | | | | | | | | | | % 149.90/21.80 | | | | | | | | | | End of split % 149.90/21.80 | | | | | | | | | | % 149.90/21.80 | | | | | | | | | End of split % 149.90/21.80 | | | | | | | | | % 149.90/21.80 | | | | | | | | End of split % 149.90/21.80 | | | | | | | | % 149.90/21.80 | | | | | | | End of split % 149.90/21.80 | | | | | | | % 149.90/21.80 | | | | | | End of split % 149.90/21.80 | | | | | | % 149.90/21.80 | | | | | End of split % 149.90/21.80 | | | | | % 149.90/21.80 | | | | Case 2: % 149.90/21.80 | | | | | % 149.90/21.80 | | | | | (179) all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2 % 149.90/21.80 | | | | | % 149.90/21.80 | | | | | REF_CLOSE: (38), (61), (85), (104), (122), (141), (179) are % 149.90/21.80 | | | | | inconsistent by sub-proof #26. % 149.90/21.80 | | | | | % 149.90/21.80 | | | | End of split % 149.90/21.80 | | | | % 149.90/21.80 | | | End of split % 149.90/21.80 | | | % 149.90/21.80 | | End of split % 149.90/21.80 | | % 149.90/21.80 | Case 2: % 149.90/21.80 | | % 149.90/21.81 | | (180) all_56_31 = e3 % 149.90/21.81 | | (181) all_56_25 = e0 % 149.90/21.81 | | % 149.90/21.81 | | COMBINE_EQS: (5), (181) imply: % 149.90/21.81 | | (182) all_52_3 = e0 % 149.90/21.81 | | % 149.90/21.81 | | SIMP: (182) implies: % 149.90/21.81 | | (183) all_52_3 = e0 % 149.90/21.81 | | % 149.90/21.81 | | COMBINE_EQS: (74), (180) imply: % 149.90/21.81 | | (184) all_4_2 = e3 % 149.90/21.81 | | % 149.90/21.81 | | COMBINE_EQS: (84), (184) imply: % 149.90/21.81 | | (185) all_58_15 = e3 % 149.90/21.81 | | % 149.90/21.81 | | COMBINE_EQS: (108), (183) imply: % 149.90/21.81 | | (186) all_58_12 = e0 % 149.90/21.81 | | % 149.90/21.81 | | REDUCE: (56), (183) imply: % 149.90/21.81 | | (187) ~ (all_52_7 = e0) % 149.90/21.81 | | % 149.90/21.81 | | SIMP: (187) implies: % 149.90/21.81 | | (188) ~ (all_52_7 = e0) % 149.90/21.81 | | % 149.90/21.81 | | REDUCE: (69), (183) imply: % 149.90/21.81 | | (189) ~ (all_52_11 = e0) % 149.90/21.81 | | % 149.90/21.81 | | SIMP: (189) implies: % 149.90/21.81 | | (190) ~ (all_52_11 = e0) % 149.90/21.81 | | % 149.90/21.81 | | REDUCE: (55), (183) imply: % 149.90/21.81 | | (191) ~ (all_10_2 = e0) % 149.90/21.81 | | % 149.90/21.81 | | SIMP: (191) implies: % 149.90/21.81 | | (192) ~ (all_10_2 = e0) % 149.90/21.81 | | % 149.90/21.81 | | REDUCE: (63), (183), (184) imply: % 149.90/21.81 | | (193) ~ (e3 = e0) % 149.90/21.81 | | % 149.90/21.81 | | REDUCE: (72), (184) imply: % 149.90/21.81 | | (194) ~ (all_52_11 = e3) % 149.90/21.81 | | % 149.90/21.81 | | REDUCE: (16), (184) imply: % 149.90/21.81 | | (195) ~ (all_52_14 = e3) % 149.90/21.81 | | % 149.90/21.81 | | REDUCE: (67), (184) imply: % 149.90/21.81 | | (196) op(e3, e3) = all_4_1 % 149.90/21.81 | | % 149.90/21.81 | | REF_CLOSE: (2), (3), (4), (6), (7), (9), (10), (11), (12), (13), (15), (16), % 149.90/21.81 | | (17), (19), (20), (22), (23), (24), (25), (26), (27), (28), (29), % 149.90/21.81 | | (30), (31), (32), (33), (34), (35), (37), (38), (39), (40), (41), % 149.90/21.81 | | (42), (43), (44), (45), (46), (47), (48), (49), (50), (51), (52), % 149.90/21.81 | | (54), (59), (60), (61), (62), (64), (65), (66), (67), (70), (71), % 149.90/21.81 | | (75), (76), (77), (78), (79), (80), (81), (83), (84), (85), (86), % 149.90/21.81 | | (87), (88), (89), (90), (91), (92), (95), (96), (97), (98), (99), % 149.90/21.81 | | (100), (101), (102), (103), (104), (105), (107), (109), (185), % 149.90/21.81 | | (186), (188), (190), (192), (194), (195), (196) are inconsistent % 149.90/21.81 | | by sub-proof #21. % 149.90/21.81 | | % 149.90/21.81 | End of split % 149.90/21.81 | % 149.90/21.81 End of proof % 149.90/21.81 % 149.90/21.81 Sub-proof #21 shows that the following formulas are inconsistent: % 149.90/21.81 ---------------------------------------------------------------- % 149.90/21.81 (1) op(e0, all_52_13) = all_56_14 % 149.90/21.81 (2) ~ (all_52_11 = all_6_2) % 149.90/21.81 (3) ~ (all_52_4 = all_52_8) % 149.90/21.81 (4) ~ (all_52_7 = all_52_11) % 149.90/21.81 (5) ~ (all_52_8 = all_52_9) % 149.90/21.81 (6) ~ (e3 = e0) % 149.90/21.81 (7) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0 % 149.90/21.81 (8) all_54_10 = all_6_2 % 149.90/21.81 (9) ~ (all_6_1 = e2) % 149.90/21.81 (10) op(e0, all_4_1) = e3 % 149.90/21.81 (11) all_54_0 = all_10_2 % 149.90/21.81 (12) ~ (all_52_14 = all_4_2) % 149.90/21.81 (13) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0 % 149.90/21.81 (14) all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2 % 149.90/21.81 (15) ~ (all_52_9 = all_8_2) % 149.90/21.81 (16) ~ (all_52_4 = all_52_7) % 149.90/21.81 (17) ~ (all_6_2 = e3) % 149.90/21.81 (18) op(e0, e0) = all_4_2 % 149.90/21.81 (19) all_58_4 = all_52_8 % 149.90/21.81 (20) all_54_5 = all_8_2 % 149.90/21.81 (21) ~ (all_6_1 = e3) % 149.90/21.81 (22) ~ (all_52_6 = all_52_14) % 149.90/21.81 (23) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 149.90/21.81 (24) ~ (all_52_11 = e0) % 149.90/21.81 (25) all_54_15 = all_4_2 % 149.90/21.81 (26) all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1 % 149.90/21.81 (27) all_56_21 = all_6_2 % 149.90/21.81 (28) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 149.90/21.81 (29) ~ (all_52_7 = all_8_2) % 149.90/21.81 (30) all_56_1 = all_10_2 % 149.90/21.81 (31) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0 % 149.90/21.81 (32) all_58_5 = all_52_9 % 149.90/21.81 (33) all_54_1 = all_52_4 % 149.90/21.81 (34) all_58_9 = all_52_12 % 149.90/21.81 (35) all_58_12 = e0 % 149.90/21.81 (36) op(e0, all_52_14) = all_56_22 % 149.90/21.81 (37) op(e0, e2) = all_52_7 % 149.90/21.81 (38) ~ (all_56_1 = e1) | all_56_5 = e3 % 149.90/21.81 (39) all_54_14 = all_52_11 % 149.90/21.81 (40) all_58_1 = all_52_4 % 149.90/21.81 (41) all_58_13 = all_52_7 % 149.90/21.81 (42) all_58_4 = e0 | all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0 % 149.90/21.81 (43) op(e3, e3) = all_10_2 % 149.90/21.81 (44) ~ (all_52_8 = all_6_2) % 149.90/21.81 (45) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0 % 149.90/21.81 (46) all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1 % 149.90/21.81 (47) all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1 % 149.90/21.81 (48) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 149.90/21.81 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 149.90/21.81 (49) ~ (all_52_11 = e3) % 149.90/21.81 (50) op(e0, e1) = all_52_11 % 149.90/21.81 (51) ~ (all_52_14 = e3) % 149.90/21.81 (52) ~ (all_4_2 = e1) % 149.90/21.81 (53) all_58_8 = all_6_2 % 149.90/21.81 (54) all_54_6 = all_52_9 % 149.90/21.81 (55) ~ (all_52_8 = all_10_2) % 149.90/21.81 (56) ~ (all_56_1 = e2) | all_56_3 = e3 % 149.90/21.81 (57) all_58_15 = e3 % 149.90/21.81 (58) all_56_5 = all_52_8 % 149.90/21.81 (59) op(all_4_2, all_4_2) = all_4_1 % 149.90/21.81 (60) all_58_3 = all_8_2 % 149.90/21.81 (61) all_56_3 = all_52_4 % 149.90/21.81 (62) all_58_11 = all_52_14 % 149.90/21.81 (63) ~ (all_52_9 = all_52_11) % 149.90/21.81 (64) op(all_6_2, all_6_2) = all_6_1 % 149.90/21.81 (65) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0 % 149.90/21.81 (66) ~ (all_52_8 = all_52_11) % 149.90/21.81 (67) all_54_2 = all_52_8 % 149.90/21.81 (68) all_56_23 = all_52_14 % 149.90/21.81 (69) ~ (all_10_2 = e0) % 149.90/21.81 (70) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0 % 149.90/21.81 (71) all_58_15 = all_4_2 % 149.90/21.81 (72) ~ (all_6_2 = e2) % 149.90/21.81 (73) all_58_2 = all_52_1 % 149.90/21.81 (74) ~ (all_52_9 = all_6_2) % 149.90/21.81 (75) all_58_7 = all_52_6 % 149.90/21.81 (76) all_58_10 = all_52_13 % 149.90/21.81 (77) all_58_0 = all_10_2 % 149.90/21.81 (78) all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1 % 149.90/21.81 (79) all_58_1 = e0 | all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0 % 149.90/21.81 (80) ~ (all_52_4 = all_52_12) % 149.90/21.81 (81) ~ (all_52_8 = all_52_12) % 149.90/21.81 (82) ~ (all_56_21 = e0) | all_56_23 = e1 % 149.90/21.81 (83) op(e0, all_4_2) = all_56_30 % 149.90/21.81 (84) ~ (all_8_2 = e0) % 149.90/21.81 (85) ~ (all_52_14 = all_6_2) % 149.90/21.81 (86) ~ (all_52_7 = e0) % 149.90/21.81 (87) ~ (all_52_4 = all_10_2) % 149.90/21.81 (88) ~ (all_52_4 = all_8_2) % 149.90/21.81 (89) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 149.90/21.81 (90) all_58_14 = all_52_11 % 149.90/21.81 (91) ~ (all_52_12 = all_10_2) % 149.90/21.81 (92) ~ (all_52_1 = all_10_2) % 149.90/21.81 (93) op(e3, e3) = all_4_1 % 149.90/21.81 (94) all_54_11 = all_52_14 % 149.90/21.81 % 149.90/21.81 Begin of proof % 149.90/21.81 | % 149.90/21.81 | GROUND_INST: instantiating (48) with all_10_2, all_4_1, e3, e3, simplifying % 149.90/21.81 | with (43), (93) gives: % 149.90/21.81 | (95) all_10_2 = all_4_1 % 149.90/21.81 | % 149.90/21.81 | COMBINE_EQS: (11), (95) imply: % 149.90/21.81 | (96) all_54_0 = all_4_1 % 149.90/21.81 | % 149.90/21.81 | COMBINE_EQS: (30), (95) imply: % 149.90/21.81 | (97) all_56_1 = all_4_1 % 149.90/21.81 | % 149.90/21.81 | COMBINE_EQS: (77), (95) imply: % 149.90/21.81 | (98) all_58_0 = all_4_1 % 149.90/21.81 | % 149.90/21.81 | REDUCE: (92), (95) imply: % 149.90/21.81 | (99) ~ (all_52_1 = all_4_1) % 149.90/21.81 | % 149.90/21.81 | REDUCE: (87), (95) imply: % 149.90/21.81 | (100) ~ (all_52_4 = all_4_1) % 149.90/21.81 | % 149.90/21.81 | REDUCE: (55), (95) imply: % 149.90/21.81 | (101) ~ (all_52_8 = all_4_1) % 149.90/21.81 | % 149.90/21.81 | REDUCE: (91), (95) imply: % 149.90/21.81 | (102) ~ (all_52_12 = all_4_1) % 149.90/21.81 | % 149.90/21.81 | REDUCE: (69), (95) imply: % 149.90/21.81 | (103) ~ (all_4_1 = e0) % 149.90/21.81 | % 149.90/21.81 | BETA: splitting (82) gives: % 149.90/21.81 | % 149.90/21.81 | Case 1: % 149.90/21.81 | | % 149.90/21.81 | | (104) ~ (all_56_21 = e0) % 149.90/21.81 | | % 149.90/21.81 | | REDUCE: (27), (104) imply: % 149.90/21.81 | | (105) ~ (all_6_2 = e0) % 149.90/21.81 | | % 149.90/21.81 | | BETA: splitting (28) gives: % 149.90/21.81 | | % 149.90/21.81 | | Case 1: % 149.90/21.81 | | | % 149.90/21.81 | | | (106) all_54_10 = e3 % 149.90/21.81 | | | % 149.90/21.81 | | | REF_CLOSE: (8), (17), (106) are inconsistent by sub-proof #736. % 149.90/21.81 | | | % 149.90/21.81 | | Case 2: % 149.90/21.81 | | | % 149.90/21.81 | | | (107) ~ (all_54_10 = e3) % 149.90/21.81 | | | (108) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 149.90/21.81 | | | % 149.90/21.81 | | | BETA: splitting (108) gives: % 149.90/21.81 | | | % 149.90/21.81 | | | Case 1: % 149.90/21.81 | | | | % 149.90/21.81 | | | | (109) all_54_10 = e2 % 149.90/21.81 | | | | % 149.90/21.81 | | | | REF_CLOSE: (8), (72), (109) are inconsistent by sub-proof #735. % 149.90/21.81 | | | | % 149.90/21.81 | | | Case 2: % 149.90/21.81 | | | | % 149.90/21.81 | | | | (110) all_54_10 = e1 | all_54_10 = e0 % 149.90/21.81 | | | | % 149.90/21.81 | | | | BETA: splitting (110) gives: % 149.90/21.81 | | | | % 149.90/21.81 | | | | Case 1: % 149.90/21.81 | | | | | % 149.90/21.81 | | | | | (111) all_54_10 = e1 % 149.90/21.81 | | | | | % 149.90/21.81 | | | | | COMBINE_EQS: (8), (111) imply: % 149.90/21.81 | | | | | (112) all_6_2 = e1 % 149.90/21.81 | | | | | % 149.90/21.81 | | | | | SIMP: (112) implies: % 149.90/21.81 | | | | | (113) all_6_2 = e1 % 149.90/21.81 | | | | | % 149.90/21.81 | | | | | REDUCE: (44), (113) imply: % 149.90/21.81 | | | | | (114) ~ (all_52_8 = e1) % 149.90/21.81 | | | | | % 149.90/21.81 | | | | | REDUCE: (74), (113) imply: % 149.90/21.81 | | | | | (115) ~ (all_52_9 = e1) % 149.90/21.81 | | | | | % 149.90/21.81 | | | | | REDUCE: (2), (113) imply: % 149.90/21.81 | | | | | (116) ~ (all_52_11 = e1) % 149.90/21.81 | | | | | % 149.90/21.81 | | | | | REDUCE: (85), (113) imply: % 149.90/21.81 | | | | | (117) ~ (all_52_14 = e1) % 149.90/21.81 | | | | | % 149.90/21.81 | | | | | REDUCE: (17), (113) imply: % 149.90/21.81 | | | | | (118) ~ (e3 = e1) % 149.90/21.81 | | | | | % 149.90/21.81 | | | | | SIMP: (118) implies: % 149.90/21.81 | | | | | (119) ~ (e3 = e1) % 149.90/21.81 | | | | | % 149.90/21.81 | | | | | REDUCE: (105), (113) imply: % 149.90/21.81 | | | | | (120) ~ (e1 = e0) % 149.90/21.81 | | | | | % 149.90/21.81 | | | | | BETA: splitting (7) gives: % 149.90/21.81 | | | | | % 149.90/21.81 | | | | | Case 1: % 149.90/21.81 | | | | | | % 149.90/21.81 | | | | | | (121) all_54_14 = e3 % 149.90/21.81 | | | | | | % 149.90/21.81 | | | | | | REF_CLOSE: (39), (49), (121) are inconsistent by sub-proof #729. % 149.90/21.81 | | | | | | % 149.90/21.81 | | | | | Case 2: % 149.90/21.81 | | | | | | % 149.90/21.81 | | | | | | (122) all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0 % 149.90/21.81 | | | | | | % 149.90/21.81 | | | | | | BETA: splitting (78) gives: % 149.90/21.81 | | | | | | % 149.90/21.81 | | | | | | Case 1: % 149.90/21.81 | | | | | | | % 149.90/21.81 | | | | | | | (123) all_58_12 = e1 % 149.90/21.81 | | | | | | | % 149.90/21.81 | | | | | | | COMBINE_EQS: (35), (123) imply: % 149.90/21.81 | | | | | | | (124) e1 = e0 % 149.90/21.81 | | | | | | | % 149.90/21.81 | | | | | | | REDUCE: (120), (124) imply: % 149.90/21.81 | | | | | | | (125) $false % 149.90/21.81 | | | | | | | % 149.90/21.81 | | | | | | | CLOSE: (125) is inconsistent. % 149.90/21.81 | | | | | | | % 149.90/21.81 | | | | | | Case 2: % 149.90/21.81 | | | | | | | % 149.90/21.81 | | | | | | | (126) all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1 % 149.90/21.81 | | | | | | | % 149.90/21.81 | | | | | | | BETA: splitting (126) gives: % 149.90/21.81 | | | | | | | % 149.90/21.81 | | | | | | | Case 1: % 149.90/21.81 | | | | | | | | % 149.90/21.81 | | | | | | | | (127) all_58_13 = e1 % 149.90/21.81 | | | | | | | | % 149.90/21.81 | | | | | | | | COMBINE_EQS: (41), (127) imply: % 149.90/21.81 | | | | | | | | (128) all_52_7 = e1 % 149.90/21.81 | | | | | | | | % 149.90/21.81 | | | | | | | | SIMP: (128) implies: % 149.90/21.81 | | | | | | | | (129) all_52_7 = e1 % 149.90/21.81 | | | | | | | | % 149.90/21.81 | | | | | | | | REDUCE: (16), (129) imply: % 149.90/21.81 | | | | | | | | (130) ~ (all_52_4 = e1) % 149.90/21.81 | | | | | | | | % 149.90/21.81 | | | | | | | | REDUCE: (4), (129) imply: % 149.90/21.81 | | | | | | | | (131) ~ (all_52_11 = e1) % 149.90/21.81 | | | | | | | | % 149.90/21.81 | | | | | | | | REDUCE: (29), (129) imply: % 149.90/21.81 | | | | | | | | (132) ~ (all_8_2 = e1) % 149.90/21.81 | | | | | | | | % 149.90/21.81 | | | | | | | | SIMP: (132) implies: % 149.90/21.81 | | | | | | | | (133) ~ (all_8_2 = e1) % 149.90/21.81 | | | | | | | | % 149.90/21.81 | | | | | | | | REDUCE: (37), (129) imply: % 149.90/21.81 | | | | | | | | (134) op(e0, e2) = e1 % 149.90/21.81 | | | | | | | | % 149.90/21.81 | | | | | | | | BETA: splitting (122) gives: % 149.90/21.81 | | | | | | | | % 149.90/21.81 | | | | | | | | Case 1: % 149.90/21.81 | | | | | | | | | % 149.90/21.81 | | | | | | | | | (135) all_54_14 = e2 % 149.90/21.81 | | | | | | | | | % 149.90/21.81 | | | | | | | | | COMBINE_EQS: (39), (135) imply: % 149.90/21.81 | | | | | | | | | (136) all_52_11 = e2 % 149.90/21.81 | | | | | | | | | % 149.90/21.81 | | | | | | | | | SIMP: (136) implies: % 149.90/21.81 | | | | | | | | | (137) all_52_11 = e2 % 149.90/21.81 | | | | | | | | | % 149.90/21.81 | | | | | | | | | REDUCE: (66), (137) imply: % 149.90/21.81 | | | | | | | | | (138) ~ (all_52_8 = e2) % 149.90/21.81 | | | | | | | | | % 149.90/21.81 | | | | | | | | | REDUCE: (63), (137) imply: % 149.90/21.81 | | | | | | | | | (139) ~ (all_52_9 = e2) % 149.90/21.81 | | | | | | | | | % 149.90/21.81 | | | | | | | | | REDUCE: (50), (137) imply: % 149.90/21.81 | | | | | | | | | (140) op(e0, e1) = e2 % 149.90/21.81 | | | | | | | | | % 149.90/21.81 | | | | | | | | | BETA: splitting (56) gives: % 149.90/21.81 | | | | | | | | | % 149.90/21.81 | | | | | | | | | Case 1: % 149.90/21.81 | | | | | | | | | | % 149.90/21.81 | | | | | | | | | | (141) ~ (all_56_1 = e2) % 149.90/21.81 | | | | | | | | | | % 149.90/21.81 | | | | | | | | | | REDUCE: (97), (141) imply: % 149.90/21.81 | | | | | | | | | | (142) ~ (all_4_1 = e2) % 149.90/21.81 | | | | | | | | | | % 149.90/21.81 | | | | | | | | | | BETA: splitting (38) gives: % 149.90/21.81 | | | | | | | | | | % 149.90/21.81 | | | | | | | | | | Case 1: % 149.90/21.81 | | | | | | | | | | | % 149.90/21.81 | | | | | | | | | | | (143) ~ (all_56_1 = e1) % 149.90/21.81 | | | | | | | | | | | % 149.90/21.81 | | | | | | | | | | | REDUCE: (97), (143) imply: % 149.90/21.81 | | | | | | | | | | | (144) ~ (all_4_1 = e1) % 149.90/21.81 | | | | | | | | | | | % 149.90/21.81 | | | | | | | | | | | BETA: splitting (23) gives: % 149.90/21.81 | | | | | | | | | | | % 149.90/21.81 | | | | | | | | | | | Case 1: % 149.90/21.81 | | | | | | | | | | | | % 149.90/21.81 | | | | | | | | | | | | (145) all_54_0 = e3 % 149.90/21.81 | | | | | | | | | | | | % 149.90/21.81 | | | | | | | | | | | | COMBINE_EQS: (96), (145) imply: % 149.90/21.81 | | | | | | | | | | | | (146) all_4_1 = e3 % 149.90/21.81 | | | | | | | | | | | | % 149.90/21.81 | | | | | | | | | | | | SIMP: (146) implies: % 149.90/21.81 | | | | | | | | | | | | (147) all_4_1 = e3 % 149.90/21.81 | | | | | | | | | | | | % 149.90/21.81 | | | | | | | | | | | | REDUCE: (101), (147) imply: % 149.90/21.81 | | | | | | | | | | | | (148) ~ (all_52_8 = e3) % 149.90/21.81 | | | | | | | | | | | | % 149.90/21.81 | | | | | | | | | | | | BETA: splitting (45) gives: % 149.90/21.81 | | | | | | | | | | | | % 149.90/21.81 | | | | | | | | | | | | Case 1: % 149.90/21.81 | | | | | | | | | | | | | % 149.90/21.81 | | | | | | | | | | | | | (149) all_54_2 = e3 % 149.90/21.81 | | | | | | | | | | | | | % 149.90/21.81 | | | | | | | | | | | | | COMBINE_EQS: (67), (149) imply: % 149.90/21.81 | | | | | | | | | | | | | (150) all_52_8 = e3 % 149.90/21.81 | | | | | | | | | | | | | % 149.90/21.81 | | | | | | | | | | | | | REDUCE: (148), (150) imply: % 149.90/21.81 | | | | | | | | | | | | | (151) $false % 149.90/21.81 | | | | | | | | | | | | | % 149.90/21.81 | | | | | | | | | | | | | CLOSE: (151) is inconsistent. % 149.90/21.81 | | | | | | | | | | | | | % 149.90/21.81 | | | | | | | | | | | | Case 2: % 149.90/21.81 | | | | | | | | | | | | | % 149.90/21.81 | | | | | | | | | | | | | (152) all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0 % 149.90/21.81 | | | | | | | | | | | | | % 149.90/21.81 | | | | | | | | | | | | | BETA: splitting (152) gives: % 149.90/21.81 | | | | | | | | | | | | | % 149.90/21.81 | | | | | | | | | | | | | Case 1: % 149.90/21.81 | | | | | | | | | | | | | | % 149.90/21.81 | | | | | | | | | | | | | | (153) all_54_2 = e2 % 149.90/21.81 | | | | | | | | | | | | | | % 149.90/21.81 | | | | | | | | | | | | | | COMBINE_EQS: (67), (153) imply: % 149.90/21.81 | | | | | | | | | | | | | | (154) all_52_8 = e2 % 149.90/21.81 | | | | | | | | | | | | | | % 149.90/21.81 | | | | | | | | | | | | | | REDUCE: (138), (154) imply: % 149.90/21.81 | | | | | | | | | | | | | | (155) $false % 149.90/21.81 | | | | | | | | | | | | | | % 149.90/21.81 | | | | | | | | | | | | | | CLOSE: (155) is inconsistent. % 149.90/21.81 | | | | | | | | | | | | | | % 149.90/21.81 | | | | | | | | | | | | | Case 2: % 149.90/21.81 | | | | | | | | | | | | | | % 149.90/21.81 | | | | | | | | | | | | | | (156) ~ (all_54_2 = e2) % 149.90/21.81 | | | | | | | | | | | | | | (157) all_54_2 = e1 | all_54_2 = e0 % 149.90/21.81 | | | | | | | | | | | | | | % 149.90/21.81 | | | | | | | | | | | | | | BETA: splitting (157) gives: % 149.90/21.81 | | | | | | | | | | | | | | % 149.90/21.81 | | | | | | | | | | | | | | Case 1: % 149.90/21.81 | | | | | | | | | | | | | | | % 149.90/21.81 | | | | | | | | | | | | | | | (158) all_54_2 = e1 % 149.90/21.81 | | | | | | | | | | | | | | | % 149.90/21.81 | | | | | | | | | | | | | | | COMBINE_EQS: (67), (158) imply: % 149.90/21.81 | | | | | | | | | | | | | | | (159) all_52_8 = e1 % 149.90/21.81 | | | | | | | | | | | | | | | % 149.90/21.81 | | | | | | | | | | | | | | | REDUCE: (114), (159) imply: % 149.90/21.81 | | | | | | | | | | | | | | | (160) $false % 149.90/21.81 | | | | | | | | | | | | | | | % 149.90/21.81 | | | | | | | | | | | | | | | CLOSE: (160) is inconsistent. % 149.90/21.81 | | | | | | | | | | | | | | | % 149.90/21.81 | | | | | | | | | | | | | | Case 2: % 149.90/21.81 | | | | | | | | | | | | | | | % 149.90/21.81 | | | | | | | | | | | | | | | (161) all_54_2 = e0 % 149.90/21.81 | | | | | | | | | | | | | | | % 149.90/21.81 | | | | | | | | | | | | | | | COMBINE_EQS: (67), (161) imply: % 149.90/21.81 | | | | | | | | | | | | | | | (162) all_52_8 = e0 % 149.90/21.81 | | | | | | | | | | | | | | | % 149.90/21.81 | | | | | | | | | | | | | | | REDUCE: (5), (162) imply: % 149.90/21.81 | | | | | | | | | | | | | | | (163) ~ (all_52_9 = e0) % 149.90/21.81 | | | | | | | | | | | | | | | % 149.90/21.81 | | | | | | | | | | | | | | | SIMP: (163) implies: % 149.90/21.81 | | | | | | | | | | | | | | | (164) ~ (all_52_9 = e0) % 149.90/21.81 | | | | | | | | | | | | | | | % 149.90/21.81 | | | | | | | | | | | | | | | BETA: splitting (31) gives: % 149.90/21.81 | | | | | | | | | | | | | | | % 149.90/21.81 | | | | | | | | | | | | | | | Case 1: % 149.90/21.81 | | | | | | | | | | | | | | | | % 149.90/21.81 | | | | | | | | | | | | | | | | (165) all_54_6 = e3 % 149.90/21.81 | | | | | | | | | | | | | | | | % 149.90/21.81 | | | | | | | | | | | | | | | | COMBINE_EQS: (54), (165) imply: % 149.90/21.81 | | | | | | | | | | | | | | | | (166) all_52_9 = e3 % 149.90/21.81 | | | | | | | | | | | | | | | | % 149.90/21.81 | | | | | | | | | | | | | | | | REDUCE: (15), (166) imply: % 149.90/21.81 | | | | | | | | | | | | | | | | (167) ~ (all_8_2 = e3) % 149.90/21.81 | | | | | | | | | | | | | | | | % 149.90/21.81 | | | | | | | | | | | | | | | | SIMP: (167) implies: % 149.90/21.81 | | | | | | | | | | | | | | | | (168) ~ (all_8_2 = e3) % 149.90/21.81 | | | | | | | | | | | | | | | | % 149.90/21.81 | | | | | | | | | | | | | | | | REF_CLOSE: (1), (3), (6), (10), (14), (19), (20), (23), (24), % 149.90/21.81 | | | | | | | | | | | | | | | | (32), (33), (34), (38), (40), (42), (45), (46), % 149.90/21.81 | | | | | | | | | | | | | | | | (47), (48), (53), (58), (60), (67), (70), (73), % 149.90/21.81 | | | | | | | | | | | | | | | | (76), (80), (81), (84), (88), (89), (90), (96), % 149.90/21.81 | | | | | | | | | | | | | | | | (97), (98), (99), (100), (102), (103), (105), % 149.90/21.81 | | | | | | | | | | | | | | | | (114), (115), (130), (133), (138), (140), (142), % 149.90/21.81 | | | | | | | | | | | | | | | | (168) are inconsistent by sub-proof #25. % 149.90/21.81 | | | | | | | | | | | | | | | | % 149.90/21.81 | | | | | | | | | | | | | | | Case 2: % 149.90/21.81 | | | | | | | | | | | | | | | | % 149.90/21.81 | | | | | | | | | | | | | | | | (169) all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0 % 149.90/21.81 | | | | | | | | | | | | | | | | % 149.90/21.81 | | | | | | | | | | | | | | | | REF_CLOSE: (54), (115), (139), (164), (169) are inconsistent % 149.90/21.81 | | | | | | | | | | | | | | | | by sub-proof #608. % 149.90/21.81 | | | | | | | | | | | | | | | | % 149.90/21.81 | | | | | | | | | | | | | | | End of split % 149.90/21.81 | | | | | | | | | | | | | | | % 149.90/21.81 | | | | | | | | | | | | | | End of split % 149.90/21.81 | | | | | | | | | | | | | | % 149.90/21.81 | | | | | | | | | | | | | End of split % 149.90/21.81 | | | | | | | | | | | | | % 149.90/21.81 | | | | | | | | | | | | End of split % 149.90/21.81 | | | | | | | | | | | | % 149.90/21.81 | | | | | | | | | | | Case 2: % 149.90/21.81 | | | | | | | | | | | | % 149.90/21.81 | | | | | | | | | | | | (170) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 149.90/21.81 | | | | | | | | | | | | % 149.90/21.81 | | | | | | | | | | | | REF_CLOSE: (96), (103), (142), (144), (170) are inconsistent % 149.90/21.81 | | | | | | | | | | | | by sub-proof #549. % 149.90/21.81 | | | | | | | | | | | | % 149.90/21.81 | | | | | | | | | | | End of split % 149.90/21.81 | | | | | | | | | | | % 149.90/21.81 | | | | | | | | | | Case 2: % 149.90/21.81 | | | | | | | | | | | % 149.90/21.81 | | | | | | | | | | | (171) all_56_5 = e3 % 149.90/21.81 | | | | | | | | | | | (172) all_56_1 = e1 % 149.90/21.81 | | | | | | | | | | | % 149.90/21.81 | | | | | | | | | | | COMBINE_EQS: (97), (172) imply: % 149.90/21.81 | | | | | | | | | | | (173) all_4_1 = e1 % 149.90/21.81 | | | | | | | | | | | % 149.90/21.81 | | | | | | | | | | | COMBINE_EQS: (58), (171) imply: % 149.90/21.81 | | | | | | | | | | | (174) all_52_8 = e3 % 149.90/21.81 | | | | | | | | | | | % 149.90/21.81 | | | | | | | | | | | SIMP: (174) implies: % 149.90/21.81 | | | | | | | | | | | (175) all_52_8 = e3 % 149.90/21.81 | | | | | | | | | | | % 149.90/21.81 | | | | | | | | | | | REDUCE: (138), (175) imply: % 149.90/21.81 | | | | | | | | | | | (176) ~ (e3 = e2) % 149.90/21.81 | | | | | | | | | | | % 149.90/21.81 | | | | | | | | | | | REDUCE: (102), (173) imply: % 149.90/21.81 | | | | | | | | | | | (177) ~ (all_52_12 = e1) % 149.90/21.81 | | | | | | | | | | | % 149.90/21.81 | | | | | | | | | | | REDUCE: (10), (173) imply: % 149.90/21.81 | | | | | | | | | | | (178) op(e0, e1) = e3 % 149.90/21.81 | | | | | | | | | | | % 149.90/21.81 | | | | | | | | | | | BETA: splitting (26) gives: % 149.90/21.81 | | | | | | | | | | | % 149.90/21.81 | | | | | | | | | | | Case 1: % 149.90/21.81 | | | | | | | | | | | | % 149.90/21.81 | | | | | | | | | | | | (179) all_58_9 = e1 % 149.90/21.81 | | | | | | | | | | | | % 149.90/21.81 | | | | | | | | | | | | COMBINE_EQS: (34), (179) imply: % 149.90/21.81 | | | | | | | | | | | | (180) all_52_12 = e1 % 149.90/21.81 | | | | | | | | | | | | % 149.90/21.81 | | | | | | | | | | | | REDUCE: (177), (180) imply: % 149.90/21.81 | | | | | | | | | | | | (181) $false % 149.90/21.81 | | | | | | | | | | | | % 149.90/21.81 | | | | | | | | | | | | CLOSE: (181) is inconsistent. % 149.90/21.81 | | | | | | | | | | | | % 149.90/21.81 | | | | | | | | | | | Case 2: % 149.90/21.81 | | | | | | | | | | | | % 149.90/21.81 | | | | | | | | | | | | (182) all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1 % 149.90/21.81 | | | | | | | | | | | | % 149.90/21.81 | | | | | | | | | | | | REF_CLOSE: (1), (48), (52), (62), (71), (76), (117), (140), % 149.90/21.81 | | | | | | | | | | | | (176), (178), (182) are inconsistent by sub-proof % 149.90/21.81 | | | | | | | | | | | | #196. % 149.90/21.81 | | | | | | | | | | | | % 149.90/21.81 | | | | | | | | | | | End of split % 149.90/21.81 | | | | | | | | | | | % 149.90/21.81 | | | | | | | | | | End of split % 149.90/21.81 | | | | | | | | | | % 149.90/21.81 | | | | | | | | | Case 2: % 149.90/21.81 | | | | | | | | | | % 149.90/21.81 | | | | | | | | | | (183) all_56_3 = e3 % 149.90/21.81 | | | | | | | | | | (184) all_56_1 = e2 % 149.90/21.81 | | | | | | | | | | % 149.90/21.81 | | | | | | | | | | COMBINE_EQS: (97), (184) imply: % 149.90/21.81 | | | | | | | | | | (185) all_4_1 = e2 % 149.90/21.81 | | | | | | | | | | % 149.90/21.81 | | | | | | | | | | COMBINE_EQS: (61), (183) imply: % 149.90/21.81 | | | | | | | | | | (186) all_52_4 = e3 % 149.90/21.81 | | | | | | | | | | % 149.90/21.81 | | | | | | | | | | SIMP: (186) implies: % 149.90/21.81 | | | | | | | | | | (187) all_52_4 = e3 % 149.90/21.81 | | | | | | | | | | % 149.90/21.81 | | | | | | | | | | COMBINE_EQS: (40), (187) imply: % 149.90/21.81 | | | | | | | | | | (188) all_58_1 = e3 % 149.90/21.81 | | | | | | | | | | % 149.90/21.81 | | | | | | | | | | REDUCE: (88), (187) imply: % 149.90/21.81 | | | | | | | | | | (189) ~ (all_8_2 = e3) % 149.90/21.81 | | | | | | | | | | % 149.90/21.81 | | | | | | | | | | SIMP: (189) implies: % 149.90/21.81 | | | | | | | | | | (190) ~ (all_8_2 = e3) % 149.90/21.81 | | | | | | | | | | % 149.90/21.81 | | | | | | | | | | REDUCE: (10), (185) imply: % 149.90/21.81 | | | | | | | | | | (191) op(e0, e2) = e3 % 149.90/21.81 | | | | | | | | | | % 149.90/21.81 | | | | | | | | | | REF_CLOSE: (6), (13), (20), (22), (36), (48), (51), (60), % 149.90/21.81 | | | | | | | | | | (75), (79), (84), (89), (94), (117), (119), (120), % 149.90/21.81 | | | | | | | | | | (127), (133), (134), (188), (190), (191) are % 149.90/21.81 | | | | | | | | | | inconsistent by sub-proof #24. % 149.90/21.81 | | | | | | | | | | % 149.90/21.81 | | | | | | | | | End of split % 149.90/21.81 | | | | | | | | | % 149.90/21.81 | | | | | | | | Case 2: % 149.90/21.81 | | | | | | | | | % 149.90/21.81 | | | | | | | | | (192) all_54_14 = e1 | all_54_14 = e0 % 149.90/21.81 | | | | | | | | | % 149.90/21.81 | | | | | | | | | REF_CLOSE: (24), (39), (116), (192) are inconsistent by % 149.90/21.81 | | | | | | | | | sub-proof #714. % 149.90/21.81 | | | | | | | | | % 149.90/21.81 | | | | | | | | End of split % 149.90/21.81 | | | | | | | | % 149.90/21.81 | | | | | | | Case 2: % 149.90/21.81 | | | | | | | | % 149.90/21.81 | | | | | | | | (193) all_58_14 = e1 | all_58_15 = e1 % 149.90/21.81 | | | | | | | | % 149.90/21.81 | | | | | | | | REF_CLOSE: (57), (90), (116), (119), (193) are inconsistent by % 149.90/21.81 | | | | | | | | sub-proof #226. % 149.90/21.81 | | | | | | | | % 149.90/21.81 | | | | | | | End of split % 149.90/21.81 | | | | | | | % 149.90/21.81 | | | | | | End of split % 149.90/21.81 | | | | | | % 149.90/21.81 | | | | | End of split % 149.90/21.81 | | | | | % 149.90/21.81 | | | | Case 2: % 149.90/21.81 | | | | | % 149.90/21.81 | | | | | (194) all_54_10 = e0 % 149.90/21.81 | | | | | % 149.90/21.81 | | | | | REF_CLOSE: (8), (105), (194) are inconsistent by sub-proof #705. % 149.90/21.81 | | | | | % 149.90/21.81 | | | | End of split % 149.90/21.81 | | | | % 149.90/21.81 | | | End of split % 149.90/21.81 | | | % 149.90/21.81 | | End of split % 149.90/21.81 | | % 149.90/21.81 | Case 2: % 149.90/21.81 | | % 149.90/21.81 | | (195) all_56_21 = e0 % 149.90/21.81 | | % 149.90/21.81 | | COMBINE_EQS: (27), (195) imply: % 149.90/21.81 | | (196) all_6_2 = e0 % 149.90/21.81 | | % 149.90/21.81 | | SIMP: (196) implies: % 149.90/21.81 | | (197) all_6_2 = e0 % 149.90/21.81 | | % 149.90/21.81 | | REDUCE: (64), (197) imply: % 149.90/21.81 | | (198) op(e0, e0) = all_6_1 % 149.90/21.81 | | % 149.90/21.81 | | REF_CLOSE: (9), (10), (12), (18), (21), (25), (48), (59), (65), (68), (82), % 149.90/21.81 | | (83), (195), (198) are inconsistent by sub-proof #22. % 149.90/21.81 | | % 149.90/21.81 | End of split % 149.90/21.81 | % 149.90/21.81 End of proof % 149.90/21.81 % 149.90/21.81 Sub-proof #22 shows that the following formulas are inconsistent: % 149.90/21.81 ---------------------------------------------------------------- % 149.90/21.81 (1) ~ (all_6_1 = e2) % 149.90/21.81 (2) op(e0, all_4_1) = e3 % 149.90/21.81 (3) ~ (all_52_14 = all_4_2) % 149.90/21.81 (4) op(e0, e0) = all_4_2 % 149.90/21.81 (5) ~ (all_6_1 = e3) % 149.90/21.81 (6) all_54_15 = all_4_2 % 149.90/21.81 (7) all_56_21 = e0 % 149.90/21.81 (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 149.90/21.81 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 149.90/21.81 (9) op(all_4_2, all_4_2) = all_4_1 % 149.90/21.81 (10) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0 % 149.90/21.81 (11) all_56_23 = all_52_14 % 149.90/21.81 (12) op(e0, e0) = all_6_1 % 149.90/21.81 (13) ~ (all_56_21 = e0) | all_56_23 = e1 % 149.90/21.81 (14) op(e0, all_4_2) = all_56_30 % 149.90/21.81 % 149.90/21.81 Begin of proof % 149.90/21.81 | % 149.90/21.81 | BETA: splitting (13) gives: % 149.90/21.81 | % 149.90/21.81 | Case 1: % 149.90/21.81 | | % 149.90/21.81 | | (15) ~ (all_56_21 = e0) % 149.90/21.81 | | % 149.90/21.81 | | REDUCE: (7), (15) imply: % 149.90/21.81 | | (16) $false % 149.90/21.81 | | % 149.90/21.82 | | CLOSE: (16) is inconsistent. % 149.90/21.82 | | % 149.90/21.82 | Case 2: % 149.90/21.82 | | % 149.90/21.82 | | (17) all_56_23 = e1 % 149.90/21.82 | | % 149.90/21.82 | | COMBINE_EQS: (11), (17) imply: % 149.90/21.82 | | (18) all_52_14 = e1 % 149.90/21.82 | | % 149.90/21.82 | | SIMP: (18) implies: % 149.90/21.82 | | (19) all_52_14 = e1 % 149.90/21.82 | | % 149.90/21.82 | | REDUCE: (3), (19) imply: % 149.90/21.82 | | (20) ~ (all_4_2 = e1) % 149.90/21.82 | | % 149.90/21.82 | | SIMP: (20) implies: % 149.90/21.82 | | (21) ~ (all_4_2 = e1) % 149.90/21.82 | | % 149.90/21.82 | | REF_CLOSE: (1), (2), (4), (5), (6), (8), (9), (10), (12), (14), (21) are % 149.90/21.82 | | inconsistent by sub-proof #23. % 149.90/21.82 | | % 149.90/21.82 | End of split % 149.90/21.82 | % 149.90/21.82 End of proof % 149.90/21.82 % 149.90/21.82 Sub-proof #23 shows that the following formulas are inconsistent: % 149.90/21.82 ---------------------------------------------------------------- % 149.90/21.82 (1) ~ (all_6_1 = e2) % 149.90/21.82 (2) op(e0, all_4_1) = e3 % 149.90/21.82 (3) op(e0, e0) = all_4_2 % 149.90/21.82 (4) ~ (all_6_1 = e3) % 149.90/21.82 (5) all_54_15 = all_4_2 % 149.90/21.82 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 149.90/21.82 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 149.90/21.82 (7) ~ (all_4_2 = e1) % 149.90/21.82 (8) op(all_4_2, all_4_2) = all_4_1 % 149.90/21.82 (9) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0 % 149.90/21.82 (10) op(e0, e0) = all_6_1 % 149.90/21.82 (11) op(e0, all_4_2) = all_56_30 % 149.90/21.82 % 149.90/21.82 Begin of proof % 149.90/21.82 | % 149.90/21.82 | GROUND_INST: instantiating (6) with all_4_2, all_6_1, e0, e0, simplifying with % 149.90/21.82 | (3), (10) gives: % 149.90/21.82 | (12) all_6_1 = all_4_2 % 149.90/21.82 | % 149.90/21.82 | REDUCE: (4), (12) imply: % 149.90/21.82 | (13) ~ (all_4_2 = e3) % 149.90/21.82 | % 149.90/21.82 | REDUCE: (1), (12) imply: % 149.90/21.82 | (14) ~ (all_4_2 = e2) % 149.90/21.82 | % 149.90/21.82 | REF_CLOSE: (2), (3), (5), (6), (7), (8), (9), (11), (13), (14) are % 149.90/21.82 | inconsistent by sub-proof #29. % 149.90/21.82 | % 149.90/21.82 End of proof % 149.90/21.82 % 149.90/21.82 Sub-proof #24 shows that the following formulas are inconsistent: % 149.90/21.82 ---------------------------------------------------------------- % 149.90/21.82 (1) ~ (e3 = e0) % 149.90/21.82 (2) ~ (all_8_2 = e1) % 149.90/21.82 (3) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0 % 149.90/21.82 (4) op(e0, e2) = e1 % 149.90/21.82 (5) all_54_5 = all_8_2 % 149.90/21.82 (6) ~ (all_52_6 = all_52_14) % 149.90/21.82 (7) op(e0, all_52_14) = all_56_22 % 149.90/21.82 (8) ~ (e1 = e0) % 149.90/21.82 (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 149.90/21.82 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 149.90/21.82 (10) ~ (all_52_14 = e1) % 149.90/21.82 (11) ~ (all_52_14 = e3) % 149.90/21.82 (12) ~ (all_8_2 = e3) % 149.90/21.82 (13) all_58_3 = all_8_2 % 149.90/21.82 (14) all_58_1 = e3 % 149.90/21.82 (15) all_58_7 = all_52_6 % 149.90/21.82 (16) all_58_1 = e0 | all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0 % 149.90/21.82 (17) ~ (e3 = e1) % 149.90/21.82 (18) ~ (all_8_2 = e0) % 149.90/21.82 (19) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 149.90/21.82 (20) all_58_13 = e1 % 149.90/21.82 (21) op(e0, e2) = e3 % 149.90/21.82 (22) all_54_11 = all_52_14 % 149.90/21.82 % 149.90/21.82 Begin of proof % 149.90/21.82 | % 149.90/21.82 | BETA: splitting (19) gives: % 149.90/21.82 | % 149.90/21.82 | Case 1: % 149.90/21.82 | | % 149.90/21.82 | | (23) all_54_5 = e3 % 149.90/21.82 | | % 149.90/21.82 | | REF_CLOSE: (5), (12), (23) are inconsistent by sub-proof #737. % 149.90/21.82 | | % 149.90/21.82 | Case 2: % 149.90/21.82 | | % 149.90/21.82 | | (24) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 149.90/21.82 | | % 149.90/21.82 | | BETA: splitting (16) gives: % 149.90/21.82 | | % 149.90/21.82 | | Case 1: % 149.90/21.82 | | | % 149.90/21.82 | | | (25) all_58_1 = e0 % 149.90/21.82 | | | % 149.90/21.82 | | | COMBINE_EQS: (14), (25) imply: % 149.90/21.82 | | | (26) e3 = e0 % 149.90/21.82 | | | % 149.90/21.82 | | | REDUCE: (1), (26) imply: % 149.90/21.82 | | | (27) $false % 149.90/21.82 | | | % 149.90/21.82 | | | CLOSE: (27) is inconsistent. % 149.90/21.82 | | | % 149.90/21.82 | | Case 2: % 149.90/21.82 | | | % 149.90/21.82 | | | (28) all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0 % 149.90/21.82 | | | % 149.90/21.82 | | | BETA: splitting (24) gives: % 149.90/21.82 | | | % 149.90/21.82 | | | Case 1: % 149.90/21.82 | | | | % 149.90/21.82 | | | | (29) all_54_5 = e2 % 149.90/21.82 | | | | % 149.90/21.82 | | | | COMBINE_EQS: (5), (29) imply: % 149.90/21.82 | | | | (30) all_8_2 = e2 % 149.90/21.82 | | | | % 149.90/21.82 | | | | SIMP: (30) implies: % 149.90/21.82 | | | | (31) all_8_2 = e2 % 149.90/21.82 | | | | % 149.90/21.82 | | | | COMBINE_EQS: (13), (31) imply: % 149.90/21.82 | | | | (32) all_58_3 = e2 % 149.90/21.82 | | | | % 149.90/21.82 | | | | REDUCE: (18), (31) imply: % 149.90/21.82 | | | | (33) ~ (e2 = e0) % 149.90/21.82 | | | | % 149.90/21.82 | | | | BETA: splitting (28) gives: % 149.90/21.82 | | | | % 149.90/21.82 | | | | Case 1: % 149.90/21.82 | | | | | % 149.90/21.82 | | | | | (34) all_58_3 = e0 % 149.90/21.82 | | | | | % 149.90/21.82 | | | | | COMBINE_EQS: (32), (34) imply: % 149.90/21.82 | | | | | (35) e2 = e0 % 149.90/21.82 | | | | | % 149.90/21.82 | | | | | REDUCE: (33), (35) imply: % 149.90/21.82 | | | | | (36) $false % 149.90/21.82 | | | | | % 149.90/21.82 | | | | | CLOSE: (36) is inconsistent. % 149.90/21.82 | | | | | % 149.90/21.82 | | | | Case 2: % 149.90/21.82 | | | | | % 149.90/21.82 | | | | | (37) all_58_7 = e0 | all_58_13 = e0 % 149.90/21.82 | | | | | % 149.90/21.82 | | | | | BETA: splitting (37) gives: % 149.90/21.82 | | | | | % 149.90/21.82 | | | | | Case 1: % 149.90/21.82 | | | | | | % 149.90/21.82 | | | | | | (38) all_58_7 = e0 % 149.90/21.82 | | | | | | % 149.90/21.82 | | | | | | COMBINE_EQS: (15), (38) imply: % 149.90/21.82 | | | | | | (39) all_52_6 = e0 % 149.90/21.82 | | | | | | % 149.90/21.82 | | | | | | REDUCE: (6), (39) imply: % 149.90/21.82 | | | | | | (40) ~ (all_52_14 = e0) % 149.90/21.82 | | | | | | % 149.90/21.82 | | | | | | SIMP: (40) implies: % 149.90/21.82 | | | | | | (41) ~ (all_52_14 = e0) % 149.90/21.82 | | | | | | % 149.90/21.82 | | | | | | BETA: splitting (3) gives: % 149.90/21.82 | | | | | | % 149.90/21.82 | | | | | | Case 1: % 149.90/21.82 | | | | | | | % 149.90/21.82 | | | | | | | (42) all_54_11 = e3 % 149.90/21.82 | | | | | | | % 149.90/21.82 | | | | | | | REF_CLOSE: (11), (22), (42) are inconsistent by sub-proof #416. % 149.90/21.82 | | | | | | | % 149.90/21.82 | | | | | | Case 2: % 149.90/21.82 | | | | | | | % 149.90/21.82 | | | | | | | (43) all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0 % 149.90/21.82 | | | | | | | % 149.90/21.82 | | | | | | | BETA: splitting (43) gives: % 149.90/21.82 | | | | | | | % 149.90/21.82 | | | | | | | Case 1: % 149.90/21.82 | | | | | | | | % 149.90/21.82 | | | | | | | | (44) all_54_11 = e2 % 149.90/21.82 | | | | | | | | % 149.90/21.82 | | | | | | | | COMBINE_EQS: (22), (44) imply: % 149.90/21.82 | | | | | | | | (45) all_52_14 = e2 % 149.90/21.82 | | | | | | | | % 149.90/21.82 | | | | | | | | SIMP: (45) implies: % 149.90/21.82 | | | | | | | | (46) all_52_14 = e2 % 149.90/21.82 | | | | | | | | % 149.90/21.82 | | | | | | | | REDUCE: (7), (46) imply: % 149.90/21.82 | | | | | | | | (47) op(e0, e2) = all_56_22 % 149.90/21.82 | | | | | | | | % 149.90/21.82 | | | | | | | | GROUND_INST: instantiating (9) with e1, all_56_22, e2, e0, % 149.90/21.82 | | | | | | | | simplifying with (4), (47) gives: % 149.90/21.82 | | | | | | | | (48) all_56_22 = e1 % 149.90/21.82 | | | | | | | | % 149.90/21.82 | | | | | | | | GROUND_INST: instantiating (9) with e3, all_56_22, e2, e0, % 149.90/21.82 | | | | | | | | simplifying with (21), (47) gives: % 149.90/21.82 | | | | | | | | (49) all_56_22 = e3 % 149.90/21.82 | | | | | | | | % 149.90/21.82 | | | | | | | | COMBINE_EQS: (48), (49) imply: % 149.90/21.82 | | | | | | | | (50) e3 = e1 % 149.90/21.82 | | | | | | | | % 149.90/21.82 | | | | | | | | SIMP: (50) implies: % 149.90/21.82 | | | | | | | | (51) e3 = e1 % 149.90/21.82 | | | | | | | | % 149.90/21.82 | | | | | | | | REDUCE: (17), (51) imply: % 149.90/21.82 | | | | | | | | (52) $false % 149.90/21.82 | | | | | | | | % 149.90/21.82 | | | | | | | | CLOSE: (52) is inconsistent. % 149.90/21.82 | | | | | | | | % 149.90/21.82 | | | | | | | Case 2: % 149.90/21.82 | | | | | | | | % 149.90/21.82 | | | | | | | | (53) all_54_11 = e1 | all_54_11 = e0 % 149.90/21.82 | | | | | | | | % 149.90/21.82 | | | | | | | | REF_CLOSE: (10), (22), (41), (53) are inconsistent by sub-proof % 149.90/21.82 | | | | | | | | #688. % 149.90/21.82 | | | | | | | | % 149.90/21.82 | | | | | | | End of split % 149.90/21.82 | | | | | | | % 149.90/21.82 | | | | | | End of split % 149.90/21.82 | | | | | | % 149.90/21.82 | | | | | Case 2: % 149.90/21.82 | | | | | | % 149.90/21.82 | | | | | | (54) all_58_13 = e0 % 149.90/21.82 | | | | | | % 149.90/21.82 | | | | | | COMBINE_EQS: (20), (54) imply: % 149.90/21.82 | | | | | | (55) e1 = e0 % 149.90/21.82 | | | | | | % 149.90/21.82 | | | | | | REDUCE: (8), (55) imply: % 149.90/21.82 | | | | | | (56) $false % 149.90/21.82 | | | | | | % 149.90/21.82 | | | | | | CLOSE: (56) is inconsistent. % 149.90/21.82 | | | | | | % 149.90/21.82 | | | | | End of split % 149.90/21.82 | | | | | % 149.90/21.82 | | | | End of split % 149.90/21.82 | | | | % 149.90/21.82 | | | Case 2: % 149.90/21.82 | | | | % 149.90/21.82 | | | | (57) all_54_5 = e1 | all_54_5 = e0 % 149.90/21.82 | | | | % 149.90/21.82 | | | | REF_CLOSE: (2), (5), (18), (57) are inconsistent by sub-proof #645. % 149.90/21.82 | | | | % 149.90/21.82 | | | End of split % 149.90/21.82 | | | % 149.90/21.82 | | End of split % 149.90/21.82 | | % 149.90/21.82 | End of split % 149.90/21.82 | % 149.90/21.82 End of proof % 149.90/21.82 % 149.90/21.82 Sub-proof #25 shows that the following formulas are inconsistent: % 149.90/21.82 ---------------------------------------------------------------- % 149.90/21.82 (1) op(e0, all_52_13) = all_56_14 % 149.90/21.82 (2) ~ (all_52_4 = all_52_8) % 149.90/21.82 (3) ~ (e3 = e0) % 149.90/21.82 (4) ~ (all_4_1 = e0) % 149.90/21.82 (5) ~ (all_52_8 = e2) % 149.90/21.82 (6) op(e0, all_4_1) = e3 % 149.90/21.82 (7) ~ (all_8_2 = e1) % 149.90/21.82 (8) all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2 % 149.90/21.82 (9) all_58_4 = all_52_8 % 149.90/21.82 (10) all_54_5 = all_8_2 % 149.90/21.82 (11) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 149.90/21.82 (12) ~ (all_52_4 = all_4_1) % 149.90/21.82 (13) ~ (all_52_11 = e0) % 149.90/21.82 (14) ~ (all_4_1 = e2) % 149.90/21.82 (15) all_58_5 = all_52_9 % 149.90/21.82 (16) all_54_1 = all_52_4 % 149.90/21.82 (17) all_58_9 = all_52_12 % 149.90/21.82 (18) all_56_1 = all_4_1 % 149.90/21.82 (19) op(e0, e1) = e2 % 149.90/21.82 (20) ~ (all_52_4 = e1) % 149.90/21.82 (21) ~ (all_52_1 = all_4_1) % 149.90/21.82 (22) ~ (all_56_1 = e1) | all_56_5 = e3 % 149.90/21.82 (23) all_58_1 = all_52_4 % 149.90/21.82 (24) all_54_0 = all_4_1 % 149.90/21.82 (25) all_58_4 = e0 | all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0 % 149.90/21.82 (26) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0 % 149.90/21.82 (27) all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1 % 149.90/21.82 (28) all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1 % 149.90/21.82 (29) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 149.90/21.82 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 149.90/21.82 (30) ~ (all_6_2 = e0) % 149.90/21.82 (31) all_58_8 = all_6_2 % 149.90/21.82 (32) all_58_0 = all_4_1 % 149.90/21.82 (33) ~ (all_52_12 = all_4_1) % 149.90/21.82 (34) ~ (all_8_2 = e3) % 149.90/21.82 (35) all_56_5 = all_52_8 % 149.90/21.82 (36) all_58_3 = all_8_2 % 149.90/21.82 (37) ~ (all_52_8 = e1) % 149.90/21.82 (38) ~ (all_52_9 = e1) % 149.90/21.82 (39) all_54_2 = all_52_8 % 149.90/21.82 (40) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0 % 149.90/21.82 (41) all_58_2 = all_52_1 % 149.90/21.82 (42) all_58_10 = all_52_13 % 149.90/21.82 (43) ~ (all_52_4 = all_52_12) % 149.90/21.82 (44) ~ (all_52_8 = all_52_12) % 149.90/21.82 (45) ~ (all_8_2 = e0) % 149.90/21.82 (46) ~ (all_52_4 = all_8_2) % 149.90/21.82 (47) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 149.90/21.82 (48) all_58_14 = all_52_11 % 149.90/21.82 % 149.90/21.82 Begin of proof % 149.90/21.82 | % 149.90/21.82 | BETA: splitting (47) gives: % 149.90/21.82 | % 149.90/21.82 | Case 1: % 149.90/21.82 | | % 149.90/21.82 | | (49) all_54_5 = e3 % 149.90/21.82 | | % 149.90/21.82 | | REF_CLOSE: (10), (34), (49) are inconsistent by sub-proof #737. % 149.90/21.82 | | % 149.90/21.82 | Case 2: % 149.90/21.82 | | % 149.90/21.82 | | (50) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 149.90/21.82 | | % 149.90/21.82 | | BETA: splitting (50) gives: % 149.90/21.82 | | % 149.90/21.82 | | Case 1: % 149.90/21.82 | | | % 149.90/21.82 | | | (51) all_54_5 = e2 % 149.90/21.82 | | | % 149.90/21.82 | | | COMBINE_EQS: (10), (51) imply: % 149.90/21.82 | | | (52) all_8_2 = e2 % 149.90/21.82 | | | % 149.90/21.82 | | | SIMP: (52) implies: % 149.90/21.82 | | | (53) all_8_2 = e2 % 149.90/21.82 | | | % 149.90/21.82 | | | COMBINE_EQS: (36), (53) imply: % 149.90/21.82 | | | (54) all_58_3 = e2 % 149.90/21.82 | | | % 149.90/21.82 | | | REDUCE: (46), (53) imply: % 149.90/21.82 | | | (55) ~ (all_52_4 = e2) % 149.90/21.82 | | | % 149.90/21.82 | | | REDUCE: (7), (53) imply: % 149.90/21.82 | | | (56) ~ (e2 = e1) % 149.90/21.82 | | | % 149.90/21.82 | | | BETA: splitting (8) gives: % 149.90/21.82 | | | % 149.90/21.82 | | | Case 1: % 149.90/21.82 | | | | % 149.90/21.82 | | | | (57) all_58_0 = e2 % 149.90/21.82 | | | | % 149.90/21.82 | | | | COMBINE_EQS: (32), (57) imply: % 149.90/21.82 | | | | (58) all_4_1 = e2 % 149.90/21.82 | | | | % 149.90/21.82 | | | | REDUCE: (14), (58) imply: % 149.90/21.82 | | | | (59) $false % 149.90/21.82 | | | | % 149.90/21.82 | | | | CLOSE: (59) is inconsistent. % 149.90/21.82 | | | | % 149.90/21.82 | | | Case 2: % 149.90/21.82 | | | | % 149.90/21.82 | | | | (60) all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2 % 149.90/21.82 | | | | % 149.90/21.82 | | | | BETA: splitting (60) gives: % 149.90/21.82 | | | | % 149.90/21.82 | | | | Case 1: % 149.90/21.82 | | | | | % 149.90/21.82 | | | | | (61) all_58_1 = e2 % 149.90/21.82 | | | | | % 149.90/21.82 | | | | | COMBINE_EQS: (23), (61) imply: % 149.90/21.82 | | | | | (62) all_52_4 = e2 % 149.90/21.82 | | | | | % 149.90/21.82 | | | | | REDUCE: (55), (62) imply: % 149.90/21.82 | | | | | (63) $false % 149.90/21.82 | | | | | % 149.90/21.82 | | | | | CLOSE: (63) is inconsistent. % 149.90/21.82 | | | | | % 149.90/21.82 | | | | Case 2: % 149.90/21.82 | | | | | % 149.90/21.82 | | | | | (64) all_58_4 = e2 | all_58_9 = e2 % 149.90/21.82 | | | | | % 149.90/21.82 | | | | | BETA: splitting (64) gives: % 149.90/21.82 | | | | | % 149.90/21.82 | | | | | Case 1: % 149.90/21.82 | | | | | | % 149.90/21.82 | | | | | | (65) all_58_4 = e2 % 149.90/21.82 | | | | | | % 149.90/21.82 | | | | | | COMBINE_EQS: (9), (65) imply: % 149.90/21.82 | | | | | | (66) all_52_8 = e2 % 149.90/21.82 | | | | | | % 149.90/21.82 | | | | | | REDUCE: (5), (66) imply: % 149.90/21.82 | | | | | | (67) $false % 149.90/21.82 | | | | | | % 149.90/21.82 | | | | | | CLOSE: (67) is inconsistent. % 149.90/21.82 | | | | | | % 149.90/21.82 | | | | | Case 2: % 149.90/21.82 | | | | | | % 149.90/21.82 | | | | | | (68) all_58_9 = e2 % 149.90/21.82 | | | | | | % 149.90/21.82 | | | | | | COMBINE_EQS: (17), (68) imply: % 149.90/21.82 | | | | | | (69) all_52_12 = e2 % 149.90/21.82 | | | | | | % 149.90/21.82 | | | | | | REDUCE: (33), (69) imply: % 149.90/21.82 | | | | | | (70) ~ (all_4_1 = e2) % 149.90/21.82 | | | | | | % 149.90/21.82 | | | | | | BETA: splitting (27) gives: % 149.90/21.82 | | | | | | % 149.90/21.82 | | | | | | Case 1: % 149.90/21.82 | | | | | | | % 149.90/21.82 | | | | | | | (71) all_58_0 = e1 % 149.90/21.82 | | | | | | | % 149.90/21.82 | | | | | | | COMBINE_EQS: (32), (71) imply: % 149.90/21.82 | | | | | | | (72) all_4_1 = e1 % 149.90/21.82 | | | | | | | % 149.90/21.82 | | | | | | | COMBINE_EQS: (18), (72) imply: % 149.90/21.82 | | | | | | | (73) all_56_1 = e1 % 149.90/21.82 | | | | | | | % 149.90/21.82 | | | | | | | REDUCE: (21), (72) imply: % 149.90/21.82 | | | | | | | (74) ~ (all_52_1 = e1) % 149.90/21.82 | | | | | | | % 149.90/21.82 | | | | | | | REDUCE: (14), (72) imply: % 149.90/21.82 | | | | | | | (75) ~ (e2 = e1) % 149.90/21.82 | | | | | | | % 149.90/21.82 | | | | | | | REDUCE: (6), (72) imply: % 149.90/21.82 | | | | | | | (76) op(e0, e1) = e3 % 149.90/21.82 | | | | | | | % 149.90/21.82 | | | | | | | BETA: splitting (22) gives: % 149.90/21.82 | | | | | | | % 149.90/21.82 | | | | | | | Case 1: % 149.90/21.82 | | | | | | | | % 149.90/21.82 | | | | | | | | (77) ~ (all_56_1 = e1) % 149.90/21.82 | | | | | | | | % 149.90/21.82 | | | | | | | | REDUCE: (73), (77) imply: % 149.90/21.82 | | | | | | | | (78) $false % 149.90/21.82 | | | | | | | | % 149.90/21.82 | | | | | | | | CLOSE: (78) is inconsistent. % 149.90/21.82 | | | | | | | | % 149.90/21.82 | | | | | | | Case 2: % 149.90/21.82 | | | | | | | | % 149.90/21.82 | | | | | | | | (79) all_56_5 = e3 % 149.90/21.82 | | | | | | | | % 149.90/21.82 | | | | | | | | COMBINE_EQS: (35), (79) imply: % 149.90/21.82 | | | | | | | | (80) all_52_8 = e3 % 149.90/21.82 | | | | | | | | % 149.90/21.82 | | | | | | | | COMBINE_EQS: (9), (80) imply: % 149.90/21.82 | | | | | | | | (81) all_58_4 = e3 % 149.90/21.82 | | | | | | | | % 149.90/21.82 | | | | | | | | REDUCE: (5), (80) imply: % 149.90/21.82 | | | | | | | | (82) ~ (e3 = e2) % 149.90/21.82 | | | | | | | | % 149.90/21.82 | | | | | | | | BETA: splitting (28) gives: % 149.90/21.82 | | | | | | | | % 149.90/21.82 | | | | | | | | Case 1: % 149.90/21.82 | | | | | | | | | % 149.90/21.82 | | | | | | | | | (83) all_58_2 = e1 % 149.90/21.82 | | | | | | | | | % 149.90/21.82 | | | | | | | | | COMBINE_EQS: (41), (83) imply: % 149.90/21.82 | | | | | | | | | (84) all_52_1 = e1 % 149.90/21.82 | | | | | | | | | % 149.90/21.82 | | | | | | | | | REDUCE: (74), (84) imply: % 149.90/21.82 | | | | | | | | | (85) $false % 149.90/21.82 | | | | | | | | | % 149.90/21.82 | | | | | | | | | CLOSE: (85) is inconsistent. % 149.90/21.82 | | | | | | | | | % 149.90/21.82 | | | | | | | | Case 2: % 149.90/21.82 | | | | | | | | | % 149.90/21.82 | | | | | | | | | (86) all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1 % 149.90/21.82 | | | | | | | | | % 149.90/21.82 | | | | | | | | | BETA: splitting (25) gives: % 149.90/21.82 | | | | | | | | | % 149.90/21.82 | | | | | | | | | Case 1: % 149.90/21.82 | | | | | | | | | | % 149.90/21.82 | | | | | | | | | | (87) all_58_4 = e0 % 149.90/21.82 | | | | | | | | | | % 149.90/21.82 | | | | | | | | | | COMBINE_EQS: (81), (87) imply: % 149.90/21.82 | | | | | | | | | | (88) e3 = e0 % 149.90/21.82 | | | | | | | | | | % 149.90/21.82 | | | | | | | | | | REDUCE: (3), (88) imply: % 149.90/21.82 | | | | | | | | | | (89) $false % 149.90/21.82 | | | | | | | | | | % 149.90/21.82 | | | | | | | | | | CLOSE: (89) is inconsistent. % 149.90/21.82 | | | | | | | | | | % 149.90/21.82 | | | | | | | | | Case 2: % 149.90/21.82 | | | | | | | | | | % 149.90/21.82 | | | | | | | | | | (90) all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0 % 149.90/21.82 | | | | | | | | | | % 149.90/21.82 | | | | | | | | | | BETA: splitting (90) gives: % 149.90/21.82 | | | | | | | | | | % 149.90/21.82 | | | | | | | | | | Case 1: % 149.90/21.82 | | | | | | | | | | | % 149.90/21.82 | | | | | | | | | | | (91) all_58_5 = e0 % 149.90/21.82 | | | | | | | | | | | % 149.90/21.82 | | | | | | | | | | | COMBINE_EQS: (15), (91) imply: % 149.90/21.82 | | | | | | | | | | | (92) all_52_9 = e0 % 149.90/21.82 | | | | | | | | | | | % 149.90/21.82 | | | | | | | | | | | REDUCE: (38), (92) imply: % 149.90/21.82 | | | | | | | | | | | (93) ~ (e1 = e0) % 149.90/21.82 | | | | | | | | | | | % 149.90/21.82 | | | | | | | | | | | SIMP: (93) implies: % 149.90/21.82 | | | | | | | | | | | (94) ~ (e1 = e0) % 149.90/21.82 | | | | | | | | | | | % 149.90/21.82 | | | | | | | | | | | BETA: splitting (86) gives: % 149.90/21.82 | | | | | | | | | | | % 149.90/21.82 | | | | | | | | | | | Case 1: % 149.90/21.82 | | | | | | | | | | | | % 149.90/21.82 | | | | | | | | | | | | (95) all_58_3 = e1 % 149.90/21.82 | | | | | | | | | | | | % 149.90/21.82 | | | | | | | | | | | | COMBINE_EQS: (54), (95) imply: % 149.90/21.82 | | | | | | | | | | | | (96) e2 = e1 % 149.90/21.82 | | | | | | | | | | | | % 149.90/21.82 | | | | | | | | | | | | REDUCE: (56), (96) imply: % 149.90/21.82 | | | | | | | | | | | | (97) $false % 149.90/21.82 | | | | | | | | | | | | % 149.90/21.82 | | | | | | | | | | | | CLOSE: (97) is inconsistent. % 149.90/21.82 | | | | | | | | | | | | % 149.90/21.82 | | | | | | | | | | | Case 2: % 149.90/21.82 | | | | | | | | | | | | % 149.90/21.82 | | | | | | | | | | | | (98) all_58_5 = e1 | all_58_10 = e1 % 149.90/21.82 | | | | | | | | | | | | % 149.90/21.82 | | | | | | | | | | | | BETA: splitting (98) gives: % 149.90/21.82 | | | | | | | | | | | | % 149.90/21.82 | | | | | | | | | | | | Case 1: % 149.90/21.82 | | | | | | | | | | | | | % 149.90/21.82 | | | | | | | | | | | | | (99) all_58_5 = e1 % 149.90/21.82 | | | | | | | | | | | | | % 149.90/21.82 | | | | | | | | | | | | | REF_CLOSE: (91), (94), (99) are inconsistent by sub-proof % 149.90/21.82 | | | | | | | | | | | | | #172. % 149.90/21.82 | | | | | | | | | | | | | % 149.90/21.82 | | | | | | | | | | | | Case 2: % 149.90/21.82 | | | | | | | | | | | | | % 149.90/21.82 | | | | | | | | | | | | | (100) all_58_10 = e1 % 149.90/21.82 | | | | | | | | | | | | | % 149.90/21.82 | | | | | | | | | | | | | COMBINE_EQS: (42), (100) imply: % 149.90/21.82 | | | | | | | | | | | | | (101) all_52_13 = e1 % 149.90/21.82 | | | | | | | | | | | | | % 149.90/21.82 | | | | | | | | | | | | | REDUCE: (1), (101) imply: % 149.90/21.82 | | | | | | | | | | | | | (102) op(e0, e1) = all_56_14 % 149.90/21.82 | | | | | | | | | | | | | % 149.90/21.82 | | | | | | | | | | | | | REF_CLOSE: (19), (29), (76), (82), (102) are inconsistent by % 149.90/21.82 | | | | | | | | | | | | | sub-proof #197. % 149.90/21.82 | | | | | | | | | | | | | % 149.90/21.82 | | | | | | | | | | | | End of split % 149.90/21.82 | | | | | | | | | | | | % 149.90/21.82 | | | | | | | | | | | End of split % 149.90/21.82 | | | | | | | | | | | % 149.90/21.82 | | | | | | | | | | Case 2: % 149.90/21.82 | | | | | | | | | | | % 149.90/21.82 | | | | | | | | | | | (103) all_58_8 = e0 | all_58_14 = e0 % 149.90/21.82 | | | | | | | | | | | % 149.90/21.82 | | | | | | | | | | | REF_CLOSE: (13), (30), (31), (48), (103) are inconsistent by % 149.90/21.82 | | | | | | | | | | | sub-proof #627. % 149.90/21.82 | | | | | | | | | | | % 149.90/21.82 | | | | | | | | | | End of split % 149.90/21.82 | | | | | | | | | | % 149.90/21.82 | | | | | | | | | End of split % 149.90/21.82 | | | | | | | | | % 149.90/21.82 | | | | | | | | End of split % 149.90/21.82 | | | | | | | | % 149.90/21.82 | | | | | | | End of split % 149.90/21.82 | | | | | | | % 149.90/21.82 | | | | | | Case 2: % 149.90/21.82 | | | | | | | % 149.90/21.82 | | | | | | | (104) ~ (all_58_0 = e1) % 149.90/21.82 | | | | | | | (105) all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1 % 149.90/21.82 | | | | | | | % 149.90/21.82 | | | | | | | REDUCE: (32), (104) imply: % 149.90/21.82 | | | | | | | (106) ~ (all_4_1 = e1) % 149.90/21.82 | | | | | | | % 149.90/21.82 | | | | | | | BETA: splitting (11) gives: % 149.90/21.82 | | | | | | | % 149.90/21.82 | | | | | | | Case 1: % 149.90/21.82 | | | | | | | | % 149.90/21.82 | | | | | | | | (107) all_54_0 = e3 % 149.90/21.82 | | | | | | | | % 149.90/21.82 | | | | | | | | COMBINE_EQS: (24), (107) imply: % 149.90/21.82 | | | | | | | | (108) all_4_1 = e3 % 149.90/21.82 | | | | | | | | % 149.90/21.82 | | | | | | | | SIMP: (108) implies: % 149.90/21.82 | | | | | | | | (109) all_4_1 = e3 % 149.90/21.82 | | | | | | | | % 149.90/21.82 | | | | | | | | REDUCE: (12), (109) imply: % 149.90/21.82 | | | | | | | | (110) ~ (all_52_4 = e3) % 149.90/21.82 | | | | | | | | % 149.90/21.82 | | | | | | | | REDUCE: (106), (109) imply: % 149.90/21.82 | | | | | | | | (111) ~ (e3 = e1) % 149.90/21.82 | | | | | | | | % 149.90/21.82 | | | | | | | | BETA: splitting (40) gives: % 149.90/21.82 | | | | | | | | % 149.90/21.82 | | | | | | | | Case 1: % 149.90/21.82 | | | | | | | | | % 149.90/21.82 | | | | | | | | | (112) all_54_1 = e3 % 149.90/21.82 | | | | | | | | | % 149.90/21.82 | | | | | | | | | REF_CLOSE: (16), (110), (112) are inconsistent by sub-proof % 149.90/21.82 | | | | | | | | | #722. % 149.90/21.82 | | | | | | | | | % 149.90/21.82 | | | | | | | | Case 2: % 149.90/21.82 | | | | | | | | | % 149.90/21.82 | | | | | | | | | (113) all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0 % 149.90/21.82 | | | | | | | | | % 149.90/21.82 | | | | | | | | | REF_CLOSE: (2), (5), (9), (16), (20), (23), (25), (26), (37), % 149.90/21.82 | | | | | | | | | (39), (55), (56), (68), (105), (111), (113) are % 149.90/21.82 | | | | | | | | | inconsistent by sub-proof #557. % 149.90/21.82 | | | | | | | | | % 149.90/21.82 | | | | | | | | End of split % 149.90/21.82 | | | | | | | | % 149.90/21.82 | | | | | | | Case 2: % 149.90/21.82 | | | | | | | | % 149.90/21.82 | | | | | | | | (114) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 149.90/21.82 | | | | | | | | % 149.90/21.82 | | | | | | | | REF_CLOSE: (4), (14), (24), (106), (114) are inconsistent by % 149.90/21.82 | | | | | | | | sub-proof #549. % 149.90/21.82 | | | | | | | | % 149.90/21.82 | | | | | | | End of split % 149.90/21.82 | | | | | | | % 149.90/21.82 | | | | | | End of split % 149.90/21.82 | | | | | | % 149.90/21.82 | | | | | End of split % 149.90/21.82 | | | | | % 149.90/21.82 | | | | End of split % 149.90/21.82 | | | | % 149.90/21.82 | | | End of split % 149.90/21.82 | | | % 149.90/21.82 | | Case 2: % 149.90/21.82 | | | % 149.90/21.82 | | | (115) all_54_5 = e1 | all_54_5 = e0 % 149.90/21.82 | | | % 149.90/21.82 | | | REF_CLOSE: (7), (10), (45), (115) are inconsistent by sub-proof #645. % 149.90/21.82 | | | % 149.90/21.82 | | End of split % 149.90/21.82 | | % 149.90/21.82 | End of split % 149.90/21.82 | % 149.90/21.82 End of proof % 149.90/21.82 % 149.90/21.82 Sub-proof #26 shows that the following formulas are inconsistent: % 149.90/21.82 ---------------------------------------------------------------- % 149.90/21.82 (1) ~ (all_52_9 = e2) % 149.90/21.82 (2) all_58_5 = all_52_9 % 149.90/21.82 (3) all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2 % 149.90/21.82 (4) ~ (all_52_11 = e2) % 149.90/21.82 (5) all_58_8 = all_6_2 % 149.90/21.82 (6) ~ (all_6_2 = e2) % 149.90/21.82 (7) all_58_14 = all_52_11 % 149.90/21.82 % 149.90/21.82 Begin of proof % 149.90/21.82 | % 149.90/21.82 | BETA: splitting (3) gives: % 149.90/21.82 | % 149.90/21.82 | Case 1: % 149.90/21.82 | | % 149.90/21.82 | | (8) all_58_5 = e2 % 149.90/21.82 | | % 149.90/21.82 | | COMBINE_EQS: (2), (8) imply: % 149.90/21.82 | | (9) all_52_9 = e2 % 149.90/21.82 | | % 149.90/21.82 | | REDUCE: (1), (9) imply: % 149.90/21.82 | | (10) $false % 149.90/21.82 | | % 149.90/21.82 | | CLOSE: (10) is inconsistent. % 149.90/21.82 | | % 149.90/21.82 | Case 2: % 149.90/21.82 | | % 149.90/21.82 | | (11) all_58_8 = e2 | all_58_14 = e2 % 149.90/21.82 | | % 149.90/21.82 | | REF_CLOSE: (4), (5), (6), (7), (11) are inconsistent by sub-proof #478. % 149.90/21.82 | | % 149.90/21.82 | End of split % 149.90/21.82 | % 149.90/21.82 End of proof % 149.90/21.82 % 149.90/21.82 Sub-proof #27 shows that the following formulas are inconsistent: % 149.90/21.82 ---------------------------------------------------------------- % 149.90/21.82 (1) ~ (e3 = e0) % 149.90/21.82 (2) ~ (all_4_1 = e3) % 149.90/21.82 (3) op(e0, all_4_1) = e3 % 149.90/21.82 (4) ~ (all_8_2 = e1) % 149.90/21.82 (5) all_54_5 = all_8_2 % 149.90/21.82 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 149.90/21.82 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 149.90/21.82 (7) all_54_5 = all_4_1 % 149.90/21.82 (8) op(e0, e2) = e0 % 149.90/21.82 (9) ~ (all_8_2 = e0) % 149.90/21.82 (10) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 149.90/21.82 % 149.90/21.82 Begin of proof % 149.90/21.82 | % 149.90/21.82 | BETA: splitting (10) gives: % 149.90/21.82 | % 149.90/21.82 | Case 1: % 149.90/21.82 | | % 149.90/21.82 | | (11) all_54_5 = e3 % 149.90/21.82 | | % 149.90/21.82 | | REF_CLOSE: (2), (7), (11) are inconsistent by sub-proof #199. % 149.90/21.82 | | % 149.90/21.82 | Case 2: % 149.90/21.82 | | % 149.90/21.82 | | (12) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 149.90/21.82 | | % 149.90/21.82 | | BETA: splitting (12) gives: % 149.90/21.82 | | % 149.90/21.82 | | Case 1: % 149.90/21.82 | | | % 149.90/21.82 | | | (13) all_54_5 = e2 % 149.90/21.82 | | | % 149.90/21.82 | | | COMBINE_EQS: (7), (13) imply: % 149.90/21.82 | | | (14) all_4_1 = e2 % 149.90/21.82 | | | % 149.90/21.82 | | | SIMP: (14) implies: % 149.90/21.82 | | | (15) all_4_1 = e2 % 149.90/21.82 | | | % 149.90/21.82 | | | REF_CLOSE: (1), (3), (6), (8), (15) are inconsistent by sub-proof #28. % 149.90/21.82 | | | % 149.90/21.82 | | Case 2: % 149.90/21.82 | | | % 149.90/21.82 | | | (16) all_54_5 = e1 | all_54_5 = e0 % 149.90/21.82 | | | % 149.90/21.82 | | | REF_CLOSE: (4), (5), (9), (16) are inconsistent by sub-proof #645. % 149.90/21.82 | | | % 149.90/21.82 | | End of split % 149.90/21.82 | | % 149.90/21.82 | End of split % 149.90/21.82 | % 149.90/21.82 End of proof % 149.90/21.82 % 149.90/21.82 Sub-proof #28 shows that the following formulas are inconsistent: % 149.90/21.82 ---------------------------------------------------------------- % 149.90/21.82 (1) ~ (e3 = e0) % 149.90/21.82 (2) op(e0, all_4_1) = e3 % 149.90/21.83 (3) all_4_1 = e2 % 149.90/21.83 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 149.90/21.83 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 149.90/21.83 (5) op(e0, e2) = e0 % 149.90/21.83 % 149.90/21.83 Begin of proof % 149.90/21.83 | % 149.90/21.83 | REDUCE: (2), (3) imply: % 149.90/21.83 | (6) op(e0, e2) = e3 % 149.90/21.83 | % 149.90/21.83 | GROUND_INST: instantiating (4) with e0, e3, e2, e0, simplifying with (5), (6) % 149.90/21.83 | gives: % 149.90/21.83 | (7) e3 = e0 % 149.90/21.83 | % 149.90/21.83 | REDUCE: (1), (7) imply: % 149.90/21.83 | (8) $false % 149.90/21.83 | % 149.90/21.83 | CLOSE: (8) is inconsistent. % 149.90/21.83 | % 149.90/21.83 End of proof % 149.90/21.83 % 149.90/21.83 Sub-proof #29 shows that the following formulas are inconsistent: % 149.90/21.83 ---------------------------------------------------------------- % 149.90/21.83 (1) op(e0, all_4_1) = e3 % 149.90/21.83 (2) op(e0, e0) = all_4_2 % 149.90/21.83 (3) all_54_15 = all_4_2 % 149.90/21.83 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 149.90/21.83 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 149.90/21.83 (5) ~ (all_4_2 = e1) % 149.90/21.83 (6) ~ (all_4_2 = e2) % 149.90/21.83 (7) op(all_4_2, all_4_2) = all_4_1 % 149.90/21.83 (8) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0 % 149.90/21.83 (9) ~ (all_4_2 = e3) % 149.90/21.83 (10) op(e0, all_4_2) = all_56_30 % 149.90/21.83 % 149.90/21.83 Begin of proof % 149.90/21.83 | % 149.90/21.83 | BETA: splitting (8) gives: % 149.90/21.83 | % 149.90/21.83 | Case 1: % 149.90/21.83 | | % 149.90/21.83 | | (11) all_54_15 = e3 % 149.90/21.83 | | % 149.90/21.83 | | REF_CLOSE: (3), (9), (11) are inconsistent by sub-proof #740. % 149.90/21.83 | | % 149.90/21.83 | Case 2: % 149.90/21.83 | | % 149.90/21.83 | | (12) ~ (all_54_15 = e3) % 149.90/21.83 | | (13) all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0 % 149.90/21.83 | | % 149.90/21.83 | | BETA: splitting (13) gives: % 149.90/21.83 | | % 149.90/21.83 | | Case 1: % 149.90/21.83 | | | % 149.90/21.83 | | | (14) all_54_15 = e2 % 149.90/21.83 | | | % 149.90/21.83 | | | REF_CLOSE: (3), (6), (14) are inconsistent by sub-proof #739. % 149.90/21.83 | | | % 149.90/21.83 | | Case 2: % 149.90/21.83 | | | % 149.90/21.83 | | | (15) all_54_15 = e1 | all_54_15 = e0 % 149.90/21.83 | | | % 149.90/21.83 | | | BETA: splitting (15) gives: % 149.90/21.83 | | | % 149.90/21.83 | | | Case 1: % 149.90/21.83 | | | | % 149.90/21.83 | | | | (16) all_54_15 = e1 % 149.90/21.83 | | | | % 149.90/21.83 | | | | REF_CLOSE: (3), (5), (16) are inconsistent by sub-proof #738. % 149.90/21.83 | | | | % 149.90/21.83 | | | Case 2: % 149.90/21.83 | | | | % 149.90/21.83 | | | | (17) all_54_15 = e0 % 149.90/21.83 | | | | % 149.90/21.83 | | | | COMBINE_EQS: (3), (17) imply: % 149.90/21.83 | | | | (18) all_4_2 = e0 % 149.90/21.83 | | | | % 149.90/21.83 | | | | SIMP: (18) implies: % 149.90/21.83 | | | | (19) all_4_2 = e0 % 149.90/21.83 | | | | % 149.90/21.83 | | | | REDUCE: (9), (19) imply: % 149.90/21.83 | | | | (20) ~ (e3 = e0) % 149.90/21.83 | | | | % 149.90/21.83 | | | | SIMP: (20) implies: % 149.90/21.83 | | | | (21) ~ (e3 = e0) % 149.90/21.83 | | | | % 149.90/21.83 | | | | REDUCE: (7), (19) imply: % 149.90/21.83 | | | | (22) op(e0, e0) = all_4_1 % 149.90/21.83 | | | | % 149.90/21.83 | | | | REDUCE: (10), (19) imply: % 149.90/21.83 | | | | (23) op(e0, e0) = all_56_30 % 149.90/21.83 | | | | % 149.90/21.83 | | | | REDUCE: (2), (19) imply: % 149.90/21.83 | | | | (24) op(e0, e0) = e0 % 149.90/21.83 | | | | % 149.90/21.83 | | | | REF_CLOSE: (1), (4), (21), (22), (23), (24) are inconsistent by % 149.90/21.83 | | | | sub-proof #30. % 149.90/21.83 | | | | % 149.90/21.83 | | | End of split % 149.90/21.83 | | | % 149.90/21.83 | | End of split % 149.90/21.83 | | % 149.90/21.83 | End of split % 149.90/21.83 | % 149.90/21.83 End of proof % 149.90/21.83 % 149.90/21.83 Sub-proof #30 shows that the following formulas are inconsistent: % 149.90/21.83 ---------------------------------------------------------------- % 149.90/21.83 (1) ~ (e3 = e0) % 149.90/21.83 (2) op(e0, all_4_1) = e3 % 149.90/21.83 (3) op(e0, e0) = all_56_30 % 149.90/21.83 (4) op(e0, e0) = all_4_1 % 149.90/21.83 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 149.90/21.83 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 149.90/21.83 (6) op(e0, e0) = e0 % 149.90/21.83 % 149.90/21.83 Begin of proof % 149.90/21.83 | % 149.90/21.83 | GROUND_INST: instantiating (5) with all_4_1, all_56_30, e0, e0, simplifying % 149.90/21.83 | with (3), (4) gives: % 149.90/21.83 | (7) all_56_30 = all_4_1 % 149.90/21.83 | % 149.90/21.83 | GROUND_INST: instantiating (5) with e0, all_56_30, e0, e0, simplifying with % 149.90/21.83 | (3), (6) gives: % 149.90/21.83 | (8) all_56_30 = e0 % 149.90/21.83 | % 149.90/21.83 | COMBINE_EQS: (7), (8) imply: % 149.90/21.83 | (9) all_4_1 = e0 % 149.90/21.83 | % 149.90/21.83 | SIMP: (9) implies: % 149.90/21.83 | (10) all_4_1 = e0 % 149.90/21.83 | % 149.90/21.83 | REDUCE: (2), (10) imply: % 149.90/21.83 | (11) op(e0, e0) = e3 % 149.90/21.83 | % 149.90/21.83 | GROUND_INST: instantiating (5) with e0, e3, e0, e0, simplifying with (6), (11) % 149.90/21.83 | gives: % 149.90/21.83 | (12) e3 = e0 % 149.90/21.83 | % 149.90/21.83 | REDUCE: (1), (12) imply: % 149.90/21.83 | (13) $false % 149.90/21.83 | % 149.90/21.83 | CLOSE: (13) is inconsistent. % 149.90/21.83 | % 149.90/21.83 End of proof % 149.90/21.83 % 149.90/21.83 Sub-proof #31 shows that the following formulas are inconsistent: % 149.90/21.83 ---------------------------------------------------------------- % 149.90/21.83 (1) all_56_11 = all_8_2 % 149.90/21.83 (2) all_56_25 = all_52_3 % 149.90/21.83 (3) op(e2, all_8_1) = all_8_0 % 149.90/21.83 (4) all_58_6 = all_52_2 % 149.90/21.83 (5) ~ (e3 = e0) % 149.90/21.83 (6) all_54_10 = all_6_2 % 149.90/21.83 (7) ~ (all_52_13 = all_8_2) % 149.90/21.83 (8) ~ (all_56_21 = e2) | all_56_19 = e1 % 149.90/21.83 (9) all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2 % 149.90/21.83 (10) all_54_0 = all_10_2 % 149.90/21.83 (11) all_54_4 = all_52_1 % 149.90/21.83 (12) ~ (all_52_14 = all_4_2) % 149.90/21.83 (13) ~ (all_8_0 = e1) % 149.90/21.83 (14) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0 % 149.90/21.83 (15) ~ (all_52_4 = all_6_0) % 149.90/21.83 (16) all_54_12 = all_52_3 % 149.90/21.83 (17) ~ (all_52_4 = all_52_7) % 149.90/21.83 (18) ~ (e3 = e2) % 149.90/21.83 (19) op(e0, e0) = all_4_2 % 149.90/21.83 (20) all_58_6 = e0 | all_58_7 = e0 | all_58_8 = e0 | all_58_11 = e0 % 149.90/21.83 (21) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 149.90/21.83 (22) all_54_15 = all_4_2 % 149.90/21.83 (23) all_54_9 = all_6_0 % 149.90/21.83 (24) all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1 % 149.90/21.83 (25) all_56_21 = all_6_2 % 149.90/21.83 (26) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 149.90/21.83 (27) all_56_1 = all_10_2 % 149.90/21.83 (28) all_56_27 = all_52_7 % 149.90/21.83 (29) all_54_1 = all_52_4 % 149.90/21.83 (30) all_56_17 = all_52_2 % 149.90/21.83 (31) all_58_9 = all_52_12 % 149.90/21.83 (32) ~ (all_52_7 = all_6_0) % 149.90/21.83 (33) all_58_1 = all_52_4 % 149.90/21.83 (34) all_58_13 = all_52_7 % 149.90/21.83 (35) op(e2, all_8_2) = all_56_10 % 149.90/21.83 (36) op(e3, e3) = all_10_2 % 149.90/21.83 (37) op(e3, all_10_1) = e2 % 149.90/21.83 (38) ~ (all_56_21 = e3) | all_56_17 = e1 % 149.90/21.83 (39) all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2 % 149.90/21.83 (40) ~ (e1 = e0) % 149.90/21.83 (41) ~ (all_52_1 = all_8_2) % 149.90/21.83 (42) all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2 % 149.90/21.83 (43) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 149.90/21.83 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 149.90/21.83 (44) ~ (all_52_3 = all_10_2) % 149.90/21.83 (45) ~ (all_52_3 = all_52_7) % 149.90/21.83 (46) op(all_6_2, all_6_2) = e2 % 149.90/21.83 (47) ~ (all_6_0 = all_6_2) % 149.90/21.83 (48) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0 % 149.90/21.83 (49) ~ (all_52_1 = all_52_13) % 149.90/21.83 (50) ~ (all_52_7 = all_4_2) % 149.90/21.83 (51) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0 % 149.90/21.83 (52) ~ (all_4_2 = e1) % 149.90/21.83 (53) all_58_8 = all_6_2 % 149.90/21.83 (54) ~ (all_6_0 = e3) % 149.90/21.83 (55) ~ (all_6_0 = e0) | ~ (all_6_2 = e3) % 149.90/21.83 (56) ~ (all_52_3 = all_4_2) % 149.90/21.83 (57) all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3 % 149.90/21.83 (58) ~ (all_52_14 = all_6_0) % 149.90/21.83 (59) ~ (all_52_2 = all_52_3) % 149.90/21.83 (60) op(all_4_2, all_4_2) = all_4_1 % 149.90/21.83 (61) all_58_3 = all_8_2 % 149.90/21.83 (62) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0 % 149.90/21.83 (63) ~ (all_52_1 = all_52_3) % 149.90/21.83 (64) all_56_31 = all_4_2 % 149.90/21.83 (65) all_58_11 = all_52_14 % 149.90/21.83 (66) all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3 % 149.90/21.83 (67) ~ (all_8_0 = e3) % 149.90/21.83 (68) ~ (all_52_2 = all_52_14) % 149.90/21.83 (69) all_56_1 = e3 | all_56_11 = e2 | all_56_21 = e1 | all_56_31 = e0 % 149.90/21.83 (70) ~ (all_52_13 = all_4_2) % 149.90/21.83 (71) ~ (all_52_2 = all_6_0) % 149.90/21.83 (72) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0 % 149.90/21.83 (73) op(e3, e2) = all_52_4 % 149.90/21.83 (74) ~ (all_10_1 = e0) | ~ (all_10_2 = e1) % 149.90/21.83 (75) all_56_23 = all_52_14 % 149.90/21.83 (76) all_54_8 = all_52_2 % 149.90/21.83 (77) op(e1, e1) = all_6_2 % 149.90/21.83 (78) all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1 % 149.90/21.83 (79) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0 % 149.90/21.83 (80) all_58_15 = all_4_2 % 149.90/21.83 (81) all_58_7 = all_6_0 % 149.90/21.83 (82) all_58_2 = all_52_1 % 149.90/21.83 (83) all_56_19 = all_6_0 % 149.90/21.83 (84) all_58_10 = all_52_13 % 149.90/21.83 (85) op(all_10_2, all_10_2) = all_10_1 % 149.90/21.83 (86) all_58_0 = all_10_2 % 149.90/21.83 (87) op(e1, all_6_2) = all_56_20 % 149.90/21.83 (88) all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1 % 149.90/21.83 (89) all_58_1 = e0 | all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0 % 149.90/21.83 (90) ~ (all_56_31 = e2) | all_56_27 = e0 % 149.90/21.83 (91) ~ (e3 = e1) % 149.90/21.83 (92) op(e2, e2) = all_8_2 % 149.90/21.83 (93) ~ (all_52_2 = all_6_2) % 149.90/21.83 (94) ~ (all_52_1 = all_52_2) % 149.90/21.83 (95) ~ (all_56_21 = e0) | all_56_23 = e1 % 149.90/21.83 (96) op(e0, all_4_2) = all_56_30 % 149.90/21.83 (97) op(e3, all_10_2) = all_56_0 % 149.90/21.83 (98) ~ (all_52_14 = all_6_2) % 149.90/21.83 (99) ~ (e2 = e0) % 149.90/21.83 (100) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0 % 149.90/21.83 (101) ~ (all_52_2 = all_10_2) % 149.90/21.83 (102) ~ (all_8_2 = all_6_0) % 149.90/21.83 (103) ~ (all_52_4 = all_10_2) % 149.90/21.83 (104) ~ (all_52_4 = all_8_2) % 149.90/21.83 (105) op(all_8_2, all_8_2) = all_8_1 % 149.90/21.83 (106) op(e3, all_52_3) = all_56_24 % 149.90/21.83 (107) ~ (all_52_12 = all_10_2) % 149.90/21.83 (108) ~ (all_52_1 = all_10_2) % 149.90/21.83 (109) all_58_12 = all_52_3 % 149.90/21.83 (110) all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2 % 149.90/21.83 (111) all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3 % 149.90/21.83 (112) all_54_11 = all_52_14 % 149.90/21.83 (113) ~ (all_56_31 = e3) | all_56_25 = e0 % 149.90/21.83 % 149.90/21.83 Begin of proof % 149.90/21.83 | % 149.90/21.83 | BETA: splitting (113) gives: % 149.90/21.83 | % 149.90/21.83 | Case 1: % 149.90/21.83 | | % 149.90/21.83 | | (114) ~ (all_56_31 = e3) % 149.90/21.83 | | % 149.90/21.83 | | REDUCE: (64), (114) imply: % 149.90/21.83 | | (115) ~ (all_4_2 = e3) % 149.90/21.83 | | % 149.90/21.83 | | BETA: splitting (8) gives: % 149.90/21.83 | | % 149.90/21.83 | | Case 1: % 149.90/21.83 | | | % 149.90/21.83 | | | (116) ~ (all_56_21 = e2) % 149.90/21.83 | | | % 149.90/21.83 | | | REDUCE: (25), (116) imply: % 149.90/21.83 | | | (117) ~ (all_6_2 = e2) % 149.90/21.83 | | | % 149.90/21.83 | | | REF_CLOSE: (1), (4), (5), (6), (12), (16), (19), (20), (22), (23), (25), % 149.90/21.83 | | | (26), (27), (28), (30), (32), (38), (40), (42), (43), (44), % 149.90/21.83 | | | (45), (46), (47), (48), (52), (53), (54), (55), (56), (57), % 149.90/21.83 | | | (58), (59), (60), (62), (64), (65), (69), (72), (75), (77), % 149.90/21.83 | | | (81), (87), (90), (91), (93), (95), (96), (98), (101), (102), % 149.90/21.83 | | | (115), (117) are inconsistent by sub-proof #74. % 149.90/21.83 | | | % 149.90/21.83 | | Case 2: % 149.90/21.83 | | | % 149.90/21.83 | | | (118) all_56_21 = e2 % 149.90/21.83 | | | (119) all_56_19 = e1 % 149.90/21.83 | | | % 149.90/21.83 | | | COMBINE_EQS: (83), (119) imply: % 149.90/21.83 | | | (120) all_6_0 = e1 % 149.90/21.83 | | | % 149.90/21.83 | | | SIMP: (120) implies: % 149.90/21.83 | | | (121) all_6_0 = e1 % 149.90/21.83 | | | % 149.90/21.83 | | | COMBINE_EQS: (25), (118) imply: % 149.90/21.83 | | | (122) all_6_2 = e2 % 149.90/21.83 | | | % 149.90/21.83 | | | SIMP: (122) implies: % 149.90/21.83 | | | (123) all_6_2 = e2 % 149.90/21.83 | | | % 149.90/21.83 | | | COMBINE_EQS: (81), (121) imply: % 149.90/21.83 | | | (124) all_58_7 = e1 % 149.90/21.83 | | | % 149.90/21.83 | | | REDUCE: (71), (121) imply: % 149.90/21.83 | | | (125) ~ (all_52_2 = e1) % 149.90/21.83 | | | % 149.90/21.83 | | | REDUCE: (93), (123) imply: % 149.90/21.83 | | | (126) ~ (all_52_2 = e2) % 149.90/21.83 | | | % 149.90/21.83 | | | REDUCE: (15), (121) imply: % 149.90/21.83 | | | (127) ~ (all_52_4 = e1) % 149.90/21.83 | | | % 149.90/21.83 | | | REDUCE: (32), (121) imply: % 149.90/21.83 | | | (128) ~ (all_52_7 = e1) % 149.90/21.83 | | | % 149.90/21.83 | | | REDUCE: (58), (121) imply: % 149.90/21.83 | | | (129) ~ (all_52_14 = e1) % 149.90/21.83 | | | % 149.90/21.83 | | | REDUCE: (98), (123) imply: % 149.90/21.83 | | | (130) ~ (all_52_14 = e2) % 149.90/21.83 | | | % 149.90/21.83 | | | REDUCE: (54), (121) imply: % 149.90/21.83 | | | (131) ~ (e3 = e1) % 149.90/21.83 | | | % 149.90/21.83 | | | REDUCE: (46), (123) imply: % 149.90/21.83 | | | (132) op(e2, e2) = e2 % 149.90/21.83 | | | % 149.90/21.83 | | | REDUCE: (77), (123) imply: % 149.90/21.83 | | | (133) op(e1, e1) = e2 % 149.90/21.83 | | | % 149.90/21.83 | | | GROUND_INST: instantiating (43) with all_8_2, e2, e2, e2, simplifying with % 149.90/21.83 | | | (92), (132) gives: % 149.90/21.83 | | | (134) all_8_2 = e2 % 149.90/21.83 | | | % 149.90/21.83 | | | COMBINE_EQS: (61), (134) imply: % 149.90/21.83 | | | (135) all_58_3 = e2 % 149.90/21.83 | | | % 149.90/21.83 | | | REDUCE: (41), (134) imply: % 149.90/21.83 | | | (136) ~ (all_52_1 = e2) % 149.90/21.83 | | | % 149.90/21.83 | | | REDUCE: (104), (134) imply: % 149.90/21.83 | | | (137) ~ (all_52_4 = e2) % 149.90/21.83 | | | % 149.90/21.83 | | | REDUCE: (7), (134) imply: % 149.90/21.83 | | | (138) ~ (all_52_13 = e2) % 149.90/21.83 | | | % 149.90/21.83 | | | REDUCE: (105), (134) imply: % 149.90/21.83 | | | (139) op(e2, e2) = all_8_1 % 149.90/21.83 | | | % 149.90/21.83 | | | REDUCE: (35), (134) imply: % 149.90/21.83 | | | (140) op(e2, e2) = all_56_10 % 149.90/21.83 | | | % 149.90/21.83 | | | GROUND_INST: instantiating (43) with e2, all_56_10, e2, e2, simplifying % 149.90/21.83 | | | with (132), (140) gives: % 149.90/21.83 | | | (141) all_56_10 = e2 % 149.90/21.83 | | | % 149.90/21.83 | | | GROUND_INST: instantiating (43) with all_8_1, all_56_10, e2, e2, % 149.90/21.83 | | | simplifying with (139), (140) gives: % 149.90/21.83 | | | (142) all_56_10 = all_8_1 % 149.90/21.83 | | | % 149.90/21.83 | | | COMBINE_EQS: (141), (142) imply: % 149.90/21.83 | | | (143) all_8_1 = e2 % 149.90/21.83 | | | % 149.90/21.83 | | | SIMP: (143) implies: % 149.90/21.83 | | | (144) all_8_1 = e2 % 149.90/21.83 | | | % 149.90/21.83 | | | REDUCE: (3), (144) imply: % 149.90/21.83 | | | (145) op(e2, e2) = all_8_0 % 149.90/21.83 | | | % 149.90/21.83 | | | GROUND_INST: instantiating (43) with e2, all_8_0, e2, e2, simplifying with % 149.90/21.83 | | | (132), (145) gives: % 149.90/21.83 | | | (146) all_8_0 = e2 % 149.90/21.83 | | | % 149.90/21.83 | | | REDUCE: (67), (146) imply: % 149.90/21.83 | | | (147) ~ (e3 = e2) % 149.90/21.83 | | | % 149.90/21.83 | | | REDUCE: (13), (146) imply: % 149.90/21.83 | | | (148) ~ (e2 = e1) % 149.90/21.83 | | | % 149.90/21.83 | | | BETA: splitting (90) gives: % 149.90/21.83 | | | % 149.90/21.83 | | | Case 1: % 149.90/21.83 | | | | % 149.90/21.83 | | | | (149) ~ (all_56_31 = e2) % 149.90/21.83 | | | | % 149.90/21.83 | | | | REDUCE: (64), (149) imply: % 149.90/21.83 | | | | (150) ~ (all_4_2 = e2) % 149.90/21.83 | | | | % 149.90/21.83 | | | | BETA: splitting (110) gives: % 149.90/21.83 | | | | % 149.90/21.83 | | | | Case 1: % 149.90/21.83 | | | | | % 149.90/21.83 | | | | | (151) all_58_12 = e2 % 149.90/21.83 | | | | | % 149.90/21.83 | | | | | COMBINE_EQS: (109), (151) imply: % 149.90/21.83 | | | | | (152) all_52_3 = e2 % 149.90/21.83 | | | | | % 149.90/21.83 | | | | | SIMP: (152) implies: % 149.90/21.83 | | | | | (153) all_52_3 = e2 % 149.90/21.83 | | | | | % 149.90/21.83 | | | | | REDUCE: (56), (153) imply: % 149.90/21.83 | | | | | (154) ~ (all_4_2 = e2) % 149.90/21.83 | | | | | % 149.90/21.83 | | | | | BETA: splitting (9) gives: % 149.90/21.83 | | | | | % 149.90/21.83 | | | | | Case 1: % 149.90/21.83 | | | | | | % 149.90/21.83 | | | | | | (155) all_58_9 = e2 % 149.90/21.83 | | | | | | % 149.90/21.83 | | | | | | COMBINE_EQS: (31), (155) imply: % 149.90/21.83 | | | | | | (156) all_52_12 = e2 % 149.90/21.83 | | | | | | % 149.90/21.83 | | | | | | REDUCE: (107), (156) imply: % 149.90/21.83 | | | | | | (157) ~ (all_10_2 = e2) % 149.90/21.83 | | | | | | % 149.90/21.83 | | | | | | SIMP: (157) implies: % 149.90/21.83 | | | | | | (158) ~ (all_10_2 = e2) % 149.90/21.83 | | | | | | % 149.90/21.83 | | | | | | BETA: splitting (24) gives: % 149.90/21.83 | | | | | | % 149.90/21.83 | | | | | | Case 1: % 149.90/21.83 | | | | | | | % 149.90/21.83 | | | | | | | (159) all_58_9 = e1 % 149.90/21.83 | | | | | | | % 149.90/21.83 | | | | | | | COMBINE_EQS: (155), (159) imply: % 149.90/21.83 | | | | | | | (160) e2 = e1 % 149.90/21.83 | | | | | | | % 149.90/21.83 | | | | | | | REDUCE: (148), (160) imply: % 149.90/21.83 | | | | | | | (161) $false % 149.90/21.83 | | | | | | | % 149.90/21.83 | | | | | | | CLOSE: (161) is inconsistent. % 149.90/21.83 | | | | | | | % 149.90/21.83 | | | | | | Case 2: % 149.90/21.83 | | | | | | | % 149.90/21.83 | | | | | | | (162) ~ (all_58_9 = e1) % 149.90/21.83 | | | | | | | (163) all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1 % 149.90/21.83 | | | | | | | % 149.90/21.83 | | | | | | | BETA: splitting (88) gives: % 149.90/21.83 | | | | | | | % 149.90/21.83 | | | | | | | Case 1: % 149.90/21.83 | | | | | | | | % 149.90/21.83 | | | | | | | | (164) all_58_12 = e1 % 149.90/21.83 | | | | | | | | % 149.90/21.83 | | | | | | | | COMBINE_EQS: (151), (164) imply: % 149.90/21.83 | | | | | | | | (165) e2 = e1 % 149.90/21.83 | | | | | | | | % 149.90/21.83 | | | | | | | | REDUCE: (148), (165) imply: % 149.90/21.83 | | | | | | | | (166) $false % 149.90/21.83 | | | | | | | | % 149.90/21.83 | | | | | | | | CLOSE: (166) is inconsistent. % 149.90/21.83 | | | | | | | | % 149.90/21.83 | | | | | | | Case 2: % 149.90/21.83 | | | | | | | | % 149.90/21.83 | | | | | | | | (167) all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1 % 149.90/21.83 | | | | | | | | % 149.90/21.83 | | | | | | | | BETA: splitting (163) gives: % 149.90/21.83 | | | | | | | | % 149.90/21.83 | | | | | | | | Case 1: % 149.90/21.83 | | | | | | | | | % 149.90/21.83 | | | | | | | | | (168) all_58_10 = e1 % 149.90/21.83 | | | | | | | | | % 149.90/21.83 | | | | | | | | | COMBINE_EQS: (84), (168) imply: % 149.90/21.83 | | | | | | | | | (169) all_52_13 = e1 % 149.90/21.83 | | | | | | | | | % 149.90/21.83 | | | | | | | | | REDUCE: (49), (169) imply: % 149.90/21.83 | | | | | | | | | (170) ~ (all_52_1 = e1) % 149.90/21.83 | | | | | | | | | % 149.90/21.83 | | | | | | | | | REDUCE: (70), (169) imply: % 149.90/21.83 | | | | | | | | | (171) ~ (all_4_2 = e1) % 149.90/21.83 | | | | | | | | | % 149.90/21.83 | | | | | | | | | BETA: splitting (167) gives: % 149.90/21.83 | | | | | | | | | % 149.90/21.83 | | | | | | | | | Case 1: % 149.90/21.83 | | | | | | | | | | % 149.90/21.83 | | | | | | | | | | (172) all_58_13 = e1 % 149.90/21.83 | | | | | | | | | | % 149.90/21.83 | | | | | | | | | | REF_CLOSE: (34), (128), (172) are inconsistent by sub-proof % 149.90/21.83 | | | | | | | | | | #704. % 149.90/21.83 | | | | | | | | | | % 149.90/21.83 | | | | | | | | | Case 2: % 149.90/21.83 | | | | | | | | | | % 149.90/21.83 | | | | | | | | | | (173) all_58_14 = e1 | all_58_15 = e1 % 149.90/21.83 | | | | | | | | | | % 149.90/21.83 | | | | | | | | | | BETA: splitting (111) gives: % 149.90/21.83 | | | | | | | | | | % 149.90/21.83 | | | | | | | | | | Case 1: % 149.90/21.83 | | | | | | | | | | | % 149.90/21.83 | | | | | | | | | | | (174) all_58_12 = e3 % 149.90/21.83 | | | | | | | | | | | % 149.90/21.83 | | | | | | | | | | | COMBINE_EQS: (151), (174) imply: % 149.90/21.83 | | | | | | | | | | | (175) e3 = e2 % 149.90/21.83 | | | | | | | | | | | % 149.90/21.83 | | | | | | | | | | | SIMP: (175) implies: % 149.90/21.83 | | | | | | | | | | | (176) e3 = e2 % 149.90/21.83 | | | | | | | | | | | % 149.90/21.83 | | | | | | | | | | | REDUCE: (18), (176) imply: % 149.90/21.83 | | | | | | | | | | | (177) $false % 149.90/21.83 | | | | | | | | | | | % 149.90/21.83 | | | | | | | | | | | CLOSE: (177) is inconsistent. % 149.90/21.83 | | | | | | | | | | | % 149.90/21.83 | | | | | | | | | | Case 2: % 149.90/21.83 | | | | | | | | | | | % 149.90/21.83 | | | | | | | | | | | (178) all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3 % 149.90/21.83 | | | | | | | | | | | % 149.90/21.83 | | | | | | | | | | | BETA: splitting (178) gives: % 149.90/21.83 | | | | | | | | | | | % 149.90/21.83 | | | | | | | | | | | Case 1: % 149.90/21.83 | | | | | | | | | | | | % 149.90/21.83 | | | | | | | | | | | | (179) all_58_13 = e3 % 149.90/21.83 | | | | | | | | | | | | % 149.90/21.83 | | | | | | | | | | | | BETA: splitting (89) gives: % 149.90/21.83 | | | | | | | | | | | | % 149.90/21.83 | | | | | | | | | | | | Case 1: % 149.90/21.83 | | | | | | | | | | | | | % 149.90/21.83 | | | | | | | | | | | | | (180) all_58_1 = e0 % 149.90/21.83 | | | | | | | | | | | | | % 149.90/21.83 | | | | | | | | | | | | | COMBINE_EQS: (33), (180) imply: % 149.90/21.83 | | | | | | | | | | | | | (181) all_52_4 = e0 % 149.90/21.83 | | | | | | | | | | | | | % 149.90/21.83 | | | | | | | | | | | | | REDUCE: (103), (181) imply: % 149.90/21.83 | | | | | | | | | | | | | (182) ~ (all_10_2 = e0) % 149.90/21.83 | | | | | | | | | | | | | % 149.90/21.83 | | | | | | | | | | | | | SIMP: (182) implies: % 149.90/21.83 | | | | | | | | | | | | | (183) ~ (all_10_2 = e0) % 149.90/21.83 | | | | | | | | | | | | | % 149.90/21.83 | | | | | | | | | | | | | REDUCE: (73), (181) imply: % 149.90/21.83 | | | | | | | | | | | | | (184) op(e3, e2) = e0 % 149.90/21.83 | | | | | | | | | | | | | % 149.90/21.83 | | | | | | | | | | | | | BETA: splitting (78) gives: % 149.90/21.83 | | | | | | | | | | | | | % 149.90/21.83 | | | | | | | | | | | | | Case 1: % 149.90/21.83 | | | | | | | | | | | | | | % 149.90/21.83 | | | | | | | | | | | | | | (185) all_58_0 = e1 % 149.90/21.83 | | | | | | | | | | | | | | % 149.90/21.83 | | | | | | | | | | | | | | COMBINE_EQS: (86), (185) imply: % 149.90/21.83 | | | | | | | | | | | | | | (186) all_10_2 = e1 % 149.90/21.83 | | | | | | | | | | | | | | % 149.90/21.83 | | | | | | | | | | | | | | REDUCE: (158), (186) imply: % 149.90/21.83 | | | | | | | | | | | | | | (187) ~ (e2 = e1) % 149.90/21.83 | | | | | | | | | | | | | | % 149.90/21.83 | | | | | | | | | | | | | | REDUCE: (85), (186) imply: % 149.90/21.83 | | | | | | | | | | | | | | (188) op(e1, e1) = all_10_1 % 149.90/21.83 | | | | | | | | | | | | | | % 149.90/21.83 | | | | | | | | | | | | | | REDUCE: (36), (186) imply: % 149.90/21.83 | | | | | | | | | | | | | | (189) op(e3, e3) = e1 % 149.90/21.83 | | | | | | | | | | | | | | % 149.90/21.83 | | | | | | | | | | | | | | BETA: splitting (74) gives: % 149.90/21.83 | | | | | | | | | | | | | | % 149.90/21.83 | | | | | | | | | | | | | | Case 1: % 149.90/21.83 | | | | | | | | | | | | | | | % 149.90/21.83 | | | | | | | | | | | | | | | (190) ~ (all_10_2 = e1) % 149.90/21.83 | | | | | | | | | | | | | | | % 149.90/21.83 | | | | | | | | | | | | | | | REF_CLOSE: (10), (21), (36), (43), (158), (183), (189), (190) % 149.90/21.83 | | | | | | | | | | | | | | | are inconsistent by sub-proof #305. % 149.90/21.83 | | | | | | | | | | | | | | | % 149.90/21.83 | | | | | | | | | | | | | | Case 2: % 149.90/21.83 | | | | | | | | | | | | | | | % 149.90/21.83 | | | | | | | | | | | | | | | (191) ~ (all_10_1 = e0) % 149.90/21.83 | | | | | | | | | | | | | | | % 149.90/21.83 | | | | | | | | | | | | | | | BETA: splitting (39) gives: % 149.90/21.83 | | | | | | | | | | | | | | | % 149.90/21.83 | | | | | | | | | | | | | | | Case 1: % 149.90/21.83 | | | | | | | | | | | | | | | | % 149.90/21.83 | | | | | | | | | | | | | | | | (192) all_58_0 = e2 % 149.90/21.83 | | | | | | | | | | | | | | | | % 149.90/21.83 | | | | | | | | | | | | | | | | REF_CLOSE: (148), (185), (192) are inconsistent by sub-proof % 149.90/21.83 | | | | | | | | | | | | | | | | #187. % 149.90/21.83 | | | | | | | | | | | | | | | | % 149.90/21.83 | | | | | | | | | | | | | | | Case 2: % 149.90/21.83 | | | | | | | | | | | | | | | | % 149.90/21.83 | | | | | | | | | | | | | | | | (193) all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2 % 149.90/21.83 | | | | | | | | | | | | | | | | % 149.90/21.83 | | | | | | | | | | | | | | | | BETA: splitting (193) gives: % 149.90/21.83 | | | | | | | | | | | | | | | | % 149.90/21.83 | | | | | | | | | | | | | | | | Case 1: % 149.90/21.83 | | | | | | | | | | | | | | | | | % 149.90/21.83 | | | | | | | | | | | | | | | | | (194) all_58_2 = e2 % 149.90/21.83 | | | | | | | | | | | | | | | | | % 149.90/21.83 | | | | | | | | | | | | | | | | | COMBINE_EQS: (82), (194) imply: % 149.90/21.83 | | | | | | | | | | | | | | | | | (195) all_52_1 = e2 % 149.90/21.83 | | | | | | | | | | | | | | | | | % 149.90/21.83 | | | | | | | | | | | | | | | | | REDUCE: (136), (195) imply: % 149.90/21.83 | | | | | | | | | | | | | | | | | (196) $false % 149.90/21.83 | | | | | | | | | | | | | | | | | % 149.90/21.83 | | | | | | | | | | | | | | | | | CLOSE: (196) is inconsistent. % 149.90/21.83 | | | | | | | | | | | | | | | | | % 149.90/21.83 | | | | | | | | | | | | | | | | Case 2: % 149.90/21.83 | | | | | | | | | | | | | | | | | % 149.90/21.83 | | | | | | | | | | | | | | | | | (197) all_58_6 = e2 | all_58_12 = e2 % 149.90/21.83 | | | | | | | | | | | | | | | | | % 149.90/21.83 | | | | | | | | | | | | | | | | | BETA: splitting (110) gives: % 149.90/21.83 | | | | | | | | | | | | | | | | | % 149.90/21.83 | | | | | | | | | | | | | | | | | Case 1: % 149.90/21.83 | | | | | | | | | | | | | | | | | | % 149.90/21.83 | | | | | | | | | | | | | | | | | | % 149.90/21.83 | | | | | | | | | | | | | | | | | | REDUCE: (106), (153) imply: % 149.90/21.83 | | | | | | | | | | | | | | | | | | (198) op(e3, e2) = all_56_24 % 149.90/21.83 | | | | | | | | | | | | | | | | | | % 149.90/21.83 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (43) with e2, all_10_1, e1, e1, % 149.90/21.83 | | | | | | | | | | | | | | | | | | simplifying with (133), (188) gives: % 149.90/21.83 | | | | | | | | | | | | | | | | | | (199) all_10_1 = e2 % 149.90/21.83 | | | | | | | | | | | | | | | | | | % 149.90/21.83 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (43) with e0, all_56_24, e2, e3, % 149.90/21.83 | | | | | | | | | | | | | | | | | | simplifying with (184), (198) gives: % 149.90/21.83 | | | | | | | | | | | | | | | | | | (200) all_56_24 = e0 % 149.90/21.83 | | | | | | | | | | | | | | | | | | % 149.90/21.83 | | | | | | | | | | | | | | | | | | REDUCE: (37), (199) imply: % 149.90/21.83 | | | | | | | | | | | | | | | | | | (201) op(e3, e2) = e2 % 149.90/21.83 | | | | | | | | | | | | | | | | | | % 149.90/21.84 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (43) with e0, e2, e2, e3, % 149.90/21.84 | | | | | | | | | | | | | | | | | | simplifying with (184), (201) gives: % 149.90/21.84 | | | | | | | | | | | | | | | | | | (202) e2 = e0 % 149.90/21.84 | | | | | | | | | | | | | | | | | | % 149.90/21.84 | | | | | | | | | | | | | | | | | | REDUCE: (99), (202) imply: % 149.90/21.84 | | | | | | | | | | | | | | | | | | (203) $false % 149.90/21.84 | | | | | | | | | | | | | | | | | | % 149.90/21.84 | | | | | | | | | | | | | | | | | | CLOSE: (203) is inconsistent. % 149.90/21.84 | | | | | | | | | | | | | | | | | | % 149.90/21.84 | | | | | | | | | | | | | | | | | Case 2: % 149.90/21.84 | | | | | | | | | | | | | | | | | | % 149.90/21.84 | | | | | | | | | | | | | | | | | | (204) ~ (all_58_12 = e2) % 149.90/21.84 | | | | | | | | | | | | | | | | | | % 149.90/21.84 | | | | | | | | | | | | | | | | | | REDUCE: (109), (204) imply: % 149.90/21.84 | | | | | | | | | | | | | | | | | | (205) ~ (all_52_3 = e2) % 149.90/21.84 | | | | | | | | | | | | | | | | | | % 149.90/21.84 | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (109), (126), (197), (205) are inconsistent % 149.90/21.84 | | | | | | | | | | | | | | | | | | by sub-proof #696. % 149.90/21.84 | | | | | | | | | | | | | | | | | | % 149.90/21.84 | | | | | | | | | | | | | | | | | End of split % 149.90/21.84 | | | | | | | | | | | | | | | | | % 149.90/21.84 | | | | | | | | | | | | | | | | End of split % 149.90/21.84 | | | | | | | | | | | | | | | | % 149.90/21.84 | | | | | | | | | | | | | | | End of split % 149.90/21.84 | | | | | | | | | | | | | | | % 149.90/21.84 | | | | | | | | | | | | | | End of split % 149.90/21.84 | | | | | | | | | | | | | | % 149.90/21.84 | | | | | | | | | | | | | Case 2: % 149.90/21.84 | | | | | | | | | | | | | | % 149.90/21.84 | | | | | | | | | | | | | | (206) ~ (all_58_0 = e1) % 149.90/21.84 | | | | | | | | | | | | | | % 149.90/21.84 | | | | | | | | | | | | | | REF_CLOSE: (10), (11), (21), (51), (76), (86), (94), (100), % 149.90/21.84 | | | | | | | | | | | | | | (101), (108), (125), (126), (136), (158), (170), % 149.90/21.84 | | | | | | | | | | | | | | (183), (206) are inconsistent by sub-proof #73. % 149.90/21.84 | | | | | | | | | | | | | | % 149.90/21.84 | | | | | | | | | | | | | End of split % 149.90/21.84 | | | | | | | | | | | | | % 149.90/21.84 | | | | | | | | | | | | Case 2: % 149.90/21.84 | | | | | | | | | | | | | % 149.90/21.84 | | | | | | | | | | | | | (207) all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0 % 149.90/21.84 | | | | | | | | | | | | | % 149.90/21.84 | | | | | | | | | | | | | REF_CLOSE: (5), (40), (99), (124), (135), (179), (207) are % 149.90/21.84 | | | | | | | | | | | | | inconsistent by sub-proof #61. % 149.90/21.84 | | | | | | | | | | | | | % 149.90/21.84 | | | | | | | | | | | | End of split % 149.90/21.84 | | | | | | | | | | | | % 149.90/21.84 | | | | | | | | | | | Case 2: % 149.90/21.84 | | | | | | | | | | | | % 149.90/21.84 | | | | | | | | | | | | (208) all_58_14 = e3 | all_58_15 = e3 % 149.90/21.84 | | | | | | | | | | | | % 149.90/21.84 | | | | | | | | | | | | BETA: splitting (208) gives: % 149.90/21.84 | | | | | | | | | | | | % 149.90/21.84 | | | | | | | | | | | | Case 1: % 149.90/21.84 | | | | | | | | | | | | | % 149.90/21.84 | | | | | | | | | | | | | (209) all_58_14 = e3 % 149.90/21.84 | | | | | | | | | | | | | % 149.90/21.84 | | | | | | | | | | | | | REF_CLOSE: (52), (80), (91), (173), (209) are inconsistent by % 149.90/21.84 | | | | | | | | | | | | | sub-proof #456. % 149.90/21.84 | | | | | | | | | | | | | % 149.90/21.84 | | | | | | | | | | | | Case 2: % 149.90/21.84 | | | | | | | | | | | | | % 149.90/21.84 | | | | | | | | | | | | | (210) all_58_15 = e3 % 149.90/21.84 | | | | | | | | | | | | | % 149.90/21.84 | | | | | | | | | | | | | COMBINE_EQS: (80), (210) imply: % 149.90/21.84 | | | | | | | | | | | | | (211) all_4_2 = e3 % 149.90/21.84 | | | | | | | | | | | | | % 149.90/21.84 | | | | | | | | | | | | | REDUCE: (115), (211) imply: % 149.90/21.84 | | | | | | | | | | | | | (212) $false % 149.90/21.84 | | | | | | | | | | | | | % 149.90/21.84 | | | | | | | | | | | | | CLOSE: (212) is inconsistent. % 149.90/21.84 | | | | | | | | | | | | | % 149.90/21.84 | | | | | | | | | | | | End of split % 149.90/21.84 | | | | | | | | | | | | % 149.90/21.84 | | | | | | | | | | | End of split % 149.90/21.84 | | | | | | | | | | | % 149.90/21.84 | | | | | | | | | | End of split % 149.90/21.84 | | | | | | | | | | % 149.90/21.84 | | | | | | | | | End of split % 149.90/21.84 | | | | | | | | | % 149.90/21.84 | | | | | | | | Case 2: % 149.90/21.84 | | | | | | | | | % 149.90/21.84 | | | | | | | | | (213) all_58_11 = e1 | all_58_15 = e1 % 149.90/21.84 | | | | | | | | | % 149.90/21.84 | | | | | | | | | REF_CLOSE: (52), (65), (80), (129), (213) are inconsistent by % 149.90/21.84 | | | | | | | | | sub-proof #672. % 149.90/21.84 | | | | | | | | | % 149.90/21.84 | | | | | | | | End of split % 149.90/21.84 | | | | | | | | % 149.90/21.84 | | | | | | | End of split % 149.90/21.84 | | | | | | | % 149.90/21.84 | | | | | | End of split % 149.90/21.84 | | | | | | % 149.90/21.84 | | | | | Case 2: % 149.90/21.84 | | | | | | % 149.90/21.84 | | | | | | (214) all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2 % 149.90/21.84 | | | | | | % 149.90/21.84 | | | | | | REF_CLOSE: (65), (80), (84), (130), (138), (150), (214) are % 149.90/21.84 | | | | | | inconsistent by sub-proof #693. % 149.90/21.84 | | | | | | % 149.90/21.84 | | | | | End of split % 149.90/21.84 | | | | | % 149.90/21.84 | | | | Case 2: % 149.90/21.84 | | | | | % 149.90/21.84 | | | | | (215) ~ (all_58_12 = e2) % 149.90/21.84 | | | | | % 149.90/21.84 | | | | | REF_CLOSE: (4), (9), (31), (39), (65), (80), (82), (84), (86), (107), % 149.90/21.84 | | | | | (109), (126), (130), (136), (138), (150), (215) are % 149.90/21.84 | | | | | inconsistent by sub-proof #39. % 149.90/21.84 | | | | | % 149.90/21.84 | | | | End of split % 149.90/21.84 | | | | % 149.90/21.84 | | | Case 2: % 149.90/21.84 | | | | % 149.90/21.84 | | | | (216) all_56_31 = e2 % 149.90/21.84 | | | | (217) all_56_27 = e0 % 149.90/21.84 | | | | % 149.90/21.84 | | | | COMBINE_EQS: (28), (217) imply: % 149.90/21.84 | | | | (218) all_52_7 = e0 % 149.90/21.84 | | | | % 149.90/21.84 | | | | SIMP: (218) implies: % 149.90/21.84 | | | | (219) all_52_7 = e0 % 149.90/21.84 | | | | % 149.90/21.84 | | | | COMBINE_EQS: (64), (216) imply: % 149.90/21.84 | | | | (220) all_4_2 = e2 % 149.90/21.84 | | | | % 149.90/21.84 | | | | REDUCE: (56), (220) imply: % 149.90/21.84 | | | | (221) ~ (all_52_3 = e2) % 149.90/21.84 | | | | % 149.90/21.84 | | | | REDUCE: (17), (219) imply: % 149.90/21.84 | | | | (222) ~ (all_52_4 = e0) % 149.90/21.84 | | | | % 149.90/21.84 | | | | BETA: splitting (79) gives: % 149.90/21.84 | | | | % 149.90/21.84 | | | | Case 1: % 149.90/21.84 | | | | | % 149.90/21.84 | | | | | (223) all_54_1 = e3 % 149.90/21.84 | | | | | % 149.90/21.84 | | | | | COMBINE_EQS: (29), (223) imply: % 149.90/21.84 | | | | | (224) all_52_4 = e3 % 149.90/21.84 | | | | | % 149.90/21.84 | | | | | SIMP: (224) implies: % 149.90/21.84 | | | | | (225) all_52_4 = e3 % 149.90/21.84 | | | | | % 149.90/21.84 | | | | | REDUCE: (103), (225) imply: % 149.90/21.84 | | | | | (226) ~ (all_10_2 = e3) % 149.90/21.84 | | | | | % 149.90/21.84 | | | | | SIMP: (226) implies: % 149.90/21.84 | | | | | (227) ~ (all_10_2 = e3) % 149.90/21.84 | | | | | % 149.90/21.84 | | | | | REDUCE: (73), (225) imply: % 149.90/21.84 | | | | | (228) op(e3, e2) = e3 % 149.90/21.84 | | | | | % 149.90/21.84 | | | | | BETA: splitting (39) gives: % 149.90/21.84 | | | | | % 149.90/21.84 | | | | | Case 1: % 149.90/21.84 | | | | | | % 149.90/21.84 | | | | | | (229) all_58_0 = e2 % 149.90/21.84 | | | | | | % 149.90/21.84 | | | | | | COMBINE_EQS: (86), (229) imply: % 149.90/21.84 | | | | | | (230) all_10_2 = e2 % 149.90/21.84 | | | | | | % 149.90/21.84 | | | | | | REDUCE: (85), (230) imply: % 149.90/21.84 | | | | | | (231) op(e2, e2) = all_10_1 % 149.90/21.84 | | | | | | % 149.90/21.84 | | | | | | REDUCE: (97), (230) imply: % 149.90/21.84 | | | | | | (232) op(e3, e2) = all_56_0 % 149.90/21.84 | | | | | | % 149.90/21.84 | | | | | | GROUND_INST: instantiating (43) with e2, all_10_1, e2, e2, % 149.90/21.84 | | | | | | simplifying with (132), (231) gives: % 149.90/21.84 | | | | | | (233) all_10_1 = e2 % 149.90/21.84 | | | | | | % 149.90/21.84 | | | | | | GROUND_INST: instantiating (43) with e3, all_56_0, e2, e3, % 149.90/21.84 | | | | | | simplifying with (228), (232) gives: % 149.90/21.84 | | | | | | (234) all_56_0 = e3 % 149.90/21.84 | | | | | | % 149.90/21.84 | | | | | | REDUCE: (37), (233) imply: % 149.90/21.84 | | | | | | (235) op(e3, e2) = e2 % 149.90/21.84 | | | | | | % 149.90/21.84 | | | | | | GROUND_INST: instantiating (43) with e3, e2, e2, e3, simplifying % 149.90/21.84 | | | | | | with (228), (235) gives: % 149.90/21.84 | | | | | | (236) e3 = e2 % 149.90/21.84 | | | | | | % 149.90/21.84 | | | | | | REDUCE: (18), (236) imply: % 149.90/21.84 | | | | | | (237) $false % 149.90/21.84 | | | | | | % 149.90/21.84 | | | | | | CLOSE: (237) is inconsistent. % 149.90/21.84 | | | | | | % 149.90/21.84 | | | | | Case 2: % 149.90/21.84 | | | | | | % 149.90/21.84 | | | | | | (238) all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2 % 149.90/21.84 | | | | | | % 149.90/21.84 | | | | | | REF_CLOSE: (4), (82), (109), (126), (136), (221), (238) are % 149.90/21.84 | | | | | | inconsistent by sub-proof #695. % 149.90/21.84 | | | | | | % 149.90/21.84 | | | | | End of split % 149.90/21.84 | | | | | % 149.90/21.84 | | | | Case 2: % 149.90/21.84 | | | | | % 149.90/21.84 | | | | | (239) all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0 % 149.90/21.84 | | | | | % 149.90/21.84 | | | | | REF_CLOSE: (29), (127), (137), (222), (239) are inconsistent by % 149.90/21.84 | | | | | sub-proof #718. % 149.90/21.84 | | | | | % 149.90/21.84 | | | | End of split % 149.90/21.84 | | | | % 149.90/21.84 | | | End of split % 149.90/21.84 | | | % 149.90/21.84 | | End of split % 149.90/21.84 | | % 149.90/21.84 | Case 2: % 149.90/21.84 | | % 149.90/21.84 | | (240) all_56_31 = e3 % 149.90/21.84 | | (241) all_56_25 = e0 % 149.90/21.84 | | % 149.90/21.84 | | REF_CLOSE: (1), (2), (4), (6), (8), (12), (14), (18), (19), (23), (25), % 149.90/21.84 | | (26), (27), (30), (34), (36), (38), (40), (43), (45), (46), (47), % 149.90/21.84 | | (50), (53), (54), (55), (56), (57), (58), (59), (60), (61), (62), % 149.90/21.84 | | (64), (65), (66), (68), (69), (71), (75), (76), (77), (81), (83), % 149.90/21.84 | | (85), (87), (89), (93), (95), (96), (97), (98), (100), (101), % 149.90/21.84 | | (102), (112), (240), (241) are inconsistent by sub-proof #55. % 149.90/21.84 | | % 149.90/21.84 | End of split % 149.90/21.84 | % 149.90/21.84 End of proof % 149.90/21.84 % 149.90/21.84 Sub-proof #32 shows that the following formulas are inconsistent: % 149.90/21.84 ---------------------------------------------------------------- % 149.90/21.84 (1) all_56_11 = all_8_2 % 149.90/21.84 (2) ~ (all_56_11 = e1) | all_56_13 = e2 % 149.90/21.84 (3) all_14_2 = all_8_2 % 149.90/21.84 (4) op(e2, all_8_1) = all_8_0 % 149.90/21.84 (5) ~ (all_8_1 = e1) % 149.90/21.84 (6) all_54_10 = all_6_2 % 149.90/21.84 (7) ~ (all_52_13 = all_8_2) % 149.90/21.84 (8) ~ (all_56_21 = e2) | all_56_19 = e1 % 149.90/21.84 (9) all_54_0 = all_10_2 % 149.90/21.84 (10) ~ (all_52_14 = all_4_2) % 149.90/21.84 (11) all_8_0 = e1 % 149.90/21.84 (12) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0 % 149.90/21.84 (13) op(e0, e0) = all_4_2 % 149.90/21.84 (14) all_54_5 = all_8_2 % 149.90/21.84 (15) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 149.90/21.84 (16) all_54_15 = all_4_2 % 149.90/21.84 (17) all_54_9 = all_6_0 % 149.90/21.84 (18) all_42_1 = all_8_1 % 149.90/21.84 (19) all_56_21 = all_6_2 % 149.90/21.84 (20) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 149.90/21.84 (21) all_56_1 = all_10_2 % 149.90/21.84 (22) all_56_17 = all_52_2 % 149.90/21.84 (23) all_14_1 = all_8_1 % 149.90/21.84 (24) op(e2, all_8_2) = all_56_10 % 149.90/21.84 (25) op(e3, e3) = all_10_2 % 149.90/21.84 (26) all_42_2 = all_8_2 % 149.90/21.84 (27) ~ (all_56_21 = e3) | all_56_17 = e1 % 149.90/21.84 (28) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 149.90/21.84 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 149.90/21.84 (29) ~ (all_56_11 = e3) | all_56_9 = e2 % 149.90/21.84 (30) op(all_6_2, all_6_2) = e2 % 149.90/21.84 (31) ~ (all_6_0 = all_6_2) % 149.90/21.84 (32) all_56_13 = all_52_9 % 149.90/21.84 (33) ~ (all_6_0 = e0) | ~ (all_6_2 = e3) % 149.90/21.84 (34) ~ (all_42_0 = e1) | ~ (all_42_1 = e0) | ~ (all_42_2 = e3) % 149.90/21.84 (35) all_42_0 = all_8_0 % 149.90/21.84 (36) ~ (all_52_14 = all_6_0) % 149.90/21.84 (37) ~ (e2 = e1) % 149.90/21.84 (38) ~ (all_14_1 = e3) | ~ (all_14_2 = e0) % 149.90/21.84 (39) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0 % 149.90/21.84 (40) all_56_31 = all_4_2 % 149.90/21.84 (41) ~ (all_52_2 = all_52_14) % 149.90/21.84 (42) all_56_1 = e3 | all_56_11 = e2 | all_56_21 = e1 | all_56_31 = e0 % 149.90/21.84 (43) ~ (all_52_13 = all_4_2) % 149.90/21.84 (44) ~ (all_52_2 = all_6_0) % 149.90/21.84 (45) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0 % 149.90/21.84 (46) all_56_23 = all_52_14 % 149.90/21.84 (47) op(e1, e1) = all_6_2 % 149.90/21.84 (48) ~ (all_52_9 = all_6_2) % 149.90/21.84 (49) op(all_10_2, all_10_2) = all_10_1 % 149.90/21.84 (50) ~ (all_56_11 = e0) | all_56_15 = e2 % 149.90/21.84 (51) op(e1, all_6_2) = all_56_20 % 149.90/21.84 (52) op(e2, e3) = all_52_1 % 149.90/21.84 (53) op(e2, e2) = all_8_2 % 149.90/21.84 (54) op(e2, e0) = all_52_13 % 149.90/21.84 (55) ~ (all_52_2 = all_6_2) % 149.90/21.84 (56) ~ (all_56_21 = e0) | all_56_23 = e1 % 149.90/21.84 (57) op(e3, all_10_2) = all_56_0 % 149.90/21.84 (58) ~ (all_52_14 = all_6_2) % 149.90/21.84 (59) ~ (all_8_2 = all_6_0) % 149.90/21.84 (60) op(all_8_2, all_8_2) = all_8_1 % 149.90/21.84 (61) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 149.90/21.84 (62) all_56_9 = all_52_1 % 149.90/21.84 (63) all_56_15 = all_52_13 % 149.90/21.84 (64) ~ (all_52_1 = all_10_2) % 149.90/21.84 (65) all_54_11 = all_52_14 % 149.90/21.84 % 149.90/21.84 Begin of proof % 149.90/21.84 | % 149.90/21.84 | COMBINE_EQS: (11), (35) imply: % 149.90/21.84 | (66) all_42_0 = e1 % 149.90/21.84 | % 149.90/21.84 | REDUCE: (4), (11) imply: % 149.90/21.84 | (67) op(e2, all_8_1) = e1 % 149.90/21.84 | % 149.90/21.84 | BETA: splitting (34) gives: % 149.90/21.84 | % 149.90/21.84 | Case 1: % 149.90/21.84 | | % 149.90/21.84 | | (68) ~ (all_42_0 = e1) % 149.90/21.84 | | % 149.90/21.84 | | REDUCE: (66), (68) imply: % 149.90/21.84 | | (69) $false % 149.90/21.84 | | % 149.90/21.84 | | CLOSE: (69) is inconsistent. % 149.90/21.84 | | % 149.90/21.84 | Case 2: % 149.90/21.84 | | % 149.90/21.84 | | (70) ~ (all_42_1 = e0) | ~ (all_42_2 = e3) % 149.90/21.84 | | % 149.90/21.84 | | BETA: splitting (8) gives: % 149.90/21.84 | | % 149.90/21.84 | | Case 1: % 149.90/21.84 | | | % 149.90/21.84 | | | (71) ~ (all_56_21 = e2) % 149.90/21.84 | | | % 149.90/21.84 | | | REDUCE: (19), (71) imply: % 149.90/21.84 | | | (72) ~ (all_6_2 = e2) % 149.90/21.84 | | | % 149.90/21.84 | | | BETA: splitting (50) gives: % 149.90/21.84 | | | % 149.90/21.84 | | | Case 1: % 149.90/21.84 | | | | % 149.90/21.84 | | | | (73) ~ (all_56_11 = e0) % 149.90/21.84 | | | | % 149.90/21.84 | | | | REDUCE: (1), (73) imply: % 149.90/21.84 | | | | (74) ~ (all_8_2 = e0) % 149.90/21.84 | | | | % 149.90/21.84 | | | | BETA: splitting (27) gives: % 149.90/21.84 | | | | % 149.90/21.84 | | | | Case 1: % 149.90/21.84 | | | | | % 149.90/21.84 | | | | | (75) ~ (all_56_21 = e3) % 149.90/21.84 | | | | | % 149.90/21.84 | | | | | REDUCE: (19), (75) imply: % 149.90/21.84 | | | | | (76) ~ (all_6_2 = e3) % 149.90/21.84 | | | | | % 149.90/21.84 | | | | | REF_CLOSE: (1), (2), (5), (6), (7), (9), (14), (15), (18), (20), (24), % 149.90/21.84 | | | | | (25), (26), (28), (29), (32), (37), (47), (48), (52), (53), % 149.90/21.84 | | | | | (54), (60), (61), (62), (64), (67), (70), (74), (76) are % 149.90/21.84 | | | | | inconsistent by sub-proof #254. % 149.90/21.84 | | | | | % 149.90/21.84 | | | | Case 2: % 149.90/21.84 | | | | | % 149.90/21.84 | | | | | (77) all_56_21 = e3 % 149.90/21.84 | | | | | (78) all_56_17 = e1 % 149.90/21.84 | | | | | % 149.90/21.84 | | | | | REF_CLOSE: (1), (6), (10), (12), (17), (19), (20), (21), (22), (25), % 149.90/21.84 | | | | | (28), (30), (31), (33), (36), (39), (40), (41), (42), (44), % 149.90/21.84 | | | | | (46), (47), (49), (51), (55), (56), (57), (58), (59), (65), % 149.90/21.84 | | | | | (72), (77), (78) are inconsistent by sub-proof #66. % 149.90/21.84 | | | | | % 149.90/21.84 | | | | End of split % 149.90/21.84 | | | | % 149.90/21.84 | | | Case 2: % 149.90/21.84 | | | | % 149.90/21.84 | | | | (79) all_56_11 = e0 % 149.90/21.84 | | | | % 149.90/21.84 | | | | REF_CLOSE: (1), (3), (5), (13), (16), (23), (24), (28), (37), (38), % 149.90/21.84 | | | | (43), (45), (50), (54), (60), (63), (67), (79) are % 149.90/21.84 | | | | inconsistent by sub-proof #156. % 149.90/21.84 | | | | % 149.90/21.84 | | | End of split % 149.90/21.84 | | | % 149.90/21.84 | | Case 2: % 149.90/21.84 | | | % 149.90/21.84 | | | (80) all_56_21 = e2 % 149.90/21.84 | | | % 149.90/21.84 | | | COMBINE_EQS: (19), (80) imply: % 149.90/21.84 | | | (81) all_6_2 = e2 % 149.90/21.84 | | | % 149.90/21.84 | | | REDUCE: (30), (81) imply: % 149.90/21.84 | | | (82) op(e2, e2) = e2 % 149.90/21.84 | | | % 149.90/21.84 | | | GROUND_INST: instantiating (28) with all_8_2, e2, e2, e2, simplifying with % 149.90/21.84 | | | (53), (82) gives: % 149.90/21.84 | | | (83) all_8_2 = e2 % 149.90/21.84 | | | % 149.90/21.84 | | | REDUCE: (60), (83) imply: % 149.90/21.84 | | | (84) op(e2, e2) = all_8_1 % 149.90/21.84 | | | % 149.90/21.84 | | | REDUCE: (24), (83) imply: % 149.90/21.84 | | | (85) op(e2, e2) = all_56_10 % 149.90/21.84 | | | % 149.90/21.84 | | | GROUND_INST: instantiating (28) with e2, all_56_10, e2, e2, simplifying % 149.90/21.84 | | | with (82), (85) gives: % 149.90/21.84 | | | (86) all_56_10 = e2 % 149.90/21.84 | | | % 149.90/21.84 | | | GROUND_INST: instantiating (28) with all_8_1, all_56_10, e2, e2, % 149.90/21.84 | | | simplifying with (84), (85) gives: % 149.90/21.84 | | | (87) all_56_10 = all_8_1 % 149.90/21.84 | | | % 149.90/21.84 | | | COMBINE_EQS: (86), (87) imply: % 149.90/21.84 | | | (88) all_8_1 = e2 % 149.90/21.84 | | | % 149.90/21.84 | | | REF_CLOSE: (5), (28), (67), (84), (88) are inconsistent by sub-proof #260. % 149.90/21.84 | | | % 149.90/21.84 | | End of split % 149.90/21.84 | | % 149.90/21.84 | End of split % 149.90/21.84 | % 149.90/21.84 End of proof % 149.90/21.84 % 149.90/21.84 Sub-proof #33 shows that the following formulas are inconsistent: % 149.90/21.84 ---------------------------------------------------------------- % 149.90/21.84 (1) all_56_11 = all_8_2 % 149.90/21.84 (2) ~ (all_34_1 = e3) | ~ (all_34_2 = e1) % 149.90/21.84 (3) op(e0, e0) = e1 % 149.90/21.84 (4) ~ (all_8_1 = e1) % 149.90/21.84 (5) all_54_10 = all_6_2 % 149.90/21.84 (6) ~ (all_56_21 = e2) | all_56_19 = e1 % 149.90/21.84 (7) all_34_2 = e1 % 149.90/21.84 (8) all_54_0 = all_10_2 % 149.90/21.84 (9) all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2 % 149.90/21.84 (10) ~ (all_52_4 = all_6_0) % 149.90/21.84 (11) all_54_12 = all_52_3 % 149.90/21.84 (12) ~ (all_52_4 = all_52_7) % 149.90/21.84 (13) all_58_4 = all_52_8 % 149.90/21.84 (14) all_54_5 = all_8_2 % 149.90/21.84 (15) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 149.90/21.84 (16) all_56_21 = all_6_2 % 149.90/21.84 (17) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 149.90/21.84 (18) ~ (all_52_7 = all_8_2) % 149.90/21.84 (19) all_56_1 = all_10_2 % 149.90/21.84 (20) all_54_1 = all_52_4 % 149.90/21.84 (21) all_58_9 = all_52_12 % 149.90/21.84 (22) ~ (all_52_7 = all_6_0) % 149.90/21.84 (23) op(e0, all_52_12) = all_56_6 % 149.90/21.84 (24) op(e0, e2) = all_52_7 % 149.90/21.84 (25) ~ (all_56_1 = e1) | all_56_5 = e3 % 149.90/21.84 (26) all_58_1 = all_52_4 % 149.90/21.84 (27) all_58_13 = all_52_7 % 149.90/21.84 (28) op(e3, e3) = all_10_2 % 149.90/21.84 (29) ~ (all_52_8 = all_6_2) % 149.90/21.84 (30) ~ (e1 = e0) % 149.90/21.84 (31) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 149.90/21.84 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 149.90/21.84 (32) ~ (all_52_3 = all_10_2) % 149.90/21.84 (33) ~ (all_6_2 = e0) % 149.90/21.84 (34) ~ (all_56_11 = e3) | all_56_9 = e2 % 149.90/21.84 (35) ~ (all_52_3 = e0) % 149.90/21.84 (36) all_56_7 = all_52_12 % 149.90/21.84 (37) op(all_6_2, all_6_2) = e2 % 149.90/21.84 (38) op(e0, all_4_1) = e2 % 149.90/21.84 (39) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0 % 149.90/21.84 (40) ~ (all_52_8 = all_10_2) % 149.90/21.84 (41) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0 % 149.90/21.84 (42) ~ (all_56_1 = e2) | all_56_3 = e3 % 149.90/21.84 (43) ~ (all_56_1 = e0) | all_56_7 = e3 % 149.90/21.84 (44) all_34_1 = all_4_1 % 149.90/21.84 (45) all_56_5 = all_52_8 % 149.90/21.84 (46) ~ (e2 = e1) % 149.90/21.84 (47) all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3 % 149.90/21.84 (48) all_58_3 = all_8_2 % 149.90/21.84 (49) all_56_3 = all_52_4 % 149.90/21.84 (50) ~ (all_52_1 = all_52_3) % 149.90/21.84 (51) all_58_14 = e0 % 149.90/21.84 (52) all_54_13 = all_52_7 % 149.90/21.84 (53) op(e1, e1) = all_6_2 % 149.90/21.84 (54) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0 % 149.90/21.84 (55) all_58_7 = all_6_0 % 149.90/21.84 (56) all_56_19 = all_6_0 % 149.90/21.84 (57) all_58_15 = e1 % 149.90/21.84 (58) ~ (all_56_11 = e0) | all_56_15 = e2 % 149.90/21.84 (59) op(e1, e1) = all_4_1 % 149.90/21.84 (60) all_58_0 = all_10_2 % 149.90/21.84 (61) op(e1, all_6_2) = all_56_20 % 149.90/21.84 (62) all_58_1 = e0 | all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0 % 149.90/21.84 (63) ~ (all_52_3 = e1) % 149.90/21.84 (64) ~ (all_52_8 = all_52_12) % 149.90/21.84 (65) ~ (e2 = e0) % 149.90/21.84 (66) ~ (all_52_7 = e0) % 149.90/21.84 (67) ~ (all_8_2 = all_6_0) % 149.90/21.84 (68) ~ (all_52_4 = all_10_2) % 149.90/21.84 (69) ~ (all_52_4 = all_8_2) % 149.90/21.84 (70) op(all_8_2, all_8_2) = all_8_1 % 149.90/21.84 (71) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 149.90/21.84 (72) all_56_9 = all_52_1 % 149.90/21.84 (73) ~ (all_52_1 = all_10_2) % 149.90/21.84 (74) all_58_12 = all_52_3 % 149.90/21.84 (75) all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2 % 149.90/21.84 % 149.90/21.84 Begin of proof % 149.90/21.84 | % 149.90/21.84 | BETA: splitting (2) gives: % 149.90/21.84 | % 149.90/21.84 | Case 1: % 149.90/21.84 | | % 149.90/21.84 | | (76) ~ (all_34_1 = e3) % 149.90/21.84 | | % 149.90/21.84 | | REDUCE: (44), (76) imply: % 149.90/21.84 | | (77) ~ (all_4_1 = e3) % 149.90/21.84 | | % 149.90/21.84 | | GROUND_INST: instantiating (31) with all_6_2, all_4_1, e1, e1, simplifying % 149.90/21.84 | | with (53), (59) gives: % 149.90/21.84 | | (78) all_6_2 = all_4_1 % 149.90/21.84 | | % 149.90/21.84 | | COMBINE_EQS: (5), (78) imply: % 149.90/21.84 | | (79) all_54_10 = all_4_1 % 149.90/21.84 | | % 149.90/21.84 | | COMBINE_EQS: (16), (78) imply: % 149.90/21.84 | | (80) all_56_21 = all_4_1 % 149.90/21.84 | | % 149.90/21.84 | | REDUCE: (29), (78) imply: % 149.90/21.84 | | (81) ~ (all_52_8 = all_4_1) % 149.90/21.84 | | % 149.90/21.84 | | REDUCE: (33), (78) imply: % 149.90/21.84 | | (82) ~ (all_4_1 = e0) % 149.90/21.84 | | % 149.90/21.84 | | REDUCE: (37), (78) imply: % 149.90/21.84 | | (83) op(all_4_1, all_4_1) = e2 % 149.90/21.84 | | % 149.90/21.84 | | REDUCE: (61), (78) imply: % 149.90/21.84 | | (84) op(e1, all_4_1) = all_56_20 % 149.90/21.84 | | % 149.90/21.84 | | BETA: splitting (58) gives: % 149.90/21.84 | | % 149.90/21.84 | | Case 1: % 149.90/21.84 | | | % 149.90/21.84 | | | (85) ~ (all_56_11 = e0) % 149.90/21.84 | | | % 149.90/21.84 | | | REDUCE: (1), (85) imply: % 149.90/21.84 | | | (86) ~ (all_8_2 = e0) % 149.90/21.84 | | | % 149.90/21.84 | | | BETA: splitting (34) gives: % 149.90/21.84 | | | % 149.90/21.84 | | | Case 1: % 149.90/21.84 | | | | % 149.90/21.84 | | | | (87) ~ (all_56_11 = e3) % 149.90/21.84 | | | | % 149.90/21.84 | | | | REDUCE: (1), (87) imply: % 149.90/21.84 | | | | (88) ~ (all_8_2 = e3) % 149.90/21.84 | | | | % 149.90/21.84 | | | | BETA: splitting (6) gives: % 149.90/21.84 | | | | % 149.90/21.84 | | | | Case 1: % 149.90/21.84 | | | | | % 149.90/21.84 | | | | | (89) ~ (all_56_21 = e2) % 149.90/21.84 | | | | | % 149.90/21.84 | | | | | REDUCE: (80), (89) imply: % 149.90/21.84 | | | | | (90) ~ (all_4_1 = e2) % 149.90/21.84 | | | | | % 149.90/21.84 | | | | | REF_CLOSE: (17), (31), (59), (77), (79), (82), (83), (84), (90) are % 149.90/21.84 | | | | | inconsistent by sub-proof #53. % 149.90/21.84 | | | | | % 149.90/21.84 | | | | Case 2: % 149.90/21.84 | | | | | % 149.90/21.84 | | | | | (91) all_56_21 = e2 % 149.90/21.84 | | | | | (92) all_56_19 = e1 % 149.90/21.84 | | | | | % 149.90/21.84 | | | | | COMBINE_EQS: (56), (92) imply: % 149.90/21.84 | | | | | (93) all_6_0 = e1 % 149.90/21.84 | | | | | % 149.90/21.84 | | | | | SIMP: (93) implies: % 149.90/21.84 | | | | | (94) all_6_0 = e1 % 149.90/21.84 | | | | | % 149.90/21.84 | | | | | COMBINE_EQS: (80), (91) imply: % 149.90/21.84 | | | | | (95) all_4_1 = e2 % 149.90/21.84 | | | | | % 149.90/21.84 | | | | | SIMP: (95) implies: % 149.90/21.84 | | | | | (96) all_4_1 = e2 % 149.90/21.84 | | | | | % 149.90/21.84 | | | | | COMBINE_EQS: (55), (94) imply: % 149.90/21.84 | | | | | (97) all_58_7 = e1 % 149.90/21.84 | | | | | % 149.90/21.84 | | | | | REDUCE: (22), (94) imply: % 149.90/21.84 | | | | | (98) ~ (all_52_7 = e1) % 149.90/21.84 | | | | | % 149.90/21.84 | | | | | REDUCE: (81), (96) imply: % 149.90/21.84 | | | | | (99) ~ (all_52_8 = e2) % 149.90/21.84 | | | | | % 149.90/21.84 | | | | | REDUCE: (67), (94) imply: % 149.90/21.84 | | | | | (100) ~ (all_8_2 = e1) % 149.90/21.84 | | | | | % 149.90/21.84 | | | | | REDUCE: (38), (96) imply: % 149.90/21.84 | | | | | (101) op(e0, e2) = e2 % 149.90/21.84 | | | | | % 149.90/21.84 | | | | | BETA: splitting (71) gives: % 149.90/21.84 | | | | | % 149.90/21.84 | | | | | Case 1: % 149.90/21.84 | | | | | | % 149.90/21.84 | | | | | | (102) all_54_5 = e3 % 149.90/21.84 | | | | | | % 149.90/21.84 | | | | | | REF_CLOSE: (14), (88), (102) are inconsistent by sub-proof #737. % 149.90/21.84 | | | | | | % 149.90/21.84 | | | | | Case 2: % 149.90/21.84 | | | | | | % 149.90/21.84 | | | | | | (103) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 149.90/21.84 | | | | | | % 149.90/21.84 | | | | | | BETA: splitting (103) gives: % 149.90/21.84 | | | | | | % 149.90/21.84 | | | | | | Case 1: % 149.90/21.84 | | | | | | | % 149.90/21.84 | | | | | | | (104) all_54_5 = e2 % 149.90/21.84 | | | | | | | % 149.90/21.84 | | | | | | | COMBINE_EQS: (14), (104) imply: % 149.90/21.84 | | | | | | | (105) all_8_2 = e2 % 149.90/21.84 | | | | | | | % 149.90/21.84 | | | | | | | SIMP: (105) implies: % 149.90/21.84 | | | | | | | (106) all_8_2 = e2 % 149.90/21.84 | | | | | | | % 149.90/21.84 | | | | | | | COMBINE_EQS: (48), (106) imply: % 149.90/21.84 | | | | | | | (107) all_58_3 = e2 % 149.90/21.84 | | | | | | | % 149.90/21.84 | | | | | | | REDUCE: (69), (106) imply: % 149.90/21.84 | | | | | | | (108) ~ (all_52_4 = e2) % 149.90/21.84 | | | | | | | % 149.90/21.84 | | | | | | | REDUCE: (18), (106) imply: % 149.90/21.84 | | | | | | | (109) ~ (all_52_7 = e2) % 149.90/21.84 | | | | | | | % 149.90/21.84 | | | | | | | BETA: splitting (41) gives: % 149.90/21.84 | | | | | | | % 149.90/21.84 | | | | | | | Case 1: % 149.90/21.84 | | | | | | | | % 149.90/21.84 | | | | | | | | (110) all_54_13 = e3 % 149.90/21.84 | | | | | | | | % 149.90/21.84 | | | | | | | | COMBINE_EQS: (52), (110) imply: % 149.90/21.84 | | | | | | | | (111) all_52_7 = e3 % 149.90/21.84 | | | | | | | | % 149.90/21.84 | | | | | | | | COMBINE_EQS: (27), (111) imply: % 149.90/21.84 | | | | | | | | (112) all_58_13 = e3 % 149.90/21.84 | | | | | | | | % 149.90/21.84 | | | | | | | | REDUCE: (12), (111) imply: % 149.90/21.84 | | | | | | | | (113) ~ (all_52_4 = e3) % 149.90/21.84 | | | | | | | | % 149.90/21.84 | | | | | | | | REDUCE: (109), (111) imply: % 149.90/21.84 | | | | | | | | (114) ~ (e3 = e2) % 149.90/21.84 | | | | | | | | % 149.90/21.84 | | | | | | | | REDUCE: (66), (111) imply: % 149.90/21.84 | | | | | | | | (115) ~ (e3 = e0) % 149.90/21.84 | | | | | | | | % 149.90/21.84 | | | | | | | | REDUCE: (24), (111) imply: % 149.90/21.84 | | | | | | | | (116) op(e0, e2) = e3 % 149.90/21.84 | | | | | | | | % 149.90/21.84 | | | | | | | | BETA: splitting (42) gives: % 149.90/21.84 | | | | | | | | % 149.90/21.84 | | | | | | | | Case 1: % 149.90/21.84 | | | | | | | | | % 149.90/21.84 | | | | | | | | | (117) ~ (all_56_1 = e2) % 149.90/21.84 | | | | | | | | | % 149.90/21.84 | | | | | | | | | REDUCE: (19), (117) imply: % 149.90/21.84 | | | | | | | | | (118) ~ (all_10_2 = e2) % 149.90/21.84 | | | | | | | | | % 149.90/21.84 | | | | | | | | | BETA: splitting (62) gives: % 149.90/21.84 | | | | | | | | | % 149.90/21.84 | | | | | | | | | Case 1: % 149.90/21.84 | | | | | | | | | | % 149.90/21.84 | | | | | | | | | | (119) all_58_1 = e0 % 149.90/21.84 | | | | | | | | | | % 149.90/21.84 | | | | | | | | | | COMBINE_EQS: (26), (119) imply: % 149.90/21.84 | | | | | | | | | | (120) all_52_4 = e0 % 149.90/21.84 | | | | | | | | | | % 149.90/21.84 | | | | | | | | | | REDUCE: (108), (120) imply: % 149.90/21.85 | | | | | | | | | | (121) ~ (e2 = e0) % 149.90/21.85 | | | | | | | | | | % 149.90/21.85 | | | | | | | | | | BETA: splitting (9) gives: % 149.90/21.85 | | | | | | | | | | % 149.90/21.85 | | | | | | | | | | Case 1: % 149.90/21.85 | | | | | | | | | | | % 149.90/21.85 | | | | | | | | | | | (122) all_58_0 = e2 % 149.90/21.85 | | | | | | | | | | | % 149.90/21.85 | | | | | | | | | | | COMBINE_EQS: (60), (122) imply: % 149.90/21.85 | | | | | | | | | | | (123) all_10_2 = e2 % 149.90/21.85 | | | | | | | | | | | % 149.90/21.85 | | | | | | | | | | | REDUCE: (118), (123) imply: % 149.90/21.85 | | | | | | | | | | | (124) $false % 149.90/21.85 | | | | | | | | | | | % 149.90/21.85 | | | | | | | | | | | CLOSE: (124) is inconsistent. % 149.90/21.85 | | | | | | | | | | | % 149.90/21.85 | | | | | | | | | | Case 2: % 149.90/21.85 | | | | | | | | | | | % 149.90/21.85 | | | | | | | | | | | (125) all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2 % 149.90/21.85 | | | | | | | | | | | % 149.90/21.85 | | | | | | | | | | | BETA: splitting (125) gives: % 149.90/21.85 | | | | | | | | | | | % 149.90/21.85 | | | | | | | | | | | Case 1: % 149.90/21.85 | | | | | | | | | | | | % 149.90/21.85 | | | | | | | | | | | | (126) all_58_1 = e2 % 149.90/21.85 | | | | | | | | | | | | % 149.90/21.85 | | | | | | | | | | | | REF_CLOSE: (65), (119), (126) are inconsistent by sub-proof % 149.90/21.85 | | | | | | | | | | | | #330. % 149.90/21.85 | | | | | | | | | | | | % 149.90/21.85 | | | | | | | | | | | Case 2: % 149.90/21.85 | | | | | | | | | | | | % 149.90/21.85 | | | | | | | | | | | | (127) all_58_4 = e2 | all_58_9 = e2 % 149.90/21.85 | | | | | | | | | | | | % 149.90/21.85 | | | | | | | | | | | | BETA: splitting (127) gives: % 149.90/21.85 | | | | | | | | | | | | % 149.90/21.85 | | | | | | | | | | | | Case 1: % 149.90/21.85 | | | | | | | | | | | | | % 149.90/21.85 | | | | | | | | | | | | | (128) all_58_4 = e2 % 149.90/21.85 | | | | | | | | | | | | | % 149.90/21.85 | | | | | | | | | | | | | COMBINE_EQS: (13), (128) imply: % 149.90/21.85 | | | | | | | | | | | | | (129) all_52_8 = e2 % 149.90/21.85 | | | | | | | | | | | | | % 149.90/21.85 | | | | | | | | | | | | | REDUCE: (99), (129) imply: % 149.90/21.85 | | | | | | | | | | | | | (130) $false % 149.90/21.85 | | | | | | | | | | | | | % 149.90/21.85 | | | | | | | | | | | | | CLOSE: (130) is inconsistent. % 149.90/21.85 | | | | | | | | | | | | | % 149.90/21.85 | | | | | | | | | | | | Case 2: % 149.90/21.85 | | | | | | | | | | | | | % 149.90/21.85 | | | | | | | | | | | | | (131) all_58_9 = e2 % 149.90/21.85 | | | | | | | | | | | | | % 149.90/21.85 | | | | | | | | | | | | | COMBINE_EQS: (21), (131) imply: % 149.90/21.85 | | | | | | | | | | | | | (132) all_52_12 = e2 % 149.90/21.85 | | | | | | | | | | | | | % 149.90/21.85 | | | | | | | | | | | | | REDUCE: (23), (132) imply: % 149.90/21.85 | | | | | | | | | | | | | (133) op(e0, e2) = all_56_6 % 149.90/21.85 | | | | | | | | | | | | | % 149.90/21.85 | | | | | | | | | | | | | GROUND_INST: instantiating (31) with e3, all_56_6, e2, e0, % 149.90/21.85 | | | | | | | | | | | | | simplifying with (116), (133) gives: % 149.90/21.85 | | | | | | | | | | | | | (134) all_56_6 = e3 % 149.90/21.85 | | | | | | | | | | | | | % 149.90/21.85 | | | | | | | | | | | | | GROUND_INST: instantiating (31) with e2, all_56_6, e2, e0, % 149.90/21.85 | | | | | | | | | | | | | simplifying with (101), (133) gives: % 149.90/21.85 | | | | | | | | | | | | | (135) all_56_6 = e2 % 149.90/21.85 | | | | | | | | | | | | | % 149.90/21.85 | | | | | | | | | | | | | REF_CLOSE: (114), (134), (135) are inconsistent by sub-proof % 149.90/21.85 | | | | | | | | | | | | | #198. % 149.90/21.85 | | | | | | | | | | | | | % 149.90/21.85 | | | | | | | | | | | | End of split % 149.90/21.85 | | | | | | | | | | | | % 149.90/21.85 | | | | | | | | | | | End of split % 149.90/21.85 | | | | | | | | | | | % 149.90/21.85 | | | | | | | | | | End of split % 149.90/21.85 | | | | | | | | | | % 149.90/21.85 | | | | | | | | | Case 2: % 149.90/21.85 | | | | | | | | | | % 149.90/21.85 | | | | | | | | | | (136) all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0 % 149.90/21.85 | | | | | | | | | | % 149.90/21.85 | | | | | | | | | | REF_CLOSE: (30), (65), (97), (107), (112), (115), (136) are % 149.90/21.85 | | | | | | | | | | inconsistent by sub-proof #61. % 149.90/21.85 | | | | | | | | | | % 149.90/21.85 | | | | | | | | | End of split % 149.90/21.85 | | | | | | | | | % 149.90/21.85 | | | | | | | | Case 2: % 149.90/21.85 | | | | | | | | | % 149.90/21.85 | | | | | | | | | (137) all_56_3 = e3 % 149.90/21.85 | | | | | | | | | % 149.90/21.85 | | | | | | | | | COMBINE_EQS: (49), (137) imply: % 149.90/21.85 | | | | | | | | | (138) all_52_4 = e3 % 149.90/21.85 | | | | | | | | | % 149.90/21.85 | | | | | | | | | REDUCE: (113), (138) imply: % 149.90/21.85 | | | | | | | | | (139) $false % 149.90/21.85 | | | | | | | | | % 149.90/21.85 | | | | | | | | | CLOSE: (139) is inconsistent. % 149.90/21.85 | | | | | | | | | % 149.90/21.85 | | | | | | | | End of split % 149.90/21.85 | | | | | | | | % 149.90/21.85 | | | | | | | Case 2: % 149.90/21.85 | | | | | | | | % 149.90/21.85 | | | | | | | | (140) all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0 % 149.90/21.85 | | | | | | | | % 149.90/21.85 | | | | | | | | REF_CLOSE: (52), (66), (98), (109), (140) are inconsistent by % 149.90/21.85 | | | | | | | | sub-proof #710. % 149.90/21.85 | | | | | | | | % 149.90/21.85 | | | | | | | End of split % 149.90/21.85 | | | | | | | % 149.90/21.85 | | | | | | Case 2: % 149.90/21.85 | | | | | | | % 149.90/21.85 | | | | | | | (141) all_54_5 = e1 | all_54_5 = e0 % 149.90/21.85 | | | | | | | % 149.90/21.85 | | | | | | | REF_CLOSE: (14), (86), (100), (141) are inconsistent by sub-proof % 149.90/21.85 | | | | | | | #645. % 149.90/21.85 | | | | | | | % 149.90/21.85 | | | | | | End of split % 149.90/21.85 | | | | | | % 149.90/21.85 | | | | | End of split % 149.90/21.85 | | | | | % 149.90/21.85 | | | | End of split % 149.90/21.85 | | | | % 149.90/21.85 | | | Case 2: % 149.90/21.85 | | | | % 149.90/21.85 | | | | (142) all_56_11 = e3 % 149.90/21.85 | | | | (143) all_56_9 = e2 % 149.90/21.85 | | | | % 149.90/21.85 | | | | COMBINE_EQS: (72), (143) imply: % 149.90/21.85 | | | | (144) all_52_1 = e2 % 149.90/21.85 | | | | % 149.90/21.85 | | | | COMBINE_EQS: (1), (142) imply: % 149.90/21.85 | | | | (145) all_8_2 = e3 % 149.90/21.85 | | | | % 149.90/21.85 | | | | REDUCE: (50), (144) imply: % 149.90/21.85 | | | | (146) ~ (all_52_3 = e2) % 149.90/21.85 | | | | % 149.90/21.85 | | | | SIMP: (146) implies: % 149.90/21.85 | | | | (147) ~ (all_52_3 = e2) % 149.90/21.85 | | | | % 149.90/21.85 | | | | REDUCE: (73), (144) imply: % 149.90/21.85 | | | | (148) ~ (all_10_2 = e2) % 149.90/21.85 | | | | % 149.90/21.85 | | | | SIMP: (148) implies: % 149.90/21.85 | | | | (149) ~ (all_10_2 = e2) % 149.90/21.85 | | | | % 149.90/21.85 | | | | REDUCE: (69), (145) imply: % 149.90/21.85 | | | | (150) ~ (all_52_4 = e3) % 149.90/21.85 | | | | % 149.90/21.85 | | | | REDUCE: (70), (145) imply: % 149.90/21.85 | | | | (151) op(e3, e3) = all_8_1 % 149.90/21.85 | | | | % 149.90/21.85 | | | | BETA: splitting (39) gives: % 149.90/21.85 | | | | % 149.90/21.85 | | | | Case 1: % 149.90/21.85 | | | | | % 149.90/21.85 | | | | | (152) all_54_12 = e3 % 149.90/21.85 | | | | | % 149.90/21.85 | | | | | COMBINE_EQS: (11), (152) imply: % 149.90/21.85 | | | | | (153) all_52_3 = e3 % 149.90/21.85 | | | | | % 149.90/21.85 | | | | | SIMP: (153) implies: % 149.90/21.85 | | | | | (154) all_52_3 = e3 % 149.90/21.85 | | | | | % 149.90/21.85 | | | | | COMBINE_EQS: (74), (154) imply: % 149.90/21.85 | | | | | (155) all_58_12 = e3 % 149.90/21.85 | | | | | % 149.90/21.85 | | | | | REDUCE: (32), (154) imply: % 149.90/21.85 | | | | | (156) ~ (all_10_2 = e3) % 149.90/21.85 | | | | | % 149.90/21.85 | | | | | SIMP: (156) implies: % 149.90/21.85 | | | | | (157) ~ (all_10_2 = e3) % 149.90/21.85 | | | | | % 149.90/21.85 | | | | | REDUCE: (147), (154) imply: % 149.90/21.85 | | | | | (158) ~ (e3 = e2) % 149.90/21.85 | | | | | % 149.90/21.85 | | | | | BETA: splitting (75) gives: % 149.90/21.85 | | | | | % 149.90/21.85 | | | | | Case 1: % 149.90/21.85 | | | | | | % 149.90/21.85 | | | | | | (159) all_58_12 = e2 % 149.90/21.85 | | | | | | % 149.90/21.85 | | | | | | COMBINE_EQS: (155), (159) imply: % 149.90/21.85 | | | | | | (160) e3 = e2 % 149.90/21.85 | | | | | | % 149.90/21.85 | | | | | | REDUCE: (158), (160) imply: % 149.90/21.85 | | | | | | (161) $false % 149.90/21.85 | | | | | | % 149.90/21.85 | | | | | | CLOSE: (161) is inconsistent. % 149.90/21.85 | | | | | | % 149.90/21.85 | | | | | Case 2: % 149.90/21.85 | | | | | | % 149.90/21.85 | | | | | | (162) all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2 % 149.90/21.85 | | | | | | % 149.90/21.85 | | | | | | BETA: splitting (162) gives: % 149.90/21.85 | | | | | | % 149.90/21.85 | | | | | | Case 1: % 149.90/21.85 | | | | | | | % 149.90/21.85 | | | | | | | (163) all_58_13 = e2 % 149.90/21.85 | | | | | | | % 149.90/21.85 | | | | | | | COMBINE_EQS: (27), (163) imply: % 149.90/21.85 | | | | | | | (164) all_52_7 = e2 % 149.90/21.85 | | | | | | | % 149.90/21.85 | | | | | | | SIMP: (164) implies: % 149.90/21.85 | | | | | | | (165) all_52_7 = e2 % 149.90/21.85 | | | | | | | % 149.90/21.85 | | | | | | | REDUCE: (12), (165) imply: % 149.90/21.85 | | | | | | | (166) ~ (all_52_4 = e2) % 149.90/21.85 | | | | | | | % 149.90/21.85 | | | | | | | BETA: splitting (47) gives: % 149.90/21.85 | | | | | | | % 149.90/21.85 | | | | | | | Case 1: % 149.90/21.85 | | | | | | | | % 149.90/21.85 | | | | | | | | (167) all_58_4 = e3 % 149.90/21.85 | | | | | | | | % 149.90/21.85 | | | | | | | | COMBINE_EQS: (13), (167) imply: % 149.90/21.85 | | | | | | | | (168) all_52_8 = e3 % 149.90/21.85 | | | | | | | | % 149.90/21.85 | | | | | | | | REDUCE: (64), (168) imply: % 149.90/21.85 | | | | | | | | (169) ~ (all_52_12 = e3) % 149.90/21.85 | | | | | | | | % 149.90/21.85 | | | | | | | | SIMP: (169) implies: % 149.90/21.85 | | | | | | | | (170) ~ (all_52_12 = e3) % 149.90/21.85 | | | | | | | | % 149.90/21.85 | | | | | | | | REF_CLOSE: (4), (8), (15), (19), (28), (31), (36), (43), (149), % 149.90/21.85 | | | | | | | | (151), (157), (170) are inconsistent by sub-proof % 149.90/21.85 | | | | | | | | #392. % 149.90/21.85 | | | | | | | | % 149.90/21.85 | | | | | | | Case 2: % 149.90/21.85 | | | | | | | | % 149.90/21.85 | | | | | | | | (171) ~ (all_58_4 = e3) % 149.90/21.85 | | | | | | | | % 149.90/21.85 | | | | | | | | REDUCE: (13), (171) imply: % 149.90/21.85 | | | | | | | | (172) ~ (all_52_8 = e3) % 149.90/21.85 | | | | | | | | % 149.90/21.85 | | | | | | | | BETA: splitting (25) gives: % 149.90/21.85 | | | | | | | | % 149.90/21.85 | | | | | | | | Case 1: % 149.90/21.85 | | | | | | | | | % 149.90/21.85 | | | | | | | | | (173) ~ (all_56_1 = e1) % 149.90/21.85 | | | | | | | | | % 149.90/21.85 | | | | | | | | | REDUCE: (19), (173) imply: % 149.90/21.85 | | | | | | | | | (174) ~ (all_10_2 = e1) % 149.90/21.85 | | | | | | | | | % 149.90/21.85 | | | | | | | | | BETA: splitting (15) gives: % 149.90/21.85 | | | | | | | | | % 149.90/21.85 | | | | | | | | | Case 1: % 149.90/21.85 | | | | | | | | | | % 149.90/21.85 | | | | | | | | | | (175) all_54_0 = e3 % 149.90/21.85 | | | | | | | | | | % 149.90/21.85 | | | | | | | | | | REF_CLOSE: (8), (157), (175) are inconsistent by sub-proof % 149.90/21.85 | | | | | | | | | | #709. % 149.90/21.85 | | | | | | | | | | % 149.90/21.85 | | | | | | | | | Case 2: % 149.90/21.85 | | | | | | | | | | % 149.90/21.85 | | | | | | | | | | (176) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 149.90/21.85 | | | | | | | | | | % 149.90/21.85 | | | | | | | | | | BETA: splitting (176) gives: % 149.90/21.85 | | | | | | | | | | % 149.90/21.85 | | | | | | | | | | Case 1: % 149.90/21.85 | | | | | | | | | | | % 149.90/21.85 | | | | | | | | | | | (177) all_54_0 = e2 % 149.90/21.85 | | | | | | | | | | | % 149.90/21.85 | | | | | | | | | | | REF_CLOSE: (8), (149), (177) are inconsistent by sub-proof % 149.90/21.85 | | | | | | | | | | | #734. % 149.90/21.85 | | | | | | | | | | | % 149.90/21.85 | | | | | | | | | | Case 2: % 149.90/21.85 | | | | | | | | | | | % 149.90/21.85 | | | | | | | | | | | (178) all_54_0 = e1 | all_54_0 = e0 % 149.90/21.85 | | | | | | | | | | | % 149.90/21.85 | | | | | | | | | | | BETA: splitting (178) gives: % 149.90/21.85 | | | | | | | | | | | % 149.90/21.85 | | | | | | | | | | | Case 1: % 149.90/21.85 | | | | | | | | | | | | % 149.90/21.85 | | | | | | | | | | | | (179) all_54_0 = e1 % 149.90/21.85 | | | | | | | | | | | | % 149.90/21.85 | | | | | | | | | | | | REF_CLOSE: (8), (174), (179) are inconsistent by sub-proof % 149.90/21.85 | | | | | | | | | | | | #733. % 149.90/21.85 | | | | | | | | | | | | % 149.90/21.85 | | | | | | | | | | | Case 2: % 149.90/21.85 | | | | | | | | | | | | % 149.90/21.85 | | | | | | | | | | | | (180) all_54_0 = e0 % 149.90/21.85 | | | | | | | | | | | | % 149.90/21.85 | | | | | | | | | | | | COMBINE_EQS: (8), (180) imply: % 149.90/21.85 | | | | | | | | | | | | (181) all_10_2 = e0 % 149.90/21.85 | | | | | | | | | | | | % 149.90/21.85 | | | | | | | | | | | | SIMP: (181) implies: % 149.90/21.85 | | | | | | | | | | | | (182) all_10_2 = e0 % 149.90/21.85 | | | | | | | | | | | | % 149.90/21.85 | | | | | | | | | | | | REDUCE: (68), (182) imply: % 149.90/21.85 | | | | | | | | | | | | (183) ~ (all_52_4 = e0) % 149.90/21.85 | | | | | | | | | | | | % 149.90/21.85 | | | | | | | | | | | | BETA: splitting (54) gives: % 149.90/21.85 | | | | | | | | | | | | % 149.90/21.85 | | | | | | | | | | | | Case 1: % 149.90/21.85 | | | | | | | | | | | | | % 149.90/21.85 | | | | | | | | | | | | | (184) all_54_1 = e3 % 149.90/21.85 | | | | | | | | | | | | | % 149.90/21.85 | | | | | | | | | | | | | REF_CLOSE: (20), (150), (184) are inconsistent by sub-proof % 149.90/21.85 | | | | | | | | | | | | | #722. % 149.90/21.85 | | | | | | | | | | | | | % 149.90/21.85 | | | | | | | | | | | | Case 2: % 149.90/21.85 | | | | | | | | | | | | | % 149.90/21.85 | | | | | | | | | | | | | (185) all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0 % 149.90/21.85 | | | | | | | | | | | | | % 149.90/21.85 | | | | | | | | | | | | | BETA: splitting (185) gives: % 149.90/21.85 | | | | | | | | | | | | | % 149.90/21.85 | | | | | | | | | | | | | Case 1: % 149.90/21.85 | | | | | | | | | | | | | | % 149.90/21.85 | | | | | | | | | | | | | | (186) all_54_1 = e2 % 149.90/21.85 | | | | | | | | | | | | | | % 149.90/21.85 | | | | | | | | | | | | | | REF_CLOSE: (20), (166), (186) are inconsistent by sub-proof % 149.90/21.85 | | | | | | | | | | | | | | #721. % 149.90/21.85 | | | | | | | | | | | | | | % 149.90/21.85 | | | | | | | | | | | | | Case 2: % 149.90/21.85 | | | | | | | | | | | | | | % 149.90/21.85 | | | | | | | | | | | | | | (187) all_54_1 = e1 | all_54_1 = e0 % 149.90/21.85 | | | | | | | | | | | | | | % 149.90/21.85 | | | | | | | | | | | | | | BETA: splitting (187) gives: % 149.90/21.85 | | | | | | | | | | | | | | % 149.90/21.85 | | | | | | | | | | | | | | Case 1: % 149.90/21.85 | | | | | | | | | | | | | | | % 149.90/21.85 | | | | | | | | | | | | | | | (188) all_54_1 = e1 % 149.90/21.85 | | | | | | | | | | | | | | | % 149.90/21.85 | | | | | | | | | | | | | | | COMBINE_EQS: (20), (188) imply: % 149.90/21.85 | | | | | | | | | | | | | | | (189) all_52_4 = e1 % 149.90/21.85 | | | | | | | | | | | | | | | % 149.90/21.85 | | | | | | | | | | | | | | | SIMP: (189) implies: % 149.90/21.85 | | | | | | | | | | | | | | | (190) all_52_4 = e1 % 149.90/21.85 | | | | | | | | | | | | | | | % 149.90/21.85 | | | | | | | | | | | | | | | REDUCE: (10), (190) imply: % 149.90/21.85 | | | | | | | | | | | | | | | (191) ~ (all_6_0 = e1) % 149.90/21.85 | | | | | | | | | | | | | | | % 149.90/21.85 | | | | | | | | | | | | | | | SIMP: (191) implies: % 149.90/21.85 | | | | | | | | | | | | | | | (192) ~ (all_6_0 = e1) % 149.90/21.85 | | | | | | | | | | | | | | | % 149.90/21.85 | | | | | | | | | | | | | | | BETA: splitting (6) gives: % 149.90/21.85 | | | | | | | | | | | | | | | % 149.90/21.85 | | | | | | | | | | | | | | | Case 1: % 149.90/21.85 | | | | | | | | | | | | | | | | % 149.90/21.85 | | | | | | | | | | | | | | | | (193) ~ (all_56_21 = e2) % 149.90/21.85 | | | | | | | | | | | | | | | | % 149.90/21.85 | | | | | | | | | | | | | | | | REDUCE: (80), (193) imply: % 149.90/21.85 | | | | | | | | | | | | | | | | (194) ~ (all_4_1 = e2) % 149.90/21.85 | | | | | | | | | | | | | | | | % 149.90/21.85 | | | | | | | | | | | | | | | | REF_CLOSE: (17), (31), (59), (77), (79), (82), (83), (84), % 149.90/21.85 | | | | | | | | | | | | | | | | (194) are inconsistent by sub-proof #53. % 149.90/21.85 | | | | | | | | | | | | | | | | % 149.90/21.85 | | | | | | | | | | | | | | | Case 2: % 149.90/21.85 | | | | | | | | | | | | | | | | % 149.90/21.85 | | | | | | | | | | | | | | | | (195) all_56_19 = e1 % 149.90/21.85 | | | | | | | | | | | | | | | | % 149.90/21.85 | | | | | | | | | | | | | | | | COMBINE_EQS: (56), (195) imply: % 149.90/21.85 | | | | | | | | | | | | | | | | (196) all_6_0 = e1 % 149.90/21.85 | | | | | | | | | | | | | | | | % 149.90/21.85 | | | | | | | | | | | | | | | | REDUCE: (192), (196) imply: % 149.90/21.85 | | | | | | | | | | | | | | | | (197) $false % 149.90/21.85 | | | | | | | | | | | | | | | | % 149.90/21.85 | | | | | | | | | | | | | | | | CLOSE: (197) is inconsistent. % 149.90/21.85 | | | | | | | | | | | | | | | | % 149.90/21.85 | | | | | | | | | | | | | | | End of split % 149.90/21.85 | | | | | | | | | | | | | | | % 149.90/21.85 | | | | | | | | | | | | | | Case 2: % 149.90/21.85 | | | | | | | | | | | | | | | % 149.90/21.85 | | | | | | | | | | | | | | | (198) all_54_1 = e0 % 149.90/21.85 | | | | | | | | | | | | | | | % 149.90/21.85 | | | | | | | | | | | | | | | REF_CLOSE: (20), (183), (198) are inconsistent by sub-proof % 149.90/21.85 | | | | | | | | | | | | | | | #719. % 149.90/21.85 | | | | | | | | | | | | | | | % 149.90/21.85 | | | | | | | | | | | | | | End of split % 149.90/21.85 | | | | | | | | | | | | | | % 149.90/21.85 | | | | | | | | | | | | | End of split % 149.90/21.85 | | | | | | | | | | | | | % 149.90/21.85 | | | | | | | | | | | | End of split % 149.90/21.85 | | | | | | | | | | | | % 149.90/21.85 | | | | | | | | | | | End of split % 149.90/21.85 | | | | | | | | | | | % 149.90/21.85 | | | | | | | | | | End of split % 149.90/21.85 | | | | | | | | | | % 149.90/21.85 | | | | | | | | | End of split % 149.90/21.85 | | | | | | | | | % 149.90/21.85 | | | | | | | | Case 2: % 149.90/21.85 | | | | | | | | | % 149.90/21.85 | | | | | | | | | (199) all_56_5 = e3 % 149.90/21.85 | | | | | | | | | % 149.90/21.85 | | | | | | | | | COMBINE_EQS: (45), (199) imply: % 149.90/21.85 | | | | | | | | | (200) all_52_8 = e3 % 149.90/21.85 | | | | | | | | | % 149.90/21.85 | | | | | | | | | REDUCE: (172), (200) imply: % 149.90/21.85 | | | | | | | | | (201) $false % 149.90/21.85 | | | | | | | | | % 149.90/21.85 | | | | | | | | | CLOSE: (201) is inconsistent. % 149.90/21.85 | | | | | | | | | % 149.90/21.85 | | | | | | | | End of split % 149.90/21.85 | | | | | | | | % 149.90/21.85 | | | | | | | End of split % 149.90/21.85 | | | | | | | % 149.90/21.85 | | | | | | Case 2: % 149.90/21.85 | | | | | | | % 149.90/21.85 | | | | | | | (202) all_58_14 = e2 | all_58_15 = e2 % 149.90/21.85 | | | | | | | % 149.90/21.85 | | | | | | | REF_CLOSE: (46), (51), (57), (65), (202) are inconsistent by % 149.90/21.85 | | | | | | | sub-proof #36. % 149.90/21.85 | | | | | | | % 149.90/21.85 | | | | | | End of split % 149.90/21.85 | | | | | | % 149.90/21.85 | | | | | End of split % 149.90/21.85 | | | | | % 149.90/21.85 | | | | Case 2: % 149.90/21.85 | | | | | % 149.90/21.85 | | | | | (203) all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0 % 149.90/21.85 | | | | | % 149.90/21.85 | | | | | REF_CLOSE: (11), (35), (63), (147), (203) are inconsistent by % 149.90/21.85 | | | | | sub-proof #615. % 149.90/21.85 | | | | | % 149.90/21.85 | | | | End of split % 149.90/21.85 | | | | % 149.90/21.85 | | | End of split % 149.90/21.85 | | | % 149.90/21.85 | | Case 2: % 149.90/21.85 | | | % 149.90/21.85 | | | (204) all_56_11 = e0 % 149.90/21.85 | | | % 149.90/21.85 | | | COMBINE_EQS: (1), (204) imply: % 149.90/21.85 | | | (205) all_8_2 = e0 % 149.90/21.85 | | | % 149.90/21.85 | | | REDUCE: (70), (205) imply: % 149.90/21.85 | | | (206) op(e0, e0) = all_8_1 % 149.90/21.85 | | | % 149.90/21.85 | | | REF_CLOSE: (3), (4), (31), (206) are inconsistent by sub-proof #519. % 149.90/21.85 | | | % 149.90/21.85 | | End of split % 149.90/21.85 | | % 149.90/21.85 | Case 2: % 149.90/21.85 | | % 149.90/21.85 | | (207) ~ (all_34_2 = e1) % 149.90/21.85 | | % 149.90/21.85 | | REDUCE: (7), (207) imply: % 149.90/21.85 | | (208) $false % 149.90/21.85 | | % 149.90/21.85 | | CLOSE: (208) is inconsistent. % 149.90/21.85 | | % 149.90/21.85 | End of split % 149.90/21.85 | % 149.90/21.85 End of proof % 149.90/21.85 % 149.90/21.85 Sub-proof #34 shows that the following formulas are inconsistent: % 149.90/21.85 ---------------------------------------------------------------- % 149.90/21.85 (1) ~ (all_34_1 = e3) | ~ (all_34_2 = e1) % 149.90/21.85 (2) ~ (all_52_7 = e2) % 149.90/21.85 (3) all_34_2 = e1 % 149.90/21.85 (4) all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2 % 149.90/21.85 (5) ~ (all_52_14 = e2) % 149.90/21.85 (6) ~ (all_52_13 = e2) % 149.90/21.85 (7) all_58_9 = all_52_12 % 149.90/21.85 (8) op(e0, all_52_12) = all_56_6 % 149.90/21.85 (9) op(e0, e2) = all_52_7 % 149.90/21.85 (10) all_58_13 = all_52_7 % 149.90/21.85 (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 149.90/21.85 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 149.90/21.85 (12) op(e0, all_4_1) = e2 % 149.90/21.85 (13) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0 % 149.90/21.85 (14) all_34_1 = all_4_1 % 149.90/21.85 (15) ~ (e2 = e1) % 149.90/21.85 (16) all_58_11 = all_52_14 % 149.90/21.85 (17) ~ (all_52_7 = e1) % 149.90/21.85 (18) all_58_14 = e0 % 149.90/21.85 (19) all_54_13 = all_52_7 % 149.90/21.85 (20) all_58_15 = e1 % 149.90/21.85 (21) all_58_10 = all_52_13 % 149.90/21.85 (22) op(e1, e1) = all_4_1 % 149.90/21.85 (23) ~ (all_52_12 = e1) % 149.90/21.85 (24) ~ (e2 = e0) % 149.90/21.85 (25) ~ (all_52_7 = e0) % 149.90/21.85 (26) op(e1, e1) = e2 % 149.90/21.85 (27) all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2 % 149.90/21.85 % 149.90/21.85 Begin of proof % 149.90/21.85 | % 149.90/21.85 | BETA: splitting (4) gives: % 149.90/21.85 | % 149.90/21.85 | Case 1: % 149.90/21.85 | | % 149.90/21.85 | | (28) all_58_9 = e2 % 149.90/21.85 | | % 149.90/21.85 | | COMBINE_EQS: (7), (28) imply: % 149.90/21.85 | | (29) all_52_12 = e2 % 149.90/21.85 | | % 149.90/21.85 | | REDUCE: (8), (29) imply: % 149.90/21.85 | | (30) op(e0, e2) = all_56_6 % 149.90/21.85 | | % 149.90/21.85 | | BETA: splitting (1) gives: % 149.90/21.85 | | % 149.90/21.85 | | Case 1: % 149.90/21.85 | | | % 149.90/21.85 | | | (31) ~ (all_34_1 = e3) % 149.90/21.85 | | | % 149.90/21.85 | | | REDUCE: (14), (31) imply: % 149.90/21.85 | | | (32) ~ (all_4_1 = e3) % 149.90/21.85 | | | % 149.90/21.85 | | | BETA: splitting (13) gives: % 149.90/21.85 | | | % 149.90/21.85 | | | Case 1: % 149.90/21.85 | | | | % 149.90/21.85 | | | | (33) all_54_13 = e3 % 149.90/21.85 | | | | % 149.90/21.85 | | | | COMBINE_EQS: (19), (33) imply: % 149.90/21.85 | | | | (34) all_52_7 = e3 % 149.90/21.85 | | | | % 149.90/21.85 | | | | REDUCE: (9), (34) imply: % 149.90/21.85 | | | | (35) op(e0, e2) = e3 % 149.90/21.85 | | | | % 149.90/21.85 | | | | BETA: splitting (27) gives: % 149.90/21.85 | | | | % 149.90/21.85 | | | | Case 1: % 149.90/21.85 | | | | | % 149.90/21.85 | | | | | % 149.90/21.85 | | | | | GROUND_INST: instantiating (11) with e3, all_56_6, e2, e0, simplifying % 149.90/21.85 | | | | | with (30), (35) gives: % 149.90/21.85 | | | | | (36) all_56_6 = e3 % 149.90/21.85 | | | | | % 149.90/21.85 | | | | | GROUND_INST: instantiating (11) with e2, all_4_1, e1, e1, simplifying % 149.90/21.85 | | | | | with (22), (26) gives: % 149.90/21.85 | | | | | (37) all_4_1 = e2 % 149.90/21.85 | | | | | % 149.90/21.85 | | | | | REDUCE: (32), (37) imply: % 149.90/21.85 | | | | | (38) ~ (e3 = e2) % 149.90/21.85 | | | | | % 149.90/21.85 | | | | | SIMP: (38) implies: % 149.90/21.85 | | | | | (39) ~ (e3 = e2) % 149.90/21.85 | | | | | % 149.90/21.85 | | | | | REDUCE: (12), (37) imply: % 149.90/21.85 | | | | | (40) op(e0, e2) = e2 % 149.90/21.85 | | | | | % 149.90/21.85 | | | | | GROUND_INST: instantiating (11) with e2, all_56_6, e2, e0, simplifying % 149.90/21.85 | | | | | with (30), (40) gives: % 149.90/21.85 | | | | | (41) all_56_6 = e2 % 149.90/21.85 | | | | | % 149.90/21.85 | | | | | REF_CLOSE: (36), (39), (41) are inconsistent by sub-proof #198. % 149.90/21.85 | | | | | % 149.90/21.85 | | | | Case 2: % 149.90/21.85 | | | | | % 149.90/21.85 | | | | | (42) all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2 % 149.90/21.85 | | | | | % 149.90/21.85 | | | | | REF_CLOSE: (2), (10), (15), (18), (20), (24), (42) are inconsistent by % 149.90/21.85 | | | | | sub-proof #35. % 149.90/21.85 | | | | | % 149.90/21.85 | | | | End of split % 149.90/21.85 | | | | % 149.90/21.85 | | | Case 2: % 149.90/21.85 | | | | % 149.90/21.85 | | | | (43) all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0 % 149.90/21.85 | | | | % 149.90/21.85 | | | | REF_CLOSE: (2), (17), (19), (25), (43) are inconsistent by sub-proof % 149.90/21.85 | | | | #710. % 149.90/21.85 | | | | % 149.90/21.85 | | | End of split % 149.90/21.85 | | | % 149.90/21.85 | | Case 2: % 149.90/21.85 | | | % 149.90/21.85 | | | (44) ~ (all_34_2 = e1) % 149.90/21.85 | | | % 149.90/21.85 | | | REDUCE: (3), (44) imply: % 149.90/21.85 | | | (45) $false % 149.90/21.85 | | | % 149.90/21.85 | | | CLOSE: (45) is inconsistent. % 149.90/21.85 | | | % 149.90/21.85 | | End of split % 149.90/21.85 | | % 149.90/21.85 | Case 2: % 149.90/21.85 | | % 149.90/21.85 | | (46) all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2 % 149.90/21.85 | | % 149.90/21.85 | | REF_CLOSE: (5), (6), (15), (16), (20), (21), (46) are inconsistent by % 149.90/21.85 | | sub-proof #69. % 149.90/21.85 | | % 149.90/21.85 | End of split % 149.90/21.85 | % 149.90/21.85 End of proof % 149.90/21.85 % 149.90/21.85 Sub-proof #35 shows that the following formulas are inconsistent: % 149.90/21.85 ---------------------------------------------------------------- % 149.90/21.85 (1) all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2 % 149.90/21.85 (2) ~ (all_52_7 = e2) % 149.90/21.85 (3) all_58_13 = all_52_7 % 149.90/21.85 (4) ~ (e2 = e1) % 149.90/21.85 (5) all_58_14 = e0 % 149.90/21.85 (6) all_58_15 = e1 % 149.90/21.85 (7) ~ (e2 = e0) % 149.90/21.85 % 149.90/21.85 Begin of proof % 149.90/21.85 | % 149.90/21.85 | BETA: splitting (1) gives: % 149.90/21.85 | % 149.90/21.85 | Case 1: % 149.90/21.85 | | % 149.90/21.85 | | (8) all_58_13 = e2 % 149.90/21.85 | | % 149.90/21.85 | | COMBINE_EQS: (3), (8) imply: % 149.90/21.85 | | (9) all_52_7 = e2 % 149.90/21.85 | | % 149.90/21.85 | | REDUCE: (2), (9) imply: % 149.90/21.85 | | (10) $false % 149.90/21.85 | | % 149.90/21.85 | | CLOSE: (10) is inconsistent. % 149.90/21.85 | | % 149.90/21.85 | Case 2: % 149.90/21.85 | | % 149.90/21.85 | | (11) all_58_14 = e2 | all_58_15 = e2 % 149.90/21.85 | | % 149.90/21.85 | | REF_CLOSE: (4), (5), (6), (7), (11) are inconsistent by sub-proof #36. % 149.90/21.85 | | % 149.90/21.85 | End of split % 149.90/21.85 | % 149.90/21.85 End of proof % 149.90/21.85 % 149.90/21.85 Sub-proof #36 shows that the following formulas are inconsistent: % 149.90/21.85 ---------------------------------------------------------------- % 149.90/21.85 (1) all_58_14 = e2 | all_58_15 = e2 % 149.90/21.85 (2) ~ (e2 = e1) % 149.90/21.85 (3) all_58_14 = e0 % 149.90/21.85 (4) all_58_15 = e1 % 149.90/21.85 (5) ~ (e2 = e0) % 149.90/21.85 % 149.90/21.85 Begin of proof % 149.90/21.85 | % 149.90/21.85 | BETA: splitting (1) gives: % 149.90/21.85 | % 149.90/21.85 | Case 1: % 149.90/21.85 | | % 149.90/21.85 | | (6) all_58_14 = e2 % 149.90/21.85 | | % 149.90/21.85 | | COMBINE_EQS: (3), (6) imply: % 149.90/21.85 | | (7) e2 = e0 % 149.90/21.85 | | % 149.90/21.85 | | REDUCE: (5), (7) imply: % 149.90/21.85 | | (8) $false % 149.90/21.85 | | % 149.90/21.85 | | CLOSE: (8) is inconsistent. % 149.90/21.85 | | % 149.90/21.85 | Case 2: % 149.90/21.85 | | % 149.90/21.85 | | (9) all_58_15 = e2 % 149.90/21.85 | | % 149.90/21.85 | | REF_CLOSE: (2), (4), (9) are inconsistent by sub-proof #70. % 149.90/21.85 | | % 149.90/21.85 | End of split % 149.90/21.85 | % 149.90/21.85 End of proof % 149.90/21.85 % 149.90/21.85 Sub-proof #37 shows that the following formulas are inconsistent: % 149.90/21.85 ---------------------------------------------------------------- % 149.90/21.85 (1) all_56_11 = all_8_2 % 149.90/21.85 (2) ~ (all_52_11 = all_6_2) % 149.90/21.85 (3) all_56_25 = all_52_3 % 149.90/21.85 (4) ~ (all_52_7 = all_52_11) % 149.90/21.85 (5) all_58_6 = all_52_2 % 149.90/21.85 (6) all_18_1 = e2 % 149.90/21.85 (7) ~ (all_8_1 = e1) % 149.90/21.85 (8) ~ (e3 = e0) % 149.90/21.85 (9) ~ (all_56_31 = e1) | all_56_29 = e0 % 149.90/21.85 (10) all_54_10 = all_6_2 % 149.90/21.85 (11) ~ (all_56_21 = e2) | all_56_19 = e1 % 149.90/21.85 (12) ~ (all_52_14 = all_4_2) % 149.90/21.85 (13) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0 % 149.90/21.85 (14) all_54_12 = all_52_3 % 149.90/21.85 (15) all_18_0 = all_6_0 % 149.90/21.85 (16) ~ (e3 = e2) % 149.90/21.85 (17) op(e0, e0) = all_4_2 % 149.90/21.85 (18) all_58_6 = e0 | all_58_7 = e0 | all_58_8 = e0 | all_58_11 = e0 % 149.90/21.85 (19) all_54_15 = all_4_2 % 149.90/21.85 (20) all_54_9 = all_6_0 % 149.90/21.85 (21) all_56_21 = all_6_2 % 149.90/21.85 (22) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 149.90/21.85 (23) all_56_1 = all_10_2 % 149.90/21.85 (24) all_56_27 = all_52_7 % 149.90/21.85 (25) all_56_17 = all_52_2 % 149.90/21.85 (26) ~ (all_52_7 = all_6_0) % 149.90/21.85 (27) op(e0, e2) = all_52_7 % 149.90/21.85 (28) all_58_13 = all_52_7 % 149.90/21.85 (29) op(e2, all_8_2) = all_56_10 % 149.90/21.85 (30) op(e3, e3) = all_10_2 % 149.90/21.85 (31) ~ (all_56_21 = e3) | all_56_17 = e1 % 149.90/21.85 (32) ~ (e1 = e0) % 149.90/21.85 (33) all_18_2 = all_6_2 % 149.90/21.85 (34) all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2 % 149.90/21.85 (35) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 149.90/21.85 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 149.90/21.85 (36) ~ (all_52_3 = all_10_2) % 149.90/21.85 (37) ~ (all_52_3 = all_52_7) % 149.90/21.85 (38) op(e0, all_4_1) = all_4_0 % 149.90/21.85 (39) op(all_6_2, all_6_2) = e2 % 149.90/21.85 (40) ~ (all_6_0 = all_6_2) % 149.90/21.85 (41) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0 % 149.90/21.85 (42) ~ (all_52_7 = all_4_2) % 149.90/21.85 (43) all_58_8 = all_6_2 % 149.90/21.85 (44) ~ (all_6_0 = e0) | ~ (all_6_2 = e3) % 149.90/21.85 (45) op(e2, all_8_1) = e1 % 149.90/21.85 (46) ~ (all_52_3 = all_4_2) % 149.90/21.85 (47) all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3 % 149.90/21.85 (48) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0 % 149.90/21.85 (49) ~ (all_52_14 = all_6_0) % 149.90/21.85 (50) ~ (all_52_2 = all_52_3) % 149.90/21.85 (51) op(all_4_2, all_4_2) = all_4_1 % 149.90/21.85 (52) all_58_3 = all_8_2 % 149.90/21.85 (53) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0 % 149.90/21.85 (54) all_56_31 = all_4_2 % 149.90/21.85 (55) all_58_11 = all_52_14 % 149.90/21.85 (56) all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3 % 149.90/21.85 (57) ~ (all_52_2 = all_52_14) % 149.90/21.85 (58) all_56_1 = e3 | all_56_11 = e2 | all_56_21 = e1 | all_56_31 = e0 % 149.90/21.85 (59) ~ (all_52_2 = all_6_0) % 149.90/21.85 (60) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0 % 149.90/21.85 (61) all_54_13 = all_52_7 % 149.90/21.85 (62) all_56_23 = all_52_14 % 149.90/21.85 (63) all_54_8 = all_52_2 % 149.90/21.85 (64) op(e1, e1) = all_6_2 % 149.90/21.85 (65) all_56_29 = all_52_11 % 149.90/21.85 (66) all_58_7 = all_6_0 % 149.90/21.85 (67) all_56_19 = all_6_0 % 149.90/21.85 (68) ~ (all_18_0 = e3) | ~ (all_18_1 = e2) | ~ (all_18_2 = e0) % 149.90/21.85 (69) op(all_10_2, all_10_2) = all_10_1 % 149.90/21.85 (70) op(e1, all_6_2) = all_56_20 % 149.90/21.85 (71) all_58_1 = e0 | all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0 % 149.90/21.85 (72) ~ (all_56_31 = e2) | all_56_27 = e0 % 149.90/21.85 (73) ~ (e3 = e1) % 149.90/21.85 (74) op(e2, e2) = all_8_2 % 149.90/21.85 (75) ~ (all_52_2 = all_6_2) % 149.90/21.85 (76) ~ (all_56_21 = e0) | all_56_23 = e1 % 149.90/21.85 (77) op(e0, all_4_2) = all_56_30 % 149.90/21.85 (78) op(e3, all_10_2) = all_56_0 % 149.90/21.85 (79) ~ (all_52_14 = all_6_2) % 149.90/21.85 (80) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0 % 149.90/21.85 (81) ~ (all_52_2 = all_10_2) % 149.90/21.85 (82) ~ (all_8_2 = all_6_0) % 149.90/21.85 (83) op(all_8_2, all_8_2) = all_8_1 % 149.90/21.85 (84) ~ (all_4_0 = e2) % 149.90/21.86 (85) ~ (all_4_0 = e3) % 149.90/21.86 (86) all_54_11 = all_52_14 % 149.90/21.86 (87) ~ (all_56_31 = e3) | all_56_25 = e0 % 149.90/21.86 % 149.90/21.86 Begin of proof % 149.90/21.86 | % 149.90/21.86 | BETA: splitting (68) gives: % 149.90/21.86 | % 149.90/21.86 | Case 1: % 149.90/21.86 | | % 149.90/21.86 | | (88) ~ (all_18_0 = e3) % 149.90/21.86 | | % 149.90/21.86 | | REDUCE: (15), (88) imply: % 149.90/21.86 | | (89) ~ (all_6_0 = e3) % 149.90/21.86 | | % 149.90/21.86 | | BETA: splitting (9) gives: % 149.90/21.86 | | % 149.90/21.86 | | Case 1: % 149.90/21.86 | | | % 149.90/21.86 | | | (90) ~ (all_56_31 = e1) % 149.90/21.86 | | | % 149.90/21.86 | | | REDUCE: (54), (90) imply: % 149.90/21.86 | | | (91) ~ (all_4_2 = e1) % 149.90/21.86 | | | % 149.90/21.86 | | | BETA: splitting (87) gives: % 149.90/21.86 | | | % 149.90/21.86 | | | Case 1: % 149.90/21.86 | | | | % 149.90/21.86 | | | | (92) ~ (all_56_31 = e3) % 149.90/21.86 | | | | % 149.90/21.86 | | | | REDUCE: (54), (92) imply: % 149.90/21.86 | | | | (93) ~ (all_4_2 = e3) % 149.90/21.86 | | | | % 149.90/21.86 | | | | BETA: splitting (11) gives: % 149.90/21.86 | | | | % 149.90/21.86 | | | | Case 1: % 149.90/21.86 | | | | | % 149.90/21.86 | | | | | (94) ~ (all_56_21 = e2) % 149.90/21.86 | | | | | % 149.90/21.86 | | | | | REDUCE: (21), (94) imply: % 149.90/21.86 | | | | | (95) ~ (all_6_2 = e2) % 149.90/21.86 | | | | | % 149.90/21.86 | | | | | REF_CLOSE: (1), (5), (8), (10), (12), (14), (17), (18), (19), (20), % 149.90/21.86 | | | | | (21), (22), (23), (24), (25), (26), (31), (32), (34), (35), % 149.90/21.86 | | | | | (36), (37), (39), (40), (41), (43), (44), (46), (47), (49), % 149.90/21.86 | | | | | (50), (51), (53), (54), (55), (58), (60), (62), (64), (66), % 149.90/21.86 | | | | | (70), (72), (73), (75), (76), (77), (79), (81), (82), (89), % 149.90/21.86 | | | | | (91), (93), (95) are inconsistent by sub-proof #74. % 149.90/21.86 | | | | | % 149.90/21.86 | | | | Case 2: % 149.90/21.86 | | | | | % 149.90/21.86 | | | | | (96) all_56_21 = e2 % 149.90/21.86 | | | | | % 149.90/21.86 | | | | | COMBINE_EQS: (21), (96) imply: % 149.90/21.86 | | | | | (97) all_6_2 = e2 % 149.90/21.86 | | | | | % 149.90/21.86 | | | | | SIMP: (97) implies: % 149.90/21.86 | | | | | (98) all_6_2 = e2 % 149.90/21.86 | | | | | % 149.90/21.86 | | | | | REDUCE: (39), (98) imply: % 149.90/21.86 | | | | | (99) op(e2, e2) = e2 % 149.90/21.86 | | | | | % 149.90/21.86 | | | | | GROUND_INST: instantiating (35) with all_8_2, e2, e2, e2, simplifying % 149.90/21.86 | | | | | with (74), (99) gives: % 149.90/21.86 | | | | | (100) all_8_2 = e2 % 149.90/21.86 | | | | | % 149.90/21.86 | | | | | REDUCE: (83), (100) imply: % 149.90/21.86 | | | | | (101) op(e2, e2) = all_8_1 % 149.90/21.86 | | | | | % 149.90/21.86 | | | | | REDUCE: (29), (100) imply: % 149.90/21.86 | | | | | (102) op(e2, e2) = all_56_10 % 149.90/21.86 | | | | | % 149.90/21.86 | | | | | GROUND_INST: instantiating (35) with e2, all_56_10, e2, e2, % 149.90/21.86 | | | | | simplifying with (99), (102) gives: % 149.90/21.86 | | | | | (103) all_56_10 = e2 % 149.90/21.86 | | | | | % 149.90/21.86 | | | | | GROUND_INST: instantiating (35) with all_8_1, all_56_10, e2, e2, % 149.90/21.86 | | | | | simplifying with (101), (102) gives: % 149.90/21.86 | | | | | (104) all_56_10 = all_8_1 % 149.90/21.86 | | | | | % 149.90/21.86 | | | | | COMBINE_EQS: (103), (104) imply: % 149.90/21.86 | | | | | (105) all_8_1 = e2 % 149.90/21.86 | | | | | % 149.90/21.86 | | | | | SIMP: (105) implies: % 149.90/21.86 | | | | | (106) all_8_1 = e2 % 149.90/21.86 | | | | | % 149.90/21.86 | | | | | REF_CLOSE: (7), (35), (45), (101), (106) are inconsistent by sub-proof % 149.90/21.86 | | | | | #260. % 149.90/21.86 | | | | | % 149.90/21.86 | | | | End of split % 149.90/21.86 | | | | % 149.90/21.86 | | | Case 2: % 149.90/21.86 | | | | % 149.90/21.86 | | | | (107) all_56_31 = e3 % 149.90/21.86 | | | | (108) all_56_25 = e0 % 149.90/21.86 | | | | % 149.90/21.86 | | | | REF_CLOSE: (1), (3), (5), (10), (11), (12), (13), (16), (17), (20), % 149.90/21.86 | | | | (21), (22), (23), (25), (28), (30), (31), (32), (35), (37), % 149.90/21.86 | | | | (39), (40), (42), (43), (44), (46), (47), (49), (50), (51), % 149.90/21.86 | | | | (52), (53), (54), (55), (56), (57), (58), (59), (62), (63), % 149.90/21.86 | | | | (64), (66), (67), (69), (70), (71), (75), (76), (77), (78), % 149.90/21.86 | | | | (79), (80), (81), (82), (86), (89), (107), (108) are % 149.90/21.86 | | | | inconsistent by sub-proof #55. % 149.90/21.86 | | | | % 149.90/21.86 | | | End of split % 149.90/21.86 | | | % 149.90/21.86 | | Case 2: % 149.90/21.86 | | | % 149.90/21.86 | | | (109) all_56_31 = e1 % 149.90/21.86 | | | (110) all_56_29 = e0 % 149.90/21.86 | | | % 149.90/21.86 | | | COMBINE_EQS: (65), (110) imply: % 149.90/21.86 | | | (111) all_52_11 = e0 % 149.90/21.86 | | | % 149.90/21.86 | | | SIMP: (111) implies: % 149.90/21.86 | | | (112) all_52_11 = e0 % 149.90/21.86 | | | % 149.90/21.86 | | | COMBINE_EQS: (54), (109) imply: % 149.90/21.86 | | | (113) all_4_2 = e1 % 149.90/21.86 | | | % 149.90/21.86 | | | REDUCE: (4), (112) imply: % 149.90/21.86 | | | (114) ~ (all_52_7 = e0) % 149.90/21.86 | | | % 149.90/21.86 | | | REDUCE: (2), (112) imply: % 149.90/21.86 | | | (115) ~ (all_6_2 = e0) % 149.90/21.86 | | | % 149.90/21.86 | | | SIMP: (115) implies: % 149.90/21.86 | | | (116) ~ (all_6_2 = e0) % 149.90/21.86 | | | % 149.90/21.86 | | | REDUCE: (51), (113) imply: % 149.90/21.86 | | | (117) op(e1, e1) = all_4_1 % 149.90/21.86 | | | % 149.90/21.86 | | | REF_CLOSE: (1), (10), (11), (12), (13), (20), (21), (22), (23), (25), % 149.90/21.86 | | | (26), (27), (30), (31), (35), (38), (39), (40), (44), (48), % 149.90/21.86 | | | (49), (53), (54), (57), (58), (59), (61), (64), (67), (69), % 149.90/21.86 | | | (70), (75), (78), (79), (82), (84), (85), (86), (114), (116), % 149.90/21.86 | | | (117) are inconsistent by sub-proof #51. % 149.90/21.86 | | | % 149.90/21.86 | | End of split % 149.90/21.86 | | % 149.90/21.86 | Case 2: % 149.90/21.86 | | % 149.90/21.86 | | (118) all_18_0 = e3 % 149.90/21.86 | | (119) ~ (all_18_1 = e2) | ~ (all_18_2 = e0) % 149.90/21.86 | | % 149.90/21.86 | | COMBINE_EQS: (15), (118) imply: % 149.90/21.86 | | (120) all_6_0 = e3 % 149.90/21.86 | | % 149.90/21.86 | | SIMP: (120) implies: % 149.90/21.86 | | (121) all_6_0 = e3 % 149.90/21.86 | | % 149.90/21.86 | | REF_CLOSE: (6), (10), (11), (21), (22), (33), (35), (39), (40), (64), (67), % 149.90/21.86 | | (70), (73), (119), (121) are inconsistent by sub-proof #40. % 149.90/21.86 | | % 149.90/21.86 | End of split % 149.90/21.86 | % 149.90/21.86 End of proof % 149.90/21.86 % 149.90/21.86 Sub-proof #38 shows that the following formulas are inconsistent: % 149.90/21.86 ---------------------------------------------------------------- % 149.90/21.86 (1) all_58_6 = all_52_2 % 149.90/21.86 (2) op(e2, e2) = e2 % 149.90/21.86 (3) ~ (all_52_3 = e2) % 149.90/21.86 (4) all_54_1 = all_52_4 % 149.90/21.86 (5) ~ (all_52_4 = e1) % 149.90/21.86 (6) all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2 % 149.90/21.86 (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 149.90/21.86 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 149.90/21.86 (8) ~ (all_52_4 = e0) % 149.90/21.86 (9) ~ (all_52_2 = e2) % 149.90/21.86 (10) all_24_2 = all_10_2 % 149.90/21.86 (11) ~ (all_52_4 = e2) % 149.90/21.86 (12) op(e3, e2) = all_52_4 % 149.90/21.86 (13) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0 % 149.90/21.86 (14) op(e3, all_10_1) = e1 % 149.90/21.86 (15) all_58_2 = all_52_1 % 149.90/21.86 (16) ~ (all_24_1 = e0) | ~ (all_24_2 = e2) % 149.90/21.86 (17) op(all_10_2, all_10_2) = all_10_1 % 149.90/21.86 (18) all_58_0 = all_10_2 % 149.90/21.86 (19) op(e3, all_10_2) = all_56_0 % 149.90/21.86 (20) ~ (all_52_1 = e2) % 149.90/21.86 (21) all_58_12 = all_52_3 % 149.90/21.86 % 149.90/21.86 Begin of proof % 149.90/21.86 | % 149.90/21.86 | BETA: splitting (13) gives: % 149.90/21.86 | % 149.90/21.86 | Case 1: % 149.90/21.86 | | % 149.90/21.86 | | (22) all_54_1 = e3 % 149.90/21.86 | | % 149.90/21.86 | | COMBINE_EQS: (4), (22) imply: % 149.90/21.86 | | (23) all_52_4 = e3 % 149.90/21.86 | | % 149.90/21.86 | | SIMP: (23) implies: % 149.90/21.86 | | (24) all_52_4 = e3 % 149.90/21.86 | | % 149.90/21.86 | | REDUCE: (5), (24) imply: % 149.90/21.86 | | (25) ~ (e3 = e1) % 149.90/21.86 | | % 149.90/21.86 | | REDUCE: (12), (24) imply: % 149.90/21.86 | | (26) op(e3, e2) = e3 % 149.90/21.86 | | % 149.90/21.86 | | BETA: splitting (6) gives: % 149.90/21.86 | | % 149.90/21.86 | | Case 1: % 149.90/21.86 | | | % 149.90/21.86 | | | (27) all_58_0 = e2 % 149.90/21.86 | | | % 149.90/21.86 | | | COMBINE_EQS: (18), (27) imply: % 149.90/21.86 | | | (28) all_10_2 = e2 % 149.90/21.86 | | | % 149.90/21.86 | | | COMBINE_EQS: (10), (28) imply: % 149.90/21.86 | | | (29) all_24_2 = e2 % 149.90/21.86 | | | % 149.90/21.86 | | | REDUCE: (17), (28) imply: % 149.90/21.86 | | | (30) op(e2, e2) = all_10_1 % 149.90/21.86 | | | % 149.90/21.86 | | | REDUCE: (19), (28) imply: % 149.90/21.86 | | | (31) op(e3, e2) = all_56_0 % 149.90/21.86 | | | % 149.90/21.86 | | | BETA: splitting (16) gives: % 149.90/21.86 | | | % 149.90/21.86 | | | Case 1: % 149.90/21.86 | | | | % 149.90/21.86 | | | | (32) ~ (all_24_2 = e2) % 149.90/21.86 | | | | % 149.90/21.86 | | | | REDUCE: (29), (32) imply: % 149.90/21.86 | | | | (33) $false % 149.90/21.86 | | | | % 149.90/21.86 | | | | CLOSE: (33) is inconsistent. % 149.90/21.86 | | | | % 149.90/21.86 | | | Case 2: % 149.90/21.86 | | | | % 149.90/21.86 | | | | % 149.90/21.86 | | | | GROUND_INST: instantiating (7) with e2, all_10_1, e2, e2, simplifying % 149.90/21.86 | | | | with (2), (30) gives: % 149.90/21.86 | | | | (34) all_10_1 = e2 % 149.90/21.86 | | | | % 149.90/21.86 | | | | GROUND_INST: instantiating (7) with e3, all_56_0, e2, e3, simplifying % 149.90/21.86 | | | | with (26), (31) gives: % 149.90/21.86 | | | | (35) all_56_0 = e3 % 149.90/21.86 | | | | % 149.90/21.86 | | | | REDUCE: (14), (34) imply: % 149.90/21.86 | | | | (36) op(e3, e2) = e1 % 149.90/21.86 | | | | % 149.90/21.86 | | | | REF_CLOSE: (7), (25), (26), (36) are inconsistent by sub-proof #267. % 149.90/21.86 | | | | % 149.90/21.86 | | | End of split % 149.90/21.86 | | | % 149.90/21.86 | | Case 2: % 149.90/21.86 | | | % 149.90/21.86 | | | (37) all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2 % 149.90/21.86 | | | % 149.90/21.86 | | | REF_CLOSE: (1), (3), (9), (15), (20), (21), (37) are inconsistent by % 149.90/21.86 | | | sub-proof #695. % 149.90/21.86 | | | % 149.90/21.86 | | End of split % 149.90/21.86 | | % 149.90/21.86 | Case 2: % 149.90/21.86 | | % 149.90/21.86 | | (38) all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0 % 149.90/21.86 | | % 149.90/21.86 | | REF_CLOSE: (4), (5), (8), (11), (38) are inconsistent by sub-proof #718. % 149.90/21.86 | | % 149.90/21.86 | End of split % 149.90/21.86 | % 149.90/21.86 End of proof % 149.90/21.86 % 149.90/21.86 Sub-proof #39 shows that the following formulas are inconsistent: % 149.90/21.86 ---------------------------------------------------------------- % 149.90/21.86 (1) all_58_6 = all_52_2 % 149.90/21.86 (2) all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2 % 149.90/21.86 (3) ~ (all_52_14 = e2) % 149.90/21.86 (4) ~ (all_52_13 = e2) % 149.90/21.86 (5) all_58_9 = all_52_12 % 149.90/21.86 (6) all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2 % 149.90/21.86 (7) ~ (all_58_12 = e2) % 149.90/21.86 (8) ~ (all_4_2 = e2) % 149.90/21.86 (9) all_58_11 = all_52_14 % 149.90/21.86 (10) ~ (all_52_2 = e2) % 149.90/21.86 (11) all_58_15 = all_4_2 % 149.90/21.86 (12) all_58_2 = all_52_1 % 149.90/21.86 (13) all_58_10 = all_52_13 % 149.90/21.86 (14) all_58_0 = all_10_2 % 149.90/21.86 (15) ~ (all_52_1 = e2) % 149.90/21.86 (16) ~ (all_52_12 = all_10_2) % 149.90/21.86 (17) all_58_12 = all_52_3 % 149.90/21.86 % 149.90/21.86 Begin of proof % 149.90/21.86 | % 149.90/21.86 | REDUCE: (7), (17) imply: % 149.90/21.86 | (18) ~ (all_52_3 = e2) % 149.90/21.86 | % 149.90/21.86 | BETA: splitting (2) gives: % 149.90/21.86 | % 149.90/21.86 | Case 1: % 149.90/21.86 | | % 149.90/21.86 | | (19) all_58_9 = e2 % 149.90/21.86 | | % 149.90/21.86 | | COMBINE_EQS: (5), (19) imply: % 149.90/21.86 | | (20) all_52_12 = e2 % 149.90/21.86 | | % 149.90/21.86 | | REDUCE: (16), (20) imply: % 149.90/21.86 | | (21) ~ (all_10_2 = e2) % 149.90/21.86 | | % 149.90/21.86 | | SIMP: (21) implies: % 149.90/21.86 | | (22) ~ (all_10_2 = e2) % 149.90/21.86 | | % 149.90/21.86 | | REF_CLOSE: (1), (6), (10), (12), (14), (15), (17), (18), (22) are % 149.90/21.86 | | inconsistent by sub-proof #597. % 149.90/21.86 | | % 149.90/21.86 | Case 2: % 149.90/21.86 | | % 149.90/21.86 | | (23) all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2 % 149.90/21.86 | | % 149.90/21.86 | | REF_CLOSE: (3), (4), (8), (9), (11), (13), (23) are inconsistent by % 149.90/21.86 | | sub-proof #693. % 149.90/21.86 | | % 149.90/21.86 | End of split % 149.90/21.86 | % 149.90/21.86 End of proof % 149.90/21.86 % 149.90/21.86 Sub-proof #40 shows that the following formulas are inconsistent: % 149.90/21.86 ---------------------------------------------------------------- % 149.90/21.86 (1) all_18_1 = e2 % 149.90/21.86 (2) all_54_10 = all_6_2 % 149.90/21.86 (3) ~ (all_56_21 = e2) | all_56_19 = e1 % 149.90/21.86 (4) all_56_21 = all_6_2 % 149.90/21.86 (5) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 149.90/21.86 (6) all_18_2 = all_6_2 % 149.90/21.86 (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 149.90/21.86 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 149.90/21.86 (8) op(all_6_2, all_6_2) = e2 % 149.90/21.86 (9) ~ (all_6_0 = all_6_2) % 149.90/21.86 (10) all_6_0 = e3 % 149.90/21.86 (11) op(e1, e1) = all_6_2 % 149.90/21.86 (12) ~ (all_18_1 = e2) | ~ (all_18_2 = e0) % 149.90/21.86 (13) all_56_19 = all_6_0 % 149.90/21.86 (14) op(e1, all_6_2) = all_56_20 % 149.90/21.86 (15) ~ (e3 = e1) % 149.90/21.86 % 149.90/21.86 Begin of proof % 149.90/21.86 | % 149.90/21.86 | COMBINE_EQS: (10), (13) imply: % 149.90/21.86 | (16) all_56_19 = e3 % 149.90/21.86 | % 149.90/21.86 | REDUCE: (9), (10) imply: % 149.90/21.86 | (17) ~ (all_6_2 = e3) % 149.90/21.86 | % 149.90/21.86 | SIMP: (17) implies: % 149.90/21.86 | (18) ~ (all_6_2 = e3) % 149.90/21.86 | % 149.90/21.86 | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (11), (12), (14), (15), % 149.90/21.86 | (16), (18) are inconsistent by sub-proof #41. % 149.90/21.86 | % 149.90/21.86 End of proof % 149.90/21.86 % 149.90/21.86 Sub-proof #41 shows that the following formulas are inconsistent: % 149.90/21.86 ---------------------------------------------------------------- % 149.90/21.86 (1) all_18_1 = e2 % 149.90/21.86 (2) all_54_10 = all_6_2 % 149.90/21.86 (3) ~ (all_56_21 = e2) | all_56_19 = e1 % 149.90/21.86 (4) ~ (all_6_2 = e3) % 149.90/21.86 (5) all_56_21 = all_6_2 % 149.90/21.86 (6) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 149.90/21.86 (7) all_18_2 = all_6_2 % 149.90/21.86 (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 149.90/21.86 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 149.90/21.86 (9) op(all_6_2, all_6_2) = e2 % 149.90/21.86 (10) all_56_19 = e3 % 149.90/21.86 (11) op(e1, e1) = all_6_2 % 149.90/21.86 (12) ~ (all_18_1 = e2) | ~ (all_18_2 = e0) % 149.90/21.86 (13) op(e1, all_6_2) = all_56_20 % 149.90/21.86 (14) ~ (e3 = e1) % 149.90/21.86 % 149.90/21.86 Begin of proof % 149.90/21.86 | % 149.90/21.86 | BETA: splitting (12) gives: % 149.90/21.86 | % 149.90/21.86 | Case 1: % 149.90/21.86 | | % 149.90/21.86 | | (15) ~ (all_18_1 = e2) % 149.90/21.86 | | % 149.90/21.86 | | REDUCE: (1), (15) imply: % 149.90/21.86 | | (16) $false % 149.90/21.86 | | % 149.90/21.86 | | CLOSE: (16) is inconsistent. % 149.90/21.86 | | % 149.90/21.86 | Case 2: % 149.90/21.86 | | % 149.90/21.86 | | (17) ~ (all_18_2 = e0) % 149.90/21.86 | | % 149.90/21.86 | | REDUCE: (7), (17) imply: % 149.90/21.86 | | (18) ~ (all_6_2 = e0) % 149.90/21.86 | | % 149.90/21.86 | | BETA: splitting (3) gives: % 149.90/21.86 | | % 149.90/21.86 | | Case 1: % 149.90/21.86 | | | % 149.90/21.86 | | | (19) ~ (all_56_21 = e2) % 149.90/21.86 | | | % 149.90/21.86 | | | REDUCE: (5), (19) imply: % 149.90/21.86 | | | (20) ~ (all_6_2 = e2) % 149.90/21.86 | | | % 149.90/21.86 | | | REF_CLOSE: (2), (4), (6), (8), (9), (11), (13), (18), (20) are % 149.90/21.86 | | | inconsistent by sub-proof #89. % 149.90/21.86 | | | % 149.90/21.86 | | Case 2: % 149.90/21.86 | | | % 149.90/21.86 | | | (21) all_56_19 = e1 % 149.90/21.86 | | | % 149.90/21.86 | | | COMBINE_EQS: (10), (21) imply: % 149.90/21.86 | | | (22) e3 = e1 % 149.90/21.86 | | | % 149.90/21.86 | | | REDUCE: (14), (22) imply: % 149.90/21.86 | | | (23) $false % 149.90/21.86 | | | % 149.90/21.86 | | | CLOSE: (23) is inconsistent. % 149.90/21.86 | | | % 149.90/21.86 | | End of split % 149.90/21.86 | | % 149.90/21.86 | End of split % 149.90/21.86 | % 149.90/21.86 End of proof % 149.90/21.86 % 149.90/21.86 Sub-proof #42 shows that the following formulas are inconsistent: % 149.90/21.86 ---------------------------------------------------------------- % 149.90/21.86 (1) all_56_11 = all_8_2 % 149.90/21.86 (2) ~ (all_52_11 = all_6_2) % 149.90/21.86 (3) ~ (all_52_4 = all_52_8) % 149.90/21.86 (4) all_56_25 = all_52_3 % 149.90/21.86 (5) op(e2, all_8_1) = all_8_0 % 149.90/21.86 (6) all_58_6 = all_52_2 % 149.90/21.86 (7) ~ (all_8_1 = e1) % 149.90/21.86 (8) ~ (e3 = e0) % 149.90/21.86 (9) ~ (all_56_31 = e1) | all_56_29 = e0 % 149.90/21.86 (10) all_54_10 = all_6_2 % 149.90/21.86 (11) ~ (all_56_21 = e2) | all_56_19 = e1 % 149.90/21.86 (12) all_54_0 = all_10_2 % 149.90/21.86 (13) ~ (all_52_14 = all_4_2) % 149.90/21.86 (14) ~ (all_8_0 = e1) % 149.90/21.86 (15) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0 % 149.90/21.86 (16) all_54_12 = all_52_3 % 149.90/21.86 (17) ~ (all_52_4 = all_52_7) % 149.90/21.86 (18) all_8_1 = e3 % 149.90/21.86 (19) ~ (e3 = e2) % 149.90/21.86 (20) op(e0, e0) = all_4_2 % 149.90/21.86 (21) all_58_6 = e0 | all_58_7 = e0 | all_58_8 = e0 | all_58_11 = e0 % 149.90/21.86 (22) all_54_5 = all_8_2 % 149.90/21.86 (23) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 149.90/21.86 (24) all_54_15 = all_4_2 % 149.90/21.86 (25) all_54_9 = all_6_0 % 149.90/21.86 (26) all_56_21 = all_6_2 % 149.90/21.86 (27) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 149.90/21.86 (28) ~ (all_52_7 = all_8_2) % 149.90/21.86 (29) all_56_1 = all_10_2 % 149.90/21.86 (30) all_56_27 = all_52_7 % 149.90/21.86 (31) all_56_17 = all_52_2 % 149.90/21.86 (32) ~ (all_52_7 = all_6_0) % 149.90/21.86 (33) ~ (all_56_1 = e1) | all_56_5 = e3 % 149.90/21.86 (34) all_58_1 = all_52_4 % 149.90/21.86 (35) all_58_13 = all_52_7 % 149.90/21.86 (36) op(e2, all_8_2) = all_56_10 % 149.90/21.86 (37) op(e3, e3) = all_10_2 % 149.90/21.86 (38) all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1 % 149.90/21.86 (39) ~ (all_56_21 = e3) | all_56_17 = e1 % 149.90/21.86 (40) ~ (e1 = e0) % 149.90/21.86 (41) all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2 % 149.90/21.86 (42) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 149.90/21.86 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 149.90/21.86 (43) ~ (all_52_3 = all_10_2) % 149.90/21.86 (44) ~ (all_52_3 = all_52_7) % 149.90/21.86 (45) op(all_6_2, all_6_2) = e2 % 149.90/21.86 (46) ~ (all_6_0 = all_6_2) % 149.90/21.86 (47) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0 % 149.90/21.86 (48) ~ (all_52_7 = all_4_2) % 149.90/21.86 (49) all_58_8 = all_6_2 % 149.90/21.86 (50) ~ (all_6_0 = e3) % 149.90/21.86 (51) ~ (all_6_0 = e0) | ~ (all_6_2 = e3) % 149.90/21.86 (52) ~ (all_52_3 = all_4_2) % 149.90/21.86 (53) all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3 % 149.90/21.86 (54) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0 % 149.90/21.86 (55) ~ (all_56_1 = e2) | all_56_3 = e3 % 149.90/21.86 (56) ~ (all_52_14 = all_6_0) % 149.90/21.86 (57) all_56_5 = all_52_8 % 149.90/21.86 (58) ~ (all_52_2 = all_52_3) % 149.90/21.86 (59) op(all_4_2, all_4_2) = all_4_1 % 149.90/21.86 (60) all_58_3 = all_8_2 % 149.90/21.86 (61) all_56_3 = all_52_4 % 149.90/21.86 (62) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0 % 149.90/21.86 (63) all_56_31 = all_4_2 % 149.90/21.86 (64) all_58_11 = all_52_14 % 149.90/21.86 (65) all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3 % 149.90/21.86 (66) ~ (all_52_2 = all_52_14) % 149.90/21.86 (67) all_56_1 = e3 | all_56_11 = e2 | all_56_21 = e1 | all_56_31 = e0 % 149.90/21.86 (68) ~ (all_52_2 = all_6_0) % 149.90/21.86 (69) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0 % 149.90/21.86 (70) all_54_13 = all_52_7 % 149.90/21.86 (71) all_56_23 = all_52_14 % 149.90/21.86 (72) all_54_8 = all_52_2 % 149.90/21.86 (73) op(e1, e1) = all_6_2 % 149.90/21.86 (74) all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1 % 149.90/21.86 (75) all_56_29 = all_52_11 % 149.90/21.86 (76) all_58_7 = all_6_0 % 149.90/21.86 (77) all_58_2 = all_52_1 % 149.90/21.86 (78) op(all_10_2, all_10_2) = all_10_1 % 149.90/21.86 (79) ~ (all_56_11 = e0) | all_56_15 = e2 % 149.90/21.86 (80) all_58_0 = all_10_2 % 149.90/21.86 (81) op(e1, all_6_2) = all_56_20 % 149.90/21.86 (82) op(e2, e3) = all_52_1 % 149.90/21.86 (83) all_58_1 = e0 | all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0 % 149.90/21.86 (84) ~ (all_56_31 = e2) | all_56_27 = e0 % 149.90/21.86 (85) op(e2, e2) = all_8_2 % 149.90/21.86 (86) ~ (all_52_2 = all_6_2) % 149.90/21.86 (87) ~ (all_56_21 = e0) | all_56_23 = e1 % 149.90/21.86 (88) op(e0, all_4_2) = all_56_30 % 149.90/21.86 (89) op(e3, all_10_2) = all_56_0 % 149.90/21.86 (90) ~ (all_52_14 = all_6_2) % 149.90/21.86 (91) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0 % 149.90/21.86 (92) ~ (all_52_2 = all_10_2) % 149.90/21.86 (93) ~ (all_8_2 = all_6_0) % 149.90/21.86 (94) ~ (all_52_4 = all_10_2) % 149.90/21.86 (95) ~ (all_52_4 = all_8_2) % 149.90/21.86 (96) op(all_8_2, all_8_2) = all_8_1 % 149.90/21.86 (97) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 149.90/21.86 (98) all_58_12 = all_52_3 % 149.90/21.86 (99) all_54_11 = all_52_14 % 149.90/21.86 (100) ~ (all_56_31 = e3) | all_56_25 = e0 % 149.90/21.86 % 149.90/21.86 Begin of proof % 149.90/21.86 | % 149.90/21.86 | REDUCE: (7), (18) imply: % 149.90/21.86 | (101) ~ (e3 = e1) % 149.90/21.86 | % 149.90/21.86 | REDUCE: (18), (96) imply: % 149.90/21.86 | (102) op(all_8_2, all_8_2) = e3 % 149.90/21.86 | % 149.90/21.86 | REDUCE: (5), (18) imply: % 149.90/21.86 | (103) op(e2, e3) = all_8_0 % 149.90/21.86 | % 149.90/21.86 | GROUND_INST: instantiating (42) with all_52_1, all_8_0, e3, e2, simplifying % 149.90/21.86 | with (82), (103) gives: % 149.90/21.86 | (104) all_52_1 = all_8_0 % 149.90/21.86 | % 149.90/21.86 | COMBINE_EQS: (77), (104) imply: % 149.90/21.86 | (105) all_58_2 = all_8_0 % 149.90/21.86 | % 149.90/21.86 | BETA: splitting (11) gives: % 149.90/21.86 | % 149.90/21.86 | Case 1: % 149.90/21.86 | | % 149.90/21.86 | | (106) ~ (all_56_21 = e2) % 149.90/21.86 | | % 149.90/21.86 | | REDUCE: (26), (106) imply: % 149.90/21.86 | | (107) ~ (all_6_2 = e2) % 149.90/21.86 | | % 149.90/21.86 | | BETA: splitting (9) gives: % 149.90/21.86 | | % 149.90/21.86 | | Case 1: % 149.90/21.86 | | | % 149.90/21.86 | | | (108) ~ (all_56_31 = e1) % 149.90/21.86 | | | % 149.90/21.86 | | | REDUCE: (63), (108) imply: % 149.90/21.86 | | | (109) ~ (all_4_2 = e1) % 149.90/21.86 | | | % 149.90/21.86 | | | BETA: splitting (100) gives: % 149.90/21.86 | | | % 149.90/21.86 | | | Case 1: % 149.90/21.86 | | | | % 149.90/21.86 | | | | (110) ~ (all_56_31 = e3) % 149.90/21.86 | | | | % 149.90/21.86 | | | | REDUCE: (63), (110) imply: % 149.90/21.86 | | | | (111) ~ (all_4_2 = e3) % 149.90/21.86 | | | | % 149.90/21.86 | | | | REF_CLOSE: (1), (6), (8), (10), (13), (16), (20), (21), (24), (25), % 149.90/21.86 | | | | (26), (27), (29), (30), (31), (32), (39), (40), (41), (42), % 149.90/21.86 | | | | (43), (44), (45), (46), (47), (49), (50), (51), (52), (53), % 149.90/21.86 | | | | (56), (58), (59), (62), (63), (64), (67), (69), (71), (73), % 149.90/21.86 | | | | (76), (81), (84), (86), (87), (88), (90), (92), (93), (101), % 149.90/21.86 | | | | (107), (109), (111) are inconsistent by sub-proof #74. % 149.90/21.86 | | | | % 149.90/21.87 | | | Case 2: % 149.90/21.87 | | | | % 149.90/21.87 | | | | (112) all_56_31 = e3 % 149.90/21.87 | | | | (113) all_56_25 = e0 % 149.90/21.87 | | | | % 149.90/21.87 | | | | COMBINE_EQS: (4), (113) imply: % 149.90/21.87 | | | | (114) all_52_3 = e0 % 149.90/21.87 | | | | % 149.90/21.87 | | | | SIMP: (114) implies: % 149.90/21.87 | | | | (115) all_52_3 = e0 % 149.90/21.87 | | | | % 149.90/21.87 | | | | COMBINE_EQS: (63), (112) imply: % 149.90/21.87 | | | | (116) all_4_2 = e3 % 149.90/21.87 | | | | % 149.90/21.87 | | | | COMBINE_EQS: (98), (115) imply: % 149.90/21.87 | | | | (117) all_58_12 = e0 % 149.90/21.87 | | | | % 149.90/21.87 | | | | REDUCE: (44), (115) imply: % 149.90/21.87 | | | | (118) ~ (all_52_7 = e0) % 149.90/21.87 | | | | % 149.90/21.87 | | | | SIMP: (118) implies: % 149.90/21.87 | | | | (119) ~ (all_52_7 = e0) % 149.90/21.87 | | | | % 149.90/21.87 | | | | REDUCE: (43), (115) imply: % 149.90/21.87 | | | | (120) ~ (all_10_2 = e0) % 149.90/21.87 | | | | % 149.90/21.87 | | | | SIMP: (120) implies: % 149.90/21.87 | | | | (121) ~ (all_10_2 = e0) % 149.90/21.87 | | | | % 149.90/21.87 | | | | REDUCE: (52), (115), (116) imply: % 149.90/21.87 | | | | (122) ~ (e3 = e0) % 149.90/21.87 | | | | % 149.90/21.87 | | | | REDUCE: (48), (116) imply: % 149.90/21.87 | | | | (123) ~ (all_52_7 = e3) % 149.90/21.87 | | | | % 149.90/21.87 | | | | REDUCE: (59), (116) imply: % 149.90/21.87 | | | | (124) op(e3, e3) = all_4_1 % 149.90/21.87 | | | | % 149.90/21.87 | | | | GROUND_INST: instantiating (42) with all_10_2, all_4_1, e3, e3, % 149.90/21.87 | | | | simplifying with (37), (124) gives: % 149.90/21.87 | | | | (125) all_10_2 = all_4_1 % 149.90/21.87 | | | | % 149.90/21.87 | | | | COMBINE_EQS: (12), (125) imply: % 149.90/21.87 | | | | (126) all_54_0 = all_4_1 % 149.90/21.87 | | | | % 149.90/21.87 | | | | COMBINE_EQS: (29), (125) imply: % 149.90/21.87 | | | | (127) all_56_1 = all_4_1 % 149.90/21.87 | | | | % 149.90/21.87 | | | | COMBINE_EQS: (80), (125) imply: % 149.90/21.87 | | | | (128) all_58_0 = all_4_1 % 149.90/21.87 | | | | % 149.90/21.87 | | | | REDUCE: (92), (125) imply: % 149.90/21.87 | | | | (129) ~ (all_52_2 = all_4_1) % 149.90/21.87 | | | | % 149.90/21.87 | | | | REDUCE: (94), (125) imply: % 149.90/21.87 | | | | (130) ~ (all_52_4 = all_4_1) % 149.90/21.87 | | | | % 149.90/21.87 | | | | REDUCE: (121), (125) imply: % 149.90/21.87 | | | | (131) ~ (all_4_1 = e0) % 149.90/21.87 | | | | % 149.90/21.87 | | | | BETA: splitting (79) gives: % 149.90/21.87 | | | | % 149.90/21.87 | | | | Case 1: % 149.90/21.87 | | | | | % 149.90/21.87 | | | | | (132) ~ (all_56_11 = e0) % 149.90/21.87 | | | | | % 149.90/21.87 | | | | | REDUCE: (1), (132) imply: % 149.90/21.87 | | | | | (133) ~ (all_8_2 = e0) % 149.90/21.87 | | | | | % 149.90/21.87 | | | | | BETA: splitting (87) gives: % 149.90/21.87 | | | | | % 149.90/21.87 | | | | | Case 1: % 149.90/21.87 | | | | | | % 149.90/21.87 | | | | | | (134) ~ (all_56_21 = e0) % 149.90/21.87 | | | | | | % 149.90/21.87 | | | | | | REDUCE: (26), (134) imply: % 149.90/21.87 | | | | | | (135) ~ (all_6_2 = e0) % 149.90/21.87 | | | | | | % 149.90/21.87 | | | | | | REF_CLOSE: (1), (10), (13), (15), (25), (26), (27), (29), (31), % 149.90/21.87 | | | | | | (37), (39), (42), (45), (46), (51), (56), (62), (63), % 149.90/21.87 | | | | | | (66), (67), (68), (71), (73), (78), (81), (86), (87), % 149.90/21.87 | | | | | | (89), (90), (93), (99), (107), (135) are inconsistent by % 149.90/21.87 | | | | | | sub-proof #58. % 149.90/21.87 | | | | | | % 149.90/21.87 | | | | | Case 2: % 149.90/21.87 | | | | | | % 149.90/21.87 | | | | | | (136) all_56_23 = e1 % 149.90/21.87 | | | | | | (137) all_56_21 = e0 % 149.90/21.87 | | | | | | % 149.90/21.87 | | | | | | COMBINE_EQS: (26), (137) imply: % 149.90/21.87 | | | | | | (138) all_6_2 = e0 % 149.90/21.87 | | | | | | % 149.90/21.87 | | | | | | SIMP: (138) implies: % 149.90/21.87 | | | | | | (139) all_6_2 = e0 % 149.90/21.87 | | | | | | % 149.90/21.87 | | | | | | COMBINE_EQS: (71), (136) imply: % 149.90/21.87 | | | | | | (140) all_52_14 = e1 % 149.90/21.87 | | | | | | % 149.90/21.87 | | | | | | SIMP: (140) implies: % 149.90/21.87 | | | | | | (141) all_52_14 = e1 % 149.90/21.87 | | | | | | % 149.90/21.87 | | | | | | REDUCE: (66), (141) imply: % 149.90/21.87 | | | | | | (142) ~ (all_52_2 = e1) % 149.90/21.87 | | | | | | % 149.90/21.87 | | | | | | REDUCE: (86), (139) imply: % 149.90/21.87 | | | | | | (143) ~ (all_52_2 = e0) % 149.90/21.87 | | | | | | % 149.90/21.87 | | | | | | REDUCE: (56), (141) imply: % 149.90/21.87 | | | | | | (144) ~ (all_6_0 = e1) % 149.90/21.87 | | | | | | % 149.90/21.87 | | | | | | SIMP: (144) implies: % 149.90/21.87 | | | | | | (145) ~ (all_6_0 = e1) % 149.90/21.87 | | | | | | % 149.90/21.87 | | | | | | REDUCE: (46), (139) imply: % 149.90/21.87 | | | | | | (146) ~ (all_6_0 = e0) % 149.90/21.87 | | | | | | % 149.90/21.87 | | | | | | REF_CLOSE: (1), (17), (22), (23), (25), (28), (32), (34), (35), % 149.90/21.87 | | | | | | (38), (50), (54), (55), (60), (61), (62), (67), (68), % 149.90/21.87 | | | | | | (70), (72), (76), (83), (91), (93), (95), (97), (112), % 149.90/21.87 | | | | | | (119), (123), (126), (127), (128), (129), (130), (133), % 149.90/21.87 | | | | | | (137), (142), (143), (145), (146) are inconsistent by % 149.90/21.87 | | | | | | sub-proof #44. % 149.90/21.87 | | | | | | % 149.90/21.87 | | | | | End of split % 149.90/21.87 | | | | | % 149.90/21.87 | | | | Case 2: % 149.90/21.87 | | | | | % 149.90/21.87 | | | | | (147) all_56_11 = e0 % 149.90/21.87 | | | | | % 149.90/21.87 | | | | | COMBINE_EQS: (1), (147) imply: % 149.90/21.87 | | | | | (148) all_8_2 = e0 % 149.90/21.87 | | | | | % 149.90/21.87 | | | | | COMBINE_EQS: (60), (148) imply: % 149.90/21.87 | | | | | (149) all_58_3 = e0 % 149.90/21.87 | | | | | % 149.90/21.87 | | | | | BETA: splitting (65) gives: % 149.90/21.87 | | | | | % 149.90/21.87 | | | | | Case 1: % 149.90/21.87 | | | | | | % 149.90/21.87 | | | | | | (150) all_58_1 = e3 % 149.90/21.87 | | | | | | % 149.90/21.87 | | | | | | COMBINE_EQS: (34), (150) imply: % 149.90/21.87 | | | | | | (151) all_52_4 = e3 % 149.90/21.87 | | | | | | % 149.90/21.87 | | | | | | REDUCE: (3), (151) imply: % 149.90/21.87 | | | | | | (152) ~ (all_52_8 = e3) % 149.90/21.87 | | | | | | % 149.90/21.87 | | | | | | SIMP: (152) implies: % 149.90/21.87 | | | | | | (153) ~ (all_52_8 = e3) % 149.90/21.87 | | | | | | % 149.90/21.87 | | | | | | REDUCE: (130), (151) imply: % 149.90/21.87 | | | | | | (154) ~ (all_4_1 = e3) % 149.90/21.87 | | | | | | % 149.90/21.87 | | | | | | SIMP: (154) implies: % 149.90/21.87 | | | | | | (155) ~ (all_4_1 = e3) % 149.90/21.87 | | | | | | % 149.90/21.87 | | | | | | BETA: splitting (33) gives: % 149.90/21.87 | | | | | | % 149.90/21.87 | | | | | | Case 1: % 149.90/21.87 | | | | | | | % 149.90/21.87 | | | | | | | (156) ~ (all_56_1 = e1) % 149.90/21.87 | | | | | | | % 149.90/21.87 | | | | | | | REDUCE: (127), (156) imply: % 149.90/21.87 | | | | | | | (157) ~ (all_4_1 = e1) % 149.90/21.87 | | | | | | | % 149.90/21.87 | | | | | | | BETA: splitting (23) gives: % 149.90/21.87 | | | | | | | % 149.90/21.87 | | | | | | | Case 1: % 149.90/21.87 | | | | | | | | % 149.90/21.87 | | | | | | | | (158) all_54_0 = e3 % 149.90/21.87 | | | | | | | | % 149.90/21.87 | | | | | | | | REF_CLOSE: (126), (155), (158) are inconsistent by sub-proof % 149.90/21.87 | | | | | | | | #554. % 149.90/21.87 | | | | | | | | % 149.90/21.87 | | | | | | | Case 2: % 149.90/21.87 | | | | | | | | % 149.90/21.87 | | | | | | | | (159) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 149.90/21.87 | | | | | | | | % 149.90/21.87 | | | | | | | | BETA: splitting (159) gives: % 149.90/21.87 | | | | | | | | % 149.90/21.87 | | | | | | | | Case 1: % 149.90/21.87 | | | | | | | | | % 149.90/21.87 | | | | | | | | | (160) all_54_0 = e2 % 149.90/21.87 | | | | | | | | | % 149.90/21.87 | | | | | | | | | COMBINE_EQS: (126), (160) imply: % 149.90/21.87 | | | | | | | | | (161) all_4_1 = e2 % 149.90/21.87 | | | | | | | | | % 149.90/21.87 | | | | | | | | | SIMP: (161) implies: % 149.90/21.87 | | | | | | | | | (162) all_4_1 = e2 % 149.90/21.87 | | | | | | | | | % 149.90/21.87 | | | | | | | | | COMBINE_EQS: (128), (162) imply: % 149.90/21.87 | | | | | | | | | (163) all_58_0 = e2 % 149.90/21.87 | | | | | | | | | % 149.90/21.87 | | | | | | | | | REDUCE: (157), (162) imply: % 149.90/21.87 | | | | | | | | | (164) ~ (e2 = e1) % 149.90/21.87 | | | | | | | | | % 149.90/21.87 | | | | | | | | | BETA: splitting (74) gives: % 149.90/21.87 | | | | | | | | | % 149.90/21.87 | | | | | | | | | Case 1: % 149.90/21.87 | | | | | | | | | | % 149.90/21.87 | | | | | | | | | | (165) all_58_0 = e1 % 149.90/21.87 | | | | | | | | | | % 149.90/21.87 | | | | | | | | | | COMBINE_EQS: (163), (165) imply: % 149.90/21.87 | | | | | | | | | | (166) e2 = e1 % 149.90/21.87 | | | | | | | | | | % 149.90/21.87 | | | | | | | | | | REDUCE: (164), (166) imply: % 149.90/21.87 | | | | | | | | | | (167) $false % 149.90/21.87 | | | | | | | | | | % 149.90/21.87 | | | | | | | | | | CLOSE: (167) is inconsistent. % 149.90/21.87 | | | | | | | | | | % 149.90/21.87 | | | | | | | | | Case 2: % 149.90/21.87 | | | | | | | | | | % 149.90/21.87 | | | | | | | | | | (168) all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1 % 149.90/21.87 | | | | | | | | | | % 149.90/21.87 | | | | | | | | | | BETA: splitting (168) gives: % 149.90/21.87 | | | | | | | | | | % 149.90/21.87 | | | | | | | | | | Case 1: % 149.90/21.87 | | | | | | | | | | | % 149.90/21.87 | | | | | | | | | | | (169) all_58_2 = e1 % 149.90/21.87 | | | | | | | | | | | % 149.90/21.87 | | | | | | | | | | | COMBINE_EQS: (105), (169) imply: % 149.90/21.87 | | | | | | | | | | | (170) all_8_0 = e1 % 149.90/21.87 | | | | | | | | | | | % 149.90/21.87 | | | | | | | | | | | REDUCE: (14), (170) imply: % 149.90/21.87 | | | | | | | | | | | (171) $false % 149.90/21.87 | | | | | | | | | | | % 149.90/21.87 | | | | | | | | | | | CLOSE: (171) is inconsistent. % 149.90/21.87 | | | | | | | | | | | % 149.90/21.87 | | | | | | | | | | Case 2: % 149.90/21.87 | | | | | | | | | | | % 149.90/21.87 | | | | | | | | | | | (172) all_58_6 = e1 | all_58_12 = e1 % 149.90/21.87 | | | | | | | | | | | % 149.90/21.87 | | | | | | | | | | | BETA: splitting (172) gives: % 149.90/21.87 | | | | | | | | | | | % 149.90/21.87 | | | | | | | | | | | Case 1: % 149.90/21.87 | | | | | | | | | | | | % 149.90/21.87 | | | | | | | | | | | | (173) all_58_6 = e1 % 149.90/21.87 | | | | | | | | | | | | % 149.90/21.87 | | | | | | | | | | | | COMBINE_EQS: (6), (173) imply: % 149.90/21.87 | | | | | | | | | | | | (174) all_52_2 = e1 % 149.90/21.87 | | | | | | | | | | | | % 149.90/21.87 | | | | | | | | | | | | SIMP: (174) implies: % 149.90/21.87 | | | | | | | | | | | | (175) all_52_2 = e1 % 149.90/21.87 | | | | | | | | | | | | % 149.90/21.87 | | | | | | | | | | | | REDUCE: (66), (175) imply: % 149.90/21.87 | | | | | | | | | | | | (176) ~ (all_52_14 = e1) % 149.90/21.87 | | | | | | | | | | | | % 149.90/21.87 | | | | | | | | | | | | SIMP: (176) implies: % 149.90/21.87 | | | | | | | | | | | | (177) ~ (all_52_14 = e1) % 149.90/21.87 | | | | | | | | | | | | % 149.90/21.87 | | | | | | | | | | | | BETA: splitting (87) gives: % 149.90/21.87 | | | | | | | | | | | | % 149.90/21.87 | | | | | | | | | | | | Case 1: % 149.90/21.87 | | | | | | | | | | | | | % 149.90/21.87 | | | | | | | | | | | | | (178) ~ (all_56_21 = e0) % 149.90/21.87 | | | | | | | | | | | | | % 149.90/21.87 | | | | | | | | | | | | | REDUCE: (26), (178) imply: % 149.90/21.87 | | | | | | | | | | | | | (179) ~ (all_6_2 = e0) % 149.90/21.87 | | | | | | | | | | | | | % 149.90/21.87 | | | | | | | | | | | | | REF_CLOSE: (1), (10), (13), (15), (25), (26), (27), (29), % 149.90/21.87 | | | | | | | | | | | | | (31), (37), (39), (42), (45), (46), (51), (56), % 149.90/21.87 | | | | | | | | | | | | | (62), (63), (66), (67), (68), (71), (73), (78), % 149.90/21.87 | | | | | | | | | | | | | (81), (86), (87), (89), (90), (93), (99), (107), % 149.90/21.87 | | | | | | | | | | | | | (179) are inconsistent by sub-proof #58. % 149.90/21.87 | | | | | | | | | | | | | % 149.90/21.87 | | | | | | | | | | | | Case 2: % 149.90/21.87 | | | | | | | | | | | | | % 149.90/21.87 | | | | | | | | | | | | | (180) all_56_23 = e1 % 149.90/21.87 | | | | | | | | | | | | | % 149.90/21.87 | | | | | | | | | | | | | REF_CLOSE: (71), (177), (180) are inconsistent by sub-proof % 149.90/21.87 | | | | | | | | | | | | | #309. % 149.90/21.87 | | | | | | | | | | | | | % 149.90/21.87 | | | | | | | | | | | | End of split % 149.90/21.87 | | | | | | | | | | | | % 149.90/21.87 | | | | | | | | | | | Case 2: % 149.90/21.87 | | | | | | | | | | | | % 149.90/21.87 | | | | | | | | | | | | (181) all_58_12 = e1 % 149.90/21.87 | | | | | | | | | | | | % 149.90/21.87 | | | | | | | | | | | | REF_CLOSE: (40), (117), (181) are inconsistent by sub-proof % 149.90/21.87 | | | | | | | | | | | | #475. % 149.90/21.87 | | | | | | | | | | | | % 149.90/21.87 | | | | | | | | | | | End of split % 149.90/21.87 | | | | | | | | | | | % 149.90/21.87 | | | | | | | | | | End of split % 149.90/21.87 | | | | | | | | | | % 149.90/21.87 | | | | | | | | | End of split % 149.90/21.87 | | | | | | | | | % 149.90/21.87 | | | | | | | | Case 2: % 149.90/21.87 | | | | | | | | | % 149.90/21.87 | | | | | | | | | (182) all_54_0 = e1 | all_54_0 = e0 % 149.90/21.87 | | | | | | | | | % 149.90/21.87 | | | | | | | | | REF_CLOSE: (126), (131), (157), (182) are inconsistent by % 149.90/21.87 | | | | | | | | | sub-proof #550. % 149.90/21.87 | | | | | | | | | % 149.90/21.87 | | | | | | | | End of split % 149.90/21.87 | | | | | | | | % 149.90/21.87 | | | | | | | End of split % 149.90/21.87 | | | | | | | % 149.90/21.87 | | | | | | Case 2: % 149.90/21.87 | | | | | | | % 149.90/21.87 | | | | | | | (183) all_56_5 = e3 % 149.90/21.87 | | | | | | | % 149.90/21.87 | | | | | | | REF_CLOSE: (57), (153), (183) are inconsistent by sub-proof #481. % 149.90/21.87 | | | | | | | % 149.90/21.87 | | | | | | End of split % 149.90/21.87 | | | | | | % 149.90/21.87 | | | | | Case 2: % 149.90/21.87 | | | | | | % 149.90/21.87 | | | | | | (184) all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3 % 149.90/21.87 | | | | | | % 149.90/21.87 | | | | | | BETA: splitting (184) gives: % 149.90/21.87 | | | | | | % 149.90/21.87 | | | | | | Case 1: % 149.90/21.87 | | | | | | | % 149.90/21.87 | | | | | | | (185) all_58_3 = e3 % 149.90/21.87 | | | | | | | % 149.90/21.87 | | | | | | | REF_CLOSE: (8), (149), (185) are inconsistent by sub-proof #632. % 149.90/21.87 | | | | | | | % 149.90/21.87 | | | | | | Case 2: % 149.90/21.87 | | | | | | | % 149.90/21.87 | | | | | | | (186) all_58_7 = e3 | all_58_13 = e3 % 149.90/21.87 | | | | | | | % 149.90/21.87 | | | | | | | BETA: splitting (186) gives: % 149.90/21.87 | | | | | | | % 149.90/21.87 | | | | | | | Case 1: % 149.90/21.87 | | | | | | | | % 149.90/21.87 | | | | | | | | (187) all_58_7 = e3 % 149.90/21.87 | | | | | | | | % 149.90/21.87 | | | | | | | | COMBINE_EQS: (76), (187) imply: % 149.90/21.87 | | | | | | | | (188) all_6_0 = e3 % 149.90/21.87 | | | | | | | | % 149.90/21.87 | | | | | | | | REDUCE: (50), (188) imply: % 149.90/21.87 | | | | | | | | (189) $false % 149.90/21.87 | | | | | | | | % 149.90/21.87 | | | | | | | | CLOSE: (189) is inconsistent. % 149.90/21.87 | | | | | | | | % 149.90/21.87 | | | | | | | Case 2: % 149.90/21.87 | | | | | | | | % 149.90/21.87 | | | | | | | | (190) all_58_13 = e3 % 149.90/21.87 | | | | | | | | % 149.90/21.87 | | | | | | | | REF_CLOSE: (35), (123), (190) are inconsistent by sub-proof % 149.90/21.87 | | | | | | | | #444. % 149.90/21.87 | | | | | | | | % 149.90/21.87 | | | | | | | End of split % 149.90/21.87 | | | | | | | % 149.90/21.87 | | | | | | End of split % 149.90/21.87 | | | | | | % 149.90/21.87 | | | | | End of split % 149.90/21.87 | | | | | % 149.90/21.87 | | | | End of split % 149.90/21.87 | | | | % 149.90/21.87 | | | End of split % 149.90/21.87 | | | % 149.90/21.87 | | Case 2: % 149.90/21.87 | | | % 149.90/21.87 | | | (191) all_56_31 = e1 % 149.90/21.87 | | | (192) all_56_29 = e0 % 149.90/21.87 | | | % 149.90/21.87 | | | COMBINE_EQS: (75), (192) imply: % 149.90/21.87 | | | (193) all_52_11 = e0 % 149.90/21.87 | | | % 149.90/21.87 | | | SIMP: (193) implies: % 149.90/21.87 | | | (194) all_52_11 = e0 % 149.90/21.87 | | | % 149.90/21.87 | | | COMBINE_EQS: (63), (191) imply: % 149.90/21.87 | | | (195) all_4_2 = e1 % 149.90/21.87 | | | % 149.90/21.87 | | | REDUCE: (2), (194) imply: % 149.90/21.87 | | | (196) ~ (all_6_2 = e0) % 149.90/21.87 | | | % 149.90/21.87 | | | SIMP: (196) implies: % 149.90/21.87 | | | (197) ~ (all_6_2 = e0) % 149.90/21.87 | | | % 149.90/21.87 | | | REDUCE: (59), (195) imply: % 149.90/21.87 | | | (198) op(e1, e1) = all_4_1 % 149.90/21.87 | | | % 149.90/21.87 | | | GROUND_INST: instantiating (42) with all_6_2, all_4_1, e1, e1, simplifying % 149.90/21.87 | | | with (73), (198) gives: % 149.90/21.87 | | | (199) all_6_2 = all_4_1 % 149.90/21.87 | | | % 149.90/21.87 | | | COMBINE_EQS: (10), (199) imply: % 149.90/21.87 | | | (200) all_54_10 = all_4_1 % 149.90/21.87 | | | % 149.90/21.87 | | | COMBINE_EQS: (26), (199) imply: % 149.90/21.87 | | | (201) all_56_21 = all_4_1 % 149.90/21.87 | | | % 149.90/21.87 | | | REDUCE: (86), (199) imply: % 149.90/21.87 | | | (202) ~ (all_52_2 = all_4_1) % 149.90/21.87 | | | % 149.90/21.87 | | | REDUCE: (90), (199) imply: % 149.90/21.87 | | | (203) ~ (all_52_14 = all_4_1) % 149.90/21.87 | | | % 149.90/21.87 | | | REDUCE: (46), (199) imply: % 149.90/21.87 | | | (204) ~ (all_6_0 = all_4_1) % 149.90/21.87 | | | % 149.90/21.87 | | | REDUCE: (45), (199) imply: % 149.90/21.87 | | | (205) op(all_4_1, all_4_1) = e2 % 149.90/21.87 | | | % 149.90/21.87 | | | BETA: splitting (39) gives: % 149.90/21.87 | | | % 149.90/21.87 | | | Case 1: % 149.90/21.87 | | | | % 149.90/21.87 | | | | (206) ~ (all_56_21 = e3) % 149.90/21.87 | | | | % 149.90/21.87 | | | | REDUCE: (201), (206) imply: % 149.90/21.87 | | | | (207) ~ (all_4_1 = e3) % 149.90/21.87 | | | | % 149.90/21.87 | | | | REF_CLOSE: (10), (27), (42), (45), (73), (81), (107), (197), (200), % 149.90/21.87 | | | | (207) are inconsistent by sub-proof #43. % 149.90/21.87 | | | | % 149.90/21.87 | | | Case 2: % 149.90/21.87 | | | | % 149.90/21.87 | | | | (208) all_56_21 = e3 % 149.90/21.87 | | | | (209) all_56_17 = e1 % 149.90/21.87 | | | | % 149.90/21.87 | | | | COMBINE_EQS: (31), (209) imply: % 149.90/21.87 | | | | (210) all_52_2 = e1 % 149.90/21.87 | | | | % 149.90/21.87 | | | | COMBINE_EQS: (201), (208) imply: % 149.90/21.87 | | | | (211) all_4_1 = e3 % 149.90/21.87 | | | | % 149.90/21.87 | | | | SIMP: (211) implies: % 149.90/21.87 | | | | (212) all_4_1 = e3 % 149.90/21.87 | | | | % 149.90/21.87 | | | | REDUCE: (66), (210) imply: % 149.90/21.87 | | | | (213) ~ (all_52_14 = e1) % 149.90/21.87 | | | | % 149.90/21.87 | | | | SIMP: (213) implies: % 149.90/21.87 | | | | (214) ~ (all_52_14 = e1) % 149.90/21.87 | | | | % 149.90/21.87 | | | | REDUCE: (68), (210) imply: % 149.90/21.87 | | | | (215) ~ (all_6_0 = e1) % 149.90/21.87 | | | | % 149.90/21.87 | | | | SIMP: (215) implies: % 149.90/21.87 | | | | (216) ~ (all_6_0 = e1) % 149.90/21.87 | | | | % 149.90/21.87 | | | | REDUCE: (202), (210), (212) imply: % 149.90/21.87 | | | | (217) ~ (e3 = e1) % 149.90/21.87 | | | | % 149.90/21.87 | | | | REDUCE: (203), (212) imply: % 149.90/21.87 | | | | (218) ~ (all_52_14 = e3) % 149.90/21.87 | | | | % 149.90/21.87 | | | | REDUCE: (205), (212) imply: % 149.90/21.87 | | | | (219) op(e3, e3) = e2 % 149.90/21.87 | | | | % 149.90/21.87 | | | | REF_CLOSE: (1), (10), (13), (15), (25), (26), (27), (29), (37), (42), % 149.90/21.87 | | | | (45), (50), (51), (56), (62), (63), (67), (71), (73), (78), % 149.90/21.87 | | | | (81), (87), (89), (93), (99), (101), (107), (208), (214), % 149.90/21.87 | | | | (216), (218), (219) are inconsistent by sub-proof #79. % 149.90/21.87 | | | | % 149.90/21.87 | | | End of split % 149.90/21.87 | | | % 149.90/21.87 | | End of split % 149.90/21.87 | | % 149.90/21.87 | Case 2: % 149.90/21.87 | | % 149.90/21.87 | | (220) all_56_21 = e2 % 149.90/21.87 | | % 149.90/21.87 | | COMBINE_EQS: (26), (220) imply: % 149.90/21.87 | | (221) all_6_2 = e2 % 149.90/21.87 | | % 149.90/21.87 | | REDUCE: (45), (221) imply: % 149.90/21.87 | | (222) op(e2, e2) = e2 % 149.90/21.87 | | % 149.90/21.87 | | REF_CLOSE: (19), (36), (42), (85), (102), (222) are inconsistent by % 149.90/21.87 | | sub-proof #349. % 149.90/21.87 | | % 149.90/21.87 | End of split % 149.90/21.87 | % 149.90/21.87 End of proof % 149.90/21.87 % 149.90/21.87 Sub-proof #43 shows that the following formulas are inconsistent: % 149.90/21.87 ---------------------------------------------------------------- % 149.90/21.87 (1) ~ (all_4_1 = e3) % 149.90/21.87 (2) all_54_10 = all_6_2 % 149.90/21.87 (3) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 149.90/21.87 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 149.90/21.87 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 149.90/21.87 (5) ~ (all_6_2 = e0) % 149.90/21.87 (6) op(all_6_2, all_6_2) = e2 % 149.90/21.87 (7) all_54_10 = all_4_1 % 149.90/21.87 (8) op(e1, e1) = all_6_2 % 149.90/21.87 (9) ~ (all_6_2 = e2) % 149.90/21.87 (10) op(e1, all_6_2) = all_56_20 % 149.90/21.87 % 149.90/21.87 Begin of proof % 149.90/21.87 | % 149.90/21.87 | BETA: splitting (3) gives: % 149.90/21.87 | % 149.90/21.87 | Case 1: % 149.90/21.87 | | % 149.90/21.87 | | (11) all_54_10 = e3 % 149.90/21.87 | | % 149.90/21.87 | | REF_CLOSE: (1), (7), (11) are inconsistent by sub-proof #282. % 149.90/21.87 | | % 149.90/21.87 | Case 2: % 149.90/21.87 | | % 149.90/21.87 | | (12) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 149.90/21.87 | | % 149.90/21.87 | | REF_CLOSE: (2), (4), (5), (6), (8), (9), (10), (12) are inconsistent by % 149.90/21.87 | | sub-proof #90. % 149.90/21.87 | | % 149.90/21.87 | End of split % 149.90/21.87 | % 149.90/21.87 End of proof % 149.90/21.87 % 149.90/21.87 Sub-proof #44 shows that the following formulas are inconsistent: % 149.90/21.87 ---------------------------------------------------------------- % 149.90/21.87 (1) all_56_11 = all_8_2 % 149.90/21.87 (2) ~ (all_52_2 = all_4_1) % 149.90/21.87 (3) all_56_31 = e3 % 149.90/21.87 (4) ~ (all_52_4 = all_52_7) % 149.90/21.87 (5) all_54_5 = all_8_2 % 149.90/21.87 (6) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 149.90/21.87 (7) ~ (all_52_4 = all_4_1) % 149.90/21.87 (8) all_54_9 = all_6_0 % 149.90/21.87 (9) ~ (all_52_7 = all_8_2) % 149.90/21.87 (10) ~ (all_52_7 = all_6_0) % 149.90/21.87 (11) all_56_21 = e0 % 149.90/21.87 (12) all_56_1 = all_4_1 % 149.90/21.87 (13) ~ (all_6_0 = e1) % 149.90/21.87 (14) all_58_1 = all_52_4 % 149.90/21.87 (15) all_54_0 = all_4_1 % 149.90/21.87 (16) all_58_13 = all_52_7 % 149.90/21.87 (17) all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1 % 149.90/21.87 (18) ~ (all_52_2 = e0) % 149.90/21.87 (19) ~ (all_6_0 = e3) % 149.90/21.87 (20) all_58_0 = all_4_1 % 149.90/21.87 (21) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0 % 149.90/21.87 (22) ~ (all_56_1 = e2) | all_56_3 = e3 % 149.90/21.87 (23) ~ (all_52_2 = e1) % 149.90/21.87 (24) all_58_3 = all_8_2 % 149.90/21.87 (25) all_56_3 = all_52_4 % 149.90/21.87 (26) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0 % 149.90/21.87 (27) all_56_1 = e3 | all_56_11 = e2 | all_56_21 = e1 | all_56_31 = e0 % 149.90/21.87 (28) ~ (all_52_2 = all_6_0) % 149.90/21.87 (29) all_54_13 = all_52_7 % 149.90/21.87 (30) all_54_8 = all_52_2 % 149.90/21.87 (31) all_58_7 = all_6_0 % 149.90/21.87 (32) ~ (all_52_7 = e3) % 149.90/21.87 (33) ~ (all_6_0 = e0) % 149.90/21.87 (34) all_58_1 = e0 | all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0 % 149.90/21.87 (35) ~ (all_8_2 = e0) % 149.90/21.87 (36) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0 % 149.90/21.87 (37) ~ (all_52_7 = e0) % 149.90/21.87 (38) ~ (all_8_2 = all_6_0) % 149.90/21.87 (39) ~ (all_52_4 = all_8_2) % 149.90/21.87 (40) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 149.90/21.87 % 149.90/21.87 Begin of proof % 149.90/21.87 | % 149.90/21.87 | BETA: splitting (26) gives: % 149.90/21.87 | % 149.90/21.87 | Case 1: % 149.90/21.87 | | % 149.90/21.87 | | (41) all_54_9 = e3 % 149.90/21.87 | | % 149.90/21.87 | | COMBINE_EQS: (8), (41) imply: % 149.90/21.87 | | (42) all_6_0 = e3 % 149.90/21.87 | | % 149.90/21.87 | | REDUCE: (19), (42) imply: % 149.90/21.87 | | (43) $false % 149.90/21.87 | | % 149.90/21.87 | | CLOSE: (43) is inconsistent. % 149.90/21.87 | | % 149.90/21.87 | Case 2: % 149.90/21.87 | | % 149.90/21.87 | | (44) all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0 % 149.90/21.87 | | % 149.90/21.87 | | BETA: splitting (44) gives: % 149.90/21.87 | | % 149.90/21.87 | | Case 1: % 149.90/21.87 | | | % 149.90/21.87 | | | (45) all_54_9 = e2 % 149.90/21.87 | | | % 149.90/21.87 | | | COMBINE_EQS: (8), (45) imply: % 149.90/21.87 | | | (46) all_6_0 = e2 % 149.90/21.87 | | | % 149.90/21.87 | | | REDUCE: (28), (46) imply: % 149.90/21.87 | | | (47) ~ (all_52_2 = e2) % 149.90/21.87 | | | % 149.90/21.87 | | | REDUCE: (10), (46) imply: % 149.90/21.87 | | | (48) ~ (all_52_7 = e2) % 149.90/21.87 | | | % 149.90/21.87 | | | REDUCE: (38), (46) imply: % 149.90/21.87 | | | (49) ~ (all_8_2 = e2) % 149.90/21.87 | | | % 149.90/21.87 | | | BETA: splitting (21) gives: % 149.90/21.87 | | | % 149.90/21.87 | | | Case 1: % 149.90/21.87 | | | | % 149.90/21.87 | | | | (50) all_54_13 = e3 % 149.90/21.87 | | | | % 149.90/21.87 | | | | REF_CLOSE: (29), (32), (50) are inconsistent by sub-proof #668. % 149.90/21.87 | | | | % 149.90/21.87 | | | Case 2: % 149.90/21.87 | | | | % 149.90/21.87 | | | | (51) all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0 % 149.90/21.87 | | | | % 149.90/21.87 | | | | BETA: splitting (36) gives: % 149.90/21.87 | | | | % 149.90/21.87 | | | | Case 1: % 149.90/21.87 | | | | | % 149.90/21.87 | | | | | (52) all_54_8 = e3 % 149.90/21.87 | | | | | % 149.90/21.87 | | | | | COMBINE_EQS: (30), (52) imply: % 149.90/21.87 | | | | | (53) all_52_2 = e3 % 149.90/21.87 | | | | | % 149.90/21.87 | | | | | SIMP: (53) implies: % 149.90/21.87 | | | | | (54) all_52_2 = e3 % 149.90/21.87 | | | | | % 149.90/21.87 | | | | | REDUCE: (2), (54) imply: % 149.90/21.87 | | | | | (55) ~ (all_4_1 = e3) % 149.90/21.87 | | | | | % 149.90/21.87 | | | | | SIMP: (55) implies: % 149.90/21.87 | | | | | (56) ~ (all_4_1 = e3) % 149.90/21.87 | | | | | % 149.90/21.87 | | | | | REDUCE: (18), (54) imply: % 149.90/21.87 | | | | | (57) ~ (e3 = e0) % 149.90/21.87 | | | | | % 149.90/21.87 | | | | | BETA: splitting (34) gives: % 149.90/21.87 | | | | | % 149.90/21.87 | | | | | Case 1: % 149.90/21.87 | | | | | | % 149.90/21.87 | | | | | | (58) all_58_1 = e0 % 149.90/21.87 | | | | | | % 149.90/21.87 | | | | | | COMBINE_EQS: (14), (58) imply: % 149.90/21.87 | | | | | | (59) all_52_4 = e0 % 149.90/21.87 | | | | | | % 149.90/21.87 | | | | | | COMBINE_EQS: (25), (59) imply: % 149.90/21.87 | | | | | | (60) all_56_3 = e0 % 149.90/21.87 | | | | | | % 149.90/21.87 | | | | | | REDUCE: (4), (59) imply: % 149.90/21.87 | | | | | | (61) ~ (all_52_7 = e0) % 149.90/21.87 | | | | | | % 149.90/21.87 | | | | | | REDUCE: (39), (59) imply: % 149.90/21.87 | | | | | | (62) ~ (all_8_2 = e0) % 149.90/21.87 | | | | | | % 149.90/21.87 | | | | | | REDUCE: (7), (59) imply: % 149.90/21.87 | | | | | | (63) ~ (all_4_1 = e0) % 149.90/21.87 | | | | | | % 149.90/21.87 | | | | | | SIMP: (63) implies: % 149.90/21.87 | | | | | | (64) ~ (all_4_1 = e0) % 149.90/21.87 | | | | | | % 149.90/21.87 | | | | | | REF_CLOSE: (1), (3), (5), (6), (9), (11), (12), (15), (17), (20), % 149.90/21.87 | | | | | | (22), (27), (29), (35), (37), (40), (48), (49), (51), % 149.90/21.87 | | | | | | (56), (57), (60), (64) are inconsistent by sub-proof #46. % 149.90/21.87 | | | | | | % 149.90/21.87 | | | | | Case 2: % 149.90/21.87 | | | | | | % 149.90/21.87 | | | | | | (65) all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0 % 149.90/21.87 | | | | | | % 149.90/21.87 | | | | | | REF_CLOSE: (16), (24), (31), (33), (35), (37), (65) are inconsistent % 149.90/21.87 | | | | | | by sub-proof #45. % 149.90/21.87 | | | | | | % 149.90/21.87 | | | | | End of split % 149.90/21.87 | | | | | % 149.90/21.87 | | | | Case 2: % 149.90/21.87 | | | | | % 149.90/21.87 | | | | | (66) all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0 % 149.90/21.87 | | | | | % 149.90/21.87 | | | | | BETA: splitting (66) gives: % 149.90/21.87 | | | | | % 149.90/21.87 | | | | | Case 1: % 149.90/21.87 | | | | | | % 149.90/21.87 | | | | | | (67) all_54_8 = e2 % 149.90/21.87 | | | | | | % 149.90/21.87 | | | | | | REF_CLOSE: (30), (47), (67) are inconsistent by sub-proof #666. % 149.90/21.87 | | | | | | % 149.90/21.87 | | | | | Case 2: % 149.90/21.87 | | | | | | % 149.90/21.87 | | | | | | (68) all_54_8 = e1 | all_54_8 = e0 % 149.90/21.87 | | | | | | % 149.90/21.87 | | | | | | REF_CLOSE: (18), (23), (30), (68) are inconsistent by sub-proof % 149.90/21.87 | | | | | | #664. % 149.90/21.87 | | | | | | % 149.90/21.87 | | | | | End of split % 149.90/21.87 | | | | | % 149.90/21.87 | | | | End of split % 149.90/21.87 | | | | % 149.90/21.87 | | | End of split % 149.90/21.87 | | | % 149.90/21.87 | | Case 2: % 149.90/21.87 | | | % 149.90/21.87 | | | (69) all_54_9 = e1 | all_54_9 = e0 % 149.90/21.87 | | | % 149.90/21.87 | | | REF_CLOSE: (8), (13), (33), (69) are inconsistent by sub-proof #81. % 149.90/21.87 | | | % 149.90/21.87 | | End of split % 149.90/21.87 | | % 149.90/21.87 | End of split % 149.90/21.87 | % 149.90/21.87 End of proof % 149.90/21.87 % 149.90/21.87 Sub-proof #45 shows that the following formulas are inconsistent: % 149.90/21.87 ---------------------------------------------------------------- % 149.90/21.87 (1) all_58_13 = all_52_7 % 149.90/21.87 (2) all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0 % 149.90/21.87 (3) all_58_3 = all_8_2 % 149.90/21.87 (4) all_58_7 = all_6_0 % 149.90/21.87 (5) ~ (all_6_0 = e0) % 149.90/21.87 (6) ~ (all_8_2 = e0) % 149.90/21.87 (7) ~ (all_52_7 = e0) % 149.90/21.87 % 149.90/21.87 Begin of proof % 149.90/21.87 | % 149.90/21.87 | BETA: splitting (2) gives: % 149.90/21.87 | % 149.90/21.87 | Case 1: % 149.90/21.87 | | % 149.90/21.87 | | (8) all_58_3 = e0 % 149.90/21.87 | | % 149.90/21.87 | | COMBINE_EQS: (3), (8) imply: % 149.90/21.87 | | (9) all_8_2 = e0 % 149.90/21.87 | | % 149.90/21.87 | | REDUCE: (6), (9) imply: % 149.90/21.87 | | (10) $false % 149.90/21.87 | | % 149.90/21.87 | | CLOSE: (10) is inconsistent. % 149.90/21.87 | | % 149.90/21.87 | Case 2: % 149.90/21.87 | | % 149.90/21.87 | | (11) all_58_7 = e0 | all_58_13 = e0 % 149.90/21.87 | | % 149.90/21.87 | | BETA: splitting (11) gives: % 149.90/21.87 | | % 149.90/21.87 | | Case 1: % 149.90/21.87 | | | % 149.90/21.87 | | | (12) all_58_7 = e0 % 149.90/21.87 | | | % 149.90/21.87 | | | COMBINE_EQS: (4), (12) imply: % 149.90/21.87 | | | (13) all_6_0 = e0 % 149.90/21.87 | | | % 149.90/21.87 | | | REDUCE: (5), (13) imply: % 149.90/21.87 | | | (14) $false % 149.90/21.87 | | | % 149.90/21.87 | | | CLOSE: (14) is inconsistent. % 149.90/21.87 | | | % 149.90/21.87 | | Case 2: % 149.90/21.87 | | | % 149.90/21.87 | | | (15) all_58_13 = e0 % 149.90/21.87 | | | % 149.90/21.87 | | | COMBINE_EQS: (1), (15) imply: % 149.90/21.87 | | | (16) all_52_7 = e0 % 149.90/21.87 | | | % 149.90/21.87 | | | REDUCE: (7), (16) imply: % 149.90/21.87 | | | (17) $false % 149.90/21.87 | | | % 149.90/21.87 | | | CLOSE: (17) is inconsistent. % 149.90/21.87 | | | % 149.90/21.87 | | End of split % 149.90/21.87 | | % 149.90/21.87 | End of split % 149.90/21.87 | % 149.90/21.87 End of proof % 149.90/21.87 % 149.90/21.87 Sub-proof #46 shows that the following formulas are inconsistent: % 149.90/21.87 ---------------------------------------------------------------- % 149.90/21.87 (1) all_56_11 = all_8_2 % 149.90/21.87 (2) ~ (all_52_7 = e2) % 149.90/21.87 (3) ~ (e3 = e0) % 149.90/21.87 (4) ~ (all_4_1 = e0) % 149.90/21.87 (5) ~ (all_4_1 = e3) % 149.90/21.87 (6) all_56_31 = e3 % 149.90/21.87 (7) all_54_5 = all_8_2 % 149.90/21.87 (8) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 149.90/21.87 (9) ~ (all_8_2 = e2) % 149.90/21.87 (10) ~ (all_52_7 = all_8_2) % 149.90/21.87 (11) all_56_21 = e0 % 149.90/21.87 (12) all_56_1 = all_4_1 % 149.90/21.87 (13) all_54_0 = all_4_1 % 149.90/21.88 (14) all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1 % 149.90/21.88 (15) all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0 % 149.90/21.88 (16) all_58_0 = all_4_1 % 149.90/21.88 (17) ~ (all_56_1 = e2) | all_56_3 = e3 % 149.90/21.88 (18) all_56_1 = e3 | all_56_11 = e2 | all_56_21 = e1 | all_56_31 = e0 % 149.90/21.88 (19) all_54_13 = all_52_7 % 149.90/21.88 (20) all_56_3 = e0 % 149.90/21.88 (21) ~ (all_8_2 = e0) % 149.90/21.88 (22) ~ (all_52_7 = e0) % 149.90/21.88 (23) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 149.90/21.88 % 149.90/21.88 Begin of proof % 149.90/21.88 | % 149.90/21.88 | BETA: splitting (17) gives: % 149.90/21.88 | % 149.90/21.88 | Case 1: % 149.90/21.88 | | % 149.90/21.88 | | (24) ~ (all_56_1 = e2) % 149.90/21.88 | | % 149.90/21.88 | | REDUCE: (12), (24) imply: % 149.90/21.88 | | (25) ~ (all_4_1 = e2) % 149.90/21.88 | | % 149.90/21.88 | | BETA: splitting (15) gives: % 149.90/21.88 | | % 149.90/21.88 | | Case 1: % 149.90/21.88 | | | % 149.90/21.88 | | | (26) all_54_13 = e2 % 149.90/21.88 | | | % 149.90/21.88 | | | COMBINE_EQS: (19), (26) imply: % 149.90/21.88 | | | (27) all_52_7 = e2 % 149.90/21.88 | | | % 149.90/21.88 | | | REDUCE: (2), (27) imply: % 149.90/21.88 | | | (28) $false % 149.90/21.88 | | | % 149.90/21.88 | | | CLOSE: (28) is inconsistent. % 149.90/21.88 | | | % 149.90/21.88 | | Case 2: % 149.90/21.88 | | | % 149.90/21.88 | | | (29) all_54_13 = e1 | all_54_13 = e0 % 149.90/21.88 | | | % 149.90/21.88 | | | BETA: splitting (29) gives: % 149.90/21.88 | | | % 149.90/21.88 | | | Case 1: % 149.90/21.88 | | | | % 149.90/21.88 | | | | (30) all_54_13 = e1 % 149.90/21.88 | | | | % 149.90/21.88 | | | | COMBINE_EQS: (19), (30) imply: % 149.90/21.88 | | | | (31) all_52_7 = e1 % 149.90/21.88 | | | | % 149.90/21.88 | | | | REDUCE: (10), (31) imply: % 149.90/21.88 | | | | (32) ~ (all_8_2 = e1) % 149.90/21.88 | | | | % 149.90/21.88 | | | | SIMP: (32) implies: % 149.90/21.88 | | | | (33) ~ (all_8_2 = e1) % 149.90/21.88 | | | | % 149.90/21.88 | | | | BETA: splitting (23) gives: % 149.90/21.88 | | | | % 149.90/21.88 | | | | Case 1: % 149.90/21.88 | | | | | % 149.90/21.88 | | | | | (34) all_54_5 = e3 % 149.90/21.88 | | | | | % 149.90/21.88 | | | | | COMBINE_EQS: (7), (34) imply: % 149.90/21.88 | | | | | (35) all_8_2 = e3 % 149.90/21.88 | | | | | % 149.90/21.88 | | | | | SIMP: (35) implies: % 149.90/21.88 | | | | | (36) all_8_2 = e3 % 149.90/21.88 | | | | | % 149.90/21.88 | | | | | COMBINE_EQS: (1), (36) imply: % 149.90/21.88 | | | | | (37) all_56_11 = e3 % 149.90/21.88 | | | | | % 149.90/21.88 | | | | | REDUCE: (9), (36) imply: % 149.90/21.88 | | | | | (38) ~ (e3 = e2) % 149.90/21.88 | | | | | % 149.90/21.88 | | | | | BETA: splitting (8) gives: % 149.90/21.88 | | | | | % 149.90/21.88 | | | | | Case 1: % 149.90/21.88 | | | | | | % 149.90/21.88 | | | | | | (39) all_54_0 = e3 % 149.90/21.88 | | | | | | % 149.90/21.88 | | | | | | REF_CLOSE: (5), (13), (39) are inconsistent by sub-proof #554. % 149.90/21.88 | | | | | | % 149.90/21.88 | | | | | Case 2: % 149.90/21.88 | | | | | | % 149.90/21.88 | | | | | | (40) ~ (all_54_0 = e3) % 149.90/21.88 | | | | | | (41) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 149.90/21.88 | | | | | | % 149.90/21.88 | | | | | | BETA: splitting (14) gives: % 149.90/21.88 | | | | | | % 149.90/21.88 | | | | | | Case 1: % 149.90/21.88 | | | | | | | % 149.90/21.88 | | | | | | | (42) all_58_0 = e1 % 149.90/21.88 | | | | | | | % 149.90/21.88 | | | | | | | COMBINE_EQS: (16), (42) imply: % 149.90/21.88 | | | | | | | (43) all_4_1 = e1 % 149.90/21.88 | | | | | | | % 149.90/21.88 | | | | | | | COMBINE_EQS: (12), (43) imply: % 149.90/21.88 | | | | | | | (44) all_56_1 = e1 % 149.90/21.88 | | | | | | | % 149.90/21.88 | | | | | | | REDUCE: (5), (43) imply: % 149.90/21.88 | | | | | | | (45) ~ (e3 = e1) % 149.90/21.88 | | | | | | | % 149.90/21.88 | | | | | | | SIMP: (45) implies: % 149.90/21.88 | | | | | | | (46) ~ (e3 = e1) % 149.90/21.88 | | | | | | | % 149.90/21.88 | | | | | | | REDUCE: (4), (43) imply: % 149.90/21.88 | | | | | | | (47) ~ (e1 = e0) % 149.90/21.88 | | | | | | | % 149.90/21.88 | | | | | | | BETA: splitting (18) gives: % 149.90/21.88 | | | | | | | % 149.90/21.88 | | | | | | | Case 1: % 149.90/21.88 | | | | | | | | % 149.90/21.88 | | | | | | | | (48) all_56_1 = e3 % 149.90/21.88 | | | | | | | | % 149.90/21.88 | | | | | | | | REF_CLOSE: (44), (46), (48) are inconsistent by sub-proof #182. % 149.90/21.88 | | | | | | | | % 149.90/21.88 | | | | | | | Case 2: % 149.90/21.88 | | | | | | | | % 149.90/21.88 | | | | | | | | (49) all_56_11 = e2 | all_56_21 = e1 | all_56_31 = e0 % 149.90/21.88 | | | | | | | | % 149.90/21.88 | | | | | | | | BETA: splitting (49) gives: % 149.90/21.88 | | | | | | | | % 149.90/21.88 | | | | | | | | Case 1: % 149.90/21.88 | | | | | | | | | % 149.90/21.88 | | | | | | | | | (50) all_56_11 = e2 % 149.90/21.88 | | | | | | | | | % 149.90/21.88 | | | | | | | | | REF_CLOSE: (37), (38), (50) are inconsistent by sub-proof #48. % 149.90/21.88 | | | | | | | | | % 149.90/21.88 | | | | | | | | Case 2: % 149.90/21.88 | | | | | | | | | % 149.90/21.88 | | | | | | | | | (51) all_56_21 = e1 | all_56_31 = e0 % 149.90/21.88 | | | | | | | | | % 149.90/21.88 | | | | | | | | | REF_CLOSE: (3), (6), (11), (47), (51) are inconsistent by % 149.90/21.88 | | | | | | | | | sub-proof #322. % 149.90/21.88 | | | | | | | | | % 149.90/21.88 | | | | | | | | End of split % 149.90/21.88 | | | | | | | | % 149.90/21.88 | | | | | | | End of split % 149.90/21.88 | | | | | | | % 149.90/21.88 | | | | | | Case 2: % 149.90/21.88 | | | | | | | % 149.90/21.88 | | | | | | | (52) ~ (all_58_0 = e1) % 149.90/21.88 | | | | | | | % 149.90/21.88 | | | | | | | REDUCE: (16), (52) imply: % 149.90/21.88 | | | | | | | (53) ~ (all_4_1 = e1) % 149.90/21.88 | | | | | | | % 149.90/21.88 | | | | | | | REF_CLOSE: (4), (13), (25), (41), (53) are inconsistent by % 149.90/21.88 | | | | | | | sub-proof #549. % 149.90/21.88 | | | | | | | % 149.90/21.88 | | | | | | End of split % 149.90/21.88 | | | | | | % 149.90/21.88 | | | | | End of split % 149.90/21.88 | | | | | % 149.90/21.88 | | | | Case 2: % 149.90/21.88 | | | | | % 149.90/21.88 | | | | | (54) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 149.90/21.88 | | | | | % 149.90/21.88 | | | | | BETA: splitting (54) gives: % 149.90/21.88 | | | | | % 149.90/21.88 | | | | | Case 1: % 149.90/21.88 | | | | | | % 149.90/21.88 | | | | | | (55) all_54_5 = e2 % 149.90/21.88 | | | | | | % 149.90/21.88 | | | | | | REF_CLOSE: (7), (9), (55) are inconsistent by sub-proof #648. % 149.90/21.88 | | | | | | % 149.90/21.88 | | | | | Case 2: % 149.90/21.88 | | | | | | % 149.90/21.88 | | | | | | (56) all_54_5 = e1 | all_54_5 = e0 % 149.90/21.88 | | | | | | % 149.90/21.88 | | | | | | REF_CLOSE: (7), (21), (33), (56) are inconsistent by sub-proof #645. % 149.90/21.88 | | | | | | % 149.90/21.88 | | | | | End of split % 149.90/21.88 | | | | | % 149.90/21.88 | | | | End of split % 149.90/21.88 | | | | % 149.90/21.88 | | | Case 2: % 149.90/21.88 | | | | % 149.90/21.88 | | | | (57) all_54_13 = e0 % 149.90/21.88 | | | | % 149.90/21.88 | | | | COMBINE_EQS: (19), (57) imply: % 149.90/21.88 | | | | (58) all_52_7 = e0 % 149.90/21.88 | | | | % 149.90/21.88 | | | | REDUCE: (22), (58) imply: % 149.90/21.88 | | | | (59) $false % 149.90/21.88 | | | | % 149.90/21.88 | | | | CLOSE: (59) is inconsistent. % 149.90/21.88 | | | | % 149.90/21.88 | | | End of split % 149.90/21.88 | | | % 149.90/21.88 | | End of split % 149.90/21.88 | | % 149.90/21.88 | Case 2: % 149.90/21.88 | | % 149.90/21.88 | | (60) all_56_3 = e3 % 149.90/21.88 | | % 149.90/21.88 | | REF_CLOSE: (3), (20), (60) are inconsistent by sub-proof #47. % 149.90/21.88 | | % 149.90/21.88 | End of split % 149.90/21.88 | % 149.90/21.88 End of proof % 149.90/21.88 % 149.90/21.88 Sub-proof #47 shows that the following formulas are inconsistent: % 149.90/21.88 ---------------------------------------------------------------- % 149.90/21.88 (1) all_56_3 = e3 % 149.90/21.88 (2) all_56_3 = e0 % 149.90/21.88 (3) ~ (e3 = e0) % 149.90/21.88 % 149.90/21.88 Begin of proof % 149.90/21.88 | % 149.90/21.88 | COMBINE_EQS: (1), (2) imply: % 149.90/21.88 | (4) e3 = e0 % 149.90/21.88 | % 149.90/21.88 | SIMP: (4) implies: % 149.90/21.88 | (5) e3 = e0 % 149.90/21.88 | % 149.90/21.88 | REDUCE: (3), (5) imply: % 149.90/21.88 | (6) $false % 149.90/21.88 | % 149.90/21.88 | CLOSE: (6) is inconsistent. % 149.90/21.88 | % 149.90/21.88 End of proof % 149.90/21.88 % 149.90/21.88 Sub-proof #48 shows that the following formulas are inconsistent: % 149.90/21.88 ---------------------------------------------------------------- % 149.90/21.88 (1) all_56_11 = e3 % 149.90/21.88 (2) all_56_11 = e2 % 149.90/21.88 (3) ~ (e3 = e2) % 149.90/21.88 % 149.90/21.88 Begin of proof % 149.90/21.88 | % 149.90/21.88 | COMBINE_EQS: (1), (2) imply: % 149.90/21.88 | (4) e3 = e2 % 149.90/21.88 | % 149.90/21.88 | SIMP: (4) implies: % 149.90/21.88 | (5) e3 = e2 % 149.90/21.88 | % 149.90/21.88 | REDUCE: (3), (5) imply: % 149.90/21.88 | (6) $false % 149.90/21.88 | % 149.90/21.88 | CLOSE: (6) is inconsistent. % 149.90/21.88 | % 149.90/21.88 End of proof % 149.90/21.88 % 149.90/21.88 Sub-proof #49 shows that the following formulas are inconsistent: % 149.90/21.88 ---------------------------------------------------------------- % 149.90/21.88 (1) all_56_11 = all_8_2 % 149.90/21.88 (2) ~ (all_56_11 = e1) | all_56_13 = e2 % 149.90/21.88 (3) ~ (all_52_11 = all_6_2) % 149.90/21.88 (4) ~ (all_52_4 = all_52_8) % 149.90/21.88 (5) all_56_25 = all_52_3 % 149.90/21.88 (6) ~ (all_52_7 = all_52_11) % 149.90/21.88 (7) op(e2, all_8_1) = all_8_0 % 149.90/21.88 (8) all_58_6 = all_52_2 % 149.90/21.88 (9) ~ (all_8_1 = e1) % 149.90/21.88 (10) ~ (all_52_1 = all_52_9) % 149.90/21.88 (11) ~ (all_56_31 = e1) | all_56_29 = e0 % 149.90/21.88 (12) all_54_10 = all_6_2 % 149.90/21.88 (13) ~ (all_56_21 = e2) | all_56_19 = e1 % 149.90/21.88 (14) all_54_0 = all_10_2 % 149.90/21.88 (15) ~ (all_52_14 = all_4_2) % 149.90/21.88 (16) ~ (all_8_0 = e1) % 149.90/21.88 (17) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0 % 149.90/21.88 (18) all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2 % 149.90/21.88 (19) ~ (all_52_9 = all_8_2) % 149.90/21.88 (20) ~ (all_8_1 = e3) % 149.90/21.88 (21) ~ (e3 = e2) % 149.90/21.88 (22) op(e0, e0) = all_4_2 % 149.90/21.88 (23) all_58_4 = all_52_8 % 149.90/21.88 (24) all_54_5 = all_8_2 % 149.90/21.88 (25) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 149.90/21.88 (26) all_54_15 = all_4_2 % 149.90/21.88 (27) all_54_9 = all_6_0 % 149.90/21.88 (28) all_56_21 = all_6_2 % 149.90/21.88 (29) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 149.90/21.88 (30) all_56_1 = all_10_2 % 149.90/21.88 (31) all_56_27 = all_52_7 % 149.90/21.88 (32) all_58_5 = all_52_9 % 149.90/21.88 (33) all_54_1 = all_52_4 % 149.90/21.88 (34) all_56_17 = all_52_2 % 149.90/21.88 (35) ~ (all_52_7 = all_6_0) % 149.90/21.88 (36) op(e0, e2) = all_52_7 % 149.90/21.88 (37) all_58_13 = all_52_7 % 149.90/21.88 (38) op(e3, e3) = all_10_2 % 149.90/21.88 (39) ~ (all_56_21 = e3) | all_56_17 = e1 % 149.90/21.88 (40) all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2 % 149.90/21.88 (41) ~ (e1 = e0) % 149.90/21.88 (42) all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1 % 149.90/21.88 (43) ~ (all_52_1 = all_8_2) % 149.90/21.88 (44) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 149.90/21.88 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 149.90/21.88 (45) all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0 % 149.90/21.88 (46) ~ (all_52_3 = all_52_7) % 149.90/21.88 (47) ~ (all_56_11 = e3) | all_56_9 = e2 % 149.90/21.88 (48) op(e0, all_4_1) = all_4_0 % 149.90/21.88 (49) all_56_7 = all_52_12 % 149.90/21.88 (50) op(all_6_2, all_6_2) = e2 % 149.90/21.88 (51) ~ (all_6_0 = all_6_2) % 149.90/21.88 (52) all_56_13 = all_52_9 % 149.90/21.88 (53) ~ (all_52_1 = all_52_13) % 149.90/21.88 (54) ~ (all_52_7 = all_4_2) % 149.90/21.88 (55) all_58_8 = all_6_2 % 149.90/21.88 (56) ~ (all_6_0 = e3) % 149.90/21.88 (57) ~ (all_6_0 = e0) | ~ (all_6_2 = e3) % 149.90/21.88 (58) all_4_0 = e1 % 149.90/21.88 (59) ~ (all_52_3 = all_4_2) % 149.90/21.88 (60) ~ (all_52_8 = all_10_2) % 149.90/21.88 (61) all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3 % 149.90/21.88 (62) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0 % 149.90/21.88 (63) ~ (all_56_1 = e0) | all_56_7 = e3 % 149.90/21.88 (64) ~ (all_52_14 = all_6_0) % 149.90/21.88 (65) ~ (all_52_2 = all_52_3) % 149.90/21.88 (66) op(all_4_2, all_4_2) = all_4_1 % 149.90/21.88 (67) all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3 % 149.90/21.88 (68) all_58_3 = all_8_2 % 149.90/21.88 (69) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0 % 149.90/21.88 (70) ~ (all_52_1 = all_52_3) % 149.90/21.88 (71) all_56_31 = all_4_2 % 149.90/21.88 (72) all_58_11 = all_52_14 % 149.90/21.88 (73) all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3 % 149.90/21.88 (74) ~ (all_52_2 = all_52_14) % 149.90/21.88 (75) all_56_1 = e3 | all_56_11 = e2 | all_56_21 = e1 | all_56_31 = e0 % 149.90/21.88 (76) ~ (all_52_13 = all_4_2) % 149.90/21.88 (77) ~ (all_52_2 = all_6_0) % 149.90/21.88 (78) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0 % 149.90/21.88 (79) all_54_13 = all_52_7 % 149.90/21.88 (80) all_56_23 = all_52_14 % 149.90/21.88 (81) all_54_8 = all_52_2 % 149.90/21.88 (82) op(e1, e1) = all_6_2 % 149.90/21.88 (83) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0 % 149.90/21.88 (84) all_56_29 = all_52_11 % 149.90/21.88 (85) all_58_7 = all_6_0 % 149.90/21.88 (86) all_58_2 = all_52_1 % 149.90/21.88 (87) all_56_19 = all_6_0 % 149.90/21.88 (88) ~ (all_52_9 = all_6_2) % 149.90/21.88 (89) all_58_10 = all_52_13 % 149.90/21.88 (90) op(all_10_2, all_10_2) = all_10_1 % 149.90/21.88 (91) ~ (all_56_11 = e0) | all_56_15 = e2 % 149.90/21.88 (92) all_58_0 = all_10_2 % 149.90/21.88 (93) op(e1, all_6_2) = all_56_20 % 149.90/21.88 (94) all_58_1 = e0 | all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0 % 149.90/21.88 (95) ~ (all_56_31 = e2) | all_56_27 = e0 % 149.90/21.88 (96) op(e2, e2) = all_8_2 % 149.90/21.88 (97) ~ (all_52_4 = all_52_12) % 149.90/21.88 (98) op(e2, e0) = all_52_13 % 149.90/21.88 (99) ~ (all_52_2 = all_6_2) % 149.90/21.88 (100) ~ (all_52_8 = all_52_12) % 149.90/21.88 (101) ~ (all_52_1 = all_52_2) % 149.90/21.88 (102) ~ (all_56_21 = e0) | all_56_23 = e1 % 149.90/21.88 (103) op(e0, all_4_2) = all_56_30 % 149.90/21.88 (104) op(e3, all_10_2) = all_56_0 % 149.90/21.88 (105) ~ (all_52_14 = all_6_2) % 149.90/21.88 (106) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0 % 149.90/21.88 (107) ~ (all_52_2 = all_10_2) % 149.90/21.88 (108) ~ (all_8_2 = all_6_0) % 149.90/21.88 (109) ~ (all_52_4 = all_10_2) % 149.90/21.88 (110) op(all_8_2, all_8_2) = all_8_1 % 149.90/21.88 (111) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 149.90/21.88 (112) ~ (all_4_0 = e2) % 149.90/21.88 (113) ~ (all_4_0 = e3) % 149.90/21.88 (114) all_56_9 = all_52_1 % 149.90/21.88 (115) all_56_15 = all_52_13 % 149.90/21.88 (116) ~ (all_52_1 = all_10_2) % 149.90/21.88 (117) all_58_12 = all_52_3 % 149.90/21.88 (118) all_54_11 = all_52_14 % 149.90/21.88 (119) ~ (all_56_31 = e3) | all_56_25 = e0 % 149.90/21.88 % 149.90/21.88 Begin of proof % 149.90/21.88 | % 149.90/21.88 | REDUCE: (48), (58) imply: % 149.90/21.88 | (120) op(e0, all_4_1) = e1 % 149.90/21.88 | % 149.90/21.88 | BETA: splitting (11) gives: % 149.90/21.88 | % 149.90/21.88 | Case 1: % 149.90/21.88 | | % 149.90/21.88 | | (121) ~ (all_56_31 = e1) % 149.90/21.88 | | % 149.90/21.88 | | REDUCE: (71), (121) imply: % 149.90/21.88 | | (122) ~ (all_4_2 = e1) % 149.90/21.88 | | % 149.90/21.88 | | BETA: splitting (119) gives: % 149.90/21.88 | | % 149.90/21.88 | | Case 1: % 149.90/21.88 | | | % 149.90/21.88 | | | (123) ~ (all_56_31 = e3) % 149.90/21.88 | | | % 149.90/21.88 | | | REDUCE: (71), (123) imply: % 149.90/21.88 | | | (124) ~ (all_4_2 = e3) % 149.90/21.88 | | | % 149.90/21.88 | | | BETA: splitting (13) gives: % 149.90/21.88 | | | % 149.90/21.88 | | | Case 1: % 149.90/21.88 | | | | % 149.90/21.88 | | | | (125) ~ (all_56_21 = e2) % 149.90/21.88 | | | | % 149.90/21.88 | | | | REDUCE: (28), (125) imply: % 149.90/21.88 | | | | (126) ~ (all_6_2 = e2) % 149.90/21.88 | | | | % 149.90/21.88 | | | | BETA: splitting (91) gives: % 149.90/21.88 | | | | % 149.90/21.88 | | | | Case 1: % 149.90/21.88 | | | | | % 149.90/21.88 | | | | | (127) ~ (all_56_11 = e0) % 149.90/21.88 | | | | | % 149.90/21.88 | | | | | REDUCE: (1), (127) imply: % 149.90/21.88 | | | | | (128) ~ (all_8_2 = e0) % 149.90/21.88 | | | | | % 149.90/21.88 | | | | | REF_CLOSE: (1), (2), (4), (7), (8), (9), (10), (12), (14), (15), (16), % 149.90/21.88 | | | | | (17), (18), (19), (20), (22), (23), (24), (25), (27), (28), % 149.90/21.88 | | | | | (29), (30), (32), (33), (34), (38), (39), (40), (42), (43), % 149.90/21.88 | | | | | (44), (45), (47), (49), (50), (51), (52), (53), (55), (56), % 149.90/21.88 | | | | | (57), (60), (61), (63), (64), (66), (67), (68), (69), (70), % 149.90/21.88 | | | | | (71), (72), (74), (75), (76), (77), (80), (82), (83), (85), % 149.90/21.88 | | | | | (86), (88), (89), (90), (91), (92), (93), (97), (98), (99), % 149.90/21.88 | | | | | (100), (101), (102), (103), (104), (105), (107), (108), % 149.90/21.88 | | | | | (109), (110), (111), (114), (115), (116), (117), (118), % 149.90/21.88 | | | | | (126), (128) are inconsistent by sub-proof #59. % 149.90/21.88 | | | | | % 149.90/21.88 | | | | Case 2: % 149.90/21.88 | | | | | % 149.90/21.88 | | | | | (129) all_56_11 = e0 % 149.90/21.88 | | | | | % 149.90/21.88 | | | | | REF_CLOSE: (1), (9), (20), (22), (26), (44), (66), (76), (78), (91), % 149.90/21.88 | | | | | (103), (110), (115), (120), (129) are inconsistent by % 149.90/21.88 | | | | | sub-proof #357. % 149.90/21.88 | | | | | % 149.90/21.88 | | | | End of split % 149.90/21.88 | | | | % 149.90/21.88 | | | Case 2: % 149.90/21.88 | | | | % 149.90/21.88 | | | | (130) all_56_21 = e2 % 149.90/21.88 | | | | (131) all_56_19 = e1 % 149.90/21.88 | | | | % 149.90/21.88 | | | | COMBINE_EQS: (87), (131) imply: % 149.90/21.88 | | | | (132) all_6_0 = e1 % 149.90/21.88 | | | | % 149.90/21.88 | | | | COMBINE_EQS: (28), (130) imply: % 149.90/21.88 | | | | (133) all_6_2 = e2 % 149.90/21.88 | | | | % 149.90/21.88 | | | | SIMP: (133) implies: % 149.90/21.88 | | | | (134) all_6_2 = e2 % 149.90/21.88 | | | | % 149.90/21.88 | | | | REDUCE: (99), (134) imply: % 149.90/21.88 | | | | (135) ~ (all_52_2 = e2) % 149.90/21.88 | | | | % 149.90/21.88 | | | | REDUCE: (35), (132) imply: % 149.90/21.88 | | | | (136) ~ (all_52_7 = e1) % 149.90/21.88 | | | | % 149.90/21.88 | | | | REDUCE: (50), (134) imply: % 149.90/21.88 | | | | (137) op(e2, e2) = e2 % 149.90/21.88 | | | | % 149.90/21.88 | | | | GROUND_INST: instantiating (44) with all_8_2, e2, e2, e2, simplifying % 149.90/21.88 | | | | with (96), (137) gives: % 149.90/21.88 | | | | (138) all_8_2 = e2 % 149.90/21.88 | | | | % 149.90/21.88 | | | | REDUCE: (43), (138) imply: % 149.90/21.88 | | | | (139) ~ (all_52_1 = e2) % 149.90/21.88 | | | | % 149.90/21.88 | | | | BETA: splitting (95) gives: % 149.90/21.88 | | | | % 149.90/21.88 | | | | Case 1: % 149.90/21.88 | | | | | % 149.90/21.88 | | | | | (140) ~ (all_56_31 = e2) % 149.90/21.88 | | | | | % 149.90/21.88 | | | | | REDUCE: (71), (140) imply: % 149.90/21.88 | | | | | (141) ~ (all_4_2 = e2) % 149.90/21.88 | | | | | % 149.90/21.88 | | | | | REF_CLOSE: (22), (26), (44), (66), (78), (103), (120), (122), (124), % 149.90/21.88 | | | | | (141) are inconsistent by sub-proof #363. % 149.90/21.88 | | | | | % 149.90/21.88 | | | | Case 2: % 149.90/21.88 | | | | | % 149.90/21.88 | | | | | (142) all_56_31 = e2 % 149.90/21.88 | | | | | (143) all_56_27 = e0 % 149.90/21.88 | | | | | % 149.90/21.88 | | | | | COMBINE_EQS: (31), (143) imply: % 149.90/21.88 | | | | | (144) all_52_7 = e0 % 149.90/21.88 | | | | | % 149.90/21.88 | | | | | SIMP: (144) implies: % 149.90/21.88 | | | | | (145) all_52_7 = e0 % 149.90/21.88 | | | | | % 149.90/21.88 | | | | | COMBINE_EQS: (71), (142) imply: % 149.90/21.88 | | | | | (146) all_4_2 = e2 % 149.90/21.88 | | | | | % 149.90/21.88 | | | | | REDUCE: (59), (146) imply: % 149.90/21.88 | | | | | (147) ~ (all_52_3 = e2) % 149.90/21.88 | | | | | % 149.90/21.88 | | | | | REDUCE: (136), (145) imply: % 149.90/21.88 | | | | | (148) ~ (e1 = e0) % 149.90/21.88 | | | | | % 149.90/21.88 | | | | | REDUCE: (66), (146) imply: % 149.90/21.88 | | | | | (149) op(e2, e2) = all_4_1 % 149.90/21.88 | | | | | % 149.90/21.88 | | | | | REDUCE: (103), (146) imply: % 149.90/21.88 | | | | | (150) op(e0, e2) = all_56_30 % 149.90/21.88 | | | | | % 149.90/21.88 | | | | | REDUCE: (36), (145) imply: % 149.90/21.88 | | | | | (151) op(e0, e2) = e0 % 149.90/21.88 | | | | | % 149.90/21.88 | | | | | BETA: splitting (40) gives: % 149.90/21.88 | | | | | % 149.90/21.88 | | | | | Case 1: % 149.90/21.88 | | | | | | % 149.90/21.88 | | | | | | (152) all_58_0 = e2 % 149.90/21.88 | | | | | | % 149.90/21.88 | | | | | | COMBINE_EQS: (92), (152) imply: % 149.90/21.88 | | | | | | (153) all_10_2 = e2 % 149.90/21.88 | | | | | | % 149.90/21.88 | | | | | | REDUCE: (90), (153) imply: % 149.90/21.88 | | | | | | (154) op(e2, e2) = all_10_1 % 149.90/21.88 | | | | | | % 149.90/21.88 | | | | | | GROUND_INST: instantiating (44) with e0, all_56_30, e2, e0, % 149.90/21.88 | | | | | | simplifying with (150), (151) gives: % 149.90/21.88 | | | | | | (155) all_56_30 = e0 % 149.90/21.88 | | | | | | % 149.90/21.88 | | | | | | GROUND_INST: instantiating (44) with e2, all_10_1, e2, e2, % 149.90/21.88 | | | | | | simplifying with (137), (154) gives: % 149.90/21.88 | | | | | | (156) all_10_1 = e2 % 149.90/21.88 | | | | | | % 149.90/21.88 | | | | | | GROUND_INST: instantiating (44) with all_4_1, all_10_1, e2, e2, % 149.90/21.88 | | | | | | simplifying with (149), (154) gives: % 149.90/21.88 | | | | | | (157) all_10_1 = all_4_1 % 149.90/21.88 | | | | | | % 149.90/21.88 | | | | | | COMBINE_EQS: (156), (157) imply: % 149.90/21.88 | | | | | | (158) all_4_1 = e2 % 149.90/21.88 | | | | | | % 149.90/21.88 | | | | | | SIMP: (158) implies: % 149.90/21.88 | | | | | | (159) all_4_1 = e2 % 149.90/21.88 | | | | | | % 149.90/21.88 | | | | | | REDUCE: (120), (159) imply: % 149.90/21.88 | | | | | | (160) op(e0, e2) = e1 % 149.90/21.88 | | | | | | % 149.90/21.88 | | | | | | GROUND_INST: instantiating (44) with e0, e1, e2, e0, simplifying % 149.90/21.88 | | | | | | with (151), (160) gives: % 149.90/21.88 | | | | | | (161) e1 = e0 % 150.32/21.88 | | | | | | % 150.32/21.88 | | | | | | REDUCE: (41), (161) imply: % 150.32/21.88 | | | | | | (162) $false % 150.32/21.88 | | | | | | % 150.32/21.88 | | | | | | CLOSE: (162) is inconsistent. % 150.32/21.88 | | | | | | % 150.32/21.88 | | | | | Case 2: % 150.32/21.88 | | | | | | % 150.32/21.88 | | | | | | (163) all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2 % 150.32/21.88 | | | | | | % 150.32/21.88 | | | | | | REF_CLOSE: (8), (86), (117), (135), (139), (147), (163) are % 150.32/21.88 | | | | | | inconsistent by sub-proof #695. % 150.32/21.88 | | | | | | % 150.32/21.88 | | | | | End of split % 150.32/21.88 | | | | | % 150.32/21.88 | | | | End of split % 150.32/21.88 | | | | % 150.32/21.88 | | | End of split % 150.32/21.88 | | | % 150.32/21.88 | | Case 2: % 150.32/21.88 | | | % 150.32/21.88 | | | (164) all_56_31 = e3 % 150.32/21.88 | | | (165) all_56_25 = e0 % 150.32/21.88 | | | % 150.32/21.88 | | | REF_CLOSE: (1), (5), (8), (12), (13), (15), (17), (21), (22), (27), (28), % 150.32/21.88 | | | (29), (30), (34), (37), (38), (39), (41), (44), (46), (50), % 150.32/21.88 | | | (51), (54), (55), (56), (57), (59), (61), (64), (65), (66), % 150.32/21.88 | | | (68), (69), (71), (72), (73), (74), (75), (77), (80), (81), % 150.32/21.88 | | | (82), (85), (87), (90), (93), (94), (99), (102), (103), (104), % 150.32/21.88 | | | (105), (106), (107), (108), (118), (164), (165) are % 150.32/21.88 | | | inconsistent by sub-proof #55. % 150.32/21.88 | | | % 150.32/21.88 | | End of split % 150.32/21.88 | | % 150.32/21.88 | Case 2: % 150.32/21.88 | | % 150.32/21.88 | | (166) all_56_31 = e1 % 150.32/21.88 | | (167) all_56_29 = e0 % 150.32/21.88 | | % 150.32/21.88 | | COMBINE_EQS: (84), (167) imply: % 150.32/21.88 | | (168) all_52_11 = e0 % 150.32/21.88 | | % 150.32/21.88 | | SIMP: (168) implies: % 150.32/21.88 | | (169) all_52_11 = e0 % 150.32/21.88 | | % 150.32/21.88 | | REF_CLOSE: (1), (3), (6), (12), (13), (15), (17), (27), (28), (29), (30), % 150.32/21.88 | | (34), (35), (36), (38), (39), (44), (48), (50), (51), (57), (62), % 150.32/21.88 | | (64), (66), (69), (71), (74), (75), (77), (79), (82), (87), (90), % 150.32/21.88 | | (93), (99), (104), (105), (108), (112), (113), (118), (166), % 150.32/21.88 | | (169) are inconsistent by sub-proof #50. % 150.32/21.88 | | % 150.32/21.88 | End of split % 150.32/21.88 | % 150.32/21.88 End of proof % 150.32/21.88 % 150.32/21.88 Sub-proof #50 shows that the following formulas are inconsistent: % 150.32/21.88 ---------------------------------------------------------------- % 150.32/21.88 (1) all_56_11 = all_8_2 % 150.32/21.88 (2) ~ (all_52_11 = all_6_2) % 150.32/21.88 (3) all_56_31 = e1 % 150.32/21.88 (4) ~ (all_52_7 = all_52_11) % 150.32/21.88 (5) all_54_10 = all_6_2 % 150.32/21.88 (6) ~ (all_56_21 = e2) | all_56_19 = e1 % 150.32/21.88 (7) ~ (all_52_14 = all_4_2) % 150.32/21.88 (8) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0 % 150.32/21.88 (9) all_52_11 = e0 % 150.32/21.88 (10) all_54_9 = all_6_0 % 150.32/21.88 (11) all_56_21 = all_6_2 % 150.32/21.88 (12) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 150.32/21.88 (13) all_56_1 = all_10_2 % 150.32/21.88 (14) all_56_17 = all_52_2 % 150.32/21.88 (15) ~ (all_52_7 = all_6_0) % 150.32/21.88 (16) op(e0, e2) = all_52_7 % 150.32/21.88 (17) op(e3, e3) = all_10_2 % 150.32/21.88 (18) ~ (all_56_21 = e3) | all_56_17 = e1 % 150.32/21.88 (19) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 150.32/21.88 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 150.32/21.88 (20) op(e0, all_4_1) = all_4_0 % 150.32/21.88 (21) op(all_6_2, all_6_2) = e2 % 150.32/21.88 (22) ~ (all_6_0 = all_6_2) % 150.32/21.88 (23) ~ (all_6_0 = e0) | ~ (all_6_2 = e3) % 150.32/21.88 (24) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0 % 150.32/21.88 (25) ~ (all_52_14 = all_6_0) % 150.32/21.88 (26) op(all_4_2, all_4_2) = all_4_1 % 150.32/21.89 (27) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0 % 150.32/21.89 (28) all_56_31 = all_4_2 % 150.32/21.89 (29) ~ (all_52_2 = all_52_14) % 150.32/21.89 (30) all_56_1 = e3 | all_56_11 = e2 | all_56_21 = e1 | all_56_31 = e0 % 150.32/21.89 (31) ~ (all_52_2 = all_6_0) % 150.32/21.89 (32) all_54_13 = all_52_7 % 150.32/21.89 (33) op(e1, e1) = all_6_2 % 150.32/21.89 (34) all_56_19 = all_6_0 % 150.32/21.89 (35) op(all_10_2, all_10_2) = all_10_1 % 150.32/21.89 (36) op(e1, all_6_2) = all_56_20 % 150.32/21.89 (37) ~ (all_52_2 = all_6_2) % 150.32/21.89 (38) op(e3, all_10_2) = all_56_0 % 150.32/21.89 (39) ~ (all_52_14 = all_6_2) % 150.32/21.89 (40) ~ (all_8_2 = all_6_0) % 150.32/21.89 (41) ~ (all_4_0 = e2) % 150.32/21.89 (42) ~ (all_4_0 = e3) % 150.32/21.89 (43) all_54_11 = all_52_14 % 150.32/21.89 % 150.32/21.89 Begin of proof % 150.32/21.89 | % 150.32/21.89 | COMBINE_EQS: (3), (28) imply: % 150.32/21.89 | (44) all_4_2 = e1 % 150.32/21.89 | % 150.32/21.89 | REDUCE: (4), (9) imply: % 150.32/21.89 | (45) ~ (all_52_7 = e0) % 150.32/21.89 | % 150.32/21.89 | REDUCE: (2), (9) imply: % 150.32/21.89 | (46) ~ (all_6_2 = e0) % 150.32/21.89 | % 150.32/21.89 | SIMP: (46) implies: % 150.32/21.89 | (47) ~ (all_6_2 = e0) % 150.32/21.89 | % 150.32/21.89 | REDUCE: (26), (44) imply: % 150.32/21.89 | (48) op(e1, e1) = all_4_1 % 150.32/21.89 | % 150.32/21.89 | REF_CLOSE: (1), (5), (6), (7), (8), (10), (11), (12), (13), (14), (15), (16), % 150.32/21.89 | (17), (18), (19), (20), (21), (22), (23), (24), (25), (27), (28), % 150.32/21.89 | (29), (30), (31), (32), (33), (34), (35), (36), (37), (38), (39), % 150.32/21.89 | (40), (41), (42), (43), (45), (47), (48) are inconsistent by % 150.32/21.89 | sub-proof #51. % 150.32/21.89 | % 150.32/21.89 End of proof % 150.32/21.89 % 150.32/21.89 Sub-proof #51 shows that the following formulas are inconsistent: % 150.32/21.89 ---------------------------------------------------------------- % 150.32/21.89 (1) all_56_11 = all_8_2 % 150.32/21.89 (2) all_54_10 = all_6_2 % 150.32/21.89 (3) ~ (all_56_21 = e2) | all_56_19 = e1 % 150.32/21.89 (4) ~ (all_52_14 = all_4_2) % 150.32/21.89 (5) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0 % 150.32/21.89 (6) all_54_9 = all_6_0 % 150.32/21.89 (7) all_56_21 = all_6_2 % 150.32/21.89 (8) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 150.32/21.89 (9) all_56_1 = all_10_2 % 150.32/21.89 (10) all_56_17 = all_52_2 % 150.32/21.89 (11) ~ (all_52_7 = all_6_0) % 150.32/21.89 (12) op(e0, e2) = all_52_7 % 150.32/21.89 (13) op(e3, e3) = all_10_2 % 150.32/21.89 (14) ~ (all_56_21 = e3) | all_56_17 = e1 % 150.32/21.89 (15) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 150.32/21.89 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 150.32/21.89 (16) ~ (all_6_2 = e0) % 150.32/21.89 (17) op(e0, all_4_1) = all_4_0 % 150.32/21.89 (18) op(all_6_2, all_6_2) = e2 % 150.32/21.89 (19) ~ (all_6_0 = all_6_2) % 150.32/21.89 (20) ~ (all_6_0 = e0) | ~ (all_6_2 = e3) % 150.32/21.89 (21) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0 % 150.32/21.89 (22) ~ (all_52_14 = all_6_0) % 150.32/21.89 (23) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0 % 150.32/21.89 (24) all_56_31 = all_4_2 % 150.32/21.89 (25) ~ (all_52_2 = all_52_14) % 150.32/21.89 (26) all_56_1 = e3 | all_56_11 = e2 | all_56_21 = e1 | all_56_31 = e0 % 150.32/21.89 (27) ~ (all_52_2 = all_6_0) % 150.32/21.89 (28) all_54_13 = all_52_7 % 150.32/21.89 (29) op(e1, e1) = all_6_2 % 150.32/21.89 (30) all_56_19 = all_6_0 % 150.32/21.89 (31) op(all_10_2, all_10_2) = all_10_1 % 150.32/21.89 (32) op(e1, e1) = all_4_1 % 150.32/21.89 (33) op(e1, all_6_2) = all_56_20 % 150.32/21.89 (34) ~ (all_52_2 = all_6_2) % 150.32/21.89 (35) op(e3, all_10_2) = all_56_0 % 150.32/21.89 (36) ~ (all_52_14 = all_6_2) % 150.32/21.89 (37) ~ (all_52_7 = e0) % 150.32/21.89 (38) ~ (all_8_2 = all_6_0) % 150.32/21.89 (39) ~ (all_4_0 = e2) % 150.32/21.89 (40) ~ (all_4_0 = e3) % 150.32/21.89 (41) all_54_11 = all_52_14 % 150.32/21.89 % 150.32/21.89 Begin of proof % 150.32/21.89 | % 150.32/21.89 | GROUND_INST: instantiating (15) with all_6_2, all_4_1, e1, e1, simplifying % 150.32/21.89 | with (29), (32) gives: % 150.32/21.89 | (42) all_6_2 = all_4_1 % 150.32/21.89 | % 150.32/21.89 | COMBINE_EQS: (2), (42) imply: % 150.32/21.89 | (43) all_54_10 = all_4_1 % 150.32/21.89 | % 150.32/21.89 | COMBINE_EQS: (7), (42) imply: % 150.32/21.89 | (44) all_56_21 = all_4_1 % 150.32/21.89 | % 150.32/21.89 | REDUCE: (34), (42) imply: % 150.32/21.89 | (45) ~ (all_52_2 = all_4_1) % 150.32/21.89 | % 150.32/21.89 | REDUCE: (36), (42) imply: % 150.32/21.89 | (46) ~ (all_52_14 = all_4_1) % 150.32/21.89 | % 150.32/21.89 | REDUCE: (19), (42) imply: % 150.32/21.89 | (47) ~ (all_6_0 = all_4_1) % 150.32/21.89 | % 150.32/21.89 | REDUCE: (16), (42) imply: % 150.32/21.89 | (48) ~ (all_4_1 = e0) % 150.32/21.89 | % 150.32/21.89 | REDUCE: (18), (42) imply: % 150.32/21.89 | (49) op(all_4_1, all_4_1) = e2 % 150.32/21.89 | % 150.32/21.89 | REDUCE: (33), (42) imply: % 150.32/21.89 | (50) op(e1, all_4_1) = all_56_20 % 150.32/21.89 | % 150.32/21.89 | BETA: splitting (3) gives: % 150.32/21.89 | % 150.32/21.89 | Case 1: % 150.32/21.89 | | % 150.32/21.89 | | (51) ~ (all_56_21 = e2) % 150.32/21.89 | | % 150.32/21.89 | | REDUCE: (44), (51) imply: % 150.32/21.89 | | (52) ~ (all_4_1 = e2) % 150.32/21.89 | | % 150.32/21.89 | | REF_CLOSE: (1), (4), (5), (6), (8), (9), (10), (13), (14), (15), (20), (22), % 150.32/21.89 | | (23), (24), (25), (26), (27), (31), (32), (35), (38), (41), (42), % 150.32/21.89 | | (43), (44), (45), (46), (47), (48), (49), (50), (52) are % 150.32/21.89 | | inconsistent by sub-proof #52. % 150.32/21.89 | | % 150.32/21.89 | Case 2: % 150.32/21.89 | | % 150.32/21.89 | | (53) all_56_21 = e2 % 150.32/21.89 | | (54) all_56_19 = e1 % 150.32/21.89 | | % 150.32/21.89 | | COMBINE_EQS: (30), (54) imply: % 150.32/21.89 | | (55) all_6_0 = e1 % 150.32/21.89 | | % 150.32/21.89 | | COMBINE_EQS: (44), (53) imply: % 150.32/21.89 | | (56) all_4_1 = e2 % 150.32/21.89 | | % 150.32/21.89 | | SIMP: (56) implies: % 150.32/21.89 | | (57) all_4_1 = e2 % 150.32/21.89 | | % 150.32/21.89 | | REDUCE: (11), (55) imply: % 150.32/21.89 | | (58) ~ (all_52_7 = e1) % 150.32/21.89 | | % 150.32/21.89 | | REDUCE: (17), (57) imply: % 150.32/21.89 | | (59) op(e0, e2) = all_4_0 % 150.32/21.89 | | % 150.32/21.89 | | REF_CLOSE: (12), (15), (21), (28), (37), (39), (40), (58), (59) are % 150.32/21.89 | | inconsistent by sub-proof #518. % 150.32/21.89 | | % 150.32/21.89 | End of split % 150.32/21.89 | % 150.32/21.89 End of proof % 150.32/21.89 % 150.32/21.89 Sub-proof #52 shows that the following formulas are inconsistent: % 150.32/21.89 ---------------------------------------------------------------- % 150.32/21.89 (1) all_56_11 = all_8_2 % 150.32/21.89 (2) ~ (all_4_1 = e0) % 150.32/21.89 (3) ~ (all_52_2 = all_4_1) % 150.32/21.89 (4) ~ (all_52_14 = all_4_1) % 150.32/21.89 (5) ~ (all_52_14 = all_4_2) % 150.32/21.89 (6) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0 % 150.32/21.89 (7) op(e1, all_4_1) = all_56_20 % 150.32/21.89 (8) all_54_9 = all_6_0 % 150.32/21.89 (9) ~ (all_4_1 = e2) % 150.32/21.89 (10) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 150.32/21.89 (11) all_56_1 = all_10_2 % 150.32/21.89 (12) all_56_17 = all_52_2 % 150.32/21.89 (13) op(e3, e3) = all_10_2 % 150.32/21.89 (14) ~ (all_56_21 = e3) | all_56_17 = e1 % 150.32/21.89 (15) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 150.32/21.89 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 150.32/21.89 (16) all_56_21 = all_4_1 % 150.32/21.89 (17) ~ (all_6_0 = e0) | ~ (all_6_2 = e3) % 150.32/21.89 (18) ~ (all_52_14 = all_6_0) % 150.32/21.89 (19) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0 % 150.32/21.89 (20) all_56_31 = all_4_2 % 150.32/21.89 (21) ~ (all_52_2 = all_52_14) % 150.32/21.89 (22) all_6_2 = all_4_1 % 150.32/21.89 (23) all_56_1 = e3 | all_56_11 = e2 | all_56_21 = e1 | all_56_31 = e0 % 150.32/21.89 (24) ~ (all_52_2 = all_6_0) % 150.32/21.89 (25) all_54_10 = all_4_1 % 150.32/21.89 (26) op(all_10_2, all_10_2) = all_10_1 % 150.32/21.89 (27) ~ (all_6_0 = all_4_1) % 150.32/21.89 (28) op(e1, e1) = all_4_1 % 150.32/21.89 (29) op(all_4_1, all_4_1) = e2 % 150.32/21.89 (30) op(e3, all_10_2) = all_56_0 % 150.32/21.89 (31) ~ (all_8_2 = all_6_0) % 150.32/21.89 (32) all_54_11 = all_52_14 % 150.32/21.89 % 150.32/21.89 Begin of proof % 150.32/21.89 | % 150.32/21.89 | BETA: splitting (14) gives: % 150.32/21.89 | % 150.32/21.89 | Case 1: % 150.32/21.89 | | % 150.32/21.89 | | (33) ~ (all_56_21 = e3) % 150.32/21.89 | | % 150.32/21.89 | | REDUCE: (16), (33) imply: % 150.32/21.89 | | (34) ~ (all_4_1 = e3) % 150.32/21.89 | | % 150.32/21.89 | | REF_CLOSE: (2), (7), (9), (10), (15), (25), (28), (29), (34) are % 150.32/21.89 | | inconsistent by sub-proof #53. % 150.32/21.89 | | % 150.32/21.89 | Case 2: % 150.32/21.89 | | % 150.32/21.89 | | (35) all_56_21 = e3 % 150.32/21.89 | | (36) all_56_17 = e1 % 150.32/21.89 | | % 150.32/21.89 | | COMBINE_EQS: (12), (36) imply: % 150.32/21.89 | | (37) all_52_2 = e1 % 150.32/21.89 | | % 150.32/21.89 | | COMBINE_EQS: (16), (35) imply: % 150.32/21.89 | | (38) all_4_1 = e3 % 150.32/21.89 | | % 150.32/21.89 | | COMBINE_EQS: (22), (38) imply: % 150.32/21.89 | | (39) all_6_2 = e3 % 150.32/21.89 | | % 150.32/21.89 | | REDUCE: (21), (37) imply: % 150.32/21.89 | | (40) ~ (all_52_14 = e1) % 150.32/21.89 | | % 150.32/21.89 | | SIMP: (40) implies: % 150.32/21.89 | | (41) ~ (all_52_14 = e1) % 150.32/21.89 | | % 150.32/21.89 | | REDUCE: (24), (37) imply: % 150.32/21.89 | | (42) ~ (all_6_0 = e1) % 150.32/21.89 | | % 150.32/21.89 | | SIMP: (42) implies: % 150.32/21.89 | | (43) ~ (all_6_0 = e1) % 150.32/21.89 | | % 150.32/21.89 | | REDUCE: (3), (37), (38) imply: % 150.32/21.89 | | (44) ~ (e3 = e1) % 150.32/21.89 | | % 150.32/21.89 | | SIMP: (44) implies: % 150.32/21.89 | | (45) ~ (e3 = e1) % 150.32/21.89 | | % 150.32/21.89 | | REDUCE: (4), (38) imply: % 150.32/21.89 | | (46) ~ (all_52_14 = e3) % 150.32/21.89 | | % 150.32/21.89 | | REDUCE: (27), (38) imply: % 150.32/21.89 | | (47) ~ (all_6_0 = e3) % 150.32/21.89 | | % 150.32/21.89 | | REDUCE: (29), (38) imply: % 150.32/21.89 | | (48) op(e3, e3) = e2 % 150.32/21.89 | | % 150.32/21.89 | | BETA: splitting (17) gives: % 150.32/21.89 | | % 150.32/21.89 | | Case 1: % 150.32/21.89 | | | % 150.32/21.89 | | | (49) ~ (all_6_2 = e3) % 150.32/21.89 | | | % 150.32/21.89 | | | REDUCE: (39), (49) imply: % 150.32/21.89 | | | (50) $false % 150.32/21.89 | | | % 150.32/21.89 | | | CLOSE: (50) is inconsistent. % 150.32/21.89 | | | % 150.32/21.89 | | Case 2: % 150.32/21.89 | | | % 150.32/21.89 | | | (51) ~ (all_6_0 = e0) % 150.32/21.89 | | | % 150.32/21.89 | | | REF_CLOSE: (1), (5), (6), (8), (11), (13), (15), (18), (19), (20), (23), % 150.32/21.89 | | | (26), (30), (31), (32), (35), (41), (43), (45), (46), (47), % 150.32/21.89 | | | (48), (51) are inconsistent by sub-proof #80. % 150.32/21.89 | | | % 150.32/21.89 | | End of split % 150.32/21.89 | | % 150.32/21.89 | End of split % 150.32/21.89 | % 150.32/21.89 End of proof % 150.32/21.89 % 150.32/21.89 Sub-proof #53 shows that the following formulas are inconsistent: % 150.32/21.89 ---------------------------------------------------------------- % 150.32/21.89 (1) ~ (all_4_1 = e0) % 150.32/21.89 (2) ~ (all_4_1 = e3) % 150.32/21.89 (3) op(e1, all_4_1) = all_56_20 % 150.32/21.89 (4) ~ (all_4_1 = e2) % 150.32/21.89 (5) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 150.32/21.89 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 150.32/21.89 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 150.32/21.89 (7) all_54_10 = all_4_1 % 150.32/21.89 (8) op(e1, e1) = all_4_1 % 150.32/21.89 (9) op(all_4_1, all_4_1) = e2 % 150.32/21.89 % 150.32/21.89 Begin of proof % 150.32/21.89 | % 150.32/21.89 | BETA: splitting (5) gives: % 150.32/21.89 | % 150.32/21.89 | Case 1: % 150.32/21.89 | | % 150.32/21.89 | | (10) all_54_10 = e3 % 150.32/21.89 | | % 150.32/21.89 | | REF_CLOSE: (2), (7), (10) are inconsistent by sub-proof #282. % 150.32/21.89 | | % 150.32/21.89 | Case 2: % 150.32/21.89 | | % 150.32/21.89 | | (11) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 150.32/21.89 | | % 150.32/21.89 | | BETA: splitting (11) gives: % 150.32/21.89 | | % 150.32/21.89 | | Case 1: % 150.32/21.89 | | | % 150.32/21.89 | | | (12) all_54_10 = e2 % 150.32/21.89 | | | % 150.32/21.89 | | | REF_CLOSE: (4), (7), (12) are inconsistent by sub-proof #281. % 150.32/21.89 | | | % 150.32/21.89 | | Case 2: % 150.32/21.89 | | | % 150.32/21.89 | | | (13) ~ (all_54_10 = e2) % 150.32/21.89 | | | (14) all_54_10 = e1 | all_54_10 = e0 % 150.32/21.89 | | | % 150.32/21.89 | | | BETA: splitting (14) gives: % 150.32/21.89 | | | % 150.32/21.89 | | | Case 1: % 150.32/21.89 | | | | % 150.32/21.89 | | | | (15) all_54_10 = e1 % 150.32/21.89 | | | | % 150.32/21.89 | | | | COMBINE_EQS: (7), (15) imply: % 150.32/21.89 | | | | (16) all_4_1 = e1 % 150.32/21.89 | | | | % 150.32/21.89 | | | | SIMP: (16) implies: % 150.32/21.89 | | | | (17) all_4_1 = e1 % 150.32/21.89 | | | | % 150.32/21.89 | | | | REF_CLOSE: (3), (4), (6), (8), (9), (17) are inconsistent by sub-proof % 150.32/21.89 | | | | #54. % 150.32/21.89 | | | | % 150.32/21.89 | | | Case 2: % 150.32/21.89 | | | | % 150.32/21.89 | | | | (18) all_54_10 = e0 % 150.32/21.89 | | | | % 150.32/21.89 | | | | REF_CLOSE: (1), (7), (18) are inconsistent by sub-proof #277. % 150.32/21.89 | | | | % 150.32/21.89 | | | End of split % 150.32/21.89 | | | % 150.32/21.89 | | End of split % 150.32/21.89 | | % 150.32/21.89 | End of split % 150.32/21.89 | % 150.32/21.89 End of proof % 150.32/21.89 % 150.32/21.89 Sub-proof #54 shows that the following formulas are inconsistent: % 150.32/21.89 ---------------------------------------------------------------- % 150.32/21.89 (1) op(e1, all_4_1) = all_56_20 % 150.32/21.89 (2) ~ (all_4_1 = e2) % 150.32/21.89 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 150.32/21.89 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 150.32/21.89 (4) all_4_1 = e1 % 150.32/21.89 (5) op(e1, e1) = all_4_1 % 150.32/21.89 (6) op(all_4_1, all_4_1) = e2 % 150.32/21.89 % 150.32/21.89 Begin of proof % 150.32/21.89 | % 150.32/21.89 | REDUCE: (2), (4) imply: % 150.32/21.89 | (7) ~ (e2 = e1) % 150.32/21.89 | % 150.32/21.89 | SIMP: (7) implies: % 150.32/21.89 | (8) ~ (e2 = e1) % 150.32/21.89 | % 150.32/21.89 | REDUCE: (4), (6) imply: % 150.32/21.89 | (9) op(e1, e1) = e2 % 150.32/21.89 | % 150.32/21.89 | REDUCE: (1), (4) imply: % 150.32/21.89 | (10) op(e1, e1) = all_56_20 % 150.32/21.89 | % 150.32/21.89 | REDUCE: (4), (5) imply: % 150.32/21.89 | (11) op(e1, e1) = e1 % 150.32/21.89 | % 150.32/21.89 | REF_CLOSE: (3), (8), (9), (10), (11) are inconsistent by sub-proof #494. % 150.32/21.89 | % 150.32/21.89 End of proof % 150.32/21.89 % 150.32/21.89 Sub-proof #55 shows that the following formulas are inconsistent: % 150.32/21.89 ---------------------------------------------------------------- % 150.32/21.89 (1) all_56_11 = all_8_2 % 150.32/21.89 (2) all_56_25 = all_52_3 % 150.32/21.89 (3) all_58_6 = all_52_2 % 150.32/21.89 (4) all_54_10 = all_6_2 % 150.32/21.89 (5) ~ (all_56_21 = e2) | all_56_19 = e1 % 150.32/21.89 (6) all_56_31 = e3 % 150.32/21.89 (7) ~ (all_52_14 = all_4_2) % 150.32/21.89 (8) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0 % 150.32/21.89 (9) ~ (e3 = e2) % 150.32/21.89 (10) op(e0, e0) = all_4_2 % 150.32/21.89 (11) all_54_9 = all_6_0 % 150.32/21.89 (12) all_56_21 = all_6_2 % 150.32/21.89 (13) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 150.32/21.89 (14) all_56_1 = all_10_2 % 150.32/21.89 (15) all_56_17 = all_52_2 % 150.32/21.89 (16) all_58_13 = all_52_7 % 150.32/21.89 (17) op(e3, e3) = all_10_2 % 150.32/21.89 (18) ~ (all_56_21 = e3) | all_56_17 = e1 % 150.32/21.89 (19) ~ (e1 = e0) % 150.32/21.89 (20) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 150.32/21.89 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 150.32/21.89 (21) all_56_25 = e0 % 150.32/21.89 (22) ~ (all_52_3 = all_52_7) % 150.32/21.89 (23) op(all_6_2, all_6_2) = e2 % 150.32/21.89 (24) ~ (all_6_0 = all_6_2) % 150.32/21.89 (25) ~ (all_52_7 = all_4_2) % 150.32/21.89 (26) all_58_8 = all_6_2 % 150.32/21.89 (27) ~ (all_6_0 = e3) % 150.32/21.89 (28) ~ (all_6_0 = e0) | ~ (all_6_2 = e3) % 150.32/21.89 (29) ~ (all_52_3 = all_4_2) % 150.32/21.89 (30) all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3 % 150.32/21.89 (31) ~ (all_52_14 = all_6_0) % 150.32/21.89 (32) ~ (all_52_2 = all_52_3) % 150.32/21.89 (33) op(all_4_2, all_4_2) = all_4_1 % 150.32/21.89 (34) all_58_3 = all_8_2 % 150.32/21.89 (35) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0 % 150.32/21.89 (36) all_56_31 = all_4_2 % 150.32/21.89 (37) all_58_11 = all_52_14 % 150.32/21.89 (38) all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3 % 150.32/21.89 (39) ~ (all_52_2 = all_52_14) % 150.32/21.89 (40) all_56_1 = e3 | all_56_11 = e2 | all_56_21 = e1 | all_56_31 = e0 % 150.32/21.89 (41) ~ (all_52_2 = all_6_0) % 150.32/21.89 (42) all_56_23 = all_52_14 % 150.32/21.89 (43) all_54_8 = all_52_2 % 150.32/21.89 (44) op(e1, e1) = all_6_2 % 150.32/21.89 (45) all_58_7 = all_6_0 % 150.32/21.89 (46) all_56_19 = all_6_0 % 150.32/21.89 (47) op(all_10_2, all_10_2) = all_10_1 % 150.32/21.89 (48) op(e1, all_6_2) = all_56_20 % 150.32/21.89 (49) all_58_1 = e0 | all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0 % 150.32/21.89 (50) ~ (all_52_2 = all_6_2) % 150.32/21.89 (51) ~ (all_56_21 = e0) | all_56_23 = e1 % 150.32/21.89 (52) op(e0, all_4_2) = all_56_30 % 150.32/21.89 (53) op(e3, all_10_2) = all_56_0 % 150.32/21.89 (54) ~ (all_52_14 = all_6_2) % 150.32/21.89 (55) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0 % 150.32/21.89 (56) ~ (all_52_2 = all_10_2) % 150.32/21.89 (57) ~ (all_8_2 = all_6_0) % 150.32/21.89 (58) all_54_11 = all_52_14 % 150.32/21.89 % 150.32/21.89 Begin of proof % 150.32/21.89 | % 150.32/21.89 | COMBINE_EQS: (2), (21) imply: % 150.32/21.89 | (59) all_52_3 = e0 % 150.32/21.89 | % 150.32/21.89 | SIMP: (59) implies: % 150.32/21.89 | (60) all_52_3 = e0 % 150.32/21.89 | % 150.32/21.89 | COMBINE_EQS: (6), (36) imply: % 150.32/21.89 | (61) all_4_2 = e3 % 150.32/21.89 | % 150.32/21.89 | REDUCE: (32), (60) imply: % 150.32/21.89 | (62) ~ (all_52_2 = e0) % 150.32/21.89 | % 150.32/21.89 | REDUCE: (22), (60) imply: % 150.32/21.89 | (63) ~ (all_52_7 = e0) % 150.32/21.89 | % 150.32/21.89 | SIMP: (63) implies: % 150.32/21.89 | (64) ~ (all_52_7 = e0) % 150.32/21.89 | % 150.32/21.89 | REDUCE: (29), (60), (61) imply: % 150.32/21.89 | (65) ~ (e3 = e0) % 150.32/21.89 | % 150.32/21.89 | SIMP: (65) implies: % 150.32/21.89 | (66) ~ (e3 = e0) % 150.32/21.89 | % 150.32/21.89 | REDUCE: (25), (61) imply: % 150.32/21.89 | (67) ~ (all_52_7 = e3) % 150.32/21.89 | % 150.32/21.89 | REDUCE: (7), (61) imply: % 150.32/21.89 | (68) ~ (all_52_14 = e3) % 150.32/21.89 | % 150.32/21.89 | REDUCE: (33), (61) imply: % 150.32/21.89 | (69) op(e3, e3) = all_4_1 % 150.32/21.89 | % 150.32/21.89 | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13), % 150.32/21.89 | (14), (15), (16), (17), (18), (19), (20), (23), (24), (26), (27), % 150.32/21.89 | (28), (30), (31), (33), (34), (35), (36), (37), (38), (39), (40), % 150.32/21.89 | (41), (42), (43), (44), (45), (46), (47), (48), (49), (50), (51), % 150.32/21.89 | (52), (53), (54), (55), (56), (57), (58), (62), (64), (66), (67), % 150.32/21.89 | (68), (69) are inconsistent by sub-proof #56. % 150.32/21.89 | % 150.32/21.89 End of proof % 150.32/21.89 % 150.32/21.89 Sub-proof #56 shows that the following formulas are inconsistent: % 150.32/21.89 ---------------------------------------------------------------- % 150.32/21.89 (1) all_56_11 = all_8_2 % 150.32/21.89 (2) all_58_6 = all_52_2 % 150.32/21.89 (3) ~ (e3 = e0) % 150.32/21.89 (4) all_54_10 = all_6_2 % 150.32/21.89 (5) ~ (all_56_21 = e2) | all_56_19 = e1 % 150.32/21.89 (6) all_56_31 = e3 % 150.32/21.89 (7) ~ (all_52_14 = all_4_2) % 150.32/21.89 (8) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0 % 150.32/21.89 (9) ~ (e3 = e2) % 150.32/21.89 (10) op(e0, e0) = all_4_2 % 150.32/21.89 (11) all_54_9 = all_6_0 % 150.32/21.89 (12) all_56_21 = all_6_2 % 150.32/21.89 (13) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 150.32/21.89 (14) all_56_1 = all_10_2 % 150.32/21.89 (15) all_56_17 = all_52_2 % 150.32/21.89 (16) all_58_13 = all_52_7 % 150.32/21.89 (17) op(e3, e3) = all_10_2 % 150.32/21.89 (18) ~ (all_56_21 = e3) | all_56_17 = e1 % 150.32/21.89 (19) ~ (e1 = e0) % 150.32/21.89 (20) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 150.32/21.89 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 150.32/21.89 (21) ~ (all_52_2 = e0) % 150.32/21.89 (22) op(all_6_2, all_6_2) = e2 % 150.32/21.89 (23) ~ (all_6_0 = all_6_2) % 150.32/21.89 (24) ~ (all_52_14 = e3) % 150.32/21.89 (25) all_58_8 = all_6_2 % 150.32/21.89 (26) ~ (all_6_0 = e3) % 150.32/21.89 (27) ~ (all_6_0 = e0) | ~ (all_6_2 = e3) % 150.32/21.89 (28) all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3 % 150.32/21.89 (29) ~ (all_52_14 = all_6_0) % 150.32/21.89 (30) op(all_4_2, all_4_2) = all_4_1 % 150.32/21.89 (31) all_58_3 = all_8_2 % 150.32/21.89 (32) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0 % 150.32/21.89 (33) all_56_31 = all_4_2 % 150.32/21.89 (34) all_58_11 = all_52_14 % 150.32/21.89 (35) all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3 % 150.32/21.89 (36) ~ (all_52_2 = all_52_14) % 150.32/21.89 (37) all_56_1 = e3 | all_56_11 = e2 | all_56_21 = e1 | all_56_31 = e0 % 150.32/21.89 (38) ~ (all_52_2 = all_6_0) % 150.32/21.89 (39) all_56_23 = all_52_14 % 150.32/21.89 (40) all_54_8 = all_52_2 % 150.32/21.89 (41) op(e1, e1) = all_6_2 % 150.32/21.89 (42) all_58_7 = all_6_0 % 150.32/21.89 (43) ~ (all_52_7 = e3) % 150.32/21.89 (44) all_56_19 = all_6_0 % 150.32/21.89 (45) op(all_10_2, all_10_2) = all_10_1 % 150.32/21.89 (46) op(e1, all_6_2) = all_56_20 % 150.32/21.90 (47) all_58_1 = e0 | all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0 % 150.32/21.90 (48) ~ (all_52_2 = all_6_2) % 150.32/21.90 (49) ~ (all_56_21 = e0) | all_56_23 = e1 % 150.32/21.90 (50) op(e0, all_4_2) = all_56_30 % 150.32/21.90 (51) op(e3, all_10_2) = all_56_0 % 150.32/21.90 (52) ~ (all_52_14 = all_6_2) % 150.32/21.90 (53) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0 % 150.32/21.90 (54) ~ (all_52_7 = e0) % 150.32/21.90 (55) ~ (all_52_2 = all_10_2) % 150.32/21.90 (56) ~ (all_8_2 = all_6_0) % 150.32/21.90 (57) op(e3, e3) = all_4_1 % 150.32/21.90 (58) all_54_11 = all_52_14 % 150.32/21.90 % 150.32/21.90 Begin of proof % 150.32/21.90 | % 150.32/21.90 | GROUND_INST: instantiating (20) with all_10_2, all_4_1, e3, e3, simplifying % 150.32/21.90 | with (17), (57) gives: % 150.32/21.90 | (59) all_10_2 = all_4_1 % 150.32/21.90 | % 150.32/21.90 | COMBINE_EQS: (14), (59) imply: % 150.32/21.90 | (60) all_56_1 = all_4_1 % 150.32/21.90 | % 150.32/21.90 | REDUCE: (55), (59) imply: % 150.32/21.90 | (61) ~ (all_52_2 = all_4_1) % 150.32/21.90 | % 150.32/21.90 | BETA: splitting (49) gives: % 150.32/21.90 | % 150.32/21.90 | Case 1: % 150.32/21.90 | | % 150.32/21.90 | | (62) ~ (all_56_21 = e0) % 150.32/21.90 | | % 150.32/21.90 | | REDUCE: (12), (62) imply: % 150.32/21.90 | | (63) ~ (all_6_2 = e0) % 150.32/21.90 | | % 150.32/21.90 | | BETA: splitting (5) gives: % 150.32/21.90 | | % 150.32/21.90 | | Case 1: % 150.32/21.90 | | | % 150.32/21.90 | | | (64) ~ (all_56_21 = e2) % 150.32/21.90 | | | % 150.32/21.90 | | | REDUCE: (12), (64) imply: % 150.32/21.90 | | | (65) ~ (all_6_2 = e2) % 150.32/21.90 | | | % 150.32/21.90 | | | REF_CLOSE: (1), (4), (7), (8), (11), (12), (13), (14), (15), (17), (18), % 150.32/21.90 | | | (20), (22), (23), (27), (29), (32), (33), (36), (37), (38), % 150.32/21.90 | | | (39), (41), (45), (46), (48), (49), (51), (52), (56), (58), % 150.32/21.90 | | | (63), (65) are inconsistent by sub-proof #58. % 150.32/21.90 | | | % 150.32/21.90 | | Case 2: % 150.32/21.90 | | | % 150.32/21.90 | | | (66) all_56_21 = e2 % 150.32/21.90 | | | (67) all_56_19 = e1 % 150.32/21.90 | | | % 150.32/21.90 | | | COMBINE_EQS: (44), (67) imply: % 150.32/21.90 | | | (68) all_6_0 = e1 % 150.32/21.90 | | | % 150.32/21.90 | | | SIMP: (68) implies: % 150.32/21.90 | | | (69) all_6_0 = e1 % 150.32/21.90 | | | % 150.32/21.90 | | | COMBINE_EQS: (12), (66) imply: % 150.32/21.90 | | | (70) all_6_2 = e2 % 150.32/21.90 | | | % 150.32/21.90 | | | SIMP: (70) implies: % 150.32/21.90 | | | (71) all_6_2 = e2 % 150.32/21.90 | | | % 150.32/21.90 | | | COMBINE_EQS: (42), (69) imply: % 150.32/21.90 | | | (72) all_58_7 = e1 % 150.32/21.90 | | | % 150.32/21.90 | | | REDUCE: (38), (69) imply: % 150.32/21.90 | | | (73) ~ (all_52_2 = e1) % 150.32/21.90 | | | % 150.32/21.90 | | | REDUCE: (48), (71) imply: % 150.32/21.90 | | | (74) ~ (all_52_2 = e2) % 150.32/21.90 | | | % 150.32/21.90 | | | REDUCE: (23), (69), (71) imply: % 150.32/21.90 | | | (75) ~ (e2 = e1) % 150.32/21.90 | | | % 150.32/21.90 | | | SIMP: (75) implies: % 150.32/21.90 | | | (76) ~ (e2 = e1) % 150.32/21.90 | | | % 150.32/21.90 | | | REDUCE: (26), (69) imply: % 150.32/21.90 | | | (77) ~ (e3 = e1) % 150.32/21.90 | | | % 150.32/21.90 | | | SIMP: (77) implies: % 150.32/21.90 | | | (78) ~ (e3 = e1) % 150.32/21.90 | | | % 150.32/21.90 | | | REF_CLOSE: (1), (3), (6), (9), (16), (19), (21), (31), (35), (37), (40), % 150.32/21.90 | | | (43), (47), (53), (54), (60), (61), (63), (66), (71), (72), % 150.32/21.90 | | | (73), (74), (76), (78) are inconsistent by sub-proof #542. % 150.32/21.90 | | | % 150.32/21.90 | | End of split % 150.32/21.90 | | % 150.32/21.90 | Case 2: % 150.32/21.90 | | % 150.32/21.90 | | (79) all_56_23 = e1 % 150.32/21.90 | | (80) all_56_21 = e0 % 150.32/21.90 | | % 150.32/21.90 | | COMBINE_EQS: (12), (80) imply: % 150.32/21.90 | | (81) all_6_2 = e0 % 150.32/21.90 | | % 150.32/21.90 | | SIMP: (81) implies: % 150.32/21.90 | | (82) all_6_2 = e0 % 150.32/21.90 | | % 150.32/21.90 | | COMBINE_EQS: (39), (79) imply: % 150.32/21.90 | | (83) all_52_14 = e1 % 150.32/21.90 | | % 150.32/21.90 | | SIMP: (83) implies: % 150.32/21.90 | | (84) all_52_14 = e1 % 150.32/21.90 | | % 150.32/21.90 | | COMBINE_EQS: (34), (84) imply: % 150.32/21.90 | | (85) all_58_11 = e1 % 150.32/21.90 | | % 150.32/21.90 | | COMBINE_EQS: (25), (82) imply: % 150.32/21.90 | | (86) all_58_8 = e0 % 150.32/21.90 | | % 150.32/21.90 | | REDUCE: (29), (84) imply: % 150.32/21.90 | | (87) ~ (all_6_0 = e1) % 150.32/21.90 | | % 150.32/21.90 | | SIMP: (87) implies: % 150.32/21.90 | | (88) ~ (all_6_0 = e1) % 150.32/21.90 | | % 150.32/21.90 | | REDUCE: (24), (84) imply: % 150.32/21.90 | | (89) ~ (e3 = e1) % 150.32/21.90 | | % 150.32/21.90 | | SIMP: (89) implies: % 150.32/21.90 | | (90) ~ (e3 = e1) % 150.32/21.90 | | % 150.32/21.90 | | REF_CLOSE: (1), (2), (3), (10), (11), (14), (19), (20), (22), (23), (26), % 150.32/21.90 | | (28), (30), (32), (33), (37), (42), (50), (55), (56), (80), (82), % 150.32/21.90 | | (85), (86), (88), (90) are inconsistent by sub-proof #57. % 150.32/21.90 | | % 150.32/21.90 | End of split % 150.32/21.90 | % 150.32/21.90 End of proof % 150.32/21.90 % 150.32/21.90 Sub-proof #57 shows that the following formulas are inconsistent: % 150.32/21.90 ---------------------------------------------------------------- % 150.32/21.90 (1) all_56_11 = all_8_2 % 150.32/21.90 (2) all_58_6 = all_52_2 % 150.32/21.90 (3) ~ (e3 = e0) % 150.32/21.90 (4) op(e0, e0) = all_4_2 % 150.32/21.90 (5) all_54_9 = all_6_0 % 150.32/21.90 (6) all_56_1 = all_10_2 % 150.32/21.90 (7) all_56_21 = e0 % 150.32/21.90 (8) ~ (all_6_0 = e1) % 150.32/21.90 (9) ~ (e1 = e0) % 150.32/21.90 (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 150.32/21.90 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 150.32/21.90 (11) all_6_2 = e0 % 150.32/21.90 (12) all_58_11 = e1 % 150.32/21.90 (13) op(all_6_2, all_6_2) = e2 % 150.32/21.90 (14) ~ (all_6_0 = all_6_2) % 150.32/21.90 (15) ~ (all_6_0 = e3) % 150.32/21.90 (16) all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3 % 150.32/21.90 (17) all_58_8 = e0 % 150.32/21.90 (18) op(all_4_2, all_4_2) = all_4_1 % 150.32/21.90 (19) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0 % 150.32/21.90 (20) all_56_31 = all_4_2 % 150.32/21.90 (21) all_56_1 = e3 | all_56_11 = e2 | all_56_21 = e1 | all_56_31 = e0 % 150.32/21.90 (22) all_58_7 = all_6_0 % 150.32/21.90 (23) ~ (e3 = e1) % 150.32/21.90 (24) op(e0, all_4_2) = all_56_30 % 150.32/21.90 (25) ~ (all_52_2 = all_10_2) % 150.32/21.90 (26) ~ (all_8_2 = all_6_0) % 150.32/21.90 % 150.32/21.90 Begin of proof % 150.32/21.90 | % 150.32/21.90 | REDUCE: (11), (14) imply: % 150.32/21.90 | (27) ~ (all_6_0 = e0) % 150.32/21.90 | % 150.32/21.90 | REDUCE: (11), (13) imply: % 150.32/21.90 | (28) op(e0, e0) = e2 % 150.32/21.90 | % 150.32/21.90 | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (12), (15), % 150.32/21.90 | (16), (17), (18), (19), (20), (21), (22), (23), (24), (25), (26), % 150.32/21.90 | (27), (28) are inconsistent by sub-proof #75. % 150.32/21.90 | % 150.32/21.90 End of proof % 150.32/21.90 % 150.32/21.90 Sub-proof #58 shows that the following formulas are inconsistent: % 150.32/21.90 ---------------------------------------------------------------- % 150.32/21.90 (1) all_56_11 = all_8_2 % 150.32/21.90 (2) all_54_10 = all_6_2 % 150.32/21.90 (3) ~ (all_52_14 = all_4_2) % 150.32/21.90 (4) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0 % 150.32/21.90 (5) all_54_9 = all_6_0 % 150.32/21.90 (6) all_56_21 = all_6_2 % 150.32/21.90 (7) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 150.32/21.90 (8) all_56_1 = all_10_2 % 150.32/21.90 (9) all_56_17 = all_52_2 % 150.32/21.90 (10) op(e3, e3) = all_10_2 % 150.32/21.90 (11) ~ (all_56_21 = e3) | all_56_17 = e1 % 150.32/21.90 (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 150.32/21.90 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 150.32/21.90 (13) ~ (all_6_2 = e0) % 150.32/21.90 (14) op(all_6_2, all_6_2) = e2 % 150.32/21.90 (15) ~ (all_6_0 = all_6_2) % 150.32/21.90 (16) ~ (all_6_0 = e0) | ~ (all_6_2 = e3) % 150.32/21.90 (17) ~ (all_52_14 = all_6_0) % 150.32/21.90 (18) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0 % 150.32/21.90 (19) all_56_31 = all_4_2 % 150.32/21.90 (20) ~ (all_52_2 = all_52_14) % 150.32/21.90 (21) all_56_1 = e3 | all_56_11 = e2 | all_56_21 = e1 | all_56_31 = e0 % 150.32/21.90 (22) ~ (all_52_2 = all_6_0) % 150.32/21.90 (23) all_56_23 = all_52_14 % 150.32/21.90 (24) op(e1, e1) = all_6_2 % 150.32/21.90 (25) ~ (all_6_2 = e2) % 150.32/21.90 (26) op(all_10_2, all_10_2) = all_10_1 % 150.32/21.90 (27) op(e1, all_6_2) = all_56_20 % 150.32/21.90 (28) ~ (all_52_2 = all_6_2) % 150.32/21.90 (29) ~ (all_56_21 = e0) | all_56_23 = e1 % 150.32/21.90 (30) op(e3, all_10_2) = all_56_0 % 150.32/21.90 (31) ~ (all_52_14 = all_6_2) % 150.32/21.90 (32) ~ (all_8_2 = all_6_0) % 150.32/21.90 (33) all_54_11 = all_52_14 % 150.32/21.90 % 150.32/21.90 Begin of proof % 150.32/21.90 | % 150.32/21.90 | BETA: splitting (11) gives: % 150.32/21.90 | % 150.32/21.90 | Case 1: % 150.32/21.90 | | % 150.32/21.90 | | (34) ~ (all_56_21 = e3) % 150.32/21.90 | | % 150.32/21.90 | | REDUCE: (6), (34) imply: % 150.32/21.90 | | (35) ~ (all_6_2 = e3) % 150.32/21.90 | | % 150.32/21.90 | | REF_CLOSE: (2), (7), (12), (13), (14), (24), (25), (27), (35) are % 150.32/21.90 | | inconsistent by sub-proof #89. % 150.32/21.90 | | % 150.32/21.90 | Case 2: % 150.32/21.90 | | % 150.32/21.90 | | (36) all_56_21 = e3 % 150.32/21.90 | | (37) all_56_17 = e1 % 150.32/21.90 | | % 150.32/21.90 | | COMBINE_EQS: (9), (37) imply: % 150.32/21.90 | | (38) all_52_2 = e1 % 150.32/21.90 | | % 150.32/21.90 | | SIMP: (38) implies: % 150.32/21.90 | | (39) all_52_2 = e1 % 150.32/21.90 | | % 150.32/21.90 | | COMBINE_EQS: (6), (36) imply: % 150.32/21.90 | | (40) all_6_2 = e3 % 150.32/21.90 | | % 150.32/21.90 | | SIMP: (40) implies: % 150.32/21.90 | | (41) all_6_2 = e3 % 150.32/21.90 | | % 150.32/21.90 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (10), (12), (14), (15), % 150.32/21.90 | | (16), (17), (18), (19), (20), (21), (22), (23), (24), (25), (26), % 150.32/21.90 | | (27), (28), (29), (30), (31), (32), (33), (36), (39), (41) are % 150.32/21.90 | | inconsistent by sub-proof #67. % 150.32/21.90 | | % 150.32/21.90 | End of split % 150.32/21.90 | % 150.32/21.90 End of proof % 150.32/21.90 % 150.32/21.90 Sub-proof #59 shows that the following formulas are inconsistent: % 150.32/21.90 ---------------------------------------------------------------- % 150.32/21.90 (1) all_56_11 = all_8_2 % 150.32/21.90 (2) ~ (all_56_11 = e1) | all_56_13 = e2 % 150.32/21.90 (3) ~ (all_52_4 = all_52_8) % 150.32/21.90 (4) op(e2, all_8_1) = all_8_0 % 150.32/21.90 (5) all_58_6 = all_52_2 % 150.32/21.90 (6) ~ (all_8_1 = e1) % 150.32/21.90 (7) ~ (all_52_1 = all_52_9) % 150.32/21.90 (8) all_54_10 = all_6_2 % 150.32/21.90 (9) all_54_0 = all_10_2 % 150.32/21.90 (10) ~ (all_52_14 = all_4_2) % 150.32/21.90 (11) ~ (all_8_0 = e1) % 150.32/21.90 (12) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0 % 150.32/21.90 (13) all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2 % 150.32/21.90 (14) ~ (all_52_9 = all_8_2) % 150.32/21.90 (15) ~ (all_8_1 = e3) % 150.32/21.90 (16) op(e0, e0) = all_4_2 % 150.32/21.90 (17) all_58_4 = all_52_8 % 150.32/21.90 (18) all_54_5 = all_8_2 % 150.32/21.90 (19) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 150.32/21.90 (20) all_54_9 = all_6_0 % 150.32/21.90 (21) all_56_21 = all_6_2 % 150.32/21.90 (22) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 150.32/21.90 (23) all_56_1 = all_10_2 % 150.32/21.90 (24) all_58_5 = all_52_9 % 150.32/21.90 (25) all_54_1 = all_52_4 % 150.32/21.90 (26) all_56_17 = all_52_2 % 150.32/21.90 (27) op(e3, e3) = all_10_2 % 150.32/21.90 (28) ~ (all_56_21 = e3) | all_56_17 = e1 % 150.32/21.90 (29) all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2 % 150.32/21.90 (30) all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1 % 150.32/21.90 (31) ~ (all_52_1 = all_8_2) % 150.32/21.90 (32) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 150.32/21.90 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 150.32/21.90 (33) all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0 % 150.32/21.90 (34) ~ (all_56_11 = e3) | all_56_9 = e2 % 150.32/21.90 (35) all_56_7 = all_52_12 % 150.32/21.90 (36) op(all_6_2, all_6_2) = e2 % 150.32/21.90 (37) ~ (all_6_0 = all_6_2) % 150.32/21.90 (38) all_56_13 = all_52_9 % 150.32/21.90 (39) ~ (all_52_1 = all_52_13) % 150.32/21.90 (40) all_58_8 = all_6_2 % 150.32/21.90 (41) ~ (all_6_0 = e3) % 150.32/21.90 (42) ~ (all_6_0 = e0) | ~ (all_6_2 = e3) % 150.32/21.90 (43) ~ (all_52_8 = all_10_2) % 150.32/21.90 (44) all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3 % 150.32/21.90 (45) ~ (all_56_1 = e0) | all_56_7 = e3 % 150.32/21.90 (46) ~ (all_52_14 = all_6_0) % 150.32/21.90 (47) op(all_4_2, all_4_2) = all_4_1 % 150.32/21.90 (48) all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3 % 150.32/21.90 (49) all_58_3 = all_8_2 % 150.32/21.90 (50) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0 % 150.32/21.90 (51) ~ (all_52_1 = all_52_3) % 150.32/21.90 (52) all_56_31 = all_4_2 % 150.32/21.90 (53) all_58_11 = all_52_14 % 150.32/21.90 (54) ~ (all_52_2 = all_52_14) % 150.32/21.90 (55) all_56_1 = e3 | all_56_11 = e2 | all_56_21 = e1 | all_56_31 = e0 % 150.32/21.90 (56) ~ (all_52_13 = all_4_2) % 150.32/21.90 (57) ~ (all_52_2 = all_6_0) % 150.32/21.90 (58) all_56_23 = all_52_14 % 150.32/21.90 (59) op(e1, e1) = all_6_2 % 150.32/21.90 (60) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0 % 150.32/21.90 (61) all_58_7 = all_6_0 % 150.32/21.90 (62) ~ (all_6_2 = e2) % 150.32/21.90 (63) all_58_2 = all_52_1 % 150.32/21.90 (64) ~ (all_52_9 = all_6_2) % 150.32/21.90 (65) all_58_10 = all_52_13 % 150.32/21.90 (66) op(all_10_2, all_10_2) = all_10_1 % 150.32/21.90 (67) ~ (all_56_11 = e0) | all_56_15 = e2 % 150.32/21.90 (68) all_58_0 = all_10_2 % 150.32/21.90 (69) op(e1, all_6_2) = all_56_20 % 150.32/21.90 (70) ~ (all_52_4 = all_52_12) % 150.32/21.90 (71) op(e2, e0) = all_52_13 % 150.32/21.90 (72) ~ (all_52_2 = all_6_2) % 150.32/21.90 (73) ~ (all_52_8 = all_52_12) % 150.32/21.90 (74) ~ (all_52_1 = all_52_2) % 150.32/21.90 (75) ~ (all_56_21 = e0) | all_56_23 = e1 % 150.32/21.90 (76) op(e0, all_4_2) = all_56_30 % 150.32/21.90 (77) ~ (all_8_2 = e0) % 150.32/21.90 (78) op(e3, all_10_2) = all_56_0 % 150.32/21.90 (79) ~ (all_52_14 = all_6_2) % 150.32/21.90 (80) ~ (all_52_2 = all_10_2) % 150.32/21.90 (81) ~ (all_8_2 = all_6_0) % 150.32/21.90 (82) ~ (all_52_4 = all_10_2) % 150.32/21.90 (83) op(all_8_2, all_8_2) = all_8_1 % 150.32/21.90 (84) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 150.32/21.90 (85) all_56_9 = all_52_1 % 150.32/21.90 (86) all_56_15 = all_52_13 % 150.32/21.90 (87) ~ (all_52_1 = all_10_2) % 150.32/21.90 (88) all_58_12 = all_52_3 % 150.32/21.90 (89) all_54_11 = all_52_14 % 150.32/21.90 % 150.32/21.90 Begin of proof % 150.32/21.90 | % 150.32/21.90 | BETA: splitting (28) gives: % 150.32/21.90 | % 150.32/21.90 | Case 1: % 150.32/21.90 | | % 150.32/21.90 | | (90) ~ (all_56_21 = e3) % 150.32/21.90 | | % 150.32/21.90 | | REDUCE: (21), (90) imply: % 150.32/21.90 | | (91) ~ (all_6_2 = e3) % 150.32/21.90 | | % 150.32/21.90 | | BETA: splitting (34) gives: % 150.32/21.90 | | % 150.32/21.90 | | Case 1: % 150.32/21.90 | | | % 150.32/21.90 | | | (92) ~ (all_56_11 = e3) % 150.32/21.90 | | | % 150.32/21.90 | | | REDUCE: (1), (92) imply: % 150.32/21.90 | | | (93) ~ (all_8_2 = e3) % 150.32/21.90 | | | % 150.32/21.90 | | | REF_CLOSE: (1), (2), (5), (6), (8), (14), (15), (16), (18), (20), (21), % 150.32/21.90 | | | (22), (23), (32), (36), (37), (38), (40), (41), (44), (46), % 150.32/21.90 | | | (47), (50), (52), (53), (55), (58), (59), (61), (62), (64), % 150.32/21.90 | | | (69), (75), (76), (77), (79), (80), (81), (83), (84), (91), % 150.32/21.90 | | | (93) are inconsistent by sub-proof #84. % 150.32/21.90 | | | % 150.32/21.90 | | Case 2: % 150.32/21.90 | | | % 150.32/21.90 | | | (94) all_56_11 = e3 % 150.32/21.90 | | | (95) all_56_9 = e2 % 150.32/21.90 | | | % 150.32/21.90 | | | COMBINE_EQS: (85), (95) imply: % 150.32/21.90 | | | (96) all_52_1 = e2 % 150.32/21.90 | | | % 150.32/21.90 | | | COMBINE_EQS: (1), (94) imply: % 150.32/21.90 | | | (97) all_8_2 = e3 % 150.32/21.90 | | | % 150.32/21.90 | | | COMBINE_EQS: (49), (97) imply: % 150.32/21.90 | | | (98) all_58_3 = e3 % 150.32/21.90 | | | % 150.32/21.90 | | | COMBINE_EQS: (63), (96) imply: % 150.32/21.90 | | | (99) all_58_2 = e2 % 150.32/21.90 | | | % 150.32/21.90 | | | REDUCE: (74), (96) imply: % 150.32/21.90 | | | (100) ~ (all_52_2 = e2) % 150.32/21.90 | | | % 150.32/21.90 | | | SIMP: (100) implies: % 150.32/21.90 | | | (101) ~ (all_52_2 = e2) % 150.32/21.90 | | | % 150.32/21.90 | | | REDUCE: (51), (96) imply: % 150.32/21.90 | | | (102) ~ (all_52_3 = e2) % 150.32/21.90 | | | % 150.32/21.90 | | | SIMP: (102) implies: % 150.32/21.90 | | | (103) ~ (all_52_3 = e2) % 150.32/21.90 | | | % 150.32/21.90 | | | REDUCE: (7), (96) imply: % 150.32/21.90 | | | (104) ~ (all_52_9 = e2) % 150.32/21.90 | | | % 150.32/21.90 | | | SIMP: (104) implies: % 150.32/21.90 | | | (105) ~ (all_52_9 = e2) % 150.32/21.90 | | | % 150.32/21.90 | | | REDUCE: (87), (96) imply: % 150.32/21.90 | | | (106) ~ (all_10_2 = e2) % 150.32/21.90 | | | % 150.32/21.90 | | | SIMP: (106) implies: % 150.32/21.90 | | | (107) ~ (all_10_2 = e2) % 150.32/21.90 | | | % 150.32/21.90 | | | REDUCE: (31), (96), (97) imply: % 150.32/21.90 | | | (108) ~ (e3 = e2) % 150.32/21.90 | | | % 150.32/21.90 | | | SIMP: (108) implies: % 150.32/21.90 | | | (109) ~ (e3 = e2) % 150.32/21.90 | | | % 150.32/21.90 | | | REDUCE: (14), (97) imply: % 150.32/21.90 | | | (110) ~ (all_52_9 = e3) % 150.32/21.90 | | | % 150.32/21.90 | | | REDUCE: (83), (97) imply: % 150.32/21.90 | | | (111) op(e3, e3) = all_8_1 % 150.32/21.90 | | | % 150.32/21.90 | | | REF_CLOSE: (3), (4), (5), (6), (9), (11), (13), (15), (17), (19), (21), % 150.32/21.90 | | | (23), (24), (25), (27), (29), (30), (32), (33), (35), (39), % 150.32/21.90 | | | (40), (43), (45), (48), (52), (55), (56), (60), (62), (63), % 150.32/21.90 | | | (64), (65), (67), (68), (70), (71), (73), (82), (86), (88), % 150.32/21.90 | | | (91), (94), (98), (99), (101), (103), (105), (107), (109), % 150.32/21.90 | | | (110), (111) are inconsistent by sub-proof #151. % 150.32/21.90 | | | % 150.32/21.90 | | End of split % 150.32/21.90 | | % 150.32/21.90 | Case 2: % 150.32/21.90 | | % 150.32/21.90 | | (112) all_56_21 = e3 % 150.32/21.90 | | (113) all_56_17 = e1 % 150.32/21.90 | | % 150.32/21.90 | | COMBINE_EQS: (26), (113) imply: % 150.32/21.90 | | (114) all_52_2 = e1 % 150.32/21.90 | | % 150.32/21.90 | | COMBINE_EQS: (21), (112) imply: % 150.32/21.90 | | (115) all_6_2 = e3 % 150.32/21.90 | | % 150.32/21.90 | | SIMP: (115) implies: % 150.32/21.90 | | (116) all_6_2 = e3 % 150.32/21.90 | | % 150.32/21.90 | | REF_CLOSE: (1), (8), (10), (12), (20), (21), (22), (23), (27), (32), (36), % 150.32/21.90 | | (37), (42), (46), (50), (52), (54), (55), (57), (58), (59), (62), % 150.32/21.90 | | (66), (69), (72), (75), (78), (79), (81), (89), (112), (114), % 150.32/21.90 | | (116) are inconsistent by sub-proof #67. % 150.32/21.90 | | % 150.32/21.90 | End of split % 150.32/21.90 | % 150.32/21.90 End of proof % 150.32/21.90 % 150.32/21.90 Sub-proof #60 shows that the following formulas are inconsistent: % 150.32/21.90 ---------------------------------------------------------------- % 150.32/21.90 (1) ~ (all_52_11 = all_6_2) % 150.32/21.90 (2) all_56_25 = all_52_3 % 150.32/21.90 (3) ~ (all_52_7 = all_52_11) % 150.32/21.90 (4) op(e2, all_8_1) = all_8_0 % 150.32/21.90 (5) ~ (all_56_31 = e1) | all_56_29 = e0 % 150.32/21.90 (6) all_56_5 = all_10_0 % 150.32/21.90 (7) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0 % 150.32/21.90 (8) ~ (all_52_13 = all_8_2) % 150.32/21.90 (9) all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2 % 150.32/21.90 (10) ~ (all_8_0 = e1) % 150.32/21.90 (11) all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2 % 150.32/21.90 (12) ~ (all_52_9 = all_8_2) % 150.32/21.90 (13) all_58_4 = all_10_0 % 150.32/21.90 (14) ~ (all_52_4 = all_6_0) % 150.32/21.90 (15) ~ (all_52_4 = all_52_7) % 150.32/21.90 (16) all_54_2 = all_10_0 % 150.32/21.90 (17) all_54_15 = all_4_2 % 150.32/21.90 (18) all_56_21 = all_6_2 % 150.32/21.90 (19) all_56_1 = all_10_2 % 150.32/21.90 (20) all_56_27 = all_52_7 % 150.32/21.90 (21) ~ (all_32_0 = e0) | ~ (all_32_2 = e2) % 150.32/21.90 (22) all_58_5 = all_52_9 % 150.32/21.90 (23) all_54_1 = all_52_4 % 150.32/21.90 (24) all_58_9 = all_52_12 % 150.32/21.90 (25) all_6_0 = e1 % 150.32/21.90 (26) ~ (all_56_1 = e1) | all_56_5 = e3 % 150.32/21.90 (27) all_54_14 = all_52_11 % 150.32/21.90 (28) all_58_1 = all_52_4 % 150.32/21.90 (29) all_58_13 = all_52_7 % 150.32/21.90 (30) op(e2, all_8_2) = all_56_10 % 150.32/21.90 (31) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0 % 150.32/21.90 (32) all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1 % 150.32/21.90 (33) ~ (e1 = e0) % 150.32/21.90 (34) all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1 % 150.32/21.90 (35) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 150.32/21.90 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 150.32/21.90 (36) ~ (all_52_11 = all_10_0) % 150.32/21.90 (37) ~ (all_52_3 = all_52_7) % 150.32/21.90 (38) op(all_6_2, all_6_2) = e2 % 150.32/21.90 (39) ~ (all_52_7 = all_4_2) % 150.32/21.90 (40) ~ (all_6_0 = e3) % 150.32/21.90 (41) ~ (all_52_3 = all_4_2) % 150.32/21.90 (42) all_56_21 = e2 % 150.32/21.90 (43) ~ (all_52_12 = all_10_0) % 150.32/21.90 (44) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0 % 150.32/21.90 (45) ~ (all_52_4 = all_10_0) % 150.32/21.90 (46) op(all_4_2, all_4_2) = all_4_1 % 150.32/21.90 (47) op(all_10_2, all_10_2) = e1 % 150.32/21.90 (48) all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1 % 150.32/21.90 (49) all_58_3 = all_8_2 % 150.32/21.90 (50) ~ (all_52_11 = all_4_2) % 150.32/21.90 (51) all_56_31 = all_4_2 % 150.32/21.90 (52) all_58_11 = all_52_14 % 150.32/21.90 (53) all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3 % 150.32/21.90 (54) ~ (all_8_0 = e3) % 150.32/21.91 (55) ~ (all_10_0 = all_6_2) % 150.32/21.91 (56) ~ (all_10_0 = e1) % 150.32/21.91 (57) all_32_0 = all_10_0 % 150.32/21.91 (58) ~ (all_52_13 = all_4_2) % 150.32/21.91 (59) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0 % 150.32/21.91 (60) all_54_13 = all_52_7 % 150.32/21.91 (61) op(e1, e1) = all_6_2 % 150.32/21.91 (62) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0 % 150.32/21.91 (63) all_58_15 = all_4_2 % 150.32/21.91 (64) all_56_29 = all_52_11 % 150.32/21.91 (65) all_58_7 = all_6_0 % 150.32/21.91 (66) all_58_2 = all_52_1 % 150.32/21.91 (67) all_58_10 = all_52_13 % 150.32/21.91 (68) ~ (all_52_12 = all_4_2) % 150.32/21.91 (69) all_58_0 = all_10_2 % 150.32/21.91 (70) all_58_1 = e0 | all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0 % 150.32/21.91 (71) op(e1, all_52_9) = all_56_12 % 150.32/21.91 (72) ~ (all_56_31 = e2) | all_56_27 = e0 % 150.32/21.91 (73) op(e2, e2) = all_8_2 % 150.32/21.91 (74) ~ (all_52_4 = all_52_12) % 150.32/21.91 (75) ~ (all_52_14 = all_6_2) % 150.32/21.91 (76) ~ (e2 = e0) % 150.32/21.91 (77) op(e1, all_52_11) = all_56_28 % 150.32/21.91 (78) ~ (all_10_0 = all_10_2) % 150.32/21.91 (79) ~ (all_52_4 = all_8_2) % 150.32/21.91 (80) op(all_8_2, all_8_2) = all_8_1 % 150.32/21.91 (81) all_32_2 = all_10_2 % 150.32/21.91 (82) ~ (all_52_1 = all_10_2) % 150.32/21.91 (83) ~ (all_56_31 = e3) | all_56_25 = e0 % 150.32/21.91 % 150.32/21.91 Begin of proof % 150.32/21.91 | % 150.32/21.91 | COMBINE_EQS: (18), (42) imply: % 150.32/21.91 | (84) all_6_2 = e2 % 150.32/21.91 | % 150.32/21.91 | SIMP: (84) implies: % 150.32/21.91 | (85) all_6_2 = e2 % 150.32/21.91 | % 150.32/21.91 | COMBINE_EQS: (25), (65) imply: % 150.32/21.91 | (86) all_58_7 = e1 % 150.32/21.91 | % 150.32/21.91 | REDUCE: (14), (25) imply: % 150.32/21.91 | (87) ~ (all_52_4 = e1) % 150.32/21.91 | % 150.32/21.91 | REDUCE: (1), (85) imply: % 150.32/21.91 | (88) ~ (all_52_11 = e2) % 150.32/21.91 | % 150.32/21.91 | REDUCE: (75), (85) imply: % 150.32/21.91 | (89) ~ (all_52_14 = e2) % 150.32/21.91 | % 150.32/21.91 | REDUCE: (55), (85) imply: % 150.32/21.91 | (90) ~ (all_10_0 = e2) % 150.32/21.91 | % 150.32/21.91 | REDUCE: (25), (40) imply: % 150.32/21.91 | (91) ~ (e3 = e1) % 150.32/21.91 | % 150.32/21.91 | SIMP: (91) implies: % 150.32/21.91 | (92) ~ (e3 = e1) % 150.32/21.91 | % 150.32/21.91 | REDUCE: (38), (85) imply: % 150.32/21.91 | (93) op(e2, e2) = e2 % 150.32/21.91 | % 150.32/21.91 | REDUCE: (61), (85) imply: % 150.32/21.91 | (94) op(e1, e1) = e2 % 150.32/21.91 | % 150.32/21.91 | GROUND_INST: instantiating (35) with all_8_2, e2, e2, e2, simplifying with % 150.32/21.91 | (73), (93) gives: % 150.32/21.91 | (95) all_8_2 = e2 % 150.32/21.91 | % 150.32/21.91 | COMBINE_EQS: (49), (95) imply: % 150.32/21.91 | (96) all_58_3 = e2 % 150.32/21.91 | % 150.32/21.91 | REDUCE: (79), (95) imply: % 150.32/21.91 | (97) ~ (all_52_4 = e2) % 150.32/21.91 | % 150.32/21.91 | REDUCE: (12), (95) imply: % 150.32/21.91 | (98) ~ (all_52_9 = e2) % 150.32/21.91 | % 150.32/21.91 | REDUCE: (8), (95) imply: % 150.32/21.91 | (99) ~ (all_52_13 = e2) % 150.32/21.91 | % 150.32/21.91 | REDUCE: (80), (95) imply: % 150.32/21.91 | (100) op(e2, e2) = all_8_1 % 150.32/21.91 | % 150.32/21.91 | REDUCE: (30), (95) imply: % 150.32/21.91 | (101) op(e2, e2) = all_56_10 % 150.32/21.91 | % 150.32/21.91 | GROUND_INST: instantiating (35) with e2, all_56_10, e2, e2, simplifying with % 150.32/21.91 | (93), (101) gives: % 150.32/21.91 | (102) all_56_10 = e2 % 150.32/21.91 | % 150.32/21.91 | GROUND_INST: instantiating (35) with all_8_1, all_56_10, e2, e2, simplifying % 150.32/21.91 | with (100), (101) gives: % 150.32/21.91 | (103) all_56_10 = all_8_1 % 150.32/21.91 | % 150.32/21.91 | COMBINE_EQS: (102), (103) imply: % 150.32/21.91 | (104) all_8_1 = e2 % 150.32/21.91 | % 150.32/21.91 | SIMP: (104) implies: % 150.32/21.91 | (105) all_8_1 = e2 % 150.32/21.91 | % 150.32/21.91 | REDUCE: (4), (105) imply: % 150.32/21.91 | (106) op(e2, e2) = all_8_0 % 150.32/21.91 | % 150.32/21.91 | GROUND_INST: instantiating (35) with e2, all_8_0, e2, e2, simplifying with % 150.32/21.91 | (93), (106) gives: % 150.32/21.91 | (107) all_8_0 = e2 % 150.32/21.91 | % 150.32/21.91 | REDUCE: (54), (107) imply: % 150.32/21.91 | (108) ~ (e3 = e2) % 150.32/21.91 | % 150.32/21.91 | SIMP: (108) implies: % 150.42/21.91 | (109) ~ (e3 = e2) % 150.42/21.91 | % 150.42/21.91 | REDUCE: (10), (107) imply: % 150.42/21.91 | (110) ~ (e2 = e1) % 150.42/21.91 | % 150.42/21.91 | BETA: splitting (5) gives: % 150.42/21.91 | % 150.42/21.91 | Case 1: % 150.42/21.91 | | % 150.42/21.91 | | (111) ~ (all_56_31 = e1) % 150.42/21.91 | | % 150.42/21.91 | | REDUCE: (51), (111) imply: % 150.42/21.91 | | (112) ~ (all_4_2 = e1) % 150.42/21.91 | | % 150.42/21.91 | | BETA: splitting (83) gives: % 150.42/21.91 | | % 150.42/21.91 | | Case 1: % 150.42/21.91 | | | % 150.42/21.91 | | | (113) ~ (all_56_31 = e3) % 150.42/21.91 | | | % 150.42/21.91 | | | REDUCE: (51), (113) imply: % 150.42/21.91 | | | (114) ~ (all_4_2 = e3) % 150.42/21.91 | | | % 150.42/21.91 | | | BETA: splitting (72) gives: % 150.42/21.91 | | | % 150.42/21.91 | | | Case 1: % 150.42/21.91 | | | | % 150.42/21.91 | | | | (115) ~ (all_56_31 = e2) % 150.42/21.91 | | | | % 150.42/21.91 | | | | REDUCE: (51), (115) imply: % 150.42/21.91 | | | | (116) ~ (all_4_2 = e2) % 150.42/21.91 | | | | % 150.42/21.91 | | | | BETA: splitting (9) gives: % 150.42/21.91 | | | | % 150.42/21.91 | | | | Case 1: % 150.42/21.91 | | | | | % 150.42/21.91 | | | | | (117) all_58_9 = e2 % 150.42/21.91 | | | | | % 150.42/21.91 | | | | | COMBINE_EQS: (24), (117) imply: % 150.42/21.91 | | | | | (118) all_52_12 = e2 % 150.42/21.91 | | | | | % 150.42/21.91 | | | | | REDUCE: (43), (118) imply: % 150.42/21.91 | | | | | (119) ~ (all_10_0 = e2) % 150.42/21.91 | | | | | % 150.42/21.91 | | | | | REDUCE: (68), (118) imply: % 150.42/21.91 | | | | | (120) ~ (all_4_2 = e2) % 150.42/21.91 | | | | | % 150.42/21.91 | | | | | BETA: splitting (59) gives: % 150.42/21.91 | | | | | % 150.42/21.91 | | | | | Case 1: % 150.42/21.91 | | | | | | % 150.42/21.91 | | | | | | (121) all_54_15 = e3 % 150.42/21.91 | | | | | | % 150.42/21.91 | | | | | | REF_CLOSE: (17), (114), (121) are inconsistent by sub-proof #740. % 150.42/21.91 | | | | | | % 150.42/21.91 | | | | | Case 2: % 150.42/21.91 | | | | | | % 150.42/21.91 | | | | | | (122) ~ (all_54_15 = e3) % 150.42/21.91 | | | | | | (123) all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0 % 150.42/21.91 | | | | | | % 150.42/21.91 | | | | | | BETA: splitting (123) gives: % 150.42/21.91 | | | | | | % 150.42/21.91 | | | | | | Case 1: % 150.42/21.91 | | | | | | | % 150.42/21.91 | | | | | | | (124) all_54_15 = e2 % 150.42/21.91 | | | | | | | % 150.42/21.91 | | | | | | | REF_CLOSE: (17), (116), (124) are inconsistent by sub-proof #739. % 150.42/21.91 | | | | | | | % 150.42/21.91 | | | | | | Case 2: % 150.42/21.91 | | | | | | | % 150.42/21.91 | | | | | | | (125) ~ (all_54_15 = e2) % 150.42/21.91 | | | | | | | (126) all_54_15 = e1 | all_54_15 = e0 % 150.42/21.91 | | | | | | | % 150.42/21.91 | | | | | | | BETA: splitting (126) gives: % 150.42/21.91 | | | | | | | % 150.42/21.91 | | | | | | | Case 1: % 150.42/21.91 | | | | | | | | % 150.42/21.91 | | | | | | | | (127) all_54_15 = e1 % 150.42/21.91 | | | | | | | | % 150.42/21.91 | | | | | | | | REF_CLOSE: (17), (112), (127) are inconsistent by sub-proof % 150.42/21.91 | | | | | | | | #738. % 150.42/21.91 | | | | | | | | % 150.42/21.91 | | | | | | | Case 2: % 150.42/21.91 | | | | | | | | % 150.42/21.91 | | | | | | | | (128) all_54_15 = e0 % 150.42/21.91 | | | | | | | | % 150.42/21.91 | | | | | | | | COMBINE_EQS: (17), (128) imply: % 150.42/21.91 | | | | | | | | (129) all_4_2 = e0 % 150.42/21.91 | | | | | | | | % 150.42/21.91 | | | | | | | | SIMP: (129) implies: % 150.42/21.91 | | | | | | | | (130) all_4_2 = e0 % 150.42/21.91 | | | | | | | | % 150.42/21.91 | | | | | | | | REDUCE: (39), (130) imply: % 150.42/21.91 | | | | | | | | (131) ~ (all_52_7 = e0) % 150.42/21.91 | | | | | | | | % 150.42/21.91 | | | | | | | | REDUCE: (50), (130) imply: % 150.42/21.91 | | | | | | | | (132) ~ (all_52_11 = e0) % 150.42/21.91 | | | | | | | | % 150.42/21.91 | | | | | | | | REDUCE: (114), (130) imply: % 150.42/21.91 | | | | | | | | (133) ~ (e3 = e0) % 150.42/21.91 | | | | | | | | % 150.42/21.91 | | | | | | | | SIMP: (133) implies: % 150.42/21.91 | | | | | | | | (134) ~ (e3 = e0) % 150.42/21.91 | | | | | | | | % 150.42/21.91 | | | | | | | | REDUCE: (116), (130) imply: % 150.42/21.91 | | | | | | | | (135) ~ (e2 = e0) % 150.42/21.91 | | | | | | | | % 150.42/21.91 | | | | | | | | REDUCE: (112), (130) imply: % 150.42/21.91 | | | | | | | | (136) ~ (e1 = e0) % 150.42/21.91 | | | | | | | | % 150.42/21.91 | | | | | | | | BETA: splitting (44) gives: % 150.42/21.91 | | | | | | | | % 150.42/21.91 | | | | | | | | Case 1: % 150.42/21.91 | | | | | | | | | % 150.42/21.91 | | | | | | | | | (137) all_54_13 = e3 % 150.42/21.91 | | | | | | | | | % 150.42/21.91 | | | | | | | | | COMBINE_EQS: (60), (137) imply: % 150.42/21.91 | | | | | | | | | (138) all_52_7 = e3 % 150.42/21.91 | | | | | | | | | % 150.42/21.91 | | | | | | | | | SIMP: (138) implies: % 150.42/21.91 | | | | | | | | | (139) all_52_7 = e3 % 150.42/21.91 | | | | | | | | | % 150.42/21.91 | | | | | | | | | COMBINE_EQS: (29), (139) imply: % 150.42/21.91 | | | | | | | | | (140) all_58_13 = e3 % 150.42/21.91 | | | | | | | | | % 150.42/21.91 | | | | | | | | | REDUCE: (3), (139) imply: % 150.42/21.91 | | | | | | | | | (141) ~ (all_52_11 = e3) % 150.42/21.91 | | | | | | | | | % 150.42/21.91 | | | | | | | | | SIMP: (141) implies: % 150.42/21.91 | | | | | | | | | (142) ~ (all_52_11 = e3) % 150.42/21.91 | | | | | | | | | % 150.42/21.91 | | | | | | | | | BETA: splitting (32) gives: % 150.42/21.91 | | | | | | | | | % 150.42/21.91 | | | | | | | | | Case 1: % 150.42/21.91 | | | | | | | | | | % 150.42/21.91 | | | | | | | | | | (143) all_58_0 = e1 % 150.42/21.91 | | | | | | | | | | % 150.42/21.91 | | | | | | | | | | COMBINE_EQS: (69), (143) imply: % 150.42/21.91 | | | | | | | | | | (144) all_10_2 = e1 % 150.42/21.91 | | | | | | | | | | % 150.42/21.91 | | | | | | | | | | REDUCE: (47), (144) imply: % 150.42/21.91 | | | | | | | | | | (145) op(e1, e1) = e1 % 150.42/21.91 | | | | | | | | | | % 150.42/21.91 | | | | | | | | | | BETA: splitting (7) gives: % 150.42/21.91 | | | | | | | | | | % 150.42/21.91 | | | | | | | | | | Case 1: % 150.42/21.91 | | | | | | | | | | | % 150.42/21.91 | | | | | | | | | | | (146) all_54_14 = e3 % 150.42/21.91 | | | | | | | | | | | % 150.42/21.91 | | | | | | | | | | | COMBINE_EQS: (27), (146) imply: % 150.42/21.91 | | | | | | | | | | | (147) all_52_11 = e3 % 150.42/21.91 | | | | | | | | | | | % 150.42/21.91 | | | | | | | | | | | REDUCE: (142), (147) imply: % 150.42/21.91 | | | | | | | | | | | (148) $false % 150.42/21.91 | | | | | | | | | | | % 150.42/21.91 | | | | | | | | | | | CLOSE: (148) is inconsistent. % 150.42/21.91 | | | | | | | | | | | % 150.42/21.91 | | | | | | | | | | Case 2: % 150.42/21.91 | | | | | | | | | | | % 150.42/21.91 | | | | | | | | | | | (149) all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0 % 150.42/21.91 | | | | | | | | | | | % 150.42/21.91 | | | | | | | | | | | BETA: splitting (149) gives: % 150.42/21.91 | | | | | | | | | | | % 150.42/21.91 | | | | | | | | | | | Case 1: % 150.42/21.91 | | | | | | | | | | | | % 150.42/21.91 | | | | | | | | | | | | (150) all_54_14 = e2 % 150.42/21.91 | | | | | | | | | | | | % 150.42/21.91 | | | | | | | | | | | | REF_CLOSE: (27), (88), (150) are inconsistent by sub-proof % 150.42/21.91 | | | | | | | | | | | | #581. % 150.42/21.91 | | | | | | | | | | | | % 150.42/21.91 | | | | | | | | | | | Case 2: % 150.42/21.91 | | | | | | | | | | | | % 150.42/21.91 | | | | | | | | | | | | (151) ~ (all_54_14 = e2) % 150.42/21.91 | | | | | | | | | | | | (152) all_54_14 = e1 | all_54_14 = e0 % 150.42/21.91 | | | | | | | | | | | | % 150.42/21.91 | | | | | | | | | | | | BETA: splitting (152) gives: % 150.42/21.91 | | | | | | | | | | | | % 150.42/21.91 | | | | | | | | | | | | Case 1: % 150.42/21.91 | | | | | | | | | | | | | % 150.42/21.91 | | | | | | | | | | | | | (153) all_54_14 = e1 % 150.42/21.91 | | | | | | | | | | | | | % 150.42/21.91 | | | | | | | | | | | | | COMBINE_EQS: (27), (153) imply: % 150.42/21.91 | | | | | | | | | | | | | (154) all_52_11 = e1 % 150.42/21.91 | | | | | | | | | | | | | % 150.42/21.91 | | | | | | | | | | | | | SIMP: (154) implies: % 150.42/21.91 | | | | | | | | | | | | | (155) all_52_11 = e1 % 150.42/21.91 | | | | | | | | | | | | | % 150.42/21.91 | | | | | | | | | | | | | REDUCE: (88), (155) imply: % 150.42/21.91 | | | | | | | | | | | | | (156) ~ (e2 = e1) % 150.42/21.91 | | | | | | | | | | | | | % 150.42/21.91 | | | | | | | | | | | | | REDUCE: (77), (155) imply: % 150.42/21.91 | | | | | | | | | | | | | (157) op(e1, e1) = all_56_28 % 150.42/21.91 | | | | | | | | | | | | | % 150.42/21.91 | | | | | | | | | | | | | GROUND_INST: instantiating (35) with e2, all_56_28, e1, e1, % 150.42/21.91 | | | | | | | | | | | | | simplifying with (94), (157) gives: % 150.42/21.91 | | | | | | | | | | | | | (158) all_56_28 = e2 % 150.42/21.91 | | | | | | | | | | | | | % 150.42/21.91 | | | | | | | | | | | | | GROUND_INST: instantiating (35) with e1, all_56_28, e1, e1, % 150.42/21.91 | | | | | | | | | | | | | simplifying with (145), (157) gives: % 150.42/21.91 | | | | | | | | | | | | | (159) all_56_28 = e1 % 150.42/21.91 | | | | | | | | | | | | | % 150.42/21.91 | | | | | | | | | | | | | COMBINE_EQS: (158), (159) imply: % 150.42/21.91 | | | | | | | | | | | | | (160) e2 = e1 % 150.42/21.91 | | | | | | | | | | | | | % 150.42/21.91 | | | | | | | | | | | | | SIMP: (160) implies: % 150.42/21.91 | | | | | | | | | | | | | (161) e2 = e1 % 150.42/21.91 | | | | | | | | | | | | | % 150.42/21.91 | | | | | | | | | | | | | REDUCE: (110), (161) imply: % 150.42/21.91 | | | | | | | | | | | | | (162) $false % 150.42/21.91 | | | | | | | | | | | | | % 150.42/21.91 | | | | | | | | | | | | | CLOSE: (162) is inconsistent. % 150.42/21.91 | | | | | | | | | | | | | % 150.42/21.91 | | | | | | | | | | | | Case 2: % 150.42/21.91 | | | | | | | | | | | | | % 150.42/21.91 | | | | | | | | | | | | | (163) all_54_14 = e0 % 150.42/21.91 | | | | | | | | | | | | | % 150.42/21.91 | | | | | | | | | | | | | REF_CLOSE: (27), (132), (163) are inconsistent by sub-proof % 150.42/21.91 | | | | | | | | | | | | | #715. % 150.42/21.91 | | | | | | | | | | | | | % 150.42/21.91 | | | | | | | | | | | | End of split % 150.42/21.91 | | | | | | | | | | | | % 150.42/21.91 | | | | | | | | | | | End of split % 150.42/21.91 | | | | | | | | | | | % 150.42/21.91 | | | | | | | | | | End of split % 150.42/21.91 | | | | | | | | | | % 150.42/21.91 | | | | | | | | | Case 2: % 150.42/21.91 | | | | | | | | | | % 150.42/21.91 | | | | | | | | | | (164) all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1 % 150.42/21.91 | | | | | | | | | | % 150.42/21.91 | | | | | | | | | | BETA: splitting (70) gives: % 150.42/21.91 | | | | | | | | | | % 150.42/21.91 | | | | | | | | | | Case 1: % 150.42/21.91 | | | | | | | | | | | % 150.42/21.91 | | | | | | | | | | | (165) all_58_1 = e0 % 150.42/21.91 | | | | | | | | | | | % 150.42/21.91 | | | | | | | | | | | COMBINE_EQS: (28), (165) imply: % 150.42/21.91 | | | | | | | | | | | (166) all_52_4 = e0 % 150.42/21.91 | | | | | | | | | | | % 150.42/21.91 | | | | | | | | | | | REDUCE: (45), (166) imply: % 150.42/21.91 | | | | | | | | | | | (167) ~ (all_10_0 = e0) % 150.42/21.91 | | | | | | | | | | | % 150.42/21.91 | | | | | | | | | | | SIMP: (167) implies: % 150.42/21.91 | | | | | | | | | | | (168) ~ (all_10_0 = e0) % 150.42/21.91 | | | | | | | | | | | % 150.42/21.91 | | | | | | | | | | | REF_CLOSE: (13), (16), (23), (28), (31), (45), (56), (62), % 150.42/21.91 | | | | | | | | | | | (87), (90), (97), (110), (117), (164), (168) are % 150.42/21.91 | | | | | | | | | | | inconsistent by sub-proof #62. % 150.42/21.91 | | | | | | | | | | | % 150.42/21.91 | | | | | | | | | | Case 2: % 150.42/21.91 | | | | | | | | | | | % 150.42/21.91 | | | | | | | | | | | (169) all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0 % 150.42/21.91 | | | | | | | | | | | % 150.42/21.91 | | | | | | | | | | | REF_CLOSE: (33), (76), (86), (96), (134), (140), (169) are % 150.42/21.91 | | | | | | | | | | | inconsistent by sub-proof #61. % 150.42/21.91 | | | | | | | | | | | % 150.42/21.91 | | | | | | | | | | End of split % 150.42/21.91 | | | | | | | | | | % 150.42/21.91 | | | | | | | | | End of split % 150.42/21.91 | | | | | | | | | % 150.42/21.91 | | | | | | | | Case 2: % 150.42/21.91 | | | | | | | | | % 150.42/21.91 | | | | | | | | | (170) ~ (all_54_13 = e3) % 150.42/21.91 | | | | | | | | | % 150.42/21.91 | | | | | | | | | REDUCE: (60), (170) imply: % 150.42/21.91 | | | | | | | | | (171) ~ (all_52_7 = e3) % 150.42/21.91 | | | | | | | | | % 150.42/21.91 | | | | | | | | | REF_CLOSE: (29), (33), (53), (70), (76), (86), (92), (96), % 150.42/21.91 | | | | | | | | | (109), (131), (134), (171) are inconsistent by % 150.42/21.91 | | | | | | | | | sub-proof #544. % 150.42/21.91 | | | | | | | | | % 150.42/21.91 | | | | | | | | End of split % 150.42/21.91 | | | | | | | | % 150.42/21.91 | | | | | | | End of split % 150.42/21.91 | | | | | | | % 150.42/21.91 | | | | | | End of split % 150.42/21.91 | | | | | | % 150.42/21.91 | | | | | End of split % 150.42/21.91 | | | | | % 150.42/21.91 | | | | Case 2: % 150.42/21.91 | | | | | % 150.42/21.91 | | | | | (172) all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2 % 150.42/21.91 | | | | | % 150.42/21.91 | | | | | REF_CLOSE: (52), (63), (67), (89), (99), (116), (172) are inconsistent % 150.42/21.91 | | | | | by sub-proof #693. % 150.42/21.91 | | | | | % 150.42/21.91 | | | | End of split % 150.42/21.91 | | | | % 150.42/21.91 | | | Case 2: % 150.42/21.91 | | | | % 150.42/21.91 | | | | (173) all_56_31 = e2 % 150.42/21.91 | | | | (174) all_56_27 = e0 % 150.42/21.91 | | | | % 150.42/21.91 | | | | COMBINE_EQS: (20), (174) imply: % 150.42/21.91 | | | | (175) all_52_7 = e0 % 150.42/21.91 | | | | % 150.42/21.91 | | | | SIMP: (175) implies: % 150.42/21.91 | | | | (176) all_52_7 = e0 % 150.42/21.91 | | | | % 150.42/21.91 | | | | COMBINE_EQS: (51), (173) imply: % 150.42/21.91 | | | | (177) all_4_2 = e2 % 150.42/21.91 | | | | % 150.42/21.91 | | | | REDUCE: (15), (176) imply: % 150.42/21.91 | | | | (178) ~ (all_52_4 = e0) % 150.42/21.91 | | | | % 150.42/21.91 | | | | REDUCE: (68), (177) imply: % 150.42/21.91 | | | | (179) ~ (all_52_12 = e2) % 150.42/21.91 | | | | % 150.42/21.91 | | | | BETA: splitting (62) gives: % 150.42/21.91 | | | | % 150.42/21.91 | | | | Case 1: % 150.42/21.91 | | | | | % 150.42/21.91 | | | | | (180) all_54_1 = e3 % 150.42/21.91 | | | | | % 150.42/21.91 | | | | | COMBINE_EQS: (23), (180) imply: % 150.42/21.91 | | | | | (181) all_52_4 = e3 % 150.42/21.91 | | | | | % 150.42/21.91 | | | | | SIMP: (181) implies: % 150.42/21.91 | | | | | (182) all_52_4 = e3 % 150.42/21.91 | | | | | % 150.42/21.91 | | | | | COMBINE_EQS: (28), (182) imply: % 150.42/21.91 | | | | | (183) all_58_1 = e3 % 150.42/21.91 | | | | | % 150.42/21.91 | | | | | REDUCE: (45), (182) imply: % 150.42/21.91 | | | | | (184) ~ (all_10_0 = e3) % 150.42/21.91 | | | | | % 150.42/21.91 | | | | | SIMP: (184) implies: % 150.42/21.91 | | | | | (185) ~ (all_10_0 = e3) % 150.42/21.91 | | | | | % 150.42/21.91 | | | | | REF_CLOSE: (11), (13), (16), (21), (24), (31), (56), (57), (69), (78), % 150.42/21.91 | | | | | (81), (90), (109), (179), (183), (185) are inconsistent by % 150.42/21.91 | | | | | sub-proof #386. % 150.42/21.91 | | | | | % 150.42/21.91 | | | | Case 2: % 150.42/21.91 | | | | | % 150.42/21.91 | | | | | (186) all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0 % 150.42/21.91 | | | | | % 150.42/21.91 | | | | | REF_CLOSE: (23), (87), (97), (178), (186) are inconsistent by % 150.42/21.91 | | | | | sub-proof #718. % 150.42/21.91 | | | | | % 150.42/21.91 | | | | End of split % 150.42/21.91 | | | | % 150.42/21.91 | | | End of split % 150.42/21.91 | | | % 150.42/21.91 | | Case 2: % 150.42/21.91 | | | % 150.42/21.91 | | | (187) all_56_31 = e3 % 150.42/21.91 | | | (188) all_56_25 = e0 % 150.42/21.91 | | | % 150.42/21.91 | | | COMBINE_EQS: (2), (188) imply: % 150.42/21.91 | | | (189) all_52_3 = e0 % 150.42/21.91 | | | % 150.42/21.91 | | | SIMP: (189) implies: % 150.42/21.91 | | | (190) all_52_3 = e0 % 150.42/21.91 | | | % 150.42/21.91 | | | COMBINE_EQS: (51), (187) imply: % 150.42/21.91 | | | (191) all_4_2 = e3 % 150.42/21.91 | | | % 150.42/21.91 | | | REDUCE: (37), (190) imply: % 150.42/21.91 | | | (192) ~ (all_52_7 = e0) % 150.42/21.91 | | | % 150.42/21.91 | | | SIMP: (192) implies: % 150.42/21.91 | | | (193) ~ (all_52_7 = e0) % 150.42/21.91 | | | % 150.42/21.91 | | | REDUCE: (41), (190), (191) imply: % 150.42/21.91 | | | (194) ~ (e3 = e0) % 150.42/21.91 | | | % 150.42/21.91 | | | SIMP: (194) implies: % 150.42/21.91 | | | (195) ~ (e3 = e0) % 150.42/21.91 | | | % 150.42/21.91 | | | REDUCE: (39), (191) imply: % 150.42/21.91 | | | (196) ~ (all_52_7 = e3) % 150.42/21.91 | | | % 150.42/21.91 | | | REF_CLOSE: (29), (33), (53), (70), (76), (86), (92), (96), (109), (193), % 150.42/21.91 | | | (195), (196) are inconsistent by sub-proof #544. % 150.42/21.91 | | | % 150.42/21.91 | | End of split % 150.42/21.91 | | % 150.42/21.91 | Case 2: % 150.42/21.91 | | % 150.42/21.91 | | (197) all_56_31 = e1 % 150.42/21.91 | | (198) all_56_29 = e0 % 150.42/21.91 | | % 150.42/21.91 | | COMBINE_EQS: (64), (198) imply: % 150.42/21.91 | | (199) all_52_11 = e0 % 150.42/21.91 | | % 150.42/21.91 | | SIMP: (199) implies: % 150.42/21.91 | | (200) all_52_11 = e0 % 150.42/21.91 | | % 150.42/21.91 | | COMBINE_EQS: (51), (197) imply: % 150.42/21.91 | | (201) all_4_2 = e1 % 150.42/21.91 | | % 150.42/21.91 | | COMBINE_EQS: (63), (201) imply: % 150.42/21.91 | | (202) all_58_15 = e1 % 150.42/21.91 | | % 150.42/21.91 | | REDUCE: (36), (200) imply: % 150.42/21.91 | | (203) ~ (all_10_0 = e0) % 150.42/21.91 | | % 150.42/21.91 | | SIMP: (203) implies: % 150.42/21.91 | | (204) ~ (all_10_0 = e0) % 150.42/21.91 | | % 150.42/21.91 | | REDUCE: (68), (201) imply: % 150.42/21.91 | | (205) ~ (all_52_12 = e1) % 150.42/21.91 | | % 150.42/21.91 | | REDUCE: (58), (201) imply: % 150.42/21.91 | | (206) ~ (all_52_13 = e1) % 150.42/21.91 | | % 150.42/21.91 | | REDUCE: (46), (201) imply: % 150.42/21.91 | | (207) op(e1, e1) = all_4_1 % 150.42/21.91 | | % 150.42/21.91 | | BETA: splitting (32) gives: % 150.42/21.91 | | % 150.42/21.91 | | Case 1: % 150.42/21.91 | | | % 150.42/21.91 | | | (208) all_58_0 = e1 % 150.42/21.91 | | | % 150.42/21.91 | | | COMBINE_EQS: (69), (208) imply: % 150.42/21.91 | | | (209) all_10_2 = e1 % 150.42/21.91 | | | % 150.42/21.91 | | | COMBINE_EQS: (19), (209) imply: % 150.42/21.91 | | | (210) all_56_1 = e1 % 150.42/21.91 | | | % 150.42/21.91 | | | REDUCE: (82), (209) imply: % 150.42/21.91 | | | (211) ~ (all_52_1 = e1) % 150.42/21.91 | | | % 150.42/21.91 | | | REDUCE: (47), (209) imply: % 150.42/21.91 | | | (212) op(e1, e1) = e1 % 150.42/21.91 | | | % 150.42/21.91 | | | BETA: splitting (26) gives: % 150.42/21.91 | | | % 150.42/21.91 | | | Case 1: % 150.42/21.91 | | | | % 150.42/21.91 | | | | (213) ~ (all_56_1 = e1) % 150.42/21.91 | | | | % 150.42/21.91 | | | | REDUCE: (210), (213) imply: % 150.42/21.91 | | | | (214) $false % 150.42/21.91 | | | | % 150.42/21.91 | | | | CLOSE: (214) is inconsistent. % 150.42/21.91 | | | | % 150.42/21.91 | | | Case 2: % 150.42/21.91 | | | | % 150.42/21.91 | | | | (215) all_56_5 = e3 % 150.42/21.91 | | | | % 150.42/21.91 | | | | COMBINE_EQS: (6), (215) imply: % 150.42/21.91 | | | | (216) all_10_0 = e3 % 150.42/21.91 | | | | % 150.42/21.91 | | | | SIMP: (216) implies: % 150.42/21.91 | | | | (217) all_10_0 = e3 % 150.42/21.91 | | | | % 150.42/21.91 | | | | COMBINE_EQS: (13), (217) imply: % 150.42/21.91 | | | | (218) all_58_4 = e3 % 150.42/21.91 | | | | % 150.42/21.91 | | | | BETA: splitting (48) gives: % 150.42/21.91 | | | | % 150.42/21.91 | | | | Case 1: % 150.42/21.91 | | | | | % 150.42/21.91 | | | | | (219) all_58_4 = e1 % 150.42/21.91 | | | | | % 150.42/21.91 | | | | | COMBINE_EQS: (218), (219) imply: % 150.42/21.91 | | | | | (220) e3 = e1 % 150.42/21.91 | | | | | % 150.42/21.91 | | | | | REDUCE: (92), (220) imply: % 150.42/21.91 | | | | | (221) $false % 150.42/21.91 | | | | | % 150.42/21.91 | | | | | CLOSE: (221) is inconsistent. % 150.42/21.91 | | | | | % 150.42/21.91 | | | | Case 2: % 150.42/21.91 | | | | | % 150.42/21.91 | | | | | (222) all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1 % 150.42/21.91 | | | | | % 150.42/21.91 | | | | | BETA: splitting (34) gives: % 150.42/21.91 | | | | | % 150.42/21.91 | | | | | Case 1: % 150.42/21.91 | | | | | | % 150.42/21.91 | | | | | | (223) all_58_2 = e1 % 150.42/21.91 | | | | | | % 150.42/21.91 | | | | | | COMBINE_EQS: (66), (223) imply: % 150.42/21.91 | | | | | | (224) all_52_1 = e1 % 150.42/21.91 | | | | | | % 150.42/21.91 | | | | | | REDUCE: (211), (224) imply: % 150.42/21.91 | | | | | | (225) $false % 150.42/21.91 | | | | | | % 150.42/21.91 | | | | | | CLOSE: (225) is inconsistent. % 150.42/21.91 | | | | | | % 150.42/21.91 | | | | | Case 2: % 150.42/21.91 | | | | | | % 150.42/21.91 | | | | | | (226) all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1 % 150.42/21.91 | | | | | | % 150.42/21.91 | | | | | | BETA: splitting (222) gives: % 150.42/21.91 | | | | | | % 150.42/21.91 | | | | | | Case 1: % 150.42/21.91 | | | | | | | % 150.42/21.91 | | | | | | | (227) all_58_5 = e1 % 150.42/21.91 | | | | | | | % 150.42/21.91 | | | | | | | COMBINE_EQS: (22), (227) imply: % 150.42/21.91 | | | | | | | (228) all_52_9 = e1 % 150.42/21.91 | | | | | | | % 150.42/21.91 | | | | | | | REDUCE: (98), (228) imply: % 150.42/21.91 | | | | | | | (229) ~ (e2 = e1) % 150.42/21.91 | | | | | | | % 150.42/21.91 | | | | | | | REDUCE: (71), (228) imply: % 150.42/21.91 | | | | | | | (230) op(e1, e1) = all_56_12 % 150.42/21.91 | | | | | | | % 150.42/21.91 | | | | | | | GROUND_INST: instantiating (35) with e2, all_56_12, e1, e1, % 150.42/21.91 | | | | | | | simplifying with (94), (230) gives: % 150.42/21.91 | | | | | | | (231) all_56_12 = e2 % 150.42/21.91 | | | | | | | % 150.42/21.91 | | | | | | | GROUND_INST: instantiating (35) with all_4_1, all_56_12, e1, e1, % 150.42/21.91 | | | | | | | simplifying with (207), (230) gives: % 150.42/21.91 | | | | | | | (232) all_56_12 = all_4_1 % 150.42/21.91 | | | | | | | % 150.42/21.91 | | | | | | | GROUND_INST: instantiating (35) with e1, all_56_12, e1, e1, % 150.42/21.91 | | | | | | | simplifying with (212), (230) gives: % 150.42/21.91 | | | | | | | (233) all_56_12 = e1 % 150.42/21.91 | | | | | | | % 150.42/21.91 | | | | | | | COMBINE_EQS: (232), (233) imply: % 150.42/21.91 | | | | | | | (234) all_4_1 = e1 % 150.42/21.91 | | | | | | | % 150.42/21.91 | | | | | | | COMBINE_EQS: (231), (232) imply: % 150.42/21.91 | | | | | | | (235) all_4_1 = e2 % 150.42/21.91 | | | | | | | % 150.42/21.91 | | | | | | | COMBINE_EQS: (234), (235) imply: % 150.42/21.91 | | | | | | | (236) e2 = e1 % 150.42/21.91 | | | | | | | % 150.42/21.91 | | | | | | | SIMP: (236) implies: % 150.42/21.91 | | | | | | | (237) e2 = e1 % 150.42/21.91 | | | | | | | % 150.42/21.91 | | | | | | | REDUCE: (110), (237) imply: % 150.42/21.91 | | | | | | | (238) $false % 150.42/21.91 | | | | | | | % 150.42/21.91 | | | | | | | CLOSE: (238) is inconsistent. % 150.42/21.91 | | | | | | | % 150.42/21.91 | | | | | | Case 2: % 150.42/21.91 | | | | | | | % 150.42/21.91 | | | | | | | (239) ~ (all_58_5 = e1) % 150.42/21.91 | | | | | | | % 150.42/21.91 | | | | | | | REDUCE: (22), (239) imply: % 150.42/21.91 | | | | | | | (240) ~ (all_52_9 = e1) % 150.42/21.91 | | | | | | | % 150.42/21.91 | | | | | | | REF_CLOSE: (22), (67), (96), (110), (206), (226), (240) are % 150.42/21.91 | | | | | | | inconsistent by sub-proof #528. % 150.42/21.91 | | | | | | | % 150.42/21.91 | | | | | | End of split % 150.42/21.91 | | | | | | % 150.42/21.91 | | | | | End of split % 150.42/21.91 | | | | | % 150.42/21.91 | | | | End of split % 150.42/21.91 | | | | % 150.42/21.91 | | | End of split % 150.42/21.91 | | | % 150.42/21.91 | | Case 2: % 150.42/21.91 | | | % 150.42/21.91 | | | (241) all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1 % 150.42/21.91 | | | % 150.42/21.91 | | | BETA: splitting (9) gives: % 150.42/21.91 | | | % 150.42/21.91 | | | Case 1: % 150.42/21.91 | | | | % 150.42/21.91 | | | | (242) all_58_9 = e2 % 150.42/21.91 | | | | % 150.42/21.91 | | | | COMBINE_EQS: (24), (242) imply: % 150.42/21.91 | | | | (243) all_52_12 = e2 % 150.42/21.91 | | | | % 150.42/21.91 | | | | REDUCE: (43), (243) imply: % 150.42/21.91 | | | | (244) ~ (all_10_0 = e2) % 150.42/21.91 | | | | % 150.42/21.91 | | | | REF_CLOSE: (13), (16), (23), (28), (31), (45), (56), (62), (87), (90), % 150.42/21.91 | | | | (97), (110), (204), (241), (242) are inconsistent by % 150.42/21.91 | | | | sub-proof #62. % 150.42/21.91 | | | | % 150.42/21.91 | | | Case 2: % 150.42/21.91 | | | | % 150.42/21.91 | | | | (245) all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2 % 150.42/21.91 | | | | % 150.42/21.91 | | | | REF_CLOSE: (52), (67), (89), (99), (110), (202), (245) are inconsistent % 150.42/21.91 | | | | by sub-proof #69. % 150.42/21.91 | | | | % 150.42/21.91 | | | End of split % 150.42/21.91 | | | % 150.42/21.91 | | End of split % 150.42/21.91 | | % 150.42/21.91 | End of split % 150.42/21.91 | % 150.42/21.91 End of proof % 150.42/21.91 % 150.42/21.91 Sub-proof #61 shows that the following formulas are inconsistent: % 150.42/21.91 ---------------------------------------------------------------- % 150.42/21.91 (1) ~ (e3 = e0) % 150.42/21.91 (2) ~ (e1 = e0) % 150.42/21.91 (3) all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0 % 150.42/21.91 (4) all_58_3 = e2 % 150.42/21.91 (5) ~ (e2 = e0) % 150.42/21.91 (6) all_58_7 = e1 % 150.42/21.91 (7) all_58_13 = e3 % 150.42/21.91 % 150.42/21.91 Begin of proof % 150.42/21.91 | % 150.42/21.91 | BETA: splitting (3) gives: % 150.42/21.91 | % 150.42/21.91 | Case 1: % 150.42/21.91 | | % 150.42/21.91 | | (8) all_58_3 = e0 % 150.42/21.91 | | % 150.42/21.91 | | COMBINE_EQS: (4), (8) imply: % 150.42/21.91 | | (9) e2 = e0 % 150.42/21.91 | | % 150.42/21.91 | | REDUCE: (5), (9) imply: % 150.42/21.91 | | (10) $false % 150.42/21.91 | | % 150.42/21.91 | | CLOSE: (10) is inconsistent. % 150.42/21.91 | | % 150.42/21.91 | Case 2: % 150.42/21.91 | | % 150.42/21.91 | | (11) all_58_7 = e0 | all_58_13 = e0 % 150.42/21.91 | | % 150.42/21.91 | | BETA: splitting (11) gives: % 150.42/21.91 | | % 150.42/21.91 | | Case 1: % 150.42/21.91 | | | % 150.42/21.91 | | | (12) all_58_7 = e0 % 150.42/21.91 | | | % 150.42/21.91 | | | COMBINE_EQS: (6), (12) imply: % 150.42/21.91 | | | (13) e1 = e0 % 150.42/21.91 | | | % 150.42/21.91 | | | REDUCE: (2), (13) imply: % 150.42/21.91 | | | (14) $false % 150.42/21.91 | | | % 150.42/21.91 | | | CLOSE: (14) is inconsistent. % 150.42/21.91 | | | % 150.42/21.91 | | Case 2: % 150.42/21.91 | | | % 150.42/21.91 | | | (15) all_58_13 = e0 % 150.42/21.91 | | | % 150.42/21.91 | | | COMBINE_EQS: (7), (15) imply: % 150.42/21.91 | | | (16) e3 = e0 % 150.42/21.91 | | | % 150.42/21.91 | | | REDUCE: (1), (16) imply: % 150.42/21.91 | | | (17) $false % 150.42/21.91 | | | % 150.42/21.91 | | | CLOSE: (17) is inconsistent. % 150.42/21.91 | | | % 150.42/21.91 | | End of split % 150.42/21.91 | | % 150.42/21.91 | End of split % 150.42/21.91 | % 150.42/21.91 End of proof % 150.42/21.91 % 150.42/21.91 Sub-proof #62 shows that the following formulas are inconsistent: % 150.42/21.91 ---------------------------------------------------------------- % 150.42/21.91 (1) all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1 % 150.42/21.91 (2) all_58_4 = all_10_0 % 150.42/21.91 (3) all_54_2 = all_10_0 % 150.42/21.91 (4) ~ (all_10_0 = e0) % 150.42/21.91 (5) all_54_1 = all_52_4 % 150.42/21.91 (6) ~ (all_52_4 = e1) % 150.42/21.91 (7) all_58_1 = all_52_4 % 150.42/21.91 (8) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0 % 150.42/21.91 (9) all_58_9 = e2 % 150.42/21.91 (10) ~ (all_52_4 = all_10_0) % 150.42/21.91 (11) ~ (e2 = e1) % 150.42/21.91 (12) ~ (all_10_0 = e1) % 150.42/21.91 (13) ~ (all_52_4 = e2) % 150.42/21.91 (14) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0 % 150.42/21.91 (15) ~ (all_10_0 = e2) % 150.42/21.91 % 150.42/21.91 Begin of proof % 150.42/21.91 | % 150.42/21.91 | BETA: splitting (8) gives: % 150.42/21.91 | % 150.42/21.91 | Case 1: % 150.42/21.91 | | % 150.42/21.91 | | (16) all_54_2 = e3 % 150.42/21.91 | | % 150.42/21.91 | | COMBINE_EQS: (3), (16) imply: % 150.42/21.91 | | (17) all_10_0 = e3 % 150.42/21.91 | | % 150.42/21.91 | | SIMP: (17) implies: % 150.42/21.91 | | (18) all_10_0 = e3 % 150.42/21.91 | | % 150.42/21.91 | | COMBINE_EQS: (2), (18) imply: % 150.42/21.92 | | (19) all_58_4 = e3 % 150.42/21.92 | | % 150.42/21.92 | | REDUCE: (10), (18) imply: % 150.42/21.92 | | (20) ~ (all_52_4 = e3) % 150.42/21.92 | | % 150.42/21.92 | | REDUCE: (12), (18) imply: % 150.42/21.92 | | (21) ~ (e3 = e1) % 150.42/21.92 | | % 150.42/21.92 | | BETA: splitting (14) gives: % 150.42/21.92 | | % 150.42/21.92 | | Case 1: % 150.42/21.92 | | | % 150.42/21.92 | | | (22) all_54_1 = e3 % 150.42/21.92 | | | % 150.42/21.92 | | | REF_CLOSE: (5), (20), (22) are inconsistent by sub-proof #722. % 150.42/21.92 | | | % 150.42/21.92 | | Case 2: % 150.42/21.92 | | | % 150.42/21.92 | | | (23) all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0 % 150.42/21.92 | | | % 150.42/21.92 | | | REF_CLOSE: (1), (5), (6), (7), (9), (11), (13), (19), (21), (23) are % 150.42/21.92 | | | inconsistent by sub-proof #701. % 150.42/21.92 | | | % 150.42/21.92 | | End of split % 150.42/21.92 | | % 150.42/21.92 | Case 2: % 150.42/21.92 | | % 150.42/21.92 | | (24) all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0 % 150.42/21.92 | | % 150.42/21.92 | | REF_CLOSE: (3), (4), (12), (15), (24) are inconsistent by sub-proof #382. % 150.42/21.92 | | % 150.42/21.92 | End of split % 150.42/21.92 | % 150.42/21.92 End of proof % 150.42/21.92 % 150.42/21.92 Sub-proof #63 shows that the following formulas are inconsistent: % 150.42/21.92 ---------------------------------------------------------------- % 150.42/21.92 (1) all_56_10 = e2 % 150.42/21.92 (2) all_56_11 = e2 % 150.42/21.92 (3) ( ~ (all_56_0 = all_56_1) & ~ (all_56_2 = all_56_3) & ~ (all_56_4 = % 150.42/21.92 all_56_5) & ~ (all_56_6 = all_56_7)) | ( ~ (all_56_8 = all_56_9) & % 150.42/21.92 ~ (all_56_10 = all_56_11) & ~ (all_56_12 = all_56_13) & ~ (all_56_14 % 150.42/21.92 = all_56_15)) % 150.42/21.92 (4) all_56_3 = e3 % 150.42/21.92 (5) all_56_2 = e3 % 150.42/21.92 % 150.42/21.92 Begin of proof % 150.42/21.92 | % 150.42/21.92 | BETA: splitting (3) gives: % 150.42/21.92 | % 150.42/21.92 | Case 1: % 150.42/21.92 | | % 150.42/21.92 | | (6) ~ (all_56_0 = all_56_1) & ~ (all_56_2 = all_56_3) & ~ (all_56_4 = % 150.42/21.92 | | all_56_5) & ~ (all_56_6 = all_56_7) % 150.42/21.92 | | % 150.42/21.92 | | ALPHA: (6) implies: % 150.42/21.92 | | (7) ~ (all_56_2 = all_56_3) % 150.42/21.92 | | % 150.42/21.92 | | REDUCE: (4), (5), (7) imply: % 150.42/21.92 | | (8) $false % 150.42/21.92 | | % 150.42/21.92 | | CLOSE: (8) is inconsistent. % 150.42/21.92 | | % 150.42/21.92 | Case 2: % 150.42/21.92 | | % 150.42/21.92 | | (9) ~ (all_56_8 = all_56_9) & ~ (all_56_10 = all_56_11) & ~ (all_56_12 % 150.42/21.92 | | = all_56_13) & ~ (all_56_14 = all_56_15) % 150.42/21.92 | | % 150.42/21.92 | | ALPHA: (9) implies: % 150.42/21.92 | | (10) ~ (all_56_10 = all_56_11) % 150.42/21.92 | | % 150.42/21.92 | | REDUCE: (1), (2), (10) imply: % 150.42/21.92 | | (11) $false % 150.42/21.92 | | % 150.42/21.92 | | CLOSE: (11) is inconsistent. % 150.42/21.92 | | % 150.42/21.92 | End of split % 150.42/21.92 | % 150.42/21.92 End of proof % 150.42/21.92 % 150.42/21.92 Sub-proof #64 shows that the following formulas are inconsistent: % 150.42/21.92 ---------------------------------------------------------------- % 150.42/21.92 (1) all_56_25 = all_52_3 % 150.42/21.92 (2) all_58_6 = all_52_2 % 150.42/21.92 (3) ~ (all_52_8 = e2) % 150.42/21.92 (4) all_54_0 = all_10_2 % 150.42/21.92 (5) ~ (all_10_2 = e1) % 150.42/21.92 (6) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 150.42/21.92 (7) all_54_15 = all_4_2 % 150.42/21.92 (8) all_54_1 = all_10_0 % 150.42/21.92 (9) ~ (all_10_2 = e2) % 150.42/21.92 (10) all_58_13 = all_52_7 % 150.42/21.92 (11) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0 % 150.42/21.92 (12) all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2 % 150.42/21.92 (13) ~ (all_52_8 = all_10_0) % 150.42/21.92 (14) ~ (all_52_3 = all_10_2) % 150.42/21.92 (15) ~ (all_4_2 = e1) % 150.42/21.92 (16) ~ (all_52_3 = all_4_2) % 150.42/21.92 (17) ~ (all_52_8 = all_10_2) % 150.42/21.92 (18) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0 % 150.42/21.92 (19) ~ (e2 = e1) % 150.42/21.92 (20) all_56_31 = all_4_2 % 150.42/21.92 (21) all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3 % 150.42/21.92 (22) ~ (all_52_2 = e2) % 150.42/21.92 (23) ~ (all_10_0 = e1) % 150.42/21.92 (24) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0 % 150.42/21.92 (25) ~ (all_52_7 = e1) % 150.42/21.92 (26) ~ (all_52_8 = all_52_11) % 150.42/21.92 (27) all_54_13 = all_52_7 % 150.42/21.92 (28) all_54_2 = all_52_8 % 150.42/21.92 (29) ~ (all_10_2 = e0) % 150.42/21.92 (30) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0 % 150.42/21.92 (31) all_58_15 = all_4_2 % 150.42/21.92 (32) all_58_2 = all_52_1 % 150.42/21.92 (33) all_58_0 = all_10_2 % 150.42/21.92 (34) all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1 % 150.42/21.92 (35) all_58_3 = e2 % 150.42/21.92 (36) all_58_1 = e0 | all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0 % 150.42/21.92 (37) all_58_7 = e1 % 150.42/21.92 (38) ~ (all_10_0 = all_10_2) % 150.42/21.92 (39) ~ (all_10_0 = e2) % 150.42/21.92 (40) ~ (all_52_7 = all_10_0) % 150.42/21.92 (41) all_58_14 = all_52_11 % 150.42/21.92 (42) ~ (all_52_1 = e2) % 150.42/21.92 (43) all_58_12 = all_52_3 % 150.42/21.92 (44) all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2 % 150.42/21.92 (45) ~ (all_56_31 = e3) | all_56_25 = e0 % 150.42/21.92 % 150.42/21.92 Begin of proof % 150.42/21.92 | % 150.42/21.92 | BETA: splitting (6) gives: % 150.42/21.92 | % 150.42/21.92 | Case 1: % 150.42/21.92 | | % 150.42/21.92 | | (46) all_54_0 = e3 % 150.42/21.92 | | % 150.42/21.92 | | COMBINE_EQS: (4), (46) imply: % 150.42/21.92 | | (47) all_10_2 = e3 % 150.42/21.92 | | % 150.42/21.92 | | SIMP: (47) implies: % 150.42/21.92 | | (48) all_10_2 = e3 % 150.42/21.92 | | % 150.42/21.92 | | COMBINE_EQS: (33), (48) imply: % 150.42/21.92 | | (49) all_58_0 = e3 % 150.42/21.92 | | % 150.42/21.92 | | REDUCE: (14), (48) imply: % 150.42/21.92 | | (50) ~ (all_52_3 = e3) % 150.42/21.92 | | % 150.42/21.92 | | REDUCE: (17), (48) imply: % 150.42/21.92 | | (51) ~ (all_52_8 = e3) % 150.42/21.92 | | % 150.42/21.92 | | REDUCE: (38), (48) imply: % 150.42/21.92 | | (52) ~ (all_10_0 = e3) % 150.42/21.92 | | % 150.42/21.92 | | REDUCE: (9), (48) imply: % 150.42/21.92 | | (53) ~ (e3 = e2) % 150.42/21.92 | | % 150.42/21.92 | | REDUCE: (5), (48) imply: % 150.42/21.92 | | (54) ~ (e3 = e1) % 150.42/21.92 | | % 150.42/21.92 | | BETA: splitting (30) gives: % 150.42/21.92 | | % 150.42/21.92 | | Case 1: % 150.42/21.92 | | | % 150.42/21.92 | | | (55) all_54_1 = e3 % 150.42/21.92 | | | % 150.42/21.92 | | | REF_CLOSE: (8), (52), (55) are inconsistent by sub-proof #493. % 150.42/21.92 | | | % 150.42/21.92 | | Case 2: % 150.42/21.92 | | | % 150.42/21.92 | | | (56) ~ (all_54_1 = e3) % 150.42/21.92 | | | (57) all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0 % 150.42/21.92 | | | % 150.42/21.92 | | | BETA: splitting (57) gives: % 150.42/21.92 | | | % 150.42/21.92 | | | Case 1: % 150.42/21.92 | | | | % 150.42/21.92 | | | | (58) all_54_1 = e2 % 150.42/21.92 | | | | % 150.42/21.92 | | | | REF_CLOSE: (8), (39), (58) are inconsistent by sub-proof #492. % 150.42/21.92 | | | | % 150.42/21.92 | | | Case 2: % 150.42/21.92 | | | | % 150.42/21.92 | | | | (59) ~ (all_54_1 = e2) % 150.42/21.92 | | | | (60) all_54_1 = e1 | all_54_1 = e0 % 150.42/21.92 | | | | % 150.42/21.92 | | | | BETA: splitting (60) gives: % 150.42/21.92 | | | | % 150.42/21.92 | | | | Case 1: % 150.42/21.92 | | | | | % 150.42/21.92 | | | | | (61) all_54_1 = e1 % 150.42/21.92 | | | | | % 150.42/21.92 | | | | | REF_CLOSE: (8), (23), (61) are inconsistent by sub-proof #491. % 150.42/21.92 | | | | | % 150.42/21.92 | | | | Case 2: % 150.42/21.92 | | | | | % 150.42/21.92 | | | | | (62) all_54_1 = e0 % 150.42/21.92 | | | | | % 150.42/21.92 | | | | | COMBINE_EQS: (8), (62) imply: % 150.42/21.92 | | | | | (63) all_10_0 = e0 % 150.42/21.92 | | | | | % 150.42/21.92 | | | | | SIMP: (63) implies: % 150.42/21.92 | | | | | (64) all_10_0 = e0 % 150.42/21.92 | | | | | % 150.42/21.92 | | | | | REDUCE: (40), (64) imply: % 150.42/21.92 | | | | | (65) ~ (all_52_7 = e0) % 150.42/21.92 | | | | | % 150.42/21.92 | | | | | REDUCE: (13), (64) imply: % 150.42/21.92 | | | | | (66) ~ (all_52_8 = e0) % 150.42/21.92 | | | | | % 150.42/21.92 | | | | | REDUCE: (52), (64) imply: % 150.42/21.92 | | | | | (67) ~ (e3 = e0) % 150.42/21.92 | | | | | % 150.42/21.92 | | | | | SIMP: (67) implies: % 150.42/21.92 | | | | | (68) ~ (e3 = e0) % 150.42/21.92 | | | | | % 150.42/21.92 | | | | | REDUCE: (39), (64) imply: % 150.42/21.92 | | | | | (69) ~ (e2 = e0) % 150.42/21.92 | | | | | % 150.42/21.92 | | | | | SIMP: (69) implies: % 150.42/21.92 | | | | | (70) ~ (e2 = e0) % 150.42/21.92 | | | | | % 150.42/21.92 | | | | | REDUCE: (23), (64) imply: % 150.42/21.92 | | | | | (71) ~ (e1 = e0) % 150.42/21.92 | | | | | % 150.42/21.92 | | | | | SIMP: (71) implies: % 150.42/21.92 | | | | | (72) ~ (e1 = e0) % 150.42/21.92 | | | | | % 150.42/21.92 | | | | | BETA: splitting (44) gives: % 150.42/21.92 | | | | | % 150.42/21.92 | | | | | Case 1: % 150.42/21.92 | | | | | | % 150.42/21.92 | | | | | | (73) all_58_12 = e2 % 150.42/21.92 | | | | | | % 150.42/21.92 | | | | | | COMBINE_EQS: (43), (73) imply: % 150.42/21.92 | | | | | | (74) all_52_3 = e2 % 150.42/21.92 | | | | | | % 150.42/21.92 | | | | | | SIMP: (74) implies: % 150.42/21.92 | | | | | | (75) all_52_3 = e2 % 150.42/21.92 | | | | | | % 150.42/21.92 | | | | | | COMBINE_EQS: (1), (75) imply: % 150.42/21.92 | | | | | | (76) all_56_25 = e2 % 150.42/21.92 | | | | | | % 150.42/21.92 | | | | | | REDUCE: (16), (75) imply: % 150.42/21.92 | | | | | | (77) ~ (all_4_2 = e2) % 150.42/21.92 | | | | | | % 150.42/21.92 | | | | | | SIMP: (77) implies: % 150.42/21.92 | | | | | | (78) ~ (all_4_2 = e2) % 150.42/21.92 | | | | | | % 150.42/21.92 | | | | | | REDUCE: (50), (75) imply: % 150.42/21.92 | | | | | | (79) ~ (e3 = e2) % 150.42/21.92 | | | | | | % 150.42/21.92 | | | | | | BETA: splitting (45) gives: % 150.42/21.92 | | | | | | % 150.42/21.92 | | | | | | Case 1: % 150.42/21.92 | | | | | | | % 150.42/21.92 | | | | | | | (80) ~ (all_56_31 = e3) % 150.42/21.92 | | | | | | | % 150.42/21.92 | | | | | | | REDUCE: (20), (80) imply: % 150.42/21.92 | | | | | | | (81) ~ (all_4_2 = e3) % 150.42/21.92 | | | | | | | % 150.42/21.92 | | | | | | | BETA: splitting (34) gives: % 150.42/21.92 | | | | | | | % 150.42/21.92 | | | | | | | Case 1: % 150.42/21.92 | | | | | | | | % 150.42/21.92 | | | | | | | | (82) all_58_12 = e1 % 150.42/21.92 | | | | | | | | % 150.42/21.92 | | | | | | | | COMBINE_EQS: (73), (82) imply: % 150.42/21.92 | | | | | | | | (83) e2 = e1 % 150.42/21.92 | | | | | | | | % 150.42/21.92 | | | | | | | | REDUCE: (19), (83) imply: % 150.42/21.92 | | | | | | | | (84) $false % 150.42/21.92 | | | | | | | | % 150.42/21.92 | | | | | | | | CLOSE: (84) is inconsistent. % 150.42/21.92 | | | | | | | | % 150.42/21.92 | | | | | | | Case 2: % 150.42/21.92 | | | | | | | | % 150.42/21.92 | | | | | | | | (85) all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1 % 150.42/21.92 | | | | | | | | % 150.42/21.92 | | | | | | | | BETA: splitting (11) gives: % 150.42/21.92 | | | | | | | | % 150.42/21.92 | | | | | | | | Case 1: % 150.42/21.92 | | | | | | | | | % 150.42/21.92 | | | | | | | | | (86) all_54_2 = e3 % 150.42/21.92 | | | | | | | | | % 150.42/21.92 | | | | | | | | | REF_CLOSE: (28), (51), (86) are inconsistent by sub-proof % 150.42/21.92 | | | | | | | | | #728. % 150.42/21.92 | | | | | | | | | % 150.42/21.92 | | | | | | | | Case 2: % 150.42/21.92 | | | | | | | | | % 150.42/21.92 | | | | | | | | | (87) all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0 % 150.42/21.92 | | | | | | | | | % 150.42/21.92 | | | | | | | | | BETA: splitting (24) gives: % 150.42/21.92 | | | | | | | | | % 150.42/21.92 | | | | | | | | | Case 1: % 150.42/21.92 | | | | | | | | | | % 150.42/21.92 | | | | | | | | | | (88) all_54_15 = e3 % 150.42/21.92 | | | | | | | | | | % 150.42/21.92 | | | | | | | | | | REF_CLOSE: (7), (81), (88) are inconsistent by sub-proof % 150.42/21.92 | | | | | | | | | | #740. % 150.42/21.92 | | | | | | | | | | % 150.42/21.92 | | | | | | | | | Case 2: % 150.42/21.92 | | | | | | | | | | % 150.42/21.92 | | | | | | | | | | (89) all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0 % 150.42/21.92 | | | | | | | | | | % 150.42/21.92 | | | | | | | | | | BETA: splitting (18) gives: % 150.42/21.92 | | | | | | | | | | % 150.42/21.92 | | | | | | | | | | Case 1: % 150.42/21.92 | | | | | | | | | | | % 150.42/21.92 | | | | | | | | | | | (90) all_54_13 = e3 % 150.42/21.92 | | | | | | | | | | | % 150.42/21.92 | | | | | | | | | | | COMBINE_EQS: (27), (90) imply: % 150.42/21.92 | | | | | | | | | | | (91) all_52_7 = e3 % 150.42/21.92 | | | | | | | | | | | % 150.42/21.92 | | | | | | | | | | | COMBINE_EQS: (10), (91) imply: % 150.42/21.92 | | | | | | | | | | | (92) all_58_13 = e3 % 150.42/21.92 | | | | | | | | | | | % 150.42/21.92 | | | | | | | | | | | BETA: splitting (89) gives: % 150.42/21.92 | | | | | | | | | | | % 150.42/21.92 | | | | | | | | | | | Case 1: % 150.42/21.92 | | | | | | | | | | | | % 150.42/21.92 | | | | | | | | | | | | (93) all_54_15 = e2 % 150.42/21.92 | | | | | | | | | | | | % 150.42/21.92 | | | | | | | | | | | | COMBINE_EQS: (7), (93) imply: % 150.42/21.92 | | | | | | | | | | | | (94) all_4_2 = e2 % 150.42/21.92 | | | | | | | | | | | | % 150.42/21.92 | | | | | | | | | | | | REDUCE: (78), (94) imply: % 150.42/21.92 | | | | | | | | | | | | (95) $false % 150.42/21.92 | | | | | | | | | | | | % 150.42/21.92 | | | | | | | | | | | | CLOSE: (95) is inconsistent. % 150.42/21.92 | | | | | | | | | | | | % 150.42/21.92 | | | | | | | | | | | Case 2: % 150.42/21.92 | | | | | | | | | | | | % 150.42/21.92 | | | | | | | | | | | | (96) all_54_15 = e1 | all_54_15 = e0 % 150.42/21.92 | | | | | | | | | | | | % 150.42/21.92 | | | | | | | | | | | | BETA: splitting (85) gives: % 150.42/21.92 | | | | | | | | | | | | % 150.42/21.92 | | | | | | | | | | | | Case 1: % 150.42/21.92 | | | | | | | | | | | | | % 150.42/21.92 | | | | | | | | | | | | | (97) all_58_13 = e1 % 150.42/21.92 | | | | | | | | | | | | | % 150.42/21.92 | | | | | | | | | | | | | COMBINE_EQS: (92), (97) imply: % 150.42/21.92 | | | | | | | | | | | | | (98) e3 = e1 % 150.42/21.92 | | | | | | | | | | | | | % 150.42/21.92 | | | | | | | | | | | | | REDUCE: (54), (98) imply: % 150.42/21.92 | | | | | | | | | | | | | (99) $false % 150.42/21.92 | | | | | | | | | | | | | % 150.42/21.92 | | | | | | | | | | | | | CLOSE: (99) is inconsistent. % 150.42/21.92 | | | | | | | | | | | | | % 150.42/21.92 | | | | | | | | | | | | Case 2: % 150.42/21.92 | | | | | | | | | | | | | % 150.42/21.92 | | | | | | | | | | | | | (100) all_58_14 = e1 | all_58_15 = e1 % 150.42/21.92 | | | | | | | | | | | | | % 150.42/21.92 | | | | | | | | | | | | | REF_CLOSE: (3), (7), (15), (26), (28), (31), (41), (66), % 150.42/21.92 | | | | | | | | | | | | | (87), (96), (100) are inconsistent by sub-proof % 150.42/21.92 | | | | | | | | | | | | | #697. % 150.42/21.92 | | | | | | | | | | | | | % 150.42/21.92 | | | | | | | | | | | | End of split % 150.42/21.92 | | | | | | | | | | | | % 150.42/21.92 | | | | | | | | | | | End of split % 150.42/21.92 | | | | | | | | | | | % 150.42/21.92 | | | | | | | | | | Case 2: % 150.42/21.92 | | | | | | | | | | | % 150.42/21.92 | | | | | | | | | | | (101) ~ (all_54_13 = e3) % 150.42/21.92 | | | | | | | | | | | % 150.42/21.92 | | | | | | | | | | | REDUCE: (27), (101) imply: % 150.42/21.92 | | | | | | | | | | | (102) ~ (all_52_7 = e3) % 150.42/21.92 | | | | | | | | | | | % 150.42/21.92 | | | | | | | | | | | REF_CLOSE: (10), (21), (35), (36), (37), (53), (54), (65), % 150.42/21.92 | | | | | | | | | | | (68), (70), (72), (102) are inconsistent by % 150.42/21.92 | | | | | | | | | | | sub-proof #544. % 150.42/21.92 | | | | | | | | | | | % 150.42/21.92 | | | | | | | | | | End of split % 150.42/21.92 | | | | | | | | | | % 150.42/21.92 | | | | | | | | | End of split % 150.42/21.92 | | | | | | | | | % 150.42/21.92 | | | | | | | | End of split % 150.42/21.92 | | | | | | | | % 150.42/21.92 | | | | | | | End of split % 150.42/21.92 | | | | | | | % 150.42/21.92 | | | | | | Case 2: % 150.42/21.92 | | | | | | | % 150.42/21.92 | | | | | | | (103) all_56_25 = e0 % 150.42/21.92 | | | | | | | % 150.42/21.92 | | | | | | | COMBINE_EQS: (76), (103) imply: % 150.42/21.92 | | | | | | | (104) e2 = e0 % 150.42/21.92 | | | | | | | % 150.42/21.92 | | | | | | | SIMP: (104) implies: % 150.42/21.92 | | | | | | | (105) e2 = e0 % 150.42/21.92 | | | | | | | % 150.42/21.92 | | | | | | | REDUCE: (70), (105) imply: % 150.42/21.92 | | | | | | | (106) $false % 150.42/21.92 | | | | | | | % 150.42/21.92 | | | | | | | CLOSE: (106) is inconsistent. % 150.42/21.92 | | | | | | | % 150.42/21.92 | | | | | | End of split % 150.42/21.92 | | | | | | % 150.42/21.92 | | | | | Case 2: % 150.42/21.92 | | | | | | % 150.42/21.92 | | | | | | (107) ~ (all_58_12 = e2) % 150.42/21.92 | | | | | | % 150.42/21.92 | | | | | | REDUCE: (43), (107) imply: % 150.42/21.92 | | | | | | (108) ~ (all_52_3 = e2) % 150.42/21.92 | | | | | | % 150.42/21.92 | | | | | | REF_CLOSE: (2), (12), (22), (32), (42), (43), (49), (53), (108) are % 150.42/21.92 | | | | | | inconsistent by sub-proof #694. % 150.42/21.92 | | | | | | % 150.42/21.92 | | | | | End of split % 150.42/21.92 | | | | | % 150.42/21.92 | | | | End of split % 150.42/21.92 | | | | % 150.42/21.92 | | | End of split % 150.42/21.92 | | | % 150.42/21.92 | | End of split % 150.42/21.92 | | % 150.42/21.92 | Case 2: % 150.42/21.92 | | % 150.42/21.92 | | (109) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 150.42/21.92 | | % 150.42/21.92 | | REF_CLOSE: (4), (5), (9), (29), (109) are inconsistent by sub-proof #731. % 150.42/21.92 | | % 150.42/21.92 | End of split % 150.42/21.92 | % 150.42/21.92 End of proof % 150.42/21.92 % 150.42/21.92 Sub-proof #65 shows that the following formulas are inconsistent: % 150.42/21.92 ---------------------------------------------------------------- % 150.42/21.92 (1) all_56_11 = all_8_2 % 150.42/21.92 (2) ~ (all_56_11 = e1) | all_56_13 = e2 % 150.42/21.92 (3) all_58_6 = all_52_2 % 150.42/21.92 (4) ~ (all_8_1 = e1) % 150.42/21.92 (5) ~ (all_10_0 = all_8_2) % 150.42/21.92 (6) all_54_10 = all_6_2 % 150.42/21.92 (7) all_54_0 = all_10_2 % 150.42/21.92 (8) ~ (all_52_14 = all_4_2) % 150.42/21.92 (9) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0 % 150.42/21.92 (10) ~ (all_52_9 = all_8_2) % 150.42/21.92 (11) ~ (all_8_1 = e3) % 150.42/21.92 (12) op(e0, e0) = all_4_2 % 150.42/21.92 (13) all_54_5 = all_8_2 % 150.42/21.92 (14) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 150.42/21.92 (15) all_54_9 = all_6_0 % 150.42/21.92 (16) all_54_1 = all_10_0 % 150.42/21.92 (17) all_56_21 = all_6_2 % 150.42/21.92 (18) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 150.42/21.92 (19) all_56_1 = all_10_2 % 150.42/21.92 (20) all_56_17 = all_52_2 % 150.42/21.92 (21) ~ (all_56_1 = e1) | all_56_5 = e3 % 150.42/21.92 (22) op(e3, e3) = all_10_2 % 150.42/21.92 (23) ~ (all_56_21 = e3) | all_56_17 = e1 % 150.42/21.92 (24) all_38_0 = all_10_0 % 150.42/21.92 (25) all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2 % 150.42/21.92 (26) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 150.42/21.92 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 150.42/21.92 (27) ~ (all_52_8 = all_10_0) % 150.42/21.92 (28) ~ (all_56_11 = e3) | all_56_9 = e2 % 150.42/21.92 (29) all_56_7 = all_52_12 % 150.42/21.92 (30) op(all_6_2, all_6_2) = e2 % 150.42/21.92 (31) ~ (all_6_0 = all_6_2) % 150.42/21.92 (32) all_56_13 = all_52_9 % 150.42/21.92 (33) all_58_8 = all_6_2 % 150.42/21.92 (34) ~ (all_6_0 = e3) % 150.42/21.92 (35) ~ (all_6_0 = e0) | ~ (all_6_2 = e3) % 150.42/21.92 (36) ~ (all_56_21 = e2) % 150.42/21.92 (37) all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3 % 150.42/21.92 (38) ~ (all_52_12 = all_10_0) % 150.42/21.92 (39) ~ (all_56_1 = e0) | all_56_7 = e3 % 150.42/21.92 (40) ~ (all_52_14 = all_6_0) % 150.42/21.92 (41) all_56_5 = all_52_8 % 150.42/21.92 (42) op(all_4_2, all_4_2) = all_4_1 % 150.42/21.92 (43) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0 % 150.42/21.92 (44) all_56_31 = all_4_2 % 150.42/21.92 (45) all_58_11 = all_52_14 % 150.42/21.92 (46) op(all_10_2, all_10_2) = e2 % 150.42/21.92 (47) ~ (all_52_2 = all_52_14) % 150.42/21.92 (48) all_56_1 = e3 | all_56_11 = e2 | all_56_21 = e1 | all_56_31 = e0 % 150.42/21.92 (49) ~ (all_10_0 = e1) % 150.42/21.92 (50) ~ (all_52_2 = all_6_0) % 150.42/21.92 (51) ~ (all_52_13 = all_52_14) % 150.42/21.92 (52) all_56_23 = all_52_14 % 150.42/21.92 (53) ~ (all_38_0 = e0) | ~ (all_38_2 = e1) % 150.42/21.92 (54) all_38_2 = all_10_2 % 150.42/21.92 (55) op(e1, e1) = all_6_2 % 150.42/21.92 (56) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0 % 150.42/21.92 (57) all_58_7 = all_6_0 % 150.42/21.92 (58) ~ (all_52_9 = all_6_2) % 150.42/21.92 (59) op(all_10_2, all_10_2) = all_10_1 % 150.42/21.92 (60) ~ (all_56_11 = e0) | all_56_15 = e2 % 150.42/21.92 (61) op(e1, all_6_2) = all_56_20 % 150.42/21.92 (62) op(e2, e2) = all_8_2 % 150.42/21.92 (63) ~ (all_52_2 = all_6_2) % 150.42/21.92 (64) ~ (all_56_21 = e0) | all_56_23 = e1 % 150.42/21.92 (65) op(e0, all_4_2) = all_56_30 % 150.42/21.92 (66) op(e3, all_10_2) = all_56_0 % 150.42/21.92 (67) ~ (all_52_14 = all_6_2) % 150.42/21.92 (68) op(e2, all_6_0) = all_56_18 % 150.42/21.92 (69) ~ (all_10_0 = all_10_2) % 150.42/21.92 (70) ~ (all_52_2 = all_10_2) % 150.42/21.92 (71) ~ (all_8_2 = all_6_0) % 150.42/21.92 (72) ~ (all_10_0 = e2) % 150.42/21.92 (73) op(all_8_2, all_8_2) = all_8_1 % 150.42/21.92 (74) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 150.42/21.92 (75) all_56_9 = all_52_1 % 150.42/21.92 (76) all_56_15 = all_52_13 % 150.42/21.92 (77) ~ (all_52_1 = all_10_2) % 150.42/21.92 (78) all_54_11 = all_52_14 % 150.42/21.92 % 150.42/21.92 Begin of proof % 150.42/21.92 | % 150.42/21.92 | REDUCE: (17), (36) imply: % 150.42/21.92 | (79) ~ (all_6_2 = e2) % 150.42/21.92 | % 150.42/21.92 | BETA: splitting (60) gives: % 150.42/21.92 | % 150.42/21.92 | Case 1: % 150.42/21.92 | | % 150.42/21.92 | | (80) ~ (all_56_11 = e0) % 150.42/21.92 | | % 150.42/21.92 | | REDUCE: (1), (80) imply: % 150.42/21.92 | | (81) ~ (all_8_2 = e0) % 150.42/21.92 | | % 150.42/21.92 | | BETA: splitting (23) gives: % 150.42/21.92 | | % 150.42/21.92 | | Case 1: % 150.42/21.92 | | | % 150.42/21.92 | | | (82) ~ (all_56_21 = e3) % 150.42/21.92 | | | % 150.42/21.92 | | | REDUCE: (17), (82) imply: % 150.42/21.92 | | | (83) ~ (all_6_2 = e3) % 150.42/21.92 | | | % 150.42/21.92 | | | BETA: splitting (28) gives: % 150.42/21.92 | | | % 150.42/21.92 | | | Case 1: % 150.42/21.92 | | | | % 150.42/21.92 | | | | (84) ~ (all_56_11 = e3) % 150.42/21.92 | | | | % 150.42/21.92 | | | | REDUCE: (1), (84) imply: % 150.42/21.92 | | | | (85) ~ (all_8_2 = e3) % 150.42/21.92 | | | | % 150.42/21.92 | | | | REF_CLOSE: (1), (2), (3), (4), (6), (10), (11), (12), (13), (15), (17), % 150.42/21.92 | | | | (18), (19), (26), (30), (31), (32), (33), (34), (37), (40), % 150.42/21.92 | | | | (42), (43), (44), (45), (48), (52), (55), (57), (58), (61), % 150.42/21.92 | | | | (64), (65), (67), (70), (71), (73), (74), (79), (81), (83), % 150.42/21.92 | | | | (85) are inconsistent by sub-proof #84. % 150.42/21.92 | | | | % 150.42/21.92 | | | Case 2: % 150.42/21.92 | | | | % 150.42/21.92 | | | | (86) all_56_11 = e3 % 150.42/21.92 | | | | (87) all_56_9 = e2 % 150.42/21.92 | | | | % 150.42/21.92 | | | | COMBINE_EQS: (75), (87) imply: % 150.42/21.92 | | | | (88) all_52_1 = e2 % 150.42/21.92 | | | | % 150.42/21.92 | | | | COMBINE_EQS: (1), (86) imply: % 150.42/21.92 | | | | (89) all_8_2 = e3 % 150.42/21.92 | | | | % 150.42/21.92 | | | | REDUCE: (77), (88) imply: % 150.42/21.92 | | | | (90) ~ (all_10_2 = e2) % 150.42/21.92 | | | | % 150.42/21.92 | | | | SIMP: (90) implies: % 150.42/21.92 | | | | (91) ~ (all_10_2 = e2) % 150.42/21.92 | | | | % 150.42/21.92 | | | | REDUCE: (5), (89) imply: % 150.42/21.92 | | | | (92) ~ (all_10_0 = e3) % 150.42/21.92 | | | | % 150.42/21.92 | | | | REDUCE: (71), (89) imply: % 150.42/21.92 | | | | (93) ~ (all_6_0 = e3) % 150.42/21.92 | | | | % 150.42/21.92 | | | | BETA: splitting (56) gives: % 150.42/21.92 | | | | % 150.42/21.92 | | | | Case 1: % 150.42/21.92 | | | | | % 150.42/21.92 | | | | | (94) all_54_1 = e3 % 150.42/21.92 | | | | | % 150.42/21.92 | | | | | REF_CLOSE: (16), (92), (94) are inconsistent by sub-proof #493. % 150.42/21.92 | | | | | % 150.42/21.92 | | | | Case 2: % 150.42/21.92 | | | | | % 150.42/21.92 | | | | | (95) all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0 % 150.42/21.92 | | | | | % 150.42/21.92 | | | | | BETA: splitting (95) gives: % 150.42/21.92 | | | | | % 150.42/21.92 | | | | | Case 1: % 150.42/21.92 | | | | | | % 150.42/21.92 | | | | | | (96) all_54_1 = e2 % 150.42/21.92 | | | | | | % 150.42/21.92 | | | | | | REF_CLOSE: (16), (72), (96) are inconsistent by sub-proof #492. % 150.42/21.92 | | | | | | % 150.42/21.92 | | | | | Case 2: % 150.42/21.92 | | | | | | % 150.42/21.92 | | | | | | (97) all_54_1 = e1 | all_54_1 = e0 % 150.42/21.92 | | | | | | % 150.42/21.92 | | | | | | BETA: splitting (97) gives: % 150.42/21.92 | | | | | | % 150.42/21.92 | | | | | | Case 1: % 150.42/21.92 | | | | | | | % 150.42/21.92 | | | | | | | (98) all_54_1 = e1 % 150.42/21.92 | | | | | | | % 150.42/21.92 | | | | | | | REF_CLOSE: (16), (49), (98) are inconsistent by sub-proof #491. % 150.42/21.92 | | | | | | | % 150.42/21.92 | | | | | | Case 2: % 150.42/21.92 | | | | | | | % 150.42/21.92 | | | | | | | (99) all_54_1 = e0 % 150.42/21.92 | | | | | | | % 150.42/21.92 | | | | | | | COMBINE_EQS: (16), (99) imply: % 150.42/21.92 | | | | | | | (100) all_10_0 = e0 % 150.42/21.92 | | | | | | | % 150.42/21.92 | | | | | | | SIMP: (100) implies: % 150.42/21.92 | | | | | | | (101) all_10_0 = e0 % 150.42/21.92 | | | | | | | % 150.42/21.92 | | | | | | | COMBINE_EQS: (24), (101) imply: % 150.42/21.92 | | | | | | | (102) all_38_0 = e0 % 150.42/21.92 | | | | | | | % 150.42/21.92 | | | | | | | REDUCE: (69), (101) imply: % 150.42/21.92 | | | | | | | (103) ~ (all_10_2 = e0) % 150.42/21.92 | | | | | | | % 150.42/21.92 | | | | | | | SIMP: (103) implies: % 150.42/21.92 | | | | | | | (104) ~ (all_10_2 = e0) % 150.42/21.92 | | | | | | | % 150.42/21.92 | | | | | | | BETA: splitting (53) gives: % 150.42/21.92 | | | | | | | % 150.42/21.92 | | | | | | | Case 1: % 150.42/21.92 | | | | | | | | % 150.42/21.92 | | | | | | | | (105) ~ (all_38_2 = e1) % 150.42/21.92 | | | | | | | | % 150.42/21.92 | | | | | | | | REDUCE: (54), (105) imply: % 150.42/21.92 | | | | | | | | (106) ~ (all_10_2 = e1) % 150.42/21.92 | | | | | | | | % 150.42/21.92 | | | | | | | | BETA: splitting (14) gives: % 150.42/21.92 | | | | | | | | % 150.42/21.92 | | | | | | | | Case 1: % 150.42/21.92 | | | | | | | | | % 150.42/21.92 | | | | | | | | | (107) all_54_0 = e3 % 150.42/21.92 | | | | | | | | | % 150.42/21.92 | | | | | | | | | COMBINE_EQS: (7), (107) imply: % 150.42/21.92 | | | | | | | | | (108) all_10_2 = e3 % 150.42/21.92 | | | | | | | | | % 150.42/21.92 | | | | | | | | | SIMP: (108) implies: % 150.42/21.92 | | | | | | | | | (109) all_10_2 = e3 % 150.42/21.92 | | | | | | | | | % 150.42/21.92 | | | | | | | | | REDUCE: (70), (109) imply: % 150.42/21.92 | | | | | | | | | (110) ~ (all_52_2 = e3) % 150.42/21.92 | | | | | | | | | % 150.42/21.92 | | | | | | | | | REDUCE: (106), (109) imply: % 150.42/21.92 | | | | | | | | | (111) ~ (e3 = e1) % 150.42/21.92 | | | | | | | | | % 150.42/21.92 | | | | | | | | | REDUCE: (104), (109) imply: % 150.42/21.92 | | | | | | | | | (112) ~ (e3 = e0) % 150.42/21.92 | | | | | | | | | % 150.42/21.92 | | | | | | | | | BETA: splitting (37) gives: % 150.42/21.92 | | | | | | | | | % 150.42/21.92 | | | | | | | | | Case 1: % 150.42/21.92 | | | | | | | | | | % 150.42/21.92 | | | | | | | | | | (113) all_58_6 = e3 % 150.42/21.92 | | | | | | | | | | % 150.42/21.92 | | | | | | | | | | COMBINE_EQS: (3), (113) imply: % 150.42/21.92 | | | | | | | | | | (114) all_52_2 = e3 % 150.42/21.92 | | | | | | | | | | % 150.42/21.92 | | | | | | | | | | REDUCE: (110), (114) imply: % 150.42/21.92 | | | | | | | | | | (115) $false % 150.42/21.92 | | | | | | | | | | % 150.42/21.92 | | | | | | | | | | CLOSE: (115) is inconsistent. % 150.42/21.92 | | | | | | | | | | % 150.42/21.92 | | | | | | | | | Case 2: % 150.42/21.92 | | | | | | | | | | % 150.42/21.92 | | | | | | | | | | (116) all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3 % 150.42/21.92 | | | | | | | | | | % 150.42/21.92 | | | | | | | | | | REF_CLOSE: (6), (17), (18), (26), (30), (33), (34), (40), % 150.42/21.92 | | | | | | | | | | (45), (52), (55), (57), (61), (64), (67), (79), % 150.42/21.92 | | | | | | | | | | (83), (111), (112), (116) are inconsistent by % 150.42/21.92 | | | | | | | | | | sub-proof #82. % 150.42/21.92 | | | | | | | | | | % 150.42/21.92 | | | | | | | | | End of split % 150.42/21.92 | | | | | | | | | % 150.42/21.92 | | | | | | | | Case 2: % 150.42/21.92 | | | | | | | | | % 150.42/21.92 | | | | | | | | | (117) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 150.42/21.92 | | | | | | | | | % 150.42/21.92 | | | | | | | | | REF_CLOSE: (7), (91), (104), (106), (117) are inconsistent by % 150.42/21.92 | | | | | | | | | sub-proof #731. % 150.42/21.92 | | | | | | | | | % 150.42/21.92 | | | | | | | | End of split % 150.42/21.92 | | | | | | | | % 150.42/21.92 | | | | | | | Case 2: % 150.42/21.92 | | | | | | | | % 150.42/21.92 | | | | | | | | (118) all_38_2 = e1 % 150.42/21.92 | | | | | | | | % 150.42/21.92 | | | | | | | | REF_CLOSE: (53), (102), (118) are inconsistent by sub-proof % 150.42/21.92 | | | | | | | | #487. % 150.42/21.92 | | | | | | | | % 150.42/21.92 | | | | | | | End of split % 150.42/21.92 | | | | | | | % 150.42/21.92 | | | | | | End of split % 150.42/21.92 | | | | | | % 150.42/21.92 | | | | | End of split % 150.42/21.92 | | | | | % 150.42/21.92 | | | | End of split % 150.42/21.92 | | | | % 150.42/21.92 | | | End of split % 150.42/21.92 | | | % 150.42/21.92 | | Case 2: % 150.42/21.92 | | | % 150.42/21.92 | | | (119) all_56_21 = e3 % 150.42/21.92 | | | (120) all_56_17 = e1 % 150.42/21.92 | | | % 150.42/21.92 | | | REF_CLOSE: (1), (6), (8), (9), (15), (17), (18), (19), (20), (22), (26), % 150.42/21.92 | | | (30), (31), (35), (40), (43), (44), (47), (48), (50), (52), % 150.42/21.92 | | | (55), (59), (61), (63), (64), (66), (67), (71), (78), (79), % 150.42/21.92 | | | (119), (120) are inconsistent by sub-proof #66. % 150.42/21.92 | | | % 150.42/21.92 | | End of split % 150.42/21.92 | | % 150.42/21.92 | Case 2: % 150.42/21.92 | | % 150.42/21.92 | | (121) all_56_15 = e2 % 150.42/21.92 | | (122) all_56_11 = e0 % 150.42/21.92 | | % 150.42/21.92 | | COMBINE_EQS: (1), (122) imply: % 150.42/21.92 | | (123) all_8_2 = e0 % 150.42/21.92 | | % 150.42/21.92 | | COMBINE_EQS: (76), (121) imply: % 150.42/21.92 | | (124) all_52_13 = e2 % 150.42/21.92 | | % 150.42/21.92 | | REDUCE: (51), (124) imply: % 150.42/21.92 | | (125) ~ (all_52_14 = e2) % 150.42/21.92 | | % 150.42/21.92 | | SIMP: (125) implies: % 150.42/21.92 | | (126) ~ (all_52_14 = e2) % 150.42/21.92 | | % 150.42/21.92 | | REDUCE: (5), (123) imply: % 150.42/21.92 | | (127) ~ (all_10_0 = e0) % 150.42/21.92 | | % 150.42/21.92 | | REDUCE: (71), (123) imply: % 150.42/21.92 | | (128) ~ (all_6_0 = e0) % 150.42/21.92 | | % 150.42/21.92 | | SIMP: (128) implies: % 150.42/21.92 | | (129) ~ (all_6_0 = e0) % 150.42/21.92 | | % 150.42/21.92 | | REDUCE: (62), (123) imply: % 150.42/21.92 | | (130) op(e2, e2) = e0 % 150.42/21.92 | | % 150.42/21.92 | | BETA: splitting (56) gives: % 150.42/21.92 | | % 150.42/21.92 | | Case 1: % 150.42/21.92 | | | % 150.42/21.92 | | | (131) all_54_1 = e3 % 150.42/21.92 | | | % 150.42/21.92 | | | COMBINE_EQS: (16), (131) imply: % 150.42/21.92 | | | (132) all_10_0 = e3 % 150.42/21.92 | | | % 150.42/21.92 | | | SIMP: (132) implies: % 150.42/21.92 | | | (133) all_10_0 = e3 % 150.42/21.92 | | | % 150.42/21.92 | | | REDUCE: (27), (133) imply: % 150.42/21.92 | | | (134) ~ (all_52_8 = e3) % 150.42/21.92 | | | % 150.42/21.92 | | | REDUCE: (38), (133) imply: % 150.42/21.92 | | | (135) ~ (all_52_12 = e3) % 150.42/21.92 | | | % 150.42/21.92 | | | REDUCE: (69), (133) imply: % 150.42/21.92 | | | (136) ~ (all_10_2 = e3) % 150.42/21.92 | | | % 150.42/21.92 | | | SIMP: (136) implies: % 150.42/21.92 | | | (137) ~ (all_10_2 = e3) % 150.42/21.92 | | | % 150.42/21.92 | | | BETA: splitting (39) gives: % 150.42/21.92 | | | % 150.42/21.92 | | | Case 1: % 150.42/21.92 | | | | % 150.42/21.92 | | | | (138) ~ (all_56_1 = e0) % 150.42/21.92 | | | | % 150.42/21.92 | | | | REDUCE: (19), (138) imply: % 150.42/21.92 | | | | (139) ~ (all_10_2 = e0) % 150.42/21.92 | | | | % 150.42/21.92 | | | | BETA: splitting (21) gives: % 150.42/21.92 | | | | % 150.42/21.92 | | | | Case 1: % 150.42/21.92 | | | | | % 150.42/21.92 | | | | | (140) ~ (all_56_1 = e1) % 150.42/21.92 | | | | | % 150.42/21.92 | | | | | REDUCE: (19), (140) imply: % 150.42/21.92 | | | | | (141) ~ (all_10_2 = e1) % 150.42/21.92 | | | | | % 150.42/21.92 | | | | | BETA: splitting (14) gives: % 150.42/21.92 | | | | | % 150.42/21.92 | | | | | Case 1: % 150.42/21.92 | | | | | | % 150.42/21.93 | | | | | | (142) all_54_0 = e3 % 150.42/21.93 | | | | | | % 150.42/21.93 | | | | | | REF_CLOSE: (7), (137), (142) are inconsistent by sub-proof #709. % 150.42/21.93 | | | | | | % 150.42/21.93 | | | | | Case 2: % 150.42/21.93 | | | | | | % 150.42/21.93 | | | | | | (143) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 150.42/21.93 | | | | | | % 150.42/21.93 | | | | | | BETA: splitting (143) gives: % 150.42/21.93 | | | | | | % 150.42/21.93 | | | | | | Case 1: % 150.42/21.93 | | | | | | | % 150.42/21.93 | | | | | | | (144) all_54_0 = e2 % 150.42/21.93 | | | | | | | % 150.42/21.93 | | | | | | | COMBINE_EQS: (7), (144) imply: % 150.42/21.93 | | | | | | | (145) all_10_2 = e2 % 150.42/21.93 | | | | | | | % 150.42/21.93 | | | | | | | SIMP: (145) implies: % 150.42/21.93 | | | | | | | (146) all_10_2 = e2 % 150.42/21.93 | | | | | | | % 150.42/21.93 | | | | | | | REDUCE: (70), (146) imply: % 150.42/21.93 | | | | | | | (147) ~ (all_52_2 = e2) % 150.42/21.93 | | | | | | | % 150.42/21.93 | | | | | | | REDUCE: (46), (146) imply: % 150.42/21.93 | | | | | | | (148) op(e2, e2) = e2 % 150.42/21.93 | | | | | | | % 150.42/21.93 | | | | | | | BETA: splitting (25) gives: % 150.42/21.93 | | | | | | | % 150.42/21.93 | | | | | | | Case 1: % 150.42/21.93 | | | | | | | | % 150.42/21.93 | | | | | | | | (149) all_58_6 = e2 % 150.42/21.93 | | | | | | | | % 150.42/21.93 | | | | | | | | COMBINE_EQS: (3), (149) imply: % 150.42/21.93 | | | | | | | | (150) all_52_2 = e2 % 150.42/21.93 | | | | | | | | % 150.42/21.93 | | | | | | | | REDUCE: (147), (150) imply: % 150.42/21.93 | | | | | | | | (151) $false % 150.42/21.93 | | | | | | | | % 150.42/21.93 | | | | | | | | CLOSE: (151) is inconsistent. % 150.42/21.93 | | | | | | | | % 150.42/21.93 | | | | | | | Case 2: % 150.42/21.93 | | | | | | | | % 150.42/21.93 | | | | | | | | (152) all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2 % 150.42/21.93 | | | | | | | | % 150.42/21.93 | | | | | | | | BETA: splitting (152) gives: % 150.42/21.93 | | | | | | | | % 150.42/21.93 | | | | | | | | Case 1: % 150.42/21.93 | | | | | | | | | % 150.42/21.93 | | | | | | | | | (153) all_58_7 = e2 % 150.42/21.93 | | | | | | | | | % 150.42/21.93 | | | | | | | | | COMBINE_EQS: (57), (153) imply: % 150.42/21.93 | | | | | | | | | (154) all_6_0 = e2 % 150.42/21.93 | | | | | | | | | % 150.42/21.93 | | | | | | | | | REDUCE: (129), (154) imply: % 150.42/21.93 | | | | | | | | | (155) ~ (e2 = e0) % 150.42/21.93 | | | | | | | | | % 150.42/21.93 | | | | | | | | | REDUCE: (68), (154) imply: % 150.42/21.93 | | | | | | | | | (156) op(e2, e2) = all_56_18 % 150.42/21.93 | | | | | | | | | % 150.42/21.93 | | | | | | | | | REF_CLOSE: (26), (130), (148), (155), (156) are inconsistent % 150.42/21.93 | | | | | | | | | by sub-proof #484. % 150.42/21.93 | | | | | | | | | % 150.42/21.93 | | | | | | | | Case 2: % 150.42/21.93 | | | | | | | | | % 150.42/21.93 | | | | | | | | | (157) all_58_8 = e2 | all_58_11 = e2 % 150.42/21.93 | | | | | | | | | % 150.42/21.93 | | | | | | | | | REF_CLOSE: (33), (45), (79), (126), (157) are inconsistent by % 150.42/21.93 | | | | | | | | | sub-proof #511. % 150.42/21.93 | | | | | | | | | % 150.42/21.93 | | | | | | | | End of split % 150.42/21.93 | | | | | | | | % 150.42/21.93 | | | | | | | End of split % 150.42/21.93 | | | | | | | % 150.42/21.93 | | | | | | Case 2: % 150.42/21.93 | | | | | | | % 150.42/21.93 | | | | | | | (158) all_54_0 = e1 | all_54_0 = e0 % 150.42/21.93 | | | | | | | % 150.42/21.93 | | | | | | | REF_CLOSE: (7), (139), (141), (158) are inconsistent by sub-proof % 150.42/21.93 | | | | | | | #483. % 150.42/21.93 | | | | | | | % 150.42/21.93 | | | | | | End of split % 150.42/21.93 | | | | | | % 150.42/21.93 | | | | | End of split % 150.42/21.93 | | | | | % 150.42/21.93 | | | | Case 2: % 150.42/21.93 | | | | | % 150.42/21.93 | | | | | (159) all_56_5 = e3 % 150.42/21.93 | | | | | % 150.42/21.93 | | | | | REF_CLOSE: (41), (134), (159) are inconsistent by sub-proof #481. % 150.42/21.93 | | | | | % 150.42/21.93 | | | | End of split % 150.42/21.93 | | | | % 150.42/21.93 | | | Case 2: % 150.42/21.93 | | | | % 150.42/21.93 | | | | (160) all_56_7 = e3 % 150.42/21.93 | | | | % 150.42/21.93 | | | | REF_CLOSE: (29), (135), (160) are inconsistent by sub-proof #691. % 150.42/21.93 | | | | % 150.42/21.93 | | | End of split % 150.42/21.93 | | | % 150.42/21.93 | | Case 2: % 150.42/21.93 | | | % 150.42/21.93 | | | (161) all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0 % 150.42/21.93 | | | % 150.42/21.93 | | | REF_CLOSE: (16), (49), (72), (127), (161) are inconsistent by sub-proof % 150.42/21.93 | | | #490. % 150.42/21.93 | | | % 150.42/21.93 | | End of split % 150.42/21.93 | | % 150.42/21.93 | End of split % 150.42/21.93 | % 150.42/21.93 End of proof % 150.42/21.93 % 150.42/21.93 Sub-proof #66 shows that the following formulas are inconsistent: % 150.42/21.93 ---------------------------------------------------------------- % 150.42/21.93 (1) all_56_11 = all_8_2 % 150.42/21.93 (2) all_54_10 = all_6_2 % 150.42/21.93 (3) all_56_21 = e3 % 150.42/21.93 (4) ~ (all_52_14 = all_4_2) % 150.42/21.93 (5) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0 % 150.42/21.93 (6) all_54_9 = all_6_0 % 150.42/21.93 (7) all_56_21 = all_6_2 % 150.42/21.93 (8) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 150.42/21.93 (9) all_56_1 = all_10_2 % 150.42/21.93 (10) all_56_17 = all_52_2 % 150.42/21.93 (11) op(e3, e3) = all_10_2 % 150.42/21.93 (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 150.42/21.93 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 150.42/21.93 (13) op(all_6_2, all_6_2) = e2 % 150.42/21.93 (14) ~ (all_6_0 = all_6_2) % 150.42/21.93 (15) ~ (all_6_0 = e0) | ~ (all_6_2 = e3) % 150.42/21.93 (16) ~ (all_52_14 = all_6_0) % 150.42/21.93 (17) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0 % 150.42/21.93 (18) all_56_31 = all_4_2 % 150.42/21.93 (19) ~ (all_52_2 = all_52_14) % 150.42/21.93 (20) all_56_1 = e3 | all_56_11 = e2 | all_56_21 = e1 | all_56_31 = e0 % 150.42/21.93 (21) ~ (all_52_2 = all_6_0) % 150.42/21.93 (22) all_56_17 = e1 % 150.42/21.93 (23) all_56_23 = all_52_14 % 150.42/21.93 (24) op(e1, e1) = all_6_2 % 150.42/21.93 (25) ~ (all_6_2 = e2) % 150.42/21.93 (26) op(all_10_2, all_10_2) = all_10_1 % 150.42/21.93 (27) op(e1, all_6_2) = all_56_20 % 150.42/21.93 (28) ~ (all_52_2 = all_6_2) % 150.42/21.93 (29) ~ (all_56_21 = e0) | all_56_23 = e1 % 150.42/21.93 (30) op(e3, all_10_2) = all_56_0 % 150.42/21.93 (31) ~ (all_52_14 = all_6_2) % 150.42/21.93 (32) ~ (all_8_2 = all_6_0) % 150.42/21.93 (33) all_54_11 = all_52_14 % 150.42/21.93 % 150.42/21.93 Begin of proof % 150.42/21.93 | % 150.42/21.93 | COMBINE_EQS: (10), (22) imply: % 150.42/21.93 | (34) all_52_2 = e1 % 150.42/21.93 | % 150.42/21.93 | COMBINE_EQS: (3), (7) imply: % 150.42/21.93 | (35) all_6_2 = e3 % 150.42/21.93 | % 150.42/21.93 | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (11), (12), (13), % 150.42/21.93 | (14), (15), (16), (17), (18), (19), (20), (21), (23), (24), (25), % 150.42/21.93 | (26), (27), (28), (29), (30), (31), (32), (33), (34), (35) are % 150.42/21.93 | inconsistent by sub-proof #67. % 150.42/21.93 | % 150.42/21.93 End of proof % 150.42/21.93 % 150.42/21.93 Sub-proof #67 shows that the following formulas are inconsistent: % 150.42/21.93 ---------------------------------------------------------------- % 150.42/21.93 (1) all_56_11 = all_8_2 % 150.42/21.93 (2) all_54_10 = all_6_2 % 150.42/21.93 (3) all_56_21 = e3 % 150.42/21.93 (4) ~ (all_52_14 = all_4_2) % 150.42/21.93 (5) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0 % 150.42/21.93 (6) all_6_2 = e3 % 150.42/21.93 (7) all_54_9 = all_6_0 % 150.42/21.93 (8) all_56_21 = all_6_2 % 150.42/21.93 (9) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 150.42/21.93 (10) all_56_1 = all_10_2 % 150.42/21.93 (11) op(e3, e3) = all_10_2 % 150.42/21.93 (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 150.42/21.93 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 150.42/21.93 (13) op(all_6_2, all_6_2) = e2 % 150.42/21.93 (14) ~ (all_6_0 = all_6_2) % 150.42/21.93 (15) ~ (all_6_0 = e0) | ~ (all_6_2 = e3) % 150.42/21.93 (16) ~ (all_52_14 = all_6_0) % 150.42/21.93 (17) all_52_2 = e1 % 150.42/21.93 (18) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0 % 150.42/21.93 (19) all_56_31 = all_4_2 % 150.42/21.93 (20) ~ (all_52_2 = all_52_14) % 150.42/21.93 (21) all_56_1 = e3 | all_56_11 = e2 | all_56_21 = e1 | all_56_31 = e0 % 150.42/21.93 (22) ~ (all_52_2 = all_6_0) % 150.42/21.93 (23) all_56_23 = all_52_14 % 150.42/21.93 (24) op(e1, e1) = all_6_2 % 150.42/21.93 (25) ~ (all_6_2 = e2) % 150.42/21.93 (26) op(all_10_2, all_10_2) = all_10_1 % 150.42/21.93 (27) op(e1, all_6_2) = all_56_20 % 150.42/21.93 (28) ~ (all_52_2 = all_6_2) % 150.42/21.93 (29) ~ (all_56_21 = e0) | all_56_23 = e1 % 150.42/21.93 (30) op(e3, all_10_2) = all_56_0 % 150.42/21.93 (31) ~ (all_52_14 = all_6_2) % 150.42/21.93 (32) ~ (all_8_2 = all_6_0) % 150.42/21.93 (33) all_54_11 = all_52_14 % 150.42/21.93 % 150.42/21.93 Begin of proof % 150.42/21.93 | % 150.42/21.93 | REDUCE: (17), (20) imply: % 150.42/21.93 | (34) ~ (all_52_14 = e1) % 150.42/21.93 | % 150.42/21.93 | SIMP: (34) implies: % 150.42/21.93 | (35) ~ (all_52_14 = e1) % 150.42/21.93 | % 150.42/21.93 | REDUCE: (17), (22) imply: % 150.42/21.93 | (36) ~ (all_6_0 = e1) % 150.42/21.93 | % 150.42/21.93 | SIMP: (36) implies: % 150.42/21.93 | (37) ~ (all_6_0 = e1) % 150.42/21.93 | % 150.42/21.93 | REDUCE: (6), (17), (28) imply: % 150.42/21.93 | (38) ~ (e3 = e1) % 150.42/21.93 | % 150.42/21.93 | SIMP: (38) implies: % 150.42/21.93 | (39) ~ (e3 = e1) % 150.42/21.93 | % 150.42/21.93 | REDUCE: (6), (31) imply: % 150.42/21.93 | (40) ~ (all_52_14 = e3) % 150.42/21.93 | % 150.42/21.93 | REDUCE: (6), (14) imply: % 150.42/21.93 | (41) ~ (all_6_0 = e3) % 150.42/21.93 | % 150.42/21.93 | REDUCE: (6), (13) imply: % 150.42/21.93 | (42) op(e3, e3) = e2 % 150.42/21.93 | % 150.42/21.93 | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (10), (11), (12), (13), % 150.42/21.93 | (15), (16), (18), (19), (21), (23), (24), (25), (26), (27), (29), % 150.42/21.93 | (30), (32), (33), (35), (37), (39), (40), (41), (42) are % 150.42/21.93 | inconsistent by sub-proof #79. % 150.42/21.93 | % 150.42/21.93 End of proof % 150.42/21.93 % 150.42/21.93 Sub-proof #68 shows that the following formulas are inconsistent: % 150.42/21.93 ---------------------------------------------------------------- % 150.42/21.93 (1) all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2 % 150.42/21.93 (2) ~ (e3 = e2) % 150.42/21.93 (3) ~ (all_52_14 = e2) % 150.42/21.93 (4) ~ (all_52_13 = e2) % 150.42/21.93 (5) all_58_9 = all_52_12 % 150.42/21.93 (6) op(e0, e2) = all_52_7 % 150.42/21.93 (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 150.42/21.93 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 150.42/21.93 (8) op(e0, all_4_1) = all_4_0 % 150.42/21.93 (9) all_56_7 = all_52_12 % 150.42/21.93 (10) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0 % 150.42/21.93 (11) ~ (all_56_1 = e0) | all_56_7 = e3 % 150.42/21.93 (12) ~ (e2 = e1) % 150.42/21.93 (13) all_58_11 = all_52_14 % 150.42/21.93 (14) ~ (all_52_7 = e1) % 150.42/21.93 (15) all_54_13 = all_52_7 % 150.42/21.93 (16) all_58_15 = e1 % 150.42/21.93 (17) all_58_10 = all_52_13 % 150.42/21.93 (18) op(e1, e1) = all_4_1 % 150.42/21.93 (19) ~ (all_52_7 = e0) % 150.42/21.93 (20) op(e1, e1) = e2 % 150.42/21.93 (21) ~ (all_4_0 = e2) % 150.42/21.93 (22) ~ (all_4_0 = e3) % 150.42/21.93 % 150.42/21.93 Begin of proof % 150.42/21.93 | % 150.42/21.93 | BETA: splitting (1) gives: % 150.42/21.93 | % 150.42/21.93 | Case 1: % 150.42/21.93 | | % 150.42/21.93 | | (23) all_58_9 = e2 % 150.42/21.93 | | % 150.42/21.93 | | COMBINE_EQS: (5), (23) imply: % 150.42/21.93 | | (24) all_52_12 = e2 % 150.42/21.93 | | % 150.42/21.93 | | COMBINE_EQS: (9), (24) imply: % 150.42/21.93 | | (25) all_56_7 = e2 % 150.42/21.93 | | % 150.42/21.93 | | BETA: splitting (11) gives: % 150.42/21.93 | | % 150.42/21.93 | | Case 1: % 150.42/21.93 | | | % 150.42/21.93 | | | % 150.42/21.93 | | | GROUND_INST: instantiating (7) with e2, all_4_1, e1, e1, simplifying with % 150.42/21.93 | | | (18), (20) gives: % 150.42/21.93 | | | (26) all_4_1 = e2 % 150.42/21.93 | | | % 150.42/21.93 | | | REDUCE: (8), (26) imply: % 150.42/21.93 | | | (27) op(e0, e2) = all_4_0 % 150.42/21.93 | | | % 150.42/21.93 | | | REF_CLOSE: (6), (7), (10), (14), (15), (19), (21), (22), (27) are % 150.42/21.93 | | | inconsistent by sub-proof #518. % 150.42/21.93 | | | % 150.42/21.93 | | Case 2: % 150.42/21.93 | | | % 150.42/21.93 | | | (28) all_56_7 = e3 % 150.42/21.93 | | | % 150.42/21.93 | | | REF_CLOSE: (2), (25), (28) are inconsistent by sub-proof #660. % 150.42/21.93 | | | % 150.42/21.93 | | End of split % 150.42/21.93 | | % 150.42/21.93 | Case 2: % 150.42/21.93 | | % 150.42/21.93 | | (29) all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2 % 150.42/21.93 | | % 150.42/21.93 | | REF_CLOSE: (3), (4), (12), (13), (16), (17), (29) are inconsistent by % 150.42/21.93 | | sub-proof #69. % 150.42/21.93 | | % 150.42/21.93 | End of split % 150.42/21.93 | % 150.42/21.93 End of proof % 150.42/21.93 % 150.42/21.93 Sub-proof #69 shows that the following formulas are inconsistent: % 150.42/21.93 ---------------------------------------------------------------- % 150.42/21.93 (1) ~ (all_52_14 = e2) % 150.42/21.93 (2) ~ (all_52_13 = e2) % 150.42/21.93 (3) ~ (e2 = e1) % 150.42/21.93 (4) all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2 % 150.42/21.93 (5) all_58_11 = all_52_14 % 150.42/21.93 (6) all_58_15 = e1 % 150.42/21.93 (7) all_58_10 = all_52_13 % 150.42/21.93 % 150.42/21.93 Begin of proof % 150.42/21.93 | % 150.42/21.93 | BETA: splitting (4) gives: % 150.42/21.93 | % 150.42/21.93 | Case 1: % 150.42/21.93 | | % 150.42/21.93 | | (8) all_58_10 = e2 % 150.42/21.93 | | % 150.42/21.93 | | COMBINE_EQS: (7), (8) imply: % 150.42/21.93 | | (9) all_52_13 = e2 % 150.42/21.93 | | % 150.42/21.93 | | REDUCE: (2), (9) imply: % 150.42/21.93 | | (10) $false % 150.42/21.93 | | % 150.42/21.93 | | CLOSE: (10) is inconsistent. % 150.42/21.93 | | % 150.42/21.93 | Case 2: % 150.42/21.93 | | % 150.42/21.93 | | (11) all_58_11 = e2 | all_58_15 = e2 % 150.42/21.93 | | % 150.42/21.93 | | BETA: splitting (11) gives: % 150.42/21.93 | | % 150.42/21.93 | | Case 1: % 150.42/21.93 | | | % 150.42/21.93 | | | (12) all_58_11 = e2 % 150.42/21.93 | | | % 150.42/21.93 | | | COMBINE_EQS: (5), (12) imply: % 150.42/21.93 | | | (13) all_52_14 = e2 % 150.42/21.93 | | | % 150.42/21.93 | | | REDUCE: (1), (13) imply: % 150.42/21.93 | | | (14) $false % 150.42/21.93 | | | % 150.42/21.93 | | | CLOSE: (14) is inconsistent. % 150.42/21.93 | | | % 150.42/21.93 | | Case 2: % 150.42/21.93 | | | % 150.42/21.93 | | | (15) all_58_15 = e2 % 150.42/21.93 | | | % 150.42/21.93 | | | REF_CLOSE: (3), (6), (15) are inconsistent by sub-proof #70. % 150.42/21.93 | | | % 150.42/21.93 | | End of split % 150.42/21.93 | | % 150.42/21.93 | End of split % 150.42/21.93 | % 150.42/21.93 End of proof % 150.42/21.93 % 150.42/21.93 Sub-proof #70 shows that the following formulas are inconsistent: % 150.42/21.93 ---------------------------------------------------------------- % 150.42/21.93 (1) all_58_15 = e2 % 150.42/21.93 (2) all_58_15 = e1 % 150.42/21.93 (3) ~ (e2 = e1) % 150.42/21.93 % 150.42/21.93 Begin of proof % 150.42/21.93 | % 150.42/21.93 | COMBINE_EQS: (1), (2) imply: % 150.42/21.93 | (4) e2 = e1 % 150.42/21.93 | % 150.42/21.93 | SIMP: (4) implies: % 150.42/21.93 | (5) e2 = e1 % 150.42/21.93 | % 150.42/21.93 | REDUCE: (3), (5) imply: % 150.42/21.93 | (6) $false % 150.42/21.93 | % 150.42/21.93 | CLOSE: (6) is inconsistent. % 150.42/21.93 | % 150.42/21.93 End of proof % 150.42/21.93 % 150.42/21.93 Sub-proof #71 shows that the following formulas are inconsistent: % 150.42/21.93 ---------------------------------------------------------------- % 150.42/21.93 (1) all_56_25 = all_52_3 % 150.42/21.93 (2) ~ (all_52_7 = e2) % 150.42/21.93 (3) all_56_31 = e3 % 150.42/21.93 (4) all_56_25 = e0 % 150.42/21.93 (5) ~ (all_52_3 = all_52_7) % 150.42/21.93 (6) ~ (all_52_7 = all_4_2) % 150.42/21.93 (7) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0 % 150.42/21.93 (8) all_56_31 = all_4_2 % 150.42/21.93 (9) ~ (all_52_7 = e1) % 150.42/21.93 (10) all_54_13 = all_52_7 % 150.42/21.93 % 150.42/21.93 Begin of proof % 150.42/21.93 | % 150.42/21.93 | COMBINE_EQS: (1), (4) imply: % 150.42/21.93 | (11) all_52_3 = e0 % 150.42/21.93 | % 150.42/21.93 | SIMP: (11) implies: % 150.42/21.93 | (12) all_52_3 = e0 % 150.42/21.93 | % 150.42/21.93 | COMBINE_EQS: (3), (8) imply: % 150.42/21.93 | (13) all_4_2 = e3 % 150.42/21.93 | % 150.42/21.93 | REDUCE: (5), (12) imply: % 150.42/21.93 | (14) ~ (all_52_7 = e0) % 150.42/21.93 | % 150.42/21.93 | SIMP: (14) implies: % 150.42/21.93 | (15) ~ (all_52_7 = e0) % 150.42/21.93 | % 150.42/21.93 | REDUCE: (6), (13) imply: % 150.42/21.93 | (16) ~ (all_52_7 = e3) % 150.42/21.93 | % 150.42/21.93 | REF_CLOSE: (2), (7), (9), (10), (15), (16) are inconsistent by sub-proof #620. % 150.42/21.93 | % 150.42/21.93 End of proof % 150.42/21.93 % 150.42/21.93 Sub-proof #72 shows that the following formulas are inconsistent: % 150.42/21.93 ---------------------------------------------------------------- % 150.42/21.93 (1) ~ (all_52_4 = all_52_8) % 150.42/21.93 (2) all_58_6 = all_52_2 % 150.42/21.93 (3) op(e2, e2) = e2 % 150.42/21.93 (4) all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2 % 150.42/21.93 (5) all_54_0 = all_10_2 % 150.42/21.93 (6) ~ (all_52_4 = all_52_7) % 150.42/21.93 (7) all_58_4 = all_52_8 % 150.42/21.93 (8) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 150.42/21.93 (9) all_54_15 = all_4_2 % 150.42/21.93 (10) ~ (all_52_14 = e2) % 150.42/21.93 (11) all_56_1 = all_10_2 % 150.42/21.93 (12) all_56_27 = all_52_7 % 150.42/21.93 (13) all_54_1 = all_52_4 % 150.42/21.93 (14) ~ (all_52_13 = e2) % 150.42/21.93 (15) all_58_9 = all_52_12 % 150.42/21.93 (16) ~ (all_52_4 = e1) % 150.42/21.93 (17) ~ (all_56_1 = e1) | all_56_5 = e3 % 150.42/21.93 (18) all_58_1 = all_52_4 % 150.42/21.93 (19) all_58_13 = all_52_7 % 150.42/21.93 (20) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0 % 150.42/21.93 (21) all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1 % 150.42/21.93 (22) all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2 % 150.42/21.93 (23) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 150.42/21.93 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 150.42/21.93 (24) all_56_7 = all_52_12 % 150.42/21.93 (25) ~ (all_10_1 = e2) % 150.42/21.93 (26) ~ (all_52_4 = e0) % 150.42/21.93 (27) ~ (all_4_2 = e1) % 150.42/21.93 (28) ~ (all_56_1 = e0) | all_56_7 = e3 % 150.42/21.93 (29) all_56_5 = all_52_8 % 150.42/21.93 (30) ~ (e2 = e1) % 150.42/21.93 (31) all_56_31 = all_4_2 % 150.42/21.93 (32) all_58_11 = all_52_14 % 150.42/21.93 (33) all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3 % 150.42/21.93 (34) ~ (all_52_2 = e2) % 150.42/21.93 (35) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0 % 150.42/21.93 (36) ~ (all_52_4 = e2) % 150.42/21.93 (37) ~ (all_52_7 = e1) % 150.42/21.93 (38) ~ (all_52_8 = all_52_11) % 150.42/21.93 (39) all_54_2 = all_52_8 % 150.42/21.93 (40) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0 % 150.42/21.93 (41) all_58_15 = all_4_2 % 150.42/21.93 (42) all_58_2 = all_52_1 % 150.42/21.93 (43) ~ (all_4_2 = e3) % 150.42/21.93 (44) all_58_10 = all_52_13 % 150.42/21.93 (45) ~ (all_52_12 = all_4_2) % 150.42/21.93 (46) op(all_10_2, all_10_2) = all_10_1 % 150.42/21.93 (47) all_58_0 = all_10_2 % 150.42/21.93 (48) all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1 % 150.42/21.93 (49) ~ (all_56_31 = e2) | all_56_27 = e0 % 150.42/21.93 (50) ~ (all_52_4 = all_52_12) % 150.42/21.93 (51) ~ (all_52_8 = all_52_12) % 150.42/21.93 (52) ~ (all_52_4 = all_10_2) % 150.42/21.93 (53) all_58_14 = all_52_11 % 150.42/21.93 (54) ~ (all_52_1 = e2) % 150.42/21.93 (55) ~ (all_52_12 = all_10_2) % 150.42/21.93 (56) all_58_12 = all_52_3 % 150.42/21.93 (57) all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2 % 150.42/21.93 % 150.42/21.93 Begin of proof % 150.42/21.93 | % 150.42/21.93 | BETA: splitting (33) gives: % 150.42/21.93 | % 150.42/21.93 | Case 1: % 150.42/21.93 | | % 150.42/21.93 | | (58) all_58_1 = e3 % 150.42/21.93 | | % 150.42/21.93 | | COMBINE_EQS: (18), (58) imply: % 150.42/21.93 | | (59) all_52_4 = e3 % 150.42/21.93 | | % 150.42/21.93 | | REDUCE: (1), (59) imply: % 150.42/21.93 | | (60) ~ (all_52_8 = e3) % 150.42/21.93 | | % 150.42/21.93 | | SIMP: (60) implies: % 150.42/21.93 | | (61) ~ (all_52_8 = e3) % 150.42/21.93 | | % 150.42/21.93 | | REDUCE: (50), (59) imply: % 150.42/21.93 | | (62) ~ (all_52_12 = e3) % 150.42/21.93 | | % 150.42/21.93 | | SIMP: (62) implies: % 150.42/21.93 | | (63) ~ (all_52_12 = e3) % 150.42/21.93 | | % 150.42/21.93 | | BETA: splitting (28) gives: % 150.42/21.93 | | % 150.42/21.93 | | Case 1: % 150.42/21.93 | | | % 150.42/21.93 | | | (64) ~ (all_56_1 = e0) % 150.42/21.93 | | | % 150.42/21.93 | | | REDUCE: (11), (64) imply: % 150.42/21.93 | | | (65) ~ (all_10_2 = e0) % 150.42/21.93 | | | % 150.42/21.93 | | | BETA: splitting (17) gives: % 150.42/21.93 | | | % 150.42/21.93 | | | Case 1: % 150.42/21.93 | | | | % 150.42/21.93 | | | | (66) ~ (all_56_1 = e1) % 150.42/21.93 | | | | % 150.42/21.93 | | | | REDUCE: (11), (66) imply: % 150.42/21.93 | | | | (67) ~ (all_10_2 = e1) % 150.42/21.93 | | | | % 150.42/21.93 | | | | BETA: splitting (49) gives: % 150.42/21.93 | | | | % 150.42/21.93 | | | | Case 1: % 150.42/21.93 | | | | | % 150.42/21.93 | | | | | (68) ~ (all_56_31 = e2) % 150.42/21.93 | | | | | % 150.42/21.93 | | | | | REDUCE: (31), (68) imply: % 150.42/21.93 | | | | | (69) ~ (all_4_2 = e2) % 150.42/21.93 | | | | | % 150.42/21.93 | | | | | REF_CLOSE: (1), (2), (4), (5), (7), (8), (9), (10), (13), (14), (15), % 150.42/21.93 | | | | | (16), (18), (19), (20), (21), (22), (27), (30), (32), (34), % 150.42/21.93 | | | | | (35), (37), (38), (39), (40), (41), (42), (43), (44), (45), % 150.42/21.93 | | | | | (47), (48), (50), (51), (52), (53), (54), (55), (56), (57), % 150.42/21.93 | | | | | (65), (67), (69) are inconsistent by sub-proof #692. % 150.42/21.93 | | | | | % 150.42/21.93 | | | | Case 2: % 150.42/21.93 | | | | | % 150.42/21.93 | | | | | (70) all_56_27 = e0 % 150.42/21.93 | | | | | % 150.42/21.93 | | | | | COMBINE_EQS: (12), (70) imply: % 150.42/21.93 | | | | | (71) all_52_7 = e0 % 150.42/21.93 | | | | | % 150.42/21.93 | | | | | SIMP: (71) implies: % 150.42/21.93 | | | | | (72) all_52_7 = e0 % 150.42/21.93 | | | | | % 150.42/21.93 | | | | | BETA: splitting (40) gives: % 150.42/21.93 | | | | | % 150.42/21.93 | | | | | Case 1: % 150.42/21.93 | | | | | | % 150.42/21.93 | | | | | | (73) all_54_1 = e3 % 150.42/21.93 | | | | | | % 150.42/21.93 | | | | | | REDUCE: (52), (59) imply: % 150.42/21.93 | | | | | | (74) ~ (all_10_2 = e3) % 150.42/21.93 | | | | | | % 150.42/21.93 | | | | | | SIMP: (74) implies: % 150.42/21.93 | | | | | | (75) ~ (all_10_2 = e3) % 150.42/21.93 | | | | | | % 150.42/21.93 | | | | | | BETA: splitting (22) gives: % 150.42/21.93 | | | | | | % 150.42/21.93 | | | | | | Case 1: % 150.42/21.93 | | | | | | | % 150.42/21.93 | | | | | | | (76) all_58_0 = e2 % 150.42/21.93 | | | | | | | % 150.42/21.93 | | | | | | | COMBINE_EQS: (47), (76) imply: % 150.42/21.93 | | | | | | | (77) all_10_2 = e2 % 150.42/21.93 | | | | | | | % 150.42/21.93 | | | | | | | REDUCE: (46), (77) imply: % 150.42/21.93 | | | | | | | (78) op(e2, e2) = all_10_1 % 150.42/21.93 | | | | | | | % 150.42/21.93 | | | | | | | GROUND_INST: instantiating (23) with e2, all_10_1, e2, e2, % 150.42/21.93 | | | | | | | simplifying with (3), (78) gives: % 150.42/21.93 | | | | | | | (79) all_10_1 = e2 % 150.42/21.93 | | | | | | | % 150.42/21.93 | | | | | | | REDUCE: (25), (79) imply: % 150.42/21.93 | | | | | | | (80) $false % 150.42/21.93 | | | | | | | % 150.42/21.93 | | | | | | | CLOSE: (80) is inconsistent. % 150.42/21.93 | | | | | | | % 150.42/21.93 | | | | | | Case 2: % 150.42/21.93 | | | | | | | % 150.42/21.93 | | | | | | | (81) ~ (all_58_0 = e2) % 150.42/21.93 | | | | | | | % 150.42/21.93 | | | | | | | REDUCE: (47), (81) imply: % 150.42/21.93 | | | | | | | (82) ~ (all_10_2 = e2) % 150.42/21.93 | | | | | | | % 150.42/21.93 | | | | | | | REF_CLOSE: (5), (8), (65), (67), (75), (82) are inconsistent by % 150.42/21.93 | | | | | | | sub-proof #708. % 150.42/21.93 | | | | | | | % 150.42/21.93 | | | | | | End of split % 150.42/21.93 | | | | | | % 150.42/21.93 | | | | | Case 2: % 150.42/21.93 | | | | | | % 150.42/21.93 | | | | | | (83) all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0 % 150.42/21.93 | | | | | | % 150.42/21.93 | | | | | | REF_CLOSE: (13), (16), (26), (36), (83) are inconsistent by % 150.42/21.93 | | | | | | sub-proof #718. % 150.42/21.93 | | | | | | % 150.42/21.93 | | | | | End of split % 150.42/21.93 | | | | | % 150.42/21.93 | | | | End of split % 150.42/21.93 | | | | % 150.42/21.93 | | | Case 2: % 150.42/21.93 | | | | % 150.42/21.93 | | | | (84) all_56_5 = e3 % 150.42/21.93 | | | | % 150.42/21.93 | | | | REF_CLOSE: (29), (61), (84) are inconsistent by sub-proof #481. % 150.42/21.93 | | | | % 150.42/21.93 | | | End of split % 150.42/21.93 | | | % 150.42/21.93 | | Case 2: % 150.42/21.93 | | | % 150.42/21.93 | | | (85) all_56_7 = e3 % 150.42/21.93 | | | % 150.42/21.93 | | | REF_CLOSE: (24), (63), (85) are inconsistent by sub-proof #691. % 150.42/21.93 | | | % 150.42/21.93 | | End of split % 150.42/21.93 | | % 150.42/21.93 | Case 2: % 150.42/21.93 | | % 150.42/21.93 | | (86) ~ (all_58_1 = e3) % 150.42/21.93 | | % 150.42/21.93 | | REDUCE: (18), (86) imply: % 150.42/21.93 | | (87) ~ (all_52_4 = e3) % 150.42/21.93 | | % 150.42/21.93 | | REF_CLOSE: (13), (16), (26), (36), (40), (87) are inconsistent by sub-proof % 150.42/21.93 | | #717. % 150.42/21.93 | | % 150.42/21.93 | End of split % 150.42/21.93 | % 150.42/21.93 End of proof % 150.42/21.93 % 150.42/21.93 Sub-proof #73 shows that the following formulas are inconsistent: % 150.42/21.93 ---------------------------------------------------------------- % 150.42/21.93 (1) all_54_0 = all_10_2 % 150.42/21.93 (2) all_54_4 = all_52_1 % 150.42/21.93 (3) ~ (all_52_1 = e1) % 150.42/21.93 (4) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 150.42/21.93 (5) ~ (all_10_2 = e2) % 150.42/21.93 (6) ~ (all_58_0 = e1) % 150.42/21.93 (7) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0 % 150.42/21.93 (8) ~ (all_52_2 = e1) % 150.42/21.93 (9) ~ (all_52_2 = e2) % 150.42/21.93 (10) all_54_8 = all_52_2 % 150.42/21.93 (11) ~ (all_10_2 = e0) % 150.42/21.93 (12) all_58_0 = all_10_2 % 150.42/21.93 (13) ~ (all_52_1 = all_52_2) % 150.42/21.93 (14) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0 % 150.42/21.93 (15) ~ (all_52_2 = all_10_2) % 150.42/21.93 (16) ~ (all_52_1 = e2) % 150.42/21.93 (17) ~ (all_52_1 = all_10_2) % 150.42/21.93 % 150.42/21.93 Begin of proof % 150.42/21.93 | % 150.42/21.93 | REDUCE: (6), (12) imply: % 150.42/21.93 | (18) ~ (all_10_2 = e1) % 150.42/21.93 | % 150.42/21.93 | BETA: splitting (4) gives: % 150.42/21.93 | % 150.42/21.93 | Case 1: % 150.42/21.93 | | % 150.42/21.93 | | (19) all_54_0 = e3 % 150.42/21.93 | | % 150.42/21.93 | | COMBINE_EQS: (1), (19) imply: % 150.42/21.93 | | (20) all_10_2 = e3 % 150.42/21.93 | | % 150.42/21.93 | | SIMP: (20) implies: % 150.42/21.93 | | (21) all_10_2 = e3 % 150.42/21.93 | | % 150.42/21.93 | | REDUCE: (17), (21) imply: % 150.42/21.93 | | (22) ~ (all_52_1 = e3) % 150.42/21.93 | | % 150.42/21.93 | | REDUCE: (15), (21) imply: % 150.42/21.93 | | (23) ~ (all_52_2 = e3) % 150.42/21.93 | | % 150.42/21.93 | | BETA: splitting (14) gives: % 150.42/21.93 | | % 150.42/21.93 | | Case 1: % 150.42/21.93 | | | % 150.42/21.93 | | | (24) all_54_8 = e3 % 150.42/21.93 | | | % 150.42/21.93 | | | COMBINE_EQS: (10), (24) imply: % 150.42/21.93 | | | (25) all_52_2 = e3 % 150.42/21.93 | | | % 150.42/21.93 | | | REDUCE: (23), (25) imply: % 150.42/21.93 | | | (26) $false % 150.42/21.93 | | | % 150.42/21.93 | | | CLOSE: (26) is inconsistent. % 150.42/21.93 | | | % 150.42/21.93 | | Case 2: % 150.42/21.93 | | | % 150.42/21.93 | | | (27) all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0 % 150.42/21.93 | | | % 150.42/21.93 | | | REF_CLOSE: (2), (3), (7), (8), (9), (10), (13), (16), (22), (27) are % 150.42/21.93 | | | inconsistent by sub-proof #108. % 150.42/21.93 | | | % 150.42/21.93 | | End of split % 150.42/21.93 | | % 150.42/21.93 | Case 2: % 150.42/21.93 | | % 150.42/21.93 | | (28) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 150.42/21.93 | | % 150.42/21.93 | | REF_CLOSE: (1), (5), (11), (18), (28) are inconsistent by sub-proof #731. % 150.42/21.93 | | % 150.42/21.93 | End of split % 150.42/21.94 | % 150.42/21.94 End of proof % 150.42/21.94 % 150.42/21.94 Sub-proof #74 shows that the following formulas are inconsistent: % 150.42/21.94 ---------------------------------------------------------------- % 150.42/21.94 (1) all_56_11 = all_8_2 % 150.42/21.94 (2) all_58_6 = all_52_2 % 150.42/21.94 (3) ~ (e3 = e0) % 150.42/21.94 (4) all_54_10 = all_6_2 % 150.42/21.94 (5) ~ (all_52_14 = all_4_2) % 150.42/21.94 (6) all_54_12 = all_52_3 % 150.42/21.94 (7) op(e0, e0) = all_4_2 % 150.42/21.94 (8) all_58_6 = e0 | all_58_7 = e0 | all_58_8 = e0 | all_58_11 = e0 % 150.42/21.94 (9) all_54_15 = all_4_2 % 150.42/21.94 (10) all_54_9 = all_6_0 % 150.42/21.94 (11) all_56_21 = all_6_2 % 150.42/21.94 (12) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 150.42/21.94 (13) all_56_1 = all_10_2 % 150.42/21.94 (14) all_56_27 = all_52_7 % 150.42/21.94 (15) all_56_17 = all_52_2 % 150.42/21.94 (16) ~ (all_52_7 = all_6_0) % 150.42/21.94 (17) ~ (all_56_21 = e3) | all_56_17 = e1 % 150.42/21.94 (18) ~ (e1 = e0) % 150.42/21.94 (19) all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2 % 150.42/21.94 (20) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 150.42/21.94 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 150.42/21.94 (21) ~ (all_52_3 = all_10_2) % 150.42/21.94 (22) ~ (all_52_3 = all_52_7) % 150.42/21.94 (23) op(all_6_2, all_6_2) = e2 % 150.42/21.94 (24) ~ (all_6_0 = all_6_2) % 150.42/21.94 (25) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0 % 150.42/21.94 (26) ~ (all_4_2 = e1) % 150.42/21.94 (27) all_58_8 = all_6_2 % 150.42/21.94 (28) ~ (all_6_0 = e3) % 150.42/21.94 (29) ~ (all_6_0 = e0) | ~ (all_6_2 = e3) % 150.42/21.94 (30) ~ (all_52_3 = all_4_2) % 150.42/21.94 (31) all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3 % 150.42/21.94 (32) ~ (all_52_14 = all_6_0) % 150.42/21.94 (33) ~ (all_52_2 = all_52_3) % 150.42/21.94 (34) op(all_4_2, all_4_2) = all_4_1 % 150.42/21.94 (35) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0 % 150.42/21.94 (36) all_56_31 = all_4_2 % 150.42/21.94 (37) all_58_11 = all_52_14 % 150.42/21.94 (38) all_56_1 = e3 | all_56_11 = e2 | all_56_21 = e1 | all_56_31 = e0 % 150.42/21.94 (39) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0 % 150.42/21.94 (40) all_56_23 = all_52_14 % 150.42/21.94 (41) op(e1, e1) = all_6_2 % 150.42/21.94 (42) all_58_7 = all_6_0 % 150.42/21.94 (43) ~ (all_6_2 = e2) % 150.42/21.94 (44) ~ (all_4_2 = e3) % 150.42/21.94 (45) op(e1, all_6_2) = all_56_20 % 150.42/21.94 (46) ~ (all_56_31 = e2) | all_56_27 = e0 % 150.42/21.94 (47) ~ (e3 = e1) % 150.42/21.94 (48) ~ (all_52_2 = all_6_2) % 150.42/21.94 (49) ~ (all_56_21 = e0) | all_56_23 = e1 % 150.42/21.94 (50) op(e0, all_4_2) = all_56_30 % 150.42/21.94 (51) ~ (all_52_14 = all_6_2) % 150.42/21.94 (52) ~ (all_52_2 = all_10_2) % 150.42/21.94 (53) ~ (all_8_2 = all_6_0) % 150.42/21.94 % 150.42/21.94 Begin of proof % 150.42/21.94 | % 150.42/21.94 | BETA: splitting (49) gives: % 150.42/21.94 | % 150.42/21.94 | Case 1: % 150.42/21.94 | | % 150.42/21.94 | | (54) ~ (all_56_21 = e0) % 150.42/21.94 | | % 150.42/21.94 | | REDUCE: (11), (54) imply: % 150.42/21.94 | | (55) ~ (all_6_2 = e0) % 150.42/21.94 | | % 150.42/21.94 | | REF_CLOSE: (1), (2), (4), (5), (6), (8), (9), (11), (12), (13), (14), (15), % 150.42/21.94 | | (16), (17), (18), (19), (20), (21), (22), (23), (25), (26), (27), % 150.42/21.94 | | (29), (30), (33), (36), (37), (38), (39), (41), (42), (43), (44), % 150.42/21.94 | | (45), (46), (48), (53), (55) are inconsistent by sub-proof #76. % 150.42/21.94 | | % 150.42/21.94 | Case 2: % 150.42/21.94 | | % 150.42/21.94 | | (56) all_56_23 = e1 % 150.42/21.94 | | (57) all_56_21 = e0 % 150.42/21.94 | | % 150.42/21.94 | | COMBINE_EQS: (11), (57) imply: % 150.42/21.94 | | (58) all_6_2 = e0 % 150.42/21.94 | | % 150.42/21.94 | | SIMP: (58) implies: % 150.42/21.94 | | (59) all_6_2 = e0 % 150.42/21.94 | | % 150.42/21.94 | | COMBINE_EQS: (40), (56) imply: % 150.42/21.94 | | (60) all_52_14 = e1 % 150.42/21.94 | | % 150.42/21.94 | | SIMP: (60) implies: % 150.42/21.94 | | (61) all_52_14 = e1 % 150.42/21.94 | | % 150.42/21.94 | | COMBINE_EQS: (37), (61) imply: % 150.42/21.94 | | (62) all_58_11 = e1 % 150.42/21.94 | | % 150.42/21.94 | | COMBINE_EQS: (27), (59) imply: % 150.42/21.94 | | (63) all_58_8 = e0 % 150.42/21.94 | | % 150.42/21.94 | | REDUCE: (32), (61) imply: % 150.42/21.94 | | (64) ~ (all_6_0 = e1) % 150.42/21.94 | | % 150.42/21.94 | | SIMP: (64) implies: % 150.42/21.94 | | (65) ~ (all_6_0 = e1) % 150.42/21.94 | | % 150.42/21.94 | | REDUCE: (24), (59) imply: % 150.42/21.94 | | (66) ~ (all_6_0 = e0) % 150.42/21.94 | | % 150.42/21.94 | | REDUCE: (23), (59) imply: % 150.42/21.94 | | (67) op(e0, e0) = e2 % 150.42/21.94 | | % 150.42/21.94 | | REF_CLOSE: (1), (2), (3), (7), (10), (13), (18), (20), (28), (31), (34), % 150.42/21.94 | | (35), (36), (38), (42), (47), (50), (52), (53), (57), (62), (63), % 150.42/21.94 | | (65), (66), (67) are inconsistent by sub-proof #75. % 150.42/21.94 | | % 150.42/21.94 | End of split % 150.42/21.94 | % 150.42/21.94 End of proof % 150.42/21.94 % 150.42/21.94 Sub-proof #75 shows that the following formulas are inconsistent: % 150.42/21.94 ---------------------------------------------------------------- % 150.42/21.94 (1) all_56_11 = all_8_2 % 150.42/21.94 (2) all_58_6 = all_52_2 % 150.42/21.94 (3) ~ (e3 = e0) % 150.42/21.94 (4) op(e0, e0) = all_4_2 % 150.42/21.94 (5) all_54_9 = all_6_0 % 150.42/21.94 (6) all_56_1 = all_10_2 % 150.42/21.94 (7) all_56_21 = e0 % 150.42/21.94 (8) ~ (all_6_0 = e1) % 150.42/21.94 (9) ~ (e1 = e0) % 150.42/21.94 (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 150.42/21.94 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 150.42/21.94 (11) all_58_11 = e1 % 150.42/21.94 (12) ~ (all_6_0 = e3) % 150.42/21.94 (13) all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3 % 150.42/21.94 (14) all_58_8 = e0 % 150.42/21.94 (15) op(all_4_2, all_4_2) = all_4_1 % 150.42/21.94 (16) op(e0, e0) = e2 % 150.42/21.94 (17) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0 % 150.42/21.94 (18) all_56_31 = all_4_2 % 150.42/21.94 (19) all_56_1 = e3 | all_56_11 = e2 | all_56_21 = e1 | all_56_31 = e0 % 150.42/21.94 (20) all_58_7 = all_6_0 % 150.42/21.94 (21) ~ (all_6_0 = e0) % 150.42/21.94 (22) ~ (e3 = e1) % 150.42/21.94 (23) op(e0, all_4_2) = all_56_30 % 150.42/21.94 (24) ~ (all_52_2 = all_10_2) % 150.42/21.94 (25) ~ (all_8_2 = all_6_0) % 150.42/21.94 % 150.42/21.94 Begin of proof % 150.42/21.94 | % 150.42/21.94 | BETA: splitting (17) gives: % 150.42/21.94 | % 150.42/21.94 | Case 1: % 150.42/21.94 | | % 150.42/21.94 | | (26) all_54_9 = e3 % 150.42/21.94 | | % 150.42/21.94 | | REF_CLOSE: (5), (12), (26) are inconsistent by sub-proof #88. % 150.42/21.94 | | % 150.42/21.94 | Case 2: % 150.42/21.94 | | % 150.42/21.94 | | (27) ~ (all_54_9 = e3) % 150.42/21.94 | | (28) all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0 % 150.42/21.94 | | % 150.42/21.94 | | BETA: splitting (13) gives: % 150.42/21.94 | | % 150.42/21.94 | | Case 1: % 150.42/21.94 | | | % 150.42/21.94 | | | (29) all_58_6 = e3 % 150.42/21.94 | | | % 150.42/21.94 | | | COMBINE_EQS: (2), (29) imply: % 150.42/21.94 | | | (30) all_52_2 = e3 % 150.42/21.94 | | | % 150.42/21.94 | | | SIMP: (30) implies: % 150.42/21.94 | | | (31) all_52_2 = e3 % 150.42/21.94 | | | % 150.42/21.94 | | | REDUCE: (24), (31) imply: % 150.42/21.94 | | | (32) ~ (all_10_2 = e3) % 150.42/21.94 | | | % 150.42/21.94 | | | SIMP: (32) implies: % 150.42/21.94 | | | (33) ~ (all_10_2 = e3) % 150.42/21.94 | | | % 150.42/21.94 | | | BETA: splitting (28) gives: % 150.42/21.94 | | | % 150.42/21.94 | | | Case 1: % 150.42/21.94 | | | | % 150.42/21.94 | | | | (34) all_54_9 = e2 % 150.42/21.94 | | | | % 150.42/21.94 | | | | COMBINE_EQS: (5), (34) imply: % 150.42/21.94 | | | | (35) all_6_0 = e2 % 150.42/21.94 | | | | % 150.42/21.94 | | | | SIMP: (35) implies: % 150.42/21.94 | | | | (36) all_6_0 = e2 % 150.42/21.94 | | | | % 150.42/21.94 | | | | REDUCE: (25), (36) imply: % 150.42/21.94 | | | | (37) ~ (all_8_2 = e2) % 150.42/21.94 | | | | % 150.42/21.94 | | | | REDUCE: (21), (36) imply: % 150.42/21.94 | | | | (38) ~ (e2 = e0) % 150.42/21.94 | | | | % 150.42/21.94 | | | | BETA: splitting (19) gives: % 150.42/21.94 | | | | % 150.42/21.94 | | | | Case 1: % 150.42/21.94 | | | | | % 150.42/21.94 | | | | | (39) all_56_1 = e3 % 150.42/21.94 | | | | | % 150.42/21.94 | | | | | COMBINE_EQS: (6), (39) imply: % 150.42/21.94 | | | | | (40) all_10_2 = e3 % 150.42/21.94 | | | | | % 150.42/21.94 | | | | | REDUCE: (33), (40) imply: % 150.42/21.94 | | | | | (41) $false % 150.42/21.94 | | | | | % 150.42/21.94 | | | | | CLOSE: (41) is inconsistent. % 150.42/21.94 | | | | | % 150.42/21.94 | | | | Case 2: % 150.42/21.94 | | | | | % 150.42/21.94 | | | | | (42) all_56_11 = e2 | all_56_21 = e1 | all_56_31 = e0 % 150.42/21.94 | | | | | % 150.42/21.94 | | | | | BETA: splitting (42) gives: % 150.42/21.94 | | | | | % 150.42/21.94 | | | | | Case 1: % 150.42/21.94 | | | | | | % 150.42/21.94 | | | | | | (43) all_56_11 = e2 % 150.42/21.94 | | | | | | % 150.42/21.94 | | | | | | COMBINE_EQS: (1), (43) imply: % 150.42/21.94 | | | | | | (44) all_8_2 = e2 % 150.42/21.94 | | | | | | % 150.42/21.94 | | | | | | REDUCE: (37), (44) imply: % 150.42/21.94 | | | | | | (45) $false % 150.42/21.94 | | | | | | % 150.42/21.94 | | | | | | CLOSE: (45) is inconsistent. % 150.42/21.94 | | | | | | % 150.42/21.94 | | | | | Case 2: % 150.42/21.94 | | | | | | % 150.42/21.94 | | | | | | (46) all_56_21 = e1 | all_56_31 = e0 % 150.42/21.94 | | | | | | % 150.42/21.94 | | | | | | REF_CLOSE: (4), (7), (9), (10), (15), (16), (18), (23), (38), (46) % 150.42/21.94 | | | | | | are inconsistent by sub-proof #86. % 150.42/21.94 | | | | | | % 150.42/21.94 | | | | | End of split % 150.42/21.94 | | | | | % 150.42/21.94 | | | | End of split % 150.42/21.94 | | | | % 150.42/21.94 | | | Case 2: % 150.42/21.94 | | | | % 150.42/21.94 | | | | (47) all_54_9 = e1 | all_54_9 = e0 % 150.42/21.94 | | | | % 150.42/21.94 | | | | REF_CLOSE: (5), (8), (21), (47) are inconsistent by sub-proof #81. % 150.42/21.94 | | | | % 150.42/21.94 | | | End of split % 150.42/21.94 | | | % 150.42/21.94 | | Case 2: % 150.42/21.94 | | | % 150.42/21.94 | | | (48) all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3 % 150.42/21.94 | | | % 150.42/21.94 | | | REF_CLOSE: (3), (11), (12), (14), (20), (22), (48) are inconsistent by % 150.42/21.94 | | | sub-proof #85. % 150.42/21.94 | | | % 150.42/21.94 | | End of split % 150.42/21.94 | | % 150.42/21.94 | End of split % 150.42/21.94 | % 150.42/21.94 End of proof % 150.42/21.94 % 150.42/21.94 Sub-proof #76 shows that the following formulas are inconsistent: % 150.42/21.94 ---------------------------------------------------------------- % 150.42/21.94 (1) all_56_11 = all_8_2 % 150.42/21.94 (2) all_58_6 = all_52_2 % 150.42/21.94 (3) all_54_10 = all_6_2 % 150.42/21.94 (4) ~ (all_52_14 = all_4_2) % 150.42/21.94 (5) all_54_12 = all_52_3 % 150.42/21.94 (6) all_58_6 = e0 | all_58_7 = e0 | all_58_8 = e0 | all_58_11 = e0 % 150.42/21.94 (7) all_54_15 = all_4_2 % 150.42/21.94 (8) all_56_21 = all_6_2 % 150.42/21.94 (9) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 150.42/21.94 (10) all_56_1 = all_10_2 % 150.42/21.94 (11) all_56_27 = all_52_7 % 150.42/21.94 (12) all_56_17 = all_52_2 % 150.42/21.94 (13) ~ (all_52_7 = all_6_0) % 150.42/21.94 (14) ~ (all_56_21 = e3) | all_56_17 = e1 % 150.42/21.94 (15) ~ (e1 = e0) % 150.42/21.94 (16) all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2 % 150.42/21.94 (17) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 150.42/21.94 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 150.42/21.94 (18) ~ (all_52_3 = all_10_2) % 150.42/21.94 (19) ~ (all_52_3 = all_52_7) % 150.42/21.94 (20) ~ (all_6_2 = e0) % 150.42/21.94 (21) op(all_6_2, all_6_2) = e2 % 150.42/21.94 (22) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0 % 150.42/21.94 (23) ~ (all_4_2 = e1) % 150.42/21.94 (24) all_58_8 = all_6_2 % 150.42/21.94 (25) ~ (all_6_0 = e0) | ~ (all_6_2 = e3) % 150.42/21.94 (26) ~ (all_52_3 = all_4_2) % 150.42/21.94 (27) ~ (all_52_2 = all_52_3) % 150.42/21.94 (28) all_56_31 = all_4_2 % 150.42/21.94 (29) all_58_11 = all_52_14 % 150.42/21.94 (30) all_56_1 = e3 | all_56_11 = e2 | all_56_21 = e1 | all_56_31 = e0 % 150.42/21.94 (31) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0 % 150.42/21.94 (32) op(e1, e1) = all_6_2 % 150.42/21.94 (33) all_58_7 = all_6_0 % 150.42/21.94 (34) ~ (all_6_2 = e2) % 150.42/21.94 (35) ~ (all_4_2 = e3) % 150.42/21.94 (36) op(e1, all_6_2) = all_56_20 % 150.42/21.94 (37) ~ (all_56_31 = e2) | all_56_27 = e0 % 150.42/21.94 (38) ~ (all_52_2 = all_6_2) % 150.42/21.94 (39) ~ (all_8_2 = all_6_0) % 150.42/21.94 % 150.42/21.94 Begin of proof % 150.42/21.94 | % 150.42/21.94 | BETA: splitting (14) gives: % 150.42/21.94 | % 150.42/21.94 | Case 1: % 150.42/21.94 | | % 150.42/21.94 | | (40) ~ (all_56_21 = e3) % 150.42/21.94 | | % 150.42/21.94 | | REDUCE: (8), (40) imply: % 150.42/21.94 | | (41) ~ (all_6_2 = e3) % 150.42/21.94 | | % 150.42/21.94 | | REF_CLOSE: (3), (9), (17), (20), (21), (32), (34), (36), (41) are % 150.42/21.94 | | inconsistent by sub-proof #89. % 150.42/21.94 | | % 150.42/21.94 | Case 2: % 150.42/21.94 | | % 150.42/21.94 | | (42) all_56_21 = e3 % 150.42/21.94 | | (43) all_56_17 = e1 % 150.42/21.94 | | % 150.42/21.94 | | COMBINE_EQS: (12), (43) imply: % 150.42/21.94 | | (44) all_52_2 = e1 % 150.42/21.94 | | % 150.42/21.94 | | COMBINE_EQS: (8), (42) imply: % 150.42/21.94 | | (45) all_6_2 = e3 % 150.42/21.94 | | % 150.42/21.94 | | SIMP: (45) implies: % 150.42/21.94 | | (46) all_6_2 = e3 % 150.42/21.94 | | % 150.42/21.94 | | COMBINE_EQS: (24), (46) imply: % 150.42/21.94 | | (47) all_58_8 = e3 % 150.42/21.94 | | % 150.42/21.94 | | COMBINE_EQS: (2), (44) imply: % 150.42/21.94 | | (48) all_58_6 = e1 % 150.42/21.94 | | % 150.42/21.94 | | REDUCE: (27), (44) imply: % 150.42/21.94 | | (49) ~ (all_52_3 = e1) % 150.42/21.94 | | % 150.42/21.94 | | SIMP: (49) implies: % 150.42/21.94 | | (50) ~ (all_52_3 = e1) % 150.42/21.94 | | % 150.42/21.94 | | REDUCE: (38), (44), (46) imply: % 150.42/21.94 | | (51) ~ (e3 = e1) % 150.42/21.94 | | % 150.42/21.94 | | SIMP: (51) implies: % 150.42/21.94 | | (52) ~ (e3 = e1) % 150.42/21.94 | | % 150.42/21.94 | | REDUCE: (20), (46) imply: % 150.42/21.94 | | (53) ~ (e3 = e0) % 150.42/21.94 | | % 150.42/21.94 | | BETA: splitting (25) gives: % 150.42/21.94 | | % 150.42/21.94 | | Case 1: % 150.42/21.94 | | | % 150.42/21.94 | | | (54) ~ (all_6_2 = e3) % 150.42/21.94 | | | % 150.42/21.94 | | | REF_CLOSE: (3), (9), (17), (20), (21), (32), (34), (36), (54) are % 150.42/21.94 | | | inconsistent by sub-proof #77. % 150.42/21.94 | | | % 150.42/21.94 | | Case 2: % 150.42/21.94 | | | % 150.42/21.94 | | | (55) ~ (all_6_0 = e0) % 150.42/21.94 | | | % 150.42/21.94 | | | BETA: splitting (6) gives: % 150.42/21.94 | | | % 150.42/21.94 | | | Case 1: % 150.42/21.94 | | | | % 150.42/21.94 | | | | (56) all_58_6 = e0 % 150.42/21.94 | | | | % 150.42/21.94 | | | | REF_CLOSE: (15), (48), (56) are inconsistent by sub-proof #344. % 150.42/21.94 | | | | % 150.42/21.94 | | | Case 2: % 150.42/21.94 | | | | % 150.42/21.94 | | | | (57) all_58_7 = e0 | all_58_8 = e0 | all_58_11 = e0 % 150.42/21.94 | | | | % 150.42/21.94 | | | | BETA: splitting (57) gives: % 150.42/21.94 | | | | % 150.42/21.94 | | | | Case 1: % 150.42/21.94 | | | | | % 150.42/21.94 | | | | | (58) all_58_7 = e0 % 150.42/21.94 | | | | | % 150.42/21.94 | | | | | COMBINE_EQS: (33), (58) imply: % 150.42/21.94 | | | | | (59) all_6_0 = e0 % 150.42/21.94 | | | | | % 150.42/21.94 | | | | | REDUCE: (55), (59) imply: % 150.42/21.94 | | | | | (60) $false % 150.42/21.94 | | | | | % 150.42/21.94 | | | | | CLOSE: (60) is inconsistent. % 150.42/21.94 | | | | | % 150.42/21.94 | | | | Case 2: % 150.42/21.94 | | | | | % 150.42/21.94 | | | | | (61) all_58_8 = e0 | all_58_11 = e0 % 150.42/21.94 | | | | | % 150.42/21.94 | | | | | BETA: splitting (61) gives: % 150.42/21.94 | | | | | % 150.42/21.94 | | | | | Case 1: % 150.42/21.94 | | | | | | % 150.42/21.94 | | | | | | (62) all_58_8 = e0 % 150.42/21.94 | | | | | | % 150.42/21.94 | | | | | | COMBINE_EQS: (47), (62) imply: % 150.42/21.94 | | | | | | (63) e3 = e0 % 150.42/21.94 | | | | | | % 150.42/21.94 | | | | | | REDUCE: (53), (63) imply: % 150.42/21.94 | | | | | | (64) $false % 150.42/21.94 | | | | | | % 150.42/21.94 | | | | | | CLOSE: (64) is inconsistent. % 150.42/21.94 | | | | | | % 150.42/21.94 | | | | | Case 2: % 150.42/21.94 | | | | | | % 150.42/21.94 | | | | | | (65) all_58_11 = e0 % 150.42/21.94 | | | | | | % 150.42/21.94 | | | | | | COMBINE_EQS: (29), (65) imply: % 150.42/21.94 | | | | | | (66) all_52_14 = e0 % 150.42/21.94 | | | | | | % 150.42/21.94 | | | | | | REDUCE: (4), (66) imply: % 150.42/21.94 | | | | | | (67) ~ (all_4_2 = e0) % 150.42/21.94 | | | | | | % 150.42/21.94 | | | | | | SIMP: (67) implies: % 150.42/21.94 | | | | | | (68) ~ (all_4_2 = e0) % 150.42/21.94 | | | | | | % 150.42/21.94 | | | | | | BETA: splitting (31) gives: % 150.42/21.94 | | | | | | % 150.42/21.94 | | | | | | Case 1: % 150.42/21.94 | | | | | | | % 150.42/21.94 | | | | | | | (69) all_54_15 = e3 % 150.42/21.94 | | | | | | | % 150.42/21.94 | | | | | | | COMBINE_EQS: (7), (69) imply: % 150.42/21.94 | | | | | | | (70) all_4_2 = e3 % 150.42/21.94 | | | | | | | % 150.42/21.94 | | | | | | | REDUCE: (35), (70) imply: % 150.42/21.94 | | | | | | | (71) $false % 150.42/21.94 | | | | | | | % 150.42/21.94 | | | | | | | CLOSE: (71) is inconsistent. % 150.42/21.94 | | | | | | | % 150.42/21.94 | | | | | | Case 2: % 150.42/21.94 | | | | | | | % 150.42/21.94 | | | | | | | (72) ~ (all_54_15 = e3) % 150.42/21.94 | | | | | | | (73) all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0 % 150.42/21.94 | | | | | | | % 150.42/21.94 | | | | | | | BETA: splitting (73) gives: % 150.42/21.94 | | | | | | | % 150.42/21.94 | | | | | | | Case 1: % 150.42/21.94 | | | | | | | | % 150.42/21.94 | | | | | | | | (74) all_54_15 = e2 % 150.42/21.94 | | | | | | | | % 150.42/21.94 | | | | | | | | COMBINE_EQS: (7), (74) imply: % 150.42/21.94 | | | | | | | | (75) all_4_2 = e2 % 150.42/21.94 | | | | | | | | % 150.42/21.94 | | | | | | | | COMBINE_EQS: (28), (75) imply: % 150.42/21.94 | | | | | | | | (76) all_56_31 = e2 % 150.42/21.94 | | | | | | | | % 150.42/21.94 | | | | | | | | REDUCE: (26), (75) imply: % 150.42/21.94 | | | | | | | | (77) ~ (all_52_3 = e2) % 150.42/21.94 | | | | | | | | % 150.42/21.94 | | | | | | | | REDUCE: (35), (75) imply: % 150.42/21.94 | | | | | | | | (78) ~ (e3 = e2) % 150.42/21.94 | | | | | | | | % 150.42/21.94 | | | | | | | | SIMP: (78) implies: % 150.42/21.94 | | | | | | | | (79) ~ (e3 = e2) % 150.42/21.94 | | | | | | | | % 150.42/21.94 | | | | | | | | REDUCE: (23), (75) imply: % 150.42/21.94 | | | | | | | | (80) ~ (e2 = e1) % 150.42/21.94 | | | | | | | | % 150.42/21.94 | | | | | | | | REDUCE: (68), (75) imply: % 150.42/21.94 | | | | | | | | (81) ~ (e2 = e0) % 150.42/21.94 | | | | | | | | % 150.42/21.94 | | | | | | | | BETA: splitting (16) gives: % 150.42/21.94 | | | | | | | | % 150.42/21.94 | | | | | | | | Case 1: % 150.42/21.94 | | | | | | | | | % 150.42/21.94 | | | | | | | | | (82) all_58_6 = e2 % 150.42/21.94 | | | | | | | | | % 150.42/21.94 | | | | | | | | | COMBINE_EQS: (48), (82) imply: % 150.42/21.94 | | | | | | | | | (83) e2 = e1 % 150.42/21.94 | | | | | | | | | % 150.42/21.94 | | | | | | | | | REDUCE: (80), (83) imply: % 150.42/21.94 | | | | | | | | | (84) $false % 150.42/21.94 | | | | | | | | | % 150.42/21.94 | | | | | | | | | CLOSE: (84) is inconsistent. % 150.42/21.94 | | | | | | | | | % 150.42/21.94 | | | | | | | | Case 2: % 150.42/21.94 | | | | | | | | | % 150.42/21.94 | | | | | | | | | (85) all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2 % 150.42/21.94 | | | | | | | | | % 150.42/21.94 | | | | | | | | | BETA: splitting (85) gives: % 150.42/21.94 | | | | | | | | | % 150.42/21.94 | | | | | | | | | Case 1: % 150.42/21.94 | | | | | | | | | | % 150.42/21.94 | | | | | | | | | | (86) all_58_7 = e2 % 150.42/21.94 | | | | | | | | | | % 150.42/21.94 | | | | | | | | | | COMBINE_EQS: (33), (86) imply: % 150.42/21.94 | | | | | | | | | | (87) all_6_0 = e2 % 150.42/21.94 | | | | | | | | | | % 150.42/21.94 | | | | | | | | | | REDUCE: (13), (87) imply: % 150.42/21.94 | | | | | | | | | | (88) ~ (all_52_7 = e2) % 150.42/21.94 | | | | | | | | | | % 150.42/21.94 | | | | | | | | | | REDUCE: (39), (87) imply: % 150.42/21.94 | | | | | | | | | | (89) ~ (all_8_2 = e2) % 150.42/21.94 | | | | | | | | | | % 150.42/21.94 | | | | | | | | | | BETA: splitting (37) gives: % 150.42/21.94 | | | | | | | | | | % 150.42/21.94 | | | | | | | | | | Case 1: % 150.42/21.94 | | | | | | | | | | | % 150.42/21.94 | | | | | | | | | | | (90) ~ (all_56_31 = e2) % 150.42/21.94 | | | | | | | | | | | % 150.42/21.94 | | | | | | | | | | | REDUCE: (76), (90) imply: % 150.42/21.94 | | | | | | | | | | | (91) $false % 150.42/21.94 | | | | | | | | | | | % 150.42/21.94 | | | | | | | | | | | CLOSE: (91) is inconsistent. % 150.42/21.94 | | | | | | | | | | | % 150.42/21.94 | | | | | | | | | | Case 2: % 150.42/21.94 | | | | | | | | | | | % 150.42/21.94 | | | | | | | | | | | (92) all_56_27 = e0 % 150.42/21.94 | | | | | | | | | | | % 150.42/21.94 | | | | | | | | | | | COMBINE_EQS: (11), (92) imply: % 150.42/21.94 | | | | | | | | | | | (93) all_52_7 = e0 % 150.42/21.94 | | | | | | | | | | | % 150.42/21.94 | | | | | | | | | | | SIMP: (93) implies: % 150.42/21.94 | | | | | | | | | | | (94) all_52_7 = e0 % 150.42/21.94 | | | | | | | | | | | % 150.42/21.94 | | | | | | | | | | | REDUCE: (19), (94) imply: % 150.42/21.94 | | | | | | | | | | | (95) ~ (all_52_3 = e0) % 150.42/21.94 | | | | | | | | | | | % 150.42/21.94 | | | | | | | | | | | REDUCE: (88), (94) imply: % 150.42/21.94 | | | | | | | | | | | (96) ~ (e2 = e0) % 150.42/21.94 | | | | | | | | | | | % 150.42/21.94 | | | | | | | | | | | BETA: splitting (30) gives: % 150.42/21.94 | | | | | | | | | | | % 150.42/21.94 | | | | | | | | | | | Case 1: % 150.42/21.94 | | | | | | | | | | | | % 150.42/21.94 | | | | | | | | | | | | (97) all_56_1 = e3 % 150.42/21.94 | | | | | | | | | | | | % 150.42/21.94 | | | | | | | | | | | | COMBINE_EQS: (10), (97) imply: % 150.42/21.94 | | | | | | | | | | | | (98) all_10_2 = e3 % 150.42/21.94 | | | | | | | | | | | | % 150.42/21.94 | | | | | | | | | | | | REDUCE: (18), (98) imply: % 150.42/21.94 | | | | | | | | | | | | (99) ~ (all_52_3 = e3) % 150.42/21.94 | | | | | | | | | | | | % 150.42/21.94 | | | | | | | | | | | | BETA: splitting (22) gives: % 150.42/21.94 | | | | | | | | | | | | % 150.42/21.94 | | | | | | | | | | | | Case 1: % 150.42/21.94 | | | | | | | | | | | | | % 150.42/21.94 | | | | | | | | | | | | | (100) all_54_12 = e3 % 150.42/21.94 | | | | | | | | | | | | | % 150.42/21.94 | | | | | | | | | | | | | REF_CLOSE: (5), (99), (100) are inconsistent by sub-proof % 150.42/21.94 | | | | | | | | | | | | | #667. % 150.42/21.94 | | | | | | | | | | | | | % 150.42/21.94 | | | | | | | | | | | | Case 2: % 150.42/21.94 | | | | | | | | | | | | | % 150.42/21.94 | | | | | | | | | | | | | (101) all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0 % 150.42/21.94 | | | | | | | | | | | | | % 150.42/21.94 | | | | | | | | | | | | | REF_CLOSE: (5), (50), (77), (95), (101) are inconsistent by % 150.42/21.94 | | | | | | | | | | | | | sub-proof #615. % 150.42/21.94 | | | | | | | | | | | | | % 150.42/21.94 | | | | | | | | | | | | End of split % 150.42/21.94 | | | | | | | | | | | | % 150.42/21.94 | | | | | | | | | | | Case 2: % 150.42/21.94 | | | | | | | | | | | | % 150.42/21.94 | | | | | | | | | | | | (102) all_56_11 = e2 | all_56_21 = e1 | all_56_31 = e0 % 150.42/21.94 | | | | | | | | | | | | % 150.42/21.94 | | | | | | | | | | | | BETA: splitting (102) gives: % 150.42/21.94 | | | | | | | | | | | | % 150.42/21.94 | | | | | | | | | | | | Case 1: % 150.42/21.94 | | | | | | | | | | | | | % 150.42/21.94 | | | | | | | | | | | | | (103) all_56_11 = e2 % 150.42/21.94 | | | | | | | | | | | | | % 150.42/21.94 | | | | | | | | | | | | | COMBINE_EQS: (1), (103) imply: % 150.42/21.94 | | | | | | | | | | | | | (104) all_8_2 = e2 % 150.42/21.94 | | | | | | | | | | | | | % 150.42/21.94 | | | | | | | | | | | | | REDUCE: (89), (104) imply: % 150.42/21.94 | | | | | | | | | | | | | (105) $false % 150.42/21.94 | | | | | | | | | | | | | % 150.42/21.94 | | | | | | | | | | | | | CLOSE: (105) is inconsistent. % 150.42/21.94 | | | | | | | | | | | | | % 150.42/21.94 | | | | | | | | | | | | Case 2: % 150.42/21.94 | | | | | | | | | | | | | % 150.42/21.94 | | | | | | | | | | | | | (106) all_56_21 = e1 | all_56_31 = e0 % 150.42/21.94 | | | | | | | | | | | | | % 150.42/21.94 | | | | | | | | | | | | | BETA: splitting (106) gives: % 150.42/21.94 | | | | | | | | | | | | | % 150.42/21.94 | | | | | | | | | | | | | Case 1: % 150.42/21.94 | | | | | | | | | | | | | | % 150.42/21.94 | | | | | | | | | | | | | | (107) all_56_21 = e1 % 150.42/21.94 | | | | | | | | | | | | | | % 150.42/21.94 | | | | | | | | | | | | | | COMBINE_EQS: (42), (107) imply: % 150.42/21.94 | | | | | | | | | | | | | | (108) e3 = e1 % 150.42/21.94 | | | | | | | | | | | | | | % 150.42/21.94 | | | | | | | | | | | | | | REDUCE: (52), (108) imply: % 150.42/21.94 | | | | | | | | | | | | | | (109) $false % 150.42/21.94 | | | | | | | | | | | | | | % 150.42/21.94 | | | | | | | | | | | | | | CLOSE: (109) is inconsistent. % 150.42/21.94 | | | | | | | | | | | | | | % 150.42/21.94 | | | | | | | | | | | | | Case 2: % 150.42/21.94 | | | | | | | | | | | | | | % 150.42/21.94 | | | | | | | | | | | | | | (110) all_56_31 = e0 % 150.42/21.94 | | | | | | | | | | | | | | % 150.42/21.94 | | | | | | | | | | | | | | REF_CLOSE: (76), (81), (110) are inconsistent by sub-proof % 150.42/21.94 | | | | | | | | | | | | | | #166. % 150.42/21.94 | | | | | | | | | | | | | | % 150.42/21.94 | | | | | | | | | | | | | End of split % 150.42/21.94 | | | | | | | | | | | | | % 150.42/21.94 | | | | | | | | | | | | End of split % 150.42/21.94 | | | | | | | | | | | | % 150.42/21.94 | | | | | | | | | | | End of split % 150.42/21.94 | | | | | | | | | | | % 150.42/21.94 | | | | | | | | | | End of split % 150.42/21.94 | | | | | | | | | | % 150.42/21.94 | | | | | | | | | Case 2: % 150.42/21.94 | | | | | | | | | | % 150.42/21.94 | | | | | | | | | | (111) all_58_8 = e2 | all_58_11 = e2 % 150.42/21.94 | | | | | | | | | | % 150.42/21.94 | | | | | | | | | | BETA: splitting (111) gives: % 150.42/21.94 | | | | | | | | | | % 150.42/21.94 | | | | | | | | | | Case 1: % 150.42/21.94 | | | | | | | | | | | % 150.42/21.94 | | | | | | | | | | | (112) all_58_8 = e2 % 150.42/21.94 | | | | | | | | | | | % 150.42/21.94 | | | | | | | | | | | COMBINE_EQS: (47), (112) imply: % 150.42/21.94 | | | | | | | | | | | (113) e3 = e2 % 150.42/21.94 | | | | | | | | | | | % 150.42/21.94 | | | | | | | | | | | REDUCE: (79), (113) imply: % 150.42/21.94 | | | | | | | | | | | (114) $false % 150.42/21.94 | | | | | | | | | | | % 150.42/21.94 | | | | | | | | | | | CLOSE: (114) is inconsistent. % 150.42/21.94 | | | | | | | | | | | % 150.42/21.94 | | | | | | | | | | Case 2: % 150.42/21.94 | | | | | | | | | | | % 150.42/21.94 | | | | | | | | | | | (115) all_58_11 = e2 % 150.42/21.94 | | | | | | | | | | | % 150.42/21.94 | | | | | | | | | | | REF_CLOSE: (65), (81), (115) are inconsistent by sub-proof % 150.42/21.94 | | | | | | | | | | | #280. % 150.42/21.94 | | | | | | | | | | | % 150.42/21.94 | | | | | | | | | | End of split % 150.42/21.94 | | | | | | | | | | % 150.42/21.94 | | | | | | | | | End of split % 150.42/21.94 | | | | | | | | | % 150.42/21.94 | | | | | | | | End of split % 150.42/21.94 | | | | | | | | % 150.42/21.94 | | | | | | | Case 2: % 150.42/21.94 | | | | | | | | % 150.42/21.94 | | | | | | | | (116) all_54_15 = e1 | all_54_15 = e0 % 150.42/21.94 | | | | | | | | % 150.42/21.94 | | | | | | | | REF_CLOSE: (7), (23), (68), (116) are inconsistent by sub-proof % 150.42/21.94 | | | | | | | | #96. % 150.42/21.94 | | | | | | | | % 150.42/21.94 | | | | | | | End of split % 150.42/21.94 | | | | | | | % 150.42/21.94 | | | | | | End of split % 150.42/21.94 | | | | | | % 150.42/21.94 | | | | | End of split % 150.42/21.94 | | | | | % 150.42/21.94 | | | | End of split % 150.42/21.94 | | | | % 150.42/21.94 | | | End of split % 150.42/21.94 | | | % 150.42/21.94 | | End of split % 150.42/21.94 | | % 150.42/21.94 | End of split % 150.42/21.94 | % 150.42/21.94 End of proof % 150.42/21.94 % 150.42/21.94 Sub-proof #77 shows that the following formulas are inconsistent: % 150.42/21.94 ---------------------------------------------------------------- % 150.42/21.94 (1) all_54_10 = all_6_2 % 150.42/21.94 (2) ~ (all_6_2 = e3) % 150.42/21.94 (3) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 150.42/21.94 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 150.42/21.94 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 150.42/21.94 (5) ~ (all_6_2 = e0) % 150.42/21.94 (6) op(all_6_2, all_6_2) = e2 % 150.42/21.94 (7) op(e1, e1) = all_6_2 % 150.42/21.94 (8) ~ (all_6_2 = e2) % 150.42/21.94 (9) op(e1, all_6_2) = all_56_20 % 150.42/21.94 % 150.42/21.94 Begin of proof % 150.42/21.94 | % 150.42/21.94 | BETA: splitting (3) gives: % 150.42/21.94 | % 150.42/21.94 | Case 1: % 150.42/21.94 | | % 150.42/21.94 | | (10) all_54_10 = e3 % 150.42/21.94 | | % 150.42/21.94 | | REF_CLOSE: (1), (2), (10) are inconsistent by sub-proof #736. % 150.42/21.94 | | % 150.42/21.94 | Case 2: % 150.42/21.94 | | % 150.42/21.94 | | (11) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 150.42/21.94 | | % 150.42/21.94 | | REF_CLOSE: (1), (4), (5), (6), (7), (8), (9), (11) are inconsistent by % 150.42/21.94 | | sub-proof #90. % 150.42/21.94 | | % 150.42/21.94 | End of split % 150.42/21.94 | % 150.42/21.94 End of proof % 150.42/21.94 % 150.42/21.94 Sub-proof #78 shows that the following formulas are inconsistent: % 150.42/21.94 ---------------------------------------------------------------- % 150.42/21.94 (1) all_56_11 = all_8_2 % 150.42/21.94 (2) ~ (all_56_11 = e1) | all_56_13 = e2 % 150.42/21.94 (3) ~ (all_52_11 = all_6_2) % 150.42/21.94 (4) ~ (all_52_4 = all_52_8) % 150.42/21.94 (5) op(e2, all_8_1) = all_8_0 % 150.42/21.94 (6) all_58_6 = all_52_2 % 150.42/21.94 (7) ~ (all_8_1 = e1) % 150.42/21.94 (8) ~ (all_52_1 = all_52_9) % 150.42/21.94 (9) all_54_10 = all_6_2 % 150.42/21.94 (10) all_54_0 = all_10_2 % 150.42/21.94 (11) ~ (all_52_14 = all_4_2) % 150.42/21.94 (12) ~ (all_8_0 = e1) % 150.42/21.94 (13) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0 % 150.42/21.94 (14) all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2 % 150.42/21.94 (15) ~ (all_52_9 = all_8_2) % 150.42/21.94 (16) all_54_12 = all_52_3 % 150.42/21.94 (17) ~ (all_52_12 = all_52_13) % 150.42/21.94 (18) ~ (all_8_1 = e3) % 150.42/21.94 (19) op(e0, e0) = all_4_2 % 150.42/21.94 (20) all_58_4 = all_52_8 % 150.42/21.94 (21) all_54_5 = all_8_2 % 150.42/21.94 (22) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 150.42/21.94 (23) all_54_15 = all_4_2 % 150.42/21.94 (24) all_54_9 = all_6_0 % 150.42/21.94 (25) ~ (all_10_1 = e1) % 150.42/21.94 (26) all_56_21 = all_6_2 % 150.57/21.94 (27) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 150.57/21.94 (28) all_56_1 = all_10_2 % 150.57/21.94 (29) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0 % 150.57/21.94 (30) all_58_5 = all_52_9 % 150.57/21.94 (31) all_54_1 = all_52_4 % 150.57/21.94 (32) all_56_17 = all_52_2 % 150.57/21.94 (33) all_58_1 = all_52_4 % 150.57/21.94 (34) all_58_13 = all_52_7 % 150.57/21.94 (35) op(e3, e3) = all_10_2 % 150.57/21.94 (36) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0 % 150.57/21.94 (37) all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1 % 150.57/21.94 (38) ~ (all_56_21 = e3) | all_56_17 = e1 % 150.57/21.94 (39) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 150.57/21.94 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 150.57/21.94 (40) ~ (all_52_3 = all_10_2) % 150.57/21.94 (41) ~ (all_52_3 = all_52_7) % 150.57/21.94 (42) ~ (all_56_11 = e3) | all_56_9 = e2 % 150.57/21.94 (43) all_56_7 = all_52_12 % 150.57/21.94 (44) ~ (all_10_1 = e2) % 150.57/21.94 (45) op(all_6_2, all_6_2) = e2 % 150.57/21.94 (46) ~ (all_6_0 = all_6_2) % 150.57/21.95 (47) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0 % 150.57/21.95 (48) all_56_13 = all_52_9 % 150.57/21.95 (49) ~ (all_52_1 = all_52_13) % 150.57/21.95 (50) all_58_8 = all_6_2 % 150.57/21.95 (51) ~ (all_6_0 = e3) % 150.57/21.95 (52) ~ (all_6_0 = e0) | ~ (all_6_2 = e3) % 150.57/21.95 (53) ~ (all_52_8 = all_10_2) % 150.57/21.95 (54) all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3 % 150.57/21.95 (55) ~ (all_56_1 = e0) | all_56_7 = e3 % 150.57/21.95 (56) ~ (all_52_14 = all_6_0) % 150.57/21.95 (57) ~ (all_52_2 = all_52_3) % 150.57/21.95 (58) op(all_4_2, all_4_2) = all_4_1 % 150.57/21.95 (59) all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3 % 150.57/21.95 (60) all_58_3 = all_8_2 % 150.57/21.95 (61) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0 % 150.57/21.95 (62) ~ (all_52_11 = all_4_2) % 150.57/21.95 (63) ~ (all_52_1 = all_52_3) % 150.57/21.95 (64) all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1 % 150.57/21.95 (65) all_56_31 = all_4_2 % 150.57/21.95 (66) all_58_11 = all_52_14 % 150.57/21.95 (67) ~ (all_52_2 = all_52_14) % 150.57/21.95 (68) all_54_7 = all_52_13 % 150.57/21.95 (69) all_56_1 = e3 | all_56_11 = e2 | all_56_21 = e1 | all_56_31 = e0 % 150.57/21.95 (70) ~ (all_52_13 = all_4_2) % 150.57/21.95 (71) ~ (all_52_2 = all_6_0) % 150.57/21.95 (72) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0 % 150.57/21.95 (73) ~ (all_56_11 = e0) % 150.57/21.95 (74) ~ (all_52_8 = all_52_11) % 150.57/21.95 (75) all_54_2 = all_52_8 % 150.57/21.95 (76) all_56_23 = all_52_14 % 150.57/21.95 (77) op(e1, e1) = all_6_2 % 150.57/21.95 (78) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0 % 150.57/21.95 (79) all_58_7 = all_6_0 % 150.57/21.95 (80) ~ (all_6_2 = e2) % 150.57/21.95 (81) ~ (all_52_9 = all_6_2) % 150.57/21.95 (82) op(all_10_2, all_10_2) = all_10_1 % 150.57/21.95 (83) all_58_0 = all_10_2 % 150.57/21.95 (84) op(e1, all_6_2) = all_56_20 % 150.57/21.95 (85) ~ (e3 = e1) % 150.57/21.95 (86) ~ (all_52_4 = all_52_12) % 150.57/21.95 (87) op(e2, e0) = all_52_13 % 150.57/21.95 (88) ~ (all_52_2 = all_6_2) % 150.57/21.95 (89) ~ (all_52_8 = all_52_12) % 150.57/21.95 (90) ~ (all_56_21 = e0) | all_56_23 = e1 % 150.57/21.95 (91) op(e0, all_4_2) = all_56_30 % 150.57/21.95 (92) op(e3, all_10_2) = all_56_0 % 150.57/21.95 (93) ~ (all_52_14 = all_6_2) % 150.57/21.95 (94) ~ (all_52_2 = all_10_2) % 150.57/21.95 (95) ~ (all_8_2 = all_6_0) % 150.57/21.95 (96) ~ (all_52_4 = all_10_2) % 150.57/21.95 (97) op(all_8_2, all_8_2) = all_8_1 % 150.57/21.95 (98) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 150.57/21.95 (99) all_58_14 = all_52_11 % 150.57/21.95 (100) ~ (all_52_12 = all_10_2) % 150.57/21.95 (101) all_56_9 = all_52_1 % 150.57/21.95 (102) ~ (all_52_1 = all_10_2) % 150.57/21.95 (103) all_54_11 = all_52_14 % 150.57/21.95 % 150.57/21.95 Begin of proof % 150.57/21.95 | % 150.57/21.95 | REDUCE: (1), (73) imply: % 150.57/21.95 | (104) ~ (all_8_2 = e0) % 150.57/21.95 | % 150.57/21.95 | BETA: splitting (38) gives: % 150.57/21.95 | % 150.57/21.95 | Case 1: % 150.57/21.95 | | % 150.57/21.95 | | (105) ~ (all_56_21 = e3) % 150.57/21.95 | | % 150.57/21.95 | | REDUCE: (26), (105) imply: % 150.57/21.95 | | (106) ~ (all_6_2 = e3) % 150.57/21.95 | | % 150.57/21.95 | | BETA: splitting (42) gives: % 150.57/21.95 | | % 150.57/21.95 | | Case 1: % 150.57/21.95 | | | % 150.57/21.95 | | | (107) ~ (all_56_11 = e3) % 150.57/21.95 | | | % 150.57/21.95 | | | REDUCE: (1), (107) imply: % 150.57/21.95 | | | (108) ~ (all_8_2 = e3) % 150.57/21.95 | | | % 150.57/21.95 | | | REF_CLOSE: (1), (2), (6), (7), (9), (15), (18), (19), (21), (24), (26), % 150.57/21.95 | | | (27), (28), (39), (45), (46), (48), (50), (51), (54), (56), % 150.57/21.95 | | | (58), (61), (65), (66), (69), (76), (77), (79), (80), (81), % 150.57/21.95 | | | (84), (90), (91), (93), (94), (95), (97), (98), (104), (106), % 150.57/21.95 | | | (108) are inconsistent by sub-proof #84. % 150.57/21.95 | | | % 150.57/21.95 | | Case 2: % 150.57/21.95 | | | % 150.57/21.95 | | | (109) all_56_11 = e3 % 150.57/21.95 | | | (110) all_56_9 = e2 % 150.57/21.95 | | | % 150.57/21.95 | | | COMBINE_EQS: (101), (110) imply: % 150.57/21.95 | | | (111) all_52_1 = e2 % 150.57/21.95 | | | % 150.57/21.95 | | | COMBINE_EQS: (1), (109) imply: % 150.57/21.95 | | | (112) all_8_2 = e3 % 150.57/21.95 | | | % 150.57/21.95 | | | COMBINE_EQS: (60), (112) imply: % 150.57/21.95 | | | (113) all_58_3 = e3 % 150.57/21.95 | | | % 150.57/21.95 | | | REDUCE: (63), (111) imply: % 150.57/21.95 | | | (114) ~ (all_52_3 = e2) % 150.57/21.95 | | | % 150.57/21.95 | | | SIMP: (114) implies: % 150.57/21.95 | | | (115) ~ (all_52_3 = e2) % 150.57/21.95 | | | % 150.57/21.95 | | | REDUCE: (8), (111) imply: % 150.57/21.95 | | | (116) ~ (all_52_9 = e2) % 150.57/21.95 | | | % 150.57/21.95 | | | SIMP: (116) implies: % 150.57/21.95 | | | (117) ~ (all_52_9 = e2) % 150.57/21.95 | | | % 150.57/21.95 | | | REDUCE: (49), (111) imply: % 150.57/21.95 | | | (118) ~ (all_52_13 = e2) % 150.57/21.95 | | | % 150.57/21.95 | | | SIMP: (118) implies: % 150.57/21.95 | | | (119) ~ (all_52_13 = e2) % 150.57/21.95 | | | % 150.57/21.95 | | | REDUCE: (102), (111) imply: % 150.57/21.95 | | | (120) ~ (all_10_2 = e2) % 150.57/21.95 | | | % 150.57/21.95 | | | SIMP: (120) implies: % 150.57/21.95 | | | (121) ~ (all_10_2 = e2) % 150.57/21.95 | | | % 150.57/21.95 | | | REDUCE: (15), (112) imply: % 150.57/21.95 | | | (122) ~ (all_52_9 = e3) % 150.57/21.95 | | | % 150.57/21.95 | | | REDUCE: (95), (112) imply: % 150.57/21.95 | | | (123) ~ (all_6_0 = e3) % 150.57/21.95 | | | % 150.57/21.95 | | | REDUCE: (97), (112) imply: % 150.57/21.95 | | | (124) op(e3, e3) = all_8_1 % 150.57/21.95 | | | % 150.57/21.95 | | | GROUND_INST: instantiating (39) with all_10_2, all_8_1, e3, e3, % 150.57/21.95 | | | simplifying with (35), (124) gives: % 150.57/21.95 | | | (125) all_10_2 = all_8_1 % 150.57/21.95 | | | % 150.57/21.95 | | | COMBINE_EQS: (10), (125) imply: % 150.57/21.95 | | | (126) all_54_0 = all_8_1 % 150.57/21.95 | | | % 150.57/21.95 | | | COMBINE_EQS: (28), (125) imply: % 150.57/21.95 | | | (127) all_56_1 = all_8_1 % 150.57/21.95 | | | % 150.57/21.95 | | | COMBINE_EQS: (83), (125) imply: % 150.57/21.95 | | | (128) all_58_0 = all_8_1 % 150.57/21.95 | | | % 150.57/21.95 | | | REDUCE: (40), (125) imply: % 150.57/21.95 | | | (129) ~ (all_52_3 = all_8_1) % 150.57/21.95 | | | % 150.57/21.95 | | | REDUCE: (96), (125) imply: % 150.57/21.95 | | | (130) ~ (all_52_4 = all_8_1) % 150.57/21.95 | | | % 150.57/21.95 | | | REDUCE: (53), (125) imply: % 150.57/21.95 | | | (131) ~ (all_52_8 = all_8_1) % 150.57/21.95 | | | % 150.57/21.95 | | | REDUCE: (100), (125) imply: % 150.57/21.95 | | | (132) ~ (all_52_12 = all_8_1) % 150.57/21.95 | | | % 150.57/21.95 | | | REDUCE: (121), (125) imply: % 150.57/21.95 | | | (133) ~ (all_8_1 = e2) % 150.57/21.95 | | | % 150.57/21.95 | | | REDUCE: (82), (125) imply: % 150.57/21.95 | | | (134) op(all_8_1, all_8_1) = all_10_1 % 150.57/21.95 | | | % 150.57/21.95 | | | BETA: splitting (22) gives: % 150.57/21.95 | | | % 150.57/21.95 | | | Case 1: % 150.57/21.95 | | | | % 150.57/21.95 | | | | (135) all_54_0 = e3 % 150.57/21.95 | | | | % 150.57/21.95 | | | | REF_CLOSE: (18), (126), (135) are inconsistent by sub-proof #600. % 150.57/21.95 | | | | % 150.57/21.95 | | | Case 2: % 150.57/21.95 | | | | % 150.57/21.95 | | | | (136) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 150.57/21.95 | | | | % 150.57/21.95 | | | | BETA: splitting (136) gives: % 150.57/21.95 | | | | % 150.57/21.95 | | | | Case 1: % 150.57/21.95 | | | | | % 150.57/21.95 | | | | | (137) all_54_0 = e2 % 150.57/21.95 | | | | | % 150.57/21.95 | | | | | REF_CLOSE: (126), (133), (137) are inconsistent by sub-proof #599. % 150.57/21.95 | | | | | % 150.57/21.95 | | | | Case 2: % 150.57/21.95 | | | | | % 150.57/21.95 | | | | | (138) all_54_0 = e1 | all_54_0 = e0 % 150.57/21.95 | | | | | % 150.57/21.95 | | | | | BETA: splitting (138) gives: % 150.57/21.95 | | | | | % 150.57/21.95 | | | | | Case 1: % 150.57/21.95 | | | | | | % 150.57/21.95 | | | | | | (139) all_54_0 = e1 % 150.57/21.95 | | | | | | % 150.57/21.95 | | | | | | REF_CLOSE: (7), (126), (139) are inconsistent by sub-proof #598. % 150.57/21.95 | | | | | | % 150.57/21.95 | | | | | Case 2: % 150.57/21.95 | | | | | | % 150.57/21.95 | | | | | | (140) all_54_0 = e0 % 150.57/21.95 | | | | | | % 150.57/21.95 | | | | | | COMBINE_EQS: (126), (140) imply: % 150.57/21.95 | | | | | | (141) all_8_1 = e0 % 150.57/21.95 | | | | | | % 150.57/21.95 | | | | | | SIMP: (141) implies: % 150.57/21.95 | | | | | | (142) all_8_1 = e0 % 150.57/21.95 | | | | | | % 150.57/21.95 | | | | | | COMBINE_EQS: (127), (142) imply: % 150.57/21.95 | | | | | | (143) all_56_1 = e0 % 150.57/21.95 | | | | | | % 150.57/21.95 | | | | | | COMBINE_EQS: (128), (142) imply: % 150.57/21.95 | | | | | | (144) all_58_0 = e0 % 150.57/21.95 | | | | | | % 150.57/21.95 | | | | | | REDUCE: (129), (142) imply: % 150.57/21.95 | | | | | | (145) ~ (all_52_3 = e0) % 150.57/21.95 | | | | | | % 150.57/21.95 | | | | | | REDUCE: (130), (142) imply: % 150.57/21.95 | | | | | | (146) ~ (all_52_4 = e0) % 150.57/21.95 | | | | | | % 150.57/21.95 | | | | | | REDUCE: (131), (142) imply: % 150.57/21.95 | | | | | | (147) ~ (all_52_8 = e0) % 150.57/21.95 | | | | | | % 150.57/21.95 | | | | | | REDUCE: (132), (142) imply: % 150.57/21.95 | | | | | | (148) ~ (all_52_12 = e0) % 150.57/21.95 | | | | | | % 150.57/21.95 | | | | | | REDUCE: (134), (142) imply: % 150.57/21.95 | | | | | | (149) op(e0, e0) = all_10_1 % 150.57/21.95 | | | | | | % 150.57/21.95 | | | | | | REDUCE: (5), (142) imply: % 150.57/21.95 | | | | | | (150) op(e2, e0) = all_8_0 % 150.57/21.95 | | | | | | % 150.57/21.95 | | | | | | BETA: splitting (55) gives: % 150.57/21.95 | | | | | | % 150.57/21.95 | | | | | | Case 1: % 150.57/21.95 | | | | | | | % 150.57/21.95 | | | | | | | (151) ~ (all_56_1 = e0) % 150.57/21.95 | | | | | | | % 150.57/21.95 | | | | | | | REDUCE: (143), (151) imply: % 150.57/21.95 | | | | | | | (152) $false % 150.57/21.95 | | | | | | | % 150.57/21.95 | | | | | | | CLOSE: (152) is inconsistent. % 150.57/21.95 | | | | | | | % 150.57/21.95 | | | | | | Case 2: % 150.57/21.95 | | | | | | | % 150.57/21.95 | | | | | | | (153) all_56_7 = e3 % 150.57/21.95 | | | | | | | % 150.57/21.95 | | | | | | | COMBINE_EQS: (43), (153) imply: % 150.57/21.95 | | | | | | | (154) all_52_12 = e3 % 150.57/21.95 | | | | | | | % 150.57/21.95 | | | | | | | REDUCE: (86), (154) imply: % 150.57/21.95 | | | | | | | (155) ~ (all_52_4 = e3) % 150.57/21.95 | | | | | | | % 150.57/21.95 | | | | | | | REDUCE: (89), (154) imply: % 150.57/21.95 | | | | | | | (156) ~ (all_52_8 = e3) % 150.57/21.95 | | | | | | | % 150.57/21.95 | | | | | | | REDUCE: (17), (154) imply: % 150.57/21.95 | | | | | | | (157) ~ (all_52_13 = e3) % 150.57/21.95 | | | | | | | % 150.57/21.95 | | | | | | | SIMP: (157) implies: % 150.57/21.95 | | | | | | | (158) ~ (all_52_13 = e3) % 150.57/21.95 | | | | | | | % 150.57/21.95 | | | | | | | REDUCE: (148), (154) imply: % 150.57/21.95 | | | | | | | (159) ~ (e3 = e0) % 150.57/21.95 | | | | | | | % 150.57/21.95 | | | | | | | BETA: splitting (54) gives: % 150.57/21.95 | | | | | | | % 150.57/21.95 | | | | | | | Case 1: % 150.57/21.95 | | | | | | | | % 150.57/21.95 | | | | | | | | (160) all_58_6 = e3 % 150.57/21.95 | | | | | | | | % 150.57/21.95 | | | | | | | | COMBINE_EQS: (6), (160) imply: % 150.57/21.95 | | | | | | | | (161) all_52_2 = e3 % 150.57/21.95 | | | | | | | | % 150.57/21.95 | | | | | | | | REDUCE: (57), (161) imply: % 150.57/21.95 | | | | | | | | (162) ~ (all_52_3 = e3) % 150.57/21.95 | | | | | | | | % 150.57/21.95 | | | | | | | | SIMP: (162) implies: % 150.57/21.95 | | | | | | | | (163) ~ (all_52_3 = e3) % 150.57/21.95 | | | | | | | | % 150.57/21.95 | | | | | | | | REDUCE: (88), (161) imply: % 150.57/21.95 | | | | | | | | (164) ~ (all_6_2 = e3) % 150.57/21.95 | | | | | | | | % 150.57/21.95 | | | | | | | | BETA: splitting (47) gives: % 150.57/21.95 | | | | | | | | % 150.57/21.95 | | | | | | | | Case 1: % 150.57/21.95 | | | | | | | | | % 150.57/21.95 | | | | | | | | | (165) all_54_12 = e3 % 150.57/21.95 | | | | | | | | | % 150.57/21.95 | | | | | | | | | REF_CLOSE: (16), (163), (165) are inconsistent by sub-proof % 150.57/21.95 | | | | | | | | | #667. % 150.57/21.95 | | | | | | | | | % 150.57/21.95 | | | | | | | | Case 2: % 150.57/21.95 | | | | | | | | | % 150.57/21.95 | | | | | | | | | (166) all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0 % 150.57/21.95 | | | | | | | | | % 150.57/21.95 | | | | | | | | | BETA: splitting (59) gives: % 150.57/21.95 | | | | | | | | | % 150.57/21.95 | | | | | | | | | Case 1: % 150.57/21.95 | | | | | | | | | | % 150.57/21.95 | | | | | | | | | | (167) all_58_4 = e3 % 150.57/21.95 | | | | | | | | | | % 150.57/21.95 | | | | | | | | | | COMBINE_EQS: (20), (167) imply: % 150.57/21.95 | | | | | | | | | | (168) all_52_8 = e3 % 150.57/21.95 | | | | | | | | | | % 150.57/21.95 | | | | | | | | | | REDUCE: (156), (168) imply: % 150.57/21.95 | | | | | | | | | | (169) $false % 150.57/21.95 | | | | | | | | | | % 150.57/21.95 | | | | | | | | | | CLOSE: (169) is inconsistent. % 150.57/21.95 | | | | | | | | | | % 150.57/21.95 | | | | | | | | | Case 2: % 150.57/21.95 | | | | | | | | | | % 150.57/21.95 | | | | | | | | | | (170) all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3 % 150.57/21.95 | | | | | | | | | | % 150.57/21.95 | | | | | | | | | | BETA: splitting (170) gives: % 150.57/21.95 | | | | | | | | | | % 150.57/21.95 | | | | | | | | | | Case 1: % 150.57/21.95 | | | | | | | | | | | % 150.57/21.95 | | | | | | | | | | | (171) all_58_5 = e3 % 150.57/21.95 | | | | | | | | | | | % 150.57/21.95 | | | | | | | | | | | COMBINE_EQS: (30), (171) imply: % 150.57/21.95 | | | | | | | | | | | (172) all_52_9 = e3 % 150.57/21.95 | | | | | | | | | | | % 150.57/21.95 | | | | | | | | | | | REDUCE: (122), (172) imply: % 150.57/21.95 | | | | | | | | | | | (173) $false % 150.57/21.95 | | | | | | | | | | | % 150.57/21.95 | | | | | | | | | | | CLOSE: (173) is inconsistent. % 150.57/21.95 | | | | | | | | | | | % 150.57/21.95 | | | | | | | | | | Case 2: % 150.57/21.95 | | | | | | | | | | | % 150.57/21.95 | | | | | | | | | | | (174) all_58_8 = e3 | all_58_14 = e3 % 150.57/21.95 | | | | | | | | | | | % 150.57/21.95 | | | | | | | | | | | BETA: splitting (174) gives: % 150.57/21.95 | | | | | | | | | | | % 150.57/21.95 | | | | | | | | | | | Case 1: % 150.57/21.95 | | | | | | | | | | | | % 150.57/21.95 | | | | | | | | | | | | (175) all_58_8 = e3 % 150.57/21.95 | | | | | | | | | | | | % 150.57/21.95 | | | | | | | | | | | | COMBINE_EQS: (50), (175) imply: % 150.57/21.95 | | | | | | | | | | | | (176) all_6_2 = e3 % 150.57/21.95 | | | | | | | | | | | | % 150.57/21.95 | | | | | | | | | | | | REDUCE: (106), (176) imply: % 150.57/21.95 | | | | | | | | | | | | (177) $false % 150.57/21.95 | | | | | | | | | | | | % 150.57/21.95 | | | | | | | | | | | | CLOSE: (177) is inconsistent. % 150.57/21.95 | | | | | | | | | | | | % 150.57/21.95 | | | | | | | | | | | Case 2: % 150.57/21.95 | | | | | | | | | | | | % 150.57/21.95 | | | | | | | | | | | | (178) all_58_14 = e3 % 150.57/21.95 | | | | | | | | | | | | % 150.57/21.95 | | | | | | | | | | | | COMBINE_EQS: (99), (178) imply: % 150.57/21.95 | | | | | | | | | | | | (179) all_52_11 = e3 % 150.57/21.95 | | | | | | | | | | | | % 150.57/21.95 | | | | | | | | | | | | SIMP: (179) implies: % 150.57/21.95 | | | | | | | | | | | | (180) all_52_11 = e3 % 150.57/21.95 | | | | | | | | | | | | % 150.57/21.95 | | | | | | | | | | | | REDUCE: (62), (180) imply: % 150.57/21.95 | | | | | | | | | | | | (181) ~ (all_4_2 = e3) % 150.57/21.95 | | | | | | | | | | | | % 150.57/21.95 | | | | | | | | | | | | SIMP: (181) implies: % 150.57/21.95 | | | | | | | | | | | | (182) ~ (all_4_2 = e3) % 150.57/21.95 | | | | | | | | | | | | % 150.57/21.95 | | | | | | | | | | | | BETA: splitting (166) gives: % 150.57/21.95 | | | | | | | | | | | | % 150.57/21.95 | | | | | | | | | | | | Case 1: % 150.57/21.95 | | | | | | | | | | | | | % 150.57/21.95 | | | | | | | | | | | | | (183) all_54_12 = e2 % 150.57/21.95 | | | | | | | | | | | | | % 150.57/21.95 | | | | | | | | | | | | | REF_CLOSE: (16), (115), (183) are inconsistent by sub-proof % 150.57/21.95 | | | | | | | | | | | | | #618. % 150.57/21.95 | | | | | | | | | | | | | % 150.57/21.95 | | | | | | | | | | | | Case 2: % 150.57/21.95 | | | | | | | | | | | | | % 150.57/21.95 | | | | | | | | | | | | | (184) all_54_12 = e1 | all_54_12 = e0 % 150.57/21.95 | | | | | | | | | | | | | % 150.57/21.95 | | | | | | | | | | | | | BETA: splitting (184) gives: % 150.57/21.95 | | | | | | | | | | | | | % 150.57/21.95 | | | | | | | | | | | | | Case 1: % 150.57/21.95 | | | | | | | | | | | | | | % 150.57/21.95 | | | | | | | | | | | | | | (185) all_54_12 = e1 % 150.57/21.95 | | | | | | | | | | | | | | % 150.57/21.95 | | | | | | | | | | | | | | COMBINE_EQS: (16), (185) imply: % 150.57/21.95 | | | | | | | | | | | | | | (186) all_52_3 = e1 % 150.57/21.95 | | | | | | | | | | | | | | % 150.57/21.95 | | | | | | | | | | | | | | SIMP: (186) implies: % 150.57/21.95 | | | | | | | | | | | | | | (187) all_52_3 = e1 % 150.57/21.95 | | | | | | | | | | | | | | % 150.57/21.95 | | | | | | | | | | | | | | REDUCE: (41), (187) imply: % 150.57/21.95 | | | | | | | | | | | | | | (188) ~ (all_52_7 = e1) % 150.57/21.95 | | | | | | | | | | | | | | % 150.57/21.95 | | | | | | | | | | | | | | SIMP: (188) implies: % 150.57/21.95 | | | | | | | | | | | | | | (189) ~ (all_52_7 = e1) % 150.57/21.95 | | | | | | | | | | | | | | % 150.57/21.95 | | | | | | | | | | | | | | REDUCE: (145), (187) imply: % 150.57/21.95 | | | | | | | | | | | | | | (190) ~ (e1 = e0) % 150.57/21.95 | | | | | | | | | | | | | | % 150.57/21.95 | | | | | | | | | | | | | | BETA: splitting (14) gives: % 150.57/21.95 | | | | | | | | | | | | | | % 150.57/21.95 | | | | | | | | | | | | | | Case 1: % 150.57/21.95 | | | | | | | | | | | | | | | % 150.57/21.95 | | | | | | | | | | | | | | | (191) all_58_4 = e2 % 150.57/21.95 | | | | | | | | | | | | | | | % 150.57/21.95 | | | | | | | | | | | | | | | COMBINE_EQS: (20), (191) imply: % 150.57/21.95 | | | | | | | | | | | | | | | (192) all_52_8 = e2 % 150.57/21.95 | | | | | | | | | | | | | | | % 150.57/21.95 | | | | | | | | | | | | | | | REDUCE: (4), (192) imply: % 150.57/21.95 | | | | | | | | | | | | | | | (193) ~ (all_52_4 = e2) % 150.57/21.95 | | | | | | | | | | | | | | | % 150.57/21.95 | | | | | | | | | | | | | | | REF_CLOSE: (12), (19), (23), (25), (29), (31), (33), (37), % 150.57/21.95 | | | | | | | | | | | | | | | (39), (44), (68), (70), (72), (78), (87), (119), % 150.57/21.95 | | | | | | | | | | | | | | | (144), (146), (149), (150), (155), (158), (182), % 150.57/21.95 | | | | | | | | | | | | | | | (190), (193) are inconsistent by sub-proof #592. % 150.57/21.95 | | | | | | | | | | | | | | | % 150.57/21.95 | | | | | | | | | | | | | | Case 2: % 150.57/21.95 | | | | | | | | | | | | | | | % 150.57/21.95 | | | | | | | | | | | | | | | (194) ~ (all_58_4 = e2) % 150.57/21.95 | | | | | | | | | | | | | | | (195) all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2 % 150.57/21.95 | | | | | | | | | | | | | | | % 150.57/21.95 | | | | | | | | | | | | | | | REDUCE: (20), (194) imply: % 150.57/21.95 | | | | | | | | | | | | | | | (196) ~ (all_52_8 = e2) % 150.57/21.95 | | | | | | | | | | | | | | | % 150.57/21.95 | | | | | | | | | | | | | | | BETA: splitting (36) gives: % 150.57/21.95 | | | | | | | | | | | | | | | % 150.57/21.95 | | | | | | | | | | | | | | | Case 1: % 150.57/21.95 | | | | | | | | | | | | | | | | % 150.57/21.95 | | | | | | | | | | | | | | | | (197) all_54_2 = e3 % 150.57/21.95 | | | | | | | | | | | | | | | | % 150.57/21.95 | | | | | | | | | | | | | | | | REF_CLOSE: (75), (156), (197) are inconsistent by sub-proof % 150.57/21.95 | | | | | | | | | | | | | | | | #728. % 150.57/21.95 | | | | | | | | | | | | | | | | % 150.57/21.95 | | | | | | | | | | | | | | | Case 2: % 150.57/21.95 | | | | | | | | | | | | | | | | % 150.57/21.95 | | | | | | | | | | | | | | | | (198) all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0 % 150.57/21.95 | | | | | | | | | | | | | | | | % 150.57/21.95 | | | | | | | | | | | | | | | | BETA: splitting (198) gives: % 150.57/21.95 | | | | | | | | | | | | | | | | % 150.57/21.95 | | | | | | | | | | | | | | | | Case 1: % 150.57/21.95 | | | | | | | | | | | | | | | | | % 150.57/21.95 | | | | | | | | | | | | | | | | | (199) all_54_2 = e2 % 150.57/21.95 | | | | | | | | | | | | | | | | | % 150.57/21.95 | | | | | | | | | | | | | | | | | REF_CLOSE: (75), (196), (199) are inconsistent by sub-proof % 150.57/21.95 | | | | | | | | | | | | | | | | | #727. % 150.57/21.95 | | | | | | | | | | | | | | | | | % 150.57/21.95 | | | | | | | | | | | | | | | | Case 2: % 150.57/21.95 | | | | | | | | | | | | | | | | | % 150.57/21.95 | | | | | | | | | | | | | | | | | (200) ~ (all_54_2 = e2) % 150.57/21.95 | | | | | | | | | | | | | | | | | (201) all_54_2 = e1 | all_54_2 = e0 % 150.57/21.95 | | | | | | | | | | | | | | | | | % 150.57/21.95 | | | | | | | | | | | | | | | | | BETA: splitting (201) gives: % 150.57/21.95 | | | | | | | | | | | | | | | | | % 150.57/21.95 | | | | | | | | | | | | | | | | | Case 1: % 150.57/21.95 | | | | | | | | | | | | | | | | | | % 150.57/21.95 | | | | | | | | | | | | | | | | | | (202) all_54_2 = e1 % 150.57/21.95 | | | | | | | | | | | | | | | | | | % 150.57/21.95 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (75), (202) imply: % 150.57/21.95 | | | | | | | | | | | | | | | | | | (203) all_52_8 = e1 % 150.57/21.95 | | | | | | | | | | | | | | | | | | % 150.57/21.95 | | | | | | | | | | | | | | | | | | SIMP: (203) implies: % 150.57/21.95 | | | | | | | | | | | | | | | | | | (204) all_52_8 = e1 % 150.57/21.95 | | | | | | | | | | | | | | | | | | % 150.57/21.95 | | | | | | | | | | | | | | | | | | REDUCE: (4), (204) imply: % 150.57/21.95 | | | | | | | | | | | | | | | | | | (205) ~ (all_52_4 = e1) % 150.57/21.95 | | | | | | | | | | | | | | | | | | % 150.57/21.95 | | | | | | | | | | | | | | | | | | REDUCE: (196), (204) imply: % 150.57/21.95 | | | | | | | | | | | | | | | | | | (206) ~ (e2 = e1) % 150.57/21.95 | | | | | | | | | | | | | | | | | | % 150.57/21.95 | | | | | | | | | | | | | | | | | | SIMP: (206) implies: % 150.57/21.95 | | | | | | | | | | | | | | | | | | (207) ~ (e2 = e1) % 150.57/21.95 | | | | | | | | | | | | | | | | | | % 150.57/21.95 | | | | | | | | | | | | | | | | | | BETA: splitting (195) gives: % 150.57/21.95 | | | | | | | | | | | | | | | | | | % 150.57/21.95 | | | | | | | | | | | | | | | | | | Case 1: % 150.57/21.95 | | | | | | | | | | | | | | | | | | | % 150.57/21.95 | | | | | | | | | | | | | | | | | | | (208) all_58_5 = e2 % 150.57/21.95 | | | | | | | | | | | | | | | | | | | % 150.57/21.95 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (30), (208) imply: % 150.57/21.95 | | | | | | | | | | | | | | | | | | | (209) all_52_9 = e2 % 150.57/21.95 | | | | | | | | | | | | | | | | | | | % 150.57/21.95 | | | | | | | | | | | | | | | | | | | REDUCE: (117), (209) imply: % 150.57/21.95 | | | | | | | | | | | | | | | | | | | (210) $false % 150.57/21.95 | | | | | | | | | | | | | | | | | | | % 150.57/21.95 | | | | | | | | | | | | | | | | | | | CLOSE: (210) is inconsistent. % 150.57/21.95 | | | | | | | | | | | | | | | | | | | % 150.57/21.95 | | | | | | | | | | | | | | | | | | Case 2: % 150.57/21.95 | | | | | | | | | | | | | | | | | | | % 150.57/21.95 | | | | | | | | | | | | | | | | | | | (211) all_58_8 = e2 | all_58_14 = e2 % 150.57/21.95 | | | | | | | | | | | | | | | | | | | % 150.57/21.95 | | | | | | | | | | | | | | | | | | | BETA: splitting (64) gives: % 150.57/21.95 | | | | | | | | | | | | | | | | | | | % 150.57/21.95 | | | | | | | | | | | | | | | | | | | Case 1: % 150.57/21.95 | | | | | | | | | | | | | | | | | | | | % 150.57/21.95 | | | | | | | | | | | | | | | | | | | | (212) all_58_1 = e1 % 150.57/21.95 | | | | | | | | | | | | | | | | | | | | % 150.57/21.95 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (33), (212) imply: % 150.57/21.95 | | | | | | | | | | | | | | | | | | | | (213) all_52_4 = e1 % 150.57/21.95 | | | | | | | | | | | | | | | | | | | | % 150.57/21.95 | | | | | | | | | | | | | | | | | | | | REDUCE: (205), (213) imply: % 150.57/21.95 | | | | | | | | | | | | | | | | | | | | (214) $false % 150.57/21.95 | | | | | | | | | | | | | | | | | | | | % 150.57/21.95 | | | | | | | | | | | | | | | | | | | | CLOSE: (214) is inconsistent. % 150.57/21.95 | | | | | | | | | | | | | | | | | | | | % 150.57/21.95 | | | | | | | | | | | | | | | | | | | Case 2: % 150.57/21.95 | | | | | | | | | | | | | | | | | | | | % 150.57/21.95 | | | | | | | | | | | | | | | | | | | | (215) all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1 % 150.57/21.95 | | | | | | | | | | | | | | | | | | | | % 150.57/21.95 | | | | | | | | | | | | | | | | | | | | BETA: splitting (215) gives: % 150.57/21.95 | | | | | | | | | | | | | | | | | | | | % 150.57/21.95 | | | | | | | | | | | | | | | | | | | | Case 1: % 150.57/21.95 | | | | | | | | | | | | | | | | | | | | | % 150.57/21.95 | | | | | | | | | | | | | | | | | | | | | (216) all_58_3 = e1 % 150.57/21.95 | | | | | | | | | | | | | | | | | | | | | % 150.57/21.95 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (113), (216) imply: % 150.57/21.95 | | | | | | | | | | | | | | | | | | | | | (217) e3 = e1 % 150.57/21.95 | | | | | | | | | | | | | | | | | | | | | % 150.57/21.95 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (178), (217) imply: % 150.57/21.95 | | | | | | | | | | | | | | | | | | | | | (218) all_58_14 = e1 % 150.57/21.95 | | | | | | | | | | | | | | | | | | | | | % 150.57/21.95 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (50), (80), (207), (211), (218) are inconsistent % 150.57/21.95 | | | | | | | | | | | | | | | | | | | | | by sub-proof #401. % 150.57/21.95 | | | | | | | | | | | | | | | | | | | | | % 150.57/21.95 | | | | | | | | | | | | | | | | | | | | Case 2: % 150.57/21.95 | | | | | | | | | | | | | | | | | | | | | % 150.57/21.95 | | | | | | | | | | | | | | | | | | | | | (219) all_58_7 = e1 | all_58_13 = e1 % 150.57/21.95 | | | | | | | | | | | | | | | | | | | | | % 150.57/21.95 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (219) gives: % 150.57/21.95 | | | | | | | | | | | | | | | | | | | | | % 150.57/21.95 | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.57/21.95 | | | | | | | | | | | | | | | | | | | | | | % 150.57/21.95 | | | | | | | | | | | | | | | | | | | | | | (220) all_58_7 = e1 % 150.57/21.95 | | | | | | | | | | | | | | | | | | | | | | % 150.57/21.95 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (79), (220) imply: % 150.57/21.95 | | | | | | | | | | | | | | | | | | | | | | (221) all_6_0 = e1 % 150.57/21.95 | | | | | | | | | | | | | | | | | | | | | | % 150.57/21.95 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (56), (221) imply: % 150.57/21.95 | | | | | | | | | | | | | | | | | | | | | | (222) ~ (all_52_14 = e1) % 150.57/21.95 | | | | | | | | | | | | | | | | | | | | | | % 150.57/21.95 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (26), (27), (39), (45), (76), (77), (80), % 150.57/21.95 | | | | | | | | | | | | | | | | | | | | | | (84), (90), (106), (222) are inconsistent by % 150.57/21.95 | | | | | | | | | | | | | | | | | | | | | | sub-proof #83. % 150.57/21.95 | | | | | | | | | | | | | | | | | | | | | | % 150.57/21.95 | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.57/21.95 | | | | | | | | | | | | | | | | | | | | | | % 150.57/21.95 | | | | | | | | | | | | | | | | | | | | | | (223) all_58_13 = e1 % 150.57/21.95 | | | | | | | | | | | | | | | | | | | | | | % 150.57/21.95 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (34), (223) imply: % 150.57/21.95 | | | | | | | | | | | | | | | | | | | | | | (224) all_52_7 = e1 % 150.57/21.95 | | | | | | | | | | | | | | | | | | | | | | % 150.57/21.95 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (189), (224) imply: % 150.57/21.95 | | | | | | | | | | | | | | | | | | | | | | (225) $false % 150.57/21.95 | | | | | | | | | | | | | | | | | | | | | | % 150.57/21.95 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (225) is inconsistent. % 150.57/21.95 | | | | | | | | | | | | | | | | | | | | | | % 150.57/21.95 | | | | | | | | | | | | | | | | | | | | | End of split % 150.57/21.95 | | | | | | | | | | | | | | | | | | | | | % 150.57/21.95 | | | | | | | | | | | | | | | | | | | | End of split % 150.57/21.95 | | | | | | | | | | | | | | | | | | | | % 150.57/21.95 | | | | | | | | | | | | | | | | | | | End of split % 150.57/21.95 | | | | | | | | | | | | | | | | | | | % 150.57/21.95 | | | | | | | | | | | | | | | | | | End of split % 150.57/21.95 | | | | | | | | | | | | | | | | | | % 150.57/21.95 | | | | | | | | | | | | | | | | | Case 2: % 150.57/21.95 | | | | | | | | | | | | | | | | | | % 150.57/21.95 | | | | | | | | | | | | | | | | | | (226) all_54_2 = e0 % 150.57/21.95 | | | | | | | | | | | | | | | | | | % 150.57/21.95 | | | | | | | | | | | | | | | | | | REF_CLOSE: (75), (147), (226) are inconsistent by sub-proof % 150.57/21.95 | | | | | | | | | | | | | | | | | | #725. % 150.57/21.95 | | | | | | | | | | | | | | | | | | % 150.57/21.95 | | | | | | | | | | | | | | | | | End of split % 150.57/21.95 | | | | | | | | | | | | | | | | | % 150.57/21.95 | | | | | | | | | | | | | | | | End of split % 150.57/21.95 | | | | | | | | | | | | | | | | % 150.57/21.95 | | | | | | | | | | | | | | | End of split % 150.57/21.95 | | | | | | | | | | | | | | | % 150.57/21.95 | | | | | | | | | | | | | | End of split % 150.57/21.95 | | | | | | | | | | | | | | % 150.57/21.95 | | | | | | | | | | | | | Case 2: % 150.57/21.95 | | | | | | | | | | | | | | % 150.57/21.95 | | | | | | | | | | | | | | (227) all_54_12 = e0 % 150.57/21.95 | | | | | | | | | | | | | | % 150.57/21.95 | | | | | | | | | | | | | | REF_CLOSE: (16), (145), (227) are inconsistent by sub-proof % 150.57/21.95 | | | | | | | | | | | | | | #617. % 150.57/21.95 | | | | | | | | | | | | | | % 150.57/21.95 | | | | | | | | | | | | | End of split % 150.57/21.95 | | | | | | | | | | | | | % 150.57/21.95 | | | | | | | | | | | | End of split % 150.57/21.95 | | | | | | | | | | | | % 150.57/21.95 | | | | | | | | | | | End of split % 150.57/21.95 | | | | | | | | | | | % 150.57/21.95 | | | | | | | | | | End of split % 150.57/21.95 | | | | | | | | | | % 150.57/21.95 | | | | | | | | | End of split % 150.57/21.95 | | | | | | | | | % 150.57/21.95 | | | | | | | | End of split % 150.57/21.95 | | | | | | | | % 150.57/21.95 | | | | | | | Case 2: % 150.57/21.95 | | | | | | | | % 150.57/21.95 | | | | | | | | (228) all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3 % 150.57/21.95 | | | | | | | | % 150.57/21.95 | | | | | | | | REF_CLOSE: (9), (26), (27), (39), (45), (50), (51), (56), (66), % 150.57/21.95 | | | | | | | | (76), (77), (79), (80), (84), (85), (90), (93), % 150.57/21.95 | | | | | | | | (106), (159), (228) are inconsistent by sub-proof % 150.57/21.95 | | | | | | | | #82. % 150.57/21.95 | | | | | | | | % 150.57/21.95 | | | | | | | End of split % 150.57/21.95 | | | | | | | % 150.57/21.95 | | | | | | End of split % 150.57/21.95 | | | | | | % 150.57/21.95 | | | | | End of split % 150.57/21.95 | | | | | % 150.57/21.95 | | | | End of split % 150.57/21.95 | | | | % 150.57/21.95 | | | End of split % 150.57/21.95 | | | % 150.57/21.95 | | End of split % 150.57/21.95 | | % 150.57/21.95 | Case 2: % 150.57/21.95 | | % 150.57/21.95 | | (229) all_56_21 = e3 % 150.57/21.95 | | (230) all_56_17 = e1 % 150.57/21.95 | | % 150.57/21.95 | | COMBINE_EQS: (32), (230) imply: % 150.57/21.95 | | (231) all_52_2 = e1 % 150.57/21.95 | | % 150.57/21.95 | | COMBINE_EQS: (26), (229) imply: % 150.57/21.95 | | (232) all_6_2 = e3 % 150.57/21.95 | | % 150.57/21.95 | | SIMP: (232) implies: % 150.57/21.95 | | (233) all_6_2 = e3 % 150.57/21.95 | | % 150.57/21.95 | | REDUCE: (67), (231) imply: % 150.57/21.95 | | (234) ~ (all_52_14 = e1) % 150.57/21.95 | | % 150.57/21.95 | | SIMP: (234) implies: % 150.57/21.95 | | (235) ~ (all_52_14 = e1) % 150.57/21.95 | | % 150.57/21.95 | | REDUCE: (71), (231) imply: % 150.57/21.95 | | (236) ~ (all_6_0 = e1) % 150.57/21.95 | | % 150.57/21.95 | | SIMP: (236) implies: % 150.57/21.95 | | (237) ~ (all_6_0 = e1) % 150.57/21.95 | | % 150.57/21.95 | | REDUCE: (88), (231), (233) imply: % 150.57/21.95 | | (238) ~ (e3 = e1) % 150.57/21.95 | | % 150.57/21.95 | | REDUCE: (93), (233) imply: % 150.57/21.95 | | (239) ~ (all_52_14 = e3) % 150.57/21.95 | | % 150.57/21.95 | | REDUCE: (45), (233) imply: % 150.57/21.95 | | (240) op(e3, e3) = e2 % 150.57/21.95 | | % 150.57/21.95 | | REF_CLOSE: (1), (9), (11), (13), (24), (26), (27), (28), (35), (39), (45), % 150.57/21.95 | | (51), (52), (56), (61), (65), (69), (76), (77), (80), (82), (84), % 150.57/21.95 | | (85), (90), (92), (95), (103), (229), (235), (237), (239), (240) % 150.57/21.95 | | are inconsistent by sub-proof #79. % 150.57/21.95 | | % 150.57/21.95 | End of split % 150.57/21.95 | % 150.57/21.95 End of proof % 150.57/21.95 % 150.57/21.95 Sub-proof #79 shows that the following formulas are inconsistent: % 150.57/21.95 ---------------------------------------------------------------- % 150.57/21.95 (1) all_56_11 = all_8_2 % 150.57/21.95 (2) all_54_10 = all_6_2 % 150.57/21.95 (3) all_56_21 = e3 % 150.57/21.95 (4) ~ (all_52_14 = all_4_2) % 150.57/21.95 (5) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0 % 150.57/21.95 (6) all_54_9 = all_6_0 % 150.57/21.95 (7) all_56_21 = all_6_2 % 150.57/21.95 (8) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 150.57/21.95 (9) op(e3, e3) = e2 % 150.57/21.95 (10) all_56_1 = all_10_2 % 150.57/21.95 (11) ~ (all_6_0 = e1) % 150.57/21.95 (12) op(e3, e3) = all_10_2 % 150.57/21.95 (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 150.57/21.95 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 150.57/21.95 (14) ~ (all_52_14 = e1) % 150.57/21.95 (15) op(all_6_2, all_6_2) = e2 % 150.57/21.95 (16) ~ (all_52_14 = e3) % 150.57/21.95 (17) ~ (all_6_0 = e3) % 150.57/21.95 (18) ~ (all_6_0 = e0) | ~ (all_6_2 = e3) % 150.57/21.95 (19) ~ (all_52_14 = all_6_0) % 150.57/21.95 (20) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0 % 150.57/21.95 (21) all_56_31 = all_4_2 % 150.57/21.95 (22) all_56_1 = e3 | all_56_11 = e2 | all_56_21 = e1 | all_56_31 = e0 % 150.57/21.95 (23) all_56_23 = all_52_14 % 150.57/21.95 (24) op(e1, e1) = all_6_2 % 150.57/21.95 (25) ~ (all_6_2 = e2) % 150.57/21.95 (26) op(all_10_2, all_10_2) = all_10_1 % 150.57/21.95 (27) op(e1, all_6_2) = all_56_20 % 150.57/21.95 (28) ~ (e3 = e1) % 150.57/21.95 (29) ~ (all_56_21 = e0) | all_56_23 = e1 % 150.57/21.95 (30) op(e3, all_10_2) = all_56_0 % 150.57/21.95 (31) ~ (all_8_2 = all_6_0) % 150.57/21.95 (32) all_54_11 = all_52_14 % 150.57/21.95 % 150.57/21.95 Begin of proof % 150.57/21.95 | % 150.57/21.95 | BETA: splitting (18) gives: % 150.57/21.95 | % 150.57/21.95 | Case 1: % 150.57/21.95 | | % 150.57/21.95 | | (33) ~ (all_6_2 = e3) % 150.57/21.95 | | % 150.57/21.95 | | REF_CLOSE: (2), (7), (8), (13), (14), (15), (23), (24), (25), (27), (29), % 150.57/21.95 | | (33) are inconsistent by sub-proof #83. % 150.57/21.95 | | % 150.57/21.95 | Case 2: % 150.57/21.95 | | % 150.57/21.95 | | (34) ~ (all_6_0 = e0) % 150.57/21.95 | | % 150.57/21.95 | | REF_CLOSE: (1), (3), (4), (5), (6), (9), (10), (11), (12), (13), (14), (16), % 150.57/21.95 | | (17), (19), (20), (21), (22), (26), (28), (30), (31), (32), (34) % 150.57/21.95 | | are inconsistent by sub-proof #80. % 150.57/21.95 | | % 150.57/21.95 | End of split % 150.57/21.95 | % 150.57/21.95 End of proof % 150.57/21.95 % 150.57/21.95 Sub-proof #80 shows that the following formulas are inconsistent: % 150.57/21.95 ---------------------------------------------------------------- % 150.57/21.95 (1) all_56_11 = all_8_2 % 150.57/21.95 (2) all_56_21 = e3 % 150.57/21.95 (3) ~ (all_52_14 = all_4_2) % 150.57/21.95 (4) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0 % 150.57/21.95 (5) all_54_9 = all_6_0 % 150.57/21.95 (6) op(e3, e3) = e2 % 150.57/21.95 (7) all_56_1 = all_10_2 % 150.57/21.95 (8) ~ (all_6_0 = e1) % 150.57/21.96 (9) op(e3, e3) = all_10_2 % 150.57/21.96 (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 150.57/21.96 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 150.57/21.96 (11) ~ (all_52_14 = e1) % 150.57/21.96 (12) ~ (all_52_14 = e3) % 150.57/21.96 (13) ~ (all_6_0 = e3) % 150.57/21.96 (14) ~ (all_52_14 = all_6_0) % 150.57/21.96 (15) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0 % 150.57/21.96 (16) all_56_31 = all_4_2 % 150.57/21.96 (17) all_56_1 = e3 | all_56_11 = e2 | all_56_21 = e1 | all_56_31 = e0 % 150.57/21.96 (18) ~ (all_6_0 = e0) % 150.57/21.96 (19) op(all_10_2, all_10_2) = all_10_1 % 150.57/21.96 (20) ~ (e3 = e1) % 150.57/21.96 (21) op(e3, all_10_2) = all_56_0 % 150.57/21.96 (22) ~ (all_8_2 = all_6_0) % 150.57/21.96 (23) all_54_11 = all_52_14 % 150.57/21.96 % 150.57/21.96 Begin of proof % 150.57/21.96 | % 150.57/21.96 | BETA: splitting (15) gives: % 150.57/21.96 | % 150.57/21.96 | Case 1: % 150.57/21.96 | | % 150.57/21.96 | | (24) all_54_9 = e3 % 150.57/21.96 | | % 150.57/21.96 | | REF_CLOSE: (5), (13), (24) are inconsistent by sub-proof #88. % 150.57/21.96 | | % 150.57/21.96 | Case 2: % 150.57/21.96 | | % 150.57/21.96 | | (25) ~ (all_54_9 = e3) % 150.57/21.96 | | (26) all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0 % 150.57/21.96 | | % 150.57/21.96 | | BETA: splitting (26) gives: % 150.57/21.96 | | % 150.57/21.96 | | Case 1: % 150.57/21.96 | | | % 150.57/21.96 | | | (27) all_54_9 = e2 % 150.57/21.96 | | | % 150.57/21.96 | | | COMBINE_EQS: (5), (27) imply: % 150.57/21.96 | | | (28) all_6_0 = e2 % 150.57/21.96 | | | % 150.57/21.96 | | | SIMP: (28) implies: % 150.57/21.96 | | | (29) all_6_0 = e2 % 150.57/21.96 | | | % 150.57/21.96 | | | REDUCE: (14), (29) imply: % 150.57/21.96 | | | (30) ~ (all_52_14 = e2) % 150.57/21.96 | | | % 150.57/21.96 | | | REDUCE: (22), (29) imply: % 150.57/21.96 | | | (31) ~ (all_8_2 = e2) % 150.57/21.96 | | | % 150.57/21.96 | | | REDUCE: (13), (29) imply: % 150.57/21.96 | | | (32) ~ (e3 = e2) % 150.57/21.96 | | | % 150.57/21.96 | | | SIMP: (32) implies: % 150.57/21.96 | | | (33) ~ (e3 = e2) % 150.57/21.96 | | | % 150.57/21.96 | | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (9), (10), (11), (12), (16), % 150.57/21.96 | | | (17), (19), (20), (21), (23), (30), (31), (33) are inconsistent % 150.57/21.96 | | | by sub-proof #414. % 150.57/21.96 | | | % 150.57/21.96 | | Case 2: % 150.57/21.96 | | | % 150.57/21.96 | | | (34) all_54_9 = e1 | all_54_9 = e0 % 150.57/21.96 | | | % 150.57/21.96 | | | REF_CLOSE: (5), (8), (18), (34) are inconsistent by sub-proof #81. % 150.57/21.96 | | | % 150.57/21.96 | | End of split % 150.57/21.96 | | % 150.57/21.96 | End of split % 150.57/21.96 | % 150.57/21.96 End of proof % 150.57/21.96 % 150.57/21.96 Sub-proof #81 shows that the following formulas are inconsistent: % 150.57/21.96 ---------------------------------------------------------------- % 150.57/21.96 (1) all_54_9 = e1 | all_54_9 = e0 % 150.57/21.96 (2) all_54_9 = all_6_0 % 150.57/21.96 (3) ~ (all_6_0 = e1) % 150.57/21.96 (4) ~ (all_6_0 = e0) % 150.57/21.96 % 150.57/21.96 Begin of proof % 150.57/21.96 | % 150.57/21.96 | BETA: splitting (1) gives: % 150.57/21.96 | % 150.57/21.96 | Case 1: % 150.57/21.96 | | % 150.57/21.96 | | (5) all_54_9 = e1 % 150.57/21.96 | | % 150.57/21.96 | | REF_CLOSE: (2), (3), (5) are inconsistent by sub-proof #87. % 150.57/21.96 | | % 150.57/21.96 | Case 2: % 150.57/21.96 | | % 150.57/21.96 | | (6) all_54_9 = e0 % 150.57/21.96 | | % 150.57/21.96 | | COMBINE_EQS: (2), (6) imply: % 150.57/21.96 | | (7) all_6_0 = e0 % 150.57/21.96 | | % 150.57/21.96 | | SIMP: (7) implies: % 150.57/21.96 | | (8) all_6_0 = e0 % 150.57/21.96 | | % 150.57/21.96 | | REDUCE: (4), (8) imply: % 150.57/21.96 | | (9) $false % 150.57/21.96 | | % 150.57/21.96 | | CLOSE: (9) is inconsistent. % 150.57/21.96 | | % 150.57/21.96 | End of split % 150.57/21.96 | % 150.57/21.96 End of proof % 150.57/21.96 % 150.57/21.96 Sub-proof #82 shows that the following formulas are inconsistent: % 150.57/21.96 ---------------------------------------------------------------- % 150.57/21.96 (1) ~ (e3 = e0) % 150.57/21.96 (2) all_54_10 = all_6_2 % 150.57/21.96 (3) ~ (all_6_2 = e3) % 150.57/21.96 (4) all_56_21 = all_6_2 % 150.57/21.96 (5) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 150.57/21.96 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 150.57/21.96 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 150.57/21.96 (7) all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3 % 150.57/21.96 (8) op(all_6_2, all_6_2) = e2 % 150.57/21.96 (9) all_58_8 = all_6_2 % 150.57/21.96 (10) ~ (all_6_0 = e3) % 150.57/21.96 (11) ~ (all_52_14 = all_6_0) % 150.57/21.96 (12) all_58_11 = all_52_14 % 150.57/21.96 (13) all_56_23 = all_52_14 % 150.57/21.96 (14) op(e1, e1) = all_6_2 % 150.57/21.96 (15) all_58_7 = all_6_0 % 150.57/21.96 (16) ~ (all_6_2 = e2) % 150.57/21.96 (17) op(e1, all_6_2) = all_56_20 % 150.57/21.96 (18) ~ (e3 = e1) % 150.57/21.96 (19) ~ (all_56_21 = e0) | all_56_23 = e1 % 150.57/21.96 (20) ~ (all_52_14 = all_6_2) % 150.57/21.96 % 150.57/21.96 Begin of proof % 150.57/21.96 | % 150.57/21.96 | BETA: splitting (7) gives: % 150.57/21.96 | % 150.57/21.96 | Case 1: % 150.57/21.96 | | % 150.57/21.96 | | (21) all_58_7 = e3 % 150.57/21.96 | | % 150.57/21.96 | | COMBINE_EQS: (15), (21) imply: % 150.57/21.96 | | (22) all_6_0 = e3 % 150.57/21.96 | | % 150.57/21.96 | | REDUCE: (10), (22) imply: % 150.57/21.96 | | (23) $false % 150.57/21.96 | | % 150.57/21.96 | | CLOSE: (23) is inconsistent. % 150.57/21.96 | | % 150.57/21.96 | Case 2: % 150.57/21.96 | | % 150.57/21.96 | | (24) all_58_8 = e3 | all_58_11 = e3 % 150.57/21.96 | | % 150.57/21.96 | | BETA: splitting (24) gives: % 150.57/21.96 | | % 150.57/21.96 | | Case 1: % 150.57/21.96 | | | % 150.57/21.96 | | | (25) all_58_8 = e3 % 150.57/21.96 | | | % 150.57/21.96 | | | COMBINE_EQS: (9), (25) imply: % 150.57/21.96 | | | (26) all_6_2 = e3 % 150.57/21.96 | | | % 150.57/21.96 | | | REDUCE: (3), (26) imply: % 150.57/21.96 | | | (27) $false % 150.57/21.96 | | | % 150.57/21.96 | | | CLOSE: (27) is inconsistent. % 150.57/21.96 | | | % 150.57/21.96 | | Case 2: % 150.57/21.96 | | | % 150.57/21.96 | | | (28) all_58_11 = e3 % 150.57/21.96 | | | % 150.57/21.96 | | | COMBINE_EQS: (12), (28) imply: % 150.57/21.96 | | | (29) all_52_14 = e3 % 150.57/21.96 | | | % 150.57/21.96 | | | COMBINE_EQS: (13), (29) imply: % 150.57/21.96 | | | (30) all_56_23 = e3 % 150.57/21.96 | | | % 150.57/21.96 | | | REDUCE: (11), (29) imply: % 150.57/21.96 | | | (31) ~ (all_6_0 = e3) % 150.57/21.96 | | | % 150.57/21.96 | | | REDUCE: (20), (29) imply: % 150.57/21.96 | | | (32) ~ (all_6_2 = e3) % 150.57/21.96 | | | % 150.57/21.96 | | | BETA: splitting (19) gives: % 150.57/21.96 | | | % 150.57/21.96 | | | Case 1: % 150.57/21.96 | | | | % 150.57/21.96 | | | | (33) ~ (all_56_21 = e0) % 150.57/21.96 | | | | % 150.57/21.96 | | | | REDUCE: (4), (33) imply: % 150.57/21.96 | | | | (34) ~ (all_6_2 = e0) % 150.57/21.96 | | | | % 150.57/21.96 | | | | REF_CLOSE: (2), (3), (5), (6), (8), (14), (16), (17), (34) are % 150.57/21.96 | | | | inconsistent by sub-proof #89. % 150.57/21.96 | | | | % 150.57/21.96 | | | Case 2: % 150.57/21.96 | | | | % 150.57/21.96 | | | | (35) all_56_23 = e1 % 150.57/21.96 | | | | (36) all_56_21 = e0 % 150.57/21.96 | | | | % 150.57/21.96 | | | | COMBINE_EQS: (4), (36) imply: % 150.57/21.96 | | | | (37) all_6_2 = e0 % 150.57/21.96 | | | | % 150.57/21.96 | | | | COMBINE_EQS: (30), (35) imply: % 150.57/21.96 | | | | (38) e3 = e1 % 150.57/21.96 | | | | % 150.57/21.96 | | | | COMBINE_EQS: (28), (38) imply: % 150.57/21.96 | | | | (39) all_58_11 = e1 % 150.57/21.96 | | | | % 150.57/21.96 | | | | COMBINE_EQS: (9), (37) imply: % 150.57/21.96 | | | | (40) all_58_8 = e0 % 150.57/21.96 | | | | % 150.57/21.96 | | | | REF_CLOSE: (1), (7), (10), (15), (18), (39), (40) are inconsistent by % 150.57/21.96 | | | | sub-proof #85. % 150.57/21.96 | | | | % 150.57/21.96 | | | End of split % 150.57/21.96 | | | % 150.57/21.96 | | End of split % 150.57/21.96 | | % 150.57/21.96 | End of split % 150.57/21.96 | % 150.57/21.96 End of proof % 150.57/21.96 % 150.57/21.96 Sub-proof #83 shows that the following formulas are inconsistent: % 150.57/21.96 ---------------------------------------------------------------- % 150.57/21.96 (1) all_54_10 = all_6_2 % 150.57/21.96 (2) ~ (all_6_2 = e3) % 150.57/21.96 (3) all_56_21 = all_6_2 % 150.57/21.96 (4) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 150.57/21.96 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 150.57/21.96 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 150.57/21.96 (6) ~ (all_52_14 = e1) % 150.57/21.96 (7) op(all_6_2, all_6_2) = e2 % 150.57/21.96 (8) all_56_23 = all_52_14 % 150.57/21.96 (9) op(e1, e1) = all_6_2 % 150.57/21.96 (10) ~ (all_6_2 = e2) % 150.57/21.96 (11) op(e1, all_6_2) = all_56_20 % 150.57/21.96 (12) ~ (all_56_21 = e0) | all_56_23 = e1 % 150.57/21.96 % 150.57/21.96 Begin of proof % 150.57/21.96 | % 150.57/21.96 | BETA: splitting (12) gives: % 150.57/21.96 | % 150.57/21.96 | Case 1: % 150.57/21.96 | | % 150.57/21.96 | | (13) ~ (all_56_21 = e0) % 150.57/21.96 | | % 150.57/21.96 | | REDUCE: (3), (13) imply: % 150.57/21.96 | | (14) ~ (all_6_2 = e0) % 150.57/21.96 | | % 150.57/21.96 | | REF_CLOSE: (1), (2), (4), (5), (7), (9), (10), (11), (14) are inconsistent % 150.57/21.96 | | by sub-proof #89. % 150.57/21.96 | | % 150.57/21.96 | Case 2: % 150.57/21.96 | | % 150.57/21.96 | | (15) all_56_23 = e1 % 150.57/21.96 | | % 150.57/21.96 | | REF_CLOSE: (6), (8), (15) are inconsistent by sub-proof #309. % 150.57/21.96 | | % 150.57/21.96 | End of split % 150.57/21.96 | % 150.57/21.96 End of proof % 150.57/21.96 % 150.57/21.96 Sub-proof #84 shows that the following formulas are inconsistent: % 150.57/21.96 ---------------------------------------------------------------- % 150.57/21.96 (1) all_56_11 = all_8_2 % 150.57/21.96 (2) ~ (all_56_11 = e1) | all_56_13 = e2 % 150.57/21.96 (3) all_58_6 = all_52_2 % 150.57/21.96 (4) ~ (all_8_1 = e1) % 150.57/21.96 (5) all_54_10 = all_6_2 % 150.57/21.96 (6) ~ (all_52_9 = all_8_2) % 150.57/21.96 (7) ~ (all_6_2 = e3) % 150.57/21.96 (8) ~ (all_8_1 = e3) % 150.57/21.96 (9) op(e0, e0) = all_4_2 % 150.57/21.96 (10) all_54_5 = all_8_2 % 150.57/21.96 (11) all_54_9 = all_6_0 % 150.57/21.96 (12) all_56_21 = all_6_2 % 150.57/21.96 (13) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 150.57/21.96 (14) all_56_1 = all_10_2 % 150.57/21.96 (15) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 150.57/21.96 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 150.57/21.96 (16) op(all_6_2, all_6_2) = e2 % 150.57/21.96 (17) ~ (all_6_0 = all_6_2) % 150.57/21.96 (18) all_56_13 = all_52_9 % 150.57/21.96 (19) all_58_8 = all_6_2 % 150.57/21.96 (20) ~ (all_6_0 = e3) % 150.57/21.96 (21) all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3 % 150.57/21.96 (22) ~ (all_52_14 = all_6_0) % 150.57/21.96 (23) ~ (all_8_2 = e3) % 150.57/21.96 (24) op(all_4_2, all_4_2) = all_4_1 % 150.57/21.96 (25) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0 % 150.57/21.96 (26) all_56_31 = all_4_2 % 150.57/21.96 (27) all_58_11 = all_52_14 % 150.57/21.96 (28) all_56_1 = e3 | all_56_11 = e2 | all_56_21 = e1 | all_56_31 = e0 % 150.57/21.96 (29) all_56_23 = all_52_14 % 150.57/21.96 (30) op(e1, e1) = all_6_2 % 150.57/21.96 (31) all_58_7 = all_6_0 % 150.57/21.96 (32) ~ (all_6_2 = e2) % 150.57/21.96 (33) ~ (all_52_9 = all_6_2) % 150.57/21.96 (34) op(e1, all_6_2) = all_56_20 % 150.57/21.96 (35) ~ (all_56_21 = e0) | all_56_23 = e1 % 150.57/21.96 (36) op(e0, all_4_2) = all_56_30 % 150.57/21.96 (37) ~ (all_8_2 = e0) % 150.57/21.96 (38) ~ (all_52_14 = all_6_2) % 150.57/21.96 (39) ~ (all_52_2 = all_10_2) % 150.57/21.96 (40) ~ (all_8_2 = all_6_0) % 150.57/21.96 (41) op(all_8_2, all_8_2) = all_8_1 % 150.57/21.96 (42) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 150.57/21.96 % 150.57/21.96 Begin of proof % 150.57/21.96 | % 150.57/21.96 | BETA: splitting (2) gives: % 150.57/21.96 | % 150.57/21.96 | Case 1: % 150.57/21.96 | | % 150.57/21.96 | | (43) ~ (all_56_11 = e1) % 150.57/21.96 | | % 150.57/21.96 | | REDUCE: (1), (43) imply: % 150.57/21.96 | | (44) ~ (all_8_2 = e1) % 150.57/21.96 | | % 150.57/21.96 | | BETA: splitting (42) gives: % 150.57/21.96 | | % 150.57/21.96 | | Case 1: % 150.57/21.96 | | | % 150.57/21.96 | | | (45) all_54_5 = e3 % 150.57/21.96 | | | % 150.57/21.96 | | | REF_CLOSE: (10), (23), (45) are inconsistent by sub-proof #737. % 150.57/21.96 | | | % 150.57/21.96 | | Case 2: % 150.57/21.96 | | | % 150.57/21.96 | | | (46) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 150.57/21.96 | | | % 150.57/21.96 | | | BETA: splitting (46) gives: % 150.57/21.96 | | | % 150.57/21.96 | | | Case 1: % 150.57/21.96 | | | | % 150.57/21.96 | | | | (47) all_54_5 = e2 % 150.57/21.96 | | | | % 150.57/21.96 | | | | COMBINE_EQS: (10), (47) imply: % 150.57/21.96 | | | | (48) all_8_2 = e2 % 150.57/21.96 | | | | % 150.57/21.96 | | | | SIMP: (48) implies: % 150.57/21.96 | | | | (49) all_8_2 = e2 % 150.57/21.96 | | | | % 150.57/21.96 | | | | REDUCE: (40), (49) imply: % 150.57/21.96 | | | | (50) ~ (all_6_0 = e2) % 150.57/21.96 | | | | % 150.57/21.96 | | | | SIMP: (50) implies: % 150.57/21.96 | | | | (51) ~ (all_6_0 = e2) % 150.57/21.96 | | | | % 150.57/21.96 | | | | BETA: splitting (35) gives: % 150.57/21.96 | | | | % 150.57/21.96 | | | | Case 1: % 150.57/21.96 | | | | | % 150.57/21.96 | | | | | (52) ~ (all_56_21 = e0) % 150.57/21.96 | | | | | % 150.57/21.96 | | | | | REDUCE: (12), (52) imply: % 150.57/21.96 | | | | | (53) ~ (all_6_2 = e0) % 150.57/21.96 | | | | | % 150.57/21.96 | | | | | REF_CLOSE: (5), (7), (13), (15), (16), (30), (32), (34), (53) are % 150.57/21.96 | | | | | inconsistent by sub-proof #89. % 150.57/21.96 | | | | | % 150.57/21.96 | | | | Case 2: % 150.57/21.96 | | | | | % 150.57/21.96 | | | | | (54) all_56_23 = e1 % 150.57/21.96 | | | | | % 150.57/21.96 | | | | | COMBINE_EQS: (29), (54) imply: % 150.57/21.96 | | | | | (55) all_52_14 = e1 % 150.57/21.96 | | | | | % 150.57/21.96 | | | | | SIMP: (55) implies: % 150.57/21.96 | | | | | (56) all_52_14 = e1 % 150.57/21.96 | | | | | % 150.57/21.96 | | | | | REDUCE: (22), (56) imply: % 150.57/21.96 | | | | | (57) ~ (all_6_0 = e1) % 150.57/21.96 | | | | | % 150.57/21.96 | | | | | SIMP: (57) implies: % 150.57/21.96 | | | | | (58) ~ (all_6_0 = e1) % 150.57/21.96 | | | | | % 150.57/21.96 | | | | | BETA: splitting (25) gives: % 150.57/21.96 | | | | | % 150.57/21.96 | | | | | Case 1: % 150.57/21.96 | | | | | | % 150.57/21.96 | | | | | | (59) all_54_9 = e3 % 150.57/21.96 | | | | | | % 150.57/21.96 | | | | | | REF_CLOSE: (11), (20), (59) are inconsistent by sub-proof #88. % 150.57/21.96 | | | | | | % 150.57/21.96 | | | | | Case 2: % 150.57/21.96 | | | | | | % 150.57/21.96 | | | | | | (60) all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0 % 150.57/21.96 | | | | | | % 150.57/21.96 | | | | | | BETA: splitting (60) gives: % 150.57/21.96 | | | | | | % 150.57/21.96 | | | | | | Case 1: % 150.57/21.96 | | | | | | | % 150.57/21.96 | | | | | | | (61) all_54_9 = e2 % 150.57/21.96 | | | | | | | % 150.57/21.96 | | | | | | | COMBINE_EQS: (11), (61) imply: % 150.57/21.96 | | | | | | | (62) all_6_0 = e2 % 150.57/21.96 | | | | | | | % 150.57/21.96 | | | | | | | SIMP: (62) implies: % 150.57/21.96 | | | | | | | (63) all_6_0 = e2 % 150.57/21.96 | | | | | | | % 150.57/21.96 | | | | | | | REDUCE: (51), (63) imply: % 150.57/21.96 | | | | | | | (64) $false % 150.57/21.96 | | | | | | | % 150.57/21.96 | | | | | | | CLOSE: (64) is inconsistent. % 150.57/21.96 | | | | | | | % 150.57/21.96 | | | | | | Case 2: % 150.57/21.96 | | | | | | | % 150.57/21.96 | | | | | | | (65) all_54_9 = e1 | all_54_9 = e0 % 150.57/21.96 | | | | | | | % 150.57/21.96 | | | | | | | BETA: splitting (65) gives: % 150.57/21.96 | | | | | | | % 150.57/21.96 | | | | | | | Case 1: % 150.57/21.96 | | | | | | | | % 150.57/21.96 | | | | | | | | (66) all_54_9 = e1 % 150.57/21.96 | | | | | | | | % 150.57/21.96 | | | | | | | | REF_CLOSE: (11), (58), (66) are inconsistent by sub-proof #87. % 150.57/21.96 | | | | | | | | % 150.57/21.96 | | | | | | | Case 2: % 150.57/21.96 | | | | | | | | % 150.57/21.96 | | | | | | | | (67) all_54_9 = e0 % 150.57/21.96 | | | | | | | | % 150.57/21.96 | | | | | | | | COMBINE_EQS: (11), (67) imply: % 150.57/21.96 | | | | | | | | (68) all_6_0 = e0 % 150.57/21.96 | | | | | | | | % 150.57/21.96 | | | | | | | | SIMP: (68) implies: % 150.57/21.96 | | | | | | | | (69) all_6_0 = e0 % 150.57/21.96 | | | | | | | | % 150.57/21.96 | | | | | | | | REDUCE: (17), (69) imply: % 150.57/21.96 | | | | | | | | (70) ~ (all_6_2 = e0) % 150.57/21.96 | | | | | | | | % 150.57/21.96 | | | | | | | | SIMP: (70) implies: % 150.57/21.96 | | | | | | | | (71) ~ (all_6_2 = e0) % 150.57/21.96 | | | | | | | | % 150.57/21.96 | | | | | | | | REF_CLOSE: (5), (7), (13), (15), (16), (30), (32), (34), (71) % 150.57/21.96 | | | | | | | | are inconsistent by sub-proof #89. % 150.57/21.96 | | | | | | | | % 150.57/21.96 | | | | | | | End of split % 150.57/21.96 | | | | | | | % 150.57/21.96 | | | | | | End of split % 150.57/21.96 | | | | | | % 150.57/21.96 | | | | | End of split % 150.57/21.96 | | | | | % 150.57/21.96 | | | | End of split % 150.57/21.96 | | | | % 150.57/21.96 | | | Case 2: % 150.57/21.96 | | | | % 150.57/21.96 | | | | (72) all_54_5 = e1 | all_54_5 = e0 % 150.57/21.96 | | | | % 150.57/21.96 | | | | REF_CLOSE: (10), (37), (44), (72) are inconsistent by sub-proof #645. % 150.57/21.96 | | | | % 150.57/21.96 | | | End of split % 150.57/21.96 | | | % 150.57/21.96 | | End of split % 150.57/21.96 | | % 150.57/21.96 | Case 2: % 150.57/21.96 | | % 150.57/21.96 | | (73) all_56_13 = e2 % 150.57/21.96 | | (74) all_56_11 = e1 % 150.57/21.96 | | % 150.57/21.96 | | COMBINE_EQS: (1), (74) imply: % 150.57/21.96 | | (75) all_8_2 = e1 % 150.57/21.96 | | % 150.57/21.96 | | COMBINE_EQS: (18), (73) imply: % 150.57/21.96 | | (76) all_52_9 = e2 % 150.57/21.96 | | % 150.57/21.96 | | REDUCE: (6), (75), (76) imply: % 150.57/21.96 | | (77) ~ (e2 = e1) % 150.57/21.96 | | % 150.57/21.96 | | REDUCE: (33), (76) imply: % 150.57/21.96 | | (78) ~ (all_6_2 = e2) % 150.57/21.96 | | % 150.57/21.96 | | REDUCE: (23), (75) imply: % 150.57/21.96 | | (79) ~ (e3 = e1) % 150.57/21.96 | | % 150.57/21.96 | | SIMP: (79) implies: % 150.57/21.96 | | (80) ~ (e3 = e1) % 150.57/21.96 | | % 150.57/21.96 | | REDUCE: (41), (75) imply: % 150.57/21.96 | | (81) op(e1, e1) = all_8_1 % 150.57/21.96 | | % 150.57/21.96 | | GROUND_INST: instantiating (15) with all_6_2, all_8_1, e1, e1, simplifying % 150.57/21.96 | | with (30), (81) gives: % 150.57/21.96 | | (82) all_8_1 = all_6_2 % 150.57/21.96 | | % 150.57/21.96 | | REDUCE: (4), (82) imply: % 150.57/21.96 | | (83) ~ (all_6_2 = e1) % 150.57/21.96 | | % 150.57/21.96 | | BETA: splitting (13) gives: % 150.57/21.96 | | % 150.57/21.96 | | Case 1: % 150.57/21.96 | | | % 150.57/21.96 | | | (84) all_54_10 = e3 % 150.57/21.96 | | | % 150.57/21.96 | | | REF_CLOSE: (5), (7), (84) are inconsistent by sub-proof #736. % 150.57/21.96 | | | % 150.57/21.96 | | Case 2: % 150.57/21.96 | | | % 150.57/21.96 | | | (85) ~ (all_54_10 = e3) % 150.57/21.96 | | | (86) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 150.57/21.96 | | | % 150.57/21.96 | | | BETA: splitting (86) gives: % 150.57/21.96 | | | % 150.57/21.96 | | | Case 1: % 150.57/21.96 | | | | % 150.57/21.96 | | | | (87) all_54_10 = e2 % 150.57/21.96 | | | | % 150.57/21.96 | | | | REF_CLOSE: (5), (32), (87) are inconsistent by sub-proof #735. % 150.57/21.96 | | | | % 150.57/21.96 | | | Case 2: % 150.57/21.96 | | | | % 150.57/21.96 | | | | (88) ~ (all_54_10 = e2) % 150.57/21.96 | | | | (89) all_54_10 = e1 | all_54_10 = e0 % 150.57/21.96 | | | | % 150.57/21.96 | | | | BETA: splitting (89) gives: % 150.57/21.96 | | | | % 150.57/21.96 | | | | Case 1: % 150.57/21.96 | | | | | % 150.57/21.96 | | | | | (90) all_54_10 = e1 % 150.57/21.96 | | | | | % 150.57/21.96 | | | | | REF_CLOSE: (5), (83), (90) are inconsistent by sub-proof #606. % 150.57/21.96 | | | | | % 150.57/21.96 | | | | Case 2: % 150.57/21.96 | | | | | % 150.57/21.96 | | | | | (91) all_54_10 = e0 % 150.57/21.96 | | | | | % 150.57/21.96 | | | | | COMBINE_EQS: (5), (91) imply: % 150.57/21.96 | | | | | (92) all_6_2 = e0 % 150.57/21.96 | | | | | % 150.57/21.96 | | | | | SIMP: (92) implies: % 150.57/21.96 | | | | | (93) all_6_2 = e0 % 150.57/21.96 | | | | | % 150.57/21.96 | | | | | COMBINE_EQS: (12), (93) imply: % 150.57/21.96 | | | | | (94) all_56_21 = e0 % 150.57/21.96 | | | | | % 150.57/21.96 | | | | | COMBINE_EQS: (19), (93) imply: % 150.57/21.96 | | | | | (95) all_58_8 = e0 % 150.57/21.96 | | | | | % 150.57/21.96 | | | | | REDUCE: (38), (93) imply: % 150.57/21.96 | | | | | (96) ~ (all_52_14 = e0) % 150.57/21.96 | | | | | % 150.57/21.96 | | | | | REDUCE: (7), (93) imply: % 150.57/21.96 | | | | | (97) ~ (e3 = e0) % 150.57/21.96 | | | | | % 150.57/21.96 | | | | | SIMP: (97) implies: % 150.57/21.96 | | | | | (98) ~ (e3 = e0) % 150.57/21.96 | | | | | % 150.57/21.96 | | | | | REDUCE: (32), (93) imply: % 150.57/21.96 | | | | | (99) ~ (e2 = e0) % 150.57/21.96 | | | | | % 150.57/21.96 | | | | | SIMP: (99) implies: % 150.57/21.96 | | | | | (100) ~ (e2 = e0) % 150.57/21.96 | | | | | % 150.57/21.96 | | | | | REDUCE: (16), (93) imply: % 150.57/21.96 | | | | | (101) op(e0, e0) = e2 % 150.57/21.96 | | | | | % 150.57/21.96 | | | | | BETA: splitting (35) gives: % 150.57/21.96 | | | | | % 150.57/21.96 | | | | | Case 1: % 150.57/21.96 | | | | | | % 150.57/21.96 | | | | | | (102) ~ (all_56_21 = e0) % 150.57/21.96 | | | | | | % 150.57/21.96 | | | | | | REDUCE: (94), (102) imply: % 150.57/21.96 | | | | | | (103) $false % 150.57/21.96 | | | | | | % 150.57/21.96 | | | | | | CLOSE: (103) is inconsistent. % 150.57/21.96 | | | | | | % 150.57/21.96 | | | | | Case 2: % 150.57/21.96 | | | | | | % 150.57/21.96 | | | | | | (104) all_56_23 = e1 % 150.57/21.96 | | | | | | % 150.57/21.96 | | | | | | COMBINE_EQS: (29), (104) imply: % 150.57/21.96 | | | | | | (105) all_52_14 = e1 % 150.57/21.96 | | | | | | % 150.57/21.96 | | | | | | SIMP: (105) implies: % 150.57/21.96 | | | | | | (106) all_52_14 = e1 % 150.57/21.96 | | | | | | % 150.57/21.96 | | | | | | COMBINE_EQS: (27), (106) imply: % 150.57/21.96 | | | | | | (107) all_58_11 = e1 % 150.57/21.96 | | | | | | % 150.57/21.96 | | | | | | REDUCE: (96), (106) imply: % 150.57/21.96 | | | | | | (108) ~ (e1 = e0) % 150.57/21.96 | | | | | | % 150.57/21.96 | | | | | | BETA: splitting (21) gives: % 150.57/21.96 | | | | | | % 150.57/21.96 | | | | | | Case 1: % 150.57/21.96 | | | | | | | % 150.57/21.96 | | | | | | | (109) all_58_6 = e3 % 150.57/21.96 | | | | | | | % 150.57/21.96 | | | | | | | COMBINE_EQS: (3), (109) imply: % 150.57/21.96 | | | | | | | (110) all_52_2 = e3 % 150.57/21.96 | | | | | | | % 150.57/21.96 | | | | | | | REDUCE: (39), (110) imply: % 150.57/21.96 | | | | | | | (111) ~ (all_10_2 = e3) % 150.57/21.96 | | | | | | | % 150.57/21.96 | | | | | | | SIMP: (111) implies: % 150.57/21.96 | | | | | | | (112) ~ (all_10_2 = e3) % 150.57/21.96 | | | | | | | % 150.57/21.96 | | | | | | | BETA: splitting (28) gives: % 150.57/21.96 | | | | | | | % 150.57/21.96 | | | | | | | Case 1: % 150.57/21.96 | | | | | | | | % 150.57/21.96 | | | | | | | | (113) all_56_1 = e3 % 150.57/21.96 | | | | | | | | % 150.57/21.96 | | | | | | | | COMBINE_EQS: (14), (113) imply: % 150.57/21.96 | | | | | | | | (114) all_10_2 = e3 % 150.57/21.96 | | | | | | | | % 150.57/21.96 | | | | | | | | REDUCE: (112), (114) imply: % 150.57/21.96 | | | | | | | | (115) $false % 150.57/21.96 | | | | | | | | % 150.57/21.96 | | | | | | | | CLOSE: (115) is inconsistent. % 150.57/21.96 | | | | | | | | % 150.57/21.96 | | | | | | | Case 2: % 150.57/21.96 | | | | | | | | % 150.57/21.96 | | | | | | | | (116) all_56_11 = e2 | all_56_21 = e1 | all_56_31 = e0 % 150.57/21.96 | | | | | | | | % 150.57/21.96 | | | | | | | | BETA: splitting (116) gives: % 150.57/21.96 | | | | | | | | % 150.57/21.96 | | | | | | | | Case 1: % 150.57/21.96 | | | | | | | | | % 150.57/21.96 | | | | | | | | | (117) all_56_11 = e2 % 150.57/21.96 | | | | | | | | | % 150.57/21.96 | | | | | | | | | REF_CLOSE: (74), (77), (117) are inconsistent by sub-proof % 150.57/21.96 | | | | | | | | | #419. % 150.57/21.96 | | | | | | | | | % 150.57/21.96 | | | | | | | | Case 2: % 150.57/21.96 | | | | | | | | | % 150.57/21.96 | | | | | | | | | (118) all_56_21 = e1 | all_56_31 = e0 % 150.57/21.96 | | | | | | | | | % 150.57/21.96 | | | | | | | | | REF_CLOSE: (9), (15), (24), (26), (36), (94), (100), (101), % 150.57/21.96 | | | | | | | | | (108), (118) are inconsistent by sub-proof #86. % 150.57/21.96 | | | | | | | | | % 150.57/21.96 | | | | | | | | End of split % 150.57/21.96 | | | | | | | | % 150.57/21.96 | | | | | | | End of split % 150.57/21.96 | | | | | | | % 150.57/21.96 | | | | | | Case 2: % 150.57/21.96 | | | | | | | % 150.57/21.96 | | | | | | | (119) all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3 % 150.57/21.96 | | | | | | | % 150.57/21.96 | | | | | | | REF_CLOSE: (20), (31), (80), (95), (98), (107), (119) are % 150.57/21.96 | | | | | | | inconsistent by sub-proof #85. % 150.57/21.96 | | | | | | | % 150.57/21.96 | | | | | | End of split % 150.57/21.96 | | | | | | % 150.57/21.96 | | | | | End of split % 150.57/21.96 | | | | | % 150.57/21.96 | | | | End of split % 150.57/21.96 | | | | % 150.57/21.96 | | | End of split % 150.57/21.96 | | | % 150.57/21.96 | | End of split % 150.57/21.96 | | % 150.57/21.96 | End of split % 150.57/21.96 | % 150.57/21.96 End of proof % 150.57/21.96 % 150.57/21.96 Sub-proof #85 shows that the following formulas are inconsistent: % 150.57/21.96 ---------------------------------------------------------------- % 150.57/21.96 (1) ~ (e3 = e0) % 150.57/21.96 (2) all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3 % 150.57/21.96 (3) all_58_11 = e1 % 150.57/21.96 (4) ~ (all_6_0 = e3) % 150.57/21.96 (5) all_58_8 = e0 % 150.57/21.96 (6) all_58_7 = all_6_0 % 150.57/21.96 (7) ~ (e3 = e1) % 150.57/21.96 % 150.57/21.96 Begin of proof % 150.57/21.96 | % 150.57/21.96 | BETA: splitting (2) gives: % 150.57/21.96 | % 150.57/21.96 | Case 1: % 150.57/21.96 | | % 150.57/21.96 | | (8) all_58_7 = e3 % 150.57/21.96 | | % 150.57/21.96 | | COMBINE_EQS: (6), (8) imply: % 150.57/21.96 | | (9) all_6_0 = e3 % 150.57/21.96 | | % 150.57/21.96 | | REDUCE: (4), (9) imply: % 150.57/21.96 | | (10) $false % 150.57/21.96 | | % 150.57/21.96 | | CLOSE: (10) is inconsistent. % 150.57/21.96 | | % 150.57/21.96 | Case 2: % 150.57/21.96 | | % 150.57/21.96 | | (11) all_58_8 = e3 | all_58_11 = e3 % 150.57/21.96 | | % 150.57/21.96 | | REF_CLOSE: (1), (3), (5), (7), (11) are inconsistent by sub-proof #343. % 150.57/21.96 | | % 150.57/21.96 | End of split % 150.57/21.96 | % 150.57/21.96 End of proof % 150.57/21.96 % 150.57/21.96 Sub-proof #86 shows that the following formulas are inconsistent: % 150.57/21.96 ---------------------------------------------------------------- % 150.57/21.96 (1) op(e0, e0) = all_4_2 % 150.57/21.96 (2) all_56_21 = e0 % 150.57/21.96 (3) ~ (e1 = e0) % 150.57/21.96 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 150.57/21.96 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 150.57/21.96 (5) op(all_4_2, all_4_2) = all_4_1 % 150.57/21.96 (6) op(e0, e0) = e2 % 150.57/21.96 (7) all_56_31 = all_4_2 % 150.57/21.96 (8) all_56_21 = e1 | all_56_31 = e0 % 150.57/21.96 (9) op(e0, all_4_2) = all_56_30 % 150.57/21.96 (10) ~ (e2 = e0) % 150.57/21.96 % 150.57/21.96 Begin of proof % 150.57/21.96 | % 150.57/21.96 | BETA: splitting (8) gives: % 150.57/21.96 | % 150.57/21.96 | Case 1: % 150.57/21.96 | | % 150.57/21.96 | | (11) all_56_21 = e1 % 150.57/21.96 | | % 150.57/21.96 | | COMBINE_EQS: (2), (11) imply: % 150.57/21.96 | | (12) e1 = e0 % 150.57/21.96 | | % 150.57/21.96 | | REDUCE: (3), (12) imply: % 150.57/21.96 | | (13) $false % 150.57/21.96 | | % 150.57/21.96 | | CLOSE: (13) is inconsistent. % 150.57/21.96 | | % 150.57/21.96 | Case 2: % 150.57/21.96 | | % 150.57/21.96 | | (14) all_56_31 = e0 % 150.57/21.96 | | % 150.57/21.96 | | COMBINE_EQS: (7), (14) imply: % 150.57/21.96 | | (15) all_4_2 = e0 % 150.57/21.96 | | % 150.57/21.96 | | SIMP: (15) implies: % 150.57/21.96 | | (16) all_4_2 = e0 % 150.57/21.96 | | % 150.57/21.96 | | REDUCE: (5), (16) imply: % 150.57/21.96 | | (17) op(e0, e0) = all_4_1 % 150.57/21.96 | | % 150.57/21.96 | | REDUCE: (9), (16) imply: % 150.57/21.96 | | (18) op(e0, e0) = all_56_30 % 150.57/21.96 | | % 150.57/21.96 | | REDUCE: (1), (16) imply: % 150.57/21.96 | | (19) op(e0, e0) = e0 % 150.57/21.96 | | % 150.57/21.96 | | REF_CLOSE: (4), (6), (10), (17), (18), (19) are inconsistent by sub-proof % 150.57/21.96 | | #231. % 150.57/21.96 | | % 150.57/21.96 | End of split % 150.57/21.96 | % 150.57/21.96 End of proof % 150.57/21.96 % 150.57/21.96 Sub-proof #87 shows that the following formulas are inconsistent: % 150.57/21.96 ---------------------------------------------------------------- % 150.57/21.96 (1) all_54_9 = all_6_0 % 150.57/21.96 (2) all_54_9 = e1 % 150.57/21.96 (3) ~ (all_6_0 = e1) % 150.57/21.96 % 150.57/21.96 Begin of proof % 150.57/21.96 | % 150.57/21.96 | COMBINE_EQS: (1), (2) imply: % 150.57/21.96 | (4) all_6_0 = e1 % 150.57/21.96 | % 150.57/21.96 | SIMP: (4) implies: % 150.57/21.96 | (5) all_6_0 = e1 % 150.57/21.96 | % 150.57/21.96 | REDUCE: (3), (5) imply: % 150.57/21.96 | (6) $false % 150.57/21.96 | % 150.57/21.96 | CLOSE: (6) is inconsistent. % 150.57/21.96 | % 150.57/21.96 End of proof % 150.57/21.96 % 150.57/21.96 Sub-proof #88 shows that the following formulas are inconsistent: % 150.57/21.96 ---------------------------------------------------------------- % 150.57/21.96 (1) all_54_9 = all_6_0 % 150.57/21.96 (2) all_54_9 = e3 % 150.57/21.96 (3) ~ (all_6_0 = e3) % 150.57/21.96 % 150.57/21.96 Begin of proof % 150.57/21.96 | % 150.57/21.96 | COMBINE_EQS: (1), (2) imply: % 150.57/21.96 | (4) all_6_0 = e3 % 150.57/21.96 | % 150.57/21.96 | SIMP: (4) implies: % 150.57/21.96 | (5) all_6_0 = e3 % 150.57/21.96 | % 150.57/21.96 | REDUCE: (3), (5) imply: % 150.57/21.96 | (6) $false % 150.57/21.96 | % 150.57/21.96 | CLOSE: (6) is inconsistent. % 150.57/21.96 | % 150.57/21.96 End of proof % 150.57/21.96 % 150.57/21.96 Sub-proof #89 shows that the following formulas are inconsistent: % 150.57/21.96 ---------------------------------------------------------------- % 150.57/21.96 (1) all_54_10 = all_6_2 % 150.57/21.96 (2) ~ (all_6_2 = e3) % 150.57/21.96 (3) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 150.57/21.96 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 150.57/21.96 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 150.57/21.96 (5) ~ (all_6_2 = e0) % 150.57/21.96 (6) op(all_6_2, all_6_2) = e2 % 150.57/21.96 (7) op(e1, e1) = all_6_2 % 150.57/21.97 (8) ~ (all_6_2 = e2) % 150.57/21.97 (9) op(e1, all_6_2) = all_56_20 % 150.57/21.97 % 150.57/21.97 Begin of proof % 150.57/21.97 | % 150.57/21.97 | BETA: splitting (3) gives: % 150.57/21.97 | % 150.57/21.97 | Case 1: % 150.57/21.97 | | % 150.57/21.97 | | (10) all_54_10 = e3 % 150.57/21.97 | | % 150.57/21.97 | | REF_CLOSE: (1), (2), (10) are inconsistent by sub-proof #736. % 150.57/21.97 | | % 150.57/21.97 | Case 2: % 150.57/21.97 | | % 150.57/21.97 | | (11) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 150.57/21.97 | | % 150.57/21.97 | | REF_CLOSE: (1), (4), (5), (6), (7), (8), (9), (11) are inconsistent by % 150.57/21.97 | | sub-proof #90. % 150.57/21.97 | | % 150.57/21.97 | End of split % 150.57/21.97 | % 150.57/21.97 End of proof % 150.57/21.97 % 150.57/21.97 Sub-proof #90 shows that the following formulas are inconsistent: % 150.57/21.97 ---------------------------------------------------------------- % 150.57/21.97 (1) all_54_10 = all_6_2 % 150.57/21.97 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 150.57/21.97 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 150.57/21.97 (3) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 150.57/21.97 (4) ~ (all_6_2 = e0) % 150.57/21.97 (5) op(all_6_2, all_6_2) = e2 % 150.57/21.97 (6) op(e1, e1) = all_6_2 % 150.57/21.97 (7) ~ (all_6_2 = e2) % 150.57/21.97 (8) op(e1, all_6_2) = all_56_20 % 150.57/21.97 % 150.57/21.97 Begin of proof % 150.57/21.97 | % 150.57/21.97 | BETA: splitting (3) gives: % 150.57/21.97 | % 150.57/21.97 | Case 1: % 150.57/21.97 | | % 150.57/21.97 | | (9) all_54_10 = e2 % 150.57/21.97 | | % 150.57/21.97 | | REF_CLOSE: (1), (7), (9) are inconsistent by sub-proof #735. % 150.57/21.97 | | % 150.57/21.97 | Case 2: % 150.57/21.97 | | % 150.57/21.97 | | (10) ~ (all_54_10 = e2) % 150.57/21.97 | | (11) all_54_10 = e1 | all_54_10 = e0 % 150.57/21.97 | | % 150.57/21.97 | | BETA: splitting (11) gives: % 150.57/21.97 | | % 150.57/21.97 | | Case 1: % 150.57/21.97 | | | % 150.57/21.97 | | | (12) all_54_10 = e1 % 150.57/21.97 | | | % 150.57/21.97 | | | COMBINE_EQS: (1), (12) imply: % 150.57/21.97 | | | (13) all_6_2 = e1 % 150.57/21.97 | | | % 150.57/21.97 | | | SIMP: (13) implies: % 150.57/21.97 | | | (14) all_6_2 = e1 % 150.57/21.97 | | | % 150.57/21.97 | | | REDUCE: (7), (14) imply: % 150.57/21.97 | | | (15) ~ (e2 = e1) % 150.57/21.97 | | | % 150.57/21.97 | | | SIMP: (15) implies: % 150.57/21.97 | | | (16) ~ (e2 = e1) % 150.57/21.97 | | | % 150.57/21.97 | | | REDUCE: (5), (14) imply: % 150.57/21.97 | | | (17) op(e1, e1) = e2 % 150.57/21.97 | | | % 150.57/21.97 | | | REDUCE: (8), (14) imply: % 150.57/21.97 | | | (18) op(e1, e1) = all_56_20 % 150.57/21.97 | | | % 150.57/21.97 | | | REDUCE: (6), (14) imply: % 150.57/21.97 | | | (19) op(e1, e1) = e1 % 150.57/21.97 | | | % 150.57/21.97 | | | REF_CLOSE: (2), (16), (17), (18), (19) are inconsistent by sub-proof #494. % 150.57/21.97 | | | % 150.57/21.97 | | Case 2: % 150.57/21.97 | | | % 150.57/21.97 | | | (20) all_54_10 = e0 % 150.57/21.97 | | | % 150.57/21.97 | | | REF_CLOSE: (1), (4), (20) are inconsistent by sub-proof #705. % 150.57/21.97 | | | % 150.57/21.97 | | End of split % 150.57/21.97 | | % 150.57/21.97 | End of split % 150.57/21.97 | % 150.57/21.97 End of proof % 150.57/21.97 % 150.57/21.97 Sub-proof #91 shows that the following formulas are inconsistent: % 150.57/21.97 ---------------------------------------------------------------- % 150.57/21.97 (1) all_58_13 = all_52_7 % 150.57/21.97 (2) all_58_13 = e2 % 150.57/21.97 (3) ~ (all_52_7 = e2) % 150.57/21.97 % 150.57/21.97 Begin of proof % 150.57/21.97 | % 150.57/21.97 | COMBINE_EQS: (1), (2) imply: % 150.57/21.97 | (4) all_52_7 = e2 % 150.57/21.97 | % 150.57/21.97 | SIMP: (4) implies: % 150.57/21.97 | (5) all_52_7 = e2 % 150.57/21.97 | % 150.57/21.97 | REDUCE: (3), (5) imply: % 150.57/21.97 | (6) $false % 150.57/21.97 | % 150.57/21.97 | CLOSE: (6) is inconsistent. % 150.57/21.97 | % 150.57/21.97 End of proof % 150.57/21.97 % 150.57/21.97 Sub-proof #92 shows that the following formulas are inconsistent: % 150.57/21.97 ---------------------------------------------------------------- % 150.57/21.97 (1) all_56_11 = all_8_2 % 150.57/21.97 (2) op(e0, all_52_13) = all_56_14 % 150.57/21.97 (3) ~ (all_56_11 = e1) | all_56_13 = e2 % 150.57/21.97 (4) ~ (all_52_11 = all_6_2) % 150.57/21.97 (5) ~ (all_52_4 = all_52_8) % 150.57/21.97 (6) all_56_25 = all_52_3 % 150.57/21.97 (7) ~ (all_34_1 = e3) | ~ (all_34_2 = e1) % 150.57/21.97 (8) ~ (all_52_7 = all_52_11) % 150.57/21.97 (9) all_54_9 = all_52_6 % 150.57/21.97 (10) all_58_6 = all_52_2 % 150.57/21.97 (11) ~ (all_8_0 = all_6_2) % 150.57/21.97 (12) ~ (e3 = e0) % 150.57/21.97 (13) ~ (all_56_31 = e1) | all_56_29 = e0 % 150.57/21.97 (14) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0 % 150.57/21.97 (15) all_54_10 = all_6_2 % 150.57/21.97 (16) ~ (all_6_1 = e2) % 150.57/21.97 (17) all_12_2 = all_4_2 % 150.57/21.97 (18) ~ (all_56_21 = e2) | all_56_19 = e1 % 150.57/21.97 (19) all_54_0 = all_10_2 % 150.57/21.97 (20) all_48_1 = e1 % 150.57/21.97 (21) all_54_4 = all_52_1 % 150.57/21.97 (22) ~ (all_52_14 = all_4_2) % 150.57/21.97 (23) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0 % 150.57/21.97 (24) all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2 % 150.57/21.97 (25) ~ (all_52_12 = all_52_13) % 150.57/21.97 (26) ~ (e3 = e2) % 150.57/21.97 (27) op(e0, e0) = all_4_2 % 150.57/21.97 (28) ~ (all_52_13 = all_8_0) % 150.57/21.97 (29) all_58_4 = all_52_8 % 150.57/21.97 (30) all_54_5 = all_8_2 % 150.57/21.97 (31) ~ (all_52_6 = all_52_14) % 150.57/21.97 (32) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 150.57/21.97 (33) ~ (all_6_0 = e2) % 150.57/21.97 (34) ~ (all_48_0 = e3) | ~ (all_48_1 = e1) | ~ (all_48_2 = e0) % 150.57/21.97 (35) all_54_15 = all_4_2 % 150.57/21.97 (36) all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1 % 150.57/21.97 (37) ~ (all_8_0 = all_8_2) % 150.57/21.97 (38) all_56_21 = all_6_2 % 150.57/21.97 (39) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 150.57/21.97 (40) ~ (all_52_7 = all_8_2) % 150.57/21.97 (41) all_56_1 = all_10_2 % 150.57/21.97 (42) all_56_27 = all_52_7 % 150.57/21.97 (43) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0 % 150.57/21.97 (44) all_58_5 = all_52_9 % 150.57/21.97 (45) all_48_0 = all_8_0 % 150.57/21.97 (46) all_56_17 = all_52_2 % 150.57/21.97 (47) all_58_9 = all_52_12 % 150.57/21.97 (48) op(e0, all_52_12) = all_56_6 % 150.57/21.97 (49) ~ (all_36_1 = e3) % 150.57/21.97 (50) op(e1, e0) = all_52_14 % 150.57/21.97 (51) all_54_14 = all_52_11 % 150.57/21.97 (52) all_58_5 = all_8_0 % 150.57/21.97 (53) op(e2, all_8_2) = all_56_10 % 150.57/21.97 (54) op(e3, e3) = all_10_2 % 150.57/21.97 (55) ~ (all_56_21 = e3) | all_56_17 = e1 % 150.57/21.97 (56) all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2 % 150.57/21.97 (57) ~ (all_52_1 = all_8_2) % 150.57/21.97 (58) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 150.57/21.97 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 150.57/21.97 (59) ~ (all_52_3 = all_10_2) % 150.57/21.97 (60) all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0 % 150.57/21.97 (61) all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) & % 150.57/21.97 (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0)) % 150.57/21.97 (62) ~ (all_56_11 = e3) | all_56_9 = e2 % 150.57/21.97 (63) ~ (all_52_2 = all_52_6) % 150.57/21.97 (64) all_56_7 = all_52_12 % 150.57/21.97 (65) op(e0, all_4_1) = e2 % 150.57/21.97 (66) op(e0, e1) = all_52_11 % 150.57/21.97 (67) ~ (all_52_1 = all_52_13) % 150.57/21.97 (68) ~ (all_52_7 = all_4_2) % 150.57/21.97 (69) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0 % 150.57/21.97 (70) all_36_1 = all_6_1 % 150.57/21.97 (71) all_58_8 = all_6_2 % 150.57/21.97 (72) ~ (all_52_3 = all_4_2) % 150.57/21.97 (73) ~ (all_52_8 = all_10_2) % 150.57/21.97 (74) ~ (all_56_1 = e2) | all_56_3 = e3 % 150.57/21.97 (75) ~ (all_56_1 = e0) | all_56_7 = e3 % 150.57/21.97 (76) ~ (all_12_1 = e1) | ~ (all_12_2 = e3) % 150.57/21.97 (77) all_34_1 = all_4_1 % 150.57/21.97 (78) ~ (e2 = e1) % 150.57/21.97 (79) op(e1, all_6_1) = all_6_0 % 150.57/21.97 (80) op(all_4_2, all_4_2) = all_4_1 % 150.57/21.97 (81) all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3 % 150.57/21.97 (82) all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1 % 150.57/21.97 (83) all_58_3 = all_8_2 % 150.57/21.97 (84) all_56_3 = all_52_4 % 150.57/21.97 (85) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0 % 150.57/21.97 (86) ~ (all_52_11 = all_4_2) % 150.57/21.97 (87) all_56_31 = all_4_2 % 150.57/21.97 (88) all_58_11 = all_52_14 % 150.57/21.97 (89) all_56_13 = all_8_0 % 150.57/21.97 (90) ~ (all_52_2 = all_52_14) % 150.57/21.97 (91) ~ (all_52_1 = all_8_0) % 150.57/21.97 (92) op(all_6_2, all_6_2) = all_6_1 % 150.57/21.97 (93) all_56_1 = e3 | all_56_11 = e2 | all_56_21 = e1 | all_56_31 = e0 % 150.57/21.97 (94) ~ (all_52_11 = all_8_0) % 150.57/21.97 (95) ~ (all_52_13 = all_4_2) % 150.57/21.97 (96) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0 % 150.57/21.97 (97) ~ (all_8_0 = e0) | ~ (all_8_2 = e3) % 150.57/21.97 (98) ~ (all_52_13 = all_52_14) % 150.57/21.97 (99) all_56_23 = all_52_14 % 150.57/21.97 (100) op(all_8_2, all_8_2) = e1 % 150.57/21.97 (101) op(e1, e1) = all_6_2 % 150.57/21.97 (102) ~ (all_52_6 = all_8_2) % 150.57/21.97 (103) all_58_15 = all_4_2 % 150.57/21.97 (104) all_56_29 = all_52_11 % 150.57/21.97 (105) all_58_2 = all_52_1 % 150.57/21.97 (106) all_58_10 = all_52_13 % 150.57/21.97 (107) all_12_1 = all_4_1 % 150.57/21.97 (108) ~ (all_56_11 = e0) | all_56_15 = e2 % 150.57/21.97 (109) all_58_0 = all_10_2 % 150.57/21.97 (110) op(e1, all_6_2) = all_56_20 % 150.57/21.97 (111) ~ (all_52_12 = all_52_14) % 150.57/21.97 (112) op(e1, all_52_9) = all_56_12 % 150.57/21.97 (113) ~ (all_56_31 = e2) | all_56_27 = e0 % 150.57/21.97 (114) ~ (e3 = e1) % 150.57/21.97 (115) op(e2, e2) = all_8_2 % 150.57/21.97 (116) ~ (all_52_2 = all_6_2) % 150.57/21.97 (117) ~ (all_52_1 = all_52_2) % 150.57/21.97 (118) ~ (all_56_21 = e0) | all_56_23 = e1 % 150.57/21.97 (119) op(e0, all_4_2) = all_56_30 % 150.57/21.97 (120) ~ (all_52_6 = all_6_2) % 150.57/21.97 (121) all_48_2 = all_8_2 % 150.57/21.97 (122) all_54_6 = all_8_0 % 150.57/21.97 (123) ~ (all_52_14 = all_6_2) % 150.57/21.97 (124) ~ (e2 = e0) % 150.57/21.97 (125) ~ (all_52_2 = all_10_2) % 150.57/21.97 (126) all_34_2 = all_4_2 % 150.57/21.97 (127) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 150.57/21.97 (128) all_58_14 = all_52_11 % 150.57/21.97 (129) all_56_19 = all_52_6 % 150.57/21.97 (130) all_56_9 = all_52_1 % 150.57/21.97 (131) all_56_15 = all_52_13 % 150.57/21.97 (132) ~ (all_52_1 = all_10_2) % 150.57/21.97 (133) all_58_12 = all_52_3 % 150.57/21.97 (134) all_54_11 = all_52_14 % 150.57/21.97 (135) ~ (all_56_31 = e3) | all_56_25 = e0 % 150.57/21.97 % 150.57/21.97 Begin of proof % 150.57/21.97 | % 150.57/21.97 | REDUCE: (49), (70) imply: % 150.57/21.97 | (136) ~ (all_6_1 = e3) % 150.57/21.97 | % 150.57/21.97 | BETA: splitting (34) gives: % 150.57/21.97 | % 150.57/21.97 | Case 1: % 150.57/21.97 | | % 150.57/21.97 | | (137) ~ (all_48_0 = e3) % 150.57/21.97 | | % 150.57/21.97 | | REDUCE: (45), (137) imply: % 150.57/21.97 | | (138) ~ (all_8_0 = e3) % 150.57/21.97 | | % 150.57/21.97 | | BETA: splitting (18) gives: % 150.57/21.97 | | % 150.57/21.97 | | Case 1: % 150.57/21.97 | | | % 150.57/21.97 | | | (139) ~ (all_56_21 = e2) % 150.57/21.97 | | | % 150.57/21.97 | | | REDUCE: (38), (139) imply: % 150.57/21.97 | | | (140) ~ (all_6_2 = e2) % 150.57/21.97 | | | % 150.57/21.97 | | | BETA: splitting (13) gives: % 150.57/21.97 | | | % 150.57/21.97 | | | Case 1: % 150.57/21.97 | | | | % 150.57/21.97 | | | | (141) ~ (all_56_31 = e1) % 150.57/21.97 | | | | % 150.57/21.97 | | | | REDUCE: (87), (141) imply: % 150.57/21.97 | | | | (142) ~ (all_4_2 = e1) % 150.57/21.97 | | | | % 150.57/21.97 | | | | BETA: splitting (135) gives: % 150.57/21.97 | | | | % 150.57/21.97 | | | | Case 1: % 150.57/21.97 | | | | | % 150.57/21.97 | | | | | (143) ~ (all_56_31 = e3) % 150.57/21.97 | | | | | % 150.57/21.97 | | | | | REDUCE: (87), (143) imply: % 150.57/21.97 | | | | | (144) ~ (all_4_2 = e3) % 150.57/21.97 | | | | | % 150.57/21.97 | | | | | BETA: splitting (118) gives: % 150.57/21.97 | | | | | % 150.57/21.97 | | | | | Case 1: % 150.57/21.97 | | | | | | % 150.57/21.97 | | | | | | (145) ~ (all_56_21 = e0) % 150.57/21.97 | | | | | | % 150.57/21.97 | | | | | | REDUCE: (38), (145) imply: % 150.57/21.97 | | | | | | (146) ~ (all_6_2 = e0) % 150.57/21.97 | | | | | | % 150.57/21.97 | | | | | | BETA: splitting (113) gives: % 150.57/21.97 | | | | | | % 150.57/21.97 | | | | | | Case 1: % 150.57/21.97 | | | | | | | % 150.57/21.97 | | | | | | | (147) ~ (all_56_31 = e2) % 150.57/21.97 | | | | | | | % 150.57/21.97 | | | | | | | REDUCE: (87), (147) imply: % 150.57/21.97 | | | | | | | (148) ~ (all_4_2 = e2) % 150.57/21.97 | | | | | | | % 150.57/21.97 | | | | | | | REF_CLOSE: (27), (35), (58), (65), (80), (96), (119), (142), % 150.57/21.97 | | | | | | | (144), (148) are inconsistent by sub-proof #229. % 150.57/21.97 | | | | | | | % 150.57/21.97 | | | | | | Case 2: % 150.57/21.97 | | | | | | | % 150.57/21.97 | | | | | | | (149) all_56_31 = e2 % 150.57/21.97 | | | | | | | (150) all_56_27 = e0 % 150.57/21.97 | | | | | | | % 150.57/21.97 | | | | | | | COMBINE_EQS: (42), (150) imply: % 150.57/21.97 | | | | | | | (151) all_52_7 = e0 % 150.57/21.97 | | | | | | | % 150.57/21.97 | | | | | | | SIMP: (151) implies: % 150.57/21.97 | | | | | | | (152) all_52_7 = e0 % 150.57/21.97 | | | | | | | % 150.57/21.97 | | | | | | | COMBINE_EQS: (87), (149) imply: % 150.57/21.97 | | | | | | | (153) all_4_2 = e2 % 150.57/21.97 | | | | | | | % 150.57/21.97 | | | | | | | REDUCE: (72), (153) imply: % 150.57/21.97 | | | | | | | (154) ~ (all_52_3 = e2) % 150.57/21.97 | | | | | | | % 150.57/21.97 | | | | | | | REDUCE: (8), (152) imply: % 150.57/21.97 | | | | | | | (155) ~ (all_52_11 = e0) % 150.57/21.97 | | | | | | | % 150.57/21.97 | | | | | | | SIMP: (155) implies: % 150.57/21.97 | | | | | | | (156) ~ (all_52_11 = e0) % 150.57/21.97 | | | | | | | % 150.57/21.97 | | | | | | | REDUCE: (40), (152) imply: % 150.57/21.97 | | | | | | | (157) ~ (all_8_2 = e0) % 150.57/21.97 | | | | | | | % 150.57/21.97 | | | | | | | SIMP: (157) implies: % 150.57/21.97 | | | | | | | (158) ~ (all_8_2 = e0) % 150.57/21.97 | | | | | | | % 150.57/21.97 | | | | | | | REDUCE: (68), (152), (153) imply: % 150.57/21.97 | | | | | | | (159) ~ (e2 = e0) % 150.57/21.97 | | | | | | | % 150.57/21.97 | | | | | | | REDUCE: (86), (153) imply: % 150.57/21.97 | | | | | | | (160) ~ (all_52_11 = e2) % 150.57/21.97 | | | | | | | % 150.57/21.97 | | | | | | | REDUCE: (80), (153) imply: % 150.57/21.97 | | | | | | | (161) op(e2, e2) = all_4_1 % 150.57/21.97 | | | | | | | % 150.57/21.97 | | | | | | | GROUND_INST: instantiating (58) with all_8_2, all_4_1, e2, e2, % 150.57/21.97 | | | | | | | simplifying with (115), (161) gives: % 150.57/21.97 | | | | | | | (162) all_8_2 = all_4_1 % 150.57/21.97 | | | | | | | % 150.57/21.97 | | | | | | | COMBINE_EQS: (30), (162) imply: % 150.57/21.97 | | | | | | | (163) all_54_5 = all_4_1 % 150.57/21.97 | | | | | | | % 150.57/21.97 | | | | | | | COMBINE_EQS: (1), (162) imply: % 150.57/21.97 | | | | | | | (164) all_56_11 = all_4_1 % 150.57/21.97 | | | | | | | % 150.57/21.97 | | | | | | | COMBINE_EQS: (83), (162) imply: % 150.57/21.97 | | | | | | | (165) all_58_3 = all_4_1 % 150.57/21.97 | | | | | | | % 150.57/21.97 | | | | | | | REDUCE: (57), (162) imply: % 150.57/21.97 | | | | | | | (166) ~ (all_52_1 = all_4_1) % 150.57/21.97 | | | | | | | % 150.57/21.97 | | | | | | | REDUCE: (37), (162) imply: % 150.57/21.97 | | | | | | | (167) ~ (all_8_0 = all_4_1) % 150.57/21.97 | | | | | | | % 150.57/21.97 | | | | | | | REDUCE: (158), (162) imply: % 150.57/21.97 | | | | | | | (168) ~ (all_4_1 = e0) % 150.57/21.97 | | | | | | | % 150.57/21.97 | | | | | | | REDUCE: (100), (162) imply: % 150.57/21.97 | | | | | | | (169) op(all_4_1, all_4_1) = e1 % 150.57/21.97 | | | | | | | % 150.57/21.97 | | | | | | | BETA: splitting (55) gives: % 150.57/21.97 | | | | | | | % 150.57/21.97 | | | | | | | Case 1: % 150.57/21.97 | | | | | | | | % 150.57/21.97 | | | | | | | | (170) ~ (all_56_21 = e3) % 150.57/21.97 | | | | | | | | % 150.57/21.97 | | | | | | | | REDUCE: (38), (170) imply: % 150.57/21.97 | | | | | | | | (171) ~ (all_6_2 = e3) % 150.57/21.97 | | | | | | | | % 150.57/21.97 | | | | | | | | BETA: splitting (39) gives: % 150.57/21.97 | | | | | | | | % 150.57/21.97 | | | | | | | | Case 1: % 150.57/21.97 | | | | | | | | | % 150.57/21.97 | | | | | | | | | (172) all_54_10 = e3 % 150.57/21.97 | | | | | | | | | % 150.57/21.97 | | | | | | | | | REF_CLOSE: (15), (171), (172) are inconsistent by sub-proof % 150.57/21.97 | | | | | | | | | #736. % 150.57/21.97 | | | | | | | | | % 150.57/21.97 | | | | | | | | Case 2: % 150.57/21.97 | | | | | | | | | % 150.57/21.97 | | | | | | | | | (173) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 150.57/21.97 | | | | | | | | | % 150.57/21.97 | | | | | | | | | BETA: splitting (173) gives: % 150.57/21.97 | | | | | | | | | % 150.57/21.97 | | | | | | | | | Case 1: % 150.57/21.97 | | | | | | | | | | % 150.57/21.97 | | | | | | | | | | (174) all_54_10 = e2 % 150.57/21.97 | | | | | | | | | | % 150.57/21.97 | | | | | | | | | | REF_CLOSE: (15), (140), (174) are inconsistent by sub-proof % 150.57/21.97 | | | | | | | | | | #735. % 150.57/21.97 | | | | | | | | | | % 150.57/21.97 | | | | | | | | | Case 2: % 150.57/21.97 | | | | | | | | | | % 150.57/21.97 | | | | | | | | | | (175) all_54_10 = e1 | all_54_10 = e0 % 150.57/21.97 | | | | | | | | | | % 150.57/21.97 | | | | | | | | | | BETA: splitting (175) gives: % 150.57/21.97 | | | | | | | | | | % 150.57/21.97 | | | | | | | | | | Case 1: % 150.57/21.97 | | | | | | | | | | | % 150.57/21.97 | | | | | | | | | | | (176) all_54_10 = e1 % 150.57/21.97 | | | | | | | | | | | % 150.57/21.97 | | | | | | | | | | | COMBINE_EQS: (15), (176) imply: % 150.57/21.97 | | | | | | | | | | | (177) all_6_2 = e1 % 150.57/21.97 | | | | | | | | | | | % 150.57/21.97 | | | | | | | | | | | SIMP: (177) implies: % 150.57/21.97 | | | | | | | | | | | (178) all_6_2 = e1 % 150.57/21.97 | | | | | | | | | | | % 150.57/21.97 | | | | | | | | | | | REDUCE: (4), (178) imply: % 150.57/21.97 | | | | | | | | | | | (179) ~ (all_52_11 = e1) % 150.57/21.97 | | | | | | | | | | | % 150.57/21.97 | | | | | | | | | | | REDUCE: (123), (178) imply: % 150.57/21.97 | | | | | | | | | | | (180) ~ (all_52_14 = e1) % 150.57/21.97 | | | | | | | | | | | % 150.57/21.97 | | | | | | | | | | | BETA: splitting (14) gives: % 150.57/21.97 | | | | | | | | | | | % 150.57/21.97 | | | | | | | | | | | Case 1: % 150.57/21.97 | | | | | | | | | | | | % 150.57/21.97 | | | | | | | | | | | | (181) all_54_14 = e3 % 150.57/21.97 | | | | | | | | | | | | % 150.57/21.97 | | | | | | | | | | | | COMBINE_EQS: (51), (181) imply: % 150.57/21.97 | | | | | | | | | | | | (182) all_52_11 = e3 % 150.57/21.97 | | | | | | | | | | | | % 150.57/21.97 | | | | | | | | | | | | SIMP: (182) implies: % 150.57/21.97 | | | | | | | | | | | | (183) all_52_11 = e3 % 150.57/21.97 | | | | | | | | | | | | % 150.57/21.97 | | | | | | | | | | | | REDUCE: (94), (183) imply: % 150.57/21.97 | | | | | | | | | | | | (184) ~ (all_8_0 = e3) % 150.57/21.97 | | | | | | | | | | | | % 150.57/21.97 | | | | | | | | | | | | REDUCE: (66), (183) imply: % 150.57/21.97 | | | | | | | | | | | | (185) op(e0, e1) = e3 % 150.57/21.97 | | | | | | | | | | | | % 150.57/21.97 | | | | | | | | | | | | BETA: splitting (62) gives: % 150.57/21.97 | | | | | | | | | | | | % 150.57/21.97 | | | | | | | | | | | | Case 1: % 150.57/21.97 | | | | | | | | | | | | | % 150.57/21.97 | | | | | | | | | | | | | (186) ~ (all_56_11 = e3) % 150.57/21.97 | | | | | | | | | | | | | % 150.57/21.97 | | | | | | | | | | | | | REDUCE: (164), (186) imply: % 150.57/21.97 | | | | | | | | | | | | | (187) ~ (all_4_1 = e3) % 150.57/21.97 | | | | | | | | | | | | | % 150.57/21.97 | | | | | | | | | | | | | BETA: splitting (3) gives: % 150.57/21.97 | | | | | | | | | | | | | % 150.57/21.97 | | | | | | | | | | | | | Case 1: % 150.57/21.97 | | | | | | | | | | | | | | % 150.57/21.97 | | | | | | | | | | | | | | (188) ~ (all_56_11 = e1) % 150.57/21.97 | | | | | | | | | | | | | | % 150.57/21.97 | | | | | | | | | | | | | | REDUCE: (164), (188) imply: % 150.57/21.97 | | | | | | | | | | | | | | (189) ~ (all_4_1 = e1) % 150.57/21.97 | | | | | | | | | | | | | | % 150.57/21.97 | | | | | | | | | | | | | | BETA: splitting (127) gives: % 150.57/21.97 | | | | | | | | | | | | | | % 150.57/21.97 | | | | | | | | | | | | | | Case 1: % 150.57/21.97 | | | | | | | | | | | | | | | % 150.57/21.97 | | | | | | | | | | | | | | | (190) all_54_5 = e3 % 150.57/21.97 | | | | | | | | | | | | | | | % 150.57/21.97 | | | | | | | | | | | | | | | REF_CLOSE: (163), (187), (190) are inconsistent by sub-proof % 150.57/21.97 | | | | | | | | | | | | | | | #199. % 150.57/21.97 | | | | | | | | | | | | | | | % 150.57/21.97 | | | | | | | | | | | | | | Case 2: % 150.57/21.97 | | | | | | | | | | | | | | | % 150.57/21.97 | | | | | | | | | | | | | | | (191) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 150.57/21.97 | | | | | | | | | | | | | | | % 150.57/21.97 | | | | | | | | | | | | | | | REF_CLOSE: (58), (161), (163), (168), (169), (189), (191) are % 150.57/21.97 | | | | | | | | | | | | | | | inconsistent by sub-proof #103. % 150.57/21.97 | | | | | | | | | | | | | | | % 150.57/21.97 | | | | | | | | | | | | | | End of split % 150.57/21.97 | | | | | | | | | | | | | | % 150.57/21.97 | | | | | | | | | | | | | Case 2: % 150.57/21.97 | | | | | | | | | | | | | | % 150.57/21.97 | | | | | | | | | | | | | | (192) all_56_13 = e2 % 150.57/21.97 | | | | | | | | | | | | | | (193) all_56_11 = e1 % 150.57/21.97 | | | | | | | | | | | | | | % 150.57/21.97 | | | | | | | | | | | | | | COMBINE_EQS: (164), (193) imply: % 150.57/21.97 | | | | | | | | | | | | | | (194) all_4_1 = e1 % 150.57/21.97 | | | | | | | | | | | | | | % 150.57/21.97 | | | | | | | | | | | | | | COMBINE_EQS: (89), (192) imply: % 150.57/21.97 | | | | | | | | | | | | | | (195) all_8_0 = e2 % 150.57/21.97 | | | | | | | | | | | | | | % 150.57/21.97 | | | | | | | | | | | | | | REDUCE: (138), (195) imply: % 150.57/21.97 | | | | | | | | | | | | | | (196) ~ (e3 = e2) % 150.57/21.97 | | | | | | | | | | | | | | % 150.57/21.97 | | | | | | | | | | | | | | REF_CLOSE: (2), (36), (47), (48), (58), (65), (88), (103), % 150.57/21.97 | | | | | | | | | | | | | | (106), (142), (180), (185), (194), (196) are % 150.57/21.97 | | | | | | | | | | | | | | inconsistent by sub-proof #195. % 150.57/21.97 | | | | | | | | | | | | | | % 150.57/21.97 | | | | | | | | | | | | | End of split % 150.57/21.97 | | | | | | | | | | | | | % 150.57/21.97 | | | | | | | | | | | | Case 2: % 150.57/21.97 | | | | | | | | | | | | | % 150.57/21.97 | | | | | | | | | | | | | (197) all_56_11 = e3 % 150.57/21.97 | | | | | | | | | | | | | (198) all_56_9 = e2 % 150.57/21.97 | | | | | | | | | | | | | % 150.57/21.97 | | | | | | | | | | | | | COMBINE_EQS: (130), (198) imply: % 150.57/21.97 | | | | | | | | | | | | | (199) all_52_1 = e2 % 150.57/21.97 | | | | | | | | | | | | | % 150.57/21.97 | | | | | | | | | | | | | COMBINE_EQS: (164), (197) imply: % 150.57/21.97 | | | | | | | | | | | | | (200) all_4_1 = e3 % 150.57/21.97 | | | | | | | | | | | | | % 150.57/21.97 | | | | | | | | | | | | | SIMP: (200) implies: % 150.57/21.97 | | | | | | | | | | | | | (201) all_4_1 = e3 % 150.57/21.97 | | | | | | | | | | | | | % 150.57/21.97 | | | | | | | | | | | | | COMBINE_EQS: (162), (201) imply: % 150.57/21.97 | | | | | | | | | | | | | (202) all_8_2 = e3 % 150.57/21.97 | | | | | | | | | | | | | % 150.57/21.97 | | | | | | | | | | | | | COMBINE_EQS: (165), (201) imply: % 150.57/21.97 | | | | | | | | | | | | | (203) all_58_3 = e3 % 150.57/21.97 | | | | | | | | | | | | | % 150.57/21.97 | | | | | | | | | | | | | COMBINE_EQS: (105), (199) imply: % 150.57/21.97 | | | | | | | | | | | | | (204) all_58_2 = e2 % 150.57/21.97 | | | | | | | | | | | | | % 150.57/21.97 | | | | | | | | | | | | | REDUCE: (117), (199) imply: % 150.57/21.97 | | | | | | | | | | | | | (205) ~ (all_52_2 = e2) % 150.57/21.97 | | | | | | | | | | | | | % 150.57/21.97 | | | | | | | | | | | | | SIMP: (205) implies: % 150.57/21.97 | | | | | | | | | | | | | (206) ~ (all_52_2 = e2) % 150.57/21.97 | | | | | | | | | | | | | % 150.57/21.97 | | | | | | | | | | | | | REDUCE: (132), (199) imply: % 150.57/21.97 | | | | | | | | | | | | | (207) ~ (all_10_2 = e2) % 150.57/21.97 | | | | | | | | | | | | | % 150.57/21.97 | | | | | | | | | | | | | SIMP: (207) implies: % 150.57/21.97 | | | | | | | | | | | | | (208) ~ (all_10_2 = e2) % 150.57/21.97 | | | | | | | | | | | | | % 150.57/21.97 | | | | | | | | | | | | | REDUCE: (91), (199) imply: % 150.57/21.97 | | | | | | | | | | | | | (209) ~ (all_8_0 = e2) % 150.57/21.97 | | | | | | | | | | | | | % 150.57/21.97 | | | | | | | | | | | | | SIMP: (209) implies: % 150.57/21.97 | | | | | | | | | | | | | (210) ~ (all_8_0 = e2) % 150.57/21.97 | | | | | | | | | | | | | % 150.57/21.97 | | | | | | | | | | | | | REDUCE: (166), (199), (201) imply: % 150.57/21.97 | | | | | | | | | | | | | (211) ~ (e3 = e2) % 150.57/21.97 | | | | | | | | | | | | | % 150.57/21.97 | | | | | | | | | | | | | REDUCE: (169), (201) imply: % 150.57/21.97 | | | | | | | | | | | | | (212) op(e3, e3) = e1 % 150.57/21.97 | | | | | | | | | | | | | % 150.57/21.97 | | | | | | | | | | | | | REF_CLOSE: (10), (11), (26), (28), (38), (41), (43), (52), % 150.57/21.97 | | | | | | | | | | | | | (54), (56), (58), (60), (67), (87), (93), (95), % 150.57/21.97 | | | | | | | | | | | | | (97), (105), (106), (108), (109), (122), (124), % 150.57/21.97 | | | | | | | | | | | | | (131), (133), (138), (154), (197), (202), (203), % 150.57/21.97 | | | | | | | | | | | | | (204), (206), (208), (210), (212) are inconsistent % 150.57/21.97 | | | | | | | | | | | | | by sub-proof #107. % 150.57/21.97 | | | | | | | | | | | | | % 150.57/21.97 | | | | | | | | | | | | End of split % 150.57/21.97 | | | | | | | | | | | | % 150.57/21.97 | | | | | | | | | | | Case 2: % 150.57/21.97 | | | | | | | | | | | | % 150.57/21.97 | | | | | | | | | | | | (213) all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0 % 150.57/21.97 | | | | | | | | | | | | % 150.57/21.97 | | | | | | | | | | | | REF_CLOSE: (51), (156), (160), (179), (213) are inconsistent % 150.57/21.97 | | | | | | | | | | | | by sub-proof #580. % 150.57/21.97 | | | | | | | | | | | | % 150.57/21.97 | | | | | | | | | | | End of split % 150.57/21.97 | | | | | | | | | | | % 150.57/21.97 | | | | | | | | | | Case 2: % 150.57/21.97 | | | | | | | | | | | % 150.57/21.97 | | | | | | | | | | | (214) all_54_10 = e0 % 150.57/21.97 | | | | | | | | | | | % 150.57/21.97 | | | | | | | | | | | REF_CLOSE: (15), (146), (214) are inconsistent by sub-proof % 150.57/21.97 | | | | | | | | | | | #705. % 150.57/21.97 | | | | | | | | | | | % 150.57/21.97 | | | | | | | | | | End of split % 150.57/21.97 | | | | | | | | | | % 150.57/21.97 | | | | | | | | | End of split % 150.57/21.97 | | | | | | | | | % 150.57/21.97 | | | | | | | | End of split % 150.57/21.97 | | | | | | | | % 150.57/21.97 | | | | | | | Case 2: % 150.57/21.97 | | | | | | | | % 150.57/21.97 | | | | | | | | (215) all_56_21 = e3 % 150.57/21.97 | | | | | | | | (216) all_56_17 = e1 % 150.57/21.97 | | | | | | | | % 150.57/21.97 | | | | | | | | REF_CLOSE: (1), (9), (16), (19), (22), (23), (25), (31), (32), % 150.57/21.97 | | | | | | | | (33), (36), (38), (41), (44), (46), (47), (50), (54), % 150.57/21.97 | | | | | | | | (58), (60), (63), (64), (75), (79), (83), (85), (87), % 150.57/21.97 | | | | | | | | (88), (90), (92), (93), (98), (102), (103), (105), % 150.57/21.97 | | | | | | | | (106), (111), (112), (116), (120), (125), (132), % 150.57/21.97 | | | | | | | | (134), (136), (142), (158), (215), (216) are % 150.57/21.97 | | | | | | | | inconsistent by sub-proof #292. % 150.57/21.97 | | | | | | | | % 150.57/21.97 | | | | | | | End of split % 150.57/21.97 | | | | | | | % 150.57/21.97 | | | | | | End of split % 150.57/21.97 | | | | | | % 150.57/21.97 | | | | | Case 2: % 150.57/21.97 | | | | | | % 150.57/21.97 | | | | | | (217) all_56_23 = e1 % 150.57/21.97 | | | | | | (218) all_56_21 = e0 % 150.57/21.97 | | | | | | % 150.57/21.97 | | | | | | REF_CLOSE: (16), (22), (27), (35), (38), (58), (65), (80), (92), % 150.57/21.97 | | | | | | (96), (99), (119), (136), (217), (218) are inconsistent % 150.57/21.97 | | | | | | by sub-proof #227. % 150.57/21.97 | | | | | | % 150.57/21.97 | | | | | End of split % 150.57/21.97 | | | | | % 150.57/21.97 | | | | Case 2: % 150.57/21.97 | | | | | % 150.57/21.97 | | | | | (219) all_56_31 = e3 % 150.57/21.97 | | | | | (220) all_56_25 = e0 % 150.57/21.97 | | | | | % 150.57/21.97 | | | | | COMBINE_EQS: (6), (220) imply: % 150.57/21.97 | | | | | (221) all_52_3 = e0 % 150.57/21.97 | | | | | % 150.57/21.97 | | | | | SIMP: (221) implies: % 150.57/21.97 | | | | | (222) all_52_3 = e0 % 150.57/21.97 | | | | | % 150.57/21.97 | | | | | COMBINE_EQS: (87), (219) imply: % 150.57/21.97 | | | | | (223) all_4_2 = e3 % 150.57/21.97 | | | | | % 150.57/21.97 | | | | | COMBINE_EQS: (17), (223) imply: % 150.57/21.97 | | | | | (224) all_12_2 = e3 % 150.57/21.97 | | | | | % 150.57/21.97 | | | | | REDUCE: (59), (222) imply: % 150.57/21.97 | | | | | (225) ~ (all_10_2 = e0) % 150.57/21.97 | | | | | % 150.57/21.97 | | | | | SIMP: (225) implies: % 150.57/21.97 | | | | | (226) ~ (all_10_2 = e0) % 150.57/21.97 | | | | | % 150.57/21.97 | | | | | REDUCE: (86), (223) imply: % 150.57/21.97 | | | | | (227) ~ (all_52_11 = e3) % 150.57/21.97 | | | | | % 150.57/21.97 | | | | | REDUCE: (80), (223) imply: % 150.57/21.97 | | | | | (228) op(e3, e3) = all_4_1 % 150.57/21.97 | | | | | % 150.57/21.97 | | | | | BETA: splitting (76) gives: % 150.57/21.97 | | | | | % 150.57/21.97 | | | | | Case 1: % 150.57/21.97 | | | | | | % 150.57/21.97 | | | | | | (229) ~ (all_12_1 = e1) % 150.57/21.97 | | | | | | % 150.57/21.97 | | | | | | REDUCE: (107), (229) imply: % 150.57/21.97 | | | | | | (230) ~ (all_4_1 = e1) % 150.57/21.97 | | | | | | % 150.57/21.97 | | | | | | GROUND_INST: instantiating (58) with all_10_2, all_4_1, e3, e3, % 150.57/21.97 | | | | | | simplifying with (54), (228) gives: % 150.57/21.97 | | | | | | (231) all_10_2 = all_4_1 % 150.57/21.97 | | | | | | % 150.57/21.97 | | | | | | COMBINE_EQS: (19), (231) imply: % 150.57/21.97 | | | | | | (232) all_54_0 = all_4_1 % 150.57/21.97 | | | | | | % 150.57/21.97 | | | | | | COMBINE_EQS: (41), (231) imply: % 150.57/21.97 | | | | | | (233) all_56_1 = all_4_1 % 150.57/21.97 | | | | | | % 150.57/21.97 | | | | | | REDUCE: (125), (231) imply: % 150.57/21.97 | | | | | | (234) ~ (all_52_2 = all_4_1) % 150.57/21.97 | | | | | | % 150.57/21.97 | | | | | | REDUCE: (73), (231) imply: % 150.57/21.97 | | | | | | (235) ~ (all_52_8 = all_4_1) % 150.57/21.97 | | | | | | % 150.57/21.97 | | | | | | REDUCE: (226), (231) imply: % 150.57/21.97 | | | | | | (236) ~ (all_4_1 = e0) % 150.57/21.97 | | | | | | % 150.57/21.97 | | | | | | REF_CLOSE: (5), (16), (29), (32), (38), (46), (52), (55), (58), % 150.57/21.97 | | | | | | (71), (74), (81), (84), (92), (128), (136), (138), (227), % 150.57/21.97 | | | | | | (228), (230), (232), (233), (234), (235), (236) are % 150.57/21.97 | | | | | | inconsistent by sub-proof #123. % 150.57/21.97 | | | | | | % 150.57/21.97 | | | | | Case 2: % 150.57/21.97 | | | | | | % 150.57/21.97 | | | | | | (237) ~ (all_12_2 = e3) % 150.57/21.97 | | | | | | % 150.57/21.97 | | | | | | REDUCE: (224), (237) imply: % 150.57/21.97 | | | | | | (238) $false % 150.57/21.97 | | | | | | % 150.57/21.97 | | | | | | CLOSE: (238) is inconsistent. % 150.57/21.97 | | | | | | % 150.57/21.97 | | | | | End of split % 150.57/21.97 | | | | | % 150.57/21.98 | | | | End of split % 150.57/21.98 | | | | % 150.57/21.98 | | | Case 2: % 150.57/21.98 | | | | % 150.57/21.98 | | | | (239) all_56_31 = e1 % 150.57/21.98 | | | | (240) all_56_29 = e0 % 150.57/21.98 | | | | % 150.57/21.98 | | | | REF_CLOSE: (4), (7), (12), (15), (24), (26), (29), (39), (52), (58), % 150.57/21.98 | | | | (65), (66), (71), (77), (78), (80), (81), (82), (86), (87), % 150.57/21.98 | | | | (92), (94), (101), (104), (110), (114), (119), (124), (126), % 150.57/21.98 | | | | (128), (138), (140), (239), (240) are inconsistent by % 150.57/21.98 | | | | sub-proof #93. % 150.57/21.98 | | | | % 150.57/21.98 | | | End of split % 150.57/21.98 | | | % 150.57/21.98 | | Case 2: % 150.57/21.98 | | | % 150.57/21.98 | | | (241) all_56_21 = e2 % 150.57/21.98 | | | (242) all_56_19 = e1 % 150.57/21.98 | | | % 150.57/21.98 | | | REF_CLOSE: (1), (16), (21), (27), (28), (30), (37), (38), (41), (43), % 150.57/21.98 | | | (57), (58), (61), (67), (69), (80), (87), (91), (92), (93), % 150.57/21.98 | | | (100), (102), (103), (108), (115), (119), (122), (127), (129), % 150.57/21.98 | | | (131), (132), (136), (138), (241), (242) are inconsistent by % 150.57/21.98 | | | sub-proof #99. % 150.57/21.98 | | | % 150.57/21.98 | | End of split % 150.57/21.98 | | % 150.57/21.98 | Case 2: % 150.57/21.98 | | % 150.57/21.98 | | (243) all_48_0 = e3 % 150.57/21.98 | | (244) ~ (all_48_1 = e1) | ~ (all_48_2 = e0) % 150.57/21.98 | | % 150.57/21.98 | | COMBINE_EQS: (45), (243) imply: % 150.57/21.98 | | (245) all_8_0 = e3 % 150.57/21.98 | | % 150.57/21.98 | | SIMP: (245) implies: % 150.57/21.98 | | (246) all_8_0 = e3 % 150.57/21.98 | | % 150.57/21.98 | | REF_CLOSE: (1), (3), (20), (26), (30), (37), (53), (58), (89), (100), (115), % 150.57/21.98 | | (121), (127), (244), (246) are inconsistent by sub-proof #115. % 150.57/21.98 | | % 150.57/21.98 | End of split % 150.57/21.98 | % 150.57/21.98 End of proof % 150.57/21.98 % 150.57/21.98 Sub-proof #93 shows that the following formulas are inconsistent: % 150.57/21.98 ---------------------------------------------------------------- % 150.57/21.98 (1) ~ (all_52_11 = all_6_2) % 150.57/21.98 (2) all_56_31 = e1 % 150.57/21.98 (3) ~ (all_34_1 = e3) | ~ (all_34_2 = e1) % 150.57/21.98 (4) ~ (e3 = e0) % 150.57/21.98 (5) all_54_10 = all_6_2 % 150.57/21.98 (6) all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2 % 150.57/21.98 (7) ~ (e3 = e2) % 150.57/21.98 (8) all_58_4 = all_52_8 % 150.57/21.98 (9) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 150.57/21.98 (10) all_58_5 = all_8_0 % 150.57/21.98 (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 150.57/21.98 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 150.57/21.98 (12) op(e0, all_4_1) = e2 % 150.57/21.98 (13) op(e0, e1) = all_52_11 % 150.57/21.98 (14) all_58_8 = all_6_2 % 150.57/21.98 (15) all_34_1 = all_4_1 % 150.57/21.98 (16) ~ (e2 = e1) % 150.57/21.98 (17) op(all_4_2, all_4_2) = all_4_1 % 150.57/21.98 (18) all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3 % 150.57/21.98 (19) all_56_29 = e0 % 150.57/21.98 (20) all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1 % 150.57/21.98 (21) ~ (all_52_11 = all_4_2) % 150.57/21.98 (22) all_56_31 = all_4_2 % 150.57/21.98 (23) ~ (all_8_0 = e3) % 150.57/21.98 (24) op(all_6_2, all_6_2) = all_6_1 % 150.57/21.98 (25) ~ (all_52_11 = all_8_0) % 150.57/21.98 (26) op(e1, e1) = all_6_2 % 150.57/21.98 (27) all_56_29 = all_52_11 % 150.57/21.98 (28) ~ (all_6_2 = e2) % 150.57/21.98 (29) op(e1, all_6_2) = all_56_20 % 150.57/21.98 (30) ~ (e3 = e1) % 150.57/21.98 (31) op(e0, all_4_2) = all_56_30 % 150.57/21.98 (32) ~ (e2 = e0) % 150.57/21.98 (33) all_34_2 = all_4_2 % 150.57/21.98 (34) all_58_14 = all_52_11 % 150.57/21.98 % 150.57/21.98 Begin of proof % 150.57/21.98 | % 150.57/21.98 | COMBINE_EQS: (19), (27) imply: % 150.57/21.98 | (35) all_52_11 = e0 % 150.57/21.98 | % 150.57/21.98 | SIMP: (35) implies: % 150.57/21.98 | (36) all_52_11 = e0 % 150.57/21.98 | % 150.57/21.98 | COMBINE_EQS: (2), (22) imply: % 150.57/21.98 | (37) all_4_2 = e1 % 150.57/21.98 | % 150.57/21.98 | COMBINE_EQS: (33), (37) imply: % 150.57/21.98 | (38) all_34_2 = e1 % 150.57/21.98 | % 150.57/21.98 | COMBINE_EQS: (34), (36) imply: % 150.57/21.98 | (39) all_58_14 = e0 % 150.57/21.98 | % 150.57/21.98 | REDUCE: (25), (36) imply: % 150.57/21.98 | (40) ~ (all_8_0 = e0) % 150.57/21.98 | % 150.57/21.98 | SIMP: (40) implies: % 150.57/21.98 | (41) ~ (all_8_0 = e0) % 150.57/21.98 | % 150.57/21.98 | REDUCE: (1), (36) imply: % 150.57/21.98 | (42) ~ (all_6_2 = e0) % 150.57/21.98 | % 150.57/21.98 | SIMP: (42) implies: % 150.57/21.98 | (43) ~ (all_6_2 = e0) % 150.57/21.98 | % 150.57/21.98 | REDUCE: (21), (36), (37) imply: % 150.57/21.98 | (44) ~ (e1 = e0) % 150.57/21.98 | % 150.57/21.98 | SIMP: (44) implies: % 150.57/21.98 | (45) ~ (e1 = e0) % 150.57/21.98 | % 150.57/21.98 | REDUCE: (17), (37) imply: % 150.57/21.98 | (46) op(e1, e1) = all_4_1 % 150.57/21.98 | % 150.57/21.98 | REDUCE: (31), (37) imply: % 150.57/21.98 | (47) op(e0, e1) = all_56_30 % 150.57/21.98 | % 150.57/21.98 | REDUCE: (13), (36) imply: % 150.57/21.98 | (48) op(e0, e1) = e0 % 150.57/21.98 | % 150.57/21.98 | BETA: splitting (3) gives: % 150.57/21.98 | % 150.57/21.98 | Case 1: % 150.57/21.98 | | % 150.57/21.98 | | (49) ~ (all_34_1 = e3) % 150.57/21.98 | | % 150.57/21.98 | | REDUCE: (15), (49) imply: % 150.57/21.98 | | (50) ~ (all_4_1 = e3) % 150.57/21.98 | | % 150.57/21.98 | | GROUND_INST: instantiating (11) with e0, all_56_30, e1, e0, simplifying with % 150.57/21.98 | | (47), (48) gives: % 150.57/21.98 | | (51) all_56_30 = e0 % 150.57/21.98 | | % 150.57/21.98 | | GROUND_INST: instantiating (11) with all_6_2, all_4_1, e1, e1, simplifying % 150.57/21.98 | | with (26), (46) gives: % 150.57/21.98 | | (52) all_6_2 = all_4_1 % 150.57/21.98 | | % 150.57/21.98 | | COMBINE_EQS: (5), (52) imply: % 150.57/21.98 | | (53) all_54_10 = all_4_1 % 150.57/21.98 | | % 150.57/21.98 | | COMBINE_EQS: (14), (52) imply: % 150.57/21.98 | | (54) all_58_8 = all_4_1 % 150.57/21.98 | | % 150.57/21.98 | | BETA: splitting (9) gives: % 150.57/21.98 | | % 150.57/21.98 | | Case 1: % 150.57/21.98 | | | % 150.57/21.98 | | | (55) all_54_10 = e3 % 150.57/21.98 | | | % 150.57/21.98 | | | REF_CLOSE: (50), (53), (55) are inconsistent by sub-proof #282. % 150.57/21.98 | | | % 150.57/21.98 | | Case 2: % 150.57/21.98 | | | % 150.57/21.98 | | | (56) ~ (all_54_10 = e3) % 150.57/21.98 | | | (57) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 150.57/21.98 | | | % 150.57/21.98 | | | BETA: splitting (18) gives: % 150.57/21.98 | | | % 150.57/21.98 | | | Case 1: % 150.57/21.98 | | | | % 150.57/21.98 | | | | (58) all_58_4 = e3 % 150.57/21.98 | | | | % 150.57/21.98 | | | | COMBINE_EQS: (8), (58) imply: % 150.57/21.98 | | | | (59) all_52_8 = e3 % 150.57/21.98 | | | | % 150.57/21.98 | | | | BETA: splitting (6) gives: % 150.57/21.98 | | | | % 150.57/21.98 | | | | Case 1: % 150.57/21.98 | | | | | % 150.57/21.98 | | | | | (60) all_58_4 = e2 % 150.57/21.98 | | | | | % 150.57/21.98 | | | | | COMBINE_EQS: (58), (60) imply: % 150.57/21.98 | | | | | (61) e3 = e2 % 150.57/21.98 | | | | | % 150.57/21.98 | | | | | REDUCE: (7), (61) imply: % 150.57/21.98 | | | | | (62) $false % 150.57/21.98 | | | | | % 150.57/21.98 | | | | | CLOSE: (62) is inconsistent. % 150.57/21.98 | | | | | % 150.57/21.98 | | | | Case 2: % 150.57/21.98 | | | | | % 150.57/21.98 | | | | | (63) all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2 % 150.57/21.98 | | | | | % 150.57/21.98 | | | | | REF_CLOSE: (5), (10), (11), (12), (14), (16), (20), (24), (26), (28), % 150.57/21.98 | | | | | (29), (30), (32), (39), (41), (43), (45), (46), (47), (48), % 150.57/21.98 | | | | | (57), (58), (63) are inconsistent by sub-proof #94. % 150.57/21.98 | | | | | % 150.57/21.98 | | | | End of split % 150.57/21.98 | | | | % 150.57/21.98 | | | Case 2: % 150.57/21.98 | | | | % 150.57/21.98 | | | | (64) all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3 % 150.57/21.98 | | | | % 150.57/21.98 | | | | REF_CLOSE: (4), (10), (23), (39), (50), (54), (64) are inconsistent by % 150.57/21.98 | | | | sub-proof #120. % 150.57/21.98 | | | | % 150.57/21.98 | | | End of split % 150.57/21.98 | | | % 150.57/21.98 | | End of split % 150.57/21.98 | | % 150.57/21.98 | Case 2: % 150.57/21.98 | | % 150.57/21.98 | | (65) ~ (all_34_2 = e1) % 150.57/21.98 | | % 150.57/21.98 | | REDUCE: (38), (65) imply: % 150.57/21.98 | | (66) $false % 150.57/21.98 | | % 150.57/21.98 | | CLOSE: (66) is inconsistent. % 150.57/21.98 | | % 150.57/21.98 | End of split % 150.57/21.98 | % 150.57/21.98 End of proof % 150.57/21.98 % 150.57/21.98 Sub-proof #94 shows that the following formulas are inconsistent: % 150.57/21.98 ---------------------------------------------------------------- % 150.57/21.98 (1) op(e0, e1) = all_56_30 % 150.57/21.98 (2) all_54_10 = all_6_2 % 150.57/21.98 (3) all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2 % 150.57/21.98 (4) all_58_5 = all_8_0 % 150.57/21.98 (5) ~ (e1 = e0) % 150.57/21.98 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 150.57/21.98 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 150.57/21.98 (7) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 150.57/21.98 (8) ~ (all_6_2 = e0) % 150.57/21.98 (9) ~ (all_8_0 = e0) % 150.57/21.98 (10) op(e0, all_4_1) = e2 % 150.57/21.98 (11) all_58_8 = all_6_2 % 150.57/21.98 (12) ~ (e2 = e1) % 150.57/21.98 (13) all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1 % 150.57/21.98 (14) op(e0, e1) = e0 % 150.57/21.98 (15) op(all_6_2, all_6_2) = all_6_1 % 150.57/21.98 (16) all_58_14 = e0 % 150.57/21.98 (17) op(e1, e1) = all_6_2 % 150.57/21.98 (18) ~ (all_6_2 = e2) % 150.57/21.98 (19) op(e1, e1) = all_4_1 % 150.57/21.98 (20) op(e1, all_6_2) = all_56_20 % 150.57/21.98 (21) ~ (e3 = e1) % 150.57/21.98 (22) ~ (e2 = e0) % 150.57/21.98 (23) all_58_4 = e3 % 150.57/21.98 % 150.57/21.98 Begin of proof % 150.57/21.98 | % 150.57/21.98 | BETA: splitting (3) gives: % 150.57/21.98 | % 150.57/21.98 | Case 1: % 150.57/21.98 | | % 150.57/21.98 | | (24) all_58_5 = e2 % 150.57/21.98 | | % 150.57/21.98 | | COMBINE_EQS: (4), (24) imply: % 150.57/21.98 | | (25) all_8_0 = e2 % 150.57/21.98 | | % 150.57/21.98 | | REF_CLOSE: (1), (5), (6), (10), (11), (12), (13), (14), (15), (16), (17), % 150.57/21.98 | | (19), (20), (21), (22), (23), (24) are inconsistent by sub-proof % 150.57/21.98 | | #179. % 150.57/21.98 | | % 150.57/21.98 | Case 2: % 150.57/21.98 | | % 150.57/21.98 | | (26) all_58_8 = e2 | all_58_14 = e2 % 150.57/21.98 | | % 150.57/21.98 | | BETA: splitting (7) gives: % 150.57/21.98 | | % 150.57/21.98 | | Case 1: % 150.57/21.98 | | | % 150.57/21.98 | | | (27) all_54_10 = e2 % 150.57/21.98 | | | % 150.57/21.98 | | | REF_CLOSE: (2), (18), (27) are inconsistent by sub-proof #735. % 150.57/21.98 | | | % 150.57/21.98 | | Case 2: % 150.57/21.98 | | | % 150.57/21.98 | | | (28) ~ (all_54_10 = e2) % 150.57/21.98 | | | (29) all_54_10 = e1 | all_54_10 = e0 % 150.57/21.98 | | | % 150.57/21.98 | | | REF_CLOSE: (2), (8), (11), (16), (18), (22), (26), (29) are inconsistent % 150.57/21.98 | | | by sub-proof #213. % 150.57/21.98 | | | % 150.57/21.98 | | End of split % 150.57/21.98 | | % 150.57/21.98 | End of split % 150.57/21.98 | % 150.57/21.98 End of proof % 150.57/21.98 % 150.57/21.98 Sub-proof #95 shows that the following formulas are inconsistent: % 150.57/21.98 ---------------------------------------------------------------- % 150.57/21.98 (1) all_56_11 = all_8_2 % 150.57/21.98 (2) all_56_31 = e1 % 150.57/21.98 (3) ~ (all_52_4 = all_52_8) % 150.57/21.98 (4) ~ (all_34_1 = e3) | ~ (all_34_2 = e1) % 150.57/21.98 (5) ~ (e3 = e0) % 150.57/21.98 (6) all_54_0 = all_10_2 % 150.57/21.98 (7) all_58_4 = all_52_8 % 150.57/21.98 (8) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 150.57/21.98 (9) ~ (all_10_1 = e1) % 150.57/21.98 (10) all_56_21 = all_6_2 % 150.57/21.98 (11) all_56_1 = all_10_2 % 150.57/21.98 (12) all_58_5 = all_8_0 % 150.57/21.98 (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 150.57/21.98 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 150.57/21.98 (14) all_56_7 = all_52_12 % 150.57/21.98 (15) all_58_8 = all_6_2 % 150.57/21.98 (16) ~ (all_52_8 = all_10_2) % 150.57/21.98 (17) ~ (all_56_1 = e2) | all_56_3 = e3 % 150.57/21.98 (18) ~ (all_56_1 = e0) | all_56_7 = e3 % 150.57/21.98 (19) all_34_1 = all_4_1 % 150.57/21.98 (20) op(all_4_2, all_4_2) = all_4_1 % 150.57/21.98 (21) all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3 % 150.57/21.98 (22) all_56_29 = e0 % 150.57/21.98 (23) all_56_3 = all_52_4 % 150.57/21.98 (24) all_56_31 = all_4_2 % 150.57/21.98 (25) ~ (all_8_0 = e3) % 150.57/21.98 (26) all_56_1 = e3 | all_56_11 = e2 | all_56_21 = e1 | all_56_31 = e0 % 150.57/21.98 (27) op(all_8_2, all_8_2) = e1 % 150.57/21.98 (28) op(e1, e1) = all_6_2 % 150.57/21.98 (29) all_56_29 = all_52_11 % 150.57/21.98 (30) op(all_10_2, all_10_2) = all_10_1 % 150.57/21.98 (31) op(e2, e2) = all_8_2 % 150.57/21.98 (32) ~ (all_52_8 = all_52_12) % 150.57/21.98 (33) all_34_2 = all_4_2 % 150.57/21.98 (34) all_58_14 = all_52_11 % 150.57/21.98 % 150.57/21.98 Begin of proof % 150.57/21.98 | % 150.57/21.98 | COMBINE_EQS: (22), (29) imply: % 150.57/21.98 | (35) all_52_11 = e0 % 150.57/21.98 | % 150.57/21.98 | SIMP: (35) implies: % 150.57/21.98 | (36) all_52_11 = e0 % 150.57/21.98 | % 150.57/21.98 | COMBINE_EQS: (2), (24) imply: % 150.57/21.98 | (37) all_4_2 = e1 % 150.57/21.98 | % 150.57/21.98 | COMBINE_EQS: (33), (37) imply: % 150.57/21.98 | (38) all_34_2 = e1 % 150.57/21.98 | % 150.57/21.98 | COMBINE_EQS: (34), (36) imply: % 150.57/21.98 | (39) all_58_14 = e0 % 150.57/21.98 | % 150.57/21.98 | REDUCE: (20), (37) imply: % 150.57/21.98 | (40) op(e1, e1) = all_4_1 % 150.57/21.98 | % 150.57/21.98 | BETA: splitting (4) gives: % 150.57/21.98 | % 150.57/21.98 | Case 1: % 150.57/21.98 | | % 150.57/21.98 | | (41) ~ (all_34_1 = e3) % 150.57/21.98 | | % 150.57/21.98 | | REDUCE: (19), (41) imply: % 150.57/21.98 | | (42) ~ (all_4_1 = e3) % 150.57/21.98 | | % 150.57/21.98 | | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (9), (10), (11), (12), (13), % 150.57/21.98 | | (14), (15), (16), (17), (18), (21), (23), (25), (26), (27), (28), % 150.57/21.98 | | (30), (31), (32), (39), (40), (42) are inconsistent by sub-proof % 150.57/21.98 | | #119. % 150.57/21.98 | | % 150.57/21.98 | Case 2: % 150.57/21.98 | | % 150.57/21.98 | | (43) ~ (all_34_2 = e1) % 150.57/21.98 | | % 150.57/21.98 | | REDUCE: (38), (43) imply: % 150.57/21.98 | | (44) $false % 150.57/21.98 | | % 150.57/21.98 | | CLOSE: (44) is inconsistent. % 150.57/21.98 | | % 150.57/21.98 | End of split % 150.57/21.98 | % 150.57/21.98 End of proof % 150.57/21.98 % 150.57/21.98 Sub-proof #96 shows that the following formulas are inconsistent: % 150.57/21.98 ---------------------------------------------------------------- % 150.57/21.98 (1) all_54_15 = e1 | all_54_15 = e0 % 150.57/21.98 (2) all_54_15 = all_4_2 % 150.57/21.98 (3) ~ (all_4_2 = e1) % 150.57/21.98 (4) ~ (all_4_2 = e0) % 150.57/21.98 % 150.57/21.98 Begin of proof % 150.57/21.98 | % 150.57/21.98 | BETA: splitting (1) gives: % 150.57/21.98 | % 150.57/21.98 | Case 1: % 150.57/21.98 | | % 150.57/21.98 | | (5) all_54_15 = e1 % 150.57/21.98 | | % 150.57/21.98 | | COMBINE_EQS: (2), (5) imply: % 150.57/21.98 | | (6) all_4_2 = e1 % 150.57/21.98 | | % 150.57/21.98 | | REDUCE: (3), (6) imply: % 150.57/21.98 | | (7) $false % 150.57/21.98 | | % 150.57/21.98 | | CLOSE: (7) is inconsistent. % 150.57/21.98 | | % 150.57/21.98 | Case 2: % 150.57/21.98 | | % 150.57/21.98 | | (8) all_54_15 = e0 % 150.57/21.98 | | % 150.57/21.98 | | COMBINE_EQS: (2), (8) imply: % 150.57/21.98 | | (9) all_4_2 = e0 % 150.57/21.98 | | % 150.57/21.98 | | REDUCE: (4), (9) imply: % 150.57/21.98 | | (10) $false % 150.57/21.98 | | % 150.57/21.98 | | CLOSE: (10) is inconsistent. % 150.57/21.98 | | % 150.57/21.98 | End of split % 150.57/21.98 | % 150.57/21.98 End of proof % 150.57/21.98 % 150.57/21.98 Sub-proof #97 shows that the following formulas are inconsistent: % 150.57/21.98 ---------------------------------------------------------------- % 150.57/21.98 (1) all_56_11 = all_8_2 % 150.57/21.98 (2) ~ (all_56_11 = e1) | all_56_13 = e2 % 150.57/21.98 (3) ~ (all_8_0 = all_6_2) % 150.57/21.98 (4) ~ (e3 = e0) % 150.57/21.98 (5) ~ (all_6_1 = e2) % 150.57/21.98 (6) ~ (all_52_13 = all_8_2) % 150.57/21.98 (7) all_48_1 = e1 % 150.57/21.98 (8) op(e0, e0) = all_4_2 % 150.57/21.98 (9) ~ (all_52_13 = all_8_0) % 150.57/21.98 (10) all_54_5 = all_8_2 % 150.57/21.98 (11) ~ (all_48_0 = e3) | ~ (all_48_1 = e1) | ~ (all_48_2 = e0) % 150.57/21.98 (12) ~ (all_8_0 = all_8_2) % 150.57/21.98 (13) all_56_21 = all_6_2 % 150.57/21.98 (14) all_56_1 = all_10_2 % 150.57/21.98 (15) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0 % 150.57/21.98 (16) all_48_0 = all_8_0 % 150.57/21.98 (17) all_56_17 = all_52_2 % 150.57/21.98 (18) all_36_1 = e3 % 150.57/21.98 (19) all_58_5 = all_8_0 % 150.57/21.98 (20) op(e2, all_8_2) = all_56_10 % 150.57/21.98 (21) op(e3, e3) = all_10_2 % 150.57/21.98 (22) ~ (all_56_21 = e3) | all_56_17 = e1 % 150.57/21.98 (23) ~ (e1 = e0) % 150.57/21.98 (24) all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1 % 150.57/21.98 (25) ~ (all_52_1 = all_8_2) % 150.57/21.98 (26) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 150.57/21.98 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 150.57/21.98 (27) all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0 % 150.57/21.98 (28) ~ (all_56_11 = e3) | all_56_9 = e2 % 150.57/21.98 (29) op(e1, e3) = all_52_2 % 150.57/21.98 (30) all_36_1 = all_6_1 % 150.57/21.98 (31) ~ (e2 = e1) % 150.57/21.98 (32) op(e1, all_6_1) = all_6_0 % 150.57/21.98 (33) op(all_4_2, all_4_2) = all_4_1 % 150.57/21.98 (34) all_58_3 = all_8_2 % 150.57/21.98 (35) all_56_31 = all_4_2 % 150.57/21.98 (36) all_56_13 = all_8_0 % 150.57/21.98 (37) ~ (all_52_1 = all_8_0) % 150.57/21.98 (38) op(all_6_2, all_6_2) = all_6_1 % 150.57/21.98 (39) all_56_1 = e3 | all_56_11 = e2 | all_56_21 = e1 | all_56_31 = e0 % 150.57/21.98 (40) ~ (all_52_13 = all_4_2) % 150.57/21.98 (41) ~ (all_8_0 = e0) | ~ (all_8_2 = e3) % 150.57/21.98 (42) op(all_8_2, all_8_2) = e1 % 150.57/21.98 (43) op(e1, e1) = all_6_2 % 150.57/21.98 (44) op(e3, all_10_1) = e1 % 150.57/21.98 (45) all_58_2 = all_52_1 % 150.57/21.98 (46) all_58_10 = all_52_13 % 150.57/21.98 (47) op(all_10_2, all_10_2) = all_10_1 % 150.57/21.98 (48) ~ (all_56_11 = e0) | all_56_15 = e2 % 150.57/21.98 (49) op(e1, all_6_2) = all_56_20 % 150.57/21.98 (50) ~ (e3 = e1) % 150.57/21.98 (51) op(e2, e2) = all_8_2 % 150.57/21.98 (52) op(e0, all_4_2) = all_56_30 % 150.57/21.98 (53) all_48_2 = all_8_2 % 150.57/21.98 (54) all_54_6 = all_8_0 % 150.57/21.98 (55) op(e3, all_10_2) = all_56_0 % 150.57/21.98 (56) ~ (e2 = e0) % 150.57/21.98 (57) ~ (all_52_2 = all_10_2) % 150.57/21.98 (58) all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3 % 150.57/21.98 (59) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 150.57/21.98 (60) all_56_9 = all_52_1 % 150.57/21.98 (61) all_56_15 = all_52_13 % 150.57/21.98 (62) ~ (all_52_1 = all_10_2) % 150.57/21.98 % 150.57/21.98 Begin of proof % 150.57/21.98 | % 150.57/21.98 | COMBINE_EQS: (18), (30) imply: % 150.57/21.98 | (63) all_6_1 = e3 % 150.57/21.98 | % 150.57/21.98 | SIMP: (63) implies: % 150.57/21.98 | (64) all_6_1 = e3 % 150.57/21.98 | % 150.57/21.98 | REDUCE: (5), (64) imply: % 150.57/21.98 | (65) ~ (e3 = e2) % 150.57/21.98 | % 150.57/21.98 | REDUCE: (38), (64) imply: % 150.57/21.98 | (66) op(all_6_2, all_6_2) = e3 % 150.57/21.98 | % 150.57/21.98 | REDUCE: (32), (64) imply: % 150.57/21.98 | (67) op(e1, e3) = all_6_0 % 150.57/21.98 | % 150.57/21.98 | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (9), (10), (11), (12), (13), % 150.57/21.98 | (14), (15), (16), (17), (19), (20), (21), (22), (23), (24), (25), % 150.57/21.98 | (26), (27), (28), (29), (31), (33), (34), (35), (36), (37), (39), % 150.57/21.98 | (40), (41), (42), (43), (44), (45), (46), (47), (48), (49), (50), % 150.57/21.98 | (51), (52), (53), (54), (55), (56), (57), (58), (59), (60), (61), % 150.57/21.98 | (62), (65), (66), (67) are inconsistent by sub-proof #98. % 150.57/21.98 | % 150.57/21.98 End of proof % 150.57/21.98 % 150.57/21.98 Sub-proof #98 shows that the following formulas are inconsistent: % 150.57/21.98 ---------------------------------------------------------------- % 150.57/21.98 (1) all_56_11 = all_8_2 % 150.57/21.98 (2) ~ (all_56_11 = e1) | all_56_13 = e2 % 150.57/21.98 (3) ~ (all_8_0 = all_6_2) % 150.57/21.98 (4) ~ (e3 = e0) % 150.57/21.98 (5) ~ (all_52_13 = all_8_2) % 150.57/21.98 (6) all_48_1 = e1 % 150.57/21.98 (7) ~ (e3 = e2) % 150.57/21.98 (8) op(e0, e0) = all_4_2 % 150.57/21.98 (9) ~ (all_52_13 = all_8_0) % 150.57/21.98 (10) all_54_5 = all_8_2 % 150.57/21.98 (11) ~ (all_48_0 = e3) | ~ (all_48_1 = e1) | ~ (all_48_2 = e0) % 150.57/21.98 (12) ~ (all_8_0 = all_8_2) % 150.57/21.98 (13) all_56_21 = all_6_2 % 150.57/21.98 (14) all_56_1 = all_10_2 % 150.57/21.98 (15) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0 % 150.57/21.98 (16) all_48_0 = all_8_0 % 150.57/21.98 (17) all_56_17 = all_52_2 % 150.57/21.98 (18) all_58_5 = all_8_0 % 150.57/21.98 (19) op(e2, all_8_2) = all_56_10 % 150.57/21.98 (20) op(e3, e3) = all_10_2 % 150.57/21.98 (21) ~ (all_56_21 = e3) | all_56_17 = e1 % 150.57/21.98 (22) ~ (e1 = e0) % 150.57/21.98 (23) all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1 % 150.57/21.98 (24) ~ (all_52_1 = all_8_2) % 150.57/21.98 (25) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 150.57/21.98 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 150.57/21.98 (26) all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0 % 150.57/21.98 (27) ~ (all_56_11 = e3) | all_56_9 = e2 % 150.57/21.98 (28) op(e1, e3) = all_52_2 % 150.57/21.98 (29) ~ (e2 = e1) % 150.57/21.98 (30) op(all_4_2, all_4_2) = all_4_1 % 150.57/21.98 (31) all_58_3 = all_8_2 % 150.57/21.98 (32) all_56_31 = all_4_2 % 150.57/21.98 (33) all_56_13 = all_8_0 % 150.57/21.98 (34) ~ (all_52_1 = all_8_0) % 150.57/21.98 (35) all_56_1 = e3 | all_56_11 = e2 | all_56_21 = e1 | all_56_31 = e0 % 150.57/21.98 (36) ~ (all_52_13 = all_4_2) % 150.57/21.98 (37) ~ (all_8_0 = e0) | ~ (all_8_2 = e3) % 150.57/21.98 (38) op(all_8_2, all_8_2) = e1 % 150.57/21.98 (39) op(e1, e1) = all_6_2 % 150.57/21.98 (40) op(e3, all_10_1) = e1 % 150.57/21.98 (41) all_58_2 = all_52_1 % 150.57/21.98 (42) all_58_10 = all_52_13 % 150.57/21.98 (43) op(all_10_2, all_10_2) = all_10_1 % 150.57/21.98 (44) ~ (all_56_11 = e0) | all_56_15 = e2 % 150.57/21.98 (45) op(e1, all_6_2) = all_56_20 % 150.57/21.98 (46) op(e1, e3) = all_6_0 % 150.57/21.98 (47) ~ (e3 = e1) % 150.57/21.98 (48) op(e2, e2) = all_8_2 % 150.57/21.98 (49) op(e0, all_4_2) = all_56_30 % 150.57/21.98 (50) all_48_2 = all_8_2 % 150.57/21.98 (51) all_54_6 = all_8_0 % 150.57/21.98 (52) op(all_6_2, all_6_2) = e3 % 150.57/21.98 (53) op(e3, all_10_2) = all_56_0 % 150.57/21.98 (54) ~ (e2 = e0) % 150.57/21.98 (55) ~ (all_52_2 = all_10_2) % 150.57/21.98 (56) all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3 % 150.57/21.99 (57) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 150.57/21.99 (58) all_56_9 = all_52_1 % 150.57/21.99 (59) all_56_15 = all_52_13 % 150.57/21.99 (60) ~ (all_52_1 = all_10_2) % 150.57/21.99 % 150.57/21.99 Begin of proof % 150.57/21.99 | % 150.57/21.99 | GROUND_INST: instantiating (25) with all_52_2, all_6_0, e3, e1, simplifying % 150.57/21.99 | with (28), (46) gives: % 150.57/21.99 | (61) all_52_2 = all_6_0 % 150.57/21.99 | % 150.57/21.99 | COMBINE_EQS: (17), (61) imply: % 150.57/21.99 | (62) all_56_17 = all_6_0 % 150.57/21.99 | % 150.57/21.99 | REDUCE: (55), (61) imply: % 150.57/21.99 | (63) ~ (all_10_2 = all_6_0) % 150.57/21.99 | % 150.57/21.99 | SIMP: (63) implies: % 150.57/21.99 | (64) ~ (all_10_2 = all_6_0) % 150.57/21.99 | % 150.57/21.99 | BETA: splitting (11) gives: % 150.57/21.99 | % 150.57/21.99 | Case 1: % 150.57/21.99 | | % 150.57/21.99 | | (65) ~ (all_48_0 = e3) % 150.57/21.99 | | % 150.57/21.99 | | REDUCE: (16), (65) imply: % 150.57/21.99 | | (66) ~ (all_8_0 = e3) % 150.57/21.99 | | % 150.57/21.99 | | BETA: splitting (44) gives: % 150.57/21.99 | | % 150.57/21.99 | | Case 1: % 150.57/21.99 | | | % 150.57/21.99 | | | (67) ~ (all_56_11 = e0) % 150.57/21.99 | | | % 150.57/21.99 | | | REDUCE: (1), (67) imply: % 150.57/21.99 | | | (68) ~ (all_8_2 = e0) % 150.57/21.99 | | | % 150.57/21.99 | | | BETA: splitting (21) gives: % 150.57/21.99 | | | % 150.57/21.99 | | | Case 1: % 150.57/21.99 | | | | % 150.57/21.99 | | | | (69) ~ (all_56_21 = e3) % 150.57/21.99 | | | | % 150.57/21.99 | | | | REDUCE: (13), (69) imply: % 150.57/21.99 | | | | (70) ~ (all_6_2 = e3) % 150.57/21.99 | | | | % 150.57/21.99 | | | | REF_CLOSE: (1), (2), (3), (9), (10), (12), (13), (14), (15), (18), (19), % 150.57/21.99 | | | | (20), (24), (25), (26), (27), (31), (32), (34), (35), (36), % 150.57/21.99 | | | | (37), (38), (39), (41), (42), (45), (48), (51), (52), (54), % 150.57/21.99 | | | | (57), (58), (68), (70) are inconsistent by sub-proof #114. % 150.57/21.99 | | | | % 150.57/21.99 | | | Case 2: % 150.57/21.99 | | | | % 150.57/21.99 | | | | (71) all_56_21 = e3 % 150.57/21.99 | | | | (72) all_56_17 = e1 % 150.57/21.99 | | | | % 150.57/21.99 | | | | REF_CLOSE: (13), (20), (25), (40), (43), (52), (53), (62), (64), (71), % 150.57/21.99 | | | | (72) are inconsistent by sub-proof #184. % 150.57/21.99 | | | | % 150.57/21.99 | | | End of split % 150.57/21.99 | | | % 150.57/21.99 | | Case 2: % 150.57/21.99 | | | % 150.57/21.99 | | | (73) all_56_15 = e2 % 150.57/21.99 | | | (74) all_56_11 = e0 % 150.57/21.99 | | | % 150.57/21.99 | | | REF_CLOSE: (1), (3), (4), (5), (7), (8), (9), (12), (13), (14), (15), % 150.57/21.99 | | | (18), (22), (23), (25), (29), (30), (31), (32), (35), (38), % 150.57/21.99 | | | (41), (42), (47), (49), (51), (56), (59), (60), (66), (73), % 150.57/21.99 | | | (74) are inconsistent by sub-proof #126. % 150.57/21.99 | | | % 150.57/21.99 | | End of split % 150.57/21.99 | | % 150.57/21.99 | Case 2: % 150.57/21.99 | | % 150.57/21.99 | | (75) all_48_0 = e3 % 150.57/21.99 | | (76) ~ (all_48_1 = e1) | ~ (all_48_2 = e0) % 150.57/21.99 | | % 150.57/21.99 | | COMBINE_EQS: (16), (75) imply: % 150.57/21.99 | | (77) all_8_0 = e3 % 150.57/21.99 | | % 150.57/21.99 | | SIMP: (77) implies: % 150.57/21.99 | | (78) all_8_0 = e3 % 150.57/21.99 | | % 150.57/21.99 | | REF_CLOSE: (1), (2), (6), (7), (10), (12), (19), (25), (33), (38), (48), % 150.57/21.99 | | (50), (57), (76), (78) are inconsistent by sub-proof #115. % 150.57/21.99 | | % 150.57/21.99 | End of split % 150.57/21.99 | % 150.57/21.99 End of proof % 150.57/21.99 % 150.57/21.99 Sub-proof #99 shows that the following formulas are inconsistent: % 150.57/21.99 ---------------------------------------------------------------- % 150.57/21.99 (1) all_56_11 = all_8_2 % 150.57/21.99 (2) ~ (all_6_1 = e2) % 150.57/21.99 (3) all_54_4 = all_52_1 % 150.57/21.99 (4) op(e0, e0) = all_4_2 % 150.57/21.99 (5) ~ (all_52_13 = all_8_0) % 150.57/21.99 (6) all_54_5 = all_8_2 % 150.57/21.99 (7) ~ (all_6_1 = e3) % 150.57/21.99 (8) ~ (all_8_0 = all_8_2) % 150.57/21.99 (9) all_56_21 = all_6_2 % 150.57/21.99 (10) all_56_1 = all_10_2 % 150.57/21.99 (11) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0 % 150.57/21.99 (12) ~ (all_52_1 = all_8_2) % 150.57/21.99 (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 150.57/21.99 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 150.57/21.99 (14) all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) & % 150.57/21.99 (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0)) % 150.57/21.99 (15) ~ (all_52_1 = all_52_13) % 150.57/21.99 (16) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0 % 150.57/21.99 (17) all_56_21 = e2 % 150.57/21.99 (18) all_56_19 = e1 % 150.57/21.99 (19) op(all_4_2, all_4_2) = all_4_1 % 150.57/21.99 (20) all_56_31 = all_4_2 % 150.57/21.99 (21) ~ (all_8_0 = e3) % 150.57/21.99 (22) ~ (all_52_1 = all_8_0) % 150.57/21.99 (23) op(all_6_2, all_6_2) = all_6_1 % 150.57/21.99 (24) all_56_1 = e3 | all_56_11 = e2 | all_56_21 = e1 | all_56_31 = e0 % 150.57/21.99 (25) op(all_8_2, all_8_2) = e1 % 150.57/21.99 (26) ~ (all_52_6 = all_8_2) % 150.57/21.99 (27) all_58_15 = all_4_2 % 150.57/21.99 (28) ~ (all_56_11 = e0) | all_56_15 = e2 % 150.57/21.99 (29) op(e2, e2) = all_8_2 % 150.57/21.99 (30) op(e0, all_4_2) = all_56_30 % 150.57/21.99 (31) all_54_6 = all_8_0 % 150.57/21.99 (32) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 150.57/21.99 (33) all_56_19 = all_52_6 % 150.57/21.99 (34) all_56_15 = all_52_13 % 150.57/21.99 (35) ~ (all_52_1 = all_10_2) % 150.57/21.99 % 150.57/21.99 Begin of proof % 150.57/21.99 | % 150.57/21.99 | COMBINE_EQS: (18), (33) imply: % 150.57/21.99 | (36) all_52_6 = e1 % 150.57/21.99 | % 150.57/21.99 | COMBINE_EQS: (9), (17) imply: % 150.57/21.99 | (37) all_6_2 = e2 % 150.57/21.99 | % 150.57/21.99 | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (10), (11), (12), (13), % 150.57/21.99 | (14), (15), (16), (17), (19), (20), (21), (22), (23), (24), (25), % 150.57/21.99 | (26), (27), (28), (29), (30), (31), (32), (34), (35), (36), (37) % 150.57/21.99 | are inconsistent by sub-proof #117. % 150.57/21.99 | % 150.57/21.99 End of proof % 150.57/21.99 % 150.57/21.99 Sub-proof #100 shows that the following formulas are inconsistent: % 150.57/21.99 ---------------------------------------------------------------- % 150.57/21.99 (1) all_56_11 = all_8_2 % 150.57/21.99 (2) ~ (all_56_11 = e1) | all_56_13 = e2 % 150.57/21.99 (3) ~ (all_52_11 = all_6_2) % 150.57/21.99 (4) ~ (all_52_4 = all_52_8) % 150.57/21.99 (5) ~ (all_8_0 = all_6_2) % 150.57/21.99 (6) ~ (e3 = e0) % 150.57/21.99 (7) ~ (all_6_1 = e2) % 150.57/21.99 (8) all_54_0 = all_10_2 % 150.57/21.99 (9) ~ (all_52_13 = all_8_0) % 150.57/21.99 (10) all_58_4 = all_52_8 % 150.57/21.99 (11) all_54_5 = all_8_2 % 150.57/21.99 (12) ~ (all_6_1 = e3) % 150.57/21.99 (13) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 150.57/21.99 (14) ~ (all_52_11 = e0) % 150.57/21.99 (15) ~ (all_8_0 = all_8_2) % 150.57/21.99 (16) all_56_21 = all_6_2 % 150.57/21.99 (17) all_56_1 = all_10_2 % 150.57/21.99 (18) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0 % 150.57/21.99 (19) all_56_17 = all_52_2 % 150.57/21.99 (20) all_58_5 = all_8_0 % 150.57/21.99 (21) all_58_4 = e0 | all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0 % 150.57/21.99 (22) op(e2, all_8_2) = all_56_10 % 150.57/21.99 (23) op(e3, e3) = all_10_2 % 150.57/21.99 (24) ~ (all_56_21 = e3) | all_56_17 = e1 % 150.57/21.99 (25) ~ (all_52_1 = all_8_2) % 150.57/21.99 (26) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 150.57/21.99 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 150.57/21.99 (27) ~ (all_52_11 = e3) % 150.57/21.99 (28) all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0 % 150.57/21.99 (29) ~ (all_26_1 = e2) | ~ (all_26_2 = e3) % 150.57/21.99 (30) ~ (all_56_11 = e3) | all_56_9 = e2 % 150.57/21.99 (31) all_58_8 = all_6_2 % 150.57/21.99 (32) ~ (all_52_8 = all_10_2) % 150.57/21.99 (33) ~ (all_56_1 = e2) | all_56_3 = e3 % 150.57/21.99 (34) all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3 % 150.57/21.99 (35) all_58_3 = all_8_2 % 150.57/21.99 (36) all_56_3 = all_52_4 % 150.57/21.99 (37) all_56_31 = all_4_2 % 150.57/21.99 (38) op(e0, e0) = e3 % 150.57/21.99 (39) ~ (all_8_0 = e3) % 150.57/21.99 (40) all_56_13 = all_8_0 % 150.57/21.99 (41) ~ (all_52_1 = all_8_0) % 150.57/21.99 (42) op(all_6_2, all_6_2) = all_6_1 % 150.57/21.99 (43) all_56_1 = e3 | all_56_11 = e2 | all_56_21 = e1 | all_56_31 = e0 % 150.57/21.99 (44) ~ (all_52_13 = all_4_2) % 150.57/21.99 (45) ~ (all_8_0 = e0) | ~ (all_8_2 = e3) % 150.57/21.99 (46) op(all_8_2, all_8_2) = e1 % 150.57/21.99 (47) ~ (all_10_2 = e0) % 150.57/21.99 (48) all_58_2 = all_52_1 % 150.57/21.99 (49) all_58_10 = all_52_13 % 150.57/21.99 (50) op(e2, e2) = all_8_2 % 150.57/21.99 (51) ~ (all_56_21 = e0) | all_56_23 = e1 % 150.57/21.99 (52) all_54_6 = all_8_0 % 150.57/21.99 (53) ~ (e2 = e0) % 150.57/21.99 (54) ~ (all_52_2 = all_10_2) % 150.57/21.99 (55) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 150.57/21.99 (56) all_58_14 = all_52_11 % 150.57/21.99 (57) all_26_2 = e3 % 150.57/21.99 (58) all_56_9 = all_52_1 % 150.57/21.99 (59) op(e3, e3) = all_4_1 % 150.57/21.99 % 150.57/21.99 Begin of proof % 150.57/21.99 | % 150.57/21.99 | BETA: splitting (29) gives: % 150.57/21.99 | % 150.57/21.99 | Case 1: % 150.57/21.99 | | % 150.57/21.99 | | % 150.57/21.99 | | GROUND_INST: instantiating (26) with all_10_2, all_4_1, e3, e3, simplifying % 150.57/21.99 | | with (23), (59) gives: % 150.57/21.99 | | (60) all_10_2 = all_4_1 % 150.57/21.99 | | % 150.57/21.99 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), % 150.57/21.99 | | (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23), % 150.57/21.99 | | (24), (25), (26), (27), (28), (30), (31), (32), (33), (34), (35), % 150.57/21.99 | | (36), (37), (38), (39), (40), (41), (42), (43), (44), (45), (46), % 150.57/21.99 | | (47), (48), (49), (50), (51), (52), (53), (54), (55), (56), (58), % 150.57/21.99 | | (60) are inconsistent by sub-proof #122. % 150.57/21.99 | | % 150.57/21.99 | Case 2: % 150.57/21.99 | | % 150.57/21.99 | | (61) ~ (all_26_2 = e3) % 150.57/21.99 | | % 150.57/21.99 | | REDUCE: (57), (61) imply: % 150.57/21.99 | | (62) $false % 150.57/21.99 | | % 150.57/21.99 | | CLOSE: (62) is inconsistent. % 150.57/21.99 | | % 150.57/21.99 | End of split % 150.57/21.99 | % 150.57/21.99 End of proof % 150.57/21.99 % 150.57/21.99 Sub-proof #101 shows that the following formulas are inconsistent: % 150.57/21.99 ---------------------------------------------------------------- % 150.57/21.99 (1) op(e0, e1) = e1 % 150.57/21.99 (2) ~ (all_52_13 = e1) % 150.57/21.99 (3) all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1 % 150.57/21.99 (4) all_58_9 = all_52_12 % 150.57/21.99 (5) op(e0, all_52_12) = all_56_6 % 150.57/21.99 (6) op(e0, e1) = e3 % 150.57/21.99 (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 150.57/21.99 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 150.57/21.99 (8) ~ (all_52_14 = e1) % 150.57/21.99 (9) ~ (all_52_12 = e3) % 150.57/21.99 (10) ~ (all_4_2 = e1) % 150.57/21.99 (11) all_58_11 = all_52_14 % 150.57/21.99 (12) all_58_15 = all_4_2 % 150.57/21.99 (13) all_58_10 = all_52_13 % 150.57/21.99 % 150.57/21.99 Begin of proof % 150.57/21.99 | % 150.57/21.99 | BETA: splitting (3) gives: % 150.57/21.99 | % 150.57/21.99 | Case 1: % 150.57/21.99 | | % 150.57/21.99 | | (14) all_58_9 = e1 % 150.57/21.99 | | % 150.57/21.99 | | COMBINE_EQS: (4), (14) imply: % 150.57/21.99 | | (15) all_52_12 = e1 % 150.57/21.99 | | % 150.57/21.99 | | REDUCE: (9), (15) imply: % 150.57/21.99 | | (16) ~ (e3 = e1) % 150.57/21.99 | | % 150.57/21.99 | | SIMP: (16) implies: % 150.57/21.99 | | (17) ~ (e3 = e1) % 150.57/21.99 | | % 150.57/21.99 | | REDUCE: (5), (15) imply: % 150.57/21.99 | | (18) op(e0, e1) = all_56_6 % 150.57/21.99 | | % 150.57/21.99 | | GROUND_INST: instantiating (7) with e3, all_56_6, e1, e0, simplifying with % 150.57/21.99 | | (6), (18) gives: % 150.57/21.99 | | (19) all_56_6 = e3 % 150.57/21.99 | | % 150.57/21.99 | | GROUND_INST: instantiating (7) with e1, all_56_6, e1, e0, simplifying with % 150.57/21.99 | | (1), (18) gives: % 150.57/21.99 | | (20) all_56_6 = e1 % 150.57/21.99 | | % 150.57/21.99 | | COMBINE_EQS: (19), (20) imply: % 150.57/21.99 | | (21) e3 = e1 % 150.57/21.99 | | % 150.57/21.99 | | SIMP: (21) implies: % 150.57/21.99 | | (22) e3 = e1 % 150.57/21.99 | | % 150.57/21.99 | | REDUCE: (17), (22) imply: % 150.57/21.99 | | (23) $false % 150.57/21.99 | | % 150.57/21.99 | | CLOSE: (23) is inconsistent. % 150.57/21.99 | | % 150.57/21.99 | Case 2: % 150.57/21.99 | | % 150.57/21.99 | | (24) all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1 % 150.57/21.99 | | % 150.57/21.99 | | REF_CLOSE: (2), (8), (10), (11), (12), (13), (24) are inconsistent by % 150.57/21.99 | | sub-proof #587. % 150.57/21.99 | | % 150.57/21.99 | End of split % 150.57/21.99 | % 150.57/21.99 End of proof % 150.57/21.99 % 150.57/21.99 Sub-proof #102 shows that the following formulas are inconsistent: % 150.57/21.99 ---------------------------------------------------------------- % 150.57/21.99 (1) ~ (all_4_1 = e0) % 150.57/21.99 (2) ~ (all_4_1 = e3) % 150.57/21.99 (3) op(all_4_1, all_4_1) = e1 % 150.57/21.99 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 150.57/21.99 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 150.57/21.99 (5) ~ (all_4_1 = e1) % 150.57/21.99 (6) op(e2, e2) = all_4_1 % 150.57/21.99 (7) all_54_5 = all_4_1 % 150.57/21.99 (8) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 150.57/21.99 % 150.57/21.99 Begin of proof % 150.57/21.99 | % 150.57/21.99 | BETA: splitting (8) gives: % 150.57/21.99 | % 150.57/21.99 | Case 1: % 150.57/21.99 | | % 150.57/21.99 | | (9) all_54_5 = e3 % 150.57/21.99 | | % 150.57/21.99 | | REF_CLOSE: (2), (7), (9) are inconsistent by sub-proof #199. % 150.57/21.99 | | % 150.57/21.99 | Case 2: % 150.57/21.99 | | % 150.57/21.99 | | (10) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 150.57/21.99 | | % 150.57/21.99 | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (10) are inconsistent by sub-proof % 150.57/21.99 | | #103. % 150.57/21.99 | | % 150.57/21.99 | End of split % 150.57/21.99 | % 150.57/21.99 End of proof % 150.57/21.99 % 150.57/21.99 Sub-proof #103 shows that the following formulas are inconsistent: % 150.57/21.99 ---------------------------------------------------------------- % 150.57/21.99 (1) ~ (all_4_1 = e0) % 150.57/21.99 (2) op(all_4_1, all_4_1) = e1 % 150.57/21.99 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 150.57/21.99 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 150.57/21.99 (4) ~ (all_4_1 = e1) % 150.57/21.99 (5) op(e2, e2) = all_4_1 % 150.57/21.99 (6) all_54_5 = all_4_1 % 150.57/21.99 (7) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 150.57/21.99 % 150.57/21.99 Begin of proof % 150.57/21.99 | % 150.57/21.99 | BETA: splitting (7) gives: % 150.57/21.99 | % 150.57/21.99 | Case 1: % 150.57/21.99 | | % 150.57/21.99 | | (8) all_54_5 = e2 % 150.57/21.99 | | % 150.57/21.99 | | COMBINE_EQS: (6), (8) imply: % 150.57/21.99 | | (9) all_4_1 = e2 % 150.57/21.99 | | % 150.57/21.99 | | SIMP: (9) implies: % 150.57/21.99 | | (10) all_4_1 = e2 % 150.57/21.99 | | % 150.57/21.99 | | REDUCE: (4), (10) imply: % 150.57/21.99 | | (11) ~ (e2 = e1) % 150.57/21.99 | | % 150.57/21.99 | | REDUCE: (2), (10) imply: % 150.57/21.99 | | (12) op(e2, e2) = e1 % 150.57/21.99 | | % 150.57/21.99 | | REDUCE: (5), (10) imply: % 150.57/21.99 | | (13) op(e2, e2) = e2 % 150.57/21.99 | | % 150.57/21.99 | | REF_CLOSE: (3), (11), (12), (13) are inconsistent by sub-proof #479. % 150.57/21.99 | | % 150.57/21.99 | Case 2: % 150.57/21.99 | | % 150.57/21.99 | | (14) all_54_5 = e1 | all_54_5 = e0 % 150.57/21.99 | | % 150.57/21.99 | | REF_CLOSE: (1), (4), (6), (14) are inconsistent by sub-proof #569. % 150.57/21.99 | | % 150.57/21.99 | End of split % 150.57/21.99 | % 150.57/21.99 End of proof % 150.57/21.99 % 150.57/21.99 Sub-proof #104 shows that the following formulas are inconsistent: % 150.57/21.99 ---------------------------------------------------------------- % 150.57/21.99 (1) all_56_11 = all_8_2 % 150.57/21.99 (2) ~ (all_56_11 = e1) | all_56_13 = e2 % 150.57/21.99 (3) ~ (all_8_0 = all_6_2) % 150.57/21.99 (4) ~ (e3 = e0) % 150.57/21.99 (5) ~ (all_6_1 = e2) % 150.57/21.99 (6) ~ (all_52_13 = all_8_2) % 150.57/21.99 (7) all_48_1 = e1 % 150.57/21.99 (8) ~ (e3 = e2) % 150.57/21.99 (9) op(e0, e0) = all_4_2 % 150.57/21.99 (10) ~ (all_52_13 = all_8_0) % 150.57/21.99 (11) all_54_5 = all_8_2 % 150.57/21.99 (12) all_6_0 = e2 % 150.57/21.99 (13) ~ (all_48_0 = e3) | ~ (all_48_1 = e1) | ~ (all_48_2 = e0) % 150.57/21.99 (14) ~ (all_8_0 = all_8_2) % 150.57/21.99 (15) all_56_21 = all_6_2 % 150.57/21.99 (16) all_56_1 = all_10_2 % 150.57/21.99 (17) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0 % 150.57/21.99 (18) all_48_0 = all_8_0 % 150.57/21.99 (19) all_58_5 = all_8_0 % 150.57/21.99 (20) op(e2, all_8_2) = all_56_10 % 150.57/21.99 (21) op(e3, e3) = all_10_2 % 150.57/21.99 (22) ~ (e1 = e0) % 150.57/21.99 (23) all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1 % 150.57/21.99 (24) ~ (all_52_1 = all_8_2) % 150.57/21.99 (25) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 150.57/21.99 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 150.57/21.99 (26) all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0 % 150.57/21.99 (27) ~ (all_56_11 = e3) | all_56_9 = e2 % 150.57/21.99 (28) ~ (e2 = e1) % 150.57/21.99 (29) op(e1, all_6_1) = all_6_0 % 150.57/21.99 (30) op(all_4_2, all_4_2) = all_4_1 % 150.57/21.99 (31) all_58_3 = all_8_2 % 150.57/21.99 (32) all_56_31 = all_4_2 % 150.57/21.99 (33) all_56_13 = all_8_0 % 150.57/21.99 (34) ~ (all_52_1 = all_8_0) % 150.57/21.99 (35) op(all_6_2, all_6_2) = all_6_1 % 150.57/21.99 (36) all_56_1 = e3 | all_56_11 = e2 | all_56_21 = e1 | all_56_31 = e0 % 150.57/21.99 (37) ~ (all_52_13 = all_4_2) % 150.57/21.99 (38) ~ (all_8_0 = e0) | ~ (all_8_2 = e3) % 150.57/21.99 (39) op(all_8_2, all_8_2) = e1 % 150.57/21.99 (40) op(e1, e1) = all_6_2 % 150.57/21.99 (41) all_58_2 = all_52_1 % 150.57/21.99 (42) all_58_10 = all_52_13 % 150.57/21.99 (43) ~ (all_56_11 = e0) | all_56_15 = e2 % 150.57/21.99 (44) op(e1, all_6_2) = all_56_20 % 150.57/21.99 (45) ~ (e3 = e1) % 150.57/21.99 (46) op(e2, e2) = all_8_2 % 150.57/21.99 (47) op(e0, all_4_2) = all_56_30 % 150.57/21.99 (48) all_48_2 = all_8_2 % 150.57/21.99 (49) all_54_6 = all_8_0 % 150.57/21.99 (50) ~ (e2 = e0) % 150.57/21.99 (51) all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3 % 150.57/21.99 (52) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 150.57/21.99 (53) all_56_9 = all_52_1 % 150.57/21.99 (54) all_56_15 = all_52_13 % 150.57/21.99 (55) ~ (all_52_1 = all_10_2) % 150.57/21.99 % 150.57/21.99 Begin of proof % 150.57/21.99 | % 150.57/21.99 | REDUCE: (12), (29) imply: % 150.57/21.99 | (56) op(e1, all_6_1) = e2 % 150.57/21.99 | % 150.57/21.99 | BETA: splitting (13) gives: % 150.57/21.99 | % 150.57/21.99 | Case 1: % 150.57/21.99 | | % 150.57/21.99 | | (57) ~ (all_48_0 = e3) % 150.57/21.99 | | % 150.57/21.99 | | REDUCE: (18), (57) imply: % 150.57/21.99 | | (58) ~ (all_8_0 = e3) % 150.57/21.99 | | % 150.57/21.99 | | BETA: splitting (43) gives: % 150.57/21.99 | | % 150.57/21.99 | | Case 1: % 150.57/21.99 | | | % 150.57/21.99 | | | (59) ~ (all_56_11 = e0) % 150.57/21.99 | | | % 150.57/21.99 | | | REDUCE: (1), (59) imply: % 150.57/21.99 | | | (60) ~ (all_8_2 = e0) % 150.57/21.99 | | | % 150.57/21.99 | | | BETA: splitting (2) gives: % 150.57/21.99 | | | % 150.57/21.99 | | | Case 1: % 150.57/21.99 | | | | % 150.57/21.99 | | | | (61) ~ (all_56_11 = e1) % 150.57/21.99 | | | | % 150.57/21.99 | | | | REDUCE: (1), (61) imply: % 150.57/21.99 | | | | (62) ~ (all_8_2 = e1) % 150.57/21.99 | | | | % 150.57/21.99 | | | | REF_CLOSE: (1), (3), (10), (11), (14), (15), (16), (17), (19), (20), % 150.57/21.99 | | | | (21), (24), (25), (26), (27), (31), (32), (34), (36), (37), % 150.57/21.99 | | | | (38), (39), (41), (42), (46), (49), (50), (52), (53), (60), % 150.57/21.99 | | | | (62) are inconsistent by sub-proof #141. % 150.57/21.99 | | | | % 150.57/21.99 | | | Case 2: % 150.57/21.99 | | | | % 150.57/21.99 | | | | (63) all_56_11 = e1 % 150.57/21.99 | | | | % 150.57/21.99 | | | | COMBINE_EQS: (1), (63) imply: % 150.57/21.99 | | | | (64) all_8_2 = e1 % 150.57/21.99 | | | | % 150.57/21.99 | | | | REDUCE: (39), (64) imply: % 150.57/21.99 | | | | (65) op(e1, e1) = e1 % 150.57/21.99 | | | | % 150.57/21.99 | | | | GROUND_INST: instantiating (25) with all_6_2, e1, e1, e1, simplifying % 150.57/21.99 | | | | with (40), (65) gives: % 150.57/21.99 | | | | (66) all_6_2 = e1 % 150.57/21.99 | | | | % 150.57/21.99 | | | | REDUCE: (35), (66) imply: % 150.57/21.99 | | | | (67) op(e1, e1) = all_6_1 % 150.57/21.99 | | | | % 150.57/21.99 | | | | REDUCE: (44), (66) imply: % 150.57/21.99 | | | | (68) op(e1, e1) = all_56_20 % 150.57/21.99 | | | | % 150.57/21.99 | | | | GROUND_INST: instantiating (25) with e1, all_56_20, e1, e1, simplifying % 150.57/21.99 | | | | with (65), (68) gives: % 150.57/21.99 | | | | (69) all_56_20 = e1 % 150.57/21.99 | | | | % 150.57/21.99 | | | | GROUND_INST: instantiating (25) with all_6_1, all_56_20, e1, e1, % 150.57/21.99 | | | | simplifying with (67), (68) gives: % 150.57/21.99 | | | | (70) all_56_20 = all_6_1 % 150.57/21.99 | | | | % 150.57/21.99 | | | | COMBINE_EQS: (69), (70) imply: % 150.57/21.99 | | | | (71) all_6_1 = e1 % 150.57/21.99 | | | | % 150.57/21.99 | | | | SIMP: (71) implies: % 150.57/21.99 | | | | (72) all_6_1 = e1 % 150.57/21.99 | | | | % 150.57/21.99 | | | | REF_CLOSE: (5), (25), (56), (67), (68), (72) are inconsistent by % 150.57/21.99 | | | | sub-proof #378. % 150.57/21.99 | | | | % 150.57/21.99 | | | End of split % 150.57/21.99 | | | % 150.57/21.99 | | Case 2: % 150.57/21.99 | | | % 150.57/21.99 | | | (73) all_56_15 = e2 % 150.57/21.99 | | | (74) all_56_11 = e0 % 150.57/21.99 | | | % 150.57/21.99 | | | REF_CLOSE: (1), (3), (4), (6), (8), (9), (10), (14), (15), (16), (17), % 150.57/21.99 | | | (19), (22), (23), (25), (28), (30), (31), (32), (36), (39), % 150.57/21.99 | | | (41), (42), (45), (47), (49), (51), (54), (55), (58), (73), % 150.57/21.99 | | | (74) are inconsistent by sub-proof #126. % 150.57/21.99 | | | % 150.57/21.99 | | End of split % 150.57/21.99 | | % 150.57/21.99 | Case 2: % 150.57/21.99 | | % 150.57/21.99 | | (75) all_48_0 = e3 % 150.57/21.99 | | (76) ~ (all_48_1 = e1) | ~ (all_48_2 = e0) % 150.57/21.99 | | % 150.57/21.99 | | COMBINE_EQS: (18), (75) imply: % 150.57/21.99 | | (77) all_8_0 = e3 % 150.57/21.99 | | % 150.57/21.99 | | SIMP: (77) implies: % 150.57/21.99 | | (78) all_8_0 = e3 % 150.57/21.99 | | % 150.57/21.99 | | REF_CLOSE: (1), (2), (7), (8), (11), (14), (20), (25), (33), (39), (46), % 150.57/21.99 | | (48), (52), (76), (78) are inconsistent by sub-proof #115. % 150.57/21.99 | | % 150.57/21.99 | End of split % 150.57/21.99 | % 150.57/21.99 End of proof % 150.57/21.99 % 150.57/21.99 Sub-proof #105 shows that the following formulas are inconsistent: % 150.57/21.99 ---------------------------------------------------------------- % 150.57/21.99 (1) all_56_11 = all_8_2 % 150.57/21.99 (2) ~ (all_56_11 = e1) | all_56_13 = e2 % 150.57/21.99 (3) ~ (all_8_0 = all_6_2) % 150.57/21.99 (4) ~ (e3 = e0) % 150.57/21.99 (5) ~ (all_52_13 = all_8_2) % 150.57/21.99 (6) all_54_0 = all_10_2 % 150.57/21.99 (7) all_48_1 = e1 % 150.57/21.99 (8) all_54_2 = all_10_0 % 150.57/21.99 (9) ~ (e3 = e2) % 150.57/21.99 (10) op(e0, e0) = all_4_2 % 150.57/21.99 (11) ~ (all_52_13 = all_8_0) % 150.57/21.99 (12) all_54_5 = all_8_2 % 150.57/21.99 (13) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 150.57/21.99 (14) ~ (all_48_0 = e3) | ~ (all_48_1 = e1) | ~ (all_48_2 = e0) % 150.57/21.99 (15) ~ (all_8_0 = all_8_2) % 150.57/21.99 (16) all_56_21 = all_6_2 % 150.57/21.99 (17) all_56_1 = all_10_2 % 150.57/21.99 (18) ~ (all_32_0 = e0) | ~ (all_32_2 = e2) % 150.57/21.99 (19) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0 % 150.57/21.99 (20) all_48_0 = all_8_0 % 150.57/21.99 (21) all_56_17 = all_52_2 % 150.57/21.99 (22) all_58_5 = all_8_0 % 150.57/21.99 (23) op(e2, all_8_2) = all_56_10 % 150.57/21.99 (24) op(e3, e3) = all_10_2 % 150.57/21.99 (25) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0 % 150.57/21.99 (26) ~ (all_56_21 = e3) | all_56_17 = e1 % 150.57/21.99 (27) ~ (e1 = e0) % 150.57/21.99 (28) all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1 % 150.57/21.99 (29) ~ (all_52_1 = all_8_2) % 150.57/21.99 (30) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 150.57/21.99 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 150.57/21.99 (31) all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0 % 150.57/21.99 (32) ~ (all_56_11 = e3) | all_56_9 = e2 % 150.57/21.99 (33) op(e1, e3) = all_52_2 % 150.57/21.99 (34) ~ (e2 = e1) % 150.57/21.99 (35) op(all_4_2, all_4_2) = all_4_1 % 150.57/22.00 (36) op(all_10_2, all_10_2) = e1 % 150.57/22.00 (37) all_58_3 = all_8_2 % 150.57/22.00 (38) all_56_31 = all_4_2 % 150.57/22.00 (39) all_56_13 = all_8_0 % 150.57/22.00 (40) ~ (all_10_0 = all_6_2) % 150.57/22.00 (41) ~ (all_52_1 = all_8_0) % 150.57/22.00 (42) all_56_1 = e3 | all_56_11 = e2 | all_56_21 = e1 | all_56_31 = e0 % 150.57/22.00 (43) ~ (all_10_0 = e1) % 150.57/22.00 (44) all_32_0 = all_10_0 % 150.57/22.00 (45) ~ (all_52_13 = all_4_2) % 150.57/22.00 (46) ~ (all_8_0 = e0) | ~ (all_8_2 = e3) % 150.57/22.00 (47) op(all_8_2, all_8_2) = e1 % 150.57/22.00 (48) op(e1, e1) = all_6_2 % 150.57/22.00 (49) all_58_2 = all_52_1 % 150.57/22.00 (50) all_58_10 = all_52_13 % 150.57/22.00 (51) ~ (all_56_11 = e0) | all_56_15 = e2 % 150.57/22.00 (52) op(e1, all_6_2) = all_56_20 % 150.57/22.00 (53) op(e1, e3) = all_6_0 % 150.57/22.00 (54) ~ (e3 = e1) % 150.57/22.00 (55) op(e2, e2) = all_8_2 % 150.57/22.00 (56) op(e0, all_4_2) = all_56_30 % 150.57/22.00 (57) all_48_2 = all_8_2 % 150.57/22.00 (58) all_54_6 = all_8_0 % 150.57/22.00 (59) op(all_6_2, all_6_2) = e3 % 150.57/22.00 (60) op(e3, all_10_2) = all_56_0 % 150.57/22.00 (61) ~ (e2 = e0) % 150.57/22.00 (62) ~ (all_10_0 = all_10_2) % 150.57/22.00 (63) ~ (all_52_2 = all_10_2) % 150.57/22.00 (64) all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3 % 150.57/22.00 (65) ~ (all_10_0 = e2) % 150.57/22.00 (66) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 150.57/22.00 (67) all_56_9 = all_52_1 % 150.57/22.00 (68) all_56_15 = all_52_13 % 150.57/22.00 (69) all_32_2 = all_10_2 % 150.57/22.00 (70) ~ (all_52_1 = all_10_2) % 150.57/22.00 % 150.57/22.00 Begin of proof % 150.57/22.00 | % 150.57/22.00 | GROUND_INST: instantiating (30) with all_52_2, all_6_0, e3, e1, simplifying % 150.57/22.00 | with (33), (53) gives: % 150.57/22.00 | (71) all_52_2 = all_6_0 % 150.57/22.00 | % 150.57/22.00 | COMBINE_EQS: (21), (71) imply: % 150.57/22.00 | (72) all_56_17 = all_6_0 % 150.57/22.00 | % 150.57/22.00 | REDUCE: (63), (71) imply: % 150.57/22.00 | (73) ~ (all_10_2 = all_6_0) % 150.57/22.00 | % 150.57/22.00 | SIMP: (73) implies: % 150.57/22.00 | (74) ~ (all_10_2 = all_6_0) % 150.57/22.00 | % 150.57/22.00 | BETA: splitting (14) gives: % 150.57/22.00 | % 150.57/22.00 | Case 1: % 150.57/22.00 | | % 150.57/22.00 | | (75) ~ (all_48_0 = e3) % 150.57/22.00 | | % 150.57/22.00 | | REDUCE: (20), (75) imply: % 150.57/22.00 | | (76) ~ (all_8_0 = e3) % 150.57/22.00 | | % 150.57/22.00 | | BETA: splitting (51) gives: % 150.57/22.00 | | % 150.57/22.00 | | Case 1: % 150.57/22.00 | | | % 150.57/22.00 | | | (77) ~ (all_56_11 = e0) % 150.57/22.00 | | | % 150.57/22.00 | | | REDUCE: (1), (77) imply: % 150.57/22.00 | | | (78) ~ (all_8_2 = e0) % 150.57/22.00 | | | % 150.57/22.00 | | | BETA: splitting (26) gives: % 150.57/22.00 | | | % 150.57/22.00 | | | Case 1: % 150.57/22.00 | | | | % 150.57/22.00 | | | | (79) ~ (all_56_21 = e3) % 150.57/22.00 | | | | % 150.57/22.00 | | | | REDUCE: (16), (79) imply: % 150.57/22.00 | | | | (80) ~ (all_6_2 = e3) % 150.57/22.00 | | | | % 150.57/22.00 | | | | REF_CLOSE: (1), (2), (3), (11), (12), (15), (16), (17), (19), (22), % 150.57/22.00 | | | | (23), (24), (29), (30), (31), (32), (37), (38), (41), (42), % 150.57/22.00 | | | | (45), (46), (47), (48), (49), (50), (52), (55), (58), (59), % 150.57/22.00 | | | | (61), (66), (67), (78), (80) are inconsistent by sub-proof % 150.57/22.00 | | | | #114. % 150.57/22.00 | | | | % 150.57/22.00 | | | Case 2: % 150.57/22.00 | | | | % 150.57/22.00 | | | | (81) all_56_21 = e3 % 150.57/22.00 | | | | (82) all_56_17 = e1 % 150.57/22.00 | | | | % 150.57/22.00 | | | | COMBINE_EQS: (72), (82) imply: % 150.57/22.00 | | | | (83) all_6_0 = e1 % 150.57/22.00 | | | | % 150.57/22.00 | | | | COMBINE_EQS: (16), (81) imply: % 150.57/22.00 | | | | (84) all_6_2 = e3 % 150.57/22.00 | | | | % 150.57/22.00 | | | | SIMP: (84) implies: % 150.57/22.00 | | | | (85) all_6_2 = e3 % 150.57/22.00 | | | | % 150.57/22.00 | | | | REDUCE: (40), (85) imply: % 150.57/22.00 | | | | (86) ~ (all_10_0 = e3) % 150.57/22.00 | | | | % 150.57/22.00 | | | | REDUCE: (74), (83) imply: % 150.57/22.00 | | | | (87) ~ (all_10_2 = e1) % 150.57/22.00 | | | | % 150.57/22.00 | | | | REF_CLOSE: (6), (8), (13), (18), (24), (25), (30), (36), (43), (44), % 150.57/22.00 | | | | (60), (62), (65), (69), (86), (87) are inconsistent by % 150.57/22.00 | | | | sub-proof #394. % 150.57/22.00 | | | | % 150.57/22.00 | | | End of split % 150.57/22.00 | | | % 150.57/22.00 | | Case 2: % 150.57/22.00 | | | % 150.57/22.00 | | | (88) all_56_15 = e2 % 150.57/22.00 | | | (89) all_56_11 = e0 % 150.57/22.00 | | | % 150.57/22.00 | | | REF_CLOSE: (1), (3), (4), (5), (9), (10), (11), (15), (16), (17), (19), % 150.57/22.00 | | | (22), (27), (28), (30), (34), (35), (37), (38), (42), (47), % 150.57/22.00 | | | (49), (50), (54), (56), (58), (64), (68), (70), (76), (88), % 150.57/22.00 | | | (89) are inconsistent by sub-proof #126. % 150.57/22.00 | | | % 150.57/22.00 | | End of split % 150.57/22.00 | | % 150.57/22.00 | Case 2: % 150.57/22.00 | | % 150.57/22.00 | | (90) all_48_0 = e3 % 150.57/22.00 | | (91) ~ (all_48_1 = e1) | ~ (all_48_2 = e0) % 150.57/22.00 | | % 150.57/22.00 | | COMBINE_EQS: (20), (90) imply: % 150.57/22.00 | | (92) all_8_0 = e3 % 150.57/22.00 | | % 150.57/22.00 | | SIMP: (92) implies: % 150.57/22.00 | | (93) all_8_0 = e3 % 150.57/22.00 | | % 150.57/22.00 | | REF_CLOSE: (1), (2), (7), (9), (12), (15), (23), (30), (39), (47), (55), % 150.57/22.00 | | (57), (66), (91), (93) are inconsistent by sub-proof #115. % 150.57/22.00 | | % 150.57/22.00 | End of split % 150.57/22.00 | % 150.57/22.00 End of proof % 150.57/22.00 % 150.57/22.00 Sub-proof #106 shows that the following formulas are inconsistent: % 150.57/22.00 ---------------------------------------------------------------- % 150.57/22.00 (1) all_56_11 = all_8_2 % 150.57/22.00 (2) ~ (all_56_11 = e1) | all_56_13 = e2 % 150.57/22.00 (3) all_58_6 = all_52_2 % 150.57/22.00 (4) ~ (all_8_0 = all_6_2) % 150.57/22.00 (5) ~ (e3 = e0) % 150.57/22.00 (6) ~ (all_52_13 = all_8_2) % 150.57/22.00 (7) all_48_1 = e1 % 150.57/22.00 (8) op(e0, e0) = all_4_2 % 150.57/22.00 (9) ~ (all_52_13 = all_8_0) % 150.57/22.00 (10) all_54_5 = all_8_2 % 150.57/22.00 (11) ~ (all_6_1 = e3) % 150.57/22.00 (12) ~ (all_6_0 = e2) % 150.57/22.00 (13) ~ (all_48_0 = e3) | ~ (all_48_1 = e1) | ~ (all_48_2 = e0) % 150.57/22.00 (14) ~ (all_8_0 = all_8_2) % 150.57/22.00 (15) all_56_21 = all_6_2 % 150.57/22.00 (16) all_56_1 = all_10_2 % 150.57/22.00 (17) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0 % 150.57/22.00 (18) all_48_0 = all_8_0 % 150.57/22.00 (19) all_58_5 = all_8_0 % 150.57/22.00 (20) op(e2, all_8_2) = all_56_10 % 150.57/22.00 (21) op(e3, e3) = all_10_2 % 150.57/22.00 (22) all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2 % 150.57/22.00 (23) ~ (e1 = e0) % 150.57/22.00 (24) all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1 % 150.57/22.00 (25) ~ (all_52_1 = all_8_2) % 150.57/22.00 (26) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 150.57/22.00 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 150.57/22.00 (27) all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0 % 150.57/22.00 (28) ~ (all_56_11 = e3) | all_56_9 = e2 % 150.57/22.00 (29) ~ (all_52_1 = all_52_13) % 150.57/22.00 (30) all_6_0 = e3 % 150.57/22.00 (31) ~ (e2 = e1) % 150.57/22.00 (32) op(e1, all_6_1) = all_6_0 % 150.57/22.00 (33) op(all_4_2, all_4_2) = all_4_1 % 150.57/22.00 (34) all_58_3 = all_8_2 % 150.57/22.00 (35) ~ (all_52_1 = all_52_3) % 150.57/22.00 (36) all_56_31 = all_4_2 % 150.57/22.00 (37) all_56_13 = all_8_0 % 150.57/22.00 (38) ~ (all_52_1 = all_8_0) % 150.57/22.00 (39) op(all_6_2, all_6_2) = all_6_1 % 150.57/22.00 (40) all_56_1 = e3 | all_56_11 = e2 | all_56_21 = e1 | all_56_31 = e0 % 150.57/22.00 (41) ~ (all_52_13 = all_4_2) % 150.57/22.00 (42) ~ (all_8_0 = e0) | ~ (all_8_2 = e3) % 150.57/22.00 (43) op(all_8_2, all_8_2) = e1 % 150.57/22.00 (44) op(e1, e1) = all_6_2 % 150.57/22.00 (45) all_58_2 = all_52_1 % 150.57/22.00 (46) all_58_10 = all_52_13 % 150.57/22.00 (47) ~ (all_56_11 = e0) | all_56_15 = e2 % 150.57/22.00 (48) all_58_0 = all_10_2 % 150.57/22.00 (49) op(e1, all_6_2) = all_56_20 % 150.57/22.00 (50) ~ (e3 = e1) % 150.57/22.00 (51) op(e2, e2) = all_8_2 % 150.57/22.00 (52) ~ (all_52_1 = all_52_2) % 150.57/22.00 (53) op(e0, all_4_2) = all_56_30 % 150.57/22.00 (54) all_48_2 = all_8_2 % 150.57/22.00 (55) all_54_6 = all_8_0 % 150.57/22.00 (56) ~ (e2 = e0) % 150.57/22.00 (57) all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3 % 150.57/22.00 (58) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 150.57/22.00 (59) all_56_9 = all_52_1 % 150.57/22.00 (60) all_56_15 = all_52_13 % 150.57/22.00 (61) ~ (all_52_1 = all_10_2) % 150.57/22.00 (62) all_58_12 = all_52_3 % 150.57/22.00 % 150.57/22.00 Begin of proof % 150.57/22.00 | % 150.57/22.00 | REDUCE: (12), (30) imply: % 150.57/22.00 | (63) ~ (e3 = e2) % 150.57/22.00 | % 150.57/22.00 | REDUCE: (30), (32) imply: % 150.57/22.00 | (64) op(e1, all_6_1) = e3 % 150.57/22.00 | % 150.57/22.00 | BETA: splitting (13) gives: % 150.57/22.00 | % 150.57/22.00 | Case 1: % 150.57/22.00 | | % 150.57/22.00 | | (65) ~ (all_48_0 = e3) % 150.57/22.00 | | % 150.57/22.00 | | REDUCE: (18), (65) imply: % 150.57/22.00 | | (66) ~ (all_8_0 = e3) % 150.57/22.00 | | % 150.57/22.00 | | BETA: splitting (47) gives: % 150.57/22.00 | | % 150.57/22.00 | | Case 1: % 150.57/22.00 | | | % 150.57/22.00 | | | (67) ~ (all_56_11 = e0) % 150.57/22.00 | | | % 150.57/22.00 | | | REDUCE: (1), (67) imply: % 150.57/22.00 | | | (68) ~ (all_8_2 = e0) % 150.57/22.00 | | | % 150.57/22.00 | | | BETA: splitting (28) gives: % 150.57/22.00 | | | % 150.57/22.00 | | | Case 1: % 150.57/22.00 | | | | % 150.57/22.00 | | | | (69) ~ (all_56_11 = e3) % 150.57/22.00 | | | | % 150.57/22.00 | | | | REDUCE: (1), (69) imply: % 150.57/22.00 | | | | (70) ~ (all_8_2 = e3) % 150.57/22.00 | | | | % 150.57/22.00 | | | | BETA: splitting (2) gives: % 150.57/22.00 | | | | % 150.57/22.00 | | | | Case 1: % 150.57/22.00 | | | | | % 150.57/22.00 | | | | | (71) ~ (all_56_11 = e1) % 150.57/22.00 | | | | | % 150.57/22.00 | | | | | REDUCE: (1), (71) imply: % 150.57/22.00 | | | | | (72) ~ (all_8_2 = e1) % 150.57/22.00 | | | | | % 150.57/22.00 | | | | | REF_CLOSE: (10), (20), (26), (43), (51), (58), (68), (70), (72) are % 150.57/22.00 | | | | | inconsistent by sub-proof #146. % 150.57/22.00 | | | | | % 150.57/22.00 | | | | Case 2: % 150.57/22.00 | | | | | % 150.57/22.00 | | | | | (73) all_56_11 = e1 % 150.57/22.00 | | | | | % 150.57/22.00 | | | | | COMBINE_EQS: (1), (73) imply: % 150.57/22.00 | | | | | (74) all_8_2 = e1 % 150.57/22.00 | | | | | % 150.57/22.00 | | | | | REDUCE: (43), (74) imply: % 150.57/22.00 | | | | | (75) op(e1, e1) = e1 % 150.57/22.00 | | | | | % 150.57/22.00 | | | | | GROUND_INST: instantiating (26) with all_6_2, e1, e1, e1, simplifying % 150.57/22.00 | | | | | with (44), (75) gives: % 150.57/22.00 | | | | | (76) all_6_2 = e1 % 150.57/22.00 | | | | | % 150.57/22.00 | | | | | REDUCE: (39), (76) imply: % 150.57/22.00 | | | | | (77) op(e1, e1) = all_6_1 % 150.57/22.00 | | | | | % 150.57/22.00 | | | | | REDUCE: (49), (76) imply: % 150.57/22.00 | | | | | (78) op(e1, e1) = all_56_20 % 150.57/22.00 | | | | | % 150.57/22.00 | | | | | GROUND_INST: instantiating (26) with e1, all_56_20, e1, e1, % 150.57/22.00 | | | | | simplifying with (75), (78) gives: % 150.57/22.00 | | | | | (79) all_56_20 = e1 % 150.57/22.00 | | | | | % 150.57/22.00 | | | | | GROUND_INST: instantiating (26) with all_6_1, all_56_20, e1, e1, % 150.57/22.00 | | | | | simplifying with (77), (78) gives: % 150.57/22.00 | | | | | (80) all_56_20 = all_6_1 % 150.57/22.00 | | | | | % 150.57/22.00 | | | | | REF_CLOSE: (11), (26), (64), (77), (78), (79), (80) are inconsistent % 150.57/22.00 | | | | | by sub-proof #515. % 150.57/22.00 | | | | | % 150.57/22.00 | | | | End of split % 150.57/22.00 | | | | % 150.57/22.00 | | | Case 2: % 150.57/22.00 | | | | % 150.57/22.00 | | | | (81) all_56_11 = e3 % 150.57/22.00 | | | | (82) all_56_9 = e2 % 150.57/22.00 | | | | % 150.57/22.00 | | | | COMBINE_EQS: (59), (82) imply: % 150.57/22.00 | | | | (83) all_52_1 = e2 % 150.57/22.00 | | | | % 150.57/22.00 | | | | COMBINE_EQS: (1), (81) imply: % 150.57/22.00 | | | | (84) all_8_2 = e3 % 150.57/22.00 | | | | % 150.57/22.00 | | | | COMBINE_EQS: (34), (84) imply: % 150.57/22.00 | | | | (85) all_58_3 = e3 % 150.57/22.00 | | | | % 150.57/22.00 | | | | COMBINE_EQS: (45), (83) imply: % 150.57/22.00 | | | | (86) all_58_2 = e2 % 150.57/22.00 | | | | % 150.57/22.00 | | | | REDUCE: (52), (83) imply: % 150.57/22.00 | | | | (87) ~ (all_52_2 = e2) % 150.57/22.00 | | | | % 150.57/22.00 | | | | SIMP: (87) implies: % 150.57/22.00 | | | | (88) ~ (all_52_2 = e2) % 150.57/22.00 | | | | % 150.57/22.00 | | | | REDUCE: (35), (83) imply: % 150.57/22.00 | | | | (89) ~ (all_52_3 = e2) % 150.57/22.00 | | | | % 150.57/22.00 | | | | SIMP: (89) implies: % 150.57/22.00 | | | | (90) ~ (all_52_3 = e2) % 150.57/22.00 | | | | % 150.57/22.00 | | | | REDUCE: (61), (83) imply: % 150.57/22.00 | | | | (91) ~ (all_10_2 = e2) % 150.57/22.00 | | | | % 150.57/22.00 | | | | SIMP: (91) implies: % 150.57/22.00 | | | | (92) ~ (all_10_2 = e2) % 150.57/22.00 | | | | % 150.57/22.00 | | | | REDUCE: (38), (83) imply: % 150.57/22.00 | | | | (93) ~ (all_8_0 = e2) % 150.57/22.00 | | | | % 150.57/22.00 | | | | SIMP: (93) implies: % 150.57/22.00 | | | | (94) ~ (all_8_0 = e2) % 150.57/22.00 | | | | % 150.57/22.00 | | | | REDUCE: (25), (83), (84) imply: % 150.57/22.00 | | | | (95) ~ (e3 = e2) % 150.57/22.00 | | | | % 150.57/22.00 | | | | REDUCE: (43), (84) imply: % 150.57/22.00 | | | | (96) op(e3, e3) = e1 % 150.57/22.00 | | | | % 150.57/22.00 | | | | REF_CLOSE: (3), (4), (9), (15), (16), (17), (19), (21), (22), (26), % 150.57/22.00 | | | | (27), (29), (36), (40), (41), (42), (45), (46), (47), (48), % 150.57/22.00 | | | | (55), (56), (60), (62), (63), (66), (81), (84), (85), (86), % 150.57/22.00 | | | | (88), (90), (92), (94), (96) are inconsistent by sub-proof % 150.57/22.00 | | | | #107. % 150.57/22.00 | | | | % 150.57/22.00 | | | End of split % 150.57/22.00 | | | % 150.57/22.00 | | Case 2: % 150.57/22.00 | | | % 150.57/22.00 | | | (97) all_56_15 = e2 % 150.57/22.00 | | | (98) all_56_11 = e0 % 150.57/22.00 | | | % 150.57/22.00 | | | REF_CLOSE: (1), (4), (5), (6), (8), (9), (14), (15), (16), (17), (19), % 150.57/22.00 | | | (23), (24), (26), (31), (33), (34), (36), (40), (43), (45), % 150.57/22.00 | | | (46), (50), (53), (55), (57), (60), (61), (63), (66), (97), % 150.57/22.00 | | | (98) are inconsistent by sub-proof #126. % 150.57/22.00 | | | % 150.57/22.00 | | End of split % 150.57/22.00 | | % 150.57/22.00 | Case 2: % 150.57/22.00 | | % 150.57/22.00 | | (99) all_48_0 = e3 % 150.57/22.00 | | (100) ~ (all_48_1 = e1) | ~ (all_48_2 = e0) % 150.57/22.00 | | % 150.57/22.00 | | COMBINE_EQS: (18), (99) imply: % 150.57/22.00 | | (101) all_8_0 = e3 % 150.57/22.00 | | % 150.57/22.00 | | SIMP: (101) implies: % 150.57/22.00 | | (102) all_8_0 = e3 % 150.57/22.00 | | % 150.57/22.00 | | REF_CLOSE: (1), (2), (7), (10), (14), (20), (26), (37), (43), (51), (54), % 150.57/22.00 | | (58), (63), (100), (102) are inconsistent by sub-proof #115. % 150.57/22.00 | | % 150.57/22.00 | End of split % 150.57/22.00 | % 150.57/22.00 End of proof % 150.57/22.00 % 150.57/22.00 Sub-proof #107 shows that the following formulas are inconsistent: % 150.57/22.00 ---------------------------------------------------------------- % 150.57/22.00 (1) all_58_6 = all_52_2 % 150.57/22.00 (2) ~ (all_8_0 = all_6_2) % 150.57/22.00 (3) ~ (e3 = e2) % 150.57/22.00 (4) all_56_11 = e3 % 150.57/22.00 (5) ~ (all_52_13 = all_8_0) % 150.57/22.00 (6) ~ (all_52_3 = e2) % 150.57/22.00 (7) all_56_21 = all_6_2 % 150.57/22.00 (8) all_56_1 = all_10_2 % 150.57/22.00 (9) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0 % 150.57/22.00 (10) ~ (all_10_2 = e2) % 150.57/22.00 (11) all_58_5 = all_8_0 % 150.57/22.00 (12) op(e3, e3) = all_10_2 % 150.57/22.00 (13) all_58_3 = e3 % 150.57/22.00 (14) all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2 % 150.57/22.00 (15) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 150.57/22.00 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 150.57/22.00 (16) all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0 % 150.57/22.00 (17) ~ (all_52_1 = all_52_13) % 150.57/22.00 (18) all_58_2 = e2 % 150.57/22.00 (19) all_8_2 = e3 % 150.57/22.00 (20) op(e3, e3) = e1 % 150.57/22.00 (21) all_56_31 = all_4_2 % 150.57/22.00 (22) ~ (all_8_0 = e3) % 150.57/22.00 (23) ~ (all_52_2 = e2) % 150.57/22.00 (24) all_56_1 = e3 | all_56_11 = e2 | all_56_21 = e1 | all_56_31 = e0 % 150.57/22.00 (25) ~ (all_8_0 = e2) % 150.57/22.00 (26) ~ (all_52_13 = all_4_2) % 150.57/22.00 (27) ~ (all_8_0 = e0) | ~ (all_8_2 = e3) % 150.57/22.00 (28) all_58_2 = all_52_1 % 150.57/22.00 (29) all_58_10 = all_52_13 % 150.57/22.00 (30) ~ (all_56_11 = e0) | all_56_15 = e2 % 150.57/22.00 (31) all_58_0 = all_10_2 % 150.57/22.00 (32) all_54_6 = all_8_0 % 150.57/22.00 (33) ~ (e2 = e0) % 150.57/22.00 (34) all_56_15 = all_52_13 % 150.57/22.00 (35) all_58_12 = all_52_3 % 150.57/22.00 % 150.57/22.00 Begin of proof % 150.57/22.00 | % 150.57/22.00 | BETA: splitting (27) gives: % 150.57/22.00 | % 150.57/22.00 | Case 1: % 150.57/22.00 | | % 150.57/22.00 | | (36) ~ (all_8_2 = e3) % 150.57/22.00 | | % 150.57/22.00 | | REDUCE: (19), (36) imply: % 150.57/22.00 | | (37) $false % 150.57/22.00 | | % 150.57/22.00 | | CLOSE: (37) is inconsistent. % 150.57/22.00 | | % 150.57/22.00 | Case 2: % 150.57/22.00 | | % 150.57/22.00 | | (38) ~ (all_8_0 = e0) % 150.57/22.00 | | % 150.57/22.00 | | BETA: splitting (9) gives: % 150.57/22.00 | | % 150.57/22.00 | | Case 1: % 150.57/22.00 | | | % 150.57/22.00 | | | (39) all_54_6 = e3 % 150.57/22.00 | | | % 150.57/22.00 | | | COMBINE_EQS: (32), (39) imply: % 150.57/22.00 | | | (40) all_8_0 = e3 % 150.57/22.00 | | | % 150.57/22.00 | | | REDUCE: (22), (40) imply: % 150.57/22.00 | | | (41) $false % 150.57/22.00 | | | % 150.57/22.00 | | | CLOSE: (41) is inconsistent. % 150.57/22.00 | | | % 150.57/22.00 | | Case 2: % 150.57/22.00 | | | % 150.57/22.00 | | | (42) ~ (all_54_6 = e3) % 150.57/22.00 | | | (43) all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0 % 150.57/22.00 | | | % 150.57/22.00 | | | BETA: splitting (43) gives: % 150.57/22.00 | | | % 150.57/22.00 | | | Case 1: % 150.57/22.00 | | | | % 150.57/22.00 | | | | (44) all_54_6 = e2 % 150.57/22.00 | | | | % 150.57/22.00 | | | | COMBINE_EQS: (32), (44) imply: % 150.57/22.00 | | | | (45) all_8_0 = e2 % 150.57/22.00 | | | | % 150.57/22.00 | | | | REDUCE: (25), (45) imply: % 150.57/22.00 | | | | (46) $false % 150.57/22.00 | | | | % 150.57/22.00 | | | | CLOSE: (46) is inconsistent. % 150.57/22.00 | | | | % 150.57/22.00 | | | Case 2: % 150.57/22.00 | | | | % 150.57/22.00 | | | | (47) all_54_6 = e1 | all_54_6 = e0 % 150.57/22.00 | | | | % 150.57/22.00 | | | | BETA: splitting (16) gives: % 150.57/22.00 | | | | % 150.57/22.00 | | | | Case 1: % 150.57/22.00 | | | | | % 150.57/22.00 | | | | | (48) all_58_2 = e0 % 150.57/22.00 | | | | | % 150.57/22.00 | | | | | COMBINE_EQS: (18), (48) imply: % 150.57/22.00 | | | | | (49) e2 = e0 % 150.57/22.00 | | | | | % 150.57/22.00 | | | | | REDUCE: (33), (49) imply: % 150.57/22.00 | | | | | (50) $false % 150.57/22.00 | | | | | % 150.57/22.00 | | | | | CLOSE: (50) is inconsistent. % 150.57/22.00 | | | | | % 150.57/22.00 | | | | Case 2: % 150.57/22.00 | | | | | % 150.57/22.00 | | | | | (51) all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0 % 150.57/22.00 | | | | | % 150.57/22.00 | | | | | BETA: splitting (51) gives: % 150.57/22.00 | | | | | % 150.57/22.00 | | | | | Case 1: % 150.57/22.00 | | | | | | % 150.57/22.00 | | | | | | (52) all_58_3 = e0 % 150.57/22.00 | | | | | | % 150.57/22.00 | | | | | | REF_CLOSE: (1), (4), (6), (10), (13), (14), (17), (23), (28), (30), % 150.57/22.00 | | | | | | (31), (34), (35), (52) are inconsistent by sub-proof % 150.57/22.00 | | | | | | #595. % 150.57/22.00 | | | | | | % 150.57/22.00 | | | | | Case 2: % 150.57/22.00 | | | | | | % 150.57/22.00 | | | | | | (53) all_58_5 = e0 | all_58_10 = e0 % 150.57/22.00 | | | | | | % 150.57/22.00 | | | | | | BETA: splitting (53) gives: % 150.57/22.00 | | | | | | % 150.57/22.00 | | | | | | Case 1: % 150.57/22.00 | | | | | | | % 150.57/22.00 | | | | | | | (54) all_58_5 = e0 % 150.57/22.00 | | | | | | | % 150.57/22.00 | | | | | | | COMBINE_EQS: (11), (54) imply: % 150.57/22.00 | | | | | | | (55) all_8_0 = e0 % 150.57/22.00 | | | | | | | % 150.57/22.00 | | | | | | | REDUCE: (38), (55) imply: % 150.57/22.00 | | | | | | | (56) $false % 150.57/22.00 | | | | | | | % 150.57/22.00 | | | | | | | CLOSE: (56) is inconsistent. % 150.57/22.00 | | | | | | | % 150.57/22.00 | | | | | | Case 2: % 150.57/22.00 | | | | | | | % 150.57/22.00 | | | | | | | (57) all_58_10 = e0 % 150.57/22.00 | | | | | | | % 150.57/22.00 | | | | | | | COMBINE_EQS: (29), (57) imply: % 150.57/22.00 | | | | | | | (58) all_52_13 = e0 % 150.57/22.00 | | | | | | | % 150.57/22.00 | | | | | | | REDUCE: (5), (58) imply: % 150.57/22.00 | | | | | | | (59) ~ (all_8_0 = e0) % 150.57/22.00 | | | | | | | % 150.57/22.00 | | | | | | | REDUCE: (26), (58) imply: % 150.57/22.00 | | | | | | | (60) ~ (all_4_2 = e0) % 150.57/22.00 | | | | | | | % 150.57/22.00 | | | | | | | SIMP: (60) implies: % 150.57/22.00 | | | | | | | (61) ~ (all_4_2 = e0) % 150.57/22.00 | | | | | | | % 150.57/22.00 | | | | | | | REF_CLOSE: (2), (3), (4), (7), (8), (12), (15), (20), (21), (22), % 150.57/22.00 | | | | | | | (24), (32), (38), (47), (61) are inconsistent by % 150.57/22.00 | | | | | | | sub-proof #142. % 150.57/22.00 | | | | | | | % 150.57/22.00 | | | | | | End of split % 150.57/22.00 | | | | | | % 150.57/22.00 | | | | | End of split % 150.57/22.00 | | | | | % 150.57/22.00 | | | | End of split % 150.57/22.00 | | | | % 150.57/22.00 | | | End of split % 150.57/22.00 | | | % 150.57/22.00 | | End of split % 150.57/22.00 | | % 150.57/22.00 | End of split % 150.57/22.00 | % 150.57/22.00 End of proof % 150.57/22.00 % 150.57/22.00 Sub-proof #108 shows that the following formulas are inconsistent: % 150.57/22.00 ---------------------------------------------------------------- % 150.57/22.00 (1) all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0 % 150.57/22.00 (2) all_54_4 = all_52_1 % 150.57/22.00 (3) ~ (all_52_1 = e3) % 150.57/22.00 (4) ~ (all_52_1 = e1) % 150.57/22.00 (5) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0 % 150.57/22.00 (6) ~ (all_52_2 = e1) % 150.57/22.00 (7) ~ (all_52_2 = e2) % 150.57/22.00 (8) all_54_8 = all_52_2 % 150.57/22.00 (9) ~ (all_52_1 = all_52_2) % 150.57/22.00 (10) ~ (all_52_1 = e2) % 150.57/22.00 % 150.57/22.00 Begin of proof % 150.57/22.00 | % 150.57/22.00 | BETA: splitting (5) gives: % 150.57/22.00 | % 150.57/22.00 | Case 1: % 150.57/22.00 | | % 150.57/22.00 | | (11) all_54_4 = e3 % 150.57/22.00 | | % 150.57/22.00 | | REF_CLOSE: (2), (3), (11) are inconsistent by sub-proof #634. % 150.57/22.00 | | % 150.57/22.00 | Case 2: % 150.57/22.00 | | % 150.57/22.00 | | (12) all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0 % 150.57/22.00 | | % 150.57/22.00 | | BETA: splitting (12) gives: % 150.57/22.00 | | % 150.57/22.00 | | Case 1: % 150.57/22.00 | | | % 150.57/22.00 | | | (13) all_54_4 = e2 % 150.57/22.00 | | | % 150.57/22.00 | | | REF_CLOSE: (2), (10), (13) are inconsistent by sub-proof #633. % 150.57/22.00 | | | % 150.57/22.00 | | Case 2: % 150.57/22.00 | | | % 150.57/22.00 | | | (14) all_54_4 = e1 | all_54_4 = e0 % 150.57/22.00 | | | % 150.57/22.00 | | | BETA: splitting (14) gives: % 150.57/22.00 | | | % 150.57/22.00 | | | Case 1: % 150.57/22.00 | | | | % 150.57/22.00 | | | | (15) all_54_4 = e1 % 150.57/22.00 | | | | % 150.57/22.00 | | | | REF_CLOSE: (2), (4), (15) are inconsistent by sub-proof #584. % 150.57/22.00 | | | | % 150.57/22.00 | | | Case 2: % 150.57/22.00 | | | | % 150.57/22.00 | | | | (16) all_54_4 = e0 % 150.57/22.00 | | | | % 150.57/22.00 | | | | COMBINE_EQS: (2), (16) imply: % 150.57/22.00 | | | | (17) all_52_1 = e0 % 150.57/22.00 | | | | % 150.57/22.00 | | | | SIMP: (17) implies: % 150.57/22.00 | | | | (18) all_52_1 = e0 % 150.57/22.00 | | | | % 150.57/22.00 | | | | REDUCE: (9), (18) imply: % 150.57/22.00 | | | | (19) ~ (all_52_2 = e0) % 150.57/22.00 | | | | % 150.57/22.00 | | | | SIMP: (19) implies: % 150.57/22.00 | | | | (20) ~ (all_52_2 = e0) % 150.57/22.00 | | | | % 150.57/22.00 | | | | REF_CLOSE: (1), (6), (7), (8), (20) are inconsistent by sub-proof #270. % 150.57/22.00 | | | | % 150.57/22.00 | | | End of split % 150.57/22.00 | | | % 150.57/22.00 | | End of split % 150.57/22.00 | | % 150.57/22.00 | End of split % 150.57/22.00 | % 150.57/22.00 End of proof % 150.57/22.00 % 150.57/22.00 Sub-proof #109 shows that the following formulas are inconsistent: % 150.57/22.00 ---------------------------------------------------------------- % 150.57/22.00 (1) all_56_11 = all_8_2 % 150.57/22.00 (2) ~ (all_56_11 = e1) | all_56_13 = e2 % 150.57/22.00 (3) ~ (all_56_31 = e1) % 150.57/22.00 (4) ~ (all_8_0 = all_6_2) % 150.57/22.00 (5) ~ (e3 = e0) % 150.57/22.00 (6) ~ (all_52_13 = all_8_2) % 150.57/22.00 (7) all_54_0 = all_10_2 % 150.57/22.00 (8) all_54_2 = all_10_0 % 150.57/22.00 (9) ~ (e3 = e2) % 150.57/22.00 (10) op(e0, e0) = all_4_2 % 150.57/22.00 (11) ~ (all_52_13 = all_8_0) % 150.57/22.00 (12) all_54_5 = all_8_2 % 150.57/22.00 (13) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 150.57/22.00 (14) all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1 % 150.57/22.00 (15) ~ (all_8_0 = all_8_2) % 150.57/22.00 (16) all_56_21 = all_6_2 % 150.57/22.00 (17) all_56_1 = all_10_2 % 150.57/22.00 (18) ~ (all_32_0 = e0) | ~ (all_32_2 = e2) % 150.57/22.00 (19) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0 % 150.57/22.00 (20) all_56_17 = all_52_2 % 150.57/22.00 (21) all_58_9 = all_52_12 % 150.57/22.00 (22) all_58_5 = all_8_0 % 150.57/22.00 (23) op(e2, all_8_2) = all_56_10 % 150.57/22.00 (24) op(e3, e3) = all_10_2 % 150.57/22.00 (25) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0 % 150.57/22.00 (26) ~ (all_56_21 = e3) | all_56_17 = e1 % 150.57/22.00 (27) ~ (e1 = e0) % 150.57/22.00 (28) all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1 % 150.57/22.00 (29) ~ (all_52_1 = all_8_2) % 150.57/22.00 (30) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 150.57/22.00 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 150.57/22.00 (31) all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0 % 150.57/22.00 (32) ~ (all_56_11 = e3) | all_56_9 = e2 % 150.57/22.00 (33) all_56_7 = all_52_12 % 150.57/22.00 (34) ~ (all_52_12 = all_10_0) % 150.57/22.00 (35) ~ (all_56_1 = e2) | all_56_3 = e3 % 150.57/22.00 (36) ~ (all_56_1 = e0) | all_56_7 = e3 % 150.57/22.00 (37) ~ (all_52_4 = all_10_0) % 150.57/22.00 (38) ~ (e2 = e1) % 150.57/22.00 (39) op(all_4_2, all_4_2) = all_4_1 % 150.57/22.00 (40) op(all_10_2, all_10_2) = e1 % 150.57/22.00 (41) all_58_3 = all_8_2 % 150.57/22.00 (42) all_56_3 = all_52_4 % 150.57/22.00 (43) all_56_31 = all_4_2 % 150.57/22.00 (44) all_58_11 = all_52_14 % 150.57/22.00 (45) ~ (all_8_0 = e3) % 150.57/22.00 (46) ~ (all_10_0 = all_6_2) % 150.57/22.00 (47) ~ (all_52_1 = all_8_0) % 150.57/22.00 (48) all_56_1 = e3 | all_56_11 = e2 | all_56_21 = e1 | all_56_31 = e0 % 150.57/22.01 (49) ~ (all_10_0 = e1) % 150.57/22.01 (50) all_32_0 = all_10_0 % 150.57/22.01 (51) ~ (all_52_13 = all_4_2) % 150.57/22.01 (52) ~ (all_8_0 = e0) | ~ (all_8_2 = e3) % 150.57/22.01 (53) op(all_8_2, all_8_2) = e1 % 150.57/22.01 (54) op(e1, e1) = all_6_2 % 150.57/22.01 (55) all_58_15 = all_4_2 % 150.57/22.01 (56) all_58_2 = all_52_1 % 150.57/22.01 (57) all_58_10 = all_52_13 % 150.57/22.01 (58) ~ (all_56_11 = e0) | all_56_15 = e2 % 150.57/22.01 (59) ~ (e3 = e1) % 150.57/22.01 (60) op(e2, e2) = all_8_2 % 150.57/22.01 (61) op(e0, all_4_2) = all_56_30 % 150.57/22.01 (62) all_54_6 = all_8_0 % 150.57/22.01 (63) op(e3, all_10_2) = all_56_0 % 150.57/22.01 (64) ~ (all_52_14 = all_6_2) % 150.57/22.01 (65) ~ (e2 = e0) % 150.57/22.01 (66) ~ (all_10_0 = all_10_2) % 150.57/22.01 (67) ~ (all_52_2 = all_10_2) % 150.57/22.01 (68) all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3 % 150.57/22.01 (69) ~ (all_10_0 = e2) % 150.57/22.01 (70) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 150.57/22.01 (71) ~ (all_52_12 = all_10_2) % 150.57/22.01 (72) all_56_9 = all_52_1 % 150.57/22.01 (73) all_56_15 = all_52_13 % 150.57/22.01 (74) all_32_2 = all_10_2 % 150.57/22.01 (75) ~ (all_52_1 = all_10_2) % 150.57/22.01 % 150.57/22.01 Begin of proof % 150.57/22.01 | % 150.57/22.01 | REDUCE: (3), (43) imply: % 150.57/22.01 | (76) ~ (all_4_2 = e1) % 150.57/22.01 | % 150.57/22.01 | BETA: splitting (58) gives: % 150.57/22.01 | % 150.57/22.01 | Case 1: % 150.57/22.01 | | % 150.57/22.01 | | (77) ~ (all_56_11 = e0) % 150.57/22.01 | | % 150.57/22.01 | | REDUCE: (1), (77) imply: % 150.57/22.01 | | (78) ~ (all_8_2 = e0) % 150.57/22.01 | | % 150.57/22.01 | | BETA: splitting (26) gives: % 150.57/22.01 | | % 150.57/22.01 | | Case 1: % 150.57/22.01 | | | % 150.57/22.01 | | | (79) ~ (all_56_21 = e3) % 150.57/22.01 | | | % 150.57/22.01 | | | REDUCE: (16), (79) imply: % 150.57/22.01 | | | (80) ~ (all_6_2 = e3) % 150.57/22.01 | | | % 150.57/22.01 | | | BETA: splitting (2) gives: % 150.57/22.01 | | | % 150.57/22.01 | | | Case 1: % 150.57/22.01 | | | | % 150.57/22.01 | | | | (81) ~ (all_56_11 = e1) % 150.57/22.01 | | | | % 150.57/22.01 | | | | REDUCE: (1), (81) imply: % 150.57/22.01 | | | | (82) ~ (all_8_2 = e1) % 150.57/22.01 | | | | % 150.57/22.01 | | | | REF_CLOSE: (1), (4), (11), (12), (15), (16), (17), (19), (22), (23), % 150.57/22.01 | | | | (24), (29), (30), (31), (32), (41), (43), (47), (48), (51), % 150.57/22.01 | | | | (52), (53), (56), (57), (60), (62), (65), (70), (72), (78), % 150.57/22.01 | | | | (82) are inconsistent by sub-proof #141. % 150.57/22.01 | | | | % 150.57/22.01 | | | Case 2: % 150.57/22.01 | | | | % 150.57/22.01 | | | | (83) all_56_11 = e1 % 150.57/22.01 | | | | % 150.57/22.01 | | | | COMBINE_EQS: (1), (83) imply: % 150.57/22.01 | | | | (84) all_8_2 = e1 % 150.57/22.01 | | | | % 150.57/22.01 | | | | REDUCE: (6), (84) imply: % 150.57/22.01 | | | | (85) ~ (all_52_13 = e1) % 150.57/22.01 | | | | % 150.57/22.01 | | | | REDUCE: (53), (84) imply: % 150.57/22.01 | | | | (86) op(e1, e1) = e1 % 150.57/22.01 | | | | % 150.57/22.01 | | | | GROUND_INST: instantiating (30) with all_6_2, e1, e1, e1, simplifying % 150.57/22.01 | | | | with (54), (86) gives: % 150.57/22.01 | | | | (87) all_6_2 = e1 % 150.57/22.01 | | | | % 150.57/22.01 | | | | REDUCE: (64), (87) imply: % 150.57/22.01 | | | | (88) ~ (all_52_14 = e1) % 150.57/22.01 | | | | % 150.57/22.01 | | | | REDUCE: (80), (87) imply: % 150.57/22.01 | | | | (89) ~ (e3 = e1) % 150.57/22.01 | | | | % 150.57/22.01 | | | | BETA: splitting (14) gives: % 150.57/22.01 | | | | % 150.57/22.01 | | | | Case 1: % 150.57/22.01 | | | | | % 150.57/22.01 | | | | | (90) all_58_9 = e1 % 150.57/22.01 | | | | | % 150.57/22.01 | | | | | COMBINE_EQS: (21), (90) imply: % 150.57/22.01 | | | | | (91) all_52_12 = e1 % 150.57/22.01 | | | | | % 150.57/22.01 | | | | | COMBINE_EQS: (33), (91) imply: % 150.57/22.01 | | | | | (92) all_56_7 = e1 % 150.57/22.01 | | | | | % 150.57/22.01 | | | | | REDUCE: (34), (91) imply: % 150.57/22.01 | | | | | (93) ~ (all_10_0 = e1) % 150.57/22.01 | | | | | % 150.57/22.01 | | | | | REDUCE: (71), (91) imply: % 150.57/22.01 | | | | | (94) ~ (all_10_2 = e1) % 150.57/22.01 | | | | | % 150.57/22.01 | | | | | SIMP: (94) implies: % 150.57/22.01 | | | | | (95) ~ (all_10_2 = e1) % 150.57/22.01 | | | | | % 150.57/22.01 | | | | | BETA: splitting (36) gives: % 150.57/22.01 | | | | | % 150.57/22.01 | | | | | Case 1: % 150.57/22.01 | | | | | | % 150.57/22.01 | | | | | | (96) ~ (all_56_1 = e0) % 150.57/22.01 | | | | | | % 150.57/22.01 | | | | | | REDUCE: (17), (96) imply: % 150.57/22.01 | | | | | | (97) ~ (all_10_2 = e0) % 150.57/22.01 | | | | | | % 150.57/22.01 | | | | | | REF_CLOSE: (7), (8), (13), (17), (18), (24), (25), (30), (35), (37), % 150.57/22.01 | | | | | | (40), (42), (49), (50), (63), (66), (74), (95), (97) are % 150.57/22.01 | | | | | | inconsistent by sub-proof #403. % 150.57/22.01 | | | | | | % 150.57/22.01 | | | | | Case 2: % 150.57/22.01 | | | | | | % 150.57/22.01 | | | | | | (98) all_56_7 = e3 % 150.57/22.01 | | | | | | % 150.57/22.01 | | | | | | REF_CLOSE: (59), (92), (98) are inconsistent by sub-proof #497. % 150.57/22.01 | | | | | | % 150.57/22.01 | | | | | End of split % 150.57/22.01 | | | | | % 150.57/22.01 | | | | Case 2: % 150.57/22.01 | | | | | % 150.57/22.01 | | | | | (99) all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1 % 150.57/22.01 | | | | | % 150.57/22.01 | | | | | REF_CLOSE: (44), (55), (57), (76), (85), (88), (99) are inconsistent % 150.57/22.01 | | | | | by sub-proof #587. % 150.57/22.01 | | | | | % 150.57/22.01 | | | | End of split % 150.57/22.01 | | | | % 150.57/22.01 | | | End of split % 150.57/22.01 | | | % 150.57/22.01 | | Case 2: % 150.57/22.01 | | | % 150.57/22.01 | | | (100) all_56_21 = e3 % 150.57/22.01 | | | (101) all_56_17 = e1 % 150.57/22.01 | | | % 150.57/22.01 | | | COMBINE_EQS: (20), (101) imply: % 150.57/22.01 | | | (102) all_52_2 = e1 % 150.57/22.01 | | | % 150.57/22.01 | | | COMBINE_EQS: (16), (100) imply: % 150.57/22.01 | | | (103) all_6_2 = e3 % 150.57/22.01 | | | % 150.57/22.01 | | | SIMP: (103) implies: % 150.57/22.01 | | | (104) all_6_2 = e3 % 150.57/22.01 | | | % 150.57/22.01 | | | REDUCE: (67), (102) imply: % 150.57/22.01 | | | (105) ~ (all_10_2 = e1) % 150.57/22.01 | | | % 150.57/22.01 | | | SIMP: (105) implies: % 150.57/22.01 | | | (106) ~ (all_10_2 = e1) % 150.57/22.01 | | | % 150.57/22.01 | | | REDUCE: (46), (104) imply: % 150.57/22.01 | | | (107) ~ (all_10_0 = e3) % 150.57/22.01 | | | % 150.57/22.01 | | | REF_CLOSE: (7), (8), (13), (18), (24), (25), (30), (40), (49), (50), (63), % 150.57/22.01 | | | (66), (69), (74), (106), (107) are inconsistent by sub-proof % 150.57/22.01 | | | #394. % 150.57/22.01 | | | % 150.57/22.01 | | End of split % 150.57/22.01 | | % 150.57/22.01 | Case 2: % 150.57/22.01 | | % 150.57/22.01 | | (108) all_56_15 = e2 % 150.57/22.01 | | (109) all_56_11 = e0 % 150.57/22.01 | | % 150.57/22.01 | | REF_CLOSE: (1), (4), (5), (6), (9), (10), (11), (15), (16), (17), (19), % 150.57/22.01 | | (22), (27), (28), (30), (38), (39), (41), (43), (45), (48), (53), % 150.57/22.01 | | (56), (57), (59), (61), (62), (68), (73), (75), (108), (109) are % 150.57/22.01 | | inconsistent by sub-proof #126. % 150.57/22.01 | | % 150.57/22.01 | End of split % 150.57/22.01 | % 150.57/22.01 End of proof % 150.57/22.01 % 150.57/22.01 Sub-proof #110 shows that the following formulas are inconsistent: % 150.57/22.01 ---------------------------------------------------------------- % 150.57/22.01 (1) all_56_11 = all_8_2 % 150.57/22.01 (2) ~ (all_56_11 = e1) | all_56_13 = e2 % 150.57/22.01 (3) ~ (all_52_11 = all_6_2) % 150.57/22.01 (4) ~ (all_8_0 = all_6_2) % 150.57/22.01 (5) ~ (e3 = e0) % 150.57/22.01 (6) ~ (all_52_13 = all_8_2) % 150.57/22.01 (7) ~ (e3 = e2) % 150.57/22.01 (8) op(e0, e0) = all_4_2 % 150.57/22.01 (9) ~ (all_52_13 = all_8_0) % 150.57/22.01 (10) all_58_4 = all_52_8 % 150.57/22.01 (11) all_54_5 = all_8_2 % 150.57/22.01 (12) all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1 % 150.57/22.01 (13) ~ (all_8_0 = all_8_2) % 150.57/22.01 (14) all_56_21 = all_6_2 % 150.57/22.01 (15) all_56_1 = all_10_2 % 150.57/22.01 (16) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0 % 150.57/22.01 (17) all_58_9 = all_52_12 % 150.57/22.01 (18) all_58_5 = all_8_0 % 150.57/22.01 (19) op(e2, all_8_2) = all_56_10 % 150.57/22.01 (20) op(e3, e3) = all_10_2 % 150.57/22.01 (21) ~ (all_56_21 = e3) | all_56_17 = e1 % 150.57/22.01 (22) ~ (e1 = e0) % 150.57/22.01 (23) all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1 % 150.57/22.01 (24) ~ (all_52_1 = all_8_2) % 150.57/22.01 (25) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 150.57/22.01 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 150.57/22.01 (26) all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0 % 150.57/22.01 (27) ~ (all_56_11 = e3) | all_56_9 = e2 % 150.57/22.01 (28) ~ (all_4_2 = e1) % 150.57/22.01 (29) all_58_8 = all_6_2 % 150.57/22.01 (30) ~ (all_52_14 = all_6_0) % 150.57/22.01 (31) ~ (e2 = e1) % 150.57/22.01 (32) op(all_4_2, all_4_2) = all_4_1 % 150.57/22.01 (33) all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1 % 150.57/22.01 (34) all_58_3 = all_8_2 % 150.57/22.01 (35) all_56_31 = all_4_2 % 150.57/22.01 (36) all_58_11 = all_52_14 % 150.57/22.01 (37) ~ (all_8_0 = e3) % 150.57/22.01 (38) all_56_13 = all_8_0 % 150.57/22.01 (39) ~ (all_52_1 = all_8_0) % 150.57/22.01 (40) all_56_1 = e3 | all_56_11 = e2 | all_56_21 = e1 | all_56_31 = e0 % 150.57/22.01 (41) ~ (all_52_13 = all_4_2) % 150.57/22.01 (42) ~ (all_8_0 = e0) | ~ (all_8_2 = e3) % 150.57/22.01 (43) op(all_8_2, all_8_2) = e1 % 150.57/22.01 (44) op(e1, e1) = all_6_2 % 150.57/22.01 (45) all_58_15 = all_4_2 % 150.57/22.01 (46) all_58_2 = all_52_1 % 150.57/22.01 (47) all_58_10 = all_52_13 % 150.57/22.01 (48) ~ (all_56_11 = e0) | all_56_15 = e2 % 150.57/22.01 (49) op(e1, all_6_2) = all_56_20 % 150.57/22.01 (50) all_56_17 = all_6_0 % 150.57/22.01 (51) ~ (e3 = e1) % 150.57/22.01 (52) op(e2, e2) = all_8_2 % 150.57/22.01 (53) ~ (all_52_8 = all_52_12) % 150.57/22.01 (54) op(e0, all_4_2) = all_56_30 % 150.57/22.01 (55) all_54_6 = all_8_0 % 150.57/22.01 (56) op(all_6_2, all_6_2) = e3 % 150.57/22.01 (57) ~ (e2 = e0) % 150.57/22.01 (58) op(e1, all_52_11) = all_56_28 % 150.57/22.01 (59) all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3 % 150.57/22.01 (60) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 150.57/22.01 (61) all_58_14 = all_52_11 % 150.57/22.01 (62) ~ (all_52_12 = all_10_2) % 150.57/22.01 (63) all_56_9 = all_52_1 % 150.57/22.01 (64) all_56_15 = all_52_13 % 150.57/22.01 (65) ~ (all_52_1 = all_10_2) % 150.57/22.01 % 150.57/22.01 Begin of proof % 150.57/22.01 | % 150.57/22.01 | BETA: splitting (48) gives: % 150.57/22.01 | % 150.57/22.01 | Case 1: % 150.57/22.01 | | % 150.57/22.01 | | (66) ~ (all_56_11 = e0) % 150.57/22.01 | | % 150.57/22.01 | | REDUCE: (1), (66) imply: % 150.57/22.01 | | (67) ~ (all_8_2 = e0) % 150.57/22.01 | | % 150.57/22.01 | | BETA: splitting (21) gives: % 150.57/22.01 | | % 150.57/22.01 | | Case 1: % 150.57/22.01 | | | % 150.57/22.01 | | | (68) ~ (all_56_21 = e3) % 150.57/22.01 | | | % 150.57/22.01 | | | REDUCE: (14), (68) imply: % 150.57/22.01 | | | (69) ~ (all_6_2 = e3) % 150.57/22.01 | | | % 150.57/22.01 | | | REF_CLOSE: (1), (2), (4), (9), (11), (13), (14), (15), (16), (18), (19), % 150.57/22.01 | | | (20), (24), (25), (26), (27), (34), (35), (39), (40), (41), % 150.57/22.01 | | | (42), (43), (44), (46), (47), (49), (52), (55), (56), (57), % 150.57/22.01 | | | (60), (63), (67), (69) are inconsistent by sub-proof #114. % 150.57/22.01 | | | % 150.57/22.01 | | Case 2: % 150.57/22.01 | | | % 150.57/22.01 | | | (70) all_56_21 = e3 % 150.57/22.01 | | | (71) all_56_17 = e1 % 150.57/22.01 | | | % 150.57/22.01 | | | COMBINE_EQS: (50), (71) imply: % 150.57/22.01 | | | (72) all_6_0 = e1 % 150.57/22.01 | | | % 150.57/22.01 | | | COMBINE_EQS: (14), (70) imply: % 150.57/22.01 | | | (73) all_6_2 = e3 % 150.57/22.01 | | | % 150.57/22.01 | | | COMBINE_EQS: (29), (73) imply: % 150.57/22.01 | | | (74) all_58_8 = e3 % 150.57/22.01 | | | % 150.57/22.01 | | | REDUCE: (3), (73) imply: % 150.57/22.01 | | | (75) ~ (all_52_11 = e3) % 150.57/22.01 | | | % 150.57/22.01 | | | REDUCE: (30), (72) imply: % 150.57/22.01 | | | (76) ~ (all_52_14 = e1) % 150.57/22.01 | | | % 150.57/22.01 | | | REDUCE: (56), (73) imply: % 150.57/22.01 | | | (77) op(e3, e3) = e3 % 150.57/22.01 | | | % 150.57/22.01 | | | REDUCE: (44), (73) imply: % 150.57/22.01 | | | (78) op(e1, e1) = e3 % 150.57/22.01 | | | % 150.57/22.01 | | | REF_CLOSE: (1), (2), (4), (6), (9), (10), (11), (12), (13), (14), (15), % 150.57/22.01 | | | (16), (17), (18), (19), (20), (24), (25), (26), (27), (28), % 150.57/22.01 | | | (33), (34), (35), (36), (38), (39), (40), (41), (42), (43), % 150.57/22.01 | | | (45), (46), (47), (52), (53), (55), (57), (58), (60), (61), % 150.57/22.01 | | | (62), (63), (67), (74), (75), (76), (77), (78) are inconsistent % 150.57/22.01 | | | by sub-proof #140. % 150.57/22.01 | | | % 150.57/22.01 | | End of split % 150.57/22.01 | | % 150.57/22.01 | Case 2: % 150.57/22.01 | | % 150.57/22.01 | | (79) all_56_15 = e2 % 150.57/22.01 | | (80) all_56_11 = e0 % 150.57/22.01 | | % 150.57/22.01 | | REF_CLOSE: (1), (4), (5), (6), (7), (8), (9), (13), (14), (15), (16), (18), % 150.57/22.01 | | (22), (23), (25), (28), (31), (32), (34), (35), (37), (40), (43), % 150.57/22.01 | | (46), (47), (51), (54), (55), (59), (64), (65), (79), (80) are % 150.57/22.01 | | inconsistent by sub-proof #111. % 150.57/22.01 | | % 150.57/22.01 | End of split % 150.57/22.01 | % 150.57/22.01 End of proof % 150.57/22.01 % 150.57/22.01 Sub-proof #111 shows that the following formulas are inconsistent: % 150.57/22.01 ---------------------------------------------------------------- % 150.57/22.01 (1) all_56_11 = all_8_2 % 150.57/22.01 (2) ~ (all_8_0 = all_6_2) % 150.57/22.01 (3) ~ (e3 = e0) % 150.57/22.01 (4) ~ (all_52_13 = all_8_2) % 150.57/22.01 (5) ~ (e3 = e2) % 150.57/22.01 (6) op(e0, e0) = all_4_2 % 150.57/22.01 (7) ~ (all_52_13 = all_8_0) % 150.57/22.01 (8) ~ (all_8_0 = all_8_2) % 150.57/22.01 (9) all_56_21 = all_6_2 % 150.57/22.01 (10) all_56_1 = all_10_2 % 150.57/22.01 (11) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0 % 150.57/22.01 (12) all_58_5 = all_8_0 % 150.57/22.01 (13) ~ (e1 = e0) % 150.57/22.01 (14) all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1 % 150.57/22.01 (15) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 150.57/22.01 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 150.57/22.01 (16) all_56_15 = e2 % 150.57/22.01 (17) ~ (all_4_2 = e1) % 150.57/22.01 (18) ~ (e2 = e1) % 150.57/22.01 (19) op(all_4_2, all_4_2) = all_4_1 % 150.57/22.01 (20) all_58_3 = all_8_2 % 150.57/22.01 (21) all_56_31 = all_4_2 % 150.57/22.01 (22) ~ (all_8_0 = e3) % 150.57/22.01 (23) all_56_1 = e3 | all_56_11 = e2 | all_56_21 = e1 | all_56_31 = e0 % 150.57/22.01 (24) all_56_11 = e0 % 150.57/22.01 (25) op(all_8_2, all_8_2) = e1 % 150.57/22.01 (26) all_58_2 = all_52_1 % 150.57/22.01 (27) all_58_10 = all_52_13 % 150.57/22.01 (28) ~ (e3 = e1) % 150.57/22.01 (29) op(e0, all_4_2) = all_56_30 % 150.57/22.01 (30) all_54_6 = all_8_0 % 150.57/22.01 (31) all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3 % 150.57/22.01 (32) all_56_15 = all_52_13 % 150.57/22.01 (33) ~ (all_52_1 = all_10_2) % 150.57/22.01 % 150.57/22.01 Begin of proof % 150.57/22.01 | % 150.57/22.01 | COMBINE_EQS: (1), (24) imply: % 150.57/22.01 | (34) all_8_2 = e0 % 150.57/22.01 | % 150.57/22.01 | COMBINE_EQS: (16), (32) imply: % 150.57/22.01 | (35) all_52_13 = e2 % 150.57/22.01 | % 150.57/22.01 | COMBINE_EQS: (27), (35) imply: % 150.57/22.01 | (36) all_58_10 = e2 % 150.57/22.01 | % 150.57/22.01 | COMBINE_EQS: (20), (34) imply: % 150.57/22.01 | (37) all_58_3 = e0 % 150.57/22.01 | % 150.57/22.01 | REDUCE: (7), (35) imply: % 150.57/22.01 | (38) ~ (all_8_0 = e2) % 150.57/22.01 | % 150.57/22.01 | SIMP: (38) implies: % 150.57/22.01 | (39) ~ (all_8_0 = e2) % 150.57/22.01 | % 150.57/22.01 | REDUCE: (4), (34), (35) imply: % 150.57/22.01 | (40) ~ (e2 = e0) % 150.57/22.01 | % 150.57/22.01 | REDUCE: (8), (34) imply: % 150.57/22.01 | (41) ~ (all_8_0 = e0) % 150.57/22.01 | % 150.57/22.01 | REDUCE: (25), (34) imply: % 150.57/22.01 | (42) op(e0, e0) = e1 % 150.57/22.01 | % 150.57/22.01 | REF_CLOSE: (2), (3), (5), (6), (9), (10), (11), (12), (13), (14), (15), (17), % 150.57/22.01 | (18), (19), (21), (22), (23), (24), (26), (28), (29), (30), (31), % 150.57/22.01 | (33), (36), (37), (39), (40), (41), (42) are inconsistent by % 150.57/22.01 | sub-proof #112. % 150.57/22.01 | % 150.57/22.01 End of proof % 150.57/22.01 % 150.57/22.01 Sub-proof #112 shows that the following formulas are inconsistent: % 150.57/22.01 ---------------------------------------------------------------- % 150.57/22.01 (1) op(e0, e0) = e1 % 150.57/22.01 (2) ~ (all_8_0 = all_6_2) % 150.57/22.01 (3) ~ (e3 = e0) % 150.57/22.01 (4) ~ (e3 = e2) % 150.57/22.01 (5) op(e0, e0) = all_4_2 % 150.57/22.01 (6) all_58_10 = e2 % 150.57/22.01 (7) all_56_21 = all_6_2 % 150.57/22.01 (8) all_56_1 = all_10_2 % 150.57/22.01 (9) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0 % 150.57/22.01 (10) all_58_5 = all_8_0 % 150.57/22.01 (11) ~ (e1 = e0) % 150.57/22.01 (12) all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1 % 150.57/22.01 (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 150.57/22.01 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 150.57/22.01 (14) ~ (all_8_0 = e0) % 150.57/22.01 (15) ~ (all_4_2 = e1) % 150.57/22.01 (16) all_58_3 = e0 % 150.57/22.01 (17) ~ (e2 = e1) % 150.57/22.01 (18) op(all_4_2, all_4_2) = all_4_1 % 150.57/22.01 (19) all_56_31 = all_4_2 % 150.57/22.01 (20) ~ (all_8_0 = e3) % 150.57/22.01 (21) all_56_1 = e3 | all_56_11 = e2 | all_56_21 = e1 | all_56_31 = e0 % 150.57/22.01 (22) ~ (all_8_0 = e2) % 150.57/22.01 (23) all_56_11 = e0 % 150.57/22.01 (24) all_58_2 = all_52_1 % 150.57/22.01 (25) ~ (e3 = e1) % 150.57/22.01 (26) op(e0, all_4_2) = all_56_30 % 150.57/22.01 (27) all_54_6 = all_8_0 % 150.57/22.01 (28) ~ (e2 = e0) % 150.57/22.01 (29) all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3 % 150.57/22.01 (30) ~ (all_52_1 = all_10_2) % 150.57/22.01 % 150.57/22.01 Begin of proof % 150.57/22.01 | % 150.57/22.01 | BETA: splitting (29) gives: % 150.57/22.01 | % 150.57/22.01 | Case 1: % 150.57/22.01 | | % 150.57/22.01 | | (31) all_58_2 = e3 % 150.57/22.01 | | % 150.57/22.01 | | COMBINE_EQS: (24), (31) imply: % 150.57/22.01 | | (32) all_52_1 = e3 % 150.57/22.01 | | % 150.57/22.01 | | REDUCE: (30), (32) imply: % 150.57/22.01 | | (33) ~ (all_10_2 = e3) % 150.57/22.01 | | % 150.57/22.01 | | SIMP: (33) implies: % 150.57/22.01 | | (34) ~ (all_10_2 = e3) % 150.57/22.01 | | % 150.57/22.01 | | BETA: splitting (12) gives: % 150.57/22.01 | | % 150.57/22.01 | | Case 1: % 150.57/22.01 | | | % 150.57/22.01 | | | (35) all_58_2 = e1 % 150.57/22.01 | | | % 150.57/22.01 | | | COMBINE_EQS: (31), (35) imply: % 150.57/22.01 | | | (36) e3 = e1 % 150.57/22.01 | | | % 150.57/22.01 | | | REDUCE: (25), (36) imply: % 150.57/22.01 | | | (37) $false % 150.57/22.01 | | | % 150.57/22.01 | | | CLOSE: (37) is inconsistent. % 150.57/22.01 | | | % 150.57/22.01 | | Case 2: % 150.57/22.01 | | | % 150.57/22.01 | | | (38) all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1 % 150.57/22.01 | | | % 150.57/22.01 | | | BETA: splitting (38) gives: % 150.57/22.01 | | | % 150.57/22.01 | | | Case 1: % 150.57/22.01 | | | | % 150.57/22.01 | | | | (39) all_58_3 = e1 % 150.57/22.01 | | | | % 150.57/22.01 | | | | REF_CLOSE: (11), (16), (39) are inconsistent by sub-proof #338. % 150.57/22.01 | | | | % 150.57/22.01 | | | Case 2: % 150.57/22.01 | | | | % 150.57/22.01 | | | | (40) all_58_5 = e1 | all_58_10 = e1 % 150.57/22.01 | | | | % 150.57/22.01 | | | | BETA: splitting (40) gives: % 150.57/22.01 | | | | % 150.57/22.01 | | | | Case 1: % 150.57/22.01 | | | | | % 150.57/22.01 | | | | | (41) all_58_5 = e1 % 150.57/22.01 | | | | | % 150.57/22.01 | | | | | COMBINE_EQS: (10), (41) imply: % 150.57/22.01 | | | | | (42) all_8_0 = e1 % 150.57/22.01 | | | | | % 150.57/22.01 | | | | | REDUCE: (2), (42) imply: % 150.57/22.01 | | | | | (43) ~ (all_6_2 = e1) % 150.57/22.01 | | | | | % 150.57/22.01 | | | | | SIMP: (43) implies: % 150.57/22.01 | | | | | (44) ~ (all_6_2 = e1) % 150.57/22.01 | | | | | % 150.57/22.01 | | | | | BETA: splitting (21) gives: % 150.57/22.01 | | | | | % 150.57/22.01 | | | | | Case 1: % 150.57/22.01 | | | | | | % 150.57/22.01 | | | | | | (45) all_56_1 = e3 % 150.57/22.01 | | | | | | % 150.57/22.01 | | | | | | COMBINE_EQS: (8), (45) imply: % 150.57/22.01 | | | | | | (46) all_10_2 = e3 % 150.57/22.01 | | | | | | % 150.57/22.01 | | | | | | REDUCE: (34), (46) imply: % 150.57/22.01 | | | | | | (47) $false % 150.57/22.01 | | | | | | % 150.57/22.01 | | | | | | CLOSE: (47) is inconsistent. % 150.57/22.01 | | | | | | % 150.57/22.01 | | | | | Case 2: % 150.57/22.01 | | | | | | % 150.57/22.01 | | | | | | (48) all_56_11 = e2 | all_56_21 = e1 | all_56_31 = e0 % 150.57/22.01 | | | | | | % 150.57/22.01 | | | | | | BETA: splitting (48) gives: % 150.57/22.01 | | | | | | % 150.57/22.01 | | | | | | Case 1: % 150.57/22.01 | | | | | | | % 150.57/22.01 | | | | | | | (49) all_56_11 = e2 % 150.57/22.01 | | | | | | | % 150.57/22.01 | | | | | | | REF_CLOSE: (23), (28), (49) are inconsistent by sub-proof #427. % 150.57/22.01 | | | | | | | % 150.57/22.01 | | | | | | Case 2: % 150.57/22.01 | | | | | | | % 150.57/22.01 | | | | | | | (50) all_56_21 = e1 | all_56_31 = e0 % 150.57/22.01 | | | | | | | % 150.57/22.01 | | | | | | | REF_CLOSE: (1), (5), (7), (13), (15), (18), (19), (26), (44), (50) % 150.57/22.01 | | | | | | | are inconsistent by sub-proof #113. % 150.57/22.01 | | | | | | | % 150.57/22.01 | | | | | | End of split % 150.57/22.01 | | | | | | % 150.57/22.01 | | | | | End of split % 150.57/22.01 | | | | | % 150.57/22.01 | | | | Case 2: % 150.57/22.01 | | | | | % 150.57/22.01 | | | | | (51) all_58_10 = e1 % 150.57/22.01 | | | | | % 150.57/22.01 | | | | | COMBINE_EQS: (6), (51) imply: % 150.57/22.01 | | | | | (52) e2 = e1 % 150.57/22.01 | | | | | % 150.57/22.01 | | | | | REDUCE: (17), (52) imply: % 150.57/22.01 | | | | | (53) $false % 150.57/22.01 | | | | | % 150.57/22.01 | | | | | CLOSE: (53) is inconsistent. % 150.57/22.01 | | | | | % 150.57/22.01 | | | | End of split % 150.57/22.01 | | | | % 150.57/22.01 | | | End of split % 150.57/22.01 | | | % 150.57/22.01 | | End of split % 150.57/22.01 | | % 150.57/22.01 | Case 2: % 150.57/22.01 | | % 150.57/22.01 | | (54) all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3 % 150.57/22.01 | | % 150.57/22.01 | | REF_CLOSE: (3), (4), (6), (9), (10), (14), (16), (20), (22), (25), (27), % 150.57/22.01 | | (54) are inconsistent by sub-proof #129. % 150.57/22.01 | | % 150.57/22.01 | End of split % 150.57/22.01 | % 150.57/22.01 End of proof % 150.57/22.01 % 150.57/22.01 Sub-proof #113 shows that the following formulas are inconsistent: % 150.57/22.01 ---------------------------------------------------------------- % 150.57/22.01 (1) op(e0, e0) = e1 % 150.57/22.01 (2) op(e0, e0) = all_4_2 % 150.57/22.01 (3) all_56_21 = all_6_2 % 150.57/22.01 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 150.57/22.01 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 150.57/22.01 (5) ~ (all_4_2 = e1) % 150.57/22.01 (6) op(all_4_2, all_4_2) = all_4_1 % 150.57/22.01 (7) all_56_31 = all_4_2 % 150.57/22.01 (8) ~ (all_6_2 = e1) % 150.57/22.01 (9) all_56_21 = e1 | all_56_31 = e0 % 150.57/22.01 (10) op(e0, all_4_2) = all_56_30 % 150.57/22.01 % 150.57/22.01 Begin of proof % 150.57/22.01 | % 150.57/22.01 | BETA: splitting (9) gives: % 150.57/22.01 | % 150.57/22.01 | Case 1: % 150.57/22.01 | | % 150.57/22.01 | | (11) all_56_21 = e1 % 150.57/22.01 | | % 150.57/22.01 | | REF_CLOSE: (3), (8), (11) are inconsistent by sub-proof #153. % 150.57/22.01 | | % 150.57/22.01 | Case 2: % 150.57/22.01 | | % 150.57/22.01 | | (12) all_56_31 = e0 % 150.57/22.01 | | % 150.57/22.01 | | COMBINE_EQS: (7), (12) imply: % 150.57/22.01 | | (13) all_4_2 = e0 % 150.57/22.01 | | % 150.57/22.01 | | SIMP: (13) implies: % 150.57/22.01 | | (14) all_4_2 = e0 % 150.57/22.01 | | % 150.57/22.01 | | REDUCE: (5), (14) imply: % 150.57/22.01 | | (15) ~ (e1 = e0) % 150.57/22.01 | | % 150.57/22.01 | | SIMP: (15) implies: % 150.57/22.01 | | (16) ~ (e1 = e0) % 150.57/22.01 | | % 150.57/22.01 | | REDUCE: (6), (14) imply: % 150.57/22.01 | | (17) op(e0, e0) = all_4_1 % 150.57/22.01 | | % 150.57/22.01 | | REDUCE: (10), (14) imply: % 150.57/22.01 | | (18) op(e0, e0) = all_56_30 % 150.57/22.01 | | % 150.57/22.01 | | REDUCE: (2), (14) imply: % 150.57/22.01 | | (19) op(e0, e0) = e0 % 150.57/22.01 | | % 150.57/22.01 | | REF_CLOSE: (1), (4), (16), (17), (18), (19) are inconsistent by sub-proof % 150.57/22.01 | | #389. % 150.57/22.01 | | % 150.57/22.01 | End of split % 150.57/22.01 | % 150.57/22.01 End of proof % 150.57/22.01 % 150.57/22.01 Sub-proof #114 shows that the following formulas are inconsistent: % 150.57/22.01 ---------------------------------------------------------------- % 150.57/22.01 (1) all_56_11 = all_8_2 % 150.57/22.01 (2) ~ (all_56_11 = e1) | all_56_13 = e2 % 150.57/22.01 (3) ~ (all_8_0 = all_6_2) % 150.57/22.01 (4) ~ (all_6_2 = e3) % 150.57/22.01 (5) ~ (all_52_13 = all_8_0) % 150.57/22.01 (6) all_54_5 = all_8_2 % 150.57/22.01 (7) ~ (all_8_0 = all_8_2) % 150.57/22.01 (8) all_56_21 = all_6_2 % 150.57/22.01 (9) all_56_1 = all_10_2 % 150.57/22.01 (10) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0 % 150.57/22.01 (11) all_58_5 = all_8_0 % 150.57/22.01 (12) op(e2, all_8_2) = all_56_10 % 150.57/22.01 (13) op(e3, e3) = all_10_2 % 150.57/22.01 (14) ~ (all_52_1 = all_8_2) % 150.57/22.01 (15) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 150.57/22.01 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 150.57/22.01 (16) all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0 % 150.57/22.01 (17) ~ (all_56_11 = e3) | all_56_9 = e2 % 150.57/22.01 (18) all_58_3 = all_8_2 % 150.57/22.01 (19) all_56_31 = all_4_2 % 150.57/22.01 (20) ~ (all_52_1 = all_8_0) % 150.57/22.01 (21) all_56_1 = e3 | all_56_11 = e2 | all_56_21 = e1 | all_56_31 = e0 % 150.57/22.01 (22) ~ (all_52_13 = all_4_2) % 150.57/22.01 (23) ~ (all_8_0 = e0) | ~ (all_8_2 = e3) % 150.57/22.01 (24) op(all_8_2, all_8_2) = e1 % 150.57/22.01 (25) op(e1, e1) = all_6_2 % 150.57/22.01 (26) all_58_2 = all_52_1 % 150.57/22.01 (27) all_58_10 = all_52_13 % 150.57/22.01 (28) op(e1, all_6_2) = all_56_20 % 150.57/22.01 (29) op(e2, e2) = all_8_2 % 150.57/22.01 (30) ~ (all_8_2 = e0) % 150.57/22.01 (31) all_54_6 = all_8_0 % 150.57/22.01 (32) op(all_6_2, all_6_2) = e3 % 150.57/22.01 (33) ~ (e2 = e0) % 150.57/22.01 (34) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 150.57/22.01 (35) all_56_9 = all_52_1 % 150.57/22.01 % 150.57/22.01 Begin of proof % 150.57/22.01 | % 150.57/22.01 | BETA: splitting (2) gives: % 150.57/22.01 | % 150.57/22.01 | Case 1: % 150.57/22.01 | | % 150.57/22.01 | | (36) ~ (all_56_11 = e1) % 150.57/22.01 | | % 150.57/22.01 | | REDUCE: (1), (36) imply: % 150.57/22.01 | | (37) ~ (all_8_2 = e1) % 150.57/22.01 | | % 150.57/22.02 | | REF_CLOSE: (1), (3), (5), (6), (7), (8), (9), (10), (11), (12), (13), (14), % 150.57/22.02 | | (15), (16), (17), (18), (19), (20), (21), (22), (23), (24), (26), % 150.57/22.02 | | (27), (29), (30), (31), (33), (34), (35), (37) are inconsistent % 150.57/22.02 | | by sub-proof #141. % 150.57/22.02 | | % 150.57/22.02 | Case 2: % 150.57/22.02 | | % 150.57/22.02 | | (38) all_56_11 = e1 % 150.57/22.02 | | % 150.57/22.02 | | COMBINE_EQS: (1), (38) imply: % 150.57/22.02 | | (39) all_8_2 = e1 % 150.57/22.02 | | % 150.57/22.02 | | REDUCE: (24), (39) imply: % 150.57/22.02 | | (40) op(e1, e1) = e1 % 150.57/22.02 | | % 150.57/22.02 | | GROUND_INST: instantiating (15) with all_6_2, e1, e1, e1, simplifying with % 150.57/22.02 | | (25), (40) gives: % 150.57/22.02 | | (41) all_6_2 = e1 % 150.57/22.02 | | % 150.57/22.02 | | REDUCE: (4), (41) imply: % 150.57/22.02 | | (42) ~ (e3 = e1) % 150.57/22.02 | | % 150.57/22.02 | | SIMP: (42) implies: % 150.57/22.02 | | (43) ~ (e3 = e1) % 150.57/22.02 | | % 150.57/22.02 | | REF_CLOSE: (15), (25), (28), (32), (41), (43) are inconsistent by sub-proof % 150.57/22.02 | | #460. % 150.57/22.02 | | % 150.57/22.02 | End of split % 150.57/22.02 | % 150.57/22.02 End of proof % 150.57/22.02 % 150.57/22.02 Sub-proof #115 shows that the following formulas are inconsistent: % 150.57/22.02 ---------------------------------------------------------------- % 150.57/22.02 (1) all_56_11 = all_8_2 % 150.57/22.02 (2) ~ (all_56_11 = e1) | all_56_13 = e2 % 150.57/22.02 (3) all_48_1 = e1 % 150.57/22.02 (4) ~ (e3 = e2) % 150.57/22.02 (5) all_54_5 = all_8_2 % 150.57/22.02 (6) ~ (all_8_0 = all_8_2) % 150.57/22.02 (7) ~ (all_48_1 = e1) | ~ (all_48_2 = e0) % 150.57/22.02 (8) op(e2, all_8_2) = all_56_10 % 150.57/22.02 (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 150.57/22.02 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 150.57/22.02 (10) all_8_0 = e3 % 150.57/22.02 (11) all_56_13 = all_8_0 % 150.57/22.02 (12) op(all_8_2, all_8_2) = e1 % 150.57/22.02 (13) op(e2, e2) = all_8_2 % 150.57/22.02 (14) all_48_2 = all_8_2 % 150.57/22.02 (15) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 150.57/22.02 % 150.57/22.02 Begin of proof % 150.57/22.02 | % 150.57/22.02 | COMBINE_EQS: (10), (11) imply: % 150.57/22.02 | (16) all_56_13 = e3 % 150.57/22.02 | % 150.57/22.02 | REDUCE: (6), (10) imply: % 150.57/22.02 | (17) ~ (all_8_2 = e3) % 150.57/22.02 | % 150.57/22.02 | SIMP: (17) implies: % 150.57/22.02 | (18) ~ (all_8_2 = e3) % 150.57/22.02 | % 150.57/22.02 | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (12), (13), (14), (15), % 150.57/22.02 | (16), (18) are inconsistent by sub-proof #116. % 150.57/22.02 | % 150.57/22.02 End of proof % 150.57/22.02 % 150.57/22.02 Sub-proof #116 shows that the following formulas are inconsistent: % 150.57/22.02 ---------------------------------------------------------------- % 150.57/22.02 (1) all_56_11 = all_8_2 % 150.57/22.02 (2) ~ (all_56_11 = e1) | all_56_13 = e2 % 150.57/22.02 (3) all_48_1 = e1 % 150.57/22.02 (4) ~ (e3 = e2) % 150.57/22.02 (5) all_54_5 = all_8_2 % 150.57/22.02 (6) ~ (all_48_1 = e1) | ~ (all_48_2 = e0) % 150.57/22.02 (7) op(e2, all_8_2) = all_56_10 % 150.57/22.02 (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 150.57/22.02 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 150.57/22.02 (9) all_56_13 = e3 % 150.57/22.02 (10) ~ (all_8_2 = e3) % 150.57/22.02 (11) op(all_8_2, all_8_2) = e1 % 150.57/22.02 (12) op(e2, e2) = all_8_2 % 150.57/22.02 (13) all_48_2 = all_8_2 % 150.57/22.02 (14) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 150.57/22.02 % 150.57/22.02 Begin of proof % 150.57/22.02 | % 150.57/22.02 | BETA: splitting (2) gives: % 150.57/22.02 | % 150.57/22.02 | Case 1: % 150.57/22.02 | | % 150.57/22.02 | | (15) ~ (all_56_11 = e1) % 150.57/22.02 | | % 150.57/22.02 | | REDUCE: (1), (15) imply: % 150.57/22.02 | | (16) ~ (all_8_2 = e1) % 150.57/22.02 | | % 150.57/22.02 | | BETA: splitting (6) gives: % 150.57/22.02 | | % 150.57/22.02 | | Case 1: % 150.57/22.02 | | | % 150.57/22.02 | | | (17) ~ (all_48_1 = e1) % 150.57/22.02 | | | % 150.57/22.02 | | | REDUCE: (3), (17) imply: % 150.57/22.02 | | | (18) $false % 150.57/22.02 | | | % 150.57/22.02 | | | CLOSE: (18) is inconsistent. % 150.57/22.02 | | | % 150.57/22.02 | | Case 2: % 150.57/22.02 | | | % 150.57/22.02 | | | (19) ~ (all_48_2 = e0) % 150.57/22.02 | | | % 150.57/22.02 | | | REDUCE: (13), (19) imply: % 150.57/22.02 | | | (20) ~ (all_8_2 = e0) % 150.57/22.02 | | | % 150.57/22.02 | | | REF_CLOSE: (5), (7), (8), (10), (11), (12), (14), (16), (20) are % 150.57/22.02 | | | inconsistent by sub-proof #146. % 150.57/22.02 | | | % 150.57/22.02 | | End of split % 150.57/22.02 | | % 150.57/22.02 | Case 2: % 150.57/22.02 | | % 150.57/22.02 | | (21) all_56_13 = e2 % 150.57/22.02 | | % 150.57/22.02 | | REF_CLOSE: (4), (9), (21) are inconsistent by sub-proof #527. % 150.57/22.02 | | % 150.57/22.02 | End of split % 150.57/22.02 | % 150.57/22.02 End of proof % 150.57/22.02 % 150.57/22.02 Sub-proof #117 shows that the following formulas are inconsistent: % 150.57/22.02 ---------------------------------------------------------------- % 150.57/22.02 (1) all_56_11 = all_8_2 % 150.57/22.02 (2) all_52_6 = e1 % 150.57/22.02 (3) ~ (all_6_1 = e2) % 150.57/22.02 (4) all_54_4 = all_52_1 % 150.57/22.02 (5) op(e0, e0) = all_4_2 % 150.57/22.02 (6) ~ (all_52_13 = all_8_0) % 150.57/22.02 (7) all_54_5 = all_8_2 % 150.57/22.02 (8) ~ (all_6_1 = e3) % 150.57/22.02 (9) ~ (all_8_0 = all_8_2) % 150.57/22.02 (10) all_56_1 = all_10_2 % 150.57/22.02 (11) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0 % 150.57/22.02 (12) ~ (all_52_1 = all_8_2) % 150.57/22.02 (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 150.57/22.02 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 150.57/22.02 (14) all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) & % 150.57/22.02 (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0)) % 150.57/22.02 (15) ~ (all_52_1 = all_52_13) % 150.57/22.02 (16) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0 % 150.57/22.02 (17) all_56_21 = e2 % 150.57/22.02 (18) op(all_4_2, all_4_2) = all_4_1 % 150.57/22.02 (19) all_56_31 = all_4_2 % 150.57/22.02 (20) ~ (all_8_0 = e3) % 150.57/22.02 (21) ~ (all_52_1 = all_8_0) % 150.57/22.02 (22) op(all_6_2, all_6_2) = all_6_1 % 150.57/22.02 (23) all_56_1 = e3 | all_56_11 = e2 | all_56_21 = e1 | all_56_31 = e0 % 150.57/22.02 (24) op(all_8_2, all_8_2) = e1 % 150.57/22.02 (25) ~ (all_52_6 = all_8_2) % 150.57/22.02 (26) all_58_15 = all_4_2 % 150.57/22.02 (27) all_6_2 = e2 % 150.57/22.02 (28) ~ (all_56_11 = e0) | all_56_15 = e2 % 150.57/22.02 (29) op(e2, e2) = all_8_2 % 150.57/22.02 (30) op(e0, all_4_2) = all_56_30 % 150.57/22.02 (31) all_54_6 = all_8_0 % 150.57/22.02 (32) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 150.57/22.02 (33) all_56_15 = all_52_13 % 150.57/22.02 (34) ~ (all_52_1 = all_10_2) % 150.57/22.02 % 150.57/22.02 Begin of proof % 150.57/22.02 | % 150.57/22.02 | REDUCE: (2), (25) imply: % 150.57/22.02 | (35) ~ (all_8_2 = e1) % 150.57/22.02 | % 150.57/22.02 | SIMP: (35) implies: % 150.57/22.02 | (36) ~ (all_8_2 = e1) % 150.57/22.02 | % 150.57/22.02 | REDUCE: (22), (27) imply: % 150.57/22.02 | (37) op(e2, e2) = all_6_1 % 150.57/22.02 | % 150.57/22.02 | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13), % 150.57/22.02 | (14), (15), (16), (17), (18), (19), (20), (21), (23), (24), (26), % 150.57/22.02 | (28), (29), (30), (31), (32), (33), (34), (36), (37) are % 150.57/22.02 | inconsistent by sub-proof #118. % 150.57/22.02 | % 150.57/22.02 End of proof % 150.57/22.02 % 150.57/22.02 Sub-proof #118 shows that the following formulas are inconsistent: % 150.57/22.02 ---------------------------------------------------------------- % 150.57/22.02 (1) all_56_11 = all_8_2 % 150.57/22.02 (2) ~ (all_6_1 = e2) % 150.57/22.02 (3) ~ (all_8_2 = e1) % 150.57/22.02 (4) all_54_4 = all_52_1 % 150.57/22.02 (5) op(e0, e0) = all_4_2 % 150.57/22.02 (6) ~ (all_52_13 = all_8_0) % 150.57/22.02 (7) op(e2, e2) = all_6_1 % 150.57/22.02 (8) all_54_5 = all_8_2 % 150.57/22.02 (9) ~ (all_6_1 = e3) % 150.57/22.02 (10) ~ (all_8_0 = all_8_2) % 150.57/22.02 (11) all_56_1 = all_10_2 % 150.57/22.02 (12) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0 % 150.57/22.02 (13) ~ (all_52_1 = all_8_2) % 150.57/22.02 (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 150.57/22.02 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 150.57/22.02 (15) all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) & % 150.57/22.02 (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0)) % 150.57/22.02 (16) ~ (all_52_1 = all_52_13) % 150.57/22.02 (17) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0 % 150.57/22.02 (18) all_56_21 = e2 % 150.57/22.02 (19) op(all_4_2, all_4_2) = all_4_1 % 150.57/22.02 (20) all_56_31 = all_4_2 % 150.57/22.02 (21) ~ (all_8_0 = e3) % 150.57/22.02 (22) ~ (all_52_1 = all_8_0) % 150.57/22.02 (23) all_56_1 = e3 | all_56_11 = e2 | all_56_21 = e1 | all_56_31 = e0 % 150.57/22.02 (24) op(all_8_2, all_8_2) = e1 % 150.57/22.02 (25) all_58_15 = all_4_2 % 150.57/22.02 (26) ~ (all_56_11 = e0) | all_56_15 = e2 % 150.57/22.02 (27) op(e2, e2) = all_8_2 % 150.57/22.02 (28) op(e0, all_4_2) = all_56_30 % 150.57/22.02 (29) all_54_6 = all_8_0 % 150.57/22.02 (30) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 150.57/22.02 (31) all_56_15 = all_52_13 % 150.57/22.02 (32) ~ (all_52_1 = all_10_2) % 150.57/22.02 % 150.57/22.02 Begin of proof % 150.57/22.02 | % 150.57/22.02 | GROUND_INST: instantiating (14) with all_8_2, all_6_1, e2, e2, simplifying % 150.57/22.02 | with (7), (27) gives: % 150.57/22.02 | (33) all_8_2 = all_6_1 % 150.57/22.02 | % 150.57/22.02 | COMBINE_EQS: (8), (33) imply: % 150.57/22.02 | (34) all_54_5 = all_6_1 % 150.57/22.02 | % 150.57/22.02 | COMBINE_EQS: (1), (33) imply: % 150.57/22.02 | (35) all_56_11 = all_6_1 % 150.57/22.02 | % 150.57/22.02 | REDUCE: (13), (33) imply: % 150.57/22.02 | (36) ~ (all_52_1 = all_6_1) % 150.57/22.02 | % 150.57/22.02 | REDUCE: (10), (33) imply: % 150.57/22.02 | (37) ~ (all_8_0 = all_6_1) % 150.57/22.02 | % 150.57/22.02 | REDUCE: (3), (33) imply: % 150.57/22.02 | (38) ~ (all_6_1 = e1) % 150.57/22.02 | % 150.57/22.02 | REDUCE: (24), (33) imply: % 150.57/22.02 | (39) op(all_6_1, all_6_1) = e1 % 150.57/22.02 | % 150.57/22.02 | BETA: splitting (30) gives: % 150.57/22.02 | % 150.57/22.02 | Case 1: % 150.57/22.02 | | % 150.57/22.02 | | (40) all_54_5 = e3 % 150.57/22.02 | | % 150.57/22.02 | | REF_CLOSE: (9), (34), (40) are inconsistent by sub-proof #509. % 150.57/22.02 | | % 150.57/22.02 | Case 2: % 150.57/22.02 | | % 150.57/22.02 | | (41) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 150.57/22.02 | | % 150.57/22.02 | | BETA: splitting (41) gives: % 150.57/22.02 | | % 150.57/22.02 | | Case 1: % 150.57/22.02 | | | % 150.57/22.02 | | | (42) all_54_5 = e2 % 150.57/22.02 | | | % 150.57/22.02 | | | REF_CLOSE: (2), (34), (42) are inconsistent by sub-proof #466. % 150.57/22.02 | | | % 150.57/22.02 | | Case 2: % 150.57/22.02 | | | % 150.57/22.02 | | | (43) ~ (all_54_5 = e2) % 150.57/22.02 | | | (44) all_54_5 = e1 | all_54_5 = e0 % 150.57/22.02 | | | % 150.57/22.02 | | | BETA: splitting (44) gives: % 150.57/22.02 | | | % 150.57/22.02 | | | Case 1: % 150.57/22.02 | | | | % 150.57/22.02 | | | | (45) all_54_5 = e1 % 150.57/22.02 | | | | % 150.57/22.02 | | | | REF_CLOSE: (34), (38), (45) are inconsistent by sub-proof #465. % 150.57/22.02 | | | | % 150.57/22.02 | | | Case 2: % 150.57/22.02 | | | | % 150.57/22.02 | | | | (46) all_54_5 = e0 % 150.57/22.02 | | | | % 150.57/22.02 | | | | COMBINE_EQS: (34), (46) imply: % 150.57/22.02 | | | | (47) all_6_1 = e0 % 150.57/22.02 | | | | % 150.57/22.02 | | | | SIMP: (47) implies: % 150.57/22.02 | | | | (48) all_6_1 = e0 % 150.57/22.02 | | | | % 150.57/22.02 | | | | COMBINE_EQS: (35), (48) imply: % 150.57/22.02 | | | | (49) all_56_11 = e0 % 150.57/22.02 | | | | % 150.57/22.02 | | | | REDUCE: (36), (48) imply: % 150.57/22.02 | | | | (50) ~ (all_52_1 = e0) % 150.57/22.02 | | | | % 150.57/22.02 | | | | REDUCE: (37), (48) imply: % 150.57/22.02 | | | | (51) ~ (all_8_0 = e0) % 150.57/22.02 | | | | % 150.57/22.02 | | | | BETA: splitting (26) gives: % 150.57/22.02 | | | | % 150.57/22.02 | | | | Case 1: % 150.57/22.02 | | | | | % 150.57/22.02 | | | | | (52) ~ (all_56_11 = e0) % 150.57/22.02 | | | | | % 150.57/22.02 | | | | | REDUCE: (49), (52) imply: % 150.57/22.02 | | | | | (53) $false % 150.57/22.02 | | | | | % 150.57/22.02 | | | | | CLOSE: (53) is inconsistent. % 150.57/22.02 | | | | | % 150.57/22.02 | | | | Case 2: % 150.57/22.02 | | | | | % 150.57/22.02 | | | | | (54) all_56_15 = e2 % 150.57/22.02 | | | | | % 150.57/22.02 | | | | | COMBINE_EQS: (31), (54) imply: % 150.57/22.02 | | | | | (55) all_52_13 = e2 % 150.57/22.02 | | | | | % 150.57/22.02 | | | | | REDUCE: (16), (55) imply: % 150.57/22.02 | | | | | (56) ~ (all_52_1 = e2) % 150.57/22.02 | | | | | % 150.57/22.02 | | | | | REDUCE: (6), (55) imply: % 150.57/22.02 | | | | | (57) ~ (all_8_0 = e2) % 150.57/22.02 | | | | | % 150.57/22.02 | | | | | SIMP: (57) implies: % 150.57/22.02 | | | | | (58) ~ (all_8_0 = e2) % 150.57/22.02 | | | | | % 150.57/22.02 | | | | | BETA: splitting (12) gives: % 150.57/22.02 | | | | | % 150.57/22.02 | | | | | Case 1: % 150.57/22.02 | | | | | | % 150.57/22.02 | | | | | | (59) all_54_6 = e3 % 150.57/22.02 | | | | | | % 150.57/22.02 | | | | | | REF_CLOSE: (21), (29), (59) are inconsistent by sub-proof #145. % 150.57/22.02 | | | | | | % 150.57/22.02 | | | | | Case 2: % 150.57/22.02 | | | | | | % 150.57/22.02 | | | | | | (60) all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0 % 150.57/22.02 | | | | | | % 150.57/22.02 | | | | | | BETA: splitting (60) gives: % 150.57/22.02 | | | | | | % 150.57/22.02 | | | | | | Case 1: % 150.57/22.02 | | | | | | | % 150.57/22.02 | | | | | | | (61) all_54_6 = e2 % 150.57/22.02 | | | | | | | % 150.57/22.02 | | | | | | | REF_CLOSE: (29), (58), (61) are inconsistent by sub-proof #144. % 150.57/22.02 | | | | | | | % 150.57/22.02 | | | | | | Case 2: % 150.57/22.02 | | | | | | | % 150.57/22.02 | | | | | | | (62) ~ (all_54_6 = e2) % 150.57/22.02 | | | | | | | (63) all_54_6 = e1 | all_54_6 = e0 % 150.57/22.02 | | | | | | | % 150.57/22.02 | | | | | | | BETA: splitting (63) gives: % 150.57/22.02 | | | | | | | % 150.57/22.02 | | | | | | | Case 1: % 150.57/22.02 | | | | | | | | % 150.57/22.02 | | | | | | | | (64) all_54_6 = e1 % 150.57/22.02 | | | | | | | | % 150.57/22.02 | | | | | | | | COMBINE_EQS: (29), (64) imply: % 150.57/22.02 | | | | | | | | (65) all_8_0 = e1 % 150.57/22.02 | | | | | | | | % 150.57/22.02 | | | | | | | | SIMP: (65) implies: % 150.57/22.02 | | | | | | | | (66) all_8_0 = e1 % 150.57/22.02 | | | | | | | | % 150.57/22.02 | | | | | | | | REDUCE: (22), (66) imply: % 150.57/22.02 | | | | | | | | (67) ~ (all_52_1 = e1) % 150.57/22.02 | | | | | | | | % 150.57/22.02 | | | | | | | | REDUCE: (58), (66) imply: % 150.57/22.02 | | | | | | | | (68) ~ (e2 = e1) % 150.57/22.02 | | | | | | | | % 150.57/22.02 | | | | | | | | SIMP: (68) implies: % 150.57/22.02 | | | | | | | | (69) ~ (e2 = e1) % 150.57/22.02 | | | | | | | | % 150.57/22.02 | | | | | | | | BETA: splitting (17) gives: % 150.57/22.02 | | | | | | | | % 150.57/22.02 | | | | | | | | Case 1: % 150.57/22.02 | | | | | | | | | % 150.57/22.02 | | | | | | | | | (70) all_54_4 = e3 % 150.57/22.02 | | | | | | | | | % 150.57/22.02 | | | | | | | | | COMBINE_EQS: (4), (70) imply: % 150.57/22.02 | | | | | | | | | (71) all_52_1 = e3 % 150.57/22.02 | | | | | | | | | % 150.57/22.02 | | | | | | | | | SIMP: (71) implies: % 150.57/22.02 | | | | | | | | | (72) all_52_1 = e3 % 150.57/22.02 | | | | | | | | | % 150.57/22.02 | | | | | | | | | REDUCE: (32), (72) imply: % 150.57/22.02 | | | | | | | | | (73) ~ (all_10_2 = e3) % 150.57/22.02 | | | | | | | | | % 150.57/22.02 | | | | | | | | | SIMP: (73) implies: % 150.57/22.02 | | | | | | | | | (74) ~ (all_10_2 = e3) % 150.57/22.02 | | | | | | | | | % 150.57/22.02 | | | | | | | | | BETA: splitting (23) gives: % 150.57/22.02 | | | | | | | | | % 150.57/22.02 | | | | | | | | | Case 1: % 150.57/22.02 | | | | | | | | | | % 150.57/22.02 | | | | | | | | | | (75) all_56_1 = e3 % 150.57/22.02 | | | | | | | | | | % 150.57/22.02 | | | | | | | | | | COMBINE_EQS: (11), (75) imply: % 150.57/22.02 | | | | | | | | | | (76) all_10_2 = e3 % 150.57/22.02 | | | | | | | | | | % 150.57/22.02 | | | | | | | | | | REDUCE: (74), (76) imply: % 150.57/22.02 | | | | | | | | | | (77) $false % 150.57/22.02 | | | | | | | | | | % 150.57/22.02 | | | | | | | | | | CLOSE: (77) is inconsistent. % 150.57/22.02 | | | | | | | | | | % 150.57/22.02 | | | | | | | | | Case 2: % 150.57/22.02 | | | | | | | | | | % 150.57/22.02 | | | | | | | | | | (78) all_56_11 = e2 | all_56_21 = e1 | all_56_31 = e0 % 150.57/22.02 | | | | | | | | | | % 150.57/22.02 | | | | | | | | | | BETA: splitting (78) gives: % 150.57/22.02 | | | | | | | | | | % 150.57/22.02 | | | | | | | | | | Case 1: % 150.57/22.02 | | | | | | | | | | | % 150.57/22.02 | | | | | | | | | | | (79) all_56_11 = e2 % 150.57/22.02 | | | | | | | | | | | % 150.57/22.02 | | | | | | | | | | | COMBINE_EQS: (35), (79) imply: % 150.57/22.02 | | | | | | | | | | | (80) all_6_1 = e2 % 150.57/22.02 | | | | | | | | | | | % 150.57/22.02 | | | | | | | | | | | REDUCE: (2), (80) imply: % 150.57/22.02 | | | | | | | | | | | (81) $false % 150.57/22.02 | | | | | | | | | | | % 150.57/22.02 | | | | | | | | | | | CLOSE: (81) is inconsistent. % 150.57/22.02 | | | | | | | | | | | % 150.57/22.02 | | | | | | | | | | Case 2: % 150.57/22.02 | | | | | | | | | | | % 150.57/22.02 | | | | | | | | | | | (82) all_56_21 = e1 | all_56_31 = e0 % 150.57/22.02 | | | | | | | | | | | % 150.57/22.02 | | | | | | | | | | | BETA: splitting (15) gives: % 150.57/22.02 | | | | | | | | | | | % 150.57/22.02 | | | | | | | | | | | Case 1: % 150.57/22.02 | | | | | | | | | | | | % 150.57/22.02 | | | | | | | | | | | | (83) all_58_15 = e0 % 150.57/22.02 | | | | | | | | | | | | % 150.57/22.02 | | | | | | | | | | | | COMBINE_EQS: (25), (83) imply: % 150.57/22.02 | | | | | | | | | | | | (84) all_4_2 = e0 % 150.57/22.02 | | | | | | | | | | | | % 150.57/22.02 | | | | | | | | | | | | REDUCE: (19), (84) imply: % 150.57/22.02 | | | | | | | | | | | | (85) op(e0, e0) = all_4_1 % 150.57/22.02 | | | | | | | | | | | | % 150.57/22.02 | | | | | | | | | | | | REDUCE: (28), (84) imply: % 150.57/22.02 | | | | | | | | | | | | (86) op(e0, e0) = all_56_30 % 150.57/22.02 | | | | | | | | | | | | % 150.57/22.02 | | | | | | | | | | | | REDUCE: (5), (84) imply: % 150.57/22.02 | | | | | | | | | | | | (87) op(e0, e0) = e0 % 150.57/22.02 | | | | | | | | | | | | % 150.57/22.02 | | | | | | | | | | | | BETA: splitting (44) gives: % 150.57/22.02 | | | | | | | | | | | | % 150.57/22.02 | | | | | | | | | | | | Case 1: % 150.57/22.02 | | | | | | | | | | | | | % 150.57/22.02 | | | | | | | | | | | | | (88) all_54_5 = e1 % 150.57/22.02 | | | | | | | | | | | | | % 150.57/22.02 | | | | | | | | | | | | | REF_CLOSE: (34), (38), (88) are inconsistent by sub-proof % 150.57/22.02 | | | | | | | | | | | | | #465. % 150.57/22.02 | | | | | | | | | | | | | % 150.57/22.02 | | | | | | | | | | | | Case 2: % 150.57/22.02 | | | | | | | | | | | | | % 150.57/22.02 | | | | | | | | | | | | | % 150.57/22.02 | | | | | | | | | | | | | REDUCE: (38), (48) imply: % 150.57/22.02 | | | | | | | | | | | | | (89) ~ (e1 = e0) % 150.57/22.02 | | | | | | | | | | | | | % 150.57/22.02 | | | | | | | | | | | | | SIMP: (89) implies: % 150.57/22.02 | | | | | | | | | | | | | (90) ~ (e1 = e0) % 150.57/22.02 | | | | | | | | | | | | | % 150.57/22.02 | | | | | | | | | | | | | REDUCE: (39), (48) imply: % 150.57/22.02 | | | | | | | | | | | | | (91) op(e0, e0) = e1 % 150.57/22.02 | | | | | | | | | | | | | % 150.57/22.02 | | | | | | | | | | | | | REF_CLOSE: (14), (85), (86), (87), (90), (91) are % 150.57/22.02 | | | | | | | | | | | | | inconsistent by sub-proof #389. % 150.57/22.02 | | | | | | | | | | | | | % 150.57/22.02 | | | | | | | | | | | | End of split % 150.57/22.02 | | | | | | | | | | | | % 150.57/22.02 | | | | | | | | | | | Case 2: % 150.57/22.02 | | | | | | | | | | | | % 150.57/22.02 | | | | | | | | | | | | (92) ~ (all_58_15 = e0) % 150.57/22.02 | | | | | | | | | | | | % 150.57/22.02 | | | | | | | | | | | | REDUCE: (25), (92) imply: % 150.57/22.02 | | | | | | | | | | | | (93) ~ (all_4_2 = e0) % 150.57/22.02 | | | | | | | | | | | | % 150.57/22.02 | | | | | | | | | | | | REF_CLOSE: (18), (20), (69), (82), (93) are inconsistent by % 150.57/22.02 | | | | | | | | | | | | sub-proof #435. % 150.57/22.02 | | | | | | | | | | | | % 150.57/22.02 | | | | | | | | | | | End of split % 150.57/22.02 | | | | | | | | | | | % 150.57/22.02 | | | | | | | | | | End of split % 150.57/22.02 | | | | | | | | | | % 150.57/22.02 | | | | | | | | | End of split % 150.57/22.02 | | | | | | | | | % 150.57/22.02 | | | | | | | | Case 2: % 150.57/22.02 | | | | | | | | | % 150.57/22.02 | | | | | | | | | (94) all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0 % 150.57/22.02 | | | | | | | | | % 150.57/22.02 | | | | | | | | | REF_CLOSE: (4), (50), (56), (67), (94) are inconsistent by % 150.57/22.02 | | | | | | | | | sub-proof #560. % 150.57/22.02 | | | | | | | | | % 150.57/22.02 | | | | | | | | End of split % 150.57/22.02 | | | | | | | | % 150.57/22.02 | | | | | | | Case 2: % 150.57/22.02 | | | | | | | | % 150.57/22.02 | | | | | | | | (95) all_54_6 = e0 % 150.57/22.02 | | | | | | | | % 150.57/22.02 | | | | | | | | REF_CLOSE: (29), (51), (95) are inconsistent by sub-proof #143. % 150.57/22.02 | | | | | | | | % 150.57/22.02 | | | | | | | End of split % 150.57/22.02 | | | | | | | % 150.57/22.02 | | | | | | End of split % 150.57/22.02 | | | | | | % 150.57/22.02 | | | | | End of split % 150.57/22.02 | | | | | % 150.57/22.02 | | | | End of split % 150.57/22.02 | | | | % 150.57/22.02 | | | End of split % 150.57/22.02 | | | % 150.57/22.02 | | End of split % 150.57/22.02 | | % 150.57/22.02 | End of split % 150.57/22.02 | % 150.57/22.02 End of proof % 150.57/22.02 % 150.57/22.02 Sub-proof #119 shows that the following formulas are inconsistent: % 150.57/22.02 ---------------------------------------------------------------- % 150.57/22.02 (1) all_56_11 = all_8_2 % 150.57/22.02 (2) all_56_31 = e1 % 150.57/22.02 (3) ~ (all_52_4 = all_52_8) % 150.57/22.02 (4) ~ (e3 = e0) % 150.57/22.02 (5) ~ (all_4_1 = e3) % 150.57/22.02 (6) all_54_0 = all_10_2 % 150.57/22.02 (7) all_58_4 = all_52_8 % 150.57/22.02 (8) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 150.57/22.02 (9) ~ (all_10_1 = e1) % 150.57/22.02 (10) all_56_21 = all_6_2 % 150.57/22.02 (11) all_56_1 = all_10_2 % 150.57/22.02 (12) all_58_5 = all_8_0 % 150.57/22.02 (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 150.57/22.02 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 150.57/22.02 (14) all_56_7 = all_52_12 % 150.57/22.02 (15) all_58_8 = all_6_2 % 150.57/22.02 (16) ~ (all_52_8 = all_10_2) % 150.57/22.02 (17) ~ (all_56_1 = e2) | all_56_3 = e3 % 150.57/22.02 (18) ~ (all_56_1 = e0) | all_56_7 = e3 % 150.57/22.02 (19) all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3 % 150.57/22.02 (20) all_56_3 = all_52_4 % 150.57/22.02 (21) ~ (all_8_0 = e3) % 150.57/22.02 (22) all_56_1 = e3 | all_56_11 = e2 | all_56_21 = e1 | all_56_31 = e0 % 150.57/22.02 (23) all_58_14 = e0 % 150.57/22.02 (24) op(all_8_2, all_8_2) = e1 % 150.57/22.02 (25) op(e1, e1) = all_6_2 % 150.57/22.02 (26) op(all_10_2, all_10_2) = all_10_1 % 150.57/22.02 (27) op(e1, e1) = all_4_1 % 150.57/22.02 (28) op(e2, e2) = all_8_2 % 150.57/22.02 (29) ~ (all_52_8 = all_52_12) % 150.57/22.02 % 150.57/22.02 Begin of proof % 150.57/22.02 | % 150.57/22.02 | GROUND_INST: instantiating (13) with all_6_2, all_4_1, e1, e1, simplifying % 150.57/22.02 | with (25), (27) gives: % 150.57/22.02 | (30) all_6_2 = all_4_1 % 150.57/22.02 | % 150.57/22.02 | COMBINE_EQS: (10), (30) imply: % 150.57/22.02 | (31) all_56_21 = all_4_1 % 150.57/22.02 | % 150.57/22.02 | COMBINE_EQS: (15), (30) imply: % 150.57/22.02 | (32) all_58_8 = all_4_1 % 150.57/22.02 | % 150.57/22.02 | BETA: splitting (19) gives: % 150.57/22.02 | % 150.57/22.02 | Case 1: % 150.57/22.02 | | % 150.57/22.02 | | (33) all_58_4 = e3 % 150.57/22.02 | | % 150.57/22.02 | | COMBINE_EQS: (7), (33) imply: % 150.57/22.02 | | (34) all_52_8 = e3 % 150.57/22.02 | | % 150.57/22.02 | | REDUCE: (3), (34) imply: % 150.57/22.02 | | (35) ~ (all_52_4 = e3) % 150.57/22.02 | | % 150.57/22.02 | | REDUCE: (29), (34) imply: % 150.57/22.02 | | (36) ~ (all_52_12 = e3) % 150.57/22.02 | | % 150.57/22.02 | | SIMP: (36) implies: % 150.57/22.02 | | (37) ~ (all_52_12 = e3) % 150.57/22.02 | | % 150.57/22.02 | | REDUCE: (16), (34) imply: % 150.57/22.02 | | (38) ~ (all_10_2 = e3) % 150.57/22.02 | | % 150.57/22.02 | | SIMP: (38) implies: % 150.57/22.02 | | (39) ~ (all_10_2 = e3) % 150.57/22.02 | | % 150.57/22.02 | | BETA: splitting (17) gives: % 150.57/22.02 | | % 150.57/22.02 | | Case 1: % 150.57/22.02 | | | % 150.57/22.02 | | | (40) ~ (all_56_1 = e2) % 150.57/22.02 | | | % 150.57/22.02 | | | REDUCE: (11), (40) imply: % 150.57/22.02 | | | (41) ~ (all_10_2 = e2) % 150.57/22.02 | | | % 150.57/22.02 | | | BETA: splitting (18) gives: % 150.57/22.02 | | | % 150.57/22.02 | | | Case 1: % 150.57/22.02 | | | | % 150.57/22.02 | | | | (42) ~ (all_56_1 = e0) % 150.57/22.02 | | | | % 150.57/22.02 | | | | REDUCE: (11), (42) imply: % 150.57/22.02 | | | | (43) ~ (all_10_2 = e0) % 150.57/22.02 | | | | % 150.57/22.02 | | | | BETA: splitting (8) gives: % 150.57/22.02 | | | | % 150.57/22.02 | | | | Case 1: % 150.57/22.02 | | | | | % 150.57/22.02 | | | | | (44) all_54_0 = e3 % 150.57/22.02 | | | | | % 150.57/22.02 | | | | | REF_CLOSE: (6), (39), (44) are inconsistent by sub-proof #709. % 150.57/22.02 | | | | | % 150.57/22.02 | | | | Case 2: % 150.57/22.02 | | | | | % 150.57/22.02 | | | | | (45) ~ (all_54_0 = e3) % 150.57/22.02 | | | | | (46) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 150.57/22.02 | | | | | % 150.57/22.02 | | | | | BETA: splitting (46) gives: % 150.57/22.02 | | | | | % 150.57/22.02 | | | | | Case 1: % 150.57/22.02 | | | | | | % 150.57/22.02 | | | | | | (47) all_54_0 = e2 % 150.57/22.02 | | | | | | % 150.57/22.02 | | | | | | REF_CLOSE: (6), (41), (47) are inconsistent by sub-proof #734. % 150.57/22.02 | | | | | | % 150.57/22.02 | | | | | Case 2: % 150.57/22.02 | | | | | | % 150.57/22.02 | | | | | | (48) ~ (all_54_0 = e2) % 150.57/22.02 | | | | | | (49) all_54_0 = e1 | all_54_0 = e0 % 150.57/22.02 | | | | | | % 150.57/22.02 | | | | | | BETA: splitting (49) gives: % 150.57/22.02 | | | | | | % 150.57/22.02 | | | | | | Case 1: % 150.57/22.02 | | | | | | | % 150.57/22.02 | | | | | | | (50) all_54_0 = e1 % 150.57/22.02 | | | | | | | % 150.57/22.02 | | | | | | | COMBINE_EQS: (6), (50) imply: % 150.57/22.02 | | | | | | | (51) all_10_2 = e1 % 150.57/22.02 | | | | | | | % 150.57/22.02 | | | | | | | SIMP: (51) implies: % 150.57/22.02 | | | | | | | (52) all_10_2 = e1 % 150.57/22.02 | | | | | | | % 150.57/22.02 | | | | | | | COMBINE_EQS: (11), (52) imply: % 150.57/22.02 | | | | | | | (53) all_56_1 = e1 % 150.57/22.02 | | | | | | | % 150.57/22.02 | | | | | | | REDUCE: (39), (52) imply: % 150.57/22.02 | | | | | | | (54) ~ (e3 = e1) % 150.57/22.02 | | | | | | | % 150.57/22.02 | | | | | | | SIMP: (54) implies: % 150.57/22.02 | | | | | | | (55) ~ (e3 = e1) % 150.57/22.02 | | | | | | | % 150.57/22.02 | | | | | | | REDUCE: (41), (52) imply: % 150.57/22.02 | | | | | | | (56) ~ (e2 = e1) % 150.57/22.02 | | | | | | | % 150.57/22.02 | | | | | | | SIMP: (56) implies: % 150.57/22.02 | | | | | | | (57) ~ (e2 = e1) % 150.57/22.02 | | | | | | | % 150.57/22.02 | | | | | | | REDUCE: (43), (52) imply: % 150.57/22.02 | | | | | | | (58) ~ (e1 = e0) % 150.57/22.02 | | | | | | | % 150.57/22.02 | | | | | | | REDUCE: (26), (52) imply: % 150.57/22.02 | | | | | | | (59) op(e1, e1) = all_10_1 % 150.57/22.02 | | | | | | | % 150.57/22.02 | | | | | | | GROUND_INST: instantiating (13) with all_4_1, all_10_1, e1, e1, % 150.57/22.02 | | | | | | | simplifying with (27), (59) gives: % 150.57/22.02 | | | | | | | (60) all_10_1 = all_4_1 % 150.57/22.02 | | | | | | | % 150.57/22.02 | | | | | | | REDUCE: (9), (60) imply: % 150.57/22.02 | | | | | | | (61) ~ (all_4_1 = e1) % 150.57/22.02 | | | | | | | % 150.57/22.02 | | | | | | | BETA: splitting (22) gives: % 150.57/22.02 | | | | | | | % 150.57/22.02 | | | | | | | Case 1: % 150.57/22.02 | | | | | | | | % 150.57/22.02 | | | | | | | | (62) all_56_1 = e3 % 150.57/22.02 | | | | | | | | % 150.57/22.02 | | | | | | | | COMBINE_EQS: (53), (62) imply: % 150.57/22.02 | | | | | | | | (63) e3 = e1 % 150.57/22.02 | | | | | | | | % 150.57/22.02 | | | | | | | | REDUCE: (55), (63) imply: % 150.57/22.02 | | | | | | | | (64) $false % 150.57/22.02 | | | | | | | | % 150.57/22.02 | | | | | | | | CLOSE: (64) is inconsistent. % 150.57/22.02 | | | | | | | | % 150.57/22.02 | | | | | | | Case 2: % 150.57/22.02 | | | | | | | | % 150.57/22.02 | | | | | | | | (65) all_56_11 = e2 | all_56_21 = e1 | all_56_31 = e0 % 150.57/22.02 | | | | | | | | % 150.57/22.02 | | | | | | | | BETA: splitting (65) gives: % 150.57/22.02 | | | | | | | | % 150.57/22.02 | | | | | | | | Case 1: % 150.57/22.02 | | | | | | | | | % 150.57/22.02 | | | | | | | | | (66) all_56_11 = e2 % 150.57/22.02 | | | | | | | | | % 150.57/22.02 | | | | | | | | | COMBINE_EQS: (1), (66) imply: % 150.57/22.02 | | | | | | | | | (67) all_8_2 = e2 % 150.57/22.02 | | | | | | | | | % 150.57/22.02 | | | | | | | | | SIMP: (67) implies: % 150.57/22.02 | | | | | | | | | (68) all_8_2 = e2 % 150.57/22.02 | | | | | | | | | % 150.57/22.02 | | | | | | | | | REDUCE: (24), (68) imply: % 150.57/22.02 | | | | | | | | | (69) op(e2, e2) = e1 % 150.57/22.02 | | | | | | | | | % 150.57/22.02 | | | | | | | | | REDUCE: (28), (68) imply: % 150.57/22.02 | | | | | | | | | (70) op(e2, e2) = e2 % 150.57/22.02 | | | | | | | | | % 150.57/22.02 | | | | | | | | | REF_CLOSE: (13), (57), (69), (70) are inconsistent by % 150.57/22.02 | | | | | | | | | sub-proof #479. % 150.57/22.02 | | | | | | | | | % 150.57/22.02 | | | | | | | | Case 2: % 150.57/22.02 | | | | | | | | | % 150.57/22.02 | | | | | | | | | (71) all_56_21 = e1 | all_56_31 = e0 % 150.57/22.02 | | | | | | | | | % 150.57/22.02 | | | | | | | | | REF_CLOSE: (2), (31), (58), (61), (71) are inconsistent by % 150.57/22.02 | | | | | | | | | sub-proof #181. % 150.57/22.02 | | | | | | | | | % 150.57/22.02 | | | | | | | | End of split % 150.57/22.02 | | | | | | | | % 150.57/22.02 | | | | | | | End of split % 150.57/22.02 | | | | | | | % 150.57/22.02 | | | | | | Case 2: % 150.57/22.02 | | | | | | | % 150.57/22.02 | | | | | | | (72) all_54_0 = e0 % 150.57/22.02 | | | | | | | % 150.57/22.02 | | | | | | | REF_CLOSE: (6), (43), (72) are inconsistent by sub-proof #732. % 150.57/22.02 | | | | | | | % 150.57/22.02 | | | | | | End of split % 150.57/22.02 | | | | | | % 150.57/22.02 | | | | | End of split % 150.57/22.02 | | | | | % 150.57/22.02 | | | | End of split % 150.57/22.02 | | | | % 150.57/22.02 | | | Case 2: % 150.57/22.02 | | | | % 150.57/22.02 | | | | (73) all_56_7 = e3 % 150.57/22.02 | | | | % 150.57/22.02 | | | | COMBINE_EQS: (14), (73) imply: % 150.57/22.02 | | | | (74) all_52_12 = e3 % 150.57/22.02 | | | | % 150.57/22.02 | | | | REDUCE: (37), (74) imply: % 150.57/22.02 | | | | (75) $false % 150.57/22.02 | | | | % 150.57/22.02 | | | | CLOSE: (75) is inconsistent. % 150.57/22.02 | | | | % 150.57/22.02 | | | End of split % 150.57/22.02 | | | % 150.57/22.02 | | Case 2: % 150.57/22.02 | | | % 150.57/22.02 | | | (76) all_56_3 = e3 % 150.57/22.02 | | | % 150.57/22.02 | | | COMBINE_EQS: (20), (76) imply: % 150.57/22.02 | | | (77) all_52_4 = e3 % 150.57/22.02 | | | % 150.57/22.02 | | | REDUCE: (35), (77) imply: % 150.57/22.02 | | | (78) $false % 150.57/22.02 | | | % 150.57/22.02 | | | CLOSE: (78) is inconsistent. % 150.57/22.02 | | | % 150.57/22.02 | | End of split % 150.57/22.02 | | % 150.57/22.02 | Case 2: % 150.57/22.02 | | % 150.57/22.02 | | (79) all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3 % 150.57/22.02 | | % 150.57/22.02 | | REF_CLOSE: (4), (5), (12), (21), (23), (32), (79) are inconsistent by % 150.57/22.02 | | sub-proof #120. % 150.57/22.02 | | % 150.57/22.02 | End of split % 150.57/22.02 | % 150.57/22.02 End of proof % 150.57/22.02 % 150.57/22.02 Sub-proof #120 shows that the following formulas are inconsistent: % 150.57/22.02 ---------------------------------------------------------------- % 150.57/22.02 (1) ~ (e3 = e0) % 150.57/22.02 (2) ~ (all_4_1 = e3) % 150.57/22.02 (3) all_58_5 = all_8_0 % 150.57/22.02 (4) ~ (all_8_0 = e3) % 150.57/22.02 (5) all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3 % 150.57/22.02 (6) all_58_14 = e0 % 150.57/22.02 (7) all_58_8 = all_4_1 % 150.57/22.02 % 150.57/22.02 Begin of proof % 150.57/22.02 | % 150.57/22.02 | BETA: splitting (5) gives: % 150.57/22.02 | % 150.57/22.02 | Case 1: % 150.57/22.02 | | % 150.57/22.02 | | (8) all_58_5 = e3 % 150.57/22.02 | | % 150.57/22.02 | | COMBINE_EQS: (3), (8) imply: % 150.57/22.02 | | (9) all_8_0 = e3 % 150.57/22.02 | | % 150.57/22.02 | | REDUCE: (4), (9) imply: % 150.57/22.02 | | (10) $false % 150.57/22.02 | | % 150.57/22.02 | | CLOSE: (10) is inconsistent. % 150.57/22.02 | | % 150.57/22.02 | Case 2: % 150.57/22.02 | | % 150.57/22.02 | | (11) all_58_8 = e3 | all_58_14 = e3 % 150.57/22.02 | | % 150.57/22.02 | | REF_CLOSE: (1), (2), (6), (7), (11) are inconsistent by sub-proof #526. % 150.57/22.02 | | % 150.57/22.02 | End of split % 150.57/22.02 | % 150.57/22.02 End of proof % 150.57/22.02 % 150.57/22.02 Sub-proof #121 shows that the following formulas are inconsistent: % 150.57/22.02 ---------------------------------------------------------------- % 150.57/22.02 (1) all_56_11 = all_8_2 % 150.57/22.02 (2) ~ (all_56_11 = e1) | all_56_13 = e2 % 150.57/22.02 (3) ~ (all_52_11 = all_6_2) % 150.57/22.02 (4) ~ (all_52_4 = all_52_8) % 150.57/22.02 (5) all_56_25 = all_52_3 % 150.57/22.02 (6) ~ (all_8_0 = all_6_2) % 150.57/22.02 (7) ~ (all_6_1 = e2) % 150.57/22.02 (8) all_54_0 = all_10_2 % 150.57/22.02 (9) all_56_31 = e3 % 150.57/22.02 (10) op(e0, e0) = all_4_2 % 150.57/22.02 (11) ~ (all_52_13 = all_8_0) % 150.57/22.02 (12) all_58_4 = all_52_8 % 150.57/22.02 (13) all_54_5 = all_8_2 % 150.57/22.02 (14) ~ (all_6_1 = e3) % 150.57/22.02 (15) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 150.57/22.02 (16) ~ (all_8_0 = all_8_2) % 150.57/22.02 (17) all_56_21 = all_6_2 % 150.57/22.02 (18) all_56_1 = all_10_2 % 150.57/22.02 (19) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0 % 150.57/22.02 (20) all_56_17 = all_52_2 % 150.57/22.02 (21) all_58_5 = all_8_0 % 150.57/22.02 (22) all_58_4 = e0 | all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0 % 150.57/22.02 (23) op(e2, all_8_2) = all_56_10 % 150.57/22.03 (24) op(e3, e3) = all_10_2 % 150.57/22.03 (25) ~ (all_56_21 = e3) | all_56_17 = e1 % 150.57/22.03 (26) ~ (all_52_1 = all_8_2) % 150.57/22.03 (27) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 150.57/22.03 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 150.57/22.03 (28) ~ (all_52_3 = all_10_2) % 150.57/22.03 (29) all_56_25 = e0 % 150.57/22.03 (30) all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0 % 150.57/22.03 (31) ~ (all_56_11 = e3) | all_56_9 = e2 % 150.57/22.03 (32) all_58_8 = all_6_2 % 150.57/22.03 (33) ~ (all_52_3 = all_4_2) % 150.57/22.03 (34) ~ (all_52_8 = all_10_2) % 150.57/22.03 (35) ~ (all_56_1 = e2) | all_56_3 = e3 % 150.57/22.03 (36) op(all_4_2, all_4_2) = all_4_1 % 150.57/22.03 (37) all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3 % 150.57/22.03 (38) ~ (all_52_3 = all_52_11) % 150.57/22.03 (39) all_58_3 = all_8_2 % 150.57/22.03 (40) all_56_3 = all_52_4 % 150.57/22.03 (41) ~ (all_52_11 = all_4_2) % 150.57/22.03 (42) all_56_31 = all_4_2 % 150.57/22.03 (43) ~ (all_8_0 = e3) % 150.57/22.03 (44) all_56_13 = all_8_0 % 150.57/22.03 (45) ~ (all_52_1 = all_8_0) % 150.57/22.03 (46) op(all_6_2, all_6_2) = all_6_1 % 150.57/22.03 (47) all_56_1 = e3 | all_56_11 = e2 | all_56_21 = e1 | all_56_31 = e0 % 150.57/22.03 (48) ~ (all_52_13 = all_4_2) % 150.57/22.03 (49) ~ (all_8_0 = e0) | ~ (all_8_2 = e3) % 150.57/22.03 (50) op(all_8_2, all_8_2) = e1 % 150.57/22.03 (51) all_58_2 = all_52_1 % 150.57/22.03 (52) all_58_10 = all_52_13 % 150.57/22.03 (53) op(e2, e2) = all_8_2 % 150.57/22.03 (54) ~ (all_56_21 = e0) | all_56_23 = e1 % 150.57/22.03 (55) all_54_6 = all_8_0 % 150.57/22.03 (56) ~ (e2 = e0) % 150.57/22.03 (57) ~ (all_52_2 = all_10_2) % 150.57/22.03 (58) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 150.57/22.03 (59) all_58_14 = all_52_11 % 150.57/22.03 (60) all_56_9 = all_52_1 % 150.57/22.03 % 150.57/22.03 Begin of proof % 150.57/22.03 | % 150.57/22.03 | COMBINE_EQS: (5), (29) imply: % 150.57/22.03 | (61) all_52_3 = e0 % 150.57/22.03 | % 150.57/22.03 | SIMP: (61) implies: % 150.57/22.03 | (62) all_52_3 = e0 % 150.57/22.03 | % 150.57/22.03 | COMBINE_EQS: (9), (42) imply: % 150.57/22.03 | (63) all_4_2 = e3 % 150.57/22.03 | % 150.57/22.03 | REDUCE: (38), (62) imply: % 150.57/22.03 | (64) ~ (all_52_11 = e0) % 150.57/22.03 | % 150.57/22.03 | SIMP: (64) implies: % 150.57/22.03 | (65) ~ (all_52_11 = e0) % 150.57/22.03 | % 150.57/22.03 | REDUCE: (28), (62) imply: % 150.57/22.03 | (66) ~ (all_10_2 = e0) % 150.57/22.03 | % 150.57/22.03 | SIMP: (66) implies: % 150.57/22.03 | (67) ~ (all_10_2 = e0) % 150.57/22.03 | % 150.57/22.03 | REDUCE: (33), (62), (63) imply: % 150.57/22.03 | (68) ~ (e3 = e0) % 150.57/22.03 | % 150.57/22.03 | SIMP: (68) implies: % 150.57/22.03 | (69) ~ (e3 = e0) % 150.57/22.03 | % 150.57/22.03 | REDUCE: (41), (63) imply: % 150.57/22.03 | (70) ~ (all_52_11 = e3) % 150.57/22.03 | % 150.57/22.03 | REDUCE: (36), (63) imply: % 150.57/22.03 | (71) op(e3, e3) = all_4_1 % 150.57/22.03 | % 150.57/22.03 | REDUCE: (10), (63) imply: % 150.57/22.03 | (72) op(e0, e0) = e3 % 150.57/22.03 | % 150.57/22.03 | GROUND_INST: instantiating (27) with all_10_2, all_4_1, e3, e3, simplifying % 150.57/22.03 | with (24), (71) gives: % 150.57/22.03 | (73) all_10_2 = all_4_1 % 150.57/22.03 | % 150.57/22.03 | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (11), (12), (13), (14), (15), % 150.57/22.03 | (16), (17), (18), (19), (20), (21), (22), (23), (24), (25), (26), % 150.57/22.03 | (27), (30), (31), (32), (34), (35), (37), (39), (40), (42), (43), % 150.57/22.03 | (44), (45), (46), (47), (48), (49), (50), (51), (52), (53), (54), % 150.57/22.03 | (55), (56), (57), (58), (59), (60), (65), (67), (69), (70), (72), % 150.57/22.03 | (73) are inconsistent by sub-proof #122. % 150.57/22.03 | % 150.57/22.03 End of proof % 150.57/22.03 % 150.57/22.03 Sub-proof #122 shows that the following formulas are inconsistent: % 150.57/22.03 ---------------------------------------------------------------- % 150.57/22.03 (1) all_56_11 = all_8_2 % 150.57/22.03 (2) ~ (all_56_11 = e1) | all_56_13 = e2 % 150.57/22.03 (3) ~ (all_52_11 = all_6_2) % 150.57/22.03 (4) ~ (all_52_4 = all_52_8) % 150.57/22.03 (5) ~ (all_8_0 = all_6_2) % 150.57/22.03 (6) ~ (e3 = e0) % 150.57/22.03 (7) ~ (all_6_1 = e2) % 150.57/22.03 (8) all_54_0 = all_10_2 % 150.57/22.03 (9) ~ (all_52_13 = all_8_0) % 150.57/22.03 (10) all_58_4 = all_52_8 % 150.57/22.03 (11) all_54_5 = all_8_2 % 150.57/22.03 (12) ~ (all_6_1 = e3) % 150.57/22.03 (13) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 150.57/22.03 (14) ~ (all_52_11 = e0) % 150.57/22.03 (15) ~ (all_8_0 = all_8_2) % 150.57/22.03 (16) all_56_21 = all_6_2 % 150.57/22.03 (17) all_56_1 = all_10_2 % 150.57/22.03 (18) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0 % 150.57/22.03 (19) all_56_17 = all_52_2 % 150.57/22.03 (20) all_58_5 = all_8_0 % 150.57/22.03 (21) all_58_4 = e0 | all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0 % 150.57/22.03 (22) op(e2, all_8_2) = all_56_10 % 150.57/22.03 (23) op(e3, e3) = all_10_2 % 150.57/22.03 (24) ~ (all_56_21 = e3) | all_56_17 = e1 % 150.57/22.03 (25) ~ (all_52_1 = all_8_2) % 150.57/22.03 (26) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 150.57/22.03 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 150.57/22.03 (27) ~ (all_52_11 = e3) % 150.57/22.03 (28) all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0 % 150.57/22.03 (29) ~ (all_56_11 = e3) | all_56_9 = e2 % 150.57/22.03 (30) all_58_8 = all_6_2 % 150.57/22.03 (31) ~ (all_52_8 = all_10_2) % 150.57/22.03 (32) ~ (all_56_1 = e2) | all_56_3 = e3 % 150.57/22.03 (33) all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3 % 150.57/22.03 (34) all_58_3 = all_8_2 % 150.57/22.03 (35) all_56_3 = all_52_4 % 150.57/22.03 (36) all_56_31 = all_4_2 % 150.57/22.03 (37) op(e0, e0) = e3 % 150.57/22.03 (38) ~ (all_8_0 = e3) % 150.57/22.03 (39) all_56_13 = all_8_0 % 150.57/22.03 (40) all_10_2 = all_4_1 % 150.57/22.03 (41) ~ (all_52_1 = all_8_0) % 150.57/22.03 (42) op(all_6_2, all_6_2) = all_6_1 % 150.57/22.03 (43) all_56_1 = e3 | all_56_11 = e2 | all_56_21 = e1 | all_56_31 = e0 % 150.57/22.03 (44) ~ (all_52_13 = all_4_2) % 150.57/22.03 (45) ~ (all_8_0 = e0) | ~ (all_8_2 = e3) % 150.57/22.03 (46) op(all_8_2, all_8_2) = e1 % 150.57/22.03 (47) ~ (all_10_2 = e0) % 150.57/22.03 (48) all_58_2 = all_52_1 % 150.57/22.03 (49) all_58_10 = all_52_13 % 150.57/22.03 (50) op(e2, e2) = all_8_2 % 150.57/22.03 (51) ~ (all_56_21 = e0) | all_56_23 = e1 % 150.57/22.03 (52) all_54_6 = all_8_0 % 150.57/22.03 (53) ~ (e2 = e0) % 150.57/22.03 (54) ~ (all_52_2 = all_10_2) % 150.57/22.03 (55) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 150.57/22.03 (56) all_58_14 = all_52_11 % 150.57/22.03 (57) all_56_9 = all_52_1 % 150.57/22.03 % 150.57/22.03 Begin of proof % 150.57/22.03 | % 150.57/22.03 | COMBINE_EQS: (8), (40) imply: % 150.57/22.03 | (58) all_54_0 = all_4_1 % 150.57/22.03 | % 150.57/22.03 | COMBINE_EQS: (17), (40) imply: % 150.57/22.03 | (59) all_56_1 = all_4_1 % 150.57/22.03 | % 150.57/22.03 | REDUCE: (40), (54) imply: % 150.57/22.03 | (60) ~ (all_52_2 = all_4_1) % 150.57/22.03 | % 150.57/22.03 | REDUCE: (31), (40) imply: % 150.57/22.03 | (61) ~ (all_52_8 = all_4_1) % 150.57/22.03 | % 150.57/22.03 | REDUCE: (40), (47) imply: % 150.57/22.03 | (62) ~ (all_4_1 = e0) % 150.57/22.03 | % 150.57/22.03 | REDUCE: (23), (40) imply: % 150.57/22.03 | (63) op(e3, e3) = all_4_1 % 150.57/22.03 | % 150.57/22.03 | BETA: splitting (51) gives: % 150.57/22.03 | % 150.57/22.03 | Case 1: % 150.57/22.03 | | % 150.57/22.03 | | (64) ~ (all_56_21 = e0) % 150.57/22.03 | | % 150.57/22.03 | | REDUCE: (16), (64) imply: % 150.57/22.03 | | (65) ~ (all_6_2 = e0) % 150.57/22.03 | | % 150.57/22.03 | | BETA: splitting (24) gives: % 150.57/22.03 | | % 150.57/22.03 | | Case 1: % 150.57/22.03 | | | % 150.57/22.03 | | | (66) ~ (all_56_21 = e3) % 150.57/22.03 | | | % 150.57/22.03 | | | REDUCE: (16), (66) imply: % 150.57/22.03 | | | (67) ~ (all_6_2 = e3) % 150.57/22.03 | | | % 150.57/22.03 | | | BETA: splitting (33) gives: % 150.57/22.03 | | | % 150.57/22.03 | | | Case 1: % 150.57/22.03 | | | | % 150.57/22.03 | | | | (68) all_58_4 = e3 % 150.57/22.03 | | | | % 150.57/22.03 | | | | COMBINE_EQS: (10), (68) imply: % 150.57/22.03 | | | | (69) all_52_8 = e3 % 150.57/22.03 | | | | % 150.57/22.03 | | | | BETA: splitting (21) gives: % 150.57/22.03 | | | | % 150.57/22.03 | | | | Case 1: % 150.57/22.03 | | | | | % 150.57/22.03 | | | | | (70) all_58_4 = e0 % 150.57/22.03 | | | | | % 150.57/22.03 | | | | | COMBINE_EQS: (68), (70) imply: % 150.57/22.03 | | | | | (71) e3 = e0 % 150.57/22.03 | | | | | % 150.57/22.03 | | | | | REDUCE: (6), (71) imply: % 150.57/22.03 | | | | | (72) $false % 150.57/22.03 | | | | | % 150.57/22.03 | | | | | CLOSE: (72) is inconsistent. % 150.57/22.03 | | | | | % 150.57/22.03 | | | | Case 2: % 150.57/22.03 | | | | | % 150.57/22.03 | | | | | (73) all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0 % 150.57/22.03 | | | | | % 150.57/22.03 | | | | | BETA: splitting (73) gives: % 150.57/22.03 | | | | | % 150.57/22.03 | | | | | Case 1: % 150.57/22.03 | | | | | | % 150.57/22.03 | | | | | | (74) all_58_5 = e0 % 150.57/22.03 | | | | | | % 150.57/22.03 | | | | | | COMBINE_EQS: (20), (74) imply: % 150.57/22.03 | | | | | | (75) all_8_0 = e0 % 150.57/22.03 | | | | | | % 150.57/22.03 | | | | | | COMBINE_EQS: (39), (75) imply: % 150.57/22.03 | | | | | | (76) all_56_13 = e0 % 150.57/22.03 | | | | | | % 150.57/22.03 | | | | | | REDUCE: (15), (75) imply: % 150.57/22.03 | | | | | | (77) ~ (all_8_2 = e0) % 150.57/22.03 | | | | | | % 150.57/22.03 | | | | | | SIMP: (77) implies: % 150.57/22.03 | | | | | | (78) ~ (all_8_2 = e0) % 150.57/22.03 | | | | | | % 150.57/22.03 | | | | | | REF_CLOSE: (1), (2), (5), (9), (11), (15), (16), (17), (18), (20), % 150.57/22.03 | | | | | | (22), (23), (25), (26), (28), (29), (34), (36), (41), % 150.57/22.03 | | | | | | (43), (44), (45), (46), (48), (49), (50), (52), (53), % 150.57/22.03 | | | | | | (55), (57), (76), (78) are inconsistent by sub-proof % 150.57/22.03 | | | | | | #134. % 150.57/22.03 | | | | | | % 150.57/22.03 | | | | | Case 2: % 150.57/22.03 | | | | | | % 150.57/22.03 | | | | | | (79) all_58_8 = e0 | all_58_14 = e0 % 150.57/22.03 | | | | | | % 150.57/22.03 | | | | | | REF_CLOSE: (14), (30), (56), (65), (79) are inconsistent by % 150.57/22.03 | | | | | | sub-proof #627. % 150.57/22.03 | | | | | | % 150.57/22.03 | | | | | End of split % 150.57/22.03 | | | | | % 150.57/22.03 | | | | End of split % 150.57/22.03 | | | | % 150.57/22.03 | | | Case 2: % 150.57/22.03 | | | | % 150.57/22.03 | | | | (80) all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3 % 150.57/22.03 | | | | % 150.57/22.03 | | | | REF_CLOSE: (20), (27), (30), (38), (56), (67), (80) are inconsistent by % 150.57/22.03 | | | | sub-proof #124. % 150.57/22.03 | | | | % 150.57/22.03 | | | End of split % 150.57/22.03 | | | % 150.57/22.03 | | Case 2: % 150.57/22.03 | | | % 150.57/22.03 | | | (81) all_56_21 = e3 % 150.57/22.03 | | | (82) all_56_17 = e1 % 150.57/22.03 | | | % 150.57/22.03 | | | COMBINE_EQS: (19), (82) imply: % 150.57/22.03 | | | (83) all_52_2 = e1 % 150.57/22.03 | | | % 150.57/22.03 | | | SIMP: (83) implies: % 150.57/22.03 | | | (84) all_52_2 = e1 % 150.57/22.03 | | | % 150.57/22.03 | | | COMBINE_EQS: (16), (81) imply: % 150.57/22.03 | | | (85) all_6_2 = e3 % 150.57/22.03 | | | % 150.57/22.03 | | | SIMP: (85) implies: % 150.57/22.03 | | | (86) all_6_2 = e3 % 150.57/22.03 | | | % 150.57/22.03 | | | REDUCE: (60), (84) imply: % 150.57/22.03 | | | (87) ~ (all_4_1 = e1) % 150.57/22.03 | | | % 150.57/22.03 | | | SIMP: (87) implies: % 150.57/22.03 | | | (88) ~ (all_4_1 = e1) % 150.57/22.03 | | | % 150.57/22.03 | | | REF_CLOSE: (4), (7), (10), (12), (13), (16), (19), (20), (24), (26), (27), % 150.57/22.03 | | | (30), (32), (33), (35), (38), (42), (56), (58), (59), (60), % 150.57/22.03 | | | (61), (62), (63), (88) are inconsistent by sub-proof #123. % 150.57/22.03 | | | % 150.57/22.03 | | End of split % 150.57/22.03 | | % 150.57/22.03 | Case 2: % 150.57/22.03 | | % 150.57/22.03 | | (89) all_56_21 = e0 % 150.57/22.03 | | % 150.57/22.03 | | REF_CLOSE: (12), (16), (26), (37), (42), (89) are inconsistent by sub-proof % 150.57/22.03 | | #539. % 150.57/22.03 | | % 150.57/22.03 | End of split % 150.57/22.03 | % 150.57/22.03 End of proof % 150.57/22.03 % 150.57/22.03 Sub-proof #123 shows that the following formulas are inconsistent: % 150.57/22.03 ---------------------------------------------------------------- % 150.57/22.03 (1) ~ (all_52_4 = all_52_8) % 150.57/22.03 (2) ~ (all_4_1 = e0) % 150.57/22.03 (3) ~ (all_52_2 = all_4_1) % 150.57/22.03 (4) ~ (all_6_1 = e2) % 150.57/22.03 (5) all_58_4 = all_52_8 % 150.57/22.03 (6) ~ (all_6_1 = e3) % 150.57/22.03 (7) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 150.57/22.03 (8) all_56_21 = all_6_2 % 150.57/22.03 (9) all_56_17 = all_52_2 % 150.57/22.03 (10) all_56_1 = all_4_1 % 150.57/22.03 (11) all_54_0 = all_4_1 % 150.57/22.03 (12) all_58_5 = all_8_0 % 150.57/22.03 (13) ~ (all_56_21 = e3) | all_56_17 = e1 % 150.57/22.03 (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 150.57/22.03 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 150.57/22.03 (15) ~ (all_52_11 = e3) % 150.57/22.03 (16) all_58_8 = all_6_2 % 150.57/22.03 (17) ~ (all_56_1 = e2) | all_56_3 = e3 % 150.57/22.03 (18) all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3 % 150.57/22.03 (19) all_56_3 = all_52_4 % 150.57/22.03 (20) ~ (all_8_0 = e3) % 150.57/22.03 (21) ~ (all_4_1 = e1) % 150.57/22.03 (22) op(all_6_2, all_6_2) = all_6_1 % 150.57/22.03 (23) ~ (all_52_8 = all_4_1) % 150.57/22.03 (24) all_58_14 = all_52_11 % 150.57/22.03 (25) op(e3, e3) = all_4_1 % 150.57/22.03 % 150.57/22.03 Begin of proof % 150.57/22.03 | % 150.57/22.03 | BETA: splitting (13) gives: % 150.57/22.03 | % 150.57/22.03 | Case 1: % 150.57/22.03 | | % 150.57/22.03 | | (26) ~ (all_56_21 = e3) % 150.57/22.03 | | % 150.57/22.03 | | REDUCE: (8), (26) imply: % 150.57/22.03 | | (27) ~ (all_6_2 = e3) % 150.57/22.03 | | % 150.57/22.03 | | BETA: splitting (18) gives: % 150.57/22.03 | | % 150.57/22.03 | | Case 1: % 150.57/22.03 | | | % 150.57/22.03 | | | (28) all_58_4 = e3 % 150.57/22.03 | | | % 150.57/22.03 | | | COMBINE_EQS: (5), (28) imply: % 150.57/22.03 | | | (29) all_52_8 = e3 % 150.57/22.03 | | | % 150.57/22.03 | | | REDUCE: (1), (29) imply: % 150.57/22.03 | | | (30) ~ (all_52_4 = e3) % 150.57/22.03 | | | % 150.57/22.03 | | | REDUCE: (23), (29) imply: % 150.57/22.03 | | | (31) ~ (all_4_1 = e3) % 150.57/22.03 | | | % 150.57/22.03 | | | SIMP: (31) implies: % 150.57/22.03 | | | (32) ~ (all_4_1 = e3) % 150.57/22.03 | | | % 150.57/22.03 | | | REF_CLOSE: (2), (7), (10), (11), (17), (19), (21), (30), (32) are % 150.57/22.03 | | | inconsistent by sub-proof #355. % 150.57/22.03 | | | % 150.57/22.03 | | Case 2: % 150.57/22.03 | | | % 150.57/22.03 | | | (33) all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3 % 150.57/22.03 | | | % 150.57/22.03 | | | REF_CLOSE: (12), (15), (16), (20), (24), (27), (33) are inconsistent by % 150.57/22.03 | | | sub-proof #124. % 150.57/22.03 | | | % 150.57/22.03 | | End of split % 150.57/22.03 | | % 150.57/22.03 | Case 2: % 150.57/22.03 | | % 150.57/22.03 | | (34) all_56_21 = e3 % 150.57/22.03 | | (35) all_56_17 = e1 % 150.57/22.03 | | % 150.57/22.03 | | COMBINE_EQS: (9), (35) imply: % 150.57/22.03 | | (36) all_52_2 = e1 % 150.57/22.03 | | % 150.57/22.03 | | REF_CLOSE: (2), (3), (4), (6), (7), (8), (11), (14), (22), (25), (34), (36) % 150.57/22.03 | | are inconsistent by sub-proof #547. % 150.57/22.03 | | % 150.57/22.03 | End of split % 150.57/22.03 | % 150.57/22.03 End of proof % 150.57/22.03 % 150.57/22.03 Sub-proof #124 shows that the following formulas are inconsistent: % 150.57/22.03 ---------------------------------------------------------------- % 150.57/22.03 (1) ~ (all_6_2 = e3) % 150.57/22.03 (2) all_58_5 = all_8_0 % 150.57/22.03 (3) ~ (all_52_11 = e3) % 150.57/22.03 (4) all_58_8 = all_6_2 % 150.57/22.03 (5) ~ (all_8_0 = e3) % 150.57/22.03 (6) all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3 % 150.57/22.03 (7) all_58_14 = all_52_11 % 150.57/22.03 % 150.57/22.03 Begin of proof % 150.57/22.03 | % 150.57/22.03 | BETA: splitting (6) gives: % 150.57/22.03 | % 150.57/22.03 | Case 1: % 150.57/22.03 | | % 150.57/22.03 | | (8) all_58_5 = e3 % 150.57/22.03 | | % 150.57/22.03 | | COMBINE_EQS: (2), (8) imply: % 150.57/22.03 | | (9) all_8_0 = e3 % 150.57/22.03 | | % 150.57/22.03 | | REDUCE: (5), (9) imply: % 150.57/22.03 | | (10) $false % 150.57/22.03 | | % 150.57/22.03 | | CLOSE: (10) is inconsistent. % 150.57/22.03 | | % 150.57/22.03 | Case 2: % 150.57/22.03 | | % 150.57/22.03 | | (11) all_58_8 = e3 | all_58_14 = e3 % 150.57/22.03 | | % 150.57/22.03 | | REF_CLOSE: (1), (3), (4), (7), (11) are inconsistent by sub-proof #149. % 150.57/22.03 | | % 150.57/22.03 | End of split % 150.57/22.03 | % 150.57/22.03 End of proof % 150.57/22.03 % 150.57/22.03 Sub-proof #125 shows that the following formulas are inconsistent: % 150.57/22.03 ---------------------------------------------------------------- % 150.57/22.03 (1) all_56_11 = all_8_2 % 150.57/22.03 (2) ~ (all_56_11 = e1) | all_56_13 = e2 % 150.57/22.03 (3) all_58_6 = all_52_2 % 150.57/22.03 (4) ~ (all_6_1 = e2) % 150.57/22.03 (5) op(e1, e1) = e0 % 150.57/22.03 (6) op(e0, e0) = all_4_2 % 150.57/22.03 (7) all_54_5 = all_8_2 % 150.57/22.03 (8) ~ (all_6_1 = e3) % 150.57/22.03 (9) all_54_15 = all_4_2 % 150.57/22.03 (10) all_58_1 = all_52_4 % 150.57/22.03 (11) all_58_13 = all_52_7 % 150.57/22.03 (12) op(e2, all_8_2) = all_56_10 % 150.57/22.03 (13) ~ (all_52_1 = all_8_2) % 150.57/22.03 (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 150.57/22.03 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 150.57/22.03 (15) all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0 % 150.57/22.03 (16) ~ (all_56_11 = e3) | all_56_9 = e2 % 150.57/22.03 (17) op(e0, all_4_1) = all_4_0 % 150.57/22.03 (18) ~ (all_52_2 = e0) % 150.57/22.03 (19) ~ (all_52_7 = all_4_2) % 150.57/22.03 (20) ~ (all_4_2 = e1) % 150.57/22.03 (21) ~ (all_4_0 = e1) % 150.57/22.03 (22) ~ (all_52_3 = all_4_2) % 150.57/22.03 (23) ~ (all_52_6 = e0) % 150.57/22.03 (24) op(all_4_2, all_4_2) = all_4_1 % 150.57/22.03 (25) all_58_3 = all_8_2 % 150.57/22.03 (26) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0 % 150.57/22.03 (27) op(all_8_2, all_8_2) = e1 % 150.57/22.03 (28) all_58_2 = all_52_1 % 150.57/22.03 (29) all_58_7 = all_52_6 % 150.57/22.03 (30) op(e0, e0) = all_6_1 % 150.57/22.03 (31) ~ (all_56_11 = e0) | all_56_15 = e2 % 150.57/22.03 (32) all_58_0 = all_10_2 % 150.57/22.03 (33) all_58_1 = e0 | all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0 % 150.57/22.03 (34) op(e2, e2) = all_8_2 % 150.57/22.03 (35) op(e0, all_4_2) = all_56_30 % 150.57/22.03 (36) all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0 % 150.57/22.03 (37) ~ (all_52_4 = all_10_2) % 150.57/22.03 (38) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 150.57/22.03 (39) ~ (all_4_0 = e2) % 150.57/22.03 (40) all_56_9 = all_52_1 % 150.57/22.03 (41) all_58_12 = all_52_3 % 150.57/22.03 % 150.57/22.03 Begin of proof % 150.57/22.03 | % 150.57/22.03 | GROUND_INST: instantiating (14) with all_4_2, all_6_1, e0, e0, simplifying % 150.57/22.03 | with (6), (30) gives: % 150.57/22.03 | (42) all_6_1 = all_4_2 % 150.57/22.03 | % 150.57/22.03 | REDUCE: (8), (42) imply: % 150.57/22.03 | (43) ~ (all_4_2 = e3) % 150.57/22.03 | % 150.57/22.03 | REDUCE: (4), (42) imply: % 150.57/22.03 | (44) ~ (all_4_2 = e2) % 150.57/22.03 | % 150.57/22.03 | BETA: splitting (26) gives: % 150.57/22.03 | % 150.57/22.03 | Case 1: % 150.57/22.03 | | % 150.57/22.03 | | (45) all_54_15 = e3 % 150.57/22.03 | | % 150.57/22.03 | | COMBINE_EQS: (9), (45) imply: % 150.57/22.03 | | (46) all_4_2 = e3 % 150.57/22.03 | | % 150.57/22.03 | | REDUCE: (43), (46) imply: % 150.57/22.03 | | (47) $false % 150.57/22.03 | | % 150.57/22.03 | | CLOSE: (47) is inconsistent. % 150.57/22.03 | | % 150.57/22.03 | Case 2: % 150.57/22.03 | | % 150.57/22.03 | | (48) all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0 % 150.57/22.03 | | % 150.57/22.03 | | BETA: splitting (48) gives: % 150.57/22.03 | | % 150.57/22.03 | | Case 1: % 150.57/22.03 | | | % 150.57/22.03 | | | (49) all_54_15 = e2 % 150.57/22.03 | | | % 150.57/22.03 | | | COMBINE_EQS: (9), (49) imply: % 150.57/22.03 | | | (50) all_4_2 = e2 % 150.57/22.03 | | | % 150.57/22.03 | | | REDUCE: (44), (50) imply: % 150.57/22.03 | | | (51) $false % 150.57/22.03 | | | % 150.57/22.03 | | | CLOSE: (51) is inconsistent. % 150.57/22.03 | | | % 150.57/22.03 | | Case 2: % 150.57/22.03 | | | % 150.57/22.03 | | | (52) all_54_15 = e1 | all_54_15 = e0 % 150.57/22.03 | | | % 150.57/22.03 | | | BETA: splitting (52) gives: % 150.57/22.03 | | | % 150.57/22.03 | | | Case 1: % 150.57/22.03 | | | | % 150.57/22.03 | | | | (53) all_54_15 = e1 % 150.57/22.03 | | | | % 150.57/22.03 | | | | COMBINE_EQS: (9), (53) imply: % 150.57/22.03 | | | | (54) all_4_2 = e1 % 150.57/22.03 | | | | % 150.57/22.03 | | | | REDUCE: (20), (54) imply: % 150.57/22.03 | | | | (55) $false % 150.57/22.03 | | | | % 150.57/22.03 | | | | CLOSE: (55) is inconsistent. % 150.57/22.03 | | | | % 150.57/22.03 | | | Case 2: % 150.57/22.03 | | | | % 150.57/22.03 | | | | (56) all_54_15 = e0 % 150.57/22.03 | | | | % 150.57/22.03 | | | | COMBINE_EQS: (9), (56) imply: % 150.57/22.03 | | | | (57) all_4_2 = e0 % 150.57/22.03 | | | | % 150.57/22.03 | | | | REDUCE: (22), (57) imply: % 150.57/22.03 | | | | (58) ~ (all_52_3 = e0) % 150.57/22.03 | | | | % 150.57/22.03 | | | | REDUCE: (19), (57) imply: % 150.57/22.03 | | | | (59) ~ (all_52_7 = e0) % 150.57/22.03 | | | | % 150.57/22.03 | | | | REDUCE: (24), (57) imply: % 150.57/22.03 | | | | (60) op(e0, e0) = all_4_1 % 150.57/22.03 | | | | % 150.57/22.03 | | | | REDUCE: (35), (57) imply: % 150.57/22.03 | | | | (61) op(e0, e0) = all_56_30 % 150.57/22.03 | | | | % 150.57/22.03 | | | | REDUCE: (6), (57) imply: % 150.57/22.03 | | | | (62) op(e0, e0) = e0 % 150.57/22.03 | | | | % 150.57/22.03 | | | | GROUND_INST: instantiating (14) with all_4_1, all_56_30, e0, e0, % 150.57/22.03 | | | | simplifying with (60), (61) gives: % 150.57/22.03 | | | | (63) all_56_30 = all_4_1 % 150.57/22.03 | | | | % 150.57/22.03 | | | | GROUND_INST: instantiating (14) with e0, all_56_30, e0, e0, simplifying % 150.57/22.03 | | | | with (61), (62) gives: % 150.57/22.03 | | | | (64) all_56_30 = e0 % 150.57/22.03 | | | | % 150.57/22.03 | | | | COMBINE_EQS: (63), (64) imply: % 150.57/22.03 | | | | (65) all_4_1 = e0 % 150.57/22.03 | | | | % 150.57/22.03 | | | | SIMP: (65) implies: % 150.57/22.03 | | | | (66) all_4_1 = e0 % 150.57/22.03 | | | | % 150.57/22.03 | | | | REDUCE: (17), (66) imply: % 150.57/22.03 | | | | (67) op(e0, e0) = all_4_0 % 150.57/22.03 | | | | % 150.57/22.03 | | | | GROUND_INST: instantiating (14) with e0, all_4_0, e0, e0, simplifying % 150.57/22.03 | | | | with (62), (67) gives: % 150.57/22.03 | | | | (68) all_4_0 = e0 % 150.57/22.03 | | | | % 150.57/22.03 | | | | REDUCE: (39), (68) imply: % 150.57/22.03 | | | | (69) ~ (e2 = e0) % 150.57/22.03 | | | | % 150.57/22.03 | | | | SIMP: (69) implies: % 150.57/22.03 | | | | (70) ~ (e2 = e0) % 150.57/22.03 | | | | % 150.57/22.03 | | | | REDUCE: (21), (68) imply: % 150.57/22.03 | | | | (71) ~ (e1 = e0) % 150.57/22.03 | | | | % 150.57/22.03 | | | | SIMP: (71) implies: % 150.57/22.03 | | | | (72) ~ (e1 = e0) % 150.57/22.03 | | | | % 150.57/22.03 | | | | BETA: splitting (31) gives: % 150.57/22.03 | | | | % 150.57/22.03 | | | | Case 1: % 150.57/22.03 | | | | | % 150.57/22.03 | | | | | (73) ~ (all_56_11 = e0) % 150.57/22.03 | | | | | % 150.57/22.03 | | | | | REDUCE: (1), (73) imply: % 150.57/22.03 | | | | | (74) ~ (all_8_2 = e0) % 150.57/22.03 | | | | | % 150.57/22.03 | | | | | BETA: splitting (15) gives: % 150.57/22.03 | | | | | % 150.57/22.03 | | | | | Case 1: % 150.57/22.03 | | | | | | % 150.57/22.03 | | | | | | (75) all_58_2 = e0 % 150.57/22.03 | | | | | | % 150.57/22.03 | | | | | | COMBINE_EQS: (28), (75) imply: % 150.57/22.03 | | | | | | (76) all_52_1 = e0 % 150.57/22.03 | | | | | | % 150.57/22.03 | | | | | | COMBINE_EQS: (40), (76) imply: % 150.57/22.03 | | | | | | (77) all_56_9 = e0 % 150.57/22.03 | | | | | | % 150.57/22.03 | | | | | | REDUCE: (13), (76) imply: % 150.57/22.03 | | | | | | (78) ~ (all_8_2 = e0) % 150.57/22.03 | | | | | | % 150.57/22.03 | | | | | | BETA: splitting (16) gives: % 150.57/22.03 | | | | | | % 150.57/22.03 | | | | | | Case 1: % 150.57/22.03 | | | | | | | % 150.57/22.03 | | | | | | | (79) ~ (all_56_11 = e3) % 150.57/22.03 | | | | | | | % 150.57/22.03 | | | | | | | REDUCE: (1), (79) imply: % 150.57/22.03 | | | | | | | (80) ~ (all_8_2 = e3) % 150.57/22.03 | | | | | | | % 150.57/22.03 | | | | | | | BETA: splitting (2) gives: % 150.57/22.03 | | | | | | | % 150.57/22.03 | | | | | | | Case 1: % 150.57/22.03 | | | | | | | | % 150.57/22.03 | | | | | | | | (81) ~ (all_56_11 = e1) % 150.57/22.03 | | | | | | | | % 150.57/22.03 | | | | | | | | REDUCE: (1), (81) imply: % 150.57/22.03 | | | | | | | | (82) ~ (all_8_2 = e1) % 150.57/22.03 | | | | | | | | % 150.57/22.03 | | | | | | | | REF_CLOSE: (7), (12), (14), (27), (34), (38), (74), (80), (82) % 150.57/22.03 | | | | | | | | are inconsistent by sub-proof #146. % 150.57/22.03 | | | | | | | | % 150.57/22.03 | | | | | | | Case 2: % 150.57/22.03 | | | | | | | | % 150.57/22.03 | | | | | | | | (83) all_56_11 = e1 % 150.57/22.03 | | | | | | | | % 150.57/22.03 | | | | | | | | COMBINE_EQS: (1), (83) imply: % 150.57/22.03 | | | | | | | | (84) all_8_2 = e1 % 150.57/22.03 | | | | | | | | % 150.57/22.03 | | | | | | | | SIMP: (84) implies: % 150.57/22.03 | | | | | | | | (85) all_8_2 = e1 % 150.57/22.03 | | | | | | | | % 150.57/22.03 | | | | | | | | REDUCE: (27), (85) imply: % 150.57/22.03 | | | | | | | | (86) op(e1, e1) = e1 % 150.57/22.03 | | | | | | | | % 150.57/22.03 | | | | | | | | GROUND_INST: instantiating (14) with e0, e1, e1, e1, simplifying % 150.57/22.03 | | | | | | | | with (5), (86) gives: % 150.57/22.03 | | | | | | | | (87) e1 = e0 % 150.57/22.03 | | | | | | | | % 150.57/22.03 | | | | | | | | REDUCE: (72), (87) imply: % 150.57/22.03 | | | | | | | | (88) $false % 150.57/22.03 | | | | | | | | % 150.57/22.03 | | | | | | | | CLOSE: (88) is inconsistent. % 150.57/22.03 | | | | | | | | % 150.57/22.03 | | | | | | | End of split % 150.57/22.03 | | | | | | | % 150.57/22.03 | | | | | | Case 2: % 150.57/22.03 | | | | | | | % 150.57/22.03 | | | | | | | (89) all_56_9 = e2 % 150.57/22.03 | | | | | | | % 150.57/22.03 | | | | | | | REF_CLOSE: (70), (77), (89) are inconsistent by sub-proof #486. % 150.57/22.03 | | | | | | | % 150.57/22.03 | | | | | | End of split % 150.57/22.03 | | | | | | % 150.57/22.03 | | | | | Case 2: % 150.57/22.03 | | | | | | % 150.57/22.03 | | | | | | (90) ~ (all_58_2 = e0) % 150.57/22.03 | | | | | | % 150.57/22.03 | | | | | | REF_CLOSE: (3), (10), (11), (18), (23), (25), (28), (29), (32), % 150.57/22.03 | | | | | | (33), (36), (37), (41), (58), (59), (74), (90) are % 150.57/22.03 | | | | | | inconsistent by sub-proof #602. % 150.57/22.03 | | | | | | % 150.57/22.03 | | | | | End of split % 150.57/22.03 | | | | | % 150.57/22.03 | | | | Case 2: % 150.57/22.03 | | | | | % 150.57/22.03 | | | | | (91) all_56_11 = e0 % 150.57/22.03 | | | | | % 150.57/22.03 | | | | | COMBINE_EQS: (1), (91) imply: % 150.57/22.03 | | | | | (92) all_8_2 = e0 % 150.57/22.03 | | | | | % 150.57/22.03 | | | | | REDUCE: (27), (92) imply: % 150.57/22.03 | | | | | (93) op(e0, e0) = e1 % 150.57/22.03 | | | | | % 150.57/22.03 | | | | | REF_CLOSE: (14), (60), (61), (62), (72), (93) are inconsistent by % 150.57/22.03 | | | | | sub-proof #389. % 150.57/22.03 | | | | | % 150.57/22.03 | | | | End of split % 150.57/22.03 | | | | % 150.57/22.03 | | | End of split % 150.57/22.03 | | | % 150.57/22.03 | | End of split % 150.57/22.03 | | % 150.57/22.03 | End of split % 150.57/22.03 | % 150.57/22.03 End of proof % 150.57/22.03 % 150.57/22.03 Sub-proof #126 shows that the following formulas are inconsistent: % 150.57/22.03 ---------------------------------------------------------------- % 150.57/22.03 (1) all_56_11 = all_8_2 % 150.82/22.03 (2) ~ (all_8_0 = all_6_2) % 150.82/22.03 (3) ~ (e3 = e0) % 150.82/22.03 (4) ~ (all_52_13 = all_8_2) % 150.82/22.03 (5) ~ (e3 = e2) % 150.82/22.03 (6) op(e0, e0) = all_4_2 % 150.82/22.03 (7) ~ (all_52_13 = all_8_0) % 150.82/22.03 (8) ~ (all_8_0 = all_8_2) % 150.82/22.03 (9) all_56_21 = all_6_2 % 150.82/22.03 (10) all_56_1 = all_10_2 % 150.82/22.03 (11) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0 % 150.82/22.03 (12) all_58_5 = all_8_0 % 150.82/22.03 (13) ~ (e1 = e0) % 150.82/22.03 (14) all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1 % 150.82/22.03 (15) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 150.82/22.03 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 150.82/22.03 (16) all_56_15 = e2 % 150.82/22.03 (17) ~ (e2 = e1) % 150.82/22.03 (18) op(all_4_2, all_4_2) = all_4_1 % 150.82/22.03 (19) all_58_3 = all_8_2 % 150.82/22.03 (20) all_56_31 = all_4_2 % 150.82/22.03 (21) ~ (all_8_0 = e3) % 150.82/22.03 (22) all_56_1 = e3 | all_56_11 = e2 | all_56_21 = e1 | all_56_31 = e0 % 150.82/22.03 (23) all_56_11 = e0 % 150.82/22.03 (24) op(all_8_2, all_8_2) = e1 % 150.82/22.03 (25) all_58_2 = all_52_1 % 150.82/22.03 (26) all_58_10 = all_52_13 % 150.82/22.04 (27) ~ (e3 = e1) % 150.82/22.04 (28) op(e0, all_4_2) = all_56_30 % 150.82/22.04 (29) all_54_6 = all_8_0 % 150.82/22.04 (30) all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3 % 150.82/22.04 (31) all_56_15 = all_52_13 % 150.82/22.04 (32) ~ (all_52_1 = all_10_2) % 150.82/22.04 % 150.82/22.04 Begin of proof % 150.82/22.04 | % 150.82/22.04 | COMBINE_EQS: (1), (23) imply: % 150.82/22.04 | (33) all_8_2 = e0 % 150.82/22.04 | % 150.82/22.04 | COMBINE_EQS: (16), (31) imply: % 150.82/22.04 | (34) all_52_13 = e2 % 150.82/22.04 | % 150.82/22.04 | COMBINE_EQS: (26), (34) imply: % 150.82/22.04 | (35) all_58_10 = e2 % 150.82/22.04 | % 150.82/22.04 | COMBINE_EQS: (19), (33) imply: % 150.82/22.04 | (36) all_58_3 = e0 % 150.82/22.04 | % 150.82/22.04 | REDUCE: (7), (34) imply: % 150.82/22.04 | (37) ~ (all_8_0 = e2) % 150.82/22.04 | % 150.82/22.04 | SIMP: (37) implies: % 150.82/22.04 | (38) ~ (all_8_0 = e2) % 150.82/22.04 | % 150.82/22.04 | REDUCE: (4), (33), (34) imply: % 150.82/22.04 | (39) ~ (e2 = e0) % 150.82/22.04 | % 150.82/22.04 | REF_CLOSE: (2), (3), (5), (6), (8), (9), (10), (11), (12), (13), (14), (15), % 150.82/22.04 | (17), (18), (20), (21), (22), (23), (24), (25), (27), (28), (29), % 150.82/22.04 | (30), (32), (33), (35), (36), (38), (39) are inconsistent by % 150.82/22.04 | sub-proof #127. % 150.82/22.04 | % 150.82/22.04 End of proof % 150.82/22.04 % 150.82/22.04 Sub-proof #127 shows that the following formulas are inconsistent: % 150.82/22.04 ---------------------------------------------------------------- % 150.82/22.04 (1) ~ (all_8_0 = all_6_2) % 150.82/22.04 (2) ~ (e3 = e0) % 150.82/22.04 (3) ~ (e3 = e2) % 150.82/22.04 (4) op(e0, e0) = all_4_2 % 150.82/22.04 (5) all_58_10 = e2 % 150.82/22.04 (6) ~ (all_8_0 = all_8_2) % 150.82/22.04 (7) all_56_21 = all_6_2 % 150.82/22.04 (8) all_56_1 = all_10_2 % 150.82/22.04 (9) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0 % 150.82/22.04 (10) all_58_5 = all_8_0 % 150.82/22.04 (11) ~ (e1 = e0) % 150.82/22.04 (12) all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1 % 150.82/22.04 (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 150.82/22.04 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 150.82/22.04 (14) all_58_3 = e0 % 150.82/22.04 (15) ~ (e2 = e1) % 150.82/22.04 (16) op(all_4_2, all_4_2) = all_4_1 % 150.82/22.04 (17) all_56_31 = all_4_2 % 150.82/22.04 (18) ~ (all_8_0 = e3) % 150.82/22.04 (19) all_56_1 = e3 | all_56_11 = e2 | all_56_21 = e1 | all_56_31 = e0 % 150.82/22.04 (20) ~ (all_8_0 = e2) % 150.82/22.04 (21) all_56_11 = e0 % 150.82/22.04 (22) op(all_8_2, all_8_2) = e1 % 150.82/22.04 (23) all_58_2 = all_52_1 % 150.82/22.04 (24) ~ (e3 = e1) % 150.82/22.04 (25) op(e0, all_4_2) = all_56_30 % 150.82/22.04 (26) all_8_2 = e0 % 150.82/22.04 (27) all_54_6 = all_8_0 % 150.82/22.04 (28) ~ (e2 = e0) % 150.82/22.04 (29) all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3 % 150.82/22.04 (30) ~ (all_52_1 = all_10_2) % 150.82/22.04 % 150.82/22.04 Begin of proof % 150.82/22.04 | % 150.82/22.04 | REDUCE: (6), (26) imply: % 150.82/22.04 | (31) ~ (all_8_0 = e0) % 150.82/22.04 | % 150.82/22.04 | REDUCE: (22), (26) imply: % 150.82/22.04 | (32) op(e0, e0) = e1 % 150.82/22.04 | % 150.82/22.04 | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (10), (11), (12), (13), % 150.82/22.04 | (14), (15), (16), (17), (18), (19), (20), (21), (23), (24), (25), % 150.82/22.04 | (27), (28), (29), (30), (31), (32) are inconsistent by sub-proof % 150.82/22.04 | #128. % 150.82/22.04 | % 150.82/22.04 End of proof % 150.82/22.04 % 150.82/22.04 Sub-proof #128 shows that the following formulas are inconsistent: % 150.82/22.04 ---------------------------------------------------------------- % 150.82/22.04 (1) op(e0, e0) = e1 % 150.82/22.04 (2) ~ (all_8_0 = all_6_2) % 150.82/22.04 (3) ~ (e3 = e0) % 150.82/22.04 (4) ~ (e3 = e2) % 150.82/22.04 (5) op(e0, e0) = all_4_2 % 150.82/22.04 (6) all_58_10 = e2 % 150.82/22.04 (7) all_56_21 = all_6_2 % 150.82/22.04 (8) all_56_1 = all_10_2 % 150.82/22.04 (9) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0 % 150.82/22.04 (10) all_58_5 = all_8_0 % 150.82/22.04 (11) ~ (e1 = e0) % 150.82/22.04 (12) all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1 % 150.82/22.04 (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 150.82/22.04 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 150.82/22.04 (14) ~ (all_8_0 = e0) % 150.82/22.04 (15) all_58_3 = e0 % 150.82/22.04 (16) ~ (e2 = e1) % 150.82/22.04 (17) op(all_4_2, all_4_2) = all_4_1 % 150.82/22.04 (18) all_56_31 = all_4_2 % 150.82/22.04 (19) ~ (all_8_0 = e3) % 150.82/22.04 (20) all_56_1 = e3 | all_56_11 = e2 | all_56_21 = e1 | all_56_31 = e0 % 150.82/22.04 (21) ~ (all_8_0 = e2) % 150.82/22.04 (22) all_56_11 = e0 % 150.82/22.04 (23) all_58_2 = all_52_1 % 150.82/22.04 (24) ~ (e3 = e1) % 150.82/22.04 (25) op(e0, all_4_2) = all_56_30 % 150.82/22.04 (26) all_54_6 = all_8_0 % 150.82/22.04 (27) ~ (e2 = e0) % 150.82/22.04 (28) all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3 % 150.82/22.04 (29) ~ (all_52_1 = all_10_2) % 150.82/22.04 % 150.82/22.04 Begin of proof % 150.82/22.04 | % 150.82/22.04 | BETA: splitting (28) gives: % 150.82/22.04 | % 150.82/22.04 | Case 1: % 150.82/22.04 | | % 150.82/22.04 | | (30) all_58_2 = e3 % 150.82/22.04 | | % 150.82/22.04 | | COMBINE_EQS: (23), (30) imply: % 150.82/22.04 | | (31) all_52_1 = e3 % 150.82/22.04 | | % 150.82/22.04 | | REDUCE: (29), (31) imply: % 150.82/22.04 | | (32) ~ (all_10_2 = e3) % 150.82/22.04 | | % 150.82/22.04 | | SIMP: (32) implies: % 150.82/22.04 | | (33) ~ (all_10_2 = e3) % 150.82/22.04 | | % 150.82/22.04 | | BETA: splitting (12) gives: % 150.82/22.04 | | % 150.82/22.04 | | Case 1: % 150.82/22.04 | | | % 150.82/22.04 | | | (34) all_58_2 = e1 % 150.82/22.04 | | | % 150.82/22.04 | | | COMBINE_EQS: (30), (34) imply: % 150.82/22.04 | | | (35) e3 = e1 % 150.82/22.04 | | | % 150.82/22.04 | | | REDUCE: (24), (35) imply: % 150.82/22.04 | | | (36) $false % 150.82/22.04 | | | % 150.82/22.04 | | | CLOSE: (36) is inconsistent. % 150.82/22.04 | | | % 150.82/22.04 | | Case 2: % 150.82/22.04 | | | % 150.82/22.04 | | | (37) all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1 % 150.82/22.04 | | | % 150.82/22.04 | | | BETA: splitting (37) gives: % 150.82/22.04 | | | % 150.82/22.04 | | | Case 1: % 150.82/22.04 | | | | % 150.82/22.04 | | | | (38) all_58_3 = e1 % 150.82/22.04 | | | | % 150.82/22.04 | | | | REF_CLOSE: (11), (15), (38) are inconsistent by sub-proof #338. % 150.82/22.04 | | | | % 150.82/22.04 | | | Case 2: % 150.82/22.04 | | | | % 150.82/22.04 | | | | (39) all_58_5 = e1 | all_58_10 = e1 % 150.82/22.04 | | | | % 150.82/22.04 | | | | BETA: splitting (39) gives: % 150.82/22.04 | | | | % 150.82/22.04 | | | | Case 1: % 150.82/22.04 | | | | | % 150.82/22.04 | | | | | (40) all_58_5 = e1 % 150.82/22.04 | | | | | % 150.82/22.04 | | | | | COMBINE_EQS: (10), (40) imply: % 150.82/22.04 | | | | | (41) all_8_0 = e1 % 150.82/22.04 | | | | | % 150.82/22.04 | | | | | REDUCE: (2), (41) imply: % 150.82/22.04 | | | | | (42) ~ (all_6_2 = e1) % 150.82/22.04 | | | | | % 150.82/22.04 | | | | | SIMP: (42) implies: % 150.82/22.04 | | | | | (43) ~ (all_6_2 = e1) % 150.82/22.04 | | | | | % 150.82/22.04 | | | | | BETA: splitting (20) gives: % 150.82/22.04 | | | | | % 150.82/22.04 | | | | | Case 1: % 150.82/22.04 | | | | | | % 150.82/22.04 | | | | | | (44) all_56_1 = e3 % 150.82/22.04 | | | | | | % 150.82/22.04 | | | | | | COMBINE_EQS: (8), (44) imply: % 150.82/22.04 | | | | | | (45) all_10_2 = e3 % 150.82/22.04 | | | | | | % 150.82/22.04 | | | | | | REDUCE: (33), (45) imply: % 150.82/22.04 | | | | | | (46) $false % 150.82/22.04 | | | | | | % 150.82/22.04 | | | | | | CLOSE: (46) is inconsistent. % 150.82/22.04 | | | | | | % 150.82/22.04 | | | | | Case 2: % 150.82/22.04 | | | | | | % 150.82/22.04 | | | | | | (47) all_56_11 = e2 | all_56_21 = e1 | all_56_31 = e0 % 150.82/22.04 | | | | | | % 150.82/22.04 | | | | | | BETA: splitting (47) gives: % 150.82/22.04 | | | | | | % 150.82/22.04 | | | | | | Case 1: % 150.82/22.04 | | | | | | | % 150.82/22.04 | | | | | | | (48) all_56_11 = e2 % 150.82/22.04 | | | | | | | % 150.82/22.04 | | | | | | | REF_CLOSE: (22), (27), (48) are inconsistent by sub-proof #427. % 150.82/22.04 | | | | | | | % 150.82/22.04 | | | | | | Case 2: % 150.82/22.04 | | | | | | | % 150.82/22.04 | | | | | | | (49) all_56_21 = e1 | all_56_31 = e0 % 150.82/22.04 | | | | | | | % 150.82/22.04 | | | | | | | BETA: splitting (49) gives: % 150.82/22.04 | | | | | | | % 150.82/22.04 | | | | | | | Case 1: % 150.82/22.04 | | | | | | | | % 150.82/22.04 | | | | | | | | (50) all_56_21 = e1 % 150.82/22.04 | | | | | | | | % 150.82/22.04 | | | | | | | | COMBINE_EQS: (7), (50) imply: % 150.82/22.04 | | | | | | | | (51) all_6_2 = e1 % 150.82/22.04 | | | | | | | | % 150.82/22.04 | | | | | | | | REDUCE: (43), (51) imply: % 150.82/22.04 | | | | | | | | (52) $false % 150.82/22.04 | | | | | | | | % 150.82/22.04 | | | | | | | | CLOSE: (52) is inconsistent. % 150.82/22.04 | | | | | | | | % 150.82/22.04 | | | | | | | Case 2: % 150.82/22.04 | | | | | | | | % 150.82/22.04 | | | | | | | | (53) all_56_31 = e0 % 150.82/22.04 | | | | | | | | % 150.82/22.04 | | | | | | | | COMBINE_EQS: (18), (53) imply: % 150.82/22.04 | | | | | | | | (54) all_4_2 = e0 % 150.82/22.04 | | | | | | | | % 150.82/22.04 | | | | | | | | SIMP: (54) implies: % 150.82/22.04 | | | | | | | | (55) all_4_2 = e0 % 150.82/22.04 | | | | | | | | % 150.82/22.04 | | | | | | | | REDUCE: (17), (55) imply: % 150.82/22.04 | | | | | | | | (56) op(e0, e0) = all_4_1 % 150.82/22.04 | | | | | | | | % 150.82/22.04 | | | | | | | | REDUCE: (25), (55) imply: % 150.82/22.04 | | | | | | | | (57) op(e0, e0) = all_56_30 % 150.82/22.04 | | | | | | | | % 150.82/22.04 | | | | | | | | REDUCE: (5), (55) imply: % 150.82/22.04 | | | | | | | | (58) op(e0, e0) = e0 % 150.82/22.04 | | | | | | | | % 150.82/22.04 | | | | | | | | REF_CLOSE: (1), (11), (13), (56), (57), (58) are inconsistent by % 150.82/22.04 | | | | | | | | sub-proof #389. % 150.82/22.04 | | | | | | | | % 150.82/22.04 | | | | | | | End of split % 150.82/22.04 | | | | | | | % 150.82/22.04 | | | | | | End of split % 150.82/22.04 | | | | | | % 150.82/22.04 | | | | | End of split % 150.82/22.04 | | | | | % 150.82/22.04 | | | | Case 2: % 150.82/22.04 | | | | | % 150.82/22.04 | | | | | (59) all_58_10 = e1 % 150.82/22.04 | | | | | % 150.82/22.04 | | | | | COMBINE_EQS: (6), (59) imply: % 150.82/22.04 | | | | | (60) e2 = e1 % 150.82/22.04 | | | | | % 150.82/22.04 | | | | | REDUCE: (16), (60) imply: % 150.82/22.04 | | | | | (61) $false % 150.82/22.04 | | | | | % 150.82/22.04 | | | | | CLOSE: (61) is inconsistent. % 150.82/22.04 | | | | | % 150.82/22.04 | | | | End of split % 150.82/22.04 | | | | % 150.82/22.04 | | | End of split % 150.82/22.04 | | | % 150.82/22.04 | | End of split % 150.82/22.04 | | % 150.82/22.04 | Case 2: % 150.82/22.04 | | % 150.82/22.04 | | (62) all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3 % 150.82/22.04 | | % 150.82/22.04 | | REF_CLOSE: (3), (4), (6), (9), (10), (14), (15), (19), (21), (24), (26), % 150.82/22.04 | | (62) are inconsistent by sub-proof #129. % 150.82/22.04 | | % 150.82/22.04 | End of split % 150.82/22.04 | % 150.82/22.04 End of proof % 150.82/22.04 % 150.82/22.04 Sub-proof #129 shows that the following formulas are inconsistent: % 150.82/22.04 ---------------------------------------------------------------- % 150.82/22.04 (1) ~ (e3 = e0) % 150.82/22.04 (2) all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3 % 150.82/22.04 (3) ~ (e3 = e2) % 150.82/22.04 (4) all_58_10 = e2 % 150.82/22.04 (5) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0 % 150.82/22.04 (6) all_58_5 = all_8_0 % 150.82/22.04 (7) ~ (all_8_0 = e0) % 150.82/22.04 (8) all_58_3 = e0 % 150.82/22.04 (9) ~ (all_8_0 = e3) % 150.82/22.04 (10) ~ (all_8_0 = e2) % 150.82/22.04 (11) ~ (e3 = e1) % 150.82/22.04 (12) all_54_6 = all_8_0 % 150.82/22.04 % 150.82/22.04 Begin of proof % 150.82/22.04 | % 150.82/22.04 | BETA: splitting (2) gives: % 150.82/22.04 | % 150.82/22.04 | Case 1: % 150.82/22.04 | | % 150.82/22.04 | | (13) all_58_3 = e3 % 150.82/22.04 | | % 150.82/22.04 | | REF_CLOSE: (1), (8), (13) are inconsistent by sub-proof #632. % 150.82/22.04 | | % 150.82/22.04 | Case 2: % 150.82/22.04 | | % 150.82/22.04 | | (14) all_58_5 = e3 | all_58_10 = e3 % 150.82/22.04 | | % 150.82/22.04 | | BETA: splitting (5) gives: % 150.82/22.04 | | % 150.82/22.04 | | Case 1: % 150.82/22.04 | | | % 150.82/22.04 | | | (15) all_54_6 = e3 % 150.82/22.04 | | | % 150.82/22.04 | | | COMBINE_EQS: (12), (15) imply: % 150.82/22.04 | | | (16) all_8_0 = e3 % 150.82/22.04 | | | % 150.82/22.04 | | | REDUCE: (9), (16) imply: % 150.82/22.04 | | | (17) $false % 150.82/22.04 | | | % 150.82/22.04 | | | CLOSE: (17) is inconsistent. % 150.82/22.04 | | | % 150.82/22.04 | | Case 2: % 150.82/22.04 | | | % 150.82/22.04 | | | (18) all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0 % 150.82/22.04 | | | % 150.82/22.04 | | | BETA: splitting (18) gives: % 150.82/22.04 | | | % 150.82/22.04 | | | Case 1: % 150.82/22.04 | | | | % 150.82/22.04 | | | | (19) all_54_6 = e2 % 150.82/22.04 | | | | % 150.82/22.04 | | | | COMBINE_EQS: (12), (19) imply: % 150.82/22.04 | | | | (20) all_8_0 = e2 % 150.82/22.04 | | | | % 150.82/22.04 | | | | REDUCE: (10), (20) imply: % 150.82/22.04 | | | | (21) $false % 150.82/22.04 | | | | % 150.82/22.04 | | | | CLOSE: (21) is inconsistent. % 150.82/22.04 | | | | % 150.82/22.04 | | | Case 2: % 150.82/22.04 | | | | % 150.82/22.04 | | | | (22) all_54_6 = e1 | all_54_6 = e0 % 150.82/22.04 | | | | % 150.82/22.04 | | | | BETA: splitting (22) gives: % 150.82/22.04 | | | | % 150.82/22.04 | | | | Case 1: % 150.82/22.04 | | | | | % 150.82/22.04 | | | | | (23) all_54_6 = e1 % 150.82/22.04 | | | | | % 150.82/22.04 | | | | | COMBINE_EQS: (12), (23) imply: % 150.82/22.04 | | | | | (24) all_8_0 = e1 % 150.82/22.04 | | | | | % 150.82/22.04 | | | | | COMBINE_EQS: (6), (24) imply: % 150.82/22.04 | | | | | (25) all_58_5 = e1 % 150.82/22.04 | | | | | % 150.82/22.04 | | | | | REF_CLOSE: (3), (4), (11), (14), (25) are inconsistent by sub-proof % 150.82/22.04 | | | | | #612. % 150.82/22.04 | | | | | % 150.82/22.04 | | | | Case 2: % 150.82/22.04 | | | | | % 150.82/22.04 | | | | | (26) all_54_6 = e0 % 150.82/22.04 | | | | | % 150.82/22.04 | | | | | COMBINE_EQS: (12), (26) imply: % 150.82/22.04 | | | | | (27) all_8_0 = e0 % 150.82/22.04 | | | | | % 150.82/22.04 | | | | | REDUCE: (7), (27) imply: % 150.82/22.04 | | | | | (28) $false % 150.82/22.04 | | | | | % 150.82/22.04 | | | | | CLOSE: (28) is inconsistent. % 150.82/22.04 | | | | | % 150.82/22.04 | | | | End of split % 150.82/22.04 | | | | % 150.82/22.04 | | | End of split % 150.82/22.04 | | | % 150.82/22.04 | | End of split % 150.82/22.04 | | % 150.82/22.04 | End of split % 150.82/22.04 | % 150.82/22.04 End of proof % 150.82/22.04 % 150.82/22.04 Sub-proof #130 shows that the following formulas are inconsistent: % 150.82/22.04 ---------------------------------------------------------------- % 150.82/22.04 (1) all_56_11 = all_8_2 % 150.82/22.04 (2) all_54_9 = all_52_6 % 150.82/22.04 (3) ~ (all_6_1 = e2) % 150.82/22.04 (4) all_54_0 = all_10_2 % 150.82/22.04 (5) all_56_21 = e3 % 150.82/22.04 (6) ~ (all_52_14 = all_4_2) % 150.82/22.04 (7) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0 % 150.82/22.04 (8) ~ (all_52_12 = all_52_13) % 150.82/22.04 (9) ~ (all_6_1 = e3) % 150.82/22.04 (10) ~ (all_52_6 = all_52_14) % 150.82/22.04 (11) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 150.82/22.04 (12) ~ (all_6_0 = e2) % 150.82/22.04 (13) all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1 % 150.82/22.04 (14) all_56_21 = all_6_2 % 150.82/22.04 (15) all_56_1 = all_10_2 % 150.82/22.04 (16) all_58_5 = all_52_9 % 150.82/22.04 (17) all_56_17 = all_52_2 % 150.82/22.04 (18) all_58_9 = all_52_12 % 150.82/22.04 (19) op(e1, e0) = all_52_14 % 150.82/22.04 (20) op(e3, e3) = all_10_2 % 150.82/22.04 (21) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 150.82/22.04 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 150.82/22.04 (22) all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0 % 150.82/22.04 (23) ~ (all_52_2 = all_52_6) % 150.82/22.04 (24) all_56_7 = all_52_12 % 150.82/22.04 (25) ~ (all_4_2 = e1) % 150.82/22.04 (26) ~ (all_56_1 = e0) | all_56_7 = e3 % 150.82/22.04 (27) op(e1, all_6_1) = all_6_0 % 150.82/22.04 (28) all_58_3 = all_8_2 % 150.82/22.04 (29) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0 % 150.82/22.04 (30) all_56_31 = all_4_2 % 150.82/22.04 (31) all_58_11 = all_52_14 % 150.82/22.04 (32) ~ (all_52_2 = all_52_14) % 150.82/22.04 (33) op(all_6_2, all_6_2) = all_6_1 % 150.82/22.04 (34) all_56_1 = e3 | all_56_11 = e2 | all_56_21 = e1 | all_56_31 = e0 % 150.82/22.04 (35) all_56_17 = e1 % 150.82/22.04 (36) ~ (all_52_13 = all_52_14) % 150.82/22.04 (37) ~ (all_52_6 = all_8_2) % 150.82/22.04 (38) all_58_15 = all_4_2 % 150.82/22.04 (39) all_58_2 = all_52_1 % 150.82/22.04 (40) all_58_10 = all_52_13 % 150.82/22.04 (41) ~ (all_52_12 = all_52_14) % 150.82/22.04 (42) op(e1, all_52_9) = all_56_12 % 150.82/22.04 (43) ~ (all_52_2 = all_6_2) % 150.82/22.04 (44) ~ (all_52_6 = all_6_2) % 150.82/22.04 (45) ~ (all_8_2 = e0) % 150.82/22.04 (46) ~ (all_52_2 = all_10_2) % 150.82/22.04 (47) ~ (all_52_1 = all_10_2) % 150.82/22.04 (48) all_54_11 = all_52_14 % 150.82/22.04 % 150.82/22.04 Begin of proof % 150.82/22.04 | % 150.82/22.04 | COMBINE_EQS: (17), (35) imply: % 150.82/22.04 | (49) all_52_2 = e1 % 150.82/22.04 | % 150.82/22.04 | SIMP: (49) implies: % 150.82/22.04 | (50) all_52_2 = e1 % 150.82/22.04 | % 150.82/22.04 | COMBINE_EQS: (5), (14) imply: % 150.82/22.04 | (51) all_6_2 = e3 % 150.82/22.04 | % 150.82/22.04 | SIMP: (51) implies: % 150.82/22.04 | (52) all_6_2 = e3 % 150.82/22.04 | % 150.82/22.04 | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), % 150.82/22.04 | (13), (15), (16), (18), (19), (20), (21), (22), (23), (24), (25), % 150.82/22.04 | (26), (27), (28), (29), (30), (31), (32), (33), (34), (36), (37), % 150.82/22.04 | (38), (39), (40), (41), (42), (43), (44), (45), (46), (47), (48), % 150.82/22.04 | (50), (52) are inconsistent by sub-proof #293. % 150.82/22.04 | % 150.82/22.04 End of proof % 150.82/22.04 % 150.82/22.04 Sub-proof #131 shows that the following formulas are inconsistent: % 150.82/22.04 ---------------------------------------------------------------- % 150.82/22.04 (1) all_54_9 = all_52_6 % 150.82/22.04 (2) ~ (all_52_6 = e1) % 150.82/22.04 (3) op(e2, e2) = all_10_1 % 150.82/22.04 (4) ~ (all_4_1 = e3) % 150.82/22.04 (5) all_54_5 = all_8_2 % 150.82/22.04 (6) ~ (all_10_1 = e1) % 150.82/22.04 (7) ~ (all_52_6 = e3) % 150.82/22.04 (8) ~ (all_52_6 = all_4_1) % 150.82/22.04 (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 150.82/22.04 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 150.82/22.04 (10) ~ (all_52_6 = e0) % 150.82/22.04 (11) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0 % 150.82/22.04 (12) all_54_5 = all_4_1 % 150.82/22.04 (13) op(e2, e2) = all_8_2 % 150.82/22.04 (14) ~ (all_8_2 = e0) % 150.82/22.04 (15) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 150.82/22.04 % 150.82/22.04 Begin of proof % 150.82/22.04 | % 150.82/22.04 | BETA: splitting (11) gives: % 150.82/22.04 | % 150.82/22.04 | Case 1: % 150.82/22.04 | | % 150.82/22.04 | | (16) all_54_9 = e3 % 150.82/22.04 | | % 150.82/22.04 | | REF_CLOSE: (1), (7), (16) are inconsistent by sub-proof #680. % 150.82/22.04 | | % 150.82/22.04 | Case 2: % 150.82/22.04 | | % 150.82/22.04 | | (17) all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0 % 150.82/22.04 | | % 150.82/22.04 | | BETA: splitting (17) gives: % 150.82/22.04 | | % 150.82/22.04 | | Case 1: % 150.82/22.04 | | | % 150.82/22.04 | | | (18) all_54_9 = e2 % 150.82/22.04 | | | % 150.82/22.04 | | | COMBINE_EQS: (1), (18) imply: % 150.82/22.04 | | | (19) all_52_6 = e2 % 150.82/22.04 | | | % 150.82/22.04 | | | SIMP: (19) implies: % 150.82/22.04 | | | (20) all_52_6 = e2 % 150.82/22.04 | | | % 150.82/22.04 | | | REDUCE: (8), (20) imply: % 150.82/22.04 | | | (21) ~ (all_4_1 = e2) % 150.82/22.04 | | | % 150.82/22.04 | | | SIMP: (21) implies: % 150.82/22.04 | | | (22) ~ (all_4_1 = e2) % 150.82/22.04 | | | % 150.82/22.04 | | | BETA: splitting (15) gives: % 150.82/22.04 | | | % 150.82/22.04 | | | Case 1: % 150.82/22.04 | | | | % 150.82/22.04 | | | | (23) all_54_5 = e3 % 150.82/22.04 | | | | % 150.82/22.04 | | | | REF_CLOSE: (4), (12), (23) are inconsistent by sub-proof #199. % 150.82/22.04 | | | | % 150.82/22.04 | | | Case 2: % 150.82/22.04 | | | | % 150.82/22.04 | | | | (24) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 150.82/22.04 | | | | % 150.82/22.04 | | | | BETA: splitting (24) gives: % 150.82/22.04 | | | | % 150.82/22.04 | | | | Case 1: % 150.82/22.04 | | | | | % 150.82/22.04 | | | | | (25) all_54_5 = e2 % 150.82/22.04 | | | | | % 150.82/22.04 | | | | | REF_CLOSE: (12), (22), (25) are inconsistent by sub-proof #570. % 150.82/22.04 | | | | | % 150.82/22.04 | | | | Case 2: % 150.82/22.04 | | | | | % 150.82/22.04 | | | | | (26) all_54_5 = e1 | all_54_5 = e0 % 150.82/22.04 | | | | | % 150.82/22.04 | | | | | REF_CLOSE: (3), (5), (6), (9), (13), (14), (26) are inconsistent by % 150.82/22.04 | | | | | sub-proof #132. % 150.82/22.04 | | | | | % 150.82/22.04 | | | | End of split % 150.82/22.04 | | | | % 150.82/22.04 | | | End of split % 150.82/22.04 | | | % 150.82/22.04 | | Case 2: % 150.82/22.04 | | | % 150.82/22.04 | | | (27) all_54_9 = e1 | all_54_9 = e0 % 150.82/22.04 | | | % 150.82/22.04 | | | REF_CLOSE: (1), (2), (10), (27) are inconsistent by sub-proof #678. % 150.82/22.04 | | | % 150.82/22.04 | | End of split % 150.82/22.04 | | % 150.82/22.04 | End of split % 150.82/22.04 | % 150.82/22.04 End of proof % 150.82/22.04 % 150.82/22.04 Sub-proof #132 shows that the following formulas are inconsistent: % 150.82/22.04 ---------------------------------------------------------------- % 150.82/22.04 (1) op(e2, e2) = all_10_1 % 150.82/22.04 (2) all_54_5 = all_8_2 % 150.82/22.04 (3) ~ (all_10_1 = e1) % 150.82/22.04 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 150.82/22.04 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 150.82/22.04 (5) all_54_5 = e1 | all_54_5 = e0 % 150.82/22.04 (6) op(e2, e2) = all_8_2 % 150.82/22.04 (7) ~ (all_8_2 = e0) % 150.82/22.04 % 150.82/22.04 Begin of proof % 150.82/22.04 | % 150.82/22.04 | BETA: splitting (5) gives: % 150.82/22.04 | % 150.82/22.04 | Case 1: % 150.82/22.04 | | % 150.82/22.04 | | (8) all_54_5 = e1 % 150.82/22.04 | | % 150.82/22.04 | | COMBINE_EQS: (2), (8) imply: % 150.82/22.04 | | (9) all_8_2 = e1 % 150.82/22.04 | | % 150.82/22.04 | | SIMP: (9) implies: % 150.82/22.04 | | (10) all_8_2 = e1 % 150.82/22.04 | | % 150.82/22.04 | | REDUCE: (6), (10) imply: % 150.82/22.04 | | (11) op(e2, e2) = e1 % 150.82/22.04 | | % 150.82/22.04 | | GROUND_INST: instantiating (4) with e1, all_10_1, e2, e2, simplifying with % 150.82/22.04 | | (1), (11) gives: % 150.82/22.04 | | (12) all_10_1 = e1 % 150.82/22.04 | | % 150.82/22.04 | | REDUCE: (3), (12) imply: % 150.82/22.04 | | (13) $false % 150.82/22.04 | | % 150.82/22.04 | | CLOSE: (13) is inconsistent. % 150.82/22.04 | | % 150.82/22.04 | Case 2: % 150.82/22.04 | | % 150.82/22.04 | | (14) all_54_5 = e0 % 150.82/22.05 | | % 150.82/22.05 | | REF_CLOSE: (2), (7), (14) are inconsistent by sub-proof #646. % 150.82/22.05 | | % 150.82/22.05 | End of split % 150.82/22.05 | % 150.82/22.05 End of proof % 150.82/22.05 % 150.82/22.05 Sub-proof #133 shows that the following formulas are inconsistent: % 150.82/22.05 ---------------------------------------------------------------- % 150.82/22.05 (1) all_56_11 = all_8_2 % 150.82/22.05 (2) ~ (all_56_11 = e1) | all_56_13 = e2 % 150.82/22.05 (3) ~ (all_8_0 = all_6_2) % 150.82/22.05 (4) ~ (all_8_0 = e1) % 150.82/22.05 (5) all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2 % 150.82/22.05 (6) ~ (all_52_12 = all_52_13) % 150.82/22.05 (7) ~ (all_52_12 = e2) % 150.82/22.05 (8) ~ (all_52_13 = all_8_0) % 150.82/22.05 (9) all_58_4 = all_52_8 % 150.82/22.05 (10) all_54_5 = all_8_2 % 150.82/22.05 (11) ~ (all_10_2 = e1) % 150.82/22.05 (12) ~ (all_52_1 = e1) % 150.82/22.05 (13) all_58_3 = all_4_1 % 150.82/22.05 (14) all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1 % 150.82/22.05 (15) ~ (all_8_0 = all_8_2) % 150.82/22.05 (16) all_56_21 = all_6_2 % 150.82/22.05 (17) all_56_1 = all_10_2 % 150.82/22.05 (18) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0 % 150.82/22.05 (19) all_58_9 = all_52_12 % 150.82/22.05 (20) op(e0, all_52_12) = all_56_6 % 150.82/22.05 (21) ~ (all_10_2 = e2) % 150.82/22.05 (22) all_58_1 = all_52_4 % 150.82/22.05 (23) all_58_5 = all_8_0 % 150.82/22.05 (24) op(e2, all_8_2) = all_56_10 % 150.82/22.05 (25) op(e3, e3) = all_10_2 % 150.82/22.05 (26) ~ (all_52_8 = all_8_0) % 150.82/22.05 (27) all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1 % 150.82/22.05 (28) ~ (all_52_13 = all_4_1) % 150.82/22.05 (29) op(e0, e1) = e3 % 150.82/22.05 (30) all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1 % 150.82/22.05 (31) ~ (all_52_1 = all_8_2) % 150.82/22.05 (32) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 150.82/22.05 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 150.82/22.05 (33) all_56_11 = all_4_1 % 150.82/22.05 (34) all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0 % 150.82/22.05 (35) ~ (all_52_14 = e1) % 150.82/22.05 (36) ~ (all_56_11 = e3) | all_56_9 = e2 % 150.82/22.05 (37) op(e0, all_4_1) = all_4_0 % 150.82/22.05 (38) ~ (all_4_2 = e1) % 150.82/22.05 (39) ~ (e2 = e1) % 150.82/22.05 (40) all_58_3 = all_8_2 % 150.82/22.05 (41) all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1 % 150.82/22.05 (42) all_56_31 = all_4_2 % 150.82/22.05 (43) all_58_11 = all_52_14 % 150.82/22.05 (44) ~ (all_8_0 = e3) % 150.82/22.05 (45) all_56_13 = all_8_0 % 150.82/22.05 (46) ~ (all_52_8 = e1) % 150.82/22.05 (47) ~ (all_52_1 = all_8_0) % 150.82/22.05 (48) all_56_1 = e3 | all_56_11 = e2 | all_56_21 = e1 | all_56_31 = e0 % 150.82/22.05 (49) ~ (all_52_13 = all_4_2) % 150.82/22.05 (50) ~ (all_8_0 = e0) | ~ (all_8_2 = e3) % 150.82/22.05 (51) op(all_8_2, all_8_2) = e1 % 150.82/22.05 (52) all_58_15 = all_4_2 % 150.82/22.05 (53) all_58_2 = all_52_1 % 150.82/22.05 (54) all_58_10 = all_52_13 % 150.82/22.05 (55) all_58_0 = all_10_2 % 150.82/22.05 (56) op(e2, e2) = all_8_2 % 150.82/22.05 (57) ~ (all_8_2 = e0) % 150.82/22.05 (58) all_54_6 = all_8_0 % 150.82/22.05 (59) ~ (e2 = e0) % 150.82/22.05 (60) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 150.82/22.05 (61) ~ (all_4_0 = e3) % 150.82/22.05 (62) all_56_9 = all_52_1 % 150.82/22.05 % 150.82/22.05 Begin of proof % 150.82/22.05 | % 150.82/22.05 | BETA: splitting (2) gives: % 150.82/22.05 | % 150.82/22.05 | Case 1: % 150.82/22.05 | | % 150.82/22.05 | | (63) ~ (all_56_11 = e1) % 150.82/22.05 | | % 150.82/22.05 | | REDUCE: (33), (63) imply: % 150.82/22.05 | | (64) ~ (all_4_1 = e1) % 150.82/22.05 | | % 150.82/22.05 | | BETA: splitting (41) gives: % 150.82/22.05 | | % 150.82/22.05 | | Case 1: % 150.82/22.05 | | | % 150.82/22.05 | | | (65) all_58_1 = e1 % 150.82/22.05 | | | % 150.82/22.05 | | | COMBINE_EQS: (22), (65) imply: % 150.82/22.05 | | | (66) all_52_4 = e1 % 150.82/22.05 | | | % 150.82/22.05 | | | BETA: splitting (5) gives: % 150.82/22.05 | | | % 150.82/22.05 | | | Case 1: % 150.82/22.05 | | | | % 150.82/22.05 | | | | (67) all_58_0 = e2 % 150.82/22.05 | | | | % 150.82/22.05 | | | | COMBINE_EQS: (55), (67) imply: % 150.82/22.05 | | | | (68) all_10_2 = e2 % 150.82/22.05 | | | | % 150.82/22.05 | | | | REDUCE: (21), (68) imply: % 150.82/22.05 | | | | (69) $false % 150.82/22.05 | | | | % 150.82/22.05 | | | | CLOSE: (69) is inconsistent. % 150.82/22.05 | | | | % 150.82/22.05 | | | Case 2: % 150.82/22.05 | | | | % 150.82/22.05 | | | | (70) all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2 % 150.82/22.05 | | | | % 150.82/22.05 | | | | BETA: splitting (70) gives: % 150.82/22.05 | | | | % 150.82/22.05 | | | | Case 1: % 150.82/22.05 | | | | | % 150.82/22.05 | | | | | (71) all_58_1 = e2 % 150.82/22.05 | | | | | % 150.82/22.05 | | | | | REF_CLOSE: (39), (65), (71) are inconsistent by sub-proof #594. % 150.82/22.05 | | | | | % 150.82/22.05 | | | | Case 2: % 150.82/22.05 | | | | | % 150.82/22.05 | | | | | (72) all_58_4 = e2 | all_58_9 = e2 % 150.82/22.05 | | | | | % 150.82/22.05 | | | | | BETA: splitting (72) gives: % 150.82/22.05 | | | | | % 150.82/22.05 | | | | | Case 1: % 150.82/22.05 | | | | | | % 150.82/22.05 | | | | | | (73) all_58_4 = e2 % 150.82/22.05 | | | | | | % 150.82/22.05 | | | | | | COMBINE_EQS: (9), (73) imply: % 150.82/22.05 | | | | | | (74) all_52_8 = e2 % 150.82/22.05 | | | | | | % 150.82/22.05 | | | | | | REDUCE: (26), (74) imply: % 150.82/22.05 | | | | | | (75) ~ (all_8_0 = e2) % 150.82/22.05 | | | | | | % 150.82/22.05 | | | | | | SIMP: (75) implies: % 150.82/22.05 | | | | | | (76) ~ (all_8_0 = e2) % 150.82/22.05 | | | | | | % 150.82/22.05 | | | | | | BETA: splitting (18) gives: % 150.82/22.05 | | | | | | % 150.82/22.05 | | | | | | Case 1: % 150.82/22.05 | | | | | | | % 150.82/22.05 | | | | | | | (77) all_54_6 = e3 % 150.82/22.05 | | | | | | | % 150.82/22.05 | | | | | | | REF_CLOSE: (44), (58), (77) are inconsistent by sub-proof #145. % 150.82/22.05 | | | | | | | % 150.82/22.05 | | | | | | Case 2: % 150.82/22.05 | | | | | | | % 150.82/22.05 | | | | | | | (78) all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0 % 150.82/22.05 | | | | | | | % 150.82/22.05 | | | | | | | BETA: splitting (78) gives: % 150.82/22.05 | | | | | | | % 150.82/22.05 | | | | | | | Case 1: % 150.82/22.05 | | | | | | | | % 150.82/22.05 | | | | | | | | (79) all_54_6 = e2 % 150.82/22.05 | | | | | | | | % 150.82/22.05 | | | | | | | | REF_CLOSE: (58), (76), (79) are inconsistent by sub-proof #144. % 150.82/22.05 | | | | | | | | % 150.82/22.05 | | | | | | | Case 2: % 150.82/22.05 | | | | | | | | % 150.82/22.05 | | | | | | | | (80) all_54_6 = e1 | all_54_6 = e0 % 150.82/22.05 | | | | | | | | % 150.82/22.05 | | | | | | | | BETA: splitting (80) gives: % 150.82/22.05 | | | | | | | | % 150.82/22.05 | | | | | | | | Case 1: % 150.82/22.05 | | | | | | | | | % 150.82/22.05 | | | | | | | | | (81) all_54_6 = e1 % 150.82/22.05 | | | | | | | | | % 150.82/22.05 | | | | | | | | | COMBINE_EQS: (58), (81) imply: % 150.82/22.05 | | | | | | | | | (82) all_8_0 = e1 % 150.82/22.05 | | | | | | | | | % 150.82/22.05 | | | | | | | | | SIMP: (82) implies: % 150.82/22.05 | | | | | | | | | (83) all_8_0 = e1 % 150.82/22.05 | | | | | | | | | % 150.82/22.05 | | | | | | | | | REDUCE: (4), (83) imply: % 150.82/22.05 | | | | | | | | | (84) $false % 150.82/22.05 | | | | | | | | | % 150.82/22.05 | | | | | | | | | CLOSE: (84) is inconsistent. % 150.82/22.05 | | | | | | | | | % 150.82/22.05 | | | | | | | | Case 2: % 150.82/22.05 | | | | | | | | | % 150.82/22.05 | | | | | | | | | (85) all_54_6 = e0 % 150.82/22.05 | | | | | | | | | % 150.82/22.05 | | | | | | | | | COMBINE_EQS: (58), (85) imply: % 150.82/22.05 | | | | | | | | | (86) all_8_0 = e0 % 150.82/22.05 | | | | | | | | | % 150.82/22.05 | | | | | | | | | SIMP: (86) implies: % 150.82/22.05 | | | | | | | | | (87) all_8_0 = e0 % 150.82/22.05 | | | | | | | | | % 150.82/22.05 | | | | | | | | | COMBINE_EQS: (45), (87) imply: % 150.82/22.05 | | | | | | | | | (88) all_56_13 = e0 % 150.82/22.05 | | | | | | | | | % 150.82/22.05 | | | | | | | | | REF_CLOSE: (1), (2), (3), (8), (10), (15), (16), (17), (18), % 150.82/22.05 | | | | | | | | | (23), (24), (25), (31), (32), (34), (36), (40), % 150.82/22.05 | | | | | | | | | (42), (47), (48), (49), (50), (51), (53), (54), % 150.82/22.05 | | | | | | | | | (56), (57), (58), (59), (60), (62), (88) are % 150.82/22.05 | | | | | | | | | inconsistent by sub-proof #134. % 150.82/22.05 | | | | | | | | | % 150.82/22.05 | | | | | | | | End of split % 150.82/22.05 | | | | | | | | % 150.82/22.05 | | | | | | | End of split % 150.82/22.05 | | | | | | | % 150.82/22.05 | | | | | | End of split % 150.82/22.05 | | | | | | % 150.82/22.05 | | | | | Case 2: % 150.82/22.05 | | | | | | % 150.82/22.05 | | | | | | (89) all_58_9 = e2 % 150.82/22.05 | | | | | | % 150.82/22.05 | | | | | | COMBINE_EQS: (19), (89) imply: % 150.82/22.05 | | | | | | (90) all_52_12 = e2 % 150.82/22.05 | | | | | | % 150.82/22.05 | | | | | | REDUCE: (7), (90) imply: % 150.82/22.05 | | | | | | (91) $false % 150.82/22.05 | | | | | | % 150.82/22.05 | | | | | | CLOSE: (91) is inconsistent. % 150.82/22.05 | | | | | | % 150.82/22.05 | | | | | End of split % 150.82/22.05 | | | | | % 150.82/22.05 | | | | End of split % 150.82/22.05 | | | | % 150.82/22.05 | | | End of split % 150.82/22.05 | | | % 150.82/22.05 | | Case 2: % 150.82/22.05 | | | % 150.82/22.05 | | | (92) ~ (all_58_1 = e1) % 150.82/22.05 | | | % 150.82/22.05 | | | REDUCE: (22), (92) imply: % 150.82/22.05 | | | (93) ~ (all_52_4 = e1) % 150.82/22.05 | | | % 150.82/22.05 | | | BETA: splitting (27) gives: % 150.82/22.05 | | | % 150.82/22.05 | | | Case 1: % 150.82/22.05 | | | | % 150.82/22.05 | | | | (94) all_58_0 = e1 % 150.82/22.05 | | | | % 150.82/22.05 | | | | COMBINE_EQS: (55), (94) imply: % 150.82/22.05 | | | | (95) all_10_2 = e1 % 150.82/22.05 | | | | % 150.82/22.05 | | | | REDUCE: (11), (95) imply: % 150.82/22.05 | | | | (96) $false % 150.82/22.05 | | | | % 150.82/22.05 | | | | CLOSE: (96) is inconsistent. % 150.82/22.05 | | | | % 150.82/22.05 | | | Case 2: % 150.82/22.05 | | | | % 150.82/22.05 | | | | (97) all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1 % 150.82/22.05 | | | | % 150.82/22.05 | | | | BETA: splitting (30) gives: % 150.82/22.05 | | | | % 150.82/22.05 | | | | Case 1: % 150.82/22.05 | | | | | % 150.82/22.05 | | | | | (98) all_58_2 = e1 % 150.82/22.05 | | | | | % 150.82/22.05 | | | | | COMBINE_EQS: (53), (98) imply: % 150.82/22.05 | | | | | (99) all_52_1 = e1 % 150.82/22.05 | | | | | % 150.82/22.05 | | | | | REDUCE: (12), (99) imply: % 150.82/22.05 | | | | | (100) $false % 150.82/22.05 | | | | | % 150.82/22.05 | | | | | CLOSE: (100) is inconsistent. % 150.82/22.05 | | | | | % 150.82/22.05 | | | | Case 2: % 150.82/22.05 | | | | | % 150.82/22.05 | | | | | (101) all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1 % 150.82/22.05 | | | | | % 150.82/22.05 | | | | | BETA: splitting (101) gives: % 150.82/22.05 | | | | | % 150.82/22.05 | | | | | Case 1: % 150.82/22.05 | | | | | | % 150.82/22.05 | | | | | | (102) all_58_3 = e1 % 150.82/22.05 | | | | | | % 150.82/22.05 | | | | | | COMBINE_EQS: (13), (102) imply: % 150.82/22.05 | | | | | | (103) all_4_1 = e1 % 150.82/22.05 | | | | | | % 150.82/22.05 | | | | | | REDUCE: (64), (103) imply: % 150.82/22.05 | | | | | | (104) $false % 150.82/22.05 | | | | | | % 150.82/22.05 | | | | | | CLOSE: (104) is inconsistent. % 150.82/22.05 | | | | | | % 150.82/22.05 | | | | | Case 2: % 150.82/22.05 | | | | | | % 150.82/22.05 | | | | | | (105) all_58_5 = e1 | all_58_10 = e1 % 150.82/22.05 | | | | | | % 150.82/22.05 | | | | | | BETA: splitting (105) gives: % 150.82/22.05 | | | | | | % 150.82/22.05 | | | | | | Case 1: % 150.82/22.05 | | | | | | | % 150.82/22.05 | | | | | | | (106) all_58_5 = e1 % 150.82/22.05 | | | | | | | % 150.82/22.05 | | | | | | | COMBINE_EQS: (23), (106) imply: % 150.82/22.05 | | | | | | | (107) all_8_0 = e1 % 150.82/22.05 | | | | | | | % 150.82/22.05 | | | | | | | REDUCE: (4), (107) imply: % 150.82/22.05 | | | | | | | (108) $false % 150.82/22.05 | | | | | | | % 150.82/22.05 | | | | | | | CLOSE: (108) is inconsistent. % 150.82/22.05 | | | | | | | % 150.82/22.05 | | | | | | Case 2: % 150.82/22.05 | | | | | | | % 150.82/22.05 | | | | | | | (109) all_58_10 = e1 % 150.82/22.05 | | | | | | | % 150.82/22.05 | | | | | | | COMBINE_EQS: (54), (109) imply: % 150.82/22.05 | | | | | | | (110) all_52_13 = e1 % 150.82/22.05 | | | | | | | % 150.82/22.05 | | | | | | | REDUCE: (6), (110) imply: % 150.82/22.05 | | | | | | | (111) ~ (all_52_12 = e1) % 150.82/22.05 | | | | | | | % 150.82/22.05 | | | | | | | REF_CLOSE: (9), (19), (22), (46), (93), (97), (111) are % 150.82/22.05 | | | | | | | inconsistent by sub-proof #577. % 150.82/22.05 | | | | | | | % 150.82/22.05 | | | | | | End of split % 150.82/22.05 | | | | | | % 150.82/22.05 | | | | | End of split % 150.82/22.05 | | | | | % 150.82/22.05 | | | | End of split % 150.82/22.05 | | | | % 150.82/22.05 | | | End of split % 150.82/22.05 | | | % 150.82/22.05 | | End of split % 150.82/22.05 | | % 150.82/22.05 | Case 2: % 150.82/22.05 | | % 150.82/22.05 | | (112) all_56_11 = e1 % 150.82/22.05 | | % 150.82/22.05 | | COMBINE_EQS: (33), (112) imply: % 150.82/22.05 | | (113) all_4_1 = e1 % 150.82/22.05 | | % 150.82/22.05 | | REDUCE: (28), (113) imply: % 150.82/22.05 | | (114) ~ (all_52_13 = e1) % 150.82/22.05 | | % 150.82/22.05 | | REF_CLOSE: (14), (19), (20), (29), (32), (35), (37), (38), (43), (52), (54), % 150.82/22.05 | | (61), (113), (114) are inconsistent by sub-proof #586. % 150.82/22.05 | | % 150.82/22.05 | End of split % 150.82/22.05 | % 150.82/22.05 End of proof % 150.82/22.05 % 150.82/22.05 Sub-proof #134 shows that the following formulas are inconsistent: % 150.82/22.05 ---------------------------------------------------------------- % 150.82/22.05 (1) all_56_11 = all_8_2 % 150.82/22.05 (2) ~ (all_56_11 = e1) | all_56_13 = e2 % 150.82/22.05 (3) ~ (all_8_0 = all_6_2) % 150.82/22.05 (4) ~ (all_52_13 = all_8_0) % 150.82/22.05 (5) all_54_5 = all_8_2 % 150.82/22.05 (6) ~ (all_8_0 = all_8_2) % 150.82/22.05 (7) all_56_21 = all_6_2 % 150.82/22.05 (8) all_56_1 = all_10_2 % 150.82/22.05 (9) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0 % 150.82/22.05 (10) all_58_5 = all_8_0 % 150.82/22.05 (11) op(e2, all_8_2) = all_56_10 % 150.82/22.05 (12) op(e3, e3) = all_10_2 % 150.82/22.05 (13) ~ (all_52_1 = all_8_2) % 150.82/22.05 (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 150.82/22.05 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 150.82/22.05 (15) all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0 % 150.82/22.05 (16) ~ (all_56_11 = e3) | all_56_9 = e2 % 150.82/22.05 (17) all_58_3 = all_8_2 % 150.82/22.05 (18) all_56_31 = all_4_2 % 150.82/22.05 (19) ~ (all_52_1 = all_8_0) % 150.82/22.05 (20) all_56_1 = e3 | all_56_11 = e2 | all_56_21 = e1 | all_56_31 = e0 % 150.82/22.05 (21) ~ (all_52_13 = all_4_2) % 150.82/22.05 (22) ~ (all_8_0 = e0) | ~ (all_8_2 = e3) % 150.82/22.05 (23) op(all_8_2, all_8_2) = e1 % 150.82/22.05 (24) all_58_2 = all_52_1 % 150.82/22.05 (25) all_58_10 = all_52_13 % 150.82/22.05 (26) op(e2, e2) = all_8_2 % 150.82/22.05 (27) ~ (all_8_2 = e0) % 150.82/22.05 (28) all_54_6 = all_8_0 % 150.82/22.05 (29) all_56_13 = e0 % 150.82/22.05 (30) ~ (e2 = e0) % 150.82/22.05 (31) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 150.82/22.05 (32) all_56_9 = all_52_1 % 150.82/22.05 % 150.82/22.05 Begin of proof % 150.82/22.05 | % 150.82/22.05 | BETA: splitting (2) gives: % 150.82/22.05 | % 150.82/22.05 | Case 1: % 150.82/22.05 | | % 150.82/22.05 | | (33) ~ (all_56_11 = e1) % 150.82/22.05 | | % 150.82/22.05 | | REDUCE: (1), (33) imply: % 150.82/22.05 | | (34) ~ (all_8_2 = e1) % 150.82/22.05 | | % 150.82/22.05 | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13), % 150.82/22.05 | | (14), (15), (16), (17), (18), (19), (20), (21), (22), (23), (24), % 150.82/22.05 | | (25), (26), (27), (28), (30), (31), (32), (34) are inconsistent % 150.82/22.05 | | by sub-proof #141. % 150.82/22.05 | | % 150.82/22.05 | Case 2: % 150.82/22.05 | | % 150.82/22.05 | | (35) all_56_13 = e2 % 150.82/22.05 | | % 150.82/22.05 | | COMBINE_EQS: (29), (35) imply: % 150.82/22.05 | | (36) e2 = e0 % 150.82/22.05 | | % 150.82/22.05 | | SIMP: (36) implies: % 150.82/22.05 | | (37) e2 = e0 % 150.82/22.05 | | % 150.82/22.05 | | REDUCE: (30), (37) imply: % 150.82/22.05 | | (38) $false % 150.82/22.05 | | % 150.82/22.05 | | CLOSE: (38) is inconsistent. % 150.82/22.05 | | % 150.82/22.05 | End of split % 150.82/22.05 | % 150.82/22.05 End of proof % 150.82/22.05 % 150.82/22.05 Sub-proof #135 shows that the following formulas are inconsistent: % 150.82/22.05 ---------------------------------------------------------------- % 150.82/22.05 (1) all_56_11 = all_8_2 % 150.82/22.05 (2) ~ (all_56_11 = e1) | all_56_13 = e2 % 150.82/22.05 (3) ~ (all_52_11 = all_6_2) % 150.82/22.05 (4) ~ (all_52_4 = all_52_8) % 150.82/22.05 (5) all_58_6 = all_52_2 % 150.82/22.05 (6) ~ (all_8_0 = all_6_2) % 150.82/22.05 (7) ~ (e3 = e0) % 150.82/22.05 (8) ~ (all_52_13 = all_8_2) % 150.82/22.05 (9) all_54_0 = all_10_2 % 150.82/22.05 (10) all_54_4 = all_52_1 % 150.82/22.05 (11) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0 % 150.82/22.05 (12) ~ (all_52_12 = all_52_13) % 150.82/22.05 (13) ~ (all_52_13 = all_8_0) % 150.82/22.05 (14) all_58_6 = e0 | all_58_7 = e0 | all_58_8 = e0 | all_58_11 = e0 % 150.82/22.05 (15) all_58_4 = all_52_8 % 150.82/22.05 (16) all_54_5 = all_8_2 % 150.82/22.05 (17) ~ (all_52_13 = e0) % 150.82/22.05 (18) ~ (all_52_6 = all_52_14) % 150.82/22.05 (19) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 150.82/22.05 (20) ~ (all_52_11 = e0) % 150.82/22.05 (21) all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1 % 150.82/22.05 (22) ~ (all_8_0 = all_8_2) % 150.82/22.05 (23) all_56_21 = all_6_2 % 150.82/22.05 (24) all_56_1 = all_10_2 % 150.82/22.05 (25) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0 % 150.82/22.05 (26) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0 % 150.82/22.05 (27) all_58_9 = all_52_12 % 150.82/22.05 (28) ~ (all_56_1 = e1) | all_56_5 = e3 % 150.82/22.05 (29) ~ (all_10_2 = e2) % 150.82/22.05 (30) all_58_1 = all_52_4 % 150.82/22.05 (31) all_58_13 = all_52_7 % 150.82/22.05 (32) all_58_5 = all_8_0 % 150.82/22.05 (33) all_58_4 = e0 | all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0 % 150.82/22.05 (34) op(e2, all_8_2) = all_56_10 % 150.82/22.05 (35) op(e3, e3) = all_10_2 % 150.82/22.05 (36) all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1 % 150.82/22.05 (37) ~ (all_52_1 = all_8_2) % 150.82/22.05 (38) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 150.82/22.05 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 150.82/22.05 (39) all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0 % 150.82/22.05 (40) ~ (all_6_2 = e0) % 150.82/22.05 (41) ~ (all_56_11 = e3) | all_56_9 = e2 % 150.82/22.05 (42) ~ (all_52_1 = all_52_13) % 150.82/22.05 (43) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0 % 150.82/22.05 (44) ~ (all_4_2 = e1) % 150.82/22.05 (45) all_58_8 = all_6_2 % 150.82/22.05 (46) ~ (all_52_8 = all_10_2) % 150.82/22.05 (47) all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3 % 150.82/22.05 (48) all_56_5 = all_52_8 % 150.82/22.05 (49) all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1 % 150.82/22.05 (50) all_58_3 = all_8_2 % 150.82/22.05 (51) all_56_31 = all_4_2 % 150.82/22.05 (52) all_58_11 = all_52_14 % 150.82/22.05 (53) all_56_13 = all_8_0 % 150.82/22.05 (54) all_54_7 = all_52_13 % 150.82/22.05 (55) ~ (all_52_1 = all_8_0) % 150.82/22.05 (56) all_56_1 = e3 | all_56_11 = e2 | all_56_21 = e1 | all_56_31 = e0 % 150.82/22.05 (57) ~ (all_52_13 = all_4_2) % 150.82/22.05 (58) ~ (all_8_0 = e0) | ~ (all_8_2 = e3) % 150.82/22.05 (59) ~ (all_52_13 = all_52_14) % 150.82/22.05 (60) op(all_8_2, all_8_2) = e1 % 150.82/22.05 (61) op(e1, e1) = all_6_2 % 150.82/22.05 (62) ~ (all_52_6 = all_8_2) % 150.82/22.05 (63) all_58_15 = all_4_2 % 150.82/22.05 (64) all_58_2 = all_52_1 % 150.82/22.05 (65) all_58_7 = all_52_6 % 150.82/22.05 (66) all_58_10 = all_52_13 % 150.82/22.05 (67) all_58_0 = all_10_2 % 150.82/22.05 (68) all_58_1 = e0 | all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0 % 150.82/22.05 (69) ~ (all_52_12 = all_52_14) % 150.82/22.05 (70) op(e2, e2) = all_8_2 % 150.82/22.05 (71) ~ (all_52_8 = all_52_12) % 150.82/22.05 (72) ~ (all_52_1 = all_52_2) % 150.82/22.05 (73) ~ (all_8_2 = e0) % 150.82/22.05 (74) all_54_6 = all_8_0 % 150.82/22.05 (75) ~ (e2 = e0) % 150.82/22.05 (76) op(e1, all_52_11) = all_56_28 % 150.82/22.05 (77) ~ (all_52_7 = e0) % 150.82/22.05 (78) ~ (all_52_2 = all_10_2) % 150.82/22.05 (79) ~ (all_52_4 = all_8_2) % 150.82/22.05 (80) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 150.82/22.05 (81) all_58_14 = all_52_11 % 150.82/22.05 (82) ~ (all_52_12 = all_10_2) % 150.82/22.05 (83) all_56_9 = all_52_1 % 150.82/22.05 (84) all_54_11 = all_52_14 % 150.82/22.05 % 150.82/22.05 Begin of proof % 150.82/22.05 | % 150.82/22.05 | BETA: splitting (2) gives: % 150.82/22.05 | % 150.82/22.05 | Case 1: % 150.82/22.05 | | % 150.82/22.05 | | (85) ~ (all_56_11 = e1) % 150.82/22.05 | | % 150.82/22.05 | | REDUCE: (1), (85) imply: % 150.82/22.05 | | (86) ~ (all_8_2 = e1) % 150.82/22.05 | | % 150.82/22.05 | | REF_CLOSE: (1), (6), (13), (16), (22), (23), (24), (26), (32), (34), (35), % 150.82/22.05 | | (37), (38), (39), (41), (50), (51), (55), (56), (57), (58), (60), % 150.82/22.05 | | (64), (66), (70), (73), (74), (75), (80), (83), (86) are % 150.82/22.05 | | inconsistent by sub-proof #141. % 150.82/22.05 | | % 150.82/22.05 | Case 2: % 150.82/22.05 | | % 150.82/22.05 | | (87) all_56_13 = e2 % 150.82/22.05 | | (88) all_56_11 = e1 % 150.82/22.05 | | % 150.82/22.05 | | COMBINE_EQS: (1), (88) imply: % 150.82/22.05 | | (89) all_8_2 = e1 % 150.82/22.05 | | % 150.82/22.05 | | COMBINE_EQS: (53), (87) imply: % 150.82/22.05 | | (90) all_8_0 = e2 % 150.82/22.05 | | % 150.82/22.05 | | COMBINE_EQS: (32), (90) imply: % 150.82/22.05 | | (91) all_58_5 = e2 % 150.82/22.05 | | % 150.82/22.05 | | REDUCE: (37), (89) imply: % 150.82/22.05 | | (92) ~ (all_52_1 = e1) % 150.82/22.05 | | % 150.82/22.05 | | REDUCE: (79), (89) imply: % 150.82/22.05 | | (93) ~ (all_52_4 = e1) % 150.82/22.05 | | % 150.82/22.05 | | REDUCE: (62), (89) imply: % 150.82/22.05 | | (94) ~ (all_52_6 = e1) % 150.82/22.05 | | % 150.82/22.05 | | REDUCE: (13), (90) imply: % 150.82/22.05 | | (95) ~ (all_52_13 = e2) % 150.82/22.05 | | % 150.82/22.05 | | REDUCE: (8), (89) imply: % 150.82/22.05 | | (96) ~ (all_52_13 = e1) % 150.82/22.05 | | % 150.82/22.05 | | BETA: splitting (33) gives: % 150.82/22.05 | | % 150.82/22.05 | | Case 1: % 150.82/22.05 | | | % 150.82/22.05 | | | (97) all_58_4 = e0 % 150.82/22.05 | | | % 150.82/22.05 | | | COMBINE_EQS: (15), (97) imply: % 150.82/22.05 | | | (98) all_52_8 = e0 % 150.82/22.05 | | | % 150.82/22.05 | | | COMBINE_EQS: (48), (98) imply: % 150.82/22.05 | | | (99) all_56_5 = e0 % 150.82/22.05 | | | % 150.82/22.05 | | | REDUCE: (4), (98) imply: % 150.82/22.05 | | | (100) ~ (all_52_4 = e0) % 150.82/22.05 | | | % 150.82/22.05 | | | REDUCE: (46), (98) imply: % 150.82/22.05 | | | (101) ~ (all_10_2 = e0) % 150.82/22.05 | | | % 150.82/22.05 | | | SIMP: (101) implies: % 150.82/22.05 | | | (102) ~ (all_10_2 = e0) % 150.82/22.05 | | | % 150.82/22.05 | | | BETA: splitting (28) gives: % 150.82/22.05 | | | % 150.82/22.05 | | | Case 1: % 150.82/22.05 | | | | % 150.82/22.05 | | | | (103) ~ (all_56_1 = e1) % 150.82/22.05 | | | | % 150.82/22.05 | | | | REDUCE: (24), (103) imply: % 150.82/22.05 | | | | (104) ~ (all_10_2 = e1) % 150.82/22.05 | | | | % 150.82/22.05 | | | | BETA: splitting (19) gives: % 150.82/22.05 | | | | % 150.82/22.05 | | | | Case 1: % 150.82/22.05 | | | | | % 150.82/22.05 | | | | | (105) all_54_0 = e3 % 150.82/22.05 | | | | | % 150.82/22.05 | | | | | COMBINE_EQS: (9), (105) imply: % 150.82/22.05 | | | | | (106) all_10_2 = e3 % 150.82/22.05 | | | | | % 150.82/22.05 | | | | | SIMP: (106) implies: % 150.82/22.05 | | | | | (107) all_10_2 = e3 % 150.82/22.05 | | | | | % 150.82/22.05 | | | | | COMBINE_EQS: (67), (107) imply: % 150.82/22.05 | | | | | (108) all_58_0 = e3 % 150.82/22.05 | | | | | % 150.82/22.05 | | | | | REDUCE: (78), (107) imply: % 150.82/22.05 | | | | | (109) ~ (all_52_2 = e3) % 150.82/22.05 | | | | | % 150.82/22.05 | | | | | REDUCE: (104), (107) imply: % 150.82/22.05 | | | | | (110) ~ (e3 = e1) % 150.82/22.05 | | | | | % 150.82/22.05 | | | | | REDUCE: (35), (107) imply: % 150.82/22.05 | | | | | (111) op(e3, e3) = e3 % 150.82/22.05 | | | | | % 150.82/22.05 | | | | | BETA: splitting (39) gives: % 150.82/22.05 | | | | | % 150.82/22.05 | | | | | Case 1: % 150.82/22.05 | | | | | | % 150.82/22.05 | | | | | | (112) all_58_2 = e0 % 150.82/22.05 | | | | | | % 150.82/22.05 | | | | | | COMBINE_EQS: (64), (112) imply: % 150.82/22.05 | | | | | | (113) all_52_1 = e0 % 150.82/22.05 | | | | | | % 150.82/22.05 | | | | | | REDUCE: (72), (113) imply: % 150.82/22.05 | | | | | | (114) ~ (all_52_2 = e0) % 150.82/22.05 | | | | | | % 150.82/22.05 | | | | | | SIMP: (114) implies: % 150.82/22.05 | | | | | | (115) ~ (all_52_2 = e0) % 150.82/22.05 | | | | | | % 150.82/22.05 | | | | | | REDUCE: (42), (113) imply: % 150.82/22.05 | | | | | | (116) ~ (all_52_13 = e0) % 150.82/22.05 | | | | | | % 150.82/22.05 | | | | | | BETA: splitting (14) gives: % 150.82/22.05 | | | | | | % 150.82/22.05 | | | | | | Case 1: % 150.82/22.05 | | | | | | | % 150.82/22.05 | | | | | | | (117) all_58_6 = e0 % 150.82/22.05 | | | | | | | % 150.82/22.05 | | | | | | | REF_CLOSE: (5), (115), (117) are inconsistent by sub-proof #273. % 150.82/22.05 | | | | | | | % 150.82/22.05 | | | | | | Case 2: % 150.82/22.05 | | | | | | | % 150.82/22.05 | | | | | | | (118) all_58_7 = e0 | all_58_8 = e0 | all_58_11 = e0 % 150.82/22.05 | | | | | | | % 150.82/22.05 | | | | | | | BETA: splitting (118) gives: % 150.82/22.05 | | | | | | | % 150.82/22.05 | | | | | | | Case 1: % 150.82/22.05 | | | | | | | | % 150.82/22.05 | | | | | | | | (119) all_58_7 = e0 % 150.82/22.05 | | | | | | | | % 150.82/22.05 | | | | | | | | COMBINE_EQS: (65), (119) imply: % 150.82/22.05 | | | | | | | | (120) all_52_6 = e0 % 150.82/22.05 | | | | | | | | % 150.82/22.05 | | | | | | | | REDUCE: (18), (120) imply: % 150.82/22.05 | | | | | | | | (121) ~ (all_52_14 = e0) % 150.82/22.05 | | | | | | | | % 150.82/22.05 | | | | | | | | SIMP: (121) implies: % 150.82/22.05 | | | | | | | | (122) ~ (all_52_14 = e0) % 150.82/22.05 | | | | | | | | % 150.82/22.05 | | | | | | | | REDUCE: (94), (120) imply: % 150.82/22.05 | | | | | | | | (123) ~ (e1 = e0) % 150.82/22.05 | | | | | | | | % 150.82/22.05 | | | | | | | | SIMP: (123) implies: % 150.82/22.05 | | | | | | | | (124) ~ (e1 = e0) % 150.82/22.05 | | | | | | | | % 150.82/22.05 | | | | | | | | BETA: splitting (36) gives: % 150.82/22.05 | | | | | | | | % 150.82/22.05 | | | | | | | | Case 1: % 150.82/22.05 | | | | | | | | | % 150.82/22.05 | | | | | | | | | (125) all_58_0 = e1 % 150.82/22.05 | | | | | | | | | % 150.82/22.05 | | | | | | | | | COMBINE_EQS: (108), (125) imply: % 150.82/22.05 | | | | | | | | | (126) e3 = e1 % 150.82/22.05 | | | | | | | | | % 150.82/22.05 | | | | | | | | | REDUCE: (110), (126) imply: % 150.82/22.05 | | | | | | | | | (127) $false % 150.82/22.05 | | | | | | | | | % 150.82/22.05 | | | | | | | | | CLOSE: (127) is inconsistent. % 150.82/22.05 | | | | | | | | | % 150.82/22.05 | | | | | | | | Case 2: % 150.82/22.05 | | | | | | | | | % 150.82/22.05 | | | | | | | | | (128) all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1 % 150.82/22.05 | | | | | | | | | % 150.82/22.05 | | | | | | | | | BETA: splitting (128) gives: % 150.82/22.05 | | | | | | | | | % 150.82/22.05 | | | | | | | | | Case 1: % 150.82/22.05 | | | | | | | | | | % 150.82/22.05 | | | | | | | | | | (129) all_58_1 = e1 % 150.82/22.05 | | | | | | | | | | % 150.82/22.05 | | | | | | | | | | COMBINE_EQS: (30), (129) imply: % 150.82/22.05 | | | | | | | | | | (130) all_52_4 = e1 % 150.82/22.05 | | | | | | | | | | % 150.82/22.05 | | | | | | | | | | REDUCE: (93), (130) imply: % 150.82/22.05 | | | | | | | | | | (131) $false % 150.82/22.05 | | | | | | | | | | % 150.82/22.05 | | | | | | | | | | CLOSE: (131) is inconsistent. % 150.82/22.05 | | | | | | | | | | % 150.82/22.05 | | | | | | | | | Case 2: % 150.82/22.05 | | | | | | | | | | % 150.82/22.05 | | | | | | | | | | (132) all_58_4 = e1 | all_58_9 = e1 % 150.82/22.05 | | | | | | | | | | % 150.82/22.05 | | | | | | | | | | BETA: splitting (132) gives: % 150.82/22.05 | | | | | | | | | | % 150.82/22.05 | | | | | | | | | | Case 1: % 150.82/22.05 | | | | | | | | | | | % 150.82/22.05 | | | | | | | | | | | (133) all_58_4 = e1 % 150.82/22.05 | | | | | | | | | | | % 150.82/22.05 | | | | | | | | | | | COMBINE_EQS: (97), (133) imply: % 150.82/22.05 | | | | | | | | | | | (134) e1 = e0 % 150.82/22.05 | | | | | | | | | | | % 150.82/22.05 | | | | | | | | | | | SIMP: (134) implies: % 150.82/22.05 | | | | | | | | | | | (135) e1 = e0 % 150.82/22.05 | | | | | | | | | | | % 150.82/22.05 | | | | | | | | | | | REDUCE: (124), (135) imply: % 150.82/22.05 | | | | | | | | | | | (136) $false % 150.82/22.05 | | | | | | | | | | | % 150.82/22.05 | | | | | | | | | | | CLOSE: (136) is inconsistent. % 150.82/22.05 | | | | | | | | | | | % 150.82/22.05 | | | | | | | | | | Case 2: % 150.82/22.05 | | | | | | | | | | | % 150.82/22.05 | | | | | | | | | | | (137) all_58_9 = e1 % 150.82/22.05 | | | | | | | | | | | % 150.82/22.05 | | | | | | | | | | | COMBINE_EQS: (27), (137) imply: % 150.82/22.05 | | | | | | | | | | | (138) all_52_12 = e1 % 150.82/22.05 | | | | | | | | | | | % 150.82/22.05 | | | | | | | | | | | REDUCE: (12), (138) imply: % 150.82/22.05 | | | | | | | | | | | (139) ~ (all_52_13 = e1) % 150.82/22.05 | | | | | | | | | | | % 150.82/22.05 | | | | | | | | | | | REDUCE: (69), (138) imply: % 150.82/22.05 | | | | | | | | | | | (140) ~ (all_52_14 = e1) % 150.82/22.05 | | | | | | | | | | | % 150.82/22.05 | | | | | | | | | | | SIMP: (140) implies: % 150.82/22.05 | | | | | | | | | | | (141) ~ (all_52_14 = e1) % 150.82/22.05 | | | | | | | | | | | % 150.82/22.05 | | | | | | | | | | | BETA: splitting (25) gives: % 150.82/22.05 | | | | | | | | | | | % 150.82/22.05 | | | | | | | | | | | Case 1: % 150.82/22.05 | | | | | | | | | | | | % 150.82/22.05 | | | | | | | | | | | | (142) all_54_7 = e3 % 150.82/22.05 | | | | | | | | | | | | % 150.82/22.05 | | | | | | | | | | | | COMBINE_EQS: (54), (142) imply: % 150.82/22.05 | | | | | | | | | | | | (143) all_52_13 = e3 % 150.82/22.05 | | | | | | | | | | | | % 150.82/22.05 | | | | | | | | | | | | SIMP: (143) implies: % 150.82/22.05 | | | | | | | | | | | | (144) all_52_13 = e3 % 150.82/22.05 | | | | | | | | | | | | % 150.82/22.05 | | | | | | | | | | | | REDUCE: (59), (144) imply: % 150.82/22.05 | | | | | | | | | | | | (145) ~ (all_52_14 = e3) % 150.82/22.05 | | | | | | | | | | | | % 150.82/22.05 | | | | | | | | | | | | SIMP: (145) implies: % 150.82/22.05 | | | | | | | | | | | | (146) ~ (all_52_14 = e3) % 150.82/22.05 | | | | | | | | | | | | % 150.82/22.05 | | | | | | | | | | | | BETA: splitting (11) gives: % 150.82/22.05 | | | | | | | | | | | | % 150.82/22.05 | | | | | | | | | | | | Case 1: % 150.82/22.05 | | | | | | | | | | | | | % 150.82/22.05 | | | | | | | | | | | | | (147) all_54_11 = e3 % 150.82/22.05 | | | | | | | | | | | | | % 150.82/22.05 | | | | | | | | | | | | | COMBINE_EQS: (84), (147) imply: % 150.82/22.05 | | | | | | | | | | | | | (148) all_52_14 = e3 % 150.82/22.05 | | | | | | | | | | | | | % 150.82/22.05 | | | | | | | | | | | | | REDUCE: (146), (148) imply: % 150.82/22.05 | | | | | | | | | | | | | (149) $false % 150.82/22.05 | | | | | | | | | | | | | % 150.82/22.05 | | | | | | | | | | | | | CLOSE: (149) is inconsistent. % 150.82/22.05 | | | | | | | | | | | | | % 150.82/22.05 | | | | | | | | | | | | Case 2: % 150.82/22.05 | | | | | | | | | | | | | % 150.82/22.05 | | | | | | | | | | | | | (150) ~ (all_54_11 = e3) % 150.82/22.05 | | | | | | | | | | | | | (151) all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0 % 150.82/22.05 | | | | | | | | | | | | | % 150.82/22.05 | | | | | | | | | | | | | BETA: splitting (47) gives: % 150.82/22.05 | | | | | | | | | | | | | % 150.82/22.05 | | | | | | | | | | | | | Case 1: % 150.82/22.05 | | | | | | | | | | | | | | % 150.82/22.05 | | | | | | | | | | | | | | (152) all_58_6 = e3 % 150.82/22.05 | | | | | | | | | | | | | | % 150.82/22.05 | | | | | | | | | | | | | | COMBINE_EQS: (5), (152) imply: % 150.82/22.05 | | | | | | | | | | | | | | (153) all_52_2 = e3 % 150.82/22.05 | | | | | | | | | | | | | | % 150.82/22.05 | | | | | | | | | | | | | | REDUCE: (109), (153) imply: % 150.82/22.05 | | | | | | | | | | | | | | (154) $false % 150.82/22.05 | | | | | | | | | | | | | | % 150.82/22.05 | | | | | | | | | | | | | | CLOSE: (154) is inconsistent. % 150.82/22.05 | | | | | | | | | | | | | | % 150.82/22.05 | | | | | | | | | | | | | Case 2: % 150.82/22.05 | | | | | | | | | | | | | | % 150.82/22.05 | | | | | | | | | | | | | | (155) all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3 % 150.82/22.05 | | | | | | | | | | | | | | % 150.82/22.05 | | | | | | | | | | | | | | BETA: splitting (155) gives: % 150.82/22.05 | | | | | | | | | | | | | | % 150.82/22.05 | | | | | | | | | | | | | | Case 1: % 150.82/22.05 | | | | | | | | | | | | | | | % 150.82/22.05 | | | | | | | | | | | | | | | (156) all_58_7 = e3 % 150.82/22.05 | | | | | | | | | | | | | | | % 150.82/22.05 | | | | | | | | | | | | | | | REF_CLOSE: (7), (119), (156) are inconsistent by sub-proof % 150.82/22.05 | | | | | | | | | | | | | | | #303. % 150.82/22.05 | | | | | | | | | | | | | | | % 150.82/22.05 | | | | | | | | | | | | | | Case 2: % 150.82/22.05 | | | | | | | | | | | | | | | % 150.82/22.05 | | | | | | | | | | | | | | | (157) all_58_8 = e3 | all_58_11 = e3 % 150.82/22.05 | | | | | | | | | | | | | | | % 150.82/22.05 | | | | | | | | | | | | | | | BETA: splitting (151) gives: % 150.82/22.05 | | | | | | | | | | | | | | | % 150.82/22.05 | | | | | | | | | | | | | | | Case 1: % 150.82/22.05 | | | | | | | | | | | | | | | | % 150.82/22.05 | | | | | | | | | | | | | | | | (158) all_54_11 = e2 % 150.82/22.05 | | | | | | | | | | | | | | | | % 150.82/22.05 | | | | | | | | | | | | | | | | COMBINE_EQS: (84), (158) imply: % 150.82/22.05 | | | | | | | | | | | | | | | | (159) all_52_14 = e2 % 150.82/22.05 | | | | | | | | | | | | | | | | % 150.82/22.05 | | | | | | | | | | | | | | | | COMBINE_EQS: (52), (159) imply: % 150.82/22.05 | | | | | | | | | | | | | | | | (160) all_58_11 = e2 % 150.82/22.05 | | | | | | | | | | | | | | | | % 150.82/22.05 | | | | | | | | | | | | | | | | REDUCE: (146), (159) imply: % 150.82/22.05 | | | | | | | | | | | | | | | | (161) ~ (e3 = e2) % 150.82/22.05 | | | | | | | | | | | | | | | | % 150.82/22.05 | | | | | | | | | | | | | | | | SIMP: (161) implies: % 150.82/22.05 | | | | | | | | | | | | | | | | (162) ~ (e3 = e2) % 150.82/22.05 | | | | | | | | | | | | | | | | % 150.82/22.05 | | | | | | | | | | | | | | | | BETA: splitting (157) gives: % 150.82/22.05 | | | | | | | | | | | | | | | | % 150.82/22.05 | | | | | | | | | | | | | | | | Case 1: % 150.82/22.05 | | | | | | | | | | | | | | | | | % 150.82/22.05 | | | | | | | | | | | | | | | | | (163) all_58_8 = e3 % 150.82/22.05 | | | | | | | | | | | | | | | | | % 150.82/22.05 | | | | | | | | | | | | | | | | | COMBINE_EQS: (45), (163) imply: % 150.82/22.05 | | | | | | | | | | | | | | | | | (164) all_6_2 = e3 % 150.82/22.05 | | | | | | | | | | | | | | | | | % 150.82/22.05 | | | | | | | | | | | | | | | | | REDUCE: (3), (164) imply: % 150.82/22.05 | | | | | | | | | | | | | | | | | (165) ~ (all_52_11 = e3) % 150.82/22.05 | | | | | | | | | | | | | | | | | % 150.82/22.05 | | | | | | | | | | | | | | | | | REDUCE: (61), (164) imply: % 150.82/22.05 | | | | | | | | | | | | | | | | | (166) op(e1, e1) = e3 % 150.82/22.05 | | | | | | | | | | | | | | | | | % 150.82/22.06 | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (2), (6), (8), (13), (15), (16), (21), (22), % 150.82/22.06 | | | | | | | | | | | | | | | | | (23), (24), (26), (27), (32), (34), (35), (37), % 150.82/22.06 | | | | | | | | | | | | | | | | | (38), (39), (41), (44), (49), (50), (51), (52), % 150.82/22.06 | | | | | | | | | | | | | | | | | (53), (55), (56), (57), (58), (60), (63), (64), % 150.82/22.06 | | | | | | | | | | | | | | | | | (66), (70), (71), (73), (74), (75), (76), (80), % 150.82/22.06 | | | | | | | | | | | | | | | | | (81), (82), (83), (111), (141), (163), (165), % 150.82/22.06 | | | | | | | | | | | | | | | | | (166) are inconsistent by sub-proof #140. % 150.82/22.06 | | | | | | | | | | | | | | | | | % 150.82/22.06 | | | | | | | | | | | | | | | | Case 2: % 150.82/22.06 | | | | | | | | | | | | | | | | | % 150.82/22.06 | | | | | | | | | | | | | | | | | (167) all_58_11 = e3 % 150.82/22.06 | | | | | | | | | | | | | | | | | % 150.82/22.06 | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (162), (167) are inconsistent by sub-proof % 150.82/22.06 | | | | | | | | | | | | | | | | | #301. % 150.82/22.06 | | | | | | | | | | | | | | | | | % 150.82/22.06 | | | | | | | | | | | | | | | | End of split % 150.82/22.06 | | | | | | | | | | | | | | | | % 150.82/22.06 | | | | | | | | | | | | | | | Case 2: % 150.82/22.06 | | | | | | | | | | | | | | | | % 150.82/22.06 | | | | | | | | | | | | | | | | (168) all_54_11 = e1 | all_54_11 = e0 % 150.82/22.06 | | | | | | | | | | | | | | | | % 150.82/22.06 | | | | | | | | | | | | | | | | REF_CLOSE: (84), (122), (141), (168) are inconsistent by % 150.82/22.06 | | | | | | | | | | | | | | | | sub-proof #688. % 150.82/22.06 | | | | | | | | | | | | | | | | % 150.82/22.06 | | | | | | | | | | | | | | | End of split % 150.82/22.06 | | | | | | | | | | | | | | | % 150.82/22.06 | | | | | | | | | | | | | | End of split % 150.82/22.06 | | | | | | | | | | | | | | % 150.82/22.06 | | | | | | | | | | | | | End of split % 150.82/22.06 | | | | | | | | | | | | | % 150.82/22.06 | | | | | | | | | | | | End of split % 150.82/22.06 | | | | | | | | | | | | % 150.82/22.06 | | | | | | | | | | | Case 2: % 150.82/22.06 | | | | | | | | | | | | % 150.82/22.06 | | | | | | | | | | | | (169) all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0 % 150.82/22.06 | | | | | | | | | | | | % 150.82/22.06 | | | | | | | | | | | | REF_CLOSE: (17), (54), (95), (96), (169) are inconsistent by % 150.82/22.06 | | | | | | | | | | | | sub-proof #649. % 150.82/22.06 | | | | | | | | | | | | % 150.82/22.06 | | | | | | | | | | | End of split % 150.82/22.06 | | | | | | | | | | | % 150.82/22.06 | | | | | | | | | | End of split % 150.82/22.06 | | | | | | | | | | % 150.82/22.06 | | | | | | | | | End of split % 150.82/22.06 | | | | | | | | | % 150.82/22.06 | | | | | | | | End of split % 150.82/22.06 | | | | | | | | % 150.82/22.06 | | | | | | | Case 2: % 150.82/22.06 | | | | | | | | % 150.82/22.06 | | | | | | | | (170) ~ (all_58_7 = e0) % 150.82/22.06 | | | | | | | | % 150.82/22.06 | | | | | | | | REDUCE: (65), (170) imply: % 150.82/22.06 | | | | | | | | (171) ~ (all_52_6 = e0) % 150.82/22.06 | | | | | | | | % 150.82/22.06 | | | | | | | | REF_CLOSE: (30), (31), (50), (65), (68), (73), (77), (100), % 150.82/22.06 | | | | | | | | (171) are inconsistent by sub-proof #240. % 150.82/22.06 | | | | | | | | % 150.82/22.06 | | | | | | | End of split % 150.82/22.06 | | | | | | | % 150.82/22.06 | | | | | | End of split % 150.82/22.06 | | | | | | % 150.82/22.06 | | | | | Case 2: % 150.82/22.06 | | | | | | % 150.82/22.06 | | | | | | (172) ~ (all_58_2 = e0) % 150.82/22.06 | | | | | | % 150.82/22.06 | | | | | | REDUCE: (64), (172) imply: % 150.82/22.06 | | | | | | (173) ~ (all_52_1 = e0) % 150.82/22.06 | | | | | | % 150.82/22.06 | | | | | | REF_CLOSE: (1), (2), (8), (10), (16), (17), (25), (37), (42), (43), % 150.82/22.06 | | | | | | (53), (54), (55), (73), (80), (92), (95), (96), (173) are % 150.82/22.06 | | | | | | inconsistent by sub-proof #136. % 150.82/22.06 | | | | | | % 150.82/22.06 | | | | | End of split % 150.82/22.06 | | | | | % 150.82/22.06 | | | | Case 2: % 150.82/22.06 | | | | | % 150.82/22.06 | | | | | (174) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 150.82/22.06 | | | | | % 150.82/22.06 | | | | | REF_CLOSE: (9), (29), (102), (104), (174) are inconsistent by % 150.82/22.06 | | | | | sub-proof #731. % 150.82/22.06 | | | | | % 150.82/22.06 | | | | End of split % 150.82/22.06 | | | | % 150.82/22.06 | | | Case 2: % 150.82/22.06 | | | | % 150.82/22.06 | | | | (175) all_56_5 = e3 % 150.82/22.06 | | | | % 150.82/22.06 | | | | COMBINE_EQS: (99), (175) imply: % 150.82/22.06 | | | | (176) e3 = e0 % 150.82/22.06 | | | | % 150.82/22.06 | | | | REDUCE: (7), (176) imply: % 150.82/22.06 | | | | (177) $false % 150.82/22.06 | | | | % 150.82/22.06 | | | | CLOSE: (177) is inconsistent. % 150.82/22.06 | | | | % 150.82/22.06 | | | End of split % 150.82/22.06 | | | % 150.82/22.06 | | Case 2: % 150.82/22.06 | | | % 150.82/22.06 | | | (178) all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0 % 150.82/22.06 | | | % 150.82/22.06 | | | REF_CLOSE: (20), (40), (45), (75), (81), (91), (178) are inconsistent by % 150.82/22.06 | | | sub-proof #572. % 150.82/22.06 | | | % 150.82/22.06 | | End of split % 150.82/22.06 | | % 150.82/22.06 | End of split % 150.82/22.06 | % 150.82/22.06 End of proof % 150.82/22.06 % 150.82/22.06 Sub-proof #136 shows that the following formulas are inconsistent: % 150.82/22.06 ---------------------------------------------------------------- % 150.82/22.06 (1) all_56_11 = all_8_2 % 150.82/22.06 (2) ~ (all_56_11 = e1) | all_56_13 = e2 % 150.82/22.06 (3) ~ (all_52_13 = e1) % 150.82/22.06 (4) ~ (all_52_13 = all_8_2) % 150.82/22.06 (5) all_54_4 = all_52_1 % 150.82/22.06 (6) all_54_5 = all_8_2 % 150.82/22.06 (7) ~ (all_52_13 = e0) % 150.82/22.06 (8) ~ (all_52_1 = e1) % 150.82/22.06 (9) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0 % 150.82/22.06 (10) ~ (all_52_13 = e2) % 150.82/22.06 (11) ~ (all_52_1 = all_8_2) % 150.82/22.06 (12) ~ (all_52_1 = all_52_13) % 150.82/22.06 (13) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0 % 150.82/22.06 (14) ~ (all_52_1 = e0) % 150.82/22.06 (15) all_56_13 = all_8_0 % 150.82/22.06 (16) all_54_7 = all_52_13 % 150.82/22.06 (17) ~ (all_52_1 = all_8_0) % 150.82/22.06 (18) ~ (all_8_2 = e0) % 150.82/22.06 (19) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 150.82/22.06 % 150.82/22.06 Begin of proof % 150.82/22.06 | % 150.82/22.06 | BETA: splitting (9) gives: % 150.82/22.06 | % 150.82/22.06 | Case 1: % 150.82/22.06 | | % 150.82/22.06 | | (20) all_54_7 = e3 % 150.82/22.06 | | % 150.82/22.06 | | COMBINE_EQS: (16), (20) imply: % 150.82/22.06 | | (21) all_52_13 = e3 % 150.82/22.06 | | % 150.82/22.06 | | SIMP: (21) implies: % 150.82/22.06 | | (22) all_52_13 = e3 % 150.82/22.06 | | % 150.82/22.06 | | REDUCE: (12), (22) imply: % 150.82/22.06 | | (23) ~ (all_52_1 = e3) % 150.82/22.06 | | % 150.82/22.06 | | REDUCE: (4), (22) imply: % 150.82/22.06 | | (24) ~ (all_8_2 = e3) % 150.82/22.06 | | % 150.82/22.06 | | SIMP: (24) implies: % 150.82/22.06 | | (25) ~ (all_8_2 = e3) % 150.82/22.06 | | % 150.82/22.06 | | REF_CLOSE: (1), (2), (5), (6), (8), (11), (13), (14), (15), (17), (18), % 150.82/22.06 | | (19), (23), (25) are inconsistent by sub-proof #137. % 150.82/22.06 | | % 150.82/22.06 | Case 2: % 150.82/22.06 | | % 150.82/22.06 | | (26) all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0 % 150.82/22.06 | | % 150.82/22.06 | | REF_CLOSE: (3), (7), (10), (16), (26) are inconsistent by sub-proof #649. % 150.82/22.06 | | % 150.82/22.06 | End of split % 150.82/22.06 | % 150.82/22.06 End of proof % 150.82/22.06 % 150.82/22.06 Sub-proof #137 shows that the following formulas are inconsistent: % 150.82/22.06 ---------------------------------------------------------------- % 150.82/22.06 (1) all_56_11 = all_8_2 % 150.82/22.06 (2) ~ (all_56_11 = e1) | all_56_13 = e2 % 150.82/22.06 (3) all_54_4 = all_52_1 % 150.82/22.06 (4) ~ (all_52_1 = e3) % 150.82/22.06 (5) all_54_5 = all_8_2 % 150.82/22.06 (6) ~ (all_52_1 = e1) % 150.82/22.06 (7) ~ (all_52_1 = all_8_2) % 150.82/22.06 (8) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0 % 150.82/22.06 (9) ~ (all_8_2 = e3) % 150.82/22.06 (10) ~ (all_52_1 = e0) % 150.82/22.06 (11) all_56_13 = all_8_0 % 150.82/22.06 (12) ~ (all_52_1 = all_8_0) % 150.82/22.06 (13) ~ (all_8_2 = e0) % 150.82/22.06 (14) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 150.82/22.06 % 150.82/22.06 Begin of proof % 150.82/22.06 | % 150.82/22.06 | BETA: splitting (8) gives: % 150.82/22.06 | % 150.82/22.06 | Case 1: % 150.82/22.06 | | % 150.82/22.06 | | (15) all_54_4 = e3 % 150.82/22.06 | | % 150.82/22.06 | | REF_CLOSE: (3), (4), (15) are inconsistent by sub-proof #634. % 150.82/22.06 | | % 150.82/22.06 | Case 2: % 150.82/22.06 | | % 150.82/22.06 | | (16) all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0 % 150.82/22.06 | | % 150.82/22.06 | | BETA: splitting (16) gives: % 150.82/22.06 | | % 150.82/22.06 | | Case 1: % 150.82/22.06 | | | % 150.82/22.06 | | | (17) all_54_4 = e2 % 150.82/22.06 | | | % 150.82/22.06 | | | COMBINE_EQS: (3), (17) imply: % 150.82/22.06 | | | (18) all_52_1 = e2 % 150.82/22.06 | | | % 150.82/22.06 | | | SIMP: (18) implies: % 150.82/22.06 | | | (19) all_52_1 = e2 % 150.82/22.06 | | | % 150.82/22.06 | | | REDUCE: (12), (19) imply: % 150.82/22.06 | | | (20) ~ (all_8_0 = e2) % 150.82/22.06 | | | % 150.82/22.06 | | | SIMP: (20) implies: % 150.82/22.06 | | | (21) ~ (all_8_0 = e2) % 150.82/22.06 | | | % 150.82/22.06 | | | REDUCE: (7), (19) imply: % 150.82/22.06 | | | (22) ~ (all_8_2 = e2) % 150.82/22.06 | | | % 150.82/22.06 | | | SIMP: (22) implies: % 150.82/22.06 | | | (23) ~ (all_8_2 = e2) % 150.82/22.06 | | | % 150.82/22.06 | | | REF_CLOSE: (1), (2), (5), (9), (11), (13), (14), (21), (23) are % 150.82/22.06 | | | inconsistent by sub-proof #138. % 150.82/22.06 | | | % 150.82/22.06 | | Case 2: % 150.82/22.06 | | | % 150.82/22.06 | | | (24) all_54_4 = e1 | all_54_4 = e0 % 150.82/22.06 | | | % 150.82/22.06 | | | REF_CLOSE: (3), (6), (10), (24) are inconsistent by sub-proof #583. % 150.82/22.06 | | | % 150.82/22.06 | | End of split % 150.82/22.06 | | % 150.82/22.06 | End of split % 150.82/22.06 | % 150.82/22.06 End of proof % 150.82/22.06 % 150.82/22.06 Sub-proof #138 shows that the following formulas are inconsistent: % 150.82/22.06 ---------------------------------------------------------------- % 150.82/22.06 (1) all_56_11 = all_8_2 % 150.82/22.06 (2) ~ (all_56_11 = e1) | all_56_13 = e2 % 150.82/22.06 (3) all_54_5 = all_8_2 % 150.82/22.06 (4) ~ (all_8_2 = e2) % 150.82/22.06 (5) ~ (all_8_2 = e3) % 150.82/22.06 (6) all_56_13 = all_8_0 % 150.82/22.06 (7) ~ (all_8_0 = e2) % 150.82/22.06 (8) ~ (all_8_2 = e0) % 150.82/22.06 (9) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 150.82/22.06 % 150.82/22.06 Begin of proof % 150.82/22.06 | % 150.82/22.06 | BETA: splitting (2) gives: % 150.82/22.06 | % 150.82/22.06 | Case 1: % 150.82/22.06 | | % 150.82/22.06 | | (10) ~ (all_56_11 = e1) % 150.82/22.06 | | % 150.82/22.06 | | REDUCE: (1), (10) imply: % 150.82/22.06 | | (11) ~ (all_8_2 = e1) % 150.82/22.06 | | % 150.82/22.06 | | BETA: splitting (9) gives: % 150.82/22.06 | | % 150.82/22.06 | | Case 1: % 150.82/22.06 | | | % 150.82/22.06 | | | (12) all_54_5 = e3 % 150.82/22.06 | | | % 150.82/22.06 | | | REF_CLOSE: (3), (5), (12) are inconsistent by sub-proof #737. % 150.82/22.06 | | | % 150.82/22.06 | | Case 2: % 150.82/22.06 | | | % 150.82/22.06 | | | (13) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 150.82/22.06 | | | % 150.82/22.06 | | | REF_CLOSE: (3), (4), (8), (11), (13) are inconsistent by sub-proof #644. % 150.82/22.06 | | | % 150.82/22.06 | | End of split % 150.82/22.06 | | % 150.82/22.06 | Case 2: % 150.82/22.06 | | % 150.82/22.06 | | (14) all_56_13 = e2 % 150.82/22.06 | | % 150.82/22.06 | | REF_CLOSE: (6), (7), (14) are inconsistent by sub-proof #139. % 150.82/22.06 | | % 150.82/22.06 | End of split % 150.82/22.06 | % 150.82/22.06 End of proof % 150.82/22.06 % 150.82/22.06 Sub-proof #139 shows that the following formulas are inconsistent: % 150.82/22.06 ---------------------------------------------------------------- % 150.82/22.06 (1) all_56_13 = all_8_0 % 150.82/22.06 (2) all_56_13 = e2 % 150.82/22.06 (3) ~ (all_8_0 = e2) % 150.82/22.06 % 150.82/22.06 Begin of proof % 150.82/22.06 | % 150.82/22.06 | COMBINE_EQS: (1), (2) imply: % 150.82/22.06 | (4) all_8_0 = e2 % 150.82/22.06 | % 150.82/22.06 | SIMP: (4) implies: % 150.82/22.06 | (5) all_8_0 = e2 % 150.82/22.06 | % 150.82/22.06 | REDUCE: (3), (5) imply: % 150.82/22.06 | (6) $false % 150.82/22.06 | % 150.82/22.06 | CLOSE: (6) is inconsistent. % 150.82/22.06 | % 150.82/22.06 End of proof % 150.82/22.06 % 150.82/22.06 Sub-proof #140 shows that the following formulas are inconsistent: % 150.82/22.06 ---------------------------------------------------------------- % 150.82/22.06 (1) all_56_11 = all_8_2 % 150.82/22.06 (2) ~ (all_56_11 = e1) | all_56_13 = e2 % 150.82/22.06 (3) ~ (all_8_0 = all_6_2) % 150.82/22.06 (4) ~ (all_52_13 = all_8_2) % 150.82/22.06 (5) op(e3, e3) = e3 % 150.82/22.06 (6) ~ (all_52_13 = all_8_0) % 150.82/22.06 (7) all_58_4 = all_52_8 % 150.82/22.06 (8) all_54_5 = all_8_2 % 150.82/22.06 (9) all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1 % 150.82/22.06 (10) ~ (all_8_0 = all_8_2) % 150.82/22.06 (11) all_56_21 = all_6_2 % 150.82/22.06 (12) all_56_1 = all_10_2 % 150.82/22.06 (13) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0 % 150.82/22.06 (14) all_58_9 = all_52_12 % 150.82/22.06 (15) all_58_5 = all_8_0 % 150.82/22.06 (16) op(e2, all_8_2) = all_56_10 % 150.82/22.06 (17) op(e3, e3) = all_10_2 % 150.82/22.06 (18) ~ (all_52_1 = all_8_2) % 150.82/22.06 (19) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 150.82/22.06 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 150.82/22.06 (20) ~ (all_52_11 = e3) % 150.82/22.06 (21) all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0 % 150.82/22.06 (22) ~ (all_52_14 = e1) % 150.82/22.06 (23) op(e1, e1) = e3 % 150.82/22.06 (24) ~ (all_56_11 = e3) | all_56_9 = e2 % 150.82/22.06 (25) ~ (all_4_2 = e1) % 150.82/22.06 (26) all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1 % 150.82/22.06 (27) all_58_3 = all_8_2 % 150.82/22.06 (28) all_56_31 = all_4_2 % 150.82/22.06 (29) all_58_11 = all_52_14 % 150.82/22.06 (30) all_56_13 = all_8_0 % 150.82/22.06 (31) ~ (all_52_1 = all_8_0) % 150.82/22.06 (32) all_56_1 = e3 | all_56_11 = e2 | all_56_21 = e1 | all_56_31 = e0 % 150.82/22.06 (33) ~ (all_52_13 = all_4_2) % 150.82/22.06 (34) ~ (all_8_0 = e0) | ~ (all_8_2 = e3) % 150.82/22.06 (35) op(all_8_2, all_8_2) = e1 % 150.82/22.06 (36) all_58_15 = all_4_2 % 150.82/22.06 (37) all_58_2 = all_52_1 % 150.82/22.06 (38) all_58_10 = all_52_13 % 150.82/22.06 (39) op(e2, e2) = all_8_2 % 150.82/22.06 (40) ~ (all_52_8 = all_52_12) % 150.82/22.06 (41) all_58_8 = e3 % 150.82/22.06 (42) ~ (all_8_2 = e0) % 150.82/22.06 (43) all_54_6 = all_8_0 % 150.82/22.06 (44) ~ (e2 = e0) % 150.82/22.06 (45) op(e1, all_52_11) = all_56_28 % 150.82/22.06 (46) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 150.82/22.06 (47) all_58_14 = all_52_11 % 150.82/22.06 (48) ~ (all_52_12 = all_10_2) % 150.82/22.06 (49) all_56_9 = all_52_1 % 150.82/22.06 % 150.82/22.06 Begin of proof % 150.82/22.06 | % 150.82/22.06 | GROUND_INST: instantiating (19) with all_10_2, e3, e3, e3, simplifying with % 150.82/22.06 | (5), (17) gives: % 150.82/22.06 | (50) all_10_2 = e3 % 150.82/22.06 | % 150.82/22.06 | REDUCE: (48), (50) imply: % 150.82/22.06 | (51) ~ (all_52_12 = e3) % 150.82/22.06 | % 150.82/22.06 | BETA: splitting (2) gives: % 150.82/22.06 | % 150.82/22.06 | Case 1: % 150.82/22.06 | | % 150.82/22.06 | | (52) ~ (all_56_11 = e1) % 150.82/22.06 | | % 150.82/22.06 | | REDUCE: (1), (52) imply: % 150.82/22.06 | | (53) ~ (all_8_2 = e1) % 150.82/22.06 | | % 150.82/22.06 | | REF_CLOSE: (1), (3), (6), (8), (10), (11), (12), (13), (15), (16), (17), % 150.82/22.06 | | (18), (19), (21), (24), (27), (28), (31), (32), (33), (34), (35), % 150.82/22.06 | | (37), (38), (39), (42), (43), (44), (46), (49), (53) are % 150.82/22.06 | | inconsistent by sub-proof #141. % 150.82/22.06 | | % 150.82/22.06 | Case 2: % 150.82/22.06 | | % 150.82/22.06 | | (54) all_56_13 = e2 % 150.82/22.06 | | (55) all_56_11 = e1 % 150.82/22.06 | | % 150.82/22.06 | | COMBINE_EQS: (1), (55) imply: % 150.82/22.06 | | (56) all_8_2 = e1 % 150.82/22.06 | | % 150.82/22.06 | | COMBINE_EQS: (30), (54) imply: % 150.82/22.06 | | (57) all_8_0 = e2 % 150.82/22.06 | | % 150.82/22.06 | | COMBINE_EQS: (15), (57) imply: % 150.82/22.06 | | (58) all_58_5 = e2 % 150.82/22.06 | | % 150.82/22.06 | | REDUCE: (4), (56) imply: % 150.82/22.06 | | (59) ~ (all_52_13 = e1) % 150.82/22.06 | | % 150.82/22.06 | | REDUCE: (10), (56), (57) imply: % 150.82/22.06 | | (60) ~ (e2 = e1) % 150.82/22.06 | | % 150.82/22.06 | | REDUCE: (35), (56) imply: % 150.82/22.06 | | (61) op(e1, e1) = e1 % 150.82/22.06 | | % 150.82/22.06 | | BETA: splitting (9) gives: % 150.82/22.06 | | % 150.82/22.06 | | Case 1: % 150.82/22.06 | | | % 150.82/22.06 | | | (62) all_58_9 = e1 % 150.82/22.06 | | | % 150.82/22.06 | | | COMBINE_EQS: (14), (62) imply: % 150.82/22.06 | | | (63) all_52_12 = e1 % 150.82/22.06 | | | % 150.82/22.06 | | | REDUCE: (40), (63) imply: % 150.82/22.06 | | | (64) ~ (all_52_8 = e1) % 150.82/22.06 | | | % 150.82/22.06 | | | REDUCE: (51), (63) imply: % 150.82/22.06 | | | (65) ~ (e3 = e1) % 150.82/22.06 | | | % 150.82/22.06 | | | SIMP: (65) implies: % 150.82/22.06 | | | (66) ~ (e3 = e1) % 150.82/22.06 | | | % 150.82/22.06 | | | BETA: splitting (26) gives: % 150.82/22.06 | | | % 150.82/22.06 | | | Case 1: % 150.82/22.06 | | | | % 150.82/22.06 | | | | (67) all_58_4 = e1 % 150.82/22.06 | | | | % 150.82/22.06 | | | | COMBINE_EQS: (7), (67) imply: % 150.82/22.06 | | | | (68) all_52_8 = e1 % 150.82/22.06 | | | | % 150.82/22.06 | | | | REDUCE: (64), (68) imply: % 150.82/22.06 | | | | (69) $false % 150.82/22.06 | | | | % 150.82/22.06 | | | | CLOSE: (69) is inconsistent. % 150.82/22.06 | | | | % 150.82/22.06 | | | Case 2: % 150.82/22.06 | | | | % 150.82/22.06 | | | | (70) all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1 % 150.82/22.06 | | | | % 150.82/22.06 | | | | BETA: splitting (70) gives: % 150.82/22.06 | | | | % 150.82/22.06 | | | | Case 1: % 150.82/22.06 | | | | | % 150.82/22.06 | | | | | (71) all_58_5 = e1 % 150.82/22.06 | | | | | % 150.82/22.06 | | | | | COMBINE_EQS: (58), (71) imply: % 150.82/22.06 | | | | | (72) e2 = e1 % 150.82/22.06 | | | | | % 150.82/22.06 | | | | | REDUCE: (60), (72) imply: % 150.82/22.06 | | | | | (73) $false % 150.82/22.06 | | | | | % 150.82/22.06 | | | | | CLOSE: (73) is inconsistent. % 150.82/22.06 | | | | | % 150.82/22.06 | | | | Case 2: % 150.82/22.06 | | | | | % 150.82/22.06 | | | | | (74) all_58_8 = e1 | all_58_14 = e1 % 150.82/22.06 | | | | | % 150.82/22.06 | | | | | BETA: splitting (74) gives: % 150.82/22.06 | | | | | % 150.82/22.06 | | | | | Case 1: % 150.82/22.06 | | | | | | % 150.82/22.06 | | | | | | (75) all_58_8 = e1 % 150.82/22.06 | | | | | | % 150.82/22.06 | | | | | | COMBINE_EQS: (41), (75) imply: % 150.82/22.06 | | | | | | (76) e3 = e1 % 150.82/22.06 | | | | | | % 150.82/22.06 | | | | | | REDUCE: (66), (76) imply: % 150.82/22.06 | | | | | | (77) $false % 150.82/22.06 | | | | | | % 150.82/22.06 | | | | | | CLOSE: (77) is inconsistent. % 150.82/22.06 | | | | | | % 150.82/22.06 | | | | | Case 2: % 150.82/22.06 | | | | | | % 150.82/22.06 | | | | | | (78) all_58_14 = e1 % 150.82/22.06 | | | | | | % 150.82/22.06 | | | | | | COMBINE_EQS: (47), (78) imply: % 150.82/22.06 | | | | | | (79) all_52_11 = e1 % 150.82/22.06 | | | | | | % 150.82/22.06 | | | | | | SIMP: (79) implies: % 150.82/22.06 | | | | | | (80) all_52_11 = e1 % 150.82/22.06 | | | | | | % 150.82/22.06 | | | | | | REDUCE: (45), (80) imply: % 150.82/22.06 | | | | | | (81) op(e1, e1) = all_56_28 % 150.82/22.06 | | | | | | % 150.82/22.06 | | | | | | GROUND_INST: instantiating (19) with e3, all_56_28, e1, e1, % 150.82/22.06 | | | | | | simplifying with (23), (81) gives: % 150.82/22.06 | | | | | | (82) all_56_28 = e3 % 150.82/22.06 | | | | | | % 150.82/22.06 | | | | | | GROUND_INST: instantiating (19) with e1, all_56_28, e1, e1, % 150.82/22.06 | | | | | | simplifying with (61), (81) gives: % 150.82/22.06 | | | | | | (83) all_56_28 = e1 % 150.82/22.06 | | | | | | % 150.82/22.06 | | | | | | COMBINE_EQS: (82), (83) imply: % 150.82/22.06 | | | | | | (84) e3 = e1 % 150.82/22.06 | | | | | | % 150.82/22.06 | | | | | | SIMP: (84) implies: % 150.82/22.06 | | | | | | (85) e3 = e1 % 150.82/22.06 | | | | | | % 150.82/22.06 | | | | | | REDUCE: (66), (85) imply: % 150.82/22.06 | | | | | | (86) $false % 150.82/22.06 | | | | | | % 150.82/22.06 | | | | | | CLOSE: (86) is inconsistent. % 150.82/22.06 | | | | | | % 150.82/22.06 | | | | | End of split % 150.82/22.06 | | | | | % 150.82/22.06 | | | | End of split % 150.82/22.06 | | | | % 150.82/22.06 | | | End of split % 150.82/22.06 | | | % 150.82/22.06 | | Case 2: % 150.82/22.06 | | | % 150.82/22.06 | | | (87) all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1 % 150.82/22.06 | | | % 150.82/22.06 | | | REF_CLOSE: (22), (25), (29), (36), (38), (59), (87) are inconsistent by % 150.82/22.06 | | | sub-proof #587. % 150.82/22.06 | | | % 150.82/22.06 | | End of split % 150.82/22.06 | | % 150.82/22.06 | End of split % 150.82/22.06 | % 150.82/22.06 End of proof % 150.82/22.06 % 150.82/22.06 Sub-proof #141 shows that the following formulas are inconsistent: % 150.82/22.06 ---------------------------------------------------------------- % 150.82/22.06 (1) all_56_11 = all_8_2 % 150.82/22.06 (2) ~ (all_8_0 = all_6_2) % 150.82/22.06 (3) ~ (all_8_2 = e1) % 150.82/22.06 (4) ~ (all_52_13 = all_8_0) % 150.82/22.06 (5) all_54_5 = all_8_2 % 150.82/22.06 (6) ~ (all_8_0 = all_8_2) % 150.82/22.06 (7) all_56_21 = all_6_2 % 150.82/22.06 (8) all_56_1 = all_10_2 % 150.82/22.06 (9) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0 % 150.82/22.06 (10) all_58_5 = all_8_0 % 150.82/22.06 (11) op(e2, all_8_2) = all_56_10 % 150.82/22.06 (12) op(e3, e3) = all_10_2 % 150.82/22.06 (13) ~ (all_52_1 = all_8_2) % 150.82/22.06 (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 150.82/22.06 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 150.82/22.06 (15) all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0 % 150.82/22.06 (16) ~ (all_56_11 = e3) | all_56_9 = e2 % 150.82/22.06 (17) all_58_3 = all_8_2 % 150.82/22.06 (18) all_56_31 = all_4_2 % 150.82/22.06 (19) ~ (all_52_1 = all_8_0) % 150.82/22.06 (20) all_56_1 = e3 | all_56_11 = e2 | all_56_21 = e1 | all_56_31 = e0 % 150.82/22.06 (21) ~ (all_52_13 = all_4_2) % 150.82/22.06 (22) ~ (all_8_0 = e0) | ~ (all_8_2 = e3) % 150.82/22.06 (23) op(all_8_2, all_8_2) = e1 % 150.82/22.06 (24) all_58_2 = all_52_1 % 150.82/22.06 (25) all_58_10 = all_52_13 % 150.82/22.06 (26) op(e2, e2) = all_8_2 % 150.82/22.06 (27) ~ (all_8_2 = e0) % 150.82/22.06 (28) all_54_6 = all_8_0 % 150.82/22.06 (29) ~ (e2 = e0) % 150.82/22.06 (30) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 150.82/22.06 (31) all_56_9 = all_52_1 % 150.82/22.06 % 150.82/22.06 Begin of proof % 150.82/22.06 | % 150.82/22.06 | BETA: splitting (16) gives: % 150.82/22.06 | % 150.82/22.06 | Case 1: % 150.82/22.06 | | % 150.82/22.06 | | (32) ~ (all_56_11 = e3) % 150.82/22.06 | | % 150.82/22.06 | | REDUCE: (1), (32) imply: % 150.82/22.06 | | (33) ~ (all_8_2 = e3) % 150.82/22.06 | | % 150.82/22.06 | | REF_CLOSE: (3), (5), (11), (14), (23), (26), (27), (30), (33) are % 150.82/22.06 | | inconsistent by sub-proof #146. % 150.82/22.06 | | % 150.82/22.06 | Case 2: % 150.82/22.06 | | % 150.82/22.06 | | (34) all_56_11 = e3 % 150.82/22.06 | | (35) all_56_9 = e2 % 150.82/22.06 | | % 150.82/22.06 | | COMBINE_EQS: (31), (35) imply: % 150.82/22.06 | | (36) all_52_1 = e2 % 150.82/22.06 | | % 150.82/22.06 | | COMBINE_EQS: (1), (34) imply: % 150.82/22.06 | | (37) all_8_2 = e3 % 150.82/22.06 | | % 150.82/22.06 | | COMBINE_EQS: (17), (37) imply: % 150.82/22.06 | | (38) all_58_3 = e3 % 150.82/22.06 | | % 150.82/22.06 | | COMBINE_EQS: (24), (36) imply: % 150.82/22.06 | | (39) all_58_2 = e2 % 150.82/22.06 | | % 150.82/22.06 | | REDUCE: (19), (36) imply: % 150.82/22.06 | | (40) ~ (all_8_0 = e2) % 150.82/22.06 | | % 150.82/22.06 | | SIMP: (40) implies: % 150.82/22.06 | | (41) ~ (all_8_0 = e2) % 150.82/22.06 | | % 150.82/22.06 | | REDUCE: (13), (36), (37) imply: % 150.82/22.06 | | (42) ~ (e3 = e2) % 150.82/22.06 | | % 150.82/22.06 | | SIMP: (42) implies: % 150.82/22.06 | | (43) ~ (e3 = e2) % 150.82/22.06 | | % 150.82/22.06 | | REDUCE: (6), (37) imply: % 150.82/22.06 | | (44) ~ (all_8_0 = e3) % 150.82/22.06 | | % 150.82/22.06 | | REDUCE: (27), (37) imply: % 150.82/22.06 | | (45) ~ (e3 = e0) % 150.82/22.06 | | % 150.82/22.06 | | REDUCE: (23), (37) imply: % 150.82/22.06 | | (46) op(e3, e3) = e1 % 150.82/22.06 | | % 150.82/22.06 | | BETA: splitting (22) gives: % 150.82/22.06 | | % 150.82/22.06 | | Case 1: % 150.82/22.06 | | | % 150.82/22.06 | | | (47) ~ (all_8_2 = e3) % 150.82/22.06 | | | % 150.82/22.06 | | | REF_CLOSE: (3), (5), (11), (14), (23), (26), (27), (30), (47) are % 150.82/22.06 | | | inconsistent by sub-proof #146. % 150.82/22.06 | | | % 150.82/22.06 | | Case 2: % 150.82/22.06 | | | % 150.82/22.06 | | | (48) ~ (all_8_0 = e0) % 150.82/22.06 | | | % 150.82/22.06 | | | BETA: splitting (9) gives: % 150.82/22.06 | | | % 150.82/22.06 | | | Case 1: % 150.82/22.06 | | | | % 150.82/22.06 | | | | (49) all_54_6 = e3 % 150.82/22.06 | | | | % 150.82/22.06 | | | | REF_CLOSE: (28), (44), (49) are inconsistent by sub-proof #145. % 150.82/22.06 | | | | % 150.82/22.06 | | | Case 2: % 150.82/22.06 | | | | % 150.82/22.06 | | | | (50) ~ (all_54_6 = e3) % 150.82/22.06 | | | | (51) all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0 % 150.82/22.06 | | | | % 150.82/22.06 | | | | BETA: splitting (15) gives: % 150.82/22.06 | | | | % 150.82/22.06 | | | | Case 1: % 150.82/22.06 | | | | | % 150.82/22.06 | | | | | (52) all_58_2 = e0 % 150.82/22.06 | | | | | % 150.82/22.06 | | | | | COMBINE_EQS: (39), (52) imply: % 150.82/22.06 | | | | | (53) e2 = e0 % 150.82/22.06 | | | | | % 150.82/22.06 | | | | | REDUCE: (29), (53) imply: % 150.82/22.06 | | | | | (54) $false % 150.82/22.06 | | | | | % 150.82/22.06 | | | | | CLOSE: (54) is inconsistent. % 150.82/22.06 | | | | | % 150.82/22.06 | | | | Case 2: % 150.82/22.06 | | | | | % 150.82/22.06 | | | | | (55) all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0 % 150.82/22.06 | | | | | % 150.82/22.06 | | | | | BETA: splitting (55) gives: % 150.82/22.06 | | | | | % 150.82/22.06 | | | | | Case 1: % 150.82/22.06 | | | | | | % 150.82/22.06 | | | | | | (56) all_58_3 = e0 % 150.82/22.06 | | | | | | % 150.82/22.06 | | | | | | COMBINE_EQS: (38), (56) imply: % 150.82/22.06 | | | | | | (57) e3 = e0 % 150.82/22.06 | | | | | | % 150.82/22.06 | | | | | | REDUCE: (45), (57) imply: % 150.82/22.06 | | | | | | (58) $false % 150.82/22.06 | | | | | | % 150.82/22.06 | | | | | | CLOSE: (58) is inconsistent. % 150.82/22.06 | | | | | | % 150.82/22.06 | | | | | Case 2: % 150.82/22.06 | | | | | | % 150.82/22.06 | | | | | | (59) all_58_5 = e0 | all_58_10 = e0 % 150.82/22.06 | | | | | | % 150.82/22.06 | | | | | | BETA: splitting (59) gives: % 150.82/22.06 | | | | | | % 150.82/22.06 | | | | | | Case 1: % 150.82/22.06 | | | | | | | % 150.82/22.06 | | | | | | | (60) all_58_5 = e0 % 150.82/22.06 | | | | | | | % 150.82/22.06 | | | | | | | COMBINE_EQS: (10), (60) imply: % 150.82/22.06 | | | | | | | (61) all_8_0 = e0 % 150.82/22.06 | | | | | | | % 150.82/22.06 | | | | | | | REDUCE: (48), (61) imply: % 150.82/22.06 | | | | | | | (62) $false % 150.82/22.06 | | | | | | | % 150.82/22.06 | | | | | | | CLOSE: (62) is inconsistent. % 150.82/22.06 | | | | | | | % 150.82/22.06 | | | | | | Case 2: % 150.82/22.06 | | | | | | | % 150.82/22.06 | | | | | | | (63) all_58_10 = e0 % 150.82/22.06 | | | | | | | % 150.82/22.06 | | | | | | | COMBINE_EQS: (25), (63) imply: % 150.82/22.06 | | | | | | | (64) all_52_13 = e0 % 150.82/22.06 | | | | | | | % 150.82/22.06 | | | | | | | REDUCE: (4), (64) imply: % 150.82/22.06 | | | | | | | (65) ~ (all_8_0 = e0) % 150.82/22.06 | | | | | | | % 150.82/22.06 | | | | | | | REDUCE: (21), (64) imply: % 150.82/22.06 | | | | | | | (66) ~ (all_4_2 = e0) % 150.82/22.06 | | | | | | | % 150.82/22.06 | | | | | | | SIMP: (66) implies: % 150.82/22.06 | | | | | | | (67) ~ (all_4_2 = e0) % 150.82/22.06 | | | | | | | % 150.82/22.06 | | | | | | | BETA: splitting (51) gives: % 150.82/22.06 | | | | | | | % 150.82/22.06 | | | | | | | Case 1: % 150.82/22.06 | | | | | | | | % 150.82/22.06 | | | | | | | | (68) all_54_6 = e2 % 150.82/22.06 | | | | | | | | % 150.82/22.06 | | | | | | | | REF_CLOSE: (28), (41), (68) are inconsistent by sub-proof #144. % 150.82/22.06 | | | | | | | | % 150.82/22.06 | | | | | | | Case 2: % 150.82/22.06 | | | | | | | | % 150.82/22.06 | | | | | | | | (69) all_54_6 = e1 | all_54_6 = e0 % 150.82/22.06 | | | | | | | | % 150.82/22.06 | | | | | | | | REF_CLOSE: (2), (7), (8), (12), (14), (18), (20), (28), (34), % 150.82/22.06 | | | | | | | | (43), (44), (46), (48), (67), (69) are inconsistent % 150.82/22.06 | | | | | | | | by sub-proof #142. % 150.82/22.06 | | | | | | | | % 150.82/22.06 | | | | | | | End of split % 150.82/22.06 | | | | | | | % 150.82/22.06 | | | | | | End of split % 150.82/22.06 | | | | | | % 150.82/22.06 | | | | | End of split % 150.82/22.06 | | | | | % 150.82/22.06 | | | | End of split % 150.82/22.06 | | | | % 150.82/22.06 | | | End of split % 150.82/22.06 | | | % 150.82/22.06 | | End of split % 150.82/22.06 | | % 150.82/22.06 | End of split % 150.82/22.06 | % 150.82/22.06 End of proof % 150.82/22.06 % 150.82/22.06 Sub-proof #142 shows that the following formulas are inconsistent: % 150.82/22.06 ---------------------------------------------------------------- % 150.82/22.06 (1) ~ (all_8_0 = all_6_2) % 150.82/22.06 (2) ~ (e3 = e2) % 150.82/22.06 (3) all_56_11 = e3 % 150.82/22.06 (4) all_56_21 = all_6_2 % 150.82/22.06 (5) all_56_1 = all_10_2 % 150.82/22.06 (6) op(e3, e3) = all_10_2 % 150.82/22.06 (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 150.82/22.06 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 150.82/22.06 (8) ~ (all_8_0 = e0) % 150.82/22.06 (9) ~ (all_4_2 = e0) % 150.82/22.06 (10) op(e3, e3) = e1 % 150.82/22.06 (11) all_56_31 = all_4_2 % 150.82/22.06 (12) ~ (all_8_0 = e3) % 150.82/22.06 (13) all_56_1 = e3 | all_56_11 = e2 | all_56_21 = e1 | all_56_31 = e0 % 150.82/22.06 (14) all_54_6 = all_8_0 % 150.82/22.06 (15) all_54_6 = e1 | all_54_6 = e0 % 150.82/22.06 % 150.82/22.06 Begin of proof % 150.82/22.06 | % 150.82/22.06 | BETA: splitting (15) gives: % 150.82/22.06 | % 150.82/22.06 | Case 1: % 150.82/22.06 | | % 150.82/22.06 | | (16) all_54_6 = e1 % 150.82/22.06 | | % 150.82/22.06 | | COMBINE_EQS: (14), (16) imply: % 150.82/22.06 | | (17) all_8_0 = e1 % 150.82/22.06 | | % 150.82/22.06 | | SIMP: (17) implies: % 150.82/22.06 | | (18) all_8_0 = e1 % 150.82/22.06 | | % 150.82/22.06 | | REDUCE: (1), (18) imply: % 150.82/22.06 | | (19) ~ (all_6_2 = e1) % 150.82/22.06 | | % 150.82/22.06 | | SIMP: (19) implies: % 150.82/22.06 | | (20) ~ (all_6_2 = e1) % 150.82/22.06 | | % 150.82/22.06 | | REDUCE: (12), (18) imply: % 150.82/22.06 | | (21) ~ (e3 = e1) % 150.82/22.06 | | % 150.82/22.06 | | SIMP: (21) implies: % 150.82/22.06 | | (22) ~ (e3 = e1) % 150.82/22.06 | | % 150.82/22.06 | | BETA: splitting (13) gives: % 150.82/22.06 | | % 150.82/22.06 | | Case 1: % 150.82/22.06 | | | % 150.82/22.06 | | | (23) all_56_1 = e3 % 150.82/22.06 | | | % 150.82/22.06 | | | COMBINE_EQS: (5), (23) imply: % 150.82/22.06 | | | (24) all_10_2 = e3 % 150.82/22.06 | | | % 150.82/22.06 | | | REF_CLOSE: (6), (7), (10), (22), (24) are inconsistent by sub-proof #306. % 150.82/22.06 | | | % 150.82/22.06 | | Case 2: % 150.82/22.06 | | | % 150.82/22.06 | | | (25) all_56_11 = e2 | all_56_21 = e1 | all_56_31 = e0 % 150.82/22.06 | | | % 150.82/22.06 | | | REF_CLOSE: (2), (3), (4), (9), (11), (20), (25) are inconsistent by % 150.82/22.06 | | | sub-proof #152. % 150.82/22.06 | | | % 150.82/22.06 | | End of split % 150.82/22.06 | | % 150.82/22.06 | Case 2: % 150.82/22.06 | | % 150.82/22.06 | | (26) all_54_6 = e0 % 150.82/22.06 | | % 150.82/22.06 | | REF_CLOSE: (8), (14), (26) are inconsistent by sub-proof #143. % 150.82/22.06 | | % 150.82/22.06 | End of split % 150.82/22.06 | % 150.82/22.06 End of proof % 150.82/22.06 % 150.82/22.06 Sub-proof #143 shows that the following formulas are inconsistent: % 150.82/22.06 ---------------------------------------------------------------- % 150.82/22.06 (1) all_54_6 = all_8_0 % 150.82/22.06 (2) all_54_6 = e0 % 150.82/22.06 (3) ~ (all_8_0 = e0) % 150.82/22.06 % 150.82/22.06 Begin of proof % 150.82/22.06 | % 150.82/22.06 | COMBINE_EQS: (1), (2) imply: % 150.82/22.06 | (4) all_8_0 = e0 % 150.82/22.06 | % 150.82/22.06 | SIMP: (4) implies: % 150.82/22.06 | (5) all_8_0 = e0 % 150.82/22.06 | % 150.82/22.06 | REDUCE: (3), (5) imply: % 150.82/22.06 | (6) $false % 150.82/22.06 | % 150.82/22.06 | CLOSE: (6) is inconsistent. % 150.82/22.06 | % 150.82/22.06 End of proof % 150.82/22.06 % 150.82/22.06 Sub-proof #144 shows that the following formulas are inconsistent: % 150.82/22.06 ---------------------------------------------------------------- % 150.82/22.06 (1) all_54_6 = all_8_0 % 150.82/22.06 (2) all_54_6 = e2 % 150.82/22.06 (3) ~ (all_8_0 = e2) % 150.82/22.06 % 150.82/22.06 Begin of proof % 150.82/22.06 | % 150.82/22.06 | COMBINE_EQS: (1), (2) imply: % 150.82/22.06 | (4) all_8_0 = e2 % 150.82/22.06 | % 150.82/22.06 | SIMP: (4) implies: % 150.82/22.06 | (5) all_8_0 = e2 % 150.82/22.06 | % 150.82/22.06 | REDUCE: (3), (5) imply: % 150.82/22.06 | (6) $false % 150.82/22.06 | % 150.82/22.06 | CLOSE: (6) is inconsistent. % 150.82/22.06 | % 150.82/22.06 End of proof % 150.82/22.06 % 150.82/22.06 Sub-proof #145 shows that the following formulas are inconsistent: % 150.82/22.06 ---------------------------------------------------------------- % 150.82/22.06 (1) all_54_6 = all_8_0 % 150.82/22.06 (2) all_54_6 = e3 % 150.82/22.06 (3) ~ (all_8_0 = e3) % 150.82/22.06 % 150.82/22.06 Begin of proof % 150.82/22.06 | % 150.82/22.06 | COMBINE_EQS: (1), (2) imply: % 150.82/22.06 | (4) all_8_0 = e3 % 150.82/22.06 | % 150.82/22.06 | SIMP: (4) implies: % 150.82/22.06 | (5) all_8_0 = e3 % 150.82/22.06 | % 150.82/22.06 | REDUCE: (3), (5) imply: % 150.82/22.06 | (6) $false % 150.82/22.06 | % 150.82/22.06 | CLOSE: (6) is inconsistent. % 150.82/22.06 | % 150.82/22.07 End of proof % 150.82/22.07 % 150.82/22.07 Sub-proof #146 shows that the following formulas are inconsistent: % 150.82/22.07 ---------------------------------------------------------------- % 150.82/22.07 (1) ~ (all_8_2 = e1) % 150.82/22.07 (2) all_54_5 = all_8_2 % 150.82/22.07 (3) op(e2, all_8_2) = all_56_10 % 150.82/22.07 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 150.82/22.07 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 150.82/22.07 (5) ~ (all_8_2 = e3) % 150.82/22.07 (6) op(all_8_2, all_8_2) = e1 % 150.82/22.07 (7) op(e2, e2) = all_8_2 % 150.82/22.07 (8) ~ (all_8_2 = e0) % 150.82/22.07 (9) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 150.82/22.07 % 150.82/22.07 Begin of proof % 150.82/22.07 | % 150.82/22.07 | BETA: splitting (9) gives: % 150.82/22.07 | % 150.82/22.07 | Case 1: % 150.82/22.07 | | % 150.82/22.07 | | (10) all_54_5 = e3 % 150.82/22.07 | | % 150.82/22.07 | | REF_CLOSE: (2), (5), (10) are inconsistent by sub-proof #737. % 150.82/22.07 | | % 150.82/22.07 | Case 2: % 150.82/22.07 | | % 150.82/22.07 | | (11) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 150.82/22.07 | | % 150.82/22.07 | | BETA: splitting (11) gives: % 150.82/22.07 | | % 150.82/22.07 | | Case 1: % 150.82/22.07 | | | % 150.82/22.07 | | | (12) all_54_5 = e2 % 150.82/22.07 | | | % 150.82/22.07 | | | COMBINE_EQS: (2), (12) imply: % 150.82/22.07 | | | (13) all_8_2 = e2 % 150.82/22.07 | | | % 150.82/22.07 | | | SIMP: (13) implies: % 150.82/22.07 | | | (14) all_8_2 = e2 % 150.82/22.07 | | | % 150.82/22.07 | | | REDUCE: (7), (14) imply: % 150.82/22.07 | | | (15) op(e2, e2) = e2 % 150.82/22.07 | | | % 150.82/22.07 | | | REF_CLOSE: (1), (3), (4), (6), (7), (15) are inconsistent by sub-proof % 150.82/22.07 | | | #147. % 150.82/22.07 | | | % 150.82/22.07 | | Case 2: % 150.82/22.07 | | | % 150.82/22.07 | | | (16) all_54_5 = e1 | all_54_5 = e0 % 150.82/22.07 | | | % 150.82/22.07 | | | REF_CLOSE: (1), (2), (8), (16) are inconsistent by sub-proof #645. % 150.82/22.07 | | | % 150.82/22.07 | | End of split % 150.82/22.07 | | % 150.82/22.07 | End of split % 150.82/22.07 | % 150.82/22.07 End of proof % 150.82/22.07 % 150.82/22.07 Sub-proof #147 shows that the following formulas are inconsistent: % 150.82/22.07 ---------------------------------------------------------------- % 150.82/22.07 (1) ~ (all_8_2 = e1) % 150.82/22.07 (2) op(e2, e2) = e2 % 150.82/22.07 (3) op(e2, all_8_2) = all_56_10 % 150.82/22.07 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 150.82/22.07 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 150.82/22.07 (5) op(all_8_2, all_8_2) = e1 % 150.82/22.07 (6) op(e2, e2) = all_8_2 % 150.82/22.07 % 150.82/22.07 Begin of proof % 150.82/22.07 | % 150.82/22.07 | GROUND_INST: instantiating (4) with all_8_2, e2, e2, e2, simplifying with (2), % 150.82/22.07 | (6) gives: % 150.82/22.07 | (7) all_8_2 = e2 % 150.82/22.07 | % 150.82/22.07 | REDUCE: (1), (7) imply: % 150.82/22.07 | (8) ~ (e2 = e1) % 150.82/22.07 | % 150.82/22.07 | REDUCE: (5), (7) imply: % 150.82/22.07 | (9) op(e2, e2) = e1 % 150.82/22.07 | % 150.82/22.07 | REDUCE: (3), (7) imply: % 150.82/22.07 | (10) op(e2, e2) = all_56_10 % 150.82/22.07 | % 150.82/22.07 | GROUND_INST: instantiating (4) with e2, all_56_10, e2, e2, simplifying with % 150.82/22.07 | (2), (10) gives: % 150.82/22.07 | (11) all_56_10 = e2 % 150.82/22.07 | % 150.82/22.07 | GROUND_INST: instantiating (4) with e1, all_56_10, e2, e2, simplifying with % 150.82/22.07 | (9), (10) gives: % 150.82/22.07 | (12) all_56_10 = e1 % 150.82/22.07 | % 150.82/22.07 | COMBINE_EQS: (11), (12) imply: % 150.82/22.07 | (13) e2 = e1 % 150.82/22.07 | % 150.82/22.07 | REDUCE: (8), (13) imply: % 150.82/22.07 | (14) $false % 150.82/22.07 | % 150.82/22.07 | CLOSE: (14) is inconsistent. % 150.82/22.07 | % 150.82/22.07 End of proof % 150.82/22.07 % 150.82/22.07 Sub-proof #148 shows that the following formulas are inconsistent: % 150.82/22.07 ---------------------------------------------------------------- % 150.82/22.07 (1) all_56_11 = all_8_2 % 150.82/22.07 (2) ~ (e3 = e0) % 150.82/22.07 (3) ~ (all_4_1 = e0) % 150.82/22.07 (4) all_54_10 = all_6_2 % 150.82/22.07 (5) ~ (all_8_2 = e1) % 150.82/22.07 (6) all_56_31 = e3 % 150.82/22.07 (7) ~ (all_52_9 = all_8_2) % 150.82/22.07 (8) ~ (all_6_2 = e3) % 150.82/22.07 (9) all_58_4 = all_52_8 % 150.82/22.07 (10) all_54_5 = all_8_2 % 150.82/22.07 (11) ~ (all_52_4 = all_4_1) % 150.82/22.07 (12) ~ (all_6_0 = e2) % 150.82/22.07 (13) all_56_21 = all_6_2 % 150.82/22.07 (14) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 150.82/22.07 (15) all_58_5 = all_52_9 % 150.82/22.07 (16) all_56_1 = all_4_1 % 150.82/22.07 (17) all_58_12 = e0 % 150.82/22.07 (18) all_58_1 = all_52_4 % 150.82/22.07 (19) all_58_13 = all_52_7 % 150.82/22.07 (20) all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2 % 150.82/22.07 (21) ~ (all_52_1 = all_8_2) % 150.82/22.07 (22) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 150.82/22.07 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 150.82/22.07 (23) ~ (all_52_11 = e3) % 150.82/22.07 (24) ~ (all_56_11 = e3) | all_56_9 = e2 % 150.82/22.07 (25) all_58_8 = all_6_2 % 150.82/22.07 (26) all_58_0 = all_4_1 % 150.82/22.07 (27) ~ (all_56_1 = e2) | all_56_3 = e3 % 150.82/22.07 (28) all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3 % 150.82/22.07 (29) all_58_3 = all_8_2 % 150.82/22.07 (30) all_56_3 = all_52_4 % 150.82/22.07 (31) all_56_1 = e3 | all_56_11 = e2 | all_56_21 = e1 | all_56_31 = e0 % 150.82/22.07 (32) all_58_6 = all_6_0 % 150.82/22.07 (33) op(e1, e1) = all_6_2 % 150.82/22.07 (34) ~ (all_6_2 = e2) % 150.82/22.07 (35) all_58_2 = all_52_1 % 150.82/22.07 (36) all_58_7 = all_52_6 % 150.82/22.07 (37) ~ (all_52_8 = all_4_1) % 150.82/22.07 (38) op(e1, all_6_2) = all_56_20 % 150.82/22.07 (39) all_58_1 = e0 | all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0 % 150.82/22.07 (40) ~ (e3 = e1) % 150.82/22.07 (41) ~ (all_52_6 = all_6_2) % 150.82/22.07 (42) ~ (all_8_2 = e0) % 150.82/22.07 (43) op(all_6_2, all_6_2) = e3 % 150.82/22.07 (44) ~ (all_52_7 = e0) % 150.82/22.07 (45) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 150.82/22.07 (46) all_58_14 = all_52_11 % 150.82/22.07 (47) all_56_9 = all_52_1 % 150.82/22.07 % 150.82/22.07 Begin of proof % 150.82/22.07 | % 150.82/22.07 | BETA: splitting (24) gives: % 150.82/22.07 | % 150.82/22.07 | Case 1: % 150.82/22.07 | | % 150.82/22.07 | | (48) ~ (all_56_11 = e3) % 150.82/22.07 | | % 150.82/22.07 | | REDUCE: (1), (48) imply: % 150.82/22.07 | | (49) ~ (all_8_2 = e3) % 150.82/22.07 | | % 150.82/22.07 | | BETA: splitting (45) gives: % 150.82/22.07 | | % 150.82/22.07 | | Case 1: % 150.82/22.07 | | | % 150.82/22.07 | | | (50) all_54_5 = e3 % 150.82/22.07 | | | % 150.82/22.07 | | | REF_CLOSE: (10), (49), (50) are inconsistent by sub-proof #737. % 150.82/22.07 | | | % 150.82/22.07 | | Case 2: % 150.82/22.07 | | | % 150.82/22.07 | | | (51) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 150.82/22.07 | | | % 150.82/22.07 | | | BETA: splitting (51) gives: % 150.82/22.07 | | | % 150.82/22.07 | | | Case 1: % 150.82/22.07 | | | | % 150.82/22.07 | | | | (52) all_54_5 = e2 % 150.82/22.07 | | | | % 150.82/22.07 | | | | COMBINE_EQS: (10), (52) imply: % 150.82/22.07 | | | | (53) all_8_2 = e2 % 150.82/22.07 | | | | % 150.82/22.07 | | | | SIMP: (53) implies: % 150.82/22.07 | | | | (54) all_8_2 = e2 % 150.82/22.07 | | | | % 150.82/22.07 | | | | COMBINE_EQS: (1), (54) imply: % 150.82/22.07 | | | | (55) all_56_11 = e2 % 150.82/22.07 | | | | % 150.82/22.07 | | | | COMBINE_EQS: (29), (54) imply: % 150.82/22.07 | | | | (56) all_58_3 = e2 % 150.82/22.07 | | | | % 150.82/22.07 | | | | REDUCE: (21), (54) imply: % 150.82/22.07 | | | | (57) ~ (all_52_1 = e2) % 150.82/22.07 | | | | % 150.82/22.07 | | | | REDUCE: (42), (54) imply: % 150.82/22.07 | | | | (58) ~ (e2 = e0) % 150.82/22.07 | | | | % 150.82/22.07 | | | | BETA: splitting (20) gives: % 150.82/22.07 | | | | % 150.82/22.07 | | | | Case 1: % 150.82/22.07 | | | | | % 150.82/22.07 | | | | | (59) all_58_0 = e2 % 150.82/22.07 | | | | | % 150.82/22.07 | | | | | COMBINE_EQS: (26), (59) imply: % 150.82/22.07 | | | | | (60) all_4_1 = e2 % 150.82/22.07 | | | | | % 150.82/22.07 | | | | | COMBINE_EQS: (16), (60) imply: % 150.82/22.07 | | | | | (61) all_56_1 = e2 % 150.82/22.07 | | | | | % 150.82/22.07 | | | | | REDUCE: (11), (60) imply: % 150.82/22.07 | | | | | (62) ~ (all_52_4 = e2) % 150.82/22.07 | | | | | % 150.82/22.07 | | | | | BETA: splitting (27) gives: % 150.82/22.07 | | | | | % 150.82/22.07 | | | | | Case 1: % 150.82/22.07 | | | | | | % 150.82/22.07 | | | | | | (63) ~ (all_56_1 = e2) % 150.82/22.07 | | | | | | % 150.82/22.07 | | | | | | REDUCE: (61), (63) imply: % 150.82/22.07 | | | | | | (64) $false % 150.82/22.07 | | | | | | % 150.82/22.07 | | | | | | CLOSE: (64) is inconsistent. % 150.82/22.07 | | | | | | % 150.82/22.07 | | | | | Case 2: % 150.82/22.07 | | | | | | % 150.82/22.07 | | | | | | (65) all_56_3 = e3 % 150.82/22.07 | | | | | | % 150.82/22.07 | | | | | | COMBINE_EQS: (30), (65) imply: % 150.82/22.07 | | | | | | (66) all_52_4 = e3 % 150.82/22.07 | | | | | | % 150.82/22.07 | | | | | | SIMP: (66) implies: % 150.82/22.07 | | | | | | (67) all_52_4 = e3 % 150.82/22.07 | | | | | | % 150.82/22.07 | | | | | | COMBINE_EQS: (18), (67) imply: % 150.82/22.07 | | | | | | (68) all_58_1 = e3 % 150.82/22.07 | | | | | | % 150.82/22.07 | | | | | | REDUCE: (62), (67) imply: % 150.82/22.07 | | | | | | (69) ~ (e3 = e2) % 150.82/22.07 | | | | | | % 150.82/22.07 | | | | | | REF_CLOSE: (2), (4), (6), (8), (13), (14), (19), (22), (31), (33), % 150.82/22.07 | | | | | | (34), (36), (38), (39), (40), (41), (43), (44), (55), % 150.82/22.07 | | | | | | (56), (58), (61), (68), (69) are inconsistent by % 150.82/22.07 | | | | | | sub-proof #424. % 150.82/22.07 | | | | | | % 150.82/22.07 | | | | | End of split % 150.82/22.07 | | | | | % 150.82/22.07 | | | | Case 2: % 150.82/22.07 | | | | | % 150.82/22.07 | | | | | (70) all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2 % 150.82/22.07 | | | | | % 150.82/22.07 | | | | | REF_CLOSE: (12), (17), (32), (35), (57), (58), (70) are inconsistent % 150.82/22.07 | | | | | by sub-proof #421. % 150.82/22.07 | | | | | % 150.82/22.07 | | | | End of split % 150.82/22.07 | | | | % 150.82/22.07 | | | Case 2: % 150.82/22.07 | | | | % 150.82/22.07 | | | | (71) all_54_5 = e1 | all_54_5 = e0 % 150.82/22.07 | | | | % 150.82/22.07 | | | | REF_CLOSE: (5), (10), (42), (71) are inconsistent by sub-proof #645. % 150.82/22.07 | | | | % 150.82/22.07 | | | End of split % 150.82/22.07 | | | % 150.82/22.07 | | End of split % 150.82/22.07 | | % 150.82/22.07 | Case 2: % 150.82/22.07 | | % 150.82/22.07 | | (72) all_56_11 = e3 % 150.82/22.07 | | (73) all_56_9 = e2 % 150.82/22.07 | | % 150.82/22.07 | | COMBINE_EQS: (47), (73) imply: % 150.82/22.07 | | (74) all_52_1 = e2 % 150.82/22.07 | | % 150.82/22.07 | | COMBINE_EQS: (1), (72) imply: % 150.82/22.07 | | (75) all_8_2 = e3 % 150.82/22.07 | | % 150.82/22.07 | | REDUCE: (21), (74), (75) imply: % 150.82/22.07 | | (76) ~ (e3 = e2) % 150.82/22.07 | | % 150.82/22.07 | | SIMP: (76) implies: % 150.82/22.07 | | (77) ~ (e3 = e2) % 150.82/22.07 | | % 150.82/22.07 | | REDUCE: (7), (75) imply: % 150.82/22.07 | | (78) ~ (all_52_9 = e3) % 150.82/22.07 | | % 150.82/22.07 | | BETA: splitting (28) gives: % 150.82/22.07 | | % 150.82/22.07 | | Case 1: % 150.82/22.07 | | | % 150.82/22.07 | | | (79) all_58_4 = e3 % 150.82/22.07 | | | % 150.82/22.07 | | | COMBINE_EQS: (9), (79) imply: % 150.82/22.07 | | | (80) all_52_8 = e3 % 150.82/22.07 | | | % 150.82/22.07 | | | REDUCE: (37), (80) imply: % 150.82/22.07 | | | (81) ~ (all_4_1 = e3) % 150.82/22.07 | | | % 150.82/22.07 | | | SIMP: (81) implies: % 150.82/22.07 | | | (82) ~ (all_4_1 = e3) % 150.82/22.07 | | | % 150.82/22.07 | | | REF_CLOSE: (2), (6), (13), (16), (22), (31), (33), (38), (40), (43), (72), % 150.82/22.07 | | | (77), (82) are inconsistent by sub-proof #262. % 150.82/22.07 | | | % 150.82/22.07 | | Case 2: % 150.82/22.07 | | | % 150.82/22.07 | | | (83) all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3 % 150.82/22.07 | | | % 150.82/22.07 | | | BETA: splitting (83) gives: % 150.82/22.07 | | | % 150.82/22.07 | | | Case 1: % 150.82/22.07 | | | | % 150.82/22.07 | | | | (84) all_58_5 = e3 % 150.82/22.07 | | | | % 150.82/22.07 | | | | COMBINE_EQS: (15), (84) imply: % 150.82/22.07 | | | | (85) all_52_9 = e3 % 150.82/22.07 | | | | % 150.82/22.07 | | | | REDUCE: (78), (85) imply: % 150.82/22.07 | | | | (86) $false % 150.82/22.07 | | | | % 150.82/22.07 | | | | CLOSE: (86) is inconsistent. % 150.82/22.07 | | | | % 150.82/22.07 | | | Case 2: % 150.82/22.07 | | | | % 150.82/22.07 | | | | (87) all_58_8 = e3 | all_58_14 = e3 % 150.82/22.07 | | | | % 150.82/22.07 | | | | REF_CLOSE: (8), (23), (25), (46), (87) are inconsistent by sub-proof % 150.82/22.07 | | | | #149. % 150.82/22.07 | | | | % 150.82/22.07 | | | End of split % 150.82/22.07 | | | % 150.82/22.07 | | End of split % 150.82/22.07 | | % 150.82/22.07 | End of split % 150.82/22.07 | % 150.82/22.07 End of proof % 150.82/22.07 % 150.82/22.07 Sub-proof #149 shows that the following formulas are inconsistent: % 150.82/22.07 ---------------------------------------------------------------- % 150.82/22.07 (1) ~ (all_6_2 = e3) % 150.82/22.07 (2) all_58_8 = e3 | all_58_14 = e3 % 150.82/22.07 (3) ~ (all_52_11 = e3) % 150.82/22.07 (4) all_58_8 = all_6_2 % 150.82/22.07 (5) all_58_14 = all_52_11 % 150.82/22.07 % 150.82/22.07 Begin of proof % 150.82/22.07 | % 150.82/22.07 | BETA: splitting (2) gives: % 150.82/22.07 | % 150.82/22.07 | Case 1: % 150.82/22.07 | | % 150.82/22.07 | | (6) all_58_8 = e3 % 150.82/22.07 | | % 150.82/22.07 | | COMBINE_EQS: (4), (6) imply: % 150.82/22.07 | | (7) all_6_2 = e3 % 150.82/22.07 | | % 150.82/22.07 | | REDUCE: (1), (7) imply: % 150.82/22.07 | | (8) $false % 150.82/22.07 | | % 150.82/22.07 | | CLOSE: (8) is inconsistent. % 150.82/22.07 | | % 150.82/22.07 | Case 2: % 150.82/22.07 | | % 150.82/22.07 | | (9) all_58_14 = e3 % 150.82/22.07 | | % 150.82/22.07 | | REF_CLOSE: (3), (5), (9) are inconsistent by sub-proof #447. % 150.82/22.07 | | % 150.82/22.07 | End of split % 150.82/22.07 | % 150.82/22.07 End of proof % 150.82/22.07 % 150.82/22.07 Sub-proof #150 shows that the following formulas are inconsistent: % 150.82/22.07 ---------------------------------------------------------------- % 150.82/22.07 (1) all_56_11 = all_8_2 % 150.82/22.07 (2) op(e0, all_52_13) = all_56_14 % 150.82/22.07 (3) ~ (all_56_11 = e1) | all_56_13 = e2 % 150.82/22.07 (4) ~ (all_52_11 = all_6_2) % 150.82/22.07 (5) ~ (all_52_4 = all_52_8) % 150.82/22.07 (6) all_56_25 = all_52_3 % 150.82/22.07 (7) ~ (all_34_1 = e3) | ~ (all_34_2 = e1) % 150.82/22.07 (8) ~ (all_52_7 = all_52_11) % 150.82/22.07 (9) ~ (all_52_8 = all_52_9) % 150.82/22.07 (10) all_54_9 = all_52_6 % 150.82/22.07 (11) op(e2, all_8_1) = all_8_0 % 150.82/22.07 (12) all_58_6 = all_52_2 % 150.82/22.07 (13) ~ (all_8_1 = e1) % 150.82/22.07 (14) ~ (all_52_1 = all_52_9) % 150.82/22.07 (15) ~ (e3 = e0) % 150.82/22.07 (16) ~ (all_56_31 = e1) | all_56_29 = e0 % 150.82/22.07 (17) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0 % 150.82/22.07 (18) all_54_10 = all_6_2 % 150.82/22.07 (19) ~ (all_6_1 = e2) % 150.82/22.07 (20) all_12_2 = all_4_2 % 150.82/22.07 (21) ~ (all_52_13 = all_8_2) % 150.82/22.07 (22) all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2 % 150.82/22.07 (23) all_54_0 = all_10_2 % 150.82/22.07 (24) all_54_4 = all_52_1 % 150.82/22.07 (25) ~ (all_52_14 = all_4_2) % 150.82/22.07 (26) ~ (all_8_0 = e1) % 150.82/22.07 (27) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0 % 150.82/22.07 (28) all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2 % 150.82/22.07 (29) ~ (all_52_9 = all_8_2) % 150.82/22.07 (30) ~ (all_52_12 = all_52_13) % 150.82/22.07 (31) ~ (all_52_4 = all_52_7) % 150.82/22.07 (32) ~ (all_8_1 = e3) % 150.82/22.07 (33) ~ (e3 = e2) % 150.82/22.07 (34) op(e0, e0) = all_4_2 % 150.82/22.07 (35) all_58_6 = e0 | all_58_7 = e0 | all_58_8 = e0 | all_58_11 = e0 % 150.82/22.07 (36) all_58_4 = all_52_8 % 150.82/22.07 (37) all_54_5 = all_8_2 % 150.82/22.07 (38) ~ (all_6_1 = e3) % 150.82/22.07 (39) ~ (all_52_6 = all_52_14) % 150.82/22.07 (40) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 150.82/22.07 (41) ~ (all_6_0 = e2) % 150.82/22.07 (42) all_54_15 = all_4_2 % 150.82/22.07 (43) all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1 % 150.82/22.07 (44) all_56_21 = all_6_2 % 150.82/22.07 (45) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 150.82/22.07 (46) ~ (all_52_7 = all_8_2) % 150.82/22.07 (47) all_56_1 = all_10_2 % 150.82/22.07 (48) all_56_27 = all_52_7 % 150.82/22.07 (49) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0 % 150.82/22.07 (50) all_58_5 = all_52_9 % 150.82/22.07 (51) all_54_1 = all_52_4 % 150.82/22.07 (52) all_56_17 = all_52_2 % 150.82/22.07 (53) all_58_9 = all_52_12 % 150.82/22.07 (54) op(e0, all_52_14) = all_56_22 % 150.82/22.07 (55) op(e0, e2) = all_52_7 % 150.82/22.07 (56) op(e1, e0) = all_52_14 % 150.82/22.07 (57) ~ (all_56_1 = e1) | all_56_5 = e3 % 150.82/22.07 (58) all_54_14 = all_52_11 % 150.82/22.07 (59) all_58_1 = all_52_4 % 150.82/22.07 (60) all_58_13 = all_52_7 % 150.82/22.07 (61) op(e2, all_8_2) = all_56_10 % 150.82/22.07 (62) op(e3, e3) = all_10_2 % 150.82/22.07 (63) ~ (all_52_8 = all_6_2) % 150.82/22.07 (64) op(e3, all_10_1) = e2 % 150.82/22.07 (65) ~ (all_56_21 = e3) | all_56_17 = e1 % 150.82/22.07 (66) all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2 % 150.82/22.07 (67) all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0 % 150.82/22.07 (68) all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1 % 150.82/22.07 (69) ~ (all_52_1 = all_8_2) % 150.82/22.07 (70) all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2 % 150.82/22.07 (71) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 150.82/22.07 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 150.82/22.07 (72) ~ (all_52_3 = all_10_2) % 150.82/22.07 (73) all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0 % 150.82/22.07 (74) ~ (all_56_11 = e3) | all_56_9 = e2 % 150.82/22.07 (75) ~ (all_52_2 = all_52_6) % 150.82/22.07 (76) all_56_7 = all_52_12 % 150.82/22.07 (77) op(e0, all_4_1) = e2 % 150.82/22.07 (78) all_56_13 = all_52_9 % 150.82/22.07 (79) op(e0, e1) = all_52_11 % 150.82/22.07 (80) ~ (all_52_1 = all_52_13) % 150.82/22.07 (81) ~ (all_52_7 = all_4_2) % 150.82/22.07 (82) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0 % 150.82/22.07 (83) all_58_8 = all_6_2 % 150.82/22.07 (84) ~ (all_52_3 = all_4_2) % 150.82/22.07 (85) ~ (all_52_8 = all_10_2) % 150.82/22.07 (86) all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3 % 150.82/22.07 (87) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0 % 150.82/22.07 (88) ~ (all_56_1 = e2) | all_56_3 = e3 % 150.82/22.07 (89) ~ (all_56_1 = e0) | all_56_7 = e3 % 150.82/22.07 (90) ~ (all_12_1 = e1) | ~ (all_12_2 = e3) % 150.82/22.07 (91) all_34_1 = all_4_1 % 150.82/22.07 (92) all_56_5 = all_52_8 % 150.82/22.07 (93) ~ (all_52_9 = all_52_13) % 150.82/22.07 (94) ~ (all_52_2 = all_52_3) % 150.82/22.07 (95) op(e1, all_6_1) = all_6_0 % 150.82/22.07 (96) op(all_4_2, all_4_2) = all_4_1 % 150.82/22.07 (97) all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3 % 150.82/22.07 (98) ~ (all_52_3 = all_52_11) % 150.82/22.07 (99) all_58_3 = all_8_2 % 150.82/22.07 (100) all_56_3 = all_52_4 % 150.82/22.07 (101) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0 % 150.82/22.07 (102) ~ (all_52_11 = all_4_2) % 150.82/22.07 (103) ~ (all_52_1 = all_52_3) % 150.82/22.07 (104) all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1 % 150.82/22.07 (105) ~ (all_52_6 = all_52_7) % 150.82/22.07 (106) all_56_31 = all_4_2 % 150.82/22.07 (107) all_58_11 = all_52_14 % 150.82/22.07 (108) ~ (all_52_2 = all_52_14) % 150.82/22.07 (109) ~ (all_52_9 = all_52_11) % 150.82/22.07 (110) all_54_7 = all_52_13 % 150.82/22.07 (111) op(all_6_2, all_6_2) = all_6_1 % 150.82/22.07 (112) all_56_1 = e3 | all_56_11 = e2 | all_56_21 = e1 | all_56_31 = e0 % 150.82/22.07 (113) ~ (all_52_13 = all_4_2) % 150.82/22.07 (114) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0 % 150.82/22.07 (115) ~ (all_52_8 = all_52_11) % 150.82/22.07 (116) all_54_13 = all_52_7 % 150.82/22.07 (117) op(e3, e2) = all_52_4 % 150.82/22.07 (118) ~ (all_52_13 = all_52_14) % 150.82/22.07 (119) ~ (all_10_1 = e0) | ~ (all_10_2 = e1) % 150.82/22.07 (120) all_56_23 = all_52_14 % 150.82/22.07 (121) all_54_8 = all_52_2 % 150.82/22.07 (122) op(e1, e1) = all_6_2 % 150.82/22.07 (123) ~ (all_52_6 = all_8_2) % 150.82/22.07 (124) all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1 % 150.82/22.07 (125) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0 % 150.82/22.07 (126) all_58_15 = all_4_2 % 150.82/22.07 (127) all_56_29 = all_52_11 % 150.82/22.07 (128) ~ (all_6_2 = e2) % 150.82/22.07 (129) all_58_2 = all_52_1 % 150.82/22.07 (130) ~ (all_52_9 = all_6_2) % 150.82/22.07 (131) all_58_7 = all_52_6 % 150.82/22.07 (132) all_58_10 = all_52_13 % 150.82/22.07 (133) all_12_1 = all_4_1 % 150.82/22.07 (134) op(all_10_2, all_10_2) = all_10_1 % 150.82/22.07 (135) ~ (all_56_11 = e0) | all_56_15 = e2 % 150.82/22.07 (136) all_58_0 = all_10_2 % 150.82/22.07 (137) op(e3, all_52_2) = all_56_16 % 150.82/22.07 (138) op(e1, all_6_2) = all_56_20 % 150.82/22.07 (139) all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1 % 150.82/22.07 (140) ~ (all_52_12 = all_52_14) % 150.82/22.07 (141) op(e1, all_52_9) = all_56_12 % 150.82/22.07 (142) op(e3, e1) = all_52_8 % 150.82/22.07 (143) ~ (all_56_31 = e2) | all_56_27 = e0 % 150.82/22.07 (144) op(e2, e2) = all_8_2 % 150.82/22.07 (145) ~ (all_52_4 = all_52_12) % 150.82/22.07 (146) op(e2, e0) = all_52_13 % 150.82/22.07 (147) ~ (all_52_2 = all_6_2) % 150.82/22.07 (148) ~ (all_52_8 = all_52_12) % 150.82/22.07 (149) ~ (all_52_1 = all_52_2) % 150.82/22.07 (150) ~ (all_56_21 = e0) | all_56_23 = e1 % 150.82/22.07 (151) op(e0, all_4_2) = all_56_30 % 150.82/22.07 (152) ~ (all_52_6 = all_6_2) % 150.82/22.07 (153) op(e3, all_10_2) = all_56_0 % 150.82/22.07 (154) ~ (all_52_14 = all_6_2) % 150.82/22.07 (155) ~ (e2 = e0) % 150.82/22.07 (156) all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3 % 150.82/22.07 (157) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0 % 150.82/22.07 (158) ~ (all_52_2 = all_10_2) % 150.82/22.07 (159) ~ (all_52_4 = all_10_2) % 150.82/22.07 (160) all_34_2 = all_4_2 % 150.82/22.07 (161) ~ (all_52_4 = all_8_2) % 150.82/22.07 (162) op(all_8_2, all_8_2) = all_8_1 % 150.82/22.07 (163) op(e3, all_52_3) = all_56_24 % 150.82/22.07 (164) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 150.82/22.07 (165) all_58_14 = all_52_11 % 150.82/22.07 (166) ~ (all_52_12 = all_10_2) % 150.82/22.07 (167) all_56_9 = all_52_1 % 150.82/22.07 (168) all_56_15 = all_52_13 % 150.82/22.07 (169) ~ (all_52_1 = all_10_2) % 150.82/22.07 (170) all_58_12 = all_52_3 % 150.82/22.07 (171) all_54_11 = all_52_14 % 150.82/22.07 (172) ~ (all_56_31 = e3) | all_56_25 = e0 % 150.82/22.07 % 150.82/22.07 Begin of proof % 150.82/22.07 | % 150.82/22.07 | BETA: splitting (16) gives: % 150.82/22.07 | % 150.82/22.07 | Case 1: % 150.82/22.07 | | % 150.82/22.07 | | (173) ~ (all_56_31 = e1) % 150.82/22.07 | | % 150.82/22.07 | | REDUCE: (106), (173) imply: % 150.82/22.07 | | (174) ~ (all_4_2 = e1) % 150.82/22.07 | | % 150.82/22.07 | | BETA: splitting (135) gives: % 150.82/22.07 | | % 150.82/22.07 | | Case 1: % 150.82/22.07 | | | % 150.82/22.07 | | | (175) ~ (all_56_11 = e0) % 150.82/22.07 | | | % 150.82/22.07 | | | REDUCE: (1), (175) imply: % 150.82/22.07 | | | (176) ~ (all_8_2 = e0) % 150.82/22.07 | | | % 150.82/22.07 | | | BETA: splitting (65) gives: % 150.82/22.07 | | | % 150.82/22.07 | | | Case 1: % 150.82/22.07 | | | | % 150.82/22.07 | | | | (177) ~ (all_56_21 = e3) % 150.82/22.07 | | | | % 150.82/22.07 | | | | REDUCE: (44), (177) imply: % 150.82/22.07 | | | | (178) ~ (all_6_2 = e3) % 150.82/22.07 | | | | % 150.82/22.07 | | | | BETA: splitting (74) gives: % 150.82/22.07 | | | | % 150.82/22.07 | | | | Case 1: % 150.82/22.07 | | | | | % 150.82/22.07 | | | | | (179) ~ (all_56_11 = e3) % 150.82/22.07 | | | | | % 150.82/22.07 | | | | | REDUCE: (1), (179) imply: % 150.82/22.07 | | | | | (180) ~ (all_8_2 = e3) % 150.82/22.07 | | | | | % 150.82/22.07 | | | | | BETA: splitting (57) gives: % 150.82/22.07 | | | | | % 150.82/22.07 | | | | | Case 1: % 150.82/22.07 | | | | | | % 150.82/22.07 | | | | | | (181) ~ (all_56_1 = e1) % 150.82/22.07 | | | | | | % 150.82/22.07 | | | | | | REDUCE: (47), (181) imply: % 150.82/22.07 | | | | | | (182) ~ (all_10_2 = e1) % 150.82/22.07 | | | | | | % 150.82/22.07 | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (9), (10), (11), (12), % 150.82/22.07 | | | | | | (13), (14), (15), (17), (18), (19), (20), (21), (22), % 150.82/22.07 | | | | | | (23), (24), (25), (27), (28), (29), (31), (32), (33), % 150.82/22.07 | | | | | | (34), (35), (36), (37), (38), (39), (40), (42), (44), % 150.82/22.07 | | | | | | (45), (46), (47), (48), (49), (50), (51), (53), (54), % 150.82/22.07 | | | | | | (55), (58), (59), (60), (61), (62), (64), (66), (67), % 150.82/22.07 | | | | | | (69), (70), (71), (72), (73), (75), (76), (77), (78), % 150.82/22.07 | | | | | | (80), (81), (82), (83), (84), (85), (86), (87), (88), % 150.82/22.07 | | | | | | (89), (90), (93), (94), (96), (97), (98), (99), (100), % 150.82/22.07 | | | | | | (101), (102), (103), (104), (105), (106), (107), (108), % 150.82/22.07 | | | | | | (109), (110), (111), (113), (114), (115), (116), (117), % 150.82/22.07 | | | | | | (118), (120), (121), (122), (123), (124), (125), (126), % 150.82/22.07 | | | | | | (128), (129), (130), (131), (132), (133), (134), (136), % 150.82/22.07 | | | | | | (137), (139), (140), (142), (143), (144), (145), (147), % 150.82/22.07 | | | | | | (148), (149), (150), (151), (152), (154), (156), (157), % 150.82/22.07 | | | | | | (158), (159), (161), (162), (163), (164), (165), (166), % 150.82/22.07 | | | | | | (169), (170), (171), (172), (174), (176), (178), (180), % 150.82/22.07 | | | | | | (182) are inconsistent by sub-proof #154. % 150.82/22.07 | | | | | | % 150.82/22.07 | | | | | Case 2: % 150.82/22.07 | | | | | | % 150.82/22.07 | | | | | | (183) all_56_5 = e3 % 150.82/22.07 | | | | | | (184) all_56_1 = e1 % 150.82/22.07 | | | | | | % 150.82/22.07 | | | | | | COMBINE_EQS: (47), (184) imply: % 150.82/22.07 | | | | | | (185) all_10_2 = e1 % 150.82/22.07 | | | | | | % 150.82/22.07 | | | | | | COMBINE_EQS: (92), (183) imply: % 150.82/22.07 | | | | | | (186) all_52_8 = e3 % 150.82/22.07 | | | | | | % 150.82/22.07 | | | | | | REDUCE: (63), (186) imply: % 150.82/22.07 | | | | | | (187) ~ (all_6_2 = e3) % 150.82/22.07 | | | | | | % 150.82/22.07 | | | | | | REDUCE: (134), (185) imply: % 150.82/22.07 | | | | | | (188) op(e1, e1) = all_10_1 % 150.82/22.07 | | | | | | % 150.82/22.07 | | | | | | REDUCE: (153), (185) imply: % 150.82/22.07 | | | | | | (189) op(e3, e1) = all_56_0 % 150.82/22.07 | | | | | | % 150.82/22.07 | | | | | | REDUCE: (142), (186) imply: % 150.82/22.07 | | | | | | (190) op(e3, e1) = e3 % 150.82/22.07 | | | | | | % 150.82/22.07 | | | | | | BETA: splitting (119) gives: % 150.82/22.07 | | | | | | % 150.82/22.07 | | | | | | Case 1: % 150.82/22.07 | | | | | | | % 150.82/22.07 | | | | | | | (191) ~ (all_10_2 = e1) % 150.82/22.07 | | | | | | | % 150.82/22.08 | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (9), (10), (11), % 150.82/22.08 | | | | | | | (12), (13), (14), (15), (17), (18), (19), (20), (21), % 150.82/22.08 | | | | | | | (22), (23), (24), (25), (27), (28), (29), (31), (32), % 150.82/22.08 | | | | | | | (33), (34), (35), (36), (37), (38), (39), (40), (42), % 150.82/22.08 | | | | | | | (44), (45), (46), (47), (48), (49), (50), (51), (53), % 150.82/22.08 | | | | | | | (54), (55), (58), (59), (60), (61), (62), (64), (66), % 150.82/22.08 | | | | | | | (67), (69), (70), (71), (72), (73), (75), (76), (77), % 150.82/22.08 | | | | | | | (78), (80), (81), (82), (83), (84), (85), (86), (87), % 150.82/22.08 | | | | | | | (88), (89), (90), (93), (94), (96), (97), (98), (99), % 150.82/22.08 | | | | | | | (100), (101), (102), (103), (104), (105), (106), (107), % 150.82/22.08 | | | | | | | (108), (109), (110), (111), (113), (114), (115), (116), % 150.82/22.08 | | | | | | | (117), (118), (120), (121), (122), (123), (124), (125), % 150.82/22.08 | | | | | | | (126), (128), (129), (130), (131), (132), (133), (134), % 150.82/22.08 | | | | | | | (136), (137), (139), (140), (142), (143), (144), (145), % 150.82/22.08 | | | | | | | (147), (148), (149), (150), (151), (152), (154), (156), % 150.82/22.08 | | | | | | | (157), (158), (159), (161), (162), (163), (164), (165), % 150.82/22.08 | | | | | | | (166), (169), (170), (171), (172), (174), (176), (178), % 150.82/22.08 | | | | | | | (180), (191) are inconsistent by sub-proof #154. % 150.82/22.08 | | | | | | | % 150.82/22.08 | | | | | | Case 2: % 150.82/22.08 | | | | | | | % 150.82/22.08 | | | | | | | (192) ~ (all_10_1 = e0) % 150.82/22.08 | | | | | | | % 150.82/22.08 | | | | | | | GROUND_INST: instantiating (71) with all_6_2, all_10_1, e1, e1, % 150.82/22.08 | | | | | | | simplifying with (122), (188) gives: % 150.82/22.08 | | | | | | | (193) all_10_1 = all_6_2 % 150.82/22.08 | | | | | | | % 150.82/22.08 | | | | | | | REF_CLOSE: (18), (33), (45), (64), (71), (128), (178), (188), % 150.82/22.08 | | | | | | | (189), (190), (192), (193) are inconsistent by % 150.82/22.08 | | | | | | | sub-proof #169. % 150.82/22.08 | | | | | | | % 150.82/22.08 | | | | | | End of split % 150.82/22.08 | | | | | | % 150.82/22.08 | | | | | End of split % 150.82/22.08 | | | | | % 150.82/22.08 | | | | Case 2: % 150.82/22.08 | | | | | % 150.82/22.08 | | | | | (194) all_56_11 = e3 % 150.82/22.08 | | | | | (195) all_56_9 = e2 % 150.82/22.08 | | | | | % 150.82/22.08 | | | | | COMBINE_EQS: (167), (195) imply: % 150.82/22.08 | | | | | (196) all_52_1 = e2 % 150.82/22.08 | | | | | % 150.82/22.08 | | | | | COMBINE_EQS: (1), (194) imply: % 150.82/22.08 | | | | | (197) all_8_2 = e3 % 150.82/22.08 | | | | | % 150.82/22.08 | | | | | COMBINE_EQS: (99), (197) imply: % 150.82/22.08 | | | | | (198) all_58_3 = e3 % 150.82/22.08 | | | | | % 150.82/22.08 | | | | | COMBINE_EQS: (129), (196) imply: % 150.82/22.08 | | | | | (199) all_58_2 = e2 % 150.82/22.08 | | | | | % 150.82/22.08 | | | | | REDUCE: (149), (196) imply: % 150.82/22.08 | | | | | (200) ~ (all_52_2 = e2) % 150.82/22.08 | | | | | % 150.82/22.08 | | | | | SIMP: (200) implies: % 150.82/22.08 | | | | | (201) ~ (all_52_2 = e2) % 150.82/22.08 | | | | | % 150.82/22.08 | | | | | REDUCE: (103), (196) imply: % 150.82/22.08 | | | | | (202) ~ (all_52_3 = e2) % 150.82/22.08 | | | | | % 150.82/22.08 | | | | | SIMP: (202) implies: % 150.82/22.08 | | | | | (203) ~ (all_52_3 = e2) % 150.82/22.08 | | | | | % 150.82/22.08 | | | | | REDUCE: (14), (196) imply: % 150.82/22.08 | | | | | (204) ~ (all_52_9 = e2) % 150.82/22.08 | | | | | % 150.82/22.08 | | | | | SIMP: (204) implies: % 150.82/22.08 | | | | | (205) ~ (all_52_9 = e2) % 150.82/22.08 | | | | | % 150.82/22.08 | | | | | REDUCE: (169), (196) imply: % 150.82/22.08 | | | | | (206) ~ (all_10_2 = e2) % 150.82/22.08 | | | | | % 150.82/22.08 | | | | | SIMP: (206) implies: % 150.82/22.08 | | | | | (207) ~ (all_10_2 = e2) % 150.82/22.08 | | | | | % 150.82/22.08 | | | | | REDUCE: (69), (196), (197) imply: % 150.82/22.08 | | | | | (208) ~ (e3 = e2) % 150.82/22.08 | | | | | % 150.82/22.08 | | | | | REDUCE: (29), (197) imply: % 150.82/22.08 | | | | | (209) ~ (all_52_9 = e3) % 150.82/22.08 | | | | | % 150.82/22.08 | | | | | REDUCE: (162), (197) imply: % 150.82/22.08 | | | | | (210) op(e3, e3) = all_8_1 % 150.82/22.08 | | | | | % 150.82/22.08 | | | | | REF_CLOSE: (5), (11), (12), (13), (23), (26), (28), (32), (33), (36), % 150.82/22.08 | | | | | (40), (44), (47), (50), (51), (62), (66), (68), (71), (73), % 150.82/22.08 | | | | | (76), (80), (83), (85), (89), (97), (106), (112), (113), % 150.82/22.08 | | | | | (125), (128), (129), (130), (132), (135), (136), (145), % 150.82/22.08 | | | | | (146), (148), (159), (168), (170), (178), (194), (198), % 150.82/22.08 | | | | | (199), (201), (203), (205), (207), (209), (210) are % 150.82/22.08 | | | | | inconsistent by sub-proof #151. % 150.82/22.08 | | | | | % 150.82/22.08 | | | | End of split % 150.82/22.08 | | | | % 150.82/22.08 | | | Case 2: % 150.82/22.08 | | | | % 150.82/22.08 | | | | (211) all_56_21 = e3 % 150.82/22.08 | | | | (212) all_56_17 = e1 % 150.82/22.08 | | | | % 150.82/22.08 | | | | REF_CLOSE: (1), (10), (19), (23), (25), (27), (30), (38), (39), (40), % 150.82/22.08 | | | | (41), (43), (44), (47), (50), (52), (53), (56), (62), (71), % 150.82/22.08 | | | | (73), (75), (76), (89), (95), (99), (101), (106), (107), % 150.82/22.08 | | | | (108), (111), (112), (118), (123), (126), (129), (132), % 150.82/22.08 | | | | (140), (141), (147), (152), (158), (169), (171), (174), % 150.82/22.08 | | | | (176), (211), (212) are inconsistent by sub-proof #292. % 150.82/22.08 | | | | % 150.82/22.08 | | | End of split % 150.82/22.08 | | | % 150.82/22.08 | | Case 2: % 150.82/22.08 | | | % 150.82/22.08 | | | (213) all_56_15 = e2 % 150.82/22.08 | | | (214) all_56_11 = e0 % 150.82/22.08 | | | % 150.82/22.08 | | | REF_CLOSE: (1), (13), (32), (34), (42), (71), (77), (96), (113), (114), % 150.82/22.08 | | | (151), (162), (168), (213), (214) are inconsistent by sub-proof % 150.82/22.08 | | | #224. % 150.82/22.08 | | | % 150.82/22.08 | | End of split % 150.82/22.08 | | % 150.82/22.08 | Case 2: % 150.82/22.08 | | % 150.82/22.08 | | (215) all_56_31 = e1 % 150.82/22.08 | | (216) all_56_29 = e0 % 150.82/22.08 | | % 150.82/22.08 | | COMBINE_EQS: (127), (216) imply: % 150.82/22.08 | | (217) all_52_11 = e0 % 150.82/22.08 | | % 150.82/22.08 | | SIMP: (217) implies: % 150.82/22.08 | | (218) all_52_11 = e0 % 150.82/22.08 | | % 150.82/22.08 | | COMBINE_EQS: (106), (215) imply: % 150.82/22.08 | | (219) all_4_2 = e1 % 150.82/22.08 | | % 150.82/22.08 | | COMBINE_EQS: (160), (219) imply: % 150.82/22.08 | | (220) all_34_2 = e1 % 150.82/22.08 | | % 150.82/22.08 | | REDUCE: (4), (218) imply: % 150.82/22.08 | | (221) ~ (all_6_2 = e0) % 150.82/22.08 | | % 150.82/22.08 | | SIMP: (221) implies: % 150.82/22.08 | | (222) ~ (all_6_2 = e0) % 150.82/22.08 | | % 150.82/22.08 | | REDUCE: (96), (219) imply: % 150.82/22.08 | | (223) op(e1, e1) = all_4_1 % 150.82/22.08 | | % 150.82/22.08 | | REDUCE: (151), (219) imply: % 150.82/22.08 | | (224) op(e0, e1) = all_56_30 % 150.82/22.08 | | % 150.82/22.08 | | REDUCE: (79), (218) imply: % 150.82/22.08 | | (225) op(e0, e1) = e0 % 150.82/22.08 | | % 150.82/22.08 | | BETA: splitting (7) gives: % 150.82/22.08 | | % 150.82/22.08 | | Case 1: % 150.82/22.08 | | | % 150.82/22.08 | | | (226) ~ (all_34_1 = e3) % 150.82/22.08 | | | % 150.82/22.08 | | | REDUCE: (91), (226) imply: % 150.82/22.08 | | | (227) ~ (all_4_1 = e3) % 150.82/22.08 | | | % 150.82/22.08 | | | GROUND_INST: instantiating (71) with e0, all_56_30, e1, e0, simplifying % 150.82/22.08 | | | with (224), (225) gives: % 150.82/22.08 | | | (228) all_56_30 = e0 % 150.82/22.08 | | | % 150.82/22.08 | | | GROUND_INST: instantiating (71) with all_6_2, all_4_1, e1, e1, simplifying % 150.82/22.08 | | | with (122), (223) gives: % 150.82/22.08 | | | (229) all_6_2 = all_4_1 % 150.82/22.08 | | | % 150.82/22.08 | | | COMBINE_EQS: (18), (229) imply: % 150.82/22.08 | | | (230) all_54_10 = all_4_1 % 150.82/22.08 | | | % 150.82/22.08 | | | REDUCE: (128), (229) imply: % 150.82/22.08 | | | (231) ~ (all_4_1 = e2) % 150.82/22.08 | | | % 150.82/22.08 | | | REDUCE: (222), (229) imply: % 150.82/22.08 | | | (232) ~ (all_4_1 = e0) % 150.82/22.08 | | | % 150.82/22.08 | | | REDUCE: (111), (229) imply: % 150.82/22.08 | | | (233) op(all_4_1, all_4_1) = all_6_1 % 150.82/22.08 | | | % 150.82/22.08 | | | REDUCE: (138), (229) imply: % 150.82/22.08 | | | (234) op(e1, all_4_1) = all_56_20 % 150.82/22.08 | | | % 150.82/22.08 | | | REF_CLOSE: (45), (71), (77), (155), (223), (224), (225), (227), (230), % 150.82/22.08 | | | (231), (232), (233), (234) are inconsistent by sub-proof #177. % 150.82/22.08 | | | % 150.82/22.08 | | Case 2: % 150.82/22.08 | | | % 150.82/22.08 | | | (235) ~ (all_34_2 = e1) % 150.82/22.08 | | | % 150.82/22.08 | | | REDUCE: (220), (235) imply: % 150.82/22.08 | | | (236) $false % 150.82/22.08 | | | % 150.82/22.08 | | | CLOSE: (236) is inconsistent. % 150.82/22.08 | | | % 150.82/22.08 | | End of split % 150.82/22.08 | | % 150.82/22.08 | End of split % 150.82/22.08 | % 150.82/22.08 End of proof % 150.82/22.08 % 150.82/22.08 Sub-proof #151 shows that the following formulas are inconsistent: % 150.82/22.08 ---------------------------------------------------------------- % 150.82/22.08 (1) ~ (all_52_4 = all_52_8) % 150.82/22.08 (2) op(e2, all_8_1) = all_8_0 % 150.82/22.08 (3) all_58_6 = all_52_2 % 150.82/22.08 (4) ~ (all_8_1 = e1) % 150.82/22.08 (5) ~ (all_52_9 = e2) % 150.82/22.08 (6) all_54_0 = all_10_2 % 150.82/22.08 (7) ~ (all_8_0 = e1) % 150.82/22.08 (8) all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2 % 150.82/22.08 (9) ~ (all_6_2 = e3) % 150.82/22.08 (10) ~ (all_8_1 = e3) % 150.82/22.08 (11) ~ (e3 = e2) % 150.82/22.08 (12) all_56_11 = e3 % 150.82/22.08 (13) all_58_4 = all_52_8 % 150.82/22.08 (14) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 150.82/22.08 (15) ~ (all_52_3 = e2) % 150.82/22.08 (16) all_56_21 = all_6_2 % 150.82/22.08 (17) all_56_1 = all_10_2 % 150.82/22.08 (18) all_58_5 = all_52_9 % 150.82/22.08 (19) all_54_1 = all_52_4 % 150.82/22.08 (20) ~ (all_10_2 = e2) % 150.82/22.08 (21) op(e3, e3) = all_10_2 % 150.82/22.08 (22) all_58_3 = e3 % 150.82/22.08 (23) all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2 % 150.82/22.08 (24) all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1 % 150.82/22.08 (25) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 150.82/22.08 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 150.82/22.08 (26) all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0 % 150.82/22.08 (27) all_56_7 = all_52_12 % 150.82/22.08 (28) ~ (all_52_1 = all_52_13) % 150.82/22.08 (29) all_58_2 = e2 % 150.82/22.08 (30) ~ (all_52_9 = e3) % 150.82/22.08 (31) all_58_8 = all_6_2 % 150.82/22.08 (32) ~ (all_52_8 = all_10_2) % 150.82/22.08 (33) ~ (all_56_1 = e0) | all_56_7 = e3 % 150.82/22.08 (34) all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3 % 150.82/22.08 (35) all_56_31 = all_4_2 % 150.82/22.08 (36) ~ (all_52_2 = e2) % 150.82/22.08 (37) all_56_1 = e3 | all_56_11 = e2 | all_56_21 = e1 | all_56_31 = e0 % 150.82/22.08 (38) ~ (all_52_13 = all_4_2) % 150.82/22.08 (39) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0 % 150.82/22.08 (40) ~ (all_6_2 = e2) % 150.82/22.08 (41) all_58_2 = all_52_1 % 150.82/22.08 (42) ~ (all_52_9 = all_6_2) % 150.82/22.08 (43) all_58_10 = all_52_13 % 150.82/22.08 (44) op(e3, e3) = all_8_1 % 150.82/22.08 (45) ~ (all_56_11 = e0) | all_56_15 = e2 % 150.82/22.08 (46) all_58_0 = all_10_2 % 150.82/22.08 (47) ~ (all_52_4 = all_52_12) % 150.82/22.08 (48) op(e2, e0) = all_52_13 % 150.82/22.08 (49) ~ (all_52_8 = all_52_12) % 150.82/22.08 (50) ~ (all_52_4 = all_10_2) % 150.82/22.08 (51) all_56_15 = all_52_13 % 150.82/22.08 (52) all_58_12 = all_52_3 % 150.82/22.08 % 150.82/22.08 Begin of proof % 150.82/22.08 | % 150.82/22.08 | GROUND_INST: instantiating (25) with all_10_2, all_8_1, e3, e3, simplifying % 150.82/22.08 | with (21), (44) gives: % 150.82/22.08 | (53) all_10_2 = all_8_1 % 150.82/22.08 | % 150.82/22.08 | COMBINE_EQS: (6), (53) imply: % 150.82/22.08 | (54) all_54_0 = all_8_1 % 150.82/22.08 | % 150.82/22.08 | COMBINE_EQS: (17), (53) imply: % 150.82/22.08 | (55) all_56_1 = all_8_1 % 150.82/22.08 | % 150.82/22.08 | REDUCE: (50), (53) imply: % 150.82/22.08 | (56) ~ (all_52_4 = all_8_1) % 150.82/22.08 | % 150.82/22.08 | REDUCE: (32), (53) imply: % 150.82/22.08 | (57) ~ (all_52_8 = all_8_1) % 150.82/22.08 | % 150.82/22.08 | REDUCE: (20), (53) imply: % 150.82/22.08 | (58) ~ (all_8_1 = e2) % 150.82/22.08 | % 150.82/22.08 | BETA: splitting (14) gives: % 150.82/22.08 | % 150.82/22.08 | Case 1: % 150.82/22.08 | | % 150.82/22.08 | | (59) all_54_0 = e3 % 150.82/22.08 | | % 150.82/22.08 | | REF_CLOSE: (10), (54), (59) are inconsistent by sub-proof #600. % 150.82/22.08 | | % 150.82/22.08 | Case 2: % 150.82/22.08 | | % 150.82/22.08 | | (60) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 150.82/22.08 | | % 150.82/22.08 | | BETA: splitting (60) gives: % 150.82/22.08 | | % 150.82/22.08 | | Case 1: % 150.82/22.08 | | | % 150.82/22.08 | | | (61) all_54_0 = e2 % 150.82/22.08 | | | % 150.82/22.08 | | | REF_CLOSE: (54), (58), (61) are inconsistent by sub-proof #599. % 150.82/22.08 | | | % 150.82/22.08 | | Case 2: % 150.82/22.08 | | | % 150.82/22.08 | | | (62) all_54_0 = e1 | all_54_0 = e0 % 150.82/22.08 | | | % 150.82/22.08 | | | BETA: splitting (62) gives: % 150.82/22.08 | | | % 150.82/22.08 | | | Case 1: % 150.82/22.08 | | | | % 150.82/22.08 | | | | (63) all_54_0 = e1 % 150.82/22.08 | | | | % 150.82/22.08 | | | | REF_CLOSE: (4), (54), (63) are inconsistent by sub-proof #598. % 150.82/22.08 | | | | % 150.82/22.08 | | | Case 2: % 150.82/22.08 | | | | % 150.82/22.08 | | | | (64) all_54_0 = e0 % 150.82/22.08 | | | | % 150.82/22.08 | | | | COMBINE_EQS: (54), (64) imply: % 150.82/22.08 | | | | (65) all_8_1 = e0 % 150.82/22.08 | | | | % 150.82/22.08 | | | | SIMP: (65) implies: % 150.82/22.08 | | | | (66) all_8_1 = e0 % 150.82/22.08 | | | | % 150.82/22.08 | | | | COMBINE_EQS: (55), (66) imply: % 150.82/22.08 | | | | (67) all_56_1 = e0 % 150.82/22.08 | | | | % 150.82/22.08 | | | | REDUCE: (56), (66) imply: % 150.82/22.08 | | | | (68) ~ (all_52_4 = e0) % 150.82/22.08 | | | | % 150.82/22.08 | | | | REDUCE: (57), (66) imply: % 150.82/22.08 | | | | (69) ~ (all_52_8 = e0) % 150.82/22.08 | | | | % 150.82/22.08 | | | | REDUCE: (2), (66) imply: % 150.82/22.08 | | | | (70) op(e2, e0) = all_8_0 % 150.82/22.08 | | | | % 150.82/22.08 | | | | BETA: splitting (33) gives: % 150.82/22.08 | | | | % 150.82/22.08 | | | | Case 1: % 150.82/22.08 | | | | | % 150.82/22.08 | | | | | (71) ~ (all_56_1 = e0) % 150.82/22.08 | | | | | % 150.82/22.08 | | | | | REDUCE: (67), (71) imply: % 150.82/22.08 | | | | | (72) $false % 150.82/22.08 | | | | | % 150.82/22.08 | | | | | CLOSE: (72) is inconsistent. % 150.82/22.08 | | | | | % 150.82/22.08 | | | | Case 2: % 150.82/22.08 | | | | | % 150.82/22.08 | | | | | (73) all_56_7 = e3 % 150.82/22.08 | | | | | % 150.82/22.08 | | | | | COMBINE_EQS: (27), (73) imply: % 150.82/22.08 | | | | | (74) all_52_12 = e3 % 150.82/22.08 | | | | | % 150.82/22.08 | | | | | REDUCE: (47), (74) imply: % 150.82/22.08 | | | | | (75) ~ (all_52_4 = e3) % 150.82/22.08 | | | | | % 150.82/22.08 | | | | | REDUCE: (49), (74) imply: % 150.82/22.08 | | | | | (76) ~ (all_52_8 = e3) % 150.82/22.08 | | | | | % 150.82/22.08 | | | | | BETA: splitting (34) gives: % 150.82/22.08 | | | | | % 150.82/22.08 | | | | | Case 1: % 150.82/22.08 | | | | | | % 150.82/22.08 | | | | | | (77) all_58_4 = e3 % 150.82/22.08 | | | | | | % 150.82/22.08 | | | | | | COMBINE_EQS: (13), (77) imply: % 150.82/22.08 | | | | | | (78) all_52_8 = e3 % 150.82/22.08 | | | | | | % 150.82/22.08 | | | | | | REDUCE: (76), (78) imply: % 150.82/22.08 | | | | | | (79) $false % 150.82/22.08 | | | | | | % 150.82/22.08 | | | | | | CLOSE: (79) is inconsistent. % 150.82/22.08 | | | | | | % 150.82/22.08 | | | | | Case 2: % 150.82/22.08 | | | | | | % 150.82/22.08 | | | | | | (80) ~ (all_58_4 = e3) % 150.82/22.08 | | | | | | (81) all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3 % 150.82/22.08 | | | | | | % 150.82/22.08 | | | | | | BETA: splitting (81) gives: % 150.82/22.08 | | | | | | % 150.82/22.08 | | | | | | Case 1: % 150.82/22.08 | | | | | | | % 150.82/22.08 | | | | | | | (82) all_58_5 = e3 % 150.82/22.08 | | | | | | | % 150.82/22.08 | | | | | | | COMBINE_EQS: (18), (82) imply: % 150.82/22.08 | | | | | | | (83) all_52_9 = e3 % 150.82/22.08 | | | | | | | % 150.82/22.08 | | | | | | | REDUCE: (30), (83) imply: % 150.82/22.08 | | | | | | | (84) $false % 150.82/22.08 | | | | | | | % 150.82/22.08 | | | | | | | CLOSE: (84) is inconsistent. % 150.82/22.08 | | | | | | | % 150.82/22.08 | | | | | | Case 2: % 150.82/22.08 | | | | | | | % 150.82/22.08 | | | | | | | (85) all_58_8 = e3 | all_58_14 = e3 % 150.82/22.08 | | | | | | | % 150.82/22.08 | | | | | | | BETA: splitting (8) gives: % 150.82/22.08 | | | | | | | % 150.82/22.08 | | | | | | | Case 1: % 150.82/22.08 | | | | | | | | % 150.82/22.08 | | | | | | | | (86) all_58_4 = e2 % 150.82/22.08 | | | | | | | | % 150.82/22.08 | | | | | | | | COMBINE_EQS: (13), (86) imply: % 150.82/22.08 | | | | | | | | (87) all_52_8 = e2 % 150.82/22.08 | | | | | | | | % 150.82/22.08 | | | | | | | | REDUCE: (1), (87) imply: % 150.82/22.08 | | | | | | | | (88) ~ (all_52_4 = e2) % 150.82/22.08 | | | | | | | | % 150.82/22.08 | | | | | | | | REDUCE: (76), (87) imply: % 150.82/22.08 | | | | | | | | (89) ~ (e3 = e2) % 150.82/22.08 | | | | | | | | % 150.82/22.08 | | | | | | | | REDUCE: (69), (87) imply: % 150.82/22.08 | | | | | | | | (90) ~ (e2 = e0) % 150.82/22.08 | | | | | | | | % 150.82/22.08 | | | | | | | | BETA: splitting (39) gives: % 150.82/22.08 | | | | | | | | % 150.82/22.08 | | | | | | | | Case 1: % 150.82/22.08 | | | | | | | | | % 150.82/22.08 | | | | | | | | | (91) all_54_1 = e3 % 150.82/22.08 | | | | | | | | | % 150.82/22.08 | | | | | | | | | REF_CLOSE: (19), (75), (91) are inconsistent by sub-proof % 150.82/22.08 | | | | | | | | | #722. % 150.82/22.08 | | | | | | | | | % 150.82/22.08 | | | | | | | | Case 2: % 150.82/22.08 | | | | | | | | | % 150.82/22.08 | | | | | | | | | (92) ~ (all_54_1 = e3) % 150.82/22.08 | | | | | | | | | (93) all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0 % 150.82/22.08 | | | | | | | | | % 150.82/22.08 | | | | | | | | | BETA: splitting (93) gives: % 150.82/22.08 | | | | | | | | | % 150.82/22.08 | | | | | | | | | Case 1: % 150.82/22.08 | | | | | | | | | | % 150.82/22.08 | | | | | | | | | | (94) all_54_1 = e2 % 150.82/22.08 | | | | | | | | | | % 150.82/22.08 | | | | | | | | | | REF_CLOSE: (19), (88), (94) are inconsistent by sub-proof % 150.82/22.08 | | | | | | | | | | #721. % 150.82/22.08 | | | | | | | | | | % 150.82/22.08 | | | | | | | | | Case 2: % 150.82/22.08 | | | | | | | | | | % 150.82/22.08 | | | | | | | | | | (95) ~ (all_54_1 = e2) % 150.82/22.08 | | | | | | | | | | (96) all_54_1 = e1 | all_54_1 = e0 % 150.82/22.08 | | | | | | | | | | % 150.82/22.08 | | | | | | | | | | BETA: splitting (96) gives: % 150.82/22.08 | | | | | | | | | | % 150.82/22.08 | | | | | | | | | | Case 1: % 150.82/22.08 | | | | | | | | | | | % 150.82/22.08 | | | | | | | | | | | (97) all_54_1 = e1 % 150.82/22.08 | | | | | | | | | | | % 150.82/22.08 | | | | | | | | | | | COMBINE_EQS: (19), (97) imply: % 150.82/22.08 | | | | | | | | | | | (98) all_52_4 = e1 % 150.82/22.08 | | | | | | | | | | | % 150.82/22.08 | | | | | | | | | | | SIMP: (98) implies: % 150.82/22.08 | | | | | | | | | | | (99) all_52_4 = e1 % 150.82/22.08 | | | | | | | | | | | % 150.82/22.08 | | | | | | | | | | | REDUCE: (75), (99) imply: % 150.82/22.08 | | | | | | | | | | | (100) ~ (e3 = e1) % 150.82/22.08 | | | | | | | | | | | % 150.82/22.08 | | | | | | | | | | | SIMP: (100) implies: % 150.82/22.08 | | | | | | | | | | | (101) ~ (e3 = e1) % 150.82/22.08 | | | | | | | | | | | % 150.82/22.08 | | | | | | | | | | | REDUCE: (88), (99) imply: % 150.82/22.08 | | | | | | | | | | | (102) ~ (e2 = e1) % 150.82/22.08 | | | | | | | | | | | % 150.82/22.08 | | | | | | | | | | | SIMP: (102) implies: % 150.82/22.08 | | | | | | | | | | | (103) ~ (e2 = e1) % 150.82/22.08 | | | | | | | | | | | % 150.82/22.08 | | | | | | | | | | | REDUCE: (68), (99) imply: % 150.82/22.08 | | | | | | | | | | | (104) ~ (e1 = e0) % 150.82/22.08 | | | | | | | | | | | % 150.82/22.08 | | | | | | | | | | | GROUND_INST: instantiating (25) with all_52_13, all_8_0, e0, % 150.82/22.08 | | | | | | | | | | | e2, simplifying with (48), (70) gives: % 150.82/22.08 | | | | | | | | | | | (105) all_52_13 = all_8_0 % 150.82/22.08 | | | | | | | | | | | % 150.82/22.08 | | | | | | | | | | | COMBINE_EQS: (43), (105) imply: % 150.82/22.08 | | | | | | | | | | | (106) all_58_10 = all_8_0 % 150.82/22.08 | | | | | | | | | | | % 150.82/22.08 | | | | | | | | | | | REDUCE: (38), (105) imply: % 150.82/22.08 | | | | | | | | | | | (107) ~ (all_8_0 = all_4_2) % 150.82/22.08 | | | | | | | | | | | % 150.82/22.08 | | | | | | | | | | | BETA: splitting (24) gives: % 150.82/22.08 | | | | | | | | | | | % 150.82/22.08 | | | | | | | | | | | Case 1: % 150.82/22.08 | | | | | | | | | | | | % 150.82/22.08 | | | | | | | | | | | | (108) all_58_2 = e1 % 150.82/22.08 | | | | | | | | | | | | % 150.82/22.08 | | | | | | | | | | | | REF_CLOSE: (29), (103), (108) are inconsistent by sub-proof % 150.82/22.08 | | | | | | | | | | | | #631. % 150.82/22.08 | | | | | | | | | | | | % 150.82/22.08 | | | | | | | | | | | Case 2: % 150.82/22.08 | | | | | | | | | | | | % 150.82/22.08 | | | | | | | | | | | | (109) all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1 % 150.82/22.08 | | | | | | | | | | | | % 150.82/22.08 | | | | | | | | | | | | BETA: splitting (109) gives: % 150.82/22.08 | | | | | | | | | | | | % 150.82/22.08 | | | | | | | | | | | | Case 1: % 150.82/22.08 | | | | | | | | | | | | | % 150.82/22.08 | | | | | | | | | | | | | (110) all_58_3 = e1 % 150.82/22.08 | | | | | | | | | | | | | % 150.82/22.08 | | | | | | | | | | | | | COMBINE_EQS: (22), (110) imply: % 150.82/22.08 | | | | | | | | | | | | | (111) e3 = e1 % 150.82/22.08 | | | | | | | | | | | | | % 150.82/22.08 | | | | | | | | | | | | | REDUCE: (101), (111) imply: % 150.82/22.08 | | | | | | | | | | | | | (112) $false % 150.82/22.08 | | | | | | | | | | | | | % 150.82/22.08 | | | | | | | | | | | | | CLOSE: (112) is inconsistent. % 150.82/22.08 | | | | | | | | | | | | | % 150.82/22.08 | | | | | | | | | | | | Case 2: % 150.82/22.08 | | | | | | | | | | | | | % 150.82/22.08 | | | | | | | | | | | | | (113) all_58_5 = e1 | all_58_10 = e1 % 150.82/22.08 | | | | | | | | | | | | | % 150.82/22.08 | | | | | | | | | | | | | BETA: splitting (113) gives: % 150.82/22.08 | | | | | | | | | | | | | % 150.82/22.08 | | | | | | | | | | | | | Case 1: % 150.82/22.08 | | | | | | | | | | | | | | % 150.82/22.08 | | | | | | | | | | | | | | (114) all_58_5 = e1 % 150.82/22.08 | | | | | | | | | | | | | | % 150.82/22.08 | | | | | | | | | | | | | | COMBINE_EQS: (18), (114) imply: % 150.82/22.08 | | | | | | | | | | | | | | (115) all_52_9 = e1 % 150.82/22.08 | | | | | | | | | | | | | | % 150.82/22.08 | | | | | | | | | | | | | | SIMP: (115) implies: % 150.82/22.08 | | | | | | | | | | | | | | (116) all_52_9 = e1 % 150.82/22.08 | | | | | | | | | | | | | | % 150.82/22.08 | | | | | | | | | | | | | | REDUCE: (42), (116) imply: % 150.82/22.08 | | | | | | | | | | | | | | (117) ~ (all_6_2 = e1) % 150.82/22.08 | | | | | | | | | | | | | | % 150.82/22.08 | | | | | | | | | | | | | | SIMP: (117) implies: % 150.82/22.08 | | | | | | | | | | | | | | (118) ~ (all_6_2 = e1) % 150.82/22.08 | | | | | | | | | | | | | | % 150.82/22.08 | | | | | | | | | | | | | | BETA: splitting (37) gives: % 150.82/22.08 | | | | | | | | | | | | | | % 150.82/22.08 | | | | | | | | | | | | | | Case 1: % 150.82/22.08 | | | | | | | | | | | | | | | % 150.82/22.08 | | | | | | | | | | | | | | | (119) all_56_1 = e3 % 150.82/22.08 | | | | | | | | | | | | | | | % 150.82/22.08 | | | | | | | | | | | | | | | COMBINE_EQS: (67), (119) imply: % 150.82/22.08 | | | | | | | | | | | | | | | (120) e3 = e0 % 150.82/22.08 | | | | | | | | | | | | | | | % 150.82/22.08 | | | | | | | | | | | | | | | REF_CLOSE: (3), (12), (15), (20), (23), (28), (36), (41), % 150.82/22.08 | | | | | | | | | | | | | | | (45), (46), (51), (52), (120) are inconsistent by % 150.82/22.08 | | | | | | | | | | | | | | | sub-proof #189. % 150.82/22.08 | | | | | | | | | | | | | | | % 150.82/22.08 | | | | | | | | | | | | | | Case 2: % 150.82/22.08 | | | | | | | | | | | | | | | % 150.82/22.08 | | | | | | | | | | | | | | | (121) all_56_11 = e2 | all_56_21 = e1 | all_56_31 = e0 % 150.82/22.08 | | | | | | | | | | | | | | | % 150.82/22.08 | | | | | | | | | | | | | | | BETA: splitting (26) gives: % 150.82/22.08 | | | | | | | | | | | | | | | % 150.82/22.08 | | | | | | | | | | | | | | | Case 1: % 150.82/22.08 | | | | | | | | | | | | | | | | % 150.82/22.08 | | | | | | | | | | | | | | | | (122) all_58_2 = e0 % 150.82/22.08 | | | | | | | | | | | | | | | | % 150.82/22.08 | | | | | | | | | | | | | | | | COMBINE_EQS: (29), (122) imply: % 150.82/22.08 | | | | | | | | | | | | | | | | (123) e2 = e0 % 150.82/22.08 | | | | | | | | | | | | | | | | % 150.82/22.08 | | | | | | | | | | | | | | | | SIMP: (123) implies: % 150.82/22.08 | | | | | | | | | | | | | | | | (124) e2 = e0 % 150.82/22.08 | | | | | | | | | | | | | | | | % 150.82/22.08 | | | | | | | | | | | | | | | | REDUCE: (90), (124) imply: % 150.82/22.08 | | | | | | | | | | | | | | | | (125) $false % 150.82/22.08 | | | | | | | | | | | | | | | | % 150.82/22.08 | | | | | | | | | | | | | | | | CLOSE: (125) is inconsistent. % 150.82/22.08 | | | | | | | | | | | | | | | | % 150.82/22.08 | | | | | | | | | | | | | | | Case 2: % 150.82/22.08 | | | | | | | | | | | | | | | | % 150.82/22.08 | | | | | | | | | | | | | | | | (126) all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0 % 150.82/22.08 | | | | | | | | | | | | | | | | % 150.82/22.08 | | | | | | | | | | | | | | | | BETA: splitting (126) gives: % 150.82/22.08 | | | | | | | | | | | | | | | | % 150.82/22.08 | | | | | | | | | | | | | | | | Case 1: % 150.82/22.08 | | | | | | | | | | | | | | | | | % 150.82/22.08 | | | | | | | | | | | | | | | | | (127) all_58_3 = e0 % 150.82/22.08 | | | | | | | | | | | | | | | | | % 150.82/22.08 | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (12), (15), (20), (22), (23), (28), (36), % 150.82/22.08 | | | | | | | | | | | | | | | | | (41), (45), (46), (51), (52), (127) are % 150.82/22.08 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #595. % 150.82/22.08 | | | | | | | | | | | | | | | | | % 150.82/22.08 | | | | | | | | | | | | | | | | Case 2: % 150.82/22.08 | | | | | | | | | | | | | | | | | % 150.82/22.08 | | | | | | | | | | | | | | | | | (128) all_58_5 = e0 | all_58_10 = e0 % 150.82/22.08 | | | | | | | | | | | | | | | | | % 150.82/22.08 | | | | | | | | | | | | | | | | | BETA: splitting (128) gives: % 150.82/22.08 | | | | | | | | | | | | | | | | | % 150.82/22.08 | | | | | | | | | | | | | | | | | Case 1: % 150.82/22.08 | | | | | | | | | | | | | | | | | | % 150.82/22.08 | | | | | | | | | | | | | | | | | | (129) all_58_5 = e0 % 150.82/22.08 | | | | | | | | | | | | | | | | | | % 150.82/22.08 | | | | | | | | | | | | | | | | | | REF_CLOSE: (104), (114), (129) are inconsistent by sub-proof % 150.82/22.08 | | | | | | | | | | | | | | | | | | #172. % 150.82/22.08 | | | | | | | | | | | | | | | | | | % 150.82/22.08 | | | | | | | | | | | | | | | | | Case 2: % 150.82/22.08 | | | | | | | | | | | | | | | | | | % 150.82/22.08 | | | | | | | | | | | | | | | | | | (130) all_58_10 = e0 % 150.82/22.08 | | | | | | | | | | | | | | | | | | % 150.82/22.08 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (106), (130) imply: % 150.82/22.08 | | | | | | | | | | | | | | | | | | (131) all_8_0 = e0 % 150.82/22.08 | | | | | | | | | | | | | | | | | | % 150.82/22.08 | | | | | | | | | | | | | | | | | | SIMP: (131) implies: % 150.82/22.08 | | | | | | | | | | | | | | | | | | (132) all_8_0 = e0 % 150.82/22.08 | | | | | | | | | | | | | | | | | | % 150.82/22.08 | | | | | | | | | | | | | | | | | | REDUCE: (107), (132) imply: % 150.82/22.08 | | | | | | | | | | | | | | | | | | (133) ~ (all_4_2 = e0) % 150.82/22.08 | | | | | | | | | | | | | | | | | | % 150.82/22.08 | | | | | | | | | | | | | | | | | | SIMP: (133) implies: % 150.82/22.08 | | | | | | | | | | | | | | | | | | (134) ~ (all_4_2 = e0) % 150.82/22.08 | | | | | | | | | | | | | | | | | | % 150.82/22.08 | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (12), (16), (35), (118), (121), (134) are % 150.82/22.08 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #152. % 150.82/22.08 | | | | | | | | | | | | | | | | | | % 150.82/22.08 | | | | | | | | | | | | | | | | | End of split % 150.82/22.08 | | | | | | | | | | | | | | | | | % 150.82/22.08 | | | | | | | | | | | | | | | | End of split % 150.82/22.08 | | | | | | | | | | | | | | | | % 150.82/22.08 | | | | | | | | | | | | | | | End of split % 150.82/22.08 | | | | | | | | | | | | | | | % 150.82/22.08 | | | | | | | | | | | | | | End of split % 150.82/22.08 | | | | | | | | | | | | | | % 150.82/22.08 | | | | | | | | | | | | | Case 2: % 150.82/22.08 | | | | | | | | | | | | | | % 150.82/22.08 | | | | | | | | | | | | | | (135) all_58_10 = e1 % 150.82/22.08 | | | | | | | | | | | | | | % 150.82/22.08 | | | | | | | | | | | | | | COMBINE_EQS: (106), (135) imply: % 150.82/22.08 | | | | | | | | | | | | | | (136) all_8_0 = e1 % 150.82/22.08 | | | | | | | | | | | | | | % 150.82/22.08 | | | | | | | | | | | | | | SIMP: (136) implies: % 150.82/22.08 | | | | | | | | | | | | | | (137) all_8_0 = e1 % 150.82/22.08 | | | | | | | | | | | | | | % 150.82/22.08 | | | | | | | | | | | | | | REDUCE: (7), (137) imply: % 150.82/22.08 | | | | | | | | | | | | | | (138) $false % 150.82/22.08 | | | | | | | | | | | | | | % 150.82/22.08 | | | | | | | | | | | | | | CLOSE: (138) is inconsistent. % 150.82/22.08 | | | | | | | | | | | | | | % 150.82/22.08 | | | | | | | | | | | | | End of split % 150.82/22.08 | | | | | | | | | | | | | % 150.82/22.08 | | | | | | | | | | | | End of split % 150.82/22.08 | | | | | | | | | | | | % 150.82/22.08 | | | | | | | | | | | End of split % 150.82/22.08 | | | | | | | | | | | % 150.82/22.08 | | | | | | | | | | Case 2: % 150.82/22.08 | | | | | | | | | | | % 150.82/22.08 | | | | | | | | | | | (139) all_54_1 = e0 % 150.82/22.08 | | | | | | | | | | | % 150.82/22.08 | | | | | | | | | | | REF_CLOSE: (19), (68), (139) are inconsistent by sub-proof % 150.82/22.08 | | | | | | | | | | | #719. % 150.82/22.08 | | | | | | | | | | | % 150.82/22.08 | | | | | | | | | | End of split % 150.82/22.08 | | | | | | | | | | % 150.82/22.08 | | | | | | | | | End of split % 150.82/22.08 | | | | | | | | | % 150.82/22.08 | | | | | | | | End of split % 150.82/22.08 | | | | | | | | % 150.82/22.08 | | | | | | | Case 2: % 150.82/22.08 | | | | | | | | % 150.82/22.08 | | | | | | | | (140) all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2 % 150.82/22.08 | | | | | | | | % 150.82/22.08 | | | | | | | | REF_CLOSE: (5), (9), (11), (18), (31), (40), (85), (140) are % 150.82/22.08 | | | | | | | | inconsistent by sub-proof #589. % 150.82/22.08 | | | | | | | | % 150.82/22.08 | | | | | | | End of split % 150.82/22.08 | | | | | | | % 150.82/22.08 | | | | | | End of split % 150.82/22.08 | | | | | | % 150.82/22.08 | | | | | End of split % 150.82/22.08 | | | | | % 150.82/22.08 | | | | End of split % 150.82/22.08 | | | | % 150.82/22.08 | | | End of split % 150.82/22.08 | | | % 150.82/22.08 | | End of split % 150.82/22.08 | | % 150.82/22.08 | End of split % 150.82/22.08 | % 150.82/22.08 End of proof % 150.82/22.08 % 150.82/22.08 Sub-proof #152 shows that the following formulas are inconsistent: % 150.82/22.08 ---------------------------------------------------------------- % 150.82/22.08 (1) ~ (e3 = e2) % 150.82/22.08 (2) all_56_11 = e3 % 150.82/22.08 (3) all_56_21 = all_6_2 % 150.82/22.08 (4) all_56_11 = e2 | all_56_21 = e1 | all_56_31 = e0 % 150.82/22.08 (5) ~ (all_4_2 = e0) % 150.82/22.08 (6) all_56_31 = all_4_2 % 150.82/22.08 (7) ~ (all_6_2 = e1) % 150.82/22.08 % 150.82/22.08 Begin of proof % 150.82/22.08 | % 150.82/22.08 | BETA: splitting (4) gives: % 150.82/22.08 | % 150.82/22.08 | Case 1: % 150.82/22.08 | | % 150.82/22.08 | | (8) all_56_11 = e2 % 150.82/22.08 | | % 150.82/22.08 | | COMBINE_EQS: (2), (8) imply: % 150.82/22.08 | | (9) e3 = e2 % 150.82/22.08 | | % 150.82/22.08 | | REDUCE: (1), (9) imply: % 150.82/22.08 | | (10) $false % 150.82/22.08 | | % 150.82/22.08 | | CLOSE: (10) is inconsistent. % 150.82/22.08 | | % 150.82/22.08 | Case 2: % 150.82/22.08 | | % 150.82/22.08 | | (11) all_56_21 = e1 | all_56_31 = e0 % 150.82/22.08 | | % 150.82/22.08 | | BETA: splitting (11) gives: % 150.82/22.08 | | % 150.82/22.08 | | Case 1: % 150.82/22.08 | | | % 150.82/22.08 | | | (12) all_56_21 = e1 % 150.82/22.08 | | | % 150.82/22.08 | | | REF_CLOSE: (3), (7), (12) are inconsistent by sub-proof #153. % 150.82/22.08 | | | % 150.82/22.08 | | Case 2: % 150.82/22.08 | | | % 150.82/22.08 | | | (13) all_56_31 = e0 % 150.82/22.08 | | | % 150.82/22.08 | | | REF_CLOSE: (5), (6), (13) are inconsistent by sub-proof #675. % 150.82/22.08 | | | % 150.82/22.08 | | End of split % 150.82/22.08 | | % 150.82/22.08 | End of split % 150.82/22.08 | % 150.82/22.08 End of proof % 150.82/22.08 % 150.82/22.08 Sub-proof #153 shows that the following formulas are inconsistent: % 150.82/22.08 ---------------------------------------------------------------- % 150.82/22.08 (1) all_56_21 = all_6_2 % 150.82/22.08 (2) all_56_21 = e1 % 150.82/22.08 (3) ~ (all_6_2 = e1) % 150.82/22.08 % 150.82/22.08 Begin of proof % 150.82/22.08 | % 150.82/22.08 | COMBINE_EQS: (1), (2) imply: % 150.82/22.08 | (4) all_6_2 = e1 % 150.82/22.08 | % 150.82/22.08 | SIMP: (4) implies: % 150.82/22.08 | (5) all_6_2 = e1 % 150.82/22.08 | % 150.82/22.08 | REDUCE: (3), (5) imply: % 150.82/22.08 | (6) $false % 150.82/22.08 | % 150.82/22.08 | CLOSE: (6) is inconsistent. % 150.82/22.08 | % 150.82/22.08 End of proof % 150.82/22.08 % 150.82/22.08 Sub-proof #154 shows that the following formulas are inconsistent: % 150.82/22.08 ---------------------------------------------------------------- % 150.82/22.08 (1) all_56_11 = all_8_2 % 150.82/22.08 (2) op(e0, all_52_13) = all_56_14 % 150.82/22.08 (3) ~ (all_56_11 = e1) | all_56_13 = e2 % 150.82/22.08 (4) ~ (all_52_11 = all_6_2) % 150.82/22.08 (5) ~ (all_52_4 = all_52_8) % 150.82/22.08 (6) all_56_25 = all_52_3 % 150.82/22.08 (7) ~ (all_52_7 = all_52_11) % 150.82/22.08 (8) ~ (all_52_8 = all_52_9) % 150.82/22.08 (9) all_54_9 = all_52_6 % 150.82/22.08 (10) op(e2, all_8_1) = all_8_0 % 150.82/22.08 (11) all_58_6 = all_52_2 % 150.82/22.08 (12) ~ (all_8_1 = e1) % 150.82/22.08 (13) ~ (all_52_1 = all_52_9) % 150.82/22.08 (14) ~ (e3 = e0) % 150.82/22.08 (15) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0 % 150.82/22.08 (16) all_54_10 = all_6_2 % 150.82/22.08 (17) ~ (all_6_1 = e2) % 150.82/22.08 (18) all_12_2 = all_4_2 % 150.82/22.08 (19) ~ (all_52_13 = all_8_2) % 150.82/22.08 (20) all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2 % 150.82/22.08 (21) all_54_0 = all_10_2 % 150.82/22.08 (22) all_54_4 = all_52_1 % 150.82/22.08 (23) ~ (all_52_14 = all_4_2) % 150.82/22.08 (24) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0 % 150.82/22.08 (25) all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2 % 150.82/22.08 (26) ~ (all_52_9 = all_8_2) % 150.82/22.08 (27) ~ (all_52_4 = all_52_7) % 150.82/22.09 (28) ~ (all_6_2 = e3) % 150.82/22.09 (29) ~ (all_8_1 = e3) % 150.82/22.09 (30) ~ (e3 = e2) % 150.82/22.09 (31) op(e0, e0) = all_4_2 % 150.82/22.09 (32) all_58_6 = e0 | all_58_7 = e0 | all_58_8 = e0 | all_58_11 = e0 % 150.82/22.09 (33) all_58_4 = all_52_8 % 150.82/22.09 (34) all_54_5 = all_8_2 % 150.82/22.09 (35) ~ (all_10_2 = e1) % 150.82/22.09 (36) ~ (all_6_1 = e3) % 150.82/22.09 (37) ~ (all_52_6 = all_52_14) % 150.82/22.09 (38) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 150.82/22.09 (39) all_54_15 = all_4_2 % 150.82/22.09 (40) all_56_21 = all_6_2 % 150.82/22.09 (41) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 150.82/22.09 (42) ~ (all_52_7 = all_8_2) % 150.82/22.09 (43) all_56_1 = all_10_2 % 150.82/22.09 (44) all_56_27 = all_52_7 % 150.82/22.09 (45) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0 % 150.82/22.09 (46) all_58_5 = all_52_9 % 150.82/22.09 (47) all_54_1 = all_52_4 % 150.82/22.09 (48) all_58_9 = all_52_12 % 150.82/22.09 (49) op(e0, all_52_14) = all_56_22 % 150.82/22.09 (50) op(e0, e2) = all_52_7 % 150.82/22.09 (51) all_54_14 = all_52_11 % 150.82/22.09 (52) all_58_1 = all_52_4 % 150.82/22.09 (53) all_58_13 = all_52_7 % 150.82/22.09 (54) op(e2, all_8_2) = all_56_10 % 150.82/22.09 (55) op(e3, e3) = all_10_2 % 150.82/22.09 (56) op(e3, all_10_1) = e2 % 150.82/22.09 (57) all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2 % 150.82/22.09 (58) all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0 % 150.82/22.09 (59) ~ (all_52_1 = all_8_2) % 150.82/22.09 (60) all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2 % 150.82/22.09 (61) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 150.82/22.09 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 150.82/22.09 (62) ~ (all_52_3 = all_10_2) % 150.82/22.09 (63) all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0 % 150.82/22.09 (64) ~ (all_52_2 = all_52_6) % 150.82/22.09 (65) all_56_7 = all_52_12 % 150.82/22.09 (66) op(e0, all_4_1) = e2 % 150.82/22.09 (67) all_56_13 = all_52_9 % 150.82/22.09 (68) ~ (all_52_1 = all_52_13) % 150.82/22.09 (69) ~ (all_52_7 = all_4_2) % 150.82/22.09 (70) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0 % 150.82/22.09 (71) ~ (all_4_2 = e1) % 150.82/22.09 (72) all_58_8 = all_6_2 % 150.82/22.09 (73) ~ (all_52_3 = all_4_2) % 150.82/22.09 (74) ~ (all_52_8 = all_10_2) % 150.82/22.09 (75) all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3 % 150.82/22.09 (76) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0 % 150.82/22.09 (77) ~ (all_56_1 = e2) | all_56_3 = e3 % 150.82/22.09 (78) ~ (all_56_1 = e0) | all_56_7 = e3 % 150.82/22.09 (79) ~ (all_8_2 = e3) % 150.82/22.09 (80) ~ (all_12_1 = e1) | ~ (all_12_2 = e3) % 150.82/22.09 (81) ~ (all_52_9 = all_52_13) % 150.82/22.09 (82) ~ (all_52_2 = all_52_3) % 150.82/22.09 (83) op(all_4_2, all_4_2) = all_4_1 % 150.82/22.09 (84) all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3 % 150.82/22.09 (85) ~ (all_52_3 = all_52_11) % 150.82/22.09 (86) all_58_3 = all_8_2 % 150.82/22.09 (87) all_56_3 = all_52_4 % 150.82/22.09 (88) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0 % 150.82/22.09 (89) ~ (all_52_11 = all_4_2) % 150.82/22.09 (90) ~ (all_52_1 = all_52_3) % 150.82/22.09 (91) all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1 % 150.82/22.09 (92) ~ (all_52_6 = all_52_7) % 150.82/22.09 (93) all_56_31 = all_4_2 % 150.82/22.09 (94) all_58_11 = all_52_14 % 150.82/22.09 (95) ~ (all_52_2 = all_52_14) % 150.82/22.09 (96) ~ (all_52_9 = all_52_11) % 150.82/22.09 (97) all_54_7 = all_52_13 % 150.82/22.09 (98) op(all_6_2, all_6_2) = all_6_1 % 150.82/22.09 (99) ~ (all_52_13 = all_4_2) % 150.82/22.09 (100) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0 % 150.82/22.09 (101) ~ (all_52_8 = all_52_11) % 150.82/22.09 (102) all_54_13 = all_52_7 % 150.82/22.09 (103) op(e3, e2) = all_52_4 % 150.82/22.09 (104) ~ (all_52_13 = all_52_14) % 150.82/22.09 (105) all_56_23 = all_52_14 % 150.82/22.09 (106) all_54_8 = all_52_2 % 150.82/22.09 (107) op(e1, e1) = all_6_2 % 150.82/22.09 (108) ~ (all_52_6 = all_8_2) % 150.82/22.09 (109) all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1 % 150.97/22.09 (110) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0 % 150.97/22.09 (111) all_58_15 = all_4_2 % 150.97/22.09 (112) ~ (all_6_2 = e2) % 150.97/22.09 (113) all_58_2 = all_52_1 % 150.97/22.09 (114) ~ (all_52_9 = all_6_2) % 150.97/22.09 (115) all_58_7 = all_52_6 % 150.97/22.09 (116) all_58_10 = all_52_13 % 150.97/22.09 (117) all_12_1 = all_4_1 % 150.97/22.09 (118) op(all_10_2, all_10_2) = all_10_1 % 150.97/22.09 (119) all_58_0 = all_10_2 % 150.97/22.09 (120) op(e3, all_52_2) = all_56_16 % 150.97/22.09 (121) all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1 % 150.97/22.09 (122) ~ (all_52_12 = all_52_14) % 150.97/22.09 (123) op(e3, e1) = all_52_8 % 150.97/22.09 (124) ~ (all_56_31 = e2) | all_56_27 = e0 % 150.97/22.09 (125) op(e2, e2) = all_8_2 % 150.97/22.09 (126) ~ (all_52_4 = all_52_12) % 150.97/22.09 (127) ~ (all_52_2 = all_6_2) % 150.97/22.09 (128) ~ (all_52_8 = all_52_12) % 150.97/22.09 (129) ~ (all_52_1 = all_52_2) % 150.97/22.09 (130) ~ (all_56_21 = e0) | all_56_23 = e1 % 150.97/22.09 (131) op(e0, all_4_2) = all_56_30 % 150.97/22.09 (132) ~ (all_52_6 = all_6_2) % 150.97/22.09 (133) ~ (all_8_2 = e0) % 150.97/22.09 (134) ~ (all_52_14 = all_6_2) % 150.97/22.09 (135) all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3 % 150.97/22.09 (136) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0 % 150.97/22.09 (137) ~ (all_52_2 = all_10_2) % 150.97/22.09 (138) ~ (all_52_4 = all_10_2) % 150.97/22.09 (139) ~ (all_52_4 = all_8_2) % 150.97/22.09 (140) op(all_8_2, all_8_2) = all_8_1 % 150.97/22.09 (141) op(e3, all_52_3) = all_56_24 % 150.97/22.09 (142) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 150.97/22.09 (143) all_58_14 = all_52_11 % 150.97/22.09 (144) ~ (all_52_12 = all_10_2) % 150.97/22.09 (145) ~ (all_52_1 = all_10_2) % 150.97/22.09 (146) all_58_12 = all_52_3 % 150.97/22.09 (147) all_54_11 = all_52_14 % 150.97/22.09 (148) ~ (all_56_31 = e3) | all_56_25 = e0 % 150.97/22.09 % 150.97/22.09 Begin of proof % 150.97/22.09 | % 150.97/22.09 | BETA: splitting (77) gives: % 150.97/22.09 | % 150.97/22.09 | Case 1: % 150.97/22.09 | | % 150.97/22.09 | | (149) ~ (all_56_1 = e2) % 150.97/22.09 | | % 150.97/22.09 | | REDUCE: (43), (149) imply: % 150.97/22.09 | | (150) ~ (all_10_2 = e2) % 150.97/22.09 | | % 150.97/22.09 | | BETA: splitting (3) gives: % 150.97/22.09 | | % 150.97/22.09 | | Case 1: % 150.97/22.09 | | | % 150.97/22.09 | | | (151) ~ (all_56_11 = e1) % 150.97/22.09 | | | % 150.97/22.09 | | | REDUCE: (1), (151) imply: % 150.97/22.09 | | | (152) ~ (all_8_2 = e1) % 150.97/22.09 | | | % 150.97/22.09 | | | BETA: splitting (142) gives: % 150.97/22.09 | | | % 150.97/22.09 | | | Case 1: % 150.97/22.09 | | | | % 150.97/22.09 | | | | (153) all_54_5 = e3 % 150.97/22.09 | | | | % 150.97/22.09 | | | | REF_CLOSE: (34), (79), (153) are inconsistent by sub-proof #737. % 150.97/22.09 | | | | % 150.97/22.09 | | | Case 2: % 150.97/22.09 | | | | % 150.97/22.09 | | | | (154) ~ (all_54_5 = e3) % 150.97/22.09 | | | | (155) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 150.97/22.09 | | | | % 150.97/22.09 | | | | BETA: splitting (155) gives: % 150.97/22.09 | | | | % 150.97/22.09 | | | | Case 1: % 150.97/22.09 | | | | | % 150.97/22.09 | | | | | (156) all_54_5 = e2 % 150.97/22.09 | | | | | % 150.97/22.09 | | | | | COMBINE_EQS: (34), (156) imply: % 150.97/22.09 | | | | | (157) all_8_2 = e2 % 150.97/22.09 | | | | | % 150.97/22.09 | | | | | SIMP: (157) implies: % 150.97/22.09 | | | | | (158) all_8_2 = e2 % 150.97/22.09 | | | | | % 150.97/22.09 | | | | | REDUCE: (59), (158) imply: % 150.97/22.09 | | | | | (159) ~ (all_52_1 = e2) % 150.97/22.09 | | | | | % 150.97/22.09 | | | | | REDUCE: (108), (158) imply: % 150.97/22.09 | | | | | (160) ~ (all_52_6 = e2) % 150.97/22.09 | | | | | % 150.97/22.09 | | | | | REDUCE: (19), (158) imply: % 150.97/22.09 | | | | | (161) ~ (all_52_13 = e2) % 150.97/22.09 | | | | | % 150.97/22.09 | | | | | REDUCE: (140), (158) imply: % 150.97/22.09 | | | | | (162) op(e2, e2) = all_8_1 % 150.97/22.09 | | | | | % 150.97/22.09 | | | | | REDUCE: (54), (158) imply: % 150.97/22.09 | | | | | (163) op(e2, e2) = all_56_10 % 150.97/22.09 | | | | | % 150.97/22.09 | | | | | REDUCE: (125), (158) imply: % 150.97/22.09 | | | | | (164) op(e2, e2) = e2 % 150.97/22.09 | | | | | % 150.97/22.09 | | | | | GROUND_INST: instantiating (61) with all_8_1, all_56_10, e2, e2, % 150.97/22.09 | | | | | simplifying with (162), (163) gives: % 150.97/22.09 | | | | | (165) all_56_10 = all_8_1 % 150.97/22.09 | | | | | % 150.97/22.09 | | | | | GROUND_INST: instantiating (61) with e2, all_56_10, e2, e2, % 150.97/22.09 | | | | | simplifying with (163), (164) gives: % 150.97/22.09 | | | | | (166) all_56_10 = e2 % 150.97/22.09 | | | | | % 150.97/22.09 | | | | | COMBINE_EQS: (165), (166) imply: % 150.97/22.09 | | | | | (167) all_8_1 = e2 % 150.97/22.09 | | | | | % 150.97/22.09 | | | | | REDUCE: (10), (167) imply: % 150.97/22.09 | | | | | (168) op(e2, e2) = all_8_0 % 150.97/22.09 | | | | | % 150.97/22.09 | | | | | GROUND_INST: instantiating (61) with e2, all_8_0, e2, e2, simplifying % 150.97/22.09 | | | | | with (164), (168) gives: % 150.97/22.09 | | | | | (169) all_8_0 = e2 % 150.97/22.09 | | | | | % 150.97/22.09 | | | | | BETA: splitting (130) gives: % 150.97/22.09 | | | | | % 150.97/22.09 | | | | | Case 1: % 150.97/22.09 | | | | | | % 150.97/22.09 | | | | | | (170) ~ (all_56_21 = e0) % 150.97/22.09 | | | | | | % 150.97/22.09 | | | | | | REDUCE: (40), (170) imply: % 150.97/22.09 | | | | | | (171) ~ (all_6_2 = e0) % 150.97/22.09 | | | | | | % 150.97/22.09 | | | | | | BETA: splitting (41) gives: % 150.97/22.09 | | | | | | % 150.97/22.09 | | | | | | Case 1: % 150.97/22.09 | | | | | | | % 150.97/22.09 | | | | | | | (172) all_54_10 = e3 % 150.97/22.09 | | | | | | | % 150.97/22.09 | | | | | | | REF_CLOSE: (16), (28), (172) are inconsistent by sub-proof #736. % 150.97/22.09 | | | | | | | % 150.97/22.09 | | | | | | Case 2: % 150.97/22.09 | | | | | | | % 150.97/22.09 | | | | | | | (173) ~ (all_54_10 = e3) % 150.97/22.09 | | | | | | | (174) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 150.97/22.09 | | | | | | | % 150.97/22.09 | | | | | | | BETA: splitting (174) gives: % 150.97/22.09 | | | | | | | % 150.97/22.09 | | | | | | | Case 1: % 150.97/22.09 | | | | | | | | % 150.97/22.09 | | | | | | | | (175) all_54_10 = e2 % 150.97/22.09 | | | | | | | | % 150.97/22.09 | | | | | | | | REF_CLOSE: (16), (112), (175) are inconsistent by sub-proof % 150.97/22.09 | | | | | | | | #735. % 150.97/22.09 | | | | | | | | % 150.97/22.09 | | | | | | | Case 2: % 150.97/22.09 | | | | | | | | % 150.97/22.09 | | | | | | | | (176) ~ (all_54_10 = e2) % 150.97/22.09 | | | | | | | | (177) all_54_10 = e1 | all_54_10 = e0 % 150.97/22.09 | | | | | | | | % 150.97/22.09 | | | | | | | | BETA: splitting (177) gives: % 150.97/22.09 | | | | | | | | % 150.97/22.09 | | | | | | | | Case 1: % 150.97/22.09 | | | | | | | | | % 150.97/22.09 | | | | | | | | | (178) all_54_10 = e1 % 150.97/22.09 | | | | | | | | | % 150.97/22.09 | | | | | | | | | COMBINE_EQS: (16), (178) imply: % 150.97/22.09 | | | | | | | | | (179) all_6_2 = e1 % 150.97/22.09 | | | | | | | | | % 150.97/22.09 | | | | | | | | | SIMP: (179) implies: % 150.97/22.09 | | | | | | | | | (180) all_6_2 = e1 % 150.97/22.09 | | | | | | | | | % 150.97/22.09 | | | | | | | | | REDUCE: (132), (180) imply: % 150.97/22.09 | | | | | | | | | (181) ~ (all_52_6 = e1) % 150.97/22.09 | | | | | | | | | % 150.97/22.09 | | | | | | | | | REDUCE: (4), (180) imply: % 150.97/22.09 | | | | | | | | | (182) ~ (all_52_11 = e1) % 150.97/22.09 | | | | | | | | | % 150.97/22.09 | | | | | | | | | REDUCE: (134), (180) imply: % 150.97/22.09 | | | | | | | | | (183) ~ (all_52_14 = e1) % 150.97/22.09 | | | | | | | | | % 150.97/22.09 | | | | | | | | | BETA: splitting (124) gives: % 150.97/22.09 | | | | | | | | | % 150.97/22.09 | | | | | | | | | Case 1: % 150.97/22.09 | | | | | | | | | | % 150.97/22.09 | | | | | | | | | | (184) ~ (all_56_31 = e2) % 150.97/22.09 | | | | | | | | | | % 150.97/22.09 | | | | | | | | | | REDUCE: (93), (184) imply: % 150.97/22.09 | | | | | | | | | | (185) ~ (all_4_2 = e2) % 150.97/22.09 | | | | | | | | | | % 150.97/22.09 | | | | | | | | | | BETA: splitting (148) gives: % 150.97/22.09 | | | | | | | | | | % 150.97/22.09 | | | | | | | | | | Case 1: % 150.97/22.09 | | | | | | | | | | | % 150.97/22.09 | | | | | | | | | | | (186) ~ (all_56_31 = e3) % 150.97/22.09 | | | | | | | | | | | % 150.97/22.09 | | | | | | | | | | | REDUCE: (93), (186) imply: % 150.97/22.09 | | | | | | | | | | | (187) ~ (all_4_2 = e3) % 150.97/22.09 | | | | | | | | | | | % 150.97/22.09 | | | | | | | | | | | REF_CLOSE: (31), (39), (61), (66), (71), (83), (100), (131), % 150.97/22.09 | | | | | | | | | | | (185), (187) are inconsistent by sub-proof #229. % 150.97/22.09 | | | | | | | | | | | % 150.97/22.09 | | | | | | | | | | Case 2: % 150.97/22.09 | | | | | | | | | | | % 150.97/22.09 | | | | | | | | | | | (188) all_56_31 = e3 % 150.97/22.09 | | | | | | | | | | | (189) all_56_25 = e0 % 150.97/22.09 | | | | | | | | | | | % 150.97/22.09 | | | | | | | | | | | COMBINE_EQS: (6), (189) imply: % 150.97/22.09 | | | | | | | | | | | (190) all_52_3 = e0 % 150.97/22.09 | | | | | | | | | | | % 150.97/22.09 | | | | | | | | | | | SIMP: (190) implies: % 150.97/22.09 | | | | | | | | | | | (191) all_52_3 = e0 % 150.97/22.09 | | | | | | | | | | | % 150.97/22.09 | | | | | | | | | | | COMBINE_EQS: (93), (188) imply: % 150.97/22.09 | | | | | | | | | | | (192) all_4_2 = e3 % 150.97/22.09 | | | | | | | | | | | % 150.97/22.09 | | | | | | | | | | | REDUCE: (90), (191) imply: % 150.97/22.09 | | | | | | | | | | | (193) ~ (all_52_1 = e0) % 150.97/22.09 | | | | | | | | | | | % 150.97/22.09 | | | | | | | | | | | REDUCE: (82), (191) imply: % 150.97/22.09 | | | | | | | | | | | (194) ~ (all_52_2 = e0) % 150.97/22.09 | | | | | | | | | | | % 150.97/22.09 | | | | | | | | | | | REDUCE: (62), (191) imply: % 150.97/22.09 | | | | | | | | | | | (195) ~ (all_10_2 = e0) % 150.97/22.09 | | | | | | | | | | | % 150.97/22.09 | | | | | | | | | | | SIMP: (195) implies: % 150.97/22.09 | | | | | | | | | | | (196) ~ (all_10_2 = e0) % 150.97/22.09 | | | | | | | | | | | % 150.97/22.09 | | | | | | | | | | | REDUCE: (99), (192) imply: % 150.97/22.09 | | | | | | | | | | | (197) ~ (all_52_13 = e3) % 150.97/22.09 | | | | | | | | | | | % 150.97/22.09 | | | | | | | | | | | REDUCE: (23), (192) imply: % 150.97/22.09 | | | | | | | | | | | (198) ~ (all_52_14 = e3) % 150.97/22.09 | | | | | | | | | | | % 150.97/22.09 | | | | | | | | | | | REDUCE: (31), (192) imply: % 150.97/22.09 | | | | | | | | | | | (199) op(e0, e0) = e3 % 150.97/22.09 | | | | | | | | | | | % 150.97/22.09 | | | | | | | | | | | REF_CLOSE: (2), (11), (21), (22), (28), (32), (35), (36), % 150.97/22.09 | | | | | | | | | | | (38), (45), (46), (61), (63), (64), (68), (70), % 150.97/22.09 | | | | | | | | | | | (72), (75), (81), (86), (94), (97), (98), (104), % 150.97/22.09 | | | | | | | | | | | (106), (113), (115), (116), (129), (133), (136), % 150.97/22.09 | | | | | | | | | | | (137), (145), (150), (159), (161), (193), (194), % 150.97/22.09 | | | | | | | | | | | (196), (197), (198), (199) are inconsistent by % 150.97/22.09 | | | | | | | | | | | sub-proof #215. % 150.97/22.09 | | | | | | | | | | | % 150.97/22.09 | | | | | | | | | | End of split % 150.97/22.09 | | | | | | | | | | % 150.97/22.09 | | | | | | | | | Case 2: % 150.97/22.09 | | | | | | | | | | % 150.97/22.09 | | | | | | | | | | (200) all_56_31 = e2 % 150.97/22.09 | | | | | | | | | | (201) all_56_27 = e0 % 150.97/22.09 | | | | | | | | | | % 150.97/22.09 | | | | | | | | | | COMBINE_EQS: (44), (201) imply: % 150.97/22.09 | | | | | | | | | | (202) all_52_7 = e0 % 150.97/22.09 | | | | | | | | | | % 150.97/22.09 | | | | | | | | | | SIMP: (202) implies: % 150.97/22.09 | | | | | | | | | | (203) all_52_7 = e0 % 150.97/22.09 | | | | | | | | | | % 150.97/22.09 | | | | | | | | | | COMBINE_EQS: (93), (200) imply: % 150.97/22.09 | | | | | | | | | | (204) all_4_2 = e2 % 150.97/22.09 | | | | | | | | | | % 150.97/22.09 | | | | | | | | | | REDUCE: (27), (203) imply: % 150.97/22.09 | | | | | | | | | | (205) ~ (all_52_4 = e0) % 150.97/22.09 | | | | | | | | | | % 150.97/22.09 | | | | | | | | | | REDUCE: (92), (203) imply: % 150.97/22.09 | | | | | | | | | | (206) ~ (all_52_6 = e0) % 150.97/22.09 | | | | | | | | | | % 150.97/22.09 | | | | | | | | | | REDUCE: (7), (203) imply: % 150.97/22.09 | | | | | | | | | | (207) ~ (all_52_11 = e0) % 150.97/22.09 | | | | | | | | | | % 150.97/22.09 | | | | | | | | | | SIMP: (207) implies: % 150.97/22.09 | | | | | | | | | | (208) ~ (all_52_11 = e0) % 150.97/22.09 | | | | | | | | | | % 150.97/22.09 | | | | | | | | | | REDUCE: (89), (204) imply: % 150.97/22.09 | | | | | | | | | | (209) ~ (all_52_11 = e2) % 150.97/22.09 | | | | | | | | | | % 150.97/22.09 | | | | | | | | | | REDUCE: (23), (204) imply: % 150.97/22.09 | | | | | | | | | | (210) ~ (all_52_14 = e2) % 150.97/22.09 | | | | | | | | | | % 150.97/22.09 | | | | | | | | | | REDUCE: (83), (204) imply: % 150.97/22.09 | | | | | | | | | | (211) op(e2, e2) = all_4_1 % 150.97/22.09 | | | | | | | | | | % 150.97/22.09 | | | | | | | | | | REDUCE: (131), (204) imply: % 150.97/22.09 | | | | | | | | | | (212) op(e0, e2) = all_56_30 % 150.97/22.09 | | | | | | | | | | % 150.97/22.09 | | | | | | | | | | REDUCE: (50), (203) imply: % 150.97/22.09 | | | | | | | | | | (213) op(e0, e2) = e0 % 150.97/22.09 | | | | | | | | | | % 150.97/22.09 | | | | | | | | | | REDUCE: (31), (204) imply: % 150.97/22.09 | | | | | | | | | | (214) op(e0, e0) = e2 % 150.97/22.09 | | | | | | | | | | % 150.97/22.09 | | | | | | | | | | BETA: splitting (88) gives: % 150.97/22.09 | | | | | | | | | | % 150.97/22.09 | | | | | | | | | | Case 1: % 150.97/22.09 | | | | | | | | | | | % 150.97/22.09 | | | | | | | | | | | (215) all_54_9 = e3 % 150.97/22.09 | | | | | | | | | | | % 150.97/22.09 | | | | | | | | | | | COMBINE_EQS: (9), (215) imply: % 150.97/22.09 | | | | | | | | | | | (216) all_52_6 = e3 % 150.97/22.09 | | | | | | | | | | | % 150.97/22.09 | | | | | | | | | | | SIMP: (216) implies: % 150.97/22.09 | | | | | | | | | | | (217) all_52_6 = e3 % 150.97/22.09 | | | | | | | | | | | % 150.97/22.09 | | | | | | | | | | | COMBINE_EQS: (115), (217) imply: % 150.97/22.09 | | | | | | | | | | | (218) all_58_7 = e3 % 150.97/22.09 | | | | | | | | | | | % 150.97/22.09 | | | | | | | | | | | REDUCE: (37), (217) imply: % 150.97/22.09 | | | | | | | | | | | (219) ~ (all_52_14 = e3) % 150.97/22.09 | | | | | | | | | | | % 150.97/22.09 | | | | | | | | | | | SIMP: (219) implies: % 150.97/22.09 | | | | | | | | | | | (220) ~ (all_52_14 = e3) % 150.97/22.09 | | | | | | | | | | | % 150.97/22.09 | | | | | | | | | | | BETA: splitting (15) gives: % 150.97/22.09 | | | | | | | | | | | % 150.97/22.09 | | | | | | | | | | | Case 1: % 150.97/22.09 | | | | | | | | | | | | % 150.97/22.09 | | | | | | | | | | | | (221) all_54_14 = e3 % 150.97/22.09 | | | | | | | | | | | | % 150.97/22.09 | | | | | | | | | | | | COMBINE_EQS: (51), (221) imply: % 150.97/22.09 | | | | | | | | | | | | (222) all_52_11 = e3 % 150.97/22.09 | | | | | | | | | | | | % 150.97/22.09 | | | | | | | | | | | | SIMP: (222) implies: % 150.97/22.09 | | | | | | | | | | | | (223) all_52_11 = e3 % 150.97/22.09 | | | | | | | | | | | | % 150.97/22.09 | | | | | | | | | | | | REDUCE: (101), (223) imply: % 150.97/22.09 | | | | | | | | | | | | (224) ~ (all_52_8 = e3) % 150.97/22.09 | | | | | | | | | | | | % 150.97/22.09 | | | | | | | | | | | | BETA: splitting (25) gives: % 150.97/22.09 | | | | | | | | | | | | % 150.97/22.09 | | | | | | | | | | | | Case 1: % 150.97/22.09 | | | | | | | | | | | | | % 150.97/22.09 | | | | | | | | | | | | | (225) all_58_4 = e2 % 150.97/22.09 | | | | | | | | | | | | | % 150.97/22.09 | | | | | | | | | | | | | COMBINE_EQS: (33), (225) imply: % 150.97/22.09 | | | | | | | | | | | | | (226) all_52_8 = e2 % 150.97/22.09 | | | | | | | | | | | | | % 150.97/22.09 | | | | | | | | | | | | | REDUCE: (5), (226) imply: % 150.97/22.09 | | | | | | | | | | | | | (227) ~ (all_52_4 = e2) % 150.97/22.09 | | | | | | | | | | | | | % 150.97/22.09 | | | | | | | | | | | | | REDUCE: (224), (226) imply: % 150.97/22.09 | | | | | | | | | | | | | (228) ~ (e3 = e2) % 150.97/22.09 | | | | | | | | | | | | | % 150.97/22.09 | | | | | | | | | | | | | BETA: splitting (60) gives: % 150.97/22.09 | | | | | | | | | | | | | % 150.97/22.09 | | | | | | | | | | | | | Case 1: % 150.97/22.09 | | | | | | | | | | | | | | % 150.97/22.09 | | | | | | | | | | | | | | (229) all_58_6 = e2 % 150.97/22.09 | | | | | | | | | | | | | | % 150.97/22.09 | | | | | | | | | | | | | | COMBINE_EQS: (11), (229) imply: % 150.97/22.09 | | | | | | | | | | | | | | (230) all_52_2 = e2 % 150.97/22.09 | | | | | | | | | | | | | | % 150.97/22.09 | | | | | | | | | | | | | | REDUCE: (95), (230) imply: % 150.97/22.09 | | | | | | | | | | | | | | (231) ~ (all_52_14 = e2) % 150.97/22.09 | | | | | | | | | | | | | | % 150.97/22.09 | | | | | | | | | | | | | | REDUCE: (137), (230) imply: % 150.97/22.09 | | | | | | | | | | | | | | (232) ~ (all_10_2 = e2) % 150.97/22.09 | | | | | | | | | | | | | | % 150.97/22.09 | | | | | | | | | | | | | | REDUCE: (120), (230) imply: % 150.97/22.09 | | | | | | | | | | | | | | (233) op(e3, e2) = all_56_16 % 150.97/22.09 | | | | | | | | | | | | | | % 150.97/22.09 | | | | | | | | | | | | | | BETA: splitting (24) gives: % 150.97/22.09 | | | | | | | | | | | | | | % 150.97/22.09 | | | | | | | | | | | | | | Case 1: % 150.97/22.09 | | | | | | | | | | | | | | | % 150.97/22.09 | | | | | | | | | | | | | | | (234) all_54_11 = e3 % 150.97/22.09 | | | | | | | | | | | | | | | % 150.97/22.09 | | | | | | | | | | | | | | | COMBINE_EQS: (147), (234) imply: % 150.97/22.09 | | | | | | | | | | | | | | | (235) all_52_14 = e3 % 150.97/22.09 | | | | | | | | | | | | | | | % 150.97/22.09 | | | | | | | | | | | | | | | REDUCE: (220), (235) imply: % 150.97/22.09 | | | | | | | | | | | | | | | (236) $false % 150.97/22.09 | | | | | | | | | | | | | | | % 150.97/22.09 | | | | | | | | | | | | | | | CLOSE: (236) is inconsistent. % 150.97/22.09 | | | | | | | | | | | | | | | % 150.97/22.09 | | | | | | | | | | | | | | Case 2: % 150.97/22.09 | | | | | | | | | | | | | | | % 150.97/22.09 | | | | | | | | | | | | | | | (237) all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0 % 150.97/22.09 | | | | | | | | | | | | | | | % 150.97/22.09 | | | | | | | | | | | | | | | BETA: splitting (91) gives: % 150.97/22.09 | | | | | | | | | | | | | | | % 150.97/22.09 | | | | | | | | | | | | | | | Case 1: % 150.97/22.09 | | | | | | | | | | | | | | | | % 150.97/22.09 | | | | | | | | | | | | | | | | (238) all_58_1 = e1 % 150.97/22.09 | | | | | | | | | | | | | | | | % 150.97/22.09 | | | | | | | | | | | | | | | | COMBINE_EQS: (52), (238) imply: % 150.97/22.09 | | | | | | | | | | | | | | | | (239) all_52_4 = e1 % 150.97/22.09 | | | | | | | | | | | | | | | | % 150.97/22.09 | | | | | | | | | | | | | | | | REDUCE: (138), (239) imply: % 150.97/22.09 | | | | | | | | | | | | | | | | (240) ~ (all_10_2 = e1) % 150.97/22.09 | | | | | | | | | | | | | | | | % 150.97/22.09 | | | | | | | | | | | | | | | | REDUCE: (103), (239) imply: % 150.97/22.09 | | | | | | | | | | | | | | | | (241) op(e3, e2) = e1 % 150.97/22.09 | | | | | | | | | | | | | | | | % 150.97/22.09 | | | | | | | | | | | | | | | | BETA: splitting (237) gives: % 150.97/22.09 | | | | | | | | | | | | | | | | % 150.97/22.09 | | | | | | | | | | | | | | | | Case 1: % 150.97/22.09 | | | | | | | | | | | | | | | | | % 150.97/22.09 | | | | | | | | | | | | | | | | | (242) all_54_11 = e2 % 150.97/22.09 | | | | | | | | | | | | | | | | | % 150.97/22.09 | | | | | | | | | | | | | | | | | REF_CLOSE: (147), (210), (242) are inconsistent by sub-proof % 150.97/22.09 | | | | | | | | | | | | | | | | | #690. % 150.97/22.09 | | | | | | | | | | | | | | | | | % 150.97/22.09 | | | | | | | | | | | | | | | | Case 2: % 150.97/22.09 | | | | | | | | | | | | | | | | | % 150.97/22.09 | | | | | | | | | | | | | | | | | (243) ~ (all_54_11 = e2) % 150.97/22.09 | | | | | | | | | | | | | | | | | (244) all_54_11 = e1 | all_54_11 = e0 % 150.97/22.09 | | | | | | | | | | | | | | | | | % 150.97/22.09 | | | | | | | | | | | | | | | | | BETA: splitting (244) gives: % 150.97/22.09 | | | | | | | | | | | | | | | | | % 150.97/22.09 | | | | | | | | | | | | | | | | | Case 1: % 150.97/22.09 | | | | | | | | | | | | | | | | | | % 150.97/22.09 | | | | | | | | | | | | | | | | | | (245) all_54_11 = e1 % 150.97/22.09 | | | | | | | | | | | | | | | | | | % 150.97/22.09 | | | | | | | | | | | | | | | | | | REF_CLOSE: (147), (183), (245) are inconsistent by sub-proof % 150.97/22.09 | | | | | | | | | | | | | | | | | | #689. % 150.97/22.09 | | | | | | | | | | | | | | | | | | % 150.97/22.09 | | | | | | | | | | | | | | | | | Case 2: % 150.97/22.09 | | | | | | | | | | | | | | | | | | % 150.97/22.09 | | | | | | | | | | | | | | | | | | (246) all_54_11 = e0 % 150.97/22.09 | | | | | | | | | | | | | | | | | | % 150.97/22.09 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (147), (246) imply: % 150.97/22.09 | | | | | | | | | | | | | | | | | | (247) all_52_14 = e0 % 150.97/22.09 | | | | | | | | | | | | | | | | | | % 150.97/22.09 | | | | | | | | | | | | | | | | | | SIMP: (247) implies: % 150.97/22.09 | | | | | | | | | | | | | | | | | | (248) all_52_14 = e0 % 150.97/22.09 | | | | | | | | | | | | | | | | | | % 150.97/22.09 | | | | | | | | | | | | | | | | | | REDUCE: (122), (248) imply: % 150.97/22.09 | | | | | | | | | | | | | | | | | | (249) ~ (all_52_12 = e0) % 150.97/22.09 | | | | | | | | | | | | | | | | | | % 150.97/22.09 | | | | | | | | | | | | | | | | | | REDUCE: (210), (248) imply: % 150.97/22.09 | | | | | | | | | | | | | | | | | | (250) ~ (e2 = e0) % 150.97/22.09 | | | | | | | | | | | | | | | | | | % 150.97/22.09 | | | | | | | | | | | | | | | | | | SIMP: (250) implies: % 150.97/22.09 | | | | | | | | | | | | | | | | | | (251) ~ (e2 = e0) % 150.97/22.09 | | | | | | | | | | | | | | | | | | % 150.97/22.09 | | | | | | | | | | | | | | | | | | REDUCE: (183), (248) imply: % 150.97/22.09 | | | | | | | | | | | | | | | | | | (252) ~ (e1 = e0) % 150.97/22.09 | | | | | | | | | | | | | | | | | | % 150.97/22.09 | | | | | | | | | | | | | | | | | | SIMP: (252) implies: % 150.97/22.09 | | | | | | | | | | | | | | | | | | (253) ~ (e1 = e0) % 150.97/22.09 | | | | | | | | | | | | | | | | | | % 150.97/22.09 | | | | | | | | | | | | | | | | | | REDUCE: (49), (248) imply: % 150.97/22.09 | | | | | | | | | | | | | | | | | | (254) op(e0, e0) = all_56_22 % 150.97/22.09 | | | | | | | | | | | | | | | | | | % 150.97/22.09 | | | | | | | | | | | | | | | | | | BETA: splitting (58) gives: % 150.97/22.09 | | | | | | | | | | | | | | | | | | % 150.97/22.09 | | | | | | | | | | | | | | | | | | Case 1: % 150.97/22.09 | | | | | | | | | | | | | | | | | | | % 150.97/22.09 | | | | | | | | | | | | | | | | | | | (255) all_58_0 = e0 % 150.97/22.09 | | | | | | | | | | | | | | | | | | | % 150.97/22.09 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (119), (255) imply: % 150.97/22.09 | | | | | | | | | | | | | | | | | | | (256) all_10_2 = e0 % 150.97/22.09 | | | | | | | | | | | | | | | | | | | % 150.97/22.09 | | | | | | | | | | | | | | | | | | | REDUCE: (118), (256) imply: % 150.97/22.09 | | | | | | | | | | | | | | | | | | | (257) op(e0, e0) = all_10_1 % 150.97/22.09 | | | | | | | | | | | | | | | | | | | % 150.97/22.09 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (61) with all_10_1, all_56_22, e0, % 150.97/22.09 | | | | | | | | | | | | | | | | | | | e0, simplifying with (254), (257) gives: % 150.97/22.09 | | | | | | | | | | | | | | | | | | | (258) all_56_22 = all_10_1 % 150.97/22.09 | | | | | | | | | | | | | | | | | | | % 150.97/22.09 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (61) with e2, all_56_22, e0, e0, % 150.97/22.09 | | | | | | | | | | | | | | | | | | | simplifying with (214), (254) gives: % 150.97/22.09 | | | | | | | | | | | | | | | | | | | (259) all_56_22 = e2 % 150.97/22.09 | | | | | | | | | | | | | | | | | | | % 150.97/22.09 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (61) with e0, all_56_30, e2, e0, % 150.97/22.09 | | | | | | | | | | | | | | | | | | | simplifying with (212), (213) gives: % 150.97/22.09 | | | | | | | | | | | | | | | | | | | (260) all_56_30 = e0 % 150.97/22.09 | | | | | | | | | | | | | | | | | | | % 150.97/22.09 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (61) with e2, all_4_1, e2, e2, % 150.97/22.09 | | | | | | | | | | | | | | | | | | | simplifying with (164), (211) gives: % 150.97/22.09 | | | | | | | | | | | | | | | | | | | (261) all_4_1 = e2 % 150.97/22.09 | | | | | | | | | | | | | | | | | | | % 150.97/22.09 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (61) with e1, all_56_16, e2, e3, % 150.97/22.09 | | | | | | | | | | | | | | | | | | | simplifying with (233), (241) gives: % 150.97/22.09 | | | | | | | | | | | | | | | | | | | (262) all_56_16 = e1 % 150.97/22.09 | | | | | | | | | | | | | | | | | | | % 150.97/22.09 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (258), (259) imply: % 150.97/22.09 | | | | | | | | | | | | | | | | | | | (263) all_10_1 = e2 % 150.97/22.09 | | | | | | | | | | | | | | | | | | | % 150.97/22.09 | | | | | | | | | | | | | | | | | | | SIMP: (263) implies: % 150.97/22.09 | | | | | | | | | | | | | | | | | | | (264) all_10_1 = e2 % 150.97/22.09 | | | | | | | | | | | | | | | | | | | % 150.97/22.09 | | | | | | | | | | | | | | | | | | | REDUCE: (56), (264) imply: % 150.97/22.09 | | | | | | | | | | | | | | | | | | | (265) op(e3, e2) = e2 % 150.97/22.09 | | | | | | | | | | | | | | | | | | | % 150.97/22.09 | | | | | | | | | | | | | | | | | | | REDUCE: (66), (261) imply: % 150.97/22.09 | | | | | | | | | | | | | | | | | | | (266) op(e0, e2) = e2 % 150.97/22.09 | | | | | | | | | | | | | | | | | | | % 150.97/22.09 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (61) with e0, e2, e2, e0, % 150.97/22.09 | | | | | | | | | | | | | | | | | | | simplifying with (213), (266) gives: % 150.97/22.09 | | | | | | | | | | | | | | | | | | | (267) e2 = e0 % 150.97/22.09 | | | | | | | | | | | | | | | | | | | % 150.97/22.09 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (61) with e1, e2, e2, e3, % 150.97/22.09 | | | | | | | | | | | | | | | | | | | simplifying with (241), (265) gives: % 150.97/22.09 | | | | | | | | | | | | | | | | | | | (268) e2 = e1 % 150.97/22.09 | | | | | | | | | | | | | | | | | | | % 150.97/22.09 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (267), (268) imply: % 150.97/22.09 | | | | | | | | | | | | | | | | | | | (269) e1 = e0 % 150.97/22.09 | | | | | | | | | | | | | | | | | | | % 150.97/22.09 | | | | | | | | | | | | | | | | | | | REDUCE: (253), (269) imply: % 150.97/22.09 | | | | | | | | | | | | | | | | | | | (270) $false % 150.97/22.09 | | | | | | | | | | | | | | | | | | | % 150.97/22.09 | | | | | | | | | | | | | | | | | | | CLOSE: (270) is inconsistent. % 150.97/22.09 | | | | | | | | | | | | | | | | | | | % 150.97/22.09 | | | | | | | | | | | | | | | | | | Case 2: % 150.97/22.09 | | | | | | | | | | | | | | | | | | | % 150.97/22.09 | | | | | | | | | | | | | | | | | | | (271) all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0 % 150.97/22.09 | | | | | | | | | | | | | | | | | | | % 150.97/22.09 | | | | | | | | | | | | | | | | | | | BETA: splitting (271) gives: % 150.97/22.09 | | | | | | | | | | | | | | | | | | | % 150.97/22.09 | | | | | | | | | | | | | | | | | | | Case 1: % 150.97/22.09 | | | | | | | | | | | | | | | | | | | | % 150.97/22.09 | | | | | | | | | | | | | | | | | | | | (272) all_58_1 = e0 % 150.97/22.09 | | | | | | | | | | | | | | | | | | | | % 150.97/22.09 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (238), (272) imply: % 150.97/22.09 | | | | | | | | | | | | | | | | | | | | (273) e1 = e0 % 150.97/22.09 | | | | | | | | | | | | | | | | | | | | % 150.97/22.09 | | | | | | | | | | | | | | | | | | | | REDUCE: (253), (273) imply: % 150.97/22.09 | | | | | | | | | | | | | | | | | | | | (274) $false % 150.97/22.09 | | | | | | | | | | | | | | | | | | | | % 150.97/22.09 | | | | | | | | | | | | | | | | | | | | CLOSE: (274) is inconsistent. % 150.97/22.09 | | | | | | | | | | | | | | | | | | | | % 150.97/22.09 | | | | | | | | | | | | | | | | | | | Case 2: % 150.97/22.09 | | | | | | | | | | | | | | | | | | | | % 150.97/22.09 | | | | | | | | | | | | | | | | | | | | (275) all_58_4 = e0 | all_58_9 = e0 % 150.97/22.09 | | | | | | | | | | | | | | | | | | | | % 150.97/22.09 | | | | | | | | | | | | | | | | | | | | BETA: splitting (275) gives: % 150.97/22.09 | | | | | | | | | | | | | | | | | | | | % 150.97/22.09 | | | | | | | | | | | | | | | | | | | | Case 1: % 150.97/22.09 | | | | | | | | | | | | | | | | | | | | | % 150.97/22.09 | | | | | | | | | | | | | | | | | | | | | (276) all_58_4 = e0 % 150.97/22.09 | | | | | | | | | | | | | | | | | | | | | % 150.97/22.09 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (225), (251), (276) are inconsistent by sub-proof % 150.97/22.09 | | | | | | | | | | | | | | | | | | | | | #630. % 150.97/22.09 | | | | | | | | | | | | | | | | | | | | | % 150.97/22.09 | | | | | | | | | | | | | | | | | | | | Case 2: % 150.97/22.09 | | | | | | | | | | | | | | | | | | | | | % 150.97/22.09 | | | | | | | | | | | | | | | | | | | | | (277) all_58_9 = e0 % 150.97/22.09 | | | | | | | | | | | | | | | | | | | | | % 150.97/22.09 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (48), (277) imply: % 150.97/22.09 | | | | | | | | | | | | | | | | | | | | | (278) all_52_12 = e0 % 150.97/22.09 | | | | | | | | | | | | | | | | | | | | | % 150.97/22.09 | | | | | | | | | | | | | | | | | | | | | SIMP: (278) implies: % 150.97/22.09 | | | | | | | | | | | | | | | | | | | | | (279) all_52_12 = e0 % 150.97/22.09 | | | | | | | | | | | | | | | | | | | | | % 150.97/22.09 | | | | | | | | | | | | | | | | | | | | | REDUCE: (249), (279) imply: % 150.97/22.09 | | | | | | | | | | | | | | | | | | | | | (280) $false % 150.97/22.09 | | | | | | | | | | | | | | | | | | | | | % 150.97/22.09 | | | | | | | | | | | | | | | | | | | | | CLOSE: (280) is inconsistent. % 150.97/22.09 | | | | | | | | | | | | | | | | | | | | | % 150.97/22.09 | | | | | | | | | | | | | | | | | | | | End of split % 150.97/22.09 | | | | | | | | | | | | | | | | | | | | % 150.97/22.09 | | | | | | | | | | | | | | | | | | | End of split % 150.97/22.09 | | | | | | | | | | | | | | | | | | | % 150.97/22.09 | | | | | | | | | | | | | | | | | | End of split % 150.97/22.09 | | | | | | | | | | | | | | | | | | % 150.97/22.09 | | | | | | | | | | | | | | | | | End of split % 150.97/22.09 | | | | | | | | | | | | | | | | | % 150.97/22.09 | | | | | | | | | | | | | | | | End of split % 150.97/22.09 | | | | | | | | | | | | | | | | % 150.97/22.09 | | | | | | | | | | | | | | | Case 2: % 150.97/22.09 | | | | | | | | | | | | | | | | % 150.97/22.09 | | | | | | | | | | | | | | | | (281) ~ (all_58_1 = e1) % 150.97/22.09 | | | | | | | | | | | | | | | | % 150.97/22.09 | | | | | | | | | | | | | | | | REDUCE: (52), (281) imply: % 150.97/22.09 | | | | | | | | | | | | | | | | (282) ~ (all_52_4 = e1) % 150.97/22.09 | | | | | | | | | | | | | | | | % 150.97/22.09 | | | | | | | | | | | | | | | | REF_CLOSE: (21), (35), (38), (43), (47), (65), (78), (110), % 150.97/22.09 | | | | | | | | | | | | | | | | (126), (138), (150), (205), (227), (282) are % 150.97/22.09 | | | | | | | | | | | | | | | | inconsistent by sub-proof #706. % 150.97/22.09 | | | | | | | | | | | | | | | | % 150.97/22.09 | | | | | | | | | | | | | | | End of split % 150.97/22.09 | | | | | | | | | | | | | | | % 150.97/22.09 | | | | | | | | | | | | | | End of split % 150.97/22.09 | | | | | | | | | | | | | | % 150.97/22.09 | | | | | | | | | | | | | Case 2: % 150.97/22.09 | | | | | | | | | | | | | | % 150.97/22.09 | | | | | | | | | | | | | | (283) all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2 % 150.97/22.09 | | | | | | | | | | | | | | % 150.97/22.09 | | | | | | | | | | | | | | REF_CLOSE: (30), (72), (94), (112), (210), (218), (283) are % 150.97/22.09 | | | | | | | | | | | | | | inconsistent by sub-proof #168. % 150.97/22.09 | | | | | | | | | | | | | | % 150.97/22.09 | | | | | | | | | | | | | End of split % 150.97/22.09 | | | | | | | | | | | | | % 150.97/22.09 | | | | | | | | | | | | Case 2: % 150.97/22.09 | | | | | | | | | | | | | % 150.97/22.09 | | | | | | | | | | | | | (284) all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2 % 150.97/22.09 | | | | | | | | | | | | | % 150.97/22.09 | | | | | | | | | | | | | REF_CLOSE: (26), (34), (46), (61), (72), (79), (112), (125), % 150.97/22.09 | | | | | | | | | | | | | (133), (142), (143), (164), (209), (284) are % 150.97/22.09 | | | | | | | | | | | | | inconsistent by sub-proof #477. % 150.97/22.09 | | | | | | | | | | | | | % 150.97/22.09 | | | | | | | | | | | | End of split % 150.97/22.09 | | | | | | | | | | | | % 150.97/22.09 | | | | | | | | | | | Case 2: % 150.97/22.09 | | | | | | | | | | | | % 150.97/22.09 | | | | | | | | | | | | (285) all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0 % 150.97/22.09 | | | | | | | | | | | | % 150.97/22.09 | | | | | | | | | | | | REF_CLOSE: (51), (182), (208), (209), (285) are inconsistent % 150.97/22.09 | | | | | | | | | | | | by sub-proof #580. % 150.97/22.09 | | | | | | | | | | | | % 150.97/22.09 | | | | | | | | | | | End of split % 150.97/22.09 | | | | | | | | | | | % 150.97/22.09 | | | | | | | | | | Case 2: % 150.97/22.09 | | | | | | | | | | | % 150.97/22.09 | | | | | | | | | | | (286) all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0 % 150.97/22.09 | | | | | | | | | | | % 150.97/22.09 | | | | | | | | | | | REF_CLOSE: (9), (34), (79), (108), (133), (142), (152), % 150.97/22.09 | | | | | | | | | | | (181), (206), (286) are inconsistent by sub-proof % 150.97/22.09 | | | | | | | | | | | #642. % 150.97/22.09 | | | | | | | | | | | % 150.97/22.09 | | | | | | | | | | End of split % 150.97/22.09 | | | | | | | | | | % 150.97/22.09 | | | | | | | | | End of split % 150.97/22.09 | | | | | | | | | % 150.97/22.09 | | | | | | | | Case 2: % 150.97/22.09 | | | | | | | | | % 150.97/22.09 | | | | | | | | | (287) all_54_10 = e0 % 150.97/22.09 | | | | | | | | | % 150.97/22.09 | | | | | | | | | REF_CLOSE: (16), (171), (287) are inconsistent by sub-proof % 150.97/22.09 | | | | | | | | | #705. % 150.97/22.09 | | | | | | | | | % 150.97/22.09 | | | | | | | | End of split % 150.97/22.09 | | | | | | | | % 150.97/22.09 | | | | | | | End of split % 150.97/22.09 | | | | | | | % 150.97/22.09 | | | | | | End of split % 150.97/22.09 | | | | | | % 150.97/22.09 | | | | | Case 2: % 150.97/22.09 | | | | | | % 150.97/22.09 | | | | | | (288) all_56_23 = e1 % 150.97/22.09 | | | | | | (289) all_56_21 = e0 % 150.97/22.09 | | | | | | % 150.97/22.09 | | | | | | COMBINE_EQS: (40), (289) imply: % 150.97/22.09 | | | | | | (290) all_6_2 = e0 % 150.97/22.09 | | | | | | % 150.97/22.09 | | | | | | SIMP: (290) implies: % 150.97/22.09 | | | | | | (291) all_6_2 = e0 % 150.97/22.09 | | | | | | % 150.97/22.09 | | | | | | COMBINE_EQS: (105), (288) imply: % 150.97/22.09 | | | | | | (292) all_52_14 = e1 % 150.97/22.09 | | | | | | % 150.97/22.09 | | | | | | SIMP: (292) implies: % 150.97/22.09 | | | | | | (293) all_52_14 = e1 % 150.97/22.09 | | | | | | % 150.97/22.09 | | | | | | REDUCE: (95), (293) imply: % 150.97/22.09 | | | | | | (294) ~ (all_52_2 = e1) % 150.97/22.09 | | | | | | % 150.97/22.09 | | | | | | REDUCE: (127), (291) imply: % 150.97/22.09 | | | | | | (295) ~ (all_52_2 = e0) % 150.97/22.09 | | | | | | % 150.97/22.09 | | | | | | REDUCE: (37), (293) imply: % 150.97/22.09 | | | | | | (296) ~ (all_52_6 = e1) % 150.97/22.09 | | | | | | % 150.97/22.09 | | | | | | REDUCE: (132), (291) imply: % 150.97/22.09 | | | | | | (297) ~ (all_52_6 = e0) % 150.97/22.09 | | | | | | % 150.97/22.09 | | | | | | REDUCE: (23), (293) imply: % 150.97/22.09 | | | | | | (298) ~ (all_4_2 = e1) % 150.97/22.09 | | | | | | % 150.97/22.09 | | | | | | REDUCE: (98), (291) imply: % 150.97/22.09 | | | | | | (299) op(e0, e0) = all_6_1 % 150.97/22.09 | | | | | | % 150.97/22.09 | | | | | | BETA: splitting (88) gives: % 150.97/22.09 | | | | | | % 150.97/22.09 | | | | | | Case 1: % 150.97/22.09 | | | | | | | % 150.97/22.09 | | | | | | | (300) all_54_9 = e3 % 150.97/22.09 | | | | | | | % 150.97/22.09 | | | | | | | COMBINE_EQS: (9), (300) imply: % 150.97/22.09 | | | | | | | (301) all_52_6 = e3 % 150.97/22.09 | | | | | | | % 150.97/22.09 | | | | | | | REDUCE: (64), (301) imply: % 150.97/22.09 | | | | | | | (302) ~ (all_52_2 = e3) % 150.97/22.09 | | | | | | | % 150.97/22.09 | | | | | | | BETA: splitting (136) gives: % 150.97/22.09 | | | | | | | % 150.97/22.09 | | | | | | | Case 1: % 150.97/22.09 | | | | | | | | % 150.97/22.09 | | | | | | | | (303) all_54_8 = e3 % 150.97/22.09 | | | | | | | | % 150.97/22.09 | | | | | | | | REF_CLOSE: (106), (302), (303) are inconsistent by sub-proof % 150.97/22.09 | | | | | | | | #345. % 150.97/22.09 | | | | | | | | % 150.97/22.09 | | | | | | | Case 2: % 150.97/22.09 | | | | | | | | % 150.97/22.09 | | | | | | | | (304) all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0 % 150.97/22.09 | | | | | | | | % 150.97/22.09 | | | | | | | | BETA: splitting (60) gives: % 150.97/22.09 | | | | | | | | % 150.97/22.09 | | | | | | | | Case 1: % 150.97/22.09 | | | | | | | | | % 150.97/22.09 | | | | | | | | | (305) all_58_6 = e2 % 150.97/22.09 | | | | | | | | | % 150.97/22.09 | | | | | | | | | REF_CLOSE: (17), (30), (31), (36), (39), (61), (66), (71), % 150.97/22.09 | | | | | | | | | (75), (83), (100), (131), (299), (305) are % 150.97/22.09 | | | | | | | | | inconsistent by sub-proof #155. % 150.97/22.09 | | | | | | | | | % 150.97/22.10 | | | | | | | | Case 2: % 150.97/22.10 | | | | | | | | | % 150.97/22.10 | | | | | | | | | (306) ~ (all_58_6 = e2) % 150.97/22.10 | | | | | | | | | % 150.97/22.10 | | | | | | | | | REDUCE: (11), (306) imply: % 150.97/22.10 | | | | | | | | | (307) ~ (all_52_2 = e2) % 150.97/22.10 | | | | | | | | | % 150.97/22.10 | | | | | | | | | REF_CLOSE: (106), (294), (295), (304), (307) are inconsistent % 150.97/22.10 | | | | | | | | | by sub-proof #270. % 150.97/22.10 | | | | | | | | | % 150.97/22.10 | | | | | | | | End of split % 150.97/22.10 | | | | | | | | % 150.97/22.10 | | | | | | | End of split % 150.97/22.10 | | | | | | | % 150.97/22.10 | | | | | | Case 2: % 150.97/22.10 | | | | | | | % 150.97/22.10 | | | | | | | (308) all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0 % 150.97/22.10 | | | | | | | % 150.97/22.10 | | | | | | | REF_CLOSE: (9), (34), (79), (108), (133), (142), (152), (296), % 150.97/22.10 | | | | | | | (297), (308) are inconsistent by sub-proof #642. % 150.97/22.10 | | | | | | | % 150.97/22.10 | | | | | | End of split % 150.97/22.10 | | | | | | % 150.97/22.10 | | | | | End of split % 150.97/22.10 | | | | | % 150.97/22.10 | | | | Case 2: % 150.97/22.10 | | | | | % 150.97/22.10 | | | | | (309) all_54_5 = e1 | all_54_5 = e0 % 150.97/22.10 | | | | | % 150.97/22.10 | | | | | REF_CLOSE: (34), (133), (152), (309) are inconsistent by sub-proof % 150.97/22.10 | | | | | #645. % 150.97/22.10 | | | | | % 150.97/22.10 | | | | End of split % 150.97/22.10 | | | | % 150.97/22.10 | | | End of split % 150.97/22.10 | | | % 150.97/22.10 | | Case 2: % 150.97/22.10 | | | % 150.97/22.10 | | | (310) all_56_13 = e2 % 150.97/22.10 | | | (311) all_56_11 = e1 % 150.97/22.10 | | | % 150.97/22.10 | | | COMBINE_EQS: (1), (311) imply: % 150.97/22.10 | | | (312) all_8_2 = e1 % 150.97/22.10 | | | % 150.97/22.10 | | | COMBINE_EQS: (67), (310) imply: % 150.97/22.10 | | | (313) all_52_9 = e2 % 150.97/22.10 | | | % 150.97/22.10 | | | COMBINE_EQS: (46), (313) imply: % 150.97/22.10 | | | (314) all_58_5 = e2 % 150.97/22.10 | | | % 150.97/22.10 | | | REDUCE: (13), (313) imply: % 150.97/22.10 | | | (315) ~ (all_52_1 = e2) % 150.97/22.10 | | | % 150.97/22.10 | | | REDUCE: (42), (312) imply: % 150.97/22.10 | | | (316) ~ (all_52_7 = e1) % 150.97/22.10 | | | % 150.97/22.10 | | | REDUCE: (26), (312), (313) imply: % 150.97/22.10 | | | (317) ~ (e2 = e1) % 150.97/22.10 | | | % 150.97/22.10 | | | REDUCE: (114), (313) imply: % 150.97/22.10 | | | (318) ~ (all_6_2 = e2) % 150.97/22.10 | | | % 150.97/22.10 | | | REDUCE: (79), (312) imply: % 150.97/22.10 | | | (319) ~ (e3 = e1) % 150.97/22.10 | | | % 150.97/22.10 | | | SIMP: (319) implies: % 150.97/22.10 | | | (320) ~ (e3 = e1) % 150.97/22.10 | | | % 150.97/22.10 | | | REDUCE: (140), (312) imply: % 150.97/22.10 | | | (321) op(e1, e1) = all_8_1 % 150.97/22.10 | | | % 150.97/22.10 | | | GROUND_INST: instantiating (61) with all_6_2, all_8_1, e1, e1, simplifying % 150.97/22.10 | | | with (107), (321) gives: % 150.97/22.10 | | | (322) all_8_1 = all_6_2 % 150.97/22.10 | | | % 150.97/22.10 | | | REDUCE: (12), (322) imply: % 150.97/22.10 | | | (323) ~ (all_6_2 = e1) % 150.97/22.10 | | | % 150.97/22.10 | | | BETA: splitting (41) gives: % 150.97/22.10 | | | % 150.97/22.10 | | | Case 1: % 150.97/22.10 | | | | % 150.97/22.10 | | | | (324) all_54_10 = e3 % 150.97/22.10 | | | | % 150.97/22.10 | | | | REF_CLOSE: (16), (28), (324) are inconsistent by sub-proof #736. % 150.97/22.10 | | | | % 150.97/22.10 | | | Case 2: % 150.97/22.10 | | | | % 150.97/22.10 | | | | (325) ~ (all_54_10 = e3) % 150.97/22.10 | | | | (326) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 150.97/22.10 | | | | % 150.97/22.10 | | | | BETA: splitting (326) gives: % 150.97/22.10 | | | | % 150.97/22.10 | | | | Case 1: % 150.97/22.10 | | | | | % 150.97/22.10 | | | | | (327) all_54_10 = e2 % 150.97/22.10 | | | | | % 150.97/22.10 | | | | | REF_CLOSE: (16), (112), (327) are inconsistent by sub-proof #735. % 150.97/22.10 | | | | | % 150.97/22.10 | | | | Case 2: % 150.97/22.10 | | | | | % 150.97/22.10 | | | | | (328) all_54_10 = e1 | all_54_10 = e0 % 150.97/22.10 | | | | | % 150.97/22.10 | | | | | BETA: splitting (328) gives: % 150.97/22.10 | | | | | % 150.97/22.10 | | | | | Case 1: % 150.97/22.10 | | | | | | % 150.97/22.10 | | | | | | (329) all_54_10 = e1 % 150.97/22.10 | | | | | | % 150.97/22.10 | | | | | | REF_CLOSE: (16), (323), (329) are inconsistent by sub-proof #606. % 150.97/22.10 | | | | | | % 150.97/22.10 | | | | | Case 2: % 150.97/22.10 | | | | | | % 150.97/22.10 | | | | | | (330) all_54_10 = e0 % 150.97/22.10 | | | | | | % 150.97/22.10 | | | | | | COMBINE_EQS: (16), (330) imply: % 150.97/22.10 | | | | | | (331) all_6_2 = e0 % 150.97/22.10 | | | | | | % 150.97/22.10 | | | | | | SIMP: (331) implies: % 150.97/22.10 | | | | | | (332) all_6_2 = e0 % 150.97/22.10 | | | | | | % 150.97/22.10 | | | | | | REDUCE: (98), (332) imply: % 150.97/22.10 | | | | | | (333) op(e0, e0) = all_6_1 % 150.97/22.10 | | | | | | % 150.97/22.10 | | | | | | BETA: splitting (57) gives: % 150.97/22.10 | | | | | | % 150.97/22.10 | | | | | | Case 1: % 150.97/22.10 | | | | | | | % 150.97/22.10 | | | | | | | (334) all_58_0 = e2 % 150.97/22.10 | | | | | | | % 150.97/22.10 | | | | | | | COMBINE_EQS: (119), (334) imply: % 150.97/22.10 | | | | | | | (335) all_10_2 = e2 % 150.97/22.10 | | | | | | | % 150.97/22.10 | | | | | | | REDUCE: (150), (335) imply: % 150.97/22.10 | | | | | | | (336) $false % 150.97/22.10 | | | | | | | % 150.97/22.10 | | | | | | | CLOSE: (336) is inconsistent. % 150.97/22.10 | | | | | | | % 150.97/22.10 | | | | | | Case 2: % 150.97/22.10 | | | | | | | % 150.97/22.10 | | | | | | | (337) ~ (all_58_0 = e2) % 150.97/22.10 | | | | | | | (338) all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2 % 150.97/22.10 | | | | | | | % 150.97/22.10 | | | | | | | BETA: splitting (338) gives: % 150.97/22.10 | | | | | | | % 150.97/22.10 | | | | | | | Case 1: % 150.97/22.10 | | | | | | | | % 150.97/22.10 | | | | | | | | (339) all_58_2 = e2 % 150.97/22.10 | | | | | | | | % 150.97/22.10 | | | | | | | | COMBINE_EQS: (113), (339) imply: % 150.97/22.10 | | | | | | | | (340) all_52_1 = e2 % 150.97/22.10 | | | | | | | | % 150.97/22.10 | | | | | | | | REDUCE: (315), (340) imply: % 150.97/22.10 | | | | | | | | (341) $false % 150.97/22.10 | | | | | | | | % 150.97/22.10 | | | | | | | | CLOSE: (341) is inconsistent. % 150.97/22.10 | | | | | | | | % 150.97/22.10 | | | | | | | Case 2: % 150.97/22.10 | | | | | | | | % 150.97/22.10 | | | | | | | | (342) all_58_6 = e2 | all_58_12 = e2 % 150.97/22.10 | | | | | | | | % 150.97/22.10 | | | | | | | | BETA: splitting (342) gives: % 150.97/22.10 | | | | | | | | % 150.97/22.10 | | | | | | | | Case 1: % 150.97/22.10 | | | | | | | | | % 150.97/22.10 | | | | | | | | | (343) all_58_6 = e2 % 150.97/22.10 | | | | | | | | | % 150.97/22.10 | | | | | | | | | COMBINE_EQS: (11), (343) imply: % 150.97/22.10 | | | | | | | | | (344) all_52_2 = e2 % 150.97/22.10 | | | | | | | | | % 150.97/22.10 | | | | | | | | | REF_CLOSE: (17), (30), (31), (36), (39), (61), (66), (71), % 150.97/22.10 | | | | | | | | | (75), (83), (100), (131), (333), (343) are % 150.97/22.10 | | | | | | | | | inconsistent by sub-proof #155. % 150.97/22.10 | | | | | | | | | % 150.97/22.10 | | | | | | | | Case 2: % 150.97/22.10 | | | | | | | | | % 150.97/22.10 | | | | | | | | | (345) all_58_12 = e2 % 150.97/22.10 | | | | | | | | | % 150.97/22.10 | | | | | | | | | REF_CLOSE: (21), (28), (30), (33), (35), (38), (43), (53), % 150.97/22.10 | | | | | | | | | (65), (71), (72), (74), (78), (84), (111), (121), % 150.97/22.10 | | | | | | | | | (128), (150), (314), (316), (317), (320), (345) are % 150.97/22.10 | | | | | | | | | inconsistent by sub-proof #455. % 150.97/22.10 | | | | | | | | | % 150.97/22.10 | | | | | | | | End of split % 150.97/22.10 | | | | | | | | % 150.97/22.10 | | | | | | | End of split % 150.97/22.10 | | | | | | | % 150.97/22.10 | | | | | | End of split % 150.97/22.10 | | | | | | % 150.97/22.10 | | | | | End of split % 150.97/22.10 | | | | | % 150.97/22.10 | | | | End of split % 150.97/22.10 | | | | % 150.97/22.10 | | | End of split % 150.97/22.10 | | | % 150.97/22.10 | | End of split % 150.97/22.10 | | % 150.97/22.10 | Case 2: % 150.97/22.10 | | % 150.97/22.10 | | (346) all_56_3 = e3 % 150.97/22.10 | | (347) all_56_1 = e2 % 150.97/22.10 | | % 150.97/22.10 | | COMBINE_EQS: (43), (347) imply: % 150.97/22.10 | | (348) all_10_2 = e2 % 150.97/22.10 | | % 150.97/22.10 | | COMBINE_EQS: (87), (346) imply: % 150.97/22.10 | | (349) all_52_4 = e3 % 150.97/22.10 | | % 150.97/22.10 | | COMBINE_EQS: (119), (348) imply: % 150.97/22.10 | | (350) all_58_0 = e2 % 150.97/22.10 | | % 150.97/22.10 | | REDUCE: (27), (349) imply: % 150.97/22.10 | | (351) ~ (all_52_7 = e3) % 150.97/22.10 | | % 150.97/22.10 | | SIMP: (351) implies: % 150.97/22.10 | | (352) ~ (all_52_7 = e3) % 150.97/22.10 | | % 150.97/22.10 | | REDUCE: (5), (349) imply: % 150.97/22.10 | | (353) ~ (all_52_8 = e3) % 150.97/22.10 | | % 150.97/22.10 | | SIMP: (353) implies: % 150.97/22.10 | | (354) ~ (all_52_8 = e3) % 150.97/22.10 | | % 150.97/22.10 | | REDUCE: (139), (349) imply: % 150.97/22.10 | | (355) ~ (all_8_2 = e3) % 150.97/22.10 | | % 150.97/22.10 | | REDUCE: (74), (348) imply: % 150.97/22.10 | | (356) ~ (all_52_8 = e2) % 150.97/22.10 | | % 150.97/22.10 | | REDUCE: (144), (348) imply: % 150.97/22.10 | | (357) ~ (all_52_12 = e2) % 150.97/22.10 | | % 150.97/22.10 | | REDUCE: (118), (348) imply: % 150.97/22.10 | | (358) op(e2, e2) = all_10_1 % 150.97/22.10 | | % 150.97/22.10 | | REDUCE: (55), (348) imply: % 150.97/22.10 | | (359) op(e3, e3) = e2 % 150.97/22.10 | | % 150.97/22.10 | | GROUND_INST: instantiating (61) with all_8_2, all_10_1, e2, e2, simplifying % 150.97/22.10 | | with (125), (358) gives: % 150.97/22.10 | | (360) all_10_1 = all_8_2 % 150.97/22.10 | | % 150.97/22.10 | | REDUCE: (56), (360) imply: % 150.97/22.10 | | (361) op(e3, all_8_2) = e2 % 150.97/22.10 | | % 150.97/22.10 | | BETA: splitting (3) gives: % 150.97/22.10 | | % 150.97/22.10 | | Case 1: % 150.97/22.10 | | | % 150.97/22.10 | | | (362) ~ (all_56_11 = e1) % 150.97/22.10 | | | % 150.97/22.10 | | | REDUCE: (1), (362) imply: % 150.97/22.10 | | | (363) ~ (all_8_2 = e1) % 150.97/22.10 | | | % 150.97/22.10 | | | BETA: splitting (142) gives: % 150.97/22.10 | | | % 150.97/22.10 | | | Case 1: % 150.97/22.10 | | | | % 150.97/22.10 | | | | (364) all_54_5 = e3 % 150.97/22.10 | | | | % 150.97/22.10 | | | | REF_CLOSE: (34), (79), (364) are inconsistent by sub-proof #737. % 150.97/22.10 | | | | % 150.97/22.10 | | | Case 2: % 150.97/22.10 | | | | % 150.97/22.10 | | | | (365) ~ (all_54_5 = e3) % 150.97/22.10 | | | | (366) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 150.97/22.10 | | | | % 150.97/22.10 | | | | BETA: splitting (366) gives: % 150.97/22.10 | | | | % 150.97/22.10 | | | | Case 1: % 150.97/22.10 | | | | | % 150.97/22.10 | | | | | (367) all_54_5 = e2 % 150.97/22.10 | | | | | % 150.97/22.10 | | | | | COMBINE_EQS: (34), (367) imply: % 150.97/22.10 | | | | | (368) all_8_2 = e2 % 150.97/22.10 | | | | | % 150.97/22.10 | | | | | SIMP: (368) implies: % 150.97/22.10 | | | | | (369) all_8_2 = e2 % 150.97/22.10 | | | | | % 150.97/22.10 | | | | | REDUCE: (59), (369) imply: % 150.97/22.10 | | | | | (370) ~ (all_52_1 = e2) % 150.97/22.10 | | | | | % 150.97/22.10 | | | | | REDUCE: (26), (369) imply: % 150.97/22.10 | | | | | (371) ~ (all_52_9 = e2) % 150.97/22.10 | | | | | % 150.97/22.10 | | | | | REDUCE: (19), (369) imply: % 150.97/22.10 | | | | | (372) ~ (all_52_13 = e2) % 150.97/22.10 | | | | | % 150.97/22.10 | | | | | REDUCE: (79), (369) imply: % 150.97/22.10 | | | | | (373) ~ (e3 = e2) % 150.97/22.10 | | | | | % 150.97/22.10 | | | | | REDUCE: (363), (369) imply: % 150.97/22.10 | | | | | (374) ~ (e2 = e1) % 150.97/22.10 | | | | | % 150.97/22.10 | | | | | REDUCE: (133), (369) imply: % 150.97/22.10 | | | | | (375) ~ (e2 = e0) % 150.97/22.10 | | | | | % 150.97/22.10 | | | | | REF_CLOSE: (7), (11), (13), (14), (16), (18), (20), (23), (25), (28), % 150.97/22.10 | | | | | (30), (31), (32), (33), (39), (40), (41), (46), (48), (49), % 150.97/22.10 | | | | | (50), (57), (61), (66), (69), (71), (72), (73), (75), (76), % 150.97/22.10 | | | | | (80), (83), (84), (85), (89), (92), (94), (95), (96), % 150.97/22.10 | | | | | (100), (102), (105), (111), (112), (113), (115), (116), % 150.97/22.10 | | | | | (117), (120), (127), (130), (131), (134), (135), (143), % 150.97/22.10 | | | | | (146), (352), (354), (356), (357), (359), (370), (371), % 150.97/22.10 | | | | | (372), (374), (375) are inconsistent by sub-proof #212. % 150.97/22.10 | | | | | % 150.97/22.10 | | | | Case 2: % 150.97/22.10 | | | | | % 150.97/22.10 | | | | | (376) all_54_5 = e1 | all_54_5 = e0 % 150.97/22.10 | | | | | % 150.97/22.10 | | | | | REF_CLOSE: (34), (133), (363), (376) are inconsistent by sub-proof % 150.97/22.10 | | | | | #645. % 150.97/22.10 | | | | | % 150.97/22.10 | | | | End of split % 150.97/22.10 | | | | % 150.97/22.10 | | | End of split % 150.97/22.10 | | | % 150.97/22.10 | | Case 2: % 150.97/22.10 | | | % 150.97/22.10 | | | (377) all_56_13 = e2 % 150.97/22.10 | | | (378) all_56_11 = e1 % 150.97/22.10 | | | % 150.97/22.10 | | | COMBINE_EQS: (1), (378) imply: % 150.97/22.10 | | | (379) all_8_2 = e1 % 150.97/22.10 | | | % 150.97/22.10 | | | COMBINE_EQS: (67), (377) imply: % 150.97/22.10 | | | (380) all_52_9 = e2 % 150.97/22.10 | | | % 150.97/22.10 | | | REDUCE: (59), (379) imply: % 150.97/22.10 | | | (381) ~ (all_52_1 = e1) % 150.97/22.10 | | | % 150.97/22.10 | | | REDUCE: (26), (379), (380) imply: % 150.97/22.10 | | | (382) ~ (e2 = e1) % 150.97/22.10 | | | % 150.97/22.10 | | | REDUCE: (114), (380) imply: % 150.97/22.10 | | | (383) ~ (all_6_2 = e2) % 150.97/22.10 | | | % 150.97/22.10 | | | REDUCE: (361), (379) imply: % 150.97/22.10 | | | (384) op(e3, e1) = e2 % 150.97/22.10 | | | % 150.97/22.10 | | | BETA: splitting (121) gives: % 150.97/22.10 | | | % 150.97/22.10 | | | Case 1: % 150.97/22.10 | | | | % 150.97/22.10 | | | | (385) all_58_12 = e1 % 150.97/22.10 | | | | % 150.97/22.10 | | | | COMBINE_EQS: (146), (385) imply: % 150.97/22.10 | | | | (386) all_52_3 = e1 % 150.97/22.10 | | | | % 150.97/22.10 | | | | REDUCE: (141), (386) imply: % 150.97/22.10 | | | | (387) op(e3, e1) = all_56_24 % 150.97/22.10 | | | | % 150.97/22.10 | | | | GROUND_INST: instantiating (61) with all_52_8, all_56_24, e1, e3, % 150.97/22.10 | | | | simplifying with (123), (387) gives: % 150.97/22.10 | | | | (388) all_56_24 = all_52_8 % 150.97/22.10 | | | | % 150.97/22.10 | | | | GROUND_INST: instantiating (61) with e2, all_56_24, e1, e3, simplifying % 150.97/22.10 | | | | with (384), (387) gives: % 150.97/22.10 | | | | (389) all_56_24 = e2 % 150.97/22.10 | | | | % 150.97/22.10 | | | | COMBINE_EQS: (388), (389) imply: % 150.97/22.10 | | | | (390) all_52_8 = e2 % 150.97/22.10 | | | | % 150.97/22.10 | | | | SIMP: (390) implies: % 150.97/22.10 | | | | (391) all_52_8 = e2 % 150.97/22.10 | | | | % 150.97/22.10 | | | | REDUCE: (356), (391) imply: % 150.97/22.10 | | | | (392) $false % 150.97/22.10 | | | | % 150.97/22.10 | | | | CLOSE: (392) is inconsistent. % 150.97/22.10 | | | | % 150.97/22.10 | | | Case 2: % 150.97/22.10 | | | | % 150.97/22.10 | | | | (393) ~ (all_58_12 = e1) % 150.97/22.10 | | | | % 150.97/22.10 | | | | REDUCE: (146), (393) imply: % 150.97/22.10 | | | | (394) ~ (all_52_3 = e1) % 150.97/22.10 | | | | % 150.97/22.10 | | | | BETA: splitting (109) gives: % 150.97/22.10 | | | | % 150.97/22.10 | | | | Case 1: % 150.97/22.10 | | | | | % 150.97/22.10 | | | | | (395) all_58_0 = e1 % 150.97/22.10 | | | | | % 150.97/22.10 | | | | | COMBINE_EQS: (350), (395) imply: % 150.97/22.10 | | | | | (396) e2 = e1 % 150.97/22.10 | | | | | % 150.97/22.10 | | | | | REDUCE: (382), (396) imply: % 150.97/22.10 | | | | | (397) $false % 150.97/22.10 | | | | | % 150.97/22.10 | | | | | CLOSE: (397) is inconsistent. % 150.97/22.10 | | | | | % 150.97/22.10 | | | | Case 2: % 150.97/22.10 | | | | | % 150.97/22.10 | | | | | (398) all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1 % 150.97/22.10 | | | | | % 150.97/22.10 | | | | | BETA: splitting (398) gives: % 150.97/22.10 | | | | | % 150.97/22.10 | | | | | Case 1: % 150.97/22.10 | | | | | | % 150.97/22.10 | | | | | | (399) all_58_2 = e1 % 150.97/22.10 | | | | | | % 150.97/22.10 | | | | | | COMBINE_EQS: (113), (399) imply: % 150.97/22.10 | | | | | | (400) all_52_1 = e1 % 150.97/22.10 | | | | | | % 150.97/22.10 | | | | | | REDUCE: (381), (400) imply: % 150.97/22.10 | | | | | | (401) $false % 150.97/22.10 | | | | | | % 150.97/22.10 | | | | | | CLOSE: (401) is inconsistent. % 150.97/22.10 | | | | | | % 150.97/22.10 | | | | | Case 2: % 150.97/22.10 | | | | | | % 150.97/22.10 | | | | | | (402) all_58_6 = e1 | all_58_12 = e1 % 150.97/22.10 | | | | | | % 150.97/22.10 | | | | | | BETA: splitting (402) gives: % 150.97/22.10 | | | | | | % 150.97/22.10 | | | | | | Case 1: % 150.97/22.10 | | | | | | | % 150.97/22.10 | | | | | | | (403) all_58_6 = e1 % 150.97/22.10 | | | | | | | % 150.97/22.10 | | | | | | | COMBINE_EQS: (11), (403) imply: % 150.97/22.10 | | | | | | | (404) all_52_2 = e1 % 150.97/22.10 | | | | | | | % 150.97/22.10 | | | | | | | SIMP: (404) implies: % 150.97/22.10 | | | | | | | (405) all_52_2 = e1 % 150.97/22.10 | | | | | | | % 150.97/22.10 | | | | | | | REDUCE: (95), (405) imply: % 150.97/22.10 | | | | | | | (406) ~ (all_52_14 = e1) % 150.97/22.10 | | | | | | | % 150.97/22.10 | | | | | | | SIMP: (406) implies: % 150.97/22.10 | | | | | | | (407) ~ (all_52_14 = e1) % 150.97/22.10 | | | | | | | % 150.97/22.10 | | | | | | | REDUCE: (127), (405) imply: % 150.97/22.10 | | | | | | | (408) ~ (all_6_2 = e1) % 150.97/22.10 | | | | | | | % 150.97/22.10 | | | | | | | SIMP: (408) implies: % 150.97/22.10 | | | | | | | (409) ~ (all_6_2 = e1) % 150.97/22.10 | | | | | | | % 150.97/22.10 | | | | | | | BETA: splitting (130) gives: % 150.97/22.10 | | | | | | | % 150.97/22.10 | | | | | | | Case 1: % 150.97/22.10 | | | | | | | | % 150.97/22.10 | | | | | | | | (410) ~ (all_56_21 = e0) % 150.97/22.10 | | | | | | | | % 150.97/22.10 | | | | | | | | REDUCE: (40), (410) imply: % 150.97/22.10 | | | | | | | | (411) ~ (all_6_2 = e0) % 150.97/22.10 | | | | | | | | % 150.97/22.10 | | | | | | | | REF_CLOSE: (16), (28), (41), (112), (409), (411) are % 150.97/22.10 | | | | | | | | inconsistent by sub-proof #573. % 150.97/22.10 | | | | | | | | % 150.97/22.10 | | | | | | | Case 2: % 150.97/22.10 | | | | | | | | % 150.97/22.10 | | | | | | | | (412) all_56_23 = e1 % 150.97/22.10 | | | | | | | | % 150.97/22.10 | | | | | | | | REF_CLOSE: (105), (407), (412) are inconsistent by sub-proof % 150.97/22.10 | | | | | | | | #309. % 150.97/22.10 | | | | | | | | % 150.97/22.10 | | | | | | | End of split % 150.97/22.10 | | | | | | | % 150.97/22.10 | | | | | | Case 2: % 150.97/22.10 | | | | | | | % 150.97/22.10 | | | | | | | (413) all_58_12 = e1 % 150.97/22.10 | | | | | | | % 150.97/22.10 | | | | | | | COMBINE_EQS: (146), (413) imply: % 150.97/22.10 | | | | | | | (414) all_52_3 = e1 % 150.97/22.10 | | | | | | | % 150.97/22.10 | | | | | | | REDUCE: (394), (414) imply: % 150.97/22.10 | | | | | | | (415) $false % 150.97/22.10 | | | | | | | % 150.97/22.10 | | | | | | | CLOSE: (415) is inconsistent. % 150.97/22.10 | | | | | | | % 150.97/22.10 | | | | | | End of split % 150.97/22.10 | | | | | | % 150.97/22.10 | | | | | End of split % 150.97/22.10 | | | | | % 150.97/22.10 | | | | End of split % 150.97/22.10 | | | | % 150.97/22.10 | | | End of split % 150.97/22.10 | | | % 150.97/22.10 | | End of split % 150.97/22.10 | | % 150.97/22.10 | End of split % 150.97/22.10 | % 150.97/22.10 End of proof % 150.97/22.10 % 150.97/22.10 Sub-proof #155 shows that the following formulas are inconsistent: % 150.97/22.10 ---------------------------------------------------------------- % 150.97/22.10 (1) all_58_6 = e2 % 150.97/22.10 (2) ~ (all_6_1 = e2) % 150.97/22.10 (3) ~ (e3 = e2) % 150.97/22.10 (4) op(e0, e0) = all_4_2 % 150.97/22.10 (5) ~ (all_6_1 = e3) % 150.97/22.10 (6) all_54_15 = all_4_2 % 150.97/22.10 (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 150.97/22.10 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 150.97/22.10 (8) op(e0, all_4_1) = e2 % 150.97/22.10 (9) ~ (all_4_2 = e1) % 150.97/22.10 (10) all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3 % 150.97/22.10 (11) op(all_4_2, all_4_2) = all_4_1 % 150.97/22.10 (12) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0 % 150.97/22.10 (13) op(e0, e0) = all_6_1 % 150.97/22.10 (14) op(e0, all_4_2) = all_56_30 % 150.97/22.10 % 150.97/22.10 Begin of proof % 150.97/22.10 | % 150.97/22.10 | BETA: splitting (10) gives: % 150.97/22.10 | % 150.97/22.10 | Case 1: % 150.97/22.10 | | % 150.97/22.10 | | (15) all_58_6 = e3 % 150.97/22.10 | | % 150.97/22.10 | | COMBINE_EQS: (1), (15) imply: % 150.97/22.10 | | (16) e3 = e2 % 150.97/22.10 | | % 150.97/22.10 | | REDUCE: (3), (16) imply: % 150.97/22.10 | | (17) $false % 150.97/22.10 | | % 150.97/22.10 | | CLOSE: (17) is inconsistent. % 150.97/22.10 | | % 150.97/22.10 | Case 2: % 150.97/22.10 | | % 150.97/22.10 | | % 150.97/22.10 | | GROUND_INST: instantiating (7) with all_4_2, all_6_1, e0, e0, simplifying % 150.97/22.10 | | with (4), (13) gives: % 150.97/22.10 | | (18) all_6_1 = all_4_2 % 150.97/22.10 | | % 150.97/22.10 | | REF_CLOSE: (2), (5), (6), (7), (8), (9), (11), (12), (13), (14), (18) are % 150.97/22.10 | | inconsistent by sub-proof #228. % 150.97/22.10 | | % 150.97/22.10 | End of split % 150.97/22.10 | % 150.97/22.10 End of proof % 150.97/22.10 % 150.97/22.10 Sub-proof #156 shows that the following formulas are inconsistent: % 150.97/22.10 ---------------------------------------------------------------- % 150.97/22.10 (1) all_56_11 = all_8_2 % 150.97/22.10 (2) all_14_2 = all_8_2 % 150.97/22.10 (3) ~ (all_8_1 = e1) % 150.97/22.10 (4) op(e0, e0) = all_4_2 % 150.97/22.10 (5) all_54_15 = all_4_2 % 150.97/22.10 (6) all_14_1 = all_8_1 % 150.97/22.10 (7) op(e2, all_8_2) = all_56_10 % 150.97/22.10 (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 150.97/22.10 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 150.97/22.10 (9) op(e2, all_8_1) = e1 % 150.97/22.10 (10) ~ (e2 = e1) % 150.97/22.10 (11) ~ (all_14_1 = e3) | ~ (all_14_2 = e0) % 150.97/22.10 (12) ~ (all_52_13 = all_4_2) % 150.97/22.10 (13) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0 % 150.97/22.10 (14) all_56_11 = e0 % 150.97/22.10 (15) ~ (all_56_11 = e0) | all_56_15 = e2 % 150.97/22.10 (16) op(e2, e0) = all_52_13 % 150.97/22.10 (17) op(all_8_2, all_8_2) = all_8_1 % 150.97/22.10 (18) all_56_15 = all_52_13 % 150.97/22.10 % 150.97/22.10 Begin of proof % 150.97/22.10 | % 150.97/22.10 | COMBINE_EQS: (1), (14) imply: % 150.97/22.10 | (19) all_8_2 = e0 % 150.97/22.10 | % 150.97/22.10 | COMBINE_EQS: (2), (19) imply: % 150.97/22.10 | (20) all_14_2 = e0 % 150.97/22.10 | % 150.97/22.10 | REF_CLOSE: (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13), (14), % 150.97/22.10 | (15), (16), (17), (18), (19), (20) are inconsistent by sub-proof % 150.97/22.10 | #237. % 150.97/22.10 | % 150.97/22.10 End of proof % 150.97/22.10 % 150.97/22.10 Sub-proof #157 shows that the following formulas are inconsistent: % 150.97/22.10 ---------------------------------------------------------------- % 150.97/22.10 (1) all_58_3 = e3 % 150.97/22.10 (2) all_58_3 = e1 % 150.97/22.10 (3) ~ (e3 = e1) % 150.97/22.10 % 150.97/22.10 Begin of proof % 150.97/22.10 | % 150.97/22.10 | COMBINE_EQS: (1), (2) imply: % 150.97/22.10 | (4) e3 = e1 % 150.97/22.10 | % 150.97/22.10 | SIMP: (4) implies: % 150.97/22.10 | (5) e3 = e1 % 150.97/22.10 | % 150.97/22.10 | REDUCE: (3), (5) imply: % 150.97/22.10 | (6) $false % 150.97/22.10 | % 150.97/22.10 | CLOSE: (6) is inconsistent. % 150.97/22.10 | % 150.97/22.10 End of proof % 150.97/22.10 % 150.97/22.10 Sub-proof #158 shows that the following formulas are inconsistent: % 150.97/22.10 ---------------------------------------------------------------- % 150.97/22.10 (1) op(e3, e3) = e3 % 150.97/22.10 (2) ~ (e3 = e2) % 150.97/22.10 (3) all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1 % 150.97/22.10 (4) op(e3, all_10_1) = e2 % 150.97/22.10 (5) ~ (e1 = e0) % 150.97/22.10 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 150.97/22.10 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 150.97/22.10 (7) op(e3, e3) = all_56_0 % 150.97/22.10 (8) all_58_9 = e0 % 150.97/22.10 (9) op(e3, e3) = all_10_1 % 150.97/22.10 % 150.97/22.10 Begin of proof % 150.97/22.10 | % 150.97/22.10 | BETA: splitting (3) gives: % 150.97/22.10 | % 150.97/22.10 | Case 1: % 150.97/22.10 | | % 150.97/22.10 | | (10) all_58_9 = e1 % 150.97/22.10 | | % 150.97/22.10 | | COMBINE_EQS: (8), (10) imply: % 150.97/22.10 | | (11) e1 = e0 % 150.97/22.10 | | % 150.97/22.10 | | REDUCE: (5), (11) imply: % 150.97/22.10 | | (12) $false % 150.97/22.10 | | % 150.97/22.10 | | CLOSE: (12) is inconsistent. % 150.97/22.10 | | % 150.97/22.10 | Case 2: % 150.97/22.10 | | % 150.97/22.10 | | % 150.97/22.10 | | GROUND_INST: instantiating (6) with e3, all_56_0, e3, e3, simplifying with % 150.97/22.10 | | (1), (7) gives: % 150.97/22.10 | | (13) all_56_0 = e3 % 150.97/22.10 | | % 150.97/22.10 | | GROUND_INST: instantiating (6) with all_10_1, all_56_0, e3, e3, simplifying % 150.97/22.10 | | with (7), (9) gives: % 150.97/22.10 | | (14) all_56_0 = all_10_1 % 150.97/22.10 | | % 150.97/22.10 | | COMBINE_EQS: (13), (14) imply: % 150.97/22.10 | | (15) all_10_1 = e3 % 150.97/22.10 | | % 150.97/22.10 | | REF_CLOSE: (2), (4), (6), (7), (9), (15) are inconsistent by sub-proof #175. % 150.97/22.10 | | % 150.97/22.10 | End of split % 150.97/22.10 | % 150.97/22.10 End of proof % 150.97/22.10 % 150.97/22.10 Sub-proof #159 shows that the following formulas are inconsistent: % 150.97/22.10 ---------------------------------------------------------------- % 150.97/22.10 (1) all_4_1 = e3 % 150.97/22.10 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 150.97/22.10 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 150.97/22.10 (3) op(e0, all_4_1) = e1 % 150.97/22.10 (4) all_52_2 = e1 % 150.97/22.10 (5) ~ (all_52_2 = all_52_3) % 150.97/22.10 (6) op(e0, e3) = all_52_3 % 150.97/22.10 % 150.97/22.10 Begin of proof % 150.97/22.10 | % 150.97/22.10 | REDUCE: (4), (5) imply: % 150.97/22.10 | (7) ~ (all_52_3 = e1) % 150.97/22.10 | % 150.97/22.10 | SIMP: (7) implies: % 150.97/22.10 | (8) ~ (all_52_3 = e1) % 150.97/22.10 | % 150.97/22.10 | REDUCE: (1), (3) imply: % 150.97/22.10 | (9) op(e0, e3) = e1 % 150.97/22.10 | % 150.97/22.10 | GROUND_INST: instantiating (2) with all_52_3, e1, e3, e0, simplifying with % 150.97/22.10 | (6), (9) gives: % 150.97/22.10 | (10) all_52_3 = e1 % 150.97/22.10 | % 150.97/22.10 | REDUCE: (8), (10) imply: % 150.97/22.10 | (11) $false % 150.97/22.10 | % 150.97/22.10 | CLOSE: (11) is inconsistent. % 150.97/22.10 | % 150.97/22.10 End of proof % 150.97/22.10 % 150.97/22.10 Sub-proof #160 shows that the following formulas are inconsistent: % 150.97/22.10 ---------------------------------------------------------------- % 150.97/22.10 (1) all_58_8 = e1 % 150.97/22.10 (2) all_58_8 = e3 | all_58_11 = e3 % 150.97/22.10 (3) ~ (all_52_14 = e3) % 150.97/22.10 (4) all_58_11 = all_52_14 % 150.97/22.10 (5) ~ (e3 = e1) % 150.97/22.10 % 150.97/22.10 Begin of proof % 150.97/22.10 | % 150.97/22.10 | BETA: splitting (2) gives: % 150.97/22.10 | % 150.97/22.10 | Case 1: % 150.97/22.10 | | % 150.97/22.10 | | (6) all_58_8 = e3 % 150.97/22.10 | | % 150.97/22.10 | | REF_CLOSE: (1), (5), (6) are inconsistent by sub-proof #161. % 150.97/22.10 | | % 150.97/22.10 | Case 2: % 150.97/22.10 | | % 150.97/22.10 | | (7) all_58_11 = e3 % 150.97/22.10 | | % 150.97/22.10 | | COMBINE_EQS: (4), (7) imply: % 150.97/22.10 | | (8) all_52_14 = e3 % 150.97/22.10 | | % 150.97/22.10 | | REDUCE: (3), (8) imply: % 150.97/22.10 | | (9) $false % 150.97/22.10 | | % 150.97/22.10 | | CLOSE: (9) is inconsistent. % 150.97/22.10 | | % 150.97/22.10 | End of split % 150.97/22.10 | % 150.97/22.10 End of proof % 150.97/22.10 % 150.97/22.10 Sub-proof #161 shows that the following formulas are inconsistent: % 150.97/22.10 ---------------------------------------------------------------- % 150.97/22.10 (1) all_58_8 = e3 % 150.97/22.10 (2) all_58_8 = e1 % 150.97/22.10 (3) ~ (e3 = e1) % 150.97/22.10 % 150.97/22.10 Begin of proof % 150.97/22.10 | % 150.97/22.10 | COMBINE_EQS: (1), (2) imply: % 150.97/22.10 | (4) e3 = e1 % 150.97/22.10 | % 150.97/22.10 | SIMP: (4) implies: % 150.97/22.10 | (5) e3 = e1 % 150.97/22.10 | % 150.97/22.10 | REDUCE: (3), (5) imply: % 150.97/22.10 | (6) $false % 150.97/22.10 | % 150.97/22.10 | CLOSE: (6) is inconsistent. % 150.97/22.10 | % 150.97/22.10 End of proof % 150.97/22.10 % 150.97/22.10 Sub-proof #162 shows that the following formulas are inconsistent: % 150.97/22.10 ---------------------------------------------------------------- % 150.97/22.10 (1) all_56_11 = all_8_2 % 150.97/22.10 (2) ~ (all_56_11 = e1) | all_56_13 = e2 % 150.97/22.10 (3) ~ (all_52_11 = all_6_2) % 150.97/22.10 (4) all_54_9 = all_52_6 % 150.97/22.10 (5) ~ (all_8_1 = e1) % 150.97/22.10 (6) all_54_10 = all_6_2 % 150.97/22.10 (7) ~ (all_56_21 = e2) | all_56_19 = e1 % 150.97/22.10 (8) ~ (all_52_14 = all_4_2) % 150.97/22.10 (9) ~ (all_52_9 = all_8_2) % 150.97/22.10 (10) ~ (all_8_1 = e3) % 150.97/22.10 (11) op(e0, e0) = all_4_2 % 150.97/22.10 (12) all_58_6 = e0 | all_58_7 = e0 | all_58_8 = e0 | all_58_11 = e0 % 150.97/22.10 (13) all_58_4 = all_52_8 % 150.97/22.10 (14) ~ (all_52_6 = all_52_14) % 150.97/22.10 (15) ~ (all_6_0 = e2) % 150.97/22.10 (16) all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1 % 150.97/22.10 (17) all_56_21 = all_6_2 % 150.97/22.10 (18) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 150.97/22.10 (19) ~ (all_52_7 = all_8_2) % 150.97/22.10 (20) all_56_1 = all_10_2 % 150.97/22.10 (21) all_58_5 = all_52_9 % 150.97/22.10 (22) all_58_9 = all_52_12 % 150.97/22.10 (23) all_58_1 = all_52_4 % 150.97/22.10 (24) all_58_13 = all_52_7 % 150.97/22.10 (25) op(e2, all_8_2) = all_56_10 % 150.97/22.10 (26) op(e3, e3) = all_10_2 % 150.97/22.10 (27) ~ (all_52_6 = all_6_0) % 150.97/22.10 (28) ~ (all_56_21 = e3) | all_56_17 = e1 % 150.97/22.10 (29) ~ (e1 = e0) % 150.97/22.10 (30) all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2 % 150.97/22.10 (31) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 150.97/22.10 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 150.97/22.10 (32) ~ (all_52_3 = all_10_2) % 150.97/22.10 (33) all_36_0 = all_6_0 % 150.97/22.10 (34) all_56_15 = e2 % 150.97/22.10 (35) ~ (all_6_0 = all_6_2) % 150.97/22.10 (36) all_56_13 = all_52_9 % 150.97/22.10 (37) all_54_8 = all_6_0 % 150.97/22.10 (38) all_58_8 = all_6_2 % 150.97/22.10 (39) ~ (all_52_14 = all_6_0) % 150.97/22.10 (40) op(all_4_2, all_4_2) = all_4_1 % 150.97/22.10 (41) all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1 % 150.97/22.10 (42) all_58_3 = all_8_2 % 150.97/22.10 (43) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0 % 150.97/22.10 (44) all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1 % 150.97/22.10 (45) all_56_31 = all_4_2 % 150.97/22.10 (46) all_58_11 = all_52_14 % 150.97/22.10 (47) all_36_2 = all_6_2 % 150.97/22.10 (48) all_56_1 = e3 | all_56_11 = e2 | all_56_21 = e1 | all_56_31 = e0 % 150.97/22.10 (49) all_56_11 = e0 % 150.97/22.10 (50) ~ (all_52_13 = all_52_14) % 150.97/22.10 (51) all_56_23 = all_52_14 % 150.97/22.10 (52) all_58_6 = all_6_0 % 150.97/22.10 (53) op(e1, e1) = all_6_2 % 150.97/22.10 (54) ~ (all_52_6 = all_8_2) % 150.97/22.10 (55) all_58_15 = all_4_2 % 150.97/22.10 (56) ~ (all_6_2 = e2) % 150.97/22.10 (57) all_58_7 = all_52_6 % 150.97/22.10 (58) op(e1, all_6_2) = all_56_20 % 150.97/22.10 (59) all_56_17 = all_6_0 % 150.97/22.10 (60) op(e2, e2) = all_8_2 % 150.97/22.10 (61) ~ (all_36_0 = e0) | ~ (all_36_2 = e2) % 150.97/22.10 (62) ~ (all_52_4 = all_52_12) % 150.97/22.10 (63) ~ (all_52_8 = all_52_12) % 150.97/22.10 (64) ~ (all_56_21 = e0) | all_56_23 = e1 % 150.97/22.10 (65) op(e0, all_4_2) = all_56_30 % 150.97/22.10 (66) ~ (all_52_6 = all_6_2) % 150.97/22.10 (67) op(all_6_2, all_6_2) = e3 % 150.97/22.10 (68) ~ (all_52_14 = all_6_2) % 150.97/22.10 (69) op(e1, all_52_11) = all_56_28 % 150.97/22.11 (70) all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3 % 150.97/22.11 (71) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0 % 150.97/22.11 (72) ~ (all_10_2 = all_6_0) % 150.97/22.11 (73) op(all_8_2, all_8_2) = all_8_1 % 150.97/22.11 (74) all_58_14 = all_52_11 % 150.97/22.11 (75) all_56_19 = all_52_6 % 150.97/22.11 (76) ~ (all_52_12 = all_10_2) % 150.97/22.11 (77) all_56_15 = all_52_13 % 150.97/22.11 (78) all_58_12 = all_52_3 % 150.97/22.11 (79) all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3 % 150.97/22.11 % 150.97/22.11 Begin of proof % 150.97/22.11 | % 150.97/22.11 | COMBINE_EQS: (1), (49) imply: % 150.97/22.11 | (80) all_8_2 = e0 % 150.97/22.11 | % 150.97/22.11 | COMBINE_EQS: (34), (77) imply: % 150.97/22.11 | (81) all_52_13 = e2 % 150.97/22.11 | % 150.97/22.11 | REDUCE: (54), (80) imply: % 150.97/22.11 | (82) ~ (all_52_6 = e0) % 150.97/22.11 | % 150.97/22.11 | REDUCE: (50), (81) imply: % 150.97/22.11 | (83) ~ (all_52_14 = e2) % 150.97/22.11 | % 150.97/22.11 | SIMP: (83) implies: % 150.97/22.11 | (84) ~ (all_52_14 = e2) % 150.97/22.11 | % 150.97/22.11 | REDUCE: (73), (80) imply: % 150.97/22.11 | (85) op(e0, e0) = all_8_1 % 150.97/22.11 | % 150.97/22.11 | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), % 150.97/22.11 | (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23), % 150.97/22.11 | (24), (25), (26), (27), (28), (29), (30), (31), (32), (33), (35), % 150.97/22.11 | (36), (37), (38), (39), (40), (41), (42), (43), (44), (45), (46), % 150.97/22.11 | (47), (48), (51), (52), (53), (54), (55), (56), (57), (58), (59), % 150.97/22.11 | (60), (61), (62), (63), (64), (65), (66), (67), (68), (69), (70), % 150.97/22.11 | (71), (72), (73), (74), (75), (76), (78), (79), (82), (84), (85) % 150.97/22.11 | are inconsistent by sub-proof #183. % 150.97/22.11 | % 150.97/22.11 End of proof % 150.97/22.11 % 150.97/22.11 Sub-proof #163 shows that the following formulas are inconsistent: % 150.97/22.11 ---------------------------------------------------------------- % 150.97/22.11 (1) all_56_21 = e3 % 150.97/22.11 (2) all_56_21 = all_6_2 % 150.97/22.11 (3) op(e3, e3) = all_10_2 % 150.97/22.11 (4) op(e3, all_10_1) = e2 % 150.97/22.11 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 150.97/22.11 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 150.97/22.11 (6) ~ (all_6_2 = e2) % 150.97/22.11 (7) op(all_10_2, all_10_2) = all_10_1 % 150.97/22.11 (8) op(all_6_2, all_6_2) = e3 % 150.97/22.11 (9) op(e3, all_10_2) = all_56_0 % 150.97/22.11 % 150.97/22.11 Begin of proof % 150.97/22.11 | % 150.97/22.11 | COMBINE_EQS: (1), (2) imply: % 150.97/22.11 | (10) all_6_2 = e3 % 150.97/22.11 | % 150.97/22.11 | SIMP: (10) implies: % 150.97/22.11 | (11) all_6_2 = e3 % 150.97/22.11 | % 150.97/22.11 | REDUCE: (6), (11) imply: % 150.97/22.11 | (12) ~ (e3 = e2) % 150.97/22.11 | % 150.97/22.11 | REDUCE: (8), (11) imply: % 150.97/22.11 | (13) op(e3, e3) = e3 % 150.97/22.11 | % 150.97/22.11 | GROUND_INST: instantiating (5) with all_10_2, e3, e3, e3, simplifying with % 150.97/22.11 | (3), (13) gives: % 150.97/22.11 | (14) all_10_2 = e3 % 150.97/22.11 | % 150.97/22.11 | REDUCE: (7), (14) imply: % 150.97/22.11 | (15) op(e3, e3) = all_10_1 % 150.97/22.11 | % 150.97/22.11 | REDUCE: (9), (14) imply: % 150.97/22.11 | (16) op(e3, e3) = all_56_0 % 150.97/22.11 | % 150.97/22.11 | GROUND_INST: instantiating (5) with e3, all_56_0, e3, e3, simplifying with % 150.97/22.11 | (13), (16) gives: % 150.97/22.11 | (17) all_56_0 = e3 % 150.97/22.11 | % 150.97/22.11 | GROUND_INST: instantiating (5) with all_10_1, all_56_0, e3, e3, simplifying % 150.97/22.11 | with (15), (16) gives: % 150.97/22.11 | (18) all_56_0 = all_10_1 % 150.97/22.11 | % 150.97/22.11 | COMBINE_EQS: (17), (18) imply: % 150.97/22.11 | (19) all_10_1 = e3 % 150.97/22.11 | % 150.97/22.11 | SIMP: (19) implies: % 150.97/22.11 | (20) all_10_1 = e3 % 150.97/22.11 | % 150.97/22.11 | REF_CLOSE: (4), (5), (12), (15), (16), (20) are inconsistent by sub-proof % 150.97/22.11 | #175. % 150.97/22.11 | % 150.97/22.11 End of proof % 150.97/22.11 % 150.97/22.11 Sub-proof #164 shows that the following formulas are inconsistent: % 150.97/22.11 ---------------------------------------------------------------- % 150.97/22.11 (1) ~ (all_52_11 = all_6_2) % 150.97/22.11 (2) all_58_6 = all_52_2 % 150.97/22.11 (3) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0 % 150.97/22.11 (4) ~ (all_4_1 = e0) % 150.97/22.11 (5) ~ (all_4_1 = e3) % 150.97/22.11 (6) all_54_0 = all_10_2 % 150.97/22.11 (7) all_54_4 = all_52_1 % 150.97/22.11 (8) all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2 % 150.97/22.11 (9) all_54_12 = all_52_3 % 150.97/22.11 (10) ~ (all_52_12 = e2) % 150.97/22.11 (11) all_58_4 = all_52_8 % 150.97/22.11 (12) ~ (all_10_2 = e1) % 150.97/22.11 (13) all_58_3 = all_4_1 % 150.97/22.11 (14) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 150.97/22.11 (15) ~ (all_52_4 = all_4_1) % 150.97/22.11 (16) ~ (all_52_11 = e0) % 150.97/22.11 (17) all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1 % 150.97/22.11 (18) ~ (all_52_3 = e2) % 150.97/22.11 (19) all_56_21 = all_6_2 % 150.97/22.11 (20) ~ (all_52_14 = e2) % 150.97/22.11 (21) all_56_1 = all_10_2 % 150.97/22.11 (22) all_58_5 = all_52_9 % 150.97/22.11 (23) ~ (all_52_13 = e2) % 150.97/22.11 (24) all_58_9 = all_52_12 % 150.97/22.11 (25) ~ (all_52_9 = all_4_1) % 150.97/22.11 (26) op(e0, all_52_12) = all_56_6 % 150.97/22.11 (27) all_54_14 = all_52_11 % 150.97/22.11 (28) all_58_1 = all_52_4 % 150.97/22.11 (29) op(e3, e3) = all_10_2 % 150.97/22.11 (30) all_58_15 = e2 % 150.97/22.11 (31) ~ (all_52_6 = all_4_1) % 150.97/22.11 (32) op(e3, all_10_1) = e2 % 150.97/22.11 (33) ~ (all_52_13 = all_4_1) % 150.97/22.11 (34) all_58_13 = e0 % 150.97/22.11 (35) all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2 % 150.97/22.11 (36) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 150.97/22.11 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 150.97/22.11 (37) ~ (all_52_3 = all_10_2) % 150.97/22.11 (38) all_56_11 = all_4_1 % 150.97/22.11 (39) ~ (all_52_2 = all_52_6) % 150.97/22.11 (40) op(e0, all_4_1) = all_4_0 % 150.97/22.11 (41) ~ (all_52_3 = e0) % 150.97/22.11 (42) all_56_7 = all_52_12 % 150.97/22.11 (43) ~ (all_52_11 = e2) % 150.97/22.11 (44) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0 % 150.97/22.11 (45) op(e0, e1) = all_52_11 % 150.97/22.11 (46) ~ (all_52_1 = all_52_13) % 150.97/22.11 (47) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0 % 150.97/22.11 (48) ~ (all_4_2 = e1) % 150.97/22.11 (49) all_58_8 = all_6_2 % 150.97/22.11 (50) ~ (all_52_8 = all_10_2) % 150.97/22.11 (51) all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3 % 150.97/22.11 (52) ~ (all_52_6 = e0) % 150.97/22.11 (53) ~ (all_56_1 = e2) | all_56_3 = e3 % 150.97/22.11 (54) ~ (all_56_1 = e0) | all_56_7 = e3 % 150.97/22.11 (55) op(e0, e0) = e2 % 150.97/22.11 (56) all_56_3 = all_52_4 % 150.97/22.11 (57) ~ (all_52_1 = all_52_3) % 150.97/22.11 (58) all_58_11 = all_52_14 % 150.97/22.11 (59) all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3 % 150.97/22.11 (60) ~ (all_52_9 = all_52_11) % 150.97/22.11 (61) all_56_1 = e3 | all_56_11 = e2 | all_56_21 = e1 | all_56_31 = e0 % 150.97/22.11 (62) all_54_5 = all_4_1 % 150.97/22.11 (63) op(e3, e2) = all_52_4 % 150.97/22.11 (64) ~ (all_52_13 = all_52_14) % 150.97/22.11 (65) all_58_15 = all_4_2 % 150.97/22.11 (66) ~ (all_6_2 = e2) % 150.97/22.11 (67) all_58_2 = all_52_1 % 150.97/22.11 (68) all_58_7 = all_52_6 % 150.97/22.11 (69) all_58_10 = all_52_13 % 150.97/22.11 (70) op(all_10_2, all_10_2) = all_10_1 % 150.97/22.11 (71) op(e3, all_52_2) = all_56_16 % 150.97/22.11 (72) all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1 % 150.97/22.11 (73) ~ (all_52_4 = all_52_12) % 150.97/22.11 (74) all_56_31 = e2 % 150.97/22.11 (75) ~ (all_52_1 = all_52_2) % 150.97/22.11 (76) op(e3, all_10_2) = all_56_0 % 150.97/22.11 (77) ~ (all_52_14 = all_6_2) % 150.97/22.11 (78) ~ (all_52_2 = all_10_2) % 150.97/22.11 (79) ~ (all_52_4 = all_10_2) % 150.97/22.11 (80) all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3 % 150.97/22.11 (81) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 150.97/22.11 (82) all_58_14 = all_52_11 % 150.97/22.11 (83) ~ (all_52_12 = all_10_2) % 150.97/22.11 (84) ~ (all_4_0 = e3) % 150.97/22.11 (85) ~ (all_52_1 = all_10_2) % 150.97/22.11 (86) all_58_12 = all_52_3 % 150.97/22.11 (87) all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3 % 150.97/22.11 % 150.97/22.11 Begin of proof % 150.97/22.11 | % 150.97/22.11 | BETA: splitting (54) gives: % 150.97/22.11 | % 150.97/22.11 | Case 1: % 150.97/22.11 | | % 150.97/22.11 | | (88) ~ (all_56_1 = e0) % 150.97/22.11 | | % 150.97/22.11 | | REDUCE: (21), (88) imply: % 150.97/22.11 | | (89) ~ (all_10_2 = e0) % 150.97/22.11 | | % 150.97/22.11 | | BETA: splitting (53) gives: % 150.97/22.11 | | % 150.97/22.11 | | Case 1: % 150.97/22.11 | | | % 150.97/22.11 | | | (90) ~ (all_56_1 = e2) % 150.97/22.11 | | | % 150.97/22.11 | | | REDUCE: (21), (90) imply: % 150.97/22.11 | | | (91) ~ (all_10_2 = e2) % 150.97/22.11 | | | % 150.97/22.11 | | | BETA: splitting (14) gives: % 150.97/22.11 | | | % 150.97/22.11 | | | Case 1: % 150.97/22.11 | | | | % 150.97/22.11 | | | | (92) all_54_0 = e3 % 150.97/22.11 | | | | % 150.97/22.11 | | | | COMBINE_EQS: (6), (92) imply: % 150.97/22.11 | | | | (93) all_10_2 = e3 % 150.97/22.11 | | | | % 150.97/22.11 | | | | SIMP: (93) implies: % 150.97/22.11 | | | | (94) all_10_2 = e3 % 150.97/22.11 | | | | % 150.97/22.11 | | | | REDUCE: (85), (94) imply: % 150.97/22.11 | | | | (95) ~ (all_52_1 = e3) % 150.97/22.11 | | | | % 150.97/22.11 | | | | REDUCE: (78), (94) imply: % 150.97/22.11 | | | | (96) ~ (all_52_2 = e3) % 150.97/22.11 | | | | % 150.97/22.11 | | | | REDUCE: (37), (94) imply: % 150.97/22.11 | | | | (97) ~ (all_52_3 = e3) % 150.97/22.11 | | | | % 150.97/22.11 | | | | REDUCE: (91), (94) imply: % 150.97/22.11 | | | | (98) ~ (e3 = e2) % 150.97/22.11 | | | | % 150.97/22.11 | | | | REDUCE: (89), (94) imply: % 150.97/22.11 | | | | (99) ~ (e3 = e0) % 150.97/22.11 | | | | % 150.97/22.11 | | | | REDUCE: (70), (94) imply: % 150.97/22.11 | | | | (100) op(e3, e3) = all_10_1 % 150.97/22.11 | | | | % 150.97/22.11 | | | | REDUCE: (76), (94) imply: % 150.97/22.11 | | | | (101) op(e3, e3) = all_56_0 % 150.97/22.11 | | | | % 150.97/22.11 | | | | REDUCE: (29), (94) imply: % 150.97/22.11 | | | | (102) op(e3, e3) = e3 % 150.97/22.11 | | | | % 150.97/22.11 | | | | BETA: splitting (44) gives: % 150.97/22.11 | | | | % 150.97/22.11 | | | | Case 1: % 150.97/22.11 | | | | | % 150.97/22.11 | | | | | (103) all_54_12 = e3 % 150.97/22.11 | | | | | % 150.97/22.11 | | | | | COMBINE_EQS: (9), (103) imply: % 150.97/22.11 | | | | | (104) all_52_3 = e3 % 150.97/22.11 | | | | | % 150.97/22.11 | | | | | REDUCE: (97), (104) imply: % 150.97/22.11 | | | | | (105) $false % 150.97/22.11 | | | | | % 150.97/22.11 | | | | | CLOSE: (105) is inconsistent. % 150.97/22.11 | | | | | % 150.97/22.11 | | | | Case 2: % 150.97/22.11 | | | | | % 150.97/22.11 | | | | | (106) ~ (all_54_12 = e3) % 150.97/22.11 | | | | | (107) all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0 % 150.97/22.11 | | | | | % 150.97/22.11 | | | | | BETA: splitting (107) gives: % 150.97/22.11 | | | | | % 150.97/22.11 | | | | | Case 1: % 150.97/22.11 | | | | | | % 150.97/22.11 | | | | | | (108) all_54_12 = e2 % 150.97/22.11 | | | | | | % 150.97/22.11 | | | | | | COMBINE_EQS: (9), (108) imply: % 150.97/22.11 | | | | | | (109) all_52_3 = e2 % 150.97/22.11 | | | | | | % 150.97/22.11 | | | | | | REDUCE: (18), (109) imply: % 150.97/22.11 | | | | | | (110) $false % 150.97/22.11 | | | | | | % 150.97/22.11 | | | | | | CLOSE: (110) is inconsistent. % 150.97/22.11 | | | | | | % 150.97/22.11 | | | | | Case 2: % 150.97/22.11 | | | | | | % 150.97/22.11 | | | | | | (111) all_54_12 = e1 | all_54_12 = e0 % 150.97/22.11 | | | | | | % 150.97/22.11 | | | | | | BETA: splitting (87) gives: % 150.97/22.11 | | | | | | % 150.97/22.11 | | | | | | Case 1: % 150.97/22.11 | | | | | | | % 150.97/22.11 | | | | | | | (112) all_58_12 = e3 % 150.97/22.11 | | | | | | | % 150.97/22.11 | | | | | | | REF_CLOSE: (86), (97), (112) are inconsistent by sub-proof #449. % 150.97/22.11 | | | | | | | % 150.97/22.11 | | | | | | Case 2: % 150.97/22.11 | | | | | | | % 150.97/22.11 | | | | | | | (113) all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3 % 150.97/22.11 | | | | | | | % 150.97/22.11 | | | | | | | BETA: splitting (113) gives: % 150.97/22.11 | | | | | | | % 150.97/22.11 | | | | | | | Case 1: % 150.97/22.11 | | | | | | | | % 150.97/22.11 | | | | | | | | (114) all_58_13 = e3 % 150.97/22.11 | | | | | | | | % 150.97/22.11 | | | | | | | | COMBINE_EQS: (34), (114) imply: % 150.97/22.11 | | | | | | | | (115) e3 = e0 % 150.97/22.11 | | | | | | | | % 150.97/22.11 | | | | | | | | REDUCE: (99), (115) imply: % 150.97/22.11 | | | | | | | | (116) $false % 150.97/22.11 | | | | | | | | % 150.97/22.11 | | | | | | | | CLOSE: (116) is inconsistent. % 150.97/22.11 | | | | | | | | % 150.97/22.11 | | | | | | | Case 2: % 150.97/22.11 | | | | | | | | % 150.97/22.11 | | | | | | | | (117) all_58_14 = e3 | all_58_15 = e3 % 150.97/22.11 | | | | | | | | % 150.97/22.11 | | | | | | | | BETA: splitting (117) gives: % 150.97/22.11 | | | | | | | | % 150.97/22.11 | | | | | | | | Case 1: % 150.97/22.11 | | | | | | | | | % 150.97/22.11 | | | | | | | | | (118) all_58_14 = e3 % 150.97/22.11 | | | | | | | | | % 150.97/22.11 | | | | | | | | | COMBINE_EQS: (82), (118) imply: % 150.97/22.11 | | | | | | | | | (119) all_52_11 = e3 % 150.97/22.11 | | | | | | | | | % 150.97/22.11 | | | | | | | | | SIMP: (119) implies: % 150.97/22.11 | | | | | | | | | (120) all_52_11 = e3 % 150.97/22.11 | | | | | | | | | % 150.97/22.11 | | | | | | | | | REDUCE: (60), (120) imply: % 150.97/22.11 | | | | | | | | | (121) ~ (all_52_9 = e3) % 150.97/22.11 | | | | | | | | | % 150.97/22.11 | | | | | | | | | REDUCE: (1), (120) imply: % 150.97/22.11 | | | | | | | | | (122) ~ (all_6_2 = e3) % 150.97/22.11 | | | | | | | | | % 150.97/22.11 | | | | | | | | | SIMP: (122) implies: % 150.97/22.11 | | | | | | | | | (123) ~ (all_6_2 = e3) % 150.97/22.11 | | | | | | | | | % 150.97/22.11 | | | | | | | | | BETA: splitting (72) gives: % 150.97/22.11 | | | | | | | | | % 150.97/22.11 | | | | | | | | | Case 1: % 150.97/22.11 | | | | | | | | | | % 150.97/22.11 | | | | | | | | | | (124) all_58_12 = e1 % 150.97/22.11 | | | | | | | | | | % 150.97/22.11 | | | | | | | | | | COMBINE_EQS: (86), (124) imply: % 150.97/22.11 | | | | | | | | | | (125) all_52_3 = e1 % 150.97/22.11 | | | | | | | | | | % 150.97/22.11 | | | | | | | | | | SIMP: (125) implies: % 150.97/22.11 | | | | | | | | | | (126) all_52_3 = e1 % 150.97/22.11 | | | | | | | | | | % 150.97/22.11 | | | | | | | | | | REDUCE: (57), (126) imply: % 150.97/22.11 | | | | | | | | | | (127) ~ (all_52_1 = e1) % 150.97/22.11 | | | | | | | | | | % 150.97/22.11 | | | | | | | | | | BETA: splitting (80) gives: % 150.97/22.11 | | | | | | | | | | % 150.97/22.11 | | | | | | | | | | Case 1: % 150.97/22.11 | | | | | | | | | | | % 150.97/22.11 | | | | | | | | | | | (128) all_58_2 = e3 % 150.97/22.11 | | | | | | | | | | | % 150.97/22.11 | | | | | | | | | | | COMBINE_EQS: (67), (128) imply: % 150.97/22.11 | | | | | | | | | | | (129) all_52_1 = e3 % 150.97/22.11 | | | | | | | | | | | % 150.97/22.11 | | | | | | | | | | | REDUCE: (95), (129) imply: % 150.97/22.11 | | | | | | | | | | | (130) $false % 150.97/22.11 | | | | | | | | | | | % 150.97/22.11 | | | | | | | | | | | CLOSE: (130) is inconsistent. % 150.97/22.11 | | | | | | | | | | | % 150.97/22.11 | | | | | | | | | | Case 2: % 150.97/22.11 | | | | | | | | | | | % 150.97/22.11 | | | | | | | | | | | (131) all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3 % 150.97/22.11 | | | | | | | | | | | % 150.97/22.11 | | | | | | | | | | | BETA: splitting (131) gives: % 150.97/22.11 | | | | | | | | | | | % 150.97/22.11 | | | | | | | | | | | Case 1: % 150.97/22.11 | | | | | | | | | | | | % 150.97/22.11 | | | | | | | | | | | | (132) all_58_3 = e3 % 150.97/22.11 | | | | | | | | | | | | % 150.97/22.11 | | | | | | | | | | | | COMBINE_EQS: (13), (132) imply: % 150.97/22.11 | | | | | | | | | | | | (133) all_4_1 = e3 % 150.97/22.11 | | | | | | | | | | | | % 150.97/22.11 | | | | | | | | | | | | REDUCE: (5), (133) imply: % 150.97/22.11 | | | | | | | | | | | | (134) $false % 150.97/22.11 | | | | | | | | | | | | % 150.97/22.11 | | | | | | | | | | | | CLOSE: (134) is inconsistent. % 150.97/22.11 | | | | | | | | | | | | % 150.97/22.11 | | | | | | | | | | | Case 2: % 150.97/22.11 | | | | | | | | | | | | % 150.97/22.11 | | | | | | | | | | | | (135) all_58_5 = e3 | all_58_10 = e3 % 150.97/22.11 | | | | | | | | | | | | % 150.97/22.11 | | | | | | | | | | | | BETA: splitting (135) gives: % 150.97/22.11 | | | | | | | | | | | | % 150.97/22.11 | | | | | | | | | | | | Case 1: % 150.97/22.11 | | | | | | | | | | | | | % 150.97/22.11 | | | | | | | | | | | | | (136) all_58_5 = e3 % 150.97/22.11 | | | | | | | | | | | | | % 150.97/22.11 | | | | | | | | | | | | | COMBINE_EQS: (22), (136) imply: % 150.97/22.11 | | | | | | | | | | | | | (137) all_52_9 = e3 % 150.97/22.11 | | | | | | | | | | | | | % 150.97/22.11 | | | | | | | | | | | | | REDUCE: (121), (137) imply: % 150.97/22.11 | | | | | | | | | | | | | (138) $false % 150.97/22.11 | | | | | | | | | | | | | % 150.97/22.11 | | | | | | | | | | | | | CLOSE: (138) is inconsistent. % 150.97/22.11 | | | | | | | | | | | | | % 150.97/22.11 | | | | | | | | | | | | Case 2: % 150.97/22.11 | | | | | | | | | | | | | % 150.97/22.11 | | | | | | | | | | | | | (139) all_58_10 = e3 % 150.97/22.11 | | | | | | | | | | | | | % 150.97/22.11 | | | | | | | | | | | | | COMBINE_EQS: (69), (139) imply: % 150.97/22.11 | | | | | | | | | | | | | (140) all_52_13 = e3 % 150.97/22.11 | | | | | | | | | | | | | % 150.97/22.11 | | | | | | | | | | | | | REDUCE: (64), (140) imply: % 150.97/22.11 | | | | | | | | | | | | | (141) ~ (all_52_14 = e3) % 150.97/22.11 | | | | | | | | | | | | | % 150.97/22.11 | | | | | | | | | | | | | SIMP: (141) implies: % 150.97/22.11 | | | | | | | | | | | | | (142) ~ (all_52_14 = e3) % 150.97/22.11 | | | | | | | | | | | | | % 150.97/22.11 | | | | | | | | | | | | | BETA: splitting (51) gives: % 150.97/22.11 | | | | | | | | | | | | | % 150.97/22.11 | | | | | | | | | | | | | Case 1: % 150.97/22.11 | | | | | | | | | | | | | | % 150.97/22.11 | | | | | | | | | | | | | | (143) all_58_6 = e3 % 150.97/22.11 | | | | | | | | | | | | | | % 150.97/22.11 | | | | | | | | | | | | | | REF_CLOSE: (2), (96), (143) are inconsistent by sub-proof % 150.97/22.11 | | | | | | | | | | | | | | #346. % 150.97/22.11 | | | | | | | | | | | | | | % 150.97/22.11 | | | | | | | | | | | | | Case 2: % 150.97/22.11 | | | | | | | | | | | | | | % 150.97/22.11 | | | | | | | | | | | | | | (144) all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3 % 150.97/22.11 | | | | | | | | | | | | | | % 150.97/22.11 | | | | | | | | | | | | | | BETA: splitting (144) gives: % 150.97/22.11 | | | | | | | | | | | | | | % 150.97/22.11 | | | | | | | | | | | | | | Case 1: % 150.97/22.11 | | | | | | | | | | | | | | | % 150.97/22.11 | | | | | | | | | | | | | | | (145) all_58_7 = e3 % 150.97/22.11 | | | | | | | | | | | | | | | % 150.97/22.11 | | | | | | | | | | | | | | | COMBINE_EQS: (68), (145) imply: % 150.97/22.11 | | | | | | | | | | | | | | | (146) all_52_6 = e3 % 150.97/22.11 | | | | | | | | | | | | | | | % 150.97/22.11 | | | | | | | | | | | | | | | BETA: splitting (35) gives: % 150.97/22.11 | | | | | | | | | | | | | | | % 150.97/22.11 | | | | | | | | | | | | | | | Case 1: % 150.97/22.11 | | | | | | | | | | | | | | | | % 150.97/22.11 | | | | | | | | | | | | | | | | (147) all_58_6 = e2 % 150.97/22.11 | | | | | | | | | | | | | | | | % 150.97/22.11 | | | | | | | | | | | | | | | | COMBINE_EQS: (2), (147) imply: % 150.97/22.11 | | | | | | | | | | | | | | | | (148) all_52_2 = e2 % 150.97/22.11 | | | | | | | | | | | | | | | | % 150.97/22.11 | | | | | | | | | | | | | | | | SIMP: (148) implies: % 150.97/22.11 | | | | | | | | | | | | | | | | (149) all_52_2 = e2 % 150.97/22.11 | | | | | | | | | | | | | | | | % 150.97/22.11 | | | | | | | | | | | | | | | | REDUCE: (75), (149) imply: % 150.97/22.11 | | | | | | | | | | | | | | | | (150) ~ (all_52_1 = e2) % 150.97/22.11 | | | | | | | | | | | | | | | | % 150.97/22.11 | | | | | | | | | | | | | | | | REDUCE: (96), (149) imply: % 150.97/22.11 | | | | | | | | | | | | | | | | (151) ~ (e3 = e2) % 150.97/22.11 | | | | | | | | | | | | | | | | % 150.97/22.11 | | | | | | | | | | | | | | | | BETA: splitting (47) gives: % 150.97/22.11 | | | | | | | | | | | | | | | | % 150.97/22.11 | | | | | | | | | | | | | | | | Case 1: % 150.97/22.11 | | | | | | | | | | | | | | | | | % 150.97/22.11 | | | | | | | | | | | | | | | | | (152) all_54_4 = e3 % 150.97/22.11 | | | | | | | | | | | | | | | | | % 150.97/22.11 | | | | | | | | | | | | | | | | | COMBINE_EQS: (7), (152) imply: % 150.97/22.11 | | | | | | | | | | | | | | | | | (153) all_52_1 = e3 % 150.97/22.11 | | | | | | | | | | | | | | | | | % 150.97/22.11 | | | | | | | | | | | | | | | | | REDUCE: (95), (153) imply: % 150.97/22.11 | | | | | | | | | | | | | | | | | (154) $false % 150.97/22.11 | | | | | | | | | | | | | | | | | % 150.97/22.11 | | | | | | | | | | | | | | | | | CLOSE: (154) is inconsistent. % 150.97/22.11 | | | | | | | | | | | | | | | | | % 150.97/22.11 | | | | | | | | | | | | | | | | Case 2: % 150.97/22.11 | | | | | | | | | | | | | | | | | % 150.97/22.11 | | | | | | | | | | | | | | | | | (155) all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0 % 150.97/22.11 | | | | | | | | | | | | | | | | | % 150.97/22.11 | | | | | | | | | | | | | | | | | BETA: splitting (155) gives: % 150.97/22.11 | | | | | | | | | | | | | | | | | % 150.97/22.11 | | | | | | | | | | | | | | | | | Case 1: % 150.97/22.11 | | | | | | | | | | | | | | | | | | % 150.97/22.11 | | | | | | | | | | | | | | | | | | (156) all_54_4 = e2 % 150.97/22.11 | | | | | | | | | | | | | | | | | | % 150.97/22.11 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (7), (156) imply: % 150.97/22.11 | | | | | | | | | | | | | | | | | | (157) all_52_1 = e2 % 150.97/22.11 | | | | | | | | | | | | | | | | | | % 150.97/22.11 | | | | | | | | | | | | | | | | | | REDUCE: (150), (157) imply: % 150.97/22.11 | | | | | | | | | | | | | | | | | | (158) $false % 150.97/22.11 | | | | | | | | | | | | | | | | | | % 150.97/22.11 | | | | | | | | | | | | | | | | | | CLOSE: (158) is inconsistent. % 150.97/22.11 | | | | | | | | | | | | | | | | | | % 150.97/22.11 | | | | | | | | | | | | | | | | | Case 2: % 150.97/22.11 | | | | | | | | | | | | | | | | | | % 150.97/22.11 | | | | | | | | | | | | | | | | | | (159) all_54_4 = e1 | all_54_4 = e0 % 150.97/22.11 | | | | | | | | | | | | | | | | | | % 150.97/22.11 | | | | | | | | | | | | | | | | | | BETA: splitting (159) gives: % 150.97/22.11 | | | | | | | | | | | | | | | | | | % 150.97/22.11 | | | | | | | | | | | | | | | | | | Case 1: % 150.97/22.11 | | | | | | | | | | | | | | | | | | | % 150.97/22.11 | | | | | | | | | | | | | | | | | | | (160) all_54_4 = e1 % 150.97/22.11 | | | | | | | | | | | | | | | | | | | % 150.97/22.11 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (7), (160) imply: % 150.97/22.11 | | | | | | | | | | | | | | | | | | | (161) all_52_1 = e1 % 150.97/22.11 | | | | | | | | | | | | | | | | | | | % 150.97/22.11 | | | | | | | | | | | | | | | | | | | REDUCE: (127), (161) imply: % 150.97/22.11 | | | | | | | | | | | | | | | | | | | (162) $false % 150.97/22.11 | | | | | | | | | | | | | | | | | | | % 150.97/22.11 | | | | | | | | | | | | | | | | | | | CLOSE: (162) is inconsistent. % 150.97/22.11 | | | | | | | | | | | | | | | | | | | % 150.97/22.11 | | | | | | | | | | | | | | | | | | Case 2: % 150.97/22.11 | | | | | | | | | | | | | | | | | | | % 150.97/22.11 | | | | | | | | | | | | | | | | | | | % 150.97/22.11 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (36) with all_10_1, all_56_0, e3, % 150.97/22.11 | | | | | | | | | | | | | | | | | | | e3, simplifying with (100), (101) gives: % 150.97/22.11 | | | | | | | | | | | | | | | | | | | (163) all_56_0 = all_10_1 % 150.97/22.11 | | | | | | | | | | | | | | | | | | | % 150.97/22.11 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (36) with e3, all_56_0, e3, e3, % 150.97/22.11 | | | | | | | | | | | | | | | | | | | simplifying with (101), (102) gives: % 150.97/22.11 | | | | | | | | | | | | | | | | | | | (164) all_56_0 = e3 % 150.97/22.11 | | | | | | | | | | | | | | | | | | | % 150.97/22.11 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (163), (164) imply: % 150.97/22.11 | | | | | | | | | | | | | | | | | | | (165) all_10_1 = e3 % 150.97/22.11 | | | | | | | | | | | | | | | | | | | % 150.97/22.11 | | | | | | | | | | | | | | | | | | | SIMP: (165) implies: % 150.97/22.11 | | | | | | | | | | | | | | | | | | | (166) all_10_1 = e3 % 150.97/22.11 | | | | | | | | | | | | | | | | | | | % 150.97/22.11 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (32), (36), (98), (100), (101), (166) are % 150.97/22.11 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #175. % 150.97/22.11 | | | | | | | | | | | | | | | | | | | % 150.97/22.11 | | | | | | | | | | | | | | | | | | End of split % 150.97/22.11 | | | | | | | | | | | | | | | | | | % 150.97/22.11 | | | | | | | | | | | | | | | | | End of split % 150.97/22.11 | | | | | | | | | | | | | | | | | % 150.97/22.11 | | | | | | | | | | | | | | | | End of split % 150.97/22.11 | | | | | | | | | | | | | | | | % 150.97/22.11 | | | | | | | | | | | | | | | Case 2: % 150.97/22.11 | | | | | | | | | | | | | | | | % 150.97/22.11 | | | | | | | | | | | | | | | | (167) all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2 % 150.97/22.11 | | | | | | | | | | | | | | | | % 150.97/22.11 | | | | | | | | | | | | | | | | REF_CLOSE: (20), (49), (58), (66), (98), (145), (167) are % 150.97/22.11 | | | | | | | | | | | | | | | | inconsistent by sub-proof #168. % 150.97/22.11 | | | | | | | | | | | | | | | | % 150.97/22.11 | | | | | | | | | | | | | | | End of split % 150.97/22.11 | | | | | | | | | | | | | | | % 150.97/22.11 | | | | | | | | | | | | | | Case 2: % 150.97/22.11 | | | | | | | | | | | | | | | % 150.97/22.11 | | | | | | | | | | | | | | | (168) all_58_8 = e3 | all_58_11 = e3 % 150.97/22.11 | | | | | | | | | | | | | | | % 150.97/22.11 | | | | | | | | | | | | | | | REF_CLOSE: (49), (58), (123), (142), (168) are inconsistent % 150.97/22.11 | | | | | | | | | | | | | | | by sub-proof #636. % 150.97/22.11 | | | | | | | | | | | | | | | % 150.97/22.11 | | | | | | | | | | | | | | End of split % 150.97/22.11 | | | | | | | | | | | | | | % 150.97/22.11 | | | | | | | | | | | | | End of split % 150.97/22.11 | | | | | | | | | | | | | % 150.97/22.11 | | | | | | | | | | | | End of split % 150.97/22.11 | | | | | | | | | | | | % 150.97/22.11 | | | | | | | | | | | End of split % 150.97/22.11 | | | | | | | | | | | % 150.97/22.11 | | | | | | | | | | End of split % 150.97/22.11 | | | | | | | | | | % 150.97/22.11 | | | | | | | | | Case 2: % 150.97/22.11 | | | | | | | | | | % 150.97/22.11 | | | | | | | | | | (169) ~ (all_58_12 = e1) % 150.97/22.11 | | | | | | | | | | % 150.97/22.11 | | | | | | | | | | REDUCE: (86), (169) imply: % 150.97/22.11 | | | | | | | | | | (170) ~ (all_52_3 = e1) % 150.97/22.11 | | | | | | | | | | % 150.97/22.11 | | | | | | | | | | REF_CLOSE: (9), (41), (111), (170) are inconsistent by % 150.97/22.11 | | | | | | | | | | sub-proof #616. % 150.97/22.11 | | | | | | | | | | % 150.97/22.11 | | | | | | | | | End of split % 150.97/22.11 | | | | | | | | | % 150.97/22.11 | | | | | | | | Case 2: % 150.97/22.11 | | | | | | | | | % 150.97/22.11 | | | | | | | | | (171) all_58_15 = e3 % 150.97/22.11 | | | | | | | | | % 150.97/22.11 | | | | | | | | | COMBINE_EQS: (30), (171) imply: % 150.97/22.11 | | | | | | | | | (172) e3 = e2 % 150.97/22.11 | | | | | | | | | % 150.97/22.11 | | | | | | | | | SIMP: (172) implies: % 150.97/22.11 | | | | | | | | | (173) e3 = e2 % 150.97/22.11 | | | | | | | | | % 150.97/22.11 | | | | | | | | | REDUCE: (98), (173) imply: % 150.97/22.11 | | | | | | | | | (174) $false % 150.97/22.11 | | | | | | | | | % 150.97/22.11 | | | | | | | | | CLOSE: (174) is inconsistent. % 150.97/22.11 | | | | | | | | | % 150.97/22.11 | | | | | | | | End of split % 150.97/22.11 | | | | | | | | % 150.97/22.11 | | | | | | | End of split % 150.97/22.11 | | | | | | | % 150.97/22.11 | | | | | | End of split % 150.97/22.11 | | | | | | % 150.97/22.11 | | | | | End of split % 150.97/22.11 | | | | | % 150.97/22.11 | | | | End of split % 150.97/22.11 | | | | % 150.97/22.11 | | | Case 2: % 150.97/22.11 | | | | % 150.97/22.11 | | | | (175) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 150.97/22.11 | | | | % 150.97/22.11 | | | | REF_CLOSE: (6), (12), (89), (91), (175) are inconsistent by sub-proof % 150.97/22.11 | | | | #731. % 150.97/22.11 | | | | % 150.97/22.11 | | | End of split % 150.97/22.11 | | | % 150.97/22.11 | | Case 2: % 150.97/22.11 | | | % 150.97/22.11 | | | (176) all_56_3 = e3 % 150.97/22.11 | | | (177) all_56_1 = e2 % 150.97/22.11 | | | % 150.97/22.11 | | | COMBINE_EQS: (21), (177) imply: % 150.97/22.11 | | | (178) all_10_2 = e2 % 150.97/22.11 | | | % 150.97/22.11 | | | COMBINE_EQS: (56), (176) imply: % 150.97/22.11 | | | (179) all_52_4 = e3 % 150.97/22.11 | | | % 150.97/22.11 | | | REDUCE: (79), (178), (179) imply: % 150.97/22.11 | | | (180) ~ (e3 = e2) % 150.97/22.11 | | | % 150.97/22.11 | | | REDUCE: (15), (179) imply: % 150.97/22.11 | | | (181) ~ (all_4_1 = e3) % 150.97/22.11 | | | % 150.97/22.11 | | | REDUCE: (50), (178) imply: % 150.97/22.11 | | | (182) ~ (all_52_8 = e2) % 150.97/22.11 | | | % 150.97/22.11 | | | REDUCE: (89), (178) imply: % 150.97/22.11 | | | (183) ~ (e2 = e0) % 150.97/22.11 | | | % 150.97/22.11 | | | BETA: splitting (8) gives: % 150.97/22.11 | | | % 150.97/22.11 | | | Case 1: % 150.97/22.11 | | | | % 150.97/22.11 | | | | (184) all_58_4 = e2 % 150.97/22.11 | | | | % 150.97/22.11 | | | | COMBINE_EQS: (11), (184) imply: % 150.97/22.11 | | | | (185) all_52_8 = e2 % 150.97/22.11 | | | | % 150.97/22.11 | | | | REDUCE: (182), (185) imply: % 150.97/22.11 | | | | (186) $false % 150.97/22.11 | | | | % 150.97/22.11 | | | | CLOSE: (186) is inconsistent. % 150.97/22.11 | | | | % 150.97/22.11 | | | Case 2: % 150.97/22.11 | | | | % 150.97/22.11 | | | | (187) all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2 % 150.97/22.11 | | | | % 150.97/22.11 | | | | BETA: splitting (187) gives: % 150.97/22.11 | | | | % 150.97/22.11 | | | | Case 1: % 150.97/22.11 | | | | | % 150.97/22.11 | | | | | (188) all_58_5 = e2 % 150.97/22.11 | | | | | % 150.97/22.11 | | | | | COMBINE_EQS: (22), (188) imply: % 150.97/22.11 | | | | | (189) all_52_9 = e2 % 150.97/22.11 | | | | | % 150.97/22.11 | | | | | REDUCE: (60), (189) imply: % 150.97/22.11 | | | | | (190) ~ (all_52_11 = e2) % 150.97/22.11 | | | | | % 150.97/22.11 | | | | | REDUCE: (25), (189) imply: % 150.97/22.11 | | | | | (191) ~ (all_4_1 = e2) % 150.97/22.11 | | | | | % 150.97/22.11 | | | | | SIMP: (191) implies: % 150.97/22.11 | | | | | (192) ~ (all_4_1 = e2) % 150.97/22.11 | | | | | % 150.97/22.11 | | | | | BETA: splitting (61) gives: % 150.97/22.11 | | | | | % 150.97/22.11 | | | | | Case 1: % 150.97/22.11 | | | | | | % 150.97/22.11 | | | | | | (193) all_56_1 = e3 % 150.97/22.11 | | | | | | % 150.97/22.11 | | | | | | REF_CLOSE: (177), (180), (193) are inconsistent by sub-proof #428. % 150.97/22.11 | | | | | | % 150.97/22.11 | | | | | Case 2: % 150.97/22.11 | | | | | | % 150.97/22.11 | | | | | | (194) all_56_11 = e2 | all_56_21 = e1 | all_56_31 = e0 % 150.97/22.11 | | | | | | % 150.97/22.11 | | | | | | REF_CLOSE: (1), (3), (4), (5), (16), (17), (19), (24), (26), (27), % 150.97/22.11 | | | | | | (33), (36), (38), (40), (43), (45), (48), (58), (62), % 150.97/22.11 | | | | | | (65), (69), (74), (77), (81), (84), (183), (192), (194) % 150.97/22.11 | | | | | | are inconsistent by sub-proof #165. % 150.97/22.11 | | | | | | % 150.97/22.11 | | | | | End of split % 150.97/22.11 | | | | | % 150.97/22.11 | | | | Case 2: % 150.97/22.11 | | | | | % 150.97/22.11 | | | | | (195) all_58_8 = e2 | all_58_14 = e2 % 150.97/22.11 | | | | | % 150.97/22.11 | | | | | REF_CLOSE: (43), (49), (66), (82), (195) are inconsistent by sub-proof % 150.97/22.11 | | | | | #478. % 150.97/22.11 | | | | | % 150.97/22.11 | | | | End of split % 150.97/22.11 | | | | % 150.97/22.11 | | | End of split % 150.97/22.11 | | | % 150.97/22.11 | | End of split % 150.97/22.11 | | % 150.97/22.11 | Case 2: % 150.97/22.11 | | % 150.97/22.11 | | (196) all_56_7 = e3 % 150.97/22.11 | | (197) all_56_1 = e0 % 150.97/22.11 | | % 150.97/22.11 | | COMBINE_EQS: (21), (197) imply: % 150.97/22.11 | | (198) all_10_2 = e0 % 150.97/22.11 | | % 150.97/22.11 | | COMBINE_EQS: (42), (196) imply: % 150.97/22.11 | | (199) all_52_12 = e3 % 150.97/22.11 | | % 150.97/22.11 | | REDUCE: (73), (199) imply: % 150.97/22.11 | | (200) ~ (all_52_4 = e3) % 150.97/22.11 | | % 150.97/22.11 | | REDUCE: (79), (198) imply: % 150.97/22.11 | | (201) ~ (all_52_4 = e0) % 150.97/22.11 | | % 150.97/22.11 | | REDUCE: (83), (198), (199) imply: % 150.97/22.11 | | (202) ~ (e3 = e0) % 150.97/22.11 | | % 150.97/22.11 | | REDUCE: (10), (199) imply: % 150.97/22.11 | | (203) ~ (e3 = e2) % 150.97/22.11 | | % 150.97/22.11 | | REDUCE: (70), (198) imply: % 150.97/22.11 | | (204) op(e0, e0) = all_10_1 % 150.97/22.11 | | % 150.97/22.11 | | BETA: splitting (59) gives: % 150.97/22.11 | | % 150.97/22.11 | | Case 1: % 150.97/22.11 | | | % 150.97/22.11 | | | (205) all_58_1 = e3 % 150.97/22.11 | | | % 150.97/22.11 | | | COMBINE_EQS: (28), (205) imply: % 150.97/22.11 | | | (206) all_52_4 = e3 % 150.97/22.11 | | | % 150.97/22.11 | | | REDUCE: (200), (206) imply: % 150.97/22.11 | | | (207) $false % 150.97/22.11 | | | % 150.97/22.11 | | | CLOSE: (207) is inconsistent. % 150.97/22.11 | | | % 150.97/22.11 | | Case 2: % 150.97/22.11 | | | % 150.97/22.11 | | | (208) all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3 % 150.97/22.11 | | | % 150.97/22.11 | | | BETA: splitting (208) gives: % 150.97/22.11 | | | % 150.97/22.11 | | | Case 1: % 150.97/22.11 | | | | % 150.97/22.11 | | | | (209) all_58_3 = e3 % 150.97/22.11 | | | | % 150.97/22.11 | | | | COMBINE_EQS: (13), (209) imply: % 150.97/22.11 | | | | (210) all_4_1 = e3 % 150.97/22.11 | | | | % 150.97/22.11 | | | | REDUCE: (5), (210) imply: % 150.97/22.11 | | | | (211) $false % 150.97/22.11 | | | | % 150.97/22.11 | | | | CLOSE: (211) is inconsistent. % 150.97/22.11 | | | | % 150.97/22.11 | | | Case 2: % 150.97/22.11 | | | | % 150.97/22.11 | | | | (212) all_58_7 = e3 | all_58_13 = e3 % 150.97/22.11 | | | | % 150.97/22.11 | | | | BETA: splitting (212) gives: % 150.97/22.11 | | | | % 150.97/22.11 | | | | Case 1: % 150.97/22.11 | | | | | % 150.97/22.11 | | | | | (213) all_58_7 = e3 % 150.97/22.11 | | | | | % 150.97/22.11 | | | | | COMBINE_EQS: (68), (213) imply: % 150.97/22.11 | | | | | (214) all_52_6 = e3 % 150.97/22.11 | | | | | % 150.97/22.11 | | | | | REDUCE: (31), (214) imply: % 150.97/22.11 | | | | | (215) ~ (all_4_1 = e3) % 150.97/22.11 | | | | | % 150.97/22.11 | | | | | BETA: splitting (35) gives: % 150.97/22.11 | | | | | % 150.97/22.11 | | | | | Case 1: % 150.97/22.11 | | | | | | % 150.97/22.11 | | | | | | (216) all_58_6 = e2 % 150.97/22.11 | | | | | | % 150.97/22.11 | | | | | | COMBINE_EQS: (2), (216) imply: % 150.97/22.11 | | | | | | (217) all_52_2 = e2 % 150.97/22.11 | | | | | | % 150.97/22.11 | | | | | | SIMP: (217) implies: % 150.97/22.11 | | | | | | (218) all_52_2 = e2 % 150.97/22.11 | | | | | | % 150.97/22.11 | | | | | | REDUCE: (71), (218) imply: % 150.97/22.11 | | | | | | (219) op(e3, e2) = all_56_16 % 150.97/22.11 | | | | | | % 150.97/22.11 | | | | | | GROUND_INST: instantiating (36) with e2, all_10_1, e0, e0, % 150.97/22.11 | | | | | | simplifying with (55), (204) gives: % 150.97/22.11 | | | | | | (220) all_10_1 = e2 % 150.97/22.11 | | | | | | % 150.97/22.11 | | | | | | GROUND_INST: instantiating (36) with all_52_4, all_56_16, e2, e3, % 150.97/22.11 | | | | | | simplifying with (63), (219) gives: % 150.97/22.11 | | | | | | (221) all_56_16 = all_52_4 % 150.97/22.11 | | | | | | % 150.97/22.11 | | | | | | REDUCE: (32), (220) imply: % 150.97/22.11 | | | | | | (222) op(e3, e2) = e2 % 150.97/22.11 | | | | | | % 150.97/22.11 | | | | | | GROUND_INST: instantiating (36) with all_52_4, e2, e2, e3, % 150.97/22.11 | | | | | | simplifying with (63), (222) gives: % 150.97/22.11 | | | | | | (223) all_52_4 = e2 % 150.97/22.11 | | | | | | % 150.97/22.11 | | | | | | REDUCE: (15), (223) imply: % 150.97/22.11 | | | | | | (224) ~ (all_4_1 = e2) % 150.97/22.11 | | | | | | % 150.97/22.11 | | | | | | SIMP: (224) implies: % 150.97/22.11 | | | | | | (225) ~ (all_4_1 = e2) % 150.97/22.11 | | | | | | % 150.97/22.11 | | | | | | REDUCE: (201), (223) imply: % 150.97/22.11 | | | | | | (226) ~ (e2 = e0) % 150.97/22.11 | | | | | | % 150.97/22.11 | | | | | | BETA: splitting (61) gives: % 150.97/22.11 | | | | | | % 150.97/22.11 | | | | | | Case 1: % 150.97/22.11 | | | | | | | % 150.97/22.11 | | | | | | | (227) all_56_1 = e3 % 150.97/22.11 | | | | | | | % 150.97/22.11 | | | | | | | COMBINE_EQS: (197), (227) imply: % 150.97/22.11 | | | | | | | (228) e3 = e0 % 150.97/22.11 | | | | | | | % 150.97/22.11 | | | | | | | SIMP: (228) implies: % 150.97/22.11 | | | | | | | (229) e3 = e0 % 150.97/22.11 | | | | | | | % 150.97/22.11 | | | | | | | REDUCE: (202), (229) imply: % 150.97/22.11 | | | | | | | (230) $false % 150.97/22.11 | | | | | | | % 150.97/22.11 | | | | | | | CLOSE: (230) is inconsistent. % 150.97/22.11 | | | | | | | % 150.97/22.11 | | | | | | Case 2: % 150.97/22.11 | | | | | | | % 150.97/22.11 | | | | | | | (231) all_56_11 = e2 | all_56_21 = e1 | all_56_31 = e0 % 150.97/22.11 | | | | | | | % 150.97/22.11 | | | | | | | REF_CLOSE: (1), (3), (4), (5), (16), (17), (19), (24), (26), (27), % 150.97/22.11 | | | | | | | (33), (36), (38), (40), (43), (45), (48), (58), (62), % 150.97/22.11 | | | | | | | (65), (69), (74), (77), (81), (84), (225), (226), (231) % 150.97/22.11 | | | | | | | are inconsistent by sub-proof #165. % 150.97/22.11 | | | | | | | % 150.97/22.11 | | | | | | End of split % 150.97/22.11 | | | | | | % 150.97/22.11 | | | | | Case 2: % 150.97/22.11 | | | | | | % 150.97/22.11 | | | | | | (232) all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2 % 150.97/22.11 | | | | | | % 150.97/22.11 | | | | | | REF_CLOSE: (20), (49), (58), (66), (203), (213), (232) are % 150.97/22.11 | | | | | | inconsistent by sub-proof #168. % 150.97/22.11 | | | | | | % 150.97/22.11 | | | | | End of split % 150.97/22.11 | | | | | % 150.97/22.11 | | | | Case 2: % 150.97/22.11 | | | | | % 150.97/22.11 | | | | | (233) all_58_13 = e3 % 150.97/22.11 | | | | | % 150.97/22.11 | | | | | COMBINE_EQS: (34), (233) imply: % 150.97/22.11 | | | | | (234) e3 = e0 % 150.97/22.11 | | | | | % 150.97/22.11 | | | | | REDUCE: (202), (234) imply: % 150.97/22.11 | | | | | (235) $false % 150.97/22.11 | | | | | % 150.97/22.11 | | | | | CLOSE: (235) is inconsistent. % 150.97/22.11 | | | | | % 150.97/22.11 | | | | End of split % 150.97/22.11 | | | | % 150.97/22.11 | | | End of split % 150.97/22.11 | | | % 150.97/22.11 | | End of split % 150.97/22.11 | | % 150.97/22.11 | End of split % 150.97/22.11 | % 150.97/22.11 End of proof % 150.97/22.11 % 150.97/22.11 Sub-proof #165 shows that the following formulas are inconsistent: % 150.97/22.11 ---------------------------------------------------------------- % 150.97/22.11 (1) ~ (all_52_11 = all_6_2) % 150.97/22.11 (2) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0 % 150.97/22.11 (3) ~ (all_4_1 = e0) % 150.97/22.11 (4) ~ (all_4_1 = e3) % 150.97/22.11 (5) ~ (all_52_11 = e0) % 150.97/22.11 (6) all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1 % 150.97/22.11 (7) ~ (all_4_1 = e2) % 150.97/22.11 (8) all_56_21 = all_6_2 % 150.97/22.11 (9) all_58_9 = all_52_12 % 150.97/22.11 (10) op(e0, all_52_12) = all_56_6 % 150.97/22.11 (11) all_54_14 = all_52_11 % 150.97/22.11 (12) all_56_11 = e2 | all_56_21 = e1 | all_56_31 = e0 % 150.97/22.11 (13) ~ (all_52_13 = all_4_1) % 150.97/22.11 (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 150.97/22.11 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 150.97/22.11 (15) all_56_11 = all_4_1 % 150.97/22.11 (16) op(e0, all_4_1) = all_4_0 % 150.97/22.12 (17) ~ (all_52_11 = e2) % 150.97/22.12 (18) op(e0, e1) = all_52_11 % 150.97/22.12 (19) ~ (all_4_2 = e1) % 150.97/22.12 (20) all_58_11 = all_52_14 % 150.97/22.12 (21) all_54_5 = all_4_1 % 150.97/22.12 (22) all_58_15 = all_4_2 % 150.97/22.12 (23) all_58_10 = all_52_13 % 150.97/22.12 (24) all_56_31 = e2 % 150.97/22.12 (25) ~ (all_52_14 = all_6_2) % 150.97/22.12 (26) ~ (e2 = e0) % 150.97/22.12 (27) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 150.97/22.12 (28) ~ (all_4_0 = e3) % 150.97/22.12 % 150.97/22.12 Begin of proof % 150.97/22.12 | % 150.97/22.12 | BETA: splitting (12) gives: % 150.97/22.12 | % 150.97/22.12 | Case 1: % 150.97/22.12 | | % 150.97/22.12 | | (29) all_56_11 = e2 % 150.97/22.12 | | % 150.97/22.12 | | COMBINE_EQS: (15), (29) imply: % 150.97/22.12 | | (30) all_4_1 = e2 % 150.97/22.12 | | % 150.97/22.12 | | REDUCE: (7), (30) imply: % 150.97/22.12 | | (31) $false % 150.97/22.12 | | % 150.97/22.12 | | CLOSE: (31) is inconsistent. % 150.97/22.12 | | % 150.97/22.12 | Case 2: % 150.97/22.12 | | % 150.97/22.12 | | (32) ~ (all_56_11 = e2) % 150.97/22.12 | | (33) all_56_21 = e1 | all_56_31 = e0 % 150.97/22.12 | | % 150.97/22.12 | | BETA: splitting (33) gives: % 150.97/22.12 | | % 150.97/22.12 | | Case 1: % 150.97/22.12 | | | % 150.97/22.12 | | | (34) all_56_21 = e1 % 150.97/22.12 | | | % 150.97/22.12 | | | COMBINE_EQS: (8), (34) imply: % 150.97/22.12 | | | (35) all_6_2 = e1 % 150.97/22.12 | | | % 150.97/22.12 | | | SIMP: (35) implies: % 150.97/22.12 | | | (36) all_6_2 = e1 % 150.97/22.12 | | | % 150.97/22.12 | | | REDUCE: (1), (36) imply: % 150.97/22.12 | | | (37) ~ (all_52_11 = e1) % 150.97/22.12 | | | % 150.97/22.12 | | | REDUCE: (25), (36) imply: % 150.97/22.12 | | | (38) ~ (all_52_14 = e1) % 150.97/22.12 | | | % 150.97/22.12 | | | BETA: splitting (2) gives: % 150.97/22.12 | | | % 150.97/22.12 | | | Case 1: % 150.97/22.12 | | | | % 150.97/22.12 | | | | (39) all_54_14 = e3 % 150.97/22.12 | | | | % 150.97/22.12 | | | | COMBINE_EQS: (11), (39) imply: % 150.97/22.12 | | | | (40) all_52_11 = e3 % 150.97/22.12 | | | | % 150.97/22.12 | | | | SIMP: (40) implies: % 150.97/22.12 | | | | (41) all_52_11 = e3 % 150.97/22.12 | | | | % 150.97/22.12 | | | | REDUCE: (18), (41) imply: % 150.97/22.12 | | | | (42) op(e0, e1) = e3 % 150.97/22.12 | | | | % 150.97/22.12 | | | | REF_CLOSE: (3), (4), (6), (7), (9), (10), (13), (14), (16), (19), (20), % 150.97/22.12 | | | | (21), (22), (23), (27), (28), (38), (42) are inconsistent by % 150.97/22.12 | | | | sub-proof #167. % 150.97/22.12 | | | | % 150.97/22.12 | | | Case 2: % 150.97/22.12 | | | | % 150.97/22.12 | | | | (43) all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0 % 150.97/22.12 | | | | % 150.97/22.12 | | | | REF_CLOSE: (5), (11), (17), (37), (43) are inconsistent by sub-proof % 150.97/22.12 | | | | #580. % 150.97/22.12 | | | | % 150.97/22.12 | | | End of split % 150.97/22.12 | | | % 150.97/22.12 | | Case 2: % 150.97/22.12 | | | % 150.97/22.12 | | | (44) all_56_31 = e0 % 150.97/22.12 | | | % 150.97/22.12 | | | REF_CLOSE: (24), (26), (44) are inconsistent by sub-proof #166. % 150.97/22.12 | | | % 150.97/22.12 | | End of split % 150.97/22.12 | | % 150.97/22.12 | End of split % 150.97/22.12 | % 150.97/22.12 End of proof % 150.97/22.12 % 150.97/22.12 Sub-proof #166 shows that the following formulas are inconsistent: % 150.97/22.12 ---------------------------------------------------------------- % 150.97/22.12 (1) all_56_31 = e2 % 150.97/22.12 (2) all_56_31 = e0 % 150.97/22.12 (3) ~ (e2 = e0) % 150.97/22.12 % 150.97/22.12 Begin of proof % 150.97/22.12 | % 150.97/22.12 | COMBINE_EQS: (1), (2) imply: % 150.97/22.12 | (4) e2 = e0 % 150.97/22.12 | % 150.97/22.12 | SIMP: (4) implies: % 150.97/22.12 | (5) e2 = e0 % 150.97/22.12 | % 150.97/22.12 | REDUCE: (3), (5) imply: % 150.97/22.12 | (6) $false % 150.97/22.12 | % 150.97/22.12 | CLOSE: (6) is inconsistent. % 150.97/22.12 | % 150.97/22.12 End of proof % 150.97/22.12 % 150.97/22.12 Sub-proof #167 shows that the following formulas are inconsistent: % 150.97/22.12 ---------------------------------------------------------------- % 150.97/22.12 (1) ~ (all_4_1 = e0) % 150.97/22.12 (2) ~ (all_4_1 = e3) % 150.97/22.12 (3) all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1 % 150.97/22.12 (4) ~ (all_4_1 = e2) % 150.97/22.12 (5) all_58_9 = all_52_12 % 150.97/22.12 (6) op(e0, all_52_12) = all_56_6 % 150.97/22.12 (7) ~ (all_52_13 = all_4_1) % 150.97/22.12 (8) op(e0, e1) = e3 % 150.97/22.12 (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 150.97/22.12 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 150.97/22.12 (10) ~ (all_52_14 = e1) % 150.97/22.12 (11) op(e0, all_4_1) = all_4_0 % 150.97/22.12 (12) ~ (all_4_2 = e1) % 150.97/22.12 (13) all_58_11 = all_52_14 % 150.97/22.12 (14) all_54_5 = all_4_1 % 150.97/22.12 (15) all_58_15 = all_4_2 % 150.97/22.12 (16) all_58_10 = all_52_13 % 150.97/22.12 (17) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 150.97/22.12 (18) ~ (all_4_0 = e3) % 150.97/22.12 % 150.97/22.12 Begin of proof % 150.97/22.12 | % 150.97/22.12 | BETA: splitting (17) gives: % 150.97/22.12 | % 150.97/22.12 | Case 1: % 150.97/22.12 | | % 150.97/22.12 | | (19) all_54_5 = e3 % 150.97/22.12 | | % 150.97/22.12 | | COMBINE_EQS: (14), (19) imply: % 150.97/22.12 | | (20) all_4_1 = e3 % 150.97/22.12 | | % 150.97/22.12 | | REDUCE: (2), (20) imply: % 150.97/22.12 | | (21) $false % 150.97/22.12 | | % 150.97/22.12 | | CLOSE: (21) is inconsistent. % 150.97/22.12 | | % 150.97/22.12 | Case 2: % 150.97/22.12 | | % 150.97/22.12 | | (22) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 150.97/22.12 | | % 150.97/22.12 | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13), % 150.97/22.12 | | (14), (15), (16), (18), (22) are inconsistent by sub-proof #585. % 150.97/22.12 | | % 150.97/22.12 | End of split % 150.97/22.12 | % 150.97/22.12 End of proof % 150.97/22.12 % 150.97/22.12 Sub-proof #168 shows that the following formulas are inconsistent: % 150.97/22.12 ---------------------------------------------------------------- % 150.97/22.12 (1) ~ (e3 = e2) % 150.97/22.12 (2) ~ (all_52_14 = e2) % 150.97/22.12 (3) all_58_8 = all_6_2 % 150.97/22.12 (4) all_58_11 = all_52_14 % 150.97/22.12 (5) ~ (all_6_2 = e2) % 150.97/22.12 (6) all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2 % 150.97/22.12 (7) all_58_7 = e3 % 150.97/22.12 % 150.97/22.12 Begin of proof % 150.97/22.12 | % 150.97/22.12 | BETA: splitting (6) gives: % 150.97/22.12 | % 150.97/22.12 | Case 1: % 150.97/22.12 | | % 150.97/22.12 | | (8) all_58_7 = e2 % 150.97/22.12 | | % 150.97/22.12 | | COMBINE_EQS: (7), (8) imply: % 150.97/22.12 | | (9) e3 = e2 % 150.97/22.12 | | % 150.97/22.12 | | REDUCE: (1), (9) imply: % 150.97/22.12 | | (10) $false % 150.97/22.12 | | % 150.97/22.12 | | CLOSE: (10) is inconsistent. % 150.97/22.12 | | % 150.97/22.12 | Case 2: % 150.97/22.12 | | % 150.97/22.12 | | (11) all_58_8 = e2 | all_58_11 = e2 % 150.97/22.12 | | % 150.97/22.12 | | REF_CLOSE: (2), (3), (4), (5), (11) are inconsistent by sub-proof #511. % 150.97/22.12 | | % 150.97/22.12 | End of split % 150.97/22.12 | % 150.97/22.12 End of proof % 150.97/22.12 % 150.97/22.12 Sub-proof #169 shows that the following formulas are inconsistent: % 150.97/22.12 ---------------------------------------------------------------- % 150.97/22.12 (1) all_10_1 = all_6_2 % 150.97/22.12 (2) all_54_10 = all_6_2 % 150.97/22.12 (3) ~ (all_6_2 = e3) % 150.97/22.12 (4) ~ (e3 = e2) % 150.97/22.12 (5) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 150.97/22.12 (6) op(e1, e1) = all_10_1 % 150.97/22.12 (7) op(e3, all_10_1) = e2 % 150.97/22.12 (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 150.97/22.12 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 150.97/22.12 (9) op(e3, e1) = all_56_0 % 150.97/22.12 (10) ~ (all_6_2 = e2) % 150.97/22.12 (11) op(e3, e1) = e3 % 150.97/22.12 (12) ~ (all_10_1 = e0) % 150.97/22.12 % 150.97/22.12 Begin of proof % 150.97/22.12 | % 150.97/22.12 | GROUND_INST: instantiating (8) with e3, all_56_0, e1, e3, simplifying with % 150.97/22.12 | (9), (11) gives: % 150.97/22.12 | (13) all_56_0 = e3 % 150.97/22.12 | % 150.97/22.12 | REDUCE: (1), (12) imply: % 150.97/22.12 | (14) ~ (all_6_2 = e0) % 150.97/22.12 | % 150.97/22.12 | REDUCE: (1), (6) imply: % 150.97/22.12 | (15) op(e1, e1) = all_6_2 % 150.97/22.12 | % 150.97/22.12 | BETA: splitting (5) gives: % 150.97/22.12 | % 150.97/22.12 | Case 1: % 150.97/22.12 | | % 150.97/22.12 | | (16) all_54_10 = e3 % 150.97/22.12 | | % 150.97/22.12 | | REF_CLOSE: (2), (3), (16) are inconsistent by sub-proof #736. % 150.97/22.12 | | % 150.97/22.12 | Case 2: % 150.97/22.12 | | % 150.97/22.12 | | (17) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 150.97/22.12 | | % 150.97/22.12 | | BETA: splitting (17) gives: % 150.97/22.12 | | % 150.97/22.12 | | Case 1: % 150.97/22.12 | | | % 150.97/22.12 | | | (18) all_54_10 = e2 % 150.97/22.12 | | | % 150.97/22.12 | | | REF_CLOSE: (2), (10), (18) are inconsistent by sub-proof #735. % 150.97/22.12 | | | % 150.97/22.12 | | Case 2: % 150.97/22.12 | | | % 150.97/22.12 | | | (19) all_54_10 = e1 | all_54_10 = e0 % 150.97/22.12 | | | % 150.97/22.12 | | | REF_CLOSE: (2), (4), (6), (7), (8), (9), (11), (14), (15), (19) are % 150.97/22.12 | | | inconsistent by sub-proof #170. % 150.97/22.12 | | | % 150.97/22.12 | | End of split % 150.97/22.12 | | % 150.97/22.12 | End of split % 150.97/22.12 | % 150.97/22.12 End of proof % 150.97/22.12 % 150.97/22.12 Sub-proof #170 shows that the following formulas are inconsistent: % 150.97/22.12 ---------------------------------------------------------------- % 150.97/22.12 (1) all_54_10 = all_6_2 % 150.97/22.12 (2) ~ (e3 = e2) % 150.97/22.12 (3) op(e1, e1) = all_10_1 % 150.97/22.12 (4) op(e3, all_10_1) = e2 % 150.97/22.12 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 150.97/22.12 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 150.97/22.12 (6) ~ (all_6_2 = e0) % 150.97/22.12 (7) op(e3, e1) = all_56_0 % 150.97/22.12 (8) op(e1, e1) = all_6_2 % 150.97/22.12 (9) op(e3, e1) = e3 % 150.97/22.12 (10) all_54_10 = e1 | all_54_10 = e0 % 150.97/22.12 % 150.97/22.12 Begin of proof % 150.97/22.12 | % 150.97/22.12 | BETA: splitting (10) gives: % 150.97/22.12 | % 150.97/22.12 | Case 1: % 150.97/22.12 | | % 150.97/22.12 | | (11) all_54_10 = e1 % 150.97/22.12 | | % 150.97/22.12 | | COMBINE_EQS: (1), (11) imply: % 150.97/22.12 | | (12) all_6_2 = e1 % 150.97/22.12 | | % 150.97/22.12 | | SIMP: (12) implies: % 150.97/22.12 | | (13) all_6_2 = e1 % 150.97/22.12 | | % 150.97/22.12 | | REDUCE: (8), (13) imply: % 150.97/22.12 | | (14) op(e1, e1) = e1 % 150.97/22.12 | | % 150.97/22.12 | | REF_CLOSE: (2), (3), (4), (5), (7), (9), (14) are inconsistent by sub-proof % 150.97/22.12 | | #171. % 150.97/22.12 | | % 150.97/22.12 | Case 2: % 150.97/22.12 | | % 150.97/22.12 | | (15) all_54_10 = e0 % 150.97/22.12 | | % 150.97/22.12 | | REF_CLOSE: (1), (6), (15) are inconsistent by sub-proof #705. % 150.97/22.12 | | % 150.97/22.12 | End of split % 150.97/22.12 | % 150.97/22.12 End of proof % 150.97/22.12 % 150.97/22.12 Sub-proof #171 shows that the following formulas are inconsistent: % 150.97/22.12 ---------------------------------------------------------------- % 150.97/22.12 (1) ~ (e3 = e2) % 150.97/22.12 (2) op(e1, e1) = all_10_1 % 150.97/22.12 (3) op(e3, all_10_1) = e2 % 150.97/22.12 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 150.97/22.12 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 150.97/22.12 (5) op(e3, e1) = all_56_0 % 150.97/22.12 (6) op(e3, e1) = e3 % 150.97/22.12 (7) op(e1, e1) = e1 % 150.97/22.12 % 150.97/22.12 Begin of proof % 150.97/22.12 | % 150.97/22.12 | GROUND_INST: instantiating (4) with e1, all_10_1, e1, e1, simplifying with % 150.97/22.12 | (2), (7) gives: % 150.97/22.12 | (8) all_10_1 = e1 % 150.97/22.12 | % 150.97/22.12 | GROUND_INST: instantiating (4) with e3, all_56_0, e1, e3, simplifying with % 150.97/22.12 | (5), (6) gives: % 150.97/22.12 | (9) all_56_0 = e3 % 150.97/22.12 | % 150.97/22.12 | REDUCE: (3), (8) imply: % 150.97/22.12 | (10) op(e3, e1) = e2 % 150.97/22.12 | % 150.97/22.12 | GROUND_INST: instantiating (4) with e3, e2, e1, e3, simplifying with (6), (10) % 150.97/22.12 | gives: % 150.97/22.12 | (11) e3 = e2 % 150.97/22.12 | % 150.97/22.12 | REDUCE: (1), (11) imply: % 150.97/22.12 | (12) $false % 150.97/22.12 | % 150.97/22.12 | CLOSE: (12) is inconsistent. % 150.97/22.12 | % 150.97/22.12 End of proof % 150.97/22.12 % 150.97/22.12 Sub-proof #172 shows that the following formulas are inconsistent: % 150.97/22.12 ---------------------------------------------------------------- % 150.97/22.12 (1) all_58_5 = e1 % 150.97/22.12 (2) all_58_5 = e0 % 150.97/22.12 (3) ~ (e1 = e0) % 150.97/22.12 % 150.97/22.12 Begin of proof % 150.97/22.12 | % 150.97/22.12 | COMBINE_EQS: (1), (2) imply: % 150.97/22.12 | (4) e1 = e0 % 150.97/22.12 | % 150.97/22.12 | SIMP: (4) implies: % 150.97/22.12 | (5) e1 = e0 % 150.97/22.12 | % 150.97/22.12 | REDUCE: (3), (5) imply: % 150.97/22.12 | (6) $false % 150.97/22.12 | % 150.97/22.12 | CLOSE: (6) is inconsistent. % 150.97/22.12 | % 150.97/22.12 End of proof % 150.97/22.12 % 150.97/22.12 Sub-proof #173 shows that the following formulas are inconsistent: % 150.97/22.12 ---------------------------------------------------------------- % 150.97/22.12 (1) all_56_11 = all_8_2 % 150.97/22.12 (2) all_52_6 = e1 % 150.97/22.12 (3) ~ (all_8_1 = e1) % 150.97/22.12 (4) ~ (all_6_1 = e2) % 150.97/22.12 (5) ~ (all_6_2 = e3) % 150.97/22.12 (6) ~ (all_8_1 = e3) % 150.97/22.12 (7) op(e0, e0) = all_4_2 % 150.97/22.12 (8) all_58_4 = all_52_8 % 150.97/22.12 (9) all_54_5 = all_8_2 % 150.97/22.12 (10) ~ (all_6_1 = e3) % 150.97/22.12 (11) all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1 % 150.97/22.12 (12) ~ (all_52_7 = all_8_2) % 150.97/22.12 (13) all_56_1 = all_10_2 % 150.97/22.12 (14) all_56_27 = all_52_7 % 150.97/22.12 (15) ~ (all_52_6 = e3) % 150.97/22.12 (16) all_58_9 = all_52_12 % 150.97/22.12 (17) op(e1, e0) = all_52_14 % 150.97/22.12 (18) all_58_1 = all_52_4 % 150.97/22.12 (19) all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0 % 150.97/22.12 (20) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 150.97/22.12 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 150.97/22.12 (21) ~ (all_52_14 = e1) % 150.97/22.12 (22) all_56_7 = all_52_12 % 150.97/22.12 (23) ~ (all_6_0 = e3) % 150.97/22.12 (24) ~ (all_56_1 = e0) | all_56_7 = e3 % 150.97/22.12 (25) op(e1, all_6_1) = all_6_0 % 150.97/22.12 (26) op(e1, all_52_8) = all_56_4 % 150.97/22.12 (27) all_58_11 = all_52_14 % 150.97/22.12 (28) op(all_6_2, all_6_2) = all_6_1 % 150.97/22.12 (29) ~ (all_52_6 = all_8_2) % 150.97/22.12 (30) all_58_15 = all_4_2 % 150.97/22.12 (31) all_6_2 = e2 % 150.97/22.12 (32) all_58_10 = all_52_13 % 150.97/22.12 (33) ~ (all_56_11 = e0) | all_56_15 = e2 % 150.97/22.12 (34) all_58_0 = all_10_2 % 150.97/22.12 (35) ~ (all_56_31 = e2) | all_56_27 = e0 % 150.97/22.12 (36) op(e2, e2) = all_8_2 % 150.97/22.12 (37) ~ (all_52_6 = all_6_2) % 150.97/22.12 (38) all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3 % 150.97/22.12 (39) ~ (all_52_4 = all_8_2) % 150.97/22.12 (40) op(all_8_2, all_8_2) = all_8_1 % 150.97/22.12 (41) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 150.97/22.12 (42) all_56_15 = all_52_13 % 150.97/22.12 % 150.97/22.12 Begin of proof % 150.97/22.12 | % 150.97/22.12 | REDUCE: (2), (29) imply: % 150.97/22.12 | (43) ~ (all_8_2 = e1) % 150.97/22.12 | % 150.97/22.12 | SIMP: (43) implies: % 150.97/22.12 | (44) ~ (all_8_2 = e1) % 150.97/22.12 | % 150.97/22.12 | REDUCE: (2), (31), (37) imply: % 150.97/22.12 | (45) ~ (e2 = e1) % 150.97/22.12 | % 150.97/22.12 | SIMP: (45) implies: % 150.97/22.12 | (46) ~ (e2 = e1) % 150.97/22.12 | % 150.97/22.12 | REDUCE: (2), (15) imply: % 150.97/22.12 | (47) ~ (e3 = e1) % 150.97/22.12 | % 150.97/22.12 | SIMP: (47) implies: % 150.97/22.12 | (48) ~ (e3 = e1) % 150.97/22.12 | % 150.97/22.12 | REDUCE: (5), (31) imply: % 150.97/22.12 | (49) ~ (e3 = e2) % 150.97/22.12 | % 150.97/22.12 | SIMP: (49) implies: % 150.97/22.12 | (50) ~ (e3 = e2) % 150.97/22.12 | % 150.97/22.12 | REDUCE: (28), (31) imply: % 150.97/22.12 | (51) op(e2, e2) = all_6_1 % 150.97/22.12 | % 150.97/22.12 | REF_CLOSE: (1), (3), (4), (6), (7), (8), (9), (10), (11), (12), (13), (14), % 150.97/22.12 | (16), (17), (18), (19), (20), (21), (22), (23), (24), (25), (26), % 150.97/22.12 | (27), (30), (32), (33), (34), (35), (36), (38), (39), (40), (41), % 150.97/22.12 | (42), (44), (46), (48), (50), (51) are inconsistent by sub-proof % 150.97/22.12 | #222. % 150.97/22.12 | % 150.97/22.12 End of proof % 150.97/22.12 % 150.97/22.12 Sub-proof #174 shows that the following formulas are inconsistent: % 150.97/22.12 ---------------------------------------------------------------- % 150.97/22.12 (1) all_58_6 = all_52_2 % 150.97/22.12 (2) all_58_7 = e0 | all_58_13 = e0 % 150.97/22.12 (3) all_58_13 = all_52_7 % 150.97/22.12 (4) ~ (all_52_2 = all_52_6) % 150.97/22.12 (5) ~ (all_52_3 = e0) % 150.97/22.12 (6) all_58_0 = e2 % 150.97/22.12 (7) ~ (all_52_1 = e0) % 150.97/22.12 (8) all_58_2 = all_52_1 % 150.97/22.12 (9) all_58_7 = all_52_6 % 150.97/22.12 (10) ~ (e2 = e0) % 150.97/22.12 (11) all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0 % 150.97/22.12 (12) ~ (all_52_7 = e0) % 150.97/22.12 (13) all_58_12 = all_52_3 % 150.97/22.12 % 150.97/22.12 Begin of proof % 150.97/22.12 | % 150.97/22.12 | BETA: splitting (2) gives: % 150.97/22.12 | % 150.97/22.12 | Case 1: % 150.97/22.12 | | % 150.97/22.12 | | (14) all_58_7 = e0 % 150.97/22.12 | | % 150.97/22.12 | | COMBINE_EQS: (9), (14) imply: % 150.97/22.12 | | (15) all_52_6 = e0 % 150.97/22.12 | | % 150.97/22.12 | | REDUCE: (4), (15) imply: % 150.97/22.12 | | (16) ~ (all_52_2 = e0) % 150.97/22.12 | | % 150.97/22.12 | | REF_CLOSE: (1), (5), (6), (7), (8), (10), (11), (13), (16) are inconsistent % 150.97/22.12 | | by sub-proof #613. % 150.97/22.12 | | % 150.97/22.12 | Case 2: % 150.97/22.12 | | % 150.97/22.12 | | (17) all_58_13 = e0 % 150.97/22.12 | | % 150.97/22.12 | | REF_CLOSE: (3), (12), (17) are inconsistent by sub-proof #605. % 150.97/22.12 | | % 150.97/22.12 | End of split % 150.97/22.12 | % 150.97/22.12 End of proof % 150.97/22.12 % 150.97/22.12 Sub-proof #175 shows that the following formulas are inconsistent: % 150.97/22.12 ---------------------------------------------------------------- % 150.97/22.12 (1) ~ (e3 = e2) % 150.97/22.12 (2) op(e3, all_10_1) = e2 % 150.97/22.12 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 150.97/22.12 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 150.97/22.12 (4) op(e3, e3) = all_56_0 % 150.97/22.12 (5) all_10_1 = e3 % 150.97/22.12 (6) op(e3, e3) = all_10_1 % 150.97/22.12 % 150.97/22.12 Begin of proof % 150.97/22.12 | % 150.97/22.12 | REDUCE: (2), (5) imply: % 150.97/22.12 | (7) op(e3, e3) = e2 % 150.97/22.12 | % 150.97/22.12 | REDUCE: (5), (6) imply: % 150.97/22.12 | (8) op(e3, e3) = e3 % 150.97/22.12 | % 150.97/22.12 | REF_CLOSE: (1), (3), (4), (6), (7), (8) are inconsistent by sub-proof #415. % 150.97/22.12 | % 150.97/22.12 End of proof % 150.97/22.12 % 150.97/22.12 Sub-proof #176 shows that the following formulas are inconsistent: % 150.97/22.12 ---------------------------------------------------------------- % 150.97/22.12 (1) all_56_11 = all_8_2 % 150.97/22.12 (2) ~ (all_56_11 = e1) | all_56_13 = e2 % 150.97/22.12 (3) ~ (all_52_11 = all_6_2) % 150.97/22.12 (4) all_56_25 = all_52_3 % 150.97/22.12 (5) ~ (all_52_7 = all_52_11) % 150.97/22.12 (6) all_14_2 = all_8_2 % 150.97/22.12 (7) op(e2, all_8_1) = all_8_0 % 150.97/22.12 (8) ~ (all_8_1 = e1) % 150.97/22.12 (9) ~ (all_52_1 = all_52_9) % 150.97/22.12 (10) ~ (all_56_31 = e1) | all_56_29 = e0 % 150.97/22.12 (11) all_54_10 = all_6_2 % 150.97/22.12 (12) ~ (all_6_1 = e2) % 150.97/22.12 (13) all_12_2 = all_4_2 % 150.97/22.12 (14) ~ (all_52_13 = all_8_2) % 150.97/22.12 (15) ~ (all_56_21 = e2) | all_56_19 = e1 % 150.97/22.12 (16) all_54_0 = all_10_2 % 150.97/22.12 (17) all_54_4 = all_52_1 % 150.97/22.12 (18) op(e0, e0) = all_4_2 % 150.97/22.12 (19) all_54_5 = all_8_2 % 150.97/22.12 (20) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 150.97/22.12 (21) all_54_15 = all_4_2 % 150.97/22.12 (22) all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1 % 150.97/22.12 (23) all_42_1 = all_8_1 % 150.97/22.12 (24) all_56_21 = all_6_2 % 150.97/22.12 (25) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 150.97/22.12 (26) ~ (all_52_7 = all_8_2) % 150.97/22.12 (27) all_56_1 = all_10_2 % 150.97/22.12 (28) all_56_27 = all_52_7 % 150.97/22.12 (29) all_56_17 = all_52_2 % 150.97/22.12 (30) all_58_9 = all_52_12 % 150.97/22.12 (31) all_14_1 = all_8_1 % 150.97/22.12 (32) all_58_13 = all_52_7 % 150.97/22.12 (33) op(e2, all_8_2) = all_56_10 % 150.97/22.12 (34) op(e3, e3) = all_10_2 % 150.97/22.12 (35) all_42_2 = all_8_2 % 150.97/22.12 (36) ~ (all_56_21 = e3) | all_56_17 = e1 % 150.97/22.12 (37) all_14_0 = e1 % 150.97/22.12 (38) ~ (all_52_1 = all_8_2) % 150.97/22.12 (39) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 150.97/22.12 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 150.97/22.12 (40) ~ (all_34_0 = e2) | ~ (all_34_1 = e3) | ~ (all_34_2 = e1) % 150.97/22.12 (41) all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0 % 150.97/22.12 (42) ~ (all_52_3 = all_52_7) % 150.97/22.12 (43) ~ (all_56_11 = e3) | all_56_9 = e2 % 150.97/22.12 (44) op(e0, all_4_1) = e2 % 150.97/22.12 (45) all_56_13 = all_52_9 % 150.97/22.12 (46) op(e0, e1) = all_52_11 % 150.97/22.12 (47) ~ (all_52_1 = all_52_13) % 150.97/22.12 (48) ~ (all_52_7 = all_4_2) % 150.97/22.12 (49) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0 % 150.97/22.12 (50) op(e1, e3) = all_52_2 % 150.97/22.12 (51) all_36_1 = all_6_1 % 150.97/22.12 (52) ~ (all_42_0 = e1) | ~ (all_42_1 = e0) | ~ (all_42_2 = e3) % 150.97/22.12 (53) all_42_0 = all_8_0 % 150.97/22.12 (54) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0 % 150.97/22.12 (55) ~ (all_12_1 = e1) | ~ (all_12_2 = e3) % 150.97/22.12 (56) all_34_1 = all_4_1 % 150.97/22.12 (57) ~ (e2 = e1) % 150.97/22.12 (58) ~ (all_14_1 = e3) | ~ (all_14_2 = e0) % 150.97/22.12 (59) op(e1, all_6_1) = all_6_0 % 150.97/22.12 (60) op(all_4_2, all_4_2) = all_4_1 % 150.97/22.12 (61) ~ (all_36_0 = e0) | ~ (all_36_1 = e3) | ~ (all_36_2 = e2) % 150.97/22.12 (62) ~ (all_52_1 = all_52_3) % 150.97/22.12 (63) all_56_31 = all_4_2 % 150.97/22.12 (64) all_58_11 = all_52_14 % 150.97/22.12 (65) ~ (all_52_2 = all_52_14) % 150.97/22.12 (66) op(all_6_2, all_6_2) = all_6_1 % 150.97/22.12 (67) all_56_1 = e3 | all_56_11 = e2 | all_56_21 = e1 | all_56_31 = e0 % 150.97/22.12 (68) ~ (all_52_13 = all_4_2) % 150.97/22.12 (69) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0 % 150.97/22.12 (70) all_54_13 = all_52_7 % 150.97/22.12 (71) op(e1, e1) = all_6_2 % 150.97/22.12 (72) ~ (all_52_6 = all_8_2) % 150.97/22.12 (73) all_58_15 = all_4_2 % 150.97/22.12 (74) all_56_29 = all_52_11 % 150.97/22.12 (75) all_58_2 = all_52_1 % 150.97/22.12 (76) ~ (all_52_9 = all_6_2) % 150.97/22.12 (77) all_58_10 = all_52_13 % 150.97/22.12 (78) ~ (all_56_11 = e0) | all_56_15 = e2 % 150.97/22.12 (79) op(e1, all_6_2) = all_56_20 % 150.97/22.12 (80) all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1 % 150.97/22.12 (81) op(e2, e3) = all_52_1 % 150.97/22.12 (82) all_14_0 = all_8_0 % 150.97/22.12 (83) ~ (all_56_31 = e2) | all_56_27 = e0 % 150.97/22.12 (84) all_34_0 = e2 % 150.97/22.12 (85) op(e2, e2) = all_8_2 % 150.97/22.12 (86) op(e2, e0) = all_52_13 % 150.97/22.12 (87) ~ (all_52_2 = all_6_2) % 150.97/22.12 (88) ~ (all_52_1 = all_52_2) % 150.97/22.12 (89) ~ (all_56_21 = e0) | all_56_23 = e1 % 150.97/22.12 (90) op(e0, all_4_2) = all_56_30 % 150.97/22.12 (91) ~ (all_52_6 = all_6_2) % 150.97/22.12 (92) ~ (all_52_14 = all_6_2) % 150.97/22.12 (93) ~ (e2 = e0) % 150.97/22.12 (94) all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3 % 150.97/22.12 (95) all_34_2 = all_4_2 % 150.97/22.12 (96) all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3 % 150.97/22.12 (97) op(all_8_2, all_8_2) = all_8_1 % 150.97/22.12 (98) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 150.97/22.12 (99) all_58_14 = all_52_11 % 150.97/22.12 (100) all_56_19 = all_52_6 % 150.97/22.12 (101) all_56_9 = all_52_1 % 150.97/22.12 (102) all_56_15 = all_52_13 % 150.97/22.12 (103) ~ (all_52_1 = all_10_2) % 150.97/22.12 (104) all_58_12 = all_52_3 % 150.97/22.12 (105) all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2 % 150.97/22.12 (106) ~ (all_56_31 = e3) | all_56_25 = e0 % 150.97/22.12 % 150.97/22.12 Begin of proof % 150.97/22.12 | % 150.97/22.12 | COMBINE_EQS: (37), (82) imply: % 150.97/22.12 | (107) all_8_0 = e1 % 150.97/22.12 | % 150.97/22.12 | SIMP: (107) implies: % 150.97/22.12 | (108) all_8_0 = e1 % 150.97/22.12 | % 150.97/22.12 | COMBINE_EQS: (53), (108) imply: % 150.97/22.12 | (109) all_42_0 = e1 % 150.97/22.12 | % 150.97/22.12 | REDUCE: (7), (108) imply: % 150.97/22.12 | (110) op(e2, all_8_1) = e1 % 150.97/22.12 | % 150.97/22.12 | BETA: splitting (40) gives: % 150.97/22.12 | % 150.97/22.12 | Case 1: % 150.97/22.12 | | % 150.97/22.12 | | (111) ~ (all_34_0 = e2) % 150.97/22.12 | | % 150.97/22.12 | | REDUCE: (84), (111) imply: % 150.97/22.12 | | (112) $false % 150.97/22.12 | | % 150.97/22.12 | | CLOSE: (112) is inconsistent. % 150.97/22.12 | | % 150.97/22.12 | Case 2: % 150.97/22.12 | | % 150.97/22.12 | | (113) ~ (all_34_1 = e3) | ~ (all_34_2 = e1) % 150.97/22.12 | | % 150.97/22.12 | | BETA: splitting (61) gives: % 150.97/22.13 | | % 150.97/22.13 | | Case 1: % 150.97/22.13 | | | % 150.97/22.13 | | | (114) ~ (all_36_1 = e3) % 150.97/22.13 | | | % 150.97/22.13 | | | REDUCE: (51), (114) imply: % 150.97/22.13 | | | (115) ~ (all_6_1 = e3) % 150.97/22.13 | | | % 150.97/22.13 | | | BETA: splitting (52) gives: % 150.97/22.13 | | | % 150.97/22.13 | | | Case 1: % 150.97/22.13 | | | | % 150.97/22.13 | | | | (116) ~ (all_42_0 = e1) % 150.97/22.13 | | | | % 150.97/22.13 | | | | REDUCE: (109), (116) imply: % 150.97/22.13 | | | | (117) $false % 150.97/22.13 | | | | % 150.97/22.13 | | | | CLOSE: (117) is inconsistent. % 150.97/22.13 | | | | % 150.97/22.13 | | | Case 2: % 150.97/22.13 | | | | % 150.97/22.13 | | | | (118) ~ (all_42_1 = e0) | ~ (all_42_2 = e3) % 150.97/22.13 | | | | % 150.97/22.13 | | | | BETA: splitting (10) gives: % 150.97/22.13 | | | | % 150.97/22.13 | | | | Case 1: % 150.97/22.13 | | | | | % 150.97/22.13 | | | | | (119) ~ (all_56_31 = e1) % 150.97/22.13 | | | | | % 150.97/22.13 | | | | | REDUCE: (63), (119) imply: % 150.97/22.13 | | | | | (120) ~ (all_4_2 = e1) % 150.97/22.13 | | | | | % 150.97/22.13 | | | | | BETA: splitting (106) gives: % 150.97/22.13 | | | | | % 150.97/22.13 | | | | | Case 1: % 150.97/22.13 | | | | | | % 150.97/22.13 | | | | | | (121) ~ (all_56_31 = e3) % 150.97/22.13 | | | | | | % 150.97/22.13 | | | | | | REDUCE: (63), (121) imply: % 150.97/22.13 | | | | | | (122) ~ (all_4_2 = e3) % 150.97/22.13 | | | | | | % 150.97/22.13 | | | | | | BETA: splitting (83) gives: % 150.97/22.13 | | | | | | % 150.97/22.13 | | | | | | Case 1: % 150.97/22.13 | | | | | | | % 150.97/22.13 | | | | | | | (123) ~ (all_56_31 = e2) % 150.97/22.13 | | | | | | | % 150.97/22.13 | | | | | | | REDUCE: (63), (123) imply: % 150.97/22.13 | | | | | | | (124) ~ (all_4_2 = e2) % 150.97/22.13 | | | | | | | % 150.97/22.13 | | | | | | | REF_CLOSE: (18), (21), (39), (44), (60), (69), (90), (120), (122), % 150.97/22.13 | | | | | | | (124) are inconsistent by sub-proof #229. % 150.97/22.13 | | | | | | | % 150.97/22.13 | | | | | | Case 2: % 150.97/22.13 | | | | | | | % 150.97/22.13 | | | | | | | (125) all_56_31 = e2 % 150.97/22.13 | | | | | | | (126) all_56_27 = e0 % 150.97/22.13 | | | | | | | % 150.97/22.13 | | | | | | | REF_CLOSE: (1), (2), (8), (9), (11), (12), (14), (16), (17), (18), % 150.97/22.13 | | | | | | | (19), (20), (22), (23), (24), (25), (26), (28), (29), % 150.97/22.13 | | | | | | | (30), (33), (34), (35), (36), (39), (41), (43), (45), % 150.97/22.13 | | | | | | | (47), (49), (63), (64), (65), (66), (71), (73), (75), % 150.97/22.13 | | | | | | | (76), (77), (81), (85), (87), (88), (89), (92), (94), % 150.97/22.13 | | | | | | | (97), (98), (101), (103), (110), (118), (120), (122), % 150.97/22.13 | | | | | | | (125), (126) are inconsistent by sub-proof #234. % 150.97/22.13 | | | | | | | % 150.97/22.13 | | | | | | End of split % 150.97/22.13 | | | | | | % 150.97/22.13 | | | | | Case 2: % 150.97/22.13 | | | | | | % 150.97/22.13 | | | | | | (127) all_56_31 = e3 % 150.97/22.13 | | | | | | (128) all_56_25 = e0 % 150.97/22.13 | | | | | | % 150.97/22.13 | | | | | | COMBINE_EQS: (4), (128) imply: % 150.97/22.13 | | | | | | (129) all_52_3 = e0 % 150.97/22.13 | | | | | | % 150.97/22.13 | | | | | | COMBINE_EQS: (63), (127) imply: % 150.97/22.13 | | | | | | (130) all_4_2 = e3 % 150.97/22.13 | | | | | | % 150.97/22.13 | | | | | | COMBINE_EQS: (13), (130) imply: % 150.97/22.13 | | | | | | (131) all_12_2 = e3 % 150.97/22.13 | | | | | | % 150.97/22.13 | | | | | | COMBINE_EQS: (73), (130) imply: % 150.97/22.13 | | | | | | (132) all_58_15 = e3 % 150.97/22.13 | | | | | | % 150.97/22.13 | | | | | | COMBINE_EQS: (104), (129) imply: % 150.97/22.13 | | | | | | (133) all_58_12 = e0 % 150.97/22.13 | | | | | | % 150.97/22.13 | | | | | | REDUCE: (62), (129) imply: % 150.97/22.13 | | | | | | (134) ~ (all_52_1 = e0) % 150.97/22.13 | | | | | | % 150.97/22.13 | | | | | | REDUCE: (42), (129) imply: % 150.97/22.13 | | | | | | (135) ~ (all_52_7 = e0) % 150.97/22.13 | | | | | | % 150.97/22.13 | | | | | | SIMP: (135) implies: % 150.97/22.13 | | | | | | (136) ~ (all_52_7 = e0) % 150.97/22.13 | | | | | | % 150.97/22.13 | | | | | | REDUCE: (48), (130) imply: % 150.97/22.13 | | | | | | (137) ~ (all_52_7 = e3) % 150.97/22.13 | | | | | | % 150.97/22.13 | | | | | | REDUCE: (60), (130) imply: % 150.97/22.13 | | | | | | (138) op(e3, e3) = all_4_1 % 150.97/22.13 | | | | | | % 150.97/22.13 | | | | | | REDUCE: (18), (130) imply: % 150.97/22.13 | | | | | | (139) op(e0, e0) = e3 % 150.97/22.13 | | | | | | % 150.97/22.13 | | | | | | BETA: splitting (55) gives: % 150.97/22.13 | | | | | | % 150.97/22.13 | | | | | | Case 1: % 150.97/22.13 | | | | | | | % 150.97/22.13 | | | | | | | % 150.97/22.13 | | | | | | | GROUND_INST: instantiating (39) with all_10_2, all_4_1, e3, e3, % 150.97/22.13 | | | | | | | simplifying with (34), (138) gives: % 150.97/22.13 | | | | | | | (140) all_10_2 = all_4_1 % 150.97/22.13 | | | | | | | % 150.97/22.13 | | | | | | | REF_CLOSE: (1), (2), (3), (5), (6), (8), (9), (16), (17), (19), % 150.97/22.13 | | | | | | | (20), (23), (24), (26), (27), (31), (32), (33), (34), % 150.97/22.13 | | | | | | | (35), (38), (39), (43), (45), (49), (54), (57), (58), % 150.97/22.13 | | | | | | | (67), (70), (75), (78), (80), (81), (85), (93), (96), % 150.97/22.13 | | | | | | | (97), (98), (99), (101), (103), (105), (110), (118), % 150.97/22.13 | | | | | | | (127), (132), (133), (134), (136), (137), (139), (140) % 150.97/22.13 | | | | | | | are inconsistent by sub-proof #244. % 150.97/22.13 | | | | | | | % 150.97/22.13 | | | | | | Case 2: % 150.97/22.13 | | | | | | | % 150.97/22.13 | | | | | | | (141) ~ (all_12_2 = e3) % 150.97/22.13 | | | | | | | % 150.97/22.13 | | | | | | | REDUCE: (131), (141) imply: % 150.97/22.13 | | | | | | | (142) $false % 150.97/22.13 | | | | | | | % 150.97/22.13 | | | | | | | CLOSE: (142) is inconsistent. % 150.97/22.13 | | | | | | | % 150.97/22.13 | | | | | | End of split % 150.97/22.13 | | | | | | % 150.97/22.13 | | | | | End of split % 150.97/22.13 | | | | | % 150.97/22.13 | | | | Case 2: % 150.97/22.13 | | | | | % 150.97/22.13 | | | | | (143) all_56_31 = e1 % 150.97/22.13 | | | | | (144) all_56_29 = e0 % 150.97/22.13 | | | | | % 150.97/22.13 | | | | | COMBINE_EQS: (74), (144) imply: % 150.97/22.13 | | | | | (145) all_52_11 = e0 % 150.97/22.13 | | | | | % 150.97/22.13 | | | | | SIMP: (145) implies: % 150.97/22.13 | | | | | (146) all_52_11 = e0 % 150.97/22.13 | | | | | % 150.97/22.13 | | | | | COMBINE_EQS: (63), (143) imply: % 150.97/22.13 | | | | | (147) all_4_2 = e1 % 150.97/22.13 | | | | | % 150.97/22.13 | | | | | COMBINE_EQS: (95), (147) imply: % 150.97/22.13 | | | | | (148) all_34_2 = e1 % 150.97/22.13 | | | | | % 150.97/22.13 | | | | | REDUCE: (3), (146) imply: % 150.97/22.13 | | | | | (149) ~ (all_6_2 = e0) % 150.97/22.13 | | | | | % 150.97/22.13 | | | | | SIMP: (149) implies: % 150.97/22.13 | | | | | (150) ~ (all_6_2 = e0) % 150.97/22.13 | | | | | % 150.97/22.13 | | | | | REDUCE: (60), (147) imply: % 150.97/22.13 | | | | | (151) op(e1, e1) = all_4_1 % 150.97/22.13 | | | | | % 150.97/22.13 | | | | | REDUCE: (90), (147) imply: % 150.97/22.13 | | | | | (152) op(e0, e1) = all_56_30 % 150.97/22.13 | | | | | % 150.97/22.13 | | | | | REDUCE: (46), (146) imply: % 150.97/22.13 | | | | | (153) op(e0, e1) = e0 % 150.97/22.13 | | | | | % 150.97/22.13 | | | | | BETA: splitting (113) gives: % 150.97/22.13 | | | | | % 150.97/22.13 | | | | | Case 1: % 150.97/22.13 | | | | | | % 150.97/22.13 | | | | | | (154) ~ (all_34_1 = e3) % 150.97/22.13 | | | | | | % 150.97/22.13 | | | | | | REDUCE: (56), (154) imply: % 150.97/22.13 | | | | | | (155) ~ (all_4_1 = e3) % 150.97/22.13 | | | | | | % 150.97/22.13 | | | | | | GROUND_INST: instantiating (39) with e0, all_56_30, e1, e0, % 150.97/22.13 | | | | | | simplifying with (152), (153) gives: % 150.97/22.13 | | | | | | (156) all_56_30 = e0 % 150.97/22.13 | | | | | | % 150.97/22.13 | | | | | | GROUND_INST: instantiating (39) with all_6_2, all_4_1, e1, e1, % 150.97/22.13 | | | | | | simplifying with (71), (151) gives: % 150.97/22.13 | | | | | | (157) all_6_2 = all_4_1 % 150.97/22.13 | | | | | | % 150.97/22.13 | | | | | | COMBINE_EQS: (11), (157) imply: % 150.97/22.13 | | | | | | (158) all_54_10 = all_4_1 % 150.97/22.13 | | | | | | % 150.97/22.13 | | | | | | COMBINE_EQS: (24), (157) imply: % 150.97/22.13 | | | | | | (159) all_56_21 = all_4_1 % 150.97/22.13 | | | | | | % 150.97/22.13 | | | | | | REDUCE: (91), (157) imply: % 150.97/22.13 | | | | | | (160) ~ (all_52_6 = all_4_1) % 150.97/22.13 | | | | | | % 150.97/22.13 | | | | | | REDUCE: (150), (157) imply: % 150.97/22.13 | | | | | | (161) ~ (all_4_1 = e0) % 150.97/22.13 | | | | | | % 150.97/22.13 | | | | | | REDUCE: (66), (157) imply: % 150.97/22.13 | | | | | | (162) op(all_4_1, all_4_1) = all_6_1 % 150.97/22.13 | | | | | | % 150.97/22.13 | | | | | | REDUCE: (79), (157) imply: % 150.97/22.13 | | | | | | (163) op(e1, all_4_1) = all_56_20 % 150.97/22.13 | | | | | | % 150.97/22.13 | | | | | | BETA: splitting (15) gives: % 150.97/22.13 | | | | | | % 150.97/22.13 | | | | | | Case 1: % 150.97/22.13 | | | | | | | % 150.97/22.13 | | | | | | | (164) ~ (all_56_21 = e2) % 150.97/22.13 | | | | | | | % 150.97/22.13 | | | | | | | REDUCE: (159), (164) imply: % 150.97/22.13 | | | | | | | (165) ~ (all_4_1 = e2) % 150.97/22.13 | | | | | | | % 150.97/22.13 | | | | | | | REF_CLOSE: (25), (39), (44), (93), (151), (152), (153), (155), % 150.97/22.13 | | | | | | | (158), (161), (162), (163), (165) are inconsistent by % 150.97/22.13 | | | | | | | sub-proof #177. % 150.97/22.13 | | | | | | | % 150.97/22.13 | | | | | | Case 2: % 150.97/22.13 | | | | | | | % 150.97/22.13 | | | | | | | (166) all_56_21 = e2 % 150.97/22.13 | | | | | | | (167) all_56_19 = e1 % 150.97/22.13 | | | | | | | % 150.97/22.13 | | | | | | | REF_CLOSE: (1), (6), (8), (12), (18), (19), (21), (31), (33), % 150.97/22.13 | | | | | | | (39), (58), (68), (69), (72), (78), (85), (86), (97), % 150.97/22.13 | | | | | | | (98), (100), (102), (110), (115), (159), (160), (162), % 150.97/22.13 | | | | | | | (166), (167) are inconsistent by sub-proof #233. % 150.97/22.13 | | | | | | | % 150.97/22.13 | | | | | | End of split % 150.97/22.13 | | | | | | % 150.97/22.13 | | | | | Case 2: % 150.97/22.13 | | | | | | % 150.97/22.13 | | | | | | (168) ~ (all_34_2 = e1) % 150.97/22.13 | | | | | | % 150.97/22.13 | | | | | | REDUCE: (148), (168) imply: % 150.97/22.13 | | | | | | (169) $false % 150.97/22.13 | | | | | | % 150.97/22.13 | | | | | | CLOSE: (169) is inconsistent. % 150.97/22.13 | | | | | | % 150.97/22.13 | | | | | End of split % 150.97/22.13 | | | | | % 150.97/22.13 | | | | End of split % 150.97/22.13 | | | | % 150.97/22.13 | | | End of split % 150.97/22.13 | | | % 150.97/22.13 | | Case 2: % 150.97/22.13 | | | % 150.97/22.13 | | | (170) all_36_1 = e3 % 150.97/22.13 | | | % 150.97/22.13 | | | COMBINE_EQS: (51), (170) imply: % 150.97/22.13 | | | (171) all_6_1 = e3 % 150.97/22.13 | | | % 150.97/22.13 | | | SIMP: (171) implies: % 150.97/22.13 | | | (172) all_6_1 = e3 % 150.97/22.13 | | | % 150.97/22.13 | | | REF_CLOSE: (1), (2), (6), (8), (11), (14), (16), (18), (19), (20), (21), % 150.97/22.13 | | | (23), (24), (25), (29), (31), (33), (34), (35), (36), (39), % 150.97/22.13 | | | (43), (45), (50), (52), (57), (58), (59), (68), (69), (71), % 150.97/22.13 | | | (76), (78), (81), (85), (86), (88), (97), (98), (101), (102), % 150.97/22.13 | | | (103), (109), (110), (172) are inconsistent by sub-proof #249. % 150.97/22.13 | | | % 150.97/22.13 | | End of split % 150.97/22.13 | | % 150.97/22.13 | End of split % 150.97/22.13 | % 150.97/22.13 End of proof % 150.97/22.13 % 150.97/22.13 Sub-proof #177 shows that the following formulas are inconsistent: % 150.97/22.13 ---------------------------------------------------------------- % 150.97/22.13 (1) op(e0, e1) = all_56_30 % 150.97/22.13 (2) ~ (all_4_1 = e0) % 150.97/22.13 (3) ~ (all_4_1 = e3) % 150.97/22.13 (4) op(e1, all_4_1) = all_56_20 % 150.97/22.13 (5) ~ (all_4_1 = e2) % 150.97/22.13 (6) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 150.97/22.13 (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 150.97/22.13 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 150.97/22.13 (8) op(e0, all_4_1) = e2 % 150.97/22.13 (9) op(all_4_1, all_4_1) = all_6_1 % 150.97/22.13 (10) op(e0, e1) = e0 % 150.97/22.13 (11) all_54_10 = all_4_1 % 150.97/22.13 (12) op(e1, e1) = all_4_1 % 150.97/22.13 (13) ~ (e2 = e0) % 150.97/22.13 % 150.97/22.13 Begin of proof % 150.97/22.13 | % 150.97/22.13 | BETA: splitting (6) gives: % 150.97/22.13 | % 150.97/22.13 | Case 1: % 150.97/22.13 | | % 150.97/22.13 | | (14) all_54_10 = e3 % 150.97/22.13 | | % 150.97/22.13 | | COMBINE_EQS: (11), (14) imply: % 150.97/22.13 | | (15) all_4_1 = e3 % 150.97/22.13 | | % 150.97/22.13 | | REDUCE: (3), (15) imply: % 150.97/22.13 | | (16) $false % 150.97/22.13 | | % 150.97/22.13 | | CLOSE: (16) is inconsistent. % 150.97/22.13 | | % 150.97/22.13 | Case 2: % 150.97/22.13 | | % 150.97/22.13 | | (17) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 150.97/22.13 | | % 150.97/22.13 | | BETA: splitting (17) gives: % 150.97/22.13 | | % 150.97/22.13 | | Case 1: % 150.97/22.13 | | | % 150.97/22.13 | | | (18) all_54_10 = e2 % 150.97/22.13 | | | % 150.97/22.13 | | | COMBINE_EQS: (11), (18) imply: % 150.97/22.13 | | | (19) all_4_1 = e2 % 150.97/22.13 | | | % 150.97/22.13 | | | REDUCE: (5), (19) imply: % 150.97/22.13 | | | (20) $false % 150.97/22.13 | | | % 150.97/22.13 | | | CLOSE: (20) is inconsistent. % 150.97/22.13 | | | % 150.97/22.13 | | Case 2: % 150.97/22.13 | | | % 150.97/22.13 | | | (21) all_54_10 = e1 | all_54_10 = e0 % 150.97/22.13 | | | % 150.97/22.13 | | | BETA: splitting (21) gives: % 150.97/22.13 | | | % 150.97/22.13 | | | Case 1: % 150.97/22.13 | | | | % 150.97/22.13 | | | | (22) all_54_10 = e1 % 150.97/22.13 | | | | % 150.97/22.13 | | | | COMBINE_EQS: (11), (22) imply: % 150.97/22.13 | | | | (23) all_4_1 = e1 % 150.97/22.13 | | | | % 150.97/22.13 | | | | REDUCE: (9), (23) imply: % 150.97/22.13 | | | | (24) op(e1, e1) = all_6_1 % 150.97/22.13 | | | | % 150.97/22.13 | | | | REDUCE: (4), (23) imply: % 150.97/22.13 | | | | (25) op(e1, e1) = all_56_20 % 150.97/22.13 | | | | % 150.97/22.13 | | | | REDUCE: (12), (23) imply: % 150.97/22.13 | | | | (26) op(e1, e1) = e1 % 150.97/22.13 | | | | % 150.97/22.13 | | | | REF_CLOSE: (1), (7), (8), (10), (12), (13), (24), (25), (26) are % 150.97/22.13 | | | | inconsistent by sub-proof #180. % 150.97/22.13 | | | | % 150.97/22.13 | | | Case 2: % 150.97/22.13 | | | | % 150.97/22.13 | | | | (27) all_54_10 = e0 % 150.97/22.13 | | | | % 150.97/22.13 | | | | COMBINE_EQS: (11), (27) imply: % 150.97/22.13 | | | | (28) all_4_1 = e0 % 150.97/22.13 | | | | % 150.97/22.13 | | | | REDUCE: (2), (28) imply: % 150.97/22.13 | | | | (29) $false % 150.97/22.13 | | | | % 150.97/22.13 | | | | CLOSE: (29) is inconsistent. % 150.97/22.13 | | | | % 150.97/22.13 | | | End of split % 150.97/22.13 | | | % 150.97/22.13 | | End of split % 150.97/22.13 | | % 150.97/22.13 | End of split % 150.97/22.13 | % 150.97/22.13 End of proof % 150.97/22.13 % 150.97/22.13 Sub-proof #178 shows that the following formulas are inconsistent: % 150.97/22.13 ---------------------------------------------------------------- % 150.97/22.13 (1) all_56_11 = all_8_2 % 150.97/22.13 (2) op(e0, all_52_13) = all_56_14 % 150.97/22.13 (3) ~ (all_56_11 = e1) | all_56_13 = e2 % 150.97/22.13 (4) ~ (all_52_11 = all_6_2) % 150.97/22.13 (5) all_56_25 = all_52_3 % 150.97/22.13 (6) ~ (all_52_7 = all_52_11) % 150.97/22.13 (7) ~ (all_52_8 = all_52_9) % 150.97/22.13 (8) all_54_9 = all_52_6 % 150.97/22.13 (9) op(e2, all_8_1) = all_8_0 % 150.97/22.13 (10) all_58_6 = all_52_2 % 150.97/22.13 (11) ~ (all_8_1 = e1) % 150.97/22.13 (12) ~ (all_52_1 = all_52_9) % 150.97/22.13 (13) ~ (all_56_31 = e1) | all_56_29 = e0 % 150.97/22.13 (14) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0 % 150.97/22.13 (15) all_54_10 = all_6_2 % 150.97/22.13 (16) ~ (all_6_1 = e2) % 150.97/22.13 (17) all_12_2 = all_4_2 % 150.97/22.13 (18) ~ (all_52_13 = all_8_2) % 150.97/22.13 (19) ~ (all_56_21 = e2) | all_56_19 = e1 % 150.97/22.13 (20) all_54_0 = all_10_2 % 150.97/22.13 (21) all_54_4 = all_52_1 % 150.97/22.13 (22) ~ (all_52_14 = all_4_2) % 150.97/22.13 (23) ~ (all_8_0 = e1) % 150.97/22.13 (24) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0 % 150.97/22.13 (25) ~ (all_52_9 = all_8_2) % 150.97/22.13 (26) all_54_12 = all_52_3 % 150.97/22.13 (27) op(e0, e0) = all_4_2 % 150.97/22.13 (28) all_58_6 = e0 | all_58_7 = e0 | all_58_8 = e0 | all_58_11 = e0 % 150.97/22.13 (29) all_58_4 = all_52_8 % 150.97/22.13 (30) all_54_5 = all_8_2 % 150.97/22.13 (31) ~ (all_52_6 = all_52_14) % 150.97/22.13 (32) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 150.97/22.13 (33) all_54_15 = all_4_2 % 150.97/22.13 (34) all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1 % 150.97/22.13 (35) all_56_21 = all_6_2 % 150.97/22.13 (36) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 150.97/22.13 (37) ~ (all_52_7 = all_8_2) % 150.97/22.13 (38) all_56_1 = all_10_2 % 150.97/22.13 (39) all_56_27 = all_52_7 % 150.97/22.13 (40) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0 % 150.97/22.13 (41) all_58_5 = all_52_9 % 150.97/22.13 (42) all_56_17 = all_52_2 % 150.97/22.13 (43) all_58_9 = all_52_12 % 150.97/22.13 (44) op(e0, all_52_12) = all_56_6 % 150.97/22.13 (45) op(e1, e0) = all_52_14 % 150.97/22.13 (46) all_28_1 = all_6_1 % 150.97/22.13 (47) ~ (all_56_1 = e1) | all_56_5 = e3 % 150.97/22.13 (48) all_54_14 = all_52_11 % 150.97/22.13 (49) ~ (all_22_0 = e0) | ~ (all_22_2 = e1) % 150.97/22.13 (50) all_22_1 = e3 % 150.97/22.13 (51) all_58_1 = all_52_4 % 150.97/22.13 (52) all_58_13 = all_52_7 % 150.97/22.13 (53) op(e2, all_8_2) = all_56_10 % 150.97/22.13 (54) op(e3, e3) = all_10_2 % 150.97/22.13 (55) ~ (all_52_8 = all_6_2) % 150.97/22.13 (56) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0 % 150.97/22.13 (57) ~ (all_56_21 = e3) | all_56_17 = e1 % 150.97/22.13 (58) all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0 % 150.97/22.13 (59) ~ (e1 = e0) % 150.97/22.13 (60) all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1 % 150.97/22.13 (61) ~ (all_52_1 = all_8_2) % 150.97/22.13 (62) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 150.97/22.13 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 150.97/22.13 (63) ~ (all_52_3 = all_10_2) % 150.97/22.13 (64) all_28_0 = all_6_0 % 150.97/22.13 (65) ~ (all_34_0 = e2) | ~ (all_34_1 = e3) | ~ (all_34_2 = e1) % 150.97/22.13 (66) all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0 % 150.97/22.13 (67) ~ (all_56_11 = e3) | all_56_9 = e2 % 150.97/22.13 (68) all_36_0 = all_6_0 % 150.97/22.13 (69) ~ (all_52_2 = all_52_6) % 150.97/22.13 (70) op(e0, all_4_1) = all_4_0 % 150.97/22.13 (71) all_56_7 = all_52_12 % 150.97/22.13 (72) all_22_0 = all_8_0 % 150.97/22.13 (73) all_46_2 = all_6_2 % 150.97/22.13 (74) op(e0, all_4_1) = e2 % 150.97/22.13 (75) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0 % 150.97/22.13 (76) all_28_2 = all_6_2 % 150.97/22.13 (77) all_56_13 = all_52_9 % 150.97/22.13 (78) op(e0, e1) = all_52_11 % 150.97/22.13 (79) ~ (all_52_1 = all_52_13) % 150.97/22.13 (80) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0 % 150.97/22.13 (81) op(e1, e3) = all_52_2 % 150.97/22.13 (82) all_36_1 = all_6_1 % 150.97/22.13 (83) all_58_8 = all_6_2 % 150.97/22.13 (84) ~ (all_52_3 = all_4_2) % 150.97/22.13 (85) ~ (all_52_8 = all_10_2) % 150.97/22.13 (86) ~ (all_56_1 = e0) | all_56_7 = e3 % 150.97/22.13 (87) all_46_0 = all_6_0 % 150.97/22.13 (88) ~ (all_12_1 = e1) | ~ (all_12_2 = e3) % 150.97/22.13 (89) all_34_1 = all_4_1 % 150.97/22.13 (90) all_56_5 = all_52_8 % 150.97/22.13 (91) ~ (e2 = e1) % 150.97/22.13 (92) ~ (all_52_9 = all_52_13) % 150.97/22.13 (93) op(e1, all_6_1) = all_6_0 % 150.97/22.13 (94) op(all_4_2, all_4_2) = all_4_1 % 150.97/22.13 (95) ~ (all_36_0 = e0) | ~ (all_36_1 = e3) | ~ (all_36_2 = e2) % 150.97/22.13 (96) all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3 % 150.97/22.13 (97) ~ (all_52_3 = all_52_11) % 150.97/22.13 (98) all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1 % 150.97/22.13 (99) all_58_3 = all_8_2 % 150.97/22.13 (100) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0 % 150.97/22.13 (101) ~ (all_52_11 = all_4_2) % 150.97/22.13 (102) ~ (all_52_1 = all_52_3) % 150.97/22.13 (103) op(e1, all_52_8) = all_56_4 % 150.97/22.13 (104) all_56_31 = all_4_2 % 150.97/22.13 (105) all_58_11 = all_52_14 % 150.97/22.13 (106) all_36_2 = all_6_2 % 150.97/22.13 (107) ~ (all_52_2 = all_52_14) % 150.97/22.13 (108) ~ (all_52_9 = all_52_11) % 150.97/22.13 (109) all_54_7 = all_52_13 % 150.97/22.13 (110) op(all_6_2, all_6_2) = all_6_1 % 150.97/22.13 (111) all_56_1 = e3 | all_56_11 = e2 | all_56_21 = e1 | all_56_31 = e0 % 150.97/22.13 (112) ~ (all_52_13 = all_4_2) % 150.97/22.13 (113) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0 % 150.97/22.13 (114) ~ (all_52_8 = all_52_11) % 150.97/22.13 (115) all_54_2 = all_52_8 % 150.97/22.13 (116) all_22_1 = all_8_1 % 150.97/22.13 (117) ~ (all_28_0 = e2) | ~ (all_28_1 = e3) | ~ (all_28_2 = e0) % 150.97/22.13 (118) ~ (all_52_13 = all_52_14) % 150.97/22.13 (119) all_56_23 = all_52_14 % 150.97/22.13 (120) all_54_8 = all_52_2 % 150.97/22.13 (121) all_46_1 = all_6_1 % 150.97/22.13 (122) op(e1, e1) = all_6_2 % 150.97/22.13 (123) ~ (all_52_6 = all_8_2) % 150.97/22.13 (124) all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1 % 150.97/22.13 (125) op(e0, e3) = all_52_3 % 150.97/22.13 (126) all_58_15 = all_4_2 % 150.97/22.13 (127) all_56_29 = all_52_11 % 150.97/22.13 (128) all_58_2 = all_52_1 % 150.97/22.13 (129) ~ (all_52_9 = all_6_2) % 150.97/22.13 (130) all_22_2 = all_8_2 % 150.97/22.13 (131) all_58_7 = all_52_6 % 150.97/22.13 (132) all_58_10 = all_52_13 % 150.97/22.13 (133) all_12_1 = all_4_1 % 150.97/22.13 (134) op(all_10_2, all_10_2) = all_10_1 % 150.97/22.13 (135) ~ (all_56_11 = e0) | all_56_15 = e2 % 150.97/22.13 (136) all_58_0 = all_10_2 % 150.97/22.13 (137) op(e1, all_6_2) = all_56_20 % 150.97/22.13 (138) op(e2, e3) = all_52_1 % 150.97/22.13 (139) ~ (all_56_31 = e2) | all_56_27 = e0 % 150.97/22.13 (140) all_34_0 = e2 % 150.97/22.13 (141) op(e2, e2) = all_8_2 % 150.97/22.13 (142) ~ (all_52_2 = all_6_2) % 150.97/22.13 (143) ~ (all_52_1 = all_52_2) % 150.97/22.13 (144) ~ (all_56_21 = e0) | all_56_23 = e1 % 150.97/22.13 (145) op(e0, all_4_2) = all_56_30 % 150.97/22.13 (146) ~ (all_52_6 = all_6_2) % 150.97/22.13 (147) ~ (all_52_14 = all_6_2) % 150.97/22.13 (148) ~ (e2 = e0) % 150.97/22.13 (149) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0 % 150.97/22.13 (150) ~ (all_52_2 = all_10_2) % 150.97/22.13 (151) ~ (all_46_0 = e2) | ~ (all_46_1 = e0) | ~ (all_46_2 = e3) % 150.97/22.13 (152) all_34_2 = all_4_2 % 150.97/22.13 (153) ~ (all_52_4 = all_8_2) % 150.97/22.13 (154) op(all_8_2, all_8_2) = all_8_1 % 150.97/22.13 (155) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 150.97/22.13 (156) all_58_14 = all_52_11 % 150.97/22.13 (157) all_56_19 = all_52_6 % 150.97/22.13 (158) all_56_9 = all_52_1 % 150.97/22.13 (159) all_56_15 = all_52_13 % 150.97/22.13 (160) ~ (all_52_1 = all_10_2) % 150.97/22.13 (161) all_58_12 = all_52_3 % 150.97/22.13 (162) all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3 % 150.97/22.13 (163) all_54_11 = all_52_14 % 150.97/22.13 (164) ~ (all_56_31 = e3) | all_56_25 = e0 % 150.97/22.13 % 150.97/22.13 Begin of proof % 150.97/22.13 | % 150.97/22.13 | COMBINE_EQS: (50), (116) imply: % 150.97/22.13 | (165) all_8_1 = e3 % 150.97/22.13 | % 150.97/22.13 | SIMP: (165) implies: % 150.97/22.13 | (166) all_8_1 = e3 % 150.97/22.13 | % 150.97/22.13 | REDUCE: (11), (166) imply: % 150.97/22.13 | (167) ~ (e3 = e1) % 150.97/22.13 | % 150.97/22.13 | REDUCE: (154), (166) imply: % 150.97/22.13 | (168) op(all_8_2, all_8_2) = e3 % 150.97/22.13 | % 150.97/22.13 | REDUCE: (9), (166) imply: % 150.97/22.13 | (169) op(e2, e3) = all_8_0 % 150.97/22.13 | % 150.97/22.13 | GROUND_INST: instantiating (62) with all_52_1, all_8_0, e3, e2, simplifying % 150.97/22.13 | with (138), (169) gives: % 150.97/22.13 | (170) all_52_1 = all_8_0 % 150.97/22.13 | % 150.97/22.13 | COMBINE_EQS: (21), (170) imply: % 150.97/22.13 | (171) all_54_4 = all_8_0 % 150.97/22.13 | % 150.97/22.13 | COMBINE_EQS: (158), (170) imply: % 150.97/22.13 | (172) all_56_9 = all_8_0 % 150.97/22.13 | % 150.97/22.13 | COMBINE_EQS: (128), (170) imply: % 150.97/22.13 | (173) all_58_2 = all_8_0 % 150.97/22.13 | % 150.97/22.13 | REDUCE: (143), (170) imply: % 150.97/22.13 | (174) ~ (all_52_2 = all_8_0) % 150.97/22.13 | % 150.97/22.13 | SIMP: (174) implies: % 150.97/22.13 | (175) ~ (all_52_2 = all_8_0) % 150.97/22.13 | % 150.97/22.13 | REDUCE: (102), (170) imply: % 150.97/22.13 | (176) ~ (all_52_3 = all_8_0) % 150.97/22.13 | % 150.97/22.13 | SIMP: (176) implies: % 150.97/22.13 | (177) ~ (all_52_3 = all_8_0) % 150.97/22.13 | % 150.97/22.13 | REDUCE: (12), (170) imply: % 150.97/22.13 | (178) ~ (all_52_9 = all_8_0) % 150.97/22.13 | % 150.97/22.13 | SIMP: (178) implies: % 150.97/22.13 | (179) ~ (all_52_9 = all_8_0) % 150.97/22.13 | % 150.97/22.13 | REDUCE: (79), (170) imply: % 150.97/22.13 | (180) ~ (all_52_13 = all_8_0) % 150.97/22.13 | % 150.97/22.13 | SIMP: (180) implies: % 150.97/22.13 | (181) ~ (all_52_13 = all_8_0) % 150.97/22.13 | % 150.97/22.13 | REDUCE: (160), (170) imply: % 150.97/22.13 | (182) ~ (all_10_2 = all_8_0) % 150.97/22.13 | % 150.97/22.13 | SIMP: (182) implies: % 150.97/22.13 | (183) ~ (all_10_2 = all_8_0) % 150.97/22.13 | % 150.97/22.13 | REDUCE: (61), (170) imply: % 150.97/22.13 | (184) ~ (all_8_0 = all_8_2) % 150.97/22.13 | % 150.97/22.13 | BETA: splitting (117) gives: % 150.97/22.13 | % 150.97/22.13 | Case 1: % 150.97/22.13 | | % 150.97/22.13 | | (185) ~ (all_28_0 = e2) % 150.97/22.13 | | % 150.97/22.13 | | REDUCE: (64), (185) imply: % 150.97/22.13 | | (186) ~ (all_6_0 = e2) % 150.97/22.13 | | % 150.97/22.13 | | BETA: splitting (65) gives: % 150.97/22.13 | | % 150.97/22.13 | | Case 1: % 150.97/22.13 | | | % 150.97/22.13 | | | (187) ~ (all_34_0 = e2) % 150.97/22.13 | | | % 150.97/22.13 | | | REDUCE: (140), (187) imply: % 150.97/22.13 | | | (188) $false % 150.97/22.13 | | | % 150.97/22.13 | | | CLOSE: (188) is inconsistent. % 150.97/22.13 | | | % 150.97/22.13 | | Case 2: % 150.97/22.13 | | | % 150.97/22.13 | | | (189) ~ (all_34_1 = e3) | ~ (all_34_2 = e1) % 150.97/22.13 | | | % 150.97/22.13 | | | BETA: splitting (95) gives: % 150.97/22.13 | | | % 150.97/22.13 | | | Case 1: % 150.97/22.13 | | | | % 150.97/22.13 | | | | (190) ~ (all_36_1 = e3) % 150.97/22.13 | | | | % 150.97/22.13 | | | | REDUCE: (82), (190) imply: % 150.97/22.13 | | | | (191) ~ (all_6_1 = e3) % 150.97/22.13 | | | | % 150.97/22.13 | | | | BETA: splitting (13) gives: % 150.97/22.13 | | | | % 150.97/22.13 | | | | Case 1: % 150.97/22.13 | | | | | % 150.97/22.13 | | | | | (192) ~ (all_56_31 = e1) % 150.97/22.13 | | | | | % 150.97/22.13 | | | | | REDUCE: (104), (192) imply: % 150.97/22.13 | | | | | (193) ~ (all_4_2 = e1) % 150.97/22.13 | | | | | % 150.97/22.13 | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (10), (14), (15), (16), (17), % 150.97/22.13 | | | | | (18), (19), (20), (22), (23), (24), (27), (30), (32), (33), % 150.97/22.13 | | | | | (34), (35), (36), (37), (38), (39), (41), (42), (43), (44), % 150.97/22.13 | | | | | (45), (47), (48), (53), (54), (57), (59), (60), (62), (63), % 150.97/22.13 | | | | | (67), (74), (77), (78), (80), (88), (90), (93), (94), (99), % 150.97/22.13 | | | | | (101), (104), (105), (107), (108), (110), (111), (113), % 150.97/22.13 | | | | | (114), (119), (123), (124), (125), (126), (129), (132), % 150.97/22.13 | | | | | (133), (135), (136), (139), (141), (142), (144), (145), % 150.97/22.13 | | | | | (146), (147), (150), (155), (157), (159), (161), (163), % 150.97/22.13 | | | | | (164), (168), (171), (172), (173), (177), (181), (183), % 150.97/22.13 | | | | | (184), (186), (191), (193) are inconsistent by sub-proof % 150.97/22.13 | | | | | #194. % 150.97/22.13 | | | | | % 150.97/22.13 | | | | Case 2: % 150.97/22.13 | | | | | % 150.97/22.13 | | | | | (194) all_56_31 = e1 % 150.97/22.13 | | | | | (195) all_56_29 = e0 % 150.97/22.13 | | | | | % 150.97/22.13 | | | | | COMBINE_EQS: (127), (195) imply: % 150.97/22.13 | | | | | (196) all_52_11 = e0 % 150.97/22.13 | | | | | % 150.97/22.13 | | | | | SIMP: (196) implies: % 150.97/22.13 | | | | | (197) all_52_11 = e0 % 150.97/22.13 | | | | | % 150.97/22.13 | | | | | COMBINE_EQS: (104), (194) imply: % 150.97/22.13 | | | | | (198) all_4_2 = e1 % 150.97/22.13 | | | | | % 150.97/22.13 | | | | | COMBINE_EQS: (152), (198) imply: % 150.97/22.13 | | | | | (199) all_34_2 = e1 % 150.97/22.13 | | | | | % 150.97/22.13 | | | | | COMBINE_EQS: (156), (197) imply: % 150.97/22.14 | | | | | (200) all_58_14 = e0 % 150.97/22.14 | | | | | % 150.97/22.14 | | | | | REDUCE: (97), (197) imply: % 150.97/22.14 | | | | | (201) ~ (all_52_3 = e0) % 150.97/22.14 | | | | | % 150.97/22.14 | | | | | REDUCE: (84), (198) imply: % 150.97/22.14 | | | | | (202) ~ (all_52_3 = e1) % 150.97/22.14 | | | | | % 150.97/22.14 | | | | | REDUCE: (108), (197) imply: % 150.97/22.14 | | | | | (203) ~ (all_52_9 = e0) % 150.97/22.14 | | | | | % 150.97/22.14 | | | | | REDUCE: (4), (197) imply: % 150.97/22.14 | | | | | (204) ~ (all_6_2 = e0) % 150.97/22.14 | | | | | % 150.97/22.14 | | | | | SIMP: (204) implies: % 150.97/22.14 | | | | | (205) ~ (all_6_2 = e0) % 150.97/22.14 | | | | | % 150.97/22.14 | | | | | REDUCE: (101), (197), (198) imply: % 150.97/22.14 | | | | | (206) ~ (e1 = e0) % 150.97/22.14 | | | | | % 150.97/22.14 | | | | | REDUCE: (112), (198) imply: % 150.97/22.14 | | | | | (207) ~ (all_52_13 = e1) % 150.97/22.14 | | | | | % 150.97/22.14 | | | | | REDUCE: (94), (198) imply: % 150.97/22.14 | | | | | (208) op(e1, e1) = all_4_1 % 150.97/22.14 | | | | | % 150.97/22.14 | | | | | REDUCE: (145), (198) imply: % 150.97/22.14 | | | | | (209) op(e0, e1) = all_56_30 % 150.97/22.14 | | | | | % 150.97/22.14 | | | | | REDUCE: (78), (197) imply: % 150.97/22.14 | | | | | (210) op(e0, e1) = e0 % 150.97/22.14 | | | | | % 150.97/22.14 | | | | | BETA: splitting (189) gives: % 150.97/22.14 | | | | | % 150.97/22.14 | | | | | Case 1: % 150.97/22.14 | | | | | | % 150.97/22.14 | | | | | | (211) ~ (all_34_1 = e3) % 150.97/22.14 | | | | | | % 150.97/22.14 | | | | | | REDUCE: (89), (211) imply: % 150.97/22.14 | | | | | | (212) ~ (all_4_1 = e3) % 150.97/22.14 | | | | | | % 150.97/22.14 | | | | | | GROUND_INST: instantiating (62) with e0, all_56_30, e1, e0, % 150.97/22.14 | | | | | | simplifying with (209), (210) gives: % 150.97/22.14 | | | | | | (213) all_56_30 = e0 % 150.97/22.14 | | | | | | % 150.97/22.14 | | | | | | GROUND_INST: instantiating (62) with all_6_2, all_4_1, e1, e1, % 150.97/22.14 | | | | | | simplifying with (122), (208) gives: % 150.97/22.14 | | | | | | (214) all_6_2 = all_4_1 % 150.97/22.14 | | | | | | % 150.97/22.14 | | | | | | COMBINE_EQS: (15), (214) imply: % 150.97/22.14 | | | | | | (215) all_54_10 = all_4_1 % 150.97/22.14 | | | | | | % 150.97/22.14 | | | | | | COMBINE_EQS: (35), (214) imply: % 150.97/22.14 | | | | | | (216) all_56_21 = all_4_1 % 150.97/22.14 | | | | | | % 150.97/22.14 | | | | | | REDUCE: (142), (214) imply: % 150.97/22.14 | | | | | | (217) ~ (all_52_2 = all_4_1) % 150.97/22.14 | | | | | | % 150.97/22.14 | | | | | | REDUCE: (129), (214) imply: % 150.97/22.14 | | | | | | (218) ~ (all_52_9 = all_4_1) % 150.97/22.14 | | | | | | % 150.97/22.14 | | | | | | REDUCE: (205), (214) imply: % 150.97/22.14 | | | | | | (219) ~ (all_4_1 = e0) % 150.97/22.14 | | | | | | % 150.97/22.14 | | | | | | BETA: splitting (67) gives: % 150.97/22.14 | | | | | | % 150.97/22.14 | | | | | | Case 1: % 150.97/22.14 | | | | | | | % 150.97/22.14 | | | | | | | (220) ~ (all_56_11 = e3) % 150.97/22.14 | | | | | | | % 150.97/22.14 | | | | | | | REDUCE: (1), (220) imply: % 150.97/22.14 | | | | | | | (221) ~ (all_8_2 = e3) % 150.97/22.14 | | | | | | | % 150.97/22.14 | | | | | | | BETA: splitting (47) gives: % 150.97/22.14 | | | | | | | % 150.97/22.14 | | | | | | | Case 1: % 150.97/22.14 | | | | | | | | % 150.97/22.14 | | | | | | | | (222) ~ (all_56_1 = e1) % 150.97/22.14 | | | | | | | | % 150.97/22.14 | | | | | | | | REDUCE: (38), (222) imply: % 150.97/22.14 | | | | | | | | (223) ~ (all_10_2 = e1) % 150.97/22.14 | | | | | | | | % 150.97/22.14 | | | | | | | | BETA: splitting (124) gives: % 150.97/22.14 | | | | | | | | % 150.97/22.14 | | | | | | | | Case 1: % 150.97/22.14 | | | | | | | | | % 150.97/22.14 | | | | | | | | | (224) all_58_0 = e1 % 150.97/22.14 | | | | | | | | | % 150.97/22.14 | | | | | | | | | COMBINE_EQS: (136), (224) imply: % 150.97/22.14 | | | | | | | | | (225) all_10_2 = e1 % 150.97/22.14 | | | | | | | | | % 150.97/22.14 | | | | | | | | | REDUCE: (223), (225) imply: % 150.97/22.14 | | | | | | | | | (226) $false % 150.97/22.14 | | | | | | | | | % 150.97/22.14 | | | | | | | | | CLOSE: (226) is inconsistent. % 150.97/22.14 | | | | | | | | | % 150.97/22.14 | | | | | | | | Case 2: % 150.97/22.14 | | | | | | | | | % 150.97/22.14 | | | | | | | | | (227) all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1 % 150.97/22.14 | | | | | | | | | % 150.97/22.14 | | | | | | | | | BETA: splitting (227) gives: % 150.97/22.14 | | | | | | | | | % 150.97/22.14 | | | | | | | | | Case 1: % 150.97/22.14 | | | | | | | | | | % 150.97/22.14 | | | | | | | | | | (228) all_58_2 = e1 % 150.97/22.14 | | | | | | | | | | % 150.97/22.14 | | | | | | | | | | COMBINE_EQS: (173), (228) imply: % 150.97/22.14 | | | | | | | | | | (229) all_8_0 = e1 % 150.97/22.14 | | | | | | | | | | % 150.97/22.14 | | | | | | | | | | REDUCE: (23), (229) imply: % 150.97/22.14 | | | | | | | | | | (230) $false % 150.97/22.14 | | | | | | | | | | % 150.97/22.14 | | | | | | | | | | CLOSE: (230) is inconsistent. % 150.97/22.14 | | | | | | | | | | % 150.97/22.14 | | | | | | | | | Case 2: % 150.97/22.14 | | | | | | | | | | % 150.97/22.14 | | | | | | | | | | (231) all_58_6 = e1 | all_58_12 = e1 % 150.97/22.14 | | | | | | | | | | % 150.97/22.14 | | | | | | | | | | BETA: splitting (231) gives: % 150.97/22.14 | | | | | | | | | | % 150.97/22.14 | | | | | | | | | | Case 1: % 150.97/22.14 | | | | | | | | | | | % 150.97/22.14 | | | | | | | | | | | (232) all_58_6 = e1 % 150.97/22.14 | | | | | | | | | | | % 150.97/22.14 | | | | | | | | | | | COMBINE_EQS: (10), (232) imply: % 150.97/22.14 | | | | | | | | | | | (233) all_52_2 = e1 % 150.97/22.14 | | | | | | | | | | | % 150.97/22.14 | | | | | | | | | | | SIMP: (233) implies: % 150.97/22.14 | | | | | | | | | | | (234) all_52_2 = e1 % 150.97/22.14 | | | | | | | | | | | % 150.97/22.14 | | | | | | | | | | | REDUCE: (69), (234) imply: % 150.97/22.14 | | | | | | | | | | | (235) ~ (all_52_6 = e1) % 150.97/22.14 | | | | | | | | | | | % 150.97/22.14 | | | | | | | | | | | SIMP: (235) implies: % 150.97/22.14 | | | | | | | | | | | (236) ~ (all_52_6 = e1) % 150.97/22.14 | | | | | | | | | | | % 150.97/22.14 | | | | | | | | | | | REDUCE: (217), (234) imply: % 150.97/22.14 | | | | | | | | | | | (237) ~ (all_4_1 = e1) % 150.97/22.14 | | | | | | | | | | | % 150.97/22.14 | | | | | | | | | | | SIMP: (237) implies: % 150.97/22.14 | | | | | | | | | | | (238) ~ (all_4_1 = e1) % 150.97/22.14 | | | | | | | | | | | % 150.97/22.14 | | | | | | | | | | | BETA: splitting (19) gives: % 150.97/22.14 | | | | | | | | | | | % 150.97/22.14 | | | | | | | | | | | Case 1: % 150.97/22.14 | | | | | | | | | | | | % 150.97/22.14 | | | | | | | | | | | | (239) ~ (all_56_21 = e2) % 150.97/22.14 | | | | | | | | | | | | % 150.97/22.14 | | | | | | | | | | | | REDUCE: (216), (239) imply: % 150.97/22.14 | | | | | | | | | | | | (240) ~ (all_4_1 = e2) % 150.97/22.14 | | | | | | | | | | | | % 150.97/22.14 | | | | | | | | | | | | BETA: splitting (36) gives: % 150.97/22.14 | | | | | | | | | | | | % 150.97/22.14 | | | | | | | | | | | | Case 1: % 150.97/22.14 | | | | | | | | | | | | | % 150.97/22.14 | | | | | | | | | | | | | (241) all_54_10 = e3 % 150.97/22.14 | | | | | | | | | | | | | % 150.97/22.14 | | | | | | | | | | | | | REF_CLOSE: (212), (215), (241) are inconsistent by sub-proof % 150.97/22.14 | | | | | | | | | | | | | #282. % 150.97/22.14 | | | | | | | | | | | | | % 150.97/22.14 | | | | | | | | | | | | Case 2: % 150.97/22.14 | | | | | | | | | | | | | % 150.97/22.14 | | | | | | | | | | | | | (242) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 150.97/22.14 | | | | | | | | | | | | | % 150.97/22.14 | | | | | | | | | | | | | BETA: splitting (242) gives: % 150.97/22.14 | | | | | | | | | | | | | % 150.97/22.14 | | | | | | | | | | | | | Case 1: % 150.97/22.14 | | | | | | | | | | | | | | % 150.97/22.14 | | | | | | | | | | | | | | (243) all_54_10 = e2 % 150.97/22.14 | | | | | | | | | | | | | | % 150.97/22.14 | | | | | | | | | | | | | | REF_CLOSE: (215), (240), (243) are inconsistent by sub-proof % 150.97/22.14 | | | | | | | | | | | | | | #281. % 150.97/22.14 | | | | | | | | | | | | | | % 150.97/22.14 | | | | | | | | | | | | | Case 2: % 150.97/22.14 | | | | | | | | | | | | | | % 150.97/22.14 | | | | | | | | | | | | | | (244) all_54_10 = e1 | all_54_10 = e0 % 150.97/22.14 | | | | | | | | | | | | | | % 150.97/22.14 | | | | | | | | | | | | | | BETA: splitting (244) gives: % 150.97/22.14 | | | | | | | | | | | | | | % 150.97/22.14 | | | | | | | | | | | | | | Case 1: % 150.97/22.14 | | | | | | | | | | | | | | | % 150.97/22.14 | | | | | | | | | | | | | | | (245) all_54_10 = e1 % 150.97/22.14 | | | | | | | | | | | | | | | % 150.97/22.14 | | | | | | | | | | | | | | | COMBINE_EQS: (215), (245) imply: % 150.97/22.14 | | | | | | | | | | | | | | | (246) all_4_1 = e1 % 150.97/22.14 | | | | | | | | | | | | | | | % 150.97/22.14 | | | | | | | | | | | | | | | SIMP: (246) implies: % 150.97/22.14 | | | | | | | | | | | | | | | (247) all_4_1 = e1 % 150.97/22.14 | | | | | | | | | | | | | | | % 150.97/22.14 | | | | | | | | | | | | | | | REDUCE: (238), (247) imply: % 150.97/22.14 | | | | | | | | | | | | | | | (248) $false % 150.97/22.14 | | | | | | | | | | | | | | | % 150.97/22.14 | | | | | | | | | | | | | | | CLOSE: (248) is inconsistent. % 150.97/22.14 | | | | | | | | | | | | | | | % 150.97/22.14 | | | | | | | | | | | | | | Case 2: % 150.97/22.14 | | | | | | | | | | | | | | | % 150.97/22.14 | | | | | | | | | | | | | | | (249) all_54_10 = e0 % 150.97/22.14 | | | | | | | | | | | | | | | % 150.97/22.14 | | | | | | | | | | | | | | | REF_CLOSE: (215), (219), (249) are inconsistent by sub-proof % 150.97/22.14 | | | | | | | | | | | | | | | #277. % 150.97/22.14 | | | | | | | | | | | | | | | % 150.97/22.14 | | | | | | | | | | | | | | End of split % 150.97/22.14 | | | | | | | | | | | | | | % 150.97/22.14 | | | | | | | | | | | | | End of split % 150.97/22.14 | | | | | | | | | | | | | % 150.97/22.14 | | | | | | | | | | | | End of split % 150.97/22.14 | | | | | | | | | | | | % 150.97/22.14 | | | | | | | | | | | Case 2: % 150.97/22.14 | | | | | | | | | | | | % 150.97/22.14 | | | | | | | | | | | | (250) all_56_19 = e1 % 150.97/22.14 | | | | | | | | | | | | % 150.97/22.14 | | | | | | | | | | | | COMBINE_EQS: (157), (250) imply: % 150.97/22.14 | | | | | | | | | | | | (251) all_52_6 = e1 % 150.97/22.14 | | | | | | | | | | | | % 150.97/22.14 | | | | | | | | | | | | REDUCE: (236), (251) imply: % 150.97/22.14 | | | | | | | | | | | | (252) $false % 150.97/22.14 | | | | | | | | | | | | % 150.97/22.14 | | | | | | | | | | | | CLOSE: (252) is inconsistent. % 150.97/22.14 | | | | | | | | | | | | % 150.97/22.14 | | | | | | | | | | | End of split % 150.97/22.14 | | | | | | | | | | | % 150.97/22.14 | | | | | | | | | | Case 2: % 150.97/22.14 | | | | | | | | | | | % 150.97/22.14 | | | | | | | | | | | (253) all_58_12 = e1 % 150.97/22.14 | | | | | | | | | | | % 150.97/22.14 | | | | | | | | | | | COMBINE_EQS: (161), (253) imply: % 150.97/22.14 | | | | | | | | | | | (254) all_52_3 = e1 % 150.97/22.14 | | | | | | | | | | | % 150.97/22.14 | | | | | | | | | | | REDUCE: (202), (254) imply: % 150.97/22.14 | | | | | | | | | | | (255) $false % 150.97/22.14 | | | | | | | | | | | % 150.97/22.14 | | | | | | | | | | | CLOSE: (255) is inconsistent. % 150.97/22.14 | | | | | | | | | | | % 150.97/22.14 | | | | | | | | | | End of split % 150.97/22.14 | | | | | | | | | | % 150.97/22.14 | | | | | | | | | End of split % 150.97/22.14 | | | | | | | | | % 150.97/22.14 | | | | | | | | End of split % 150.97/22.14 | | | | | | | | % 150.97/22.14 | | | | | | | Case 2: % 150.97/22.14 | | | | | | | | % 150.97/22.14 | | | | | | | | (256) all_56_5 = e3 % 150.97/22.14 | | | | | | | | (257) all_56_1 = e1 % 150.97/22.14 | | | | | | | | % 150.97/22.14 | | | | | | | | COMBINE_EQS: (38), (257) imply: % 150.97/22.14 | | | | | | | | (258) all_10_2 = e1 % 150.97/22.14 | | | | | | | | % 150.97/22.14 | | | | | | | | COMBINE_EQS: (90), (256) imply: % 150.97/22.14 | | | | | | | | (259) all_52_8 = e3 % 150.97/22.14 | | | | | | | | % 150.97/22.14 | | | | | | | | COMBINE_EQS: (29), (259) imply: % 150.97/22.14 | | | | | | | | (260) all_58_4 = e3 % 150.97/22.14 | | | | | | | | % 150.97/22.14 | | | | | | | | REDUCE: (7), (259) imply: % 150.97/22.14 | | | | | | | | (261) ~ (all_52_9 = e3) % 150.97/22.14 | | | | | | | | % 150.97/22.14 | | | | | | | | SIMP: (261) implies: % 150.97/22.14 | | | | | | | | (262) ~ (all_52_9 = e3) % 150.97/22.14 | | | | | | | | % 150.97/22.14 | | | | | | | | REDUCE: (183), (258) imply: % 150.97/22.14 | | | | | | | | (263) ~ (all_8_0 = e1) % 150.97/22.14 | | | | | | | | % 150.97/22.14 | | | | | | | | REDUCE: (134), (258) imply: % 150.97/22.14 | | | | | | | | (264) op(e1, e1) = all_10_1 % 150.97/22.14 | | | | | | | | % 150.97/22.14 | | | | | | | | GROUND_INST: instantiating (62) with all_4_1, all_10_1, e1, e1, % 150.97/22.14 | | | | | | | | simplifying with (208), (264) gives: % 150.97/22.14 | | | | | | | | (265) all_10_1 = all_4_1 % 150.97/22.14 | | | | | | | | % 150.97/22.14 | | | | | | | | BETA: splitting (3) gives: % 150.97/22.14 | | | | | | | | % 150.97/22.14 | | | | | | | | Case 1: % 150.97/22.14 | | | | | | | | | % 150.97/22.14 | | | | | | | | | (266) ~ (all_56_11 = e1) % 150.97/22.14 | | | | | | | | | % 150.97/22.14 | | | | | | | | | REDUCE: (1), (266) imply: % 150.97/22.14 | | | | | | | | | (267) ~ (all_8_2 = e1) % 150.97/22.14 | | | | | | | | | % 150.97/22.14 | | | | | | | | | BETA: splitting (60) gives: % 150.97/22.14 | | | | | | | | | % 150.97/22.14 | | | | | | | | | Case 1: % 150.97/22.14 | | | | | | | | | | % 150.97/22.14 | | | | | | | | | | (268) all_58_2 = e1 % 150.97/22.14 | | | | | | | | | | % 150.97/22.14 | | | | | | | | | | COMBINE_EQS: (173), (268) imply: % 150.97/22.14 | | | | | | | | | | (269) all_8_0 = e1 % 150.97/22.14 | | | | | | | | | | % 150.97/22.14 | | | | | | | | | | REDUCE: (23), (269) imply: % 150.97/22.14 | | | | | | | | | | (270) $false % 150.97/22.14 | | | | | | | | | | % 150.97/22.14 | | | | | | | | | | CLOSE: (270) is inconsistent. % 150.97/22.14 | | | | | | | | | | % 150.97/22.14 | | | | | | | | | Case 2: % 150.97/22.14 | | | | | | | | | | % 150.97/22.14 | | | | | | | | | | (271) all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1 % 150.97/22.14 | | | | | | | | | | % 150.97/22.14 | | | | | | | | | | BETA: splitting (271) gives: % 150.97/22.14 | | | | | | | | | | % 150.97/22.14 | | | | | | | | | | Case 1: % 150.97/22.14 | | | | | | | | | | | % 150.97/22.14 | | | | | | | | | | | (272) all_58_3 = e1 % 150.97/22.14 | | | | | | | | | | | % 150.97/22.14 | | | | | | | | | | | COMBINE_EQS: (99), (272) imply: % 150.97/22.14 | | | | | | | | | | | (273) all_8_2 = e1 % 150.97/22.14 | | | | | | | | | | | % 150.97/22.14 | | | | | | | | | | | REDUCE: (267), (273) imply: % 150.97/22.14 | | | | | | | | | | | (274) $false % 150.97/22.14 | | | | | | | | | | | % 150.97/22.14 | | | | | | | | | | | CLOSE: (274) is inconsistent. % 150.97/22.14 | | | | | | | | | | | % 150.97/22.14 | | | | | | | | | | Case 2: % 150.97/22.14 | | | | | | | | | | | % 150.97/22.14 | | | | | | | | | | | (275) all_58_5 = e1 | all_58_10 = e1 % 150.97/22.14 | | | | | | | | | | | % 150.97/22.14 | | | | | | | | | | | BETA: splitting (275) gives: % 150.97/22.14 | | | | | | | | | | | % 150.97/22.14 | | | | | | | | | | | Case 1: % 150.97/22.14 | | | | | | | | | | | | % 150.97/22.14 | | | | | | | | | | | | (276) all_58_5 = e1 % 150.97/22.14 | | | | | | | | | | | | % 150.97/22.14 | | | | | | | | | | | | COMBINE_EQS: (41), (276) imply: % 150.97/22.14 | | | | | | | | | | | | (277) all_52_9 = e1 % 150.97/22.14 | | | | | | | | | | | | % 150.97/22.14 | | | | | | | | | | | | REDUCE: (218), (277) imply: % 150.97/22.14 | | | | | | | | | | | | (278) ~ (all_4_1 = e1) % 150.97/22.14 | | | | | | | | | | | | % 150.97/22.14 | | | | | | | | | | | | SIMP: (278) implies: % 150.97/22.14 | | | | | | | | | | | | (279) ~ (all_4_1 = e1) % 150.97/22.14 | | | | | | | | | | | | % 150.97/22.14 | | | | | | | | | | | | REDUCE: (262), (277) imply: % 150.97/22.14 | | | | | | | | | | | | (280) ~ (e3 = e1) % 150.97/22.14 | | | | | | | | | | | | % 150.97/22.14 | | | | | | | | | | | | BETA: splitting (111) gives: % 150.97/22.14 | | | | | | | | | | | | % 150.97/22.14 | | | | | | | | | | | | Case 1: % 150.97/22.14 | | | | | | | | | | | | | % 150.97/22.14 | | | | | | | | | | | | | (281) all_56_1 = e3 % 150.97/22.14 | | | | | | | | | | | | | % 150.97/22.14 | | | | | | | | | | | | | REF_CLOSE: (167), (257), (281) are inconsistent by sub-proof % 150.97/22.14 | | | | | | | | | | | | | #182. % 150.97/22.14 | | | | | | | | | | | | | % 150.97/22.14 | | | | | | | | | | | | Case 2: % 150.97/22.14 | | | | | | | | | | | | | % 150.97/22.14 | | | | | | | | | | | | | (282) all_56_11 = e2 | all_56_21 = e1 | all_56_31 = e0 % 150.97/22.14 | | | | | | | | | | | | | % 150.97/22.14 | | | | | | | | | | | | | BETA: splitting (282) gives: % 150.97/22.14 | | | | | | | | | | | | | % 150.97/22.14 | | | | | | | | | | | | | Case 1: % 150.97/22.14 | | | | | | | | | | | | | | % 150.97/22.14 | | | | | | | | | | | | | | (283) all_56_11 = e2 % 150.97/22.14 | | | | | | | | | | | | | | % 150.97/22.14 | | | | | | | | | | | | | | COMBINE_EQS: (1), (283) imply: % 150.97/22.14 | | | | | | | | | | | | | | (284) all_8_2 = e2 % 150.97/22.14 | | | | | | | | | | | | | | % 150.97/22.14 | | | | | | | | | | | | | | REF_CLOSE: (53), (62), (141), (168), (221), (284) are % 150.97/22.14 | | | | | | | | | | | | | | inconsistent by sub-proof #348. % 150.97/22.14 | | | | | | | | | | | | | | % 150.97/22.14 | | | | | | | | | | | | | Case 2: % 150.97/22.14 | | | | | | | | | | | | | | % 150.97/22.14 | | | | | | | | | | | | | | (285) all_56_21 = e1 | all_56_31 = e0 % 150.97/22.14 | | | | | | | | | | | | | | % 150.97/22.14 | | | | | | | | | | | | | | REF_CLOSE: (59), (194), (216), (279), (285) are inconsistent % 150.97/22.14 | | | | | | | | | | | | | | by sub-proof #181. % 150.97/22.14 | | | | | | | | | | | | | | % 150.97/22.14 | | | | | | | | | | | | | End of split % 150.97/22.14 | | | | | | | | | | | | | % 150.97/22.14 | | | | | | | | | | | | End of split % 150.97/22.14 | | | | | | | | | | | | % 150.97/22.14 | | | | | | | | | | | Case 2: % 150.97/22.14 | | | | | | | | | | | | % 150.97/22.14 | | | | | | | | | | | | (286) all_58_10 = e1 % 150.97/22.14 | | | | | | | | | | | | % 150.97/22.14 | | | | | | | | | | | | COMBINE_EQS: (132), (286) imply: % 150.97/22.14 | | | | | | | | | | | | (287) all_52_13 = e1 % 150.97/22.14 | | | | | | | | | | | | % 150.97/22.14 | | | | | | | | | | | | REDUCE: (207), (287) imply: % 150.97/22.14 | | | | | | | | | | | | (288) $false % 150.97/22.14 | | | | | | | | | | | | % 150.97/22.14 | | | | | | | | | | | | CLOSE: (288) is inconsistent. % 150.97/22.14 | | | | | | | | | | | | % 150.97/22.14 | | | | | | | | | | | End of split % 150.97/22.14 | | | | | | | | | | | % 150.97/22.14 | | | | | | | | | | End of split % 150.97/22.14 | | | | | | | | | | % 150.97/22.14 | | | | | | | | | End of split % 150.97/22.14 | | | | | | | | | % 150.97/22.14 | | | | | | | | Case 2: % 150.97/22.14 | | | | | | | | | % 150.97/22.14 | | | | | | | | | (289) all_56_13 = e2 % 150.97/22.14 | | | | | | | | | % 150.97/22.14 | | | | | | | | | COMBINE_EQS: (77), (289) imply: % 150.97/22.14 | | | | | | | | | (290) all_52_9 = e2 % 150.97/22.14 | | | | | | | | | % 150.97/22.14 | | | | | | | | | COMBINE_EQS: (41), (290) imply: % 150.97/22.14 | | | | | | | | | (291) all_58_5 = e2 % 150.97/22.14 | | | | | | | | | % 150.97/22.14 | | | | | | | | | REF_CLOSE: (59), (62), (74), (83), (91), (98), (110), (122), % 150.97/22.14 | | | | | | | | | (137), (148), (167), (200), (208), (209), (210), % 150.97/22.14 | | | | | | | | | (260), (291) are inconsistent by sub-proof #179. % 150.97/22.14 | | | | | | | | | % 150.97/22.14 | | | | | | | | End of split % 150.97/22.14 | | | | | | | | % 150.97/22.14 | | | | | | | End of split % 150.97/22.14 | | | | | | | % 150.97/22.14 | | | | | | Case 2: % 150.97/22.14 | | | | | | | % 150.97/22.14 | | | | | | | (292) all_56_11 = e3 % 150.97/22.14 | | | | | | | (293) all_56_9 = e2 % 150.97/22.14 | | | | | | | % 150.97/22.14 | | | | | | | COMBINE_EQS: (172), (293) imply: % 150.97/22.14 | | | | | | | (294) all_8_0 = e2 % 150.97/22.14 | | | | | | | % 150.97/22.14 | | | | | | | COMBINE_EQS: (1), (292) imply: % 150.97/22.14 | | | | | | | (295) all_8_2 = e3 % 150.97/22.14 | | | | | | | % 150.97/22.14 | | | | | | | REDUCE: (177), (294) imply: % 150.97/22.14 | | | | | | | (296) ~ (all_52_3 = e2) % 150.97/22.14 | | | | | | | % 150.97/22.14 | | | | | | | REDUCE: (168), (295) imply: % 150.97/22.14 | | | | | | | (297) op(e3, e3) = e3 % 150.97/22.14 | | | | | | | % 150.97/22.14 | | | | | | | REF_CLOSE: (26), (54), (62), (63), (75), (125), (201), (202), % 150.97/22.14 | | | | | | | (296), (297) are inconsistent by sub-proof #313. % 150.97/22.14 | | | | | | | % 150.97/22.14 | | | | | | End of split % 150.97/22.14 | | | | | | % 150.97/22.14 | | | | | Case 2: % 150.97/22.14 | | | | | | % 150.97/22.14 | | | | | | (298) ~ (all_34_2 = e1) % 150.97/22.14 | | | | | | % 150.97/22.14 | | | | | | REDUCE: (199), (298) imply: % 150.97/22.14 | | | | | | (299) $false % 150.97/22.14 | | | | | | % 150.97/22.14 | | | | | | CLOSE: (299) is inconsistent. % 150.97/22.14 | | | | | | % 150.97/22.14 | | | | | End of split % 150.97/22.14 | | | | | % 150.97/22.14 | | | | End of split % 150.97/22.14 | | | | % 150.97/22.14 | | | Case 2: % 150.97/22.14 | | | | % 150.97/22.14 | | | | (300) all_36_1 = e3 % 150.97/22.14 | | | | (301) ~ (all_36_0 = e0) | ~ (all_36_2 = e2) % 150.97/22.14 | | | | % 150.97/22.14 | | | | REF_CLOSE: (1), (3), (4), (5), (8), (10), (15), (18), (19), (22), (23), % 150.97/22.14 | | | | (25), (27), (28), (29), (30), (31), (35), (36), (37), (38), % 150.97/22.14 | | | | (40), (41), (42), (49), (52), (53), (54), (57), (59), (60), % 150.97/22.14 | | | | (62), (63), (66), (67), (68), (69), (72), (74), (77), (80), % 150.97/22.14 | | | | (81), (82), (83), (85), (91), (92), (93), (94), (96), (99), % 150.97/22.14 | | | | (100), (101), (104), (105), (106), (107), (109), (110), % 150.97/22.14 | | | | (111), (112), (119), (120), (122), (123), (125), (126), % 150.97/22.14 | | | | (129), (130), (131), (132), (135), (137), (141), (142), % 150.97/22.14 | | | | (144), (145), (146), (147), (148), (149), (150), (154), % 150.97/22.14 | | | | (155), (156), (157), (159), (161), (162), (164), (168), % 150.97/22.14 | | | | (171), (172), (173), (175), (177), (179), (181), (183), % 150.97/22.14 | | | | (184), (300), (301) are inconsistent by sub-proof #191. % 150.97/22.14 | | | | % 150.97/22.14 | | | End of split % 150.97/22.14 | | | % 150.97/22.14 | | End of split % 150.97/22.14 | | % 150.97/22.14 | Case 2: % 150.97/22.14 | | % 150.97/22.14 | | (302) all_28_0 = e2 % 150.97/22.14 | | (303) ~ (all_28_1 = e3) | ~ (all_28_2 = e0) % 150.97/22.14 | | % 150.97/22.14 | | COMBINE_EQS: (64), (302) imply: % 150.97/22.14 | | (304) all_6_0 = e2 % 150.97/22.14 | | % 150.97/22.14 | | SIMP: (304) implies: % 150.97/22.14 | | (305) all_6_0 = e2 % 150.97/22.14 | | % 150.97/22.14 | | REF_CLOSE: (1), (4), (7), (11), (13), (15), (16), (19), (20), (27), (29), % 150.97/22.14 | | (30), (31), (32), (33), (34), (35), (36), (38), (41), (42), (43), % 150.97/22.14 | | (45), (46), (51), (54), (55), (56), (57), (58), (60), (61), (62), % 150.97/22.14 | | (66), (70), (71), (73), (76), (81), (85), (86), (87), (91), (93), % 150.97/22.14 | | (94), (99), (101), (103), (104), (105), (110), (111), (112), % 150.97/22.14 | | (113), (114), (115), (118), (119), (121), (122), (123), (126), % 150.97/22.14 | | (127), (128), (132), (135), (136), (137), (139), (141), (142), % 150.97/22.14 | | (144), (145), (146), (150), (151), (153), (154), (155), (157), % 150.97/22.14 | | (159), (164), (167), (303), (305) are inconsistent by sub-proof % 150.97/22.14 | | #200. % 150.97/22.14 | | % 150.97/22.14 | End of split % 150.97/22.14 | % 150.97/22.14 End of proof % 150.97/22.14 % 150.97/22.14 Sub-proof #179 shows that the following formulas are inconsistent: % 150.97/22.14 ---------------------------------------------------------------- % 150.97/22.14 (1) op(e0, e1) = all_56_30 % 150.97/22.14 (2) ~ (e1 = e0) % 150.97/22.14 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 150.97/22.14 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 150.97/22.14 (4) op(e0, all_4_1) = e2 % 150.97/22.14 (5) all_58_8 = all_6_2 % 150.97/22.14 (6) all_58_5 = e2 % 150.97/22.14 (7) ~ (e2 = e1) % 150.97/22.14 (8) all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1 % 150.97/22.14 (9) op(e0, e1) = e0 % 150.97/22.14 (10) op(all_6_2, all_6_2) = all_6_1 % 150.97/22.14 (11) all_58_14 = e0 % 150.97/22.14 (12) op(e1, e1) = all_6_2 % 150.97/22.14 (13) op(e1, e1) = all_4_1 % 150.97/22.14 (14) op(e1, all_6_2) = all_56_20 % 150.97/22.14 (15) ~ (e3 = e1) % 150.97/22.14 (16) ~ (e2 = e0) % 150.97/22.14 (17) all_58_4 = e3 % 150.97/22.14 % 150.97/22.14 Begin of proof % 150.97/22.14 | % 150.97/22.14 | BETA: splitting (8) gives: % 150.97/22.14 | % 150.97/22.14 | Case 1: % 150.97/22.14 | | % 150.97/22.14 | | (18) all_58_4 = e1 % 150.97/22.14 | | % 150.97/22.14 | | COMBINE_EQS: (17), (18) imply: % 150.97/22.14 | | (19) e3 = e1 % 150.97/22.14 | | % 150.97/22.14 | | REDUCE: (15), (19) imply: % 150.97/22.14 | | (20) $false % 150.97/22.14 | | % 150.97/22.14 | | CLOSE: (20) is inconsistent. % 150.97/22.14 | | % 150.97/22.14 | Case 2: % 150.97/22.14 | | % 150.97/22.14 | | (21) all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1 % 150.97/22.14 | | % 150.97/22.14 | | BETA: splitting (21) gives: % 150.97/22.14 | | % 150.97/22.14 | | Case 1: % 150.97/22.14 | | | % 150.97/22.14 | | | (22) all_58_5 = e1 % 150.97/22.14 | | | % 150.97/22.14 | | | COMBINE_EQS: (6), (22) imply: % 150.97/22.14 | | | (23) e2 = e1 % 150.97/22.14 | | | % 150.97/22.14 | | | REDUCE: (7), (23) imply: % 150.97/22.14 | | | (24) $false % 150.97/22.14 | | | % 150.97/22.14 | | | CLOSE: (24) is inconsistent. % 150.97/22.14 | | | % 150.97/22.14 | | Case 2: % 150.97/22.14 | | | % 150.97/22.14 | | | (25) all_58_8 = e1 | all_58_14 = e1 % 150.97/22.14 | | | % 150.97/22.14 | | | BETA: splitting (25) gives: % 150.97/22.14 | | | % 150.97/22.14 | | | Case 1: % 150.97/22.14 | | | | % 150.97/22.14 | | | | (26) all_58_8 = e1 % 150.97/22.14 | | | | % 150.97/22.14 | | | | COMBINE_EQS: (5), (26) imply: % 150.97/22.14 | | | | (27) all_6_2 = e1 % 150.97/22.14 | | | | % 150.97/22.14 | | | | REDUCE: (10), (27) imply: % 150.97/22.14 | | | | (28) op(e1, e1) = all_6_1 % 150.97/22.14 | | | | % 150.97/22.14 | | | | REDUCE: (14), (27) imply: % 150.97/22.14 | | | | (29) op(e1, e1) = all_56_20 % 150.97/22.14 | | | | % 150.97/22.14 | | | | REDUCE: (12), (27) imply: % 150.97/22.14 | | | | (30) op(e1, e1) = e1 % 150.97/22.14 | | | | % 150.97/22.14 | | | | REF_CLOSE: (1), (3), (4), (9), (13), (16), (28), (29), (30) are % 150.97/22.14 | | | | inconsistent by sub-proof #180. % 150.97/22.14 | | | | % 150.97/22.14 | | | Case 2: % 150.97/22.14 | | | | % 150.97/22.14 | | | | (31) all_58_14 = e1 % 150.97/22.14 | | | | % 150.97/22.14 | | | | REF_CLOSE: (2), (11), (31) are inconsistent by sub-proof #396. % 150.97/22.14 | | | | % 150.97/22.14 | | | End of split % 150.97/22.14 | | | % 150.97/22.14 | | End of split % 150.97/22.14 | | % 150.97/22.14 | End of split % 150.97/22.14 | % 150.97/22.14 End of proof % 150.97/22.14 % 150.97/22.14 Sub-proof #180 shows that the following formulas are inconsistent: % 150.97/22.14 ---------------------------------------------------------------- % 150.97/22.14 (1) op(e0, e1) = all_56_30 % 150.97/22.14 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 150.97/22.14 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 150.97/22.14 (3) op(e0, all_4_1) = e2 % 150.97/22.14 (4) op(e0, e1) = e0 % 150.97/22.14 (5) op(e1, e1) = all_56_20 % 150.97/22.14 (6) op(e1, e1) = all_4_1 % 150.97/22.14 (7) ~ (e2 = e0) % 150.97/22.14 (8) op(e1, e1) = all_6_1 % 150.97/22.14 (9) op(e1, e1) = e1 % 150.97/22.14 % 150.97/22.14 Begin of proof % 150.97/22.14 | % 150.97/22.14 | GROUND_INST: instantiating (2) with e0, all_56_30, e1, e0, simplifying with % 150.97/22.14 | (1), (4) gives: % 150.97/22.14 | (10) all_56_30 = e0 % 150.97/22.14 | % 150.97/22.14 | GROUND_INST: instantiating (2) with all_4_1, all_6_1, e1, e1, simplifying with % 150.97/22.14 | (6), (8) gives: % 150.97/22.14 | (11) all_6_1 = all_4_1 % 150.97/22.14 | % 150.97/22.14 | GROUND_INST: instantiating (2) with all_6_1, all_56_20, e1, e1, simplifying % 150.97/22.14 | with (5), (8) gives: % 150.97/22.14 | (12) all_56_20 = all_6_1 % 150.97/22.14 | % 150.97/22.14 | GROUND_INST: instantiating (2) with e1, all_56_20, e1, e1, simplifying with % 150.97/22.14 | (5), (9) gives: % 150.97/22.14 | (13) all_56_20 = e1 % 150.97/22.14 | % 150.97/22.14 | COMBINE_EQS: (12), (13) imply: % 150.97/22.14 | (14) all_6_1 = e1 % 150.97/22.14 | % 150.97/22.14 | SIMP: (14) implies: % 150.97/22.14 | (15) all_6_1 = e1 % 150.97/22.14 | % 150.97/22.14 | COMBINE_EQS: (11), (15) imply: % 150.97/22.14 | (16) all_4_1 = e1 % 150.97/22.14 | % 150.97/22.14 | SIMP: (16) implies: % 150.97/22.14 | (17) all_4_1 = e1 % 150.97/22.14 | % 150.97/22.14 | REDUCE: (3), (17) imply: % 150.97/22.14 | (18) op(e0, e1) = e2 % 150.97/22.14 | % 150.97/22.14 | GROUND_INST: instantiating (2) with e0, e2, e1, e0, simplifying with (4), (18) % 150.97/22.14 | gives: % 150.97/22.14 | (19) e2 = e0 % 150.97/22.14 | % 150.97/22.14 | REDUCE: (7), (19) imply: % 150.97/22.14 | (20) $false % 150.97/22.14 | % 150.97/22.14 | CLOSE: (20) is inconsistent. % 150.97/22.14 | % 150.97/22.14 End of proof % 150.97/22.14 % 150.97/22.14 Sub-proof #181 shows that the following formulas are inconsistent: % 150.97/22.14 ---------------------------------------------------------------- % 150.97/22.14 (1) all_56_31 = e1 % 150.97/22.14 (2) ~ (e1 = e0) % 150.97/22.14 (3) all_56_21 = all_4_1 % 150.97/22.14 (4) ~ (all_4_1 = e1) % 150.97/22.14 (5) all_56_21 = e1 | all_56_31 = e0 % 150.97/22.14 % 150.97/22.14 Begin of proof % 150.97/22.14 | % 150.97/22.14 | BETA: splitting (5) gives: % 150.97/22.14 | % 150.97/22.14 | Case 1: % 150.97/22.14 | | % 150.97/22.14 | | (6) all_56_21 = e1 % 150.97/22.14 | | % 150.97/22.14 | | COMBINE_EQS: (3), (6) imply: % 150.97/22.14 | | (7) all_4_1 = e1 % 150.97/22.14 | | % 150.97/22.14 | | SIMP: (7) implies: % 150.97/22.14 | | (8) all_4_1 = e1 % 150.97/22.14 | | % 150.97/22.14 | | REDUCE: (4), (8) imply: % 150.97/22.14 | | (9) $false % 150.97/22.14 | | % 150.97/22.14 | | CLOSE: (9) is inconsistent. % 150.97/22.14 | | % 150.97/22.14 | Case 2: % 150.97/22.14 | | % 150.97/22.14 | | (10) all_56_31 = e0 % 150.97/22.14 | | % 150.97/22.14 | | REF_CLOSE: (1), (2), (10) are inconsistent by sub-proof #201. % 150.97/22.14 | | % 150.97/22.14 | End of split % 150.97/22.14 | % 150.97/22.14 End of proof % 150.97/22.14 % 150.97/22.14 Sub-proof #182 shows that the following formulas are inconsistent: % 150.97/22.14 ---------------------------------------------------------------- % 150.97/22.14 (1) all_56_1 = e3 % 150.97/22.14 (2) all_56_1 = e1 % 150.97/22.14 (3) ~ (e3 = e1) % 150.97/22.14 % 150.97/22.14 Begin of proof % 150.97/22.14 | % 150.97/22.14 | COMBINE_EQS: (1), (2) imply: % 150.97/22.14 | (4) e3 = e1 % 150.97/22.14 | % 150.97/22.14 | SIMP: (4) implies: % 150.97/22.14 | (5) e3 = e1 % 150.97/22.14 | % 150.97/22.14 | REDUCE: (3), (5) imply: % 150.97/22.14 | (6) $false % 150.97/22.14 | % 150.97/22.14 | CLOSE: (6) is inconsistent. % 150.97/22.14 | % 150.97/22.14 End of proof % 150.97/22.14 % 150.97/22.14 Sub-proof #183 shows that the following formulas are inconsistent: % 150.97/22.14 ---------------------------------------------------------------- % 150.97/22.14 (1) all_56_11 = all_8_2 % 150.97/22.14 (2) ~ (all_56_11 = e1) | all_56_13 = e2 % 150.97/22.14 (3) ~ (all_52_11 = all_6_2) % 150.97/22.14 (4) all_54_9 = all_52_6 % 150.97/22.14 (5) ~ (all_8_1 = e1) % 150.97/22.14 (6) all_54_10 = all_6_2 % 150.97/22.14 (7) ~ (all_56_21 = e2) | all_56_19 = e1 % 150.97/22.14 (8) ~ (all_52_14 = all_4_2) % 150.97/22.14 (9) ~ (all_52_9 = all_8_2) % 150.97/22.14 (10) ~ (all_8_1 = e3) % 150.97/22.14 (11) op(e0, e0) = all_4_2 % 150.97/22.14 (12) all_58_6 = e0 | all_58_7 = e0 | all_58_8 = e0 | all_58_11 = e0 % 150.97/22.14 (13) all_58_4 = all_52_8 % 150.97/22.14 (14) ~ (all_52_6 = all_52_14) % 150.97/22.14 (15) ~ (all_6_0 = e2) % 150.97/22.14 (16) all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1 % 150.97/22.14 (17) all_56_21 = all_6_2 % 150.97/22.14 (18) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 150.97/22.14 (19) ~ (all_52_14 = e2) % 150.97/22.14 (20) ~ (all_52_7 = all_8_2) % 150.97/22.14 (21) all_56_1 = all_10_2 % 150.97/22.14 (22) all_58_5 = all_52_9 % 150.97/22.14 (23) all_58_9 = all_52_12 % 150.97/22.14 (24) all_58_1 = all_52_4 % 150.97/22.14 (25) all_58_13 = all_52_7 % 150.97/22.14 (26) op(e2, all_8_2) = all_56_10 % 150.97/22.14 (27) op(e3, e3) = all_10_2 % 150.97/22.14 (28) ~ (all_52_6 = all_6_0) % 150.97/22.14 (29) ~ (all_56_21 = e3) | all_56_17 = e1 % 150.97/22.14 (30) ~ (e1 = e0) % 150.97/22.14 (31) all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2 % 150.97/22.14 (32) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 150.97/22.14 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 150.97/22.14 (33) ~ (all_52_3 = all_10_2) % 150.97/22.14 (34) all_36_0 = all_6_0 % 150.97/22.14 (35) ~ (all_6_0 = all_6_2) % 150.97/22.14 (36) all_56_13 = all_52_9 % 150.97/22.14 (37) all_54_8 = all_6_0 % 150.97/22.14 (38) all_58_8 = all_6_2 % 150.97/22.14 (39) ~ (all_52_6 = e0) % 150.97/22.14 (40) op(e0, e0) = all_8_1 % 150.97/22.14 (41) ~ (all_52_14 = all_6_0) % 150.97/22.14 (42) op(all_4_2, all_4_2) = all_4_1 % 150.97/22.14 (43) all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1 % 150.97/22.14 (44) all_58_3 = all_8_2 % 150.97/22.14 (45) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0 % 150.97/22.14 (46) all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1 % 150.97/22.14 (47) all_56_31 = all_4_2 % 150.97/22.14 (48) all_58_11 = all_52_14 % 150.97/22.14 (49) all_36_2 = all_6_2 % 150.97/22.14 (50) all_56_1 = e3 | all_56_11 = e2 | all_56_21 = e1 | all_56_31 = e0 % 150.97/22.14 (51) all_56_23 = all_52_14 % 150.97/22.14 (52) all_58_6 = all_6_0 % 150.97/22.14 (53) op(e1, e1) = all_6_2 % 150.97/22.14 (54) ~ (all_52_6 = all_8_2) % 150.97/22.14 (55) all_58_15 = all_4_2 % 150.97/22.14 (56) ~ (all_6_2 = e2) % 150.97/22.14 (57) all_58_7 = all_52_6 % 150.97/22.14 (58) op(e1, all_6_2) = all_56_20 % 150.97/22.14 (59) all_56_17 = all_6_0 % 150.97/22.14 (60) op(e2, e2) = all_8_2 % 150.97/22.14 (61) ~ (all_36_0 = e0) | ~ (all_36_2 = e2) % 150.97/22.14 (62) ~ (all_52_4 = all_52_12) % 150.97/22.14 (63) ~ (all_52_8 = all_52_12) % 150.97/22.14 (64) ~ (all_56_21 = e0) | all_56_23 = e1 % 150.97/22.14 (65) op(e0, all_4_2) = all_56_30 % 150.97/22.14 (66) ~ (all_52_6 = all_6_2) % 150.97/22.14 (67) op(all_6_2, all_6_2) = e3 % 150.97/22.14 (68) ~ (all_52_14 = all_6_2) % 150.97/22.14 (69) op(e1, all_52_11) = all_56_28 % 150.97/22.14 (70) all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3 % 150.97/22.14 (71) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0 % 150.97/22.14 (72) ~ (all_10_2 = all_6_0) % 150.97/22.14 (73) op(all_8_2, all_8_2) = all_8_1 % 150.97/22.14 (74) all_58_14 = all_52_11 % 150.97/22.14 (75) all_56_19 = all_52_6 % 150.97/22.14 (76) ~ (all_52_12 = all_10_2) % 150.97/22.14 (77) all_58_12 = all_52_3 % 150.97/22.14 (78) all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3 % 150.97/22.14 % 150.97/22.14 Begin of proof % 150.97/22.14 | % 150.97/22.14 | BETA: splitting (31) gives: % 150.97/22.14 | % 150.97/22.14 | Case 1: % 150.97/22.14 | | % 150.97/22.14 | | (79) all_58_6 = e2 % 150.97/22.14 | | % 150.97/22.14 | | COMBINE_EQS: (52), (79) imply: % 150.97/22.14 | | (80) all_6_0 = e2 % 150.97/22.14 | | % 150.97/22.14 | | REDUCE: (15), (80) imply: % 150.97/22.14 | | (81) $false % 150.97/22.14 | | % 150.97/22.14 | | CLOSE: (81) is inconsistent. % 150.97/22.14 | | % 150.97/22.14 | Case 2: % 150.97/22.14 | | % 150.97/22.14 | | (82) all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2 % 150.97/22.14 | | % 150.97/22.14 | | BETA: splitting (82) gives: % 150.97/22.14 | | % 150.97/22.14 | | Case 1: % 150.97/22.14 | | | % 150.97/22.14 | | | (83) all_58_7 = e2 % 150.97/22.14 | | | % 150.97/22.14 | | | COMBINE_EQS: (57), (83) imply: % 150.97/22.14 | | | (84) all_52_6 = e2 % 150.97/22.14 | | | % 150.97/22.14 | | | REDUCE: (28), (84) imply: % 150.97/22.14 | | | (85) ~ (all_6_0 = e2) % 150.97/22.14 | | | % 150.97/22.14 | | | REDUCE: (39), (84) imply: % 150.97/22.14 | | | (86) ~ (e2 = e0) % 150.97/22.14 | | | % 150.97/22.14 | | | GROUND_INST: instantiating (32) with all_4_2, all_8_1, e0, e0, simplifying % 150.97/22.14 | | | with (11), (40) gives: % 150.97/22.14 | | | (87) all_8_1 = all_4_2 % 150.97/22.14 | | | % 150.97/22.14 | | | REDUCE: (10), (87) imply: % 150.97/22.14 | | | (88) ~ (all_4_2 = e3) % 150.97/22.14 | | | % 150.97/22.14 | | | REDUCE: (5), (87) imply: % 150.97/22.14 | | | (89) ~ (all_4_2 = e1) % 150.97/22.14 | | | % 150.97/22.15 | | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (9), (10), (11), (12), (13), % 150.97/22.15 | | | (14), (15), (16), (17), (18), (20), (21), (22), (23), (24), % 150.97/22.15 | | | (25), (26), (27), (28), (29), (30), (32), (33), (34), (35), % 150.97/22.15 | | | (36), (37), (38), (41), (42), (43), (44), (45), (46), (47), % 150.97/22.15 | | | (48), (49), (50), (51), (52), (53), (54), (55), (57), (58), % 150.97/22.15 | | | (59), (60), (61), (62), (63), (64), (65), (66), (67), (68), % 150.97/22.15 | | | (69), (70), (71), (72), (73), (74), (75), (76), (77), (78), % 150.97/22.15 | | | (86), (88), (89) are inconsistent by sub-proof #274. % 150.97/22.15 | | | % 150.97/22.15 | | Case 2: % 150.97/22.15 | | | % 150.97/22.15 | | | (90) all_58_8 = e2 | all_58_11 = e2 % 150.97/22.15 | | | % 150.97/22.15 | | | REF_CLOSE: (19), (38), (48), (56), (90) are inconsistent by sub-proof % 150.97/22.15 | | | #511. % 150.97/22.15 | | | % 150.97/22.15 | | End of split % 150.97/22.15 | | % 150.97/22.15 | End of split % 150.97/22.15 | % 150.97/22.15 End of proof % 150.97/22.15 % 150.97/22.15 Sub-proof #184 shows that the following formulas are inconsistent: % 150.97/22.15 ---------------------------------------------------------------- % 150.97/22.15 (1) all_56_21 = e3 % 150.97/22.15 (2) all_56_21 = all_6_2 % 150.97/22.15 (3) op(e3, e3) = all_10_2 % 150.97/22.15 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 150.97/22.15 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 150.97/22.15 (5) all_56_17 = e1 % 150.97/22.15 (6) op(e3, all_10_1) = e1 % 150.97/22.15 (7) op(all_10_2, all_10_2) = all_10_1 % 150.97/22.15 (8) all_56_17 = all_6_0 % 150.97/22.15 (9) op(all_6_2, all_6_2) = e3 % 150.97/22.15 (10) op(e3, all_10_2) = all_56_0 % 150.97/22.15 (11) ~ (all_10_2 = all_6_0) % 150.97/22.15 % 150.97/22.15 Begin of proof % 150.97/22.15 | % 150.97/22.15 | COMBINE_EQS: (5), (8) imply: % 150.97/22.15 | (12) all_6_0 = e1 % 150.97/22.15 | % 150.97/22.15 | COMBINE_EQS: (1), (2) imply: % 150.97/22.15 | (13) all_6_2 = e3 % 150.97/22.15 | % 150.97/22.15 | REDUCE: (11), (12) imply: % 150.97/22.15 | (14) ~ (all_10_2 = e1) % 150.97/22.15 | % 150.97/22.15 | REDUCE: (9), (13) imply: % 150.97/22.15 | (15) op(e3, e3) = e3 % 150.97/22.15 | % 150.97/22.15 | GROUND_INST: instantiating (4) with all_10_2, e3, e3, e3, simplifying with % 150.97/22.15 | (3), (15) gives: % 150.97/22.15 | (16) all_10_2 = e3 % 150.97/22.15 | % 150.97/22.15 | REDUCE: (14), (16) imply: % 150.97/22.15 | (17) ~ (e3 = e1) % 150.97/22.15 | % 150.97/22.15 | REDUCE: (7), (16) imply: % 150.97/22.15 | (18) op(e3, e3) = all_10_1 % 150.97/22.15 | % 150.97/22.15 | REDUCE: (10), (16) imply: % 150.97/22.15 | (19) op(e3, e3) = all_56_0 % 150.97/22.15 | % 150.97/22.15 | GROUND_INST: instantiating (4) with e3, all_56_0, e3, e3, simplifying with % 150.97/22.15 | (15), (19) gives: % 150.97/22.15 | (20) all_56_0 = e3 % 150.97/22.15 | % 150.97/22.15 | GROUND_INST: instantiating (4) with all_10_1, all_56_0, e3, e3, simplifying % 150.97/22.15 | with (18), (19) gives: % 150.97/22.15 | (21) all_56_0 = all_10_1 % 150.97/22.15 | % 150.97/22.15 | COMBINE_EQS: (20), (21) imply: % 150.97/22.15 | (22) all_10_1 = e3 % 150.97/22.15 | % 150.97/22.15 | SIMP: (22) implies: % 150.97/22.15 | (23) all_10_1 = e3 % 150.97/22.15 | % 150.97/22.15 | REDUCE: (6), (23) imply: % 150.97/22.15 | (24) op(e3, e3) = e1 % 150.97/22.15 | % 150.97/22.15 | REF_CLOSE: (4), (15), (17), (19), (24) are inconsistent by sub-proof #410. % 150.97/22.15 | % 150.97/22.15 End of proof % 150.97/22.15 % 150.97/22.15 Sub-proof #185 shows that the following formulas are inconsistent: % 150.97/22.15 ---------------------------------------------------------------- % 150.97/22.15 (1) all_56_11 = all_8_2 % 150.97/22.15 (2) ~ (all_52_3 = all_6_0) % 150.97/22.15 (3) ~ (all_56_11 = e1) | all_56_13 = e2 % 150.97/22.15 (4) all_56_25 = all_52_3 % 150.97/22.15 (5) all_54_9 = all_52_6 % 150.97/22.15 (6) ~ (all_8_1 = e1) % 150.97/22.15 (7) ~ (all_52_1 = all_52_9) % 150.97/22.15 (8) all_54_10 = all_6_2 % 150.97/22.15 (9) all_54_0 = all_10_2 % 150.97/22.15 (10) ~ (all_52_9 = all_8_2) % 150.97/22.15 (11) ~ (all_6_2 = e3) % 150.97/22.15 (12) ~ (all_8_1 = e3) % 150.97/22.15 (13) op(e0, e0) = all_4_2 % 150.97/22.15 (14) all_54_5 = all_8_2 % 150.97/22.15 (15) ~ (all_52_6 = all_52_14) % 150.97/22.15 (16) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 150.97/22.15 (17) ~ (all_6_0 = e2) % 150.97/22.15 (18) all_56_21 = all_6_2 % 150.97/22.15 (19) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 150.97/22.15 (20) all_56_1 = all_10_2 % 150.97/22.15 (21) ~ (all_52_1 = all_6_0) % 150.97/22.15 (22) op(e3, e3) = all_10_2 % 150.97/22.15 (23) ~ (all_52_6 = all_6_0) % 150.97/22.15 (24) all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2 % 150.97/22.15 (25) ~ (all_52_1 = all_8_2) % 150.97/22.15 (26) all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2 % 150.97/22.15 (27) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 150.97/22.15 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 150.97/22.15 (28) ~ (all_52_3 = all_10_2) % 150.97/22.15 (29) ~ (all_56_11 = e3) | all_56_9 = e2 % 150.97/22.15 (30) ~ (all_6_0 = all_6_2) % 150.97/22.15 (31) all_56_13 = all_52_9 % 150.97/22.15 (32) all_54_8 = all_6_0 % 150.97/22.15 (33) all_58_8 = all_6_2 % 150.97/22.15 (34) ~ (all_52_14 = all_6_0) % 150.97/22.15 (35) op(all_4_2, all_4_2) = all_4_1 % 150.97/22.15 (36) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0 % 150.97/22.15 (37) all_56_31 = all_4_2 % 150.97/22.15 (38) all_58_11 = all_52_14 % 150.97/22.15 (39) all_56_1 = e3 | all_56_11 = e2 | all_56_21 = e1 | all_56_31 = e0 % 150.97/22.15 (40) all_56_23 = all_52_14 % 150.97/22.15 (41) all_58_6 = all_6_0 % 150.97/22.15 (42) op(e1, e1) = all_6_2 % 150.97/22.15 (43) ~ (all_52_6 = all_8_2) % 150.97/22.15 (44) all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1 % 150.97/22.15 (45) ~ (all_6_2 = e2) % 150.97/22.15 (46) all_58_2 = all_52_1 % 150.97/22.15 (47) ~ (all_52_9 = all_6_2) % 150.97/22.15 (48) all_58_7 = all_52_6 % 150.97/22.15 (49) op(e1, all_6_2) = all_56_20 % 150.97/22.15 (50) ~ (all_56_21 = e0) | all_56_23 = e1 % 150.97/22.15 (51) op(e0, all_4_2) = all_56_30 % 150.97/22.15 (52) ~ (all_52_6 = all_6_2) % 150.97/22.15 (53) ~ (all_8_2 = e0) % 150.97/22.15 (54) op(all_6_2, all_6_2) = e3 % 150.97/22.15 (55) ~ (all_52_14 = all_6_2) % 150.97/22.15 (56) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0 % 150.97/22.15 (57) ~ (all_10_2 = all_6_0) % 150.97/22.15 (58) op(all_8_2, all_8_2) = all_8_1 % 150.97/22.15 (59) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 150.97/22.15 (60) all_56_9 = all_52_1 % 150.97/22.15 (61) ~ (all_52_1 = all_10_2) % 150.97/22.15 (62) all_58_12 = all_52_3 % 150.97/22.15 (63) ~ (all_56_31 = e3) | all_56_25 = e0 % 150.97/22.15 % 150.97/22.15 Begin of proof % 150.97/22.15 | % 150.97/22.15 | BETA: splitting (29) gives: % 150.97/22.15 | % 150.97/22.15 | Case 1: % 150.97/22.15 | | % 150.97/22.15 | | (64) ~ (all_56_11 = e3) % 150.97/22.15 | | % 150.97/22.15 | | REDUCE: (1), (64) imply: % 150.97/22.15 | | (65) ~ (all_8_2 = e3) % 150.97/22.15 | | % 150.97/22.15 | | BETA: splitting (3) gives: % 150.97/22.15 | | % 150.97/22.15 | | Case 1: % 150.97/22.15 | | | % 150.97/22.15 | | | (66) ~ (all_56_11 = e1) % 150.97/22.15 | | | % 150.97/22.15 | | | REDUCE: (1), (66) imply: % 150.97/22.15 | | | (67) ~ (all_8_2 = e1) % 150.97/22.15 | | | % 150.97/22.15 | | | REF_CLOSE: (8), (11), (14), (17), (18), (19), (26), (27), (33), (38), % 150.97/22.15 | | | (40), (41), (42), (43), (45), (48), (49), (50), (53), (54), % 150.97/22.15 | | | (55), (59), (65), (67) are inconsistent by sub-proof #458. % 150.97/22.15 | | | % 150.97/22.15 | | Case 2: % 150.97/22.15 | | | % 150.97/22.15 | | | (68) all_56_13 = e2 % 150.97/22.15 | | | (69) all_56_11 = e1 % 150.97/22.15 | | | % 150.97/22.15 | | | COMBINE_EQS: (1), (69) imply: % 150.97/22.15 | | | (70) all_8_2 = e1 % 150.97/22.15 | | | % 150.97/22.15 | | | COMBINE_EQS: (31), (68) imply: % 150.97/22.15 | | | (71) all_52_9 = e2 % 150.97/22.15 | | | % 150.97/22.15 | | | REDUCE: (7), (71) imply: % 150.97/22.15 | | | (72) ~ (all_52_1 = e2) % 150.97/22.15 | | | % 150.97/22.15 | | | REDUCE: (25), (70) imply: % 150.97/22.15 | | | (73) ~ (all_52_1 = e1) % 150.97/22.15 | | | % 150.97/22.15 | | | REDUCE: (10), (70), (71) imply: % 150.97/22.15 | | | (74) ~ (e2 = e1) % 150.97/22.15 | | | % 150.97/22.15 | | | REDUCE: (47), (71) imply: % 150.97/22.15 | | | (75) ~ (all_6_2 = e2) % 150.97/22.15 | | | % 150.97/22.15 | | | REDUCE: (58), (70) imply: % 150.97/22.15 | | | (76) op(e1, e1) = all_8_1 % 150.97/22.15 | | | % 150.97/22.15 | | | REF_CLOSE: (1), (2), (4), (5), (6), (8), (12), (13), (15), (17), (18), % 150.97/22.15 | | | (19), (20), (23), (24), (27), (30), (32), (34), (35), (36), % 150.97/22.15 | | | (37), (39), (40), (41), (42), (43), (44), (45), (46), (49), % 150.97/22.15 | | | (50), (51), (52), (54), (55), (56), (57), (62), (63), (72), % 150.97/22.15 | | | (73), (74), (76) are inconsistent by sub-proof #186. % 150.97/22.15 | | | % 150.97/22.15 | | End of split % 150.97/22.15 | | % 150.97/22.15 | Case 2: % 150.97/22.15 | | % 150.97/22.15 | | (77) all_56_11 = e3 % 150.97/22.15 | | (78) all_56_9 = e2 % 150.97/22.15 | | % 150.97/22.15 | | COMBINE_EQS: (60), (78) imply: % 150.97/22.15 | | (79) all_52_1 = e2 % 150.97/22.15 | | % 150.97/22.15 | | COMBINE_EQS: (1), (77) imply: % 150.97/22.15 | | (80) all_8_2 = e3 % 150.97/22.15 | | % 150.97/22.15 | | REDUCE: (61), (79) imply: % 150.97/22.15 | | (81) ~ (all_10_2 = e2) % 150.97/22.15 | | % 150.97/22.15 | | SIMP: (81) implies: % 150.97/22.15 | | (82) ~ (all_10_2 = e2) % 150.97/22.15 | | % 150.97/22.15 | | REDUCE: (21), (79) imply: % 150.97/22.15 | | (83) ~ (all_6_0 = e2) % 150.97/22.15 | | % 150.97/22.15 | | REDUCE: (58), (80) imply: % 150.97/22.15 | | (84) op(e3, e3) = all_8_1 % 150.97/22.15 | | % 150.97/22.15 | | GROUND_INST: instantiating (27) with all_10_2, all_8_1, e3, e3, simplifying % 150.97/22.15 | | with (22), (84) gives: % 150.97/22.15 | | (85) all_10_2 = all_8_1 % 150.97/22.15 | | % 150.97/22.15 | | COMBINE_EQS: (9), (85) imply: % 150.97/22.15 | | (86) all_54_0 = all_8_1 % 150.97/22.15 | | % 150.97/22.15 | | REDUCE: (28), (85) imply: % 150.97/22.15 | | (87) ~ (all_52_3 = all_8_1) % 150.97/22.15 | | % 150.97/22.15 | | REDUCE: (82), (85) imply: % 150.97/22.15 | | (88) ~ (all_8_1 = e2) % 150.97/22.15 | | % 150.97/22.15 | | BETA: splitting (16) gives: % 150.97/22.15 | | % 150.97/22.15 | | Case 1: % 150.97/22.15 | | | % 150.97/22.15 | | | (89) all_54_0 = e3 % 150.97/22.15 | | | % 150.97/22.15 | | | REF_CLOSE: (12), (86), (89) are inconsistent by sub-proof #600. % 150.97/22.15 | | | % 150.97/22.15 | | Case 2: % 150.97/22.15 | | | % 150.97/22.15 | | | (90) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 150.97/22.15 | | | % 150.97/22.15 | | | BETA: splitting (90) gives: % 150.97/22.15 | | | % 150.97/22.15 | | | Case 1: % 150.97/22.15 | | | | % 150.97/22.15 | | | | (91) all_54_0 = e2 % 150.97/22.15 | | | | % 150.97/22.15 | | | | REF_CLOSE: (86), (88), (91) are inconsistent by sub-proof #599. % 150.97/22.15 | | | | % 150.97/22.15 | | | Case 2: % 150.97/22.15 | | | | % 150.97/22.15 | | | | (92) all_54_0 = e1 | all_54_0 = e0 % 150.97/22.15 | | | | % 150.97/22.15 | | | | BETA: splitting (92) gives: % 150.97/22.15 | | | | % 150.97/22.15 | | | | Case 1: % 150.97/22.15 | | | | | % 150.97/22.15 | | | | | (93) all_54_0 = e1 % 150.97/22.15 | | | | | % 150.97/22.15 | | | | | REF_CLOSE: (6), (86), (93) are inconsistent by sub-proof #598. % 150.97/22.15 | | | | | % 150.97/22.15 | | | | Case 2: % 150.97/22.15 | | | | | % 150.97/22.15 | | | | | (94) all_54_0 = e0 % 150.97/22.15 | | | | | % 150.97/22.15 | | | | | COMBINE_EQS: (86), (94) imply: % 150.97/22.15 | | | | | (95) all_8_1 = e0 % 150.97/22.15 | | | | | % 150.97/22.15 | | | | | SIMP: (95) implies: % 150.97/22.15 | | | | | (96) all_8_1 = e0 % 150.97/22.15 | | | | | % 150.97/22.15 | | | | | REDUCE: (87), (96) imply: % 150.97/22.15 | | | | | (97) ~ (all_52_3 = e0) % 150.97/22.15 | | | | | % 150.97/22.15 | | | | | BETA: splitting (63) gives: % 150.97/22.15 | | | | | % 150.97/22.15 | | | | | Case 1: % 150.97/22.15 | | | | | | % 150.97/22.15 | | | | | | (98) ~ (all_56_31 = e3) % 150.97/22.15 | | | | | | % 150.97/22.15 | | | | | | REDUCE: (37), (98) imply: % 150.97/22.15 | | | | | | (99) ~ (all_4_2 = e3) % 150.97/22.15 | | | | | | % 151.11/22.15 | | | | | | REF_CLOSE: (1), (5), (8), (11), (13), (15), (17), (18), (19), (20), % 151.11/22.15 | | | | | | (23), (27), (30), (32), (34), (35), (36), (37), (39), % 151.11/22.15 | | | | | | (40), (42), (43), (45), (49), (50), (51), (52), (54), % 151.11/22.15 | | | | | | (55), (56), (57), (99) are inconsistent by sub-proof % 151.11/22.15 | | | | | | #429. % 151.11/22.15 | | | | | | % 151.11/22.15 | | | | | Case 2: % 151.11/22.15 | | | | | | % 151.11/22.15 | | | | | | (100) all_56_25 = e0 % 151.11/22.15 | | | | | | % 151.11/22.15 | | | | | | COMBINE_EQS: (4), (100) imply: % 151.11/22.15 | | | | | | (101) all_52_3 = e0 % 151.11/22.15 | | | | | | % 151.11/22.15 | | | | | | SIMP: (101) implies: % 151.11/22.15 | | | | | | (102) all_52_3 = e0 % 151.11/22.15 | | | | | | % 151.11/22.15 | | | | | | REDUCE: (97), (102) imply: % 151.11/22.15 | | | | | | (103) $false % 151.11/22.15 | | | | | | % 151.11/22.15 | | | | | | CLOSE: (103) is inconsistent. % 151.11/22.15 | | | | | | % 151.11/22.15 | | | | | End of split % 151.11/22.15 | | | | | % 151.11/22.15 | | | | End of split % 151.11/22.15 | | | | % 151.11/22.15 | | | End of split % 151.11/22.15 | | | % 151.11/22.15 | | End of split % 151.11/22.15 | | % 151.11/22.15 | End of split % 151.11/22.15 | % 151.11/22.15 End of proof % 151.11/22.15 % 151.11/22.15 Sub-proof #186 shows that the following formulas are inconsistent: % 151.11/22.15 ---------------------------------------------------------------- % 151.11/22.15 (1) all_56_11 = all_8_2 % 151.11/22.15 (2) ~ (all_52_3 = all_6_0) % 151.11/22.15 (3) all_56_25 = all_52_3 % 151.11/22.15 (4) all_54_9 = all_52_6 % 151.11/22.15 (5) ~ (all_8_1 = e1) % 151.11/22.15 (6) all_54_10 = all_6_2 % 151.11/22.15 (7) ~ (all_8_1 = e3) % 151.11/22.15 (8) op(e0, e0) = all_4_2 % 151.11/22.15 (9) ~ (all_52_1 = e1) % 151.11/22.15 (10) ~ (all_52_6 = all_52_14) % 151.11/22.15 (11) ~ (all_6_0 = e2) % 151.11/22.15 (12) all_56_21 = all_6_2 % 151.11/22.15 (13) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 151.11/22.15 (14) all_56_1 = all_10_2 % 151.11/22.15 (15) ~ (all_52_6 = all_6_0) % 151.11/22.15 (16) all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2 % 151.11/22.15 (17) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 151.11/22.15 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 151.11/22.15 (18) ~ (all_6_0 = all_6_2) % 151.11/22.15 (19) all_54_8 = all_6_0 % 151.11/22.15 (20) ~ (all_52_14 = all_6_0) % 151.11/22.15 (21) ~ (e2 = e1) % 151.11/22.15 (22) op(all_4_2, all_4_2) = all_4_1 % 151.11/22.15 (23) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0 % 151.11/22.15 (24) all_56_31 = all_4_2 % 151.11/22.15 (25) all_56_1 = e3 | all_56_11 = e2 | all_56_21 = e1 | all_56_31 = e0 % 151.11/22.15 (26) op(e1, e1) = all_8_1 % 151.11/22.15 (27) all_56_23 = all_52_14 % 151.11/22.15 (28) all_58_6 = all_6_0 % 151.11/22.15 (29) op(e1, e1) = all_6_2 % 151.11/22.15 (30) ~ (all_52_6 = all_8_2) % 151.11/22.15 (31) all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1 % 151.11/22.15 (32) ~ (all_6_2 = e2) % 151.11/22.15 (33) all_58_2 = all_52_1 % 151.11/22.15 (34) op(e1, all_6_2) = all_56_20 % 151.11/22.15 (35) ~ (all_56_21 = e0) | all_56_23 = e1 % 151.11/22.15 (36) op(e0, all_4_2) = all_56_30 % 151.11/22.15 (37) ~ (all_52_6 = all_6_2) % 151.11/22.15 (38) op(all_6_2, all_6_2) = e3 % 151.11/22.15 (39) ~ (all_52_14 = all_6_2) % 151.11/22.15 (40) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0 % 151.11/22.15 (41) ~ (all_10_2 = all_6_0) % 151.11/22.15 (42) ~ (all_52_1 = e2) % 151.11/22.15 (43) all_58_12 = all_52_3 % 151.11/22.15 (44) ~ (all_56_31 = e3) | all_56_25 = e0 % 151.11/22.15 % 151.11/22.15 Begin of proof % 151.11/22.15 | % 151.11/22.15 | GROUND_INST: instantiating (17) with all_6_2, all_8_1, e1, e1, simplifying % 151.11/22.15 | with (26), (29) gives: % 151.11/22.15 | (45) all_8_1 = all_6_2 % 151.11/22.15 | % 151.11/22.15 | REDUCE: (7), (45) imply: % 151.11/22.15 | (46) ~ (all_6_2 = e3) % 151.11/22.15 | % 151.11/22.15 | REDUCE: (5), (45) imply: % 151.11/22.15 | (47) ~ (all_6_2 = e1) % 151.11/22.15 | % 151.11/22.15 | BETA: splitting (13) gives: % 151.11/22.15 | % 151.11/22.15 | Case 1: % 151.11/22.15 | | % 151.11/22.15 | | (48) all_54_10 = e3 % 151.11/22.15 | | % 151.11/22.15 | | REF_CLOSE: (6), (46), (48) are inconsistent by sub-proof #736. % 151.11/22.15 | | % 151.11/22.15 | Case 2: % 151.11/22.15 | | % 151.11/22.15 | | (49) ~ (all_54_10 = e3) % 151.11/22.15 | | (50) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 151.11/22.15 | | % 151.11/22.15 | | BETA: splitting (50) gives: % 151.11/22.15 | | % 151.11/22.15 | | Case 1: % 151.11/22.15 | | | % 151.11/22.15 | | | (51) all_54_10 = e2 % 151.11/22.15 | | | % 151.11/22.15 | | | REF_CLOSE: (6), (32), (51) are inconsistent by sub-proof #735. % 151.11/22.15 | | | % 151.11/22.15 | | Case 2: % 151.11/22.15 | | | % 151.11/22.15 | | | (52) ~ (all_54_10 = e2) % 151.11/22.15 | | | (53) all_54_10 = e1 | all_54_10 = e0 % 151.11/22.15 | | | % 151.11/22.15 | | | BETA: splitting (53) gives: % 151.11/22.15 | | | % 151.11/22.15 | | | Case 1: % 151.11/22.15 | | | | % 151.11/22.15 | | | | (54) all_54_10 = e1 % 151.11/22.15 | | | | % 151.11/22.15 | | | | REF_CLOSE: (6), (47), (54) are inconsistent by sub-proof #606. % 151.11/22.15 | | | | % 151.11/22.15 | | | Case 2: % 151.11/22.15 | | | | % 151.11/22.15 | | | | (55) all_54_10 = e0 % 151.11/22.15 | | | | % 151.11/22.15 | | | | COMBINE_EQS: (6), (55) imply: % 151.11/22.15 | | | | (56) all_6_2 = e0 % 151.11/22.15 | | | | % 151.11/22.15 | | | | SIMP: (56) implies: % 151.11/22.15 | | | | (57) all_6_2 = e0 % 151.11/22.15 | | | | % 151.11/22.15 | | | | COMBINE_EQS: (12), (57) imply: % 151.11/22.15 | | | | (58) all_56_21 = e0 % 151.11/22.15 | | | | % 151.11/22.15 | | | | REDUCE: (37), (57) imply: % 151.11/22.15 | | | | (59) ~ (all_52_6 = e0) % 151.11/22.15 | | | | % 151.11/22.15 | | | | REDUCE: (39), (57) imply: % 151.11/22.15 | | | | (60) ~ (all_52_14 = e0) % 151.11/22.15 | | | | % 151.11/22.15 | | | | REDUCE: (18), (57) imply: % 151.11/22.15 | | | | (61) ~ (all_6_0 = e0) % 151.11/22.15 | | | | % 151.11/22.15 | | | | REDUCE: (32), (57) imply: % 151.11/22.15 | | | | (62) ~ (e2 = e0) % 151.11/22.15 | | | | % 151.11/22.15 | | | | SIMP: (62) implies: % 151.11/22.15 | | | | (63) ~ (e2 = e0) % 151.11/22.15 | | | | % 151.11/22.15 | | | | REDUCE: (38), (57) imply: % 151.11/22.15 | | | | (64) op(e0, e0) = e3 % 151.11/22.15 | | | | % 151.11/22.15 | | | | BETA: splitting (35) gives: % 151.11/22.15 | | | | % 151.11/22.15 | | | | Case 1: % 151.11/22.15 | | | | | % 151.11/22.15 | | | | | (65) ~ (all_56_21 = e0) % 151.11/22.15 | | | | | % 151.11/22.15 | | | | | REDUCE: (58), (65) imply: % 151.11/22.15 | | | | | (66) $false % 151.11/22.15 | | | | | % 151.11/22.15 | | | | | CLOSE: (66) is inconsistent. % 151.11/22.15 | | | | | % 151.11/22.15 | | | | Case 2: % 151.11/22.15 | | | | | % 151.11/22.15 | | | | | (67) all_56_23 = e1 % 151.11/22.15 | | | | | % 151.11/22.15 | | | | | COMBINE_EQS: (27), (67) imply: % 151.11/22.15 | | | | | (68) all_52_14 = e1 % 151.11/22.15 | | | | | % 151.11/22.15 | | | | | SIMP: (68) implies: % 151.11/22.15 | | | | | (69) all_52_14 = e1 % 151.11/22.15 | | | | | % 151.11/22.15 | | | | | REDUCE: (10), (69) imply: % 151.11/22.15 | | | | | (70) ~ (all_52_6 = e1) % 151.11/22.15 | | | | | % 151.11/22.15 | | | | | REDUCE: (20), (69) imply: % 151.11/22.15 | | | | | (71) ~ (all_6_0 = e1) % 151.11/22.15 | | | | | % 151.11/22.15 | | | | | SIMP: (71) implies: % 151.11/22.15 | | | | | (72) ~ (all_6_0 = e1) % 151.11/22.15 | | | | | % 151.11/22.15 | | | | | REDUCE: (60), (69) imply: % 151.11/22.15 | | | | | (73) ~ (e1 = e0) % 151.11/22.15 | | | | | % 151.11/22.15 | | | | | BETA: splitting (31) gives: % 151.11/22.15 | | | | | % 151.11/22.15 | | | | | Case 1: % 151.11/22.15 | | | | | | % 151.11/22.15 | | | | | | (74) all_58_0 = e1 % 151.11/22.15 | | | | | | % 151.11/22.15 | | | | | | BETA: splitting (16) gives: % 151.11/22.15 | | | | | | % 151.11/22.15 | | | | | | Case 1: % 151.11/22.15 | | | | | | | % 151.11/22.15 | | | | | | | (75) all_58_0 = e2 % 151.11/22.15 | | | | | | | % 151.11/22.15 | | | | | | | REF_CLOSE: (21), (74), (75) are inconsistent by sub-proof #187. % 151.11/22.15 | | | | | | | % 151.11/22.15 | | | | | | Case 2: % 151.11/22.15 | | | | | | | % 151.11/22.15 | | | | | | | (76) all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2 % 151.11/22.15 | | | | | | | % 151.11/22.15 | | | | | | | BETA: splitting (76) gives: % 151.11/22.15 | | | | | | | % 151.11/22.15 | | | | | | | Case 1: % 151.11/22.15 | | | | | | | | % 151.11/22.15 | | | | | | | | (77) all_58_2 = e2 % 151.11/22.15 | | | | | | | | % 151.11/22.15 | | | | | | | | COMBINE_EQS: (33), (77) imply: % 151.11/22.15 | | | | | | | | (78) all_52_1 = e2 % 151.11/22.15 | | | | | | | | % 151.11/22.15 | | | | | | | | REDUCE: (42), (78) imply: % 151.11/22.15 | | | | | | | | (79) $false % 151.11/22.15 | | | | | | | | % 151.11/22.15 | | | | | | | | CLOSE: (79) is inconsistent. % 151.11/22.15 | | | | | | | | % 151.11/22.15 | | | | | | | Case 2: % 151.11/22.15 | | | | | | | | % 151.11/22.15 | | | | | | | | (80) all_58_6 = e2 | all_58_12 = e2 % 151.11/22.15 | | | | | | | | % 151.11/22.15 | | | | | | | | BETA: splitting (80) gives: % 151.11/22.15 | | | | | | | | % 151.11/22.15 | | | | | | | | Case 1: % 151.11/22.15 | | | | | | | | | % 151.11/22.15 | | | | | | | | | (81) all_58_6 = e2 % 151.11/22.15 | | | | | | | | | % 151.11/22.15 | | | | | | | | | REF_CLOSE: (11), (28), (81) are inconsistent by sub-proof % 151.11/22.15 | | | | | | | | | #461. % 151.11/22.15 | | | | | | | | | % 151.11/22.15 | | | | | | | | Case 2: % 151.11/22.15 | | | | | | | | | % 151.11/22.15 | | | | | | | | | (82) all_58_12 = e2 % 151.11/22.15 | | | | | | | | | % 151.11/22.15 | | | | | | | | | COMBINE_EQS: (43), (82) imply: % 151.11/22.15 | | | | | | | | | (83) all_52_3 = e2 % 151.11/22.15 | | | | | | | | | % 151.11/22.15 | | | | | | | | | COMBINE_EQS: (3), (83) imply: % 151.11/22.15 | | | | | | | | | (84) all_56_25 = e2 % 151.11/22.15 | | | | | | | | | % 151.11/22.15 | | | | | | | | | REDUCE: (2), (83) imply: % 151.11/22.15 | | | | | | | | | (85) ~ (all_6_0 = e2) % 151.11/22.15 | | | | | | | | | % 151.11/22.15 | | | | | | | | | BETA: splitting (44) gives: % 151.11/22.15 | | | | | | | | | % 151.11/22.15 | | | | | | | | | Case 1: % 151.11/22.15 | | | | | | | | | | % 151.11/22.15 | | | | | | | | | | (86) ~ (all_56_31 = e3) % 151.11/22.15 | | | | | | | | | | % 151.11/22.15 | | | | | | | | | | REDUCE: (24), (86) imply: % 151.11/22.15 | | | | | | | | | | (87) ~ (all_4_2 = e3) % 151.11/22.15 | | | | | | | | | | % 151.11/22.15 | | | | | | | | | | REF_CLOSE: (1), (4), (6), (8), (10), (11), (12), (13), (14), % 151.11/22.15 | | | | | | | | | | (15), (17), (18), (19), (20), (22), (23), (24), % 151.11/22.15 | | | | | | | | | | (25), (27), (29), (30), (32), (34), (35), (36), % 151.11/22.15 | | | | | | | | | | (37), (38), (39), (40), (41), (46), (87) are % 151.11/22.15 | | | | | | | | | | inconsistent by sub-proof #429. % 151.11/22.15 | | | | | | | | | | % 151.11/22.15 | | | | | | | | | Case 2: % 151.11/22.15 | | | | | | | | | | % 151.11/22.15 | | | | | | | | | | (88) all_56_25 = e0 % 151.11/22.15 | | | | | | | | | | % 151.11/22.15 | | | | | | | | | | COMBINE_EQS: (84), (88) imply: % 151.11/22.15 | | | | | | | | | | (89) e2 = e0 % 151.11/22.15 | | | | | | | | | | % 151.11/22.15 | | | | | | | | | | SIMP: (89) implies: % 151.11/22.15 | | | | | | | | | | (90) e2 = e0 % 151.11/22.15 | | | | | | | | | | % 151.11/22.15 | | | | | | | | | | COMBINE_EQS: (82), (90) imply: % 151.11/22.15 | | | | | | | | | | (91) all_58_12 = e0 % 151.11/22.15 | | | | | | | | | | % 151.11/22.15 | | | | | | | | | | REF_CLOSE: (11), (28), (63), (80), (91) are inconsistent by % 151.11/22.15 | | | | | | | | | | sub-proof #422. % 151.11/22.15 | | | | | | | | | | % 151.11/22.15 | | | | | | | | | End of split % 151.11/22.15 | | | | | | | | | % 151.11/22.15 | | | | | | | | End of split % 151.11/22.15 | | | | | | | | % 151.11/22.15 | | | | | | | End of split % 151.11/22.15 | | | | | | | % 151.11/22.15 | | | | | | End of split % 151.11/22.15 | | | | | | % 151.11/22.15 | | | | | Case 2: % 151.11/22.15 | | | | | | % 151.11/22.15 | | | | | | (92) all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1 % 151.11/22.15 | | | | | | % 151.11/22.15 | | | | | | BETA: splitting (92) gives: % 151.11/22.15 | | | | | | % 151.11/22.15 | | | | | | Case 1: % 151.11/22.15 | | | | | | | % 151.11/22.15 | | | | | | | (93) all_58_2 = e1 % 151.11/22.15 | | | | | | | % 151.11/22.15 | | | | | | | COMBINE_EQS: (33), (93) imply: % 151.11/22.15 | | | | | | | (94) all_52_1 = e1 % 151.11/22.15 | | | | | | | % 151.11/22.15 | | | | | | | SIMP: (94) implies: % 151.11/22.15 | | | | | | | (95) all_52_1 = e1 % 151.11/22.15 | | | | | | | % 151.11/22.15 | | | | | | | REDUCE: (9), (95) imply: % 151.11/22.15 | | | | | | | (96) $false % 151.11/22.15 | | | | | | | % 151.11/22.15 | | | | | | | CLOSE: (96) is inconsistent. % 151.11/22.15 | | | | | | | % 151.11/22.15 | | | | | | Case 2: % 151.11/22.15 | | | | | | | % 151.11/22.15 | | | | | | | (97) all_58_6 = e1 | all_58_12 = e1 % 151.11/22.15 | | | | | | | % 151.11/22.15 | | | | | | | BETA: splitting (97) gives: % 151.11/22.15 | | | | | | | % 151.11/22.15 | | | | | | | Case 1: % 151.11/22.15 | | | | | | | | % 151.11/22.15 | | | | | | | | (98) all_58_6 = e1 % 151.11/22.15 | | | | | | | | % 151.11/22.15 | | | | | | | | COMBINE_EQS: (28), (98) imply: % 151.11/22.15 | | | | | | | | (99) all_6_0 = e1 % 151.11/22.15 | | | | | | | | % 151.11/22.15 | | | | | | | | SIMP: (99) implies: % 151.11/22.15 | | | | | | | | (100) all_6_0 = e1 % 151.11/22.15 | | | | | | | | % 151.11/22.15 | | | | | | | | REDUCE: (72), (100) imply: % 151.11/22.15 | | | | | | | | (101) $false % 151.11/22.15 | | | | | | | | % 151.11/22.15 | | | | | | | | CLOSE: (101) is inconsistent. % 151.11/22.15 | | | | | | | | % 151.11/22.15 | | | | | | | Case 2: % 151.11/22.15 | | | | | | | | % 151.11/22.15 | | | | | | | | (102) all_58_12 = e1 % 151.11/22.15 | | | | | | | | % 151.11/22.15 | | | | | | | | COMBINE_EQS: (43), (102) imply: % 151.11/22.15 | | | | | | | | (103) all_52_3 = e1 % 151.11/22.15 | | | | | | | | % 151.11/22.15 | | | | | | | | SIMP: (103) implies: % 151.11/22.15 | | | | | | | | (104) all_52_3 = e1 % 151.11/22.15 | | | | | | | | % 151.11/22.15 | | | | | | | | COMBINE_EQS: (3), (104) imply: % 151.11/22.15 | | | | | | | | (105) all_56_25 = e1 % 151.11/22.15 | | | | | | | | % 151.11/22.15 | | | | | | | | BETA: splitting (44) gives: % 151.11/22.15 | | | | | | | | % 151.11/22.15 | | | | | | | | Case 1: % 151.11/22.15 | | | | | | | | | % 151.11/22.15 | | | | | | | | | (106) ~ (all_56_31 = e3) % 151.11/22.15 | | | | | | | | | % 151.11/22.15 | | | | | | | | | REDUCE: (24), (106) imply: % 151.11/22.15 | | | | | | | | | (107) ~ (all_4_2 = e3) % 151.11/22.15 | | | | | | | | | % 151.11/22.15 | | | | | | | | | REF_CLOSE: (1), (4), (8), (11), (14), (15), (17), (19), (22), % 151.11/22.15 | | | | | | | | | (23), (24), (25), (30), (36), (40), (41), (58), % 151.11/22.15 | | | | | | | | | (59), (61), (64), (70), (72), (73), (107) are % 151.11/22.15 | | | | | | | | | inconsistent by sub-proof #450. % 151.11/22.15 | | | | | | | | | % 151.11/22.15 | | | | | | | | Case 2: % 151.11/22.15 | | | | | | | | | % 151.11/22.15 | | | | | | | | | (108) all_56_25 = e0 % 151.11/22.15 | | | | | | | | | % 151.11/22.15 | | | | | | | | | COMBINE_EQS: (105), (108) imply: % 151.11/22.15 | | | | | | | | | (109) e1 = e0 % 151.11/22.15 | | | | | | | | | % 151.11/22.15 | | | | | | | | | SIMP: (109) implies: % 151.11/22.15 | | | | | | | | | (110) e1 = e0 % 151.11/22.15 | | | | | | | | | % 151.11/22.15 | | | | | | | | | REDUCE: (73), (110) imply: % 151.11/22.15 | | | | | | | | | (111) $false % 151.11/22.15 | | | | | | | | | % 151.11/22.15 | | | | | | | | | CLOSE: (111) is inconsistent. % 151.11/22.15 | | | | | | | | | % 151.11/22.15 | | | | | | | | End of split % 151.11/22.15 | | | | | | | | % 151.11/22.15 | | | | | | | End of split % 151.11/22.15 | | | | | | | % 151.11/22.15 | | | | | | End of split % 151.11/22.15 | | | | | | % 151.11/22.15 | | | | | End of split % 151.11/22.15 | | | | | % 151.11/22.15 | | | | End of split % 151.11/22.15 | | | | % 151.11/22.15 | | | End of split % 151.11/22.15 | | | % 151.11/22.15 | | End of split % 151.11/22.15 | | % 151.11/22.15 | End of split % 151.11/22.15 | % 151.11/22.15 End of proof % 151.11/22.15 % 151.11/22.15 Sub-proof #187 shows that the following formulas are inconsistent: % 151.11/22.15 ---------------------------------------------------------------- % 151.11/22.15 (1) all_58_0 = e2 % 151.11/22.15 (2) all_58_0 = e1 % 151.11/22.15 (3) ~ (e2 = e1) % 151.11/22.15 % 151.11/22.15 Begin of proof % 151.11/22.15 | % 151.11/22.15 | COMBINE_EQS: (1), (2) imply: % 151.11/22.15 | (4) e2 = e1 % 151.11/22.15 | % 151.11/22.15 | SIMP: (4) implies: % 151.11/22.15 | (5) e2 = e1 % 151.11/22.15 | % 151.11/22.15 | REDUCE: (3), (5) imply: % 151.11/22.15 | (6) $false % 151.11/22.15 | % 151.11/22.15 | CLOSE: (6) is inconsistent. % 151.11/22.15 | % 151.11/22.15 End of proof % 151.11/22.15 % 151.11/22.15 Sub-proof #188 shows that the following formulas are inconsistent: % 151.11/22.15 ---------------------------------------------------------------- % 151.11/22.15 (1) all_56_11 = all_8_2 % 151.11/22.15 (2) all_54_9 = all_52_6 % 151.11/22.15 (3) ~ (all_6_1 = e2) % 151.11/22.15 (4) all_54_0 = all_10_2 % 151.11/22.15 (5) all_56_21 = e3 % 151.11/22.15 (6) ~ (all_52_14 = all_4_2) % 151.11/22.15 (7) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0 % 151.11/22.15 (8) all_6_2 = e3 % 151.11/22.15 (9) ~ (all_6_1 = e3) % 151.11/22.15 (10) ~ (all_52_6 = all_52_14) % 151.11/22.15 (11) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 151.11/22.15 (12) ~ (all_6_0 = e2) % 151.11/22.15 (13) all_56_1 = all_10_2 % 151.11/22.15 (14) op(e1, e0) = all_52_14 % 151.11/22.15 (15) op(e3, e3) = all_10_2 % 151.11/22.15 (16) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 151.11/22.15 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 151.11/22.15 (17) ~ (all_52_2 = all_52_6) % 151.11/22.15 (18) all_52_2 = e1 % 151.11/22.15 (19) op(e1, all_6_1) = all_6_0 % 151.11/22.15 (20) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0 % 151.11/22.15 (21) all_56_31 = all_4_2 % 151.11/22.15 (22) ~ (all_52_2 = all_52_14) % 151.11/22.15 (23) op(all_6_2, all_6_2) = all_6_1 % 151.11/22.15 (24) all_56_1 = e3 | all_56_11 = e2 | all_56_21 = e1 | all_56_31 = e0 % 151.11/22.15 (25) ~ (all_16_1 = e2) | ~ (all_16_2 = e0) % 151.11/22.15 (26) all_16_2 = all_10_2 % 151.11/22.15 (27) ~ (all_52_6 = all_8_2) % 151.11/22.15 (28) ~ (all_52_2 = all_6_2) % 151.11/22.15 (29) ~ (all_52_6 = all_6_2) % 151.11/22.15 (30) ~ (all_52_14 = all_6_2) % 151.11/22.15 (31) ~ (all_52_2 = all_10_2) % 151.11/22.15 (32) all_54_11 = all_52_14 % 151.11/22.15 % 151.11/22.15 Begin of proof % 151.11/22.15 | % 151.11/22.15 | REDUCE: (17), (18) imply: % 151.11/22.15 | (33) ~ (all_52_6 = e1) % 151.11/22.15 | % 151.11/22.15 | SIMP: (33) implies: % 151.11/22.15 | (34) ~ (all_52_6 = e1) % 151.11/22.15 | % 151.11/22.15 | REDUCE: (18), (22) imply: % 151.11/22.15 | (35) ~ (all_52_14 = e1) % 151.11/22.15 | % 151.11/22.15 | SIMP: (35) implies: % 151.11/22.15 | (36) ~ (all_52_14 = e1) % 151.11/22.15 | % 151.11/22.15 | REDUCE: (18), (31) imply: % 151.11/22.15 | (37) ~ (all_10_2 = e1) % 151.11/22.15 | % 151.11/22.15 | SIMP: (37) implies: % 151.11/22.15 | (38) ~ (all_10_2 = e1) % 151.11/22.15 | % 151.11/22.15 | REDUCE: (8), (18), (28) imply: % 151.11/22.15 | (39) ~ (e3 = e1) % 151.11/22.15 | % 151.11/22.15 | SIMP: (39) implies: % 151.11/22.15 | (40) ~ (e3 = e1) % 151.11/22.15 | % 151.11/22.15 | REDUCE: (8), (29) imply: % 151.11/22.15 | (41) ~ (all_52_6 = e3) % 151.11/22.15 | % 151.11/22.15 | REDUCE: (8), (30) imply: % 151.11/22.15 | (42) ~ (all_52_14 = e3) % 151.11/22.15 | % 151.11/22.16 | REDUCE: (8), (23) imply: % 151.11/22.16 | (43) op(e3, e3) = all_6_1 % 151.11/22.16 | % 151.11/22.16 | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (9), (10), (11), (12), (13), % 151.11/22.16 | (14), (15), (16), (19), (20), (21), (24), (25), (26), (27), (32), % 151.11/22.16 | (34), (36), (38), (40), (41), (42), (43) are inconsistent by % 151.11/22.16 | sub-proof #264. % 151.11/22.16 | % 151.11/22.16 End of proof % 151.11/22.16 % 151.11/22.16 Sub-proof #189 shows that the following formulas are inconsistent: % 151.11/22.16 ---------------------------------------------------------------- % 151.11/22.16 (1) all_58_6 = all_52_2 % 151.11/22.16 (2) all_56_11 = e3 % 151.11/22.16 (3) ~ (all_52_3 = e2) % 151.11/22.16 (4) e3 = e0 % 151.11/22.16 (5) ~ (all_10_2 = e2) % 151.11/22.16 (6) all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2 % 151.11/22.16 (7) ~ (all_52_1 = all_52_13) % 151.11/22.16 (8) ~ (all_52_2 = e2) % 151.11/22.16 (9) all_58_2 = all_52_1 % 151.11/22.16 (10) ~ (all_56_11 = e0) | all_56_15 = e2 % 151.11/22.16 (11) all_58_0 = all_10_2 % 151.11/22.16 (12) all_56_15 = all_52_13 % 151.11/22.16 (13) all_58_12 = all_52_3 % 151.11/22.16 % 151.11/22.16 Begin of proof % 151.11/22.16 | % 151.11/22.16 | SIMP: (4) implies: % 151.11/22.16 | (14) e3 = e0 % 151.11/22.16 | % 151.11/22.16 | COMBINE_EQS: (2), (14) imply: % 151.11/22.16 | (15) all_56_11 = e0 % 151.11/22.16 | % 151.11/22.16 | REF_CLOSE: (1), (3), (5), (6), (7), (8), (9), (10), (11), (12), (13), (15) are % 151.11/22.16 | inconsistent by sub-proof #596. % 151.11/22.16 | % 151.11/22.16 End of proof % 151.11/22.16 % 151.11/22.16 Sub-proof #190 shows that the following formulas are inconsistent: % 151.11/22.16 ---------------------------------------------------------------- % 151.11/22.16 (1) ~ (all_52_4 = all_52_8) % 151.11/22.16 (2) ~ (all_52_9 = e2) % 151.11/22.16 (3) all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2 % 151.11/22.16 (4) ~ (all_6_2 = e3) % 151.11/22.16 (5) ~ (e3 = e2) % 151.11/22.16 (6) op(e0, e0) = all_4_2 % 151.11/22.16 (7) all_58_4 = all_52_8 % 151.11/22.16 (8) all_54_15 = all_4_2 % 151.11/22.16 (9) all_58_5 = all_52_9 % 151.11/22.16 (10) all_54_1 = all_52_4 % 151.11/22.16 (11) all_16_2 = e0 % 151.11/22.16 (12) all_58_1 = all_52_4 % 151.11/22.16 (13) all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1 % 151.11/22.16 (14) ~ (e1 = e0) % 151.11/22.16 (15) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 151.11/22.16 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 151.11/22.16 (16) ~ (all_52_4 = e0) % 151.11/22.16 (17) op(e0, all_4_1) = e2 % 151.11/22.16 (18) all_58_0 = e0 % 151.11/22.16 (19) ~ (all_4_2 = e1) % 151.11/22.16 (20) ~ (all_52_9 = e3) % 151.11/22.16 (21) all_58_8 = all_6_2 % 151.11/22.16 (22) op(e0, e0) = all_10_1 % 151.11/22.16 (23) op(all_4_2, all_4_2) = all_4_1 % 151.11/22.16 (24) ~ (all_52_11 = all_4_2) % 151.11/22.16 (25) all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3 % 151.11/22.16 (26) ~ (all_16_1 = e2) | ~ (all_16_2 = e0) % 151.11/22.16 (27) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0 % 151.11/22.16 (28) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0 % 151.11/22.16 (29) ~ (all_6_2 = e2) % 151.11/22.16 (30) all_16_1 = all_10_1 % 151.11/22.16 (31) ~ (all_52_4 = e3) % 151.11/22.16 (32) op(e0, all_4_2) = all_56_30 % 151.11/22.16 (33) all_58_14 = all_52_11 % 151.11/22.16 % 151.11/22.16 Begin of proof % 151.11/22.16 | % 151.11/22.16 | BETA: splitting (26) gives: % 151.11/22.16 | % 151.11/22.16 | Case 1: % 151.11/22.16 | | % 151.11/22.16 | | (34) ~ (all_16_1 = e2) % 151.11/22.16 | | % 151.11/22.16 | | REDUCE: (30), (34) imply: % 151.11/22.16 | | (35) ~ (all_10_1 = e2) % 151.11/22.16 | | % 151.11/22.16 | | BETA: splitting (3) gives: % 151.11/22.16 | | % 151.11/22.16 | | Case 1: % 151.11/22.16 | | | % 151.11/22.16 | | | (36) all_58_4 = e2 % 151.11/22.16 | | | % 151.11/22.16 | | | COMBINE_EQS: (7), (36) imply: % 151.11/22.16 | | | (37) all_52_8 = e2 % 151.11/22.16 | | | % 151.11/22.16 | | | SIMP: (37) implies: % 151.11/22.16 | | | (38) all_52_8 = e2 % 151.11/22.16 | | | % 151.11/22.16 | | | REDUCE: (1), (38) imply: % 151.11/22.16 | | | (39) ~ (all_52_4 = e2) % 151.11/22.16 | | | % 151.11/22.16 | | | BETA: splitting (13) gives: % 151.11/22.16 | | | % 151.11/22.16 | | | Case 1: % 151.11/22.16 | | | | % 151.11/22.16 | | | | (40) all_58_0 = e1 % 151.11/22.16 | | | | % 151.11/22.16 | | | | REF_CLOSE: (14), (18), (40) are inconsistent by sub-proof #730. % 151.11/22.16 | | | | % 151.11/22.16 | | | Case 2: % 151.11/22.16 | | | | % 151.11/22.16 | | | | (41) all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1 % 151.11/22.16 | | | | % 151.11/22.16 | | | | BETA: splitting (28) gives: % 151.11/22.16 | | | | % 151.11/22.16 | | | | Case 1: % 151.11/22.16 | | | | | % 151.11/22.16 | | | | | (42) all_54_1 = e3 % 151.11/22.16 | | | | | % 151.11/22.16 | | | | | REF_CLOSE: (10), (31), (42) are inconsistent by sub-proof #722. % 151.11/22.16 | | | | | % 151.11/22.16 | | | | Case 2: % 151.11/22.16 | | | | | % 151.11/22.16 | | | | | (43) all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0 % 151.11/22.16 | | | | | % 151.11/22.16 | | | | | BETA: splitting (43) gives: % 151.11/22.16 | | | | | % 151.11/22.16 | | | | | Case 1: % 151.11/22.16 | | | | | | % 151.11/22.16 | | | | | | (44) all_54_1 = e2 % 151.11/22.16 | | | | | | % 151.11/22.16 | | | | | | REF_CLOSE: (10), (39), (44) are inconsistent by sub-proof #721. % 151.11/22.16 | | | | | | % 151.11/22.16 | | | | | Case 2: % 151.11/22.16 | | | | | | % 151.11/22.16 | | | | | | (45) all_54_1 = e1 | all_54_1 = e0 % 151.11/22.16 | | | | | | % 151.11/22.16 | | | | | | BETA: splitting (41) gives: % 151.11/22.16 | | | | | | % 151.11/22.16 | | | | | | Case 1: % 151.11/22.16 | | | | | | | % 151.11/22.16 | | | | | | | % 151.11/22.16 | | | | | | | GROUND_INST: instantiating (15) with all_4_2, all_10_1, e0, e0, % 151.11/22.16 | | | | | | | simplifying with (6), (22) gives: % 151.11/22.16 | | | | | | | (46) all_10_1 = all_4_2 % 151.11/22.16 | | | | | | | % 151.11/22.16 | | | | | | | REDUCE: (35), (46) imply: % 151.11/22.16 | | | | | | | (47) ~ (all_4_2 = e2) % 151.11/22.16 | | | | | | | % 151.11/22.16 | | | | | | | REF_CLOSE: (4), (6), (8), (9), (15), (17), (19), (20), (21), (23), % 151.11/22.16 | | | | | | | (24), (25), (27), (32), (33), (47) are inconsistent by % 151.11/22.16 | | | | | | | sub-proof #210. % 151.11/22.16 | | | | | | | % 151.11/22.16 | | | | | | Case 2: % 151.11/22.16 | | | | | | | % 151.11/22.16 | | | | | | | (48) ~ (all_58_1 = e1) % 151.11/22.16 | | | | | | | % 151.11/22.16 | | | | | | | REF_CLOSE: (10), (12), (16), (45), (48) are inconsistent by % 151.11/22.16 | | | | | | | sub-proof #593. % 151.11/22.16 | | | | | | | % 151.11/22.16 | | | | | | End of split % 151.11/22.16 | | | | | | % 151.11/22.16 | | | | | End of split % 151.11/22.16 | | | | | % 151.11/22.16 | | | | End of split % 151.11/22.16 | | | | % 151.11/22.16 | | | End of split % 151.11/22.16 | | | % 151.11/22.16 | | Case 2: % 151.11/22.16 | | | % 151.11/22.16 | | | (49) all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2 % 151.11/22.16 | | | % 151.11/22.16 | | | REF_CLOSE: (2), (4), (5), (9), (20), (21), (25), (29), (49) are % 151.11/22.16 | | | inconsistent by sub-proof #315. % 151.11/22.16 | | | % 151.11/22.16 | | End of split % 151.11/22.16 | | % 151.11/22.16 | Case 2: % 151.11/22.16 | | % 151.11/22.16 | | (50) ~ (all_16_2 = e0) % 151.11/22.16 | | % 151.11/22.16 | | REDUCE: (11), (50) imply: % 151.11/22.16 | | (51) $false % 151.11/22.16 | | % 151.11/22.16 | | CLOSE: (51) is inconsistent. % 151.11/22.16 | | % 151.11/22.16 | End of split % 151.11/22.16 | % 151.11/22.16 End of proof % 151.11/22.16 % 151.11/22.16 Sub-proof #191 shows that the following formulas are inconsistent: % 151.11/22.16 ---------------------------------------------------------------- % 151.11/22.16 (1) all_56_11 = all_8_2 % 151.11/22.16 (2) ~ (all_56_11 = e1) | all_56_13 = e2 % 151.11/22.16 (3) ~ (all_52_11 = all_6_2) % 151.11/22.16 (4) all_56_25 = all_52_3 % 151.11/22.16 (5) all_54_9 = all_52_6 % 151.11/22.16 (6) all_58_6 = all_52_2 % 151.11/22.16 (7) ~ (all_52_3 = all_8_0) % 151.11/22.16 (8) all_54_10 = all_6_2 % 151.11/22.16 (9) ~ (all_52_2 = all_8_0) % 151.11/22.16 (10) ~ (all_52_13 = all_8_2) % 151.11/22.16 (11) ~ (all_56_21 = e2) | all_56_19 = e1 % 151.11/22.16 (12) ~ (all_52_14 = all_4_2) % 151.11/22.16 (13) ~ (all_8_0 = e1) % 151.11/22.16 (14) ~ (all_52_9 = all_8_2) % 151.11/22.16 (15) op(e0, e0) = all_4_2 % 151.11/22.16 (16) ~ (all_52_13 = all_8_0) % 151.11/22.16 (17) all_58_6 = e0 | all_58_7 = e0 | all_58_8 = e0 | all_58_11 = e0 % 151.11/22.16 (18) all_58_4 = all_52_8 % 151.11/22.16 (19) all_54_5 = all_8_2 % 151.11/22.16 (20) ~ (all_52_6 = all_52_14) % 151.11/22.16 (21) ~ (all_8_0 = all_8_2) % 151.11/22.16 (22) all_56_21 = all_6_2 % 151.11/22.16 (23) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 151.11/22.16 (24) ~ (all_52_7 = all_8_2) % 151.11/22.16 (25) all_56_1 = all_10_2 % 151.11/22.16 (26) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0 % 151.11/22.16 (27) all_58_5 = all_52_9 % 151.11/22.16 (28) all_56_17 = all_52_2 % 151.11/22.16 (29) all_36_1 = e3 % 151.11/22.16 (30) ~ (all_22_0 = e0) | ~ (all_22_2 = e1) % 151.11/22.16 (31) all_58_13 = all_52_7 % 151.11/22.16 (32) op(e2, all_8_2) = all_56_10 % 151.11/22.16 (33) op(e3, e3) = all_10_2 % 151.11/22.16 (34) ~ (all_56_21 = e3) | all_56_17 = e1 % 151.11/22.16 (35) ~ (e1 = e0) % 151.11/22.16 (36) all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1 % 151.11/22.16 (37) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 151.11/22.16 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 151.11/22.16 (38) ~ (all_10_2 = all_8_0) % 151.11/22.16 (39) ~ (all_52_3 = all_10_2) % 151.11/22.16 (40) all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0 % 151.11/22.16 (41) ~ (all_56_11 = e3) | all_56_9 = e2 % 151.11/22.16 (42) all_36_0 = all_6_0 % 151.11/22.16 (43) ~ (all_52_2 = all_52_6) % 151.11/22.16 (44) all_22_0 = all_8_0 % 151.11/22.16 (45) op(e0, all_4_1) = e2 % 151.11/22.16 (46) all_56_13 = all_52_9 % 151.11/22.16 (47) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0 % 151.11/22.16 (48) op(e1, e3) = all_52_2 % 151.11/22.16 (49) all_36_1 = all_6_1 % 151.11/22.16 (50) all_58_8 = all_6_2 % 151.11/22.16 (51) ~ (all_52_8 = all_10_2) % 151.11/22.16 (52) ~ (e2 = e1) % 151.11/22.16 (53) ~ (all_52_9 = all_52_13) % 151.11/22.16 (54) op(e1, all_6_1) = all_6_0 % 151.11/22.16 (55) all_56_9 = all_8_0 % 151.11/22.16 (56) op(all_4_2, all_4_2) = all_4_1 % 151.11/22.16 (57) all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3 % 151.11/22.16 (58) all_58_3 = all_8_2 % 151.11/22.16 (59) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0 % 151.11/22.16 (60) ~ (all_52_11 = all_4_2) % 151.11/22.16 (61) all_56_31 = all_4_2 % 151.11/22.16 (62) all_58_11 = all_52_14 % 151.11/22.16 (63) all_36_2 = all_6_2 % 151.11/22.16 (64) ~ (all_52_2 = all_52_14) % 151.11/22.16 (65) all_54_7 = all_52_13 % 151.11/22.16 (66) op(all_6_2, all_6_2) = all_6_1 % 151.11/22.16 (67) all_56_1 = e3 | all_56_11 = e2 | all_56_21 = e1 | all_56_31 = e0 % 151.11/22.16 (68) ~ (all_52_13 = all_4_2) % 151.11/22.16 (69) op(all_8_2, all_8_2) = e3 % 151.11/22.16 (70) all_56_23 = all_52_14 % 151.11/22.16 (71) all_54_8 = all_52_2 % 151.11/22.16 (72) op(e1, e1) = all_6_2 % 151.11/22.16 (73) ~ (all_52_6 = all_8_2) % 151.11/22.16 (74) op(e0, e3) = all_52_3 % 151.11/22.16 (75) all_58_15 = all_4_2 % 151.11/22.16 (76) ~ (all_52_9 = all_6_2) % 151.11/22.16 (77) all_22_2 = all_8_2 % 151.11/22.16 (78) all_58_7 = all_52_6 % 151.11/22.16 (79) all_58_10 = all_52_13 % 151.11/22.16 (80) all_58_2 = all_8_0 % 151.11/22.16 (81) ~ (all_56_11 = e0) | all_56_15 = e2 % 151.11/22.16 (82) op(e1, all_6_2) = all_56_20 % 151.11/22.16 (83) all_54_4 = all_8_0 % 151.11/22.16 (84) op(e2, e2) = all_8_2 % 151.11/22.16 (85) ~ (all_36_0 = e0) | ~ (all_36_2 = e2) % 151.13/22.16 (86) ~ (all_52_2 = all_6_2) % 151.13/22.16 (87) ~ (all_56_21 = e0) | all_56_23 = e1 % 151.13/22.16 (88) op(e0, all_4_2) = all_56_30 % 151.13/22.16 (89) ~ (all_52_6 = all_6_2) % 151.13/22.16 (90) ~ (all_52_14 = all_6_2) % 151.13/22.16 (91) ~ (e2 = e0) % 151.13/22.16 (92) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0 % 151.13/22.16 (93) ~ (all_52_2 = all_10_2) % 151.13/22.16 (94) op(all_8_2, all_8_2) = all_8_1 % 151.13/22.16 (95) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 151.13/22.16 (96) all_58_14 = all_52_11 % 151.13/22.16 (97) all_56_19 = all_52_6 % 151.13/22.16 (98) ~ (all_52_9 = all_8_0) % 151.13/22.16 (99) all_56_15 = all_52_13 % 151.13/22.16 (100) all_58_12 = all_52_3 % 151.13/22.16 (101) all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3 % 151.13/22.16 (102) ~ (all_56_31 = e3) | all_56_25 = e0 % 151.13/22.16 % 151.13/22.16 Begin of proof % 151.13/22.16 | % 151.13/22.16 | COMBINE_EQS: (29), (49) imply: % 151.13/22.16 | (103) all_6_1 = e3 % 151.13/22.16 | % 151.13/22.16 | SIMP: (103) implies: % 151.13/22.16 | (104) all_6_1 = e3 % 151.13/22.16 | % 151.13/22.16 | REDUCE: (66), (104) imply: % 151.13/22.16 | (105) op(all_6_2, all_6_2) = e3 % 151.13/22.16 | % 151.13/22.16 | REDUCE: (54), (104) imply: % 151.13/22.16 | (106) op(e1, e3) = all_6_0 % 151.13/22.16 | % 151.13/22.16 | GROUND_INST: instantiating (37) with all_52_2, all_6_0, e3, e1, simplifying % 151.13/22.16 | with (48), (106) gives: % 151.13/22.16 | (107) all_52_2 = all_6_0 % 151.13/22.16 | % 151.13/22.16 | COMBINE_EQS: (71), (107) imply: % 151.13/22.16 | (108) all_54_8 = all_6_0 % 151.13/22.16 | % 151.13/22.16 | COMBINE_EQS: (28), (107) imply: % 151.13/22.16 | (109) all_56_17 = all_6_0 % 151.13/22.16 | % 151.13/22.16 | COMBINE_EQS: (6), (107) imply: % 151.13/22.16 | (110) all_58_6 = all_6_0 % 151.13/22.16 | % 151.13/22.16 | REDUCE: (43), (107) imply: % 151.13/22.16 | (111) ~ (all_52_6 = all_6_0) % 151.13/22.16 | % 151.13/22.16 | SIMP: (111) implies: % 151.13/22.16 | (112) ~ (all_52_6 = all_6_0) % 151.13/22.16 | % 151.13/22.16 | REDUCE: (64), (107) imply: % 151.13/22.16 | (113) ~ (all_52_14 = all_6_0) % 151.13/22.16 | % 151.13/22.16 | SIMP: (113) implies: % 151.13/22.16 | (114) ~ (all_52_14 = all_6_0) % 151.13/22.16 | % 151.13/22.16 | REDUCE: (93), (107) imply: % 151.13/22.16 | (115) ~ (all_10_2 = all_6_0) % 151.13/22.16 | % 151.13/22.16 | SIMP: (115) implies: % 151.13/22.16 | (116) ~ (all_10_2 = all_6_0) % 151.13/22.16 | % 151.13/22.16 | REDUCE: (9), (107) imply: % 151.13/22.16 | (117) ~ (all_8_0 = all_6_0) % 151.13/22.16 | % 151.13/22.16 | SIMP: (117) implies: % 151.13/22.16 | (118) ~ (all_8_0 = all_6_0) % 151.13/22.16 | % 151.13/22.16 | REDUCE: (86), (107) imply: % 151.13/22.16 | (119) ~ (all_6_0 = all_6_2) % 151.13/22.16 | % 151.13/22.16 | BETA: splitting (11) gives: % 151.13/22.16 | % 151.13/22.16 | Case 1: % 151.13/22.16 | | % 151.13/22.16 | | (120) ~ (all_56_21 = e2) % 151.13/22.16 | | % 151.13/22.16 | | REDUCE: (22), (120) imply: % 151.13/22.16 | | (121) ~ (all_6_2 = e2) % 151.13/22.16 | | % 151.13/22.16 | | BETA: splitting (81) gives: % 151.13/22.16 | | % 151.13/22.16 | | Case 1: % 151.13/22.16 | | | % 151.13/22.16 | | | (122) ~ (all_56_11 = e0) % 151.13/22.16 | | | % 151.13/22.16 | | | REDUCE: (1), (122) imply: % 151.13/22.16 | | | (123) ~ (all_8_2 = e0) % 151.13/22.16 | | | % 151.13/22.16 | | | BETA: splitting (34) gives: % 151.13/22.16 | | | % 151.13/22.16 | | | Case 1: % 151.13/22.16 | | | | % 151.13/22.16 | | | | (124) ~ (all_56_21 = e3) % 151.13/22.16 | | | | % 151.13/22.16 | | | | REDUCE: (22), (124) imply: % 151.13/22.16 | | | | (125) ~ (all_6_2 = e3) % 151.13/22.16 | | | | % 151.13/22.16 | | | | BETA: splitting (2) gives: % 151.13/22.16 | | | | % 151.13/22.16 | | | | Case 1: % 151.13/22.16 | | | | | % 151.13/22.16 | | | | | (126) ~ (all_56_11 = e1) % 151.13/22.16 | | | | | % 151.13/22.16 | | | | | REDUCE: (1), (126) imply: % 151.13/22.16 | | | | | (127) ~ (all_8_2 = e1) % 151.13/22.16 | | | | | % 151.13/22.16 | | | | | BETA: splitting (41) gives: % 151.13/22.16 | | | | | % 151.13/22.16 | | | | | Case 1: % 151.13/22.16 | | | | | | % 151.13/22.16 | | | | | | (128) ~ (all_56_11 = e3) % 151.13/22.16 | | | | | | % 151.13/22.16 | | | | | | REDUCE: (1), (128) imply: % 151.13/22.16 | | | | | | (129) ~ (all_8_2 = e3) % 151.13/22.16 | | | | | | % 151.13/22.16 | | | | | | REF_CLOSE: (19), (32), (37), (69), (84), (95), (123), (127), (129) % 151.13/22.16 | | | | | | are inconsistent by sub-proof #347. % 151.13/22.16 | | | | | | % 151.13/22.16 | | | | | Case 2: % 151.13/22.16 | | | | | | % 151.13/22.16 | | | | | | (130) all_56_11 = e3 % 151.13/22.16 | | | | | | (131) all_56_9 = e2 % 151.13/22.16 | | | | | | % 151.13/22.16 | | | | | | COMBINE_EQS: (55), (131) imply: % 151.13/22.16 | | | | | | (132) all_8_0 = e2 % 151.13/22.16 | | | | | | % 151.13/22.16 | | | | | | COMBINE_EQS: (1), (130) imply: % 151.13/22.16 | | | | | | (133) all_8_2 = e3 % 151.13/22.16 | | | | | | % 151.13/22.16 | | | | | | REDUCE: (14), (133) imply: % 151.13/22.16 | | | | | | (134) ~ (all_52_9 = e3) % 151.13/22.16 | | | | | | % 151.13/22.16 | | | | | | REDUCE: (118), (132) imply: % 151.13/22.16 | | | | | | (135) ~ (all_6_0 = e2) % 151.13/22.16 | | | | | | % 151.13/22.16 | | | | | | SIMP: (135) implies: % 151.13/22.16 | | | | | | (136) ~ (all_6_0 = e2) % 151.13/22.16 | | | | | | % 151.13/22.16 | | | | | | REDUCE: (69), (133) imply: % 151.13/22.16 | | | | | | (137) op(e3, e3) = e3 % 151.13/22.16 | | | | | | % 151.13/22.16 | | | | | | GROUND_INST: instantiating (37) with all_10_2, e3, e3, e3, % 151.13/22.16 | | | | | | simplifying with (33), (137) gives: % 151.13/22.16 | | | | | | (138) all_10_2 = e3 % 151.13/22.16 | | | | | | % 151.13/22.16 | | | | | | REDUCE: (51), (138) imply: % 151.13/22.16 | | | | | | (139) ~ (all_52_8 = e3) % 151.13/22.16 | | | | | | % 151.13/22.16 | | | | | | BETA: splitting (57) gives: % 151.13/22.16 | | | | | | % 151.13/22.16 | | | | | | Case 1: % 151.13/22.16 | | | | | | | % 151.13/22.16 | | | | | | | (140) all_58_4 = e3 % 151.13/22.16 | | | | | | | % 151.13/22.16 | | | | | | | COMBINE_EQS: (18), (140) imply: % 151.13/22.16 | | | | | | | (141) all_52_8 = e3 % 151.13/22.16 | | | | | | | % 151.13/22.16 | | | | | | | REDUCE: (139), (141) imply: % 151.13/22.16 | | | | | | | (142) $false % 151.13/22.16 | | | | | | | % 151.13/22.16 | | | | | | | CLOSE: (142) is inconsistent. % 151.13/22.16 | | | | | | | % 151.13/22.16 | | | | | | Case 2: % 151.13/22.16 | | | | | | | % 151.13/22.16 | | | | | | | (143) all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3 % 151.13/22.16 | | | | | | | % 151.13/22.16 | | | | | | | BETA: splitting (143) gives: % 151.13/22.16 | | | | | | | % 151.13/22.16 | | | | | | | Case 1: % 151.13/22.16 | | | | | | | | % 151.13/22.16 | | | | | | | | (144) all_58_5 = e3 % 151.13/22.16 | | | | | | | | % 151.13/22.16 | | | | | | | | COMBINE_EQS: (27), (144) imply: % 151.13/22.16 | | | | | | | | (145) all_52_9 = e3 % 151.13/22.16 | | | | | | | | % 151.13/22.16 | | | | | | | | REDUCE: (134), (145) imply: % 151.13/22.16 | | | | | | | | (146) $false % 151.13/22.16 | | | | | | | | % 151.13/22.16 | | | | | | | | CLOSE: (146) is inconsistent. % 151.13/22.16 | | | | | | | | % 151.13/22.16 | | | | | | | Case 2: % 151.13/22.16 | | | | | | | | % 151.13/22.16 | | | | | | | | (147) all_58_8 = e3 | all_58_14 = e3 % 151.13/22.16 | | | | | | | | % 151.13/22.16 | | | | | | | | BETA: splitting (147) gives: % 151.13/22.16 | | | | | | | | % 151.13/22.16 | | | | | | | | Case 1: % 151.13/22.16 | | | | | | | | | % 151.13/22.16 | | | | | | | | | (148) all_58_8 = e3 % 151.13/22.16 | | | | | | | | | % 151.13/22.16 | | | | | | | | | COMBINE_EQS: (50), (148) imply: % 151.13/22.16 | | | | | | | | | (149) all_6_2 = e3 % 151.13/22.16 | | | | | | | | | % 151.13/22.16 | | | | | | | | | REDUCE: (125), (149) imply: % 151.13/22.16 | | | | | | | | | (150) $false % 151.13/22.16 | | | | | | | | | % 151.13/22.16 | | | | | | | | | CLOSE: (150) is inconsistent. % 151.13/22.16 | | | | | | | | | % 151.13/22.16 | | | | | | | | Case 2: % 151.13/22.16 | | | | | | | | | % 151.13/22.16 | | | | | | | | | (151) all_58_14 = e3 % 151.13/22.16 | | | | | | | | | % 151.13/22.16 | | | | | | | | | COMBINE_EQS: (96), (151) imply: % 151.13/22.16 | | | | | | | | | (152) all_52_11 = e3 % 151.13/22.16 | | | | | | | | | % 151.13/22.16 | | | | | | | | | SIMP: (152) implies: % 151.13/22.16 | | | | | | | | | (153) all_52_11 = e3 % 151.13/22.16 | | | | | | | | | % 151.13/22.16 | | | | | | | | | REDUCE: (3), (153) imply: % 151.13/22.16 | | | | | | | | | (154) ~ (all_6_2 = e3) % 151.13/22.16 | | | | | | | | | % 151.13/22.16 | | | | | | | | | REDUCE: (60), (153) imply: % 151.13/22.16 | | | | | | | | | (155) ~ (all_4_2 = e3) % 151.13/22.16 | | | | | | | | | % 151.13/22.16 | | | | | | | | | SIMP: (155) implies: % 151.13/22.16 | | | | | | | | | (156) ~ (all_4_2 = e3) % 151.13/22.16 | | | | | | | | | % 151.13/22.16 | | | | | | | | | REF_CLOSE: (1), (5), (8), (15), (20), (22), (23), (25), (37), % 151.13/22.16 | | | | | | | | | (56), (59), (61), (67), (70), (72), (73), (82), % 151.13/22.16 | | | | | | | | | (87), (88), (89), (90), (92), (105), (108), (112), % 151.13/22.16 | | | | | | | | | (114), (116), (119), (121), (125), (136), (156) are % 151.13/22.16 | | | | | | | | | inconsistent by sub-proof #429. % 151.13/22.16 | | | | | | | | | % 151.13/22.16 | | | | | | | | End of split % 151.13/22.16 | | | | | | | | % 151.13/22.16 | | | | | | | End of split % 151.13/22.16 | | | | | | | % 151.13/22.16 | | | | | | End of split % 151.13/22.16 | | | | | | % 151.13/22.16 | | | | | End of split % 151.13/22.16 | | | | | % 151.13/22.16 | | | | Case 2: % 151.13/22.16 | | | | | % 151.13/22.16 | | | | | (157) all_56_13 = e2 % 151.13/22.16 | | | | | (158) all_56_11 = e1 % 151.13/22.16 | | | | | % 151.13/22.16 | | | | | REF_CLOSE: (1), (10), (14), (16), (21), (22), (25), (26), (30), (37), % 151.13/22.16 | | | | | (38), (44), (46), (47), (53), (61), (65), (67), (68), (69), % 151.13/22.16 | | | | | (72), (77), (82), (83), (98), (125), (157), (158) are % 151.13/22.16 | | | | | inconsistent by sub-proof #340. % 151.13/22.16 | | | | | % 151.13/22.16 | | | | End of split % 151.13/22.16 | | | | % 151.13/22.16 | | | Case 2: % 151.13/22.16 | | | | % 151.13/22.16 | | | | (159) all_56_21 = e3 % 151.13/22.16 | | | | (160) all_56_17 = e1 % 151.13/22.16 | | | | % 151.13/22.16 | | | | COMBINE_EQS: (109), (160) imply: % 151.13/22.16 | | | | (161) all_6_0 = e1 % 151.13/22.16 | | | | % 151.13/22.16 | | | | COMBINE_EQS: (22), (159) imply: % 151.13/22.16 | | | | (162) all_6_2 = e3 % 151.13/22.16 | | | | % 151.13/22.16 | | | | REDUCE: (3), (162) imply: % 151.13/22.16 | | | | (163) ~ (all_52_11 = e3) % 151.13/22.16 | | | | % 151.13/22.16 | | | | REDUCE: (105), (162) imply: % 151.13/22.16 | | | | (164) op(e3, e3) = e3 % 151.13/22.16 | | | | % 151.13/22.16 | | | | GROUND_INST: instantiating (37) with all_10_2, e3, e3, e3, simplifying % 151.13/22.16 | | | | with (33), (164) gives: % 151.13/22.16 | | | | (165) all_10_2 = e3 % 151.13/22.16 | | | | % 151.13/22.16 | | | | REDUCE: (39), (165) imply: % 151.13/22.16 | | | | (166) ~ (all_52_3 = e3) % 151.13/22.16 | | | | % 151.13/22.16 | | | | REDUCE: (38), (165) imply: % 151.13/22.16 | | | | (167) ~ (all_8_0 = e3) % 151.13/22.16 | | | | % 151.13/22.16 | | | | SIMP: (167) implies: % 151.13/22.16 | | | | (168) ~ (all_8_0 = e3) % 151.13/22.16 | | | | % 151.13/22.16 | | | | BETA: splitting (2) gives: % 151.13/22.16 | | | | % 151.13/22.16 | | | | Case 1: % 151.13/22.16 | | | | | % 151.13/22.16 | | | | | (169) ~ (all_56_11 = e1) % 151.13/22.16 | | | | | % 151.13/22.16 | | | | | REDUCE: (1), (169) imply: % 151.13/22.16 | | | | | (170) ~ (all_8_2 = e1) % 151.13/22.16 | | | | | % 151.13/22.16 | | | | | BETA: splitting (41) gives: % 151.13/22.16 | | | | | % 151.13/22.16 | | | | | Case 1: % 151.13/22.16 | | | | | | % 151.13/22.16 | | | | | | (171) ~ (all_56_11 = e3) % 151.13/22.16 | | | | | | % 151.13/22.16 | | | | | | REDUCE: (1), (171) imply: % 151.13/22.16 | | | | | | (172) ~ (all_8_2 = e3) % 151.13/22.16 | | | | | | % 151.13/22.16 | | | | | | REF_CLOSE: (19), (32), (37), (69), (84), (95), (123), (170), (172) % 151.13/22.16 | | | | | | are inconsistent by sub-proof #347. % 151.13/22.16 | | | | | | % 151.13/22.16 | | | | | Case 2: % 151.13/22.16 | | | | | | % 151.13/22.16 | | | | | | (173) all_56_11 = e3 % 151.13/22.16 | | | | | | (174) all_56_9 = e2 % 151.13/22.16 | | | | | | % 151.13/22.16 | | | | | | COMBINE_EQS: (55), (174) imply: % 151.13/22.16 | | | | | | (175) all_8_0 = e2 % 151.13/22.16 | | | | | | % 151.13/22.16 | | | | | | COMBINE_EQS: (1), (173) imply: % 151.13/22.16 | | | | | | (176) all_8_2 = e3 % 151.13/22.16 | | | | | | % 151.13/22.16 | | | | | | REDUCE: (7), (175) imply: % 151.13/22.16 | | | | | | (177) ~ (all_52_3 = e2) % 151.13/22.16 | | | | | | % 151.13/22.16 | | | | | | REDUCE: (24), (176) imply: % 151.13/22.16 | | | | | | (178) ~ (all_52_7 = e3) % 151.13/22.16 | | | | | | % 151.13/22.16 | | | | | | BETA: splitting (101) gives: % 151.13/22.16 | | | | | | % 151.13/22.16 | | | | | | Case 1: % 151.13/22.16 | | | | | | | % 151.13/22.16 | | | | | | | (179) all_58_12 = e3 % 151.13/22.16 | | | | | | | % 151.13/22.16 | | | | | | | COMBINE_EQS: (100), (179) imply: % 151.13/22.16 | | | | | | | (180) all_52_3 = e3 % 151.13/22.16 | | | | | | | % 151.13/22.16 | | | | | | | REDUCE: (166), (180) imply: % 151.13/22.16 | | | | | | | (181) $false % 151.13/22.16 | | | | | | | % 151.13/22.16 | | | | | | | CLOSE: (181) is inconsistent. % 151.13/22.16 | | | | | | | % 151.13/22.16 | | | | | | Case 2: % 151.13/22.16 | | | | | | | % 151.13/22.16 | | | | | | | (182) all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3 % 151.13/22.16 | | | | | | | % 151.13/22.16 | | | | | | | BETA: splitting (182) gives: % 151.13/22.16 | | | | | | | % 151.13/22.16 | | | | | | | Case 1: % 151.13/22.16 | | | | | | | | % 151.13/22.16 | | | | | | | | (183) all_58_13 = e3 % 151.13/22.16 | | | | | | | | % 151.13/22.16 | | | | | | | | REF_CLOSE: (31), (178), (183) are inconsistent by sub-proof % 151.13/22.16 | | | | | | | | #444. % 151.13/22.16 | | | | | | | | % 151.13/22.16 | | | | | | | Case 2: % 151.13/22.16 | | | | | | | | % 151.13/22.16 | | | | | | | | (184) all_58_14 = e3 | all_58_15 = e3 % 151.13/22.16 | | | | | | | | % 151.13/22.16 | | | | | | | | BETA: splitting (184) gives: % 151.13/22.16 | | | | | | | | % 151.13/22.16 | | | | | | | | Case 1: % 151.13/22.16 | | | | | | | | | % 151.13/22.16 | | | | | | | | | (185) all_58_14 = e3 % 151.13/22.16 | | | | | | | | | % 151.13/22.16 | | | | | | | | | REF_CLOSE: (96), (163), (185) are inconsistent by sub-proof % 151.13/22.16 | | | | | | | | | #447. % 151.13/22.16 | | | | | | | | | % 151.13/22.16 | | | | | | | | Case 2: % 151.13/22.16 | | | | | | | | | % 151.13/22.16 | | | | | | | | | (186) all_58_15 = e3 % 151.13/22.16 | | | | | | | | | % 151.13/22.16 | | | | | | | | | COMBINE_EQS: (75), (186) imply: % 151.13/22.16 | | | | | | | | | (187) all_4_2 = e3 % 151.13/22.16 | | | | | | | | | % 151.13/22.16 | | | | | | | | | COMBINE_EQS: (61), (187) imply: % 151.13/22.16 | | | | | | | | | (188) all_56_31 = e3 % 151.13/22.16 | | | | | | | | | % 151.13/22.16 | | | | | | | | | REDUCE: (56), (187) imply: % 151.13/22.16 | | | | | | | | | (189) op(e3, e3) = all_4_1 % 151.13/22.16 | | | | | | | | | % 151.13/22.16 | | | | | | | | | REDUCE: (88), (187) imply: % 151.13/22.16 | | | | | | | | | (190) op(e0, e3) = all_56_30 % 151.13/22.16 | | | | | | | | | % 151.13/22.16 | | | | | | | | | BETA: splitting (102) gives: % 151.13/22.16 | | | | | | | | | % 151.13/22.16 | | | | | | | | | Case 1: % 151.13/22.16 | | | | | | | | | | % 151.13/22.16 | | | | | | | | | | (191) ~ (all_56_31 = e3) % 151.13/22.16 | | | | | | | | | | % 151.13/22.16 | | | | | | | | | | REDUCE: (188), (191) imply: % 151.13/22.16 | | | | | | | | | | (192) $false % 151.13/22.16 | | | | | | | | | | % 151.13/22.16 | | | | | | | | | | CLOSE: (192) is inconsistent. % 151.13/22.16 | | | | | | | | | | % 151.13/22.16 | | | | | | | | | Case 2: % 151.13/22.16 | | | | | | | | | | % 151.13/22.16 | | | | | | | | | | (193) all_56_25 = e0 % 151.13/22.16 | | | | | | | | | | % 151.13/22.16 | | | | | | | | | | COMBINE_EQS: (4), (193) imply: % 151.13/22.16 | | | | | | | | | | (194) all_52_3 = e0 % 151.13/22.16 | | | | | | | | | | % 151.13/22.16 | | | | | | | | | | SIMP: (194) implies: % 151.13/22.16 | | | | | | | | | | (195) all_52_3 = e0 % 151.13/22.16 | | | | | | | | | | % 151.13/22.16 | | | | | | | | | | REDUCE: (177), (195) imply: % 151.13/22.16 | | | | | | | | | | (196) ~ (e2 = e0) % 151.13/22.16 | | | | | | | | | | % 151.13/22.16 | | | | | | | | | | REDUCE: (74), (195) imply: % 151.13/22.16 | | | | | | | | | | (197) op(e0, e3) = e0 % 151.13/22.16 | | | | | | | | | | % 151.13/22.16 | | | | | | | | | | REF_CLOSE: (37), (45), (91), (164), (189), (190), (197) are % 151.13/22.16 | | | | | | | | | | inconsistent by sub-proof #192. % 151.13/22.16 | | | | | | | | | | % 151.13/22.16 | | | | | | | | | End of split % 151.13/22.16 | | | | | | | | | % 151.13/22.16 | | | | | | | | End of split % 151.13/22.16 | | | | | | | | % 151.13/22.16 | | | | | | | End of split % 151.13/22.16 | | | | | | | % 151.13/22.16 | | | | | | End of split % 151.13/22.16 | | | | | | % 151.13/22.16 | | | | | End of split % 151.13/22.16 | | | | | % 151.13/22.16 | | | | Case 2: % 151.13/22.16 | | | | | % 151.13/22.16 | | | | | (198) all_56_11 = e1 % 151.13/22.16 | | | | | % 151.13/22.16 | | | | | COMBINE_EQS: (1), (198) imply: % 151.13/22.16 | | | | | (199) all_8_2 = e1 % 151.13/22.16 | | | | | % 151.13/22.16 | | | | | COMBINE_EQS: (77), (199) imply: % 151.13/22.16 | | | | | (200) all_22_2 = e1 % 151.13/22.16 | | | | | % 151.13/22.16 | | | | | REF_CLOSE: (2), (13), (30), (40), (44), (46), (47), (80), (83), (98), % 151.13/22.16 | | | | | (168), (198), (200) are inconsistent by sub-proof #332. % 151.13/22.16 | | | | | % 151.13/22.16 | | | | End of split % 151.13/22.16 | | | | % 151.13/22.16 | | | End of split % 151.13/22.16 | | | % 151.13/22.16 | | Case 2: % 151.13/22.16 | | | % 151.13/22.16 | | | (201) all_56_15 = e2 % 151.13/22.16 | | | (202) all_56_11 = e0 % 151.13/22.16 | | | % 151.13/22.16 | | | COMBINE_EQS: (1), (202) imply: % 151.13/22.16 | | | (203) all_8_2 = e0 % 151.13/22.16 | | | % 151.13/22.16 | | | COMBINE_EQS: (99), (201) imply: % 151.13/22.16 | | | (204) all_52_13 = e2 % 151.13/22.16 | | | % 151.13/22.16 | | | REF_CLOSE: (1), (10), (13), (15), (16), (21), (22), (25), (27), (35), % 151.13/22.16 | | | (36), (37), (38), (47), (52), (56), (58), (61), (67), (69), % 151.13/22.16 | | | (76), (79), (80), (83), (88), (203), (204) are inconsistent by % 151.13/22.16 | | | sub-proof #336. % 151.13/22.16 | | | % 151.13/22.16 | | End of split % 151.13/22.16 | | % 151.13/22.16 | Case 2: % 151.13/22.16 | | % 151.13/22.16 | | (205) all_56_21 = e2 % 151.13/22.16 | | (206) all_56_19 = e1 % 151.13/22.16 | | % 151.13/22.16 | | COMBINE_EQS: (97), (206) imply: % 151.13/22.16 | | (207) all_52_6 = e1 % 151.13/22.16 | | % 151.13/22.16 | | REF_CLOSE: (1), (12), (17), (22), (25), (32), (35), (37), (42), (50), (61), % 151.13/22.16 | | (62), (63), (67), (78), (84), (85), (89), (91), (92), (94), % 151.13/22.16 | | (105), (108), (110), (112), (114), (116), (119), (205), (207) are % 151.13/22.16 | | inconsistent by sub-proof #431. % 151.13/22.16 | | % 151.13/22.16 | End of split % 151.13/22.16 | % 151.13/22.16 End of proof % 151.13/22.16 % 151.13/22.16 Sub-proof #192 shows that the following formulas are inconsistent: % 151.13/22.16 ---------------------------------------------------------------- % 151.13/22.16 (1) op(e3, e3) = e3 % 151.13/22.16 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 151.13/22.16 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 151.13/22.17 (3) op(e0, all_4_1) = e2 % 151.13/22.17 (4) op(e0, e3) = all_56_30 % 151.13/22.17 (5) ~ (e2 = e0) % 151.13/22.17 (6) op(e3, e3) = all_4_1 % 151.13/22.17 (7) op(e0, e3) = e0 % 151.13/22.17 % 151.13/22.17 Begin of proof % 151.13/22.17 | % 151.13/22.17 | GROUND_INST: instantiating (2) with e0, all_56_30, e3, e0, simplifying with % 151.13/22.17 | (4), (7) gives: % 151.13/22.17 | (8) all_56_30 = e0 % 151.13/22.17 | % 151.13/22.17 | GROUND_INST: instantiating (2) with e3, all_4_1, e3, e3, simplifying with (1), % 151.13/22.17 | (6) gives: % 151.13/22.17 | (9) all_4_1 = e3 % 151.13/22.17 | % 151.13/22.17 | REDUCE: (3), (9) imply: % 151.13/22.17 | (10) op(e0, e3) = e2 % 151.13/22.17 | % 151.13/22.17 | GROUND_INST: instantiating (2) with e0, e2, e3, e0, simplifying with (7), (10) % 151.13/22.17 | gives: % 151.13/22.17 | (11) e2 = e0 % 151.13/22.17 | % 151.13/22.17 | REDUCE: (5), (11) imply: % 151.13/22.17 | (12) $false % 151.13/22.17 | % 151.13/22.17 | CLOSE: (12) is inconsistent. % 151.13/22.17 | % 151.13/22.17 End of proof % 151.13/22.17 % 151.13/22.17 Sub-proof #193 shows that the following formulas are inconsistent: % 151.13/22.17 ---------------------------------------------------------------- % 151.13/22.17 (1) ~ (all_52_11 = all_6_2) % 151.13/22.17 (2) all_56_31 = e1 % 151.13/22.17 (3) ~ (all_34_1 = e3) | ~ (all_34_2 = e1) % 151.13/22.17 (4) op(e1, all_6_1) = e3 % 151.13/22.17 (5) all_54_10 = all_6_2 % 151.13/22.17 (6) ~ (all_6_1 = e2) % 151.13/22.17 (7) ~ (all_56_21 = e2) | all_56_19 = e1 % 151.13/22.17 (8) all_40_2 = all_6_2 % 151.13/22.17 (9) all_54_5 = all_8_2 % 151.13/22.17 (10) ~ (all_6_1 = e3) % 151.13/22.17 (11) all_56_21 = all_6_2 % 151.13/22.17 (12) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 151.13/22.17 (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 151.13/22.17 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 151.13/22.17 (14) all_34_1 = all_4_1 % 151.13/22.17 (15) op(all_4_2, all_4_2) = all_4_1 % 151.13/22.17 (16) all_56_29 = e0 % 151.13/22.17 (17) all_56_31 = all_4_2 % 151.13/22.17 (18) op(all_6_2, all_6_2) = all_6_1 % 151.13/22.17 (19) op(e1, e1) = all_6_2 % 151.13/22.17 (20) ~ (all_52_6 = all_8_2) % 151.13/22.17 (21) all_56_29 = all_52_11 % 151.13/22.17 (22) all_40_1 = all_6_1 % 151.13/22.17 (23) op(e1, all_6_2) = all_56_20 % 151.13/22.17 (24) op(e2, e2) = all_8_2 % 151.13/22.17 (25) ~ (all_40_1 = e0) | ~ (all_40_2 = e2) % 151.13/22.17 (26) all_34_2 = all_4_2 % 151.13/22.17 (27) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 151.13/22.17 (28) all_56_19 = all_52_6 % 151.13/22.17 % 151.13/22.17 Begin of proof % 151.13/22.17 | % 151.13/22.17 | COMBINE_EQS: (16), (21) imply: % 151.13/22.17 | (29) all_52_11 = e0 % 151.13/22.17 | % 151.13/22.17 | SIMP: (29) implies: % 151.13/22.17 | (30) all_52_11 = e0 % 151.13/22.17 | % 151.13/22.17 | COMBINE_EQS: (2), (17) imply: % 151.13/22.17 | (31) all_4_2 = e1 % 151.13/22.17 | % 151.13/22.17 | COMBINE_EQS: (26), (31) imply: % 151.13/22.17 | (32) all_34_2 = e1 % 151.13/22.17 | % 151.13/22.17 | REDUCE: (1), (30) imply: % 151.13/22.17 | (33) ~ (all_6_2 = e0) % 151.13/22.17 | % 151.13/22.17 | SIMP: (33) implies: % 151.13/22.17 | (34) ~ (all_6_2 = e0) % 151.13/22.17 | % 151.13/22.17 | REDUCE: (15), (31) imply: % 151.13/22.17 | (35) op(e1, e1) = all_4_1 % 151.13/22.17 | % 151.13/22.17 | REF_CLOSE: (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13), (14), % 151.13/22.17 | (18), (19), (20), (22), (23), (24), (25), (27), (28), (32), (34), % 151.13/22.17 | (35) are inconsistent by sub-proof #218. % 151.13/22.17 | % 151.13/22.17 End of proof % 151.13/22.17 % 151.13/22.17 Sub-proof #194 shows that the following formulas are inconsistent: % 151.13/22.17 ---------------------------------------------------------------- % 151.13/22.17 (1) all_56_11 = all_8_2 % 151.13/22.17 (2) op(e0, all_52_13) = all_56_14 % 151.13/22.17 (3) ~ (all_56_11 = e1) | all_56_13 = e2 % 151.13/22.17 (4) ~ (all_52_11 = all_6_2) % 151.13/22.17 (5) all_56_25 = all_52_3 % 151.13/22.17 (6) ~ (all_52_7 = all_52_11) % 151.13/22.17 (7) all_58_6 = all_52_2 % 151.13/22.17 (8) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0 % 151.13/22.17 (9) ~ (all_52_3 = all_8_0) % 151.13/22.17 (10) all_54_10 = all_6_2 % 151.13/22.17 (11) ~ (all_6_1 = e2) % 151.13/22.17 (12) all_12_2 = all_4_2 % 151.13/22.17 (13) ~ (all_52_13 = all_8_2) % 151.13/22.17 (14) ~ (all_56_21 = e2) | all_56_19 = e1 % 151.13/22.17 (15) all_54_0 = all_10_2 % 151.13/22.17 (16) ~ (all_52_14 = all_4_2) % 151.13/22.17 (17) ~ (all_8_0 = e1) % 151.13/22.17 (18) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0 % 151.13/22.17 (19) op(e0, e0) = all_4_2 % 151.13/22.17 (20) ~ (all_52_13 = all_8_0) % 151.13/22.17 (21) all_54_5 = all_8_2 % 151.13/22.17 (22) ~ (all_6_1 = e3) % 151.13/22.17 (23) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 151.13/22.17 (24) ~ (all_6_0 = e2) % 151.13/22.17 (25) all_54_15 = all_4_2 % 151.13/22.17 (26) all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1 % 151.13/22.17 (27) ~ (all_8_0 = all_8_2) % 151.13/22.17 (28) all_56_21 = all_6_2 % 151.13/22.17 (29) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 151.13/22.17 (30) ~ (all_52_7 = all_8_2) % 151.13/22.17 (31) all_56_1 = all_10_2 % 151.13/22.17 (32) all_56_27 = all_52_7 % 151.13/22.17 (33) all_58_5 = all_52_9 % 151.13/22.17 (34) all_56_17 = all_52_2 % 151.13/22.17 (35) all_58_9 = all_52_12 % 151.13/22.17 (36) op(e0, all_52_12) = all_56_6 % 151.13/22.17 (37) op(e1, e0) = all_52_14 % 151.13/22.17 (38) ~ (all_56_1 = e1) | all_56_5 = e3 % 151.13/22.17 (39) all_54_14 = all_52_11 % 151.13/22.17 (40) op(e2, all_8_2) = all_56_10 % 151.13/22.17 (41) op(e3, e3) = all_10_2 % 151.13/22.17 (42) ~ (all_56_21 = e3) | all_56_17 = e1 % 151.13/22.17 (43) ~ (e1 = e0) % 151.13/22.17 (44) all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1 % 151.13/22.17 (45) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 151.13/22.17 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 151.13/22.17 (46) ~ (all_10_2 = all_8_0) % 151.13/22.17 (47) ~ (all_52_3 = all_10_2) % 151.13/22.17 (48) ~ (all_56_11 = e3) | all_56_9 = e2 % 151.13/22.17 (49) op(e0, all_4_1) = e2 % 151.13/22.17 (50) all_56_13 = all_52_9 % 151.13/22.17 (51) op(e0, e1) = all_52_11 % 151.13/22.17 (52) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0 % 151.13/22.17 (53) ~ (all_4_2 = e1) % 151.13/22.17 (54) ~ (all_12_1 = e1) | ~ (all_12_2 = e3) % 151.13/22.17 (55) all_56_5 = all_52_8 % 151.13/22.17 (56) op(e1, all_6_1) = all_6_0 % 151.13/22.17 (57) all_56_9 = all_8_0 % 151.13/22.17 (58) op(all_4_2, all_4_2) = all_4_1 % 151.13/22.17 (59) all_58_3 = all_8_2 % 151.13/22.17 (60) ~ (all_52_11 = all_4_2) % 151.13/22.17 (61) all_56_31 = all_4_2 % 151.13/22.17 (62) all_58_11 = all_52_14 % 151.13/22.17 (63) ~ (all_52_2 = all_52_14) % 151.13/22.17 (64) ~ (all_52_9 = all_52_11) % 151.13/22.17 (65) op(all_6_2, all_6_2) = all_6_1 % 151.13/22.17 (66) all_56_1 = e3 | all_56_11 = e2 | all_56_21 = e1 | all_56_31 = e0 % 151.13/22.17 (67) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0 % 151.13/22.17 (68) ~ (all_52_8 = all_52_11) % 151.13/22.17 (69) op(all_8_2, all_8_2) = e3 % 151.13/22.17 (70) all_56_23 = all_52_14 % 151.13/22.17 (71) ~ (all_52_6 = all_8_2) % 151.13/22.17 (72) all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1 % 151.13/22.17 (73) op(e0, e3) = all_52_3 % 151.13/22.17 (74) all_58_15 = all_4_2 % 151.13/22.17 (75) ~ (all_52_9 = all_6_2) % 151.13/22.17 (76) all_58_10 = all_52_13 % 151.13/22.17 (77) all_12_1 = all_4_1 % 151.13/22.17 (78) all_58_2 = all_8_0 % 151.13/22.17 (79) ~ (all_56_11 = e0) | all_56_15 = e2 % 151.13/22.17 (80) all_58_0 = all_10_2 % 151.13/22.17 (81) all_54_4 = all_8_0 % 151.13/22.17 (82) ~ (all_56_31 = e2) | all_56_27 = e0 % 151.13/22.17 (83) op(e2, e2) = all_8_2 % 151.13/22.17 (84) ~ (all_52_2 = all_6_2) % 151.13/22.17 (85) ~ (all_56_21 = e0) | all_56_23 = e1 % 151.13/22.17 (86) op(e0, all_4_2) = all_56_30 % 151.13/22.17 (87) ~ (all_52_6 = all_6_2) % 151.13/22.17 (88) ~ (all_52_14 = all_6_2) % 151.13/22.17 (89) ~ (all_52_2 = all_10_2) % 151.13/22.17 (90) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 151.13/22.17 (91) all_56_19 = all_52_6 % 151.13/22.17 (92) all_56_15 = all_52_13 % 151.13/22.17 (93) all_58_12 = all_52_3 % 151.13/22.17 (94) all_54_11 = all_52_14 % 151.13/22.17 (95) ~ (all_56_31 = e3) | all_56_25 = e0 % 151.13/22.17 % 151.13/22.17 Begin of proof % 151.13/22.17 | % 151.13/22.17 | BETA: splitting (14) gives: % 151.13/22.17 | % 151.13/22.17 | Case 1: % 151.13/22.17 | | % 151.13/22.17 | | (96) ~ (all_56_21 = e2) % 151.13/22.17 | | % 151.13/22.17 | | REDUCE: (28), (96) imply: % 151.13/22.17 | | (97) ~ (all_6_2 = e2) % 151.13/22.17 | | % 151.13/22.17 | | BETA: splitting (95) gives: % 151.13/22.17 | | % 151.13/22.17 | | Case 1: % 151.13/22.17 | | | % 151.13/22.17 | | | (98) ~ (all_56_31 = e3) % 151.13/22.17 | | | % 151.13/22.17 | | | REDUCE: (61), (98) imply: % 151.13/22.17 | | | (99) ~ (all_4_2 = e3) % 151.13/22.17 | | | % 151.13/22.17 | | | BETA: splitting (85) gives: % 151.13/22.17 | | | % 151.13/22.17 | | | Case 1: % 151.13/22.17 | | | | % 151.13/22.17 | | | | (100) ~ (all_56_21 = e0) % 151.13/22.17 | | | | % 151.13/22.17 | | | | REDUCE: (28), (100) imply: % 151.13/22.17 | | | | (101) ~ (all_6_2 = e0) % 151.13/22.17 | | | | % 151.13/22.17 | | | | BETA: splitting (82) gives: % 151.13/22.17 | | | | % 151.13/22.17 | | | | Case 1: % 151.13/22.17 | | | | | % 151.13/22.17 | | | | | (102) ~ (all_56_31 = e2) % 151.13/22.17 | | | | | % 151.13/22.17 | | | | | REDUCE: (61), (102) imply: % 151.13/22.17 | | | | | (103) ~ (all_4_2 = e2) % 151.13/22.17 | | | | | % 151.13/22.17 | | | | | REF_CLOSE: (19), (25), (45), (49), (53), (58), (67), (86), (99), (103) % 151.13/22.17 | | | | | are inconsistent by sub-proof #229. % 151.13/22.17 | | | | | % 151.13/22.17 | | | | Case 2: % 151.13/22.17 | | | | | % 151.13/22.17 | | | | | (104) all_56_31 = e2 % 151.13/22.17 | | | | | (105) all_56_27 = e0 % 151.13/22.17 | | | | | % 151.13/22.17 | | | | | COMBINE_EQS: (32), (105) imply: % 151.13/22.17 | | | | | (106) all_52_7 = e0 % 151.13/22.17 | | | | | % 151.13/22.17 | | | | | SIMP: (106) implies: % 151.13/22.17 | | | | | (107) all_52_7 = e0 % 151.13/22.17 | | | | | % 151.13/22.17 | | | | | COMBINE_EQS: (61), (104) imply: % 151.13/22.17 | | | | | (108) all_4_2 = e2 % 151.13/22.17 | | | | | % 151.13/22.17 | | | | | REDUCE: (6), (107) imply: % 151.13/22.17 | | | | | (109) ~ (all_52_11 = e0) % 151.13/22.17 | | | | | % 151.13/22.17 | | | | | SIMP: (109) implies: % 151.13/22.17 | | | | | (110) ~ (all_52_11 = e0) % 151.13/22.17 | | | | | % 151.13/22.17 | | | | | REDUCE: (30), (107) imply: % 151.13/22.17 | | | | | (111) ~ (all_8_2 = e0) % 151.13/22.17 | | | | | % 151.13/22.17 | | | | | SIMP: (111) implies: % 151.13/22.17 | | | | | (112) ~ (all_8_2 = e0) % 151.13/22.17 | | | | | % 151.13/22.17 | | | | | REDUCE: (60), (108) imply: % 151.13/22.17 | | | | | (113) ~ (all_52_11 = e2) % 151.13/22.17 | | | | | % 151.13/22.17 | | | | | REDUCE: (58), (108) imply: % 151.13/22.17 | | | | | (114) op(e2, e2) = all_4_1 % 151.13/22.17 | | | | | % 151.13/22.17 | | | | | GROUND_INST: instantiating (45) with all_8_2, all_4_1, e2, e2, % 151.13/22.17 | | | | | simplifying with (83), (114) gives: % 151.13/22.17 | | | | | (115) all_8_2 = all_4_1 % 151.13/22.17 | | | | | % 151.13/22.17 | | | | | COMBINE_EQS: (21), (115) imply: % 151.13/22.17 | | | | | (116) all_54_5 = all_4_1 % 151.13/22.17 | | | | | % 151.13/22.17 | | | | | COMBINE_EQS: (1), (115) imply: % 151.13/22.17 | | | | | (117) all_56_11 = all_4_1 % 151.13/22.17 | | | | | % 151.13/22.17 | | | | | REDUCE: (112), (115) imply: % 151.13/22.17 | | | | | (118) ~ (all_4_1 = e0) % 151.13/22.17 | | | | | % 151.13/22.17 | | | | | BETA: splitting (42) gives: % 151.13/22.17 | | | | | % 151.13/22.17 | | | | | Case 1: % 151.13/22.17 | | | | | | % 151.13/22.17 | | | | | | (119) ~ (all_56_21 = e3) % 151.13/22.17 | | | | | | % 151.13/22.17 | | | | | | REDUCE: (28), (119) imply: % 151.13/22.17 | | | | | | (120) ~ (all_6_2 = e3) % 151.13/22.17 | | | | | | % 151.13/22.17 | | | | | | BETA: splitting (29) gives: % 151.13/22.17 | | | | | | % 151.13/22.17 | | | | | | Case 1: % 151.13/22.17 | | | | | | | % 151.13/22.17 | | | | | | | (121) all_54_10 = e3 % 151.13/22.17 | | | | | | | % 151.13/22.17 | | | | | | | COMBINE_EQS: (10), (121) imply: % 151.13/22.17 | | | | | | | (122) all_6_2 = e3 % 151.13/22.17 | | | | | | | % 151.13/22.17 | | | | | | | REDUCE: (120), (122) imply: % 151.13/22.17 | | | | | | | (123) $false % 151.13/22.17 | | | | | | | % 151.13/22.17 | | | | | | | CLOSE: (123) is inconsistent. % 151.13/22.17 | | | | | | | % 151.13/22.17 | | | | | | Case 2: % 151.13/22.17 | | | | | | | % 151.13/22.17 | | | | | | | (124) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 151.13/22.17 | | | | | | | % 151.13/22.17 | | | | | | | BETA: splitting (124) gives: % 151.13/22.17 | | | | | | | % 151.13/22.17 | | | | | | | Case 1: % 151.13/22.17 | | | | | | | | % 151.13/22.17 | | | | | | | | (125) all_54_10 = e2 % 151.13/22.17 | | | | | | | | % 151.13/22.17 | | | | | | | | COMBINE_EQS: (10), (125) imply: % 151.13/22.17 | | | | | | | | (126) all_6_2 = e2 % 151.13/22.17 | | | | | | | | % 151.13/22.17 | | | | | | | | REDUCE: (97), (126) imply: % 151.13/22.17 | | | | | | | | (127) $false % 151.13/22.17 | | | | | | | | % 151.13/22.17 | | | | | | | | CLOSE: (127) is inconsistent. % 151.13/22.17 | | | | | | | | % 151.13/22.17 | | | | | | | Case 2: % 151.13/22.17 | | | | | | | | % 151.13/22.17 | | | | | | | | (128) all_54_10 = e1 | all_54_10 = e0 % 151.13/22.17 | | | | | | | | % 151.13/22.17 | | | | | | | | BETA: splitting (128) gives: % 151.13/22.17 | | | | | | | | % 151.13/22.17 | | | | | | | | Case 1: % 151.13/22.17 | | | | | | | | | % 151.13/22.17 | | | | | | | | | (129) all_54_10 = e1 % 151.13/22.17 | | | | | | | | | % 151.13/22.17 | | | | | | | | | COMBINE_EQS: (10), (129) imply: % 151.13/22.17 | | | | | | | | | (130) all_6_2 = e1 % 151.13/22.17 | | | | | | | | | % 151.13/22.17 | | | | | | | | | REDUCE: (84), (130) imply: % 151.13/22.17 | | | | | | | | | (131) ~ (all_52_2 = e1) % 151.13/22.17 | | | | | | | | | % 151.13/22.17 | | | | | | | | | REDUCE: (4), (130) imply: % 151.13/22.17 | | | | | | | | | (132) ~ (all_52_11 = e1) % 151.13/22.17 | | | | | | | | | % 151.13/22.17 | | | | | | | | | REDUCE: (88), (130) imply: % 151.13/22.17 | | | | | | | | | (133) ~ (all_52_14 = e1) % 151.13/22.17 | | | | | | | | | % 151.13/22.17 | | | | | | | | | BETA: splitting (8) gives: % 151.13/22.17 | | | | | | | | | % 151.13/22.17 | | | | | | | | | Case 1: % 151.13/22.17 | | | | | | | | | | % 151.13/22.17 | | | | | | | | | | (134) all_54_14 = e3 % 151.13/22.17 | | | | | | | | | | % 151.13/22.17 | | | | | | | | | | COMBINE_EQS: (39), (134) imply: % 151.13/22.17 | | | | | | | | | | (135) all_52_11 = e3 % 151.13/22.17 | | | | | | | | | | % 151.13/22.17 | | | | | | | | | | SIMP: (135) implies: % 151.13/22.17 | | | | | | | | | | (136) all_52_11 = e3 % 151.13/22.17 | | | | | | | | | | % 151.13/22.17 | | | | | | | | | | REDUCE: (68), (136) imply: % 151.13/22.17 | | | | | | | | | | (137) ~ (all_52_8 = e3) % 151.13/22.17 | | | | | | | | | | % 151.13/22.17 | | | | | | | | | | REDUCE: (64), (136) imply: % 151.13/22.17 | | | | | | | | | | (138) ~ (all_52_9 = e3) % 151.13/22.17 | | | | | | | | | | % 151.13/22.17 | | | | | | | | | | REDUCE: (51), (136) imply: % 151.13/22.17 | | | | | | | | | | (139) op(e0, e1) = e3 % 151.13/22.17 | | | | | | | | | | % 151.13/22.17 | | | | | | | | | | BETA: splitting (38) gives: % 151.13/22.17 | | | | | | | | | | % 151.13/22.17 | | | | | | | | | | Case 1: % 151.13/22.17 | | | | | | | | | | | % 151.13/22.17 | | | | | | | | | | | (140) ~ (all_56_1 = e1) % 151.13/22.17 | | | | | | | | | | | % 151.13/22.17 | | | | | | | | | | | REDUCE: (31), (140) imply: % 151.13/22.17 | | | | | | | | | | | (141) ~ (all_10_2 = e1) % 151.13/22.17 | | | | | | | | | | | % 151.13/22.17 | | | | | | | | | | | BETA: splitting (72) gives: % 151.13/22.17 | | | | | | | | | | | % 151.13/22.17 | | | | | | | | | | | Case 1: % 151.13/22.17 | | | | | | | | | | | | % 151.13/22.17 | | | | | | | | | | | | (142) all_58_0 = e1 % 151.13/22.17 | | | | | | | | | | | | % 151.13/22.17 | | | | | | | | | | | | COMBINE_EQS: (80), (142) imply: % 151.13/22.17 | | | | | | | | | | | | (143) all_10_2 = e1 % 151.13/22.17 | | | | | | | | | | | | % 151.13/22.17 | | | | | | | | | | | | REDUCE: (141), (143) imply: % 151.13/22.17 | | | | | | | | | | | | (144) $false % 151.13/22.17 | | | | | | | | | | | | % 151.13/22.17 | | | | | | | | | | | | CLOSE: (144) is inconsistent. % 151.13/22.17 | | | | | | | | | | | | % 151.13/22.17 | | | | | | | | | | | Case 2: % 151.13/22.17 | | | | | | | | | | | | % 151.13/22.17 | | | | | | | | | | | | (145) all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1 % 151.13/22.17 | | | | | | | | | | | | % 151.13/22.17 | | | | | | | | | | | | BETA: splitting (145) gives: % 151.13/22.17 | | | | | | | | | | | | % 151.13/22.17 | | | | | | | | | | | | Case 1: % 151.13/22.17 | | | | | | | | | | | | | % 151.13/22.17 | | | | | | | | | | | | | (146) all_58_2 = e1 % 151.13/22.17 | | | | | | | | | | | | | % 151.13/22.17 | | | | | | | | | | | | | COMBINE_EQS: (78), (146) imply: % 151.13/22.17 | | | | | | | | | | | | | (147) all_8_0 = e1 % 151.13/22.17 | | | | | | | | | | | | | % 151.13/22.17 | | | | | | | | | | | | | REDUCE: (17), (147) imply: % 151.13/22.17 | | | | | | | | | | | | | (148) $false % 151.13/22.17 | | | | | | | | | | | | | % 151.13/22.17 | | | | | | | | | | | | | CLOSE: (148) is inconsistent. % 151.13/22.17 | | | | | | | | | | | | | % 151.13/22.17 | | | | | | | | | | | | Case 2: % 151.13/22.17 | | | | | | | | | | | | | % 151.13/22.17 | | | | | | | | | | | | | (149) all_58_6 = e1 | all_58_12 = e1 % 151.13/22.17 | | | | | | | | | | | | | % 151.13/22.17 | | | | | | | | | | | | | BETA: splitting (149) gives: % 151.13/22.17 | | | | | | | | | | | | | % 151.13/22.17 | | | | | | | | | | | | | Case 1: % 151.13/22.17 | | | | | | | | | | | | | | % 151.13/22.17 | | | | | | | | | | | | | | (150) all_58_6 = e1 % 151.13/22.17 | | | | | | | | | | | | | | % 151.13/22.17 | | | | | | | | | | | | | | REF_CLOSE: (7), (131), (150) are inconsistent by sub-proof % 151.13/22.17 | | | | | | | | | | | | | | #472. % 151.13/22.17 | | | | | | | | | | | | | | % 151.13/22.17 | | | | | | | | | | | | | Case 2: % 151.13/22.17 | | | | | | | | | | | | | | % 151.13/22.17 | | | | | | | | | | | | | | (151) all_58_12 = e1 % 151.13/22.17 | | | | | | | | | | | | | | % 151.13/22.17 | | | | | | | | | | | | | | COMBINE_EQS: (93), (151) imply: % 151.13/22.17 | | | | | | | | | | | | | | (152) all_52_3 = e1 % 151.13/22.17 | | | | | | | | | | | | | | % 151.13/22.17 | | | | | | | | | | | | | | REDUCE: (9), (152) imply: % 151.13/22.17 | | | | | | | | | | | | | | (153) ~ (all_8_0 = e1) % 151.13/22.17 | | | | | | | | | | | | | | % 151.13/22.17 | | | | | | | | | | | | | | REDUCE: (73), (152) imply: % 151.13/22.17 | | | | | | | | | | | | | | (154) op(e0, e3) = e1 % 151.13/22.17 | | | | | | | | | | | | | | % 151.13/22.17 | | | | | | | | | | | | | | BETA: splitting (48) gives: % 151.13/22.17 | | | | | | | | | | | | | | % 151.13/22.17 | | | | | | | | | | | | | | Case 1: % 151.13/22.17 | | | | | | | | | | | | | | | % 151.13/22.17 | | | | | | | | | | | | | | | (155) ~ (all_56_11 = e3) % 151.13/22.17 | | | | | | | | | | | | | | | % 151.13/22.17 | | | | | | | | | | | | | | | REDUCE: (117), (155) imply: % 151.13/22.17 | | | | | | | | | | | | | | | (156) ~ (all_4_1 = e3) % 151.13/22.17 | | | | | | | | | | | | | | | % 151.13/22.17 | | | | | | | | | | | | | | | BETA: splitting (3) gives: % 151.13/22.17 | | | | | | | | | | | | | | | % 151.13/22.17 | | | | | | | | | | | | | | | Case 1: % 151.13/22.17 | | | | | | | | | | | | | | | | % 151.13/22.17 | | | | | | | | | | | | | | | | (157) ~ (all_56_11 = e1) % 151.13/22.17 | | | | | | | | | | | | | | | | % 151.13/22.17 | | | | | | | | | | | | | | | | REDUCE: (117), (157) imply: % 151.13/22.17 | | | | | | | | | | | | | | | | (158) ~ (all_4_1 = e1) % 151.13/22.17 | | | | | | | | | | | | | | | | % 151.13/22.17 | | | | | | | | | | | | | | | | BETA: splitting (90) gives: % 151.13/22.17 | | | | | | | | | | | | | | | | % 151.13/22.17 | | | | | | | | | | | | | | | | Case 1: % 151.13/22.17 | | | | | | | | | | | | | | | | | % 151.13/22.17 | | | | | | | | | | | | | | | | | (159) all_54_5 = e3 % 151.13/22.17 | | | | | | | | | | | | | | | | | % 151.13/22.17 | | | | | | | | | | | | | | | | | REF_CLOSE: (116), (156), (159) are inconsistent by sub-proof % 151.13/22.17 | | | | | | | | | | | | | | | | | #199. % 151.13/22.17 | | | | | | | | | | | | | | | | | % 151.13/22.17 | | | | | | | | | | | | | | | | Case 2: % 151.13/22.17 | | | | | | | | | | | | | | | | | % 151.13/22.17 | | | | | | | | | | | | | | | | | (160) ~ (all_54_5 = e3) % 151.13/22.17 | | | | | | | | | | | | | | | | | (161) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 151.13/22.17 | | | | | | | | | | | | | | | | | % 151.13/22.17 | | | | | | | | | | | | | | | | | BETA: splitting (161) gives: % 151.13/22.17 | | | | | | | | | | | | | | | | | % 151.13/22.17 | | | | | | | | | | | | | | | | | Case 1: % 151.13/22.17 | | | | | | | | | | | | | | | | | | % 151.13/22.17 | | | | | | | | | | | | | | | | | | (162) all_54_5 = e2 % 151.13/22.17 | | | | | | | | | | | | | | | | | | % 151.13/22.17 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (116), (162) imply: % 151.13/22.17 | | | | | | | | | | | | | | | | | | (163) all_4_1 = e2 % 151.13/22.17 | | | | | | | | | | | | | | | | | | % 151.13/22.17 | | | | | | | | | | | | | | | | | | SIMP: (163) implies: % 151.13/22.17 | | | | | | | | | | | | | | | | | | (164) all_4_1 = e2 % 151.13/22.17 | | | | | | | | | | | | | | | | | | % 151.13/22.17 | | | | | | | | | | | | | | | | | | REDUCE: (156), (164) imply: % 151.13/22.17 | | | | | | | | | | | | | | | | | | (165) ~ (e3 = e2) % 151.13/22.17 | | | | | | | | | | | | | | | | | | % 151.13/22.17 | | | | | | | | | | | | | | | | | | SIMP: (165) implies: % 151.13/22.17 | | | | | | | | | | | | | | | | | | (166) ~ (e3 = e2) % 151.13/22.17 | | | | | | | | | | | | | | | | | | % 151.13/22.17 | | | | | | | | | | | | | | | | | | REDUCE: (114), (164) imply: % 151.13/22.17 | | | | | | | | | | | | | | | | | | (167) op(e2, e2) = e2 % 151.13/22.17 | | | | | | | | | | | | | | | | | | % 151.13/22.17 | | | | | | | | | | | | | | | | | | REF_CLOSE: (40), (45), (69), (83), (166), (167) are % 151.13/22.17 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #349. % 151.13/22.17 | | | | | | | | | | | | | | | | | | % 151.13/22.17 | | | | | | | | | | | | | | | | | Case 2: % 151.13/22.17 | | | | | | | | | | | | | | | | | | % 151.13/22.17 | | | | | | | | | | | | | | | | | | (168) all_54_5 = e1 | all_54_5 = e0 % 151.13/22.17 | | | | | | | | | | | | | | | | | | % 151.13/22.17 | | | | | | | | | | | | | | | | | | REF_CLOSE: (116), (118), (158), (168) are inconsistent by % 151.13/22.17 | | | | | | | | | | | | | | | | | | sub-proof #569. % 151.13/22.17 | | | | | | | | | | | | | | | | | | % 151.13/22.17 | | | | | | | | | | | | | | | | | End of split % 151.13/22.17 | | | | | | | | | | | | | | | | | % 151.13/22.17 | | | | | | | | | | | | | | | | End of split % 151.13/22.17 | | | | | | | | | | | | | | | | % 151.13/22.17 | | | | | | | | | | | | | | | Case 2: % 151.13/22.17 | | | | | | | | | | | | | | | | % 151.13/22.17 | | | | | | | | | | | | | | | | (169) all_56_13 = e2 % 151.13/22.17 | | | | | | | | | | | | | | | | (170) all_56_11 = e1 % 151.13/22.17 | | | | | | | | | | | | | | | | % 151.13/22.17 | | | | | | | | | | | | | | | | COMBINE_EQS: (117), (170) imply: % 151.13/22.17 | | | | | | | | | | | | | | | | (171) all_4_1 = e1 % 151.13/22.17 | | | | | | | | | | | | | | | | % 151.13/22.17 | | | | | | | | | | | | | | | | COMBINE_EQS: (50), (169) imply: % 151.13/22.17 | | | | | | | | | | | | | | | | (172) all_52_9 = e2 % 151.13/22.17 | | | | | | | | | | | | | | | | % 151.13/22.17 | | | | | | | | | | | | | | | | REDUCE: (138), (172) imply: % 151.13/22.17 | | | | | | | | | | | | | | | | (173) ~ (e3 = e2) % 151.13/22.17 | | | | | | | | | | | | | | | | % 151.13/22.17 | | | | | | | | | | | | | | | | REF_CLOSE: (2), (26), (35), (36), (45), (49), (53), (62), % 151.13/22.17 | | | | | | | | | | | | | | | | (74), (76), (133), (139), (171), (173) are % 151.13/22.17 | | | | | | | | | | | | | | | | inconsistent by sub-proof #195. % 151.13/22.17 | | | | | | | | | | | | | | | | % 151.13/22.17 | | | | | | | | | | | | | | | End of split % 151.13/22.17 | | | | | | | | | | | | | | | % 151.13/22.17 | | | | | | | | | | | | | | Case 2: % 151.13/22.17 | | | | | | | | | | | | | | | % 151.13/22.17 | | | | | | | | | | | | | | | (174) all_56_11 = e3 % 151.13/22.17 | | | | | | | | | | | | | | | (175) all_56_9 = e2 % 151.13/22.17 | | | | | | | | | | | | | | | % 151.13/22.17 | | | | | | | | | | | | | | | COMBINE_EQS: (57), (175) imply: % 151.13/22.17 | | | | | | | | | | | | | | | (176) all_8_0 = e2 % 151.13/22.17 | | | | | | | | | | | | | | | % 151.13/22.17 | | | | | | | | | | | | | | | COMBINE_EQS: (117), (174) imply: % 151.13/22.17 | | | | | | | | | | | | | | | (177) all_4_1 = e3 % 151.13/22.17 | | | | | | | | | | | | | | | % 151.13/22.17 | | | | | | | | | | | | | | | REDUCE: (17), (176) imply: % 151.13/22.17 | | | | | | | | | | | | | | | (178) ~ (e2 = e1) % 151.13/22.17 | | | | | | | | | | | | | | | % 151.13/22.17 | | | | | | | | | | | | | | | REDUCE: (49), (177) imply: % 151.13/22.17 | | | | | | | | | | | | | | | (179) op(e0, e3) = e2 % 151.13/22.17 | | | | | | | | | | | | | | | % 151.13/22.17 | | | | | | | | | | | | | | | GROUND_INST: instantiating (45) with e1, e2, e3, e0, % 151.13/22.17 | | | | | | | | | | | | | | | simplifying with (154), (179) gives: % 151.13/22.17 | | | | | | | | | | | | | | | (180) e2 = e1 % 151.13/22.17 | | | | | | | | | | | | | | | % 151.13/22.17 | | | | | | | | | | | | | | | REDUCE: (178), (180) imply: % 151.13/22.17 | | | | | | | | | | | | | | | (181) $false % 151.13/22.17 | | | | | | | | | | | | | | | % 151.13/22.17 | | | | | | | | | | | | | | | CLOSE: (181) is inconsistent. % 151.13/22.17 | | | | | | | | | | | | | | | % 151.13/22.17 | | | | | | | | | | | | | | End of split % 151.13/22.17 | | | | | | | | | | | | | | % 151.13/22.17 | | | | | | | | | | | | | End of split % 151.13/22.17 | | | | | | | | | | | | | % 151.13/22.17 | | | | | | | | | | | | End of split % 151.13/22.17 | | | | | | | | | | | | % 151.13/22.17 | | | | | | | | | | | End of split % 151.13/22.17 | | | | | | | | | | | % 151.13/22.17 | | | | | | | | | | Case 2: % 151.13/22.17 | | | | | | | | | | | % 151.13/22.17 | | | | | | | | | | | (182) all_56_5 = e3 % 151.13/22.17 | | | | | | | | | | | % 151.13/22.17 | | | | | | | | | | | COMBINE_EQS: (55), (182) imply: % 151.13/22.17 | | | | | | | | | | | (183) all_52_8 = e3 % 151.13/22.17 | | | | | | | | | | | % 151.13/22.17 | | | | | | | | | | | REDUCE: (137), (183) imply: % 151.13/22.17 | | | | | | | | | | | (184) $false % 151.13/22.17 | | | | | | | | | | | % 151.13/22.17 | | | | | | | | | | | CLOSE: (184) is inconsistent. % 151.13/22.17 | | | | | | | | | | | % 151.13/22.17 | | | | | | | | | | End of split % 151.13/22.17 | | | | | | | | | | % 151.13/22.17 | | | | | | | | | Case 2: % 151.13/22.17 | | | | | | | | | | % 151.13/22.17 | | | | | | | | | | (185) all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0 % 151.13/22.17 | | | | | | | | | | % 151.13/22.17 | | | | | | | | | | REF_CLOSE: (39), (110), (113), (132), (185) are inconsistent % 151.13/22.17 | | | | | | | | | | by sub-proof #580. % 151.13/22.17 | | | | | | | | | | % 151.13/22.17 | | | | | | | | | End of split % 151.13/22.17 | | | | | | | | | % 151.13/22.17 | | | | | | | | Case 2: % 151.13/22.17 | | | | | | | | | % 151.13/22.17 | | | | | | | | | (186) all_54_10 = e0 % 151.13/22.17 | | | | | | | | | % 151.13/22.17 | | | | | | | | | COMBINE_EQS: (10), (186) imply: % 151.13/22.17 | | | | | | | | | (187) all_6_2 = e0 % 151.13/22.17 | | | | | | | | | % 151.13/22.17 | | | | | | | | | REDUCE: (101), (187) imply: % 151.13/22.17 | | | | | | | | | (188) $false % 151.13/22.17 | | | | | | | | | % 151.13/22.17 | | | | | | | | | CLOSE: (188) is inconsistent. % 151.13/22.17 | | | | | | | | | % 151.13/22.17 | | | | | | | | End of split % 151.13/22.17 | | | | | | | | % 151.13/22.17 | | | | | | | End of split % 151.13/22.17 | | | | | | | % 151.13/22.17 | | | | | | End of split % 151.13/22.17 | | | | | | % 151.13/22.17 | | | | | Case 2: % 151.13/22.17 | | | | | | % 151.13/22.17 | | | | | | (189) all_56_21 = e3 % 151.13/22.17 | | | | | | (190) all_56_17 = e1 % 151.13/22.17 | | | | | | % 151.13/22.17 | | | | | | REF_CLOSE: (1), (11), (15), (16), (18), (22), (23), (24), (28), % 151.13/22.17 | | | | | | (31), (34), (37), (40), (41), (45), (56), (61), (63), % 151.13/22.17 | | | | | | (65), (66), (69), (83), (84), (88), (89), (94), (97), % 151.13/22.17 | | | | | | (189), (190) are inconsistent by sub-proof #339. % 151.13/22.17 | | | | | | % 151.13/22.17 | | | | | End of split % 151.13/22.17 | | | | | % 151.13/22.17 | | | | End of split % 151.13/22.17 | | | | % 151.13/22.17 | | | Case 2: % 151.13/22.17 | | | | % 151.13/22.17 | | | | (191) all_56_23 = e1 % 151.13/22.17 | | | | (192) all_56_21 = e0 % 151.13/22.17 | | | | % 151.13/22.17 | | | | REF_CLOSE: (11), (16), (19), (22), (25), (28), (45), (49), (58), (65), % 151.13/22.17 | | | | (67), (70), (86), (191), (192) are inconsistent by sub-proof % 151.13/22.17 | | | | #227. % 151.13/22.17 | | | | % 151.13/22.17 | | | End of split % 151.13/22.17 | | | % 151.13/22.17 | | Case 2: % 151.13/22.17 | | | % 151.13/22.17 | | | (193) all_56_31 = e3 % 151.13/22.17 | | | (194) all_56_25 = e0 % 151.13/22.17 | | | % 151.13/22.17 | | | COMBINE_EQS: (5), (194) imply: % 151.13/22.17 | | | (195) all_52_3 = e0 % 151.13/22.17 | | | % 151.13/22.17 | | | SIMP: (195) implies: % 151.13/22.17 | | | (196) all_52_3 = e0 % 151.13/22.17 | | | % 151.13/22.17 | | | COMBINE_EQS: (61), (193) imply: % 151.13/22.17 | | | (197) all_4_2 = e3 % 151.13/22.17 | | | % 151.13/22.17 | | | COMBINE_EQS: (12), (197) imply: % 151.13/22.17 | | | (198) all_12_2 = e3 % 151.13/22.17 | | | % 151.13/22.17 | | | COMBINE_EQS: (93), (196) imply: % 151.13/22.17 | | | (199) all_58_12 = e0 % 151.13/22.17 | | | % 151.13/22.17 | | | REDUCE: (47), (196) imply: % 151.13/22.17 | | | (200) ~ (all_10_2 = e0) % 151.13/22.17 | | | % 151.13/22.17 | | | SIMP: (200) implies: % 151.13/22.17 | | | (201) ~ (all_10_2 = e0) % 151.13/22.17 | | | % 151.13/22.17 | | | REDUCE: (58), (197) imply: % 151.13/22.17 | | | (202) op(e3, e3) = all_4_1 % 151.13/22.17 | | | % 151.13/22.17 | | | BETA: splitting (54) gives: % 151.13/22.17 | | | % 151.13/22.17 | | | Case 1: % 151.13/22.17 | | | | % 151.13/22.17 | | | | (203) ~ (all_12_1 = e1) % 151.13/22.17 | | | | % 151.13/22.17 | | | | REDUCE: (77), (203) imply: % 151.13/22.17 | | | | (204) ~ (all_4_1 = e1) % 151.13/22.17 | | | | % 151.13/22.17 | | | | GROUND_INST: instantiating (45) with all_10_2, all_4_1, e3, e3, % 151.13/22.17 | | | | simplifying with (41), (202) gives: % 151.13/22.17 | | | | (205) all_10_2 = all_4_1 % 151.13/22.17 | | | | % 151.13/22.17 | | | | COMBINE_EQS: (15), (205) imply: % 151.13/22.17 | | | | (206) all_54_0 = all_4_1 % 151.13/22.17 | | | | % 151.13/22.17 | | | | COMBINE_EQS: (80), (205) imply: % 151.13/22.17 | | | | (207) all_58_0 = all_4_1 % 151.13/22.17 | | | | % 151.13/22.17 | | | | REDUCE: (89), (205) imply: % 151.13/22.17 | | | | (208) ~ (all_52_2 = all_4_1) % 151.13/22.17 | | | | % 151.13/22.17 | | | | REDUCE: (201), (205) imply: % 151.13/22.17 | | | | (209) ~ (all_4_1 = e0) % 151.13/22.17 | | | | % 151.13/22.17 | | | | BETA: splitting (72) gives: % 151.13/22.17 | | | | % 151.13/22.17 | | | | Case 1: % 151.13/22.17 | | | | | % 151.13/22.17 | | | | | (210) all_58_0 = e1 % 151.13/22.17 | | | | | % 151.13/22.17 | | | | | COMBINE_EQS: (207), (210) imply: % 151.13/22.17 | | | | | (211) all_4_1 = e1 % 151.13/22.17 | | | | | % 151.13/22.17 | | | | | REDUCE: (204), (211) imply: % 151.13/22.17 | | | | | (212) $false % 151.13/22.17 | | | | | % 151.13/22.17 | | | | | CLOSE: (212) is inconsistent. % 151.13/22.17 | | | | | % 151.13/22.17 | | | | Case 2: % 151.13/22.17 | | | | | % 151.13/22.17 | | | | | (213) all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1 % 151.13/22.17 | | | | | % 151.13/22.17 | | | | | BETA: splitting (213) gives: % 151.13/22.17 | | | | | % 151.13/22.17 | | | | | Case 1: % 151.13/22.17 | | | | | | % 151.13/22.17 | | | | | | (214) all_58_2 = e1 % 151.13/22.17 | | | | | | % 151.13/22.17 | | | | | | COMBINE_EQS: (78), (214) imply: % 151.13/22.17 | | | | | | (215) all_8_0 = e1 % 151.13/22.17 | | | | | | % 151.13/22.17 | | | | | | REDUCE: (17), (215) imply: % 151.13/22.17 | | | | | | (216) $false % 151.13/22.17 | | | | | | % 151.13/22.17 | | | | | | CLOSE: (216) is inconsistent. % 151.13/22.17 | | | | | | % 151.13/22.17 | | | | | Case 2: % 151.13/22.17 | | | | | | % 151.13/22.17 | | | | | | (217) all_58_6 = e1 | all_58_12 = e1 % 151.13/22.17 | | | | | | % 151.13/22.17 | | | | | | BETA: splitting (217) gives: % 151.13/22.17 | | | | | | % 151.13/22.17 | | | | | | Case 1: % 151.13/22.17 | | | | | | | % 151.13/22.17 | | | | | | | (218) all_58_6 = e1 % 151.13/22.17 | | | | | | | % 151.13/22.17 | | | | | | | COMBINE_EQS: (7), (218) imply: % 151.13/22.17 | | | | | | | (219) all_52_2 = e1 % 151.13/22.17 | | | | | | | % 151.13/22.17 | | | | | | | REDUCE: (63), (219) imply: % 151.13/22.17 | | | | | | | (220) ~ (all_52_14 = e1) % 151.13/22.17 | | | | | | | % 151.13/22.17 | | | | | | | SIMP: (220) implies: % 151.13/22.17 | | | | | | | (221) ~ (all_52_14 = e1) % 151.13/22.17 | | | | | | | % 151.13/22.17 | | | | | | | REDUCE: (84), (219) imply: % 151.13/22.17 | | | | | | | (222) ~ (all_6_2 = e1) % 151.13/22.17 | | | | | | | % 151.13/22.17 | | | | | | | SIMP: (222) implies: % 151.13/22.17 | | | | | | | (223) ~ (all_6_2 = e1) % 151.13/22.17 | | | | | | | % 151.13/22.17 | | | | | | | REDUCE: (208), (219) imply: % 151.13/22.17 | | | | | | | (224) ~ (all_4_1 = e1) % 151.13/22.17 | | | | | | | % 151.13/22.17 | | | | | | | BETA: splitting (85) gives: % 151.13/22.17 | | | | | | | % 151.13/22.17 | | | | | | | Case 1: % 151.13/22.17 | | | | | | | | % 151.13/22.17 | | | | | | | | (225) ~ (all_56_21 = e0) % 151.13/22.17 | | | | | | | | % 151.13/22.17 | | | | | | | | REDUCE: (28), (225) imply: % 151.13/22.17 | | | | | | | | (226) ~ (all_6_2 = e0) % 151.13/22.17 | | | | | | | | % 151.13/22.17 | | | | | | | | BETA: splitting (29) gives: % 151.13/22.17 | | | | | | | | % 151.13/22.17 | | | | | | | | Case 1: % 151.13/22.17 | | | | | | | | | % 151.13/22.17 | | | | | | | | | (227) all_54_10 = e3 % 151.13/22.17 | | | | | | | | | % 151.13/22.17 | | | | | | | | | COMBINE_EQS: (10), (227) imply: % 151.13/22.17 | | | | | | | | | (228) all_6_2 = e3 % 151.13/22.17 | | | | | | | | | % 151.13/22.17 | | | | | | | | | REF_CLOSE: (4), (8), (11), (22), (23), (39), (45), (65), % 151.13/22.17 | | | | | | | | | (202), (204), (206), (209), (228) are inconsistent % 151.13/22.17 | | | | | | | | | by sub-proof #469. % 151.13/22.17 | | | | | | | | | % 151.13/22.17 | | | | | | | | Case 2: % 151.13/22.17 | | | | | | | | | % 151.13/22.17 | | | | | | | | | (229) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 151.13/22.17 | | | | | | | | | % 151.13/22.17 | | | | | | | | | REF_CLOSE: (10), (97), (223), (226), (229) are inconsistent by % 151.13/22.17 | | | | | | | | | sub-proof #574. % 151.13/22.17 | | | | | | | | | % 151.13/22.17 | | | | | | | | End of split % 151.13/22.17 | | | | | | | | % 151.13/22.17 | | | | | | | Case 2: % 151.13/22.17 | | | | | | | | % 151.13/22.17 | | | | | | | | (230) all_56_23 = e1 % 151.13/22.17 | | | | | | | | % 151.13/22.17 | | | | | | | | COMBINE_EQS: (70), (230) imply: % 151.13/22.17 | | | | | | | | (231) all_52_14 = e1 % 151.13/22.17 | | | | | | | | % 151.13/22.17 | | | | | | | | REDUCE: (221), (231) imply: % 151.13/22.17 | | | | | | | | (232) $false % 151.13/22.17 | | | | | | | | % 151.13/22.17 | | | | | | | | CLOSE: (232) is inconsistent. % 151.13/22.17 | | | | | | | | % 151.13/22.17 | | | | | | | End of split % 151.13/22.17 | | | | | | | % 151.13/22.17 | | | | | | Case 2: % 151.13/22.17 | | | | | | | % 151.13/22.17 | | | | | | | (233) all_58_12 = e1 % 151.13/22.17 | | | | | | | % 151.13/22.17 | | | | | | | REF_CLOSE: (43), (199), (233) are inconsistent by sub-proof #475. % 151.13/22.17 | | | | | | | % 151.13/22.17 | | | | | | End of split % 151.13/22.17 | | | | | | % 151.13/22.17 | | | | | End of split % 151.13/22.17 | | | | | % 151.13/22.17 | | | | End of split % 151.13/22.17 | | | | % 151.13/22.17 | | | Case 2: % 151.13/22.17 | | | | % 151.13/22.17 | | | | (234) ~ (all_12_2 = e3) % 151.13/22.17 | | | | % 151.13/22.17 | | | | REDUCE: (198), (234) imply: % 151.13/22.17 | | | | (235) $false % 151.13/22.17 | | | | % 151.13/22.17 | | | | CLOSE: (235) is inconsistent. % 151.13/22.17 | | | | % 151.13/22.17 | | | End of split % 151.13/22.17 | | | % 151.13/22.17 | | End of split % 151.13/22.17 | | % 151.13/22.17 | Case 2: % 151.13/22.17 | | % 151.13/22.17 | | (236) all_56_21 = e2 % 151.13/22.17 | | (237) all_56_19 = e1 % 151.13/22.17 | | % 151.13/22.17 | | COMBINE_EQS: (91), (237) imply: % 151.13/22.17 | | (238) all_52_6 = e1 % 151.13/22.17 | | % 151.13/22.17 | | COMBINE_EQS: (28), (236) imply: % 151.13/22.17 | | (239) all_6_2 = e2 % 151.13/22.17 | | % 151.13/22.17 | | REF_CLOSE: (1), (11), (13), (17), (19), (20), (21), (22), (27), (28), (31), % 151.13/22.17 | | (33), (44), (45), (46), (52), (58), (59), (61), (65), (66), (69), % 151.13/22.17 | | (71), (75), (76), (78), (79), (81), (83), (86), (87), (90), (92), % 151.13/22.17 | | (238), (239) are inconsistent by sub-proof #334. % 151.13/22.17 | | % 151.13/22.17 | End of split % 151.13/22.17 | % 151.13/22.17 End of proof % 151.13/22.17 % 151.13/22.17 Sub-proof #195 shows that the following formulas are inconsistent: % 151.13/22.17 ---------------------------------------------------------------- % 151.13/22.17 (1) op(e0, all_52_13) = all_56_14 % 151.13/22.18 (2) all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1 % 151.13/22.18 (3) all_58_9 = all_52_12 % 151.13/22.18 (4) op(e0, all_52_12) = all_56_6 % 151.13/22.18 (5) op(e0, e1) = e3 % 151.13/22.18 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 151.13/22.18 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 151.13/22.18 (7) ~ (all_52_14 = e1) % 151.13/22.18 (8) op(e0, all_4_1) = e2 % 151.13/22.18 (9) ~ (all_4_2 = e1) % 151.13/22.18 (10) all_58_11 = all_52_14 % 151.13/22.18 (11) all_4_1 = e1 % 151.13/22.18 (12) all_58_15 = all_4_2 % 151.13/22.18 (13) all_58_10 = all_52_13 % 151.13/22.18 (14) ~ (e3 = e2) % 151.13/22.18 % 151.13/22.18 Begin of proof % 151.13/22.18 | % 151.13/22.18 | SIMP: (14) implies: % 151.13/22.18 | (15) ~ (e3 = e2) % 151.13/22.18 | % 151.13/22.18 | REDUCE: (8), (11) imply: % 151.13/22.18 | (16) op(e0, e1) = e2 % 151.13/22.18 | % 151.13/22.18 | BETA: splitting (2) gives: % 151.13/22.18 | % 151.13/22.18 | Case 1: % 151.13/22.18 | | % 151.13/22.18 | | (17) all_58_9 = e1 % 151.13/22.18 | | % 151.13/22.18 | | COMBINE_EQS: (3), (17) imply: % 151.13/22.18 | | (18) all_52_12 = e1 % 151.13/22.18 | | % 151.13/22.18 | | REDUCE: (4), (18) imply: % 151.13/22.18 | | (19) op(e0, e1) = all_56_6 % 151.13/22.18 | | % 151.13/22.18 | | GROUND_INST: instantiating (6) with e3, all_56_6, e1, e0, simplifying with % 151.13/22.18 | | (5), (19) gives: % 151.13/22.18 | | (20) all_56_6 = e3 % 151.13/22.18 | | % 151.13/22.18 | | GROUND_INST: instantiating (6) with e2, all_56_6, e1, e0, simplifying with % 151.13/22.18 | | (16), (19) gives: % 151.13/22.18 | | (21) all_56_6 = e2 % 151.13/22.18 | | % 151.13/22.18 | | REF_CLOSE: (15), (20), (21) are inconsistent by sub-proof #198. % 151.13/22.18 | | % 151.13/22.18 | Case 2: % 151.13/22.18 | | % 151.13/22.18 | | (22) all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1 % 151.13/22.18 | | % 151.13/22.18 | | REF_CLOSE: (1), (5), (6), (7), (9), (10), (12), (13), (15), (16), (22) are % 151.13/22.18 | | inconsistent by sub-proof #196. % 151.13/22.18 | | % 151.13/22.18 | End of split % 151.13/22.18 | % 151.13/22.18 End of proof % 151.13/22.18 % 151.13/22.18 Sub-proof #196 shows that the following formulas are inconsistent: % 151.13/22.18 ---------------------------------------------------------------- % 151.13/22.18 (1) op(e0, all_52_13) = all_56_14 % 151.13/22.18 (2) ~ (e3 = e2) % 151.13/22.18 (3) op(e0, e1) = e2 % 151.13/22.18 (4) op(e0, e1) = e3 % 151.13/22.18 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 151.13/22.18 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 151.13/22.18 (6) ~ (all_52_14 = e1) % 151.13/22.18 (7) ~ (all_4_2 = e1) % 151.13/22.18 (8) all_58_11 = all_52_14 % 151.13/22.18 (9) all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1 % 151.13/22.18 (10) all_58_15 = all_4_2 % 151.13/22.18 (11) all_58_10 = all_52_13 % 151.13/22.18 % 151.13/22.18 Begin of proof % 151.13/22.18 | % 151.13/22.18 | BETA: splitting (9) gives: % 151.13/22.18 | % 151.13/22.18 | Case 1: % 151.13/22.18 | | % 151.13/22.18 | | (12) all_58_10 = e1 % 151.13/22.18 | | % 151.13/22.18 | | COMBINE_EQS: (11), (12) imply: % 151.13/22.18 | | (13) all_52_13 = e1 % 151.13/22.18 | | % 151.13/22.18 | | REDUCE: (1), (13) imply: % 151.13/22.18 | | (14) op(e0, e1) = all_56_14 % 151.13/22.18 | | % 151.13/22.18 | | REF_CLOSE: (2), (3), (4), (5), (14) are inconsistent by sub-proof #197. % 151.13/22.18 | | % 151.13/22.18 | Case 2: % 151.13/22.18 | | % 151.13/22.18 | | (15) all_58_11 = e1 | all_58_15 = e1 % 151.13/22.18 | | % 151.13/22.18 | | REF_CLOSE: (6), (7), (8), (10), (15) are inconsistent by sub-proof #672. % 151.13/22.18 | | % 151.13/22.18 | End of split % 151.13/22.18 | % 151.13/22.18 End of proof % 151.13/22.18 % 151.13/22.18 Sub-proof #197 shows that the following formulas are inconsistent: % 151.13/22.18 ---------------------------------------------------------------- % 151.13/22.18 (1) ~ (e3 = e2) % 151.13/22.18 (2) op(e0, e1) = e2 % 151.13/22.18 (3) op(e0, e1) = e3 % 151.13/22.18 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 151.13/22.18 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 151.13/22.18 (5) op(e0, e1) = all_56_14 % 151.13/22.18 % 151.13/22.18 Begin of proof % 151.13/22.18 | % 151.13/22.18 | GROUND_INST: instantiating (4) with e2, all_56_14, e1, e0, simplifying with % 151.13/22.18 | (2), (5) gives: % 151.13/22.18 | (6) all_56_14 = e2 % 151.13/22.18 | % 151.13/22.18 | GROUND_INST: instantiating (4) with e3, all_56_14, e1, e0, simplifying with % 151.13/22.18 | (3), (5) gives: % 151.13/22.18 | (7) all_56_14 = e3 % 151.13/22.18 | % 151.13/22.18 | COMBINE_EQS: (6), (7) imply: % 151.13/22.18 | (8) e3 = e2 % 151.13/22.18 | % 151.13/22.18 | REDUCE: (1), (8) imply: % 151.13/22.18 | (9) $false % 151.13/22.18 | % 151.13/22.18 | CLOSE: (9) is inconsistent. % 151.13/22.18 | % 151.13/22.18 End of proof % 151.13/22.18 % 151.13/22.18 Sub-proof #198 shows that the following formulas are inconsistent: % 151.13/22.18 ---------------------------------------------------------------- % 151.13/22.18 (1) all_56_6 = e3 % 151.13/22.18 (2) all_56_6 = e2 % 151.13/22.18 (3) ~ (e3 = e2) % 151.13/22.18 % 151.13/22.18 Begin of proof % 151.13/22.18 | % 151.13/22.18 | COMBINE_EQS: (1), (2) imply: % 151.13/22.18 | (4) e3 = e2 % 151.13/22.18 | % 151.13/22.18 | SIMP: (4) implies: % 151.13/22.18 | (5) e3 = e2 % 151.13/22.18 | % 151.13/22.18 | REDUCE: (3), (5) imply: % 151.13/22.18 | (6) $false % 151.13/22.18 | % 151.13/22.18 | CLOSE: (6) is inconsistent. % 151.13/22.18 | % 151.13/22.18 End of proof % 151.13/22.18 % 151.13/22.18 Sub-proof #199 shows that the following formulas are inconsistent: % 151.13/22.18 ---------------------------------------------------------------- % 151.13/22.18 (1) all_54_5 = all_4_1 % 151.13/22.18 (2) all_54_5 = e3 % 151.13/22.18 (3) ~ (all_4_1 = e3) % 151.13/22.18 % 151.13/22.18 Begin of proof % 151.13/22.18 | % 151.13/22.18 | COMBINE_EQS: (1), (2) imply: % 151.13/22.18 | (4) all_4_1 = e3 % 151.13/22.18 | % 151.13/22.18 | SIMP: (4) implies: % 151.13/22.18 | (5) all_4_1 = e3 % 151.13/22.18 | % 151.13/22.18 | REDUCE: (3), (5) imply: % 151.13/22.18 | (6) $false % 151.13/22.18 | % 151.13/22.18 | CLOSE: (6) is inconsistent. % 151.13/22.18 | % 151.13/22.18 End of proof % 151.13/22.18 % 151.13/22.18 Sub-proof #200 shows that the following formulas are inconsistent: % 151.13/22.18 ---------------------------------------------------------------- % 151.13/22.18 (1) all_56_11 = all_8_2 % 151.13/22.18 (2) ~ (all_52_11 = all_6_2) % 151.13/22.18 (3) ~ (all_52_8 = all_52_9) % 151.13/22.18 (4) ~ (all_8_1 = e1) % 151.13/22.18 (5) ~ (all_56_31 = e1) | all_56_29 = e0 % 151.13/22.18 (6) all_54_10 = all_6_2 % 151.13/22.18 (7) ~ (all_6_1 = e2) % 151.13/22.18 (8) ~ (all_56_21 = e2) | all_56_19 = e1 % 151.13/22.18 (9) all_54_0 = all_10_2 % 151.13/22.18 (10) op(e0, e0) = all_4_2 % 151.13/22.18 (11) all_58_4 = all_52_8 % 151.13/22.18 (12) all_54_5 = all_8_2 % 151.13/22.18 (13) ~ (all_52_6 = all_52_14) % 151.13/22.18 (14) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 151.13/22.18 (15) all_6_0 = e2 % 151.13/22.18 (16) all_54_15 = all_4_2 % 151.13/22.18 (17) all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1 % 151.13/22.18 (18) all_56_21 = all_6_2 % 151.13/22.18 (19) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 151.13/22.18 (20) all_56_1 = all_10_2 % 151.13/22.18 (21) all_58_5 = all_52_9 % 151.13/22.18 (22) all_56_17 = all_52_2 % 151.13/22.18 (23) all_58_9 = all_52_12 % 151.13/22.18 (24) op(e1, e0) = all_52_14 % 151.13/22.18 (25) all_28_1 = all_6_1 % 151.13/22.18 (26) all_58_1 = all_52_4 % 151.13/22.18 (27) op(e3, e3) = all_10_2 % 151.13/22.18 (28) ~ (all_52_8 = all_6_2) % 151.13/22.18 (29) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0 % 151.13/22.18 (30) ~ (all_56_21 = e3) | all_56_17 = e1 % 151.13/22.18 (31) all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0 % 151.13/22.18 (32) all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1 % 151.13/22.18 (33) ~ (all_52_1 = all_8_2) % 151.13/22.18 (34) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 151.13/22.18 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 151.13/22.18 (35) all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0 % 151.13/22.18 (36) op(e0, all_4_1) = all_4_0 % 151.13/22.18 (37) all_56_7 = all_52_12 % 151.13/22.18 (38) all_46_2 = all_6_2 % 151.13/22.18 (39) all_28_2 = all_6_2 % 151.13/22.18 (40) op(e1, e3) = all_52_2 % 151.13/22.18 (41) ~ (all_52_8 = all_10_2) % 151.13/22.18 (42) ~ (all_56_1 = e0) | all_56_7 = e3 % 151.13/22.18 (43) all_46_0 = all_6_0 % 151.13/22.18 (44) ~ (e2 = e1) % 151.13/22.18 (45) op(e1, all_6_1) = all_6_0 % 151.13/22.18 (46) op(all_4_2, all_4_2) = all_4_1 % 151.13/22.18 (47) all_58_3 = all_8_2 % 151.13/22.18 (48) ~ (all_52_11 = all_4_2) % 151.13/22.18 (49) op(e1, all_52_8) = all_56_4 % 151.13/22.18 (50) all_56_31 = all_4_2 % 151.13/22.18 (51) all_58_11 = all_52_14 % 151.13/22.18 (52) op(all_6_2, all_6_2) = all_6_1 % 151.13/22.18 (53) all_56_1 = e3 | all_56_11 = e2 | all_56_21 = e1 | all_56_31 = e0 % 151.13/22.18 (54) ~ (all_52_13 = all_4_2) % 151.13/22.18 (55) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0 % 151.13/22.18 (56) ~ (all_52_8 = all_52_11) % 151.13/22.18 (57) all_54_2 = all_52_8 % 151.13/22.18 (58) ~ (all_52_13 = all_52_14) % 151.13/22.18 (59) ~ (all_28_1 = e3) | ~ (all_28_2 = e0) % 151.13/22.18 (60) all_56_23 = all_52_14 % 151.13/22.18 (61) all_46_1 = all_6_1 % 151.13/22.18 (62) op(e1, e1) = all_6_2 % 151.13/22.18 (63) ~ (all_52_6 = all_8_2) % 151.13/22.18 (64) all_58_15 = all_4_2 % 151.13/22.18 (65) all_56_29 = all_52_11 % 151.13/22.18 (66) all_58_2 = all_52_1 % 151.13/22.18 (67) all_58_10 = all_52_13 % 151.13/22.18 (68) ~ (all_56_11 = e0) | all_56_15 = e2 % 151.13/22.18 (69) all_58_0 = all_10_2 % 151.13/22.18 (70) op(e1, all_6_2) = all_56_20 % 151.13/22.18 (71) ~ (all_56_31 = e2) | all_56_27 = e0 % 151.13/22.18 (72) ~ (e3 = e1) % 151.13/22.18 (73) op(e2, e2) = all_8_2 % 151.13/22.18 (74) ~ (all_52_2 = all_6_2) % 151.13/22.18 (75) ~ (all_56_21 = e0) | all_56_23 = e1 % 151.13/22.18 (76) op(e0, all_4_2) = all_56_30 % 151.13/22.18 (77) ~ (all_52_6 = all_6_2) % 151.13/22.18 (78) ~ (all_52_2 = all_10_2) % 151.13/22.18 (79) ~ (all_46_0 = e2) | ~ (all_46_1 = e0) | ~ (all_46_2 = e3) % 151.13/22.18 (80) ~ (all_52_4 = all_8_2) % 151.13/22.18 (81) op(all_8_2, all_8_2) = all_8_1 % 151.13/22.18 (82) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 151.13/22.18 (83) all_56_19 = all_52_6 % 151.13/22.18 (84) all_56_15 = all_52_13 % 151.13/22.18 (85) ~ (all_56_31 = e3) | all_56_25 = e0 % 151.13/22.18 % 151.13/22.18 Begin of proof % 151.13/22.18 | % 151.13/22.18 | COMBINE_EQS: (15), (43) imply: % 151.13/22.18 | (86) all_46_0 = e2 % 151.13/22.18 | % 151.13/22.18 | REDUCE: (15), (45) imply: % 151.13/22.18 | (87) op(e1, all_6_1) = e2 % 151.13/22.18 | % 151.13/22.18 | BETA: splitting (79) gives: % 151.13/22.18 | % 151.13/22.18 | Case 1: % 151.13/22.18 | | % 151.13/22.18 | | (88) ~ (all_46_0 = e2) % 151.13/22.18 | | % 151.13/22.18 | | REDUCE: (86), (88) imply: % 151.13/22.18 | | (89) $false % 151.13/22.18 | | % 151.13/22.18 | | CLOSE: (89) is inconsistent. % 151.13/22.18 | | % 151.13/22.18 | Case 2: % 151.13/22.18 | | % 151.13/22.18 | | (90) ~ (all_46_1 = e0) | ~ (all_46_2 = e3) % 151.13/22.18 | | % 151.13/22.18 | | BETA: splitting (8) gives: % 151.13/22.18 | | % 151.13/22.18 | | Case 1: % 151.13/22.18 | | | % 151.13/22.18 | | | (91) ~ (all_56_21 = e2) % 151.13/22.18 | | | % 151.13/22.18 | | | REDUCE: (18), (91) imply: % 151.13/22.18 | | | (92) ~ (all_6_2 = e2) % 151.13/22.18 | | | % 151.13/22.18 | | | BETA: splitting (5) gives: % 151.13/22.18 | | | % 151.13/22.18 | | | Case 1: % 151.13/22.18 | | | | % 151.13/22.18 | | | | (93) ~ (all_56_31 = e1) % 151.13/22.18 | | | | % 151.13/22.18 | | | | REDUCE: (50), (93) imply: % 151.13/22.18 | | | | (94) ~ (all_4_2 = e1) % 151.13/22.18 | | | | % 151.13/22.18 | | | | REF_CLOSE: (1), (6), (7), (8), (9), (10), (11), (12), (13), (14), (16), % 151.13/22.18 | | | | (17), (18), (19), (20), (22), (23), (24), (25), (26), (27), % 151.13/22.18 | | | | (30), (31), (34), (36), (37), (38), (39), (40), (42), (44), % 151.13/22.18 | | | | (46), (49), (50), (51), (52), (55), (58), (59), (60), (61), % 151.13/22.18 | | | | (62), (63), (64), (67), (68), (69), (70), (71), (72), (73), % 151.13/22.18 | | | | (74), (75), (76), (77), (78), (80), (82), (83), (84), (85), % 151.13/22.18 | | | | (87), (90), (94) are inconsistent by sub-proof #366. % 151.13/22.18 | | | | % 151.13/22.18 | | | Case 2: % 151.13/22.18 | | | | % 151.13/22.18 | | | | (95) all_56_29 = e0 % 151.13/22.18 | | | | % 151.13/22.18 | | | | COMBINE_EQS: (65), (95) imply: % 151.13/22.18 | | | | (96) all_52_11 = e0 % 151.13/22.18 | | | | % 151.13/22.18 | | | | SIMP: (96) implies: % 151.13/22.18 | | | | (97) all_52_11 = e0 % 151.13/22.18 | | | | % 151.13/22.18 | | | | REDUCE: (2), (97) imply: % 151.13/22.18 | | | | (98) ~ (all_6_2 = e0) % 151.13/22.18 | | | | % 151.13/22.18 | | | | SIMP: (98) implies: % 151.13/22.18 | | | | (99) ~ (all_6_2 = e0) % 151.13/22.18 | | | | % 151.13/22.18 | | | | REF_CLOSE: (6), (7), (9), (14), (18), (19), (22), (27), (30), (34), % 151.13/22.18 | | | | (38), (40), (44), (52), (61), (62), (70), (78), (87), (90), % 151.13/22.18 | | | | (92), (99) are inconsistent by sub-proof #372. % 151.13/22.18 | | | | % 151.13/22.18 | | | End of split % 151.13/22.18 | | | % 151.13/22.18 | | Case 2: % 151.13/22.18 | | | % 151.13/22.18 | | | (100) all_56_21 = e2 % 151.13/22.18 | | | (101) all_56_19 = e1 % 151.13/22.18 | | | % 151.13/22.18 | | | COMBINE_EQS: (83), (101) imply: % 151.13/22.18 | | | (102) all_52_6 = e1 % 151.13/22.18 | | | % 151.13/22.18 | | | COMBINE_EQS: (18), (100) imply: % 151.13/22.18 | | | (103) all_6_2 = e2 % 151.13/22.18 | | | % 151.13/22.18 | | | REDUCE: (74), (103) imply: % 151.13/22.18 | | | (104) ~ (all_52_2 = e2) % 151.13/22.18 | | | % 151.13/22.18 | | | REDUCE: (13), (102) imply: % 151.13/22.18 | | | (105) ~ (all_52_14 = e1) % 151.13/22.18 | | | % 151.13/22.18 | | | SIMP: (105) implies: % 151.13/22.18 | | | (106) ~ (all_52_14 = e1) % 151.13/22.18 | | | % 151.13/22.18 | | | REDUCE: (63), (102) imply: % 151.13/22.18 | | | (107) ~ (all_8_2 = e1) % 151.13/22.18 | | | % 151.13/22.18 | | | SIMP: (107) implies: % 151.13/22.18 | | | (108) ~ (all_8_2 = e1) % 151.13/22.18 | | | % 151.13/22.18 | | | REDUCE: (77), (102), (103) imply: % 151.13/22.18 | | | (109) ~ (e2 = e1) % 151.13/22.18 | | | % 151.13/22.18 | | | REDUCE: (28), (103) imply: % 151.13/22.18 | | | (110) ~ (all_52_8 = e2) % 151.13/22.18 | | | % 151.13/22.18 | | | REDUCE: (52), (103) imply: % 151.13/22.18 | | | (111) op(e2, e2) = all_6_1 % 151.13/22.18 | | | % 151.13/22.18 | | | GROUND_INST: instantiating (34) with all_8_2, all_6_1, e2, e2, simplifying % 151.13/22.18 | | | with (73), (111) gives: % 151.13/22.18 | | | (112) all_8_2 = all_6_1 % 151.13/22.18 | | | % 151.13/22.18 | | | COMBINE_EQS: (12), (112) imply: % 151.13/22.18 | | | (113) all_54_5 = all_6_1 % 151.13/22.18 | | | % 151.13/22.18 | | | COMBINE_EQS: (1), (112) imply: % 151.13/22.18 | | | (114) all_56_11 = all_6_1 % 151.13/22.18 | | | % 151.13/22.18 | | | COMBINE_EQS: (47), (112) imply: % 151.13/22.18 | | | (115) all_58_3 = all_6_1 % 151.13/22.18 | | | % 151.13/22.18 | | | REDUCE: (33), (112) imply: % 151.13/22.18 | | | (116) ~ (all_52_1 = all_6_1) % 151.13/22.18 | | | % 151.13/22.18 | | | REDUCE: (81), (112) imply: % 151.13/22.18 | | | (117) op(all_6_1, all_6_1) = all_8_1 % 151.13/22.18 | | | % 151.13/22.18 | | | BETA: splitting (5) gives: % 151.13/22.18 | | | % 151.13/22.18 | | | Case 1: % 151.13/22.18 | | | | % 151.13/22.18 | | | | (118) ~ (all_56_31 = e1) % 151.13/22.18 | | | | % 151.13/22.18 | | | | REDUCE: (50), (118) imply: % 151.13/22.18 | | | | (119) ~ (all_4_2 = e1) % 151.13/22.18 | | | | % 151.13/22.18 | | | | REF_CLOSE: (1), (7), (11), (12), (17), (20), (23), (24), (26), (31), % 151.13/22.18 | | | | (34), (37), (40), (42), (44), (49), (51), (58), (64), (67), % 151.13/22.18 | | | | (68), (69), (72), (73), (80), (82), (84), (87), (104), (106), % 151.13/22.18 | | | | (108), (111), (119) are inconsistent by sub-proof #369. % 151.13/22.18 | | | | % 151.13/22.18 | | | Case 2: % 151.13/22.18 | | | | % 151.13/22.18 | | | | (120) all_56_31 = e1 % 151.13/22.18 | | | | (121) all_56_29 = e0 % 151.13/22.18 | | | | % 151.13/22.18 | | | | COMBINE_EQS: (65), (121) imply: % 151.13/22.18 | | | | (122) all_52_11 = e0 % 151.13/22.18 | | | | % 151.13/22.18 | | | | SIMP: (122) implies: % 151.13/22.18 | | | | (123) all_52_11 = e0 % 151.13/22.18 | | | | % 151.13/22.18 | | | | COMBINE_EQS: (50), (120) imply: % 151.13/22.18 | | | | (124) all_4_2 = e1 % 151.13/22.18 | | | | % 151.13/22.18 | | | | REDUCE: (56), (123) imply: % 151.13/22.18 | | | | (125) ~ (all_52_8 = e0) % 151.13/22.18 | | | | % 151.13/22.18 | | | | REDUCE: (48), (123), (124) imply: % 151.13/22.18 | | | | (126) ~ (e1 = e0) % 151.13/22.18 | | | | % 151.13/22.18 | | | | SIMP: (126) implies: % 151.13/22.18 | | | | (127) ~ (e1 = e0) % 151.13/22.18 | | | | % 151.13/22.18 | | | | REDUCE: (54), (124) imply: % 151.13/22.18 | | | | (128) ~ (all_52_13 = e1) % 151.13/22.18 | | | | % 151.13/22.18 | | | | REDUCE: (10), (124) imply: % 151.13/22.18 | | | | (129) op(e0, e0) = e1 % 151.13/22.18 | | | | % 151.13/22.18 | | | | BETA: splitting (53) gives: % 151.13/22.18 | | | | % 151.13/22.18 | | | | Case 1: % 151.13/22.18 | | | | | % 151.13/22.18 | | | | | (130) all_56_1 = e3 % 151.13/22.18 | | | | | % 151.13/22.18 | | | | | COMBINE_EQS: (20), (130) imply: % 151.13/22.18 | | | | | (131) all_10_2 = e3 % 151.13/22.18 | | | | | % 151.13/22.18 | | | | | REDUCE: (41), (131) imply: % 151.13/22.18 | | | | | (132) ~ (all_52_8 = e3) % 151.13/22.18 | | | | | % 151.13/22.18 | | | | | BETA: splitting (29) gives: % 151.13/22.18 | | | | | % 151.13/22.18 | | | | | Case 1: % 151.13/22.18 | | | | | | % 151.13/22.18 | | | | | | (133) all_54_2 = e3 % 151.13/22.18 | | | | | | % 151.13/22.18 | | | | | | REF_CLOSE: (57), (132), (133) are inconsistent by sub-proof #728. % 151.13/22.18 | | | | | | % 151.13/22.18 | | | | | Case 2: % 151.13/22.18 | | | | | | % 151.13/22.18 | | | | | | (134) all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0 % 151.13/22.18 | | | | | | % 151.13/22.18 | | | | | | BETA: splitting (134) gives: % 151.13/22.18 | | | | | | % 151.13/22.18 | | | | | | Case 1: % 151.13/22.18 | | | | | | | % 151.13/22.18 | | | | | | | (135) all_54_2 = e2 % 151.13/22.18 | | | | | | | % 151.13/22.18 | | | | | | | REF_CLOSE: (57), (110), (135) are inconsistent by sub-proof #727. % 151.13/22.18 | | | | | | | % 151.13/22.18 | | | | | | Case 2: % 151.13/22.18 | | | | | | | % 151.13/22.18 | | | | | | | (136) all_54_2 = e1 | all_54_2 = e0 % 151.13/22.18 | | | | | | | % 151.13/22.18 | | | | | | | BETA: splitting (136) gives: % 151.13/22.18 | | | | | | | % 151.13/22.18 | | | | | | | Case 1: % 151.13/22.18 | | | | | | | | % 151.13/22.18 | | | | | | | | (137) all_54_2 = e1 % 151.13/22.18 | | | | | | | | % 151.13/22.18 | | | | | | | | COMBINE_EQS: (57), (137) imply: % 151.13/22.18 | | | | | | | | (138) all_52_8 = e1 % 151.13/22.18 | | | | | | | | % 151.13/22.18 | | | | | | | | SIMP: (138) implies: % 151.13/22.18 | | | | | | | | (139) all_52_8 = e1 % 151.13/22.18 | | | | | | | | % 151.13/22.18 | | | | | | | | REDUCE: (3), (139) imply: % 151.13/22.18 | | | | | | | | (140) ~ (all_52_9 = e1) % 151.13/22.18 | | | | | | | | % 151.13/22.18 | | | | | | | | SIMP: (140) implies: % 151.13/22.18 | | | | | | | | (141) ~ (all_52_9 = e1) % 151.13/22.18 | | | | | | | | % 151.13/22.18 | | | | | | | | BETA: splitting (32) gives: % 151.13/22.18 | | | | | | | | % 151.13/22.18 | | | | | | | | Case 1: % 151.13/22.18 | | | | | | | | | % 151.13/22.18 | | | | | | | | | (142) all_58_2 = e1 % 151.13/22.18 | | | | | | | | | % 151.13/22.18 | | | | | | | | | COMBINE_EQS: (66), (142) imply: % 151.13/22.18 | | | | | | | | | (143) all_52_1 = e1 % 151.13/22.18 | | | | | | | | | % 151.13/22.18 | | | | | | | | | REDUCE: (116), (143) imply: % 151.13/22.18 | | | | | | | | | (144) ~ (all_6_1 = e1) % 151.13/22.18 | | | | | | | | | % 151.13/22.18 | | | | | | | | | SIMP: (144) implies: % 151.13/22.18 | | | | | | | | | (145) ~ (all_6_1 = e1) % 151.13/22.18 | | | | | | | | | % 151.13/22.18 | | | | | | | | | BETA: splitting (35) gives: % 151.13/22.18 | | | | | | | | | % 151.13/22.18 | | | | | | | | | Case 1: % 151.13/22.18 | | | | | | | | | | % 151.13/22.18 | | | | | | | | | | (146) all_58_2 = e0 % 151.13/22.18 | | | | | | | | | | % 151.13/22.18 | | | | | | | | | | REF_CLOSE: (127), (142), (146) are inconsistent by sub-proof % 151.13/22.18 | | | | | | | | | | #241. % 151.13/22.18 | | | | | | | | | | % 151.13/22.18 | | | | | | | | | Case 2: % 151.13/22.18 | | | | | | | | | | % 151.13/22.18 | | | | | | | | | | (147) all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0 % 151.13/22.18 | | | | | | | | | | % 151.13/22.18 | | | | | | | | | | BETA: splitting (147) gives: % 151.13/22.18 | | | | | | | | | | % 151.13/22.18 | | | | | | | | | | Case 1: % 151.13/22.18 | | | | | | | | | | | % 151.13/22.18 | | | | | | | | | | | (148) all_58_3 = e0 % 151.13/22.18 | | | | | | | | | | | % 151.13/22.18 | | | | | | | | | | | COMBINE_EQS: (115), (148) imply: % 151.13/22.18 | | | | | | | | | | | (149) all_6_1 = e0 % 151.13/22.18 | | | | | | | | | | | % 151.13/22.18 | | | | | | | | | | | REDUCE: (117), (149) imply: % 151.13/22.18 | | | | | | | | | | | (150) op(e0, e0) = all_8_1 % 151.13/22.18 | | | | | | | | | | | % 151.13/22.18 | | | | | | | | | | | REF_CLOSE: (4), (34), (129), (150) are inconsistent by % 151.13/22.18 | | | | | | | | | | | sub-proof #519. % 151.13/22.18 | | | | | | | | | | | % 151.13/22.18 | | | | | | | | | | Case 2: % 151.13/22.18 | | | | | | | | | | | % 151.13/22.18 | | | | | | | | | | | (151) ~ (all_58_3 = e0) % 151.13/22.18 | | | | | | | | | | | % 151.13/22.18 | | | | | | | | | | | REDUCE: (115), (151) imply: % 151.13/22.18 | | | | | | | | | | | (152) ~ (all_6_1 = e0) % 151.13/22.18 | | | | | | | | | | | % 151.13/22.18 | | | | | | | | | | | REF_CLOSE: (7), (34), (40), (82), (87), (104), (113), (145), % 151.13/22.18 | | | | | | | | | | | (152) are inconsistent by sub-proof #371. % 151.13/22.18 | | | | | | | | | | | % 151.13/22.18 | | | | | | | | | | End of split % 151.13/22.18 | | | | | | | | | | % 151.13/22.18 | | | | | | | | | End of split % 151.13/22.18 | | | | | | | | | % 151.13/22.18 | | | | | | | | Case 2: % 151.13/22.18 | | | | | | | | | % 151.13/22.18 | | | | | | | | | (153) all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1 % 151.13/22.18 | | | | | | | | | % 151.13/22.18 | | | | | | | | | REF_CLOSE: (21), (47), (67), (108), (128), (141), (153) are % 151.13/22.18 | | | | | | | | | inconsistent by sub-proof #495. % 151.13/22.18 | | | | | | | | | % 151.13/22.18 | | | | | | | | End of split % 151.13/22.18 | | | | | | | | % 151.13/22.18 | | | | | | | Case 2: % 151.13/22.18 | | | | | | | | % 151.13/22.18 | | | | | | | | (154) all_54_2 = e0 % 151.13/22.18 | | | | | | | | % 151.13/22.18 | | | | | | | | REF_CLOSE: (57), (125), (154) are inconsistent by sub-proof % 151.13/22.18 | | | | | | | | #725. % 151.13/22.18 | | | | | | | | % 151.13/22.18 | | | | | | | End of split % 151.13/22.18 | | | | | | | % 151.13/22.18 | | | | | | End of split % 151.13/22.18 | | | | | | % 151.13/22.18 | | | | | End of split % 151.13/22.18 | | | | | % 151.13/22.18 | | | | Case 2: % 151.13/22.18 | | | | | % 151.13/22.18 | | | | | (155) all_56_11 = e2 | all_56_21 = e1 | all_56_31 = e0 % 151.13/22.18 | | | | | % 151.13/22.18 | | | | | BETA: splitting (155) gives: % 151.13/22.18 | | | | | % 151.13/22.18 | | | | | Case 1: % 151.13/22.18 | | | | | | % 151.13/22.18 | | | | | | (156) all_56_11 = e2 % 151.13/22.18 | | | | | | % 151.13/22.18 | | | | | | COMBINE_EQS: (114), (156) imply: % 151.13/22.18 | | | | | | (157) all_6_1 = e2 % 151.13/22.18 | | | | | | % 151.13/22.18 | | | | | | REDUCE: (7), (157) imply: % 151.13/22.18 | | | | | | (158) $false % 151.13/22.18 | | | | | | % 151.13/22.18 | | | | | | CLOSE: (158) is inconsistent. % 151.13/22.18 | | | | | | % 151.13/22.18 | | | | | Case 2: % 151.13/22.18 | | | | | | % 151.13/22.18 | | | | | | (159) all_56_21 = e1 | all_56_31 = e0 % 151.13/22.18 | | | | | | % 151.13/22.18 | | | | | | BETA: splitting (159) gives: % 151.13/22.18 | | | | | | % 151.13/22.18 | | | | | | Case 1: % 151.13/22.18 | | | | | | | % 151.13/22.18 | | | | | | | (160) all_56_21 = e1 % 151.13/22.18 | | | | | | | % 151.13/22.18 | | | | | | | COMBINE_EQS: (100), (160) imply: % 151.13/22.18 | | | | | | | (161) e2 = e1 % 151.13/22.18 | | | | | | | % 151.13/22.18 | | | | | | | REDUCE: (44), (161) imply: % 151.13/22.18 | | | | | | | (162) $false % 151.13/22.18 | | | | | | | % 151.13/22.18 | | | | | | | CLOSE: (162) is inconsistent. % 151.13/22.18 | | | | | | | % 151.13/22.18 | | | | | | Case 2: % 151.13/22.18 | | | | | | | % 151.13/22.18 | | | | | | | (163) all_56_31 = e0 % 151.13/22.18 | | | | | | | % 151.13/22.18 | | | | | | | REF_CLOSE: (120), (127), (163) are inconsistent by sub-proof #201. % 151.13/22.18 | | | | | | | % 151.13/22.18 | | | | | | End of split % 151.13/22.18 | | | | | | % 151.13/22.18 | | | | | End of split % 151.13/22.18 | | | | | % 151.13/22.18 | | | | End of split % 151.13/22.18 | | | | % 151.13/22.18 | | | End of split % 151.13/22.18 | | | % 151.13/22.18 | | End of split % 151.13/22.18 | | % 151.13/22.18 | End of split % 151.13/22.18 | % 151.13/22.18 End of proof % 151.13/22.18 % 151.13/22.18 Sub-proof #201 shows that the following formulas are inconsistent: % 151.13/22.18 ---------------------------------------------------------------- % 151.13/22.18 (1) all_56_31 = e1 % 151.13/22.18 (2) all_56_31 = e0 % 151.13/22.18 (3) ~ (e1 = e0) % 151.13/22.18 % 151.13/22.18 Begin of proof % 151.13/22.18 | % 151.13/22.18 | COMBINE_EQS: (1), (2) imply: % 151.13/22.18 | (4) e1 = e0 % 151.13/22.18 | % 151.13/22.18 | SIMP: (4) implies: % 151.13/22.18 | (5) e1 = e0 % 151.13/22.18 | % 151.13/22.18 | REDUCE: (3), (5) imply: % 151.13/22.18 | (6) $false % 151.13/22.18 | % 151.13/22.18 | CLOSE: (6) is inconsistent. % 151.13/22.18 | % 151.13/22.18 End of proof % 151.13/22.18 % 151.13/22.18 Sub-proof #202 shows that the following formulas are inconsistent: % 151.13/22.18 ---------------------------------------------------------------- % 151.13/22.18 (1) all_56_11 = all_8_2 % 151.13/22.18 (2) all_56_25 = all_52_3 % 151.13/22.18 (3) ~ (all_52_7 = all_52_11) % 151.13/22.18 (4) all_58_6 = all_52_2 % 151.13/22.18 (5) ~ (all_8_1 = e1) % 151.13/22.18 (6) ~ (e3 = e0) % 151.13/22.18 (7) ~ (all_56_31 = e1) | all_56_29 = e0 % 151.13/22.18 (8) all_56_5 = all_10_0 % 151.13/22.18 (9) all_12_2 = all_4_2 % 151.13/22.18 (10) ~ (all_56_21 = e2) | all_56_19 = e1 % 151.13/22.18 (11) all_54_0 = all_10_2 % 151.13/22.18 (12) ~ (all_52_14 = all_4_2) % 151.13/22.18 (13) all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2 % 151.13/22.18 (14) all_58_4 = all_10_0 % 151.13/22.18 (15) all_54_2 = all_10_0 % 151.13/22.18 (16) op(e0, e0) = all_4_2 % 151.13/22.18 (17) all_58_6 = e0 | all_58_7 = e0 | all_58_8 = e0 | all_58_11 = e0 % 151.13/22.18 (18) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 151.13/22.18 (19) all_54_15 = all_4_2 % 151.13/22.18 (20) all_56_21 = all_6_2 % 151.13/22.18 (21) all_56_1 = all_10_2 % 151.13/22.18 (22) all_56_27 = all_52_7 % 151.13/22.18 (23) ~ (all_32_0 = e0) | ~ (all_32_2 = e2) % 151.13/22.18 (24) all_58_5 = all_52_9 % 151.13/22.18 (25) ~ (all_56_1 = e1) | all_56_5 = e3 % 151.13/22.18 (26) all_58_1 = all_52_4 % 151.13/22.18 (27) all_58_13 = all_52_7 % 151.13/22.18 (28) all_58_4 = e0 | all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0 % 151.13/22.18 (29) op(e2, all_8_2) = all_56_10 % 151.13/22.18 (30) op(e3, e3) = all_10_2 % 151.13/22.18 (31) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0 % 151.13/22.18 (32) ~ (e1 = e0) % 151.13/22.18 (33) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 151.13/22.18 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 151.13/22.18 (34) ~ (all_52_3 = all_10_2) % 151.13/22.18 (35) ~ (all_52_11 = all_10_0) % 151.13/22.18 (36) all_36_0 = all_6_0 % 151.13/22.18 (37) ~ (all_52_2 = all_52_6) % 151.13/22.18 (38) all_56_7 = all_52_12 % 151.13/22.18 (39) op(e0, all_4_1) = e2 % 151.13/22.18 (40) ~ (all_52_7 = all_4_2) % 151.13/22.18 (41) op(e1, e3) = all_52_2 % 151.13/22.18 (42) all_58_8 = all_6_2 % 151.13/22.18 (43) ~ (all_52_3 = all_4_2) % 151.13/22.18 (44) ~ (all_52_12 = all_10_0) % 151.13/22.18 (45) ~ (all_56_1 = e2) | all_56_3 = e3 % 151.13/22.18 (46) ~ (all_56_1 = e0) | all_56_7 = e3 % 151.13/22.18 (47) ~ (all_12_1 = e1) | ~ (all_12_2 = e3) % 151.13/22.18 (48) ~ (all_52_4 = all_10_0) % 151.13/22.18 (49) op(all_4_2, all_4_2) = all_4_1 % 151.13/22.18 (50) op(all_10_2, all_10_2) = e1 % 151.13/22.18 (51) all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3 % 151.13/22.18 (52) all_58_3 = all_8_2 % 151.13/22.19 (53) all_56_3 = all_52_4 % 151.13/22.19 (54) ~ (all_52_11 = all_4_2) % 151.13/22.19 (55) all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1 % 151.13/22.19 (56) all_56_31 = all_4_2 % 151.13/22.19 (57) all_58_11 = all_52_14 % 151.13/22.19 (58) ~ (all_10_0 = all_6_2) % 151.13/22.19 (59) all_36_2 = all_6_2 % 151.13/22.19 (60) ~ (all_52_2 = all_52_14) % 151.13/22.19 (61) all_56_1 = e3 | all_56_11 = e2 | all_56_21 = e1 | all_56_31 = e0 % 151.13/22.19 (62) ~ (all_10_0 = e1) % 151.13/22.19 (63) all_32_0 = all_10_0 % 151.13/22.19 (64) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0 % 151.13/22.19 (65) all_54_8 = all_52_2 % 151.13/22.19 (66) op(e1, e1) = all_6_2 % 151.13/22.19 (67) all_56_29 = all_52_11 % 151.13/22.19 (68) all_58_7 = all_52_6 % 151.13/22.19 (69) all_12_1 = all_4_1 % 151.13/22.19 (70) op(e1, all_6_2) = all_56_20 % 151.13/22.19 (71) op(e1, e3) = all_6_0 % 151.13/22.19 (72) ~ (all_56_31 = e2) | all_56_27 = e0 % 151.13/22.19 (73) op(e2, e2) = all_8_2 % 151.13/22.19 (74) ~ (all_36_0 = e0) | ~ (all_36_2 = e2) % 151.13/22.19 (75) ~ (all_52_2 = all_6_2) % 151.13/22.19 (76) ~ (all_56_21 = e0) | all_56_23 = e1 % 151.13/22.19 (77) op(e0, all_4_2) = all_56_30 % 151.13/22.19 (78) ~ (all_52_6 = all_6_2) % 151.13/22.19 (79) op(all_6_2, all_6_2) = e3 % 151.13/22.19 (80) op(e3, all_10_2) = all_56_0 % 151.13/22.19 (81) ~ (e2 = e0) % 151.13/22.19 (82) ~ (all_10_0 = all_10_2) % 151.13/22.19 (83) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0 % 151.13/22.19 (84) ~ (all_52_2 = all_10_2) % 151.13/22.19 (85) ~ (all_52_4 = all_10_2) % 151.13/22.19 (86) ~ (all_10_0 = e2) % 151.13/22.19 (87) op(all_8_2, all_8_2) = all_8_1 % 151.13/22.19 (88) all_58_14 = all_52_11 % 151.13/22.19 (89) all_56_19 = all_52_6 % 151.13/22.19 (90) all_32_2 = all_10_2 % 151.13/22.19 (91) ~ (all_56_31 = e3) | all_56_25 = e0 % 151.13/22.19 % 151.13/22.19 Begin of proof % 151.13/22.19 | % 151.13/22.19 | GROUND_INST: instantiating (33) with all_52_2, all_6_0, e3, e1, simplifying % 151.13/22.19 | with (41), (71) gives: % 151.13/22.19 | (92) all_52_2 = all_6_0 % 151.13/22.19 | % 151.13/22.19 | COMBINE_EQS: (65), (92) imply: % 151.13/22.19 | (93) all_54_8 = all_6_0 % 151.13/22.19 | % 151.13/22.19 | COMBINE_EQS: (4), (92) imply: % 151.13/22.19 | (94) all_58_6 = all_6_0 % 151.13/22.19 | % 151.13/22.19 | REDUCE: (37), (92) imply: % 151.13/22.19 | (95) ~ (all_52_6 = all_6_0) % 151.13/22.19 | % 151.13/22.19 | SIMP: (95) implies: % 151.13/22.19 | (96) ~ (all_52_6 = all_6_0) % 151.13/22.19 | % 151.13/22.19 | REDUCE: (60), (92) imply: % 151.13/22.19 | (97) ~ (all_52_14 = all_6_0) % 151.13/22.19 | % 151.13/22.19 | SIMP: (97) implies: % 151.13/22.19 | (98) ~ (all_52_14 = all_6_0) % 151.13/22.19 | % 151.13/22.19 | REDUCE: (84), (92) imply: % 151.13/22.19 | (99) ~ (all_10_2 = all_6_0) % 151.13/22.19 | % 151.13/22.19 | SIMP: (99) implies: % 151.13/22.19 | (100) ~ (all_10_2 = all_6_0) % 151.13/22.19 | % 151.13/22.19 | REDUCE: (75), (92) imply: % 151.13/22.19 | (101) ~ (all_6_0 = all_6_2) % 151.13/22.19 | % 151.13/22.19 | BETA: splitting (10) gives: % 151.13/22.19 | % 151.13/22.19 | Case 1: % 151.13/22.19 | | % 151.13/22.19 | | (102) ~ (all_56_21 = e2) % 151.13/22.19 | | % 151.13/22.19 | | REDUCE: (20), (102) imply: % 151.13/22.19 | | (103) ~ (all_6_2 = e2) % 151.13/22.19 | | % 151.13/22.19 | | REF_CLOSE: (2), (3), (5), (6), (7), (8), (9), (11), (13), (14), (15), (16), % 151.13/22.19 | | (18), (19), (20), (21), (22), (23), (24), (25), (26), (27), (28), % 151.13/22.19 | | (30), (31), (33), (34), (35), (38), (39), (40), (42), (43), (44), % 151.13/22.19 | | (45), (46), (47), (48), (49), (50), (51), (52), (53), (54), (55), % 151.13/22.19 | | (56), (58), (62), (63), (64), (66), (67), (68), (69), (70), (72), % 151.13/22.19 | | (76), (77), (78), (80), (82), (85), (86), (87), (88), (90), (91), % 151.13/22.19 | | (103) are inconsistent by sub-proof #203. % 151.13/22.19 | | % 151.13/22.19 | Case 2: % 151.13/22.19 | | % 151.13/22.19 | | (104) all_56_21 = e2 % 151.13/22.19 | | (105) all_56_19 = e1 % 151.13/22.19 | | % 151.13/22.19 | | REF_CLOSE: (1), (12), (17), (20), (21), (29), (32), (33), (36), (42), (56), % 151.13/22.19 | | (57), (59), (61), (68), (73), (74), (78), (79), (81), (83), (87), % 151.13/22.19 | | (89), (93), (94), (96), (98), (100), (101), (104), (105) are % 151.13/22.19 | | inconsistent by sub-proof #412. % 151.13/22.19 | | % 151.13/22.19 | End of split % 151.13/22.19 | % 151.13/22.19 End of proof % 151.13/22.19 % 151.13/22.19 Sub-proof #203 shows that the following formulas are inconsistent: % 151.13/22.19 ---------------------------------------------------------------- % 151.13/22.19 (1) all_56_25 = all_52_3 % 151.13/22.19 (2) ~ (all_52_7 = all_52_11) % 151.13/22.19 (3) ~ (all_8_1 = e1) % 151.13/22.19 (4) ~ (e3 = e0) % 151.13/22.19 (5) ~ (all_56_31 = e1) | all_56_29 = e0 % 151.13/22.19 (6) all_56_5 = all_10_0 % 151.13/22.19 (7) all_12_2 = all_4_2 % 151.13/22.19 (8) all_54_0 = all_10_2 % 151.13/22.19 (9) all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2 % 151.13/22.19 (10) all_58_4 = all_10_0 % 151.13/22.19 (11) all_54_2 = all_10_0 % 151.13/22.19 (12) op(e0, e0) = all_4_2 % 151.13/22.19 (13) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 151.13/22.19 (14) all_54_15 = all_4_2 % 151.13/22.19 (15) all_56_21 = all_6_2 % 151.13/22.19 (16) all_56_1 = all_10_2 % 151.13/22.19 (17) all_56_27 = all_52_7 % 151.13/22.19 (18) ~ (all_32_0 = e0) | ~ (all_32_2 = e2) % 151.13/22.19 (19) all_58_5 = all_52_9 % 151.13/22.19 (20) ~ (all_56_1 = e1) | all_56_5 = e3 % 151.13/22.19 (21) all_58_1 = all_52_4 % 151.13/22.19 (22) all_58_13 = all_52_7 % 151.13/22.19 (23) all_58_4 = e0 | all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0 % 151.13/22.19 (24) op(e3, e3) = all_10_2 % 151.13/22.19 (25) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0 % 151.13/22.19 (26) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 151.13/22.19 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 151.13/22.19 (27) ~ (all_52_3 = all_10_2) % 151.13/22.19 (28) ~ (all_52_11 = all_10_0) % 151.13/22.19 (29) all_56_7 = all_52_12 % 151.13/22.19 (30) op(e0, all_4_1) = e2 % 151.13/22.19 (31) ~ (all_52_7 = all_4_2) % 151.13/22.19 (32) all_58_8 = all_6_2 % 151.13/22.19 (33) ~ (all_52_3 = all_4_2) % 151.13/22.19 (34) ~ (all_52_12 = all_10_0) % 151.13/22.19 (35) ~ (all_56_1 = e2) | all_56_3 = e3 % 151.13/22.19 (36) ~ (all_56_1 = e0) | all_56_7 = e3 % 151.13/22.19 (37) ~ (all_12_1 = e1) | ~ (all_12_2 = e3) % 151.13/22.19 (38) ~ (all_52_4 = all_10_0) % 151.13/22.19 (39) op(all_4_2, all_4_2) = all_4_1 % 151.13/22.19 (40) op(all_10_2, all_10_2) = e1 % 151.13/22.19 (41) all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3 % 151.13/22.19 (42) all_58_3 = all_8_2 % 151.13/22.19 (43) all_56_3 = all_52_4 % 151.13/22.19 (44) ~ (all_52_11 = all_4_2) % 151.13/22.19 (45) all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1 % 151.13/22.19 (46) all_56_31 = all_4_2 % 151.13/22.19 (47) ~ (all_10_0 = all_6_2) % 151.13/22.19 (48) ~ (all_10_0 = e1) % 151.13/22.19 (49) all_32_0 = all_10_0 % 151.13/22.19 (50) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0 % 151.13/22.19 (51) op(e1, e1) = all_6_2 % 151.13/22.19 (52) all_56_29 = all_52_11 % 151.13/22.19 (53) ~ (all_6_2 = e2) % 151.13/22.19 (54) all_58_7 = all_52_6 % 151.13/22.19 (55) all_12_1 = all_4_1 % 151.13/22.19 (56) op(e1, all_6_2) = all_56_20 % 151.13/22.19 (57) ~ (all_56_31 = e2) | all_56_27 = e0 % 151.13/22.19 (58) ~ (all_56_21 = e0) | all_56_23 = e1 % 151.13/22.19 (59) op(e0, all_4_2) = all_56_30 % 151.13/22.19 (60) ~ (all_52_6 = all_6_2) % 151.13/22.19 (61) op(e3, all_10_2) = all_56_0 % 151.13/22.19 (62) ~ (all_10_0 = all_10_2) % 151.13/22.19 (63) ~ (all_52_4 = all_10_2) % 151.13/22.19 (64) ~ (all_10_0 = e2) % 151.13/22.19 (65) op(all_8_2, all_8_2) = all_8_1 % 151.13/22.19 (66) all_58_14 = all_52_11 % 151.13/22.19 (67) all_32_2 = all_10_2 % 151.13/22.19 (68) ~ (all_56_31 = e3) | all_56_25 = e0 % 151.13/22.19 % 151.13/22.19 Begin of proof % 151.13/22.19 | % 151.13/22.19 | BETA: splitting (5) gives: % 151.13/22.19 | % 151.13/22.19 | Case 1: % 151.13/22.19 | | % 151.13/22.19 | | (69) ~ (all_56_31 = e1) % 151.13/22.19 | | % 151.13/22.19 | | REDUCE: (46), (69) imply: % 151.13/22.19 | | (70) ~ (all_4_2 = e1) % 151.13/22.19 | | % 151.13/22.19 | | REF_CLOSE: (1), (2), (4), (6), (7), (8), (9), (10), (11), (12), (13), (14), % 151.13/22.19 | | (15), (16), (17), (18), (19), (20), (23), (24), (25), (26), (27), % 151.13/22.19 | | (29), (30), (31), (32), (33), (34), (35), (36), (37), (38), (39), % 151.13/22.19 | | (40), (41), (43), (44), (46), (47), (48), (49), (50), (51), (53), % 151.13/22.19 | | (55), (57), (58), (59), (61), (62), (64), (66), (67), (68), (70) % 151.13/22.19 | | are inconsistent by sub-proof #204. % 151.13/22.19 | | % 151.13/22.19 | Case 2: % 151.13/22.19 | | % 151.13/22.19 | | (71) all_56_31 = e1 % 151.13/22.19 | | (72) all_56_29 = e0 % 151.13/22.19 | | % 151.13/22.19 | | COMBINE_EQS: (52), (72) imply: % 151.13/22.19 | | (73) all_52_11 = e0 % 151.13/22.19 | | % 151.13/22.19 | | SIMP: (73) implies: % 151.13/22.19 | | (74) all_52_11 = e0 % 151.13/22.19 | | % 151.13/22.19 | | REF_CLOSE: (3), (8), (11), (13), (16), (21), (22), (25), (26), (28), (29), % 151.13/22.19 | | (31), (34), (35), (36), (38), (39), (40), (42), (43), (45), (46), % 151.13/22.19 | | (48), (51), (54), (56), (60), (62), (63), (64), (65), (71), (74) % 151.13/22.19 | | are inconsistent by sub-proof #381. % 151.13/22.19 | | % 151.13/22.19 | End of split % 151.13/22.19 | % 151.13/22.19 End of proof % 151.13/22.19 % 151.13/22.19 Sub-proof #204 shows that the following formulas are inconsistent: % 151.13/22.19 ---------------------------------------------------------------- % 151.13/22.19 (1) all_56_25 = all_52_3 % 151.13/22.19 (2) ~ (all_52_7 = all_52_11) % 151.13/22.19 (3) ~ (e3 = e0) % 151.13/22.19 (4) all_56_5 = all_10_0 % 151.13/22.19 (5) all_12_2 = all_4_2 % 151.13/22.19 (6) all_54_0 = all_10_2 % 151.13/22.19 (7) all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2 % 151.13/22.19 (8) all_58_4 = all_10_0 % 151.13/22.19 (9) all_54_2 = all_10_0 % 151.13/22.19 (10) op(e0, e0) = all_4_2 % 151.13/22.19 (11) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 151.13/22.19 (12) all_54_15 = all_4_2 % 151.13/22.19 (13) all_56_21 = all_6_2 % 151.13/22.19 (14) all_56_1 = all_10_2 % 151.13/22.19 (15) all_56_27 = all_52_7 % 151.13/22.19 (16) ~ (all_32_0 = e0) | ~ (all_32_2 = e2) % 151.13/22.19 (17) all_58_5 = all_52_9 % 151.13/22.19 (18) ~ (all_56_1 = e1) | all_56_5 = e3 % 151.13/22.19 (19) all_58_4 = e0 | all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0 % 151.13/22.19 (20) op(e3, e3) = all_10_2 % 151.13/22.19 (21) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0 % 151.13/22.19 (22) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 151.13/22.19 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 151.13/22.19 (23) ~ (all_52_3 = all_10_2) % 151.13/22.19 (24) all_56_7 = all_52_12 % 151.13/22.19 (25) op(e0, all_4_1) = e2 % 151.13/22.19 (26) ~ (all_52_7 = all_4_2) % 151.13/22.19 (27) ~ (all_4_2 = e1) % 151.13/22.19 (28) all_58_8 = all_6_2 % 151.13/22.19 (29) ~ (all_52_3 = all_4_2) % 151.13/22.19 (30) ~ (all_52_12 = all_10_0) % 151.13/22.19 (31) ~ (all_56_1 = e2) | all_56_3 = e3 % 151.13/22.19 (32) ~ (all_56_1 = e0) | all_56_7 = e3 % 151.13/22.19 (33) ~ (all_12_1 = e1) | ~ (all_12_2 = e3) % 151.13/22.19 (34) ~ (all_52_4 = all_10_0) % 151.13/22.19 (35) op(all_4_2, all_4_2) = all_4_1 % 151.13/22.19 (36) op(all_10_2, all_10_2) = e1 % 151.13/22.19 (37) all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3 % 151.13/22.19 (38) all_56_3 = all_52_4 % 151.13/22.19 (39) ~ (all_52_11 = all_4_2) % 151.13/22.19 (40) all_56_31 = all_4_2 % 151.13/22.19 (41) ~ (all_10_0 = all_6_2) % 151.13/22.19 (42) ~ (all_10_0 = e1) % 151.13/22.19 (43) all_32_0 = all_10_0 % 151.13/22.19 (44) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0 % 151.13/22.19 (45) op(e1, e1) = all_6_2 % 151.13/22.19 (46) ~ (all_6_2 = e2) % 151.13/22.19 (47) all_12_1 = all_4_1 % 151.13/22.19 (48) ~ (all_56_31 = e2) | all_56_27 = e0 % 151.13/22.19 (49) ~ (all_56_21 = e0) | all_56_23 = e1 % 151.13/22.19 (50) op(e0, all_4_2) = all_56_30 % 151.13/22.19 (51) op(e3, all_10_2) = all_56_0 % 151.13/22.19 (52) ~ (all_10_0 = all_10_2) % 151.13/22.19 (53) ~ (all_10_0 = e2) % 151.13/22.19 (54) all_58_14 = all_52_11 % 151.13/22.19 (55) all_32_2 = all_10_2 % 151.13/22.19 (56) ~ (all_56_31 = e3) | all_56_25 = e0 % 151.13/22.19 % 151.13/22.19 Begin of proof % 151.13/22.19 | % 151.13/22.19 | BETA: splitting (56) gives: % 151.13/22.19 | % 151.13/22.19 | Case 1: % 151.13/22.19 | | % 151.13/22.19 | | (57) ~ (all_56_31 = e3) % 151.13/22.19 | | % 151.13/22.19 | | REDUCE: (40), (57) imply: % 151.13/22.19 | | (58) ~ (all_4_2 = e3) % 151.13/22.19 | | % 151.13/22.19 | | BETA: splitting (49) gives: % 151.13/22.19 | | % 151.13/22.19 | | Case 1: % 151.13/22.19 | | | % 151.13/22.19 | | | (59) ~ (all_56_21 = e0) % 151.13/22.19 | | | % 151.13/22.19 | | | REDUCE: (13), (59) imply: % 151.13/22.19 | | | (60) ~ (all_6_2 = e0) % 151.13/22.19 | | | % 151.13/22.19 | | | BETA: splitting (48) gives: % 151.13/22.19 | | | % 151.13/22.19 | | | Case 1: % 151.13/22.19 | | | | % 151.13/22.19 | | | | (61) ~ (all_56_31 = e2) % 151.13/22.19 | | | | % 151.13/22.19 | | | | REDUCE: (40), (61) imply: % 151.13/22.19 | | | | (62) ~ (all_4_2 = e2) % 151.13/22.19 | | | | % 151.13/22.19 | | | | REF_CLOSE: (10), (12), (22), (25), (27), (35), (44), (50), (58), (62) % 151.13/22.19 | | | | are inconsistent by sub-proof #229. % 151.13/22.19 | | | | % 151.13/22.19 | | | Case 2: % 151.13/22.19 | | | | % 151.13/22.19 | | | | (63) all_56_31 = e2 % 151.13/22.19 | | | | (64) all_56_27 = e0 % 151.13/22.19 | | | | % 151.13/22.19 | | | | COMBINE_EQS: (15), (64) imply: % 151.13/22.19 | | | | (65) all_52_7 = e0 % 151.13/22.19 | | | | % 151.13/22.19 | | | | SIMP: (65) implies: % 151.13/22.19 | | | | (66) all_52_7 = e0 % 151.13/22.19 | | | | % 151.13/22.19 | | | | COMBINE_EQS: (40), (63) imply: % 151.13/22.19 | | | | (67) all_4_2 = e2 % 151.13/22.19 | | | | % 151.13/22.19 | | | | REDUCE: (2), (66) imply: % 151.13/22.19 | | | | (68) ~ (all_52_11 = e0) % 151.13/22.19 | | | | % 151.13/22.19 | | | | SIMP: (68) implies: % 151.13/22.19 | | | | (69) ~ (all_52_11 = e0) % 151.13/22.19 | | | | % 151.13/22.19 | | | | REDUCE: (26), (66), (67) imply: % 151.13/22.19 | | | | (70) ~ (e2 = e0) % 151.13/22.19 | | | | % 151.13/22.19 | | | | SIMP: (70) implies: % 151.13/22.19 | | | | (71) ~ (e2 = e0) % 151.13/22.19 | | | | % 151.13/22.19 | | | | REDUCE: (39), (67) imply: % 151.13/22.19 | | | | (72) ~ (all_52_11 = e2) % 151.13/22.19 | | | | % 151.13/22.19 | | | | BETA: splitting (7) gives: % 151.13/22.19 | | | | % 151.13/22.19 | | | | Case 1: % 151.13/22.19 | | | | | % 151.13/22.19 | | | | | (73) all_58_4 = e2 % 151.13/22.19 | | | | | % 151.13/22.19 | | | | | COMBINE_EQS: (8), (73) imply: % 151.13/22.19 | | | | | (74) all_10_0 = e2 % 151.13/22.19 | | | | | % 151.13/22.19 | | | | | REDUCE: (53), (74) imply: % 151.13/22.19 | | | | | (75) $false % 151.13/22.19 | | | | | % 151.13/22.19 | | | | | CLOSE: (75) is inconsistent. % 151.13/22.19 | | | | | % 151.13/22.19 | | | | Case 2: % 151.13/22.19 | | | | | % 151.13/22.19 | | | | | (76) all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2 % 151.13/22.19 | | | | | % 151.13/22.19 | | | | | BETA: splitting (76) gives: % 151.13/22.19 | | | | | % 151.13/22.19 | | | | | Case 1: % 151.13/22.19 | | | | | | % 151.13/22.19 | | | | | | (77) all_58_5 = e2 % 151.13/22.19 | | | | | | % 151.13/22.19 | | | | | | COMBINE_EQS: (17), (77) imply: % 151.13/22.19 | | | | | | (78) all_52_9 = e2 % 151.13/22.19 | | | | | | % 151.13/22.19 | | | | | | BETA: splitting (19) gives: % 151.13/22.19 | | | | | | % 151.13/22.19 | | | | | | Case 1: % 151.13/22.19 | | | | | | | % 151.13/22.19 | | | | | | | (79) all_58_4 = e0 % 151.13/22.19 | | | | | | | % 151.13/22.19 | | | | | | | COMBINE_EQS: (8), (79) imply: % 151.13/22.19 | | | | | | | (80) all_10_0 = e0 % 151.13/22.19 | | | | | | | % 151.13/22.19 | | | | | | | COMBINE_EQS: (43), (80) imply: % 151.13/22.19 | | | | | | | (81) all_32_0 = e0 % 151.13/22.19 | | | | | | | % 151.13/22.19 | | | | | | | COMBINE_EQS: (4), (80) imply: % 151.13/22.19 | | | | | | | (82) all_56_5 = e0 % 151.13/22.19 | | | | | | | % 151.13/22.19 | | | | | | | REDUCE: (52), (80) imply: % 151.13/22.19 | | | | | | | (83) ~ (all_10_2 = e0) % 151.13/22.19 | | | | | | | % 151.13/22.19 | | | | | | | SIMP: (83) implies: % 151.13/22.19 | | | | | | | (84) ~ (all_10_2 = e0) % 151.13/22.19 | | | | | | | % 151.13/22.19 | | | | | | | REF_CLOSE: (3), (6), (11), (14), (16), (18), (20), (22), (36), % 151.13/22.19 | | | | | | | (51), (55), (81), (82), (84) are inconsistent by % 151.13/22.19 | | | | | | | sub-proof #398. % 151.13/22.19 | | | | | | | % 151.13/22.19 | | | | | | Case 2: % 151.13/22.19 | | | | | | | % 151.13/22.19 | | | | | | | (85) all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0 % 151.13/22.19 | | | | | | | % 151.13/22.19 | | | | | | | REF_CLOSE: (28), (54), (60), (69), (71), (77), (85) are % 151.13/22.19 | | | | | | | inconsistent by sub-proof #572. % 151.13/22.19 | | | | | | | % 151.13/22.19 | | | | | | End of split % 151.13/22.19 | | | | | | % 151.13/22.19 | | | | | Case 2: % 151.13/22.19 | | | | | | % 151.13/22.19 | | | | | | (86) all_58_8 = e2 | all_58_14 = e2 % 151.13/22.19 | | | | | | % 151.13/22.19 | | | | | | REF_CLOSE: (28), (46), (54), (72), (86) are inconsistent by % 151.13/22.19 | | | | | | sub-proof #478. % 151.13/22.19 | | | | | | % 151.13/22.19 | | | | | End of split % 151.13/22.19 | | | | | % 151.13/22.19 | | | | End of split % 151.13/22.19 | | | | % 151.13/22.19 | | | End of split % 151.13/22.19 | | | % 151.13/22.19 | | Case 2: % 151.13/22.19 | | | % 151.13/22.19 | | | (87) all_56_21 = e0 % 151.13/22.19 | | | % 151.13/22.19 | | | COMBINE_EQS: (13), (87) imply: % 151.13/22.19 | | | (88) all_6_2 = e0 % 151.13/22.19 | | | % 151.13/22.19 | | | SIMP: (88) implies: % 151.13/22.19 | | | (89) all_6_2 = e0 % 151.13/22.19 | | | % 151.13/22.19 | | | REDUCE: (41), (89) imply: % 151.13/22.19 | | | (90) ~ (all_10_0 = e0) % 151.13/22.19 | | | % 151.13/22.19 | | | REDUCE: (45), (89) imply: % 151.13/22.19 | | | (91) op(e1, e1) = e0 % 151.13/22.19 | | | % 151.13/22.19 | | | REF_CLOSE: (6), (9), (11), (14), (21), (22), (24), (30), (31), (32), (34), % 151.13/22.19 | | | (36), (38), (42), (52), (53), (90), (91) are inconsistent by % 151.13/22.19 | | | sub-proof #245. % 151.13/22.19 | | | % 151.13/22.19 | | End of split % 151.13/22.19 | | % 151.13/22.19 | Case 2: % 151.13/22.19 | | % 151.13/22.19 | | (92) all_56_31 = e3 % 151.13/22.19 | | (93) all_56_25 = e0 % 151.13/22.19 | | % 151.13/22.19 | | COMBINE_EQS: (1), (93) imply: % 151.13/22.19 | | (94) all_52_3 = e0 % 151.13/22.19 | | % 151.13/22.19 | | SIMP: (94) implies: % 151.13/22.19 | | (95) all_52_3 = e0 % 151.13/22.19 | | % 151.13/22.19 | | COMBINE_EQS: (40), (92) imply: % 151.13/22.19 | | (96) all_4_2 = e3 % 151.13/22.19 | | % 151.13/22.19 | | COMBINE_EQS: (5), (96) imply: % 151.13/22.19 | | (97) all_12_2 = e3 % 151.13/22.19 | | % 151.13/22.19 | | REDUCE: (23), (95) imply: % 151.13/22.19 | | (98) ~ (all_10_2 = e0) % 151.13/22.19 | | % 151.13/22.19 | | SIMP: (98) implies: % 151.13/22.19 | | (99) ~ (all_10_2 = e0) % 151.13/22.19 | | % 151.13/22.19 | | REDUCE: (29), (95), (96) imply: % 151.13/22.19 | | (100) ~ (e3 = e0) % 151.13/22.19 | | % 151.13/22.19 | | REDUCE: (35), (96) imply: % 151.13/22.19 | | (101) op(e3, e3) = all_4_1 % 151.13/22.19 | | % 151.13/22.19 | | BETA: splitting (33) gives: % 151.13/22.19 | | % 151.13/22.19 | | Case 1: % 151.13/22.19 | | | % 151.13/22.19 | | | (102) ~ (all_12_1 = e1) % 151.13/22.19 | | | % 151.13/22.19 | | | REDUCE: (47), (102) imply: % 151.13/22.19 | | | (103) ~ (all_4_1 = e1) % 151.13/22.19 | | | % 151.13/22.19 | | | GROUND_INST: instantiating (22) with all_10_2, all_4_1, e3, e3, % 151.13/22.19 | | | simplifying with (20), (101) gives: % 151.13/22.19 | | | (104) all_10_2 = all_4_1 % 151.13/22.19 | | | % 151.13/22.19 | | | COMBINE_EQS: (6), (104) imply: % 151.13/22.19 | | | (105) all_54_0 = all_4_1 % 151.13/22.19 | | | % 151.13/22.19 | | | COMBINE_EQS: (14), (104) imply: % 151.13/22.19 | | | (106) all_56_1 = all_4_1 % 151.13/22.19 | | | % 151.13/22.19 | | | REDUCE: (52), (104) imply: % 151.13/22.19 | | | (107) ~ (all_10_0 = all_4_1) % 151.13/22.19 | | | % 151.13/22.19 | | | REDUCE: (99), (104) imply: % 151.13/22.19 | | | (108) ~ (all_4_1 = e0) % 151.13/22.19 | | | % 151.13/22.19 | | | REF_CLOSE: (3), (4), (6), (8), (9), (11), (14), (16), (18), (20), (21), % 151.13/22.19 | | | (22), (31), (34), (36), (37), (38), (42), (43), (51), (53), % 151.13/22.19 | | | (55), (99), (103), (105), (106), (107), (108) are inconsistent % 151.13/22.19 | | | by sub-proof #354. % 151.13/22.19 | | | % 151.13/22.19 | | Case 2: % 151.13/22.19 | | | % 151.13/22.19 | | | (109) ~ (all_12_2 = e3) % 151.13/22.19 | | | % 151.13/22.19 | | | REDUCE: (97), (109) imply: % 151.13/22.19 | | | (110) $false % 151.13/22.19 | | | % 151.13/22.19 | | | CLOSE: (110) is inconsistent. % 151.13/22.19 | | | % 151.13/22.19 | | End of split % 151.13/22.19 | | % 151.13/22.19 | End of split % 151.13/22.19 | % 151.13/22.19 End of proof % 151.13/22.19 % 151.13/22.19 Sub-proof #205 shows that the following formulas are inconsistent: % 151.13/22.19 ---------------------------------------------------------------- % 151.13/22.19 (1) all_56_11 = all_8_2 % 151.13/22.19 (2) ~ (all_52_11 = all_6_2) % 151.13/22.19 (3) all_56_31 = e1 % 151.13/22.19 (4) ~ (all_34_1 = e3) | ~ (all_34_2 = e1) % 151.13/22.19 (5) all_54_10 = all_6_2 % 151.13/22.19 (6) ~ (all_56_21 = e2) | all_56_19 = e1 % 151.13/22.19 (7) ~ (all_52_14 = all_4_2) % 151.13/22.19 (8) all_58_6 = e0 | all_58_7 = e0 | all_58_8 = e0 | all_58_11 = e0 % 151.13/22.19 (9) all_56_21 = all_6_2 % 151.13/22.19 (10) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 151.13/22.19 (11) all_56_1 = all_10_2 % 151.13/22.19 (12) op(e2, all_8_2) = all_56_10 % 151.13/22.19 (13) ~ (all_52_6 = all_6_0) % 151.13/22.19 (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 151.13/22.19 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 151.13/22.19 (15) all_36_0 = all_6_0 % 151.13/22.19 (16) ~ (all_6_0 = all_6_2) % 151.13/22.19 (17) all_54_8 = all_6_0 % 151.13/22.19 (18) all_58_8 = all_6_2 % 151.13/22.19 (19) ~ (all_52_14 = all_6_0) % 151.13/22.19 (20) all_34_1 = all_4_1 % 151.13/22.19 (21) op(all_4_2, all_4_2) = all_4_1 % 151.13/22.19 (22) all_56_29 = e0 % 151.13/22.19 (23) ~ (all_52_11 = all_4_2) % 151.13/22.19 (24) all_56_31 = all_4_2 % 151.13/22.19 (25) all_58_11 = all_52_14 % 151.13/22.19 (26) all_36_2 = all_6_2 % 151.13/22.19 (27) all_56_1 = e3 | all_56_11 = e2 | all_56_21 = e1 | all_56_31 = e0 % 151.13/22.19 (28) all_58_6 = all_6_0 % 151.13/22.19 (29) op(e1, e1) = all_6_2 % 151.13/22.19 (30) all_56_29 = all_52_11 % 151.13/22.19 (31) all_58_7 = all_52_6 % 151.13/22.19 (32) op(e1, all_6_2) = all_56_20 % 151.13/22.19 (33) op(e2, e2) = all_8_2 % 151.13/22.19 (34) ~ (all_36_0 = e0) | ~ (all_36_2 = e2) % 151.13/22.19 (35) ~ (all_52_6 = all_6_2) % 151.13/22.19 (36) op(all_6_2, all_6_2) = e3 % 151.13/22.19 (37) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0 % 151.13/22.19 (38) ~ (all_10_2 = all_6_0) % 151.13/22.19 (39) all_34_2 = all_4_2 % 151.13/22.19 (40) op(all_8_2, all_8_2) = all_8_1 % 151.13/22.19 (41) all_56_19 = all_52_6 % 151.13/22.19 % 151.13/22.19 Begin of proof % 151.13/22.19 | % 151.13/22.19 | COMBINE_EQS: (22), (30) imply: % 151.13/22.19 | (42) all_52_11 = e0 % 151.13/22.19 | % 151.13/22.19 | SIMP: (42) implies: % 151.13/22.19 | (43) all_52_11 = e0 % 151.13/22.19 | % 151.13/22.19 | COMBINE_EQS: (3), (24) imply: % 151.13/22.19 | (44) all_4_2 = e1 % 151.13/22.19 | % 151.13/22.19 | COMBINE_EQS: (39), (44) imply: % 151.13/22.19 | (45) all_34_2 = e1 % 151.13/22.19 | % 151.13/22.19 | REDUCE: (2), (43) imply: % 151.13/22.19 | (46) ~ (all_6_2 = e0) % 151.13/22.19 | % 151.13/22.19 | SIMP: (46) implies: % 151.13/22.19 | (47) ~ (all_6_2 = e0) % 151.13/22.19 | % 151.13/22.19 | REDUCE: (23), (43), (44) imply: % 151.13/22.19 | (48) ~ (e1 = e0) % 151.13/22.19 | % 151.13/22.19 | SIMP: (48) implies: % 151.13/22.19 | (49) ~ (e1 = e0) % 151.13/22.19 | % 151.13/22.19 | REDUCE: (21), (44) imply: % 151.13/22.19 | (50) op(e1, e1) = all_4_1 % 151.13/22.19 | % 151.13/22.19 | REF_CLOSE: (1), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13), (14), % 151.13/22.19 | (15), (16), (17), (18), (19), (20), (24), (25), (26), (27), (28), % 151.13/22.19 | (29), (31), (32), (33), (34), (35), (36), (37), (38), (40), (41), % 151.13/22.19 | (45), (47), (49), (50) are inconsistent by sub-proof #206. % 151.13/22.19 | % 151.13/22.19 End of proof % 151.13/22.19 % 151.13/22.19 Sub-proof #206 shows that the following formulas are inconsistent: % 151.13/22.19 ---------------------------------------------------------------- % 151.13/22.19 (1) all_56_11 = all_8_2 % 151.13/22.19 (2) ~ (all_34_1 = e3) | ~ (all_34_2 = e1) % 151.13/22.19 (3) all_54_10 = all_6_2 % 151.13/22.19 (4) ~ (all_56_21 = e2) | all_56_19 = e1 % 151.13/22.19 (5) all_34_2 = e1 % 151.13/22.19 (6) ~ (all_52_14 = all_4_2) % 151.13/22.19 (7) all_58_6 = e0 | all_58_7 = e0 | all_58_8 = e0 | all_58_11 = e0 % 151.13/22.19 (8) all_56_21 = all_6_2 % 151.13/22.19 (9) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 151.13/22.19 (10) all_56_1 = all_10_2 % 151.13/22.19 (11) op(e2, all_8_2) = all_56_10 % 151.13/22.19 (12) ~ (all_52_6 = all_6_0) % 151.13/22.19 (13) ~ (e1 = e0) % 151.13/22.19 (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 151.13/22.19 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 151.13/22.19 (15) ~ (all_6_2 = e0) % 151.13/22.19 (16) all_36_0 = all_6_0 % 151.13/22.19 (17) ~ (all_6_0 = all_6_2) % 151.13/22.19 (18) all_54_8 = all_6_0 % 151.13/22.19 (19) all_58_8 = all_6_2 % 151.13/22.19 (20) ~ (all_52_14 = all_6_0) % 151.13/22.19 (21) all_34_1 = all_4_1 % 151.13/22.19 (22) all_56_31 = all_4_2 % 151.13/22.19 (23) all_58_11 = all_52_14 % 151.13/22.19 (24) all_36_2 = all_6_2 % 151.13/22.19 (25) all_56_1 = e3 | all_56_11 = e2 | all_56_21 = e1 | all_56_31 = e0 % 151.13/22.19 (26) all_58_6 = all_6_0 % 151.13/22.19 (27) op(e1, e1) = all_6_2 % 151.13/22.19 (28) all_58_7 = all_52_6 % 151.13/22.19 (29) op(e1, e1) = all_4_1 % 151.13/22.19 (30) op(e1, all_6_2) = all_56_20 % 151.13/22.19 (31) op(e2, e2) = all_8_2 % 151.13/22.19 (32) ~ (all_36_0 = e0) | ~ (all_36_2 = e2) % 151.13/22.19 (33) ~ (all_52_6 = all_6_2) % 151.13/22.19 (34) op(all_6_2, all_6_2) = e3 % 151.13/22.19 (35) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0 % 151.13/22.19 (36) ~ (all_10_2 = all_6_0) % 151.13/22.19 (37) op(all_8_2, all_8_2) = all_8_1 % 151.13/22.19 (38) all_56_19 = all_52_6 % 151.13/22.19 % 151.13/22.19 Begin of proof % 151.13/22.19 | % 151.13/22.19 | BETA: splitting (2) gives: % 151.13/22.19 | % 151.13/22.19 | Case 1: % 151.13/22.19 | | % 151.13/22.20 | | (39) ~ (all_34_1 = e3) % 151.13/22.20 | | % 151.13/22.20 | | REDUCE: (21), (39) imply: % 151.13/22.20 | | (40) ~ (all_4_1 = e3) % 151.13/22.20 | | % 151.13/22.20 | | GROUND_INST: instantiating (14) with all_6_2, all_4_1, e1, e1, simplifying % 151.13/22.20 | | with (27), (29) gives: % 151.13/22.20 | | (41) all_6_2 = all_4_1 % 151.13/22.20 | | % 151.13/22.20 | | COMBINE_EQS: (24), (41) imply: % 151.13/22.20 | | (42) all_36_2 = all_4_1 % 151.13/22.20 | | % 151.13/22.20 | | COMBINE_EQS: (3), (41) imply: % 151.13/22.20 | | (43) all_54_10 = all_4_1 % 151.13/22.20 | | % 151.13/22.20 | | COMBINE_EQS: (8), (41) imply: % 151.13/22.20 | | (44) all_56_21 = all_4_1 % 151.13/22.20 | | % 151.13/22.20 | | COMBINE_EQS: (19), (41) imply: % 151.13/22.20 | | (45) all_58_8 = all_4_1 % 151.13/22.20 | | % 151.13/22.20 | | REDUCE: (33), (41) imply: % 151.13/22.20 | | (46) ~ (all_52_6 = all_4_1) % 151.13/22.20 | | % 151.13/22.20 | | REDUCE: (17), (41) imply: % 151.13/22.20 | | (47) ~ (all_6_0 = all_4_1) % 151.13/22.20 | | % 151.13/22.20 | | REDUCE: (15), (41) imply: % 151.13/22.20 | | (48) ~ (all_4_1 = e0) % 151.13/22.20 | | % 151.13/22.20 | | REDUCE: (34), (41) imply: % 151.13/22.20 | | (49) op(all_4_1, all_4_1) = e3 % 151.13/22.20 | | % 151.13/22.20 | | REDUCE: (30), (41) imply: % 151.13/22.20 | | (50) op(e1, all_4_1) = all_56_20 % 151.13/22.20 | | % 151.13/22.20 | | BETA: splitting (4) gives: % 151.13/22.20 | | % 151.13/22.20 | | Case 1: % 151.13/22.20 | | | % 151.13/22.20 | | | (51) ~ (all_56_21 = e2) % 151.13/22.20 | | | % 151.13/22.20 | | | REDUCE: (44), (51) imply: % 151.13/22.20 | | | (52) ~ (all_4_1 = e2) % 151.13/22.20 | | | % 151.13/22.20 | | | REF_CLOSE: (9), (14), (29), (40), (43), (48), (49), (50), (52) are % 151.13/22.20 | | | inconsistent by sub-proof #439. % 151.13/22.20 | | | % 151.13/22.20 | | Case 2: % 151.13/22.20 | | | % 151.13/22.20 | | | (53) all_56_21 = e2 % 151.13/22.20 | | | (54) all_56_19 = e1 % 151.13/22.20 | | | % 151.13/22.20 | | | COMBINE_EQS: (38), (54) imply: % 151.13/22.20 | | | (55) all_52_6 = e1 % 151.13/22.20 | | | % 151.13/22.20 | | | SIMP: (55) implies: % 151.13/22.20 | | | (56) all_52_6 = e1 % 151.13/22.20 | | | % 151.13/22.20 | | | COMBINE_EQS: (44), (53) imply: % 151.13/22.20 | | | (57) all_4_1 = e2 % 151.13/22.20 | | | % 151.13/22.20 | | | SIMP: (57) implies: % 151.13/22.20 | | | (58) all_4_1 = e2 % 151.13/22.20 | | | % 151.13/22.20 | | | COMBINE_EQS: (42), (58) imply: % 151.13/22.20 | | | (59) all_36_2 = e2 % 151.13/22.20 | | | % 151.13/22.20 | | | REF_CLOSE: (1), (6), (7), (10), (11), (12), (13), (14), (16), (18), (20), % 151.13/22.20 | | | (22), (23), (25), (26), (28), (31), (32), (35), (36), (37), % 151.13/22.20 | | | (45), (46), (47), (48), (49), (53), (56), (58), (59) are % 151.13/22.20 | | | inconsistent by sub-proof #318. % 151.13/22.20 | | | % 151.13/22.20 | | End of split % 151.13/22.20 | | % 151.13/22.20 | Case 2: % 151.13/22.20 | | % 151.13/22.20 | | (60) ~ (all_34_2 = e1) % 151.13/22.20 | | % 151.13/22.20 | | REDUCE: (5), (60) imply: % 151.13/22.20 | | (61) $false % 151.13/22.20 | | % 151.13/22.20 | | CLOSE: (61) is inconsistent. % 151.13/22.20 | | % 151.13/22.20 | End of split % 151.13/22.20 | % 151.13/22.20 End of proof % 151.13/22.20 % 151.13/22.20 Sub-proof #207 shows that the following formulas are inconsistent: % 151.13/22.20 ---------------------------------------------------------------- % 151.13/22.20 (1) all_56_11 = all_8_2 % 151.13/22.20 (2) ~ (all_52_14 = all_4_2) % 151.13/22.20 (3) all_58_6 = e0 | all_58_7 = e0 | all_58_8 = e0 | all_58_11 = e0 % 151.13/22.20 (4) all_56_21 = all_6_2 % 151.13/22.20 (5) all_56_1 = all_10_2 % 151.13/22.20 (6) op(e2, all_8_2) = all_56_10 % 151.13/22.20 (7) ~ (all_52_6 = all_6_0) % 151.13/22.20 (8) ~ (e1 = e0) % 151.13/22.20 (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 151.13/22.20 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 151.13/22.20 (10) ~ (all_6_2 = e0) % 151.13/22.20 (11) ~ (all_6_0 = all_6_2) % 151.13/22.20 (12) all_54_8 = all_6_0 % 151.13/22.20 (13) all_58_8 = all_6_2 % 151.13/22.20 (14) all_56_21 = e2 % 151.13/22.20 (15) all_56_19 = e1 % 151.13/22.20 (16) ~ (all_52_14 = all_6_0) % 151.13/22.20 (17) all_56_31 = all_4_2 % 151.13/22.20 (18) all_58_11 = all_52_14 % 151.13/22.20 (19) all_56_1 = e3 | all_56_11 = e2 | all_56_21 = e1 | all_56_31 = e0 % 151.13/22.20 (20) all_58_6 = all_6_0 % 151.13/22.20 (21) ~ (all_6_0 = e0) % 151.13/22.20 (22) all_58_7 = all_52_6 % 151.13/22.20 (23) op(e2, e2) = all_8_2 % 151.13/22.20 (24) ~ (all_52_6 = all_6_2) % 151.13/22.20 (25) op(all_6_2, all_6_2) = e3 % 151.13/22.20 (26) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0 % 151.13/22.20 (27) ~ (all_10_2 = all_6_0) % 151.13/22.20 (28) op(all_8_2, all_8_2) = all_8_1 % 151.13/22.20 (29) all_56_19 = all_52_6 % 151.13/22.20 % 151.13/22.20 Begin of proof % 151.13/22.20 | % 151.13/22.20 | COMBINE_EQS: (15), (29) imply: % 151.13/22.20 | (30) all_52_6 = e1 % 151.13/22.20 | % 151.13/22.20 | SIMP: (30) implies: % 151.13/22.20 | (31) all_52_6 = e1 % 151.13/22.20 | % 151.13/22.20 | COMBINE_EQS: (4), (14) imply: % 151.13/22.20 | (32) all_6_2 = e2 % 151.13/22.20 | % 151.13/22.20 | SIMP: (32) implies: % 151.13/22.20 | (33) all_6_2 = e2 % 151.13/22.20 | % 151.13/22.20 | COMBINE_EQS: (13), (33) imply: % 151.13/22.20 | (34) all_58_8 = e2 % 151.13/22.20 | % 151.13/22.20 | COMBINE_EQS: (22), (31) imply: % 151.13/22.20 | (35) all_58_7 = e1 % 151.13/22.20 | % 151.13/22.20 | REDUCE: (7), (31) imply: % 151.13/22.20 | (36) ~ (all_6_0 = e1) % 151.13/22.20 | % 151.13/22.20 | SIMP: (36) implies: % 151.13/22.20 | (37) ~ (all_6_0 = e1) % 151.13/22.20 | % 151.13/22.20 | REDUCE: (24), (31), (33) imply: % 151.13/22.20 | (38) ~ (e2 = e1) % 151.13/22.20 | % 151.13/22.20 | SIMP: (38) implies: % 151.13/22.20 | (39) ~ (e2 = e1) % 151.13/22.20 | % 151.13/22.20 | REDUCE: (11), (33) imply: % 151.13/22.20 | (40) ~ (all_6_0 = e2) % 151.13/22.20 | % 151.13/22.20 | REDUCE: (10), (33) imply: % 151.13/22.20 | (41) ~ (e2 = e0) % 151.13/22.20 | % 151.13/22.20 | REDUCE: (25), (33) imply: % 151.13/22.20 | (42) op(e2, e2) = e3 % 151.13/22.20 | % 151.13/22.20 | REF_CLOSE: (1), (2), (3), (5), (6), (8), (9), (12), (14), (16), (17), (18), % 151.13/22.20 | (19), (20), (21), (23), (26), (27), (28), (34), (35), (37), (39), % 151.13/22.20 | (40), (41), (42) are inconsistent by sub-proof #434. % 151.13/22.20 | % 151.13/22.20 End of proof % 151.13/22.20 % 151.13/22.20 Sub-proof #208 shows that the following formulas are inconsistent: % 151.13/22.20 ---------------------------------------------------------------- % 151.13/22.20 (1) all_56_11 = all_8_2 % 151.13/22.20 (2) ~ (all_52_3 = all_6_0) % 151.13/22.20 (3) all_54_9 = all_52_6 % 151.13/22.20 (4) all_54_10 = all_6_2 % 151.13/22.20 (5) ~ (all_56_21 = e2) | all_56_19 = e1 % 151.13/22.20 (6) ~ (all_52_14 = all_4_2) % 151.13/22.20 (7) all_54_12 = all_52_3 % 151.13/22.20 (8) op(e0, e0) = all_4_2 % 151.13/22.20 (9) all_58_6 = e0 | all_58_7 = e0 | all_58_8 = e0 | all_58_11 = e0 % 151.13/22.20 (10) ~ (all_52_6 = all_52_14) % 151.13/22.20 (11) ~ (all_6_0 = e2) % 151.13/22.20 (12) all_54_15 = all_4_2 % 151.13/22.20 (13) all_56_21 = all_6_2 % 151.13/22.20 (14) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 151.13/22.20 (15) all_56_1 = all_10_2 % 151.13/22.20 (16) all_56_27 = all_52_7 % 151.13/22.20 (17) op(e2, all_8_2) = all_56_10 % 151.13/22.20 (18) op(e3, e3) = all_10_2 % 151.13/22.20 (19) ~ (all_52_6 = all_6_0) % 151.13/22.20 (20) ~ (all_56_21 = e3) | all_56_17 = e1 % 151.13/22.20 (21) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 151.13/22.20 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 151.13/22.20 (22) ~ (all_52_3 = all_10_2) % 151.13/22.20 (23) ~ (all_52_3 = all_52_7) % 151.13/22.20 (24) all_36_0 = all_6_0 % 151.13/22.20 (25) op(e0, all_4_1) = e2 % 151.13/22.20 (26) ~ (all_6_0 = all_6_2) % 151.13/22.20 (27) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0 % 151.13/22.20 (28) ~ (all_4_2 = e1) % 151.13/22.20 (29) all_54_8 = all_6_0 % 151.13/22.20 (30) all_58_8 = all_6_2 % 151.13/22.20 (31) ~ (all_52_3 = all_4_2) % 151.13/22.20 (32) ~ (all_52_14 = all_6_0) % 151.13/22.20 (33) op(all_4_2, all_4_2) = all_4_1 % 151.13/22.20 (34) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0 % 151.13/22.20 (35) ~ (all_52_6 = all_52_7) % 151.13/22.20 (36) all_56_31 = all_4_2 % 151.13/22.20 (37) all_58_11 = all_52_14 % 151.13/22.20 (38) all_36_2 = all_6_2 % 151.13/22.20 (39) all_56_1 = e3 | all_56_11 = e2 | all_56_21 = e1 | all_56_31 = e0 % 151.13/22.20 (40) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0 % 151.13/22.20 (41) all_56_23 = all_52_14 % 151.13/22.20 (42) all_58_6 = all_6_0 % 151.13/22.20 (43) op(e1, e1) = all_6_2 % 151.13/22.20 (44) ~ (all_52_6 = all_8_2) % 151.13/22.20 (45) op(e0, e3) = all_52_3 % 151.13/22.20 (46) ~ (all_4_2 = e3) % 151.13/22.20 (47) all_58_7 = all_52_6 % 151.13/22.20 (48) op(e1, all_6_2) = all_56_20 % 151.13/22.20 (49) all_56_17 = all_6_0 % 151.13/22.20 (50) ~ (all_56_31 = e2) | all_56_27 = e0 % 151.13/22.20 (51) op(e2, e2) = all_8_2 % 151.13/22.20 (52) ~ (all_36_0 = e0) | ~ (all_36_2 = e2) % 151.13/22.20 (53) ~ (all_56_21 = e0) | all_56_23 = e1 % 151.13/22.20 (54) op(e0, all_4_2) = all_56_30 % 151.13/22.20 (55) ~ (all_52_6 = all_6_2) % 151.13/22.20 (56) op(all_6_2, all_6_2) = e3 % 151.13/22.20 (57) ~ (all_52_14 = all_6_2) % 151.13/22.20 (58) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0 % 151.13/22.20 (59) ~ (all_10_2 = all_6_0) % 151.13/22.20 (60) op(all_8_2, all_8_2) = all_8_1 % 151.13/22.20 (61) all_56_19 = all_52_6 % 151.13/22.20 % 151.13/22.20 Begin of proof % 151.13/22.20 | % 151.13/22.20 | BETA: splitting (53) gives: % 151.13/22.20 | % 151.13/22.20 | Case 1: % 151.13/22.20 | | % 151.13/22.20 | | (62) ~ (all_56_21 = e0) % 151.13/22.20 | | % 151.13/22.20 | | REDUCE: (13), (62) imply: % 151.13/22.20 | | (63) ~ (all_6_2 = e0) % 151.13/22.20 | | % 151.13/22.20 | | BETA: splitting (50) gives: % 151.13/22.20 | | % 151.13/22.20 | | Case 1: % 151.13/22.20 | | | % 151.13/22.20 | | | (64) ~ (all_56_31 = e2) % 151.13/22.20 | | | % 151.13/22.20 | | | REDUCE: (36), (64) imply: % 151.13/22.20 | | | (65) ~ (all_4_2 = e2) % 151.13/22.20 | | | % 151.13/22.20 | | | BETA: splitting (40) gives: % 151.13/22.20 | | | % 151.13/22.20 | | | Case 1: % 151.13/22.20 | | | | % 151.13/22.20 | | | | (66) all_54_15 = e3 % 151.13/22.20 | | | | % 151.13/22.20 | | | | REF_CLOSE: (12), (46), (66) are inconsistent by sub-proof #740. % 151.13/22.20 | | | | % 151.13/22.20 | | | Case 2: % 151.13/22.20 | | | | % 151.13/22.20 | | | | (67) all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0 % 151.13/22.20 | | | | % 151.13/22.20 | | | | REF_CLOSE: (8), (12), (21), (25), (28), (33), (54), (65), (67) are % 151.13/22.20 | | | | inconsistent by sub-proof #230. % 151.13/22.20 | | | | % 151.13/22.20 | | | End of split % 151.13/22.20 | | | % 151.13/22.20 | | Case 2: % 151.13/22.20 | | | % 151.13/22.20 | | | (68) all_56_31 = e2 % 151.13/22.20 | | | (69) all_56_27 = e0 % 151.13/22.20 | | | % 151.13/22.20 | | | COMBINE_EQS: (16), (69) imply: % 151.13/22.20 | | | (70) all_52_7 = e0 % 151.13/22.20 | | | % 151.13/22.20 | | | SIMP: (70) implies: % 151.13/22.20 | | | (71) all_52_7 = e0 % 151.13/22.20 | | | % 151.13/22.20 | | | COMBINE_EQS: (36), (68) imply: % 151.13/22.20 | | | (72) all_4_2 = e2 % 151.13/22.20 | | | % 151.13/22.20 | | | REDUCE: (23), (71) imply: % 151.13/22.20 | | | (73) ~ (all_52_3 = e0) % 151.13/22.20 | | | % 151.13/22.20 | | | REDUCE: (31), (72) imply: % 151.13/22.20 | | | (74) ~ (all_52_3 = e2) % 151.13/22.20 | | | % 151.13/22.20 | | | REDUCE: (35), (71) imply: % 151.13/22.20 | | | (75) ~ (all_52_6 = e0) % 151.13/22.20 | | | % 151.13/22.20 | | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (9), (13), (14), (15), (17), % 151.13/22.20 | | | (18), (19), (20), (21), (22), (24), (26), (27), (29), (30), % 151.13/22.20 | | | (32), (36), (37), (38), (39), (42), (43), (45), (47), (48), % 151.13/22.20 | | | (49), (51), (52), (55), (56), (58), (59), (60), (61), (63), % 151.13/22.20 | | | (73), (74), (75) are inconsistent by sub-proof #311. % 151.13/22.20 | | | % 151.13/22.20 | | End of split % 151.13/22.20 | | % 151.13/22.20 | Case 2: % 151.13/22.20 | | % 151.13/22.20 | | (76) all_56_23 = e1 % 151.13/22.20 | | (77) all_56_21 = e0 % 151.13/22.20 | | % 151.13/22.20 | | COMBINE_EQS: (13), (77) imply: % 151.13/22.20 | | (78) all_6_2 = e0 % 151.13/22.20 | | % 151.13/22.20 | | SIMP: (78) implies: % 151.13/22.20 | | (79) all_6_2 = e0 % 151.13/22.20 | | % 151.13/22.20 | | COMBINE_EQS: (41), (76) imply: % 151.13/22.20 | | (80) all_52_14 = e1 % 151.13/22.20 | | % 151.13/22.20 | | SIMP: (80) implies: % 151.13/22.20 | | (81) all_52_14 = e1 % 151.13/22.20 | | % 151.13/22.20 | | REDUCE: (10), (81) imply: % 151.13/22.20 | | (82) ~ (all_52_6 = e1) % 151.13/22.20 | | % 151.13/22.20 | | REDUCE: (55), (79) imply: % 151.13/22.20 | | (83) ~ (all_52_6 = e0) % 151.13/22.20 | | % 151.13/22.20 | | REDUCE: (32), (81) imply: % 151.13/22.20 | | (84) ~ (all_6_0 = e1) % 151.13/22.20 | | % 151.13/22.20 | | SIMP: (84) implies: % 151.13/22.20 | | (85) ~ (all_6_0 = e1) % 151.13/22.20 | | % 151.13/22.20 | | REDUCE: (57), (79), (81) imply: % 151.13/22.20 | | (86) ~ (e1 = e0) % 151.13/22.20 | | % 151.13/22.20 | | REDUCE: (26), (79) imply: % 151.13/22.20 | | (87) ~ (all_6_0 = e0) % 151.13/22.20 | | % 151.13/22.20 | | REDUCE: (56), (79) imply: % 151.13/22.20 | | (88) op(e0, e0) = e3 % 151.13/22.20 | | % 151.13/22.20 | | REF_CLOSE: (1), (3), (8), (11), (15), (19), (21), (29), (33), (34), (36), % 151.13/22.20 | | (39), (44), (46), (54), (58), (59), (77), (82), (83), (85), (86), % 151.13/22.20 | | (87), (88) are inconsistent by sub-proof #450. % 151.13/22.20 | | % 151.13/22.20 | End of split % 151.13/22.20 | % 151.13/22.20 End of proof % 151.13/22.20 % 151.13/22.20 Sub-proof #209 shows that the following formulas are inconsistent: % 151.13/22.20 ---------------------------------------------------------------- % 151.13/22.20 (1) all_56_11 = all_8_2 % 151.13/22.20 (2) all_52_6 = e1 % 151.13/22.20 (3) ~ (all_8_1 = e1) % 151.13/22.20 (4) ~ (all_6_1 = e2) % 151.13/22.20 (5) ~ (all_8_1 = e3) % 151.13/22.20 (6) ~ (e3 = e2) % 151.13/22.20 (7) op(e0, e0) = all_4_2 % 151.13/22.20 (8) all_58_4 = all_52_8 % 151.13/22.20 (9) all_54_5 = all_8_2 % 151.13/22.20 (10) ~ (all_6_1 = e3) % 151.13/22.20 (11) ~ (all_52_6 = all_52_14) % 151.13/22.20 (12) all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1 % 151.13/22.20 (13) ~ (all_52_7 = all_8_2) % 151.13/22.20 (14) all_56_1 = all_10_2 % 151.13/22.20 (15) all_56_27 = all_52_7 % 151.13/22.20 (16) all_58_9 = all_52_12 % 151.13/22.20 (17) op(e1, e0) = all_52_14 % 151.13/22.20 (18) all_58_1 = all_52_4 % 151.13/22.20 (19) all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0 % 151.13/22.20 (20) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 151.13/22.20 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 151.13/22.20 (21) all_56_7 = all_52_12 % 151.13/22.20 (22) ~ (all_6_0 = e3) % 151.13/22.20 (23) ~ (all_56_1 = e0) | all_56_7 = e3 % 151.13/22.20 (24) op(e1, all_6_1) = all_6_0 % 151.13/22.20 (25) op(e1, all_52_8) = all_56_4 % 151.13/22.20 (26) all_58_11 = all_52_14 % 151.13/22.20 (27) op(all_6_2, all_6_2) = all_6_1 % 151.13/22.20 (28) ~ (all_52_6 = all_8_2) % 151.13/22.20 (29) all_58_15 = all_4_2 % 151.13/22.20 (30) all_6_2 = e2 % 151.13/22.20 (31) all_58_10 = all_52_13 % 151.13/22.20 (32) ~ (all_56_11 = e0) | all_56_15 = e2 % 151.13/22.20 (33) all_58_0 = all_10_2 % 151.13/22.20 (34) ~ (all_56_31 = e2) | all_56_27 = e0 % 151.13/22.20 (35) ~ (e3 = e1) % 151.13/22.20 (36) op(e2, e2) = all_8_2 % 151.13/22.20 (37) ~ (all_52_6 = all_6_2) % 151.13/22.20 (38) all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3 % 151.13/22.20 (39) ~ (all_52_4 = all_8_2) % 151.13/22.20 (40) op(all_8_2, all_8_2) = all_8_1 % 151.13/22.20 (41) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 151.13/22.20 (42) all_56_15 = all_52_13 % 151.13/22.20 % 151.13/22.20 Begin of proof % 151.13/22.20 | % 151.13/22.20 | REDUCE: (2), (11) imply: % 151.13/22.20 | (43) ~ (all_52_14 = e1) % 151.13/22.20 | % 151.13/22.20 | SIMP: (43) implies: % 151.13/22.20 | (44) ~ (all_52_14 = e1) % 151.13/22.20 | % 151.13/22.20 | REDUCE: (2), (28) imply: % 151.13/22.20 | (45) ~ (all_8_2 = e1) % 151.13/22.20 | % 151.13/22.20 | SIMP: (45) implies: % 151.13/22.20 | (46) ~ (all_8_2 = e1) % 151.13/22.20 | % 151.13/22.20 | REDUCE: (2), (30), (37) imply: % 151.13/22.20 | (47) ~ (e2 = e1) % 151.13/22.20 | % 151.13/22.20 | SIMP: (47) implies: % 151.13/22.20 | (48) ~ (e2 = e1) % 151.13/22.20 | % 151.13/22.20 | REDUCE: (27), (30) imply: % 151.13/22.20 | (49) op(e2, e2) = all_6_1 % 151.13/22.20 | % 151.13/22.20 | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (10), (12), (13), (14), % 151.13/22.20 | (15), (16), (17), (18), (19), (20), (21), (22), (23), (24), (25), % 151.13/22.20 | (26), (29), (31), (32), (33), (34), (35), (36), (38), (39), (40), % 151.13/22.20 | (41), (42), (44), (46), (48), (49) are inconsistent by sub-proof % 151.13/22.20 | #222. % 151.13/22.20 | % 151.13/22.20 End of proof % 151.13/22.20 % 151.13/22.20 Sub-proof #210 shows that the following formulas are inconsistent: % 151.13/22.20 ---------------------------------------------------------------- % 151.13/22.20 (1) ~ (all_6_2 = e3) % 151.13/22.20 (2) op(e0, e0) = all_4_2 % 151.13/22.20 (3) all_54_15 = all_4_2 % 151.13/22.20 (4) all_58_5 = all_52_9 % 151.13/22.20 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 151.13/22.20 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 151.13/22.20 (6) op(e0, all_4_1) = e2 % 151.13/22.20 (7) ~ (all_4_2 = e1) % 151.13/22.20 (8) ~ (all_52_9 = e3) % 151.13/22.20 (9) all_58_8 = all_6_2 % 151.13/22.20 (10) ~ (all_4_2 = e2) % 151.13/22.20 (11) op(all_4_2, all_4_2) = all_4_1 % 151.13/22.20 (12) ~ (all_52_11 = all_4_2) % 151.13/22.20 (13) all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3 % 151.13/22.20 (14) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0 % 151.13/22.20 (15) op(e0, all_4_2) = all_56_30 % 151.13/22.20 (16) all_58_14 = all_52_11 % 151.13/22.20 % 151.13/22.20 Begin of proof % 151.13/22.20 | % 151.13/22.20 | BETA: splitting (13) gives: % 151.13/22.20 | % 151.13/22.20 | Case 1: % 151.13/22.20 | | % 151.13/22.20 | | (17) all_58_5 = e3 % 151.13/22.20 | | % 151.13/22.20 | | COMBINE_EQS: (4), (17) imply: % 151.13/22.20 | | (18) all_52_9 = e3 % 151.13/22.20 | | % 151.13/22.20 | | REDUCE: (8), (18) imply: % 151.13/22.20 | | (19) $false % 151.13/22.20 | | % 151.13/22.20 | | CLOSE: (19) is inconsistent. % 151.13/22.20 | | % 151.13/22.20 | Case 2: % 151.13/22.20 | | % 151.13/22.20 | | (20) all_58_8 = e3 | all_58_14 = e3 % 151.13/22.20 | | % 151.13/22.20 | | BETA: splitting (20) gives: % 151.13/22.20 | | % 151.13/22.20 | | Case 1: % 151.13/22.20 | | | % 151.13/22.20 | | | (21) all_58_8 = e3 % 151.13/22.20 | | | % 151.13/22.20 | | | COMBINE_EQS: (9), (21) imply: % 151.13/22.20 | | | (22) all_6_2 = e3 % 151.13/22.20 | | | % 151.13/22.20 | | | REDUCE: (1), (22) imply: % 151.13/22.20 | | | (23) $false % 151.13/22.20 | | | % 151.13/22.20 | | | CLOSE: (23) is inconsistent. % 151.13/22.20 | | | % 151.13/22.20 | | Case 2: % 151.13/22.20 | | | % 151.13/22.20 | | | (24) all_58_14 = e3 % 151.13/22.20 | | | % 151.13/22.20 | | | COMBINE_EQS: (16), (24) imply: % 151.13/22.20 | | | (25) all_52_11 = e3 % 151.13/22.20 | | | % 151.13/22.20 | | | SIMP: (25) implies: % 151.13/22.20 | | | (26) all_52_11 = e3 % 151.13/22.20 | | | % 151.13/22.20 | | | REDUCE: (12), (26) imply: % 151.13/22.20 | | | (27) ~ (all_4_2 = e3) % 151.13/22.20 | | | % 151.13/22.20 | | | SIMP: (27) implies: % 151.13/22.20 | | | (28) ~ (all_4_2 = e3) % 151.13/22.20 | | | % 151.13/22.20 | | | REF_CLOSE: (2), (3), (5), (6), (7), (10), (11), (14), (15), (28) are % 151.13/22.20 | | | inconsistent by sub-proof #229. % 151.13/22.20 | | | % 151.13/22.20 | | End of split % 151.13/22.20 | | % 151.13/22.20 | End of split % 151.13/22.20 | % 151.13/22.20 End of proof % 151.13/22.20 % 151.13/22.20 Sub-proof #211 shows that the following formulas are inconsistent: % 151.13/22.20 ---------------------------------------------------------------- % 151.13/22.20 (1) all_54_1 = all_10_0 % 151.13/22.20 (2) all_56_1 = all_10_2 % 151.13/22.20 (3) all_38_0 = all_10_0 % 151.13/22.20 (4) ~ (all_52_8 = all_10_0) % 151.13/22.20 (5) all_56_5 = all_52_8 % 151.13/22.20 (6) all_56_1 = e1 % 151.13/22.20 (7) ~ (all_38_0 = e0) | ~ (all_38_2 = e1) % 151.13/22.20 (8) all_38_2 = all_10_2 % 151.13/22.20 (9) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0 % 151.13/22.20 (10) all_56_5 = e3 % 151.13/22.20 (11) ~ (all_10_0 = all_10_2) % 151.13/22.20 (12) ~ (all_10_0 = e2) % 151.13/22.20 % 151.13/22.20 Begin of proof % 151.13/22.20 | % 151.13/22.20 | COMBINE_EQS: (2), (6) imply: % 151.13/22.20 | (13) all_10_2 = e1 % 151.13/22.20 | % 151.13/22.20 | COMBINE_EQS: (5), (10) imply: % 151.13/22.20 | (14) all_52_8 = e3 % 151.13/22.20 | % 151.13/22.20 | COMBINE_EQS: (8), (13) imply: % 151.13/22.20 | (15) all_38_2 = e1 % 151.13/22.20 | % 151.13/22.20 | REDUCE: (4), (14) imply: % 151.13/22.20 | (16) ~ (all_10_0 = e3) % 151.13/22.20 | % 151.13/22.20 | SIMP: (16) implies: % 151.13/22.20 | (17) ~ (all_10_0 = e3) % 151.13/22.20 | % 151.13/22.20 | REDUCE: (11), (13) imply: % 151.13/22.20 | (18) ~ (all_10_0 = e1) % 151.13/22.20 | % 151.13/22.20 | BETA: splitting (9) gives: % 151.13/22.20 | % 151.13/22.20 | Case 1: % 151.13/22.20 | | % 151.13/22.20 | | (19) all_54_1 = e3 % 151.13/22.20 | | % 151.13/22.20 | | REF_CLOSE: (1), (17), (19) are inconsistent by sub-proof #493. % 151.13/22.20 | | % 151.13/22.20 | Case 2: % 151.13/22.20 | | % 151.13/22.20 | | (20) all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0 % 151.13/22.20 | | % 151.13/22.20 | | BETA: splitting (20) gives: % 151.13/22.20 | | % 151.13/22.20 | | Case 1: % 151.13/22.20 | | | % 151.13/22.20 | | | (21) all_54_1 = e2 % 151.13/22.20 | | | % 151.13/22.20 | | | REF_CLOSE: (1), (12), (21) are inconsistent by sub-proof #492. % 151.13/22.20 | | | % 151.13/22.20 | | Case 2: % 151.13/22.20 | | | % 151.13/22.20 | | | (22) all_54_1 = e1 | all_54_1 = e0 % 151.13/22.20 | | | % 151.13/22.20 | | | BETA: splitting (22) gives: % 151.13/22.20 | | | % 151.13/22.20 | | | Case 1: % 151.13/22.20 | | | | % 151.13/22.20 | | | | (23) all_54_1 = e1 % 151.13/22.20 | | | | % 151.13/22.20 | | | | REF_CLOSE: (1), (18), (23) are inconsistent by sub-proof #491. % 151.13/22.20 | | | | % 151.13/22.20 | | | Case 2: % 151.13/22.20 | | | | % 151.13/22.20 | | | | (24) all_54_1 = e0 % 151.13/22.20 | | | | % 151.13/22.20 | | | | COMBINE_EQS: (1), (24) imply: % 151.13/22.20 | | | | (25) all_10_0 = e0 % 151.13/22.20 | | | | % 151.13/22.20 | | | | SIMP: (25) implies: % 151.13/22.20 | | | | (26) all_10_0 = e0 % 151.13/22.20 | | | | % 151.13/22.20 | | | | COMBINE_EQS: (3), (26) imply: % 151.13/22.20 | | | | (27) all_38_0 = e0 % 151.13/22.20 | | | | % 151.13/22.20 | | | | REF_CLOSE: (7), (15), (27) are inconsistent by sub-proof #487. % 151.13/22.20 | | | | % 151.13/22.20 | | | End of split % 151.13/22.20 | | | % 151.13/22.20 | | End of split % 151.13/22.20 | | % 151.13/22.20 | End of split % 151.13/22.20 | % 151.13/22.20 End of proof % 151.13/22.20 % 151.13/22.20 Sub-proof #212 shows that the following formulas are inconsistent: % 151.13/22.20 ---------------------------------------------------------------- % 151.13/22.20 (1) ~ (all_52_7 = all_52_11) % 151.13/22.20 (2) all_58_6 = all_52_2 % 151.13/22.20 (3) ~ (all_52_1 = all_52_9) % 151.13/22.20 (4) ~ (e3 = e0) % 151.13/22.20 (5) ~ (all_52_9 = e2) % 151.13/22.20 (6) all_54_10 = all_6_2 % 151.13/22.20 (7) ~ (all_52_8 = e2) % 151.13/22.20 (8) all_12_2 = all_4_2 % 151.13/22.20 (9) all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2 % 151.13/22.20 (10) ~ (all_52_14 = all_4_2) % 151.13/22.20 (11) all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2 % 151.13/22.20 (12) ~ (all_52_12 = e2) % 151.13/22.20 (13) ~ (all_6_2 = e3) % 151.13/22.20 (14) ~ (e3 = e2) % 151.13/22.20 (15) op(e0, e0) = all_4_2 % 151.13/22.20 (16) all_58_6 = e0 | all_58_7 = e0 | all_58_8 = e0 | all_58_11 = e0 % 151.13/22.20 (17) all_58_4 = all_52_8 % 151.13/22.20 (18) all_54_15 = all_4_2 % 151.13/22.20 (19) all_56_21 = all_6_2 % 151.13/22.20 (20) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 151.13/22.20 (21) op(e3, e3) = e2 % 151.13/22.20 (22) all_58_5 = all_52_9 % 151.13/22.20 (23) ~ (all_52_13 = e2) % 151.13/22.20 (24) all_58_9 = all_52_12 % 151.13/22.20 (25) op(e0, all_52_14) = all_56_22 % 151.13/22.20 (26) op(e0, e2) = all_52_7 % 151.13/22.20 (27) all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2 % 151.13/22.20 (28) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 151.13/22.20 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 151.13/22.20 (29) op(e0, all_4_1) = e2 % 151.13/22.20 (30) ~ (all_52_7 = all_4_2) % 151.13/22.20 (31) ~ (all_4_2 = e1) % 151.13/22.20 (32) all_58_8 = all_6_2 % 151.13/22.20 (33) ~ (all_52_3 = all_4_2) % 151.13/22.20 (34) all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3 % 151.13/22.20 (35) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0 % 151.13/22.20 (36) ~ (all_12_1 = e1) | ~ (all_12_2 = e3) % 151.13/22.20 (37) ~ (e2 = e1) % 151.13/22.20 (38) op(all_4_2, all_4_2) = all_4_1 % 151.13/22.20 (39) all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3 % 151.13/22.20 (40) ~ (all_52_3 = all_52_11) % 151.13/22.20 (41) ~ (all_52_11 = all_4_2) % 151.13/22.20 (42) ~ (all_52_6 = all_52_7) % 151.13/22.20 (43) ~ (all_52_8 = e3) % 151.13/22.20 (44) all_58_11 = all_52_14 % 151.13/22.20 (45) ~ (all_52_2 = all_52_14) % 151.13/22.20 (46) ~ (all_52_9 = all_52_11) % 151.13/22.20 (47) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0 % 151.13/22.20 (48) all_54_13 = all_52_7 % 151.13/22.20 (49) all_56_23 = all_52_14 % 151.13/22.20 (50) all_58_15 = all_4_2 % 151.13/22.20 (51) ~ (all_52_7 = e3) % 151.13/22.20 (52) ~ (all_6_2 = e2) % 151.13/22.20 (53) all_58_2 = all_52_1 % 151.13/22.20 (54) all_58_7 = all_52_6 % 151.13/22.20 (55) all_58_10 = all_52_13 % 151.13/22.20 (56) all_12_1 = all_4_1 % 151.13/22.20 (57) op(e3, all_52_2) = all_56_16 % 151.13/22.20 (58) ~ (all_52_2 = all_6_2) % 151.13/22.20 (59) ~ (all_56_21 = e0) | all_56_23 = e1 % 151.13/22.20 (60) op(e0, all_4_2) = all_56_30 % 151.13/22.20 (61) ~ (all_52_14 = all_6_2) % 151.13/22.21 (62) ~ (e2 = e0) % 151.13/22.21 (63) all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3 % 151.13/22.21 (64) all_58_14 = all_52_11 % 151.13/22.21 (65) ~ (all_52_1 = e2) % 151.13/22.21 (66) all_58_12 = all_52_3 % 151.13/22.21 % 151.13/22.21 Begin of proof % 151.13/22.21 | % 151.13/22.21 | BETA: splitting (11) gives: % 151.13/22.21 | % 151.13/22.21 | Case 1: % 151.13/22.21 | | % 151.13/22.21 | | (67) all_58_4 = e2 % 151.13/22.21 | | % 151.13/22.21 | | COMBINE_EQS: (17), (67) imply: % 151.13/22.21 | | (68) all_52_8 = e2 % 151.13/22.21 | | % 151.13/22.21 | | REDUCE: (7), (68) imply: % 151.13/22.21 | | (69) $false % 151.13/22.21 | | % 151.13/22.21 | | CLOSE: (69) is inconsistent. % 151.13/22.21 | | % 151.13/22.21 | Case 2: % 151.13/22.21 | | % 151.13/22.21 | | (70) all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2 % 151.13/22.21 | | % 151.13/22.21 | | BETA: splitting (70) gives: % 151.13/22.21 | | % 151.13/22.21 | | Case 1: % 151.13/22.21 | | | % 151.13/22.21 | | | (71) all_58_5 = e2 % 151.13/22.21 | | | % 151.13/22.21 | | | COMBINE_EQS: (22), (71) imply: % 151.13/22.21 | | | (72) all_52_9 = e2 % 151.13/22.21 | | | % 151.13/22.21 | | | REDUCE: (5), (72) imply: % 151.13/22.21 | | | (73) $false % 151.13/22.21 | | | % 151.13/22.21 | | | CLOSE: (73) is inconsistent. % 151.13/22.21 | | | % 151.13/22.21 | | Case 2: % 151.13/22.21 | | | % 151.13/22.21 | | | (74) all_58_8 = e2 | all_58_14 = e2 % 151.13/22.21 | | | % 151.13/22.21 | | | BETA: splitting (74) gives: % 151.13/22.21 | | | % 151.13/22.21 | | | Case 1: % 151.13/22.21 | | | | % 151.13/22.21 | | | | (75) all_58_8 = e2 % 151.13/22.21 | | | | % 151.13/22.21 | | | | COMBINE_EQS: (32), (75) imply: % 151.13/22.21 | | | | (76) all_6_2 = e2 % 151.13/22.21 | | | | % 151.13/22.21 | | | | REDUCE: (52), (76) imply: % 151.13/22.21 | | | | (77) $false % 151.13/22.21 | | | | % 151.13/22.21 | | | | CLOSE: (77) is inconsistent. % 151.13/22.21 | | | | % 151.13/22.21 | | | Case 2: % 151.13/22.21 | | | | % 151.13/22.21 | | | | (78) all_58_14 = e2 % 151.13/22.21 | | | | % 151.13/22.21 | | | | COMBINE_EQS: (64), (78) imply: % 151.13/22.21 | | | | (79) all_52_11 = e2 % 151.13/22.21 | | | | % 151.13/22.21 | | | | SIMP: (79) implies: % 151.13/22.21 | | | | (80) all_52_11 = e2 % 151.13/22.21 | | | | % 151.13/22.21 | | | | REDUCE: (40), (80) imply: % 151.13/22.21 | | | | (81) ~ (all_52_3 = e2) % 151.13/22.21 | | | | % 151.13/22.21 | | | | REDUCE: (1), (80) imply: % 151.13/22.21 | | | | (82) ~ (all_52_7 = e2) % 151.13/22.21 | | | | % 151.13/22.21 | | | | REDUCE: (41), (80) imply: % 151.13/22.21 | | | | (83) ~ (all_4_2 = e2) % 151.13/22.21 | | | | % 151.13/22.21 | | | | SIMP: (83) implies: % 151.13/22.21 | | | | (84) ~ (all_4_2 = e2) % 151.13/22.21 | | | | % 151.13/22.21 | | | | BETA: splitting (39) gives: % 151.13/22.21 | | | | % 151.13/22.21 | | | | Case 1: % 151.13/22.21 | | | | | % 151.13/22.21 | | | | | (85) all_58_4 = e3 % 151.13/22.21 | | | | | % 151.13/22.21 | | | | | COMBINE_EQS: (17), (85) imply: % 151.13/22.21 | | | | | (86) all_52_8 = e3 % 151.13/22.21 | | | | | % 151.13/22.21 | | | | | REDUCE: (43), (86) imply: % 151.13/22.21 | | | | | (87) $false % 151.13/22.21 | | | | | % 151.13/22.21 | | | | | CLOSE: (87) is inconsistent. % 151.13/22.21 | | | | | % 151.13/22.21 | | | | Case 2: % 151.13/22.21 | | | | | % 151.13/22.21 | | | | | (88) all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3 % 151.13/22.21 | | | | | % 151.13/22.21 | | | | | BETA: splitting (9) gives: % 151.13/22.21 | | | | | % 151.13/22.21 | | | | | Case 1: % 151.13/22.21 | | | | | | % 151.13/22.21 | | | | | | (89) all_58_9 = e2 % 151.13/22.21 | | | | | | % 151.13/22.21 | | | | | | COMBINE_EQS: (24), (89) imply: % 151.13/22.21 | | | | | | (90) all_52_12 = e2 % 151.13/22.21 | | | | | | % 151.13/22.21 | | | | | | REDUCE: (12), (90) imply: % 151.13/22.21 | | | | | | (91) $false % 151.13/22.21 | | | | | | % 151.13/22.21 | | | | | | CLOSE: (91) is inconsistent. % 151.13/22.21 | | | | | | % 151.13/22.21 | | | | | Case 2: % 151.13/22.21 | | | | | | % 151.13/22.21 | | | | | | (92) all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2 % 151.13/22.21 | | | | | | % 151.13/22.21 | | | | | | BETA: splitting (92) gives: % 151.13/22.21 | | | | | | % 151.13/22.21 | | | | | | Case 1: % 151.13/22.21 | | | | | | | % 151.13/22.21 | | | | | | | (93) all_58_10 = e2 % 151.13/22.21 | | | | | | | % 151.13/22.21 | | | | | | | COMBINE_EQS: (55), (93) imply: % 151.13/22.21 | | | | | | | (94) all_52_13 = e2 % 151.13/22.21 | | | | | | | % 151.13/22.21 | | | | | | | REDUCE: (23), (94) imply: % 151.13/22.21 | | | | | | | (95) $false % 151.13/22.21 | | | | | | | % 151.13/22.21 | | | | | | | CLOSE: (95) is inconsistent. % 151.13/22.21 | | | | | | | % 151.13/22.21 | | | | | | Case 2: % 151.13/22.21 | | | | | | | % 151.13/22.21 | | | | | | | (96) all_58_11 = e2 | all_58_15 = e2 % 151.13/22.21 | | | | | | | % 151.13/22.21 | | | | | | | BETA: splitting (96) gives: % 151.13/22.21 | | | | | | | % 151.13/22.21 | | | | | | | Case 1: % 151.13/22.21 | | | | | | | | % 151.13/22.21 | | | | | | | | (97) all_58_11 = e2 % 151.13/22.21 | | | | | | | | % 151.13/22.21 | | | | | | | | COMBINE_EQS: (44), (97) imply: % 151.13/22.21 | | | | | | | | (98) all_52_14 = e2 % 151.13/22.21 | | | | | | | | % 151.13/22.21 | | | | | | | | COMBINE_EQS: (49), (98) imply: % 151.13/22.21 | | | | | | | | (99) all_56_23 = e2 % 151.13/22.21 | | | | | | | | % 151.13/22.21 | | | | | | | | REDUCE: (45), (98) imply: % 151.13/22.21 | | | | | | | | (100) ~ (all_52_2 = e2) % 151.13/22.21 | | | | | | | | % 151.13/22.21 | | | | | | | | REDUCE: (61), (98) imply: % 151.13/22.21 | | | | | | | | (101) ~ (all_6_2 = e2) % 151.13/22.21 | | | | | | | | % 151.13/22.21 | | | | | | | | REDUCE: (25), (98) imply: % 151.13/22.21 | | | | | | | | (102) op(e0, e2) = all_56_22 % 151.13/22.21 | | | | | | | | % 151.13/22.21 | | | | | | | | BETA: splitting (34) gives: % 151.13/22.21 | | | | | | | | % 151.13/22.21 | | | | | | | | Case 1: % 151.13/22.21 | | | | | | | | | % 151.13/22.21 | | | | | | | | | (103) all_58_6 = e3 % 151.13/22.21 | | | | | | | | | % 151.13/22.21 | | | | | | | | | COMBINE_EQS: (2), (103) imply: % 151.13/22.21 | | | | | | | | | (104) all_52_2 = e3 % 151.13/22.21 | | | | | | | | | % 151.13/22.21 | | | | | | | | | SIMP: (104) implies: % 151.13/22.21 | | | | | | | | | (105) all_52_2 = e3 % 151.13/22.21 | | | | | | | | | % 151.13/22.21 | | | | | | | | | REDUCE: (58), (105) imply: % 151.13/22.21 | | | | | | | | | (106) ~ (all_6_2 = e3) % 151.13/22.21 | | | | | | | | | % 151.13/22.21 | | | | | | | | | REDUCE: (57), (105) imply: % 151.13/22.21 | | | | | | | | | (107) op(e3, e3) = all_56_16 % 151.13/22.21 | | | | | | | | | % 151.13/22.21 | | | | | | | | | BETA: splitting (59) gives: % 151.13/22.21 | | | | | | | | | % 151.13/22.21 | | | | | | | | | Case 1: % 151.13/22.21 | | | | | | | | | | % 151.13/22.21 | | | | | | | | | | (108) ~ (all_56_21 = e0) % 151.13/22.21 | | | | | | | | | | % 151.13/22.21 | | | | | | | | | | REDUCE: (19), (108) imply: % 151.13/22.21 | | | | | | | | | | (109) ~ (all_6_2 = e0) % 151.13/22.21 | | | | | | | | | | % 151.13/22.21 | | | | | | | | | | BETA: splitting (20) gives: % 151.13/22.21 | | | | | | | | | | % 151.13/22.21 | | | | | | | | | | Case 1: % 151.13/22.21 | | | | | | | | | | | % 151.13/22.21 | | | | | | | | | | | (110) all_54_10 = e3 % 151.13/22.21 | | | | | | | | | | | % 151.13/22.21 | | | | | | | | | | | REF_CLOSE: (6), (13), (110) are inconsistent by sub-proof % 151.13/22.21 | | | | | | | | | | | #736. % 151.13/22.21 | | | | | | | | | | | % 151.13/22.21 | | | | | | | | | | Case 2: % 151.13/22.21 | | | | | | | | | | | % 151.29/22.21 | | | | | | | | | | | (111) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 151.29/22.21 | | | | | | | | | | | % 151.29/22.21 | | | | | | | | | | | BETA: splitting (111) gives: % 151.29/22.21 | | | | | | | | | | | % 151.29/22.21 | | | | | | | | | | | Case 1: % 151.29/22.21 | | | | | | | | | | | | % 151.29/22.21 | | | | | | | | | | | | (112) all_54_10 = e2 % 151.29/22.21 | | | | | | | | | | | | % 151.29/22.21 | | | | | | | | | | | | REF_CLOSE: (6), (52), (112) are inconsistent by sub-proof % 151.29/22.21 | | | | | | | | | | | | #735. % 151.29/22.21 | | | | | | | | | | | | % 151.29/22.21 | | | | | | | | | | | Case 2: % 151.29/22.21 | | | | | | | | | | | | % 151.29/22.21 | | | | | | | | | | | | (113) ~ (all_54_10 = e2) % 151.29/22.21 | | | | | | | | | | | | (114) all_54_10 = e1 | all_54_10 = e0 % 151.29/22.21 | | | | | | | | | | | | % 151.29/22.21 | | | | | | | | | | | | BETA: splitting (16) gives: % 151.29/22.21 | | | | | | | | | | | | % 151.29/22.21 | | | | | | | | | | | | Case 1: % 151.29/22.21 | | | | | | | | | | | | | % 151.29/22.21 | | | | | | | | | | | | | (115) all_58_6 = e0 % 151.29/22.21 | | | | | | | | | | | | | % 151.29/22.21 | | | | | | | | | | | | | COMBINE_EQS: (103), (115) imply: % 151.29/22.21 | | | | | | | | | | | | | (116) e3 = e0 % 151.29/22.21 | | | | | | | | | | | | | % 151.29/22.21 | | | | | | | | | | | | | REDUCE: (4), (116) imply: % 151.29/22.21 | | | | | | | | | | | | | (117) $false % 151.29/22.21 | | | | | | | | | | | | | % 151.29/22.21 | | | | | | | | | | | | | CLOSE: (117) is inconsistent. % 151.29/22.21 | | | | | | | | | | | | | % 151.29/22.21 | | | | | | | | | | | | Case 2: % 151.29/22.21 | | | | | | | | | | | | | % 151.29/22.21 | | | | | | | | | | | | | (118) all_58_7 = e0 | all_58_8 = e0 | all_58_11 = e0 % 151.29/22.21 | | | | | | | | | | | | | % 151.29/22.21 | | | | | | | | | | | | | BETA: splitting (118) gives: % 151.29/22.21 | | | | | | | | | | | | | % 151.29/22.21 | | | | | | | | | | | | | Case 1: % 151.29/22.21 | | | | | | | | | | | | | | % 151.29/22.21 | | | | | | | | | | | | | | (119) all_58_7 = e0 % 151.29/22.21 | | | | | | | | | | | | | | % 151.29/22.21 | | | | | | | | | | | | | | COMBINE_EQS: (54), (119) imply: % 151.29/22.21 | | | | | | | | | | | | | | (120) all_52_6 = e0 % 151.29/22.21 | | | | | | | | | | | | | | % 151.29/22.21 | | | | | | | | | | | | | | REDUCE: (42), (120) imply: % 151.29/22.21 | | | | | | | | | | | | | | (121) ~ (all_52_7 = e0) % 151.29/22.21 | | | | | | | | | | | | | | % 151.29/22.21 | | | | | | | | | | | | | | SIMP: (121) implies: % 151.29/22.21 | | | | | | | | | | | | | | (122) ~ (all_52_7 = e0) % 151.29/22.21 | | | | | | | | | | | | | | % 151.29/22.21 | | | | | | | | | | | | | | BETA: splitting (35) gives: % 151.29/22.21 | | | | | | | | | | | | | | % 151.29/22.21 | | | | | | | | | | | | | | Case 1: % 151.29/22.21 | | | | | | | | | | | | | | | % 151.29/22.21 | | | | | | | | | | | | | | | (123) all_54_13 = e3 % 151.29/22.21 | | | | | | | | | | | | | | | % 151.29/22.21 | | | | | | | | | | | | | | | COMBINE_EQS: (48), (123) imply: % 151.29/22.21 | | | | | | | | | | | | | | | (124) all_52_7 = e3 % 151.29/22.21 | | | | | | | | | | | | | | | % 151.29/22.21 | | | | | | | | | | | | | | | REDUCE: (51), (124) imply: % 151.29/22.21 | | | | | | | | | | | | | | | (125) $false % 151.29/22.21 | | | | | | | | | | | | | | | % 151.29/22.21 | | | | | | | | | | | | | | | CLOSE: (125) is inconsistent. % 151.29/22.21 | | | | | | | | | | | | | | | % 151.29/22.21 | | | | | | | | | | | | | | Case 2: % 151.29/22.21 | | | | | | | | | | | | | | | % 151.29/22.21 | | | | | | | | | | | | | | | (126) all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0 % 151.29/22.21 | | | | | | | | | | | | | | | % 151.29/22.21 | | | | | | | | | | | | | | | BETA: splitting (126) gives: % 151.29/22.21 | | | | | | | | | | | | | | | % 151.29/22.21 | | | | | | | | | | | | | | | Case 1: % 151.29/22.21 | | | | | | | | | | | | | | | | % 151.29/22.21 | | | | | | | | | | | | | | | | (127) all_54_13 = e2 % 151.29/22.21 | | | | | | | | | | | | | | | | % 151.29/22.21 | | | | | | | | | | | | | | | | COMBINE_EQS: (48), (127) imply: % 151.29/22.21 | | | | | | | | | | | | | | | | (128) all_52_7 = e2 % 151.29/22.21 | | | | | | | | | | | | | | | | % 151.29/22.21 | | | | | | | | | | | | | | | | REDUCE: (82), (128) imply: % 151.29/22.21 | | | | | | | | | | | | | | | | (129) $false % 151.29/22.21 | | | | | | | | | | | | | | | | % 151.29/22.21 | | | | | | | | | | | | | | | | CLOSE: (129) is inconsistent. % 151.29/22.21 | | | | | | | | | | | | | | | | % 151.29/22.21 | | | | | | | | | | | | | | | Case 2: % 151.29/22.21 | | | | | | | | | | | | | | | | % 151.29/22.21 | | | | | | | | | | | | | | | | (130) all_54_13 = e1 | all_54_13 = e0 % 151.29/22.21 | | | | | | | | | | | | | | | | % 151.29/22.21 | | | | | | | | | | | | | | | | BETA: splitting (130) gives: % 151.29/22.21 | | | | | | | | | | | | | | | | % 151.29/22.21 | | | | | | | | | | | | | | | | Case 1: % 151.29/22.21 | | | | | | | | | | | | | | | | | % 151.29/22.21 | | | | | | | | | | | | | | | | | (131) all_54_13 = e1 % 151.29/22.21 | | | | | | | | | | | | | | | | | % 151.29/22.21 | | | | | | | | | | | | | | | | | COMBINE_EQS: (48), (131) imply: % 151.29/22.21 | | | | | | | | | | | | | | | | | (132) all_52_7 = e1 % 151.29/22.21 | | | | | | | | | | | | | | | | | % 151.29/22.21 | | | | | | | | | | | | | | | | | SIMP: (132) implies: % 151.29/22.21 | | | | | | | | | | | | | | | | | (133) all_52_7 = e1 % 151.29/22.21 | | | | | | | | | | | | | | | | | % 151.29/22.21 | | | | | | | | | | | | | | | | | REDUCE: (30), (133) imply: % 151.29/22.21 | | | | | | | | | | | | | | | | | (134) ~ (all_4_2 = e1) % 151.29/22.21 | | | | | | | | | | | | | | | | | % 151.29/22.21 | | | | | | | | | | | | | | | | | REDUCE: (26), (133) imply: % 151.29/22.21 | | | | | | | | | | | | | | | | | (135) op(e0, e2) = e1 % 151.29/22.21 | | | | | | | | | | | | | | | | | % 151.29/22.21 | | | | | | | | | | | | | | | | | BETA: splitting (47) gives: % 151.29/22.21 | | | | | | | | | | | | | | | | | % 151.29/22.21 | | | | | | | | | | | | | | | | | Case 1: % 151.29/22.21 | | | | | | | | | | | | | | | | | | % 151.29/22.21 | | | | | | | | | | | | | | | | | | (136) all_54_15 = e3 % 151.29/22.21 | | | | | | | | | | | | | | | | | | % 151.29/22.21 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (18), (136) imply: % 151.29/22.21 | | | | | | | | | | | | | | | | | | (137) all_4_2 = e3 % 151.29/22.21 | | | | | | | | | | | | | | | | | | % 151.29/22.21 | | | | | | | | | | | | | | | | | | SIMP: (137) implies: % 151.29/22.21 | | | | | | | | | | | | | | | | | | (138) all_4_2 = e3 % 151.29/22.21 | | | | | | | | | | | | | | | | | | % 151.29/22.21 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (8), (138) imply: % 151.29/22.21 | | | | | | | | | | | | | | | | | | (139) all_12_2 = e3 % 151.29/22.21 | | | | | | | | | | | | | | | | | | % 151.29/22.21 | | | | | | | | | | | | | | | | | | REDUCE: (38), (138) imply: % 151.29/22.21 | | | | | | | | | | | | | | | | | | (140) op(e3, e3) = all_4_1 % 151.29/22.21 | | | | | | | | | | | | | | | | | | % 151.29/22.21 | | | | | | | | | | | | | | | | | | BETA: splitting (36) gives: % 151.29/22.21 | | | | | | | | | | | | | | | | | | % 151.29/22.21 | | | | | | | | | | | | | | | | | | Case 1: % 151.29/22.21 | | | | | | | | | | | | | | | | | | | % 151.29/22.21 | | | | | | | | | | | | | | | | | | | (141) ~ (all_12_1 = e1) % 151.29/22.21 | | | | | | | | | | | | | | | | | | | % 151.29/22.21 | | | | | | | | | | | | | | | | | | | REDUCE: (56), (141) imply: % 151.29/22.21 | | | | | | | | | | | | | | | | | | | (142) ~ (all_4_1 = e1) % 151.29/22.21 | | | | | | | | | | | | | | | | | | | % 151.29/22.21 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (28) with e1, all_56_22, e2, e0, % 151.29/22.21 | | | | | | | | | | | | | | | | | | | simplifying with (102), (135) gives: % 151.29/22.21 | | | | | | | | | | | | | | | | | | | (143) all_56_22 = e1 % 151.29/22.21 | | | | | | | | | | | | | | | | | | | % 151.29/22.21 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (28) with all_4_1, all_56_16, e3, % 151.29/22.21 | | | | | | | | | | | | | | | | | | | e3, simplifying with (107), (140) gives: % 151.29/22.21 | | | | | | | | | | | | | | | | | | | (144) all_56_16 = all_4_1 % 151.29/22.21 | | | | | | | | | | | | | | | | | | | % 151.29/22.21 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (28) with e2, all_56_16, e3, e3, % 151.29/22.21 | | | | | | | | | | | | | | | | | | | simplifying with (21), (107) gives: % 151.29/22.21 | | | | | | | | | | | | | | | | | | | (145) all_56_16 = e2 % 151.29/22.21 | | | | | | | | | | | | | | | | | | | % 151.29/22.21 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (144), (145) imply: % 151.29/22.21 | | | | | | | | | | | | | | | | | | | (146) all_4_1 = e2 % 151.29/22.21 | | | | | | | | | | | | | | | | | | | % 151.29/22.21 | | | | | | | | | | | | | | | | | | | SIMP: (146) implies: % 151.29/22.21 | | | | | | | | | | | | | | | | | | | (147) all_4_1 = e2 % 151.29/22.21 | | | | | | | | | | | | | | | | | | | % 151.29/22.21 | | | | | | | | | | | | | | | | | | | REDUCE: (29), (147) imply: % 151.29/22.21 | | | | | | | | | | | | | | | | | | | (148) op(e0, e2) = e2 % 151.29/22.21 | | | | | | | | | | | | | | | | | | | % 151.29/22.21 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (28) with e1, e2, e2, e0, % 151.29/22.21 | | | | | | | | | | | | | | | | | | | simplifying with (135), (148) gives: % 151.29/22.21 | | | | | | | | | | | | | | | | | | | (149) e2 = e1 % 151.29/22.21 | | | | | | | | | | | | | | | | | | | % 151.29/22.21 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (97), (149) imply: % 151.29/22.21 | | | | | | | | | | | | | | | | | | | (150) all_58_11 = e1 % 151.29/22.21 | | | | | | | | | | | | | | | | | | | % 151.29/22.21 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (37), (50), (84), (96), (150) are inconsistent by % 151.29/22.21 | | | | | | | | | | | | | | | | | | | sub-proof #272. % 151.29/22.21 | | | | | | | | | | | | | | | | | | | % 151.29/22.21 | | | | | | | | | | | | | | | | | | Case 2: % 151.29/22.21 | | | | | | | | | | | | | | | | | | | % 151.29/22.21 | | | | | | | | | | | | | | | | | | | (151) ~ (all_12_2 = e3) % 151.29/22.21 | | | | | | | | | | | | | | | | | | | % 151.29/22.21 | | | | | | | | | | | | | | | | | | | REDUCE: (139), (151) imply: % 151.29/22.21 | | | | | | | | | | | | | | | | | | | (152) $false % 151.29/22.21 | | | | | | | | | | | | | | | | | | | % 151.29/22.21 | | | | | | | | | | | | | | | | | | | CLOSE: (152) is inconsistent. % 151.29/22.21 | | | | | | | | | | | | | | | | | | | % 151.29/22.21 | | | | | | | | | | | | | | | | | | End of split % 151.29/22.21 | | | | | | | | | | | | | | | | | | % 151.29/22.21 | | | | | | | | | | | | | | | | | Case 2: % 151.29/22.21 | | | | | | | | | | | | | | | | | | % 151.29/22.21 | | | | | | | | | | | | | | | | | | (153) all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0 % 151.29/22.21 | | | | | | | | | | | | | | | | | | % 151.29/22.21 | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (18), (28), (29), (31), (38), (60), (84), % 151.29/22.21 | | | | | | | | | | | | | | | | | | (153) are inconsistent by sub-proof #230. % 151.29/22.21 | | | | | | | | | | | | | | | | | | % 151.29/22.21 | | | | | | | | | | | | | | | | | End of split % 151.29/22.21 | | | | | | | | | | | | | | | | | % 151.29/22.21 | | | | | | | | | | | | | | | | Case 2: % 151.29/22.21 | | | | | | | | | | | | | | | | | % 151.29/22.21 | | | | | | | | | | | | | | | | | (154) all_54_13 = e0 % 151.29/22.21 | | | | | | | | | | | | | | | | | % 151.29/22.21 | | | | | | | | | | | | | | | | | REF_CLOSE: (48), (122), (154) are inconsistent by sub-proof % 151.29/22.21 | | | | | | | | | | | | | | | | | #712. % 151.29/22.21 | | | | | | | | | | | | | | | | | % 151.29/22.21 | | | | | | | | | | | | | | | | End of split % 151.29/22.21 | | | | | | | | | | | | | | | | % 151.29/22.21 | | | | | | | | | | | | | | | End of split % 151.29/22.21 | | | | | | | | | | | | | | | % 151.29/22.21 | | | | | | | | | | | | | | End of split % 151.29/22.21 | | | | | | | | | | | | | | % 151.29/22.21 | | | | | | | | | | | | | Case 2: % 151.29/22.21 | | | | | | | | | | | | | | % 151.29/22.21 | | | | | | | | | | | | | | (155) all_58_8 = e0 | all_58_11 = e0 % 151.29/22.21 | | | | | | | | | | | | | | % 151.29/22.21 | | | | | | | | | | | | | | BETA: splitting (155) gives: % 151.29/22.21 | | | | | | | | | | | | | | % 151.29/22.21 | | | | | | | | | | | | | | Case 1: % 151.29/22.21 | | | | | | | | | | | | | | | % 151.29/22.21 | | | | | | | | | | | | | | | (156) all_58_8 = e0 % 151.29/22.21 | | | | | | | | | | | | | | | % 151.29/22.21 | | | | | | | | | | | | | | | COMBINE_EQS: (32), (156) imply: % 151.29/22.21 | | | | | | | | | | | | | | | (157) all_6_2 = e0 % 151.29/22.21 | | | | | | | | | | | | | | | % 151.29/22.21 | | | | | | | | | | | | | | | REDUCE: (109), (157) imply: % 151.29/22.21 | | | | | | | | | | | | | | | (158) $false % 151.29/22.21 | | | | | | | | | | | | | | | % 151.29/22.21 | | | | | | | | | | | | | | | CLOSE: (158) is inconsistent. % 151.29/22.21 | | | | | | | | | | | | | | | % 151.29/22.21 | | | | | | | | | | | | | | Case 2: % 151.29/22.21 | | | | | | | | | | | | | | | % 151.29/22.21 | | | | | | | | | | | | | | | (159) all_58_11 = e0 % 151.29/22.21 | | | | | | | | | | | | | | | % 151.29/22.21 | | | | | | | | | | | | | | | COMBINE_EQS: (97), (159) imply: % 151.29/22.21 | | | | | | | | | | | | | | | (160) e2 = e0 % 151.29/22.21 | | | | | | | | | | | | | | | % 151.29/22.21 | | | | | | | | | | | | | | | COMBINE_EQS: (78), (160) imply: % 151.29/22.21 | | | | | | | | | | | | | | | (161) all_58_14 = e0 % 151.29/22.21 | | | | | | | | | | | | | | | % 151.29/22.21 | | | | | | | | | | | | | | | REF_CLOSE: (6), (32), (52), (62), (74), (109), (114), (161) % 151.29/22.21 | | | | | | | | | | | | | | | are inconsistent by sub-proof #213. % 151.29/22.21 | | | | | | | | | | | | | | | % 151.29/22.21 | | | | | | | | | | | | | | End of split % 151.29/22.21 | | | | | | | | | | | | | | % 151.29/22.21 | | | | | | | | | | | | | End of split % 151.29/22.21 | | | | | | | | | | | | | % 151.29/22.21 | | | | | | | | | | | | End of split % 151.29/22.21 | | | | | | | | | | | | % 151.29/22.21 | | | | | | | | | | | End of split % 151.29/22.21 | | | | | | | | | | | % 151.29/22.21 | | | | | | | | | | End of split % 151.29/22.21 | | | | | | | | | | % 151.29/22.21 | | | | | | | | | Case 2: % 151.29/22.21 | | | | | | | | | | % 151.29/22.21 | | | | | | | | | | (162) all_56_23 = e1 % 151.29/22.21 | | | | | | | | | | % 151.29/22.21 | | | | | | | | | | COMBINE_EQS: (99), (162) imply: % 151.29/22.21 | | | | | | | | | | (163) e2 = e1 % 151.29/22.21 | | | | | | | | | | % 151.29/22.21 | | | | | | | | | | REF_CLOSE: (37), (50), (84), (96), (97), (163) are % 151.29/22.21 | | | | | | | | | | inconsistent by sub-proof #271. % 151.29/22.21 | | | | | | | | | | % 151.29/22.21 | | | | | | | | | End of split % 151.29/22.21 | | | | | | | | | % 151.29/22.21 | | | | | | | | Case 2: % 151.29/22.21 | | | | | | | | | % 151.29/22.21 | | | | | | | | | (164) ~ (all_58_6 = e3) % 151.29/22.21 | | | | | | | | | % 151.29/22.21 | | | | | | | | | REDUCE: (2), (164) imply: % 151.29/22.21 | | | | | | | | | (165) ~ (all_52_2 = e3) % 151.29/22.21 | | | | | | | | | % 151.29/22.21 | | | | | | | | | BETA: splitting (88) gives: % 151.29/22.21 | | | | | | | | | % 151.29/22.21 | | | | | | | | | Case 1: % 151.29/22.21 | | | | | | | | | | % 151.29/22.21 | | | | | | | | | | (166) all_58_5 = e3 % 151.29/22.21 | | | | | | | | | | % 151.29/22.21 | | | | | | | | | | COMBINE_EQS: (22), (166) imply: % 151.29/22.21 | | | | | | | | | | (167) all_52_9 = e3 % 151.29/22.21 | | | | | | | | | | % 151.29/22.21 | | | | | | | | | | REDUCE: (3), (167) imply: % 151.29/22.21 | | | | | | | | | | (168) ~ (all_52_1 = e3) % 151.29/22.21 | | | | | | | | | | % 151.29/22.21 | | | | | | | | | | BETA: splitting (63) gives: % 151.29/22.21 | | | | | | | | | | % 151.29/22.21 | | | | | | | | | | Case 1: % 151.29/22.21 | | | | | | | | | | | % 151.29/22.21 | | | | | | | | | | | (169) all_58_0 = e3 % 151.29/22.21 | | | | | | | | | | | % 151.29/22.21 | | | | | | | | | | | REF_CLOSE: (2), (14), (27), (53), (65), (66), (81), (100), % 151.29/22.21 | | | | | | | | | | | (169) are inconsistent by sub-proof #694. % 151.29/22.21 | | | | | | | | | | | % 151.29/22.21 | | | | | | | | | | Case 2: % 151.29/22.21 | | | | | | | | | | | % 151.29/22.21 | | | | | | | | | | | (170) all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3 % 151.29/22.21 | | | | | | | | | | | % 151.29/22.21 | | | | | | | | | | | BETA: splitting (170) gives: % 151.29/22.21 | | | | | | | | | | | % 151.29/22.21 | | | | | | | | | | | Case 1: % 151.29/22.21 | | | | | | | | | | | | % 151.29/22.21 | | | | | | | | | | | | (171) all_58_2 = e3 % 151.29/22.21 | | | | | | | | | | | | % 151.29/22.21 | | | | | | | | | | | | COMBINE_EQS: (53), (171) imply: % 151.29/22.21 | | | | | | | | | | | | (172) all_52_1 = e3 % 151.29/22.21 | | | | | | | | | | | | % 151.29/22.21 | | | | | | | | | | | | REDUCE: (168), (172) imply: % 151.29/22.21 | | | | | | | | | | | | (173) $false % 151.29/22.21 | | | | | | | | | | | | % 151.29/22.21 | | | | | | | | | | | | CLOSE: (173) is inconsistent. % 151.29/22.21 | | | | | | | | | | | | % 151.29/22.21 | | | | | | | | | | | Case 2: % 151.29/22.21 | | | | | | | | | | | | % 151.29/22.21 | | | | | | | | | | | | (174) all_58_6 = e3 | all_58_12 = e3 % 151.29/22.21 | | | | | | | | | | | | % 151.29/22.21 | | | | | | | | | | | | BETA: splitting (174) gives: % 151.29/22.21 | | | | | | | | | | | | % 151.29/22.21 | | | | | | | | | | | | Case 1: % 151.29/22.21 | | | | | | | | | | | | | % 151.29/22.21 | | | | | | | | | | | | | (175) all_58_6 = e3 % 151.29/22.21 | | | | | | | | | | | | | % 151.29/22.21 | | | | | | | | | | | | | COMBINE_EQS: (2), (175) imply: % 151.29/22.21 | | | | | | | | | | | | | (176) all_52_2 = e3 % 151.29/22.21 | | | | | | | | | | | | | % 151.29/22.21 | | | | | | | | | | | | | REDUCE: (165), (176) imply: % 151.29/22.21 | | | | | | | | | | | | | (177) $false % 151.29/22.21 | | | | | | | | | | | | | % 151.29/22.21 | | | | | | | | | | | | | CLOSE: (177) is inconsistent. % 151.29/22.21 | | | | | | | | | | | | | % 151.29/22.21 | | | | | | | | | | | | Case 2: % 151.29/22.21 | | | | | | | | | | | | | % 151.29/22.21 | | | | | | | | | | | | | (178) all_58_12 = e3 % 151.29/22.21 | | | | | | | | | | | | | % 151.29/22.21 | | | | | | | | | | | | | COMBINE_EQS: (66), (178) imply: % 151.29/22.21 | | | | | | | | | | | | | (179) all_52_3 = e3 % 151.29/22.21 | | | | | | | | | | | | | % 151.29/22.21 | | | | | | | | | | | | | REDUCE: (33), (179) imply: % 151.29/22.21 | | | | | | | | | | | | | (180) ~ (all_4_2 = e3) % 151.29/22.21 | | | | | | | | | | | | | % 151.29/22.21 | | | | | | | | | | | | | SIMP: (180) implies: % 151.29/22.21 | | | | | | | | | | | | | (181) ~ (all_4_2 = e3) % 151.29/22.21 | | | | | | | | | | | | | % 151.29/22.21 | | | | | | | | | | | | | REF_CLOSE: (15), (18), (28), (29), (31), (38), (47), (60), % 151.29/22.21 | | | | | | | | | | | | | (84), (181) are inconsistent by sub-proof #229. % 151.29/22.21 | | | | | | | | | | | | | % 151.29/22.21 | | | | | | | | | | | | End of split % 151.29/22.21 | | | | | | | | | | | | % 151.29/22.21 | | | | | | | | | | | End of split % 151.29/22.21 | | | | | | | | | | | % 151.29/22.21 | | | | | | | | | | End of split % 151.29/22.21 | | | | | | | | | | % 151.29/22.21 | | | | | | | | | Case 2: % 151.29/22.21 | | | | | | | | | | % 151.29/22.21 | | | | | | | | | | (182) all_58_8 = e3 | all_58_14 = e3 % 151.29/22.21 | | | | | | | | | | % 151.29/22.21 | | | | | | | | | | REF_CLOSE: (13), (14), (32), (78), (182) are inconsistent by % 151.29/22.21 | | | | | | | | | | sub-proof #591. % 151.29/22.21 | | | | | | | | | | % 151.29/22.21 | | | | | | | | | End of split % 151.29/22.21 | | | | | | | | | % 151.29/22.21 | | | | | | | | End of split % 151.29/22.21 | | | | | | | | % 151.29/22.21 | | | | | | | Case 2: % 151.29/22.21 | | | | | | | | % 151.29/22.21 | | | | | | | | (183) all_58_15 = e2 % 151.29/22.21 | | | | | | | | % 151.29/22.21 | | | | | | | | COMBINE_EQS: (50), (183) imply: % 151.29/22.21 | | | | | | | | (184) all_4_2 = e2 % 151.29/22.21 | | | | | | | | % 151.29/22.21 | | | | | | | | REDUCE: (84), (184) imply: % 151.29/22.21 | | | | | | | | (185) $false % 151.29/22.21 | | | | | | | | % 151.29/22.21 | | | | | | | | CLOSE: (185) is inconsistent. % 151.29/22.21 | | | | | | | | % 151.29/22.21 | | | | | | | End of split % 151.29/22.21 | | | | | | | % 151.29/22.21 | | | | | | End of split % 151.29/22.21 | | | | | | % 151.29/22.21 | | | | | End of split % 151.29/22.21 | | | | | % 151.29/22.21 | | | | End of split % 151.29/22.21 | | | | % 151.29/22.21 | | | End of split % 151.29/22.21 | | | % 151.29/22.21 | | End of split % 151.29/22.21 | | % 151.29/22.21 | End of split % 151.29/22.21 | % 151.29/22.21 End of proof % 151.29/22.21 % 151.29/22.21 Sub-proof #213 shows that the following formulas are inconsistent: % 151.29/22.21 ---------------------------------------------------------------- % 151.29/22.21 (1) all_54_10 = all_6_2 % 151.29/22.21 (2) all_58_8 = e2 | all_58_14 = e2 % 151.29/22.21 (3) ~ (all_6_2 = e0) % 151.29/22.21 (4) all_58_8 = all_6_2 % 151.29/22.21 (5) all_58_14 = e0 % 151.29/22.21 (6) ~ (all_6_2 = e2) % 151.29/22.21 (7) all_54_10 = e1 | all_54_10 = e0 % 151.29/22.21 (8) ~ (e2 = e0) % 151.29/22.21 % 151.29/22.21 Begin of proof % 151.29/22.21 | % 151.29/22.21 | BETA: splitting (7) gives: % 151.29/22.21 | % 151.29/22.21 | Case 1: % 151.29/22.21 | | % 151.29/22.21 | | (9) all_54_10 = e1 % 151.29/22.21 | | % 151.29/22.21 | | COMBINE_EQS: (1), (9) imply: % 151.29/22.21 | | (10) all_6_2 = e1 % 151.29/22.21 | | % 151.29/22.21 | | SIMP: (10) implies: % 151.29/22.21 | | (11) all_6_2 = e1 % 151.29/22.21 | | % 151.29/22.21 | | COMBINE_EQS: (4), (11) imply: % 151.29/22.21 | | (12) all_58_8 = e1 % 151.29/22.21 | | % 151.29/22.21 | | REDUCE: (6), (11) imply: % 151.29/22.21 | | (13) ~ (e2 = e1) % 151.29/22.21 | | % 151.29/22.21 | | SIMP: (13) implies: % 151.29/22.21 | | (14) ~ (e2 = e1) % 151.29/22.21 | | % 151.29/22.21 | | REF_CLOSE: (2), (5), (8), (12), (14) are inconsistent by sub-proof #214. % 151.29/22.21 | | % 151.29/22.21 | Case 2: % 151.29/22.21 | | % 151.29/22.21 | | (15) all_54_10 = e0 % 151.29/22.21 | | % 151.29/22.21 | | REF_CLOSE: (1), (3), (15) are inconsistent by sub-proof #705. % 151.29/22.21 | | % 151.29/22.21 | End of split % 151.29/22.21 | % 151.29/22.21 End of proof % 151.29/22.21 % 151.29/22.21 Sub-proof #214 shows that the following formulas are inconsistent: % 151.29/22.21 ---------------------------------------------------------------- % 151.29/22.21 (1) all_58_8 = e1 % 151.29/22.21 (2) all_58_8 = e2 | all_58_14 = e2 % 151.29/22.21 (3) ~ (e2 = e1) % 151.29/22.21 (4) all_58_14 = e0 % 151.29/22.21 (5) ~ (e2 = e0) % 151.29/22.21 % 151.29/22.21 Begin of proof % 151.29/22.21 | % 151.29/22.21 | BETA: splitting (2) gives: % 151.29/22.21 | % 151.29/22.21 | Case 1: % 151.29/22.21 | | % 151.29/22.21 | | (6) all_58_8 = e2 % 151.29/22.21 | | % 151.29/22.21 | | COMBINE_EQS: (1), (6) imply: % 151.29/22.21 | | (7) e2 = e1 % 151.29/22.21 | | % 151.29/22.21 | | SIMP: (7) implies: % 151.29/22.21 | | (8) e2 = e1 % 151.29/22.21 | | % 151.29/22.21 | | REDUCE: (3), (8) imply: % 151.29/22.21 | | (9) $false % 151.29/22.21 | | % 151.29/22.21 | | CLOSE: (9) is inconsistent. % 151.29/22.21 | | % 151.29/22.21 | Case 2: % 151.29/22.21 | | % 151.29/22.21 | | (10) all_58_14 = e2 % 151.29/22.21 | | % 151.29/22.21 | | COMBINE_EQS: (4), (10) imply: % 151.29/22.21 | | (11) e2 = e0 % 151.29/22.21 | | % 151.29/22.21 | | REDUCE: (5), (11) imply: % 151.29/22.21 | | (12) $false % 151.29/22.21 | | % 151.29/22.21 | | CLOSE: (12) is inconsistent. % 151.29/22.21 | | % 151.29/22.21 | End of split % 151.29/22.21 | % 151.29/22.21 End of proof % 151.29/22.21 % 151.29/22.21 Sub-proof #215 shows that the following formulas are inconsistent: % 151.29/22.21 ---------------------------------------------------------------- % 151.29/22.21 (1) op(e0, all_52_13) = all_56_14 % 151.29/22.21 (2) all_58_6 = all_52_2 % 151.29/22.21 (3) all_54_0 = all_10_2 % 151.29/22.21 (4) all_54_4 = all_52_1 % 151.29/22.21 (5) ~ (all_6_2 = e3) % 151.29/22.21 (6) all_58_6 = e0 | all_58_7 = e0 | all_58_8 = e0 | all_58_11 = e0 % 151.29/22.21 (7) ~ (all_10_2 = e1) % 151.29/22.21 (8) ~ (all_6_1 = e3) % 151.29/22.21 (9) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 151.29/22.21 (10) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0 % 151.29/22.21 (11) all_58_5 = all_52_9 % 151.29/22.21 (12) ~ (all_52_13 = e2) % 151.29/22.21 (13) ~ (all_10_2 = e2) % 151.29/22.21 (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 151.29/22.21 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 151.29/22.21 (15) all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0 % 151.29/22.21 (16) ~ (all_52_2 = all_52_6) % 151.29/22.21 (17) ~ (all_52_2 = e0) % 151.29/22.21 (18) ~ (all_52_1 = all_52_13) % 151.29/22.21 (19) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0 % 151.29/22.21 (20) ~ (all_52_14 = e3) % 151.29/22.21 (21) all_58_8 = all_6_2 % 151.29/22.21 (22) all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3 % 151.29/22.21 (23) ~ (all_52_9 = all_52_13) % 151.29/22.21 (24) ~ (all_52_1 = e0) % 151.29/22.21 (25) all_58_3 = all_8_2 % 151.29/22.21 (26) all_58_11 = all_52_14 % 151.29/22.21 (27) op(e0, e0) = e3 % 151.29/22.21 (28) all_54_7 = all_52_13 % 151.29/22.21 (29) op(all_6_2, all_6_2) = all_6_1 % 151.29/22.21 (30) ~ (all_52_13 = all_52_14) % 151.29/22.21 (31) all_54_8 = all_52_2 % 151.29/22.21 (32) ~ (all_10_2 = e0) % 151.29/22.21 (33) ~ (all_52_13 = e3) % 151.29/22.21 (34) all_58_2 = all_52_1 % 151.29/22.21 (35) all_58_7 = all_52_6 % 151.29/22.21 (36) all_58_10 = all_52_13 % 151.29/22.21 (37) ~ (all_52_1 = all_52_2) % 151.29/22.21 (38) ~ (all_8_2 = e0) % 151.29/22.21 (39) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0 % 151.29/22.21 (40) ~ (all_52_2 = all_10_2) % 151.29/22.21 (41) ~ (all_52_1 = e2) % 151.29/22.21 (42) ~ (all_52_1 = all_10_2) % 151.29/22.21 % 151.29/22.21 Begin of proof % 151.29/22.21 | % 151.29/22.21 | BETA: splitting (9) gives: % 151.29/22.21 | % 151.29/22.21 | Case 1: % 151.29/22.21 | | % 151.29/22.21 | | (43) all_54_0 = e3 % 151.29/22.21 | | % 151.29/22.21 | | COMBINE_EQS: (3), (43) imply: % 151.29/22.21 | | (44) all_10_2 = e3 % 151.29/22.21 | | % 151.29/22.21 | | SIMP: (44) implies: % 151.29/22.21 | | (45) all_10_2 = e3 % 151.29/22.21 | | % 151.29/22.21 | | REDUCE: (42), (45) imply: % 151.29/22.21 | | (46) ~ (all_52_1 = e3) % 151.29/22.21 | | % 151.29/22.21 | | REDUCE: (40), (45) imply: % 151.29/22.21 | | (47) ~ (all_52_2 = e3) % 151.29/22.21 | | % 151.29/22.21 | | BETA: splitting (19) gives: % 151.29/22.21 | | % 151.29/22.21 | | Case 1: % 151.29/22.21 | | | % 151.29/22.21 | | | (48) all_54_4 = e3 % 151.29/22.21 | | | % 151.29/22.21 | | | REF_CLOSE: (4), (46), (48) are inconsistent by sub-proof #634. % 151.29/22.21 | | | % 151.29/22.21 | | Case 2: % 151.29/22.21 | | | % 151.29/22.21 | | | (49) all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0 % 151.29/22.21 | | | % 151.29/22.21 | | | BETA: splitting (49) gives: % 151.29/22.21 | | | % 151.29/22.21 | | | Case 1: % 151.29/22.21 | | | | % 151.29/22.21 | | | | (50) all_54_4 = e2 % 151.29/22.21 | | | | % 151.29/22.21 | | | | REF_CLOSE: (4), (41), (50) are inconsistent by sub-proof #633. % 151.29/22.21 | | | | % 151.29/22.21 | | | Case 2: % 151.29/22.21 | | | | % 151.29/22.21 | | | | (51) all_54_4 = e1 | all_54_4 = e0 % 151.29/22.21 | | | | % 151.29/22.21 | | | | BETA: splitting (51) gives: % 151.29/22.21 | | | | % 151.29/22.21 | | | | Case 1: % 151.29/22.21 | | | | | % 151.29/22.21 | | | | | (52) all_54_4 = e1 % 151.29/22.21 | | | | | % 151.29/22.21 | | | | | COMBINE_EQS: (4), (52) imply: % 151.29/22.21 | | | | | (53) all_52_1 = e1 % 151.29/22.21 | | | | | % 151.29/22.21 | | | | | SIMP: (53) implies: % 151.29/22.21 | | | | | (54) all_52_1 = e1 % 151.29/22.21 | | | | | % 151.29/22.21 | | | | | REDUCE: (37), (54) imply: % 151.29/22.21 | | | | | (55) ~ (all_52_2 = e1) % 151.29/22.21 | | | | | % 151.29/22.21 | | | | | SIMP: (55) implies: % 151.29/22.21 | | | | | (56) ~ (all_52_2 = e1) % 151.29/22.21 | | | | | % 151.29/22.21 | | | | | REDUCE: (18), (54) imply: % 151.29/22.21 | | | | | (57) ~ (all_52_13 = e1) % 151.29/22.21 | | | | | % 151.29/22.21 | | | | | SIMP: (57) implies: % 151.29/22.21 | | | | | (58) ~ (all_52_13 = e1) % 151.29/22.21 | | | | | % 151.29/22.21 | | | | | BETA: splitting (22) gives: % 151.29/22.21 | | | | | % 151.29/22.21 | | | | | Case 1: % 151.29/22.21 | | | | | | % 151.29/22.21 | | | | | | (59) all_58_6 = e3 % 151.29/22.21 | | | | | | % 151.29/22.21 | | | | | | REF_CLOSE: (2), (47), (59) are inconsistent by sub-proof #346. % 151.29/22.21 | | | | | | % 151.29/22.21 | | | | | Case 2: % 151.29/22.21 | | | | | | % 151.29/22.21 | | | | | | (60) all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3 % 151.29/22.21 | | | | | | % 151.29/22.21 | | | | | | BETA: splitting (60) gives: % 151.29/22.21 | | | | | | % 151.29/22.21 | | | | | | Case 1: % 151.29/22.21 | | | | | | | % 151.29/22.21 | | | | | | | (61) all_58_7 = e3 % 151.29/22.21 | | | | | | | % 151.29/22.21 | | | | | | | COMBINE_EQS: (35), (61) imply: % 151.29/22.21 | | | | | | | (62) all_52_6 = e3 % 151.29/22.21 | | | | | | | % 151.29/22.21 | | | | | | | REF_CLOSE: (1), (2), (6), (8), (10), (11), (12), (14), (15), (17), % 151.29/22.21 | | | | | | | (21), (23), (24), (25), (26), (27), (28), (29), (30), % 151.29/22.21 | | | | | | | (31), (33), (34), (36), (38), (39), (47), (56), (58), % 151.29/22.21 | | | | | | | (61) are inconsistent by sub-proof #216. % 151.29/22.21 | | | | | | | % 151.29/22.21 | | | | | | Case 2: % 151.29/22.21 | | | | | | | % 151.29/22.21 | | | | | | | (63) all_58_8 = e3 | all_58_11 = e3 % 151.29/22.21 | | | | | | | % 151.29/22.21 | | | | | | | REF_CLOSE: (5), (20), (21), (26), (63) are inconsistent by % 151.29/22.21 | | | | | | | sub-proof #636. % 151.29/22.21 | | | | | | | % 151.29/22.21 | | | | | | End of split % 151.29/22.21 | | | | | | % 151.29/22.21 | | | | | End of split % 151.29/22.21 | | | | | % 151.29/22.21 | | | | Case 2: % 151.29/22.21 | | | | | % 151.29/22.21 | | | | | (64) all_54_4 = e0 % 151.29/22.21 | | | | | % 151.29/22.21 | | | | | REF_CLOSE: (4), (24), (64) are inconsistent by sub-proof #614. % 151.29/22.21 | | | | | % 151.29/22.21 | | | | End of split % 151.29/22.21 | | | | % 151.29/22.21 | | | End of split % 151.29/22.21 | | | % 151.29/22.21 | | End of split % 151.29/22.21 | | % 151.29/22.21 | Case 2: % 151.29/22.21 | | % 151.29/22.21 | | (65) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 151.29/22.21 | | % 151.29/22.21 | | REF_CLOSE: (3), (7), (13), (32), (65) are inconsistent by sub-proof #731. % 151.29/22.21 | | % 151.29/22.21 | End of split % 151.29/22.21 | % 151.29/22.21 End of proof % 151.29/22.21 % 151.29/22.21 Sub-proof #216 shows that the following formulas are inconsistent: % 151.29/22.21 ---------------------------------------------------------------- % 151.29/22.21 (1) op(e0, all_52_13) = all_56_14 % 151.29/22.21 (2) ~ (all_52_2 = e3) % 151.29/22.21 (3) all_58_6 = all_52_2 % 151.29/22.21 (4) ~ (all_52_13 = e1) % 151.29/22.21 (5) all_58_6 = e0 | all_58_7 = e0 | all_58_8 = e0 | all_58_11 = e0 % 151.29/22.21 (6) ~ (all_6_1 = e3) % 151.29/22.21 (7) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0 % 151.29/22.21 (8) all_58_5 = all_52_9 % 151.29/22.21 (9) ~ (all_52_13 = e2) % 151.29/22.21 (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 151.29/22.21 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 151.29/22.21 (11) all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0 % 151.29/22.21 (12) ~ (all_52_2 = e0) % 151.29/22.21 (13) all_58_8 = all_6_2 % 151.29/22.21 (14) ~ (all_52_2 = e1) % 151.29/22.21 (15) ~ (all_52_9 = all_52_13) % 151.29/22.21 (16) ~ (all_52_1 = e0) % 151.29/22.21 (17) all_58_3 = all_8_2 % 151.29/22.21 (18) all_58_11 = all_52_14 % 151.29/22.21 (19) op(e0, e0) = e3 % 151.29/22.21 (20) all_54_7 = all_52_13 % 151.29/22.21 (21) op(all_6_2, all_6_2) = all_6_1 % 151.29/22.21 (22) ~ (all_52_13 = all_52_14) % 151.29/22.21 (23) all_54_8 = all_52_2 % 151.29/22.21 (24) ~ (all_52_13 = e3) % 151.29/22.21 (25) all_58_2 = all_52_1 % 151.29/22.21 (26) all_58_10 = all_52_13 % 151.29/22.21 (27) all_58_7 = e3 % 151.29/22.21 (28) ~ (all_8_2 = e0) % 151.29/22.21 (29) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0 % 151.29/22.21 % 151.29/22.21 Begin of proof % 151.29/22.21 | % 151.29/22.21 | BETA: splitting (29) gives: % 151.29/22.21 | % 151.29/22.21 | Case 1: % 151.29/22.21 | | % 151.29/22.21 | | (30) all_54_8 = e3 % 151.29/22.21 | | % 151.29/22.21 | | REF_CLOSE: (2), (23), (30) are inconsistent by sub-proof #345. % 151.29/22.21 | | % 151.29/22.21 | Case 2: % 151.29/22.21 | | % 151.29/22.21 | | (31) all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0 % 151.29/22.21 | | % 151.29/22.21 | | BETA: splitting (7) gives: % 151.29/22.21 | | % 151.29/22.21 | | Case 1: % 151.29/22.21 | | | % 151.29/22.21 | | | (32) all_54_7 = e3 % 151.29/22.21 | | | % 151.29/22.21 | | | REF_CLOSE: (20), (24), (32) are inconsistent by sub-proof #601. % 151.29/22.21 | | | % 151.29/22.21 | | Case 2: % 151.29/22.21 | | | % 151.29/22.21 | | | (33) ~ (all_54_7 = e3) % 151.29/22.21 | | | (34) all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0 % 151.29/22.21 | | | % 151.29/22.21 | | | BETA: splitting (34) gives: % 151.29/22.21 | | | % 151.29/22.21 | | | Case 1: % 151.29/22.21 | | | | % 151.29/22.21 | | | | (35) all_54_7 = e2 % 151.29/22.21 | | | | % 151.29/22.21 | | | | REF_CLOSE: (9), (20), (35) are inconsistent by sub-proof #652. % 151.29/22.21 | | | | % 151.29/22.21 | | | Case 2: % 151.29/22.21 | | | | % 151.29/22.22 | | | | (36) ~ (all_54_7 = e2) % 151.29/22.22 | | | | (37) all_54_7 = e1 | all_54_7 = e0 % 151.29/22.22 | | | | % 151.29/22.22 | | | | BETA: splitting (31) gives: % 151.29/22.22 | | | | % 151.29/22.22 | | | | Case 1: % 151.29/22.22 | | | | | % 151.29/22.22 | | | | | (38) all_54_8 = e2 % 151.29/22.22 | | | | | % 151.29/22.22 | | | | | COMBINE_EQS: (23), (38) imply: % 151.29/22.22 | | | | | (39) all_52_2 = e2 % 151.29/22.22 | | | | | % 151.29/22.22 | | | | | SIMP: (39) implies: % 151.29/22.22 | | | | | (40) all_52_2 = e2 % 151.29/22.22 | | | | | % 151.29/22.22 | | | | | COMBINE_EQS: (3), (40) imply: % 151.29/22.22 | | | | | (41) all_58_6 = e2 % 151.29/22.22 | | | | | % 151.29/22.22 | | | | | BETA: splitting (37) gives: % 151.29/22.22 | | | | | % 151.29/22.22 | | | | | Case 1: % 151.29/22.22 | | | | | | % 151.29/22.22 | | | | | | (42) all_54_7 = e1 % 151.29/22.22 | | | | | | % 151.29/22.22 | | | | | | REF_CLOSE: (4), (20), (42) are inconsistent by sub-proof #651. % 151.29/22.22 | | | | | | % 151.29/22.22 | | | | | Case 2: % 151.29/22.22 | | | | | | % 151.29/22.22 | | | | | | (43) all_54_7 = e0 % 151.29/22.22 | | | | | | % 151.29/22.22 | | | | | | COMBINE_EQS: (20), (43) imply: % 151.29/22.22 | | | | | | (44) all_52_13 = e0 % 151.29/22.22 | | | | | | % 151.29/22.22 | | | | | | SIMP: (44) implies: % 151.29/22.22 | | | | | | (45) all_52_13 = e0 % 151.29/22.22 | | | | | | % 151.29/22.22 | | | | | | REDUCE: (15), (45) imply: % 151.29/22.22 | | | | | | (46) ~ (all_52_9 = e0) % 151.29/22.22 | | | | | | % 151.29/22.22 | | | | | | REDUCE: (22), (45) imply: % 151.29/22.22 | | | | | | (47) ~ (all_52_14 = e0) % 151.29/22.22 | | | | | | % 151.29/22.22 | | | | | | SIMP: (47) implies: % 151.29/22.22 | | | | | | (48) ~ (all_52_14 = e0) % 151.29/22.22 | | | | | | % 151.29/22.22 | | | | | | REDUCE: (24), (45) imply: % 151.29/22.22 | | | | | | (49) ~ (e3 = e0) % 151.29/22.22 | | | | | | % 151.29/22.22 | | | | | | SIMP: (49) implies: % 151.29/22.22 | | | | | | (50) ~ (e3 = e0) % 151.29/22.22 | | | | | | % 151.29/22.22 | | | | | | REDUCE: (9), (45) imply: % 151.29/22.22 | | | | | | (51) ~ (e2 = e0) % 151.29/22.22 | | | | | | % 151.29/22.22 | | | | | | SIMP: (51) implies: % 151.29/22.22 | | | | | | (52) ~ (e2 = e0) % 151.29/22.22 | | | | | | % 151.29/22.22 | | | | | | BETA: splitting (5) gives: % 151.29/22.22 | | | | | | % 151.29/22.22 | | | | | | Case 1: % 151.29/22.22 | | | | | | | % 151.29/22.22 | | | | | | | (53) all_58_6 = e0 % 151.29/22.22 | | | | | | | % 151.29/22.22 | | | | | | | COMBINE_EQS: (41), (53) imply: % 151.29/22.22 | | | | | | | (54) e2 = e0 % 151.29/22.22 | | | | | | | % 151.29/22.22 | | | | | | | REDUCE: (52), (54) imply: % 151.29/22.22 | | | | | | | (55) $false % 151.29/22.22 | | | | | | | % 151.29/22.22 | | | | | | | CLOSE: (55) is inconsistent. % 151.29/22.22 | | | | | | | % 151.29/22.22 | | | | | | Case 2: % 151.29/22.22 | | | | | | | % 151.29/22.22 | | | | | | | (56) all_58_7 = e0 | all_58_8 = e0 | all_58_11 = e0 % 151.29/22.22 | | | | | | | % 151.29/22.22 | | | | | | | BETA: splitting (56) gives: % 151.29/22.22 | | | | | | | % 151.29/22.22 | | | | | | | Case 1: % 151.29/22.22 | | | | | | | | % 151.29/22.22 | | | | | | | | (57) all_58_7 = e0 % 151.29/22.22 | | | | | | | | % 151.29/22.22 | | | | | | | | COMBINE_EQS: (27), (57) imply: % 151.29/22.22 | | | | | | | | (58) e3 = e0 % 151.29/22.22 | | | | | | | | % 151.29/22.22 | | | | | | | | REDUCE: (50), (58) imply: % 151.29/22.22 | | | | | | | | (59) $false % 151.29/22.22 | | | | | | | | % 151.29/22.22 | | | | | | | | CLOSE: (59) is inconsistent. % 151.29/22.22 | | | | | | | | % 151.29/22.22 | | | | | | | Case 2: % 151.29/22.22 | | | | | | | | % 151.29/22.22 | | | | | | | | (60) all_58_8 = e0 | all_58_11 = e0 % 151.29/22.22 | | | | | | | | % 151.29/22.22 | | | | | | | | BETA: splitting (60) gives: % 151.29/22.22 | | | | | | | | % 151.29/22.22 | | | | | | | | Case 1: % 151.29/22.22 | | | | | | | | | % 151.29/22.22 | | | | | | | | | (61) all_58_8 = e0 % 151.29/22.22 | | | | | | | | | % 151.29/22.22 | | | | | | | | | COMBINE_EQS: (13), (61) imply: % 151.29/22.22 | | | | | | | | | (62) all_6_2 = e0 % 151.29/22.22 | | | | | | | | | % 151.29/22.22 | | | | | | | | | REF_CLOSE: (1), (6), (8), (10), (11), (16), (17), (19), (21), % 151.29/22.22 | | | | | | | | | (25), (26), (28), (46), (62) are inconsistent by % 151.29/22.22 | | | | | | | | | sub-proof #220. % 151.29/22.22 | | | | | | | | | % 151.29/22.22 | | | | | | | | Case 2: % 151.29/22.22 | | | | | | | | | % 151.29/22.22 | | | | | | | | | (63) all_58_11 = e0 % 151.29/22.22 | | | | | | | | | % 151.29/22.22 | | | | | | | | | COMBINE_EQS: (18), (63) imply: % 151.29/22.22 | | | | | | | | | (64) all_52_14 = e0 % 151.29/22.22 | | | | | | | | | % 151.29/22.22 | | | | | | | | | REDUCE: (48), (64) imply: % 151.29/22.22 | | | | | | | | | (65) $false % 151.29/22.22 | | | | | | | | | % 151.29/22.22 | | | | | | | | | CLOSE: (65) is inconsistent. % 151.29/22.22 | | | | | | | | | % 151.29/22.22 | | | | | | | | End of split % 151.29/22.22 | | | | | | | | % 151.29/22.22 | | | | | | | End of split % 151.29/22.22 | | | | | | | % 151.29/22.22 | | | | | | End of split % 151.29/22.22 | | | | | | % 151.29/22.22 | | | | | End of split % 151.29/22.22 | | | | | % 151.29/22.22 | | | | Case 2: % 151.29/22.22 | | | | | % 151.29/22.22 | | | | | (66) all_54_8 = e1 | all_54_8 = e0 % 151.29/22.22 | | | | | % 151.29/22.22 | | | | | REF_CLOSE: (12), (14), (23), (66) are inconsistent by sub-proof #664. % 151.29/22.22 | | | | | % 151.29/22.22 | | | | End of split % 151.29/22.22 | | | | % 151.29/22.22 | | | End of split % 151.29/22.22 | | | % 151.29/22.22 | | End of split % 151.29/22.22 | | % 151.29/22.22 | End of split % 151.29/22.22 | % 151.29/22.22 End of proof % 151.29/22.22 % 151.29/22.22 Sub-proof #217 shows that the following formulas are inconsistent: % 151.29/22.22 ---------------------------------------------------------------- % 151.29/22.22 (1) all_56_11 = all_8_2 % 151.29/22.22 (2) op(e0, all_52_13) = all_56_14 % 151.29/22.22 (3) ~ (all_52_11 = all_6_2) % 151.29/22.22 (4) all_56_25 = all_52_3 % 151.29/22.22 (5) ~ (all_34_1 = e3) | ~ (all_34_2 = e1) % 151.29/22.22 (6) ~ (all_52_7 = all_52_11) % 151.29/22.22 (7) all_54_9 = all_52_6 % 151.29/22.22 (8) all_58_6 = all_52_2 % 151.29/22.22 (9) ~ (all_56_31 = e1) | all_56_29 = e0 % 151.29/22.22 (10) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0 % 151.29/22.22 (11) op(e1, all_6_1) = e3 % 151.29/22.22 (12) all_54_10 = all_6_2 % 151.29/22.22 (13) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0 % 151.29/22.22 (14) ~ (all_6_1 = e2) % 151.29/22.22 (15) ~ (all_56_21 = e2) | all_56_19 = e1 % 151.29/22.22 (16) all_40_2 = all_6_2 % 151.29/22.22 (17) all_54_0 = all_10_2 % 151.29/22.22 (18) ~ (all_52_14 = all_4_2) % 151.29/22.22 (19) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0 % 151.29/22.22 (20) ~ (all_52_9 = all_8_2) % 151.29/22.22 (21) ~ (all_52_12 = all_52_13) % 151.29/22.22 (22) ~ (all_52_4 = all_52_7) % 151.29/22.22 (23) ~ (all_8_1 = e3) % 151.29/22.22 (24) op(e0, e0) = all_4_2 % 151.29/22.22 (25) all_58_6 = e0 | all_58_7 = e0 | all_58_8 = e0 | all_58_11 = e0 % 151.29/22.22 (26) all_58_4 = all_52_8 % 151.29/22.22 (27) all_54_5 = all_8_2 % 151.29/22.22 (28) ~ (all_6_1 = e3) % 151.29/22.22 (29) ~ (all_52_6 = all_52_14) % 151.29/22.22 (30) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 151.29/22.22 (31) ~ (all_6_0 = e2) % 151.29/22.22 (32) all_54_15 = all_4_2 % 151.29/22.22 (33) all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1 % 151.29/22.22 (34) ~ (all_10_1 = e1) % 151.29/22.22 (35) all_56_21 = all_6_2 % 151.29/22.22 (36) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 151.29/22.22 (37) all_56_1 = all_10_2 % 151.29/22.22 (38) all_58_5 = all_52_9 % 151.29/22.22 (39) all_54_1 = all_52_4 % 151.29/22.22 (40) all_56_17 = all_52_2 % 151.29/22.22 (41) all_58_9 = all_52_12 % 151.29/22.22 (42) op(e1, e0) = all_52_14 % 151.29/22.22 (43) all_54_14 = all_52_11 % 151.29/22.22 (44) all_58_4 = e0 | all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0 % 151.29/22.22 (45) op(e3, e3) = all_10_2 % 151.29/22.22 (46) ~ (all_56_21 = e3) | all_56_17 = e1 % 151.29/22.22 (47) all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2 % 151.29/22.22 (48) ~ (all_52_1 = all_8_2) % 151.29/22.22 (49) all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2 % 151.29/22.22 (50) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 151.29/22.22 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 151.29/22.22 (51) ~ (all_52_3 = all_10_2) % 151.29/22.22 (52) all_54_3 = all_52_12 % 151.29/22.22 (53) all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0 % 151.29/22.22 (54) ~ (all_52_3 = all_52_7) % 151.29/22.22 (55) ~ (all_52_2 = all_52_6) % 151.29/22.22 (56) all_56_7 = all_52_12 % 151.29/22.22 (57) ~ (all_52_7 = all_4_2) % 151.29/22.22 (58) all_58_8 = all_6_2 % 151.29/22.22 (59) ~ (all_52_3 = all_4_2) % 151.29/22.22 (60) ~ (all_52_8 = all_10_2) % 151.29/22.22 (61) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0 % 151.29/22.22 (62) ~ (all_56_1 = e2) | all_56_3 = e3 % 151.29/22.22 (63) ~ (all_56_1 = e0) | all_56_7 = e3 % 151.29/22.22 (64) all_34_1 = all_4_1 % 151.29/22.22 (65) op(e1, all_6_1) = all_6_0 % 151.29/22.22 (66) op(all_4_2, all_4_2) = all_4_1 % 151.29/22.22 (67) ~ (all_52_3 = all_52_11) % 151.29/22.22 (68) all_58_3 = all_8_2 % 151.29/22.22 (69) all_56_3 = all_52_4 % 151.29/22.22 (70) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0 % 151.29/22.22 (71) ~ (all_52_11 = all_4_2) % 151.29/22.22 (72) ~ (all_52_1 = all_52_3) % 151.29/22.22 (73) ~ (all_52_6 = all_52_7) % 151.29/22.22 (74) all_56_31 = all_4_2 % 151.29/22.22 (75) all_58_11 = all_52_14 % 151.29/22.22 (76) ~ (all_52_2 = all_52_14) % 151.29/22.22 (77) op(all_6_2, all_6_2) = all_6_1 % 151.29/22.22 (78) all_56_1 = e3 | all_56_11 = e2 | all_56_21 = e1 | all_56_31 = e0 % 151.29/22.22 (79) ~ (all_52_13 = all_4_2) % 151.29/22.22 (80) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0 % 151.29/22.22 (81) all_54_13 = all_52_7 % 151.29/22.22 (82) ~ (all_52_13 = all_52_14) % 151.29/22.22 (83) all_56_23 = all_52_14 % 151.29/22.22 (84) op(e1, e1) = all_6_2 % 151.29/22.22 (85) ~ (all_52_6 = all_8_2) % 151.29/22.22 (86) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0 % 151.29/22.22 (87) all_58_15 = all_4_2 % 151.29/22.22 (88) all_56_29 = all_52_11 % 151.29/22.22 (89) all_58_2 = all_52_1 % 151.29/22.22 (90) ~ (all_52_9 = all_6_2) % 151.29/22.22 (91) all_58_7 = all_52_6 % 151.29/22.22 (92) all_58_10 = all_52_13 % 151.29/22.22 (93) all_40_1 = all_6_1 % 151.29/22.22 (94) ~ (all_52_12 = all_4_2) % 151.29/22.22 (95) op(all_10_2, all_10_2) = all_10_1 % 151.29/22.22 (96) ~ (all_56_11 = e0) | all_56_15 = e2 % 151.29/22.22 (97) all_58_0 = all_10_2 % 151.29/22.22 (98) op(e1, all_6_2) = all_56_20 % 151.29/22.22 (99) ~ (all_52_12 = all_52_14) % 151.29/22.22 (100) op(e1, all_52_9) = all_56_12 % 151.29/22.22 (101) ~ (e3 = e1) % 151.29/22.22 (102) op(e2, e2) = all_8_2 % 151.29/22.22 (103) ~ (all_52_4 = all_52_12) % 151.29/22.22 (104) ~ (all_52_2 = all_6_2) % 151.29/22.22 (105) ~ (all_56_21 = e0) | all_56_23 = e1 % 151.29/22.22 (106) ~ (all_52_6 = all_6_2) % 151.29/22.22 (107) ~ (all_40_1 = e0) | ~ (all_40_2 = e2) % 151.29/22.22 (108) ~ (all_52_14 = all_6_2) % 151.29/22.22 (109) all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0 % 151.29/22.22 (110) ~ (all_52_2 = all_10_2) % 151.29/22.22 (111) ~ (all_52_4 = all_10_2) % 151.29/22.22 (112) all_34_2 = all_4_2 % 151.29/22.22 (113) ~ (all_52_4 = all_8_2) % 151.29/22.22 (114) op(all_8_2, all_8_2) = all_8_1 % 151.29/22.22 (115) ~ (all_52_4 = all_52_6) % 151.29/22.22 (116) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 151.29/22.22 (117) all_58_14 = all_52_11 % 151.29/22.22 (118) all_56_19 = all_52_6 % 151.29/22.22 (119) ~ (all_52_12 = all_10_2) % 151.29/22.22 (120) all_56_15 = all_52_13 % 151.29/22.22 (121) ~ (all_52_1 = all_10_2) % 151.29/22.22 (122) all_58_12 = all_52_3 % 151.29/22.22 (123) all_54_11 = all_52_14 % 151.29/22.22 (124) ~ (all_56_31 = e3) | all_56_25 = e0 % 151.29/22.22 % 151.29/22.22 Begin of proof % 151.29/22.22 | % 151.29/22.22 | BETA: splitting (9) gives: % 151.29/22.22 | % 151.29/22.22 | Case 1: % 151.29/22.22 | | % 151.29/22.22 | | (125) ~ (all_56_31 = e1) % 151.29/22.22 | | % 151.29/22.22 | | REDUCE: (74), (125) imply: % 151.29/22.22 | | (126) ~ (all_4_2 = e1) % 151.29/22.22 | | % 151.29/22.22 | | BETA: splitting (15) gives: % 151.29/22.22 | | % 151.29/22.22 | | Case 1: % 151.29/22.22 | | | % 151.29/22.22 | | | (127) ~ (all_56_21 = e2) % 151.29/22.22 | | | % 151.29/22.22 | | | REDUCE: (35), (127) imply: % 151.29/22.22 | | | (128) ~ (all_6_2 = e2) % 151.29/22.22 | | | % 151.29/22.22 | | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (10), (11), (12), (13), % 151.29/22.22 | | | (14), (15), (16), (17), (18), (19), (20), (21), (22), (23), % 151.29/22.22 | | | (24), (25), (26), (27), (28), (29), (30), (31), (32), (33), % 151.29/22.22 | | | (34), (35), (36), (37), (38), (39), (40), (41), (42), (43), % 151.29/22.22 | | | (44), (45), (46), (47), (48), (49), (50), (51), (52), (53), % 151.29/22.22 | | | (54), (55), (56), (57), (58), (59), (60), (61), (62), (63), % 151.29/22.22 | | | (65), (66), (67), (68), (69), (70), (71), (72), (73), (74), % 151.29/22.22 | | | (75), (76), (77), (78), (79), (80), (81), (82), (83), (84), % 151.29/22.22 | | | (85), (86), (87), (89), (90), (91), (92), (93), (94), (95), % 151.29/22.22 | | | (96), (97), (98), (99), (100), (101), (102), (103), (104), % 151.29/22.22 | | | (105), (106), (107), (108), (109), (110), (111), (113), (114), % 151.29/22.22 | | | (115), (116), (117), (118), (119), (120), (121), (122), (123), % 151.29/22.22 | | | (124), (126), (128) are inconsistent by sub-proof #219. % 151.29/22.22 | | | % 151.29/22.22 | | Case 2: % 151.29/22.22 | | | % 151.29/22.22 | | | (129) all_56_21 = e2 % 151.29/22.22 | | | (130) all_56_19 = e1 % 151.29/22.22 | | | % 151.29/22.22 | | | REF_CLOSE: (14), (16), (27), (28), (35), (50), (77), (85), (93), (102), % 151.29/22.22 | | | (107), (116), (118), (129), (130) are inconsistent by sub-proof % 151.29/22.22 | | | #276. % 151.29/22.22 | | | % 151.29/22.22 | | End of split % 151.29/22.22 | | % 151.29/22.22 | Case 2: % 151.29/22.22 | | % 151.29/22.22 | | (131) all_56_31 = e1 % 151.29/22.22 | | (132) all_56_29 = e0 % 151.29/22.22 | | % 151.29/22.22 | | COMBINE_EQS: (88), (132) imply: % 151.29/22.22 | | (133) all_52_11 = e0 % 151.29/22.22 | | % 151.29/22.22 | | SIMP: (133) implies: % 151.29/22.22 | | (134) all_52_11 = e0 % 151.29/22.22 | | % 151.29/22.22 | | COMBINE_EQS: (74), (131) imply: % 151.29/22.22 | | (135) all_4_2 = e1 % 151.29/22.22 | | % 151.29/22.22 | | COMBINE_EQS: (112), (135) imply: % 151.29/22.22 | | (136) all_34_2 = e1 % 151.29/22.22 | | % 151.29/22.22 | | REDUCE: (3), (134) imply: % 151.29/22.22 | | (137) ~ (all_6_2 = e0) % 151.29/22.22 | | % 151.29/22.22 | | SIMP: (137) implies: % 151.29/22.22 | | (138) ~ (all_6_2 = e0) % 151.29/22.22 | | % 151.29/22.22 | | REDUCE: (66), (135) imply: % 151.29/22.22 | | (139) op(e1, e1) = all_4_1 % 151.29/22.22 | | % 151.29/22.22 | | REF_CLOSE: (5), (11), (12), (14), (15), (16), (27), (28), (35), (36), (50), % 151.29/22.22 | | (64), (77), (84), (85), (93), (98), (102), (107), (116), (118), % 151.29/22.22 | | (136), (138), (139) are inconsistent by sub-proof #218. % 151.29/22.22 | | % 151.29/22.22 | End of split % 151.29/22.22 | % 151.29/22.22 End of proof % 151.29/22.22 % 151.29/22.22 Sub-proof #218 shows that the following formulas are inconsistent: % 151.29/22.22 ---------------------------------------------------------------- % 151.29/22.22 (1) ~ (all_34_1 = e3) | ~ (all_34_2 = e1) % 151.29/22.22 (2) op(e1, all_6_1) = e3 % 151.29/22.22 (3) all_54_10 = all_6_2 % 151.29/22.22 (4) ~ (all_6_1 = e2) % 151.29/22.22 (5) ~ (all_56_21 = e2) | all_56_19 = e1 % 151.29/22.22 (6) all_34_2 = e1 % 151.29/22.22 (7) all_40_2 = all_6_2 % 151.29/22.22 (8) all_54_5 = all_8_2 % 151.29/22.22 (9) ~ (all_6_1 = e3) % 151.29/22.22 (10) all_56_21 = all_6_2 % 151.29/22.22 (11) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 151.29/22.22 (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 151.29/22.22 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 151.29/22.22 (13) ~ (all_6_2 = e0) % 151.29/22.22 (14) all_34_1 = all_4_1 % 151.29/22.22 (15) op(all_6_2, all_6_2) = all_6_1 % 151.29/22.22 (16) op(e1, e1) = all_6_2 % 151.29/22.22 (17) ~ (all_52_6 = all_8_2) % 151.29/22.22 (18) all_40_1 = all_6_1 % 151.29/22.22 (19) op(e1, e1) = all_4_1 % 151.29/22.22 (20) op(e1, all_6_2) = all_56_20 % 151.29/22.22 (21) op(e2, e2) = all_8_2 % 151.29/22.22 (22) ~ (all_40_1 = e0) | ~ (all_40_2 = e2) % 151.29/22.22 (23) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 151.29/22.22 (24) all_56_19 = all_52_6 % 151.29/22.22 % 151.29/22.22 Begin of proof % 151.29/22.22 | % 151.29/22.22 | BETA: splitting (1) gives: % 151.29/22.22 | % 151.29/22.22 | Case 1: % 151.29/22.22 | | % 151.29/22.22 | | (25) ~ (all_34_1 = e3) % 151.29/22.22 | | % 151.29/22.22 | | REDUCE: (14), (25) imply: % 151.29/22.22 | | (26) ~ (all_4_1 = e3) % 151.29/22.22 | | % 151.29/22.22 | | GROUND_INST: instantiating (12) with all_6_2, all_4_1, e1, e1, simplifying % 151.29/22.22 | | with (16), (19) gives: % 151.29/22.22 | | (27) all_6_2 = all_4_1 % 151.29/22.22 | | % 151.29/22.22 | | COMBINE_EQS: (7), (27) imply: % 151.29/22.22 | | (28) all_40_2 = all_4_1 % 151.29/22.22 | | % 151.29/22.22 | | COMBINE_EQS: (3), (27) imply: % 151.29/22.22 | | (29) all_54_10 = all_4_1 % 151.29/22.22 | | % 151.29/22.22 | | COMBINE_EQS: (10), (27) imply: % 151.29/22.22 | | (30) all_56_21 = all_4_1 % 151.29/22.22 | | % 151.29/22.22 | | REDUCE: (13), (27) imply: % 151.29/22.22 | | (31) ~ (all_4_1 = e0) % 151.29/22.22 | | % 151.29/22.22 | | REDUCE: (15), (27) imply: % 151.29/22.22 | | (32) op(all_4_1, all_4_1) = all_6_1 % 151.29/22.22 | | % 151.29/22.22 | | REDUCE: (20), (27) imply: % 151.29/22.22 | | (33) op(e1, all_4_1) = all_56_20 % 151.29/22.22 | | % 151.29/22.22 | | BETA: splitting (5) gives: % 151.29/22.22 | | % 151.29/22.22 | | Case 1: % 151.29/22.22 | | | % 151.29/22.22 | | | (34) ~ (all_56_21 = e2) % 151.29/22.22 | | | % 151.29/22.22 | | | REDUCE: (30), (34) imply: % 151.29/22.22 | | | (35) ~ (all_4_1 = e2) % 151.29/22.22 | | | % 151.29/22.22 | | | REF_CLOSE: (2), (9), (11), (12), (19), (26), (29), (31), (32), (33), (35) % 151.29/22.22 | | | are inconsistent by sub-proof #502. % 151.29/22.22 | | | % 151.29/22.22 | | Case 2: % 151.29/22.22 | | | % 151.29/22.22 | | | (36) all_56_21 = e2 % 151.29/22.22 | | | (37) all_56_19 = e1 % 151.29/22.22 | | | % 151.29/22.22 | | | COMBINE_EQS: (24), (37) imply: % 151.29/22.22 | | | (38) all_52_6 = e1 % 151.29/22.22 | | | % 151.29/22.22 | | | COMBINE_EQS: (30), (36) imply: % 151.29/22.22 | | | (39) all_4_1 = e2 % 151.29/22.22 | | | % 151.29/22.22 | | | COMBINE_EQS: (28), (39) imply: % 151.29/22.22 | | | (40) all_40_2 = e2 % 151.29/22.22 | | | % 151.29/22.22 | | | REDUCE: (17), (38) imply: % 151.29/22.22 | | | (41) ~ (all_8_2 = e1) % 151.29/22.22 | | | % 151.29/22.22 | | | SIMP: (41) implies: % 151.29/22.22 | | | (42) ~ (all_8_2 = e1) % 151.29/22.22 | | | % 151.29/22.22 | | | REDUCE: (32), (39) imply: % 151.29/22.22 | | | (43) op(e2, e2) = all_6_1 % 151.29/22.22 | | | % 151.29/22.22 | | | REF_CLOSE: (4), (8), (9), (12), (18), (21), (22), (23), (40), (42), (43) % 151.29/22.22 | | | are inconsistent by sub-proof #507. % 151.29/22.22 | | | % 151.29/22.22 | | End of split % 151.29/22.22 | | % 151.29/22.22 | Case 2: % 151.29/22.22 | | % 151.29/22.22 | | (44) ~ (all_34_2 = e1) % 151.29/22.22 | | % 151.29/22.22 | | REDUCE: (6), (44) imply: % 151.29/22.22 | | (45) $false % 151.29/22.22 | | % 151.29/22.22 | | CLOSE: (45) is inconsistent. % 151.29/22.22 | | % 151.29/22.22 | End of split % 151.29/22.22 | % 151.29/22.22 End of proof % 151.29/22.22 % 151.29/22.22 Sub-proof #219 shows that the following formulas are inconsistent: % 151.29/22.22 ---------------------------------------------------------------- % 151.29/22.22 (1) all_56_11 = all_8_2 % 151.29/22.22 (2) op(e0, all_52_13) = all_56_14 % 151.29/22.22 (3) ~ (all_52_11 = all_6_2) % 151.29/22.22 (4) all_56_25 = all_52_3 % 151.29/22.22 (5) ~ (all_52_7 = all_52_11) % 151.29/22.22 (6) all_54_9 = all_52_6 % 151.29/22.22 (7) all_58_6 = all_52_2 % 151.29/22.22 (8) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0 % 151.29/22.22 (9) op(e1, all_6_1) = e3 % 151.29/22.22 (10) all_54_10 = all_6_2 % 151.29/22.22 (11) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0 % 151.29/22.22 (12) ~ (all_6_1 = e2) % 151.29/22.22 (13) ~ (all_56_21 = e2) | all_56_19 = e1 % 151.29/22.22 (14) all_40_2 = all_6_2 % 151.29/22.22 (15) all_54_0 = all_10_2 % 151.29/22.22 (16) ~ (all_52_14 = all_4_2) % 151.29/22.22 (17) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0 % 151.29/22.22 (18) ~ (all_52_9 = all_8_2) % 151.29/22.22 (19) ~ (all_52_12 = all_52_13) % 151.29/22.22 (20) ~ (all_52_4 = all_52_7) % 151.29/22.22 (21) ~ (all_8_1 = e3) % 151.29/22.22 (22) op(e0, e0) = all_4_2 % 151.29/22.22 (23) all_58_6 = e0 | all_58_7 = e0 | all_58_8 = e0 | all_58_11 = e0 % 151.29/22.22 (24) all_58_4 = all_52_8 % 151.29/22.22 (25) all_54_5 = all_8_2 % 151.29/22.22 (26) ~ (all_6_1 = e3) % 151.29/22.22 (27) ~ (all_52_6 = all_52_14) % 151.29/22.22 (28) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 151.29/22.22 (29) ~ (all_6_0 = e2) % 151.29/22.22 (30) all_54_15 = all_4_2 % 151.29/22.22 (31) all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1 % 151.29/22.22 (32) ~ (all_10_1 = e1) % 151.29/22.22 (33) all_56_21 = all_6_2 % 151.29/22.22 (34) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 151.29/22.22 (35) all_56_1 = all_10_2 % 151.29/22.22 (36) all_58_5 = all_52_9 % 151.29/22.22 (37) all_54_1 = all_52_4 % 151.29/22.22 (38) all_56_17 = all_52_2 % 151.29/22.22 (39) all_58_9 = all_52_12 % 151.29/22.22 (40) op(e1, e0) = all_52_14 % 151.29/22.22 (41) all_54_14 = all_52_11 % 151.29/22.22 (42) all_58_4 = e0 | all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0 % 151.29/22.22 (43) op(e3, e3) = all_10_2 % 151.29/22.22 (44) ~ (all_56_21 = e3) | all_56_17 = e1 % 151.29/22.22 (45) all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2 % 151.29/22.22 (46) ~ (all_52_1 = all_8_2) % 151.29/22.22 (47) all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2 % 151.29/22.22 (48) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 151.29/22.22 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 151.29/22.22 (49) ~ (all_52_3 = all_10_2) % 151.29/22.22 (50) all_54_3 = all_52_12 % 151.29/22.22 (51) all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0 % 151.29/22.22 (52) ~ (all_52_3 = all_52_7) % 151.29/22.22 (53) ~ (all_52_2 = all_52_6) % 151.29/22.22 (54) all_56_7 = all_52_12 % 151.29/22.22 (55) ~ (all_52_7 = all_4_2) % 151.29/22.22 (56) ~ (all_4_2 = e1) % 151.29/22.22 (57) all_58_8 = all_6_2 % 151.29/22.22 (58) ~ (all_52_3 = all_4_2) % 151.29/22.22 (59) ~ (all_52_8 = all_10_2) % 151.29/22.22 (60) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0 % 151.29/22.22 (61) ~ (all_56_1 = e2) | all_56_3 = e3 % 151.29/22.22 (62) ~ (all_56_1 = e0) | all_56_7 = e3 % 151.29/22.22 (63) op(e1, all_6_1) = all_6_0 % 151.29/22.22 (64) op(all_4_2, all_4_2) = all_4_1 % 151.29/22.22 (65) ~ (all_52_3 = all_52_11) % 151.29/22.22 (66) all_58_3 = all_8_2 % 151.29/22.22 (67) all_56_3 = all_52_4 % 151.29/22.22 (68) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0 % 151.29/22.22 (69) ~ (all_52_11 = all_4_2) % 151.29/22.22 (70) ~ (all_52_1 = all_52_3) % 151.29/22.22 (71) ~ (all_52_6 = all_52_7) % 151.29/22.22 (72) all_56_31 = all_4_2 % 151.29/22.22 (73) all_58_11 = all_52_14 % 151.29/22.22 (74) ~ (all_52_2 = all_52_14) % 151.29/22.22 (75) op(all_6_2, all_6_2) = all_6_1 % 151.29/22.22 (76) all_56_1 = e3 | all_56_11 = e2 | all_56_21 = e1 | all_56_31 = e0 % 151.29/22.22 (77) ~ (all_52_13 = all_4_2) % 151.29/22.22 (78) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0 % 151.29/22.22 (79) all_54_13 = all_52_7 % 151.29/22.22 (80) ~ (all_52_13 = all_52_14) % 151.29/22.22 (81) all_56_23 = all_52_14 % 151.29/22.22 (82) op(e1, e1) = all_6_2 % 151.29/22.22 (83) ~ (all_52_6 = all_8_2) % 151.29/22.22 (84) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0 % 151.29/22.22 (85) all_58_15 = all_4_2 % 151.29/22.22 (86) ~ (all_6_2 = e2) % 151.29/22.22 (87) all_58_2 = all_52_1 % 151.29/22.22 (88) ~ (all_52_9 = all_6_2) % 151.29/22.22 (89) all_58_7 = all_52_6 % 151.29/22.22 (90) all_58_10 = all_52_13 % 151.29/22.22 (91) all_40_1 = all_6_1 % 151.29/22.22 (92) ~ (all_52_12 = all_4_2) % 151.29/22.22 (93) op(all_10_2, all_10_2) = all_10_1 % 151.29/22.22 (94) ~ (all_56_11 = e0) | all_56_15 = e2 % 151.29/22.22 (95) all_58_0 = all_10_2 % 151.29/22.22 (96) op(e1, all_6_2) = all_56_20 % 151.29/22.22 (97) ~ (all_52_12 = all_52_14) % 151.29/22.22 (98) op(e1, all_52_9) = all_56_12 % 151.29/22.22 (99) ~ (e3 = e1) % 151.29/22.22 (100) op(e2, e2) = all_8_2 % 151.29/22.22 (101) ~ (all_52_4 = all_52_12) % 151.29/22.22 (102) ~ (all_52_2 = all_6_2) % 151.29/22.22 (103) ~ (all_56_21 = e0) | all_56_23 = e1 % 151.29/22.22 (104) ~ (all_52_6 = all_6_2) % 151.29/22.22 (105) ~ (all_40_1 = e0) | ~ (all_40_2 = e2) % 151.29/22.22 (106) ~ (all_52_14 = all_6_2) % 151.29/22.22 (107) all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0 % 151.29/22.22 (108) ~ (all_52_2 = all_10_2) % 151.29/22.22 (109) ~ (all_52_4 = all_10_2) % 151.29/22.22 (110) ~ (all_52_4 = all_8_2) % 151.29/22.22 (111) op(all_8_2, all_8_2) = all_8_1 % 151.29/22.22 (112) ~ (all_52_4 = all_52_6) % 151.29/22.22 (113) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 151.29/22.22 (114) all_58_14 = all_52_11 % 151.29/22.22 (115) all_56_19 = all_52_6 % 151.29/22.22 (116) ~ (all_52_12 = all_10_2) % 151.29/22.22 (117) all_56_15 = all_52_13 % 151.29/22.22 (118) ~ (all_52_1 = all_10_2) % 151.29/22.22 (119) all_58_12 = all_52_3 % 151.29/22.22 (120) all_54_11 = all_52_14 % 151.29/22.22 (121) ~ (all_56_31 = e3) | all_56_25 = e0 % 151.29/22.22 % 151.29/22.22 Begin of proof % 151.29/22.22 | % 151.29/22.22 | BETA: splitting (121) gives: % 151.29/22.22 | % 151.29/22.22 | Case 1: % 151.29/22.22 | | % 151.29/22.22 | | (122) ~ (all_56_31 = e3) % 151.29/22.22 | | % 151.29/22.22 | | REDUCE: (72), (122) imply: % 151.29/22.22 | | (123) ~ (all_4_2 = e3) % 151.29/22.22 | | % 151.29/22.22 | | REF_CLOSE: (1), (6), (7), (9), (10), (11), (12), (13), (14), (15), (16), % 151.29/22.22 | | (17), (18), (19), (20), (22), (23), (24), (25), (26), (27), (28), % 151.29/22.22 | | (29), (30), (31), (32), (33), (34), (35), (36), (37), (38), (39), % 151.29/22.22 | | (40), (42), (43), (44), (45), (46), (47), (48), (50), (51), (53), % 151.29/22.22 | | (54), (55), (56), (57), (58), (59), (60), (61), (62), (63), (66), % 151.29/22.22 | | (67), (68), (69), (71), (72), (73), (74), (75), (76), (77), (78), % 151.29/22.22 | | (79), (80), (81), (82), (83), (84), (85), (87), (89), (90), (91), % 151.29/22.22 | | (92), (93), (94), (95), (96), (97), (98), (99), (100), (101), % 151.29/22.22 | | (102), (103), (104), (105), (106), (107), (108), (109), (110), % 151.29/22.22 | | (112), (113), (114), (115), (116), (117), (118), (119), (120), % 151.29/22.22 | | (123) are inconsistent by sub-proof #504. % 151.29/22.22 | | % 151.29/22.22 | Case 2: % 151.29/22.22 | | % 151.29/22.22 | | (124) all_56_31 = e3 % 151.29/22.22 | | (125) all_56_25 = e0 % 151.29/22.23 | | % 151.29/22.23 | | COMBINE_EQS: (4), (125) imply: % 151.29/22.23 | | (126) all_52_3 = e0 % 151.29/22.23 | | % 151.29/22.23 | | SIMP: (126) implies: % 151.29/22.23 | | (127) all_52_3 = e0 % 151.29/22.23 | | % 151.29/22.23 | | COMBINE_EQS: (72), (124) imply: % 151.29/22.23 | | (128) all_4_2 = e3 % 151.29/22.23 | | % 151.29/22.23 | | REDUCE: (70), (127) imply: % 151.29/22.23 | | (129) ~ (all_52_1 = e0) % 151.29/22.23 | | % 151.29/22.23 | | REDUCE: (52), (127) imply: % 151.29/22.23 | | (130) ~ (all_52_7 = e0) % 151.29/22.23 | | % 151.29/22.23 | | SIMP: (130) implies: % 151.29/22.23 | | (131) ~ (all_52_7 = e0) % 151.29/22.23 | | % 151.29/22.23 | | REDUCE: (65), (127) imply: % 151.29/22.23 | | (132) ~ (all_52_11 = e0) % 151.29/22.23 | | % 151.29/22.23 | | SIMP: (132) implies: % 151.29/22.23 | | (133) ~ (all_52_11 = e0) % 151.29/22.23 | | % 151.29/22.23 | | REDUCE: (49), (127) imply: % 151.29/22.23 | | (134) ~ (all_10_2 = e0) % 151.29/22.23 | | % 151.29/22.23 | | SIMP: (134) implies: % 151.29/22.23 | | (135) ~ (all_10_2 = e0) % 151.29/22.23 | | % 151.29/22.23 | | REDUCE: (55), (128) imply: % 151.29/22.23 | | (136) ~ (all_52_7 = e3) % 151.29/22.23 | | % 151.29/22.23 | | REDUCE: (69), (128) imply: % 151.29/22.23 | | (137) ~ (all_52_11 = e3) % 151.29/22.23 | | % 151.29/22.23 | | REDUCE: (64), (128) imply: % 151.29/22.23 | | (138) op(e3, e3) = all_4_1 % 151.29/22.23 | | % 151.29/22.23 | | REDUCE: (22), (128) imply: % 151.29/22.23 | | (139) op(e0, e0) = e3 % 151.29/22.23 | | % 151.29/22.23 | | GROUND_INST: instantiating (48) with all_10_2, all_4_1, e3, e3, simplifying % 151.29/22.23 | | with (43), (138) gives: % 151.29/22.23 | | (140) all_10_2 = all_4_1 % 151.29/22.23 | | % 151.29/22.23 | | BETA: splitting (94) gives: % 151.29/22.23 | | % 151.29/22.23 | | Case 1: % 151.29/22.23 | | | % 151.29/22.23 | | | (141) ~ (all_56_11 = e0) % 151.29/22.23 | | | % 151.29/22.23 | | | REDUCE: (1), (141) imply: % 151.29/22.23 | | | (142) ~ (all_8_2 = e0) % 151.29/22.23 | | | % 151.29/22.23 | | | COMBINE_EQS: (15), (140) imply: % 151.29/22.23 | | | (143) all_54_0 = all_4_1 % 151.29/22.23 | | | % 151.29/22.23 | | | REDUCE: (108), (140) imply: % 151.29/22.23 | | | (144) ~ (all_52_2 = all_4_1) % 151.29/22.23 | | | % 151.29/22.23 | | | REDUCE: (135), (140) imply: % 151.29/22.23 | | | (145) ~ (all_4_1 = e0) % 151.29/22.23 | | | % 151.29/22.23 | | | BETA: splitting (103) gives: % 151.29/22.23 | | | % 151.29/22.23 | | | Case 1: % 151.29/22.23 | | | | % 151.29/22.23 | | | | (146) ~ (all_56_21 = e0) % 151.29/22.23 | | | | % 151.29/22.23 | | | | REDUCE: (33), (146) imply: % 151.29/22.23 | | | | (147) ~ (all_6_2 = e0) % 151.29/22.23 | | | | % 151.29/22.23 | | | | BETA: splitting (44) gives: % 151.29/22.23 | | | | % 151.29/22.23 | | | | Case 1: % 151.29/22.23 | | | | | % 151.29/22.23 | | | | | (148) ~ (all_56_21 = e3) % 151.29/22.23 | | | | | % 151.29/22.23 | | | | | REDUCE: (33), (148) imply: % 151.29/22.23 | | | | | (149) ~ (all_6_2 = e3) % 151.29/22.23 | | | | | % 151.29/22.23 | | | | | BETA: splitting (34) gives: % 151.29/22.23 | | | | | % 151.29/22.23 | | | | | Case 1: % 151.29/22.23 | | | | | | % 151.29/22.23 | | | | | | (150) all_54_10 = e3 % 151.29/22.23 | | | | | | % 151.29/22.23 | | | | | | REF_CLOSE: (10), (149), (150) are inconsistent by sub-proof #736. % 151.29/22.23 | | | | | | % 151.29/22.23 | | | | | Case 2: % 151.29/22.23 | | | | | | % 151.29/22.23 | | | | | | (151) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 151.29/22.23 | | | | | | % 151.29/22.23 | | | | | | BETA: splitting (151) gives: % 151.29/22.23 | | | | | | % 151.29/22.23 | | | | | | Case 1: % 151.29/22.23 | | | | | | | % 151.29/22.23 | | | | | | | (152) all_54_10 = e2 % 151.29/22.23 | | | | | | | % 151.29/22.23 | | | | | | | REF_CLOSE: (10), (86), (152) are inconsistent by sub-proof #735. % 151.29/22.23 | | | | | | | % 151.29/22.23 | | | | | | Case 2: % 151.29/22.23 | | | | | | | % 151.29/22.23 | | | | | | | (153) all_54_10 = e1 | all_54_10 = e0 % 151.29/22.23 | | | | | | | % 151.29/22.23 | | | | | | | BETA: splitting (153) gives: % 151.29/22.23 | | | | | | | % 151.29/22.23 | | | | | | | Case 1: % 151.29/22.23 | | | | | | | | % 151.29/22.23 | | | | | | | | (154) all_54_10 = e1 % 151.29/22.23 | | | | | | | | % 151.29/22.23 | | | | | | | | COMBINE_EQS: (10), (154) imply: % 151.29/22.23 | | | | | | | | (155) all_6_2 = e1 % 151.29/22.23 | | | | | | | | % 151.29/22.23 | | | | | | | | SIMP: (155) implies: % 151.29/22.23 | | | | | | | | (156) all_6_2 = e1 % 151.29/22.23 | | | | | | | | % 151.29/22.23 | | | | | | | | REDUCE: (3), (156) imply: % 151.29/22.23 | | | | | | | | (157) ~ (all_52_11 = e1) % 151.29/22.23 | | | | | | | | % 151.29/22.23 | | | | | | | | REDUCE: (75), (156) imply: % 151.29/22.23 | | | | | | | | (158) op(e1, e1) = all_6_1 % 151.29/22.23 | | | | | | | | % 151.29/22.23 | | | | | | | | REDUCE: (96), (156) imply: % 151.29/22.23 | | | | | | | | (159) op(e1, e1) = all_56_20 % 151.29/22.23 | | | | | | | | % 151.29/22.23 | | | | | | | | REDUCE: (82), (156) imply: % 151.29/22.23 | | | | | | | | (160) op(e1, e1) = e1 % 151.29/22.23 | | | | | | | | % 151.29/22.23 | | | | | | | | BETA: splitting (8) gives: % 151.29/22.23 | | | | | | | | % 151.29/22.23 | | | | | | | | Case 1: % 151.29/22.23 | | | | | | | | | % 151.29/22.23 | | | | | | | | | (161) all_54_14 = e3 % 151.29/22.23 | | | | | | | | | % 151.29/22.23 | | | | | | | | | REF_CLOSE: (41), (137), (161) are inconsistent by sub-proof % 151.29/22.23 | | | | | | | | | #729. % 151.29/22.23 | | | | | | | | | % 151.29/22.23 | | | | | | | | Case 2: % 151.29/22.23 | | | | | | | | | % 151.29/22.23 | | | | | | | | | (162) all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0 % 151.29/22.23 | | | | | | | | | % 151.29/22.23 | | | | | | | | | BETA: splitting (162) gives: % 151.29/22.23 | | | | | | | | | % 151.29/22.23 | | | | | | | | | Case 1: % 151.29/22.23 | | | | | | | | | | % 151.29/22.23 | | | | | | | | | | (163) all_54_14 = e2 % 151.29/22.23 | | | | | | | | | | % 151.29/22.23 | | | | | | | | | | COMBINE_EQS: (41), (163) imply: % 151.29/22.23 | | | | | | | | | | (164) all_52_11 = e2 % 151.29/22.23 | | | | | | | | | | % 151.29/22.23 | | | | | | | | | | SIMP: (164) implies: % 151.29/22.23 | | | | | | | | | | (165) all_52_11 = e2 % 151.29/22.23 | | | | | | | | | | % 151.29/22.23 | | | | | | | | | | REDUCE: (5), (165) imply: % 151.29/22.23 | | | | | | | | | | (166) ~ (all_52_7 = e2) % 151.29/22.23 | | | | | | | | | | % 151.29/22.23 | | | | | | | | | | REF_CLOSE: (9), (26), (48), (60), (79), (131), (136), (158), % 151.29/22.23 | | | | | | | | | | (159), (160), (166) are inconsistent by sub-proof % 151.29/22.23 | | | | | | | | | | #512. % 151.29/22.23 | | | | | | | | | | % 151.29/22.23 | | | | | | | | | Case 2: % 151.29/22.23 | | | | | | | | | | % 151.29/22.23 | | | | | | | | | | (167) all_54_14 = e1 | all_54_14 = e0 % 151.29/22.23 | | | | | | | | | | % 151.29/22.23 | | | | | | | | | | REF_CLOSE: (41), (133), (157), (167) are inconsistent by % 151.29/22.23 | | | | | | | | | | sub-proof #714. % 151.29/22.23 | | | | | | | | | | % 151.29/22.23 | | | | | | | | | End of split % 151.29/22.23 | | | | | | | | | % 151.29/22.23 | | | | | | | | End of split % 151.29/22.23 | | | | | | | | % 151.29/22.23 | | | | | | | Case 2: % 151.29/22.23 | | | | | | | | % 151.29/22.23 | | | | | | | | (168) all_54_10 = e0 % 151.29/22.23 | | | | | | | | % 151.29/22.23 | | | | | | | | REF_CLOSE: (10), (147), (168) are inconsistent by sub-proof % 151.29/22.23 | | | | | | | | #705. % 151.29/22.23 | | | | | | | | % 151.29/22.23 | | | | | | | End of split % 151.29/22.23 | | | | | | | % 151.29/22.23 | | | | | | End of split % 151.29/22.23 | | | | | | % 151.29/22.23 | | | | | End of split % 151.29/22.23 | | | | | % 151.29/22.23 | | | | Case 2: % 151.29/22.23 | | | | | % 151.29/22.23 | | | | | (169) all_56_21 = e3 % 151.29/22.23 | | | | | (170) all_56_17 = e1 % 151.29/22.23 | | | | | % 151.29/22.23 | | | | | COMBINE_EQS: (38), (170) imply: % 151.29/22.23 | | | | | (171) all_52_2 = e1 % 151.29/22.23 | | | | | % 151.29/22.23 | | | | | REF_CLOSE: (12), (26), (28), (33), (48), (75), (138), (143), (144), % 151.29/22.23 | | | | | (145), (169), (171) are inconsistent by sub-proof #547. % 151.29/22.23 | | | | | % 151.29/22.23 | | | | End of split % 151.29/22.23 | | | | % 151.29/22.23 | | | Case 2: % 151.29/22.23 | | | | % 151.29/22.23 | | | | (172) all_56_21 = e0 % 151.29/22.23 | | | | % 151.29/22.23 | | | | COMBINE_EQS: (33), (172) imply: % 151.29/22.23 | | | | (173) all_6_2 = e0 % 151.29/22.23 | | | | % 151.29/22.23 | | | | SIMP: (173) implies: % 151.29/22.23 | | | | (174) all_6_2 = e0 % 151.29/22.23 | | | | % 151.29/22.23 | | | | REDUCE: (88), (174) imply: % 151.29/22.23 | | | | (175) ~ (all_52_9 = e0) % 151.29/22.23 | | | | % 151.29/22.23 | | | | REF_CLOSE: (2), (26), (36), (48), (51), (66), (75), (87), (90), (129), % 151.29/22.23 | | | | (139), (142), (174), (175) are inconsistent by sub-proof % 151.29/22.23 | | | | #220. % 151.29/22.23 | | | | % 151.29/22.23 | | | End of split % 151.29/22.23 | | | % 151.29/22.23 | | Case 2: % 151.29/22.23 | | | % 151.29/22.23 | | | (176) all_56_11 = e0 % 151.29/22.23 | | | % 151.29/22.23 | | | COMBINE_EQS: (1), (176) imply: % 151.29/22.23 | | | (177) all_8_2 = e0 % 151.29/22.23 | | | % 151.29/22.23 | | | REDUCE: (111), (177) imply: % 151.29/22.23 | | | (178) op(e0, e0) = all_8_1 % 151.29/22.23 | | | % 151.29/22.23 | | | REF_CLOSE: (21), (48), (139), (178) are inconsistent by sub-proof #546. % 151.29/22.23 | | | % 151.29/22.23 | | End of split % 151.29/22.23 | | % 151.29/22.23 | End of split % 151.29/22.23 | % 151.29/22.23 End of proof % 151.29/22.23 % 151.29/22.23 Sub-proof #220 shows that the following formulas are inconsistent: % 151.29/22.23 ---------------------------------------------------------------- % 151.29/22.23 (1) op(e0, all_52_13) = all_56_14 % 151.29/22.23 (2) ~ (all_6_1 = e3) % 151.29/22.23 (3) all_58_5 = all_52_9 % 151.29/22.23 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 151.29/22.23 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 151.29/22.23 (5) all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0 % 151.29/22.23 (6) all_6_2 = e0 % 151.29/22.23 (7) ~ (all_52_9 = e0) % 151.29/22.23 (8) ~ (all_52_1 = e0) % 151.29/22.23 (9) all_58_3 = all_8_2 % 151.29/22.23 (10) op(e0, e0) = e3 % 151.29/22.23 (11) op(all_6_2, all_6_2) = all_6_1 % 151.29/22.23 (12) all_58_2 = all_52_1 % 151.29/22.23 (13) all_58_10 = all_52_13 % 151.29/22.23 (14) ~ (all_8_2 = e0) % 151.29/22.23 % 151.29/22.23 Begin of proof % 151.29/22.23 | % 151.29/22.23 | REDUCE: (6), (11) imply: % 151.29/22.23 | (15) op(e0, e0) = all_6_1 % 151.29/22.23 | % 151.29/22.23 | BETA: splitting (5) gives: % 151.29/22.23 | % 151.29/22.23 | Case 1: % 151.29/22.23 | | % 151.29/22.23 | | (16) all_58_2 = e0 % 151.29/22.23 | | % 151.29/22.23 | | COMBINE_EQS: (12), (16) imply: % 151.29/22.23 | | (17) all_52_1 = e0 % 151.29/22.23 | | % 151.29/22.23 | | REDUCE: (8), (17) imply: % 151.29/22.23 | | (18) $false % 151.29/22.23 | | % 151.29/22.23 | | CLOSE: (18) is inconsistent. % 151.29/22.23 | | % 151.29/22.23 | Case 2: % 151.29/22.23 | | % 151.29/22.23 | | (19) all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0 % 151.29/22.23 | | % 151.29/22.23 | | BETA: splitting (19) gives: % 151.29/22.23 | | % 151.29/22.23 | | Case 1: % 151.29/22.23 | | | % 151.29/22.23 | | | (20) all_58_3 = e0 % 151.29/22.23 | | | % 151.29/22.23 | | | COMBINE_EQS: (9), (20) imply: % 151.29/22.23 | | | (21) all_8_2 = e0 % 151.29/22.23 | | | % 151.29/22.23 | | | REDUCE: (14), (21) imply: % 151.29/22.23 | | | (22) $false % 151.29/22.23 | | | % 151.29/22.23 | | | CLOSE: (22) is inconsistent. % 151.29/22.23 | | | % 151.29/22.23 | | Case 2: % 151.29/22.23 | | | % 151.29/22.23 | | | (23) all_58_5 = e0 | all_58_10 = e0 % 151.29/22.23 | | | % 151.29/22.23 | | | BETA: splitting (23) gives: % 151.29/22.23 | | | % 151.29/22.23 | | | Case 1: % 151.29/22.23 | | | | % 151.29/22.23 | | | | (24) all_58_5 = e0 % 151.29/22.23 | | | | % 151.29/22.23 | | | | COMBINE_EQS: (3), (24) imply: % 151.29/22.23 | | | | (25) all_52_9 = e0 % 151.29/22.23 | | | | % 151.29/22.23 | | | | REDUCE: (7), (25) imply: % 151.29/22.23 | | | | (26) $false % 151.29/22.23 | | | | % 151.29/22.23 | | | | CLOSE: (26) is inconsistent. % 151.29/22.23 | | | | % 151.29/22.23 | | | Case 2: % 151.29/22.23 | | | | % 151.29/22.23 | | | | (27) all_58_10 = e0 % 151.29/22.23 | | | | % 151.29/22.23 | | | | COMBINE_EQS: (13), (27) imply: % 151.29/22.23 | | | | (28) all_52_13 = e0 % 151.29/22.23 | | | | % 151.29/22.23 | | | | REDUCE: (1), (28) imply: % 151.29/22.23 | | | | (29) op(e0, e0) = all_56_14 % 151.29/22.23 | | | | % 151.29/22.23 | | | | GROUND_INST: instantiating (4) with e3, all_56_14, e0, e0, simplifying % 151.29/22.23 | | | | with (10), (29) gives: % 151.29/22.23 | | | | (30) all_56_14 = e3 % 151.29/22.23 | | | | % 151.29/22.23 | | | | GROUND_INST: instantiating (4) with all_6_1, all_56_14, e0, e0, % 151.29/22.23 | | | | simplifying with (15), (29) gives: % 151.29/22.23 | | | | (31) all_56_14 = all_6_1 % 151.29/22.23 | | | | % 151.29/22.23 | | | | COMBINE_EQS: (30), (31) imply: % 151.29/22.23 | | | | (32) all_6_1 = e3 % 151.29/22.23 | | | | % 151.29/22.23 | | | | REDUCE: (2), (32) imply: % 151.29/22.23 | | | | (33) $false % 151.29/22.23 | | | | % 151.29/22.23 | | | | CLOSE: (33) is inconsistent. % 151.29/22.23 | | | | % 151.29/22.23 | | | End of split % 151.29/22.23 | | | % 151.29/22.23 | | End of split % 151.29/22.23 | | % 151.29/22.23 | End of split % 151.29/22.23 | % 151.29/22.23 End of proof % 151.29/22.23 % 151.29/22.23 Sub-proof #221 shows that the following formulas are inconsistent: % 151.29/22.23 ---------------------------------------------------------------- % 151.29/22.23 (1) all_56_11 = all_8_2 % 151.29/22.23 (2) op(e0, all_52_13) = all_56_14 % 151.29/22.23 (3) ~ (all_56_11 = e1) | all_56_13 = e2 % 151.29/22.23 (4) ~ (all_34_1 = e3) | ~ (all_34_2 = e1) % 151.29/22.23 (5) op(e0, e0) = e1 % 151.29/22.23 (6) ~ (all_8_1 = e1) % 151.29/22.23 (7) ~ (all_52_1 = all_52_9) % 151.29/22.23 (8) ~ (all_52_13 = e1) % 151.29/22.23 (9) all_54_10 = all_6_2 % 151.29/22.23 (10) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0 % 151.29/22.23 (11) ~ (all_6_1 = e2) % 151.29/22.23 (12) ~ (all_52_13 = all_8_2) % 151.29/22.23 (13) ~ (all_56_21 = e2) | all_56_19 = e1 % 151.29/22.23 (14) all_34_2 = e1 % 151.29/22.23 (15) all_54_0 = all_10_2 % 151.29/22.23 (16) all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2 % 151.29/22.23 (17) ~ (all_52_9 = all_8_2) % 151.29/22.23 (18) ~ (all_52_12 = all_52_13) % 151.29/22.23 (19) ~ (all_8_1 = e3) % 151.29/22.23 (20) ~ (e3 = e2) % 151.29/22.23 (21) op(e0, e0) = all_4_2 % 151.29/22.23 (22) all_58_4 = all_52_8 % 151.29/22.23 (23) all_54_5 = all_8_2 % 151.29/22.23 (24) ~ (all_6_1 = e3) % 151.29/22.23 (25) ~ (all_52_6 = all_52_14) % 151.29/22.23 (26) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 151.29/22.23 (27) all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1 % 151.29/22.23 (28) ~ (all_10_1 = e1) % 151.29/22.23 (29) all_56_21 = all_6_2 % 151.29/22.23 (30) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 151.29/22.23 (31) ~ (all_52_7 = all_8_2) % 151.29/22.23 (32) all_56_1 = all_10_2 % 151.29/22.23 (33) all_56_27 = all_52_7 % 151.29/22.23 (34) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0 % 151.29/22.23 (35) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0 % 151.29/22.23 (36) all_58_5 = all_52_9 % 151.29/22.23 (37) all_58_9 = all_52_12 % 151.29/22.23 (38) op(e1, e0) = all_52_14 % 151.29/22.23 (39) ~ (all_56_1 = e1) | all_56_5 = e3 % 151.29/22.23 (40) all_58_1 = all_52_4 % 151.29/22.23 (41) all_58_13 = all_52_7 % 151.29/22.23 (42) ~ (all_52_8 = all_6_2) % 151.29/22.23 (43) all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1 % 151.29/22.23 (44) all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0 % 151.29/22.23 (45) all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1 % 151.29/22.23 (46) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 151.29/22.23 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 151.29/22.23 (47) all_54_3 = all_52_12 % 151.29/22.23 (48) all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0 % 151.29/22.23 (49) ~ (all_6_2 = e0) % 151.29/22.23 (50) ~ (all_56_11 = e3) | all_56_9 = e2 % 151.29/22.23 (51) all_56_7 = all_52_12 % 151.29/22.23 (52) all_56_13 = all_52_9 % 151.29/22.23 (53) ~ (all_52_9 = e0) % 151.29/22.23 (54) all_58_8 = all_6_2 % 151.29/22.23 (55) ~ (all_6_0 = e3) % 151.29/22.23 (56) all_54_6 = all_52_9 % 151.29/22.23 (57) ~ (all_56_1 = e2) | all_56_3 = e3 % 151.29/22.23 (58) ~ (all_56_1 = e0) | all_56_7 = e3 % 151.29/22.23 (59) all_34_1 = all_4_1 % 151.29/22.23 (60) ~ (all_52_9 = all_52_13) % 151.29/22.23 (61) op(e1, all_6_1) = all_6_0 % 151.29/22.23 (62) all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3 % 151.29/22.23 (63) all_58_3 = all_8_2 % 151.29/22.23 (64) all_56_3 = all_52_4 % 151.29/22.23 (65) all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1 % 151.29/22.23 (66) op(e1, all_52_8) = all_56_4 % 151.29/22.23 (67) all_58_11 = all_52_14 % 151.29/22.23 (68) all_54_7 = all_52_13 % 151.29/22.23 (69) op(all_6_2, all_6_2) = all_6_1 % 151.29/22.23 (70) ~ (all_52_7 = e1) % 151.29/22.23 (71) all_58_14 = e0 % 151.29/22.23 (72) op(e1, e1) = all_6_2 % 151.29/22.23 (73) ~ (all_52_6 = all_8_2) % 151.29/22.23 (74) all_58_15 = all_4_2 % 151.29/22.23 (75) all_58_2 = all_52_1 % 151.29/22.23 (76) ~ (all_52_9 = all_6_2) % 151.29/22.23 (77) all_58_7 = all_52_6 % 151.29/22.23 (78) all_58_10 = all_52_13 % 151.29/22.23 (79) op(all_10_2, all_10_2) = all_10_1 % 151.29/22.23 (80) ~ (all_56_11 = e0) | all_56_15 = e2 % 151.29/22.23 (81) op(e1, e1) = all_4_1 % 151.29/22.23 (82) all_58_0 = all_10_2 % 151.29/22.23 (83) op(e1, all_6_2) = all_56_20 % 151.29/22.23 (84) ~ (all_52_12 = e1) % 151.29/22.23 (85) ~ (all_56_31 = e2) | all_56_27 = e0 % 151.29/22.23 (86) ~ (e3 = e1) % 151.29/22.23 (87) op(e2, e2) = all_8_2 % 151.29/22.23 (88) ~ (all_52_4 = all_52_12) % 151.29/22.23 (89) ~ (all_52_8 = all_52_12) % 151.29/22.23 (90) ~ (all_52_6 = all_6_2) % 151.29/22.23 (91) op(e1, e0) = all_56_28 % 151.29/22.23 (92) all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3 % 151.29/22.23 (93) ~ (all_52_4 = all_10_2) % 151.29/22.23 (94) ~ (all_52_4 = all_8_2) % 151.29/22.23 (95) op(all_8_2, all_8_2) = all_8_1 % 151.29/22.23 (96) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 151.29/22.23 (97) all_56_19 = all_52_6 % 151.29/22.23 (98) ~ (all_52_12 = all_10_2) % 151.29/22.23 (99) all_56_9 = all_52_1 % 151.29/22.23 (100) all_56_15 = all_52_13 % 151.29/22.23 (101) ~ (all_52_1 = all_10_2) % 151.29/22.23 % 151.29/22.23 Begin of proof % 151.29/22.23 | % 151.29/22.23 | BETA: splitting (4) gives: % 151.29/22.23 | % 151.29/22.23 | Case 1: % 151.29/22.23 | | % 151.29/22.23 | | (102) ~ (all_34_1 = e3) % 151.29/22.23 | | % 151.29/22.23 | | REDUCE: (59), (102) imply: % 151.29/22.23 | | (103) ~ (all_4_1 = e3) % 151.29/22.23 | | % 151.29/22.23 | | GROUND_INST: instantiating (46) with all_52_14, all_56_28, e0, e1, % 151.29/22.23 | | simplifying with (38), (91) gives: % 151.29/22.23 | | (104) all_56_28 = all_52_14 % 151.29/22.23 | | % 151.29/22.23 | | GROUND_INST: instantiating (46) with all_6_2, all_4_1, e1, e1, simplifying % 151.29/22.23 | | with (72), (81) gives: % 151.29/22.23 | | (105) all_6_2 = all_4_1 % 151.29/22.23 | | % 151.29/22.23 | | COMBINE_EQS: (9), (105) imply: % 151.29/22.23 | | (106) all_54_10 = all_4_1 % 151.29/22.23 | | % 151.29/22.23 | | COMBINE_EQS: (29), (105) imply: % 151.29/22.23 | | (107) all_56_21 = all_4_1 % 151.29/22.23 | | % 151.29/22.23 | | COMBINE_EQS: (54), (105) imply: % 151.29/22.23 | | (108) all_58_8 = all_4_1 % 151.29/22.23 | | % 151.29/22.23 | | REDUCE: (90), (105) imply: % 151.29/22.23 | | (109) ~ (all_52_6 = all_4_1) % 151.29/22.23 | | % 151.29/22.23 | | REDUCE: (42), (105) imply: % 151.29/22.23 | | (110) ~ (all_52_8 = all_4_1) % 151.29/22.23 | | % 151.29/22.23 | | REDUCE: (76), (105) imply: % 151.29/22.23 | | (111) ~ (all_52_9 = all_4_1) % 151.29/22.23 | | % 151.29/22.23 | | REDUCE: (49), (105) imply: % 151.29/22.23 | | (112) ~ (all_4_1 = e0) % 151.29/22.23 | | % 151.29/22.23 | | REDUCE: (69), (105) imply: % 151.29/22.23 | | (113) op(all_4_1, all_4_1) = all_6_1 % 151.29/22.23 | | % 151.29/22.23 | | REDUCE: (83), (105) imply: % 151.29/22.23 | | (114) op(e1, all_4_1) = all_56_20 % 151.29/22.23 | | % 151.29/22.23 | | BETA: splitting (80) gives: % 151.29/22.23 | | % 151.29/22.23 | | Case 1: % 151.29/22.23 | | | % 151.29/22.23 | | | (115) ~ (all_56_11 = e0) % 151.29/22.23 | | | % 151.29/22.23 | | | REDUCE: (1), (115) imply: % 151.29/22.23 | | | (116) ~ (all_8_2 = e0) % 151.29/22.23 | | | % 151.29/22.23 | | | BETA: splitting (13) gives: % 151.29/22.23 | | | % 151.29/22.23 | | | Case 1: % 151.29/22.23 | | | | % 151.29/22.23 | | | | (117) ~ (all_56_21 = e2) % 151.29/22.23 | | | | % 151.29/22.23 | | | | REDUCE: (107), (117) imply: % 151.29/22.23 | | | | (118) ~ (all_4_1 = e2) % 151.29/22.23 | | | | % 151.29/22.23 | | | | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (10), (12), (15), (16), % 151.29/22.23 | | | | (17), (18), (20), (22), (23), (26), (28), (30), (32), (34), % 151.29/22.23 | | | | (35), (36), (37), (39), (40), (41), (43), (45), (46), (47), % 151.29/22.23 | | | | (48), (50), (51), (52), (53), (55), (56), (57), (58), (60), % 151.29/22.23 | | | | (61), (62), (63), (64), (65), (68), (70), (71), (75), (77), % 151.29/22.23 | | | | (78), (79), (81), (82), (84), (88), (89), (93), (94), (95), % 151.29/22.23 | | | | (96), (98), (99), (101), (103), (106), (108), (109), (110), % 151.29/22.23 | | | | (111), (112), (113), (114), (116), (118) are inconsistent by % 151.29/22.23 | | | | sub-proof #525. % 151.29/22.23 | | | | % 151.29/22.23 | | | Case 2: % 151.29/22.23 | | | | % 151.29/22.23 | | | | (119) all_56_21 = e2 % 151.29/22.23 | | | | (120) all_56_19 = e1 % 151.29/22.23 | | | | % 151.29/22.23 | | | | COMBINE_EQS: (97), (120) imply: % 151.29/22.23 | | | | (121) all_52_6 = e1 % 151.29/22.23 | | | | % 151.29/22.23 | | | | SIMP: (121) implies: % 151.29/22.23 | | | | (122) all_52_6 = e1 % 151.29/22.23 | | | | % 151.29/22.23 | | | | COMBINE_EQS: (107), (119) imply: % 151.29/22.23 | | | | (123) all_4_1 = e2 % 151.29/22.23 | | | | % 151.29/22.23 | | | | SIMP: (123) implies: % 151.29/22.23 | | | | (124) all_4_1 = e2 % 151.29/22.23 | | | | % 151.29/22.23 | | | | REDUCE: (25), (122) imply: % 151.29/22.23 | | | | (125) ~ (all_52_14 = e1) % 151.29/22.23 | | | | % 151.29/22.23 | | | | SIMP: (125) implies: % 151.29/22.23 | | | | (126) ~ (all_52_14 = e1) % 151.29/22.23 | | | | % 151.29/22.23 | | | | REDUCE: (73), (122) imply: % 151.29/22.23 | | | | (127) ~ (all_8_2 = e1) % 151.29/22.23 | | | | % 151.29/22.23 | | | | SIMP: (127) implies: % 151.29/22.23 | | | | (128) ~ (all_8_2 = e1) % 151.29/22.23 | | | | % 151.29/22.23 | | | | REDUCE: (109), (122), (124) imply: % 151.29/22.23 | | | | (129) ~ (e2 = e1) % 151.29/22.23 | | | | % 151.29/22.23 | | | | SIMP: (129) implies: % 151.29/22.23 | | | | (130) ~ (e2 = e1) % 151.29/22.23 | | | | % 151.29/22.23 | | | | REDUCE: (103), (124) imply: % 151.29/22.23 | | | | (131) ~ (e3 = e2) % 151.29/22.23 | | | | % 151.29/22.23 | | | | REDUCE: (113), (124) imply: % 151.29/22.23 | | | | (132) op(e2, e2) = all_6_1 % 151.29/22.23 | | | | % 151.29/22.23 | | | | REF_CLOSE: (1), (6), (11), (19), (20), (21), (22), (23), (24), (27), % 151.29/22.23 | | | | (31), (32), (33), (37), (38), (40), (44), (46), (51), (55), % 151.29/22.23 | | | | (58), (61), (66), (67), (74), (78), (80), (82), (85), (86), % 151.29/22.23 | | | | (87), (92), (94), (95), (96), (100), (126), (128), (130), % 151.29/22.23 | | | | (132) are inconsistent by sub-proof #222. % 151.29/22.23 | | | | % 151.29/22.23 | | | End of split % 151.29/22.23 | | | % 151.29/22.23 | | Case 2: % 151.29/22.23 | | | % 151.29/22.23 | | | (133) all_56_11 = e0 % 151.29/22.23 | | | % 151.29/22.23 | | | COMBINE_EQS: (1), (133) imply: % 151.29/22.23 | | | (134) all_8_2 = e0 % 151.29/22.23 | | | % 151.29/22.23 | | | REDUCE: (95), (134) imply: % 151.29/22.23 | | | (135) op(e0, e0) = all_8_1 % 151.29/22.23 | | | % 151.29/22.23 | | | REF_CLOSE: (5), (6), (46), (135) are inconsistent by sub-proof #519. % 151.29/22.23 | | | % 151.29/22.23 | | End of split % 151.29/22.23 | | % 151.29/22.23 | Case 2: % 151.29/22.23 | | % 151.29/22.23 | | (136) ~ (all_34_2 = e1) % 151.29/22.23 | | % 151.29/22.23 | | REDUCE: (14), (136) imply: % 151.29/22.23 | | (137) $false % 151.29/22.23 | | % 151.29/22.23 | | CLOSE: (137) is inconsistent. % 151.29/22.23 | | % 151.29/22.23 | End of split % 151.29/22.23 | % 151.29/22.23 End of proof % 151.29/22.23 % 151.29/22.23 Sub-proof #222 shows that the following formulas are inconsistent: % 151.29/22.23 ---------------------------------------------------------------- % 151.29/22.23 (1) all_56_11 = all_8_2 % 151.29/22.23 (2) ~ (all_8_1 = e1) % 151.29/22.23 (3) ~ (all_6_1 = e2) % 151.29/22.23 (4) ~ (all_8_2 = e1) % 151.29/22.23 (5) ~ (all_8_1 = e3) % 151.29/22.23 (6) ~ (e3 = e2) % 151.29/22.23 (7) op(e0, e0) = all_4_2 % 151.29/22.23 (8) all_58_4 = all_52_8 % 151.29/22.23 (9) op(e2, e2) = all_6_1 % 151.29/22.23 (10) all_54_5 = all_8_2 % 151.29/22.23 (11) ~ (all_6_1 = e3) % 151.29/22.23 (12) all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1 % 151.29/22.23 (13) ~ (all_52_7 = all_8_2) % 151.29/22.23 (14) all_56_1 = all_10_2 % 151.29/22.23 (15) all_56_27 = all_52_7 % 151.29/22.23 (16) all_58_9 = all_52_12 % 151.29/22.23 (17) op(e1, e0) = all_52_14 % 151.29/22.23 (18) all_58_1 = all_52_4 % 151.29/22.23 (19) all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0 % 151.29/22.23 (20) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 151.29/22.23 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 151.29/22.23 (21) ~ (all_52_14 = e1) % 151.29/22.23 (22) all_56_7 = all_52_12 % 151.29/22.23 (23) ~ (all_6_0 = e3) % 151.29/22.23 (24) ~ (all_56_1 = e0) | all_56_7 = e3 % 151.29/22.23 (25) ~ (e2 = e1) % 151.29/22.23 (26) op(e1, all_6_1) = all_6_0 % 151.29/22.23 (27) op(e1, all_52_8) = all_56_4 % 151.29/22.23 (28) all_58_11 = all_52_14 % 151.29/22.23 (29) all_58_15 = all_4_2 % 151.29/22.23 (30) all_58_10 = all_52_13 % 151.29/22.23 (31) ~ (all_56_11 = e0) | all_56_15 = e2 % 151.29/22.23 (32) all_58_0 = all_10_2 % 151.29/22.23 (33) ~ (all_56_31 = e2) | all_56_27 = e0 % 151.29/22.23 (34) ~ (e3 = e1) % 151.29/22.23 (35) op(e2, e2) = all_8_2 % 151.29/22.23 (36) all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3 % 151.29/22.23 (37) ~ (all_52_4 = all_8_2) % 151.29/22.23 (38) op(all_8_2, all_8_2) = all_8_1 % 151.29/22.23 (39) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 151.29/22.23 (40) all_56_15 = all_52_13 % 151.29/22.23 % 151.29/22.23 Begin of proof % 151.29/22.23 | % 151.29/22.23 | GROUND_INST: instantiating (20) with all_8_2, all_6_1, e2, e2, simplifying % 151.29/22.23 | with (9), (35) gives: % 151.29/22.23 | (41) all_8_2 = all_6_1 % 151.29/22.23 | % 151.29/22.23 | COMBINE_EQS: (10), (41) imply: % 151.29/22.23 | (42) all_54_5 = all_6_1 % 151.29/22.23 | % 151.29/22.23 | COMBINE_EQS: (1), (41) imply: % 151.29/22.23 | (43) all_56_11 = all_6_1 % 151.29/22.23 | % 151.29/22.23 | REDUCE: (37), (41) imply: % 151.29/22.23 | (44) ~ (all_52_4 = all_6_1) % 151.29/22.23 | % 151.29/22.23 | REDUCE: (13), (41) imply: % 151.29/22.23 | (45) ~ (all_52_7 = all_6_1) % 151.29/22.23 | % 151.29/22.23 | REDUCE: (4), (41) imply: % 151.29/22.23 | (46) ~ (all_6_1 = e1) % 151.29/22.23 | % 151.29/22.23 | REDUCE: (38), (41) imply: % 151.29/22.23 | (47) op(all_6_1, all_6_1) = all_8_1 % 151.29/22.23 | % 151.29/22.23 | BETA: splitting (39) gives: % 151.29/22.23 | % 151.29/22.23 | Case 1: % 151.29/22.23 | | % 151.29/22.23 | | (48) all_54_5 = e3 % 151.29/22.24 | | % 151.29/22.24 | | REF_CLOSE: (11), (42), (48) are inconsistent by sub-proof #509. % 151.29/22.24 | | % 151.29/22.24 | Case 2: % 151.29/22.24 | | % 151.29/22.24 | | (49) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 151.29/22.24 | | % 151.29/22.24 | | BETA: splitting (49) gives: % 151.29/22.24 | | % 151.29/22.24 | | Case 1: % 151.29/22.24 | | | % 151.29/22.24 | | | (50) all_54_5 = e2 % 151.29/22.24 | | | % 151.29/22.24 | | | REF_CLOSE: (3), (42), (50) are inconsistent by sub-proof #466. % 151.29/22.24 | | | % 151.29/22.24 | | Case 2: % 151.29/22.24 | | | % 151.29/22.24 | | | (51) all_54_5 = e1 | all_54_5 = e0 % 151.29/22.24 | | | % 151.29/22.24 | | | BETA: splitting (51) gives: % 151.29/22.24 | | | % 151.29/22.24 | | | Case 1: % 151.29/22.24 | | | | % 151.29/22.24 | | | | (52) all_54_5 = e1 % 151.29/22.24 | | | | % 151.29/22.24 | | | | REF_CLOSE: (42), (46), (52) are inconsistent by sub-proof #465. % 151.29/22.24 | | | | % 151.29/22.24 | | | Case 2: % 151.29/22.24 | | | | % 151.29/22.24 | | | | (53) all_54_5 = e0 % 151.29/22.24 | | | | % 151.29/22.24 | | | | COMBINE_EQS: (42), (53) imply: % 151.29/22.24 | | | | (54) all_6_1 = e0 % 151.29/22.24 | | | | % 151.29/22.24 | | | | SIMP: (54) implies: % 151.29/22.24 | | | | (55) all_6_1 = e0 % 151.29/22.24 | | | | % 151.29/22.24 | | | | COMBINE_EQS: (43), (55) imply: % 151.29/22.24 | | | | (56) all_56_11 = e0 % 151.29/22.24 | | | | % 151.29/22.24 | | | | REDUCE: (44), (55) imply: % 151.29/22.24 | | | | (57) ~ (all_52_4 = e0) % 151.29/22.24 | | | | % 151.29/22.24 | | | | REDUCE: (45), (55) imply: % 151.29/22.24 | | | | (58) ~ (all_52_7 = e0) % 151.29/22.24 | | | | % 151.29/22.24 | | | | REDUCE: (46), (55) imply: % 151.29/22.24 | | | | (59) ~ (e1 = e0) % 151.29/22.24 | | | | % 151.29/22.24 | | | | SIMP: (59) implies: % 151.29/22.24 | | | | (60) ~ (e1 = e0) % 151.29/22.24 | | | | % 151.29/22.24 | | | | REDUCE: (47), (55) imply: % 151.29/22.24 | | | | (61) op(e0, e0) = all_8_1 % 151.29/22.24 | | | | % 151.29/22.24 | | | | REDUCE: (26), (55) imply: % 151.29/22.24 | | | | (62) op(e1, e0) = all_6_0 % 151.29/22.24 | | | | % 151.29/22.24 | | | | BETA: splitting (33) gives: % 151.29/22.24 | | | | % 151.29/22.24 | | | | Case 1: % 151.29/22.24 | | | | | % 151.29/22.24 | | | | | % 151.29/22.24 | | | | | GROUND_INST: instantiating (20) with all_4_2, all_8_1, e0, e0, % 151.29/22.24 | | | | | simplifying with (7), (61) gives: % 151.29/22.24 | | | | | (63) all_8_1 = all_4_2 % 151.29/22.24 | | | | | % 151.29/22.24 | | | | | GROUND_INST: instantiating (20) with all_52_14, all_6_0, e0, e1, % 151.29/22.24 | | | | | simplifying with (17), (62) gives: % 151.29/22.24 | | | | | (64) all_52_14 = all_6_0 % 151.29/22.24 | | | | | % 151.29/22.24 | | | | | REDUCE: (2), (63) imply: % 151.29/22.24 | | | | | (65) ~ (all_4_2 = e1) % 151.29/22.24 | | | | | % 151.29/22.24 | | | | | REF_CLOSE: (5), (6), (7), (8), (12), (14), (16), (17), (18), (19), % 151.29/22.24 | | | | | (20), (21), (22), (23), (24), (25), (27), (28), (29), (30), % 151.29/22.24 | | | | | (31), (32), (34), (36), (40), (56), (57), (60), (61), (62), % 151.29/22.24 | | | | | (65) are inconsistent by sub-proof #284. % 151.29/22.24 | | | | | % 151.29/22.24 | | | | Case 2: % 151.29/22.24 | | | | | % 151.29/22.24 | | | | | (66) all_56_27 = e0 % 151.29/22.24 | | | | | % 151.29/22.24 | | | | | REF_CLOSE: (15), (58), (66) are inconsistent by sub-proof #223. % 151.29/22.24 | | | | | % 151.29/22.24 | | | | End of split % 151.29/22.24 | | | | % 151.29/22.24 | | | End of split % 151.29/22.24 | | | % 151.29/22.24 | | End of split % 151.29/22.24 | | % 151.29/22.24 | End of split % 151.29/22.24 | % 151.29/22.24 End of proof % 151.29/22.24 % 151.29/22.24 Sub-proof #223 shows that the following formulas are inconsistent: % 151.29/22.24 ---------------------------------------------------------------- % 151.29/22.24 (1) all_56_27 = all_52_7 % 151.29/22.24 (2) all_56_27 = e0 % 151.29/22.24 (3) ~ (all_52_7 = e0) % 151.29/22.24 % 151.29/22.24 Begin of proof % 151.29/22.24 | % 151.29/22.24 | COMBINE_EQS: (1), (2) imply: % 151.29/22.24 | (4) all_52_7 = e0 % 151.29/22.24 | % 151.29/22.24 | SIMP: (4) implies: % 151.29/22.24 | (5) all_52_7 = e0 % 151.29/22.24 | % 151.29/22.24 | REDUCE: (3), (5) imply: % 151.29/22.24 | (6) $false % 151.29/22.24 | % 151.29/22.24 | CLOSE: (6) is inconsistent. % 151.29/22.24 | % 151.29/22.24 End of proof % 151.29/22.24 % 151.29/22.24 Sub-proof #224 shows that the following formulas are inconsistent: % 151.29/22.24 ---------------------------------------------------------------- % 151.29/22.24 (1) all_56_11 = all_8_2 % 151.29/22.24 (2) ~ (all_8_1 = e1) % 151.29/22.24 (3) ~ (all_8_1 = e3) % 151.29/22.24 (4) op(e0, e0) = all_4_2 % 151.29/22.24 (5) all_54_15 = all_4_2 % 151.29/22.24 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 151.29/22.24 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 151.29/22.24 (7) all_56_15 = e2 % 151.29/22.24 (8) op(e0, all_4_1) = e2 % 151.29/22.24 (9) op(all_4_2, all_4_2) = all_4_1 % 151.29/22.24 (10) ~ (all_52_13 = all_4_2) % 151.29/22.24 (11) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0 % 151.29/22.24 (12) all_56_11 = e0 % 151.29/22.24 (13) op(e0, all_4_2) = all_56_30 % 151.29/22.24 (14) op(all_8_2, all_8_2) = all_8_1 % 151.29/22.24 (15) all_56_15 = all_52_13 % 151.29/22.24 % 151.29/22.24 Begin of proof % 151.29/22.24 | % 151.29/22.24 | COMBINE_EQS: (1), (12) imply: % 151.29/22.24 | (16) all_8_2 = e0 % 151.29/22.24 | % 151.29/22.24 | COMBINE_EQS: (7), (15) imply: % 151.29/22.24 | (17) all_52_13 = e2 % 151.29/22.24 | % 151.29/22.24 | REDUCE: (10), (17) imply: % 151.29/22.24 | (18) ~ (all_4_2 = e2) % 151.29/22.24 | % 151.29/22.24 | SIMP: (18) implies: % 151.29/22.24 | (19) ~ (all_4_2 = e2) % 151.29/22.24 | % 151.29/22.24 | REDUCE: (14), (16) imply: % 151.29/22.24 | (20) op(e0, e0) = all_8_1 % 151.29/22.24 | % 151.29/22.24 | GROUND_INST: instantiating (6) with all_4_2, all_8_1, e0, e0, simplifying with % 151.29/22.24 | (4), (20) gives: % 151.29/22.24 | (21) all_8_1 = all_4_2 % 151.29/22.24 | % 151.29/22.24 | REDUCE: (3), (21) imply: % 151.29/22.24 | (22) ~ (all_4_2 = e3) % 151.29/22.24 | % 151.29/22.24 | REDUCE: (2), (21) imply: % 151.29/22.24 | (23) ~ (all_4_2 = e1) % 151.29/22.24 | % 151.29/22.24 | REF_CLOSE: (4), (5), (6), (8), (9), (11), (13), (19), (22), (23) are % 151.29/22.24 | inconsistent by sub-proof #229. % 151.29/22.24 | % 151.29/22.24 End of proof % 151.29/22.24 % 151.29/22.24 Sub-proof #225 shows that the following formulas are inconsistent: % 151.29/22.24 ---------------------------------------------------------------- % 151.29/22.24 (1) all_56_11 = all_8_2 % 151.29/22.24 (2) all_54_9 = all_52_6 % 151.29/22.24 (3) ~ (all_6_1 = e2) % 151.29/22.24 (4) all_54_0 = all_10_2 % 151.29/22.24 (5) all_56_21 = e3 % 151.29/22.24 (6) ~ (all_52_14 = all_4_2) % 151.29/22.24 (7) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0 % 151.29/22.24 (8) ~ (all_52_12 = all_52_13) % 151.29/22.24 (9) ~ (all_6_1 = e3) % 151.29/22.24 (10) ~ (all_52_6 = all_52_14) % 151.29/22.24 (11) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 151.29/22.24 (12) ~ (all_6_0 = e2) % 151.29/22.24 (13) all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1 % 151.29/22.24 (14) all_56_21 = all_6_2 % 151.29/22.24 (15) all_56_1 = all_10_2 % 151.29/22.24 (16) all_58_5 = all_52_9 % 151.29/22.24 (17) all_56_17 = all_52_2 % 151.29/22.24 (18) all_58_9 = all_52_12 % 151.29/22.24 (19) op(e1, e0) = all_52_14 % 151.29/22.24 (20) op(e3, e3) = all_10_2 % 151.29/22.24 (21) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 151.29/22.24 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 151.29/22.24 (22) all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0 % 151.29/22.24 (23) ~ (all_52_2 = all_52_6) % 151.29/22.24 (24) all_56_7 = all_52_12 % 151.29/22.24 (25) ~ (all_4_2 = e1) % 151.29/22.24 (26) ~ (all_56_1 = e0) | all_56_7 = e3 % 151.29/22.24 (27) op(e1, all_6_1) = all_6_0 % 151.29/22.24 (28) all_58_3 = all_8_2 % 151.29/22.24 (29) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0 % 151.29/22.24 (30) all_56_31 = all_4_2 % 151.29/22.24 (31) all_58_11 = all_52_14 % 151.29/22.24 (32) ~ (all_52_2 = all_52_14) % 151.29/22.24 (33) op(all_6_2, all_6_2) = all_6_1 % 151.29/22.24 (34) all_56_1 = e3 | all_56_11 = e2 | all_56_21 = e1 | all_56_31 = e0 % 151.29/22.24 (35) all_56_17 = e1 % 151.29/22.24 (36) ~ (all_52_13 = all_52_14) % 151.29/22.24 (37) ~ (all_52_6 = all_8_2) % 151.29/22.24 (38) all_58_15 = all_4_2 % 151.29/22.24 (39) all_58_2 = all_52_1 % 151.29/22.24 (40) all_58_10 = all_52_13 % 151.29/22.24 (41) ~ (all_52_12 = all_52_14) % 151.29/22.24 (42) op(e1, all_52_9) = all_56_12 % 151.29/22.24 (43) ~ (all_52_2 = all_6_2) % 151.29/22.24 (44) ~ (all_52_6 = all_6_2) % 151.29/22.24 (45) ~ (all_8_2 = e0) % 151.29/22.24 (46) ~ (all_52_2 = all_10_2) % 151.29/22.24 (47) ~ (all_52_1 = all_10_2) % 151.29/22.24 (48) all_54_11 = all_52_14 % 151.29/22.24 % 151.29/22.24 Begin of proof % 151.29/22.24 | % 151.29/22.24 | COMBINE_EQS: (17), (35) imply: % 151.29/22.24 | (49) all_52_2 = e1 % 151.29/22.24 | % 151.29/22.24 | COMBINE_EQS: (5), (14) imply: % 151.29/22.24 | (50) all_6_2 = e3 % 151.29/22.24 | % 151.29/22.24 | SIMP: (50) implies: % 151.29/22.24 | (51) all_6_2 = e3 % 151.29/22.24 | % 151.29/22.24 | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), % 151.29/22.24 | (13), (15), (16), (18), (19), (20), (21), (22), (23), (24), (25), % 151.29/22.24 | (26), (27), (28), (29), (30), (31), (32), (33), (34), (36), (37), % 151.29/22.24 | (38), (39), (40), (41), (42), (43), (44), (45), (46), (47), (48), % 151.29/22.24 | (49), (51) are inconsistent by sub-proof #293. % 151.29/22.24 | % 151.29/22.24 End of proof % 151.29/22.24 % 151.29/22.24 Sub-proof #226 shows that the following formulas are inconsistent: % 151.29/22.24 ---------------------------------------------------------------- % 151.29/22.24 (1) all_58_14 = e1 | all_58_15 = e1 % 151.29/22.24 (2) ~ (all_52_11 = e1) % 151.29/22.24 (3) all_58_15 = e3 % 151.29/22.24 (4) ~ (e3 = e1) % 151.29/22.24 (5) all_58_14 = all_52_11 % 151.29/22.24 % 151.29/22.24 Begin of proof % 151.29/22.24 | % 151.29/22.24 | BETA: splitting (1) gives: % 151.29/22.24 | % 151.29/22.24 | Case 1: % 151.29/22.24 | | % 151.29/22.24 | | (6) all_58_14 = e1 % 151.29/22.24 | | % 151.29/22.24 | | REF_CLOSE: (2), (5), (6) are inconsistent by sub-proof #699. % 151.29/22.24 | | % 151.29/22.24 | Case 2: % 151.29/22.24 | | % 151.29/22.24 | | (7) all_58_15 = e1 % 151.29/22.24 | | % 151.29/22.24 | | COMBINE_EQS: (3), (7) imply: % 151.29/22.24 | | (8) e3 = e1 % 151.29/22.24 | | % 151.29/22.24 | | REDUCE: (4), (8) imply: % 151.29/22.24 | | (9) $false % 151.29/22.24 | | % 151.29/22.24 | | CLOSE: (9) is inconsistent. % 151.29/22.24 | | % 151.29/22.24 | End of split % 151.29/22.24 | % 151.29/22.24 End of proof % 151.29/22.24 % 151.29/22.24 Sub-proof #227 shows that the following formulas are inconsistent: % 151.29/22.24 ---------------------------------------------------------------- % 151.29/22.24 (1) ~ (all_6_1 = e2) % 151.29/22.24 (2) ~ (all_52_14 = all_4_2) % 151.29/22.24 (3) op(e0, e0) = all_4_2 % 151.29/22.24 (4) ~ (all_6_1 = e3) % 151.29/22.24 (5) all_54_15 = all_4_2 % 151.29/22.24 (6) all_56_21 = all_6_2 % 151.29/22.24 (7) all_56_21 = e0 % 151.29/22.24 (8) all_56_23 = e1 % 151.29/22.24 (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 151.29/22.24 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 151.29/22.24 (10) op(e0, all_4_1) = e2 % 151.29/22.24 (11) op(all_4_2, all_4_2) = all_4_1 % 151.29/22.24 (12) op(all_6_2, all_6_2) = all_6_1 % 151.29/22.24 (13) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0 % 151.29/22.24 (14) all_56_23 = all_52_14 % 151.29/22.24 (15) op(e0, all_4_2) = all_56_30 % 151.29/22.24 % 151.29/22.24 Begin of proof % 151.29/22.24 | % 151.29/22.24 | COMBINE_EQS: (6), (7) imply: % 151.29/22.24 | (16) all_6_2 = e0 % 151.29/22.24 | % 151.29/22.24 | SIMP: (16) implies: % 151.29/22.24 | (17) all_6_2 = e0 % 151.29/22.24 | % 151.29/22.24 | COMBINE_EQS: (8), (14) imply: % 151.29/22.24 | (18) all_52_14 = e1 % 151.29/22.24 | % 151.29/22.24 | SIMP: (18) implies: % 151.29/22.24 | (19) all_52_14 = e1 % 151.29/22.24 | % 151.29/22.24 | REDUCE: (2), (19) imply: % 151.29/22.24 | (20) ~ (all_4_2 = e1) % 151.29/22.24 | % 151.29/22.24 | SIMP: (20) implies: % 151.29/22.24 | (21) ~ (all_4_2 = e1) % 151.29/22.24 | % 151.29/22.24 | REDUCE: (12), (17) imply: % 151.29/22.24 | (22) op(e0, e0) = all_6_1 % 151.29/22.24 | % 151.29/22.24 | GROUND_INST: instantiating (9) with all_4_2, all_6_1, e0, e0, simplifying with % 151.29/22.24 | (3), (22) gives: % 151.29/22.24 | (23) all_6_1 = all_4_2 % 151.29/22.24 | % 151.29/22.24 | REF_CLOSE: (1), (4), (5), (9), (10), (11), (13), (15), (21), (22), (23) are % 151.29/22.24 | inconsistent by sub-proof #228. % 151.29/22.24 | % 151.29/22.24 End of proof % 151.29/22.24 % 151.29/22.24 Sub-proof #228 shows that the following formulas are inconsistent: % 151.29/22.24 ---------------------------------------------------------------- % 151.29/22.24 (1) ~ (all_6_1 = e2) % 151.29/22.24 (2) ~ (all_6_1 = e3) % 151.29/22.24 (3) all_54_15 = all_4_2 % 151.29/22.24 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 151.29/22.24 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 151.29/22.24 (5) all_6_1 = all_4_2 % 151.29/22.24 (6) op(e0, all_4_1) = e2 % 151.29/22.24 (7) ~ (all_4_2 = e1) % 151.29/22.24 (8) op(all_4_2, all_4_2) = all_4_1 % 151.29/22.24 (9) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0 % 151.29/22.24 (10) op(e0, e0) = all_6_1 % 151.29/22.24 (11) op(e0, all_4_2) = all_56_30 % 151.29/22.24 % 151.29/22.24 Begin of proof % 151.29/22.24 | % 151.29/22.24 | REDUCE: (2), (5) imply: % 151.29/22.24 | (12) ~ (all_4_2 = e3) % 151.29/22.24 | % 151.29/22.24 | REDUCE: (1), (5) imply: % 151.29/22.24 | (13) ~ (all_4_2 = e2) % 151.29/22.24 | % 151.29/22.24 | REDUCE: (5), (10) imply: % 151.29/22.24 | (14) op(e0, e0) = all_4_2 % 151.29/22.24 | % 151.29/22.24 | REF_CLOSE: (3), (4), (6), (7), (8), (9), (11), (12), (13), (14) are % 151.29/22.24 | inconsistent by sub-proof #229. % 151.29/22.24 | % 151.29/22.24 End of proof % 151.29/22.24 % 151.29/22.24 Sub-proof #229 shows that the following formulas are inconsistent: % 151.29/22.24 ---------------------------------------------------------------- % 151.29/22.24 (1) op(e0, e0) = all_4_2 % 151.29/22.24 (2) all_54_15 = all_4_2 % 151.29/22.24 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 151.29/22.24 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 151.29/22.24 (4) op(e0, all_4_1) = e2 % 151.29/22.24 (5) ~ (all_4_2 = e1) % 151.29/22.24 (6) ~ (all_4_2 = e2) % 151.29/22.24 (7) op(all_4_2, all_4_2) = all_4_1 % 151.29/22.24 (8) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0 % 151.29/22.24 (9) ~ (all_4_2 = e3) % 151.29/22.24 (10) op(e0, all_4_2) = all_56_30 % 151.29/22.24 % 151.29/22.24 Begin of proof % 151.29/22.24 | % 151.29/22.24 | BETA: splitting (8) gives: % 151.29/22.24 | % 151.29/22.24 | Case 1: % 151.29/22.24 | | % 151.29/22.24 | | (11) all_54_15 = e3 % 151.29/22.24 | | % 151.29/22.24 | | REF_CLOSE: (2), (9), (11) are inconsistent by sub-proof #740. % 151.29/22.24 | | % 151.29/22.24 | Case 2: % 151.29/22.24 | | % 151.29/22.24 | | (12) all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0 % 151.29/22.24 | | % 151.29/22.24 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (10), (12) are inconsistent by % 151.29/22.24 | | sub-proof #230. % 151.29/22.24 | | % 151.29/22.24 | End of split % 151.29/22.24 | % 151.29/22.24 End of proof % 151.29/22.24 % 151.29/22.24 Sub-proof #230 shows that the following formulas are inconsistent: % 151.29/22.24 ---------------------------------------------------------------- % 151.29/22.24 (1) op(e0, e0) = all_4_2 % 151.29/22.24 (2) all_54_15 = all_4_2 % 151.29/22.24 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 151.29/22.24 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 151.29/22.24 (4) op(e0, all_4_1) = e2 % 151.29/22.24 (5) ~ (all_4_2 = e1) % 151.29/22.24 (6) ~ (all_4_2 = e2) % 151.29/22.24 (7) op(all_4_2, all_4_2) = all_4_1 % 151.29/22.24 (8) op(e0, all_4_2) = all_56_30 % 151.29/22.24 (9) all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0 % 151.29/22.24 % 151.29/22.24 Begin of proof % 151.29/22.24 | % 151.29/22.24 | BETA: splitting (9) gives: % 151.29/22.24 | % 151.29/22.24 | Case 1: % 151.29/22.24 | | % 151.29/22.24 | | (10) all_54_15 = e2 % 151.29/22.24 | | % 151.29/22.24 | | REF_CLOSE: (2), (6), (10) are inconsistent by sub-proof #739. % 151.29/22.24 | | % 151.29/22.24 | Case 2: % 151.29/22.24 | | % 151.29/22.24 | | (11) ~ (all_54_15 = e2) % 151.29/22.24 | | (12) all_54_15 = e1 | all_54_15 = e0 % 151.29/22.24 | | % 151.29/22.24 | | BETA: splitting (12) gives: % 151.29/22.24 | | % 151.29/22.24 | | Case 1: % 151.29/22.24 | | | % 151.29/22.24 | | | (13) all_54_15 = e1 % 151.29/22.24 | | | % 151.29/22.24 | | | REF_CLOSE: (2), (5), (13) are inconsistent by sub-proof #738. % 151.29/22.24 | | | % 151.29/22.24 | | Case 2: % 151.29/22.24 | | | % 151.29/22.24 | | | (14) all_54_15 = e0 % 151.29/22.24 | | | % 151.29/22.24 | | | COMBINE_EQS: (2), (14) imply: % 151.29/22.24 | | | (15) all_4_2 = e0 % 151.29/22.24 | | | % 151.29/22.24 | | | SIMP: (15) implies: % 151.29/22.24 | | | (16) all_4_2 = e0 % 151.29/22.24 | | | % 151.29/22.24 | | | REDUCE: (6), (16) imply: % 151.29/22.24 | | | (17) ~ (e2 = e0) % 151.29/22.24 | | | % 151.29/22.24 | | | SIMP: (17) implies: % 151.29/22.24 | | | (18) ~ (e2 = e0) % 151.29/22.24 | | | % 151.29/22.24 | | | REDUCE: (7), (16) imply: % 151.29/22.24 | | | (19) op(e0, e0) = all_4_1 % 151.29/22.24 | | | % 151.29/22.24 | | | REDUCE: (8), (16) imply: % 151.29/22.24 | | | (20) op(e0, e0) = all_56_30 % 151.29/22.24 | | | % 151.29/22.24 | | | REDUCE: (1), (16) imply: % 151.29/22.24 | | | (21) op(e0, e0) = e0 % 151.29/22.24 | | | % 151.29/22.24 | | | GROUND_INST: instantiating (3) with all_4_1, all_56_30, e0, e0, % 151.29/22.24 | | | simplifying with (19), (20) gives: % 151.29/22.24 | | | (22) all_56_30 = all_4_1 % 151.29/22.24 | | | % 151.29/22.24 | | | GROUND_INST: instantiating (3) with e0, all_56_30, e0, e0, simplifying % 151.29/22.24 | | | with (20), (21) gives: % 151.29/22.24 | | | (23) all_56_30 = e0 % 151.29/22.24 | | | % 151.29/22.24 | | | COMBINE_EQS: (22), (23) imply: % 151.29/22.24 | | | (24) all_4_1 = e0 % 151.29/22.24 | | | % 151.29/22.24 | | | SIMP: (24) implies: % 151.29/22.24 | | | (25) all_4_1 = e0 % 151.29/22.24 | | | % 151.29/22.24 | | | REDUCE: (4), (25) imply: % 151.29/22.24 | | | (26) op(e0, e0) = e2 % 151.29/22.24 | | | % 151.29/22.24 | | | REF_CLOSE: (3), (18), (19), (20), (21), (26) are inconsistent by sub-proof % 151.29/22.24 | | | #231. % 151.29/22.24 | | | % 151.29/22.24 | | End of split % 151.29/22.24 | | % 151.29/22.24 | End of split % 151.29/22.24 | % 151.29/22.24 End of proof % 151.29/22.24 % 151.29/22.24 Sub-proof #231 shows that the following formulas are inconsistent: % 151.29/22.24 ---------------------------------------------------------------- % 151.29/22.24 (1) op(e0, e0) = all_56_30 % 151.29/22.24 (2) op(e0, e0) = all_4_1 % 151.29/22.24 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 151.29/22.24 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 151.29/22.24 (4) op(e0, e0) = e2 % 151.29/22.24 (5) op(e0, e0) = e0 % 151.29/22.24 (6) ~ (e2 = e0) % 151.29/22.24 % 151.29/22.24 Begin of proof % 151.29/22.24 | % 151.29/22.24 | GROUND_INST: instantiating (3) with all_4_1, all_56_30, e0, e0, simplifying % 151.29/22.24 | with (1), (2) gives: % 151.29/22.24 | (7) all_56_30 = all_4_1 % 151.29/22.24 | % 151.29/22.24 | GROUND_INST: instantiating (3) with e2, all_56_30, e0, e0, simplifying with % 151.29/22.24 | (1), (4) gives: % 151.29/22.24 | (8) all_56_30 = e2 % 151.29/22.24 | % 151.29/22.24 | GROUND_INST: instantiating (3) with e0, all_56_30, e0, e0, simplifying with % 151.29/22.24 | (1), (5) gives: % 151.29/22.24 | (9) all_56_30 = e0 % 151.29/22.24 | % 151.29/22.24 | COMBINE_EQS: (7), (9) imply: % 151.29/22.24 | (10) all_4_1 = e0 % 151.29/22.24 | % 151.29/22.24 | COMBINE_EQS: (7), (8) imply: % 151.29/22.24 | (11) all_4_1 = e2 % 151.29/22.24 | % 151.29/22.24 | COMBINE_EQS: (10), (11) imply: % 151.29/22.24 | (12) e2 = e0 % 151.29/22.24 | % 151.29/22.24 | SIMP: (12) implies: % 151.29/22.24 | (13) e2 = e0 % 151.29/22.24 | % 151.29/22.24 | REDUCE: (6), (13) imply: % 151.29/22.24 | (14) $false % 151.29/22.24 | % 151.29/22.24 | CLOSE: (14) is inconsistent. % 151.29/22.24 | % 151.29/22.24 End of proof % 151.29/22.24 % 151.29/22.24 Sub-proof #232 shows that the following formulas are inconsistent: % 151.29/22.24 ---------------------------------------------------------------- % 151.29/22.24 (1) all_56_11 = all_8_2 % 151.29/22.24 (2) ~ (all_56_11 = e1) | all_56_13 = e2 % 151.29/22.24 (3) all_14_2 = all_8_2 % 151.29/22.24 (4) ~ (all_8_1 = e1) % 151.29/22.24 (5) ~ (all_52_13 = e1) % 151.29/22.24 (6) all_54_10 = all_6_2 % 151.29/22.24 (7) ~ (all_6_1 = e2) % 151.29/22.24 (8) ~ (all_56_21 = e2) | all_56_19 = e1 % 151.29/22.24 (9) all_54_0 = all_10_2 % 151.29/22.24 (10) all_54_12 = all_52_3 % 151.29/22.24 (11) op(e0, e0) = all_4_2 % 151.29/22.24 (12) all_54_5 = all_8_2 % 151.29/22.24 (13) ~ (all_6_1 = e3) % 151.29/22.24 (14) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 151.29/22.24 (15) ~ (all_6_0 = e2) % 151.29/22.24 (16) all_54_15 = all_4_2 % 151.29/22.24 (17) all_42_1 = all_8_1 % 151.29/22.24 (18) all_56_21 = all_6_2 % 151.29/22.24 (19) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 151.29/22.24 (20) all_56_17 = all_52_2 % 151.29/22.24 (21) all_14_1 = all_8_1 % 151.29/22.24 (22) op(e2, all_8_2) = all_56_10 % 151.29/22.24 (23) op(e3, e3) = all_10_2 % 151.29/22.24 (24) all_42_2 = all_8_2 % 151.29/22.24 (25) ~ (all_56_21 = e3) | all_56_17 = e1 % 151.29/22.24 (26) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 151.29/22.24 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 151.29/22.24 (27) ~ (all_6_2 = e0) % 151.29/22.24 (28) ~ (all_56_11 = e3) | all_56_9 = e2 % 151.29/22.24 (29) op(e0, all_4_1) = all_4_0 % 151.29/22.24 (30) ~ (all_52_3 = e0) % 151.29/22.24 (31) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0 % 151.29/22.24 (32) op(e2, all_8_1) = e1 % 151.29/22.24 (33) ~ (all_52_2 = all_52_3) % 151.29/22.24 (34) ~ (all_14_1 = e3) | ~ (all_14_2 = e0) % 151.29/22.24 (35) op(e1, all_6_1) = all_6_0 % 151.29/22.24 (36) ~ (all_42_1 = e0) | ~ (all_42_2 = e3) % 151.29/22.24 (37) op(all_6_2, all_6_2) = all_6_1 % 151.29/22.24 (38) ~ (all_52_13 = all_4_2) % 151.29/22.24 (39) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0 % 151.29/22.24 (40) op(e1, e1) = all_6_2 % 151.29/22.24 (41) ~ (all_52_6 = all_8_2) % 151.29/22.24 (42) op(e0, e3) = all_52_3 % 151.29/22.24 (43) ~ (all_56_11 = e0) | all_56_15 = e2 % 151.29/22.24 (44) op(e1, e1) = all_4_1 % 151.29/22.24 (45) op(e1, all_6_2) = all_56_20 % 151.29/22.24 (46) op(e2, e3) = all_52_1 % 151.29/22.24 (47) op(e2, e2) = all_8_2 % 151.29/22.24 (48) op(e2, e0) = all_52_13 % 151.29/22.24 (49) ~ (all_52_6 = all_6_2) % 151.29/22.24 (50) op(all_8_2, all_8_2) = all_8_1 % 151.29/22.24 (51) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 151.29/22.24 (52) all_56_19 = all_52_6 % 151.29/22.24 (53) ~ (all_4_0 = e2) % 151.29/22.24 (54) ~ (all_4_0 = e3) % 151.29/22.24 (55) all_56_9 = all_52_1 % 151.29/22.24 (56) all_56_15 = all_52_13 % 151.29/22.24 (57) ~ (all_52_1 = all_10_2) % 151.29/22.24 % 151.29/22.24 Begin of proof % 151.29/22.24 | % 151.29/22.24 | GROUND_INST: instantiating (26) with all_6_2, all_4_1, e1, e1, simplifying % 151.29/22.24 | with (40), (44) gives: % 151.29/22.24 | (58) all_6_2 = all_4_1 % 151.29/22.24 | % 151.29/22.24 | COMBINE_EQS: (6), (58) imply: % 151.29/22.24 | (59) all_54_10 = all_4_1 % 151.29/22.24 | % 151.29/22.24 | COMBINE_EQS: (18), (58) imply: % 151.29/22.24 | (60) all_56_21 = all_4_1 % 151.29/22.24 | % 151.29/22.24 | REDUCE: (49), (58) imply: % 151.29/22.24 | (61) ~ (all_52_6 = all_4_1) % 151.29/22.24 | % 151.29/22.24 | REDUCE: (27), (58) imply: % 151.29/22.24 | (62) ~ (all_4_1 = e0) % 151.29/22.24 | % 151.29/22.24 | REDUCE: (37), (58) imply: % 151.44/22.24 | (63) op(all_4_1, all_4_1) = all_6_1 % 151.44/22.24 | % 151.44/22.24 | REDUCE: (45), (58) imply: % 151.44/22.24 | (64) op(e1, all_4_1) = all_56_20 % 151.44/22.24 | % 151.44/22.24 | BETA: splitting (8) gives: % 151.44/22.24 | % 151.44/22.24 | Case 1: % 151.44/22.24 | | % 151.44/22.24 | | (65) ~ (all_56_21 = e2) % 151.44/22.24 | | % 151.44/22.24 | | REDUCE: (60), (65) imply: % 151.44/22.24 | | (66) ~ (all_4_1 = e2) % 151.44/22.24 | | % 151.44/22.24 | | BETA: splitting (43) gives: % 151.44/22.24 | | % 151.44/22.24 | | Case 1: % 151.44/22.24 | | | % 151.44/22.24 | | | (67) ~ (all_56_11 = e0) % 151.44/22.24 | | | % 151.44/22.24 | | | REDUCE: (1), (67) imply: % 151.44/22.24 | | | (68) ~ (all_8_2 = e0) % 151.44/22.24 | | | % 151.44/22.24 | | | REF_CLOSE: (1), (2), (4), (9), (10), (12), (14), (15), (17), (19), (20), % 151.44/22.24 | | | (22), (23), (24), (25), (26), (28), (29), (30), (31), (32), % 151.44/22.24 | | | (33), (35), (36), (42), (44), (46), (47), (50), (51), (53), % 151.44/22.24 | | | (54), (55), (57), (59), (60), (62), (63), (64), (66), (68) are % 151.44/22.24 | | | inconsistent by sub-proof #239. % 151.44/22.24 | | | % 151.44/22.24 | | Case 2: % 151.44/22.24 | | | % 151.44/22.24 | | | (69) all_56_15 = e2 % 151.44/22.24 | | | (70) all_56_11 = e0 % 151.44/22.24 | | | % 151.44/22.24 | | | REF_CLOSE: (1), (3), (4), (5), (11), (16), (21), (22), (26), (32), (34), % 151.44/22.24 | | | (38), (39), (43), (48), (50), (56), (69), (70) are inconsistent % 151.44/22.24 | | | by sub-proof #236. % 151.44/22.24 | | | % 151.44/22.24 | | End of split % 151.44/22.24 | | % 151.44/22.24 | Case 2: % 151.44/22.24 | | % 151.44/22.24 | | (71) all_56_21 = e2 % 151.44/22.24 | | (72) all_56_19 = e1 % 151.44/22.24 | | % 151.44/22.24 | | REF_CLOSE: (1), (3), (4), (7), (11), (12), (13), (16), (21), (22), (26), % 151.44/22.24 | | (32), (34), (38), (39), (41), (43), (47), (48), (50), (51), (52), % 151.44/22.24 | | (56), (60), (61), (63), (71), (72) are inconsistent by sub-proof % 151.44/22.24 | | #233. % 151.44/22.24 | | % 151.44/22.24 | End of split % 151.44/22.24 | % 151.44/22.24 End of proof % 151.44/22.24 % 151.44/22.24 Sub-proof #233 shows that the following formulas are inconsistent: % 151.44/22.24 ---------------------------------------------------------------- % 151.44/22.25 (1) all_56_11 = all_8_2 % 151.44/22.25 (2) all_14_2 = all_8_2 % 151.44/22.25 (3) ~ (all_8_1 = e1) % 151.44/22.25 (4) ~ (all_6_1 = e2) % 151.44/22.25 (5) op(e0, e0) = all_4_2 % 151.44/22.25 (6) all_54_5 = all_8_2 % 151.44/22.25 (7) ~ (all_6_1 = e3) % 151.44/22.25 (8) all_54_15 = all_4_2 % 151.44/22.25 (9) all_14_1 = all_8_1 % 151.44/22.25 (10) op(e2, all_8_2) = all_56_10 % 151.44/22.25 (11) ~ (all_52_6 = all_4_1) % 151.44/22.25 (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 151.44/22.25 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 151.44/22.25 (13) all_56_21 = all_4_1 % 151.44/22.25 (14) op(e2, all_8_1) = e1 % 151.44/22.25 (15) all_56_21 = e2 % 151.44/22.25 (16) all_56_19 = e1 % 151.44/22.25 (17) op(all_4_1, all_4_1) = all_6_1 % 151.44/22.25 (18) ~ (all_14_1 = e3) | ~ (all_14_2 = e0) % 151.44/22.25 (19) ~ (all_52_13 = all_4_2) % 151.44/22.25 (20) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0 % 151.44/22.25 (21) ~ (all_52_6 = all_8_2) % 151.44/22.25 (22) ~ (all_56_11 = e0) | all_56_15 = e2 % 151.44/22.25 (23) op(e2, e2) = all_8_2 % 151.44/22.25 (24) op(e2, e0) = all_52_13 % 151.44/22.25 (25) op(all_8_2, all_8_2) = all_8_1 % 151.44/22.25 (26) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 151.44/22.25 (27) all_56_19 = all_52_6 % 151.44/22.25 (28) all_56_15 = all_52_13 % 151.44/22.25 % 151.44/22.25 Begin of proof % 151.44/22.25 | % 151.44/22.25 | COMBINE_EQS: (16), (27) imply: % 151.44/22.25 | (29) all_52_6 = e1 % 151.44/22.25 | % 151.44/22.25 | COMBINE_EQS: (13), (15) imply: % 151.44/22.25 | (30) all_4_1 = e2 % 151.44/22.25 | % 151.44/22.25 | REDUCE: (21), (29) imply: % 151.44/22.25 | (31) ~ (all_8_2 = e1) % 151.44/22.25 | % 151.44/22.25 | SIMP: (31) implies: % 151.44/22.25 | (32) ~ (all_8_2 = e1) % 151.44/22.25 | % 151.44/22.25 | REDUCE: (11), (29), (30) imply: % 151.44/22.25 | (33) ~ (e2 = e1) % 151.44/22.25 | % 151.44/22.25 | SIMP: (33) implies: % 151.44/22.25 | (34) ~ (e2 = e1) % 151.44/22.25 | % 151.44/22.25 | REDUCE: (17), (30) imply: % 151.44/22.25 | (35) op(e2, e2) = all_6_1 % 151.44/22.25 | % 151.44/22.25 | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (12), (14), % 151.44/22.25 | (18), (19), (20), (22), (23), (24), (25), (26), (28), (32), (34), % 151.44/22.25 | (35) are inconsistent by sub-proof #235. % 151.44/22.25 | % 151.44/22.25 End of proof % 151.44/22.25 % 151.44/22.25 Sub-proof #234 shows that the following formulas are inconsistent: % 151.44/22.25 ---------------------------------------------------------------- % 151.44/22.25 (1) all_56_11 = all_8_2 % 151.44/22.25 (2) ~ (all_56_11 = e1) | all_56_13 = e2 % 151.44/22.25 (3) ~ (all_8_1 = e1) % 151.44/22.25 (4) ~ (all_52_1 = all_52_9) % 151.44/22.25 (5) all_54_10 = all_6_2 % 151.44/22.25 (6) ~ (all_6_1 = e2) % 151.44/22.25 (7) ~ (all_52_13 = all_8_2) % 151.44/22.25 (8) all_54_0 = all_10_2 % 151.44/22.25 (9) all_54_4 = all_52_1 % 151.44/22.25 (10) op(e0, e0) = all_4_2 % 151.44/22.25 (11) all_54_5 = all_8_2 % 151.44/22.25 (12) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 151.44/22.25 (13) all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1 % 151.44/22.25 (14) all_42_1 = all_8_1 % 151.44/22.25 (15) all_56_21 = all_6_2 % 151.44/22.25 (16) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 151.44/22.25 (17) ~ (all_52_7 = all_8_2) % 151.44/22.25 (18) all_56_27 = all_52_7 % 151.44/22.25 (19) all_56_17 = all_52_2 % 151.44/22.25 (20) all_58_9 = all_52_12 % 151.44/22.25 (21) op(e2, all_8_2) = all_56_10 % 151.44/22.25 (22) op(e3, e3) = all_10_2 % 151.44/22.25 (23) all_42_2 = all_8_2 % 151.44/22.25 (24) ~ (all_56_21 = e3) | all_56_17 = e1 % 151.44/22.25 (25) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 151.44/22.25 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 151.44/22.25 (26) all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0 % 151.44/22.25 (27) ~ (all_56_11 = e3) | all_56_9 = e2 % 151.44/22.25 (28) all_56_13 = all_52_9 % 151.44/22.25 (29) ~ (all_52_1 = all_52_13) % 151.44/22.25 (30) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0 % 151.44/22.25 (31) ~ (all_4_2 = e1) % 151.44/22.25 (32) op(e2, all_8_1) = e1 % 151.44/22.25 (33) all_56_31 = all_4_2 % 151.44/22.25 (34) all_58_11 = all_52_14 % 151.44/22.25 (35) ~ (all_42_1 = e0) | ~ (all_42_2 = e3) % 151.44/22.25 (36) ~ (all_52_2 = all_52_14) % 151.44/22.25 (37) op(all_6_2, all_6_2) = all_6_1 % 151.44/22.25 (38) op(e1, e1) = all_6_2 % 151.44/22.25 (39) all_58_15 = all_4_2 % 151.44/22.25 (40) all_58_2 = all_52_1 % 151.44/22.25 (41) ~ (all_4_2 = e3) % 151.44/22.25 (42) ~ (all_52_9 = all_6_2) % 151.44/22.25 (43) all_58_10 = all_52_13 % 151.44/22.25 (44) all_56_27 = e0 % 151.44/22.25 (45) op(e2, e3) = all_52_1 % 151.44/22.25 (46) op(e2, e2) = all_8_2 % 151.44/22.25 (47) all_56_31 = e2 % 151.44/22.25 (48) ~ (all_52_2 = all_6_2) % 151.44/22.25 (49) ~ (all_52_1 = all_52_2) % 151.44/22.25 (50) ~ (all_56_21 = e0) | all_56_23 = e1 % 151.44/22.25 (51) ~ (all_52_14 = all_6_2) % 151.44/22.25 (52) all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3 % 151.44/22.25 (53) op(all_8_2, all_8_2) = all_8_1 % 151.44/22.25 (54) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 151.44/22.25 (55) all_56_9 = all_52_1 % 151.44/22.25 (56) ~ (all_52_1 = all_10_2) % 151.44/22.25 % 151.44/22.25 Begin of proof % 151.44/22.25 | % 151.44/22.25 | COMBINE_EQS: (18), (44) imply: % 151.44/22.25 | (57) all_52_7 = e0 % 151.44/22.25 | % 151.44/22.25 | SIMP: (57) implies: % 151.44/22.25 | (58) all_52_7 = e0 % 151.44/22.25 | % 151.44/22.25 | COMBINE_EQS: (33), (47) imply: % 151.44/22.25 | (59) all_4_2 = e2 % 151.44/22.25 | % 151.44/22.25 | REDUCE: (17), (58) imply: % 151.44/22.25 | (60) ~ (all_8_2 = e0) % 151.44/22.25 | % 151.44/22.25 | SIMP: (60) implies: % 151.44/22.25 | (61) ~ (all_8_2 = e0) % 151.44/22.25 | % 151.44/22.25 | REDUCE: (31), (59) imply: % 151.44/22.25 | (62) ~ (e2 = e1) % 151.44/22.25 | % 151.44/22.25 | REDUCE: (10), (59) imply: % 151.44/22.25 | (63) op(e0, e0) = e2 % 151.44/22.25 | % 151.44/22.25 | BETA: splitting (50) gives: % 151.44/22.25 | % 151.44/22.25 | Case 1: % 151.44/22.25 | | % 151.44/22.25 | | (64) ~ (all_56_21 = e0) % 151.44/22.25 | | % 151.44/22.25 | | REDUCE: (15), (64) imply: % 151.44/22.25 | | (65) ~ (all_6_2 = e0) % 151.44/22.25 | | % 151.44/22.25 | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (11), (12), (13), (14), % 151.44/22.25 | | (15), (16), (19), (20), (21), (22), (23), (24), (25), (26), (27), % 151.44/22.25 | | (28), (29), (30), (31), (32), (34), (35), (36), (38), (39), (40), % 151.44/22.25 | | (41), (42), (43), (45), (46), (48), (49), (51), (52), (53), (54), % 151.44/22.25 | | (55), (56), (61), (62), (65) are inconsistent by sub-proof #247. % 151.44/22.25 | | % 151.44/22.25 | Case 2: % 151.44/22.25 | | % 151.44/22.25 | | (66) all_56_21 = e0 % 151.44/22.25 | | % 151.44/22.25 | | REF_CLOSE: (6), (15), (25), (37), (63), (66) are inconsistent by sub-proof % 151.44/22.25 | | #565. % 151.44/22.25 | | % 151.44/22.25 | End of split % 151.44/22.25 | % 151.44/22.25 End of proof % 151.44/22.25 % 151.44/22.25 Sub-proof #235 shows that the following formulas are inconsistent: % 151.44/22.25 ---------------------------------------------------------------- % 151.44/22.25 (1) all_56_11 = all_8_2 % 151.44/22.25 (2) all_14_2 = all_8_2 % 151.44/22.25 (3) ~ (all_8_1 = e1) % 151.44/22.25 (4) ~ (all_6_1 = e2) % 151.44/22.25 (5) ~ (all_8_2 = e1) % 151.44/22.25 (6) op(e0, e0) = all_4_2 % 151.44/22.25 (7) op(e2, e2) = all_6_1 % 151.44/22.25 (8) all_54_5 = all_8_2 % 151.44/22.25 (9) ~ (all_6_1 = e3) % 151.44/22.25 (10) all_54_15 = all_4_2 % 151.44/22.25 (11) all_14_1 = all_8_1 % 151.44/22.25 (12) op(e2, all_8_2) = all_56_10 % 151.44/22.25 (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 151.44/22.25 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 151.44/22.25 (14) op(e2, all_8_1) = e1 % 151.44/22.25 (15) ~ (e2 = e1) % 151.44/22.25 (16) ~ (all_14_1 = e3) | ~ (all_14_2 = e0) % 151.44/22.25 (17) ~ (all_52_13 = all_4_2) % 151.44/22.25 (18) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0 % 151.44/22.25 (19) ~ (all_56_11 = e0) | all_56_15 = e2 % 151.44/22.25 (20) op(e2, e2) = all_8_2 % 151.44/22.25 (21) op(e2, e0) = all_52_13 % 151.44/22.25 (22) op(all_8_2, all_8_2) = all_8_1 % 151.44/22.25 (23) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 151.44/22.25 (24) all_56_15 = all_52_13 % 151.44/22.25 % 151.44/22.25 Begin of proof % 151.44/22.25 | % 151.44/22.25 | GROUND_INST: instantiating (13) with all_8_2, all_6_1, e2, e2, simplifying % 151.44/22.25 | with (7), (20) gives: % 151.44/22.25 | (25) all_8_2 = all_6_1 % 151.44/22.25 | % 151.44/22.25 | COMBINE_EQS: (2), (25) imply: % 151.44/22.25 | (26) all_14_2 = all_6_1 % 151.44/22.25 | % 151.44/22.25 | COMBINE_EQS: (8), (25) imply: % 151.44/22.25 | (27) all_54_5 = all_6_1 % 151.44/22.25 | % 151.44/22.25 | COMBINE_EQS: (1), (25) imply: % 151.44/22.25 | (28) all_56_11 = all_6_1 % 151.44/22.25 | % 151.44/22.25 | REDUCE: (5), (25) imply: % 151.44/22.25 | (29) ~ (all_6_1 = e1) % 151.44/22.25 | % 151.44/22.25 | REDUCE: (22), (25) imply: % 151.44/22.25 | (30) op(all_6_1, all_6_1) = all_8_1 % 151.44/22.25 | % 151.44/22.25 | REDUCE: (12), (25) imply: % 151.44/22.25 | (31) op(e2, all_6_1) = all_56_10 % 151.44/22.25 | % 151.44/22.25 | BETA: splitting (23) gives: % 151.44/22.25 | % 151.44/22.25 | Case 1: % 151.44/22.25 | | % 151.44/22.25 | | (32) all_54_5 = e3 % 151.44/22.25 | | % 151.44/22.25 | | REF_CLOSE: (9), (27), (32) are inconsistent by sub-proof #509. % 151.44/22.25 | | % 151.44/22.25 | Case 2: % 151.44/22.25 | | % 151.44/22.25 | | (33) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 151.44/22.25 | | % 151.44/22.25 | | BETA: splitting (33) gives: % 151.44/22.25 | | % 151.44/22.25 | | Case 1: % 151.44/22.25 | | | % 151.44/22.25 | | | (34) all_54_5 = e2 % 151.44/22.25 | | | % 151.44/22.25 | | | REF_CLOSE: (4), (27), (34) are inconsistent by sub-proof #466. % 151.44/22.25 | | | % 151.44/22.25 | | Case 2: % 151.44/22.25 | | | % 151.44/22.25 | | | (35) all_54_5 = e1 | all_54_5 = e0 % 151.44/22.25 | | | % 151.44/22.25 | | | BETA: splitting (35) gives: % 151.44/22.25 | | | % 151.44/22.25 | | | Case 1: % 151.44/22.25 | | | | % 151.44/22.25 | | | | (36) all_54_5 = e1 % 151.44/22.25 | | | | % 151.44/22.25 | | | | REF_CLOSE: (27), (29), (36) are inconsistent by sub-proof #465. % 151.44/22.25 | | | | % 151.44/22.25 | | | Case 2: % 151.44/22.25 | | | | % 151.44/22.25 | | | | (37) all_54_5 = e0 % 151.44/22.25 | | | | % 151.44/22.25 | | | | COMBINE_EQS: (27), (37) imply: % 151.44/22.25 | | | | (38) all_6_1 = e0 % 151.44/22.25 | | | | % 151.44/22.25 | | | | SIMP: (38) implies: % 151.44/22.25 | | | | (39) all_6_1 = e0 % 151.44/22.25 | | | | % 151.44/22.25 | | | | COMBINE_EQS: (26), (39) imply: % 151.44/22.25 | | | | (40) all_14_2 = e0 % 151.44/22.25 | | | | % 151.44/22.25 | | | | COMBINE_EQS: (28), (39) imply: % 151.44/22.25 | | | | (41) all_56_11 = e0 % 151.44/22.25 | | | | % 151.44/22.25 | | | | REDUCE: (30), (39) imply: % 151.44/22.25 | | | | (42) op(e0, e0) = all_8_1 % 151.44/22.25 | | | | % 151.44/22.25 | | | | REDUCE: (31), (39) imply: % 151.44/22.25 | | | | (43) op(e2, e0) = all_56_10 % 151.44/22.25 | | | | % 151.44/22.25 | | | | REF_CLOSE: (3), (6), (10), (11), (13), (14), (15), (16), (17), (18), % 151.44/22.25 | | | | (19), (21), (24), (40), (41), (42), (43) are inconsistent by % 151.44/22.25 | | | | sub-proof #238. % 151.44/22.25 | | | | % 151.44/22.25 | | | End of split % 151.44/22.25 | | | % 151.44/22.25 | | End of split % 151.44/22.25 | | % 151.44/22.25 | End of split % 151.44/22.25 | % 151.44/22.25 End of proof % 151.44/22.25 % 151.44/22.25 Sub-proof #236 shows that the following formulas are inconsistent: % 151.44/22.25 ---------------------------------------------------------------- % 151.44/22.25 (1) all_56_11 = all_8_2 % 151.44/22.25 (2) all_14_2 = all_8_2 % 151.44/22.25 (3) ~ (all_8_1 = e1) % 151.44/22.25 (4) ~ (all_52_13 = e1) % 151.44/22.25 (5) op(e0, e0) = all_4_2 % 151.44/22.25 (6) all_54_15 = all_4_2 % 151.44/22.25 (7) all_14_1 = all_8_1 % 151.44/22.25 (8) op(e2, all_8_2) = all_56_10 % 151.44/22.25 (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 151.44/22.25 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 151.44/22.25 (10) all_56_15 = e2 % 151.44/22.25 (11) op(e2, all_8_1) = e1 % 151.44/22.25 (12) ~ (all_14_1 = e3) | ~ (all_14_2 = e0) % 151.44/22.25 (13) ~ (all_52_13 = all_4_2) % 151.44/22.25 (14) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0 % 151.44/22.25 (15) all_56_11 = e0 % 151.44/22.25 (16) ~ (all_56_11 = e0) | all_56_15 = e2 % 151.44/22.25 (17) op(e2, e0) = all_52_13 % 151.44/22.25 (18) op(all_8_2, all_8_2) = all_8_1 % 151.44/22.25 (19) all_56_15 = all_52_13 % 151.44/22.25 % 151.44/22.25 Begin of proof % 151.44/22.25 | % 151.44/22.25 | COMBINE_EQS: (1), (15) imply: % 151.44/22.25 | (20) all_8_2 = e0 % 151.44/22.25 | % 151.44/22.25 | COMBINE_EQS: (10), (19) imply: % 151.44/22.25 | (21) all_52_13 = e2 % 151.44/22.25 | % 151.44/22.25 | COMBINE_EQS: (2), (20) imply: % 151.44/22.25 | (22) all_14_2 = e0 % 151.44/22.25 | % 151.44/22.25 | REDUCE: (4), (21) imply: % 151.44/22.25 | (23) ~ (e2 = e1) % 151.44/22.25 | % 151.44/22.25 | REF_CLOSE: (3), (5), (6), (7), (8), (9), (11), (12), (13), (14), (15), (16), % 151.44/22.25 | (17), (18), (19), (20), (22), (23) are inconsistent by sub-proof % 151.44/22.25 | #237. % 151.44/22.25 | % 151.44/22.25 End of proof % 151.44/22.25 % 151.44/22.25 Sub-proof #237 shows that the following formulas are inconsistent: % 151.44/22.25 ---------------------------------------------------------------- % 151.44/22.25 (1) ~ (all_8_1 = e1) % 151.44/22.25 (2) op(e0, e0) = all_4_2 % 151.44/22.25 (3) all_54_15 = all_4_2 % 151.44/22.25 (4) all_14_1 = all_8_1 % 151.44/22.25 (5) op(e2, all_8_2) = all_56_10 % 151.44/22.25 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 151.44/22.25 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 151.44/22.25 (7) op(e2, all_8_1) = e1 % 151.44/22.25 (8) ~ (e2 = e1) % 151.44/22.25 (9) ~ (all_14_1 = e3) | ~ (all_14_2 = e0) % 151.44/22.25 (10) all_14_2 = e0 % 151.44/22.25 (11) ~ (all_52_13 = all_4_2) % 151.44/22.25 (12) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0 % 151.44/22.25 (13) all_56_11 = e0 % 151.44/22.25 (14) ~ (all_56_11 = e0) | all_56_15 = e2 % 151.44/22.25 (15) op(e2, e0) = all_52_13 % 151.44/22.25 (16) all_8_2 = e0 % 151.44/22.25 (17) op(all_8_2, all_8_2) = all_8_1 % 151.44/22.25 (18) all_56_15 = all_52_13 % 151.44/22.25 % 151.44/22.25 Begin of proof % 151.44/22.25 | % 151.44/22.25 | REDUCE: (16), (17) imply: % 151.44/22.25 | (19) op(e0, e0) = all_8_1 % 151.44/22.25 | % 151.44/22.25 | REDUCE: (5), (16) imply: % 151.44/22.25 | (20) op(e2, e0) = all_56_10 % 151.44/22.25 | % 151.44/22.25 | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (9), (10), (11), (12), (13), % 151.44/22.25 | (14), (15), (18), (19), (20) are inconsistent by sub-proof #238. % 151.44/22.25 | % 151.44/22.25 End of proof % 151.44/22.25 % 151.44/22.25 Sub-proof #238 shows that the following formulas are inconsistent: % 151.44/22.25 ---------------------------------------------------------------- % 151.44/22.25 (1) ~ (all_8_1 = e1) % 151.44/22.25 (2) op(e0, e0) = all_4_2 % 151.44/22.25 (3) all_54_15 = all_4_2 % 151.44/22.25 (4) all_14_1 = all_8_1 % 151.44/22.25 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 151.44/22.25 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 151.44/22.25 (6) op(e2, all_8_1) = e1 % 151.44/22.25 (7) op(e0, e0) = all_8_1 % 151.44/22.25 (8) op(e2, e0) = all_56_10 % 151.44/22.25 (9) ~ (e2 = e1) % 151.44/22.25 (10) ~ (all_14_1 = e3) | ~ (all_14_2 = e0) % 151.44/22.25 (11) all_14_2 = e0 % 151.44/22.25 (12) ~ (all_52_13 = all_4_2) % 151.44/22.25 (13) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0 % 151.44/22.25 (14) all_56_11 = e0 % 151.44/22.25 (15) ~ (all_56_11 = e0) | all_56_15 = e2 % 151.44/22.25 (16) op(e2, e0) = all_52_13 % 151.44/22.25 (17) all_56_15 = all_52_13 % 151.44/22.25 % 151.44/22.25 Begin of proof % 151.44/22.25 | % 151.44/22.25 | BETA: splitting (15) gives: % 151.44/22.25 | % 151.44/22.25 | Case 1: % 151.44/22.25 | | % 151.44/22.25 | | (18) ~ (all_56_11 = e0) % 151.44/22.25 | | % 151.44/22.25 | | REDUCE: (14), (18) imply: % 151.44/22.25 | | (19) $false % 151.44/22.25 | | % 151.44/22.25 | | CLOSE: (19) is inconsistent. % 151.44/22.25 | | % 151.44/22.25 | Case 2: % 151.44/22.25 | | % 151.44/22.25 | | (20) all_56_15 = e2 % 151.44/22.25 | | % 151.44/22.25 | | COMBINE_EQS: (17), (20) imply: % 151.44/22.25 | | (21) all_52_13 = e2 % 151.44/22.25 | | % 151.44/22.25 | | SIMP: (21) implies: % 151.44/22.25 | | (22) all_52_13 = e2 % 151.44/22.25 | | % 151.44/22.25 | | REDUCE: (12), (22) imply: % 151.44/22.25 | | (23) ~ (all_4_2 = e2) % 151.44/22.25 | | % 151.44/22.25 | | SIMP: (23) implies: % 151.44/22.25 | | (24) ~ (all_4_2 = e2) % 151.44/22.25 | | % 151.44/22.25 | | REDUCE: (16), (22) imply: % 151.44/22.25 | | (25) op(e2, e0) = e2 % 151.44/22.25 | | % 151.44/22.25 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (13), % 151.44/22.25 | | (24), (25) are inconsistent by sub-proof #253. % 151.44/22.25 | | % 151.44/22.25 | End of split % 151.44/22.25 | % 151.44/22.25 End of proof % 151.44/22.25 % 151.44/22.25 Sub-proof #239 shows that the following formulas are inconsistent: % 151.44/22.25 ---------------------------------------------------------------- % 151.44/22.25 (1) all_56_11 = all_8_2 % 151.44/22.25 (2) ~ (all_56_11 = e1) | all_56_13 = e2 % 151.44/22.25 (3) ~ (all_8_1 = e1) % 151.44/22.25 (4) ~ (all_4_1 = e0) % 151.44/22.25 (5) all_54_0 = all_10_2 % 151.44/22.25 (6) all_54_12 = all_52_3 % 151.44/22.25 (7) all_54_5 = all_8_2 % 151.44/22.25 (8) op(e1, all_4_1) = all_56_20 % 151.44/22.25 (9) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 151.44/22.25 (10) ~ (all_6_0 = e2) % 151.44/22.25 (11) all_42_1 = all_8_1 % 151.44/22.25 (12) ~ (all_4_1 = e2) % 151.44/22.25 (13) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 151.44/22.25 (14) all_56_17 = all_52_2 % 151.44/22.25 (15) op(e2, all_8_2) = all_56_10 % 151.44/22.25 (16) op(e3, e3) = all_10_2 % 151.44/22.25 (17) all_42_2 = all_8_2 % 151.44/22.25 (18) ~ (all_56_21 = e3) | all_56_17 = e1 % 151.44/22.25 (19) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 151.44/22.25 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 151.44/22.25 (20) ~ (all_56_11 = e3) | all_56_9 = e2 % 151.44/22.25 (21) op(e0, all_4_1) = all_4_0 % 151.44/22.25 (22) ~ (all_52_3 = e0) % 151.44/22.25 (23) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0 % 151.44/22.25 (24) all_56_21 = all_4_1 % 151.44/22.25 (25) op(e2, all_8_1) = e1 % 151.44/22.25 (26) op(all_4_1, all_4_1) = all_6_1 % 151.44/22.25 (27) ~ (all_52_2 = all_52_3) % 151.44/22.25 (28) op(e1, all_6_1) = all_6_0 % 151.44/22.25 (29) ~ (all_42_1 = e0) | ~ (all_42_2 = e3) % 151.44/22.25 (30) all_54_10 = all_4_1 % 151.44/22.25 (31) op(e0, e3) = all_52_3 % 151.44/22.25 (32) op(e1, e1) = all_4_1 % 151.44/22.25 (33) op(e2, e3) = all_52_1 % 151.44/22.25 (34) op(e2, e2) = all_8_2 % 151.44/22.25 (35) ~ (all_8_2 = e0) % 151.44/22.25 (36) op(all_8_2, all_8_2) = all_8_1 % 151.44/22.25 (37) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 151.44/22.25 (38) ~ (all_4_0 = e2) % 151.44/22.25 (39) ~ (all_4_0 = e3) % 151.44/22.25 (40) all_56_9 = all_52_1 % 151.44/22.25 (41) ~ (all_52_1 = all_10_2) % 151.44/22.25 % 151.44/22.25 Begin of proof % 151.44/22.25 | % 151.44/22.25 | BETA: splitting (18) gives: % 151.44/22.25 | % 151.44/22.25 | Case 1: % 151.44/22.25 | | % 151.44/22.25 | | (42) ~ (all_56_21 = e3) % 151.44/22.25 | | % 151.44/22.25 | | REDUCE: (24), (42) imply: % 151.44/22.25 | | (43) ~ (all_4_1 = e3) % 151.44/22.25 | | % 151.44/22.25 | | BETA: splitting (13) gives: % 151.44/22.25 | | % 151.44/22.25 | | Case 1: % 151.44/22.25 | | | % 151.44/22.25 | | | (44) all_54_10 = e3 % 151.44/22.25 | | | % 151.44/22.25 | | | COMBINE_EQS: (30), (44) imply: % 151.44/22.25 | | | (45) all_4_1 = e3 % 151.44/22.25 | | | % 151.44/22.25 | | | REDUCE: (43), (45) imply: % 151.44/22.25 | | | (46) $false % 151.44/22.25 | | | % 151.44/22.25 | | | CLOSE: (46) is inconsistent. % 151.44/22.25 | | | % 151.44/22.25 | | Case 2: % 151.44/22.25 | | | % 151.44/22.25 | | | (47) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 151.44/22.25 | | | % 151.44/22.25 | | | BETA: splitting (47) gives: % 151.44/22.25 | | | % 151.44/22.25 | | | Case 1: % 151.44/22.25 | | | | % 151.44/22.25 | | | | (48) all_54_10 = e2 % 151.44/22.25 | | | | % 151.44/22.25 | | | | COMBINE_EQS: (30), (48) imply: % 151.44/22.25 | | | | (49) all_4_1 = e2 % 151.44/22.25 | | | | % 151.44/22.25 | | | | REDUCE: (12), (49) imply: % 151.44/22.25 | | | | (50) $false % 151.44/22.25 | | | | % 151.44/22.25 | | | | CLOSE: (50) is inconsistent. % 151.44/22.25 | | | | % 151.44/22.25 | | | Case 2: % 151.44/22.25 | | | | % 151.44/22.25 | | | | (51) all_54_10 = e1 | all_54_10 = e0 % 151.44/22.25 | | | | % 151.44/22.25 | | | | BETA: splitting (51) gives: % 151.44/22.25 | | | | % 151.44/22.25 | | | | Case 1: % 151.44/22.25 | | | | | % 151.44/22.25 | | | | | (52) all_54_10 = e1 % 151.44/22.25 | | | | | % 151.44/22.25 | | | | | COMBINE_EQS: (30), (52) imply: % 151.44/22.25 | | | | | (53) all_4_1 = e1 % 151.44/22.25 | | | | | % 151.44/22.25 | | | | | REDUCE: (26), (53) imply: % 151.44/22.25 | | | | | (54) op(e1, e1) = all_6_1 % 151.44/22.25 | | | | | % 151.44/22.25 | | | | | REDUCE: (8), (53) imply: % 151.44/22.25 | | | | | (55) op(e1, e1) = all_56_20 % 151.44/22.25 | | | | | % 151.44/22.25 | | | | | REDUCE: (32), (53) imply: % 151.44/22.25 | | | | | (56) op(e1, e1) = e1 % 151.44/22.25 | | | | | % 151.44/22.25 | | | | | GROUND_INST: instantiating (19) with all_6_1, all_56_20, e1, e1, % 151.44/22.25 | | | | | simplifying with (54), (55) gives: % 151.44/22.25 | | | | | (57) all_56_20 = all_6_1 % 151.44/22.25 | | | | | % 151.44/22.25 | | | | | GROUND_INST: instantiating (19) with e1, all_56_20, e1, e1, % 151.44/22.25 | | | | | simplifying with (55), (56) gives: % 151.44/22.25 | | | | | (58) all_56_20 = e1 % 151.44/22.25 | | | | | % 151.44/22.25 | | | | | COMBINE_EQS: (57), (58) imply: % 151.44/22.25 | | | | | (59) all_6_1 = e1 % 151.44/22.25 | | | | | % 151.44/22.25 | | | | | REDUCE: (28), (59) imply: % 151.44/22.25 | | | | | (60) op(e1, e1) = all_6_0 % 151.44/22.25 | | | | | % 151.44/22.25 | | | | | GROUND_INST: instantiating (19) with e1, all_6_0, e1, e1, simplifying % 151.44/22.25 | | | | | with (56), (60) gives: % 151.44/22.25 | | | | | (61) all_6_0 = e1 % 151.44/22.25 | | | | | % 151.44/22.25 | | | | | REDUCE: (10), (61) imply: % 151.44/22.25 | | | | | (62) ~ (e2 = e1) % 151.44/22.25 | | | | | % 151.44/22.25 | | | | | SIMP: (62) implies: % 151.44/22.25 | | | | | (63) ~ (e2 = e1) % 151.44/22.25 | | | | | % 151.44/22.25 | | | | | BETA: splitting (20) gives: % 151.44/22.25 | | | | | % 151.44/22.25 | | | | | Case 1: % 151.44/22.25 | | | | | | % 151.44/22.25 | | | | | | (64) ~ (all_56_11 = e3) % 151.44/22.25 | | | | | | % 151.44/22.25 | | | | | | REDUCE: (1), (64) imply: % 151.44/22.25 | | | | | | (65) ~ (all_8_2 = e3) % 151.44/22.25 | | | | | | % 151.44/22.25 | | | | | | BETA: splitting (2) gives: % 151.44/22.25 | | | | | | % 151.44/22.25 | | | | | | Case 1: % 151.44/22.25 | | | | | | | % 151.44/22.25 | | | | | | | (66) ~ (all_56_11 = e1) % 151.44/22.25 | | | | | | | % 151.44/22.25 | | | | | | | REDUCE: (1), (66) imply: % 151.44/22.25 | | | | | | | (67) ~ (all_8_2 = e1) % 151.44/22.25 | | | | | | | % 151.44/22.25 | | | | | | | REF_CLOSE: (3), (7), (15), (19), (25), (34), (35), (36), (37), % 151.44/22.25 | | | | | | | (65), (67) are inconsistent by sub-proof #259. % 151.44/22.25 | | | | | | | % 151.44/22.25 | | | | | | Case 2: % 151.44/22.25 | | | | | | | % 151.44/22.25 | | | | | | | (68) all_56_11 = e1 % 151.44/22.25 | | | | | | | % 151.44/22.25 | | | | | | | COMBINE_EQS: (1), (68) imply: % 151.44/22.25 | | | | | | | (69) all_8_2 = e1 % 151.44/22.25 | | | | | | | % 151.44/22.25 | | | | | | | REF_CLOSE: (3), (19), (36), (55), (56), (69) are inconsistent by % 151.44/22.25 | | | | | | | sub-proof #535. % 151.44/22.25 | | | | | | | % 151.44/22.25 | | | | | | End of split % 151.44/22.25 | | | | | | % 151.44/22.25 | | | | | Case 2: % 151.44/22.25 | | | | | | % 151.44/22.25 | | | | | | (70) all_56_11 = e3 % 151.44/22.25 | | | | | | % 151.44/22.25 | | | | | | COMBINE_EQS: (1), (70) imply: % 151.44/22.25 | | | | | | (71) all_8_2 = e3 % 151.44/22.25 | | | | | | % 151.44/22.25 | | | | | | REF_CLOSE: (1), (3), (5), (9), (11), (15), (16), (17), (19), (20), % 151.44/22.25 | | | | | | (25), (29), (33), (36), (40), (41), (63), (71) are % 151.44/22.25 | | | | | | inconsistent by sub-proof #255. % 151.44/22.25 | | | | | | % 151.44/22.25 | | | | | End of split % 151.44/22.25 | | | | | % 151.44/22.25 | | | | Case 2: % 151.44/22.25 | | | | | % 151.44/22.25 | | | | | (72) all_54_10 = e0 % 151.44/22.25 | | | | | % 151.44/22.25 | | | | | COMBINE_EQS: (30), (72) imply: % 151.44/22.25 | | | | | (73) all_4_1 = e0 % 151.44/22.25 | | | | | % 151.44/22.25 | | | | | REDUCE: (4), (73) imply: % 151.44/22.25 | | | | | (74) $false % 151.44/22.25 | | | | | % 151.44/22.25 | | | | | CLOSE: (74) is inconsistent. % 151.44/22.25 | | | | | % 151.44/22.25 | | | | End of split % 151.44/22.25 | | | | % 151.44/22.25 | | | End of split % 151.44/22.25 | | | % 151.44/22.25 | | End of split % 151.44/22.25 | | % 151.44/22.25 | Case 2: % 151.44/22.25 | | % 151.44/22.25 | | (75) all_56_21 = e3 % 151.44/22.25 | | (76) all_56_17 = e1 % 151.44/22.25 | | % 151.44/22.25 | | REF_CLOSE: (6), (14), (19), (21), (22), (23), (24), (27), (31), (38), (39), % 151.44/22.25 | | (75), (76) are inconsistent by sub-proof #365. % 151.44/22.25 | | % 151.44/22.25 | End of split % 151.44/22.25 | % 151.44/22.25 End of proof % 151.44/22.25 % 151.44/22.25 Sub-proof #240 shows that the following formulas are inconsistent: % 151.44/22.25 ---------------------------------------------------------------- % 151.44/22.25 (1) all_58_1 = all_52_4 % 151.44/22.25 (2) all_58_13 = all_52_7 % 151.44/22.25 (3) ~ (all_52_4 = e0) % 151.44/22.25 (4) ~ (all_52_6 = e0) % 151.44/22.25 (5) all_58_3 = all_8_2 % 151.44/22.25 (6) all_58_7 = all_52_6 % 151.44/22.25 (7) all_58_1 = e0 | all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0 % 151.44/22.25 (8) ~ (all_8_2 = e0) % 151.44/22.25 (9) ~ (all_52_7 = e0) % 151.44/22.25 % 151.44/22.25 Begin of proof % 151.44/22.25 | % 151.44/22.25 | BETA: splitting (7) gives: % 151.44/22.25 | % 151.44/22.25 | Case 1: % 151.44/22.25 | | % 151.44/22.25 | | (10) all_58_1 = e0 % 151.44/22.25 | | % 151.44/22.25 | | COMBINE_EQS: (1), (10) imply: % 151.44/22.25 | | (11) all_52_4 = e0 % 151.44/22.25 | | % 151.44/22.25 | | REDUCE: (3), (11) imply: % 151.44/22.25 | | (12) $false % 151.44/22.25 | | % 151.44/22.25 | | CLOSE: (12) is inconsistent. % 151.44/22.25 | | % 151.44/22.25 | Case 2: % 151.44/22.25 | | % 151.44/22.25 | | (13) all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0 % 151.44/22.25 | | % 151.44/22.25 | | REF_CLOSE: (2), (4), (5), (6), (8), (9), (13) are inconsistent by sub-proof % 151.44/22.25 | | #603. % 151.44/22.25 | | % 151.44/22.25 | End of split % 151.44/22.25 | % 151.44/22.25 End of proof % 151.44/22.25 % 151.44/22.25 Sub-proof #241 shows that the following formulas are inconsistent: % 151.44/22.25 ---------------------------------------------------------------- % 151.44/22.25 (1) all_58_2 = e1 % 151.44/22.25 (2) all_58_2 = e0 % 151.44/22.25 (3) ~ (e1 = e0) % 151.44/22.25 % 151.44/22.25 Begin of proof % 151.44/22.25 | % 151.44/22.26 | COMBINE_EQS: (1), (2) imply: % 151.44/22.26 | (4) e1 = e0 % 151.44/22.26 | % 151.44/22.26 | SIMP: (4) implies: % 151.44/22.26 | (5) e1 = e0 % 151.44/22.26 | % 151.44/22.26 | REDUCE: (3), (5) imply: % 151.44/22.26 | (6) $false % 151.44/22.26 | % 151.44/22.26 | CLOSE: (6) is inconsistent. % 151.44/22.26 | % 151.44/22.26 End of proof % 151.44/22.26 % 151.44/22.26 Sub-proof #242 shows that the following formulas are inconsistent: % 151.44/22.26 ---------------------------------------------------------------- % 151.44/22.26 (1) all_56_11 = all_8_2 % 151.44/22.26 (2) ~ (all_56_11 = e1) | all_56_13 = e2 % 151.44/22.26 (3) all_14_2 = all_8_2 % 151.44/22.26 (4) ~ (all_8_1 = e1) % 151.44/22.26 (5) all_54_10 = all_6_2 % 151.44/22.26 (6) ~ (all_6_1 = e2) % 151.44/22.26 (7) ~ (all_52_13 = all_8_2) % 151.44/22.26 (8) all_54_0 = all_10_2 % 151.44/22.26 (9) ~ (all_52_9 = all_8_2) % 151.44/22.26 (10) op(e0, e0) = all_4_2 % 151.44/22.26 (11) all_54_5 = all_8_2 % 151.44/22.26 (12) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 151.44/22.26 (13) all_6_0 = e2 % 151.44/22.26 (14) all_54_15 = all_4_2 % 151.44/22.26 (15) all_42_1 = all_8_1 % 151.44/22.26 (16) all_56_21 = all_6_2 % 151.44/22.26 (17) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 151.44/22.26 (18) all_56_17 = all_52_2 % 151.44/22.26 (19) all_14_1 = all_8_1 % 151.44/22.26 (20) op(e2, all_8_2) = all_56_10 % 151.44/22.26 (21) op(e3, e3) = all_10_2 % 151.44/22.26 (22) all_42_2 = all_8_2 % 151.44/22.26 (23) ~ (all_56_21 = e3) | all_56_17 = e1 % 151.44/22.26 (24) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 151.44/22.26 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 151.44/22.26 (25) all_42_0 = e1 % 151.44/22.26 (26) ~ (all_56_11 = e3) | all_56_9 = e2 % 151.44/22.26 (27) all_46_2 = all_6_2 % 151.44/22.26 (28) all_56_13 = all_52_9 % 151.44/22.26 (29) op(e1, e3) = all_52_2 % 151.44/22.26 (30) ~ (all_42_0 = e1) | ~ (all_42_1 = e0) | ~ (all_42_2 = e3) % 151.44/22.26 (31) op(e2, all_8_1) = e1 % 151.44/22.26 (32) all_46_0 = all_6_0 % 151.44/22.26 (33) ~ (e2 = e1) % 151.44/22.26 (34) ~ (all_14_1 = e3) | ~ (all_14_2 = e0) % 151.44/22.26 (35) op(e1, all_6_1) = all_6_0 % 151.44/22.26 (36) op(all_6_2, all_6_2) = all_6_1 % 151.44/22.26 (37) ~ (all_52_13 = all_4_2) % 151.44/22.26 (38) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0 % 151.44/22.26 (39) all_46_1 = all_6_1 % 151.44/22.26 (40) op(e1, e1) = all_6_2 % 151.44/22.26 (41) ~ (all_52_9 = all_6_2) % 151.44/22.26 (42) ~ (all_56_11 = e0) | all_56_15 = e2 % 151.44/22.26 (43) op(e1, all_6_2) = all_56_20 % 151.44/22.26 (44) op(e2, e3) = all_52_1 % 151.44/22.26 (45) op(e2, e2) = all_8_2 % 151.44/22.26 (46) op(e2, e0) = all_52_13 % 151.44/22.26 (47) ~ (all_52_2 = all_10_2) % 151.44/22.26 (48) ~ (all_46_0 = e2) | ~ (all_46_1 = e0) | ~ (all_46_2 = e3) % 151.44/22.26 (49) op(all_8_2, all_8_2) = all_8_1 % 151.44/22.26 (50) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 151.44/22.26 (51) all_56_9 = all_52_1 % 151.44/22.26 (52) all_56_15 = all_52_13 % 151.44/22.26 (53) ~ (all_52_1 = all_10_2) % 151.44/22.26 % 151.44/22.26 Begin of proof % 151.44/22.26 | % 151.44/22.26 | COMBINE_EQS: (13), (32) imply: % 151.44/22.26 | (54) all_46_0 = e2 % 151.44/22.26 | % 151.44/22.26 | REDUCE: (13), (35) imply: % 151.44/22.26 | (55) op(e1, all_6_1) = e2 % 151.44/22.26 | % 151.44/22.26 | BETA: splitting (30) gives: % 151.44/22.26 | % 151.44/22.26 | Case 1: % 151.44/22.26 | | % 151.44/22.26 | | (56) ~ (all_42_0 = e1) % 151.44/22.26 | | % 151.44/22.26 | | REDUCE: (25), (56) imply: % 151.44/22.26 | | (57) $false % 151.44/22.26 | | % 151.44/22.26 | | CLOSE: (57) is inconsistent. % 151.44/22.26 | | % 151.44/22.26 | Case 2: % 151.44/22.26 | | % 151.44/22.26 | | (58) ~ (all_42_1 = e0) | ~ (all_42_2 = e3) % 151.44/22.26 | | % 151.44/22.26 | | BETA: splitting (48) gives: % 151.44/22.26 | | % 151.44/22.26 | | Case 1: % 151.44/22.26 | | | % 151.44/22.26 | | | (59) ~ (all_46_0 = e2) % 151.44/22.26 | | | % 151.44/22.26 | | | REDUCE: (54), (59) imply: % 151.44/22.26 | | | (60) $false % 151.44/22.26 | | | % 151.44/22.26 | | | CLOSE: (60) is inconsistent. % 151.44/22.26 | | | % 151.44/22.26 | | Case 2: % 151.44/22.26 | | | % 151.44/22.26 | | | (61) ~ (all_46_1 = e0) | ~ (all_46_2 = e3) % 151.44/22.26 | | | % 151.44/22.26 | | | BETA: splitting (42) gives: % 151.44/22.26 | | | % 151.44/22.26 | | | Case 1: % 151.44/22.26 | | | | % 151.44/22.26 | | | | (62) ~ (all_56_11 = e0) % 151.44/22.26 | | | | % 151.44/22.26 | | | | REDUCE: (1), (62) imply: % 151.44/22.26 | | | | (63) ~ (all_8_2 = e0) % 151.44/22.26 | | | | % 151.44/22.26 | | | | BETA: splitting (2) gives: % 151.44/22.26 | | | | % 151.44/22.26 | | | | Case 1: % 151.44/22.26 | | | | | % 151.44/22.26 | | | | | (64) ~ (all_56_11 = e1) % 151.44/22.26 | | | | | % 151.44/22.26 | | | | | REF_CLOSE: (1), (4), (8), (11), (12), (15), (20), (21), (22), (24), % 151.44/22.26 | | | | | (26), (31), (33), (44), (45), (49), (50), (51), (53), (58), % 151.44/22.26 | | | | | (63), (64) are inconsistent by sub-proof #250. % 151.44/22.26 | | | | | % 151.44/22.26 | | | | Case 2: % 151.44/22.26 | | | | | % 151.44/22.26 | | | | | (65) all_56_13 = e2 % 151.44/22.26 | | | | | (66) all_56_11 = e1 % 151.44/22.26 | | | | | % 151.44/22.26 | | | | | COMBINE_EQS: (1), (66) imply: % 151.44/22.26 | | | | | (67) all_8_2 = e1 % 151.44/22.26 | | | | | % 151.44/22.26 | | | | | COMBINE_EQS: (28), (65) imply: % 151.44/22.26 | | | | | (68) all_52_9 = e2 % 151.44/22.26 | | | | | % 151.44/22.26 | | | | | REDUCE: (41), (68) imply: % 151.44/22.26 | | | | | (69) ~ (all_6_2 = e2) % 151.44/22.26 | | | | | % 151.44/22.26 | | | | | SIMP: (69) implies: % 151.44/22.26 | | | | | (70) ~ (all_6_2 = e2) % 151.44/22.26 | | | | | % 151.44/22.26 | | | | | REDUCE: (7), (67) imply: % 151.44/22.26 | | | | | (71) ~ (all_52_13 = e1) % 151.44/22.26 | | | | | % 151.44/22.26 | | | | | REDUCE: (49), (67) imply: % 151.44/22.26 | | | | | (72) op(e1, e1) = all_8_1 % 151.44/22.26 | | | | | % 151.44/22.26 | | | | | GROUND_INST: instantiating (24) with all_6_2, all_8_1, e1, e1, % 151.44/22.26 | | | | | simplifying with (40), (72) gives: % 151.44/22.26 | | | | | (73) all_8_1 = all_6_2 % 151.44/22.26 | | | | | % 151.44/22.26 | | | | | REDUCE: (4), (73) imply: % 151.44/22.26 | | | | | (74) ~ (all_6_2 = e1) % 151.44/22.26 | | | | | % 151.44/22.26 | | | | | REDUCE: (31), (73) imply: % 151.44/22.26 | | | | | (75) op(e2, all_6_2) = e1 % 151.44/22.26 | | | | | % 151.44/22.26 | | | | | BETA: splitting (23) gives: % 151.44/22.26 | | | | | % 151.44/22.26 | | | | | Case 1: % 151.44/22.26 | | | | | | % 151.44/22.26 | | | | | | (76) ~ (all_56_21 = e3) % 151.44/22.26 | | | | | | % 151.44/22.26 | | | | | | REDUCE: (16), (76) imply: % 151.44/22.26 | | | | | | (77) ~ (all_6_2 = e3) % 151.44/22.26 | | | | | | % 151.44/22.26 | | | | | | REF_CLOSE: (5), (17), (24), (46), (70), (71), (74), (75), (77) are % 151.44/22.26 | | | | | | inconsistent by sub-proof #257. % 151.44/22.26 | | | | | | % 151.44/22.26 | | | | | Case 2: % 151.44/22.26 | | | | | | % 151.44/22.26 | | | | | | (78) all_56_21 = e3 % 151.44/22.26 | | | | | | % 151.44/22.26 | | | | | | REF_CLOSE: (6), (8), (12), (16), (18), (21), (23), (24), (27), (29), % 151.44/22.26 | | | | | | (33), (36), (39), (43), (47), (55), (61), (78) are % 151.44/22.26 | | | | | | inconsistent by sub-proof #373. % 151.44/22.26 | | | | | | % 151.44/22.26 | | | | | End of split % 151.44/22.26 | | | | | % 151.44/22.26 | | | | End of split % 151.44/22.26 | | | | % 151.44/22.26 | | | Case 2: % 151.44/22.26 | | | | % 151.44/22.26 | | | | (79) all_56_15 = e2 % 151.44/22.26 | | | | (80) all_56_11 = e0 % 151.44/22.26 | | | | % 151.44/22.26 | | | | COMBINE_EQS: (1), (80) imply: % 151.44/22.26 | | | | (81) all_8_2 = e0 % 151.44/22.26 | | | | % 151.44/22.26 | | | | COMBINE_EQS: (52), (79) imply: % 151.44/22.26 | | | | (82) all_52_13 = e2 % 151.44/22.26 | | | | % 151.44/22.26 | | | | COMBINE_EQS: (3), (81) imply: % 151.44/22.26 | | | | (83) all_14_2 = e0 % 151.44/22.26 | | | | % 151.44/22.26 | | | | REDUCE: (37), (82) imply: % 151.44/22.26 | | | | (84) ~ (all_4_2 = e2) % 151.44/22.26 | | | | % 151.44/22.26 | | | | SIMP: (84) implies: % 151.44/22.26 | | | | (85) ~ (all_4_2 = e2) % 151.44/22.26 | | | | % 151.44/22.26 | | | | REDUCE: (49), (81) imply: % 151.44/22.26 | | | | (86) op(e0, e0) = all_8_1 % 151.44/22.26 | | | | % 151.44/22.26 | | | | REDUCE: (20), (81) imply: % 151.44/22.26 | | | | (87) op(e2, e0) = all_56_10 % 151.44/22.26 | | | | % 151.44/22.26 | | | | REDUCE: (46), (82) imply: % 151.44/22.26 | | | | (88) op(e2, e0) = e2 % 151.44/22.26 | | | | % 151.44/22.26 | | | | REF_CLOSE: (4), (10), (14), (19), (24), (31), (33), (34), (38), (83), % 151.44/22.26 | | | | (85), (86), (87), (88) are inconsistent by sub-proof #253. % 151.44/22.26 | | | | % 151.44/22.26 | | | End of split % 151.44/22.26 | | | % 151.44/22.26 | | End of split % 151.44/22.26 | | % 151.44/22.26 | End of split % 151.44/22.26 | % 151.44/22.26 End of proof % 151.44/22.26 % 151.44/22.26 Sub-proof #243 shows that the following formulas are inconsistent: % 151.44/22.26 ---------------------------------------------------------------- % 151.44/22.26 (1) all_56_11 = all_8_2 % 151.44/22.26 (2) ~ (all_56_11 = e1) | all_56_13 = e2 % 151.44/22.26 (3) ~ (all_52_11 = all_6_2) % 151.44/22.26 (4) all_56_25 = all_52_3 % 151.44/22.26 (5) ~ (all_52_7 = all_52_11) % 151.44/22.26 (6) all_14_2 = all_8_2 % 151.44/22.26 (7) ~ (all_8_1 = e1) % 151.44/22.26 (8) ~ (all_52_1 = all_52_9) % 151.44/22.26 (9) all_54_0 = all_10_2 % 151.44/22.26 (10) all_56_31 = e3 % 151.44/22.26 (11) all_54_4 = all_52_1 % 151.44/22.26 (12) op(e0, e0) = all_4_2 % 151.44/22.26 (13) all_54_5 = all_8_2 % 151.44/22.26 (14) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 151.44/22.26 (15) all_42_1 = all_8_1 % 151.44/22.26 (16) all_56_21 = all_6_2 % 151.44/22.26 (17) ~ (all_52_7 = all_8_2) % 151.44/22.26 (18) all_56_1 = all_10_2 % 151.44/22.26 (19) all_14_1 = all_8_1 % 151.44/22.26 (20) all_58_13 = all_52_7 % 151.44/22.26 (21) op(e2, all_8_2) = all_56_10 % 151.44/22.26 (22) op(e3, e3) = all_10_2 % 151.44/22.26 (23) all_42_2 = all_8_2 % 151.44/22.26 (24) ~ (all_52_1 = all_8_2) % 151.44/22.26 (25) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 151.44/22.26 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 151.44/22.26 (26) all_56_25 = e0 % 151.44/22.26 (27) ~ (all_52_3 = all_52_7) % 151.44/22.26 (28) ~ (all_56_11 = e3) | all_56_9 = e2 % 151.44/22.26 (29) all_56_13 = all_52_9 % 151.44/22.26 (30) ~ (all_52_7 = all_4_2) % 151.44/22.26 (31) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0 % 151.44/22.26 (32) op(e2, all_8_1) = e1 % 151.44/22.26 (33) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0 % 151.44/22.26 (34) ~ (e2 = e1) % 151.44/22.26 (35) ~ (all_14_1 = e3) | ~ (all_14_2 = e0) % 151.44/22.26 (36) op(all_4_2, all_4_2) = all_4_1 % 151.44/22.26 (37) ~ (all_52_1 = all_52_3) % 151.44/22.26 (38) all_56_31 = all_4_2 % 151.44/22.26 (39) ~ (all_42_1 = e0) | ~ (all_42_2 = e3) % 151.44/22.26 (40) all_56_1 = e3 | all_56_11 = e2 | all_56_21 = e1 | all_56_31 = e0 % 151.44/22.26 (41) all_54_13 = all_52_7 % 151.44/22.26 (42) all_58_15 = all_4_2 % 151.44/22.26 (43) all_58_2 = all_52_1 % 151.44/22.26 (44) ~ (all_56_11 = e0) | all_56_15 = e2 % 151.44/22.26 (45) all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1 % 151.44/22.26 (46) op(e2, e3) = all_52_1 % 151.44/22.26 (47) op(e2, e2) = all_8_2 % 151.44/22.26 (48) ~ (e2 = e0) % 151.44/22.26 (49) all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3 % 151.44/22.26 (50) op(all_8_2, all_8_2) = all_8_1 % 151.44/22.26 (51) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 151.44/22.26 (52) all_58_14 = all_52_11 % 151.44/22.26 (53) all_56_9 = all_52_1 % 151.44/22.26 (54) ~ (all_52_1 = all_10_2) % 151.44/22.26 (55) all_58_12 = all_52_3 % 151.44/22.26 (56) all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2 % 151.44/22.26 % 151.44/22.26 Begin of proof % 151.44/22.26 | % 151.44/22.26 | COMBINE_EQS: (4), (26) imply: % 151.44/22.26 | (57) all_52_3 = e0 % 151.44/22.26 | % 151.44/22.26 | SIMP: (57) implies: % 151.44/22.26 | (58) all_52_3 = e0 % 151.44/22.26 | % 151.44/22.26 | COMBINE_EQS: (10), (38) imply: % 151.44/22.26 | (59) all_4_2 = e3 % 151.44/22.26 | % 151.44/22.26 | COMBINE_EQS: (42), (59) imply: % 151.44/22.26 | (60) all_58_15 = e3 % 151.44/22.26 | % 151.44/22.26 | COMBINE_EQS: (55), (58) imply: % 151.44/22.26 | (61) all_58_12 = e0 % 151.44/22.26 | % 151.44/22.26 | REDUCE: (37), (58) imply: % 151.44/22.26 | (62) ~ (all_52_1 = e0) % 151.44/22.26 | % 151.44/22.26 | REDUCE: (27), (58) imply: % 151.44/22.26 | (63) ~ (all_52_7 = e0) % 151.44/22.26 | % 151.44/22.26 | SIMP: (63) implies: % 151.44/22.26 | (64) ~ (all_52_7 = e0) % 151.44/22.26 | % 151.44/22.26 | REDUCE: (30), (59) imply: % 151.44/22.26 | (65) ~ (all_52_7 = e3) % 151.44/22.26 | % 151.44/22.26 | REDUCE: (36), (59) imply: % 151.44/22.26 | (66) op(e3, e3) = all_4_1 % 151.44/22.26 | % 151.44/22.26 | REDUCE: (12), (59) imply: % 151.44/22.26 | (67) op(e0, e0) = e3 % 151.44/22.26 | % 151.44/22.26 | GROUND_INST: instantiating (25) with all_10_2, all_4_1, e3, e3, simplifying % 151.44/22.26 | with (22), (66) gives: % 151.44/22.26 | (68) all_10_2 = all_4_1 % 151.44/22.26 | % 151.44/22.26 | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (9), (10), (11), (13), (14), % 151.44/22.26 | (15), (16), (17), (18), (19), (20), (21), (22), (23), (24), (25), % 151.44/22.26 | (28), (29), (31), (32), (33), (34), (35), (39), (40), (41), (43), % 151.44/22.26 | (44), (45), (46), (47), (48), (49), (50), (51), (52), (53), (54), % 151.44/22.26 | (56), (60), (61), (62), (64), (65), (67), (68) are inconsistent by % 151.44/22.26 | sub-proof #244. % 151.44/22.26 | % 151.44/22.26 End of proof % 151.44/22.26 % 151.44/22.26 Sub-proof #244 shows that the following formulas are inconsistent: % 151.44/22.26 ---------------------------------------------------------------- % 151.44/22.26 (1) all_56_11 = all_8_2 % 151.44/22.26 (2) ~ (all_56_11 = e1) | all_56_13 = e2 % 151.44/22.26 (3) ~ (all_52_11 = all_6_2) % 151.44/22.26 (4) ~ (all_52_7 = all_52_11) % 151.44/22.26 (5) all_14_2 = all_8_2 % 151.44/22.26 (6) ~ (all_8_1 = e1) % 151.44/22.26 (7) ~ (all_52_1 = all_52_9) % 151.44/22.26 (8) all_54_0 = all_10_2 % 151.44/22.26 (9) all_56_31 = e3 % 151.44/22.26 (10) all_54_4 = all_52_1 % 151.44/22.26 (11) all_54_5 = all_8_2 % 151.44/22.26 (12) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 151.44/22.26 (13) all_42_1 = all_8_1 % 151.44/22.26 (14) all_56_21 = all_6_2 % 151.44/22.26 (15) ~ (all_52_7 = all_8_2) % 151.44/22.26 (16) all_56_1 = all_10_2 % 151.44/22.26 (17) all_14_1 = all_8_1 % 151.44/22.26 (18) all_58_12 = e0 % 151.44/22.26 (19) all_58_13 = all_52_7 % 151.44/22.26 (20) op(e2, all_8_2) = all_56_10 % 151.44/22.26 (21) op(e3, e3) = all_10_2 % 151.44/22.26 (22) all_42_2 = all_8_2 % 151.44/22.26 (23) ~ (all_52_1 = all_8_2) % 151.44/22.26 (24) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 151.44/22.26 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 151.44/22.26 (25) ~ (all_56_11 = e3) | all_56_9 = e2 % 151.44/22.26 (26) all_56_13 = all_52_9 % 151.44/22.26 (27) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0 % 151.44/22.26 (28) op(e2, all_8_1) = e1 % 151.44/22.26 (29) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0 % 151.44/22.26 (30) all_58_15 = e3 % 151.44/22.26 (31) ~ (e2 = e1) % 151.44/22.26 (32) ~ (all_14_1 = e3) | ~ (all_14_2 = e0) % 151.44/22.26 (33) ~ (all_52_1 = e0) % 151.44/22.26 (34) op(e0, e0) = e3 % 151.44/22.26 (35) all_10_2 = all_4_1 % 151.44/22.26 (36) ~ (all_42_1 = e0) | ~ (all_42_2 = e3) % 151.44/22.26 (37) all_56_1 = e3 | all_56_11 = e2 | all_56_21 = e1 | all_56_31 = e0 % 151.44/22.26 (38) all_54_13 = all_52_7 % 151.44/22.26 (39) ~ (all_52_7 = e3) % 151.44/22.26 (40) all_58_2 = all_52_1 % 151.44/22.26 (41) ~ (all_56_11 = e0) | all_56_15 = e2 % 151.44/22.26 (42) all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1 % 151.44/22.26 (43) op(e2, e3) = all_52_1 % 151.44/22.26 (44) op(e2, e2) = all_8_2 % 151.44/22.26 (45) ~ (e2 = e0) % 151.44/22.26 (46) ~ (all_52_7 = e0) % 151.44/22.26 (47) all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3 % 151.44/22.26 (48) op(all_8_2, all_8_2) = all_8_1 % 151.44/22.26 (49) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 151.44/22.26 (50) all_58_14 = all_52_11 % 151.44/22.26 (51) all_56_9 = all_52_1 % 151.44/22.26 (52) ~ (all_52_1 = all_10_2) % 151.44/22.26 (53) all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2 % 151.44/22.26 % 151.44/22.26 Begin of proof % 151.44/22.26 | % 151.44/22.26 | COMBINE_EQS: (16), (35) imply: % 151.44/22.26 | (54) all_56_1 = all_4_1 % 151.44/22.26 | % 151.44/22.26 | REDUCE: (35), (52) imply: % 151.44/22.26 | (55) ~ (all_52_1 = all_4_1) % 151.44/22.26 | % 151.44/22.26 | BETA: splitting (41) gives: % 151.44/22.26 | % 151.44/22.26 | Case 1: % 151.44/22.26 | | % 151.44/22.26 | | (56) ~ (all_56_11 = e0) % 151.44/22.26 | | % 151.44/22.26 | | REDUCE: (1), (56) imply: % 151.44/22.26 | | (57) ~ (all_8_2 = e0) % 151.44/22.26 | | % 151.44/22.26 | | BETA: splitting (2) gives: % 151.44/22.26 | | % 151.44/22.26 | | Case 1: % 151.44/22.26 | | | % 151.44/22.26 | | | (58) ~ (all_56_11 = e1) % 151.44/22.26 | | | % 151.44/22.26 | | | REF_CLOSE: (1), (6), (8), (11), (12), (13), (20), (21), (22), (24), (25), % 151.44/22.26 | | | (28), (31), (36), (43), (44), (48), (49), (51), (52), (57), % 151.44/22.26 | | | (58) are inconsistent by sub-proof #250. % 151.44/22.26 | | | % 151.44/22.26 | | Case 2: % 151.44/22.26 | | | % 151.44/22.26 | | | (59) all_56_13 = e2 % 151.44/22.26 | | | (60) all_56_11 = e1 % 151.44/22.26 | | | % 151.44/22.26 | | | COMBINE_EQS: (1), (60) imply: % 151.44/22.26 | | | (61) all_8_2 = e1 % 151.44/22.26 | | | % 151.44/22.26 | | | COMBINE_EQS: (26), (59) imply: % 151.44/22.26 | | | (62) all_52_9 = e2 % 151.44/22.26 | | | % 151.44/22.26 | | | REDUCE: (7), (62) imply: % 151.44/22.26 | | | (63) ~ (all_52_1 = e2) % 151.44/22.26 | | | % 151.44/22.26 | | | REDUCE: (23), (61) imply: % 151.44/22.26 | | | (64) ~ (all_52_1 = e1) % 151.44/22.26 | | | % 151.44/22.26 | | | REDUCE: (15), (61) imply: % 151.44/22.26 | | | (65) ~ (all_52_7 = e1) % 151.44/22.26 | | | % 151.44/22.26 | | | REDUCE: (57), (61) imply: % 151.44/22.26 | | | (66) ~ (e1 = e0) % 151.44/22.26 | | | % 151.44/22.26 | | | BETA: splitting (53) gives: % 151.44/22.26 | | | % 151.44/22.26 | | | Case 1: % 151.44/22.26 | | | | % 151.44/22.26 | | | | (67) all_58_12 = e2 % 151.44/22.26 | | | | % 151.44/22.26 | | | | REF_CLOSE: (18), (45), (67) are inconsistent by sub-proof #423. % 151.44/22.26 | | | | % 151.44/22.26 | | | Case 2: % 151.44/22.26 | | | | % 151.44/22.26 | | | | (68) all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2 % 151.44/22.26 | | | | % 151.44/22.26 | | | | BETA: splitting (68) gives: % 151.44/22.26 | | | | % 151.44/22.26 | | | | Case 1: % 151.44/22.26 | | | | | % 151.44/22.26 | | | | | (69) all_58_13 = e2 % 151.44/22.26 | | | | | % 151.44/22.26 | | | | | COMBINE_EQS: (19), (69) imply: % 151.44/22.26 | | | | | (70) all_52_7 = e2 % 151.44/22.26 | | | | | % 151.44/22.26 | | | | | SIMP: (70) implies: % 151.44/22.26 | | | | | (71) all_52_7 = e2 % 151.44/22.26 | | | | | % 151.44/22.26 | | | | | REDUCE: (4), (71) imply: % 151.44/22.26 | | | | | (72) ~ (all_52_11 = e2) % 151.44/22.26 | | | | | % 151.44/22.26 | | | | | SIMP: (72) implies: % 151.44/22.26 | | | | | (73) ~ (all_52_11 = e2) % 151.44/22.26 | | | | | % 151.44/22.26 | | | | | BETA: splitting (47) gives: % 151.44/22.26 | | | | | % 151.44/22.26 | | | | | Case 1: % 151.44/22.26 | | | | | | % 151.44/22.26 | | | | | | (74) all_58_2 = e3 % 151.44/22.26 | | | | | | % 151.44/22.26 | | | | | | COMBINE_EQS: (40), (74) imply: % 151.44/22.26 | | | | | | (75) all_52_1 = e3 % 151.44/22.26 | | | | | | % 151.44/22.26 | | | | | | REDUCE: (55), (75) imply: % 151.44/22.26 | | | | | | (76) ~ (all_4_1 = e3) % 151.44/22.26 | | | | | | % 151.44/22.26 | | | | | | SIMP: (76) implies: % 151.44/22.26 | | | | | | (77) ~ (all_4_1 = e3) % 151.44/22.26 | | | | | | % 151.44/22.26 | | | | | | REDUCE: (64), (75) imply: % 151.44/22.26 | | | | | | (78) ~ (e3 = e1) % 151.44/22.26 | | | | | | % 151.44/22.26 | | | | | | REDUCE: (33), (75) imply: % 151.44/22.26 | | | | | | (79) ~ (e3 = e0) % 151.44/22.26 | | | | | | % 151.44/22.26 | | | | | | BETA: splitting (42) gives: % 151.44/22.26 | | | | | | % 151.44/22.26 | | | | | | Case 1: % 151.44/22.26 | | | | | | | % 151.44/22.26 | | | | | | | (80) all_58_12 = e1 % 151.44/22.26 | | | | | | | % 151.44/22.26 | | | | | | | REF_CLOSE: (18), (66), (80) are inconsistent by sub-proof #475. % 151.44/22.26 | | | | | | | % 151.44/22.26 | | | | | | Case 2: % 151.44/22.26 | | | | | | | % 151.44/22.26 | | | | | | | (81) all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1 % 151.44/22.26 | | | | | | | % 151.44/22.26 | | | | | | | BETA: splitting (81) gives: % 151.44/22.26 | | | | | | | % 151.44/22.26 | | | | | | | Case 1: % 151.44/22.26 | | | | | | | | % 151.44/22.26 | | | | | | | | (82) all_58_13 = e1 % 151.44/22.26 | | | | | | | | % 151.44/22.26 | | | | | | | | COMBINE_EQS: (69), (82) imply: % 151.44/22.26 | | | | | | | | (83) e2 = e1 % 151.44/22.26 | | | | | | | | % 151.44/22.26 | | | | | | | | REDUCE: (31), (83) imply: % 151.44/22.26 | | | | | | | | (84) $false % 151.44/22.26 | | | | | | | | % 151.44/22.26 | | | | | | | | CLOSE: (84) is inconsistent. % 151.44/22.26 | | | | | | | | % 151.44/22.26 | | | | | | | Case 2: % 151.44/22.26 | | | | | | | | % 151.44/22.26 | | | | | | | | (85) all_58_14 = e1 | all_58_15 = e1 % 151.44/22.26 | | | | | | | | % 151.44/22.26 | | | | | | | | BETA: splitting (85) gives: % 151.44/22.26 | | | | | | | | % 151.44/22.26 | | | | | | | | Case 1: % 151.44/22.26 | | | | | | | | | % 151.44/22.26 | | | | | | | | | (86) all_58_14 = e1 % 151.44/22.26 | | | | | | | | | % 151.44/22.26 | | | | | | | | | COMBINE_EQS: (50), (86) imply: % 151.44/22.26 | | | | | | | | | (87) all_52_11 = e1 % 151.44/22.26 | | | | | | | | | % 151.44/22.26 | | | | | | | | | SIMP: (87) implies: % 151.44/22.26 | | | | | | | | | (88) all_52_11 = e1 % 151.44/22.26 | | | | | | | | | % 151.44/22.26 | | | | | | | | | REDUCE: (3), (88) imply: % 151.44/22.26 | | | | | | | | | (89) ~ (all_6_2 = e1) % 151.44/22.26 | | | | | | | | | % 151.44/22.26 | | | | | | | | | SIMP: (89) implies: % 151.44/22.26 | | | | | | | | | (90) ~ (all_6_2 = e1) % 151.44/22.26 | | | | | | | | | % 151.44/22.26 | | | | | | | | | REDUCE: (73), (88) imply: % 151.44/22.26 | | | | | | | | | (91) ~ (e2 = e1) % 151.44/22.26 | | | | | | | | | % 151.44/22.26 | | | | | | | | | BETA: splitting (37) gives: % 151.44/22.26 | | | | | | | | | % 151.44/22.26 | | | | | | | | | Case 1: % 151.44/22.26 | | | | | | | | | | % 151.44/22.26 | | | | | | | | | | (92) all_56_1 = e3 % 151.44/22.26 | | | | | | | | | | % 151.44/22.26 | | | | | | | | | | COMBINE_EQS: (54), (92) imply: % 151.44/22.26 | | | | | | | | | | (93) all_4_1 = e3 % 151.44/22.26 | | | | | | | | | | % 151.44/22.26 | | | | | | | | | | REDUCE: (77), (93) imply: % 151.44/22.26 | | | | | | | | | | (94) $false % 151.44/22.26 | | | | | | | | | | % 151.44/22.26 | | | | | | | | | | CLOSE: (94) is inconsistent. % 151.44/22.26 | | | | | | | | | | % 151.44/22.26 | | | | | | | | | Case 2: % 151.44/22.26 | | | | | | | | | | % 151.44/22.26 | | | | | | | | | | (95) all_56_11 = e2 | all_56_21 = e1 | all_56_31 = e0 % 151.44/22.26 | | | | | | | | | | % 151.44/22.26 | | | | | | | | | | REF_CLOSE: (9), (14), (31), (60), (79), (90), (95) are % 151.44/22.26 | | | | | | | | | | inconsistent by sub-proof #418. % 151.44/22.26 | | | | | | | | | | % 151.44/22.26 | | | | | | | | | End of split % 151.44/22.26 | | | | | | | | | % 151.44/22.26 | | | | | | | | Case 2: % 151.44/22.26 | | | | | | | | | % 151.44/22.26 | | | | | | | | | (96) all_58_15 = e1 % 151.44/22.26 | | | | | | | | | % 151.44/22.26 | | | | | | | | | COMBINE_EQS: (30), (96) imply: % 151.44/22.26 | | | | | | | | | (97) e3 = e1 % 151.44/22.26 | | | | | | | | | % 151.44/22.26 | | | | | | | | | REDUCE: (78), (97) imply: % 151.44/22.26 | | | | | | | | | (98) $false % 151.44/22.26 | | | | | | | | | % 151.44/22.26 | | | | | | | | | CLOSE: (98) is inconsistent. % 151.44/22.26 | | | | | | | | | % 151.44/22.26 | | | | | | | | End of split % 151.44/22.26 | | | | | | | | % 151.44/22.26 | | | | | | | End of split % 151.44/22.26 | | | | | | | % 151.44/22.26 | | | | | | End of split % 151.44/22.26 | | | | | | % 151.44/22.26 | | | | | Case 2: % 151.44/22.26 | | | | | | % 151.44/22.26 | | | | | | (99) ~ (all_58_2 = e3) % 151.44/22.26 | | | | | | % 151.44/22.26 | | | | | | REDUCE: (40), (99) imply: % 151.44/22.26 | | | | | | (100) ~ (all_52_1 = e3) % 151.44/22.26 | | | | | | % 151.44/22.26 | | | | | | REF_CLOSE: (10), (27), (33), (63), (64), (100) are inconsistent by % 151.44/22.26 | | | | | | sub-proof #559. % 151.44/22.26 | | | | | | % 151.44/22.26 | | | | | End of split % 151.44/22.26 | | | | | % 151.44/22.26 | | | | Case 2: % 151.44/22.26 | | | | | % 151.44/22.26 | | | | | (101) ~ (all_58_13 = e2) % 151.44/22.26 | | | | | % 151.44/22.26 | | | | | REDUCE: (19), (101) imply: % 151.44/22.26 | | | | | (102) ~ (all_52_7 = e2) % 151.44/22.26 | | | | | % 151.44/22.26 | | | | | REF_CLOSE: (29), (38), (39), (46), (65), (102) are inconsistent by % 151.44/22.26 | | | | | sub-proof #620. % 151.44/22.26 | | | | | % 151.44/22.26 | | | | End of split % 151.44/22.26 | | | | % 151.44/22.26 | | | End of split % 151.44/22.26 | | | % 151.44/22.26 | | End of split % 151.44/22.26 | | % 151.44/22.26 | Case 2: % 151.44/22.26 | | % 151.44/22.26 | | (103) all_56_11 = e0 % 151.44/22.26 | | % 151.44/22.26 | | COMBINE_EQS: (1), (103) imply: % 151.44/22.26 | | (104) all_8_2 = e0 % 151.44/22.26 | | % 151.44/22.26 | | COMBINE_EQS: (5), (104) imply: % 151.44/22.26 | | (105) all_14_2 = e0 % 151.44/22.26 | | % 151.44/22.26 | | REDUCE: (48), (104) imply: % 151.44/22.26 | | (106) op(e0, e0) = all_8_1 % 151.44/22.26 | | % 151.44/22.26 | | BETA: splitting (32) gives: % 151.44/22.26 | | % 151.44/22.26 | | Case 1: % 151.44/22.26 | | | % 151.44/22.26 | | | (107) ~ (all_14_1 = e3) % 151.44/22.26 | | | % 151.44/22.26 | | | REDUCE: (17), (107) imply: % 151.44/22.26 | | | (108) ~ (all_8_1 = e3) % 151.44/22.26 | | | % 151.44/22.26 | | | REF_CLOSE: (24), (34), (106), (108) are inconsistent by sub-proof #546. % 151.44/22.26 | | | % 151.44/22.26 | | Case 2: % 151.44/22.26 | | | % 151.44/22.26 | | | (109) ~ (all_14_2 = e0) % 151.44/22.26 | | | % 151.44/22.26 | | | REDUCE: (105), (109) imply: % 151.44/22.26 | | | (110) $false % 151.44/22.26 | | | % 151.44/22.26 | | | CLOSE: (110) is inconsistent. % 151.44/22.26 | | | % 151.44/22.26 | | End of split % 151.44/22.26 | | % 151.44/22.26 | End of split % 151.44/22.26 | % 151.44/22.26 End of proof % 151.44/22.26 % 151.44/22.26 Sub-proof #245 shows that the following formulas are inconsistent: % 151.44/22.26 ---------------------------------------------------------------- % 151.44/22.26 (1) all_54_0 = all_10_2 % 151.44/22.26 (2) all_54_2 = all_10_0 % 151.44/22.26 (3) op(e1, e1) = e0 % 151.44/22.26 (4) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 151.44/22.26 (5) ~ (all_10_0 = e0) % 151.44/22.26 (6) all_56_1 = all_10_2 % 151.44/22.26 (7) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0 % 151.44/22.26 (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 151.44/22.26 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 151.44/22.26 (9) all_56_7 = all_52_12 % 151.44/22.26 (10) ~ (all_52_12 = all_10_0) % 151.44/22.26 (11) ~ (all_56_1 = e2) | all_56_3 = e3 % 151.44/22.26 (12) ~ (all_56_1 = e0) | all_56_7 = e3 % 151.44/22.26 (13) ~ (all_52_4 = all_10_0) % 151.44/22.26 (14) op(all_10_2, all_10_2) = e1 % 151.44/22.26 (15) all_56_3 = all_52_4 % 151.44/22.26 (16) ~ (all_10_0 = e1) % 151.44/22.26 (17) ~ (all_10_0 = all_10_2) % 151.44/22.26 (18) ~ (all_10_0 = e2) % 151.44/22.26 % 151.44/22.26 Begin of proof % 151.44/22.26 | % 151.44/22.26 | BETA: splitting (7) gives: % 151.44/22.26 | % 151.44/22.26 | Case 1: % 151.44/22.26 | | % 151.44/22.26 | | (19) all_54_2 = e3 % 151.44/22.26 | | % 151.44/22.26 | | COMBINE_EQS: (2), (19) imply: % 151.44/22.26 | | (20) all_10_0 = e3 % 151.44/22.26 | | % 151.44/22.26 | | SIMP: (20) implies: % 151.44/22.26 | | (21) all_10_0 = e3 % 151.44/22.26 | | % 151.44/22.26 | | REDUCE: (13), (21) imply: % 151.44/22.26 | | (22) ~ (all_52_4 = e3) % 151.44/22.26 | | % 151.44/22.26 | | REDUCE: (10), (21) imply: % 151.44/22.26 | | (23) ~ (all_52_12 = e3) % 151.44/22.26 | | % 151.44/22.26 | | REDUCE: (17), (21) imply: % 151.44/22.26 | | (24) ~ (all_10_2 = e3) % 151.44/22.26 | | % 151.44/22.26 | | SIMP: (24) implies: % 151.44/22.26 | | (25) ~ (all_10_2 = e3) % 151.44/22.26 | | % 151.44/22.26 | | BETA: splitting (12) gives: % 151.44/22.26 | | % 151.44/22.26 | | Case 1: % 151.44/22.26 | | | % 151.44/22.26 | | | (26) ~ (all_56_1 = e0) % 151.44/22.26 | | | % 151.44/22.26 | | | REDUCE: (6), (26) imply: % 151.44/22.26 | | | (27) ~ (all_10_2 = e0) % 151.44/22.26 | | | % 151.44/22.26 | | | BETA: splitting (11) gives: % 151.44/22.26 | | | % 151.44/22.26 | | | Case 1: % 151.44/22.26 | | | | % 151.44/22.26 | | | | (28) ~ (all_56_1 = e2) % 151.44/22.26 | | | | % 151.44/22.26 | | | | REDUCE: (6), (28) imply: % 151.44/22.26 | | | | (29) ~ (all_10_2 = e2) % 151.44/22.26 | | | | % 151.44/22.26 | | | | BETA: splitting (4) gives: % 151.44/22.26 | | | | % 151.44/22.26 | | | | Case 1: % 151.44/22.26 | | | | | % 151.44/22.26 | | | | | (30) all_54_0 = e3 % 151.44/22.26 | | | | | % 151.44/22.26 | | | | | REF_CLOSE: (1), (25), (30) are inconsistent by sub-proof #709. % 151.44/22.26 | | | | | % 151.44/22.26 | | | | Case 2: % 151.44/22.26 | | | | | % 151.44/22.26 | | | | | (31) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 151.44/22.26 | | | | | % 151.44/22.26 | | | | | BETA: splitting (31) gives: % 151.44/22.26 | | | | | % 151.44/22.26 | | | | | Case 1: % 151.44/22.26 | | | | | | % 151.44/22.26 | | | | | | (32) all_54_0 = e2 % 151.44/22.26 | | | | | | % 151.44/22.26 | | | | | | REF_CLOSE: (1), (29), (32) are inconsistent by sub-proof #734. % 151.44/22.26 | | | | | | % 151.44/22.26 | | | | | Case 2: % 151.44/22.26 | | | | | | % 151.44/22.26 | | | | | | (33) all_54_0 = e1 | all_54_0 = e0 % 151.44/22.26 | | | | | | % 151.44/22.26 | | | | | | REF_CLOSE: (1), (3), (8), (14), (27), (33) are inconsistent by % 151.44/22.26 | | | | | | sub-proof #397. % 151.44/22.26 | | | | | | % 151.44/22.26 | | | | | End of split % 151.44/22.26 | | | | | % 151.44/22.26 | | | | End of split % 151.44/22.26 | | | | % 151.44/22.26 | | | Case 2: % 151.44/22.26 | | | | % 151.44/22.26 | | | | (34) all_56_3 = e3 % 151.44/22.26 | | | | % 151.44/22.26 | | | | REF_CLOSE: (15), (22), (34) are inconsistent by sub-proof #395. % 151.44/22.26 | | | | % 151.44/22.26 | | | End of split % 151.44/22.26 | | | % 151.44/22.26 | | Case 2: % 151.44/22.26 | | | % 151.44/22.26 | | | (35) all_56_7 = e3 % 151.44/22.26 | | | % 151.44/22.26 | | | COMBINE_EQS: (9), (35) imply: % 151.44/22.26 | | | (36) all_52_12 = e3 % 151.44/22.26 | | | % 151.44/22.26 | | | REDUCE: (23), (36) imply: % 151.44/22.26 | | | (37) $false % 151.44/22.26 | | | % 151.44/22.26 | | | CLOSE: (37) is inconsistent. % 151.44/22.26 | | | % 151.44/22.26 | | End of split % 151.44/22.26 | | % 151.44/22.26 | Case 2: % 151.44/22.26 | | % 151.44/22.26 | | (38) all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0 % 151.44/22.26 | | % 151.44/22.26 | | REF_CLOSE: (2), (5), (16), (18), (38) are inconsistent by sub-proof #382. % 151.44/22.26 | | % 151.44/22.26 | End of split % 151.44/22.26 | % 151.44/22.26 End of proof % 151.44/22.26 % 151.44/22.26 Sub-proof #246 shows that the following formulas are inconsistent: % 151.44/22.26 ---------------------------------------------------------------- % 151.44/22.26 (1) all_56_11 = all_8_2 % 151.44/22.26 (2) ~ (all_56_11 = e1) | all_56_13 = e2 % 151.44/22.26 (3) all_14_2 = all_8_2 % 151.44/22.26 (4) ~ (all_8_1 = e1) % 151.44/22.26 (5) ~ (all_52_1 = all_52_9) % 151.44/22.26 (6) all_54_10 = all_6_2 % 151.44/22.26 (7) ~ (all_52_13 = all_8_2) % 151.44/22.26 (8) all_54_0 = all_10_2 % 151.44/22.26 (9) all_54_4 = all_52_1 % 151.44/22.26 (10) op(e0, e0) = all_4_2 % 151.44/22.26 (11) all_54_5 = all_8_2 % 151.44/22.26 (12) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 151.44/22.26 (13) all_54_15 = all_4_2 % 151.44/22.27 (14) all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1 % 151.44/22.27 (15) all_42_1 = all_8_1 % 151.44/22.27 (16) all_56_21 = all_6_2 % 151.44/22.27 (17) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 151.44/22.27 (18) all_56_17 = all_52_2 % 151.44/22.27 (19) all_58_9 = all_52_12 % 151.44/22.27 (20) all_14_1 = all_8_1 % 151.44/22.27 (21) op(e2, all_8_2) = all_56_10 % 151.44/22.27 (22) op(e3, e3) = all_10_2 % 151.44/22.27 (23) all_42_2 = all_8_2 % 151.44/22.27 (24) ~ (all_56_21 = e3) | all_56_17 = e1 % 151.44/22.27 (25) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 151.44/22.27 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 151.44/22.27 (26) all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0 % 151.44/22.27 (27) ~ (all_6_2 = e0) % 151.44/22.27 (28) ~ (all_56_11 = e3) | all_56_9 = e2 % 151.44/22.27 (29) all_56_13 = all_52_9 % 151.44/22.27 (30) ~ (all_52_1 = all_52_13) % 151.44/22.27 (31) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0 % 151.44/22.27 (32) ~ (all_4_2 = e1) % 151.44/22.27 (33) op(e2, all_8_1) = e1 % 151.44/22.27 (34) ~ (e2 = e1) % 151.44/22.27 (35) ~ (all_14_1 = e3) | ~ (all_14_2 = e0) % 151.44/22.27 (36) all_58_11 = all_52_14 % 151.44/22.27 (37) ~ (all_42_1 = e0) | ~ (all_42_2 = e3) % 151.44/22.27 (38) ~ (all_52_2 = all_52_14) % 151.44/22.27 (39) ~ (all_52_13 = all_4_2) % 151.44/22.27 (40) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0 % 151.44/22.27 (41) op(e1, e1) = all_6_2 % 151.44/22.27 (42) all_58_15 = all_4_2 % 151.44/22.27 (43) all_58_2 = all_52_1 % 151.44/22.27 (44) ~ (all_4_2 = e3) % 151.44/22.27 (45) ~ (all_52_9 = all_6_2) % 151.44/22.27 (46) all_58_10 = all_52_13 % 151.44/22.27 (47) ~ (all_56_11 = e0) | all_56_15 = e2 % 151.44/22.27 (48) op(e2, e3) = all_52_1 % 151.44/22.27 (49) op(e2, e2) = all_8_2 % 151.44/22.27 (50) op(e2, e0) = all_52_13 % 151.44/22.27 (51) ~ (all_52_2 = all_6_2) % 151.44/22.27 (52) ~ (all_52_1 = all_52_2) % 151.44/22.27 (53) ~ (all_52_14 = all_6_2) % 151.44/22.27 (54) all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3 % 151.44/22.27 (55) op(all_8_2, all_8_2) = all_8_1 % 151.44/22.27 (56) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 151.44/22.27 (57) all_56_9 = all_52_1 % 151.44/22.27 (58) all_56_15 = all_52_13 % 151.44/22.27 (59) ~ (all_52_1 = all_10_2) % 151.44/22.27 % 151.44/22.27 Begin of proof % 151.44/22.27 | % 151.44/22.27 | BETA: splitting (47) gives: % 151.44/22.27 | % 151.44/22.27 | Case 1: % 151.44/22.27 | | % 151.44/22.27 | | (60) ~ (all_56_11 = e0) % 151.44/22.27 | | % 151.44/22.27 | | REDUCE: (1), (60) imply: % 151.44/22.27 | | (61) ~ (all_8_2 = e0) % 151.44/22.27 | | % 151.44/22.27 | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (8), (9), (11), (12), (14), (15), % 151.44/22.27 | | (16), (17), (18), (19), (21), (22), (23), (24), (25), (26), (27), % 151.44/22.27 | | (28), (29), (30), (31), (32), (33), (34), (36), (37), (38), (41), % 151.44/22.27 | | (42), (43), (44), (45), (46), (48), (49), (51), (52), (53), (54), % 151.44/22.27 | | (55), (56), (57), (59), (61) are inconsistent by sub-proof #247. % 151.44/22.27 | | % 151.44/22.27 | Case 2: % 151.44/22.27 | | % 151.44/22.27 | | (62) all_56_15 = e2 % 151.44/22.27 | | (63) all_56_11 = e0 % 151.44/22.27 | | % 151.44/22.27 | | REF_CLOSE: (1), (3), (4), (10), (13), (20), (21), (25), (33), (34), (35), % 151.44/22.27 | | (39), (40), (50), (55), (58), (62), (63) are inconsistent by % 151.44/22.27 | | sub-proof #251. % 151.44/22.27 | | % 151.44/22.27 | End of split % 151.44/22.27 | % 151.44/22.27 End of proof % 151.44/22.27 % 151.44/22.27 Sub-proof #247 shows that the following formulas are inconsistent: % 151.44/22.27 ---------------------------------------------------------------- % 151.44/22.27 (1) all_56_11 = all_8_2 % 151.44/22.27 (2) ~ (all_56_11 = e1) | all_56_13 = e2 % 151.44/22.27 (3) ~ (all_8_1 = e1) % 151.44/22.27 (4) ~ (all_52_1 = all_52_9) % 151.44/22.27 (5) all_54_10 = all_6_2 % 151.44/22.27 (6) ~ (all_52_13 = all_8_2) % 151.44/22.27 (7) all_54_0 = all_10_2 % 151.44/22.27 (8) all_54_4 = all_52_1 % 151.44/22.27 (9) all_54_5 = all_8_2 % 151.44/22.27 (10) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 151.44/22.27 (11) all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1 % 151.44/22.27 (12) all_42_1 = all_8_1 % 151.44/22.27 (13) all_56_21 = all_6_2 % 151.44/22.27 (14) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 151.44/22.27 (15) all_56_17 = all_52_2 % 151.44/22.27 (16) all_58_9 = all_52_12 % 151.44/22.27 (17) op(e2, all_8_2) = all_56_10 % 151.44/22.27 (18) op(e3, e3) = all_10_2 % 151.44/22.27 (19) all_42_2 = all_8_2 % 151.44/22.27 (20) ~ (all_56_21 = e3) | all_56_17 = e1 % 151.44/22.27 (21) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 151.44/22.27 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 151.44/22.27 (22) all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0 % 151.44/22.27 (23) ~ (all_6_2 = e0) % 151.44/22.27 (24) ~ (all_56_11 = e3) | all_56_9 = e2 % 151.44/22.27 (25) all_56_13 = all_52_9 % 151.44/22.27 (26) ~ (all_52_1 = all_52_13) % 151.44/22.27 (27) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0 % 151.44/22.27 (28) ~ (all_4_2 = e1) % 151.44/22.27 (29) op(e2, all_8_1) = e1 % 151.44/22.27 (30) ~ (e2 = e1) % 151.44/22.27 (31) all_58_11 = all_52_14 % 151.44/22.27 (32) ~ (all_42_1 = e0) | ~ (all_42_2 = e3) % 151.44/22.27 (33) ~ (all_52_2 = all_52_14) % 151.44/22.27 (34) op(e1, e1) = all_6_2 % 151.44/22.27 (35) all_58_15 = all_4_2 % 151.44/22.27 (36) all_58_2 = all_52_1 % 151.44/22.27 (37) ~ (all_4_2 = e3) % 151.44/22.27 (38) ~ (all_52_9 = all_6_2) % 151.44/22.27 (39) all_58_10 = all_52_13 % 151.44/22.27 (40) op(e2, e3) = all_52_1 % 151.44/22.27 (41) op(e2, e2) = all_8_2 % 151.44/22.27 (42) ~ (all_52_2 = all_6_2) % 151.44/22.27 (43) ~ (all_52_1 = all_52_2) % 151.44/22.27 (44) ~ (all_8_2 = e0) % 151.44/22.27 (45) ~ (all_52_14 = all_6_2) % 151.44/22.27 (46) all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3 % 151.44/22.27 (47) op(all_8_2, all_8_2) = all_8_1 % 151.44/22.27 (48) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 151.44/22.27 (49) all_56_9 = all_52_1 % 151.44/22.27 (50) ~ (all_52_1 = all_10_2) % 151.44/22.27 % 151.44/22.27 Begin of proof % 151.44/22.27 | % 151.44/22.27 | BETA: splitting (2) gives: % 151.44/22.27 | % 151.44/22.27 | Case 1: % 151.44/22.27 | | % 151.44/22.27 | | (51) ~ (all_56_11 = e1) % 151.44/22.27 | | % 151.44/22.27 | | REF_CLOSE: (1), (3), (7), (9), (10), (12), (17), (18), (19), (21), (24), % 151.44/22.27 | | (29), (30), (32), (40), (41), (44), (47), (48), (49), (50), (51) % 151.44/22.27 | | are inconsistent by sub-proof #250. % 151.44/22.27 | | % 151.44/22.27 | Case 2: % 151.44/22.27 | | % 151.44/22.27 | | (52) all_56_13 = e2 % 151.44/22.27 | | (53) all_56_11 = e1 % 151.44/22.27 | | % 151.44/22.27 | | COMBINE_EQS: (1), (53) imply: % 151.44/22.27 | | (54) all_8_2 = e1 % 151.44/22.27 | | % 151.44/22.27 | | COMBINE_EQS: (25), (52) imply: % 151.44/22.27 | | (55) all_52_9 = e2 % 151.44/22.27 | | % 151.44/22.27 | | REDUCE: (4), (55) imply: % 151.44/22.27 | | (56) ~ (all_52_1 = e2) % 151.44/22.27 | | % 151.44/22.27 | | REDUCE: (38), (55) imply: % 151.44/22.27 | | (57) ~ (all_6_2 = e2) % 151.44/22.27 | | % 151.44/22.27 | | SIMP: (57) implies: % 151.44/22.27 | | (58) ~ (all_6_2 = e2) % 151.44/22.27 | | % 151.44/22.27 | | REDUCE: (6), (54) imply: % 151.44/22.27 | | (59) ~ (all_52_13 = e1) % 151.44/22.27 | | % 151.44/22.27 | | REDUCE: (47), (54) imply: % 151.44/22.27 | | (60) op(e1, e1) = all_8_1 % 151.44/22.27 | | % 151.44/22.27 | | REF_CLOSE: (3), (5), (8), (11), (13), (14), (15), (16), (20), (21), (22), % 151.44/22.27 | | (23), (26), (27), (28), (29), (31), (33), (34), (35), (36), (37), % 151.44/22.27 | | (39), (40), (42), (43), (45), (46), (56), (58), (59), (60) are % 151.44/22.27 | | inconsistent by sub-proof #248. % 151.44/22.27 | | % 151.44/22.27 | End of split % 151.44/22.27 | % 151.44/22.27 End of proof % 151.44/22.27 % 151.44/22.27 Sub-proof #248 shows that the following formulas are inconsistent: % 151.44/22.27 ---------------------------------------------------------------- % 151.44/22.27 (1) ~ (all_8_1 = e1) % 151.44/22.27 (2) ~ (all_52_13 = e1) % 151.44/22.27 (3) all_54_10 = all_6_2 % 151.44/22.27 (4) all_54_4 = all_52_1 % 151.44/22.27 (5) all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1 % 151.44/22.27 (6) all_56_21 = all_6_2 % 151.44/22.27 (7) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 151.44/22.27 (8) all_56_17 = all_52_2 % 151.44/22.27 (9) all_58_9 = all_52_12 % 151.44/22.27 (10) ~ (all_56_21 = e3) | all_56_17 = e1 % 151.44/22.27 (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 151.44/22.27 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 151.44/22.27 (12) all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0 % 151.44/22.27 (13) ~ (all_6_2 = e0) % 151.44/22.27 (14) ~ (all_52_1 = all_52_13) % 151.44/22.27 (15) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0 % 151.44/22.27 (16) ~ (all_4_2 = e1) % 151.44/22.27 (17) op(e2, all_8_1) = e1 % 151.44/22.27 (18) all_58_11 = all_52_14 % 151.44/22.27 (19) ~ (all_52_2 = all_52_14) % 151.44/22.27 (20) op(e1, e1) = all_8_1 % 151.44/22.27 (21) op(e1, e1) = all_6_2 % 151.44/22.27 (22) all_58_15 = all_4_2 % 151.44/22.27 (23) ~ (all_6_2 = e2) % 151.44/22.27 (24) all_58_2 = all_52_1 % 151.44/22.27 (25) ~ (all_4_2 = e3) % 151.44/22.27 (26) all_58_10 = all_52_13 % 151.44/22.27 (27) op(e2, e3) = all_52_1 % 151.44/22.27 (28) ~ (all_52_2 = all_6_2) % 151.44/22.27 (29) ~ (all_52_1 = all_52_2) % 151.44/22.27 (30) ~ (all_52_14 = all_6_2) % 151.44/22.27 (31) all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3 % 151.44/22.27 (32) ~ (all_52_1 = e2) % 151.44/22.27 % 151.44/22.27 Begin of proof % 151.44/22.27 | % 151.44/22.27 | GROUND_INST: instantiating (11) with all_6_2, all_8_1, e1, e1, simplifying % 151.44/22.27 | with (20), (21) gives: % 151.44/22.27 | (33) all_8_1 = all_6_2 % 151.44/22.27 | % 151.44/22.27 | REDUCE: (1), (33) imply: % 151.44/22.27 | (34) ~ (all_6_2 = e1) % 151.44/22.27 | % 151.44/22.27 | REDUCE: (17), (33) imply: % 151.44/22.27 | (35) op(e2, all_6_2) = e1 % 151.44/22.27 | % 151.44/22.27 | BETA: splitting (7) gives: % 151.44/22.27 | % 151.44/22.27 | Case 1: % 151.44/22.27 | | % 151.44/22.27 | | (36) all_54_10 = e3 % 151.44/22.27 | | % 151.44/22.27 | | COMBINE_EQS: (3), (36) imply: % 151.44/22.27 | | (37) all_6_2 = e3 % 151.44/22.27 | | % 151.44/22.27 | | SIMP: (37) implies: % 151.44/22.27 | | (38) all_6_2 = e3 % 151.44/22.27 | | % 151.44/22.27 | | COMBINE_EQS: (6), (38) imply: % 151.44/22.27 | | (39) all_56_21 = e3 % 151.44/22.27 | | % 151.44/22.27 | | REDUCE: (28), (38) imply: % 151.44/22.27 | | (40) ~ (all_52_2 = e3) % 151.44/22.27 | | % 151.44/22.27 | | REDUCE: (30), (38) imply: % 151.44/22.27 | | (41) ~ (all_52_14 = e3) % 151.44/22.27 | | % 151.44/22.27 | | REDUCE: (35), (38) imply: % 151.44/22.27 | | (42) op(e2, e3) = e1 % 151.44/22.27 | | % 151.44/22.27 | | BETA: splitting (10) gives: % 151.44/22.27 | | % 151.44/22.27 | | Case 1: % 151.44/22.27 | | | % 151.44/22.27 | | | (43) ~ (all_56_21 = e3) % 151.44/22.27 | | | % 151.44/22.27 | | | REDUCE: (39), (43) imply: % 151.44/22.27 | | | (44) $false % 151.44/22.27 | | | % 151.44/22.27 | | | CLOSE: (44) is inconsistent. % 151.44/22.27 | | | % 151.44/22.27 | | Case 2: % 151.44/22.27 | | | % 151.44/22.27 | | | (45) all_56_17 = e1 % 151.44/22.27 | | | % 151.44/22.27 | | | COMBINE_EQS: (8), (45) imply: % 151.44/22.27 | | | (46) all_52_2 = e1 % 151.44/22.27 | | | % 151.44/22.27 | | | REDUCE: (29), (46) imply: % 151.44/22.27 | | | (47) ~ (all_52_1 = e1) % 151.44/22.27 | | | % 151.44/22.27 | | | REDUCE: (19), (46) imply: % 151.44/22.27 | | | (48) ~ (all_52_14 = e1) % 151.44/22.27 | | | % 151.44/22.27 | | | SIMP: (48) implies: % 151.44/22.27 | | | (49) ~ (all_52_14 = e1) % 151.44/22.27 | | | % 151.44/22.27 | | | REDUCE: (40), (46) imply: % 151.44/22.27 | | | (50) ~ (e3 = e1) % 151.44/22.27 | | | % 151.44/22.27 | | | SIMP: (50) implies: % 151.44/22.27 | | | (51) ~ (e3 = e1) % 151.44/22.27 | | | % 151.44/22.27 | | | BETA: splitting (5) gives: % 151.44/22.27 | | | % 151.44/22.27 | | | Case 1: % 151.44/22.27 | | | | % 151.44/22.27 | | | | (52) all_58_9 = e1 % 151.44/22.27 | | | | % 151.44/22.27 | | | | COMBINE_EQS: (9), (52) imply: % 151.44/22.27 | | | | (53) all_52_12 = e1 % 151.44/22.27 | | | | % 151.44/22.27 | | | | BETA: splitting (31) gives: % 151.44/22.27 | | | | % 151.44/22.27 | | | | Case 1: % 151.44/22.27 | | | | | % 151.44/22.27 | | | | | (54) all_58_9 = e3 % 151.44/22.27 | | | | | % 151.44/22.27 | | | | | COMBINE_EQS: (52), (54) imply: % 151.44/22.27 | | | | | (55) e3 = e1 % 151.44/22.27 | | | | | % 151.44/22.27 | | | | | SIMP: (55) implies: % 151.44/22.27 | | | | | (56) e3 = e1 % 151.44/22.27 | | | | | % 151.44/22.27 | | | | | REDUCE: (51), (56) imply: % 151.44/22.27 | | | | | (57) $false % 151.44/22.27 | | | | | % 151.44/22.27 | | | | | CLOSE: (57) is inconsistent. % 151.44/22.27 | | | | | % 151.44/22.27 | | | | Case 2: % 151.44/22.27 | | | | | % 151.44/22.27 | | | | | (58) all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3 % 151.44/22.27 | | | | | % 151.44/22.27 | | | | | BETA: splitting (58) gives: % 151.44/22.27 | | | | | % 151.44/22.27 | | | | | Case 1: % 151.44/22.27 | | | | | | % 151.44/22.27 | | | | | | (59) all_58_10 = e3 % 151.44/22.27 | | | | | | % 151.44/22.27 | | | | | | COMBINE_EQS: (26), (59) imply: % 151.44/22.27 | | | | | | (60) all_52_13 = e3 % 151.44/22.27 | | | | | | % 151.44/22.27 | | | | | | REDUCE: (14), (60) imply: % 151.44/22.27 | | | | | | (61) ~ (all_52_1 = e3) % 151.44/22.27 | | | | | | % 151.44/22.27 | | | | | | BETA: splitting (15) gives: % 151.44/22.27 | | | | | | % 151.44/22.27 | | | | | | Case 1: % 151.44/22.27 | | | | | | | % 151.44/22.27 | | | | | | | (62) all_54_4 = e3 % 151.44/22.27 | | | | | | | % 151.44/22.27 | | | | | | | REF_CLOSE: (4), (61), (62) are inconsistent by sub-proof #634. % 151.44/22.27 | | | | | | | % 151.44/22.27 | | | | | | Case 2: % 151.44/22.27 | | | | | | | % 151.44/22.27 | | | | | | | (63) all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0 % 151.44/22.27 | | | | | | | % 151.44/22.27 | | | | | | | BETA: splitting (63) gives: % 151.44/22.27 | | | | | | | % 151.44/22.27 | | | | | | | Case 1: % 151.44/22.27 | | | | | | | | % 151.44/22.27 | | | | | | | | (64) all_54_4 = e2 % 151.44/22.27 | | | | | | | | % 151.44/22.27 | | | | | | | | REF_CLOSE: (4), (32), (64) are inconsistent by sub-proof #633. % 151.44/22.27 | | | | | | | | % 151.44/22.27 | | | | | | | Case 2: % 151.44/22.27 | | | | | | | | % 151.44/22.27 | | | | | | | | (65) all_54_4 = e1 | all_54_4 = e0 % 151.44/22.27 | | | | | | | | % 151.44/22.27 | | | | | | | | BETA: splitting (12) gives: % 151.44/22.27 | | | | | | | | % 151.44/22.27 | | | | | | | | Case 1: % 151.44/22.27 | | | | | | | | | % 151.44/22.27 | | | | | | | | | (66) all_58_2 = e0 % 151.44/22.27 | | | | | | | | | % 151.44/22.27 | | | | | | | | | COMBINE_EQS: (24), (66) imply: % 151.44/22.27 | | | | | | | | | (67) all_52_1 = e0 % 151.44/22.27 | | | | | | | | | % 151.44/22.27 | | | | | | | | | SIMP: (67) implies: % 151.44/22.27 | | | | | | | | | (68) all_52_1 = e0 % 151.44/22.27 | | | | | | | | | % 151.44/22.27 | | | | | | | | | REDUCE: (47), (68) imply: % 151.44/22.27 | | | | | | | | | (69) ~ (e1 = e0) % 151.44/22.27 | | | | | | | | | % 151.44/22.27 | | | | | | | | | SIMP: (69) implies: % 151.44/22.27 | | | | | | | | | (70) ~ (e1 = e0) % 151.44/22.27 | | | | | | | | | % 151.44/22.27 | | | | | | | | | REDUCE: (27), (68) imply: % 151.44/22.27 | | | | | | | | | (71) op(e2, e3) = e0 % 151.44/22.27 | | | | | | | | | % 151.44/22.27 | | | | | | | | | GROUND_INST: instantiating (11) with e0, e1, e3, e2, % 151.44/22.27 | | | | | | | | | simplifying with (42), (71) gives: % 151.44/22.27 | | | | | | | | | (72) e1 = e0 % 151.44/22.27 | | | | | | | | | % 151.44/22.27 | | | | | | | | | REDUCE: (70), (72) imply: % 151.44/22.27 | | | | | | | | | (73) $false % 151.44/22.27 | | | | | | | | | % 151.44/22.27 | | | | | | | | | CLOSE: (73) is inconsistent. % 151.44/22.27 | | | | | | | | | % 151.44/22.27 | | | | | | | | Case 2: % 151.44/22.27 | | | | | | | | | % 151.44/22.27 | | | | | | | | | (74) ~ (all_58_2 = e0) % 151.44/22.27 | | | | | | | | | % 151.44/22.27 | | | | | | | | | REDUCE: (24), (74) imply: % 151.44/22.27 | | | | | | | | | (75) ~ (all_52_1 = e0) % 151.44/22.27 | | | | | | | | | % 151.44/22.27 | | | | | | | | | BETA: splitting (65) gives: % 151.44/22.27 | | | | | | | | | % 151.44/22.27 | | | | | | | | | Case 1: % 151.44/22.27 | | | | | | | | | | % 151.44/22.27 | | | | | | | | | | (76) all_54_4 = e1 % 151.44/22.27 | | | | | | | | | | % 151.44/22.27 | | | | | | | | | | REF_CLOSE: (4), (47), (76) are inconsistent by sub-proof % 151.44/22.27 | | | | | | | | | | #584. % 151.44/22.27 | | | | | | | | | | % 151.44/22.27 | | | | | | | | | Case 2: % 151.44/22.27 | | | | | | | | | | % 151.44/22.27 | | | | | | | | | | (77) all_54_4 = e0 % 151.44/22.27 | | | | | | | | | | % 151.44/22.27 | | | | | | | | | | REF_CLOSE: (4), (75), (77) are inconsistent by sub-proof % 151.44/22.27 | | | | | | | | | | #614. % 151.44/22.27 | | | | | | | | | | % 151.44/22.27 | | | | | | | | | End of split % 151.44/22.27 | | | | | | | | | % 151.44/22.27 | | | | | | | | End of split % 151.44/22.27 | | | | | | | | % 151.44/22.27 | | | | | | | End of split % 151.44/22.27 | | | | | | | % 151.44/22.27 | | | | | | End of split % 151.44/22.27 | | | | | | % 151.44/22.27 | | | | | Case 2: % 151.44/22.27 | | | | | | % 151.44/22.27 | | | | | | (78) all_58_11 = e3 | all_58_15 = e3 % 151.44/22.27 | | | | | | % 151.44/22.27 | | | | | | REF_CLOSE: (18), (22), (25), (41), (78) are inconsistent by % 151.44/22.27 | | | | | | sub-proof #331. % 151.44/22.27 | | | | | | % 151.44/22.27 | | | | | End of split % 151.44/22.27 | | | | | % 151.44/22.27 | | | | End of split % 151.44/22.27 | | | | % 151.44/22.27 | | | Case 2: % 151.44/22.27 | | | | % 151.44/22.27 | | | | (79) all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1 % 151.44/22.27 | | | | % 151.44/22.27 | | | | REF_CLOSE: (2), (16), (18), (22), (26), (49), (79) are inconsistent by % 151.44/22.27 | | | | sub-proof #587. % 151.44/22.27 | | | | % 151.44/22.27 | | | End of split % 151.44/22.27 | | | % 151.44/22.27 | | End of split % 151.44/22.27 | | % 151.44/22.27 | Case 2: % 151.44/22.27 | | % 151.44/22.27 | | (80) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 151.44/22.27 | | % 151.44/22.27 | | REF_CLOSE: (3), (13), (23), (34), (80) are inconsistent by sub-proof #574. % 151.44/22.27 | | % 151.44/22.27 | End of split % 151.44/22.27 | % 151.44/22.27 End of proof % 151.44/22.27 % 151.44/22.27 Sub-proof #249 shows that the following formulas are inconsistent: % 151.44/22.27 ---------------------------------------------------------------- % 151.44/22.27 (1) all_56_11 = all_8_2 % 151.44/22.27 (2) ~ (all_56_11 = e1) | all_56_13 = e2 % 151.44/22.27 (3) all_14_2 = all_8_2 % 151.44/22.27 (4) ~ (all_8_1 = e1) % 151.44/22.27 (5) all_54_10 = all_6_2 % 151.44/22.27 (6) ~ (all_52_13 = all_8_2) % 151.44/22.27 (7) all_54_0 = all_10_2 % 151.44/22.27 (8) op(e0, e0) = all_4_2 % 151.44/22.27 (9) all_54_5 = all_8_2 % 151.44/22.27 (10) all_6_1 = e3 % 151.44/22.27 (11) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 151.44/22.27 (12) all_54_15 = all_4_2 % 151.44/22.27 (13) all_42_1 = all_8_1 % 151.44/22.27 (14) all_56_21 = all_6_2 % 151.44/22.27 (15) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 151.44/22.27 (16) all_56_17 = all_52_2 % 151.44/22.27 (17) all_14_1 = all_8_1 % 151.44/22.27 (18) op(e2, all_8_2) = all_56_10 % 151.44/22.27 (19) op(e3, e3) = all_10_2 % 151.44/22.27 (20) all_42_2 = all_8_2 % 151.44/22.27 (21) ~ (all_56_21 = e3) | all_56_17 = e1 % 151.44/22.27 (22) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 151.44/22.27 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 151.44/22.27 (23) all_42_0 = e1 % 151.44/22.27 (24) ~ (all_56_11 = e3) | all_56_9 = e2 % 151.44/22.27 (25) all_56_13 = all_52_9 % 151.44/22.27 (26) op(e1, e3) = all_52_2 % 151.44/22.27 (27) ~ (all_42_0 = e1) | ~ (all_42_1 = e0) | ~ (all_42_2 = e3) % 151.44/22.27 (28) op(e2, all_8_1) = e1 % 151.44/22.27 (29) ~ (e2 = e1) % 151.44/22.27 (30) ~ (all_14_1 = e3) | ~ (all_14_2 = e0) % 151.44/22.27 (31) op(e1, all_6_1) = all_6_0 % 151.44/22.27 (32) ~ (all_52_13 = all_4_2) % 151.44/22.27 (33) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0 % 151.44/22.27 (34) op(e1, e1) = all_6_2 % 151.44/22.27 (35) ~ (all_52_9 = all_6_2) % 151.44/22.27 (36) ~ (all_56_11 = e0) | all_56_15 = e2 % 151.44/22.27 (37) op(e2, e3) = all_52_1 % 151.44/22.27 (38) op(e2, e2) = all_8_2 % 151.44/22.27 (39) op(e2, e0) = all_52_13 % 151.44/22.27 (40) ~ (all_52_1 = all_52_2) % 151.44/22.27 (41) op(all_8_2, all_8_2) = all_8_1 % 151.44/22.27 (42) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 151.44/22.27 (43) all_56_9 = all_52_1 % 151.44/22.27 (44) all_56_15 = all_52_13 % 151.44/22.27 (45) ~ (all_52_1 = all_10_2) % 151.44/22.27 % 151.44/22.27 Begin of proof % 151.44/22.27 | % 151.44/22.27 | REDUCE: (10), (31) imply: % 151.44/22.27 | (46) op(e1, e3) = all_6_0 % 151.44/22.27 | % 151.44/22.27 | GROUND_INST: instantiating (22) with all_52_2, all_6_0, e3, e1, simplifying % 151.44/22.27 | with (26), (46) gives: % 151.44/22.27 | (47) all_52_2 = all_6_0 % 151.44/22.27 | % 151.44/22.27 | COMBINE_EQS: (16), (47) imply: % 151.44/22.27 | (48) all_56_17 = all_6_0 % 151.44/22.27 | % 151.44/22.27 | REDUCE: (40), (47) imply: % 151.44/22.27 | (49) ~ (all_52_1 = all_6_0) % 151.44/22.27 | % 151.44/22.27 | BETA: splitting (27) gives: % 151.44/22.27 | % 151.44/22.27 | Case 1: % 151.44/22.27 | | % 151.44/22.27 | | (50) ~ (all_42_0 = e1) % 151.44/22.27 | | % 151.44/22.27 | | REDUCE: (23), (50) imply: % 151.44/22.27 | | (51) $false % 151.44/22.27 | | % 151.44/22.27 | | CLOSE: (51) is inconsistent. % 151.44/22.27 | | % 151.44/22.27 | Case 2: % 151.44/22.27 | | % 151.44/22.27 | | (52) ~ (all_42_1 = e0) | ~ (all_42_2 = e3) % 151.44/22.27 | | % 151.44/22.27 | | BETA: splitting (36) gives: % 151.44/22.27 | | % 151.44/22.27 | | Case 1: % 151.44/22.27 | | | % 151.44/22.27 | | | (53) ~ (all_56_11 = e0) % 151.44/22.27 | | | % 151.44/22.27 | | | REDUCE: (1), (53) imply: % 151.44/22.27 | | | (54) ~ (all_8_2 = e0) % 151.44/22.27 | | | % 151.44/22.27 | | | BETA: splitting (2) gives: % 151.44/22.27 | | | % 151.44/22.27 | | | Case 1: % 151.44/22.27 | | | | % 151.44/22.27 | | | | (55) ~ (all_56_11 = e1) % 151.44/22.27 | | | | % 151.44/22.27 | | | | REF_CLOSE: (1), (4), (7), (9), (11), (13), (18), (19), (20), (22), (24), % 151.44/22.27 | | | | (28), (29), (37), (38), (41), (42), (43), (45), (52), (54), % 151.44/22.27 | | | | (55) are inconsistent by sub-proof #250. % 151.44/22.27 | | | | % 151.44/22.27 | | | Case 2: % 151.44/22.27 | | | | % 151.44/22.27 | | | | (56) all_56_13 = e2 % 151.44/22.27 | | | | (57) all_56_11 = e1 % 151.44/22.27 | | | | % 151.44/22.27 | | | | COMBINE_EQS: (1), (57) imply: % 151.44/22.27 | | | | (58) all_8_2 = e1 % 151.44/22.27 | | | | % 151.44/22.27 | | | | COMBINE_EQS: (25), (56) imply: % 151.44/22.27 | | | | (59) all_52_9 = e2 % 151.44/22.27 | | | | % 151.44/22.27 | | | | REDUCE: (35), (59) imply: % 151.44/22.27 | | | | (60) ~ (all_6_2 = e2) % 151.44/22.27 | | | | % 151.44/22.27 | | | | SIMP: (60) implies: % 151.44/22.27 | | | | (61) ~ (all_6_2 = e2) % 151.44/22.27 | | | | % 151.44/22.27 | | | | REDUCE: (6), (58) imply: % 151.44/22.27 | | | | (62) ~ (all_52_13 = e1) % 151.44/22.27 | | | | % 151.44/22.27 | | | | REDUCE: (41), (58) imply: % 151.44/22.27 | | | | (63) op(e1, e1) = all_8_1 % 151.44/22.27 | | | | % 151.44/22.27 | | | | GROUND_INST: instantiating (22) with all_6_2, all_8_1, e1, e1, % 151.44/22.27 | | | | simplifying with (34), (63) gives: % 151.44/22.27 | | | | (64) all_8_1 = all_6_2 % 151.44/22.27 | | | | % 151.44/22.27 | | | | REDUCE: (4), (64) imply: % 151.44/22.27 | | | | (65) ~ (all_6_2 = e1) % 151.44/22.27 | | | | % 151.44/22.27 | | | | REDUCE: (28), (64) imply: % 151.44/22.27 | | | | (66) op(e2, all_6_2) = e1 % 151.44/22.27 | | | | % 151.44/22.27 | | | | BETA: splitting (21) gives: % 151.44/22.27 | | | | % 151.44/22.27 | | | | Case 1: % 151.44/22.27 | | | | | % 151.44/22.27 | | | | | (67) ~ (all_56_21 = e3) % 151.44/22.27 | | | | | % 151.44/22.27 | | | | | REDUCE: (14), (67) imply: % 151.44/22.27 | | | | | (68) ~ (all_6_2 = e3) % 151.44/22.27 | | | | | % 151.44/22.27 | | | | | REF_CLOSE: (5), (15), (22), (39), (61), (62), (65), (66), (68) are % 151.44/22.27 | | | | | inconsistent by sub-proof #257. % 151.44/22.27 | | | | | % 151.44/22.27 | | | | Case 2: % 151.44/22.27 | | | | | % 151.44/22.27 | | | | | (69) all_56_21 = e3 % 151.44/22.27 | | | | | (70) all_56_17 = e1 % 151.44/22.27 | | | | | % 151.44/22.27 | | | | | COMBINE_EQS: (48), (70) imply: % 151.44/22.27 | | | | | (71) all_6_0 = e1 % 151.44/22.27 | | | | | % 151.44/22.27 | | | | | SIMP: (71) implies: % 151.44/22.27 | | | | | (72) all_6_0 = e1 % 151.44/22.27 | | | | | % 151.44/22.27 | | | | | COMBINE_EQS: (14), (69) imply: % 151.44/22.27 | | | | | (73) all_6_2 = e3 % 151.44/22.27 | | | | | % 151.44/22.27 | | | | | SIMP: (73) implies: % 151.44/22.27 | | | | | (74) all_6_2 = e3 % 151.44/22.27 | | | | | % 151.44/22.27 | | | | | REDUCE: (49), (72) imply: % 151.44/22.27 | | | | | (75) ~ (all_52_1 = e1) % 151.44/22.27 | | | | | % 151.44/22.27 | | | | | REDUCE: (66), (74) imply: % 151.44/22.27 | | | | | (76) op(e2, e3) = e1 % 151.44/22.27 | | | | | % 151.44/22.27 | | | | | GROUND_INST: instantiating (22) with all_52_1, e1, e3, e2, simplifying % 151.44/22.27 | | | | | with (37), (76) gives: % 151.44/22.27 | | | | | (77) all_52_1 = e1 % 151.44/22.27 | | | | | % 151.44/22.27 | | | | | REDUCE: (75), (77) imply: % 151.44/22.27 | | | | | (78) $false % 151.44/22.27 | | | | | % 151.44/22.27 | | | | | CLOSE: (78) is inconsistent. % 151.44/22.27 | | | | | % 151.44/22.27 | | | | End of split % 151.44/22.27 | | | | % 151.44/22.27 | | | End of split % 151.44/22.27 | | | % 151.44/22.27 | | Case 2: % 151.44/22.27 | | | % 151.44/22.27 | | | (79) all_56_15 = e2 % 151.44/22.27 | | | (80) all_56_11 = e0 % 151.44/22.27 | | | % 151.44/22.27 | | | REF_CLOSE: (1), (3), (4), (8), (12), (17), (18), (22), (28), (29), (30), % 151.44/22.27 | | | (32), (33), (39), (41), (44), (79), (80) are inconsistent by % 151.44/22.27 | | | sub-proof #251. % 151.44/22.27 | | | % 151.44/22.27 | | End of split % 151.44/22.27 | | % 151.44/22.27 | End of split % 151.44/22.27 | % 151.44/22.27 End of proof % 151.44/22.27 % 151.44/22.27 Sub-proof #250 shows that the following formulas are inconsistent: % 151.44/22.27 ---------------------------------------------------------------- % 151.44/22.27 (1) all_56_11 = all_8_2 % 151.44/22.27 (2) ~ (all_8_1 = e1) % 151.44/22.27 (3) all_54_0 = all_10_2 % 151.44/22.27 (4) all_54_5 = all_8_2 % 151.44/22.27 (5) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 151.44/22.27 (6) all_42_1 = all_8_1 % 151.44/22.27 (7) op(e2, all_8_2) = all_56_10 % 151.44/22.27 (8) op(e3, e3) = all_10_2 % 151.44/22.27 (9) all_42_2 = all_8_2 % 151.44/22.27 (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 151.44/22.27 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 151.44/22.27 (11) ~ (all_56_11 = e3) | all_56_9 = e2 % 151.44/22.27 (12) ~ (all_56_11 = e1) % 151.44/22.27 (13) op(e2, all_8_1) = e1 % 151.44/22.27 (14) ~ (e2 = e1) % 151.44/22.27 (15) ~ (all_42_1 = e0) | ~ (all_42_2 = e3) % 151.44/22.27 (16) op(e2, e3) = all_52_1 % 151.44/22.27 (17) op(e2, e2) = all_8_2 % 151.44/22.27 (18) ~ (all_8_2 = e0) % 151.44/22.27 (19) op(all_8_2, all_8_2) = all_8_1 % 151.44/22.27 (20) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 151.44/22.27 (21) all_56_9 = all_52_1 % 151.44/22.27 (22) ~ (all_52_1 = all_10_2) % 151.44/22.27 % 151.44/22.27 Begin of proof % 151.44/22.27 | % 151.44/22.27 | REDUCE: (1), (12) imply: % 151.44/22.27 | (23) ~ (all_8_2 = e1) % 151.44/22.27 | % 151.44/22.27 | BETA: splitting (11) gives: % 151.44/22.27 | % 151.44/22.27 | Case 1: % 151.44/22.27 | | % 151.44/22.27 | | (24) ~ (all_56_11 = e3) % 151.44/22.27 | | % 151.44/22.27 | | REDUCE: (1), (24) imply: % 151.44/22.27 | | (25) ~ (all_8_2 = e3) % 151.44/22.27 | | % 151.44/22.27 | | REF_CLOSE: (2), (4), (7), (10), (13), (17), (18), (19), (20), (23), (25) are % 151.44/22.27 | | inconsistent by sub-proof #259. % 151.44/22.27 | | % 151.44/22.27 | Case 2: % 151.44/22.27 | | % 151.44/22.27 | | (26) all_56_11 = e3 % 151.44/22.27 | | % 151.44/22.27 | | COMBINE_EQS: (1), (26) imply: % 151.44/22.27 | | (27) all_8_2 = e3 % 151.44/22.27 | | % 151.44/22.27 | | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (9), (10), (11), (13), (14), % 151.44/22.27 | | (15), (16), (19), (21), (22), (27) are inconsistent by sub-proof % 151.44/22.27 | | #255. % 151.44/22.27 | | % 151.44/22.27 | End of split % 151.44/22.27 | % 151.44/22.27 End of proof % 151.44/22.27 % 151.44/22.27 Sub-proof #251 shows that the following formulas are inconsistent: % 151.44/22.27 ---------------------------------------------------------------- % 151.44/22.27 (1) all_56_11 = all_8_2 % 151.44/22.27 (2) all_14_2 = all_8_2 % 151.44/22.27 (3) ~ (all_8_1 = e1) % 151.44/22.27 (4) op(e0, e0) = all_4_2 % 151.44/22.27 (5) all_54_15 = all_4_2 % 151.44/22.27 (6) all_14_1 = all_8_1 % 151.44/22.27 (7) op(e2, all_8_2) = all_56_10 % 151.44/22.28 (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 151.44/22.28 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 151.44/22.28 (9) all_56_15 = e2 % 151.44/22.28 (10) op(e2, all_8_1) = e1 % 151.44/22.28 (11) ~ (e2 = e1) % 151.44/22.28 (12) ~ (all_14_1 = e3) | ~ (all_14_2 = e0) % 151.44/22.28 (13) ~ (all_52_13 = all_4_2) % 151.44/22.28 (14) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0 % 151.44/22.28 (15) all_56_11 = e0 % 151.44/22.28 (16) op(e2, e0) = all_52_13 % 151.44/22.28 (17) op(all_8_2, all_8_2) = all_8_1 % 151.44/22.28 (18) all_56_15 = all_52_13 % 151.44/22.28 % 151.44/22.28 Begin of proof % 151.44/22.28 | % 151.44/22.28 | COMBINE_EQS: (1), (15) imply: % 151.44/22.28 | (19) all_8_2 = e0 % 151.44/22.28 | % 151.44/22.28 | COMBINE_EQS: (9), (18) imply: % 151.44/22.28 | (20) all_52_13 = e2 % 151.44/22.28 | % 151.44/22.28 | COMBINE_EQS: (2), (19) imply: % 151.44/22.28 | (21) all_14_2 = e0 % 151.44/22.28 | % 151.44/22.28 | REDUCE: (13), (20) imply: % 151.44/22.28 | (22) ~ (all_4_2 = e2) % 151.44/22.28 | % 151.44/22.28 | SIMP: (22) implies: % 151.44/22.28 | (23) ~ (all_4_2 = e2) % 151.44/22.28 | % 151.44/22.28 | REF_CLOSE: (3), (4), (5), (6), (7), (8), (10), (11), (12), (14), (16), (17), % 151.44/22.28 | (19), (20), (21), (23) are inconsistent by sub-proof #252. % 151.44/22.28 | % 151.44/22.28 End of proof % 151.44/22.28 % 151.44/22.28 Sub-proof #252 shows that the following formulas are inconsistent: % 151.44/22.28 ---------------------------------------------------------------- % 151.44/22.28 (1) ~ (all_8_1 = e1) % 151.44/22.28 (2) op(e0, e0) = all_4_2 % 151.44/22.28 (3) all_54_15 = all_4_2 % 151.44/22.28 (4) all_52_13 = e2 % 151.44/22.28 (5) all_14_1 = all_8_1 % 151.44/22.28 (6) op(e2, all_8_2) = all_56_10 % 151.44/22.28 (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 151.44/22.28 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 151.44/22.28 (8) op(e2, all_8_1) = e1 % 151.44/22.28 (9) ~ (all_4_2 = e2) % 151.44/22.28 (10) ~ (e2 = e1) % 151.44/22.28 (11) ~ (all_14_1 = e3) | ~ (all_14_2 = e0) % 151.44/22.28 (12) all_14_2 = e0 % 151.44/22.28 (13) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0 % 151.44/22.28 (14) op(e2, e0) = all_52_13 % 151.44/22.28 (15) all_8_2 = e0 % 151.44/22.28 (16) op(all_8_2, all_8_2) = all_8_1 % 151.44/22.28 % 151.44/22.28 Begin of proof % 151.44/22.28 | % 151.44/22.28 | REDUCE: (15), (16) imply: % 151.44/22.28 | (17) op(e0, e0) = all_8_1 % 151.44/22.28 | % 151.44/22.28 | REDUCE: (6), (15) imply: % 151.44/22.28 | (18) op(e2, e0) = all_56_10 % 151.44/22.28 | % 151.44/22.28 | REDUCE: (4), (14) imply: % 151.44/22.28 | (19) op(e2, e0) = e2 % 151.44/22.28 | % 151.44/22.28 | REF_CLOSE: (1), (2), (3), (5), (7), (8), (9), (10), (11), (12), (13), (17), % 151.44/22.28 | (18), (19) are inconsistent by sub-proof #253. % 151.44/22.28 | % 151.44/22.28 End of proof % 151.44/22.28 % 151.44/22.28 Sub-proof #253 shows that the following formulas are inconsistent: % 151.44/22.28 ---------------------------------------------------------------- % 151.44/22.28 (1) ~ (all_8_1 = e1) % 151.44/22.28 (2) op(e0, e0) = all_4_2 % 151.44/22.28 (3) all_54_15 = all_4_2 % 151.44/22.28 (4) all_14_1 = all_8_1 % 151.44/22.28 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 151.44/22.28 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 151.44/22.28 (6) op(e2, all_8_1) = e1 % 151.44/22.28 (7) op(e0, e0) = all_8_1 % 151.44/22.28 (8) ~ (all_4_2 = e2) % 151.44/22.28 (9) op(e2, e0) = all_56_10 % 151.44/22.28 (10) ~ (e2 = e1) % 151.44/22.28 (11) ~ (all_14_1 = e3) | ~ (all_14_2 = e0) % 151.44/22.28 (12) all_14_2 = e0 % 151.44/22.28 (13) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0 % 151.44/22.28 (14) op(e2, e0) = e2 % 151.44/22.28 % 151.44/22.28 Begin of proof % 151.44/22.28 | % 151.44/22.28 | BETA: splitting (11) gives: % 151.44/22.28 | % 151.44/22.28 | Case 1: % 151.44/22.28 | | % 151.44/22.28 | | (15) ~ (all_14_1 = e3) % 151.44/22.28 | | % 151.44/22.28 | | REDUCE: (4), (15) imply: % 151.44/22.28 | | (16) ~ (all_8_1 = e3) % 151.44/22.28 | | % 151.44/22.28 | | GROUND_INST: instantiating (5) with all_4_2, all_8_1, e0, e0, simplifying % 151.44/22.28 | | with (2), (7) gives: % 151.44/22.28 | | (17) all_8_1 = all_4_2 % 151.44/22.28 | | % 151.44/22.28 | | GROUND_INST: instantiating (5) with e2, all_56_10, e0, e2, simplifying with % 151.44/22.28 | | (9), (14) gives: % 151.44/22.28 | | (18) all_56_10 = e2 % 151.44/22.28 | | % 151.44/22.28 | | REDUCE: (16), (17) imply: % 151.44/22.28 | | (19) ~ (all_4_2 = e3) % 151.44/22.28 | | % 151.44/22.28 | | REDUCE: (1), (17) imply: % 151.44/22.28 | | (20) ~ (all_4_2 = e1) % 151.44/22.28 | | % 151.44/22.28 | | REDUCE: (6), (17) imply: % 151.44/22.28 | | (21) op(e2, all_4_2) = e1 % 151.44/22.28 | | % 151.44/22.28 | | BETA: splitting (13) gives: % 151.44/22.28 | | % 151.44/22.28 | | Case 1: % 151.44/22.28 | | | % 151.44/22.28 | | | (22) all_54_15 = e3 % 151.44/22.28 | | | % 151.44/22.28 | | | REF_CLOSE: (3), (19), (22) are inconsistent by sub-proof #740. % 151.44/22.28 | | | % 151.44/22.28 | | Case 2: % 151.44/22.28 | | | % 151.44/22.28 | | | (23) all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0 % 151.44/22.28 | | | % 151.44/22.28 | | | BETA: splitting (23) gives: % 151.44/22.28 | | | % 151.44/22.28 | | | Case 1: % 151.44/22.28 | | | | % 151.44/22.28 | | | | (24) all_54_15 = e2 % 151.44/22.28 | | | | % 151.44/22.28 | | | | REF_CLOSE: (3), (8), (24) are inconsistent by sub-proof #739. % 151.44/22.28 | | | | % 151.44/22.28 | | | Case 2: % 151.44/22.28 | | | | % 151.44/22.28 | | | | (25) all_54_15 = e1 | all_54_15 = e0 % 151.44/22.28 | | | | % 151.44/22.28 | | | | BETA: splitting (25) gives: % 151.44/22.28 | | | | % 151.44/22.28 | | | | Case 1: % 151.44/22.28 | | | | | % 151.44/22.28 | | | | | (26) all_54_15 = e1 % 151.44/22.28 | | | | | % 151.44/22.28 | | | | | REF_CLOSE: (3), (20), (26) are inconsistent by sub-proof #738. % 151.44/22.28 | | | | | % 151.44/22.28 | | | | Case 2: % 151.44/22.28 | | | | | % 151.44/22.28 | | | | | (27) all_54_15 = e0 % 151.44/22.28 | | | | | % 151.44/22.28 | | | | | COMBINE_EQS: (3), (27) imply: % 151.44/22.28 | | | | | (28) all_4_2 = e0 % 151.44/22.28 | | | | | % 151.44/22.28 | | | | | SIMP: (28) implies: % 151.44/22.28 | | | | | (29) all_4_2 = e0 % 151.44/22.28 | | | | | % 151.44/22.28 | | | | | REDUCE: (21), (29) imply: % 151.44/22.28 | | | | | (30) op(e2, e0) = e1 % 151.44/22.28 | | | | | % 151.44/22.28 | | | | | GROUND_INST: instantiating (5) with e2, e1, e0, e2, simplifying with % 151.44/22.28 | | | | | (14), (30) gives: % 151.44/22.28 | | | | | (31) e2 = e1 % 151.44/22.28 | | | | | % 151.44/22.28 | | | | | REDUCE: (10), (31) imply: % 151.44/22.28 | | | | | (32) $false % 151.44/22.28 | | | | | % 151.44/22.28 | | | | | CLOSE: (32) is inconsistent. % 151.44/22.28 | | | | | % 151.44/22.28 | | | | End of split % 151.44/22.28 | | | | % 151.44/22.28 | | | End of split % 151.44/22.28 | | | % 151.44/22.28 | | End of split % 151.44/22.28 | | % 151.44/22.28 | Case 2: % 151.44/22.28 | | % 151.44/22.28 | | (33) ~ (all_14_2 = e0) % 151.44/22.28 | | % 151.44/22.28 | | REDUCE: (12), (33) imply: % 151.44/22.28 | | (34) $false % 151.44/22.28 | | % 151.44/22.28 | | CLOSE: (34) is inconsistent. % 151.44/22.28 | | % 151.44/22.28 | End of split % 151.44/22.28 | % 151.44/22.28 End of proof % 151.44/22.28 % 151.44/22.28 Sub-proof #254 shows that the following formulas are inconsistent: % 151.44/22.28 ---------------------------------------------------------------- % 151.44/22.28 (1) all_56_11 = all_8_2 % 151.44/22.28 (2) ~ (all_56_11 = e1) | all_56_13 = e2 % 151.44/22.28 (3) ~ (all_8_1 = e1) % 151.44/22.28 (4) all_54_10 = all_6_2 % 151.44/22.28 (5) ~ (all_52_13 = all_8_2) % 151.44/22.28 (6) all_54_0 = all_10_2 % 151.44/22.28 (7) ~ (all_6_2 = e3) % 151.44/22.28 (8) all_54_5 = all_8_2 % 151.44/22.28 (9) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 151.44/22.28 (10) all_42_1 = all_8_1 % 151.44/22.28 (11) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 151.44/22.28 (12) op(e2, all_8_2) = all_56_10 % 151.44/22.28 (13) op(e3, e3) = all_10_2 % 151.44/22.28 (14) all_42_2 = all_8_2 % 151.44/22.28 (15) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 151.44/22.28 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 151.44/22.28 (16) ~ (all_56_11 = e3) | all_56_9 = e2 % 151.44/22.28 (17) all_56_13 = all_52_9 % 151.44/22.28 (18) op(e2, all_8_1) = e1 % 151.44/22.28 (19) ~ (e2 = e1) % 151.44/22.28 (20) ~ (all_42_1 = e0) | ~ (all_42_2 = e3) % 151.44/22.28 (21) op(e1, e1) = all_6_2 % 151.44/22.28 (22) ~ (all_52_9 = all_6_2) % 151.44/22.28 (23) op(e2, e3) = all_52_1 % 151.44/22.28 (24) op(e2, e2) = all_8_2 % 151.44/22.28 (25) op(e2, e0) = all_52_13 % 151.44/22.28 (26) ~ (all_8_2 = e0) % 151.44/22.28 (27) op(all_8_2, all_8_2) = all_8_1 % 151.44/22.28 (28) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 151.44/22.28 (29) all_56_9 = all_52_1 % 151.44/22.28 (30) ~ (all_52_1 = all_10_2) % 151.44/22.28 % 151.44/22.28 Begin of proof % 151.44/22.28 | % 151.44/22.28 | BETA: splitting (16) gives: % 151.44/22.28 | % 151.44/22.28 | Case 1: % 151.44/22.28 | | % 151.44/22.28 | | (31) ~ (all_56_11 = e3) % 151.44/22.28 | | % 151.44/22.28 | | REDUCE: (1), (31) imply: % 151.44/22.28 | | (32) ~ (all_8_2 = e3) % 151.44/22.28 | | % 151.44/22.28 | | BETA: splitting (2) gives: % 151.44/22.28 | | % 151.44/22.28 | | Case 1: % 151.44/22.28 | | | % 151.44/22.28 | | | (33) ~ (all_56_11 = e1) % 151.44/22.28 | | | % 151.44/22.28 | | | REDUCE: (1), (33) imply: % 151.44/22.28 | | | (34) ~ (all_8_2 = e1) % 151.44/22.28 | | | % 151.44/22.28 | | | REF_CLOSE: (3), (8), (12), (15), (18), (24), (26), (27), (28), (32), (34) % 151.44/22.28 | | | are inconsistent by sub-proof #259. % 151.44/22.28 | | | % 151.44/22.28 | | Case 2: % 151.44/22.28 | | | % 151.44/22.28 | | | (35) all_56_13 = e2 % 151.44/22.28 | | | (36) all_56_11 = e1 % 151.44/22.28 | | | % 151.44/22.28 | | | COMBINE_EQS: (1), (36) imply: % 151.44/22.28 | | | (37) all_8_2 = e1 % 151.44/22.28 | | | % 151.44/22.28 | | | COMBINE_EQS: (17), (35) imply: % 151.44/22.28 | | | (38) all_52_9 = e2 % 151.44/22.28 | | | % 151.44/22.28 | | | REDUCE: (22), (38) imply: % 151.44/22.28 | | | (39) ~ (all_6_2 = e2) % 151.44/22.28 | | | % 151.44/22.28 | | | SIMP: (39) implies: % 151.44/22.28 | | | (40) ~ (all_6_2 = e2) % 151.44/22.28 | | | % 151.44/22.28 | | | REDUCE: (5), (37) imply: % 151.44/22.28 | | | (41) ~ (all_52_13 = e1) % 151.44/22.28 | | | % 151.44/22.28 | | | REDUCE: (27), (37) imply: % 151.44/22.28 | | | (42) op(e1, e1) = all_8_1 % 151.44/22.28 | | | % 151.44/22.28 | | | GROUND_INST: instantiating (15) with all_6_2, all_8_1, e1, e1, simplifying % 151.44/22.28 | | | with (21), (42) gives: % 151.44/22.28 | | | (43) all_8_1 = all_6_2 % 151.44/22.28 | | | % 151.44/22.28 | | | REDUCE: (3), (43) imply: % 151.44/22.28 | | | (44) ~ (all_6_2 = e1) % 151.44/22.28 | | | % 151.44/22.28 | | | REDUCE: (18), (43) imply: % 151.44/22.28 | | | (45) op(e2, all_6_2) = e1 % 151.44/22.28 | | | % 151.44/22.28 | | | REF_CLOSE: (4), (7), (11), (15), (25), (40), (41), (44), (45) are % 151.44/22.28 | | | inconsistent by sub-proof #257. % 151.44/22.28 | | | % 151.44/22.28 | | End of split % 151.44/22.28 | | % 151.44/22.28 | Case 2: % 151.44/22.28 | | % 151.44/22.28 | | (46) all_56_11 = e3 % 151.44/22.28 | | % 151.44/22.28 | | COMBINE_EQS: (1), (46) imply: % 151.44/22.28 | | (47) all_8_2 = e3 % 151.44/22.28 | | % 151.44/22.28 | | REF_CLOSE: (1), (3), (6), (9), (10), (12), (13), (14), (15), (16), (18), % 151.44/22.28 | | (19), (20), (23), (27), (29), (30), (47) are inconsistent by % 151.44/22.28 | | sub-proof #255. % 151.44/22.28 | | % 151.44/22.28 | End of split % 151.44/22.28 | % 151.44/22.28 End of proof % 151.44/22.28 % 151.44/22.28 Sub-proof #255 shows that the following formulas are inconsistent: % 151.44/22.28 ---------------------------------------------------------------- % 151.44/22.28 (1) all_56_11 = all_8_2 % 151.44/22.28 (2) ~ (all_8_1 = e1) % 151.44/22.28 (3) all_54_0 = all_10_2 % 151.44/22.28 (4) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 151.44/22.28 (5) all_42_1 = all_8_1 % 151.44/22.28 (6) op(e2, all_8_2) = all_56_10 % 151.44/22.28 (7) op(e3, e3) = all_10_2 % 151.44/22.28 (8) all_42_2 = all_8_2 % 151.44/22.28 (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 151.44/22.28 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 151.44/22.28 (10) ~ (all_56_11 = e3) | all_56_9 = e2 % 151.44/22.28 (11) op(e2, all_8_1) = e1 % 151.44/22.28 (12) all_8_2 = e3 % 151.44/22.28 (13) ~ (e2 = e1) % 151.44/22.28 (14) ~ (all_42_1 = e0) | ~ (all_42_2 = e3) % 151.44/22.28 (15) op(e2, e3) = all_52_1 % 151.44/22.28 (16) op(all_8_2, all_8_2) = all_8_1 % 151.44/22.28 (17) all_56_9 = all_52_1 % 151.44/22.28 (18) ~ (all_52_1 = all_10_2) % 151.44/22.28 % 151.44/22.28 Begin of proof % 151.44/22.28 | % 151.44/22.28 | COMBINE_EQS: (8), (12) imply: % 151.44/22.28 | (19) all_42_2 = e3 % 151.44/22.28 | % 151.44/22.28 | COMBINE_EQS: (1), (12) imply: % 151.44/22.28 | (20) all_56_11 = e3 % 151.44/22.28 | % 151.44/22.28 | REDUCE: (12), (16) imply: % 151.44/22.28 | (21) op(e3, e3) = all_8_1 % 151.44/22.28 | % 151.44/22.28 | REDUCE: (6), (12) imply: % 151.44/22.28 | (22) op(e2, e3) = all_56_10 % 151.44/22.28 | % 151.44/22.28 | REF_CLOSE: (2), (3), (4), (5), (7), (9), (10), (11), (13), (14), (15), (17), % 151.44/22.28 | (18), (19), (20), (21), (22) are inconsistent by sub-proof #256. % 151.44/22.28 | % 151.44/22.28 End of proof % 151.44/22.28 % 151.44/22.28 Sub-proof #256 shows that the following formulas are inconsistent: % 151.44/22.28 ---------------------------------------------------------------- % 151.44/22.28 (1) ~ (all_8_1 = e1) % 151.44/22.28 (2) all_54_0 = all_10_2 % 151.44/22.28 (3) all_56_11 = e3 % 151.44/22.28 (4) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 151.44/22.28 (5) all_42_1 = all_8_1 % 151.44/22.28 (6) op(e3, e3) = all_10_2 % 151.44/22.28 (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 151.44/22.28 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 151.44/22.28 (8) ~ (all_56_11 = e3) | all_56_9 = e2 % 151.44/22.28 (9) op(e2, all_8_1) = e1 % 151.44/22.28 (10) ~ (e2 = e1) % 151.44/22.28 (11) ~ (all_42_1 = e0) | ~ (all_42_2 = e3) % 151.44/22.28 (12) op(e2, e3) = all_56_10 % 151.44/22.28 (13) op(e3, e3) = all_8_1 % 151.44/22.28 (14) op(e2, e3) = all_52_1 % 151.44/22.28 (15) all_42_2 = e3 % 151.44/22.28 (16) all_56_9 = all_52_1 % 151.44/22.28 (17) ~ (all_52_1 = all_10_2) % 151.44/22.28 % 151.44/22.28 Begin of proof % 151.44/22.28 | % 151.44/22.28 | BETA: splitting (8) gives: % 151.44/22.28 | % 151.44/22.28 | Case 1: % 151.44/22.28 | | % 151.44/22.28 | | (18) ~ (all_56_11 = e3) % 151.44/22.28 | | % 151.44/22.28 | | REDUCE: (3), (18) imply: % 151.44/22.28 | | (19) $false % 151.44/22.28 | | % 151.44/22.28 | | CLOSE: (19) is inconsistent. % 151.44/22.28 | | % 151.44/22.28 | Case 2: % 151.44/22.28 | | % 151.44/22.28 | | (20) all_56_9 = e2 % 151.44/22.28 | | % 151.44/22.28 | | COMBINE_EQS: (16), (20) imply: % 151.44/22.28 | | (21) all_52_1 = e2 % 151.44/22.28 | | % 151.44/22.28 | | REDUCE: (17), (21) imply: % 151.44/22.28 | | (22) ~ (all_10_2 = e2) % 151.44/22.28 | | % 151.44/22.28 | | SIMP: (22) implies: % 151.44/22.28 | | (23) ~ (all_10_2 = e2) % 151.44/22.28 | | % 151.44/22.28 | | REDUCE: (14), (21) imply: % 151.44/22.28 | | (24) op(e2, e3) = e2 % 151.44/22.28 | | % 151.44/22.28 | | BETA: splitting (11) gives: % 151.44/22.28 | | % 151.44/22.28 | | Case 1: % 151.44/22.28 | | | % 151.44/22.28 | | | (25) ~ (all_42_2 = e3) % 151.44/22.28 | | | % 151.44/22.28 | | | REDUCE: (15), (25) imply: % 151.44/22.28 | | | (26) $false % 151.44/22.28 | | | % 151.44/22.28 | | | CLOSE: (26) is inconsistent. % 151.44/22.28 | | | % 151.44/22.28 | | Case 2: % 151.44/22.28 | | | % 151.44/22.28 | | | (27) ~ (all_42_1 = e0) % 151.44/22.28 | | | % 151.44/22.28 | | | REDUCE: (5), (27) imply: % 151.44/22.28 | | | (28) ~ (all_8_1 = e0) % 151.44/22.28 | | | % 151.44/22.28 | | | GROUND_INST: instantiating (7) with e2, all_56_10, e3, e2, simplifying % 151.44/22.28 | | | with (12), (24) gives: % 151.44/22.28 | | | (29) all_56_10 = e2 % 151.44/22.28 | | | % 151.44/22.28 | | | GROUND_INST: instantiating (7) with all_10_2, all_8_1, e3, e3, simplifying % 151.44/22.28 | | | with (6), (13) gives: % 151.44/22.28 | | | (30) all_10_2 = all_8_1 % 151.44/22.28 | | | % 151.44/22.28 | | | COMBINE_EQS: (2), (30) imply: % 151.44/22.28 | | | (31) all_54_0 = all_8_1 % 151.44/22.28 | | | % 151.44/22.28 | | | REDUCE: (23), (30) imply: % 151.44/22.28 | | | (32) ~ (all_8_1 = e2) % 151.44/22.28 | | | % 151.44/22.28 | | | BETA: splitting (4) gives: % 151.44/22.28 | | | % 151.44/22.28 | | | Case 1: % 151.44/22.28 | | | | % 151.44/22.28 | | | | (33) all_54_0 = e3 % 151.44/22.28 | | | | % 151.44/22.28 | | | | COMBINE_EQS: (31), (33) imply: % 151.44/22.28 | | | | (34) all_8_1 = e3 % 151.44/22.28 | | | | % 151.44/22.28 | | | | SIMP: (34) implies: % 151.44/22.28 | | | | (35) all_8_1 = e3 % 151.44/22.28 | | | | % 151.44/22.28 | | | | REDUCE: (9), (35) imply: % 151.44/22.28 | | | | (36) op(e2, e3) = e1 % 151.44/22.28 | | | | % 151.44/22.28 | | | | GROUND_INST: instantiating (7) with e2, e1, e3, e2, simplifying with % 151.44/22.28 | | | | (24), (36) gives: % 151.44/22.28 | | | | (37) e2 = e1 % 151.44/22.28 | | | | % 151.44/22.28 | | | | REDUCE: (10), (37) imply: % 151.44/22.28 | | | | (38) $false % 151.44/22.28 | | | | % 151.44/22.28 | | | | CLOSE: (38) is inconsistent. % 151.44/22.28 | | | | % 151.44/22.28 | | | Case 2: % 151.44/22.28 | | | | % 151.44/22.28 | | | | (39) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 151.44/22.28 | | | | % 151.44/22.28 | | | | BETA: splitting (39) gives: % 151.44/22.28 | | | | % 151.44/22.28 | | | | Case 1: % 151.44/22.28 | | | | | % 151.44/22.28 | | | | | (40) all_54_0 = e2 % 151.44/22.28 | | | | | % 151.44/22.28 | | | | | REF_CLOSE: (31), (32), (40) are inconsistent by sub-proof #599. % 151.44/22.28 | | | | | % 151.44/22.28 | | | | Case 2: % 151.44/22.28 | | | | | % 151.44/22.28 | | | | | (41) all_54_0 = e1 | all_54_0 = e0 % 151.44/22.28 | | | | | % 151.44/22.28 | | | | | BETA: splitting (41) gives: % 151.44/22.28 | | | | | % 151.44/22.28 | | | | | Case 1: % 151.44/22.28 | | | | | | % 151.44/22.28 | | | | | | (42) all_54_0 = e1 % 151.44/22.28 | | | | | | % 151.44/22.28 | | | | | | REF_CLOSE: (1), (31), (42) are inconsistent by sub-proof #598. % 151.44/22.28 | | | | | | % 151.44/22.28 | | | | | Case 2: % 151.44/22.28 | | | | | | % 151.44/22.28 | | | | | | (43) all_54_0 = e0 % 151.44/22.28 | | | | | | % 151.44/22.28 | | | | | | COMBINE_EQS: (31), (43) imply: % 151.44/22.28 | | | | | | (44) all_8_1 = e0 % 151.44/22.28 | | | | | | % 151.44/22.28 | | | | | | SIMP: (44) implies: % 151.44/22.28 | | | | | | (45) all_8_1 = e0 % 151.44/22.28 | | | | | | % 151.44/22.28 | | | | | | REDUCE: (28), (45) imply: % 151.44/22.28 | | | | | | (46) $false % 151.44/22.28 | | | | | | % 151.44/22.28 | | | | | | CLOSE: (46) is inconsistent. % 151.44/22.28 | | | | | | % 151.44/22.28 | | | | | End of split % 151.44/22.28 | | | | | % 151.44/22.28 | | | | End of split % 151.44/22.28 | | | | % 151.44/22.28 | | | End of split % 151.44/22.28 | | | % 151.44/22.28 | | End of split % 151.44/22.28 | | % 151.44/22.28 | End of split % 151.44/22.28 | % 151.44/22.28 End of proof % 151.44/22.28 % 151.44/22.28 Sub-proof #257 shows that the following formulas are inconsistent: % 151.44/22.28 ---------------------------------------------------------------- % 151.44/22.28 (1) ~ (all_52_13 = e1) % 151.44/22.28 (2) all_54_10 = all_6_2 % 151.44/22.28 (3) ~ (all_6_2 = e3) % 151.44/22.28 (4) op(e2, all_6_2) = e1 % 151.44/22.28 (5) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 151.44/22.28 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 151.44/22.28 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 151.44/22.28 (7) ~ (all_6_2 = e1) % 151.44/22.28 (8) ~ (all_6_2 = e2) % 151.44/22.28 (9) op(e2, e0) = all_52_13 % 151.44/22.28 % 151.44/22.28 Begin of proof % 151.44/22.28 | % 151.44/22.28 | BETA: splitting (5) gives: % 151.44/22.28 | % 151.44/22.28 | Case 1: % 151.44/22.28 | | % 151.44/22.28 | | (10) all_54_10 = e3 % 151.44/22.28 | | % 151.44/22.28 | | REF_CLOSE: (2), (3), (10) are inconsistent by sub-proof #736. % 151.44/22.28 | | % 151.44/22.28 | Case 2: % 151.44/22.28 | | % 151.44/22.28 | | (11) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 151.44/22.28 | | % 151.44/22.28 | | BETA: splitting (11) gives: % 151.44/22.28 | | % 151.44/22.28 | | Case 1: % 151.44/22.28 | | | % 151.44/22.28 | | | (12) all_54_10 = e2 % 151.44/22.28 | | | % 151.44/22.28 | | | REF_CLOSE: (2), (8), (12) are inconsistent by sub-proof #735. % 151.44/22.28 | | | % 151.44/22.28 | | Case 2: % 151.44/22.28 | | | % 151.44/22.28 | | | (13) all_54_10 = e1 | all_54_10 = e0 % 151.44/22.28 | | | % 151.44/22.28 | | | BETA: splitting (13) gives: % 151.44/22.28 | | | % 151.44/22.28 | | | Case 1: % 151.44/22.28 | | | | % 151.44/22.28 | | | | (14) all_54_10 = e1 % 151.44/22.28 | | | | % 151.44/22.28 | | | | REF_CLOSE: (2), (7), (14) are inconsistent by sub-proof #606. % 151.44/22.28 | | | | % 151.44/22.28 | | | Case 2: % 151.44/22.28 | | | | % 151.44/22.28 | | | | (15) all_54_10 = e0 % 151.44/22.28 | | | | % 151.44/22.28 | | | | COMBINE_EQS: (2), (15) imply: % 151.44/22.28 | | | | (16) all_6_2 = e0 % 151.44/22.28 | | | | % 151.44/22.28 | | | | SIMP: (16) implies: % 151.44/22.28 | | | | (17) all_6_2 = e0 % 151.44/22.28 | | | | % 151.44/22.28 | | | | REDUCE: (4), (17) imply: % 151.44/22.28 | | | | (18) op(e2, e0) = e1 % 151.44/22.28 | | | | % 151.44/22.28 | | | | REF_CLOSE: (1), (6), (9), (18) are inconsistent by sub-proof #258. % 151.44/22.28 | | | | % 151.44/22.28 | | | End of split % 151.44/22.28 | | | % 151.44/22.28 | | End of split % 151.44/22.28 | | % 151.44/22.28 | End of split % 151.44/22.28 | % 151.44/22.28 End of proof % 151.44/22.28 % 151.44/22.28 Sub-proof #258 shows that the following formulas are inconsistent: % 151.44/22.28 ---------------------------------------------------------------- % 151.44/22.28 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 151.44/22.28 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 151.44/22.28 (2) op(e2, e0) = all_52_13 % 151.44/22.28 (3) op(e2, e0) = e1 % 151.44/22.28 (4) ~ (all_52_13 = e1) % 151.44/22.28 % 151.44/22.28 Begin of proof % 151.44/22.28 | % 151.44/22.28 | GROUND_INST: instantiating (1) with all_52_13, e1, e0, e2, simplifying with % 151.44/22.28 | (2), (3) gives: % 151.44/22.28 | (5) all_52_13 = e1 % 151.44/22.28 | % 151.44/22.28 | REDUCE: (4), (5) imply: % 151.44/22.28 | (6) $false % 151.44/22.28 | % 151.44/22.28 | CLOSE: (6) is inconsistent. % 151.44/22.28 | % 151.44/22.28 End of proof % 151.44/22.28 % 151.44/22.28 Sub-proof #259 shows that the following formulas are inconsistent: % 151.44/22.28 ---------------------------------------------------------------- % 151.44/22.28 (1) ~ (all_8_1 = e1) % 151.44/22.28 (2) ~ (all_8_2 = e1) % 151.44/22.28 (3) all_54_5 = all_8_2 % 151.44/22.28 (4) op(e2, all_8_2) = all_56_10 % 151.44/22.28 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 151.44/22.28 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 151.44/22.28 (6) op(e2, all_8_1) = e1 % 151.44/22.28 (7) ~ (all_8_2 = e3) % 151.44/22.28 (8) op(e2, e2) = all_8_2 % 151.44/22.28 (9) ~ (all_8_2 = e0) % 151.44/22.28 (10) op(all_8_2, all_8_2) = all_8_1 % 151.44/22.28 (11) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 151.44/22.28 % 151.44/22.28 Begin of proof % 151.44/22.28 | % 151.44/22.28 | BETA: splitting (11) gives: % 151.44/22.28 | % 151.44/22.28 | Case 1: % 151.44/22.28 | | % 151.44/22.28 | | (12) all_54_5 = e3 % 151.44/22.28 | | % 151.44/22.28 | | REF_CLOSE: (3), (7), (12) are inconsistent by sub-proof #737. % 151.44/22.28 | | % 151.44/22.28 | Case 2: % 151.44/22.28 | | % 151.44/22.28 | | (13) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 151.44/22.28 | | % 151.44/22.28 | | BETA: splitting (13) gives: % 151.44/22.28 | | % 151.44/22.28 | | Case 1: % 151.44/22.28 | | | % 151.44/22.28 | | | (14) all_54_5 = e2 % 151.44/22.28 | | | % 151.44/22.28 | | | COMBINE_EQS: (3), (14) imply: % 151.44/22.28 | | | (15) all_8_2 = e2 % 151.44/22.28 | | | % 151.44/22.28 | | | SIMP: (15) implies: % 151.44/22.28 | | | (16) all_8_2 = e2 % 151.44/22.28 | | | % 151.44/22.28 | | | REDUCE: (10), (16) imply: % 151.44/22.28 | | | (17) op(e2, e2) = all_8_1 % 151.44/22.28 | | | % 151.44/22.28 | | | REDUCE: (4), (16) imply: % 151.44/22.28 | | | (18) op(e2, e2) = all_56_10 % 151.44/22.28 | | | % 151.44/22.28 | | | REDUCE: (8), (16) imply: % 151.44/22.28 | | | (19) op(e2, e2) = e2 % 151.44/22.28 | | | % 151.44/22.28 | | | GROUND_INST: instantiating (5) with all_8_1, all_56_10, e2, e2, % 151.44/22.28 | | | simplifying with (17), (18) gives: % 151.44/22.28 | | | (20) all_56_10 = all_8_1 % 151.44/22.28 | | | % 151.44/22.28 | | | GROUND_INST: instantiating (5) with e2, all_56_10, e2, e2, simplifying % 151.44/22.28 | | | with (18), (19) gives: % 151.44/22.28 | | | (21) all_56_10 = e2 % 151.44/22.28 | | | % 151.44/22.28 | | | COMBINE_EQS: (20), (21) imply: % 151.44/22.28 | | | (22) all_8_1 = e2 % 151.44/22.28 | | | % 151.44/22.28 | | | REF_CLOSE: (1), (5), (6), (17), (22) are inconsistent by sub-proof #260. % 151.44/22.28 | | | % 151.44/22.28 | | Case 2: % 151.44/22.28 | | | % 151.44/22.28 | | | (23) all_54_5 = e1 | all_54_5 = e0 % 151.44/22.28 | | | % 151.44/22.28 | | | REF_CLOSE: (2), (3), (9), (23) are inconsistent by sub-proof #645. % 151.44/22.28 | | | % 151.44/22.28 | | End of split % 151.44/22.28 | | % 151.44/22.28 | End of split % 151.44/22.28 | % 151.44/22.28 End of proof % 151.44/22.28 % 151.44/22.28 Sub-proof #260 shows that the following formulas are inconsistent: % 151.44/22.28 ---------------------------------------------------------------- % 151.44/22.28 (1) ~ (all_8_1 = e1) % 151.44/22.28 (2) op(e2, e2) = all_8_1 % 151.44/22.28 (3) all_8_1 = e2 % 151.44/22.28 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 151.44/22.28 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 151.44/22.28 (5) op(e2, all_8_1) = e1 % 151.44/22.28 % 151.44/22.28 Begin of proof % 151.44/22.28 | % 151.44/22.28 | REDUCE: (1), (3) imply: % 151.44/22.28 | (6) ~ (e2 = e1) % 151.44/22.28 | % 151.44/22.28 | REDUCE: (3), (5) imply: % 151.44/22.28 | (7) op(e2, e2) = e1 % 151.44/22.28 | % 151.44/22.28 | REDUCE: (2), (3) imply: % 151.44/22.28 | (8) op(e2, e2) = e2 % 151.44/22.28 | % 151.44/22.28 | REF_CLOSE: (4), (6), (7), (8) are inconsistent by sub-proof #479. % 151.44/22.28 | % 151.44/22.28 End of proof % 151.44/22.28 % 151.44/22.28 Sub-proof #261 shows that the following formulas are inconsistent: % 151.44/22.28 ---------------------------------------------------------------- % 151.44/22.28 (1) all_56_11 = all_8_2 % 151.44/22.28 (2) ~ (all_56_11 = e1) | all_56_13 = e2 % 151.44/22.28 (3) ~ (all_52_11 = all_6_2) % 151.44/22.28 (4) all_56_25 = all_52_3 % 151.44/22.28 (5) all_54_9 = all_52_6 % 151.44/22.28 (6) all_58_6 = all_52_2 % 151.44/22.28 (7) ~ (all_8_1 = e1) % 151.44/22.28 (8) ~ (all_52_1 = all_52_9) % 151.44/22.28 (9) ~ (all_56_31 = e1) | all_56_29 = e0 % 151.44/22.28 (10) all_54_10 = all_6_2 % 151.44/22.28 (11) ~ (all_56_21 = e2) | all_56_19 = e1 % 151.44/22.28 (12) ~ (all_52_14 = all_4_2) % 151.44/22.28 (13) all_54_12 = all_52_3 % 151.44/22.28 (14) ~ (all_8_1 = e3) % 151.44/22.28 (15) op(e0, e0) = all_4_2 % 151.44/22.28 (16) all_58_6 = e0 | all_58_7 = e0 | all_58_8 = e0 | all_58_11 = e0 % 151.44/22.28 (17) all_54_5 = all_8_2 % 151.44/22.28 (18) all_6_1 = e3 % 151.44/22.28 (19) ~ (all_52_6 = all_52_14) % 151.44/22.28 (20) ~ (all_6_0 = e2) % 151.44/22.28 (21) all_54_15 = all_4_2 % 151.44/22.28 (22) all_56_21 = all_6_2 % 151.44/22.28 (23) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 151.44/22.28 (24) all_56_1 = all_10_2 % 151.44/22.28 (25) all_56_27 = all_52_7 % 151.44/22.28 (26) all_56_17 = all_52_2 % 151.44/22.28 (27) op(e2, all_8_2) = all_56_10 % 151.44/22.28 (28) op(e3, e3) = all_10_2 % 151.44/22.28 (29) ~ (all_56_21 = e3) | all_56_17 = e1 % 151.44/22.28 (30) all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2 % 151.44/22.28 (31) ~ (all_52_1 = all_8_2) % 151.44/22.28 (32) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 151.44/22.28 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 151.44/22.29 (33) ~ (all_52_3 = all_10_2) % 151.44/22.29 (34) ~ (all_52_3 = all_52_7) % 151.44/22.29 (35) ~ (all_26_1 = e2) | ~ (all_26_2 = e3) % 151.44/22.29 (36) all_36_0 = all_6_0 % 151.44/22.29 (37) ~ (all_52_2 = all_52_6) % 151.44/22.29 (38) op(e0, all_4_1) = all_4_0 % 151.44/22.29 (39) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0 % 151.44/22.29 (40) all_56_13 = all_52_9 % 151.44/22.29 (41) op(e1, e3) = all_52_2 % 151.44/22.29 (42) op(e0, all_4_1) = e1 % 151.44/22.29 (43) all_58_8 = all_6_2 % 151.44/22.29 (44) ~ (all_52_3 = all_4_2) % 151.44/22.29 (45) ~ (all_52_2 = all_52_3) % 151.44/22.29 (46) all_26_2 = all_4_2 % 151.44/22.29 (47) op(e1, all_6_1) = all_6_0 % 151.44/22.29 (48) op(all_4_2, all_4_2) = all_4_1 % 151.44/22.29 (49) ~ (all_52_3 = all_52_11) % 151.44/22.29 (50) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0 % 151.44/22.29 (51) ~ (all_52_11 = all_4_2) % 151.44/22.29 (52) ~ (all_52_6 = all_52_7) % 151.44/22.29 (53) all_56_31 = all_4_2 % 151.44/22.29 (54) all_58_11 = all_52_14 % 151.44/22.29 (55) all_36_2 = all_6_2 % 151.44/22.29 (56) ~ (all_52_2 = all_52_14) % 151.44/22.29 (57) op(all_6_2, all_6_2) = all_6_1 % 151.44/22.29 (58) all_56_1 = e3 | all_56_11 = e2 | all_56_21 = e1 | all_56_31 = e0 % 151.44/22.29 (59) ~ (all_52_13 = all_4_2) % 151.44/22.29 (60) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0 % 151.44/22.29 (61) all_56_23 = all_52_14 % 151.44/22.29 (62) all_54_8 = all_52_2 % 151.44/22.29 (63) op(e1, e1) = all_6_2 % 151.44/22.29 (64) ~ (all_52_6 = all_8_2) % 151.44/22.29 (65) op(e0, e3) = all_52_3 % 151.44/22.29 (66) all_56_29 = all_52_11 % 151.44/22.29 (67) all_58_2 = all_52_1 % 151.44/22.29 (68) all_58_7 = all_52_6 % 151.44/22.29 (69) ~ (all_56_11 = e0) | all_56_15 = e2 % 151.44/22.29 (70) all_58_0 = all_10_2 % 151.44/22.29 (71) op(e1, all_6_2) = all_56_20 % 151.44/22.29 (72) ~ (all_56_31 = e2) | all_56_27 = e0 % 151.44/22.29 (73) op(e2, e2) = all_8_2 % 151.44/22.29 (74) ~ (all_36_0 = e0) | ~ (all_36_2 = e2) % 151.44/22.29 (75) ~ (all_52_2 = all_6_2) % 151.44/22.29 (76) ~ (all_56_21 = e0) | all_56_23 = e1 % 151.44/22.29 (77) op(e0, all_4_2) = all_56_30 % 151.44/22.29 (78) ~ (all_52_6 = all_6_2) % 151.44/22.29 (79) ~ (all_52_14 = all_6_2) % 151.44/22.29 (80) ~ (e2 = e0) % 151.44/22.29 (81) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0 % 151.44/22.29 (82) ~ (all_52_2 = all_10_2) % 151.44/22.29 (83) all_26_1 = all_4_1 % 151.44/22.29 (84) op(all_8_2, all_8_2) = all_8_1 % 151.44/22.29 (85) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 151.44/22.29 (86) all_56_19 = all_52_6 % 151.44/22.29 (87) ~ (all_4_0 = e2) % 151.44/22.29 (88) ~ (all_4_0 = e3) % 151.44/22.29 (89) all_56_15 = all_52_13 % 151.44/22.29 (90) all_58_12 = all_52_3 % 151.44/22.29 (91) ~ (all_56_31 = e3) | all_56_25 = e0 % 151.44/22.29 % 151.44/22.29 Begin of proof % 151.44/22.29 | % 151.44/22.29 | REDUCE: (18), (57) imply: % 151.44/22.29 | (92) op(all_6_2, all_6_2) = e3 % 151.44/22.29 | % 151.44/22.29 | REDUCE: (18), (47) imply: % 151.44/22.29 | (93) op(e1, e3) = all_6_0 % 151.44/22.29 | % 151.44/22.29 | GROUND_INST: instantiating (32) with all_52_2, all_6_0, e3, e1, simplifying % 151.44/22.29 | with (41), (93) gives: % 151.44/22.29 | (94) all_52_2 = all_6_0 % 151.44/22.29 | % 151.44/22.29 | COMBINE_EQS: (62), (94) imply: % 151.44/22.29 | (95) all_54_8 = all_6_0 % 151.44/22.29 | % 151.44/22.29 | COMBINE_EQS: (26), (94) imply: % 151.44/22.29 | (96) all_56_17 = all_6_0 % 151.44/22.29 | % 151.44/22.29 | COMBINE_EQS: (6), (94) imply: % 151.44/22.29 | (97) all_58_6 = all_6_0 % 151.44/22.29 | % 151.44/22.29 | REDUCE: (45), (94) imply: % 151.44/22.29 | (98) ~ (all_52_3 = all_6_0) % 151.44/22.29 | % 151.44/22.29 | SIMP: (98) implies: % 151.44/22.29 | (99) ~ (all_52_3 = all_6_0) % 151.44/22.29 | % 151.44/22.29 | REDUCE: (37), (94) imply: % 151.44/22.29 | (100) ~ (all_52_6 = all_6_0) % 151.44/22.29 | % 151.44/22.29 | SIMP: (100) implies: % 151.44/22.29 | (101) ~ (all_52_6 = all_6_0) % 151.44/22.29 | % 151.44/22.29 | REDUCE: (56), (94) imply: % 151.44/22.29 | (102) ~ (all_52_14 = all_6_0) % 151.44/22.29 | % 151.44/22.29 | SIMP: (102) implies: % 151.44/22.29 | (103) ~ (all_52_14 = all_6_0) % 151.44/22.29 | % 151.44/22.29 | REDUCE: (82), (94) imply: % 151.44/22.29 | (104) ~ (all_10_2 = all_6_0) % 151.44/22.29 | % 151.44/22.29 | SIMP: (104) implies: % 151.44/22.29 | (105) ~ (all_10_2 = all_6_0) % 151.44/22.29 | % 151.44/22.29 | REDUCE: (75), (94) imply: % 151.44/22.29 | (106) ~ (all_6_0 = all_6_2) % 151.44/22.29 | % 151.44/22.29 | BETA: splitting (9) gives: % 151.44/22.29 | % 151.44/22.29 | Case 1: % 151.44/22.29 | | % 151.44/22.29 | | (107) ~ (all_56_31 = e1) % 151.44/22.29 | | % 151.44/22.29 | | REDUCE: (53), (107) imply: % 151.44/22.29 | | (108) ~ (all_4_2 = e1) % 151.44/22.29 | | % 151.44/22.29 | | BETA: splitting (69) gives: % 151.44/22.29 | | % 151.44/22.29 | | Case 1: % 151.44/22.29 | | | % 151.44/22.29 | | | (109) ~ (all_56_11 = e0) % 151.44/22.29 | | | % 151.44/22.29 | | | REDUCE: (1), (109) imply: % 151.44/22.29 | | | (110) ~ (all_8_2 = e0) % 151.44/22.29 | | | % 151.44/22.29 | | | BETA: splitting (91) gives: % 151.44/22.29 | | | % 151.44/22.29 | | | Case 1: % 151.44/22.29 | | | | % 151.44/22.29 | | | | (111) ~ (all_56_31 = e3) % 151.44/22.29 | | | | % 151.44/22.29 | | | | REDUCE: (53), (111) imply: % 151.44/22.29 | | | | (112) ~ (all_4_2 = e3) % 151.44/22.29 | | | | % 151.44/22.29 | | | | REF_CLOSE: (1), (5), (10), (11), (12), (13), (15), (16), (19), (20), % 151.44/22.29 | | | | (21), (22), (23), (24), (25), (27), (28), (29), (32), (33), % 151.44/22.29 | | | | (34), (36), (39), (42), (43), (44), (48), (50), (52), (53), % 151.44/22.29 | | | | (54), (55), (58), (60), (61), (63), (64), (65), (68), (71), % 151.44/22.29 | | | | (72), (73), (74), (76), (77), (78), (79), (81), (84), (86), % 151.44/22.29 | | | | (92), (95), (96), (97), (99), (101), (103), (105), (106), % 151.44/22.29 | | | | (108), (112) are inconsistent by sub-proof #310. % 151.44/22.29 | | | | % 151.44/22.29 | | | Case 2: % 151.44/22.29 | | | | % 151.44/22.29 | | | | (113) all_56_31 = e3 % 151.44/22.29 | | | | (114) all_56_25 = e0 % 151.44/22.29 | | | | % 151.44/22.29 | | | | COMBINE_EQS: (4), (114) imply: % 151.44/22.29 | | | | (115) all_52_3 = e0 % 151.44/22.29 | | | | % 151.44/22.29 | | | | SIMP: (115) implies: % 151.44/22.29 | | | | (116) all_52_3 = e0 % 151.44/22.29 | | | | % 151.44/22.29 | | | | COMBINE_EQS: (53), (113) imply: % 151.44/22.29 | | | | (117) all_4_2 = e3 % 151.44/22.29 | | | | % 151.44/22.29 | | | | COMBINE_EQS: (46), (117) imply: % 151.44/22.29 | | | | (118) all_26_2 = e3 % 151.44/22.29 | | | | % 151.44/22.29 | | | | COMBINE_EQS: (90), (116) imply: % 151.44/22.29 | | | | (119) all_58_12 = e0 % 151.44/22.29 | | | | % 151.44/22.29 | | | | REDUCE: (48), (117) imply: % 151.44/22.29 | | | | (120) op(e3, e3) = all_4_1 % 151.44/22.29 | | | | % 151.44/22.29 | | | | BETA: splitting (35) gives: % 151.44/22.29 | | | | % 151.44/22.29 | | | | Case 1: % 151.44/22.29 | | | | | % 151.44/22.29 | | | | | (121) ~ (all_26_1 = e2) % 151.44/22.29 | | | | | % 151.44/22.29 | | | | | REDUCE: (83), (121) imply: % 151.44/22.29 | | | | | (122) ~ (all_4_1 = e2) % 151.44/22.29 | | | | | % 151.44/22.29 | | | | | GROUND_INST: instantiating (32) with all_10_2, all_4_1, e3, e3, % 151.44/22.29 | | | | | simplifying with (28), (120) gives: % 151.44/22.29 | | | | | (123) all_10_2 = all_4_1 % 151.44/22.29 | | | | | % 151.44/22.29 | | | | | COMBINE_EQS: (24), (123) imply: % 151.44/22.29 | | | | | (124) all_56_1 = all_4_1 % 151.44/22.29 | | | | | % 151.44/22.29 | | | | | COMBINE_EQS: (70), (123) imply: % 151.44/22.29 | | | | | (125) all_58_0 = all_4_1 % 151.44/22.29 | | | | | % 151.44/22.29 | | | | | BETA: splitting (30) gives: % 151.44/22.29 | | | | | % 151.44/22.29 | | | | | Case 1: % 151.44/22.29 | | | | | | % 151.44/22.29 | | | | | | (126) all_58_0 = e2 % 151.44/22.29 | | | | | | % 151.44/22.29 | | | | | | COMBINE_EQS: (125), (126) imply: % 151.44/22.29 | | | | | | (127) all_4_1 = e2 % 151.44/22.29 | | | | | | % 151.44/22.29 | | | | | | REDUCE: (122), (127) imply: % 151.44/22.29 | | | | | | (128) $false % 151.44/22.29 | | | | | | % 151.44/22.29 | | | | | | CLOSE: (128) is inconsistent. % 151.44/22.29 | | | | | | % 151.44/22.29 | | | | | Case 2: % 151.44/22.29 | | | | | | % 151.44/22.29 | | | | | | (129) all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2 % 151.44/22.29 | | | | | | % 151.44/22.29 | | | | | | BETA: splitting (129) gives: % 151.44/22.29 | | | | | | % 151.44/22.29 | | | | | | Case 1: % 151.44/22.29 | | | | | | | % 151.44/22.29 | | | | | | | (130) all_58_2 = e2 % 151.44/22.29 | | | | | | | % 151.44/22.29 | | | | | | | COMBINE_EQS: (67), (130) imply: % 151.44/22.29 | | | | | | | (131) all_52_1 = e2 % 151.44/22.29 | | | | | | | % 151.44/22.29 | | | | | | | REDUCE: (8), (131) imply: % 151.44/22.29 | | | | | | | (132) ~ (all_52_9 = e2) % 151.44/22.29 | | | | | | | % 151.44/22.29 | | | | | | | SIMP: (132) implies: % 151.44/22.29 | | | | | | | (133) ~ (all_52_9 = e2) % 151.44/22.29 | | | | | | | % 151.44/22.29 | | | | | | | REDUCE: (31), (131) imply: % 151.44/22.29 | | | | | | | (134) ~ (all_8_2 = e2) % 151.44/22.29 | | | | | | | % 151.44/22.29 | | | | | | | SIMP: (134) implies: % 151.44/22.29 | | | | | | | (135) ~ (all_8_2 = e2) % 151.44/22.29 | | | | | | | % 151.44/22.29 | | | | | | | BETA: splitting (2) gives: % 151.44/22.29 | | | | | | | % 151.44/22.29 | | | | | | | Case 1: % 151.44/22.29 | | | | | | | | % 151.44/22.29 | | | | | | | | (136) ~ (all_56_11 = e1) % 151.44/22.29 | | | | | | | | % 151.44/22.29 | | | | | | | | REDUCE: (1), (136) imply: % 151.44/22.29 | | | | | | | | (137) ~ (all_8_2 = e1) % 151.44/22.29 | | | | | | | | % 151.44/22.29 | | | | | | | | BETA: splitting (85) gives: % 151.44/22.29 | | | | | | | | % 151.44/22.29 | | | | | | | | Case 1: % 151.44/22.29 | | | | | | | | | % 151.44/22.29 | | | | | | | | | (138) all_54_5 = e3 % 151.44/22.29 | | | | | | | | | % 151.44/22.29 | | | | | | | | | COMBINE_EQS: (17), (138) imply: % 151.44/22.29 | | | | | | | | | (139) all_8_2 = e3 % 151.44/22.29 | | | | | | | | | % 151.44/22.29 | | | | | | | | | SIMP: (139) implies: % 151.44/22.29 | | | | | | | | | (140) all_8_2 = e3 % 151.44/22.29 | | | | | | | | | % 151.44/22.29 | | | | | | | | | COMBINE_EQS: (1), (140) imply: % 151.44/22.29 | | | | | | | | | (141) all_56_11 = e3 % 151.44/22.29 | | | | | | | | | % 151.44/22.29 | | | | | | | | | REDUCE: (135), (140) imply: % 151.44/22.29 | | | | | | | | | (142) ~ (e3 = e2) % 151.44/22.29 | | | | | | | | | % 151.44/22.29 | | | | | | | | | REDUCE: (137), (140) imply: % 151.44/22.29 | | | | | | | | | (143) ~ (e3 = e1) % 151.44/22.29 | | | | | | | | | % 151.44/22.29 | | | | | | | | | REDUCE: (110), (140) imply: % 151.44/22.29 | | | | | | | | | (144) ~ (e3 = e0) % 151.44/22.29 | | | | | | | | | % 151.44/22.29 | | | | | | | | | REDUCE: (84), (140) imply: % 151.44/22.29 | | | | | | | | | (145) op(e3, e3) = all_8_1 % 151.44/22.29 | | | | | | | | | % 151.44/22.29 | | | | | | | | | GROUND_INST: instantiating (32) with all_4_1, all_8_1, e3, e3, % 151.44/22.29 | | | | | | | | | simplifying with (120), (145) gives: % 151.44/22.29 | | | | | | | | | (146) all_8_1 = all_4_1 % 151.44/22.29 | | | | | | | | | % 151.44/22.29 | | | | | | | | | REDUCE: (14), (146) imply: % 151.44/22.29 | | | | | | | | | (147) ~ (all_4_1 = e3) % 151.44/22.29 | | | | | | | | | % 151.44/22.29 | | | | | | | | | REF_CLOSE: (22), (32), (58), (63), (71), (92), (113), (124), % 151.44/22.29 | | | | | | | | | (141), (142), (143), (144), (147) are inconsistent % 151.44/22.29 | | | | | | | | | by sub-proof #262. % 151.44/22.29 | | | | | | | | | % 151.44/22.29 | | | | | | | | Case 2: % 151.44/22.29 | | | | | | | | | % 151.44/22.29 | | | | | | | | | (148) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 151.44/22.29 | | | | | | | | | % 151.44/22.29 | | | | | | | | | REF_CLOSE: (17), (110), (135), (137), (148) are inconsistent % 151.44/22.29 | | | | | | | | | by sub-proof #644. % 151.44/22.29 | | | | | | | | | % 151.44/22.29 | | | | | | | | End of split % 151.44/22.29 | | | | | | | | % 151.44/22.29 | | | | | | | Case 2: % 151.44/22.29 | | | | | | | | % 151.44/22.29 | | | | | | | | (149) all_56_13 = e2 % 151.44/22.29 | | | | | | | | % 151.44/22.29 | | | | | | | | REF_CLOSE: (40), (133), (149) are inconsistent by sub-proof % 151.44/22.29 | | | | | | | | #353. % 151.44/22.29 | | | | | | | | % 151.44/22.29 | | | | | | | End of split % 151.44/22.29 | | | | | | | % 151.44/22.29 | | | | | | Case 2: % 151.44/22.29 | | | | | | | % 151.44/22.29 | | | | | | | (150) all_58_6 = e2 | all_58_12 = e2 % 151.44/22.29 | | | | | | | % 151.44/22.29 | | | | | | | REF_CLOSE: (20), (80), (97), (119), (150) are inconsistent by % 151.44/22.29 | | | | | | | sub-proof #422. % 151.44/22.29 | | | | | | | % 151.44/22.29 | | | | | | End of split % 151.44/22.29 | | | | | | % 151.44/22.29 | | | | | End of split % 151.44/22.29 | | | | | % 151.44/22.29 | | | | Case 2: % 151.44/22.29 | | | | | % 151.44/22.29 | | | | | (151) ~ (all_26_2 = e3) % 151.44/22.29 | | | | | % 151.44/22.29 | | | | | REDUCE: (118), (151) imply: % 151.44/22.29 | | | | | (152) $false % 151.44/22.29 | | | | | % 151.44/22.29 | | | | | CLOSE: (152) is inconsistent. % 151.44/22.29 | | | | | % 151.44/22.29 | | | | End of split % 151.44/22.29 | | | | % 151.44/22.29 | | | End of split % 151.44/22.29 | | | % 151.44/22.29 | | Case 2: % 151.44/22.29 | | | % 151.44/22.29 | | | (153) all_56_11 = e0 % 151.44/22.29 | | | % 151.44/22.29 | | | REF_CLOSE: (1), (7), (14), (15), (21), (32), (42), (48), (59), (60), (69), % 151.44/22.29 | | | (77), (84), (89), (153) are inconsistent by sub-proof #357. % 151.44/22.29 | | | % 151.44/22.29 | | End of split % 151.44/22.29 | | % 151.44/22.29 | Case 2: % 151.44/22.29 | | % 151.44/22.29 | | (154) all_56_31 = e1 % 151.44/22.29 | | (155) all_56_29 = e0 % 151.44/22.29 | | % 151.44/22.29 | | REF_CLOSE: (1), (3), (10), (11), (12), (13), (16), (22), (23), (24), (27), % 151.44/22.29 | | (29), (32), (36), (38), (39), (43), (48), (49), (51), (53), (54), % 151.44/22.29 | | (55), (58), (63), (65), (66), (68), (71), (73), (74), (78), (81), % 151.44/22.29 | | (84), (86), (87), (88), (92), (95), (96), (97), (99), (101), % 151.44/22.29 | | (103), (105), (106), (154), (155) are inconsistent by sub-proof % 151.44/22.29 | | #316. % 151.44/22.29 | | % 151.44/22.29 | End of split % 151.44/22.29 | % 151.44/22.29 End of proof % 151.44/22.29 % 151.44/22.29 Sub-proof #262 shows that the following formulas are inconsistent: % 151.44/22.29 ---------------------------------------------------------------- % 151.44/22.29 (1) ~ (e3 = e0) % 151.44/22.29 (2) ~ (all_4_1 = e3) % 151.44/22.29 (3) all_56_31 = e3 % 151.44/22.29 (4) ~ (e3 = e2) % 151.44/22.29 (5) all_56_11 = e3 % 151.44/22.29 (6) all_56_21 = all_6_2 % 151.44/22.29 (7) all_56_1 = all_4_1 % 151.44/22.29 (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 151.44/22.29 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 151.44/22.29 (9) all_56_1 = e3 | all_56_11 = e2 | all_56_21 = e1 | all_56_31 = e0 % 151.44/22.29 (10) op(e1, e1) = all_6_2 % 151.44/22.29 (11) op(e1, all_6_2) = all_56_20 % 151.44/22.29 (12) ~ (e3 = e1) % 151.44/22.29 (13) op(all_6_2, all_6_2) = e3 % 151.44/22.29 % 151.44/22.29 Begin of proof % 151.44/22.29 | % 151.44/22.29 | BETA: splitting (9) gives: % 151.44/22.29 | % 151.44/22.29 | Case 1: % 151.44/22.29 | | % 151.44/22.29 | | (14) all_56_1 = e3 % 151.44/22.29 | | % 151.44/22.29 | | COMBINE_EQS: (7), (14) imply: % 151.44/22.29 | | (15) all_4_1 = e3 % 151.44/22.29 | | % 151.44/22.29 | | REDUCE: (2), (15) imply: % 151.44/22.29 | | (16) $false % 151.44/22.29 | | % 151.44/22.29 | | CLOSE: (16) is inconsistent. % 151.44/22.29 | | % 151.44/22.29 | Case 2: % 151.44/22.29 | | % 151.44/22.29 | | (17) all_56_11 = e2 | all_56_21 = e1 | all_56_31 = e0 % 151.44/22.29 | | % 151.44/22.29 | | BETA: splitting (17) gives: % 151.44/22.29 | | % 151.44/22.29 | | Case 1: % 151.44/22.29 | | | % 151.44/22.29 | | | (18) all_56_11 = e2 % 151.44/22.29 | | | % 151.44/22.29 | | | COMBINE_EQS: (5), (18) imply: % 151.44/22.29 | | | (19) e3 = e2 % 151.44/22.29 | | | % 151.44/22.29 | | | REDUCE: (4), (19) imply: % 151.44/22.29 | | | (20) $false % 151.44/22.29 | | | % 151.44/22.29 | | | CLOSE: (20) is inconsistent. % 151.44/22.29 | | | % 151.44/22.29 | | Case 2: % 151.44/22.29 | | | % 151.44/22.29 | | | (21) all_56_21 = e1 | all_56_31 = e0 % 151.44/22.29 | | | % 151.44/22.29 | | | REF_CLOSE: (1), (3), (6), (8), (10), (11), (12), (13), (21) are % 151.44/22.29 | | | inconsistent by sub-proof #426. % 151.44/22.29 | | | % 151.44/22.29 | | End of split % 151.44/22.29 | | % 151.44/22.29 | End of split % 151.44/22.29 | % 151.44/22.29 End of proof % 151.44/22.29 % 151.44/22.29 Sub-proof #263 shows that the following formulas are inconsistent: % 151.44/22.29 ---------------------------------------------------------------- % 151.44/22.29 (1) all_56_11 = all_8_2 % 151.44/22.29 (2) all_52_6 = e1 % 151.44/22.29 (3) ~ (all_8_1 = e1) % 151.44/22.29 (4) ~ (all_6_1 = e2) % 151.44/22.29 (5) ~ (all_8_1 = e3) % 151.44/22.29 (6) op(e0, e0) = all_4_2 % 151.44/22.29 (7) all_54_5 = all_8_2 % 151.44/22.29 (8) ~ (all_6_1 = e3) % 151.44/22.29 (9) all_54_15 = all_4_2 % 151.44/22.29 (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 151.44/22.29 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 151.44/22.29 (11) op(e0, all_4_1) = e1 % 151.44/22.29 (12) op(all_4_2, all_4_2) = all_4_1 % 151.44/22.29 (13) op(all_6_2, all_6_2) = all_6_1 % 151.44/22.29 (14) ~ (all_52_13 = all_4_2) % 151.44/22.29 (15) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0 % 151.44/22.29 (16) ~ (all_52_6 = all_8_2) % 151.44/22.29 (17) all_6_2 = e2 % 151.44/22.29 (18) ~ (all_56_11 = e0) | all_56_15 = e2 % 151.44/22.29 (19) op(e2, e2) = all_8_2 % 151.44/22.29 (20) op(e0, all_4_2) = all_56_30 % 151.44/22.29 (21) op(all_8_2, all_8_2) = all_8_1 % 151.44/22.29 (22) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 151.44/22.29 (23) all_56_15 = all_52_13 % 151.44/22.29 % 151.44/22.29 Begin of proof % 151.44/22.29 | % 151.44/22.29 | REDUCE: (2), (16) imply: % 151.44/22.29 | (24) ~ (all_8_2 = e1) % 151.44/22.29 | % 151.44/22.29 | SIMP: (24) implies: % 151.44/22.29 | (25) ~ (all_8_2 = e1) % 151.44/22.29 | % 151.44/22.29 | REDUCE: (13), (17) imply: % 151.44/22.29 | (26) op(e2, e2) = all_6_1 % 151.44/22.29 | % 151.44/22.29 | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), (14), % 151.44/22.29 | (15), (18), (19), (20), (21), (22), (23), (25), (26) are % 151.44/22.29 | inconsistent by sub-proof #356. % 151.44/22.29 | % 151.44/22.29 End of proof % 151.44/22.29 % 151.44/22.29 Sub-proof #264 shows that the following formulas are inconsistent: % 151.44/22.29 ---------------------------------------------------------------- % 151.44/22.29 (1) all_56_11 = all_8_2 % 151.44/22.29 (2) all_54_9 = all_52_6 % 151.44/22.29 (3) ~ (all_52_6 = e1) % 151.44/22.29 (4) ~ (all_6_1 = e2) % 151.44/22.29 (5) all_54_0 = all_10_2 % 151.44/22.29 (6) all_56_21 = e3 % 151.44/22.29 (7) ~ (all_52_14 = all_4_2) % 151.44/22.29 (8) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0 % 151.44/22.29 (9) ~ (all_10_2 = e1) % 151.44/22.29 (10) ~ (all_6_1 = e3) % 151.44/22.29 (11) ~ (all_52_6 = all_52_14) % 151.44/22.29 (12) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 151.44/22.29 (13) ~ (all_6_0 = e2) % 151.44/22.29 (14) all_56_1 = all_10_2 % 151.44/22.29 (15) ~ (all_52_6 = e3) % 151.44/22.29 (16) op(e3, e3) = all_6_1 % 151.44/22.29 (17) op(e1, e0) = all_52_14 % 151.44/22.29 (18) op(e3, e3) = all_10_2 % 151.44/22.29 (19) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 151.44/22.29 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 151.44/22.29 (20) ~ (all_52_14 = e1) % 151.44/22.29 (21) ~ (all_52_14 = e3) % 151.44/22.29 (22) op(e1, all_6_1) = all_6_0 % 151.44/22.29 (23) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0 % 151.44/22.29 (24) all_56_31 = all_4_2 % 151.44/22.29 (25) all_56_1 = e3 | all_56_11 = e2 | all_56_21 = e1 | all_56_31 = e0 % 151.44/22.29 (26) ~ (all_16_1 = e2) | ~ (all_16_2 = e0) % 151.44/22.29 (27) all_16_2 = all_10_2 % 151.44/22.29 (28) ~ (all_52_6 = all_8_2) % 151.44/22.29 (29) ~ (e3 = e1) % 151.44/22.29 (30) all_54_11 = all_52_14 % 151.44/22.29 % 151.44/22.29 Begin of proof % 151.44/22.29 | % 151.44/22.29 | GROUND_INST: instantiating (19) with all_10_2, all_6_1, e3, e3, simplifying % 151.44/22.29 | with (16), (18) gives: % 151.44/22.29 | (31) all_10_2 = all_6_1 % 151.44/22.29 | % 151.44/22.29 | COMBINE_EQS: (27), (31) imply: % 151.44/22.29 | (32) all_16_2 = all_6_1 % 151.44/22.29 | % 151.44/22.29 | COMBINE_EQS: (5), (31) imply: % 151.44/22.29 | (33) all_54_0 = all_6_1 % 151.44/22.29 | % 151.44/22.29 | COMBINE_EQS: (14), (31) imply: % 151.44/22.29 | (34) all_56_1 = all_6_1 % 151.44/22.29 | % 151.44/22.29 | REDUCE: (9), (31) imply: % 151.44/22.29 | (35) ~ (all_6_1 = e1) % 151.44/22.29 | % 151.44/22.29 | BETA: splitting (12) gives: % 151.44/22.29 | % 151.44/22.29 | Case 1: % 151.44/22.29 | | % 151.44/22.29 | | (36) all_54_0 = e3 % 151.44/22.29 | | % 151.44/22.29 | | REF_CLOSE: (10), (33), (36) are inconsistent by sub-proof #686. % 151.44/22.29 | | % 151.44/22.29 | Case 2: % 151.44/22.29 | | % 151.44/22.29 | | (37) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 151.44/22.29 | | % 151.44/22.29 | | BETA: splitting (37) gives: % 151.44/22.29 | | % 151.44/22.29 | | Case 1: % 151.44/22.29 | | | % 151.44/22.29 | | | (38) all_54_0 = e2 % 151.44/22.29 | | | % 151.44/22.29 | | | REF_CLOSE: (4), (33), (38) are inconsistent by sub-proof #685. % 151.44/22.29 | | | % 151.44/22.29 | | Case 2: % 151.44/22.29 | | | % 151.44/22.29 | | | (39) all_54_0 = e1 | all_54_0 = e0 % 151.44/22.29 | | | % 151.44/22.29 | | | BETA: splitting (39) gives: % 151.44/22.29 | | | % 151.44/22.29 | | | Case 1: % 151.44/22.29 | | | | % 151.44/22.29 | | | | (40) all_54_0 = e1 % 151.44/22.29 | | | | % 151.44/22.29 | | | | REF_CLOSE: (33), (35), (40) are inconsistent by sub-proof #684. % 151.44/22.29 | | | | % 151.44/22.29 | | | Case 2: % 151.44/22.29 | | | | % 151.44/22.29 | | | | (41) all_54_0 = e0 % 151.44/22.29 | | | | % 151.44/22.29 | | | | COMBINE_EQS: (33), (41) imply: % 151.44/22.29 | | | | (42) all_6_1 = e0 % 151.44/22.29 | | | | % 151.44/22.29 | | | | SIMP: (42) implies: % 151.44/22.29 | | | | (43) all_6_1 = e0 % 151.44/22.29 | | | | % 151.44/22.29 | | | | COMBINE_EQS: (32), (43) imply: % 151.44/22.29 | | | | (44) all_16_2 = e0 % 151.44/22.29 | | | | % 151.44/22.29 | | | | COMBINE_EQS: (34), (43) imply: % 151.44/22.29 | | | | (45) all_56_1 = e0 % 151.44/22.29 | | | | % 151.44/22.29 | | | | REDUCE: (22), (43) imply: % 151.44/22.29 | | | | (46) op(e1, e0) = all_6_0 % 151.44/22.29 | | | | % 151.44/22.29 | | | | BETA: splitting (26) gives: % 151.44/22.29 | | | | % 151.44/22.29 | | | | Case 1: % 151.44/22.29 | | | | | % 151.44/22.29 | | | | | % 151.44/22.29 | | | | | GROUND_INST: instantiating (19) with all_52_14, all_6_0, e0, e1, % 151.44/22.29 | | | | | simplifying with (17), (46) gives: % 151.44/22.29 | | | | | (47) all_52_14 = all_6_0 % 151.44/22.29 | | | | | % 151.44/22.29 | | | | | REF_CLOSE: (1), (2), (3), (6), (7), (8), (11), (13), (15), (20), (21), % 151.44/22.29 | | | | | (23), (24), (25), (28), (29), (30), (45), (47) are % 151.44/22.29 | | | | | inconsistent by sub-proof #673. % 151.44/22.29 | | | | | % 151.44/22.29 | | | | Case 2: % 151.44/22.29 | | | | | % 151.44/22.29 | | | | | (48) ~ (all_16_2 = e0) % 151.44/22.29 | | | | | % 151.44/22.29 | | | | | REDUCE: (44), (48) imply: % 151.44/22.29 | | | | | (49) $false % 151.44/22.29 | | | | | % 151.44/22.29 | | | | | CLOSE: (49) is inconsistent. % 151.44/22.29 | | | | | % 151.44/22.29 | | | | End of split % 151.44/22.29 | | | | % 151.44/22.29 | | | End of split % 151.44/22.29 | | | % 151.44/22.29 | | End of split % 151.44/22.29 | | % 151.44/22.29 | End of split % 151.44/22.29 | % 151.44/22.29 End of proof % 151.44/22.29 % 151.44/22.29 Sub-proof #265 shows that the following formulas are inconsistent: % 151.44/22.29 ---------------------------------------------------------------- % 151.44/22.29 (1) all_56_11 = all_8_2 % 151.44/22.29 (2) op(e0, all_52_13) = all_56_14 % 151.44/22.29 (3) ~ (all_56_11 = e1) | all_56_13 = e2 % 151.44/22.29 (4) ~ (all_52_11 = all_6_2) % 151.44/22.29 (5) ~ (all_52_4 = all_52_8) % 151.44/22.29 (6) ~ (all_52_7 = all_52_11) % 151.44/22.29 (7) all_54_9 = all_52_6 % 151.44/22.29 (8) all_58_6 = all_52_2 % 151.44/22.29 (9) ~ (all_8_1 = e1) % 151.44/22.29 (10) ~ (all_56_31 = e1) | all_56_29 = e0 % 151.44/22.29 (11) all_54_10 = all_6_2 % 151.44/22.29 (12) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0 % 151.44/22.29 (13) ~ (all_6_1 = e2) % 151.44/22.29 (14) ~ (all_52_13 = all_8_2) % 151.44/22.29 (15) all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2 % 151.44/22.29 (16) all_54_0 = all_10_2 % 151.44/22.29 (17) all_54_4 = all_52_1 % 151.44/22.29 (18) ~ (all_52_14 = all_4_2) % 151.44/22.29 (19) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0 % 151.44/22.29 (20) all_54_12 = all_52_3 % 151.44/22.29 (21) ~ (all_52_12 = all_52_13) % 151.44/22.29 (22) ~ (all_52_4 = all_52_7) % 151.44/22.29 (23) ~ (all_6_2 = e3) % 151.44/22.29 (24) ~ (all_8_1 = e3) % 151.44/22.29 (25) op(e0, e0) = all_4_2 % 151.44/22.29 (26) all_58_6 = e0 | all_58_7 = e0 | all_58_8 = e0 | all_58_11 = e0 % 151.44/22.29 (27) all_54_5 = all_8_2 % 151.44/22.29 (28) ~ (all_6_1 = e3) % 151.44/22.29 (29) ~ (all_52_6 = all_52_14) % 151.44/22.29 (30) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 151.44/22.29 (31) all_54_15 = all_4_2 % 151.44/22.29 (32) all_56_21 = all_6_2 % 151.44/22.29 (33) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 151.44/22.29 (34) op(e3, all_52_1) = all_56_8 % 151.44/22.29 (35) ~ (all_52_7 = all_8_2) % 151.44/22.29 (36) all_56_1 = all_10_2 % 151.44/22.29 (37) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0 % 151.44/22.29 (38) all_54_1 = all_52_4 % 151.44/22.29 (39) all_58_9 = all_52_12 % 151.44/22.29 (40) ~ (all_56_1 = e1) | all_56_5 = e3 % 151.44/22.29 (41) all_58_1 = all_52_4 % 151.44/22.29 (42) all_58_13 = all_52_7 % 151.44/22.29 (43) op(e2, all_8_2) = all_56_10 % 151.44/22.29 (44) op(e3, e3) = all_10_2 % 151.44/22.29 (45) ~ (all_52_8 = all_6_2) % 151.44/22.29 (46) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0 % 151.44/22.29 (47) all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2 % 151.44/22.29 (48) ~ (all_52_1 = all_8_2) % 151.44/22.29 (49) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 151.44/22.29 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 151.44/22.29 (50) ~ (all_52_3 = all_10_2) % 151.44/22.29 (51) all_54_3 = all_52_12 % 151.44/22.29 (52) ~ (all_52_3 = all_52_7) % 151.44/22.29 (53) all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2 % 151.44/22.29 (54) all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) & % 151.44/22.29 (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0)) % 151.44/22.29 (55) ~ (all_52_2 = all_52_6) % 151.44/22.29 (56) op(e0, all_4_1) = all_4_0 % 151.44/22.29 (57) all_56_7 = all_52_12 % 151.44/22.29 (58) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0 % 151.44/22.29 (59) all_56_13 = all_52_9 % 151.44/22.29 (60) ~ (all_52_7 = all_4_2) % 151.44/22.29 (61) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0 % 151.44/22.29 (62) all_58_8 = all_6_2 % 151.44/22.29 (63) ~ (all_52_3 = all_4_2) % 151.44/22.29 (64) ~ (all_52_8 = all_10_2) % 151.44/22.29 (65) all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3 % 151.44/22.29 (66) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0 % 151.44/22.29 (67) ~ (all_56_1 = e2) | all_56_3 = e3 % 151.44/22.29 (68) ~ (all_56_1 = e0) | all_56_7 = e3 % 151.44/22.29 (69) ~ (all_8_2 = e3) % 151.44/22.29 (70) all_56_5 = all_52_8 % 151.44/22.29 (71) ~ (all_52_2 = all_52_3) % 151.44/22.29 (72) op(all_4_2, all_4_2) = all_4_1 % 151.44/22.29 (73) all_58_3 = all_8_2 % 151.44/22.29 (74) all_56_3 = all_52_4 % 151.44/22.29 (75) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0 % 151.44/22.29 (76) ~ (all_52_1 = all_52_3) % 151.44/22.29 (77) ~ (all_52_6 = all_52_7) % 151.44/22.29 (78) all_56_31 = all_4_2 % 151.44/22.29 (79) all_58_11 = all_52_14 % 151.44/22.29 (80) ~ (all_52_2 = all_52_14) % 151.44/22.29 (81) all_54_7 = all_52_13 % 151.44/22.29 (82) all_24_2 = all_10_2 % 151.44/22.29 (83) op(all_6_2, all_6_2) = all_6_1 % 151.44/22.29 (84) ~ (all_52_13 = all_4_2) % 151.44/22.29 (85) op(e3, e0) = all_52_12 % 151.44/22.29 (86) ~ (all_16_1 = e2) | ~ (all_16_2 = e0) % 151.44/22.29 (87) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0 % 151.44/22.29 (88) all_16_2 = all_10_2 % 151.44/22.29 (89) all_54_13 = all_52_7 % 151.44/22.29 (90) all_54_2 = all_52_8 % 151.44/22.29 (91) op(e3, e2) = all_52_4 % 151.44/22.29 (92) ~ (all_52_13 = all_52_14) % 151.44/22.29 (93) all_56_23 = all_52_14 % 151.44/22.29 (94) all_54_8 = all_52_2 % 151.44/22.29 (95) all_24_1 = all_10_1 % 151.44/22.29 (96) op(e1, e1) = all_6_2 % 151.44/22.29 (97) ~ (all_52_6 = all_8_2) % 151.44/22.29 (98) all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1 % 151.44/22.29 (99) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0 % 151.44/22.29 (100) all_58_15 = all_4_2 % 151.44/22.29 (101) op(e3, all_10_1) = e1 % 151.44/22.29 (102) all_56_29 = all_52_11 % 151.44/22.29 (103) ~ (all_6_2 = e2) % 151.44/22.29 (104) all_58_2 = all_52_1 % 151.44/22.29 (105) ~ (all_52_9 = all_6_2) % 151.44/22.29 (106) all_16_1 = all_10_1 % 151.44/22.29 (107) all_58_7 = all_52_6 % 151.44/22.29 (108) all_58_10 = all_52_13 % 151.44/22.29 (109) ~ (all_52_12 = all_4_2) % 151.44/22.29 (110) ~ (all_24_1 = e0) | ~ (all_24_2 = e2) % 151.44/22.29 (111) op(all_10_2, all_10_2) = all_10_1 % 151.44/22.29 (112) all_58_0 = all_10_2 % 151.44/22.29 (113) op(e1, all_6_2) = all_56_20 % 151.44/22.29 (114) all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1 % 151.44/22.29 (115) all_58_1 = e0 | all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0 % 151.44/22.29 (116) ~ (all_52_12 = all_52_14) % 151.44/22.29 (117) op(e3, e1) = all_52_8 % 151.44/22.29 (118) ~ (e3 = e1) % 151.44/22.29 (119) op(e2, e2) = all_8_2 % 151.44/22.29 (120) ~ (all_52_4 = all_52_12) % 151.44/22.29 (121) ~ (all_52_2 = all_6_2) % 151.44/22.29 (122) ~ (all_52_8 = all_52_12) % 151.44/22.29 (123) all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1 % 151.44/22.29 (124) ~ (all_52_1 = all_52_2) % 151.44/22.29 (125) ~ (all_56_21 = e0) | all_56_23 = e1 % 151.44/22.30 (126) op(e0, all_4_2) = all_56_30 % 151.44/22.30 (127) ~ (all_52_6 = all_6_2) % 151.44/22.30 (128) ~ (all_8_2 = e0) % 151.44/22.30 (129) op(e3, all_10_2) = all_56_0 % 151.44/22.30 (130) ~ (all_52_14 = all_6_2) % 151.44/22.30 (131) all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0 % 151.44/22.30 (132) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0 % 151.44/22.30 (133) ~ (all_52_2 = all_10_2) % 151.44/22.30 (134) ~ (all_52_4 = all_10_2) % 151.44/22.30 (135) ~ (all_52_4 = all_8_2) % 151.44/22.30 (136) op(all_8_2, all_8_2) = all_8_1 % 151.44/22.30 (137) op(e3, all_52_3) = all_56_24 % 151.44/22.30 (138) ~ (all_52_4 = all_52_6) % 151.44/22.30 (139) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 151.44/22.30 (140) all_58_14 = all_52_11 % 151.44/22.30 (141) ~ (all_52_12 = all_10_2) % 151.44/22.30 (142) ~ (all_52_1 = all_10_2) % 151.44/22.30 (143) all_58_12 = all_52_3 % 151.44/22.30 (144) all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2 % 151.44/22.30 (145) all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3 % 151.44/22.30 (146) all_54_11 = all_52_14 % 151.44/22.30 % 151.44/22.30 Begin of proof % 151.44/22.30 | % 151.44/22.30 | BETA: splitting (40) gives: % 151.44/22.30 | % 151.44/22.30 | Case 1: % 151.44/22.30 | | % 151.44/22.30 | | (147) ~ (all_56_1 = e1) % 151.44/22.30 | | % 151.44/22.30 | | REDUCE: (36), (147) imply: % 151.44/22.30 | | (148) ~ (all_10_2 = e1) % 151.44/22.30 | | % 151.44/22.30 | | BETA: splitting (67) gives: % 151.44/22.30 | | % 151.44/22.30 | | Case 1: % 151.44/22.30 | | | % 151.44/22.30 | | | (149) ~ (all_56_1 = e2) % 151.44/22.30 | | | % 151.44/22.30 | | | REDUCE: (36), (149) imply: % 151.44/22.30 | | | (150) ~ (all_10_2 = e2) % 151.44/22.30 | | | % 151.44/22.30 | | | BETA: splitting (3) gives: % 151.44/22.30 | | | % 151.44/22.30 | | | Case 1: % 151.44/22.30 | | | | % 151.44/22.30 | | | | (151) ~ (all_56_11 = e1) % 151.44/22.30 | | | | % 151.44/22.30 | | | | REDUCE: (1), (151) imply: % 151.44/22.30 | | | | (152) ~ (all_8_2 = e1) % 151.44/22.30 | | | | % 151.44/22.30 | | | | BETA: splitting (139) gives: % 151.44/22.30 | | | | % 151.44/22.30 | | | | Case 1: % 151.44/22.30 | | | | | % 151.44/22.30 | | | | | (153) all_54_5 = e3 % 151.44/22.30 | | | | | % 151.44/22.30 | | | | | REF_CLOSE: (27), (69), (153) are inconsistent by sub-proof #737. % 151.44/22.30 | | | | | % 151.44/22.30 | | | | Case 2: % 151.44/22.30 | | | | | % 151.44/22.30 | | | | | (154) ~ (all_54_5 = e3) % 151.44/22.30 | | | | | (155) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 151.44/22.30 | | | | | % 151.44/22.30 | | | | | BETA: splitting (155) gives: % 151.44/22.30 | | | | | % 151.44/22.30 | | | | | Case 1: % 151.44/22.30 | | | | | | % 151.44/22.30 | | | | | | (156) all_54_5 = e2 % 151.44/22.30 | | | | | | % 151.44/22.30 | | | | | | COMBINE_EQS: (27), (156) imply: % 151.44/22.30 | | | | | | (157) all_8_2 = e2 % 151.44/22.30 | | | | | | % 151.44/22.30 | | | | | | SIMP: (157) implies: % 151.44/22.30 | | | | | | (158) all_8_2 = e2 % 151.44/22.30 | | | | | | % 151.44/22.30 | | | | | | REDUCE: (48), (158) imply: % 151.44/22.30 | | | | | | (159) ~ (all_52_1 = e2) % 151.44/22.30 | | | | | | % 151.44/22.30 | | | | | | REDUCE: (135), (158) imply: % 151.44/22.30 | | | | | | (160) ~ (all_52_4 = e2) % 151.44/22.30 | | | | | | % 151.44/22.30 | | | | | | REDUCE: (14), (158) imply: % 151.44/22.30 | | | | | | (161) ~ (all_52_13 = e2) % 151.44/22.30 | | | | | | % 151.44/22.30 | | | | | | BETA: splitting (68) gives: % 151.44/22.30 | | | | | | % 151.44/22.30 | | | | | | Case 1: % 151.44/22.30 | | | | | | | % 151.44/22.30 | | | | | | | (162) ~ (all_56_1 = e0) % 151.44/22.30 | | | | | | | % 151.44/22.30 | | | | | | | REDUCE: (36), (162) imply: % 151.44/22.30 | | | | | | | (163) ~ (all_10_2 = e0) % 151.44/22.30 | | | | | | | % 151.44/22.30 | | | | | | | REF_CLOSE: (16), (30), (44), (49), (101), (111), (129), (148), % 151.44/22.30 | | | | | | | (150), (163) are inconsistent by sub-proof #304. % 151.44/22.30 | | | | | | | % 151.44/22.30 | | | | | | Case 2: % 151.44/22.30 | | | | | | | % 151.44/22.30 | | | | | | | (164) all_56_7 = e3 % 151.44/22.30 | | | | | | | (165) all_56_1 = e0 % 151.44/22.30 | | | | | | | % 151.44/22.30 | | | | | | | COMBINE_EQS: (36), (165) imply: % 151.44/22.30 | | | | | | | (166) all_10_2 = e0 % 151.44/22.30 | | | | | | | % 151.44/22.30 | | | | | | | COMBINE_EQS: (57), (164) imply: % 151.44/22.30 | | | | | | | (167) all_52_12 = e3 % 151.44/22.30 | | | | | | | % 151.44/22.30 | | | | | | | COMBINE_EQS: (88), (166) imply: % 151.44/22.30 | | | | | | | (168) all_16_2 = e0 % 151.44/22.30 | | | | | | | % 151.44/22.30 | | | | | | | COMBINE_EQS: (39), (167) imply: % 151.44/22.30 | | | | | | | (169) all_58_9 = e3 % 151.44/22.30 | | | | | | | % 151.44/22.30 | | | | | | | REDUCE: (142), (166) imply: % 151.44/22.30 | | | | | | | (170) ~ (all_52_1 = e0) % 151.44/22.30 | | | | | | | % 151.44/22.30 | | | | | | | REDUCE: (133), (166) imply: % 151.44/22.30 | | | | | | | (171) ~ (all_52_2 = e0) % 151.44/22.30 | | | | | | | % 151.44/22.30 | | | | | | | REDUCE: (50), (166) imply: % 151.44/22.30 | | | | | | | (172) ~ (all_52_3 = e0) % 151.44/22.30 | | | | | | | % 151.44/22.30 | | | | | | | REDUCE: (120), (167) imply: % 151.44/22.30 | | | | | | | (173) ~ (all_52_4 = e3) % 151.44/22.30 | | | | | | | % 151.44/22.30 | | | | | | | REDUCE: (134), (166) imply: % 151.44/22.30 | | | | | | | (174) ~ (all_52_4 = e0) % 151.44/22.30 | | | | | | | % 151.44/22.30 | | | | | | | REDUCE: (122), (167) imply: % 151.44/22.30 | | | | | | | (175) ~ (all_52_8 = e3) % 151.44/22.30 | | | | | | | % 151.44/22.30 | | | | | | | REDUCE: (64), (166) imply: % 151.44/22.30 | | | | | | | (176) ~ (all_52_8 = e0) % 151.44/22.30 | | | | | | | % 151.44/22.30 | | | | | | | REDUCE: (109), (167) imply: % 151.44/22.30 | | | | | | | (177) ~ (all_4_2 = e3) % 151.44/22.30 | | | | | | | % 151.44/22.30 | | | | | | | SIMP: (177) implies: % 151.44/22.30 | | | | | | | (178) ~ (all_4_2 = e3) % 151.44/22.30 | | | | | | | % 151.44/22.30 | | | | | | | REDUCE: (111), (166) imply: % 151.44/22.30 | | | | | | | (179) op(e0, e0) = all_10_1 % 151.44/22.30 | | | | | | | % 151.44/22.30 | | | | | | | BETA: splitting (99) gives: % 151.44/22.30 | | | | | | | % 151.44/22.30 | | | | | | | Case 1: % 151.44/22.30 | | | | | | | | % 151.44/22.30 | | | | | | | | (180) all_54_1 = e3 % 151.44/22.30 | | | | | | | | % 151.44/22.30 | | | | | | | | REF_CLOSE: (38), (173), (180) are inconsistent by sub-proof % 151.44/22.30 | | | | | | | | #722. % 151.44/22.30 | | | | | | | | % 151.44/22.30 | | | | | | | Case 2: % 151.44/22.30 | | | | | | | | % 151.44/22.30 | | | | | | | | (181) all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0 % 151.44/22.30 | | | | | | | | % 151.44/22.30 | | | | | | | | BETA: splitting (181) gives: % 151.44/22.30 | | | | | | | | % 151.44/22.30 | | | | | | | | Case 1: % 151.44/22.30 | | | | | | | | | % 151.44/22.30 | | | | | | | | | (182) all_54_1 = e2 % 151.44/22.30 | | | | | | | | | % 151.44/22.30 | | | | | | | | | REF_CLOSE: (38), (160), (182) are inconsistent by sub-proof % 151.44/22.30 | | | | | | | | | #721. % 151.44/22.30 | | | | | | | | | % 151.44/22.30 | | | | | | | | Case 2: % 151.44/22.30 | | | | | | | | | % 151.44/22.30 | | | | | | | | | (183) all_54_1 = e1 | all_54_1 = e0 % 151.44/22.30 | | | | | | | | | % 151.44/22.30 | | | | | | | | | BETA: splitting (183) gives: % 151.44/22.30 | | | | | | | | | % 151.44/22.30 | | | | | | | | | Case 1: % 151.44/22.30 | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | (184) all_54_1 = e1 % 151.44/22.30 | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | COMBINE_EQS: (38), (184) imply: % 151.44/22.30 | | | | | | | | | | (185) all_52_4 = e1 % 151.44/22.30 | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | SIMP: (185) implies: % 151.44/22.30 | | | | | | | | | | (186) all_52_4 = e1 % 151.44/22.30 | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | REDUCE: (138), (186) imply: % 151.44/22.30 | | | | | | | | | | (187) ~ (all_52_6 = e1) % 151.44/22.30 | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | SIMP: (187) implies: % 151.44/22.30 | | | | | | | | | | (188) ~ (all_52_6 = e1) % 151.44/22.30 | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | REDUCE: (22), (186) imply: % 151.44/22.30 | | | | | | | | | | (189) ~ (all_52_7 = e1) % 151.44/22.30 | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | SIMP: (189) implies: % 151.44/22.30 | | | | | | | | | | (190) ~ (all_52_7 = e1) % 151.44/22.30 | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | REDUCE: (5), (186) imply: % 151.44/22.30 | | | | | | | | | | (191) ~ (all_52_8 = e1) % 151.44/22.30 | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | SIMP: (191) implies: % 151.44/22.30 | | | | | | | | | | (192) ~ (all_52_8 = e1) % 151.44/22.30 | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | BETA: splitting (46) gives: % 151.44/22.30 | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | Case 1: % 151.44/22.30 | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | (193) all_54_2 = e3 % 151.44/22.30 | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | REF_CLOSE: (90), (175), (193) are inconsistent by sub-proof % 151.44/22.30 | | | | | | | | | | | #728. % 151.44/22.30 | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | Case 2: % 151.44/22.30 | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | (194) ~ (all_54_2 = e3) % 151.44/22.30 | | | | | | | | | | | (195) all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0 % 151.44/22.30 | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | BETA: splitting (195) gives: % 151.44/22.30 | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | Case 1: % 151.44/22.30 | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | (196) all_54_2 = e2 % 151.44/22.30 | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | COMBINE_EQS: (90), (196) imply: % 151.44/22.30 | | | | | | | | | | | | (197) all_52_8 = e2 % 151.44/22.30 | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | SIMP: (197) implies: % 151.44/22.30 | | | | | | | | | | | | (198) all_52_8 = e2 % 151.44/22.30 | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | REDUCE: (175), (198) imply: % 151.44/22.30 | | | | | | | | | | | | (199) ~ (e3 = e2) % 151.44/22.30 | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | SIMP: (199) implies: % 151.44/22.30 | | | | | | | | | | | | (200) ~ (e3 = e2) % 151.44/22.30 | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | REDUCE: (192), (198) imply: % 151.44/22.30 | | | | | | | | | | | | (201) ~ (e2 = e1) % 151.44/22.30 | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | REDUCE: (176), (198) imply: % 151.44/22.30 | | | | | | | | | | | | (202) ~ (e2 = e0) % 151.44/22.30 | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | REDUCE: (117), (198) imply: % 151.44/22.30 | | | | | | | | | | | | (203) op(e3, e1) = e2 % 151.44/22.30 | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | BETA: splitting (86) gives: % 151.44/22.30 | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | Case 1: % 151.44/22.30 | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | (204) ~ (all_16_1 = e2) % 151.44/22.30 | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | REDUCE: (106), (204) imply: % 151.44/22.30 | | | | | | | | | | | | | (205) ~ (all_10_1 = e2) % 151.44/22.30 | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | GROUND_INST: instantiating (49) with all_4_2, all_10_1, e0, e0, % 151.44/22.30 | | | | | | | | | | | | | simplifying with (25), (179) gives: % 151.44/22.30 | | | | | | | | | | | | | (206) all_10_1 = all_4_2 % 151.44/22.30 | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | REDUCE: (205), (206) imply: % 151.44/22.30 | | | | | | | | | | | | | (207) ~ (all_4_2 = e2) % 151.44/22.30 | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | BETA: splitting (144) gives: % 151.44/22.30 | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | Case 1: % 151.44/22.30 | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | (208) all_58_12 = e2 % 151.44/22.30 | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | COMBINE_EQS: (143), (208) imply: % 151.44/22.30 | | | | | | | | | | | | | | (209) all_52_3 = e2 % 151.44/22.30 | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | REDUCE: (52), (209) imply: % 151.44/22.30 | | | | | | | | | | | | | | (210) ~ (all_52_7 = e2) % 151.44/22.30 | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | SIMP: (210) implies: % 151.44/22.30 | | | | | | | | | | | | | | (211) ~ (all_52_7 = e2) % 151.44/22.30 | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | REDUCE: (63), (209) imply: % 151.44/22.30 | | | | | | | | | | | | | | (212) ~ (all_4_2 = e2) % 151.44/22.30 | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | BETA: splitting (15) gives: % 151.44/22.30 | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | Case 1: % 151.44/22.30 | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | (213) all_58_9 = e2 % 151.44/22.30 | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | COMBINE_EQS: (169), (213) imply: % 151.44/22.30 | | | | | | | | | | | | | | | (214) e3 = e2 % 151.44/22.30 | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | REDUCE: (200), (214) imply: % 151.44/22.30 | | | | | | | | | | | | | | | (215) $false % 151.44/22.30 | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | CLOSE: (215) is inconsistent. % 151.44/22.30 | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | Case 2: % 151.44/22.30 | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | (216) all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2 % 151.44/22.30 | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | BETA: splitting (216) gives: % 151.44/22.30 | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | Case 1: % 151.44/22.30 | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | (217) all_58_10 = e2 % 151.44/22.30 | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | COMBINE_EQS: (108), (217) imply: % 151.44/22.30 | | | | | | | | | | | | | | | | (218) all_52_13 = e2 % 151.44/22.30 | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | REDUCE: (161), (218) imply: % 151.44/22.30 | | | | | | | | | | | | | | | | (219) $false % 151.44/22.30 | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | CLOSE: (219) is inconsistent. % 151.44/22.30 | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | Case 2: % 151.44/22.30 | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | (220) all_58_11 = e2 | all_58_15 = e2 % 151.44/22.30 | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | BETA: splitting (220) gives: % 151.44/22.30 | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | Case 1: % 151.44/22.30 | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | (221) all_58_11 = e2 % 151.44/22.30 | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | COMBINE_EQS: (79), (221) imply: % 151.44/22.30 | | | | | | | | | | | | | | | | | (222) all_52_14 = e2 % 151.44/22.30 | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | COMBINE_EQS: (93), (222) imply: % 151.44/22.30 | | | | | | | | | | | | | | | | | (223) all_56_23 = e2 % 151.44/22.30 | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | REDUCE: (80), (222) imply: % 151.44/22.30 | | | | | | | | | | | | | | | | | (224) ~ (all_52_2 = e2) % 151.44/22.30 | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | REDUCE: (130), (222) imply: % 151.44/22.30 | | | | | | | | | | | | | | | | | (225) ~ (all_6_2 = e2) % 151.44/22.30 | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | BETA: splitting (125) gives: % 151.44/22.30 | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | Case 1: % 151.44/22.30 | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | (226) ~ (all_56_21 = e0) % 151.44/22.30 | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | REDUCE: (32), (226) imply: % 151.44/22.30 | | | | | | | | | | | | | | | | | | (227) ~ (all_6_2 = e0) % 151.44/22.30 | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | BETA: splitting (26) gives: % 151.44/22.30 | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | Case 1: % 151.44/22.30 | | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | | (228) all_58_6 = e0 % 151.44/22.30 | | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (171), (228) are inconsistent by sub-proof % 151.44/22.30 | | | | | | | | | | | | | | | | | | | #273. % 151.44/22.30 | | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | Case 2: % 151.44/22.30 | | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | | (229) all_58_7 = e0 | all_58_8 = e0 | all_58_11 = e0 % 151.44/22.30 | | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | | BETA: splitting (229) gives: % 151.44/22.30 | | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | | Case 1: % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | (230) all_58_7 = e0 % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (107), (230) imply: % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | (231) all_52_6 = e0 % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | REDUCE: (77), (231) imply: % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | (232) ~ (all_52_7 = e0) % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | SIMP: (232) implies: % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | (233) ~ (all_52_7 = e0) % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | REDUCE: (127), (231) imply: % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | (234) ~ (all_6_2 = e0) % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | REDUCE: (188), (231) imply: % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | (235) ~ (e1 = e0) % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | SIMP: (235) implies: % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | (236) ~ (e1 = e0) % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | BETA: splitting (33) gives: % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | Case 1: % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | (237) all_54_10 = e3 % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (23), (237) are inconsistent by sub-proof % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | #736. % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | Case 2: % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | (238) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives: % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | Case 1: % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | (239) all_54_10 = e2 % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (103), (239) are inconsistent by sub-proof % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | #735. % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | Case 2: % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | (240) all_54_10 = e1 | all_54_10 = e0 % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (66) gives: % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | (241) all_54_13 = e3 % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (89), (241) imply: % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | (242) all_52_7 = e3 % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (242) implies: % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | (243) all_52_7 = e3 % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (42), (243) imply: % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | (244) all_58_13 = e3 % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (65) gives: % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | (245) all_58_6 = e3 % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (8), (245) imply: % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | (246) all_52_2 = e3 % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (246) implies: % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | (247) all_52_2 = e3 % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (124), (247) imply: % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | (248) ~ (all_52_1 = e3) % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (171), (247) imply: % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | (249) ~ (e3 = e0) % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (123) gives: % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | (250) all_58_6 = e1 % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (245), (250) imply: % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | (251) e3 = e1 % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (251) implies: % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | (252) e3 = e1 % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (118), (252) imply: % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | (253) $false % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (253) is inconsistent. % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | (254) all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1 % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (61) gives: % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | (255) all_54_4 = e3 % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (248), (255) are inconsistent by sub-proof % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | #634. % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | (256) ~ (all_54_4 = e3) % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | (257) all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0 % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (254) gives: % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | (258) all_58_7 = e1 % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (230), (258) imply: % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | (259) e1 = e0 % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (259) implies: % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | (260) e1 = e0 % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (236), (260) imply: % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | (261) $false % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (261) is inconsistent. % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | (262) all_58_8 = e1 | all_58_11 = e1 % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (262) gives: % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (263) all_58_8 = e1 % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (62), (263) imply: % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (264) all_6_2 = e1 % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (264) implies: % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (265) all_6_2 = e1 % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4), (265) imply: % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (266) ~ (all_52_11 = e1) % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (257) gives: % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (267) all_54_4 = e2 % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (159), (267) are inconsistent by sub-proof % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #633. % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (268) ~ (all_54_4 = e2) % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (269) all_54_4 = e1 | all_54_4 = e0 % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (269) gives: % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (270) all_54_4 = e1 % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (17), (270) imply: % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (271) all_52_1 = e1 % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (271) implies: % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (272) all_52_1 = e1 % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (104), (272) imply: % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (273) all_58_2 = e1 % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (248), (272) imply: % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (274) ~ (e3 = e1) % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (159), (272) imply: % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (275) ~ (e2 = e1) % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (34), (272) imply: % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (276) op(e3, e1) = all_56_8 % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (114) gives: % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (277) all_58_12 = e1 % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (208), (277) imply: % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (278) e2 = e1 % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (100), (201), (207), (220), (221), (278) are % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #271. % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (279) all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1 % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (279) gives: % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (280) all_58_13 = e1 % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (118), (244), (280) are inconsistent by sub-proof % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #561. % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (281) all_58_14 = e1 | all_58_15 = e1 % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (281) gives: % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (282) all_58_14 = e1 % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (140), (266), (282) are inconsistent by sub-proof % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #699. % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (283) all_58_15 = e1 % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (100), (283) imply: % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (284) all_4_2 = e1 % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (25), (284) imply: % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (285) op(e0, e0) = e1 % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (9), (27), (43), (49), (53), (54), (73), % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (101), (108), (119), (128), (136), (152), (155), % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (169), (179), (201), (203), (221), (236), (249), % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (273), (276), (283), (285) are inconsistent by % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #278. % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (286) all_54_4 = e0 % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (170), (286) are inconsistent by sub-proof % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #614. % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (287) all_58_11 = e1 % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (100), (201), (207), (220), (287) are inconsistent % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #272. % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | (288) ~ (all_58_6 = e3) % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8), (288) imply: % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | (289) ~ (all_52_2 = e3) % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (132) gives: % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | (290) all_54_8 = e3 % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (94), (289), (290) are inconsistent by sub-proof % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | #345. % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | (291) all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0 % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (240) gives: % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | (292) all_54_10 = e1 % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (11), (292) imply: % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | (293) all_6_2 = e1 % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (293) implies: % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | (294) all_6_2 = e1 % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (121), (294) imply: % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | (295) ~ (all_52_2 = e1) % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (94), (171), (224), (291), (295) are inconsistent % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #270. % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | (296) all_54_10 = e0 % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (227), (296) are inconsistent by sub-proof % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | #705. % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | End of split % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | (297) all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0 % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (297) gives: % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | (298) all_54_13 = e2 % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (89), (298) imply: % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | (299) all_52_7 = e2 % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (299) implies: % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | (300) all_52_7 = e2 % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (35), (300) imply: % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | (301) ~ (all_8_2 = e2) % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (27), (69), (128), (139), (152), (301) are % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #643. % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | (302) all_54_13 = e1 | all_54_13 = e0 % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (89), (190), (233), (302) are inconsistent by % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #711. % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | End of split % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | End of split % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | End of split % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | End of split % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | | Case 2: % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | (303) ~ (all_58_7 = e0) % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | REDUCE: (107), (303) imply: % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | (304) ~ (all_52_6 = e0) % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | BETA: splitting (75) gives: % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | Case 1: % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | (305) all_54_9 = e3 % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (7), (305) imply: % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | (306) all_52_6 = e3 % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | SIMP: (306) implies: % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | (307) all_52_6 = e3 % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | REDUCE: (77), (307) imply: % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | (308) ~ (all_52_7 = e3) % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | SIMP: (308) implies: % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | (309) ~ (all_52_7 = e3) % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (66) gives: % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | Case 1: % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | (310) all_54_13 = e3 % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (89), (309), (310) are inconsistent by sub-proof % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | #668. % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | Case 2: % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | (311) all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0 % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (311) gives: % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | (312) all_54_13 = e2 % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (89), (211), (312) are inconsistent by sub-proof % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | #513. % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | (313) all_54_13 = e1 | all_54_13 = e0 % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (313) gives: % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | (314) all_54_13 = e1 % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (89), (190), (314) are inconsistent by sub-proof % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | #713. % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | (315) all_54_13 = e0 % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (89), (315) imply: % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | (316) all_52_7 = e0 % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (316) implies: % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | (317) all_52_7 = e0 % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6), (317) imply: % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | (318) ~ (all_52_11 = e0) % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (318) implies: % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | (319) ~ (all_52_11 = e0) % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10) gives: % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | (320) ~ (all_56_31 = e1) % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (78), (320) imply: % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | (321) ~ (all_4_2 = e1) % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (11), (12), (13), (14), (16), (19), (20), % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | (21), (22), (25), (27), (28), (29), (30), (31), % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | (33), (35), (36), (37), (40), (41), (42), (44), % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | (45), (49), (50), (51), (52), (56), (57), (58), % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | (60), (62), (63), (65), (66), (67), (68), (70), % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | (71), (72), (73), (74), (77), (79), (81), (83), % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | (84), (85), (87), (89), (92), (96), (101), (103), % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | (107), (109), (111), (113), (115), (116), (117), % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | (118), (120), (126), (128), (129), (135), (137), % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | (139), (141), (143), (145), (146), (152), (178), % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | (207), (227), (321) are inconsistent by sub-proof % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | #297. % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | (322) all_56_29 = e0 % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (102), (319), (322) are inconsistent by sub-proof % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | #269. % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | End of split % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | End of split % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | End of split % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | Case 2: % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | (323) all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0 % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (27), (69), (97), (128), (139), (152), (188), % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | (304), (323) are inconsistent by sub-proof #642. % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | End of split % 151.44/22.30 | | | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | | End of split % 151.44/22.30 | | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | End of split % 151.44/22.30 | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | Case 2: % 151.44/22.30 | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | (324) all_56_23 = e1 % 151.44/22.30 | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (223), (324) imply: % 151.44/22.30 | | | | | | | | | | | | | | | | | | (325) e2 = e1 % 151.44/22.30 | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (221), (325) imply: % 151.44/22.30 | | | | | | | | | | | | | | | | | | (326) all_58_11 = e1 % 151.44/22.30 | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | REF_CLOSE: (100), (201), (207), (220), (326) are inconsistent % 151.44/22.30 | | | | | | | | | | | | | | | | | | by sub-proof #272. % 151.44/22.30 | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | End of split % 151.44/22.30 | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | Case 2: % 151.44/22.30 | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | (327) all_58_15 = e2 % 151.44/22.30 | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | COMBINE_EQS: (100), (327) imply: % 151.44/22.30 | | | | | | | | | | | | | | | | | (328) all_4_2 = e2 % 151.44/22.30 | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | REDUCE: (207), (328) imply: % 151.44/22.30 | | | | | | | | | | | | | | | | | (329) $false % 151.44/22.30 | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | CLOSE: (329) is inconsistent. % 151.44/22.30 | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | End of split % 151.44/22.30 | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | End of split % 151.44/22.30 | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | End of split % 151.44/22.30 | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | Case 2: % 151.44/22.30 | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | (330) ~ (all_58_12 = e2) % 151.44/22.30 | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | REDUCE: (143), (330) imply: % 151.44/22.30 | | | | | | | | | | | | | | (331) ~ (all_52_3 = e2) % 151.44/22.30 | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | BETA: splitting (47) gives: % 151.44/22.30 | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | Case 1: % 151.44/22.30 | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | (332) all_58_0 = e2 % 151.44/22.30 | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | REF_CLOSE: (8), (104), (131), (143), (170), (171), (172), % 151.44/22.30 | | | | | | | | | | | | | | | (202), (332) are inconsistent by sub-proof #613. % 151.44/22.30 | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | Case 2: % 151.44/22.30 | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | (333) all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2 % 151.44/22.30 | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | BETA: splitting (15) gives: % 151.44/22.30 | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | Case 1: % 151.44/22.30 | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | (334) all_58_9 = e2 % 151.44/22.30 | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | COMBINE_EQS: (169), (334) imply: % 151.44/22.30 | | | | | | | | | | | | | | | | (335) e3 = e2 % 151.44/22.30 | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | REDUCE: (200), (335) imply: % 151.44/22.30 | | | | | | | | | | | | | | | | (336) $false % 151.44/22.30 | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | CLOSE: (336) is inconsistent. % 151.44/22.30 | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | Case 2: % 151.44/22.30 | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | (337) all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2 % 151.44/22.30 | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | BETA: splitting (337) gives: % 151.44/22.30 | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | Case 1: % 151.44/22.30 | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | (338) all_58_10 = e2 % 151.44/22.30 | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | COMBINE_EQS: (108), (338) imply: % 151.44/22.30 | | | | | | | | | | | | | | | | | (339) all_52_13 = e2 % 151.44/22.30 | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | REDUCE: (161), (339) imply: % 151.44/22.30 | | | | | | | | | | | | | | | | | (340) $false % 151.44/22.30 | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | CLOSE: (340) is inconsistent. % 151.44/22.30 | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | Case 2: % 151.44/22.30 | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | (341) all_58_11 = e2 | all_58_15 = e2 % 151.44/22.30 | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | BETA: splitting (341) gives: % 151.44/22.30 | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | Case 1: % 151.44/22.30 | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | (342) all_58_11 = e2 % 151.44/22.30 | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (79), (342) imply: % 151.44/22.30 | | | | | | | | | | | | | | | | | | (343) all_52_14 = e2 % 151.44/22.30 | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | REDUCE: (80), (343) imply: % 151.44/22.30 | | | | | | | | | | | | | | | | | | (344) ~ (all_52_2 = e2) % 151.44/22.30 | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (104), (143), (159), (331), (333), (344) are % 151.44/22.30 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #695. % 151.44/22.30 | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | Case 2: % 151.44/22.30 | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | (345) all_58_15 = e2 % 151.44/22.30 | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (100), (345) imply: % 151.44/22.30 | | | | | | | | | | | | | | | | | | (346) all_4_2 = e2 % 151.44/22.30 | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | REDUCE: (207), (346) imply: % 151.44/22.30 | | | | | | | | | | | | | | | | | | (347) $false % 151.44/22.30 | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | | CLOSE: (347) is inconsistent. % 151.44/22.30 | | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | | End of split % 151.44/22.30 | | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | | End of split % 151.44/22.30 | | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | | End of split % 151.44/22.30 | | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | | End of split % 151.44/22.30 | | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | End of split % 151.44/22.30 | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | Case 2: % 151.44/22.30 | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | (348) ~ (all_16_2 = e0) % 151.44/22.30 | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | REDUCE: (168), (348) imply: % 151.44/22.30 | | | | | | | | | | | | | (349) $false % 151.44/22.30 | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | | CLOSE: (349) is inconsistent. % 151.44/22.30 | | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | End of split % 151.44/22.30 | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | Case 2: % 151.44/22.30 | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | (350) all_54_2 = e1 | all_54_2 = e0 % 151.44/22.30 | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | | REF_CLOSE: (90), (176), (192), (350) are inconsistent by % 151.44/22.30 | | | | | | | | | | | | sub-proof #724. % 151.44/22.30 | | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | | End of split % 151.44/22.30 | | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | End of split % 151.44/22.30 | | | | | | | | | | % 151.44/22.30 | | | | | | | | | Case 2: % 151.44/22.30 | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | (351) all_54_1 = e0 % 151.44/22.30 | | | | | | | | | | % 151.44/22.30 | | | | | | | | | | REF_CLOSE: (38), (174), (351) are inconsistent by sub-proof % 151.44/22.30 | | | | | | | | | | #719. % 151.44/22.30 | | | | | | | | | | % 151.44/22.30 | | | | | | | | | End of split % 151.44/22.30 | | | | | | | | | % 151.44/22.30 | | | | | | | | End of split % 151.44/22.30 | | | | | | | | % 151.44/22.30 | | | | | | | End of split % 151.44/22.30 | | | | | | | % 151.44/22.30 | | | | | | End of split % 151.44/22.30 | | | | | | % 151.44/22.30 | | | | | Case 2: % 151.44/22.30 | | | | | | % 151.44/22.30 | | | | | | (352) all_54_5 = e1 | all_54_5 = e0 % 151.44/22.30 | | | | | | % 151.44/22.30 | | | | | | REF_CLOSE: (27), (128), (152), (352) are inconsistent by sub-proof % 151.44/22.30 | | | | | | #645. % 151.44/22.30 | | | | | | % 151.44/22.30 | | | | | End of split % 151.44/22.30 | | | | | % 151.44/22.30 | | | | End of split % 151.44/22.30 | | | | % 151.44/22.30 | | | Case 2: % 151.44/22.30 | | | | % 151.44/22.30 | | | | (353) all_56_13 = e2 % 151.44/22.30 | | | | (354) all_56_11 = e1 % 151.44/22.30 | | | | % 151.44/22.30 | | | | COMBINE_EQS: (1), (354) imply: % 151.44/22.30 | | | | (355) all_8_2 = e1 % 151.44/22.30 | | | | % 151.44/22.30 | | | | COMBINE_EQS: (59), (353) imply: % 151.44/22.30 | | | | (356) all_52_9 = e2 % 151.44/22.30 | | | | % 151.44/22.30 | | | | REDUCE: (105), (356) imply: % 151.44/22.30 | | | | (357) ~ (all_6_2 = e2) % 151.44/22.30 | | | | % 151.44/22.30 | | | | REDUCE: (136), (355) imply: % 151.44/22.30 | | | | (358) op(e1, e1) = all_8_1 % 151.44/22.30 | | | | % 151.44/22.31 | | | | REF_CLOSE: (4), (9), (10), (11), (12), (13), (15), (16), (24), (25), % 151.44/22.31 | | | | (28), (30), (31), (33), (36), (39), (40), (41), (42), (44), % 151.44/22.31 | | | | (49), (51), (60), (67), (70), (73), (74), (78), (83), (85), % 151.44/22.31 | | | | (87), (96), (98), (101), (102), (103), (107), (111), (112), % 151.44/22.31 | | | | (115), (120), (122), (127), (128), (129), (134), (141), (358) % 151.44/22.31 | | | | are inconsistent by sub-proof #268. % 151.44/22.31 | | | | % 151.44/22.31 | | | End of split % 151.44/22.31 | | | % 151.44/22.31 | | Case 2: % 151.44/22.31 | | | % 151.44/22.31 | | | (359) all_56_3 = e3 % 151.44/22.31 | | | (360) all_56_1 = e2 % 151.44/22.31 | | | % 151.44/22.31 | | | COMBINE_EQS: (36), (360) imply: % 151.44/22.31 | | | (361) all_10_2 = e2 % 151.44/22.31 | | | % 151.44/22.31 | | | COMBINE_EQS: (74), (359) imply: % 151.44/22.31 | | | (362) all_52_4 = e3 % 151.44/22.31 | | | % 151.44/22.31 | | | COMBINE_EQS: (82), (361) imply: % 151.44/22.31 | | | (363) all_24_2 = e2 % 151.44/22.31 | | | % 151.44/22.31 | | | REDUCE: (135), (362) imply: % 151.44/22.31 | | | (364) ~ (all_8_2 = e3) % 151.44/22.31 | | | % 151.44/22.31 | | | REDUCE: (111), (361) imply: % 151.44/22.31 | | | (365) op(e2, e2) = all_10_1 % 151.44/22.31 | | | % 151.44/22.31 | | | REDUCE: (129), (361) imply: % 151.44/22.31 | | | (366) op(e3, e2) = all_56_0 % 151.44/22.31 | | | % 151.44/22.31 | | | REDUCE: (91), (362) imply: % 151.44/22.31 | | | (367) op(e3, e2) = e3 % 151.44/22.31 | | | % 151.44/22.31 | | | BETA: splitting (110) gives: % 151.44/22.31 | | | % 151.44/22.31 | | | Case 1: % 151.44/22.31 | | | | % 151.44/22.31 | | | | (368) ~ (all_24_2 = e2) % 151.44/22.31 | | | | % 151.44/22.31 | | | | REDUCE: (363), (368) imply: % 151.44/22.31 | | | | (369) $false % 151.44/22.31 | | | | % 151.44/22.31 | | | | CLOSE: (369) is inconsistent. % 151.44/22.31 | | | | % 151.44/22.31 | | | Case 2: % 151.44/22.31 | | | | % 151.44/22.31 | | | | (370) ~ (all_24_1 = e0) % 151.44/22.31 | | | | % 151.44/22.31 | | | | REDUCE: (95), (370) imply: % 151.44/22.31 | | | | (371) ~ (all_10_1 = e0) % 151.44/22.31 | | | | % 151.44/22.31 | | | | GROUND_INST: instantiating (49) with all_8_2, all_10_1, e2, e2, % 151.44/22.31 | | | | simplifying with (119), (365) gives: % 151.44/22.31 | | | | (372) all_10_1 = all_8_2 % 151.44/22.31 | | | | % 151.44/22.31 | | | | GROUND_INST: instantiating (49) with e3, all_56_0, e2, e3, simplifying % 151.44/22.31 | | | | with (366), (367) gives: % 151.44/22.31 | | | | (373) all_56_0 = e3 % 151.44/22.31 | | | | % 151.44/22.31 | | | | REDUCE: (101), (372) imply: % 151.44/22.31 | | | | (374) op(e3, all_8_2) = e1 % 151.44/22.31 | | | | % 151.44/22.31 | | | | BETA: splitting (3) gives: % 151.44/22.31 | | | | % 151.44/22.31 | | | | Case 1: % 151.44/22.31 | | | | | % 151.44/22.31 | | | | | (375) ~ (all_56_11 = e1) % 151.44/22.31 | | | | | % 151.44/22.31 | | | | | REDUCE: (1), (375) imply: % 151.44/22.31 | | | | | (376) ~ (all_8_2 = e1) % 151.44/22.31 | | | | | % 151.44/22.31 | | | | | BETA: splitting (139) gives: % 151.44/22.31 | | | | | % 151.44/22.31 | | | | | Case 1: % 151.44/22.31 | | | | | | % 151.44/22.31 | | | | | | (377) all_54_5 = e3 % 151.44/22.31 | | | | | | % 151.44/22.31 | | | | | | REF_CLOSE: (27), (69), (377) are inconsistent by sub-proof #737. % 151.44/22.31 | | | | | | % 151.44/22.31 | | | | | Case 2: % 151.44/22.31 | | | | | | % 151.44/22.31 | | | | | | (378) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 151.44/22.31 | | | | | | % 151.44/22.31 | | | | | | BETA: splitting (378) gives: % 151.44/22.31 | | | | | | % 151.44/22.31 | | | | | | Case 1: % 151.44/22.31 | | | | | | | % 151.44/22.31 | | | | | | | (379) all_54_5 = e2 % 151.44/22.31 | | | | | | | % 151.44/22.31 | | | | | | | COMBINE_EQS: (27), (379) imply: % 151.44/22.31 | | | | | | | (380) all_8_2 = e2 % 151.44/22.31 | | | | | | | % 151.44/22.31 | | | | | | | SIMP: (380) implies: % 151.44/22.31 | | | | | | | (381) all_8_2 = e2 % 151.44/22.31 | | | | | | | % 151.44/22.31 | | | | | | | REDUCE: (374), (381) imply: % 151.44/22.31 | | | | | | | (382) op(e3, e2) = e1 % 151.44/22.31 | | | | | | | % 151.44/22.31 | | | | | | | REF_CLOSE: (49), (118), (367), (382) are inconsistent by sub-proof % 151.44/22.31 | | | | | | | #267. % 151.44/22.31 | | | | | | | % 151.44/22.31 | | | | | | Case 2: % 151.44/22.31 | | | | | | | % 151.44/22.31 | | | | | | | (383) all_54_5 = e1 | all_54_5 = e0 % 151.44/22.31 | | | | | | | % 151.44/22.31 | | | | | | | REF_CLOSE: (27), (128), (376), (383) are inconsistent by sub-proof % 151.44/22.31 | | | | | | | #645. % 151.44/22.31 | | | | | | | % 151.44/22.31 | | | | | | End of split % 151.44/22.31 | | | | | | % 151.44/22.31 | | | | | End of split % 151.44/22.31 | | | | | % 151.44/22.31 | | | | Case 2: % 151.44/22.31 | | | | | % 151.44/22.31 | | | | | (384) all_56_13 = e2 % 151.44/22.31 | | | | | (385) all_56_11 = e1 % 151.44/22.31 | | | | | % 151.44/22.31 | | | | | REF_CLOSE: (1), (4), (9), (10), (11), (12), (13), (15), (16), (24), % 151.44/22.31 | | | | | (25), (28), (30), (31), (33), (36), (39), (40), (41), (42), % 151.44/22.31 | | | | | (44), (49), (51), (59), (60), (67), (70), (73), (74), (78), % 151.44/22.31 | | | | | (83), (85), (87), (96), (98), (101), (102), (105), (107), % 151.44/22.31 | | | | | (111), (112), (115), (120), (122), (127), (128), (129), % 151.44/22.31 | | | | | (134), (136), (141), (384), (385) are inconsistent by % 151.44/22.31 | | | | | sub-proof #266. % 151.44/22.31 | | | | | % 151.44/22.31 | | | | End of split % 151.44/22.31 | | | | % 151.44/22.31 | | | End of split % 151.44/22.31 | | | % 151.44/22.31 | | End of split % 151.44/22.31 | | % 151.44/22.31 | Case 2: % 151.44/22.31 | | % 151.44/22.31 | | (386) all_56_5 = e3 % 151.44/22.31 | | (387) all_56_1 = e1 % 151.44/22.31 | | % 151.44/22.31 | | COMBINE_EQS: (36), (387) imply: % 151.44/22.31 | | (388) all_10_2 = e1 % 151.44/22.31 | | % 151.44/22.31 | | COMBINE_EQS: (70), (386) imply: % 151.44/22.31 | | (389) all_52_8 = e3 % 151.44/22.31 | | % 151.44/22.31 | | REDUCE: (5), (389) imply: % 151.44/22.31 | | (390) ~ (all_52_4 = e3) % 151.44/22.31 | | % 151.44/22.31 | | REDUCE: (134), (388) imply: % 151.44/22.31 | | (391) ~ (all_52_4 = e1) % 151.44/22.31 | | % 151.44/22.31 | | REDUCE: (122), (389) imply: % 151.44/22.31 | | (392) ~ (all_52_12 = e3) % 151.44/22.31 | | % 151.44/22.31 | | SIMP: (392) implies: % 151.44/22.31 | | (393) ~ (all_52_12 = e3) % 151.44/22.31 | | % 151.44/22.31 | | REDUCE: (45), (389) imply: % 151.44/22.31 | | (394) ~ (all_6_2 = e3) % 151.44/22.31 | | % 151.44/22.31 | | REDUCE: (141), (388) imply: % 151.44/22.31 | | (395) ~ (all_52_12 = e1) % 151.44/22.31 | | % 151.44/22.31 | | REDUCE: (111), (388) imply: % 151.44/22.31 | | (396) op(e1, e1) = all_10_1 % 151.44/22.31 | | % 151.44/22.31 | | REDUCE: (129), (388) imply: % 151.44/22.31 | | (397) op(e3, e1) = all_56_0 % 151.44/22.31 | | % 151.44/22.31 | | REDUCE: (117), (389) imply: % 151.44/22.31 | | (398) op(e3, e1) = e3 % 151.44/22.31 | | % 151.44/22.31 | | GROUND_INST: instantiating (49) with all_6_2, all_10_1, e1, e1, simplifying % 151.44/22.31 | | with (96), (396) gives: % 151.44/22.31 | | (399) all_10_1 = all_6_2 % 151.44/22.31 | | % 151.44/22.31 | | GROUND_INST: instantiating (49) with e3, all_56_0, e1, e3, simplifying with % 151.44/22.31 | | (397), (398) gives: % 151.44/22.31 | | (400) all_56_0 = e3 % 151.44/22.31 | | % 151.44/22.31 | | BETA: splitting (3) gives: % 151.44/22.31 | | % 151.44/22.31 | | Case 1: % 151.44/22.31 | | | % 151.44/22.31 | | | (401) ~ (all_56_11 = e1) % 151.44/22.31 | | | % 151.44/22.31 | | | REDUCE: (1), (401) imply: % 151.44/22.31 | | | (402) ~ (all_8_2 = e1) % 151.44/22.31 | | | % 151.44/22.31 | | | BETA: splitting (139) gives: % 151.44/22.31 | | | % 151.44/22.31 | | | Case 1: % 151.44/22.31 | | | | % 151.44/22.31 | | | | (403) all_54_5 = e3 % 151.44/22.31 | | | | % 151.44/22.31 | | | | REF_CLOSE: (27), (69), (403) are inconsistent by sub-proof #737. % 151.44/22.31 | | | | % 151.44/22.31 | | | Case 2: % 151.44/22.31 | | | | % 151.44/22.31 | | | | (404) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 151.44/22.31 | | | | % 151.44/22.31 | | | | BETA: splitting (404) gives: % 151.44/22.31 | | | | % 151.44/22.31 | | | | Case 1: % 151.44/22.31 | | | | | % 151.44/22.31 | | | | | (405) all_54_5 = e2 % 151.44/22.31 | | | | | % 151.44/22.31 | | | | | COMBINE_EQS: (27), (405) imply: % 151.44/22.31 | | | | | (406) all_8_2 = e2 % 151.44/22.31 | | | | | % 151.44/22.31 | | | | | SIMP: (406) implies: % 151.44/22.31 | | | | | (407) all_8_2 = e2 % 151.44/22.31 | | | | | % 151.44/22.31 | | | | | REDUCE: (135), (407) imply: % 151.44/22.31 | | | | | (408) ~ (all_52_4 = e2) % 151.44/22.31 | | | | | % 151.44/22.31 | | | | | BETA: splitting (99) gives: % 151.44/22.31 | | | | | % 151.44/22.31 | | | | | Case 1: % 151.44/22.31 | | | | | | % 151.44/22.31 | | | | | | (409) all_54_1 = e3 % 151.44/22.31 | | | | | | % 151.44/22.31 | | | | | | REF_CLOSE: (38), (390), (409) are inconsistent by sub-proof #722. % 151.44/22.31 | | | | | | % 151.44/22.31 | | | | | Case 2: % 151.44/22.31 | | | | | | % 151.44/22.31 | | | | | | (410) all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0 % 151.44/22.31 | | | | | | % 151.44/22.31 | | | | | | BETA: splitting (410) gives: % 151.44/22.31 | | | | | | % 151.44/22.31 | | | | | | Case 1: % 151.44/22.31 | | | | | | | % 151.44/22.31 | | | | | | | (411) all_54_1 = e2 % 151.44/22.31 | | | | | | | % 151.44/22.31 | | | | | | | REF_CLOSE: (38), (408), (411) are inconsistent by sub-proof #721. % 151.44/22.31 | | | | | | | % 151.44/22.31 | | | | | | Case 2: % 151.44/22.31 | | | | | | | % 151.44/22.31 | | | | | | | (412) all_54_1 = e1 | all_54_1 = e0 % 151.44/22.31 | | | | | | | % 151.44/22.31 | | | | | | | BETA: splitting (412) gives: % 151.44/22.31 | | | | | | | % 151.44/22.31 | | | | | | | Case 1: % 151.44/22.31 | | | | | | | | % 151.44/22.31 | | | | | | | | (413) all_54_1 = e1 % 151.44/22.31 | | | | | | | | % 151.44/22.31 | | | | | | | | REF_CLOSE: (38), (391), (413) are inconsistent by sub-proof % 151.44/22.31 | | | | | | | | #720. % 151.44/22.31 | | | | | | | | % 151.44/22.31 | | | | | | | Case 2: % 151.44/22.31 | | | | | | | | % 151.44/22.31 | | | | | | | | (414) all_54_1 = e0 % 151.44/22.31 | | | | | | | | % 151.44/22.31 | | | | | | | | COMBINE_EQS: (38), (414) imply: % 151.44/22.31 | | | | | | | | (415) all_52_4 = e0 % 151.44/22.31 | | | | | | | | % 151.44/22.31 | | | | | | | | SIMP: (415) implies: % 151.44/22.31 | | | | | | | | (416) all_52_4 = e0 % 151.44/22.31 | | | | | | | | % 151.44/22.31 | | | | | | | | REDUCE: (120), (416) imply: % 151.44/22.31 | | | | | | | | (417) ~ (all_52_12 = e0) % 151.44/22.31 | | | | | | | | % 151.44/22.31 | | | | | | | | SIMP: (417) implies: % 151.44/22.31 | | | | | | | | (418) ~ (all_52_12 = e0) % 151.44/22.31 | | | | | | | | % 151.44/22.31 | | | | | | | | BETA: splitting (12) gives: % 151.44/22.31 | | | | | | | | % 151.44/22.31 | | | | | | | | Case 1: % 151.44/22.31 | | | | | | | | | % 151.44/22.31 | | | | | | | | | (419) all_54_3 = e3 % 151.44/22.31 | | | | | | | | | % 151.44/22.31 | | | | | | | | | REF_CLOSE: (51), (393), (419) are inconsistent by sub-proof % 151.44/22.31 | | | | | | | | | #659. % 151.44/22.31 | | | | | | | | | % 151.44/22.31 | | | | | | | | Case 2: % 151.44/22.31 | | | | | | | | | % 151.44/22.31 | | | | | | | | | (420) all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0 % 151.44/22.31 | | | | | | | | | % 151.44/22.31 | | | | | | | | | BETA: splitting (420) gives: % 151.44/22.31 | | | | | | | | | % 151.44/22.31 | | | | | | | | | Case 1: % 151.44/22.31 | | | | | | | | | | % 151.44/22.31 | | | | | | | | | | (421) all_54_3 = e2 % 151.44/22.31 | | | | | | | | | | % 151.44/22.31 | | | | | | | | | | COMBINE_EQS: (51), (421) imply: % 151.44/22.31 | | | | | | | | | | (422) all_52_12 = e2 % 151.44/22.31 | | | | | | | | | | % 151.44/22.31 | | | | | | | | | | SIMP: (422) implies: % 151.44/22.31 | | | | | | | | | | (423) all_52_12 = e2 % 151.44/22.31 | | | | | | | | | | % 151.44/22.31 | | | | | | | | | | REDUCE: (116), (423) imply: % 151.44/22.31 | | | | | | | | | | (424) ~ (all_52_14 = e2) % 151.44/22.31 | | | | | | | | | | % 151.44/22.31 | | | | | | | | | | SIMP: (424) implies: % 151.44/22.31 | | | | | | | | | | (425) ~ (all_52_14 = e2) % 151.44/22.31 | | | | | | | | | | % 151.44/22.31 | | | | | | | | | | REDUCE: (85), (423) imply: % 151.44/22.31 | | | | | | | | | | (426) op(e3, e0) = e2 % 151.44/22.31 | | | | | | | | | | % 151.44/22.31 | | | | | | | | | | BETA: splitting (125) gives: % 151.44/22.31 | | | | | | | | | | % 151.44/22.31 | | | | | | | | | | Case 1: % 151.44/22.31 | | | | | | | | | | | % 151.44/22.31 | | | | | | | | | | | (427) ~ (all_56_21 = e0) % 151.44/22.31 | | | | | | | | | | | % 151.44/22.31 | | | | | | | | | | | REDUCE: (32), (427) imply: % 151.44/22.31 | | | | | | | | | | | (428) ~ (all_6_2 = e0) % 151.44/22.31 | | | | | | | | | | | % 151.44/22.31 | | | | | | | | | | | REF_CLOSE: (11), (23), (28), (33), (49), (83), (96), (101), % 151.44/22.31 | | | | | | | | | | | (103), (113), (396), (397), (398), (428) are % 151.44/22.31 | | | | | | | | | | | inconsistent by sub-proof #298. % 151.44/22.31 | | | | | | | | | | | % 151.44/22.31 | | | | | | | | | | Case 2: % 151.44/22.31 | | | | | | | | | | | % 151.44/22.31 | | | | | | | | | | | (429) all_56_23 = e1 % 151.44/22.31 | | | | | | | | | | | (430) all_56_21 = e0 % 151.44/22.31 | | | | | | | | | | | % 151.44/22.31 | | | | | | | | | | | COMBINE_EQS: (32), (430) imply: % 151.44/22.31 | | | | | | | | | | | (431) all_6_2 = e0 % 151.44/22.31 | | | | | | | | | | | % 151.44/22.31 | | | | | | | | | | | COMBINE_EQS: (93), (429) imply: % 151.44/22.31 | | | | | | | | | | | (432) all_52_14 = e1 % 151.44/22.31 | | | | | | | | | | | % 151.44/22.31 | | | | | | | | | | | SIMP: (432) implies: % 151.44/22.31 | | | | | | | | | | | (433) all_52_14 = e1 % 151.44/22.31 | | | | | | | | | | | % 151.44/22.31 | | | | | | | | | | | REDUCE: (425), (433) imply: % 151.44/22.31 | | | | | | | | | | | (434) ~ (e2 = e1) % 151.44/22.31 | | | | | | | | | | | % 151.44/22.31 | | | | | | | | | | | SIMP: (434) implies: % 151.44/22.31 | | | | | | | | | | | (435) ~ (e2 = e1) % 151.44/22.31 | | | | | | | | | | | % 151.44/22.31 | | | | | | | | | | | REDUCE: (96), (431) imply: % 151.44/22.31 | | | | | | | | | | | (436) op(e1, e1) = e0 % 151.44/22.31 | | | | | | | | | | | % 151.44/22.31 | | | | | | | | | | | REF_CLOSE: (49), (101), (396), (426), (435), (436) are % 151.44/22.31 | | | | | | | | | | | inconsistent by sub-proof #291. % 151.44/22.31 | | | | | | | | | | | % 151.44/22.31 | | | | | | | | | | End of split % 151.44/22.31 | | | | | | | | | | % 151.44/22.31 | | | | | | | | | Case 2: % 151.44/22.31 | | | | | | | | | | % 151.44/22.31 | | | | | | | | | | (437) all_54_3 = e1 | all_54_3 = e0 % 151.44/22.31 | | | | | | | | | | % 151.44/22.31 | | | | | | | | | | REF_CLOSE: (51), (395), (418), (437) are inconsistent by % 151.44/22.31 | | | | | | | | | | sub-proof #655. % 151.44/22.31 | | | | | | | | | | % 151.44/22.31 | | | | | | | | | End of split % 151.44/22.31 | | | | | | | | | % 151.44/22.31 | | | | | | | | End of split % 151.44/22.31 | | | | | | | | % 151.44/22.31 | | | | | | | End of split % 151.44/22.31 | | | | | | | % 151.44/22.31 | | | | | | End of split % 151.44/22.31 | | | | | | % 151.44/22.31 | | | | | End of split % 151.44/22.31 | | | | | % 151.44/22.31 | | | | Case 2: % 151.44/22.31 | | | | | % 151.44/22.31 | | | | | (438) all_54_5 = e1 | all_54_5 = e0 % 151.44/22.31 | | | | | % 151.44/22.31 | | | | | REF_CLOSE: (27), (128), (402), (438) are inconsistent by sub-proof % 151.44/22.31 | | | | | #645. % 151.44/22.31 | | | | | % 151.44/22.31 | | | | End of split % 151.44/22.31 | | | | % 151.44/22.31 | | | End of split % 151.44/22.31 | | | % 151.44/22.31 | | Case 2: % 151.44/22.31 | | | % 151.44/22.31 | | | (439) all_56_13 = e2 % 151.44/22.31 | | | (440) all_56_11 = e1 % 151.44/22.31 | | | % 151.44/22.31 | | | REF_CLOSE: (1), (4), (9), (10), (11), (12), (13), (15), (16), (24), (25), % 151.44/22.31 | | | (28), (30), (31), (33), (36), (39), (40), (41), (42), (44), % 151.44/22.31 | | | (49), (51), (59), (60), (67), (70), (73), (74), (78), (83), % 151.44/22.31 | | | (85), (87), (96), (98), (101), (102), (105), (107), (111), % 151.44/22.31 | | | (112), (115), (120), (122), (127), (128), (129), (134), (136), % 151.44/22.31 | | | (141), (439), (440) are inconsistent by sub-proof #266. % 151.44/22.31 | | | % 151.44/22.31 | | End of split % 151.44/22.31 | | % 151.44/22.31 | End of split % 151.44/22.31 | % 151.44/22.31 End of proof % 151.44/22.31 % 151.44/22.31 Sub-proof #266 shows that the following formulas are inconsistent: % 151.44/22.31 ---------------------------------------------------------------- % 151.44/22.31 (1) all_56_11 = all_8_2 % 151.44/22.31 (2) ~ (all_52_11 = all_6_2) % 151.44/22.31 (3) ~ (all_8_1 = e1) % 151.44/22.31 (4) ~ (all_56_31 = e1) | all_56_29 = e0 % 151.44/22.31 (5) all_54_10 = all_6_2 % 151.44/22.31 (6) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0 % 151.44/22.31 (7) ~ (all_6_1 = e2) % 151.44/22.31 (8) all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2 % 151.44/22.31 (9) all_54_0 = all_10_2 % 151.44/22.31 (10) ~ (all_8_1 = e3) % 151.44/22.31 (11) op(e0, e0) = all_4_2 % 151.44/22.31 (12) ~ (all_6_1 = e3) % 151.44/22.31 (13) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 151.44/22.31 (14) all_54_15 = all_4_2 % 151.44/22.31 (15) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 151.44/22.31 (16) all_56_1 = all_10_2 % 151.44/22.31 (17) all_58_9 = all_52_12 % 151.44/22.31 (18) ~ (all_56_1 = e1) | all_56_5 = e3 % 151.44/22.31 (19) all_58_1 = all_52_4 % 151.44/22.31 (20) all_58_13 = all_52_7 % 151.44/22.31 (21) op(e3, e3) = all_10_2 % 151.44/22.31 (22) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 151.44/22.31 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 151.44/22.31 (23) all_54_3 = all_52_12 % 151.44/22.31 (24) all_56_13 = all_52_9 % 151.44/22.31 (25) ~ (all_52_7 = all_4_2) % 151.44/22.31 (26) all_56_11 = e1 % 151.44/22.31 (27) ~ (all_56_1 = e2) | all_56_3 = e3 % 151.44/22.31 (28) all_56_5 = all_52_8 % 151.44/22.31 (29) all_58_3 = all_8_2 % 151.44/22.31 (30) all_56_3 = all_52_4 % 151.44/22.31 (31) all_56_31 = all_4_2 % 151.44/22.31 (32) op(all_6_2, all_6_2) = all_6_1 % 151.44/22.31 (33) op(e3, e0) = all_52_12 % 151.44/22.31 (34) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0 % 151.44/22.31 (35) op(e1, e1) = all_6_2 % 151.44/22.31 (36) all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1 % 151.44/22.31 (37) op(e3, all_10_1) = e1 % 151.44/22.31 (38) all_56_29 = all_52_11 % 151.44/22.31 (39) ~ (all_52_9 = all_6_2) % 151.44/22.31 (40) all_58_7 = all_52_6 % 151.44/22.31 (41) op(all_10_2, all_10_2) = all_10_1 % 151.44/22.31 (42) all_58_0 = all_10_2 % 151.44/22.31 (43) all_58_1 = e0 | all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0 % 151.44/22.31 (44) ~ (all_52_4 = all_52_12) % 151.44/22.31 (45) ~ (all_52_8 = all_52_12) % 151.44/22.31 (46) ~ (all_52_6 = all_6_2) % 151.44/22.31 (47) ~ (all_8_2 = e0) % 151.44/22.31 (48) op(e3, all_10_2) = all_56_0 % 151.44/22.31 (49) all_56_13 = e2 % 151.44/22.31 (50) ~ (all_52_4 = all_10_2) % 151.44/22.31 (51) op(all_8_2, all_8_2) = all_8_1 % 151.44/22.31 (52) ~ (all_52_12 = all_10_2) % 151.44/22.31 % 151.44/22.31 Begin of proof % 151.44/22.31 | % 151.44/22.31 | COMBINE_EQS: (1), (26) imply: % 151.44/22.31 | (53) all_8_2 = e1 % 151.44/22.31 | % 151.44/22.31 | COMBINE_EQS: (24), (49) imply: % 151.44/22.31 | (54) all_52_9 = e2 % 151.44/22.31 | % 151.44/22.31 | REDUCE: (39), (54) imply: % 151.44/22.31 | (55) ~ (all_6_2 = e2) % 151.44/22.31 | % 151.44/22.31 | SIMP: (55) implies: % 151.44/22.31 | (56) ~ (all_6_2 = e2) % 151.44/22.31 | % 151.44/22.31 | REDUCE: (51), (53) imply: % 151.44/22.31 | (57) op(e1, e1) = all_8_1 % 151.44/22.31 | % 151.44/22.31 | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13), % 151.44/22.31 | (14), (15), (16), (17), (18), (19), (20), (21), (22), (23), (25), % 151.44/22.31 | (27), (28), (29), (30), (31), (32), (33), (34), (35), (36), (37), % 151.44/22.31 | (38), (40), (41), (42), (43), (44), (45), (46), (47), (48), (50), % 151.44/22.31 | (52), (56), (57) are inconsistent by sub-proof #268. % 151.44/22.31 | % 151.44/22.31 End of proof % 151.44/22.31 % 151.44/22.31 Sub-proof #267 shows that the following formulas are inconsistent: % 151.44/22.31 ---------------------------------------------------------------- % 151.44/22.31 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 151.44/22.31 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 151.44/22.31 (2) op(e3, e2) = e3 % 151.44/22.31 (3) op(e3, e2) = e1 % 151.44/22.31 (4) ~ (e3 = e1) % 151.44/22.31 % 151.44/22.31 Begin of proof % 151.44/22.31 | % 151.44/22.31 | GROUND_INST: instantiating (1) with e3, e1, e2, e3, simplifying with (2), (3) % 151.44/22.31 | gives: % 151.44/22.31 | (5) e3 = e1 % 151.44/22.31 | % 151.44/22.31 | REDUCE: (4), (5) imply: % 151.44/22.31 | (6) $false % 151.44/22.31 | % 151.44/22.31 | CLOSE: (6) is inconsistent. % 151.44/22.31 | % 151.44/22.31 End of proof % 151.44/22.31 % 151.44/22.31 Sub-proof #268 shows that the following formulas are inconsistent: % 151.44/22.31 ---------------------------------------------------------------- % 151.44/22.31 (1) ~ (all_52_11 = all_6_2) % 151.44/22.31 (2) ~ (all_8_1 = e1) % 151.44/22.31 (3) ~ (all_56_31 = e1) | all_56_29 = e0 % 151.44/22.31 (4) all_54_10 = all_6_2 % 151.44/22.31 (5) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0 % 151.44/22.31 (6) ~ (all_6_1 = e2) % 151.44/22.31 (7) all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2 % 151.44/22.31 (8) all_54_0 = all_10_2 % 151.44/22.31 (9) ~ (all_8_1 = e3) % 151.44/22.31 (10) op(e0, e0) = all_4_2 % 151.44/22.31 (11) ~ (all_6_1 = e3) % 151.44/22.31 (12) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 151.44/22.31 (13) all_54_15 = all_4_2 % 151.44/22.31 (14) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 151.44/22.31 (15) all_56_1 = all_10_2 % 151.44/22.31 (16) all_58_9 = all_52_12 % 151.44/22.31 (17) ~ (all_56_1 = e1) | all_56_5 = e3 % 151.44/22.31 (18) all_58_1 = all_52_4 % 151.44/22.31 (19) all_58_13 = all_52_7 % 151.44/22.31 (20) op(e3, e3) = all_10_2 % 151.44/22.31 (21) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 151.44/22.31 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 151.44/22.31 (22) all_54_3 = all_52_12 % 151.44/22.31 (23) ~ (all_52_7 = all_4_2) % 151.44/22.31 (24) ~ (all_56_1 = e2) | all_56_3 = e3 % 151.44/22.31 (25) all_56_5 = all_52_8 % 151.44/22.31 (26) all_58_3 = all_8_2 % 151.44/22.31 (27) all_56_3 = all_52_4 % 151.44/22.31 (28) all_56_31 = all_4_2 % 151.44/22.31 (29) op(all_6_2, all_6_2) = all_6_1 % 151.44/22.31 (30) op(e3, e0) = all_52_12 % 151.44/22.31 (31) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0 % 151.44/22.31 (32) op(e1, e1) = all_8_1 % 151.44/22.31 (33) op(e1, e1) = all_6_2 % 151.44/22.31 (34) all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1 % 151.44/22.31 (35) op(e3, all_10_1) = e1 % 151.44/22.31 (36) all_56_29 = all_52_11 % 151.44/22.31 (37) ~ (all_6_2 = e2) % 151.44/22.31 (38) all_58_7 = all_52_6 % 151.44/22.31 (39) op(all_10_2, all_10_2) = all_10_1 % 151.44/22.31 (40) all_58_0 = all_10_2 % 151.44/22.31 (41) all_58_1 = e0 | all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0 % 151.44/22.31 (42) ~ (all_52_4 = all_52_12) % 151.44/22.31 (43) ~ (all_52_8 = all_52_12) % 151.44/22.31 (44) ~ (all_52_6 = all_6_2) % 151.44/22.31 (45) ~ (all_8_2 = e0) % 151.44/22.31 (46) op(e3, all_10_2) = all_56_0 % 151.44/22.31 (47) ~ (all_52_4 = all_10_2) % 151.44/22.31 (48) ~ (all_52_12 = all_10_2) % 151.44/22.31 % 151.44/22.31 Begin of proof % 151.44/22.31 | % 151.44/22.31 | GROUND_INST: instantiating (21) with all_6_2, all_8_1, e1, e1, simplifying % 151.44/22.31 | with (32), (33) gives: % 151.44/22.31 | (49) all_8_1 = all_6_2 % 151.44/22.31 | % 151.44/22.31 | REDUCE: (9), (49) imply: % 151.44/22.31 | (50) ~ (all_6_2 = e3) % 151.44/22.31 | % 151.44/22.31 | REDUCE: (2), (49) imply: % 151.44/22.31 | (51) ~ (all_6_2 = e1) % 151.44/22.31 | % 151.44/22.31 | BETA: splitting (14) gives: % 151.44/22.31 | % 151.44/22.31 | Case 1: % 151.44/22.31 | | % 151.44/22.31 | | (52) all_54_10 = e3 % 151.44/22.31 | | % 151.44/22.31 | | REF_CLOSE: (4), (50), (52) are inconsistent by sub-proof #736. % 151.44/22.31 | | % 151.44/22.31 | Case 2: % 151.44/22.31 | | % 151.44/22.31 | | (53) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 151.44/22.31 | | % 151.44/22.31 | | BETA: splitting (53) gives: % 151.44/22.31 | | % 151.44/22.31 | | Case 1: % 151.44/22.31 | | | % 151.44/22.31 | | | (54) all_54_10 = e2 % 151.44/22.31 | | | % 151.44/22.31 | | | REF_CLOSE: (4), (37), (54) are inconsistent by sub-proof #735. % 151.44/22.31 | | | % 151.44/22.31 | | Case 2: % 151.44/22.31 | | | % 151.44/22.31 | | | (55) all_54_10 = e1 | all_54_10 = e0 % 151.44/22.31 | | | % 151.44/22.31 | | | BETA: splitting (55) gives: % 151.44/22.31 | | | % 151.44/22.31 | | | Case 1: % 151.44/22.31 | | | | % 151.44/22.31 | | | | (56) all_54_10 = e1 % 151.44/22.31 | | | | % 151.44/22.31 | | | | REF_CLOSE: (4), (51), (56) are inconsistent by sub-proof #606. % 151.44/22.31 | | | | % 151.44/22.31 | | | Case 2: % 151.44/22.31 | | | | % 151.44/22.31 | | | | (57) all_54_10 = e0 % 151.44/22.31 | | | | % 151.44/22.31 | | | | COMBINE_EQS: (4), (57) imply: % 151.44/22.31 | | | | (58) all_6_2 = e0 % 151.44/22.31 | | | | % 151.44/22.31 | | | | SIMP: (58) implies: % 151.44/22.31 | | | | (59) all_6_2 = e0 % 151.44/22.31 | | | | % 151.44/22.31 | | | | REDUCE: (1), (59) imply: % 151.44/22.31 | | | | (60) ~ (all_52_11 = e0) % 151.44/22.31 | | | | % 151.44/22.31 | | | | BETA: splitting (3) gives: % 151.44/22.31 | | | | % 151.44/22.31 | | | | Case 1: % 151.44/22.31 | | | | | % 151.44/22.31 | | | | | (61) ~ (all_56_31 = e1) % 151.44/22.31 | | | | | % 151.44/22.31 | | | | | REDUCE: (28), (61) imply: % 151.44/22.31 | | | | | (62) ~ (all_4_2 = e1) % 151.44/22.31 | | | | | % 151.44/22.31 | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (10), (11), (12), (13), (15), % 151.44/22.31 | | | | | (16), (17), (18), (19), (20), (21), (22), (23), (24), (25), % 151.44/22.31 | | | | | (26), (27), (29), (30), (31), (33), (34), (35), (38), (39), % 151.44/22.31 | | | | | (40), (41), (42), (43), (44), (45), (46), (47), (48), (51), % 151.44/22.31 | | | | | (55), (62) are inconsistent by sub-proof #287. % 151.44/22.31 | | | | | % 151.44/22.31 | | | | Case 2: % 151.44/22.31 | | | | | % 151.44/22.31 | | | | | (63) all_56_29 = e0 % 151.44/22.31 | | | | | % 151.44/22.31 | | | | | REF_CLOSE: (36), (60), (63) are inconsistent by sub-proof #269. % 151.44/22.31 | | | | | % 151.44/22.31 | | | | End of split % 151.44/22.31 | | | | % 151.44/22.31 | | | End of split % 151.44/22.31 | | | % 151.44/22.31 | | End of split % 151.44/22.31 | | % 151.44/22.31 | End of split % 151.44/22.31 | % 151.44/22.31 End of proof % 151.44/22.31 % 151.44/22.31 Sub-proof #269 shows that the following formulas are inconsistent: % 151.44/22.31 ---------------------------------------------------------------- % 151.44/22.31 (1) all_56_29 = all_52_11 % 151.44/22.31 (2) all_56_29 = e0 % 151.44/22.31 (3) ~ (all_52_11 = e0) % 151.44/22.31 % 151.44/22.31 Begin of proof % 151.44/22.31 | % 151.44/22.31 | COMBINE_EQS: (1), (2) imply: % 151.44/22.31 | (4) all_52_11 = e0 % 151.44/22.31 | % 151.44/22.31 | SIMP: (4) implies: % 151.44/22.31 | (5) all_52_11 = e0 % 151.44/22.31 | % 151.44/22.31 | REDUCE: (3), (5) imply: % 151.44/22.31 | (6) $false % 151.44/22.31 | % 151.44/22.31 | CLOSE: (6) is inconsistent. % 151.44/22.31 | % 151.44/22.31 End of proof % 151.44/22.31 % 151.44/22.31 Sub-proof #270 shows that the following formulas are inconsistent: % 151.44/22.31 ---------------------------------------------------------------- % 151.44/22.31 (1) all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0 % 151.44/22.31 (2) ~ (all_52_2 = e0) % 151.44/22.31 (3) ~ (all_52_2 = e1) % 151.44/22.31 (4) ~ (all_52_2 = e2) % 151.44/22.31 (5) all_54_8 = all_52_2 % 151.44/22.31 % 151.44/22.31 Begin of proof % 151.44/22.31 | % 151.44/22.31 | BETA: splitting (1) gives: % 151.44/22.31 | % 151.44/22.31 | Case 1: % 151.44/22.31 | | % 151.44/22.31 | | (6) all_54_8 = e2 % 151.44/22.31 | | % 151.44/22.31 | | REF_CLOSE: (4), (5), (6) are inconsistent by sub-proof #666. % 151.44/22.31 | | % 151.44/22.31 | Case 2: % 151.44/22.31 | | % 151.44/22.31 | | (7) all_54_8 = e1 | all_54_8 = e0 % 151.44/22.31 | | % 151.44/22.31 | | REF_CLOSE: (2), (3), (5), (7) are inconsistent by sub-proof #664. % 151.44/22.31 | | % 151.44/22.31 | End of split % 151.44/22.31 | % 151.44/22.31 End of proof % 151.44/22.31 % 151.44/22.31 Sub-proof #271 shows that the following formulas are inconsistent: % 151.44/22.31 ---------------------------------------------------------------- % 151.44/22.31 (1) all_58_11 = e2 % 151.44/22.31 (2) e2 = e1 % 151.44/22.31 (3) ~ (all_4_2 = e2) % 151.44/22.31 (4) ~ (e2 = e1) % 151.44/22.31 (5) all_58_15 = all_4_2 % 151.44/22.31 (6) all_58_11 = e2 | all_58_15 = e2 % 151.44/22.31 % 151.44/22.31 Begin of proof % 151.44/22.31 | % 151.44/22.31 | SIMP: (2) implies: % 151.44/22.31 | (7) e2 = e1 % 151.44/22.31 | % 151.44/22.31 | COMBINE_EQS: (1), (7) imply: % 151.44/22.31 | (8) all_58_11 = e1 % 151.44/22.31 | % 151.44/22.31 | REF_CLOSE: (3), (4), (5), (6), (8) are inconsistent by sub-proof #272. % 151.44/22.31 | % 151.44/22.31 End of proof % 151.44/22.31 % 151.44/22.31 Sub-proof #272 shows that the following formulas are inconsistent: % 151.44/22.31 ---------------------------------------------------------------- % 151.44/22.31 (1) all_58_11 = e1 % 151.44/22.31 (2) ~ (all_4_2 = e2) % 151.44/22.31 (3) ~ (e2 = e1) % 151.44/22.31 (4) all_58_15 = all_4_2 % 151.44/22.31 (5) all_58_11 = e2 | all_58_15 = e2 % 151.44/22.31 % 151.44/22.31 Begin of proof % 151.44/22.31 | % 151.44/22.31 | BETA: splitting (5) gives: % 151.44/22.31 | % 151.44/22.31 | Case 1: % 151.44/22.31 | | % 151.44/22.31 | | (6) all_58_11 = e2 % 151.44/22.31 | | % 151.44/22.31 | | COMBINE_EQS: (1), (6) imply: % 151.44/22.31 | | (7) e2 = e1 % 151.44/22.31 | | % 151.44/22.31 | | SIMP: (7) implies: % 151.44/22.31 | | (8) e2 = e1 % 151.44/22.31 | | % 151.44/22.31 | | REDUCE: (3), (8) imply: % 151.44/22.31 | | (9) $false % 151.44/22.31 | | % 151.44/22.31 | | CLOSE: (9) is inconsistent. % 151.44/22.31 | | % 151.44/22.31 | Case 2: % 151.44/22.31 | | % 151.44/22.31 | | (10) all_58_15 = e2 % 151.44/22.31 | | % 151.44/22.31 | | COMBINE_EQS: (4), (10) imply: % 151.44/22.31 | | (11) all_4_2 = e2 % 151.44/22.31 | | % 151.44/22.31 | | REDUCE: (2), (11) imply: % 151.44/22.31 | | (12) $false % 151.44/22.31 | | % 151.44/22.31 | | CLOSE: (12) is inconsistent. % 151.44/22.31 | | % 151.44/22.31 | End of split % 151.44/22.31 | % 151.44/22.31 End of proof % 151.44/22.31 % 151.44/22.31 Sub-proof #273 shows that the following formulas are inconsistent: % 151.44/22.31 ---------------------------------------------------------------- % 151.44/22.31 (1) all_58_6 = all_52_2 % 151.44/22.31 (2) all_58_6 = e0 % 151.44/22.31 (3) ~ (all_52_2 = e0) % 151.44/22.31 % 151.44/22.31 Begin of proof % 151.44/22.31 | % 151.44/22.31 | COMBINE_EQS: (1), (2) imply: % 151.44/22.31 | (4) all_52_2 = e0 % 151.44/22.31 | % 151.44/22.31 | SIMP: (4) implies: % 151.44/22.31 | (5) all_52_2 = e0 % 151.44/22.31 | % 151.44/22.31 | REDUCE: (3), (5) imply: % 151.44/22.31 | (6) $false % 151.44/22.31 | % 151.44/22.31 | CLOSE: (6) is inconsistent. % 151.44/22.31 | % 151.44/22.31 End of proof % 151.44/22.31 % 151.44/22.31 Sub-proof #274 shows that the following formulas are inconsistent: % 151.44/22.31 ---------------------------------------------------------------- % 151.44/22.31 (1) all_56_11 = all_8_2 % 151.44/22.31 (2) ~ (all_56_11 = e1) | all_56_13 = e2 % 151.44/22.31 (3) ~ (all_52_11 = all_6_2) % 151.44/22.31 (4) all_54_9 = all_52_6 % 151.44/22.31 (5) all_54_10 = all_6_2 % 151.44/22.31 (6) ~ (all_56_21 = e2) | all_56_19 = e1 % 151.44/22.31 (7) ~ (all_52_14 = all_4_2) % 151.44/22.31 (8) ~ (all_52_9 = all_8_2) % 151.44/22.31 (9) ~ (all_8_1 = e3) % 151.44/22.31 (10) op(e0, e0) = all_4_2 % 151.44/22.31 (11) all_58_6 = e0 | all_58_7 = e0 | all_58_8 = e0 | all_58_11 = e0 % 151.44/22.31 (12) all_58_4 = all_52_8 % 151.44/22.31 (13) ~ (all_52_6 = all_52_14) % 151.44/22.31 (14) ~ (all_6_0 = e2) % 151.44/22.31 (15) all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1 % 151.44/22.31 (16) all_56_21 = all_6_2 % 151.44/22.31 (17) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 151.44/22.31 (18) ~ (all_52_7 = all_8_2) % 151.44/22.31 (19) all_56_1 = all_10_2 % 151.44/22.31 (20) all_58_5 = all_52_9 % 151.44/22.31 (21) all_58_9 = all_52_12 % 151.44/22.31 (22) all_58_1 = all_52_4 % 151.44/22.31 (23) all_58_13 = all_52_7 % 151.44/22.31 (24) op(e2, all_8_2) = all_56_10 % 151.44/22.31 (25) op(e3, e3) = all_10_2 % 151.44/22.31 (26) ~ (all_52_6 = all_6_0) % 151.44/22.31 (27) ~ (all_56_21 = e3) | all_56_17 = e1 % 151.44/22.31 (28) ~ (e1 = e0) % 151.44/22.31 (29) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 151.44/22.31 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 151.44/22.31 (30) ~ (all_52_3 = all_10_2) % 151.44/22.31 (31) all_36_0 = all_6_0 % 151.44/22.31 (32) ~ (all_6_0 = all_6_2) % 151.44/22.31 (33) all_56_13 = all_52_9 % 151.44/22.31 (34) ~ (all_4_2 = e1) % 151.44/22.31 (35) all_54_8 = all_6_0 % 151.44/22.31 (36) all_58_8 = all_6_2 % 151.44/22.31 (37) ~ (all_52_14 = all_6_0) % 151.44/22.31 (38) op(all_4_2, all_4_2) = all_4_1 % 151.44/22.31 (39) all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1 % 151.44/22.31 (40) all_58_3 = all_8_2 % 151.44/22.31 (41) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0 % 151.44/22.31 (42) all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1 % 151.44/22.31 (43) all_56_31 = all_4_2 % 151.44/22.31 (44) all_58_11 = all_52_14 % 151.44/22.31 (45) all_36_2 = all_6_2 % 151.44/22.32 (46) all_56_1 = e3 | all_56_11 = e2 | all_56_21 = e1 | all_56_31 = e0 % 151.44/22.32 (47) all_56_23 = all_52_14 % 151.44/22.32 (48) all_58_6 = all_6_0 % 151.44/22.32 (49) op(e1, e1) = all_6_2 % 151.44/22.32 (50) ~ (all_52_6 = all_8_2) % 151.44/22.32 (51) all_58_15 = all_4_2 % 151.44/22.32 (52) ~ (all_4_2 = e3) % 151.44/22.32 (53) all_58_7 = all_52_6 % 151.44/22.32 (54) op(e1, all_6_2) = all_56_20 % 151.44/22.32 (55) all_56_17 = all_6_0 % 151.44/22.32 (56) op(e2, e2) = all_8_2 % 151.44/22.32 (57) ~ (all_36_0 = e0) | ~ (all_36_2 = e2) % 151.44/22.32 (58) ~ (all_52_4 = all_52_12) % 151.44/22.32 (59) ~ (all_52_8 = all_52_12) % 151.44/22.32 (60) ~ (all_56_21 = e0) | all_56_23 = e1 % 151.44/22.32 (61) op(e0, all_4_2) = all_56_30 % 151.44/22.32 (62) ~ (all_52_6 = all_6_2) % 151.44/22.32 (63) op(all_6_2, all_6_2) = e3 % 151.44/22.32 (64) ~ (all_52_14 = all_6_2) % 151.44/22.32 (65) ~ (e2 = e0) % 151.44/22.32 (66) op(e1, all_52_11) = all_56_28 % 151.44/22.32 (67) all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3 % 151.44/22.32 (68) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0 % 151.44/22.32 (69) ~ (all_10_2 = all_6_0) % 151.44/22.32 (70) op(all_8_2, all_8_2) = all_8_1 % 151.44/22.32 (71) all_58_14 = all_52_11 % 151.44/22.32 (72) all_56_19 = all_52_6 % 151.44/22.32 (73) ~ (all_52_12 = all_10_2) % 151.44/22.32 (74) all_58_12 = all_52_3 % 151.44/22.32 (75) all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3 % 151.44/22.32 % 151.44/22.32 Begin of proof % 151.44/22.32 | % 151.44/22.32 | BETA: splitting (6) gives: % 151.44/22.32 | % 151.44/22.32 | Case 1: % 151.44/22.32 | | % 151.44/22.32 | | (76) ~ (all_56_21 = e2) % 151.44/22.32 | | % 151.44/22.32 | | REDUCE: (16), (76) imply: % 151.44/22.32 | | (77) ~ (all_6_2 = e2) % 151.44/22.32 | | % 151.44/22.32 | | REF_CLOSE: (1), (2), (3), (4), (5), (8), (9), (10), (12), (13), (14), (15), % 151.44/22.32 | | (16), (17), (18), (19), (20), (21), (22), (23), (25), (26), (27), % 151.44/22.32 | | (29), (30), (32), (33), (34), (35), (36), (37), (38), (39), (40), % 151.44/22.32 | | (41), (42), (43), (44), (46), (47), (49), (50), (51), (52), (53), % 151.44/22.32 | | (54), (55), (58), (59), (60), (61), (62), (63), (64), (66), (67), % 151.44/22.32 | | (68), (69), (70), (71), (73), (74), (75), (77) are inconsistent % 151.44/22.32 | | by sub-proof #275. % 151.44/22.32 | | % 151.44/22.32 | Case 2: % 151.44/22.32 | | % 151.44/22.32 | | (78) all_56_21 = e2 % 151.44/22.32 | | (79) all_56_19 = e1 % 151.44/22.32 | | % 151.44/22.32 | | COMBINE_EQS: (72), (79) imply: % 151.44/22.32 | | (80) all_52_6 = e1 % 151.44/22.32 | | % 151.44/22.32 | | REF_CLOSE: (1), (7), (11), (16), (19), (24), (26), (28), (29), (31), (32), % 151.44/22.32 | | (35), (36), (37), (43), (44), (45), (46), (48), (53), (56), (57), % 151.44/22.32 | | (62), (63), (65), (68), (69), (70), (78), (80) are inconsistent % 151.44/22.32 | | by sub-proof #431. % 151.44/22.32 | | % 151.44/22.32 | End of split % 151.44/22.32 | % 151.44/22.32 End of proof % 151.44/22.32 % 151.44/22.32 Sub-proof #275 shows that the following formulas are inconsistent: % 151.44/22.32 ---------------------------------------------------------------- % 151.44/22.32 (1) all_56_11 = all_8_2 % 151.44/22.32 (2) ~ (all_56_11 = e1) | all_56_13 = e2 % 151.44/22.32 (3) ~ (all_52_11 = all_6_2) % 151.44/22.32 (4) all_54_9 = all_52_6 % 151.44/22.32 (5) all_54_10 = all_6_2 % 151.44/22.32 (6) ~ (all_52_9 = all_8_2) % 151.44/22.32 (7) ~ (all_8_1 = e3) % 151.44/22.32 (8) op(e0, e0) = all_4_2 % 151.44/22.32 (9) all_58_4 = all_52_8 % 151.44/22.32 (10) ~ (all_52_6 = all_52_14) % 151.44/22.32 (11) ~ (all_6_0 = e2) % 151.44/22.32 (12) all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1 % 151.44/22.32 (13) all_56_21 = all_6_2 % 151.44/22.32 (14) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 151.44/22.32 (15) ~ (all_52_7 = all_8_2) % 151.44/22.32 (16) all_56_1 = all_10_2 % 151.44/22.32 (17) all_58_5 = all_52_9 % 151.44/22.32 (18) all_58_9 = all_52_12 % 151.44/22.32 (19) all_58_1 = all_52_4 % 151.44/22.32 (20) all_58_13 = all_52_7 % 151.44/22.32 (21) op(e3, e3) = all_10_2 % 151.44/22.32 (22) ~ (all_52_6 = all_6_0) % 151.44/22.32 (23) ~ (all_56_21 = e3) | all_56_17 = e1 % 151.44/22.32 (24) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 151.44/22.32 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 151.44/22.32 (25) ~ (all_52_3 = all_10_2) % 151.44/22.32 (26) ~ (all_6_0 = all_6_2) % 151.44/22.32 (27) all_56_13 = all_52_9 % 151.44/22.32 (28) ~ (all_4_2 = e1) % 151.44/22.32 (29) all_54_8 = all_6_0 % 151.44/22.32 (30) all_58_8 = all_6_2 % 151.44/22.32 (31) ~ (all_52_14 = all_6_0) % 151.44/22.32 (32) op(all_4_2, all_4_2) = all_4_1 % 151.44/22.32 (33) all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1 % 151.44/22.32 (34) all_58_3 = all_8_2 % 151.44/22.32 (35) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0 % 151.44/22.32 (36) all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1 % 151.44/22.32 (37) all_56_31 = all_4_2 % 151.44/22.32 (38) all_58_11 = all_52_14 % 151.44/22.32 (39) all_56_1 = e3 | all_56_11 = e2 | all_56_21 = e1 | all_56_31 = e0 % 151.44/22.32 (40) all_56_23 = all_52_14 % 151.44/22.32 (41) op(e1, e1) = all_6_2 % 151.44/22.32 (42) ~ (all_52_6 = all_8_2) % 151.44/22.32 (43) all_58_15 = all_4_2 % 151.44/22.32 (44) ~ (all_6_2 = e2) % 151.44/22.32 (45) ~ (all_4_2 = e3) % 151.44/22.32 (46) all_58_7 = all_52_6 % 151.44/22.32 (47) op(e1, all_6_2) = all_56_20 % 151.44/22.32 (48) all_56_17 = all_6_0 % 151.44/22.32 (49) ~ (all_52_4 = all_52_12) % 151.44/22.32 (50) ~ (all_52_8 = all_52_12) % 151.44/22.32 (51) ~ (all_56_21 = e0) | all_56_23 = e1 % 151.44/22.32 (52) op(e0, all_4_2) = all_56_30 % 151.44/22.32 (53) ~ (all_52_6 = all_6_2) % 151.44/22.32 (54) op(all_6_2, all_6_2) = e3 % 151.44/22.32 (55) ~ (all_52_14 = all_6_2) % 151.44/22.32 (56) op(e1, all_52_11) = all_56_28 % 151.44/22.32 (57) all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3 % 151.44/22.32 (58) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0 % 151.44/22.32 (59) ~ (all_10_2 = all_6_0) % 151.44/22.32 (60) op(all_8_2, all_8_2) = all_8_1 % 151.44/22.32 (61) all_58_14 = all_52_11 % 151.44/22.32 (62) ~ (all_52_12 = all_10_2) % 151.44/22.32 (63) all_58_12 = all_52_3 % 151.44/22.32 (64) all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3 % 151.44/22.32 % 151.44/22.32 Begin of proof % 151.44/22.32 | % 151.44/22.32 | BETA: splitting (23) gives: % 151.44/22.32 | % 151.44/22.32 | Case 1: % 151.44/22.32 | | % 151.44/22.32 | | (65) ~ (all_56_21 = e3) % 151.44/22.32 | | % 151.44/22.32 | | REDUCE: (13), (65) imply: % 151.44/22.32 | | (66) ~ (all_6_2 = e3) % 151.44/22.32 | | % 151.44/22.32 | | REF_CLOSE: (1), (4), (5), (8), (10), (11), (13), (14), (16), (22), (24), % 151.44/22.32 | | (26), (29), (31), (32), (35), (37), (39), (40), (41), (42), (44), % 151.44/22.32 | | (45), (47), (51), (52), (53), (54), (55), (58), (59), (66) are % 151.44/22.32 | | inconsistent by sub-proof #429. % 151.44/22.32 | | % 151.44/22.32 | Case 2: % 151.44/22.32 | | % 151.44/22.32 | | (67) all_56_21 = e3 % 151.44/22.32 | | (68) all_56_17 = e1 % 151.44/22.32 | | % 151.44/22.32 | | COMBINE_EQS: (48), (68) imply: % 151.44/22.32 | | (69) all_6_0 = e1 % 151.44/22.32 | | % 151.44/22.32 | | COMBINE_EQS: (13), (67) imply: % 151.44/22.32 | | (70) all_6_2 = e3 % 151.44/22.32 | | % 151.44/22.32 | | COMBINE_EQS: (30), (70) imply: % 151.44/22.32 | | (71) all_58_8 = e3 % 151.44/22.32 | | % 151.44/22.32 | | REDUCE: (22), (69) imply: % 151.44/22.32 | | (72) ~ (all_52_6 = e1) % 151.44/22.32 | | % 151.44/22.32 | | REDUCE: (3), (70) imply: % 151.44/22.32 | | (73) ~ (all_52_11 = e3) % 151.44/22.32 | | % 151.44/22.32 | | REDUCE: (31), (69) imply: % 151.44/22.32 | | (74) ~ (all_52_14 = e1) % 151.44/22.32 | | % 151.44/22.32 | | REDUCE: (55), (70) imply: % 151.44/22.32 | | (75) ~ (all_52_14 = e3) % 151.44/22.32 | | % 151.44/22.32 | | REDUCE: (59), (69) imply: % 151.44/22.32 | | (76) ~ (all_10_2 = e1) % 151.44/22.32 | | % 151.44/22.32 | | REDUCE: (54), (70) imply: % 151.44/22.32 | | (77) op(e3, e3) = e3 % 151.44/22.32 | | % 151.44/22.32 | | REDUCE: (41), (70) imply: % 151.44/22.32 | | (78) op(e1, e1) = e3 % 151.44/22.32 | | % 151.44/22.32 | | GROUND_INST: instantiating (24) with all_10_2, e3, e3, e3, simplifying with % 151.44/22.32 | | (21), (77) gives: % 151.44/22.32 | | (79) all_10_2 = e3 % 151.44/22.32 | | % 151.44/22.32 | | REDUCE: (25), (79) imply: % 151.44/22.32 | | (80) ~ (all_52_3 = e3) % 151.44/22.32 | | % 151.44/22.32 | | REDUCE: (62), (79) imply: % 151.44/22.32 | | (81) ~ (all_52_12 = e3) % 151.44/22.32 | | % 151.44/22.32 | | REDUCE: (76), (79) imply: % 151.44/22.32 | | (82) ~ (e3 = e1) % 151.44/22.32 | | % 151.44/22.32 | | BETA: splitting (57) gives: % 151.44/22.32 | | % 151.44/22.32 | | Case 1: % 151.44/22.32 | | | % 151.44/22.32 | | | (83) all_58_9 = e3 % 151.44/22.32 | | | % 151.44/22.32 | | | COMBINE_EQS: (18), (83) imply: % 151.44/22.32 | | | (84) all_52_12 = e3 % 151.44/22.32 | | | % 151.44/22.32 | | | REDUCE: (81), (84) imply: % 151.44/22.32 | | | (85) $false % 151.44/22.32 | | | % 151.44/22.32 | | | CLOSE: (85) is inconsistent. % 151.44/22.32 | | | % 151.44/22.32 | | Case 2: % 151.44/22.32 | | | % 151.44/22.32 | | | (86) ~ (all_58_9 = e3) % 151.44/22.32 | | | (87) all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3 % 151.44/22.32 | | | % 151.44/22.32 | | | BETA: splitting (87) gives: % 151.44/22.32 | | | % 151.44/22.32 | | | Case 1: % 151.44/22.32 | | | | % 151.44/22.32 | | | | (88) all_58_10 = e3 % 151.44/22.32 | | | | % 151.44/22.32 | | | | REF_CLOSE: (1), (2), (6), (7), (9), (12), (15), (17), (18), (19), (20), % 151.44/22.32 | | | | (24), (27), (28), (33), (34), (36), (38), (43), (45), (46), % 151.44/22.32 | | | | (49), (50), (56), (60), (61), (63), (64), (71), (72), (73), % 151.44/22.32 | | | | (74), (78), (80), (81), (82), (88) are inconsistent by % 151.44/22.32 | | | | sub-proof #445. % 151.44/22.32 | | | | % 151.44/22.32 | | | Case 2: % 151.44/22.32 | | | | % 151.44/22.32 | | | | (89) all_58_11 = e3 | all_58_15 = e3 % 151.44/22.32 | | | | % 151.44/22.32 | | | | REF_CLOSE: (38), (43), (45), (75), (89) are inconsistent by sub-proof % 151.44/22.32 | | | | #331. % 151.44/22.32 | | | | % 151.44/22.32 | | | End of split % 151.44/22.32 | | | % 151.44/22.32 | | End of split % 151.44/22.32 | | % 151.44/22.32 | End of split % 151.44/22.32 | % 151.44/22.32 End of proof % 151.44/22.32 % 151.44/22.32 Sub-proof #276 shows that the following formulas are inconsistent: % 151.44/22.32 ---------------------------------------------------------------- % 151.44/22.32 (1) ~ (all_6_1 = e2) % 151.44/22.32 (2) all_40_2 = all_6_2 % 151.44/22.32 (3) all_54_5 = all_8_2 % 151.44/22.32 (4) ~ (all_6_1 = e3) % 151.44/22.32 (5) all_56_21 = all_6_2 % 151.44/22.32 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 151.44/22.32 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 151.44/22.32 (7) all_56_21 = e2 % 151.44/22.32 (8) all_56_19 = e1 % 151.44/22.32 (9) op(all_6_2, all_6_2) = all_6_1 % 151.44/22.32 (10) ~ (all_52_6 = all_8_2) % 151.44/22.32 (11) all_40_1 = all_6_1 % 151.44/22.32 (12) op(e2, e2) = all_8_2 % 151.44/22.32 (13) ~ (all_40_1 = e0) | ~ (all_40_2 = e2) % 151.44/22.32 (14) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 151.44/22.32 (15) all_56_19 = all_52_6 % 151.44/22.32 % 151.44/22.32 Begin of proof % 151.44/22.32 | % 151.44/22.32 | COMBINE_EQS: (8), (15) imply: % 151.44/22.32 | (16) all_52_6 = e1 % 151.44/22.32 | % 151.44/22.32 | COMBINE_EQS: (5), (7) imply: % 151.44/22.32 | (17) all_6_2 = e2 % 151.44/22.32 | % 151.44/22.32 | SIMP: (17) implies: % 151.44/22.32 | (18) all_6_2 = e2 % 151.44/22.32 | % 151.44/22.32 | REF_CLOSE: (1), (2), (3), (4), (6), (9), (10), (11), (12), (13), (14), (16), % 151.44/22.32 | (18) are inconsistent by sub-proof #506. % 151.44/22.32 | % 151.44/22.32 End of proof % 151.44/22.32 % 151.44/22.32 Sub-proof #277 shows that the following formulas are inconsistent: % 151.44/22.32 ---------------------------------------------------------------- % 151.44/22.32 (1) all_54_10 = all_4_1 % 151.44/22.32 (2) all_54_10 = e0 % 151.44/22.32 (3) ~ (all_4_1 = e0) % 151.44/22.32 % 151.44/22.32 Begin of proof % 151.44/22.32 | % 151.44/22.32 | COMBINE_EQS: (1), (2) imply: % 151.44/22.32 | (4) all_4_1 = e0 % 151.44/22.32 | % 151.44/22.32 | SIMP: (4) implies: % 151.44/22.32 | (5) all_4_1 = e0 % 151.44/22.32 | % 151.44/22.32 | REDUCE: (3), (5) imply: % 151.44/22.32 | (6) $false % 151.44/22.32 | % 151.44/22.32 | CLOSE: (6) is inconsistent. % 151.44/22.32 | % 151.44/22.32 End of proof % 151.44/22.32 % 151.44/22.32 Sub-proof #278 shows that the following formulas are inconsistent: % 151.44/22.32 ---------------------------------------------------------------- % 151.44/22.32 (1) op(e0, all_52_13) = all_56_14 % 151.44/22.32 (2) op(e0, e0) = e1 % 151.44/22.32 (3) ~ (all_8_1 = e1) % 151.44/22.32 (4) ~ (e3 = e0) % 151.44/22.32 (5) ~ (all_8_2 = e1) % 151.44/22.32 (6) all_58_9 = e3 % 151.44/22.32 (7) all_54_5 = all_8_2 % 151.44/22.32 (8) all_58_11 = e2 % 151.44/22.32 (9) op(e2, all_8_2) = all_56_10 % 151.44/22.32 (10) ~ (e1 = e0) % 151.44/22.32 (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 151.44/22.32 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 151.44/22.32 (12) all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2 % 151.44/22.32 (13) all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) & % 151.44/22.32 (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0)) % 151.44/22.32 (14) op(e3, e1) = e2 % 151.44/22.32 (15) op(e0, e0) = all_10_1 % 151.44/22.32 (16) ~ (e2 = e1) % 151.44/22.32 (17) all_58_3 = all_8_2 % 151.44/22.32 (18) op(e3, all_10_1) = e1 % 151.44/22.32 (19) all_58_15 = e1 % 151.44/22.32 (20) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 151.44/22.32 (21) all_58_2 = e1 % 151.44/22.32 (22) all_58_10 = all_52_13 % 151.44/22.32 (23) op(e2, e2) = all_8_2 % 151.44/22.32 (24) ~ (all_8_2 = e0) % 151.44/22.32 (25) op(all_8_2, all_8_2) = all_8_1 % 151.44/22.32 (26) op(e3, e1) = all_56_8 % 151.44/22.32 % 151.44/22.32 Begin of proof % 151.44/22.32 | % 151.44/22.32 | BETA: splitting (13) gives: % 151.44/22.32 | % 151.44/22.32 | Case 1: % 151.44/22.32 | | % 151.44/22.32 | | (27) all_58_15 = e0 % 151.44/22.32 | | % 151.44/22.32 | | COMBINE_EQS: (19), (27) imply: % 151.44/22.32 | | (28) e1 = e0 % 151.44/22.32 | | % 151.44/22.32 | | REDUCE: (10), (28) imply: % 151.44/22.32 | | (29) $false % 151.44/22.32 | | % 151.44/22.32 | | CLOSE: (29) is inconsistent. % 151.44/22.32 | | % 151.44/22.32 | Case 2: % 151.44/22.32 | | % 151.44/22.32 | | (30) (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) & (all_58_12 = e0 % 151.44/22.32 | | | all_58_13 = e0 | all_58_14 = e0) % 151.44/22.32 | | % 151.44/22.32 | | ALPHA: (30) implies: % 151.44/22.32 | | (31) all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0 % 151.44/22.32 | | % 151.44/22.32 | | BETA: splitting (31) gives: % 151.44/22.32 | | % 151.44/22.32 | | Case 1: % 151.44/22.32 | | | % 151.44/22.32 | | | (32) all_58_9 = e0 % 151.44/22.32 | | | % 151.44/22.32 | | | COMBINE_EQS: (6), (32) imply: % 151.44/22.32 | | | (33) e3 = e0 % 151.44/22.32 | | | % 151.44/22.32 | | | REDUCE: (4), (33) imply: % 151.44/22.32 | | | (34) $false % 151.44/22.32 | | | % 151.44/22.32 | | | CLOSE: (34) is inconsistent. % 151.44/22.32 | | | % 151.44/22.32 | | Case 2: % 151.44/22.32 | | | % 151.44/22.32 | | | (35) all_58_10 = e0 | all_58_11 = e0 % 151.44/22.32 | | | % 151.44/22.32 | | | BETA: splitting (12) gives: % 151.44/22.32 | | | % 151.44/22.32 | | | Case 1: % 151.44/22.32 | | | | % 151.44/22.32 | | | | (36) all_58_2 = e2 % 151.44/22.32 | | | | % 151.44/22.32 | | | | COMBINE_EQS: (21), (36) imply: % 151.44/22.32 | | | | (37) e2 = e1 % 151.44/22.32 | | | | % 151.44/22.32 | | | | REDUCE: (16), (37) imply: % 151.44/22.32 | | | | (38) $false % 151.44/22.32 | | | | % 151.44/22.32 | | | | CLOSE: (38) is inconsistent. % 151.44/22.32 | | | | % 151.44/22.32 | | | Case 2: % 151.44/22.32 | | | | % 151.44/22.32 | | | | (39) all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2 % 151.44/22.32 | | | | % 151.44/22.32 | | | | BETA: splitting (39) gives: % 151.44/22.32 | | | | % 151.44/22.32 | | | | Case 1: % 151.44/22.32 | | | | | % 151.44/22.32 | | | | | (40) all_58_3 = e2 % 151.44/22.32 | | | | | % 151.44/22.32 | | | | | COMBINE_EQS: (17), (40) imply: % 151.44/22.32 | | | | | (41) all_8_2 = e2 % 151.44/22.32 | | | | | % 151.44/22.32 | | | | | REDUCE: (24), (41) imply: % 151.44/22.32 | | | | | (42) ~ (e2 = e0) % 151.44/22.32 | | | | | % 151.44/22.32 | | | | | REDUCE: (25), (41) imply: % 151.44/22.32 | | | | | (43) op(e2, e2) = all_8_1 % 151.44/22.32 | | | | | % 151.44/22.32 | | | | | REDUCE: (9), (41) imply: % 151.44/22.32 | | | | | (44) op(e2, e2) = all_56_10 % 151.44/22.32 | | | | | % 151.44/22.32 | | | | | REDUCE: (23), (41) imply: % 151.44/22.32 | | | | | (45) op(e2, e2) = e2 % 151.44/22.32 | | | | | % 151.44/22.32 | | | | | BETA: splitting (35) gives: % 151.44/22.32 | | | | | % 151.44/22.32 | | | | | Case 1: % 151.44/22.32 | | | | | | % 151.44/22.32 | | | | | | (46) all_58_10 = e0 % 151.44/22.32 | | | | | | % 151.44/22.32 | | | | | | COMBINE_EQS: (22), (46) imply: % 151.44/22.32 | | | | | | (47) all_52_13 = e0 % 151.44/22.32 | | | | | | % 151.44/22.32 | | | | | | SIMP: (47) implies: % 151.44/22.32 | | | | | | (48) all_52_13 = e0 % 151.44/22.32 | | | | | | % 151.44/22.32 | | | | | | REDUCE: (1), (48) imply: % 151.44/22.32 | | | | | | (49) op(e0, e0) = all_56_14 % 151.44/22.32 | | | | | | % 151.44/22.32 | | | | | | GROUND_INST: instantiating (11) with e1, all_56_14, e0, e0, % 151.44/22.32 | | | | | | simplifying with (2), (49) gives: % 151.44/22.32 | | | | | | (50) all_56_14 = e1 % 151.44/22.32 | | | | | | % 151.44/22.32 | | | | | | GROUND_INST: instantiating (11) with all_10_1, all_56_14, e0, e0, % 151.44/22.32 | | | | | | simplifying with (15), (49) gives: % 151.44/22.32 | | | | | | (51) all_56_14 = all_10_1 % 151.44/22.32 | | | | | | % 151.44/22.32 | | | | | | GROUND_INST: instantiating (11) with all_8_1, all_56_10, e2, e2, % 151.44/22.32 | | | | | | simplifying with (43), (44) gives: % 151.44/22.32 | | | | | | (52) all_56_10 = all_8_1 % 151.44/22.32 | | | | | | % 151.44/22.32 | | | | | | GROUND_INST: instantiating (11) with e2, all_56_10, e2, e2, % 151.44/22.32 | | | | | | simplifying with (44), (45) gives: % 151.44/22.32 | | | | | | (53) all_56_10 = e2 % 151.44/22.32 | | | | | | % 151.44/22.32 | | | | | | GROUND_INST: instantiating (11) with e2, all_56_8, e1, e3, % 151.44/22.32 | | | | | | simplifying with (14), (26) gives: % 151.44/22.32 | | | | | | (54) all_56_8 = e2 % 151.44/22.32 | | | | | | % 151.44/22.32 | | | | | | COMBINE_EQS: (52), (53) imply: % 151.44/22.32 | | | | | | (55) all_8_1 = e2 % 151.44/22.32 | | | | | | % 151.44/22.32 | | | | | | SIMP: (55) implies: % 151.44/22.32 | | | | | | (56) all_8_1 = e2 % 151.44/22.32 | | | | | | % 151.44/22.32 | | | | | | COMBINE_EQS: (50), (51) imply: % 151.44/22.32 | | | | | | (57) all_10_1 = e1 % 151.44/22.32 | | | | | | % 151.44/22.32 | | | | | | REDUCE: (18), (57) imply: % 151.44/22.32 | | | | | | (58) op(e3, e1) = e1 % 151.44/22.32 | | | | | | % 151.44/22.32 | | | | | | GROUND_INST: instantiating (11) with e2, e1, e1, e3, simplifying % 151.44/22.32 | | | | | | with (14), (58) gives: % 151.44/22.32 | | | | | | (59) e2 = e1 % 151.44/22.32 | | | | | | % 151.44/22.32 | | | | | | REDUCE: (16), (59) imply: % 151.44/22.32 | | | | | | (60) $false % 151.44/22.32 | | | | | | % 151.44/22.32 | | | | | | CLOSE: (60) is inconsistent. % 151.44/22.32 | | | | | | % 151.44/22.32 | | | | | Case 2: % 151.44/22.32 | | | | | | % 151.44/22.32 | | | | | | (61) all_58_11 = e0 % 151.44/22.32 | | | | | | % 151.44/22.32 | | | | | | REF_CLOSE: (8), (42), (61) are inconsistent by sub-proof #280. % 151.44/22.32 | | | | | | % 151.44/22.32 | | | | | End of split % 151.44/22.32 | | | | | % 151.44/22.32 | | | | Case 2: % 151.44/22.32 | | | | | % 151.44/22.32 | | | | | (62) ~ (all_58_3 = e2) % 151.44/22.32 | | | | | % 151.44/22.32 | | | | | REDUCE: (17), (62) imply: % 151.44/22.32 | | | | | (63) ~ (all_8_2 = e2) % 151.44/22.32 | | | | | % 151.44/22.32 | | | | | REF_CLOSE: (5), (7), (20), (24), (63) are inconsistent by sub-proof % 151.44/22.32 | | | | | #279. % 151.44/22.32 | | | | | % 151.44/22.32 | | | | End of split % 151.44/22.32 | | | | % 151.44/22.32 | | | End of split % 151.44/22.32 | | | % 151.44/22.32 | | End of split % 151.44/22.32 | | % 151.44/22.32 | End of split % 151.44/22.32 | % 151.44/22.32 End of proof % 151.44/22.32 % 151.44/22.32 Sub-proof #279 shows that the following formulas are inconsistent: % 151.44/22.32 ---------------------------------------------------------------- % 151.44/22.32 (1) ~ (all_8_2 = e1) % 151.44/22.32 (2) all_54_5 = all_8_2 % 151.44/22.32 (3) ~ (all_8_2 = e2) % 151.44/22.32 (4) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 151.44/22.32 (5) ~ (all_8_2 = e0) % 151.44/22.32 % 151.44/22.32 Begin of proof % 151.44/22.32 | % 151.44/22.32 | BETA: splitting (4) gives: % 151.44/22.32 | % 151.44/22.32 | Case 1: % 151.44/22.32 | | % 151.44/22.32 | | (6) all_54_5 = e2 % 151.44/22.32 | | % 151.44/22.32 | | REF_CLOSE: (2), (3), (6) are inconsistent by sub-proof #648. % 151.44/22.32 | | % 151.44/22.32 | Case 2: % 151.44/22.32 | | % 151.44/22.32 | | (7) all_54_5 = e1 | all_54_5 = e0 % 151.44/22.32 | | % 151.44/22.32 | | REF_CLOSE: (1), (2), (5), (7) are inconsistent by sub-proof #645. % 151.44/22.32 | | % 151.44/22.32 | End of split % 151.44/22.32 | % 151.44/22.32 End of proof % 151.44/22.32 % 151.44/22.32 Sub-proof #280 shows that the following formulas are inconsistent: % 151.44/22.32 ---------------------------------------------------------------- % 151.44/22.32 (1) all_58_11 = e2 % 151.44/22.32 (2) all_58_11 = e0 % 151.44/22.32 (3) ~ (e2 = e0) % 151.44/22.32 % 151.44/22.32 Begin of proof % 151.44/22.32 | % 151.44/22.32 | COMBINE_EQS: (1), (2) imply: % 151.44/22.32 | (4) e2 = e0 % 151.44/22.32 | % 151.44/22.32 | SIMP: (4) implies: % 151.44/22.32 | (5) e2 = e0 % 151.44/22.32 | % 151.44/22.32 | REDUCE: (3), (5) imply: % 151.44/22.32 | (6) $false % 151.44/22.32 | % 151.44/22.32 | CLOSE: (6) is inconsistent. % 151.44/22.32 | % 151.44/22.32 End of proof % 151.44/22.32 % 151.44/22.32 Sub-proof #281 shows that the following formulas are inconsistent: % 151.44/22.32 ---------------------------------------------------------------- % 151.44/22.32 (1) all_54_10 = all_4_1 % 151.44/22.32 (2) all_54_10 = e2 % 151.44/22.32 (3) ~ (all_4_1 = e2) % 151.44/22.32 % 151.44/22.32 Begin of proof % 151.44/22.32 | % 151.44/22.32 | COMBINE_EQS: (1), (2) imply: % 151.44/22.32 | (4) all_4_1 = e2 % 151.44/22.32 | % 151.44/22.32 | SIMP: (4) implies: % 151.44/22.32 | (5) all_4_1 = e2 % 151.44/22.32 | % 151.44/22.32 | REDUCE: (3), (5) imply: % 151.44/22.32 | (6) $false % 151.44/22.32 | % 151.44/22.32 | CLOSE: (6) is inconsistent. % 151.44/22.32 | % 151.44/22.32 End of proof % 151.44/22.32 % 151.44/22.32 Sub-proof #282 shows that the following formulas are inconsistent: % 151.44/22.32 ---------------------------------------------------------------- % 151.44/22.32 (1) all_54_10 = all_4_1 % 151.44/22.32 (2) all_54_10 = e3 % 151.44/22.32 (3) ~ (all_4_1 = e3) % 151.44/22.32 % 151.44/22.32 Begin of proof % 151.44/22.32 | % 151.44/22.32 | COMBINE_EQS: (1), (2) imply: % 151.44/22.32 | (4) all_4_1 = e3 % 151.44/22.32 | % 151.44/22.32 | SIMP: (4) implies: % 151.44/22.32 | (5) all_4_1 = e3 % 151.44/22.32 | % 151.44/22.32 | REDUCE: (3), (5) imply: % 151.44/22.32 | (6) $false % 151.44/22.32 | % 151.44/22.32 | CLOSE: (6) is inconsistent. % 151.44/22.32 | % 151.44/22.32 End of proof % 151.44/22.32 % 151.44/22.32 Sub-proof #283 shows that the following formulas are inconsistent: % 151.44/22.32 ---------------------------------------------------------------- % 151.44/22.32 (1) all_56_11 = all_8_2 % 151.44/22.32 (2) ~ (all_6_1 = e2) % 151.44/22.32 (3) ~ (all_8_2 = e1) % 151.44/22.32 (4) ~ (all_8_1 = e3) % 151.44/22.32 (5) ~ (e3 = e2) % 151.44/22.32 (6) op(e0, e0) = all_4_2 % 151.44/22.32 (7) all_58_4 = all_52_8 % 151.44/22.32 (8) op(e2, e2) = all_6_1 % 151.44/22.32 (9) all_54_5 = all_8_2 % 151.44/22.32 (10) ~ (all_6_1 = e3) % 151.44/22.32 (11) all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1 % 151.44/22.32 (12) all_56_1 = all_10_2 % 151.44/22.32 (13) all_58_9 = all_52_12 % 151.44/22.32 (14) op(e1, e0) = all_52_14 % 151.44/22.32 (15) all_58_1 = all_52_4 % 151.44/22.32 (16) all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0 % 151.44/22.32 (17) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 151.44/22.32 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 151.44/22.32 (18) ~ (all_52_14 = e1) % 151.44/22.32 (19) all_56_7 = all_52_12 % 151.44/22.32 (20) ~ (all_4_2 = e1) % 151.44/22.32 (21) ~ (all_6_0 = e3) % 151.44/22.32 (22) ~ (all_56_1 = e0) | all_56_7 = e3 % 151.44/22.32 (23) ~ (e2 = e1) % 151.44/22.32 (24) op(e1, all_6_1) = all_6_0 % 151.44/22.32 (25) op(e1, all_52_8) = all_56_4 % 151.44/22.32 (26) all_58_11 = all_52_14 % 151.44/22.32 (27) all_58_15 = all_4_2 % 151.44/22.32 (28) all_58_10 = all_52_13 % 151.44/22.32 (29) ~ (all_56_11 = e0) | all_56_15 = e2 % 151.44/22.32 (30) all_58_0 = all_10_2 % 151.44/22.32 (31) ~ (e3 = e1) % 151.44/22.32 (32) op(e2, e2) = all_8_2 % 151.44/22.32 (33) all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3 % 151.44/22.32 (34) ~ (all_52_4 = all_8_2) % 151.44/22.32 (35) op(all_8_2, all_8_2) = all_8_1 % 151.44/22.32 (36) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 151.44/22.32 (37) all_56_15 = all_52_13 % 151.44/22.32 % 151.44/22.32 Begin of proof % 151.44/22.32 | % 151.44/22.32 | GROUND_INST: instantiating (17) with all_8_2, all_6_1, e2, e2, simplifying % 151.44/22.32 | with (8), (32) gives: % 151.44/22.32 | (38) all_8_2 = all_6_1 % 151.44/22.32 | % 151.44/22.32 | COMBINE_EQS: (9), (38) imply: % 151.44/22.32 | (39) all_54_5 = all_6_1 % 151.44/22.32 | % 151.44/22.32 | COMBINE_EQS: (1), (38) imply: % 151.44/22.32 | (40) all_56_11 = all_6_1 % 151.44/22.32 | % 151.44/22.32 | REDUCE: (34), (38) imply: % 151.44/22.32 | (41) ~ (all_52_4 = all_6_1) % 151.44/22.32 | % 151.44/22.32 | REDUCE: (3), (38) imply: % 151.44/22.32 | (42) ~ (all_6_1 = e1) % 151.44/22.32 | % 151.44/22.32 | REDUCE: (35), (38) imply: % 151.44/22.32 | (43) op(all_6_1, all_6_1) = all_8_1 % 151.44/22.32 | % 151.44/22.32 | BETA: splitting (36) gives: % 151.44/22.32 | % 151.44/22.32 | Case 1: % 151.44/22.32 | | % 151.44/22.32 | | (44) all_54_5 = e3 % 151.44/22.32 | | % 151.44/22.32 | | REF_CLOSE: (10), (39), (44) are inconsistent by sub-proof #509. % 151.44/22.32 | | % 151.44/22.32 | Case 2: % 151.44/22.32 | | % 151.44/22.32 | | (45) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 151.44/22.32 | | % 151.44/22.32 | | BETA: splitting (45) gives: % 151.44/22.32 | | % 151.44/22.32 | | Case 1: % 151.44/22.32 | | | % 151.44/22.32 | | | (46) all_54_5 = e2 % 151.44/22.32 | | | % 151.44/22.32 | | | REF_CLOSE: (2), (39), (46) are inconsistent by sub-proof #466. % 151.44/22.32 | | | % 151.44/22.32 | | Case 2: % 151.44/22.32 | | | % 151.44/22.32 | | | (47) all_54_5 = e1 | all_54_5 = e0 % 151.44/22.32 | | | % 151.44/22.32 | | | BETA: splitting (47) gives: % 151.44/22.32 | | | % 151.44/22.32 | | | Case 1: % 151.44/22.32 | | | | % 151.44/22.32 | | | | (48) all_54_5 = e1 % 151.44/22.32 | | | | % 151.44/22.32 | | | | REF_CLOSE: (39), (42), (48) are inconsistent by sub-proof #465. % 151.44/22.32 | | | | % 151.44/22.32 | | | Case 2: % 151.44/22.32 | | | | % 151.44/22.32 | | | | (49) all_54_5 = e0 % 151.44/22.32 | | | | % 151.44/22.32 | | | | COMBINE_EQS: (39), (49) imply: % 151.44/22.32 | | | | (50) all_6_1 = e0 % 151.44/22.32 | | | | % 151.44/22.32 | | | | SIMP: (50) implies: % 151.44/22.32 | | | | (51) all_6_1 = e0 % 151.44/22.32 | | | | % 151.44/22.32 | | | | COMBINE_EQS: (40), (51) imply: % 151.44/22.32 | | | | (52) all_56_11 = e0 % 151.44/22.32 | | | | % 151.44/22.32 | | | | REDUCE: (41), (51) imply: % 151.44/22.32 | | | | (53) ~ (all_52_4 = e0) % 151.44/22.32 | | | | % 151.44/22.32 | | | | REDUCE: (42), (51) imply: % 151.44/22.32 | | | | (54) ~ (e1 = e0) % 151.44/22.32 | | | | % 151.44/22.32 | | | | SIMP: (54) implies: % 151.44/22.32 | | | | (55) ~ (e1 = e0) % 151.44/22.32 | | | | % 151.44/22.32 | | | | REDUCE: (43), (51) imply: % 151.44/22.32 | | | | (56) op(e0, e0) = all_8_1 % 151.44/22.32 | | | | % 151.44/22.32 | | | | REDUCE: (24), (51) imply: % 151.44/22.32 | | | | (57) op(e1, e0) = all_6_0 % 151.44/22.32 | | | | % 151.44/22.32 | | | | REF_CLOSE: (4), (5), (6), (7), (11), (12), (13), (14), (15), (16), (17), % 151.44/22.32 | | | | (18), (19), (20), (21), (22), (23), (25), (26), (27), (28), % 151.44/22.32 | | | | (29), (30), (31), (33), (37), (52), (53), (55), (56), (57) % 151.44/22.32 | | | | are inconsistent by sub-proof #284. % 151.44/22.32 | | | | % 151.44/22.32 | | | End of split % 151.44/22.32 | | | % 151.44/22.32 | | End of split % 151.44/22.32 | | % 151.44/22.32 | End of split % 151.44/22.32 | % 151.44/22.32 End of proof % 151.44/22.32 % 151.44/22.32 Sub-proof #284 shows that the following formulas are inconsistent: % 151.44/22.32 ---------------------------------------------------------------- % 151.44/22.32 (1) ~ (all_8_1 = e3) % 151.44/22.32 (2) ~ (e3 = e2) % 151.44/22.32 (3) op(e0, e0) = all_4_2 % 151.44/22.32 (4) all_58_4 = all_52_8 % 151.44/22.32 (5) all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1 % 151.44/22.32 (6) all_56_1 = all_10_2 % 151.44/22.32 (7) all_58_9 = all_52_12 % 151.44/22.32 (8) op(e1, e0) = all_6_0 % 151.44/22.32 (9) op(e1, e0) = all_52_14 % 151.44/22.32 (10) all_58_1 = all_52_4 % 151.44/22.32 (11) all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0 % 151.44/22.32 (12) ~ (e1 = e0) % 151.44/22.32 (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 151.44/22.32 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 151.44/22.32 (14) ~ (all_52_14 = e1) % 151.44/22.32 (15) all_56_7 = all_52_12 % 151.44/22.32 (16) ~ (all_52_4 = e0) % 151.44/22.32 (17) ~ (all_4_2 = e1) % 151.44/22.32 (18) ~ (all_6_0 = e3) % 151.44/22.32 (19) op(e0, e0) = all_8_1 % 151.44/22.32 (20) ~ (all_56_1 = e0) | all_56_7 = e3 % 151.44/22.32 (21) ~ (e2 = e1) % 151.44/22.32 (22) op(e1, all_52_8) = all_56_4 % 151.44/22.32 (23) all_58_11 = all_52_14 % 151.44/22.32 (24) all_56_11 = e0 % 151.44/22.32 (25) all_58_15 = all_4_2 % 151.44/22.32 (26) all_58_10 = all_52_13 % 151.44/22.32 (27) ~ (all_56_11 = e0) | all_56_15 = e2 % 151.44/22.32 (28) all_58_0 = all_10_2 % 151.44/22.32 (29) ~ (e3 = e1) % 151.44/22.32 (30) all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3 % 151.44/22.32 (31) all_56_15 = all_52_13 % 151.44/22.32 % 151.44/22.32 Begin of proof % 151.44/22.32 | % 151.44/22.32 | BETA: splitting (27) gives: % 151.44/22.32 | % 151.44/22.32 | Case 1: % 151.44/22.32 | | % 151.44/22.32 | | (32) ~ (all_56_11 = e0) % 151.44/22.32 | | % 151.44/22.32 | | REDUCE: (24), (32) imply: % 151.44/22.32 | | (33) $false % 151.44/22.32 | | % 151.44/22.32 | | CLOSE: (33) is inconsistent. % 151.44/22.32 | | % 151.44/22.32 | Case 2: % 151.44/22.32 | | % 151.44/22.32 | | (34) all_56_15 = e2 % 151.44/22.32 | | % 151.44/22.33 | | COMBINE_EQS: (31), (34) imply: % 151.44/22.33 | | (35) all_52_13 = e2 % 151.44/22.33 | | % 151.44/22.33 | | COMBINE_EQS: (26), (35) imply: % 151.44/22.33 | | (36) all_58_10 = e2 % 151.44/22.33 | | % 151.44/22.33 | | BETA: splitting (5) gives: % 151.44/22.33 | | % 151.44/22.33 | | Case 1: % 151.44/22.33 | | | % 151.44/22.33 | | | (37) all_58_9 = e1 % 151.44/22.33 | | | % 151.44/22.33 | | | COMBINE_EQS: (7), (37) imply: % 151.44/22.33 | | | (38) all_52_12 = e1 % 151.44/22.33 | | | % 151.44/22.33 | | | COMBINE_EQS: (15), (38) imply: % 151.44/22.33 | | | (39) all_56_7 = e1 % 151.44/22.33 | | | % 151.44/22.33 | | | BETA: splitting (20) gives: % 151.44/22.33 | | | % 151.44/22.33 | | | Case 1: % 151.44/22.33 | | | | % 151.44/22.33 | | | | (40) ~ (all_56_1 = e0) % 151.44/22.33 | | | | % 151.44/22.33 | | | | REDUCE: (6), (40) imply: % 151.44/22.33 | | | | (41) ~ (all_10_2 = e0) % 151.44/22.33 | | | | % 151.44/22.33 | | | | BETA: splitting (11) gives: % 151.44/22.33 | | | | % 151.44/22.33 | | | | Case 1: % 151.44/22.33 | | | | | % 151.44/22.33 | | | | | (42) all_58_0 = e0 % 151.44/22.33 | | | | | % 151.44/22.33 | | | | | COMBINE_EQS: (28), (42) imply: % 151.44/22.33 | | | | | (43) all_10_2 = e0 % 151.44/22.33 | | | | | % 151.44/22.33 | | | | | REDUCE: (41), (43) imply: % 151.44/22.33 | | | | | (44) $false % 151.44/22.33 | | | | | % 151.44/22.33 | | | | | CLOSE: (44) is inconsistent. % 151.44/22.33 | | | | | % 151.44/22.33 | | | | Case 2: % 151.44/22.33 | | | | | % 151.44/22.33 | | | | | (45) all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0 % 151.44/22.33 | | | | | % 151.44/22.33 | | | | | BETA: splitting (45) gives: % 151.44/22.33 | | | | | % 151.44/22.33 | | | | | Case 1: % 151.44/22.33 | | | | | | % 151.44/22.33 | | | | | | (46) all_58_1 = e0 % 151.44/22.33 | | | | | | % 151.44/22.33 | | | | | | COMBINE_EQS: (10), (46) imply: % 151.44/22.33 | | | | | | (47) all_52_4 = e0 % 151.44/22.33 | | | | | | % 151.44/22.33 | | | | | | REDUCE: (16), (47) imply: % 151.44/22.33 | | | | | | (48) $false % 151.44/22.33 | | | | | | % 151.44/22.33 | | | | | | CLOSE: (48) is inconsistent. % 151.44/22.33 | | | | | | % 151.44/22.33 | | | | | Case 2: % 151.44/22.33 | | | | | | % 151.44/22.33 | | | | | | (49) all_58_4 = e0 | all_58_9 = e0 % 151.44/22.33 | | | | | | % 151.44/22.33 | | | | | | BETA: splitting (49) gives: % 151.44/22.33 | | | | | | % 151.44/22.33 | | | | | | Case 1: % 151.44/22.33 | | | | | | | % 151.44/22.33 | | | | | | | (50) all_58_4 = e0 % 151.44/22.33 | | | | | | | % 151.44/22.33 | | | | | | | COMBINE_EQS: (4), (50) imply: % 151.44/22.33 | | | | | | | (51) all_52_8 = e0 % 151.44/22.33 | | | | | | | % 151.44/22.33 | | | | | | | REDUCE: (22), (51) imply: % 151.44/22.33 | | | | | | | (52) op(e1, e0) = all_56_4 % 151.44/22.33 | | | | | | | % 151.44/22.33 | | | | | | | GROUND_INST: instantiating (13) with all_4_2, all_8_1, e0, e0, % 151.44/22.33 | | | | | | | simplifying with (3), (19) gives: % 151.44/22.33 | | | | | | | (53) all_8_1 = all_4_2 % 151.44/22.33 | | | | | | | % 151.44/22.33 | | | | | | | GROUND_INST: instantiating (13) with all_52_14, all_56_4, e0, e1, % 151.44/22.33 | | | | | | | simplifying with (9), (52) gives: % 151.44/22.33 | | | | | | | (54) all_56_4 = all_52_14 % 151.44/22.33 | | | | | | | % 151.44/22.33 | | | | | | | GROUND_INST: instantiating (13) with all_6_0, all_56_4, e0, e1, % 151.44/22.33 | | | | | | | simplifying with (8), (52) gives: % 151.44/22.33 | | | | | | | (55) all_56_4 = all_6_0 % 151.44/22.33 | | | | | | | % 151.44/22.33 | | | | | | | COMBINE_EQS: (54), (55) imply: % 151.44/22.33 | | | | | | | (56) all_52_14 = all_6_0 % 151.44/22.33 | | | | | | | % 151.44/22.33 | | | | | | | COMBINE_EQS: (23), (56) imply: % 151.44/22.33 | | | | | | | (57) all_58_11 = all_6_0 % 151.44/22.33 | | | | | | | % 151.44/22.33 | | | | | | | REDUCE: (1), (53) imply: % 151.44/22.33 | | | | | | | (58) ~ (all_4_2 = e3) % 151.44/22.33 | | | | | | | % 151.44/22.33 | | | | | | | BETA: splitting (30) gives: % 151.44/22.33 | | | | | | | % 151.44/22.33 | | | | | | | Case 1: % 151.44/22.33 | | | | | | | | % 151.44/22.33 | | | | | | | | (59) all_58_9 = e3 % 151.44/22.33 | | | | | | | | % 151.44/22.33 | | | | | | | | COMBINE_EQS: (37), (59) imply: % 151.44/22.33 | | | | | | | | (60) e3 = e1 % 151.44/22.33 | | | | | | | | % 151.44/22.33 | | | | | | | | REDUCE: (29), (60) imply: % 151.44/22.33 | | | | | | | | (61) $false % 151.44/22.33 | | | | | | | | % 151.44/22.33 | | | | | | | | CLOSE: (61) is inconsistent. % 151.44/22.33 | | | | | | | | % 151.44/22.33 | | | | | | | Case 2: % 151.44/22.33 | | | | | | | | % 151.44/22.33 | | | | | | | | (62) all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3 % 151.44/22.33 | | | | | | | | % 151.44/22.33 | | | | | | | | BETA: splitting (62) gives: % 151.44/22.33 | | | | | | | | % 151.44/22.33 | | | | | | | | Case 1: % 151.44/22.33 | | | | | | | | | % 151.44/22.33 | | | | | | | | | (63) all_58_10 = e3 % 151.44/22.33 | | | | | | | | | % 151.44/22.33 | | | | | | | | | COMBINE_EQS: (36), (63) imply: % 151.44/22.33 | | | | | | | | | (64) e3 = e2 % 151.44/22.33 | | | | | | | | | % 151.44/22.33 | | | | | | | | | REDUCE: (2), (64) imply: % 151.44/22.33 | | | | | | | | | (65) $false % 151.44/22.33 | | | | | | | | | % 151.44/22.33 | | | | | | | | | CLOSE: (65) is inconsistent. % 151.44/22.33 | | | | | | | | | % 151.44/22.33 | | | | | | | | Case 2: % 151.44/22.33 | | | | | | | | | % 151.44/22.33 | | | | | | | | | (66) all_58_11 = e3 | all_58_15 = e3 % 151.44/22.33 | | | | | | | | | % 151.44/22.33 | | | | | | | | | BETA: splitting (66) gives: % 151.44/22.33 | | | | | | | | | % 151.44/22.33 | | | | | | | | | Case 1: % 151.44/22.33 | | | | | | | | | | % 151.44/22.33 | | | | | | | | | | (67) all_58_11 = e3 % 151.44/22.33 | | | | | | | | | | % 151.44/22.33 | | | | | | | | | | COMBINE_EQS: (57), (67) imply: % 151.44/22.33 | | | | | | | | | | (68) all_6_0 = e3 % 151.44/22.33 | | | | | | | | | | % 151.44/22.33 | | | | | | | | | | SIMP: (68) implies: % 151.44/22.33 | | | | | | | | | | (69) all_6_0 = e3 % 151.44/22.33 | | | | | | | | | | % 151.44/22.33 | | | | | | | | | | REDUCE: (18), (69) imply: % 151.44/22.33 | | | | | | | | | | (70) $false % 151.44/22.33 | | | | | | | | | | % 151.44/22.33 | | | | | | | | | | CLOSE: (70) is inconsistent. % 151.44/22.33 | | | | | | | | | | % 151.44/22.33 | | | | | | | | | Case 2: % 151.44/22.33 | | | | | | | | | | % 151.44/22.33 | | | | | | | | | | (71) all_58_15 = e3 % 151.44/22.33 | | | | | | | | | | % 151.44/22.33 | | | | | | | | | | COMBINE_EQS: (25), (71) imply: % 151.44/22.33 | | | | | | | | | | (72) all_4_2 = e3 % 151.44/22.33 | | | | | | | | | | % 151.44/22.33 | | | | | | | | | | REDUCE: (58), (72) imply: % 151.44/22.33 | | | | | | | | | | (73) $false % 151.44/22.33 | | | | | | | | | | % 151.44/22.33 | | | | | | | | | | CLOSE: (73) is inconsistent. % 151.44/22.33 | | | | | | | | | | % 151.44/22.33 | | | | | | | | | End of split % 151.44/22.33 | | | | | | | | | % 151.44/22.33 | | | | | | | | End of split % 151.44/22.33 | | | | | | | | % 151.44/22.33 | | | | | | | End of split % 151.44/22.33 | | | | | | | % 151.44/22.33 | | | | | | Case 2: % 151.44/22.33 | | | | | | | % 151.44/22.33 | | | | | | | (74) all_58_9 = e0 % 151.44/22.33 | | | | | | | % 151.44/22.33 | | | | | | | COMBINE_EQS: (37), (74) imply: % 151.44/22.33 | | | | | | | (75) e1 = e0 % 151.44/22.33 | | | | | | | % 151.44/22.33 | | | | | | | REDUCE: (12), (75) imply: % 151.44/22.33 | | | | | | | (76) $false % 151.44/22.33 | | | | | | | % 151.44/22.33 | | | | | | | CLOSE: (76) is inconsistent. % 151.44/22.33 | | | | | | | % 151.44/22.33 | | | | | | End of split % 151.44/22.33 | | | | | | % 151.44/22.33 | | | | | End of split % 151.44/22.33 | | | | | % 151.44/22.33 | | | | End of split % 151.44/22.33 | | | | % 151.44/22.33 | | | Case 2: % 151.44/22.33 | | | | % 151.44/22.33 | | | | (77) all_56_7 = e3 % 151.44/22.33 | | | | % 151.44/22.33 | | | | REF_CLOSE: (29), (39), (77) are inconsistent by sub-proof #497. % 151.44/22.33 | | | | % 151.44/22.33 | | | End of split % 151.44/22.33 | | | % 151.44/22.33 | | Case 2: % 151.44/22.33 | | | % 151.44/22.33 | | | (78) all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1 % 151.44/22.33 | | | % 151.44/22.33 | | | REF_CLOSE: (14), (17), (21), (23), (25), (36), (78) are inconsistent by % 151.44/22.33 | | | sub-proof #370. % 151.44/22.33 | | | % 151.44/22.33 | | End of split % 151.44/22.33 | | % 151.44/22.33 | End of split % 151.44/22.33 | % 151.44/22.33 End of proof % 151.44/22.33 % 151.44/22.33 Sub-proof #285 shows that the following formulas are inconsistent: % 151.44/22.33 ---------------------------------------------------------------- % 151.44/22.33 (1) all_56_11 = all_8_2 % 151.44/22.33 (2) op(e0, all_52_13) = all_56_14 % 151.44/22.33 (3) ~ (all_56_11 = e1) | all_56_13 = e2 % 151.44/22.33 (4) ~ (all_52_11 = all_6_2) % 151.44/22.33 (5) ~ (all_52_4 = all_52_8) % 151.44/22.33 (6) all_56_25 = all_52_3 % 151.44/22.33 (7) ~ (all_52_7 = all_52_11) % 151.44/22.33 (8) ~ (all_52_8 = all_52_9) % 151.44/22.33 (9) all_54_9 = all_52_6 % 151.44/22.33 (10) op(e2, all_8_1) = all_8_0 % 151.44/22.33 (11) all_58_6 = all_52_2 % 151.44/22.33 (12) ~ (all_8_1 = e1) % 151.44/22.33 (13) ~ (all_52_1 = all_52_9) % 151.44/22.33 (14) op(e2, all_52_4) = all_56_2 % 151.44/22.33 (15) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0 % 151.44/22.33 (16) all_54_10 = all_6_2 % 151.44/22.33 (17) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0 % 151.44/22.33 (18) ~ (all_6_1 = e2) % 151.44/22.33 (19) ~ (all_52_13 = all_8_2) % 151.44/22.33 (20) all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2 % 151.44/22.33 (21) all_54_0 = all_10_2 % 151.44/22.33 (22) all_54_4 = all_52_1 % 151.44/22.33 (23) ~ (all_52_14 = all_4_2) % 151.44/22.33 (24) ~ (all_8_0 = e1) % 151.44/22.33 (25) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0 % 151.44/22.33 (26) all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2 % 151.44/22.33 (27) all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2 % 151.44/22.33 (28) ~ (all_52_9 = all_8_2) % 151.44/22.33 (29) all_54_12 = all_52_3 % 151.44/22.33 (30) ~ (all_52_12 = all_52_13) % 151.44/22.33 (31) ~ (all_52_4 = all_52_7) % 151.44/22.33 (32) ~ (all_8_1 = e3) % 151.44/22.33 (33) op(e0, e0) = all_4_2 % 151.44/22.33 (34) all_58_6 = e0 | all_58_7 = e0 | all_58_8 = e0 | all_58_11 = e0 % 151.44/22.33 (35) all_58_4 = all_52_8 % 151.44/22.33 (36) all_54_5 = all_8_2 % 151.44/22.33 (37) ~ (all_6_1 = e3) % 151.44/22.33 (38) ~ (all_52_6 = all_52_14) % 151.44/22.33 (39) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 151.44/22.33 (40) ~ (all_6_0 = e2) % 151.44/22.33 (41) all_54_15 = all_4_2 % 151.44/22.33 (42) all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1 % 151.44/22.33 (43) op(e2, e1) = all_52_9 % 151.44/22.33 (44) all_56_21 = all_6_2 % 151.44/22.33 (45) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 151.44/22.33 (46) op(e3, all_52_1) = all_56_8 % 151.44/22.33 (47) ~ (all_52_7 = all_8_2) % 151.44/22.33 (48) all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2 % 151.44/22.33 (49) all_56_1 = all_10_2 % 151.44/22.33 (50) all_56_27 = all_52_7 % 151.44/22.33 (51) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0 % 151.44/22.33 (52) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0 % 151.44/22.33 (53) all_58_5 = all_52_9 % 151.44/22.33 (54) all_54_1 = all_52_4 % 151.44/22.33 (55) all_56_17 = all_52_2 % 151.44/22.33 (56) all_58_9 = all_52_12 % 151.44/22.33 (57) op(e0, all_52_12) = all_56_6 % 151.44/22.33 (58) op(e0, all_52_14) = all_56_22 % 151.44/22.33 (59) op(e0, e2) = all_52_7 % 151.44/22.33 (60) op(e1, e0) = all_52_14 % 151.44/22.33 (61) ~ (all_56_1 = e1) | all_56_5 = e3 % 151.44/22.33 (62) all_54_14 = all_52_11 % 151.44/22.33 (63) ( ~ (all_56_0 = all_56_1) & ~ (all_56_2 = all_56_3) & ~ (all_56_4 = % 151.44/22.33 all_56_5) & ~ (all_56_6 = all_56_7)) | ( ~ (all_56_8 = all_56_9) & % 151.44/22.33 ~ (all_56_10 = all_56_11) & ~ (all_56_12 = all_56_13) & ~ (all_56_14 % 151.44/22.33 = all_56_15)) | ( ~ (all_56_16 = all_56_17) & ~ (all_56_18 = % 151.44/22.33 all_56_19) & ~ (all_56_20 = all_56_21) & ~ (all_56_22 = % 151.44/22.33 all_56_23)) | ( ~ (all_56_24 = all_56_25) & ~ (all_56_26 = % 151.44/22.33 all_56_27) & ~ (all_56_28 = all_56_29) & ~ (all_56_30 = % 151.44/22.33 all_56_31)) % 151.44/22.33 (64) all_58_1 = all_52_4 % 151.44/22.33 (65) all_58_13 = all_52_7 % 151.44/22.33 (66) all_58_4 = e0 | all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0 % 151.44/22.33 (67) op(e2, all_8_2) = all_56_10 % 151.44/22.33 (68) op(e3, e3) = all_10_2 % 151.44/22.33 (69) ~ (all_52_8 = all_6_2) % 151.44/22.33 (70) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0 % 151.44/22.33 (71) all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1 % 151.44/22.33 (72) ~ (all_56_21 = e3) | all_56_17 = e1 % 151.44/22.33 (73) all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0 % 151.44/22.33 (74) all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1 % 151.44/22.33 (75) ~ (all_52_1 = all_8_2) % 151.44/22.33 (76) all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2 % 151.44/22.33 (77) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 151.44/22.33 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 151.44/22.33 (78) ~ (all_52_3 = all_10_2) % 151.44/22.33 (79) all_54_3 = all_52_12 % 151.44/22.33 (80) all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0 % 151.44/22.33 (81) ~ (all_52_3 = all_52_7) % 151.44/22.33 (82) all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) & % 151.44/22.33 (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0)) % 151.44/22.33 (83) ~ (all_56_11 = e3) | all_56_9 = e2 % 151.44/22.33 (84) ~ (all_52_2 = all_52_6) % 151.44/22.33 (85) op(e0, all_4_1) = all_4_0 % 151.44/22.33 (86) all_56_7 = all_52_12 % 151.44/22.33 (87) op(e1, e2) = all_52_6 % 151.44/22.33 (88) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0 % 151.44/22.33 (89) all_56_13 = all_52_9 % 151.44/22.33 (90) op(e2, all_52_6) = all_56_18 % 151.44/22.33 (91) op(e0, e1) = all_52_11 % 151.44/22.33 (92) ~ (all_52_1 = all_52_13) % 151.44/22.33 (93) ~ (all_52_7 = all_4_2) % 151.44/22.33 (94) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0 % 151.44/22.33 (95) op(e1, e3) = all_52_2 % 151.44/22.33 (96) ~ (all_4_2 = e1) % 151.44/22.33 (97) all_58_8 = all_6_2 % 151.44/22.33 (98) all_54_6 = all_52_9 % 151.44/22.33 (99) ~ (all_4_0 = e1) % 151.44/22.33 (100) ~ (all_52_3 = all_4_2) % 151.44/22.33 (101) ~ (all_52_8 = all_10_2) % 151.44/22.33 (102) all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3 % 151.44/22.33 (103) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0 % 151.44/22.33 (104) ~ (all_56_1 = e2) | all_56_3 = e3 % 151.44/22.33 (105) ~ (all_56_1 = e0) | all_56_7 = e3 % 151.44/22.33 (106) all_56_5 = all_52_8 % 151.44/22.33 (107) ~ (all_52_9 = all_52_13) % 151.44/22.33 (108) ~ (all_52_2 = all_52_3) % 151.44/22.33 (109) op(e1, all_6_1) = all_6_0 % 151.44/22.33 (110) op(all_4_2, all_4_2) = all_4_1 % 151.44/22.33 (111) ~ (all_52_3 = all_52_11) % 151.44/22.33 (112) all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1 % 151.44/22.33 (113) all_58_3 = all_8_2 % 151.44/22.33 (114) all_56_3 = all_52_4 % 151.44/22.33 (115) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0 % 151.44/22.33 (116) ~ (all_52_11 = all_4_2) % 151.44/22.33 (117) ~ (all_52_1 = all_52_3) % 151.44/22.33 (118) all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1 % 151.44/22.33 (119) ~ (all_52_6 = all_52_7) % 151.44/22.33 (120) op(e1, all_52_8) = all_56_4 % 151.44/22.33 (121) all_56_31 = all_4_2 % 151.44/22.33 (122) all_58_11 = all_52_14 % 151.44/22.33 (123) all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3 % 151.44/22.33 (124) ~ (all_52_2 = all_52_14) % 151.44/22.33 (125) all_54_7 = all_52_13 % 151.44/22.33 (126) all_24_2 = all_10_2 % 151.44/22.33 (127) op(all_6_2, all_6_2) = all_6_1 % 151.44/22.33 (128) all_56_1 = e3 | all_56_11 = e2 | all_56_21 = e1 | all_56_31 = e0 % 151.44/22.33 (129) ~ (all_52_13 = all_4_2) % 151.44/22.33 (130) op(e3, e0) = all_52_12 % 151.44/22.33 (131) ~ (all_16_1 = e2) | ~ (all_16_2 = e0) % 151.44/22.33 (132) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0 % 151.44/22.33 (133) all_16_2 = all_10_2 % 151.44/22.33 (134) ~ (all_52_8 = all_52_11) % 151.44/22.33 (135) all_54_13 = all_52_7 % 151.44/22.33 (136) all_54_2 = all_52_8 % 151.44/22.33 (137) op(e3, e2) = all_52_4 % 151.44/22.33 (138) ~ (all_52_13 = all_52_14) % 151.44/22.33 (139) all_56_23 = all_52_14 % 151.44/22.33 (140) all_54_8 = all_52_2 % 151.44/22.33 (141) all_24_1 = all_10_1 % 151.44/22.33 (142) op(e1, e1) = all_6_2 % 151.44/22.33 (143) ~ (all_52_6 = all_8_2) % 151.44/22.33 (144) all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1 % 151.44/22.33 (145) op(e0, e3) = all_52_3 % 151.44/22.33 (146) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0 % 151.44/22.33 (147) all_58_15 = all_4_2 % 151.44/22.33 (148) op(e3, all_10_1) = e1 % 151.44/22.33 (149) ~ (all_6_2 = e2) % 151.44/22.33 (150) all_58_2 = all_52_1 % 151.44/22.33 (151) ~ (all_52_9 = all_6_2) % 151.44/22.33 (152) all_16_1 = all_10_1 % 151.44/22.33 (153) all_58_7 = all_52_6 % 151.44/22.33 (154) all_58_10 = all_52_13 % 151.44/22.33 (155) ~ (all_52_12 = all_4_2) % 151.44/22.33 (156) ~ (all_24_1 = e0) | ~ (all_24_2 = e2) % 151.44/22.33 (157) op(all_10_2, all_10_2) = all_10_1 % 151.44/22.33 (158) ~ (all_56_11 = e0) | all_56_15 = e2 % 151.44/22.33 (159) all_58_0 = all_10_2 % 151.44/22.33 (160) op(e3, all_52_2) = all_56_16 % 151.44/22.33 (161) op(e1, all_6_2) = all_56_20 % 151.44/22.33 (162) all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1 % 151.44/22.33 (163) op(e2, e3) = all_52_1 % 151.44/22.33 (164) all_58_1 = e0 | all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0 % 151.44/22.33 (165) ~ (all_52_12 = all_52_14) % 151.44/22.33 (166) op(e1, all_52_9) = all_56_12 % 151.44/22.33 (167) op(e3, e1) = all_52_8 % 151.44/22.33 (168) ~ (all_56_31 = e2) | all_56_27 = e0 % 151.44/22.33 (169) ~ (e3 = e1) % 151.44/22.33 (170) op(e2, e2) = all_8_2 % 151.44/22.33 (171) ~ (all_52_4 = all_52_12) % 151.44/22.33 (172) ~ (all_52_2 = all_6_2) % 151.44/22.33 (173) ~ (all_52_8 = all_52_12) % 151.44/22.33 (174) ~ (all_52_1 = all_52_2) % 151.44/22.33 (175) ~ (all_56_21 = e0) | all_56_23 = e1 % 151.44/22.33 (176) op(e0, all_4_2) = all_56_30 % 151.44/22.33 (177) ~ (all_52_6 = all_6_2) % 151.44/22.33 (178) op(e3, all_10_2) = all_56_0 % 151.44/22.33 (179) ~ (all_52_14 = all_6_2) % 151.44/22.33 (180) all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0 % 151.44/22.33 (181) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0 % 151.44/22.33 (182) ~ (all_52_2 = all_10_2) % 151.44/22.33 (183) ~ (all_52_4 = all_10_2) % 151.44/22.33 (184) all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3 % 151.44/22.33 (185) ~ (all_52_4 = all_8_2) % 151.44/22.33 (186) op(all_8_2, all_8_2) = all_8_1 % 151.44/22.33 (187) op(e3, all_52_3) = all_56_24 % 151.44/22.33 (188) ~ (all_52_4 = all_52_6) % 151.44/22.33 (189) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 151.44/22.33 (190) all_58_14 = all_52_11 % 151.44/22.33 (191) all_56_19 = all_52_6 % 151.44/22.33 (192) ~ (all_52_12 = all_10_2) % 151.44/22.33 (193) ~ (all_4_0 = e2) % 151.44/22.33 (194) all_56_9 = all_52_1 % 151.44/22.33 (195) all_56_15 = all_52_13 % 151.44/22.33 (196) ~ (all_52_1 = all_10_2) % 151.44/22.33 (197) all_58_12 = all_52_3 % 151.44/22.33 (198) all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2 % 151.44/22.33 (199) all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3 % 151.44/22.33 (200) all_54_11 = all_52_14 % 151.44/22.33 (201) ~ (all_56_31 = e3) | all_56_25 = e0 % 151.44/22.33 % 151.44/22.33 Begin of proof % 151.44/22.33 | % 151.44/22.33 | BETA: splitting (158) gives: % 151.44/22.33 | % 151.44/22.33 | Case 1: % 151.44/22.33 | | % 151.44/22.33 | | (202) ~ (all_56_11 = e0) % 151.44/22.33 | | % 151.44/22.33 | | REDUCE: (1), (202) imply: % 151.44/22.33 | | (203) ~ (all_8_2 = e0) % 151.44/22.33 | | % 151.44/22.33 | | BETA: splitting (3) gives: % 151.44/22.33 | | % 151.44/22.33 | | Case 1: % 151.44/22.33 | | | % 151.44/22.33 | | | (204) ~ (all_56_11 = e1) % 151.44/22.33 | | | % 151.44/22.33 | | | REDUCE: (1), (204) imply: % 151.44/22.33 | | | (205) ~ (all_8_2 = e1) % 151.44/22.33 | | | % 151.44/22.33 | | | BETA: splitting (201) gives: % 151.44/22.33 | | | % 151.44/22.33 | | | Case 1: % 151.44/22.33 | | | | % 151.44/22.33 | | | | (206) ~ (all_56_31 = e3) % 151.44/22.33 | | | | % 151.44/22.33 | | | | REDUCE: (121), (206) imply: % 151.44/22.33 | | | | (207) ~ (all_4_2 = e3) % 151.44/22.33 | | | | % 151.44/22.33 | | | | BETA: splitting (175) gives: % 151.44/22.33 | | | | % 151.44/22.33 | | | | Case 1: % 151.44/22.33 | | | | | % 151.44/22.33 | | | | | (208) ~ (all_56_21 = e0) % 151.44/22.33 | | | | | % 151.44/22.33 | | | | | REDUCE: (44), (208) imply: % 151.44/22.33 | | | | | (209) ~ (all_6_2 = e0) % 151.44/22.33 | | | | | % 151.44/22.33 | | | | | BETA: splitting (168) gives: % 151.44/22.33 | | | | | % 151.44/22.33 | | | | | Case 1: % 151.44/22.33 | | | | | | % 151.44/22.33 | | | | | | (210) ~ (all_56_31 = e2) % 151.44/22.33 | | | | | | % 151.44/22.33 | | | | | | REDUCE: (121), (210) imply: % 151.44/22.33 | | | | | | (211) ~ (all_4_2 = e2) % 151.44/22.33 | | | | | | % 151.44/22.33 | | | | | | REF_CLOSE: (11), (16), (17), (18), (19), (21), (25), (29), (30), % 151.44/22.33 | | | | | | (31), (33), (36), (37), (38), (39), (41), (45), (47), % 151.44/22.33 | | | | | | (49), (51), (61), (64), (65), (68), (69), (77), (78), % 151.44/22.33 | | | | | | (79), (81), (85), (86), (88), (93), (96), (97), (100), % 151.44/22.33 | | | | | | (102), (103), (104), (105), (106), (108), (110), (113), % 151.44/22.33 | | | | | | (114), (119), (122), (125), (127), (129), (130), (132), % 151.44/22.33 | | | | | | (135), (138), (142), (148), (149), (153), (155), (157), % 151.44/22.33 | | | | | | (161), (164), (165), (167), (169), (171), (176), (178), % 151.44/22.33 | | | | | | (185), (187), (189), (192), (197), (199), (200), (203), % 151.44/22.33 | | | | | | (205), (207), (209), (211) are inconsistent by sub-proof % 151.44/22.33 | | | | | | #297. % 151.44/22.33 | | | | | | % 151.44/22.33 | | | | | Case 2: % 151.44/22.33 | | | | | | % 151.44/22.33 | | | | | | (212) all_56_31 = e2 % 151.44/22.33 | | | | | | (213) all_56_27 = e0 % 151.44/22.33 | | | | | | % 151.44/22.33 | | | | | | COMBINE_EQS: (50), (213) imply: % 151.44/22.33 | | | | | | (214) all_52_7 = e0 % 151.44/22.33 | | | | | | % 151.44/22.33 | | | | | | SIMP: (214) implies: % 151.44/22.33 | | | | | | (215) all_52_7 = e0 % 151.44/22.33 | | | | | | % 151.44/22.33 | | | | | | COMBINE_EQS: (121), (212) imply: % 151.44/22.33 | | | | | | (216) all_4_2 = e2 % 151.44/22.33 | | | | | | % 151.44/22.33 | | | | | | COMBINE_EQS: (147), (216) imply: % 151.44/22.33 | | | | | | (217) all_58_15 = e2 % 151.44/22.33 | | | | | | % 151.44/22.33 | | | | | | COMBINE_EQS: (65), (215) imply: % 151.44/22.33 | | | | | | (218) all_58_13 = e0 % 151.44/22.33 | | | | | | % 151.44/22.33 | | | | | | REDUCE: (7), (215) imply: % 151.44/22.33 | | | | | | (219) ~ (all_52_11 = e0) % 151.44/22.33 | | | | | | % 151.44/22.33 | | | | | | SIMP: (219) implies: % 151.44/22.33 | | | | | | (220) ~ (all_52_11 = e0) % 151.44/22.33 | | | | | | % 151.44/22.33 | | | | | | REDUCE: (47), (215) imply: % 151.44/22.33 | | | | | | (221) ~ (all_8_2 = e0) % 151.44/22.33 | | | | | | % 151.44/22.33 | | | | | | REDUCE: (93), (215), (216) imply: % 151.44/22.33 | | | | | | (222) ~ (e2 = e0) % 151.44/22.33 | | | | | | % 151.44/22.33 | | | | | | SIMP: (222) implies: % 151.44/22.33 | | | | | | (223) ~ (e2 = e0) % 151.44/22.33 | | | | | | % 151.44/22.33 | | | | | | REDUCE: (116), (216) imply: % 151.44/22.33 | | | | | | (224) ~ (all_52_11 = e2) % 151.44/22.33 | | | | | | % 151.44/22.33 | | | | | | REDUCE: (155), (216) imply: % 151.44/22.33 | | | | | | (225) ~ (all_52_12 = e2) % 151.44/22.33 | | | | | | % 151.44/22.33 | | | | | | REDUCE: (129), (216) imply: % 151.44/22.33 | | | | | | (226) ~ (all_52_13 = e2) % 151.44/22.33 | | | | | | % 151.44/22.33 | | | | | | REDUCE: (110), (216) imply: % 151.44/22.33 | | | | | | (227) op(e2, e2) = all_4_1 % 151.44/22.33 | | | | | | % 151.44/22.33 | | | | | | REDUCE: (33), (216) imply: % 151.44/22.33 | | | | | | (228) op(e0, e0) = e2 % 151.44/22.33 | | | | | | % 151.44/22.33 | | | | | | GROUND_INST: instantiating (77) with all_8_2, all_4_1, e2, e2, % 151.44/22.33 | | | | | | simplifying with (170), (227) gives: % 151.44/22.33 | | | | | | (229) all_8_2 = all_4_1 % 151.44/22.33 | | | | | | % 151.44/22.33 | | | | | | COMBINE_EQS: (36), (229) imply: % 151.44/22.33 | | | | | | (230) all_54_5 = all_4_1 % 151.44/22.33 | | | | | | % 151.44/22.33 | | | | | | COMBINE_EQS: (1), (229) imply: % 151.44/22.33 | | | | | | (231) all_56_11 = all_4_1 % 151.44/22.33 | | | | | | % 151.44/22.33 | | | | | | COMBINE_EQS: (113), (229) imply: % 151.44/22.33 | | | | | | (232) all_58_3 = all_4_1 % 151.44/22.33 | | | | | | % 151.44/22.33 | | | | | | REDUCE: (75), (229) imply: % 151.44/22.33 | | | | | | (233) ~ (all_52_1 = all_4_1) % 151.44/22.33 | | | | | | % 151.44/22.33 | | | | | | REDUCE: (28), (229) imply: % 151.44/22.33 | | | | | | (234) ~ (all_52_9 = all_4_1) % 151.44/22.33 | | | | | | % 151.44/22.33 | | | | | | REDUCE: (19), (229) imply: % 151.44/22.33 | | | | | | (235) ~ (all_52_13 = all_4_1) % 151.44/22.33 | | | | | | % 151.44/22.33 | | | | | | REDUCE: (205), (229) imply: % 151.44/22.33 | | | | | | (236) ~ (all_4_1 = e1) % 151.44/22.33 | | | | | | % 151.44/22.33 | | | | | | BETA: splitting (72) gives: % 151.44/22.33 | | | | | | % 151.44/22.33 | | | | | | Case 1: % 151.44/22.33 | | | | | | | % 151.44/22.33 | | | | | | | (237) ~ (all_56_21 = e3) % 151.44/22.33 | | | | | | | % 151.44/22.33 | | | | | | | REDUCE: (44), (237) imply: % 151.44/22.33 | | | | | | | (238) ~ (all_6_2 = e3) % 151.44/22.33 | | | | | | | % 151.44/22.33 | | | | | | | BETA: splitting (45) gives: % 151.44/22.33 | | | | | | | % 151.44/22.33 | | | | | | | Case 1: % 151.44/22.33 | | | | | | | | % 151.44/22.33 | | | | | | | | (239) all_54_10 = e3 % 151.44/22.33 | | | | | | | | % 151.44/22.33 | | | | | | | | REF_CLOSE: (16), (238), (239) are inconsistent by sub-proof % 151.44/22.33 | | | | | | | | #736. % 151.44/22.33 | | | | | | | | % 151.44/22.33 | | | | | | | Case 2: % 151.44/22.33 | | | | | | | | % 151.44/22.33 | | | | | | | | (240) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 151.44/22.33 | | | | | | | | % 151.44/22.33 | | | | | | | | BETA: splitting (240) gives: % 151.44/22.33 | | | | | | | | % 151.44/22.33 | | | | | | | | Case 1: % 151.44/22.33 | | | | | | | | | % 151.44/22.33 | | | | | | | | | (241) all_54_10 = e2 % 151.44/22.33 | | | | | | | | | % 151.44/22.33 | | | | | | | | | REF_CLOSE: (16), (149), (241) are inconsistent by sub-proof % 151.44/22.33 | | | | | | | | | #735. % 151.44/22.33 | | | | | | | | | % 151.44/22.33 | | | | | | | | Case 2: % 151.44/22.33 | | | | | | | | | % 151.44/22.33 | | | | | | | | | (242) all_54_10 = e1 | all_54_10 = e0 % 151.44/22.33 | | | | | | | | | % 151.44/22.33 | | | | | | | | | BETA: splitting (242) gives: % 151.44/22.33 | | | | | | | | | % 151.44/22.33 | | | | | | | | | Case 1: % 151.44/22.33 | | | | | | | | | | % 151.44/22.33 | | | | | | | | | | (243) all_54_10 = e1 % 151.44/22.33 | | | | | | | | | | % 151.44/22.33 | | | | | | | | | | COMBINE_EQS: (16), (243) imply: % 151.44/22.33 | | | | | | | | | | (244) all_6_2 = e1 % 151.44/22.33 | | | | | | | | | | % 151.44/22.33 | | | | | | | | | | SIMP: (244) implies: % 151.44/22.33 | | | | | | | | | | (245) all_6_2 = e1 % 151.44/22.33 | | | | | | | | | | % 151.44/22.33 | | | | | | | | | | REDUCE: (69), (245) imply: % 151.44/22.33 | | | | | | | | | | (246) ~ (all_52_8 = e1) % 151.44/22.33 | | | | | | | | | | % 151.44/22.33 | | | | | | | | | | REDUCE: (151), (245) imply: % 151.44/22.33 | | | | | | | | | | (247) ~ (all_52_9 = e1) % 151.44/22.33 | | | | | | | | | | % 151.44/22.33 | | | | | | | | | | REDUCE: (4), (245) imply: % 151.44/22.33 | | | | | | | | | | (248) ~ (all_52_11 = e1) % 151.44/22.33 | | | | | | | | | | % 151.44/22.33 | | | | | | | | | | REDUCE: (179), (245) imply: % 151.44/22.33 | | | | | | | | | | (249) ~ (all_52_14 = e1) % 151.44/22.33 | | | | | | | | | | % 151.44/22.33 | | | | | | | | | | REDUCE: (209), (245) imply: % 151.44/22.33 | | | | | | | | | | (250) ~ (e1 = e0) % 151.44/22.33 | | | | | | | | | | % 151.44/22.33 | | | | | | | | | | BETA: splitting (15) gives: % 151.44/22.33 | | | | | | | | | | % 151.44/22.33 | | | | | | | | | | Case 1: % 151.44/22.33 | | | | | | | | | | | % 151.44/22.33 | | | | | | | | | | | (251) all_54_14 = e3 % 151.44/22.33 | | | | | | | | | | | % 151.44/22.33 | | | | | | | | | | | COMBINE_EQS: (62), (251) imply: % 151.44/22.33 | | | | | | | | | | | (252) all_52_11 = e3 % 151.44/22.33 | | | | | | | | | | | % 151.44/22.33 | | | | | | | | | | | REDUCE: (111), (252) imply: % 151.44/22.33 | | | | | | | | | | | (253) ~ (all_52_3 = e3) % 151.44/22.33 | | | | | | | | | | | % 151.44/22.33 | | | | | | | | | | | REDUCE: (134), (252) imply: % 151.44/22.33 | | | | | | | | | | | (254) ~ (all_52_8 = e3) % 151.44/22.33 | | | | | | | | | | | % 151.44/22.33 | | | | | | | | | | | BETA: splitting (162) gives: % 151.44/22.33 | | | | | | | | | | | % 151.44/22.33 | | | | | | | | | | | Case 1: % 151.44/22.33 | | | | | | | | | | | | % 151.44/22.33 | | | | | | | | | | | | (255) all_58_12 = e1 % 151.44/22.33 | | | | | | | | | | | | % 151.44/22.33 | | | | | | | | | | | | COMBINE_EQS: (197), (255) imply: % 151.44/22.33 | | | | | | | | | | | | (256) all_52_3 = e1 % 151.56/22.33 | | | | | | | | | | | | % 151.56/22.33 | | | | | | | | | | | | REDUCE: (117), (256) imply: % 151.56/22.33 | | | | | | | | | | | | (257) ~ (all_52_1 = e1) % 151.56/22.33 | | | | | | | | | | | | % 151.56/22.33 | | | | | | | | | | | | REDUCE: (78), (256) imply: % 151.56/22.33 | | | | | | | | | | | | (258) ~ (all_10_2 = e1) % 151.56/22.33 | | | | | | | | | | | | % 151.56/22.33 | | | | | | | | | | | | SIMP: (258) implies: % 151.56/22.33 | | | | | | | | | | | | (259) ~ (all_10_2 = e1) % 151.56/22.33 | | | | | | | | | | | | % 151.56/22.33 | | | | | | | | | | | | REDUCE: (253), (256) imply: % 151.56/22.33 | | | | | | | | | | | | (260) ~ (e3 = e1) % 151.56/22.33 | | | | | | | | | | | | % 151.56/22.33 | | | | | | | | | | | | REDUCE: (145), (256) imply: % 151.56/22.33 | | | | | | | | | | | | (261) op(e0, e3) = e1 % 151.56/22.33 | | | | | | | | | | | | % 151.56/22.33 | | | | | | | | | | | | BETA: splitting (118) gives: % 151.56/22.33 | | | | | | | | | | | | % 151.56/22.33 | | | | | | | | | | | | Case 1: % 151.56/22.33 | | | | | | | | | | | | | % 151.56/22.33 | | | | | | | | | | | | | (262) all_58_1 = e1 % 151.56/22.33 | | | | | | | | | | | | | % 151.56/22.33 | | | | | | | | | | | | | COMBINE_EQS: (64), (262) imply: % 151.56/22.33 | | | | | | | | | | | | | (263) all_52_4 = e1 % 151.56/22.33 | | | | | | | | | | | | | % 151.56/22.33 | | | | | | | | | | | | | COMBINE_EQS: (114), (263) imply: % 151.56/22.33 | | | | | | | | | | | | | (264) all_56_3 = e1 % 151.56/22.33 | | | | | | | | | | | | | % 151.56/22.33 | | | | | | | | | | | | | REDUCE: (171), (263) imply: % 151.56/22.33 | | | | | | | | | | | | | (265) ~ (all_52_12 = e1) % 151.56/22.33 | | | | | | | | | | | | | % 151.56/22.33 | | | | | | | | | | | | | SIMP: (265) implies: % 151.56/22.33 | | | | | | | | | | | | | (266) ~ (all_52_12 = e1) % 151.56/22.33 | | | | | | | | | | | | | % 151.56/22.33 | | | | | | | | | | | | | BETA: splitting (104) gives: % 151.56/22.33 | | | | | | | | | | | | | % 151.56/22.33 | | | | | | | | | | | | | Case 1: % 151.56/22.33 | | | | | | | | | | | | | | % 151.56/22.33 | | | | | | | | | | | | | | (267) ~ (all_56_1 = e2) % 151.56/22.33 | | | | | | | | | | | | | | % 151.56/22.33 | | | | | | | | | | | | | | REDUCE: (49), (267) imply: % 151.56/22.33 | | | | | | | | | | | | | | (268) ~ (all_10_2 = e2) % 151.56/22.33 | | | | | | | | | | | | | | % 151.56/22.33 | | | | | | | | | | | | | | BETA: splitting (42) gives: % 151.56/22.33 | | | | | | | | | | | | | | % 151.56/22.33 | | | | | | | | | | | | | | Case 1: % 151.56/22.33 | | | | | | | | | | | | | | | % 151.56/22.33 | | | | | | | | | | | | | | | (269) all_58_9 = e1 % 151.56/22.33 | | | | | | | | | | | | | | | % 151.56/22.33 | | | | | | | | | | | | | | | COMBINE_EQS: (56), (269) imply: % 151.56/22.33 | | | | | | | | | | | | | | | (270) all_52_12 = e1 % 151.56/22.33 | | | | | | | | | | | | | | | % 151.56/22.33 | | | | | | | | | | | | | | | REDUCE: (266), (270) imply: % 151.56/22.33 | | | | | | | | | | | | | | | (271) $false % 151.56/22.33 | | | | | | | | | | | | | | | % 151.56/22.33 | | | | | | | | | | | | | | | CLOSE: (271) is inconsistent. % 151.56/22.33 | | | | | | | | | | | | | | | % 151.56/22.33 | | | | | | | | | | | | | | Case 2: % 151.56/22.33 | | | | | | | | | | | | | | | % 151.56/22.33 | | | | | | | | | | | | | | | (272) all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1 % 151.56/22.33 | | | | | | | | | | | | | | | % 151.56/22.33 | | | | | | | | | | | | | | | BETA: splitting (27) gives: % 151.56/22.33 | | | | | | | | | | | | | | | % 151.56/22.33 | | | | | | | | | | | | | | | Case 1: % 151.56/22.33 | | | | | | | | | | | | | | | | % 151.56/22.33 | | | | | | | | | | | | | | | | (273) all_58_0 = e2 % 151.56/22.33 | | | | | | | | | | | | | | | | % 151.56/22.33 | | | | | | | | | | | | | | | | COMBINE_EQS: (159), (273) imply: % 151.56/22.33 | | | | | | | | | | | | | | | | (274) all_10_2 = e2 % 151.56/22.33 | | | | | | | | | | | | | | | | % 151.56/22.33 | | | | | | | | | | | | | | | | REDUCE: (268), (274) imply: % 151.56/22.33 | | | | | | | | | | | | | | | | (275) $false % 151.56/22.33 | | | | | | | | | | | | | | | | % 151.56/22.33 | | | | | | | | | | | | | | | | CLOSE: (275) is inconsistent. % 151.56/22.33 | | | | | | | | | | | | | | | | % 151.56/22.33 | | | | | | | | | | | | | | | Case 2: % 151.56/22.33 | | | | | | | | | | | | | | | | % 151.56/22.33 | | | | | | | | | | | | | | | | (276) all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2 % 151.56/22.33 | | | | | | | | | | | | | | | | % 151.56/22.33 | | | | | | | | | | | | | | | | BETA: splitting (272) gives: % 151.56/22.33 | | | | | | | | | | | | | | | | % 151.56/22.33 | | | | | | | | | | | | | | | | Case 1: % 151.56/22.33 | | | | | | | | | | | | | | | | | % 151.56/22.33 | | | | | | | | | | | | | | | | | (277) all_58_10 = e1 % 151.56/22.33 | | | | | | | | | | | | | | | | | % 151.56/22.33 | | | | | | | | | | | | | | | | | COMBINE_EQS: (154), (277) imply: % 151.56/22.33 | | | | | | | | | | | | | | | | | (278) all_52_13 = e1 % 151.56/22.33 | | | | | | | | | | | | | | | | | % 151.56/22.33 | | | | | | | | | | | | | | | | | REDUCE: (235), (278) imply: % 151.56/22.33 | | | | | | | | | | | | | | | | | (279) ~ (all_4_1 = e1) % 151.56/22.33 | | | | | | | | | | | | | | | | | % 151.56/22.33 | | | | | | | | | | | | | | | | | REDUCE: (226), (278) imply: % 151.56/22.33 | | | | | | | | | | | | | | | | | (280) ~ (e2 = e1) % 151.56/22.33 | | | | | | | | | | | | | | | | | % 151.56/22.33 | | | | | | | | | | | | | | | | | SIMP: (280) implies: % 151.56/22.33 | | | | | | | | | | | | | | | | | (281) ~ (e2 = e1) % 151.56/22.33 | | | | | | | | | | | | | | | | | % 151.56/22.33 | | | | | | | | | | | | | | | | | BETA: splitting (276) gives: % 151.56/22.33 | | | | | | | | | | | | | | | | | % 151.56/22.33 | | | | | | | | | | | | | | | | | Case 1: % 151.56/22.33 | | | | | | | | | | | | | | | | | | % 151.56/22.33 | | | | | | | | | | | | | | | | | | (282) all_58_1 = e2 % 151.56/22.33 | | | | | | | | | | | | | | | | | | % 151.56/22.33 | | | | | | | | | | | | | | | | | | REF_CLOSE: (262), (281), (282) are inconsistent by sub-proof % 151.56/22.33 | | | | | | | | | | | | | | | | | | #594. % 151.56/22.33 | | | | | | | | | | | | | | | | | | % 151.56/22.33 | | | | | | | | | | | | | | | | | Case 2: % 151.56/22.33 | | | | | | | | | | | | | | | | | | % 151.56/22.33 | | | | | | | | | | | | | | | | | | (283) all_58_4 = e2 | all_58_9 = e2 % 151.56/22.33 | | | | | | | | | | | | | | | | | | % 151.56/22.33 | | | | | | | | | | | | | | | | | | BETA: splitting (283) gives: % 151.56/22.33 | | | | | | | | | | | | | | | | | | % 151.56/22.33 | | | | | | | | | | | | | | | | | | Case 1: % 151.56/22.33 | | | | | | | | | | | | | | | | | | | % 151.56/22.33 | | | | | | | | | | | | | | | | | | | (284) all_58_4 = e2 % 151.56/22.33 | | | | | | | | | | | | | | | | | | | % 151.56/22.33 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (35), (284) imply: % 151.56/22.33 | | | | | | | | | | | | | | | | | | | (285) all_52_8 = e2 % 151.56/22.33 | | | | | | | | | | | | | | | | | | | % 151.56/22.33 | | | | | | | | | | | | | | | | | | | REDUCE: (101), (285) imply: % 151.56/22.33 | | | | | | | | | | | | | | | | | | | (286) ~ (all_10_2 = e2) % 151.56/22.33 | | | | | | | | | | | | | | | | | | | % 151.56/22.33 | | | | | | | | | | | | | | | | | | | REDUCE: (254), (285) imply: % 151.56/22.33 | | | | | | | | | | | | | | | | | | | (287) ~ (e3 = e2) % 151.56/22.33 | | | | | | | | | | | | | | | | | | | % 151.56/22.33 | | | | | | | | | | | | | | | | | | | SIMP: (287) implies: % 151.56/22.33 | | | | | | | | | | | | | | | | | | | (288) ~ (e3 = e2) % 151.56/22.33 | | | | | | | | | | | | | | | | | | | % 151.56/22.33 | | | | | | | | | | | | | | | | | | | BETA: splitting (66) gives: % 151.56/22.33 | | | | | | | | | | | | | | | | | | | % 151.56/22.33 | | | | | | | | | | | | | | | | | | | Case 1: % 151.56/22.33 | | | | | | | | | | | | | | | | | | | | % 151.56/22.33 | | | | | | | | | | | | | | | | | | | | (289) all_58_4 = e0 % 151.56/22.33 | | | | | | | | | | | | | | | | | | | | % 151.56/22.33 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (284), (289) imply: % 151.56/22.33 | | | | | | | | | | | | | | | | | | | | (290) e2 = e0 % 151.56/22.33 | | | | | | | | | | | | | | | | | | | | % 151.56/22.33 | | | | | | | | | | | | | | | | | | | | REDUCE: (223), (290) imply: % 151.56/22.33 | | | | | | | | | | | | | | | | | | | | (291) $false % 151.56/22.33 | | | | | | | | | | | | | | | | | | | | % 151.56/22.33 | | | | | | | | | | | | | | | | | | | | CLOSE: (291) is inconsistent. % 151.56/22.33 | | | | | | | | | | | | | | | | | | | | % 151.56/22.33 | | | | | | | | | | | | | | | | | | | Case 2: % 151.56/22.33 | | | | | | | | | | | | | | | | | | | | % 151.56/22.33 | | | | | | | | | | | | | | | | | | | | (292) all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0 % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | BETA: splitting (292) gives: % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | Case 1: % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | (293) all_58_5 = e0 % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (53), (293) imply: % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | (294) all_52_9 = e0 % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | REDUCE: (13), (294) imply: % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | (295) ~ (all_52_1 = e0) % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | REDUCE: (234), (294) imply: % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | (296) ~ (all_4_1 = e0) % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | SIMP: (296) implies: % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | (297) ~ (all_4_1 = e0) % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (83) gives: % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | Case 1: % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | (298) ~ (all_56_11 = e3) % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (231), (298) imply: % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | (299) ~ (all_4_1 = e3) % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (184) gives: % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | (300) all_58_2 = e3 % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (150), (300) imply: % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | (301) all_52_1 = e3 % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (196), (301) imply: % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | (302) ~ (all_10_2 = e3) % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (302) implies: % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | (303) ~ (all_10_2 = e3) % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (39) gives: % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | (304) all_54_0 = e3 % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (21), (303), (304) are inconsistent by sub-proof % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | #709. % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | (305) ~ (all_54_0 = e3) % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | (306) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (306) gives: % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | (307) all_54_0 = e2 % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (21), (268), (307) are inconsistent by sub-proof % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | #734. % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | (308) ~ (all_54_0 = e2) % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | (309) all_54_0 = e1 | all_54_0 = e0 % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (123) gives: % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | | (310) all_58_0 = e3 % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (159), (310) imply: % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | | (311) all_10_2 = e3 % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (303), (311) imply: % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | | (312) $false % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (312) is inconsistent. % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | | (313) all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3 % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (313) gives: % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | (314) all_58_1 = e3 % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (262), (314) imply: % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | (315) e3 = e1 % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (315) implies: % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | (316) e3 = e1 % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (169), (316) imply: % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | (317) $false % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (317) is inconsistent. % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | (318) all_58_4 = e3 | all_58_9 = e3 % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (318) gives: % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (319) all_58_4 = e3 % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (284), (288), (319) are inconsistent by sub-proof % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | #296. % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (320) all_58_9 = e3 % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (56), (320) imply: % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (321) all_52_12 = e3 % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (73) gives: % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (322) all_58_0 = e0 % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (159), (322) imply: % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (323) all_10_2 = e0 % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (133), (323) imply: % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (324) all_16_2 = e0 % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (303), (323) imply: % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (325) ~ (e3 = e0) % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (325) implies: % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (326) ~ (e3 = e0) % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (259), (323) imply: % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (327) ~ (e1 = e0) % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (157), (323) imply: % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (328) op(e0, e0) = all_10_1 % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (82) gives: % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (329) all_58_15 = e0 % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (217), (329) imply: % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (330) e2 = e0 % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (223), (330) imply: % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (331) $false % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (331) is inconsistent. % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (332) (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (332) implies: % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (333) all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0 % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (333) gives: % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (334) all_58_9 = e0 % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (320), (334) imply: % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (335) e3 = e0 % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (326), (335) imply: % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (336) $false % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (336) is inconsistent. % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (337) all_58_10 = e0 | all_58_11 = e0 % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (337) gives: % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (338) all_58_10 = e0 % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (277), (338) imply: % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (339) e1 = e0 % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (250), (339) imply: % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (340) $false % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (340) is inconsistent. % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (341) all_58_11 = e0 % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (122), (341) imply: % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (342) all_52_14 = e0 % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (58), (342) imply: % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (343) op(e0, e0) = all_56_22 % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (131) gives: % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (344) ~ (all_16_1 = e2) % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (152), (344) imply: % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (345) ~ (all_10_1 = e2) % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (77), (228), (328), (343), (345) are inconsistent % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #582. % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (346) ~ (all_16_2 = e0) % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (324), (346) imply: % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (347) $false % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (347) is inconsistent. % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (348) ~ (all_58_0 = e0) % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (159), (348) imply: % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (349) ~ (all_10_2 = e0) % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (309) gives: % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (350) all_54_0 = e1 % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (21), (259), (350) are inconsistent by sub-proof % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #733. % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (351) all_54_0 = e0 % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (21), (349), (351) are inconsistent by sub-proof % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #732. % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | End of split % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | (352) ~ (all_58_2 = e3) % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (150), (352) imply: % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | (353) ~ (all_52_1 = e3) % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (94) gives: % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | (354) all_54_4 = e3 % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (22), (354) imply: % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | (355) all_52_1 = e3 % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (353), (355) imply: % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | (356) $false % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (356) is inconsistent. % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | (357) all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0 % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (357) gives: % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | (358) all_54_4 = e2 % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (22), (358) imply: % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | (359) all_52_1 = e2 % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (233), (359) imply: % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | (360) ~ (all_4_1 = e2) % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (360) implies: % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | (361) ~ (all_4_1 = e2) % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (189), (230), (236), (297), (299), (361) are % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #567. % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | (362) all_54_4 = e1 | all_54_4 = e0 % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (22), (257), (295), (362) are inconsistent by % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #583. % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | | % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | | % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | End of split % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | | % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | End of split % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | Case 2: % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | (363) all_56_11 = e3 % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (77), (85), (99), (231), (261), (363) are % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #295. % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | | % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | End of split % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | Case 2: % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | (364) all_58_8 = e0 | all_58_14 = e0 % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (97), (190), (209), (220), (364) are inconsistent % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | by sub-proof #627. % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | | % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | End of split % 151.56/22.34 | | | | | | | | | | | | | | | | | | | | % 151.56/22.34 | | | | | | | | | | | | | | | | | | | End of split % 151.56/22.34 | | | | | | | | | | | | | | | | | | | % 151.56/22.34 | | | | | | | | | | | | | | | | | | Case 2: % 151.56/22.34 | | | | | | | | | | | | | | | | | | | % 151.56/22.34 | | | | | | | | | | | | | | | | | | | (365) all_58_9 = e2 % 151.56/22.34 | | | | | | | | | | | | | | | | | | | % 151.56/22.34 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (56), (365) imply: % 151.56/22.34 | | | | | | | | | | | | | | | | | | | (366) all_52_12 = e2 % 151.56/22.34 | | | | | | | | | | | | | | | | | | | % 151.56/22.34 | | | | | | | | | | | | | | | | | | | REDUCE: (225), (366) imply: % 151.56/22.34 | | | | | | | | | | | | | | | | | | | (367) $false % 151.56/22.34 | | | | | | | | | | | | | | | | | | | % 151.56/22.34 | | | | | | | | | | | | | | | | | | | CLOSE: (367) is inconsistent. % 151.56/22.34 | | | | | | | | | | | | | | | | | | | % 151.56/22.34 | | | | | | | | | | | | | | | | | | End of split % 151.56/22.34 | | | | | | | | | | | | | | | | | | % 151.56/22.34 | | | | | | | | | | | | | | | | | End of split % 151.56/22.34 | | | | | | | | | | | | | | | | | % 151.56/22.34 | | | | | | | | | | | | | | | | Case 2: % 151.56/22.34 | | | | | | | | | | | | | | | | | % 151.56/22.34 | | | | | | | | | | | | | | | | | (368) all_58_11 = e1 | all_58_15 = e1 % 151.56/22.34 | | | | | | | | | | | | | | | | | % 151.56/22.34 | | | | | | | | | | | | | | | | | REF_CLOSE: (96), (122), (147), (249), (368) are inconsistent % 151.56/22.34 | | | | | | | | | | | | | | | | | by sub-proof #672. % 151.56/22.34 | | | | | | | | | | | | | | | | | % 151.56/22.34 | | | | | | | | | | | | | | | | End of split % 151.56/22.34 | | | | | | | | | | | | | | | | % 151.56/22.34 | | | | | | | | | | | | | | | End of split % 151.56/22.34 | | | | | | | | | | | | | | | % 151.56/22.34 | | | | | | | | | | | | | | End of split % 151.56/22.34 | | | | | | | | | | | | | | % 151.56/22.34 | | | | | | | | | | | | | Case 2: % 151.56/22.34 | | | | | | | | | | | | | | % 151.56/22.34 | | | | | | | | | | | | | | (369) all_56_3 = e3 % 151.56/22.34 | | | | | | | | | | | | | | % 151.56/22.34 | | | | | | | | | | | | | | REF_CLOSE: (169), (264), (369) are inconsistent by sub-proof % 151.56/22.34 | | | | | | | | | | | | | | #579. % 151.56/22.34 | | | | | | | | | | | | | | % 151.56/22.34 | | | | | | | | | | | | | End of split % 151.56/22.34 | | | | | | | | | | | | | % 151.56/22.34 | | | | | | | | | | | | Case 2: % 151.56/22.34 | | | | | | | | | | | | | % 151.56/22.34 | | | | | | | | | | | | | (370) ~ (all_58_1 = e1) % 151.56/22.34 | | | | | | | | | | | | | % 151.56/22.34 | | | | | | | | | | | | | REDUCE: (64), (370) imply: % 151.56/22.34 | | | | | | | | | | | | | (371) ~ (all_52_4 = e1) % 151.56/22.34 | | | | | | | | | | | | | % 151.56/22.34 | | | | | | | | | | | | | REF_CLOSE: (30), (35), (53), (56), (64), (71), (74), (150), % 151.56/22.34 | | | | | | | | | | | | | (154), (159), (232), (236), (246), (247), (257), % 151.56/22.34 | | | | | | | | | | | | | (259), (371) are inconsistent by sub-proof #576. % 151.56/22.34 | | | | | | | | | | | | | % 151.56/22.34 | | | | | | | | | | | | End of split % 151.56/22.34 | | | | | | | | | | | | % 151.56/22.34 | | | | | | | | | | | Case 2: % 151.56/22.34 | | | | | | | | | | | | % 151.56/22.34 | | | | | | | | | | | | (372) all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1 % 151.56/22.34 | | | | | | | | | | | | % 151.56/22.34 | | | | | | | | | | | | REF_CLOSE: (96), (147), (190), (218), (248), (250), (372) are % 151.56/22.34 | | | | | | | | | | | | inconsistent by sub-proof #575. % 151.56/22.34 | | | | | | | | | | | | % 151.56/22.34 | | | | | | | | | | | End of split % 151.56/22.34 | | | | | | | | | | | % 151.56/22.34 | | | | | | | | | | Case 2: % 151.56/22.34 | | | | | | | | | | | % 151.56/22.34 | | | | | | | | | | | (373) all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0 % 151.56/22.34 | | | | | | | | | | | % 151.56/22.34 | | | | | | | | | | | REF_CLOSE: (62), (220), (224), (248), (373) are inconsistent % 151.56/22.34 | | | | | | | | | | | by sub-proof #580. % 151.56/22.34 | | | | | | | | | | | % 151.56/22.34 | | | | | | | | | | End of split % 151.56/22.34 | | | | | | | | | | % 151.56/22.34 | | | | | | | | | Case 2: % 151.56/22.34 | | | | | | | | | | % 151.56/22.34 | | | | | | | | | | (374) all_54_10 = e0 % 151.56/22.34 | | | | | | | | | | % 151.56/22.34 | | | | | | | | | | REF_CLOSE: (16), (209), (374) are inconsistent by sub-proof % 151.56/22.34 | | | | | | | | | | #705. % 151.56/22.34 | | | | | | | | | | % 151.56/22.34 | | | | | | | | | End of split % 151.56/22.34 | | | | | | | | | % 151.56/22.34 | | | | | | | | End of split % 151.56/22.34 | | | | | | | | % 151.56/22.34 | | | | | | | End of split % 151.56/22.34 | | | | | | | % 151.56/22.34 | | | | | | Case 2: % 151.56/22.34 | | | | | | | % 151.56/22.34 | | | | | | | (375) all_56_21 = e3 % 151.56/22.34 | | | | | | | (376) all_56_17 = e1 % 151.56/22.34 | | | | | | | % 151.56/22.34 | | | | | | | REF_CLOSE: (1), (9), (18), (21), (23), (25), (30), (37), (38), % 151.56/22.34 | | | | | | | (39), (40), (42), (44), (49), (53), (55), (56), (60), % 151.56/22.34 | | | | | | | (68), (77), (80), (84), (86), (96), (105), (109), % 151.56/22.34 | | | | | | | (113), (115), (121), (122), (124), (127), (128), (138), % 151.56/22.34 | | | | | | | (143), (147), (150), (154), (165), (166), (172), (177), % 151.56/22.34 | | | | | | | (182), (196), (200), (203), (375), (376) are % 151.56/22.34 | | | | | | | inconsistent by sub-proof #292. % 151.56/22.34 | | | | | | | % 151.56/22.34 | | | | | | End of split % 151.56/22.34 | | | | | | % 151.56/22.34 | | | | | End of split % 151.56/22.34 | | | | | % 151.56/22.34 | | | | Case 2: % 151.56/22.34 | | | | | % 151.56/22.34 | | | | | (377) all_56_23 = e1 % 151.56/22.34 | | | | | (378) all_56_21 = e0 % 151.56/22.34 | | | | | % 151.56/22.34 | | | | | COMBINE_EQS: (44), (378) imply: % 151.56/22.34 | | | | | (379) all_6_2 = e0 % 151.56/22.34 | | | | | % 151.56/22.34 | | | | | SIMP: (379) implies: % 151.56/22.34 | | | | | (380) all_6_2 = e0 % 151.56/22.34 | | | | | % 151.56/22.34 | | | | | COMBINE_EQS: (139), (377) imply: % 151.56/22.34 | | | | | (381) all_52_14 = e1 % 151.56/22.34 | | | | | % 151.56/22.34 | | | | | SIMP: (381) implies: % 151.56/22.34 | | | | | (382) all_52_14 = e1 % 151.56/22.34 | | | | | % 151.56/22.34 | | | | | REDUCE: (177), (380) imply: % 151.56/22.34 | | | | | (383) ~ (all_52_6 = e0) % 151.56/22.34 | | | | | % 151.56/22.34 | | | | | REDUCE: (23), (382) imply: % 151.56/22.34 | | | | | (384) ~ (all_4_2 = e1) % 151.56/22.34 | | | | | % 151.56/22.34 | | | | | REDUCE: (127), (380) imply: % 151.56/22.34 | | | | | (385) op(e0, e0) = all_6_1 % 151.56/22.34 | | | | | % 151.56/22.34 | | | | | REDUCE: (142), (380) imply: % 151.56/22.34 | | | | | (386) op(e1, e1) = e0 % 151.56/22.34 | | | | | % 151.56/22.34 | | | | | REF_CLOSE: (17), (18), (20), (21), (33), (37), (39), (41), (49), (56), % 151.56/22.34 | | | | | (61), (64), (65), (68), (77), (79), (93), (96), (104), % 151.56/22.34 | | | | | (106), (113), (114), (130), (132), (144), (148), (153), % 151.56/22.34 | | | | | (157), (159), (164), (171), (173), (178), (183), (192), % 151.56/22.34 | | | | | (203), (383), (385), (386) are inconsistent by sub-proof % 151.56/22.34 | | | | | #289. % 151.56/22.34 | | | | | % 151.56/22.34 | | | | End of split % 151.56/22.34 | | | | % 151.56/22.34 | | | Case 2: % 151.56/22.34 | | | | % 151.56/22.34 | | | | (387) all_56_31 = e3 % 151.56/22.34 | | | | (388) all_56_25 = e0 % 151.56/22.34 | | | | % 151.56/22.34 | | | | COMBINE_EQS: (6), (388) imply: % 151.56/22.34 | | | | (389) all_52_3 = e0 % 151.56/22.34 | | | | % 151.56/22.34 | | | | SIMP: (389) implies: % 151.56/22.34 | | | | (390) all_52_3 = e0 % 151.56/22.34 | | | | % 151.56/22.34 | | | | COMBINE_EQS: (121), (387) imply: % 151.56/22.34 | | | | (391) all_4_2 = e3 % 151.56/22.34 | | | | % 151.56/22.34 | | | | COMBINE_EQS: (147), (391) imply: % 151.56/22.34 | | | | (392) all_58_15 = e3 % 151.56/22.34 | | | | % 151.56/22.34 | | | | COMBINE_EQS: (197), (390) imply: % 151.56/22.34 | | | | (393) all_58_12 = e0 % 151.56/22.34 | | | | % 151.56/22.34 | | | | REDUCE: (117), (390) imply: % 151.56/22.34 | | | | (394) ~ (all_52_1 = e0) % 151.56/22.34 | | | | % 151.56/22.34 | | | | REDUCE: (108), (390) imply: % 151.56/22.34 | | | | (395) ~ (all_52_2 = e0) % 151.56/22.34 | | | | % 151.56/22.34 | | | | REDUCE: (111), (390) imply: % 151.56/22.34 | | | | (396) ~ (all_52_11 = e0) % 151.56/22.34 | | | | % 151.56/22.34 | | | | SIMP: (396) implies: % 151.56/22.34 | | | | (397) ~ (all_52_11 = e0) % 151.56/22.34 | | | | % 151.56/22.34 | | | | REDUCE: (78), (390) imply: % 151.56/22.34 | | | | (398) ~ (all_10_2 = e0) % 151.56/22.34 | | | | % 151.56/22.34 | | | | SIMP: (398) implies: % 151.56/22.34 | | | | (399) ~ (all_10_2 = e0) % 151.56/22.34 | | | | % 151.56/22.34 | | | | REDUCE: (116), (391) imply: % 151.56/22.34 | | | | (400) ~ (all_52_11 = e3) % 151.56/22.34 | | | | % 151.56/22.34 | | | | REDUCE: (23), (391) imply: % 151.56/22.34 | | | | (401) ~ (all_52_14 = e3) % 151.56/22.34 | | | | % 151.56/22.34 | | | | REDUCE: (110), (391) imply: % 151.56/22.34 | | | | (402) op(e3, e3) = all_4_1 % 151.56/22.34 | | | | % 151.56/22.34 | | | | REDUCE: (33), (391) imply: % 151.56/22.34 | | | | (403) op(e0, e0) = e3 % 151.56/22.34 | | | | % 151.56/22.34 | | | | REF_CLOSE: (1), (2), (4), (5), (8), (9), (10), (12), (13), (15), (16), % 151.56/22.34 | | | | (18), (19), (20), (21), (22), (24), (25), (27), (28), (31), % 151.56/22.34 | | | | (35), (36), (37), (38), (39), (42), (44), (45), (46), (47), % 151.56/22.34 | | | | (49), (52), (53), (54), (55), (56), (58), (59), (61), (62), % 151.56/22.34 | | | | (64), (65), (66), (67), (68), (69), (70), (71), (72), (75), % 151.56/22.34 | | | | (77), (83), (85), (91), (92), (94), (96), (98), (99), (104), % 151.56/22.34 | | | | (106), (107), (110), (115), (117), (119), (122), (127), % 151.56/22.34 | | | | (134), (136), (140), (143), (146), (147), (149), (150), % 151.56/22.34 | | | | (154), (159), (162), (165), (170), (171), (172), (173), % 151.56/22.34 | | | | (174), (175), (179), (181), (182), (184), (185), (186), % 151.56/22.34 | | | | (188), (189), (190), (193), (194), (196), (197), (199), % 151.56/22.34 | | | | (200), (203), (392), (393), (394), (395), (397), (399), % 151.56/22.34 | | | | (400), (401), (402), (403) are inconsistent by sub-proof % 151.56/22.34 | | | | #288. % 151.56/22.34 | | | | % 151.56/22.34 | | | End of split % 151.56/22.34 | | | % 151.56/22.34 | | Case 2: % 151.56/22.34 | | | % 151.56/22.34 | | | (404) all_56_13 = e2 % 151.56/22.34 | | | (405) all_56_11 = e1 % 151.56/22.34 | | | % 151.56/22.34 | | | COMBINE_EQS: (1), (405) imply: % 151.56/22.34 | | | (406) all_8_2 = e1 % 151.56/22.34 | | | % 151.56/22.34 | | | COMBINE_EQS: (89), (404) imply: % 151.56/22.34 | | | (407) all_52_9 = e2 % 151.56/22.34 | | | % 151.56/22.34 | | | REDUCE: (151), (407) imply: % 151.56/22.34 | | | (408) ~ (all_6_2 = e2) % 151.56/22.34 | | | % 151.56/22.34 | | | REDUCE: (186), (406) imply: % 151.56/22.34 | | | (409) op(e1, e1) = all_8_1 % 151.56/22.34 | | | % 151.56/22.34 | | | GROUND_INST: instantiating (77) with all_6_2, all_8_1, e1, e1, simplifying % 151.56/22.34 | | | with (142), (409) gives: % 151.56/22.34 | | | (410) all_8_1 = all_6_2 % 151.56/22.34 | | | % 151.56/22.34 | | | REDUCE: (32), (410) imply: % 151.56/22.34 | | | (411) ~ (all_6_2 = e3) % 151.56/22.34 | | | % 151.56/22.34 | | | REDUCE: (12), (410) imply: % 151.56/22.34 | | | (412) ~ (all_6_2 = e1) % 151.56/22.34 | | | % 151.56/22.34 | | | BETA: splitting (45) gives: % 151.56/22.34 | | | % 151.56/22.34 | | | Case 1: % 151.56/22.34 | | | | % 151.56/22.34 | | | | (413) all_54_10 = e3 % 151.56/22.34 | | | | % 151.56/22.34 | | | | REF_CLOSE: (16), (411), (413) are inconsistent by sub-proof #736. % 151.56/22.34 | | | | % 151.56/22.34 | | | Case 2: % 151.56/22.34 | | | | % 151.56/22.34 | | | | (414) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 151.56/22.34 | | | | % 151.56/22.34 | | | | BETA: splitting (414) gives: % 151.56/22.34 | | | | % 151.56/22.34 | | | | Case 1: % 151.56/22.34 | | | | | % 151.56/22.34 | | | | | (415) all_54_10 = e2 % 151.56/22.34 | | | | | % 151.56/22.34 | | | | | REF_CLOSE: (16), (149), (415) are inconsistent by sub-proof #735. % 151.56/22.34 | | | | | % 151.56/22.34 | | | | Case 2: % 151.56/22.34 | | | | | % 151.56/22.34 | | | | | (416) all_54_10 = e1 | all_54_10 = e0 % 151.56/22.34 | | | | | % 151.56/22.34 | | | | | REF_CLOSE: (16), (17), (18), (20), (21), (33), (37), (39), (41), (49), % 151.56/22.34 | | | | | (56), (61), (64), (65), (68), (77), (79), (93), (96), % 151.56/22.34 | | | | | (104), (106), (113), (114), (127), (130), (132), (142), % 151.56/22.34 | | | | | (144), (148), (153), (157), (159), (164), (171), (173), % 151.56/22.34 | | | | | (177), (178), (183), (192), (203), (412), (416) are % 151.56/22.34 | | | | | inconsistent by sub-proof #287. % 151.56/22.34 | | | | | % 151.56/22.34 | | | | End of split % 151.56/22.34 | | | | % 151.56/22.34 | | | End of split % 151.56/22.34 | | | % 151.56/22.34 | | End of split % 151.56/22.34 | | % 151.56/22.34 | Case 2: % 151.56/22.34 | | % 151.56/22.34 | | (417) all_56_15 = e2 % 151.56/22.34 | | (418) all_56_11 = e0 % 151.56/22.34 | | % 151.56/22.34 | | COMBINE_EQS: (1), (418) imply: % 151.56/22.34 | | (419) all_8_2 = e0 % 151.56/22.34 | | % 151.56/22.34 | | COMBINE_EQS: (195), (417) imply: % 151.56/22.34 | | (420) all_52_13 = e2 % 151.56/22.34 | | % 151.56/22.34 | | COMBINE_EQS: (154), (420) imply: % 151.56/22.34 | | (421) all_58_10 = e2 % 151.56/22.34 | | % 151.56/22.34 | | COMBINE_EQS: (113), (419) imply: % 151.56/22.34 | | (422) all_58_3 = e0 % 151.56/22.34 | | % 151.56/22.34 | | REDUCE: (92), (420) imply: % 151.56/22.34 | | (423) ~ (all_52_1 = e2) % 151.56/22.34 | | % 151.56/22.34 | | REDUCE: (75), (419) imply: % 151.56/22.34 | | (424) ~ (all_52_1 = e0) % 151.56/22.34 | | % 151.56/22.34 | | REDUCE: (185), (419) imply: % 151.56/22.34 | | (425) ~ (all_52_4 = e0) % 151.56/22.34 | | % 151.56/22.34 | | REDUCE: (107), (420) imply: % 151.56/22.34 | | (426) ~ (all_52_9 = e2) % 151.56/22.34 | | % 151.56/22.34 | | REDUCE: (28), (419) imply: % 151.56/22.34 | | (427) ~ (all_52_9 = e0) % 151.56/22.34 | | % 151.56/22.34 | | REDUCE: (30), (420) imply: % 151.56/22.34 | | (428) ~ (all_52_12 = e2) % 151.56/22.34 | | % 151.56/22.34 | | REDUCE: (138), (420) imply: % 151.56/22.34 | | (429) ~ (all_52_14 = e2) % 151.56/22.34 | | % 151.56/22.34 | | SIMP: (429) implies: % 151.56/22.34 | | (430) ~ (all_52_14 = e2) % 151.56/22.34 | | % 151.56/22.34 | | REDUCE: (129), (420) imply: % 151.56/22.34 | | (431) ~ (all_4_2 = e2) % 151.56/22.34 | | % 151.56/22.34 | | SIMP: (431) implies: % 151.56/22.34 | | (432) ~ (all_4_2 = e2) % 151.56/22.34 | | % 151.56/22.34 | | REDUCE: (186), (419) imply: % 151.56/22.34 | | (433) op(e0, e0) = all_8_1 % 151.56/22.34 | | % 151.56/22.34 | | REDUCE: (170), (419) imply: % 151.56/22.34 | | (434) op(e2, e2) = e0 % 151.56/22.34 | | % 151.56/22.34 | | REDUCE: (2), (420) imply: % 151.56/22.34 | | (435) op(e0, e2) = all_56_14 % 151.56/22.34 | | % 151.56/22.34 | | REF_CLOSE: (5), (8), (9), (11), (12), (13), (14), (16), (17), (21), (22), % 151.56/22.34 | | (26), (27), (29), (31), (32), (33), (34), (35), (38), (39), (41), % 151.56/22.34 | | (42), (43), (44), (45), (46), (48), (52), (53), (54), (55), (56), % 151.56/22.34 | | (57), (58), (59), (63), (64), (65), (66), (69), (70), (72), (76), % 151.56/22.34 | | (77), (79), (81), (84), (85), (86), (87), (88), (89), (90), (91), % 151.56/22.34 | | (93), (94), (95), (97), (98), (99), (100), (101), (103), (106), % 151.56/22.34 | | (108), (110), (111), (112), (114), (115), (116), (117), (118), % 151.56/22.34 | | (119), (120), (121), (122), (124), (126), (132), (135), (136), % 151.56/22.34 | | (137), (139), (140), (141), (145), (146), (147), (149), (150), % 151.56/22.34 | | (151), (153), (155), (156), (157), (159), (160), (162), (163), % 151.56/22.34 | | (165), (166), (167), (171), (172), (173), (174), (175), (176), % 151.56/22.34 | | (177), (179), (180), (181), (182), (183), (184), (188), (190), % 151.56/22.34 | | (191), (192), (193), (194), (197), (198), (417), (421), (422), % 151.56/22.34 | | (423), (424), (425), (426), (427), (428), (430), (432), (433), % 151.56/22.34 | | (434), (435) are inconsistent by sub-proof #286. % 151.56/22.34 | | % 151.56/22.34 | End of split % 151.56/22.34 | % 151.56/22.34 End of proof % 151.56/22.34 % 151.56/22.34 Sub-proof #286 shows that the following formulas are inconsistent: % 151.56/22.34 ---------------------------------------------------------------- % 151.56/22.34 (1) ~ (all_52_4 = all_52_8) % 151.56/22.34 (2) ~ (all_52_8 = all_52_9) % 151.56/22.34 (3) all_54_9 = all_52_6 % 151.56/22.34 (4) all_58_6 = all_52_2 % 151.56/22.34 (5) ~ (all_8_1 = e1) % 151.56/22.34 (6) ~ (all_52_1 = all_52_9) % 151.56/22.34 (7) op(e2, all_52_4) = all_56_2 % 151.56/22.34 (8) ~ (all_52_9 = e2) % 151.56/22.34 (9) all_54_10 = all_6_2 % 151.56/22.34 (10) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0 % 151.56/22.34 (11) all_54_0 = all_10_2 % 151.56/22.34 (12) all_54_4 = all_52_1 % 151.56/22.34 (13) all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2 % 151.56/22.34 (14) all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2 % 151.56/22.34 (15) all_54_12 = all_52_3 % 151.56/22.34 (16) ~ (all_52_4 = all_52_7) % 151.56/22.34 (17) ~ (all_52_12 = e2) % 151.56/22.34 (18) ~ (all_8_1 = e3) % 151.56/22.34 (19) op(e0, e0) = all_4_2 % 151.56/22.34 (20) all_58_6 = e0 | all_58_7 = e0 | all_58_8 = e0 | all_58_11 = e0 % 151.56/22.34 (21) all_58_4 = all_52_8 % 151.56/22.34 (22) ~ (all_52_6 = all_52_14) % 151.56/22.34 (23) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 151.56/22.34 (24) all_54_15 = all_4_2 % 151.56/22.34 (25) all_58_10 = e2 % 151.56/22.34 (26) all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1 % 151.56/22.34 (27) op(e2, e1) = all_52_9 % 151.56/22.34 (28) all_56_21 = all_6_2 % 151.56/22.34 (29) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 151.56/22.34 (30) ~ (all_52_14 = e2) % 151.56/22.34 (31) op(e3, all_52_1) = all_56_8 % 151.56/22.34 (32) all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2 % 151.56/22.34 (33) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0 % 151.56/22.34 (34) all_58_5 = all_52_9 % 151.56/22.34 (35) all_54_1 = all_52_4 % 151.56/22.34 (36) all_56_17 = all_52_2 % 151.56/22.34 (37) all_58_9 = all_52_12 % 151.56/22.34 (38) op(e0, all_52_12) = all_56_6 % 151.56/22.34 (39) op(e0, all_52_14) = all_56_22 % 151.56/22.34 (40) op(e0, e2) = all_52_7 % 151.56/22.34 (41) ( ~ (all_56_0 = all_56_1) & ~ (all_56_2 = all_56_3) & ~ (all_56_4 = % 151.56/22.34 all_56_5) & ~ (all_56_6 = all_56_7)) | ( ~ (all_56_8 = all_56_9) & % 151.56/22.34 ~ (all_56_10 = all_56_11) & ~ (all_56_12 = all_56_13) & ~ (all_56_14 % 151.56/22.34 = all_56_15)) | ( ~ (all_56_16 = all_56_17) & ~ (all_56_18 = % 151.56/22.34 all_56_19) & ~ (all_56_20 = all_56_21) & ~ (all_56_22 = % 151.56/22.34 all_56_23)) | ( ~ (all_56_24 = all_56_25) & ~ (all_56_26 = % 151.56/22.34 all_56_27) & ~ (all_56_28 = all_56_29) & ~ (all_56_30 = % 151.56/22.34 all_56_31)) % 151.56/22.34 (42) all_58_1 = all_52_4 % 151.56/22.34 (43) all_58_13 = all_52_7 % 151.56/22.34 (44) all_58_4 = e0 | all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0 % 151.56/22.34 (45) ~ (all_52_8 = all_6_2) % 151.56/22.34 (46) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0 % 151.56/22.34 (47) ~ (all_56_21 = e3) | all_56_17 = e1 % 151.56/22.34 (48) op(e2, e2) = e0 % 151.56/22.34 (49) all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2 % 151.56/22.34 (50) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 151.56/22.34 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 151.56/22.34 (51) all_54_3 = all_52_12 % 151.56/22.34 (52) ~ (all_52_3 = all_52_7) % 151.56/22.34 (53) ~ (all_52_2 = all_52_6) % 151.56/22.34 (54) op(e0, all_4_1) = all_4_0 % 151.56/22.34 (55) all_56_15 = e2 % 151.56/22.34 (56) all_56_7 = all_52_12 % 151.56/22.34 (57) ~ (all_52_4 = e0) % 151.56/22.34 (58) op(e1, e2) = all_52_6 % 151.56/22.34 (59) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0 % 151.56/22.34 (60) all_56_13 = all_52_9 % 151.56/22.34 (61) op(e2, all_52_6) = all_56_18 % 151.56/22.34 (62) op(e0, e1) = all_52_11 % 151.56/22.34 (63) ~ (all_52_7 = all_4_2) % 151.56/22.34 (64) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0 % 151.56/22.34 (65) ~ (all_52_9 = e0) % 151.56/22.34 (66) op(e1, e3) = all_52_2 % 151.56/22.34 (67) all_58_8 = all_6_2 % 151.56/22.34 (68) all_54_6 = all_52_9 % 151.56/22.34 (69) ~ (all_4_0 = e1) % 151.56/22.34 (70) ~ (all_52_3 = all_4_2) % 151.56/22.34 (71) ~ (all_52_8 = all_10_2) % 151.56/22.34 (72) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0 % 151.56/22.34 (73) op(e0, e0) = all_8_1 % 151.56/22.34 (74) all_56_5 = all_52_8 % 151.56/22.34 (75) ~ (all_4_2 = e2) % 151.56/22.34 (76) all_58_3 = e0 % 151.56/22.34 (77) ~ (all_52_2 = all_52_3) % 151.56/22.34 (78) ~ (all_52_1 = e0) % 151.56/22.35 (79) op(all_4_2, all_4_2) = all_4_1 % 151.56/22.35 (80) op(e0, e2) = all_56_14 % 151.56/22.35 (81) ~ (all_52_3 = all_52_11) % 151.56/22.35 (82) all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1 % 151.56/22.35 (83) all_56_3 = all_52_4 % 151.56/22.35 (84) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0 % 151.56/22.35 (85) ~ (all_52_11 = all_4_2) % 151.56/22.35 (86) ~ (all_52_1 = all_52_3) % 151.56/22.35 (87) all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1 % 151.56/22.35 (88) ~ (all_52_6 = all_52_7) % 151.56/22.35 (89) op(e1, all_52_8) = all_56_4 % 151.56/22.35 (90) all_56_31 = all_4_2 % 151.56/22.35 (91) all_58_11 = all_52_14 % 151.56/22.35 (92) ~ (all_52_2 = all_52_14) % 151.56/22.35 (93) all_24_2 = all_10_2 % 151.56/22.35 (94) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0 % 151.56/22.35 (95) all_54_13 = all_52_7 % 151.56/22.35 (96) all_54_2 = all_52_8 % 151.56/22.35 (97) op(e3, e2) = all_52_4 % 151.56/22.35 (98) all_56_23 = all_52_14 % 151.56/22.35 (99) all_54_8 = all_52_2 % 151.56/22.35 (100) all_24_1 = all_10_1 % 151.56/22.35 (101) op(e0, e3) = all_52_3 % 151.56/22.35 (102) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0 % 151.56/22.35 (103) all_58_15 = all_4_2 % 151.56/22.35 (104) ~ (all_6_2 = e2) % 151.56/22.35 (105) all_58_2 = all_52_1 % 151.56/22.35 (106) ~ (all_52_9 = all_6_2) % 151.56/22.35 (107) all_58_7 = all_52_6 % 151.56/22.35 (108) ~ (all_52_12 = all_4_2) % 151.56/22.35 (109) ~ (all_24_1 = e0) | ~ (all_24_2 = e2) % 151.56/22.35 (110) op(all_10_2, all_10_2) = all_10_1 % 151.56/22.35 (111) all_58_0 = all_10_2 % 151.56/22.35 (112) op(e3, all_52_2) = all_56_16 % 151.56/22.35 (113) all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1 % 151.56/22.35 (114) op(e2, e3) = all_52_1 % 151.56/22.35 (115) ~ (all_52_12 = all_52_14) % 151.56/22.35 (116) op(e1, all_52_9) = all_56_12 % 151.56/22.35 (117) op(e3, e1) = all_52_8 % 151.56/22.35 (118) ~ (all_52_4 = all_52_12) % 151.56/22.35 (119) ~ (all_52_2 = all_6_2) % 151.56/22.35 (120) ~ (all_52_8 = all_52_12) % 151.56/22.35 (121) ~ (all_52_1 = all_52_2) % 151.56/22.35 (122) ~ (all_56_21 = e0) | all_56_23 = e1 % 151.56/22.35 (123) op(e0, all_4_2) = all_56_30 % 151.56/22.35 (124) ~ (all_52_6 = all_6_2) % 151.56/22.35 (125) ~ (all_52_14 = all_6_2) % 151.56/22.35 (126) all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0 % 151.56/22.35 (127) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0 % 151.56/22.35 (128) ~ (all_52_2 = all_10_2) % 151.56/22.35 (129) ~ (all_52_4 = all_10_2) % 151.56/22.35 (130) all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3 % 151.56/22.35 (131) ~ (all_52_4 = all_52_6) % 151.56/22.35 (132) all_58_14 = all_52_11 % 151.56/22.35 (133) ~ (all_52_1 = e2) % 151.56/22.35 (134) all_56_19 = all_52_6 % 151.56/22.35 (135) ~ (all_52_12 = all_10_2) % 151.56/22.35 (136) ~ (all_4_0 = e2) % 151.56/22.35 (137) all_56_9 = all_52_1 % 151.56/22.35 (138) all_58_12 = all_52_3 % 151.56/22.35 (139) all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2 % 151.56/22.35 % 151.56/22.35 Begin of proof % 151.56/22.35 | % 151.56/22.35 | GROUND_INST: instantiating (50) with all_4_2, all_8_1, e0, e0, simplifying % 151.56/22.35 | with (19), (73) gives: % 151.56/22.35 | (140) all_8_1 = all_4_2 % 151.56/22.35 | % 151.56/22.35 | GROUND_INST: instantiating (50) with all_52_7, all_56_14, e2, e0, simplifying % 151.56/22.35 | with (40), (80) gives: % 151.56/22.35 | (141) all_56_14 = all_52_7 % 151.56/22.35 | % 151.56/22.35 | REDUCE: (18), (140) imply: % 151.56/22.35 | (142) ~ (all_4_2 = e3) % 151.56/22.35 | % 151.56/22.35 | REDUCE: (5), (140) imply: % 151.56/22.35 | (143) ~ (all_4_2 = e1) % 151.56/22.35 | % 151.56/22.35 | BETA: splitting (94) gives: % 151.56/22.35 | % 151.56/22.35 | Case 1: % 151.56/22.35 | | % 151.56/22.35 | | (144) all_54_15 = e3 % 151.56/22.35 | | % 151.56/22.35 | | COMBINE_EQS: (24), (144) imply: % 151.56/22.35 | | (145) all_4_2 = e3 % 151.56/22.35 | | % 151.56/22.35 | | REDUCE: (142), (145) imply: % 151.56/22.35 | | (146) $false % 151.56/22.35 | | % 151.56/22.35 | | CLOSE: (146) is inconsistent. % 151.56/22.35 | | % 151.56/22.35 | Case 2: % 151.56/22.35 | | % 151.56/22.35 | | (147) all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0 % 151.56/22.35 | | % 151.56/22.35 | | BETA: splitting (147) gives: % 151.56/22.35 | | % 151.56/22.35 | | Case 1: % 151.56/22.35 | | | % 151.56/22.35 | | | (148) all_54_15 = e2 % 151.56/22.35 | | | % 151.56/22.35 | | | COMBINE_EQS: (24), (148) imply: % 151.56/22.35 | | | (149) all_4_2 = e2 % 151.56/22.35 | | | % 151.56/22.35 | | | REDUCE: (75), (149) imply: % 151.56/22.35 | | | (150) $false % 151.56/22.35 | | | % 151.56/22.35 | | | CLOSE: (150) is inconsistent. % 151.56/22.35 | | | % 151.56/22.35 | | Case 2: % 151.56/22.35 | | | % 151.56/22.35 | | | (151) all_54_15 = e1 | all_54_15 = e0 % 151.56/22.35 | | | % 151.56/22.35 | | | BETA: splitting (151) gives: % 151.56/22.35 | | | % 151.56/22.35 | | | Case 1: % 151.56/22.35 | | | | % 151.56/22.35 | | | | (152) all_54_15 = e1 % 151.56/22.35 | | | | % 151.56/22.35 | | | | COMBINE_EQS: (24), (152) imply: % 151.56/22.35 | | | | (153) all_4_2 = e1 % 151.56/22.35 | | | | % 151.56/22.35 | | | | REDUCE: (143), (153) imply: % 151.56/22.35 | | | | (154) $false % 151.56/22.35 | | | | % 151.56/22.35 | | | | CLOSE: (154) is inconsistent. % 151.56/22.35 | | | | % 151.56/22.35 | | | Case 2: % 151.56/22.35 | | | | % 151.56/22.35 | | | | (155) all_54_15 = e0 % 151.56/22.35 | | | | % 151.56/22.35 | | | | COMBINE_EQS: (24), (155) imply: % 151.56/22.35 | | | | (156) all_4_2 = e0 % 151.56/22.35 | | | | % 151.56/22.35 | | | | COMBINE_EQS: (90), (156) imply: % 151.56/22.35 | | | | (157) all_56_31 = e0 % 151.56/22.35 | | | | % 151.56/22.35 | | | | REDUCE: (70), (156) imply: % 151.56/22.35 | | | | (158) ~ (all_52_3 = e0) % 151.56/22.35 | | | | % 151.56/22.35 | | | | REDUCE: (63), (156) imply: % 151.56/22.35 | | | | (159) ~ (all_52_7 = e0) % 151.56/22.35 | | | | % 151.56/22.35 | | | | REDUCE: (85), (156) imply: % 151.56/22.35 | | | | (160) ~ (all_52_11 = e0) % 151.56/22.35 | | | | % 151.56/22.35 | | | | REDUCE: (108), (156) imply: % 151.56/22.35 | | | | (161) ~ (all_52_12 = e0) % 151.56/22.35 | | | | % 151.56/22.35 | | | | REDUCE: (79), (156) imply: % 151.56/22.35 | | | | (162) op(e0, e0) = all_4_1 % 151.56/22.35 | | | | % 151.56/22.35 | | | | REDUCE: (123), (156) imply: % 151.56/22.35 | | | | (163) op(e0, e0) = all_56_30 % 151.56/22.35 | | | | % 151.56/22.35 | | | | REDUCE: (19), (156) imply: % 151.56/22.35 | | | | (164) op(e0, e0) = e0 % 151.56/22.35 | | | | % 151.56/22.35 | | | | GROUND_INST: instantiating (50) with all_4_1, all_56_30, e0, e0, % 151.56/22.35 | | | | simplifying with (162), (163) gives: % 151.56/22.35 | | | | (165) all_56_30 = all_4_1 % 151.56/22.35 | | | | % 151.56/22.35 | | | | GROUND_INST: instantiating (50) with e0, all_56_30, e0, e0, simplifying % 151.56/22.35 | | | | with (163), (164) gives: % 151.56/22.35 | | | | (166) all_56_30 = e0 % 151.56/22.35 | | | | % 151.56/22.35 | | | | COMBINE_EQS: (165), (166) imply: % 151.56/22.35 | | | | (167) all_4_1 = e0 % 151.56/22.35 | | | | % 151.56/22.35 | | | | SIMP: (167) implies: % 151.56/22.35 | | | | (168) all_4_1 = e0 % 151.56/22.35 | | | | % 151.56/22.35 | | | | REDUCE: (54), (168) imply: % 151.56/22.35 | | | | (169) op(e0, e0) = all_4_0 % 151.56/22.35 | | | | % 151.56/22.35 | | | | GROUND_INST: instantiating (50) with e0, all_4_0, e0, e0, simplifying % 151.56/22.35 | | | | with (164), (169) gives: % 151.56/22.35 | | | | (170) all_4_0 = e0 % 151.56/22.35 | | | | % 151.56/22.35 | | | | REDUCE: (136), (170) imply: % 151.56/22.35 | | | | (171) ~ (e2 = e0) % 151.56/22.35 | | | | % 151.56/22.35 | | | | SIMP: (171) implies: % 151.56/22.35 | | | | (172) ~ (e2 = e0) % 151.56/22.35 | | | | % 151.56/22.35 | | | | REDUCE: (69), (170) imply: % 151.56/22.35 | | | | (173) ~ (e1 = e0) % 151.56/22.35 | | | | % 151.56/22.35 | | | | SIMP: (173) implies: % 151.56/22.35 | | | | (174) ~ (e1 = e0) % 151.56/22.35 | | | | % 151.56/22.35 | | | | BETA: splitting (122) gives: % 151.56/22.35 | | | | % 151.56/22.35 | | | | Case 1: % 151.56/22.35 | | | | | % 151.56/22.35 | | | | | (175) ~ (all_56_21 = e0) % 151.56/22.35 | | | | | % 151.56/22.35 | | | | | REDUCE: (28), (175) imply: % 151.56/22.35 | | | | | (176) ~ (all_6_2 = e0) % 151.56/22.35 | | | | | % 151.56/22.35 | | | | | BETA: splitting (20) gives: % 151.56/22.35 | | | | | % 151.56/22.35 | | | | | Case 1: % 151.56/22.35 | | | | | | % 151.56/22.35 | | | | | | (177) all_58_6 = e0 % 151.56/22.35 | | | | | | % 151.56/22.35 | | | | | | COMBINE_EQS: (4), (177) imply: % 151.56/22.35 | | | | | | (178) all_52_2 = e0 % 151.56/22.35 | | | | | | % 151.56/22.35 | | | | | | SIMP: (178) implies: % 151.56/22.35 | | | | | | (179) all_52_2 = e0 % 151.56/22.35 | | | | | | % 151.56/22.35 | | | | | | COMBINE_EQS: (36), (179) imply: % 151.56/22.35 | | | | | | (180) all_56_17 = e0 % 151.56/22.35 | | | | | | % 151.56/22.35 | | | | | | REDUCE: (128), (179) imply: % 151.56/22.35 | | | | | | (181) ~ (all_10_2 = e0) % 151.56/22.35 | | | | | | % 151.56/22.35 | | | | | | SIMP: (181) implies: % 151.56/22.35 | | | | | | (182) ~ (all_10_2 = e0) % 151.56/22.35 | | | | | | % 151.56/22.35 | | | | | | REDUCE: (119), (179) imply: % 151.56/22.35 | | | | | | (183) ~ (all_6_2 = e0) % 151.56/22.35 | | | | | | % 151.56/22.35 | | | | | | BETA: splitting (49) gives: % 151.56/22.35 | | | | | | % 151.56/22.35 | | | | | | Case 1: % 151.56/22.35 | | | | | | | % 151.56/22.35 | | | | | | | (184) all_58_6 = e2 % 151.56/22.35 | | | | | | | % 151.56/22.35 | | | | | | | COMBINE_EQS: (177), (184) imply: % 151.56/22.35 | | | | | | | (185) e2 = e0 % 151.56/22.35 | | | | | | | % 151.56/22.35 | | | | | | | REDUCE: (172), (185) imply: % 151.56/22.35 | | | | | | | (186) $false % 151.56/22.35 | | | | | | | % 151.56/22.35 | | | | | | | CLOSE: (186) is inconsistent. % 151.56/22.35 | | | | | | | % 151.56/22.35 | | | | | | Case 2: % 151.56/22.35 | | | | | | | % 151.56/22.35 | | | | | | | (187) all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2 % 151.56/22.35 | | | | | | | % 151.56/22.35 | | | | | | | BETA: splitting (47) gives: % 151.56/22.35 | | | | | | | % 151.56/22.35 | | | | | | | Case 1: % 151.56/22.35 | | | | | | | | % 151.56/22.35 | | | | | | | | (188) ~ (all_56_21 = e3) % 151.56/22.35 | | | | | | | | % 151.56/22.35 | | | | | | | | REDUCE: (28), (188) imply: % 151.56/22.35 | | | | | | | | (189) ~ (all_6_2 = e3) % 151.56/22.35 | | | | | | | | % 151.56/22.35 | | | | | | | | BETA: splitting (29) gives: % 151.56/22.35 | | | | | | | | % 151.56/22.35 | | | | | | | | Case 1: % 151.56/22.35 | | | | | | | | | % 151.56/22.35 | | | | | | | | | (190) all_54_10 = e3 % 151.56/22.35 | | | | | | | | | % 151.56/22.35 | | | | | | | | | REF_CLOSE: (9), (189), (190) are inconsistent by sub-proof % 151.56/22.35 | | | | | | | | | #736. % 151.56/22.35 | | | | | | | | | % 151.56/22.35 | | | | | | | | Case 2: % 151.56/22.35 | | | | | | | | | % 151.56/22.35 | | | | | | | | | (191) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 151.56/22.35 | | | | | | | | | % 151.56/22.35 | | | | | | | | | BETA: splitting (187) gives: % 151.56/22.35 | | | | | | | | | % 151.56/22.35 | | | | | | | | | Case 1: % 151.56/22.35 | | | | | | | | | | % 151.56/22.35 | | | | | | | | | | (192) all_58_7 = e2 % 151.56/22.35 | | | | | | | | | | % 151.56/22.35 | | | | | | | | | | COMBINE_EQS: (107), (192) imply: % 151.56/22.35 | | | | | | | | | | (193) all_52_6 = e2 % 151.56/22.35 | | | | | | | | | | % 151.56/22.35 | | | | | | | | | | REDUCE: (131), (193) imply: % 151.56/22.35 | | | | | | | | | | (194) ~ (all_52_4 = e2) % 151.56/22.35 | | | | | | | | | | % 151.56/22.35 | | | | | | | | | | REDUCE: (124), (193) imply: % 151.56/22.35 | | | | | | | | | | (195) ~ (all_6_2 = e2) % 151.56/22.35 | | | | | | | | | | % 151.56/22.35 | | | | | | | | | | REDUCE: (61), (193) imply: % 151.56/22.35 | | | | | | | | | | (196) op(e2, e2) = all_56_18 % 151.56/22.35 | | | | | | | | | | % 151.56/22.35 | | | | | | | | | | BETA: splitting (191) gives: % 151.56/22.35 | | | | | | | | | | % 151.56/22.35 | | | | | | | | | | Case 1: % 151.56/22.35 | | | | | | | | | | | % 151.56/22.35 | | | | | | | | | | | (197) all_54_10 = e2 % 151.56/22.35 | | | | | | | | | | | % 151.56/22.35 | | | | | | | | | | | REF_CLOSE: (9), (104), (197) are inconsistent by sub-proof % 151.56/22.35 | | | | | | | | | | | #735. % 151.56/22.35 | | | | | | | | | | | % 151.56/22.35 | | | | | | | | | | Case 2: % 151.56/22.35 | | | | | | | | | | | % 151.56/22.35 | | | | | | | | | | | (198) ~ (all_54_10 = e2) % 151.56/22.35 | | | | | | | | | | | (199) all_54_10 = e1 | all_54_10 = e0 % 151.56/22.35 | | | | | | | | | | | % 151.56/22.35 | | | | | | | | | | | BETA: splitting (199) gives: % 151.56/22.35 | | | | | | | | | | | % 151.56/22.35 | | | | | | | | | | | Case 1: % 151.56/22.35 | | | | | | | | | | | | % 151.56/22.35 | | | | | | | | | | | | (200) all_54_10 = e1 % 151.56/22.35 | | | | | | | | | | | | % 151.56/22.35 | | | | | | | | | | | | COMBINE_EQS: (9), (200) imply: % 151.56/22.35 | | | | | | | | | | | | (201) all_6_2 = e1 % 151.56/22.35 | | | | | | | | | | | | % 151.56/22.35 | | | | | | | | | | | | SIMP: (201) implies: % 151.56/22.35 | | | | | | | | | | | | (202) all_6_2 = e1 % 151.56/22.35 | | | | | | | | | | | | % 151.56/22.35 | | | | | | | | | | | | REDUCE: (125), (202) imply: % 151.56/22.35 | | | | | | | | | | | | (203) ~ (all_52_14 = e1) % 151.56/22.35 | | | | | | | | | | | | % 151.56/22.35 | | | | | | | | | | | | REDUCE: (104), (202) imply: % 151.56/22.35 | | | | | | | | | | | | (204) ~ (e2 = e1) % 151.56/22.35 | | | | | | | | | | | | % 151.56/22.35 | | | | | | | | | | | | SIMP: (204) implies: % 151.56/22.35 | | | | | | | | | | | | (205) ~ (e2 = e1) % 151.56/22.35 | | | | | | | | | | | | % 151.56/22.35 | | | | | | | | | | | | BETA: splitting (26) gives: % 151.56/22.35 | | | | | | | | | | | | % 151.56/22.35 | | | | | | | | | | | | Case 1: % 151.56/22.35 | | | | | | | | | | | | | % 151.56/22.35 | | | | | | | | | | | | | (206) all_58_9 = e1 % 151.56/22.35 | | | | | | | | | | | | | % 151.56/22.35 | | | | | | | | | | | | | COMBINE_EQS: (37), (206) imply: % 151.56/22.35 | | | | | | | | | | | | | (207) all_52_12 = e1 % 151.56/22.35 | | | | | | | | | | | | | % 151.56/22.35 | | | | | | | | | | | | | REDUCE: (118), (207) imply: % 151.56/22.35 | | | | | | | | | | | | | (208) ~ (all_52_4 = e1) % 151.56/22.35 | | | | | | | | | | | | | % 151.56/22.35 | | | | | | | | | | | | | REDUCE: (135), (207) imply: % 151.56/22.35 | | | | | | | | | | | | | (209) ~ (all_10_2 = e1) % 151.56/22.35 | | | | | | | | | | | | | % 151.56/22.35 | | | | | | | | | | | | | SIMP: (209) implies: % 151.56/22.35 | | | | | | | | | | | | | (210) ~ (all_10_2 = e1) % 151.56/22.35 | | | | | | | | | | | | | % 151.56/22.35 | | | | | | | | | | | | | BETA: splitting (102) gives: % 151.56/22.35 | | | | | | | | | | | | | % 151.56/22.35 | | | | | | | | | | | | | Case 1: % 151.56/22.35 | | | | | | | | | | | | | | % 151.56/22.35 | | | | | | | | | | | | | | (211) all_54_1 = e3 % 151.56/22.35 | | | | | | | | | | | | | | % 151.56/22.35 | | | | | | | | | | | | | | COMBINE_EQS: (35), (211) imply: % 151.56/22.35 | | | | | | | | | | | | | | (212) all_52_4 = e3 % 151.56/22.35 | | | | | | | | | | | | | | % 151.56/22.35 | | | | | | | | | | | | | | SIMP: (212) implies: % 151.56/22.35 | | | | | | | | | | | | | | (213) all_52_4 = e3 % 151.56/22.35 | | | | | | | | | | | | | | % 151.56/22.35 | | | | | | | | | | | | | | REDUCE: (129), (213) imply: % 151.56/22.35 | | | | | | | | | | | | | | (214) ~ (all_10_2 = e3) % 151.56/22.35 | | | | | | | | | | | | | | % 151.56/22.35 | | | | | | | | | | | | | | SIMP: (214) implies: % 151.56/22.35 | | | | | | | | | | | | | | (215) ~ (all_10_2 = e3) % 151.56/22.35 | | | | | | | | | | | | | | % 151.56/22.35 | | | | | | | | | | | | | | BETA: splitting (23) gives: % 151.56/22.35 | | | | | | | | | | | | | | % 151.56/22.35 | | | | | | | | | | | | | | Case 1: % 151.56/22.35 | | | | | | | | | | | | | | | % 151.56/22.35 | | | | | | | | | | | | | | | (216) all_54_0 = e3 % 151.56/22.35 | | | | | | | | | | | | | | | % 151.56/22.35 | | | | | | | | | | | | | | | REF_CLOSE: (11), (215), (216) are inconsistent by sub-proof % 151.56/22.35 | | | | | | | | | | | | | | | #709. % 151.56/22.35 | | | | | | | | | | | | | | | % 151.56/22.35 | | | | | | | | | | | | | | Case 2: % 151.56/22.35 | | | | | | | | | | | | | | | % 151.56/22.35 | | | | | | | | | | | | | | | (217) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 151.56/22.35 | | | | | | | | | | | | | | | % 151.56/22.35 | | | | | | | | | | | | | | | BETA: splitting (14) gives: % 151.56/22.35 | | | | | | | | | | | | | | | % 151.56/22.35 | | | | | | | | | | | | | | | Case 1: % 151.56/22.35 | | | | | | | | | | | | | | | | % 151.56/22.35 | | | | | | | | | | | | | | | | (218) all_58_0 = e2 % 151.56/22.35 | | | | | | | | | | | | | | | | % 151.56/22.35 | | | | | | | | | | | | | | | | COMBINE_EQS: (111), (218) imply: % 151.56/22.35 | | | | | | | | | | | | | | | | (219) all_10_2 = e2 % 151.56/22.35 | | | | | | | | | | | | | | | | % 151.56/22.35 | | | | | | | | | | | | | | | | COMBINE_EQS: (93), (219) imply: % 151.56/22.35 | | | | | | | | | | | | | | | | (220) all_24_2 = e2 % 151.56/22.35 | | | | | | | | | | | | | | | | % 151.56/22.35 | | | | | | | | | | | | | | | | REDUCE: (110), (219) imply: % 151.56/22.35 | | | | | | | | | | | | | | | | (221) op(e2, e2) = all_10_1 % 151.56/22.35 | | | | | | | | | | | | | | | | % 151.56/22.35 | | | | | | | | | | | | | | | | BETA: splitting (109) gives: % 151.56/22.35 | | | | | | | | | | | | | | | | % 151.56/22.35 | | | | | | | | | | | | | | | | Case 1: % 151.56/22.35 | | | | | | | | | | | | | | | | | % 151.56/22.35 | | | | | | | | | | | | | | | | | (222) ~ (all_24_2 = e2) % 151.56/22.35 | | | | | | | | | | | | | | | | | % 151.56/22.35 | | | | | | | | | | | | | | | | | REDUCE: (220), (222) imply: % 151.56/22.35 | | | | | | | | | | | | | | | | | (223) $false % 151.56/22.35 | | | | | | | | | | | | | | | | | % 151.56/22.35 | | | | | | | | | | | | | | | | | CLOSE: (223) is inconsistent. % 151.56/22.35 | | | | | | | | | | | | | | | | | % 151.56/22.35 | | | | | | | | | | | | | | | | Case 2: % 151.56/22.35 | | | | | | | | | | | | | | | | | % 151.56/22.35 | | | | | | | | | | | | | | | | | (224) ~ (all_24_1 = e0) % 151.56/22.35 | | | | | | | | | | | | | | | | | % 151.56/22.35 | | | | | | | | | | | | | | | | | REDUCE: (100), (224) imply: % 151.56/22.35 | | | | | | | | | | | | | | | | | (225) ~ (all_10_1 = e0) % 151.56/22.35 | | | | | | | | | | | | | | | | | % 151.56/22.35 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (50) with e0, all_56_18, e2, e2, % 151.56/22.35 | | | | | | | | | | | | | | | | | simplifying with (48), (196) gives: % 151.56/22.35 | | | | | | | | | | | | | | | | | (226) all_56_18 = e0 % 151.56/22.35 | | | | | | | | | | | | | | | | | % 151.56/22.35 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (50) with all_10_1, all_56_18, e2, % 151.56/22.35 | | | | | | | | | | | | | | | | | e2, simplifying with (196), (221) gives: % 151.56/22.35 | | | | | | | | | | | | | | | | | (227) all_56_18 = all_10_1 % 151.56/22.35 | | | | | | | | | | | | | | | | | % 151.56/22.35 | | | | | | | | | | | | | | | | | COMBINE_EQS: (226), (227) imply: % 151.56/22.35 | | | | | | | | | | | | | | | | | (228) all_10_1 = e0 % 151.56/22.35 | | | | | | | | | | | | | | | | | % 151.56/22.35 | | | | | | | | | | | | | | | | | REDUCE: (225), (228) imply: % 151.56/22.35 | | | | | | | | | | | | | | | | | (229) $false % 151.56/22.35 | | | | | | | | | | | | | | | | | % 151.56/22.35 | | | | | | | | | | | | | | | | | CLOSE: (229) is inconsistent. % 151.56/22.35 | | | | | | | | | | | | | | | | | % 151.56/22.35 | | | | | | | | | | | | | | | | End of split % 151.56/22.35 | | | | | | | | | | | | | | | | % 151.56/22.35 | | | | | | | | | | | | | | | Case 2: % 151.56/22.35 | | | | | | | | | | | | | | | | % 151.56/22.35 | | | | | | | | | | | | | | | | (230) ~ (all_58_0 = e2) % 151.56/22.35 | | | | | | | | | | | | | | | | % 151.56/22.35 | | | | | | | | | | | | | | | | REDUCE: (111), (230) imply: % 151.56/22.35 | | | | | | | | | | | | | | | | (231) ~ (all_10_2 = e2) % 151.56/22.35 | | | | | | | | | | | | | | | | % 151.56/22.35 | | | | | | | | | | | | | | | | REF_CLOSE: (11), (182), (210), (217), (231) are inconsistent % 151.56/22.35 | | | | | | | | | | | | | | | | by sub-proof #731. % 151.56/22.35 | | | | | | | | | | | | | | | | % 151.56/22.35 | | | | | | | | | | | | | | | End of split % 151.56/22.35 | | | | | | | | | | | | | | | % 151.56/22.35 | | | | | | | | | | | | | | End of split % 151.56/22.35 | | | | | | | | | | | | | | % 151.56/22.35 | | | | | | | | | | | | | Case 2: % 151.56/22.35 | | | | | | | | | | | | | | % 151.56/22.35 | | | | | | | | | | | | | | (232) all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0 % 151.56/22.35 | | | | | | | | | | | | | | % 151.56/22.35 | | | | | | | | | | | | | | REF_CLOSE: (35), (57), (194), (208), (232) are inconsistent % 151.56/22.35 | | | | | | | | | | | | | | by sub-proof #718. % 151.56/22.35 | | | | | | | | | | | | | | % 151.56/22.35 | | | | | | | | | | | | | End of split % 151.56/22.35 | | | | | | | | | | | | | % 151.56/22.35 | | | | | | | | | | | | Case 2: % 151.56/22.35 | | | | | | | | | | | | | % 151.56/22.35 | | | | | | | | | | | | | (233) all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1 % 151.56/22.35 | | | | | | | | | | | | | % 151.56/22.35 | | | | | | | | | | | | | REF_CLOSE: (25), (91), (103), (143), (203), (205), (233) are % 151.56/22.35 | | | | | | | | | | | | | inconsistent by sub-proof #370. % 151.56/22.35 | | | | | | | | | | | | | % 151.56/22.35 | | | | | | | | | | | | End of split % 151.56/22.35 | | | | | | | | | | | | % 151.56/22.35 | | | | | | | | | | | Case 2: % 151.56/22.35 | | | | | | | | | | | | % 151.56/22.35 | | | | | | | | | | | | (234) all_54_10 = e0 % 151.56/22.35 | | | | | | | | | | | | % 151.56/22.35 | | | | | | | | | | | | REF_CLOSE: (9), (176), (234) are inconsistent by sub-proof % 151.56/22.35 | | | | | | | | | | | | #705. % 151.56/22.35 | | | | | | | | | | | | % 151.56/22.35 | | | | | | | | | | | End of split % 151.56/22.35 | | | | | | | | | | | % 151.56/22.35 | | | | | | | | | | End of split % 151.56/22.35 | | | | | | | | | | % 151.56/22.35 | | | | | | | | | Case 2: % 151.56/22.35 | | | | | | | | | | % 151.56/22.35 | | | | | | | | | | (235) all_58_8 = e2 | all_58_11 = e2 % 151.56/22.35 | | | | | | | | | | % 151.56/22.35 | | | | | | | | | | REF_CLOSE: (30), (67), (91), (104), (235) are inconsistent by % 151.56/22.35 | | | | | | | | | | sub-proof #511. % 151.56/22.35 | | | | | | | | | | % 151.56/22.35 | | | | | | | | | End of split % 151.56/22.35 | | | | | | | | | % 151.56/22.35 | | | | | | | | End of split % 151.56/22.35 | | | | | | | | % 151.56/22.35 | | | | | | | Case 2: % 151.56/22.35 | | | | | | | | % 151.56/22.35 | | | | | | | | (236) all_56_17 = e1 % 151.56/22.35 | | | | | | | | % 151.56/22.35 | | | | | | | | COMBINE_EQS: (180), (236) imply: % 151.56/22.35 | | | | | | | | (237) e1 = e0 % 151.56/22.35 | | | | | | | | % 151.56/22.35 | | | | | | | | REDUCE: (174), (237) imply: % 151.56/22.35 | | | | | | | | (238) $false % 151.56/22.35 | | | | | | | | % 151.56/22.35 | | | | | | | | CLOSE: (238) is inconsistent. % 151.56/22.35 | | | | | | | | % 151.56/22.35 | | | | | | | End of split % 151.56/22.35 | | | | | | | % 151.56/22.35 | | | | | | End of split % 151.56/22.35 | | | | | | % 151.56/22.35 | | | | | Case 2: % 151.56/22.35 | | | | | | % 151.56/22.35 | | | | | | (239) ~ (all_58_6 = e0) % 151.56/22.35 | | | | | | % 151.56/22.35 | | | | | | REF_CLOSE: (4), (21), (34), (44), (65), (67), (71), (78), (105), % 151.56/22.35 | | | | | | (111), (126), (132), (138), (158), (160), (176), (239) % 151.56/22.35 | | | | | | are inconsistent by sub-proof #623. % 151.56/22.35 | | | | | | % 151.56/22.35 | | | | | End of split % 151.56/22.35 | | | | | % 151.56/22.35 | | | | Case 2: % 151.56/22.35 | | | | | % 151.56/22.35 | | | | | (240) all_56_23 = e1 % 151.56/22.35 | | | | | (241) all_56_21 = e0 % 151.56/22.35 | | | | | % 151.56/22.35 | | | | | COMBINE_EQS: (28), (241) imply: % 151.56/22.35 | | | | | (242) all_6_2 = e0 % 151.56/22.35 | | | | | % 151.56/22.35 | | | | | SIMP: (242) implies: % 151.56/22.35 | | | | | (243) all_6_2 = e0 % 151.56/22.35 | | | | | % 151.56/22.35 | | | | | COMBINE_EQS: (98), (240) imply: % 151.56/22.35 | | | | | (244) all_52_14 = e1 % 151.56/22.35 | | | | | % 151.56/22.35 | | | | | SIMP: (244) implies: % 151.56/22.35 | | | | | (245) all_52_14 = e1 % 151.56/22.35 | | | | | % 151.56/22.35 | | | | | COMBINE_EQS: (67), (243) imply: % 151.56/22.35 | | | | | (246) all_58_8 = e0 % 151.56/22.35 | | | | | % 151.56/22.35 | | | | | REDUCE: (92), (245) imply: % 151.56/22.35 | | | | | (247) ~ (all_52_2 = e1) % 151.56/22.35 | | | | | % 151.56/22.35 | | | | | REDUCE: (119), (243) imply: % 151.56/22.35 | | | | | (248) ~ (all_52_2 = e0) % 151.56/22.35 | | | | | % 151.56/22.35 | | | | | REDUCE: (22), (245) imply: % 151.56/22.35 | | | | | (249) ~ (all_52_6 = e1) % 151.56/22.35 | | | | | % 151.56/22.35 | | | | | REDUCE: (124), (243) imply: % 151.56/22.35 | | | | | (250) ~ (all_52_6 = e0) % 151.56/22.35 | | | | | % 151.56/22.35 | | | | | REDUCE: (45), (243) imply: % 151.56/22.35 | | | | | (251) ~ (all_52_8 = e0) % 151.56/22.35 | | | | | % 151.56/22.35 | | | | | REDUCE: (115), (245) imply: % 151.56/22.35 | | | | | (252) ~ (all_52_12 = e1) % 151.56/22.35 | | | | | % 151.56/22.35 | | | | | REDUCE: (39), (245) imply: % 151.56/22.35 | | | | | (253) op(e0, e1) = all_56_22 % 151.56/22.35 | | | | | % 151.56/22.35 | | | | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (10), (12), (13), (14), % 151.56/22.35 | | | | | (15), (16), (17), (21), (25), (27), (31), (32), (33), (34), % 151.56/22.35 | | | | | (35), (36), (37), (38), (41), (42), (43), (46), (50), (51), % 151.56/22.35 | | | | | (52), (53), (55), (56), (57), (58), (59), (60), (61), (62), % 151.56/22.35 | | | | | (64), (65), (66), (68), (72), (74), (76), (77), (78), (81), % 151.56/22.35 | | | | | (82), (83), (84), (86), (87), (88), (89), (95), (96), (97), % 151.56/22.35 | | | | | (99), (101), (102), (103), (105), (107), (112), (113), % 151.56/22.35 | | | | | (114), (116), (117), (118), (120), (121), (126), (127), % 151.56/22.35 | | | | | (130), (131), (132), (133), (134), (137), (138), (139), % 151.56/22.35 | | | | | (141), (143), (157), (158), (159), (161), (166), (240), % 151.56/22.35 | | | | | (246), (247), (248), (249), (250), (251), (252), (253) are % 151.56/22.35 | | | | | inconsistent by sub-proof #607. % 151.56/22.35 | | | | | % 151.56/22.35 | | | | End of split % 151.56/22.35 | | | | % 151.56/22.35 | | | End of split % 151.56/22.35 | | | % 151.56/22.35 | | End of split % 151.56/22.35 | | % 151.56/22.35 | End of split % 151.56/22.35 | % 151.56/22.35 End of proof % 151.56/22.35 % 151.56/22.35 Sub-proof #287 shows that the following formulas are inconsistent: % 151.56/22.35 ---------------------------------------------------------------- % 151.56/22.35 (1) all_54_10 = all_6_2 % 151.56/22.35 (2) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0 % 151.56/22.35 (3) ~ (all_6_1 = e2) % 151.56/22.35 (4) all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2 % 151.56/22.35 (5) all_54_0 = all_10_2 % 151.56/22.35 (6) op(e0, e0) = all_4_2 % 151.56/22.35 (7) ~ (all_6_1 = e3) % 151.56/22.35 (8) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 151.56/22.35 (9) all_54_15 = all_4_2 % 151.56/22.35 (10) all_56_1 = all_10_2 % 151.56/22.35 (11) all_58_9 = all_52_12 % 151.56/22.35 (12) ~ (all_56_1 = e1) | all_56_5 = e3 % 151.56/22.35 (13) all_58_1 = all_52_4 % 151.56/22.35 (14) all_58_13 = all_52_7 % 151.56/22.35 (15) op(e3, e3) = all_10_2 % 151.56/22.35 (16) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 151.56/22.35 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 151.56/22.35 (17) all_54_3 = all_52_12 % 151.56/22.35 (18) ~ (all_52_7 = all_4_2) % 151.56/22.35 (19) ~ (all_4_2 = e1) % 151.56/22.35 (20) ~ (all_56_1 = e2) | all_56_3 = e3 % 151.56/22.35 (21) all_56_5 = all_52_8 % 151.56/22.35 (22) all_58_3 = all_8_2 % 151.56/22.35 (23) all_56_3 = all_52_4 % 151.56/22.35 (24) op(all_6_2, all_6_2) = all_6_1 % 151.56/22.35 (25) op(e3, e0) = all_52_12 % 151.56/22.35 (26) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0 % 151.56/22.35 (27) op(e1, e1) = all_6_2 % 151.56/22.35 (28) all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1 % 151.56/22.35 (29) ~ (all_6_2 = e1) % 151.56/22.35 (30) op(e3, all_10_1) = e1 % 151.56/22.35 (31) all_58_7 = all_52_6 % 151.56/22.35 (32) op(all_10_2, all_10_2) = all_10_1 % 151.56/22.35 (33) all_58_0 = all_10_2 % 151.56/22.35 (34) all_58_1 = e0 | all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0 % 151.56/22.35 (35) ~ (all_52_4 = all_52_12) % 151.56/22.35 (36) ~ (all_52_8 = all_52_12) % 151.56/22.35 (37) ~ (all_52_6 = all_6_2) % 151.56/22.35 (38) all_54_10 = e1 | all_54_10 = e0 % 151.56/22.35 (39) ~ (all_8_2 = e0) % 151.56/22.35 (40) op(e3, all_10_2) = all_56_0 % 151.56/22.35 (41) ~ (all_52_4 = all_10_2) % 151.56/22.35 (42) ~ (all_52_12 = all_10_2) % 151.56/22.35 % 151.56/22.35 Begin of proof % 151.56/22.35 | % 151.56/22.35 | BETA: splitting (38) gives: % 151.56/22.35 | % 151.56/22.35 | Case 1: % 151.56/22.35 | | % 151.56/22.35 | | (43) all_54_10 = e1 % 151.56/22.35 | | % 151.56/22.35 | | REF_CLOSE: (1), (29), (43) are inconsistent by sub-proof #606. % 151.56/22.35 | | % 151.56/22.35 | Case 2: % 151.56/22.35 | | % 151.56/22.35 | | (44) all_54_10 = e0 % 151.56/22.35 | | % 151.56/22.35 | | COMBINE_EQS: (1), (44) imply: % 151.56/22.35 | | (45) all_6_2 = e0 % 151.56/22.35 | | % 151.56/22.35 | | SIMP: (45) implies: % 151.56/22.35 | | (46) all_6_2 = e0 % 151.56/22.35 | | % 151.56/22.35 | | REDUCE: (37), (46) imply: % 151.56/22.35 | | (47) ~ (all_52_6 = e0) % 151.56/22.35 | | % 151.56/22.35 | | REDUCE: (24), (46) imply: % 151.56/22.35 | | (48) op(e0, e0) = all_6_1 % 151.56/22.35 | | % 151.56/22.35 | | REDUCE: (27), (46) imply: % 151.56/22.35 | | (49) op(e1, e1) = e0 % 151.56/22.35 | | % 151.56/22.35 | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13), % 151.56/22.35 | | (14), (15), (16), (17), (18), (19), (20), (21), (22), (23), (25), % 151.56/22.35 | | (26), (28), (30), (31), (32), (33), (34), (35), (36), (39), (40), % 151.56/22.35 | | (41), (42), (47), (48), (49) are inconsistent by sub-proof #289. % 151.56/22.35 | | % 151.56/22.35 | End of split % 151.56/22.35 | % 151.56/22.35 End of proof % 151.56/22.35 % 151.56/22.35 Sub-proof #288 shows that the following formulas are inconsistent: % 151.56/22.35 ---------------------------------------------------------------- % 151.56/22.35 (1) all_56_11 = all_8_2 % 151.56/22.35 (2) op(e0, all_52_13) = all_56_14 % 151.56/22.35 (3) ~ (all_52_11 = all_6_2) % 151.56/22.35 (4) ~ (all_52_4 = all_52_8) % 151.56/22.35 (5) ~ (all_52_8 = all_52_9) % 151.56/22.35 (6) all_54_9 = all_52_6 % 151.56/22.35 (7) op(e2, all_8_1) = all_8_0 % 151.56/22.35 (8) ~ (all_8_1 = e1) % 151.56/22.35 (9) ~ (all_52_1 = all_52_9) % 151.56/22.35 (10) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0 % 151.56/22.35 (11) all_54_10 = all_6_2 % 151.56/22.35 (12) ~ (all_6_1 = e2) % 151.56/22.35 (13) ~ (all_52_13 = all_8_2) % 151.56/22.35 (14) all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2 % 151.56/22.35 (15) all_54_0 = all_10_2 % 151.56/22.35 (16) all_54_4 = all_52_1 % 151.56/22.35 (17) ~ (all_8_0 = e1) % 151.56/22.35 (18) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0 % 151.56/22.35 (19) all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2 % 151.56/22.35 (20) ~ (all_52_9 = all_8_2) % 151.56/22.35 (21) ~ (all_52_4 = all_52_7) % 151.56/22.35 (22) all_58_4 = all_52_8 % 151.56/22.35 (23) all_54_5 = all_8_2 % 151.56/22.35 (24) ~ (all_6_1 = e3) % 151.56/22.35 (25) ~ (all_52_6 = all_52_14) % 151.56/22.35 (26) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 151.56/22.35 (27) ~ (all_52_11 = e0) % 151.56/22.35 (28) all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1 % 151.56/22.35 (29) all_56_21 = all_6_2 % 151.56/22.35 (30) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 151.56/22.35 (31) op(e3, all_52_1) = all_56_8 % 151.56/22.35 (32) ~ (all_52_7 = all_8_2) % 151.56/22.35 (33) all_56_1 = all_10_2 % 151.56/22.35 (34) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0 % 151.56/22.35 (35) all_58_5 = all_52_9 % 151.56/22.35 (36) all_54_1 = all_52_4 % 151.56/22.35 (37) all_56_17 = all_52_2 % 151.56/22.35 (38) all_58_9 = all_52_12 % 151.56/22.35 (39) all_58_12 = e0 % 151.56/22.35 (40) op(e0, all_52_14) = all_56_22 % 151.56/22.35 (41) op(e0, e2) = all_52_7 % 151.56/22.35 (42) ~ (all_56_1 = e1) | all_56_5 = e3 % 151.56/22.35 (43) all_54_14 = all_52_11 % 151.56/22.35 (44) all_58_1 = all_52_4 % 151.56/22.35 (45) all_58_13 = all_52_7 % 151.56/22.35 (46) all_58_4 = e0 | all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0 % 151.56/22.35 (47) op(e2, all_8_2) = all_56_10 % 151.56/22.35 (48) op(e3, e3) = all_10_2 % 151.56/22.35 (49) ~ (all_52_8 = all_6_2) % 151.56/22.35 (50) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0 % 151.56/22.35 (51) all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1 % 151.56/22.35 (52) ~ (all_56_21 = e3) | all_56_17 = e1 % 151.56/22.35 (53) ~ (all_52_1 = all_8_2) % 151.56/22.35 (54) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 151.56/22.35 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 151.56/22.35 (55) ~ (all_52_11 = e3) % 151.56/22.35 (56) ~ (all_56_11 = e3) | all_56_9 = e2 % 151.56/22.35 (57) op(e0, all_4_1) = all_4_0 % 151.56/22.35 (58) ~ (all_52_2 = e0) % 151.56/22.35 (59) op(e0, e1) = all_52_11 % 151.56/22.35 (60) ~ (all_52_1 = all_52_13) % 151.56/22.35 (61) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0 % 151.56/22.35 (62) ~ (all_52_14 = e3) % 151.56/22.35 (63) ~ (all_4_2 = e1) % 151.56/22.35 (64) all_54_6 = all_52_9 % 151.56/22.35 (65) ~ (all_4_0 = e1) % 151.56/22.35 (66) ~ (all_56_1 = e2) | all_56_3 = e3 % 151.56/22.35 (67) all_58_15 = e3 % 151.56/22.35 (68) all_56_5 = all_52_8 % 151.56/22.35 (69) ~ (all_52_9 = all_52_13) % 151.56/22.35 (70) ~ (all_52_1 = e0) % 151.56/22.35 (71) op(all_4_2, all_4_2) = all_4_1 % 151.56/22.35 (72) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0 % 151.56/22.35 (73) ~ (all_52_1 = all_52_3) % 151.56/22.35 (74) ~ (all_52_6 = all_52_7) % 151.56/22.35 (75) all_58_11 = all_52_14 % 151.56/22.35 (76) op(e0, e0) = e3 % 151.56/22.35 (77) op(all_6_2, all_6_2) = all_6_1 % 151.56/22.35 (78) ~ (all_52_8 = all_52_11) % 151.56/22.35 (79) all_54_2 = all_52_8 % 151.56/22.35 (80) all_54_8 = all_52_2 % 151.56/22.35 (81) ~ (all_52_6 = all_8_2) % 151.56/22.35 (82) ~ (all_10_2 = e0) % 151.56/22.35 (83) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0 % 151.56/22.35 (84) all_58_15 = all_4_2 % 151.56/22.35 (85) ~ (all_6_2 = e2) % 151.56/22.35 (86) all_58_2 = all_52_1 % 151.56/22.35 (87) all_58_10 = all_52_13 % 151.56/22.35 (88) all_58_0 = all_10_2 % 151.56/22.35 (89) all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1 % 151.56/22.35 (90) ~ (all_52_12 = all_52_14) % 151.56/22.35 (91) op(e2, e2) = all_8_2 % 151.56/22.35 (92) ~ (all_52_4 = all_52_12) % 151.56/22.35 (93) ~ (all_52_2 = all_6_2) % 151.56/22.35 (94) ~ (all_52_8 = all_52_12) % 151.56/22.35 (95) ~ (all_52_1 = all_52_2) % 151.56/22.35 (96) ~ (all_56_21 = e0) | all_56_23 = e1 % 151.56/22.35 (97) ~ (all_8_2 = e0) % 151.56/22.35 (98) ~ (all_52_14 = all_6_2) % 151.56/22.35 (99) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0 % 151.56/22.35 (100) ~ (all_52_2 = all_10_2) % 151.56/22.35 (101) all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3 % 151.56/22.35 (102) ~ (all_52_4 = all_8_2) % 151.56/22.35 (103) op(all_8_2, all_8_2) = all_8_1 % 151.56/22.35 (104) ~ (all_52_4 = all_52_6) % 151.56/22.35 (105) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 151.56/22.35 (106) all_58_14 = all_52_11 % 151.56/22.35 (107) ~ (all_4_0 = e2) % 151.56/22.36 (108) all_56_9 = all_52_1 % 151.56/22.36 (109) ~ (all_52_1 = all_10_2) % 151.56/22.36 (110) op(e3, e3) = all_4_1 % 151.56/22.36 (111) all_58_12 = all_52_3 % 151.56/22.36 (112) all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3 % 151.56/22.36 (113) all_54_11 = all_52_14 % 151.56/22.36 % 151.56/22.36 Begin of proof % 151.56/22.36 | % 151.56/22.36 | GROUND_INST: instantiating (54) with all_10_2, all_4_1, e3, e3, simplifying % 151.56/22.36 | with (48), (110) gives: % 151.56/22.36 | (114) all_10_2 = all_4_1 % 151.56/22.36 | % 151.56/22.36 | COMBINE_EQS: (15), (114) imply: % 151.56/22.36 | (115) all_54_0 = all_4_1 % 151.56/22.36 | % 151.56/22.36 | COMBINE_EQS: (33), (114) imply: % 151.56/22.36 | (116) all_56_1 = all_4_1 % 151.56/22.36 | % 151.56/22.36 | COMBINE_EQS: (88), (114) imply: % 151.56/22.36 | (117) all_58_0 = all_4_1 % 151.56/22.36 | % 151.56/22.36 | REDUCE: (109), (114) imply: % 151.56/22.36 | (118) ~ (all_52_1 = all_4_1) % 151.56/22.36 | % 151.56/22.36 | REDUCE: (100), (114) imply: % 151.56/22.36 | (119) ~ (all_52_2 = all_4_1) % 151.56/22.36 | % 151.56/22.36 | REDUCE: (82), (114) imply: % 151.56/22.36 | (120) ~ (all_4_1 = e0) % 151.56/22.36 | % 151.56/22.36 | BETA: splitting (96) gives: % 151.56/22.36 | % 151.56/22.36 | Case 1: % 151.56/22.36 | | % 151.56/22.36 | | (121) ~ (all_56_21 = e0) % 151.56/22.36 | | % 151.56/22.36 | | REDUCE: (29), (121) imply: % 151.56/22.36 | | (122) ~ (all_6_2 = e0) % 151.56/22.36 | | % 151.56/22.36 | | BETA: splitting (52) gives: % 151.56/22.36 | | % 151.56/22.36 | | Case 1: % 151.56/22.36 | | | % 151.56/22.36 | | | (123) ~ (all_56_21 = e3) % 151.56/22.36 | | | % 151.56/22.36 | | | REDUCE: (29), (123) imply: % 151.56/22.36 | | | (124) ~ (all_6_2 = e3) % 151.56/22.36 | | | % 151.56/22.36 | | | BETA: splitting (30) gives: % 151.56/22.36 | | | % 151.56/22.36 | | | Case 1: % 151.56/22.36 | | | | % 151.56/22.36 | | | | (125) all_54_10 = e3 % 151.56/22.36 | | | | % 151.56/22.36 | | | | COMBINE_EQS: (11), (125) imply: % 151.56/22.36 | | | | (126) all_6_2 = e3 % 151.56/22.36 | | | | % 151.56/22.36 | | | | REDUCE: (124), (126) imply: % 151.56/22.36 | | | | (127) $false % 151.56/22.36 | | | | % 151.56/22.36 | | | | CLOSE: (127) is inconsistent. % 151.56/22.36 | | | | % 151.56/22.36 | | | Case 2: % 151.56/22.36 | | | | % 151.56/22.36 | | | | (128) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 151.56/22.36 | | | | % 151.56/22.36 | | | | BETA: splitting (128) gives: % 151.56/22.36 | | | | % 151.56/22.36 | | | | Case 1: % 151.56/22.36 | | | | | % 151.56/22.36 | | | | | (129) all_54_10 = e2 % 151.56/22.36 | | | | | % 151.56/22.36 | | | | | COMBINE_EQS: (11), (129) imply: % 151.56/22.36 | | | | | (130) all_6_2 = e2 % 151.56/22.36 | | | | | % 151.56/22.36 | | | | | REDUCE: (85), (130) imply: % 151.56/22.36 | | | | | (131) $false % 151.56/22.36 | | | | | % 151.56/22.36 | | | | | CLOSE: (131) is inconsistent. % 151.56/22.36 | | | | | % 151.56/22.36 | | | | Case 2: % 151.56/22.36 | | | | | % 151.56/22.36 | | | | | (132) all_54_10 = e1 | all_54_10 = e0 % 151.56/22.36 | | | | | % 151.56/22.36 | | | | | BETA: splitting (132) gives: % 151.56/22.36 | | | | | % 151.56/22.36 | | | | | Case 1: % 151.56/22.36 | | | | | | % 151.56/22.36 | | | | | | (133) all_54_10 = e1 % 151.56/22.36 | | | | | | % 151.56/22.36 | | | | | | COMBINE_EQS: (11), (133) imply: % 151.56/22.36 | | | | | | (134) all_6_2 = e1 % 151.56/22.36 | | | | | | % 151.56/22.36 | | | | | | REDUCE: (93), (134) imply: % 151.56/22.36 | | | | | | (135) ~ (all_52_2 = e1) % 151.56/22.36 | | | | | | % 151.56/22.36 | | | | | | REDUCE: (49), (134) imply: % 151.56/22.36 | | | | | | (136) ~ (all_52_8 = e1) % 151.56/22.36 | | | | | | % 151.56/22.36 | | | | | | REDUCE: (3), (134) imply: % 151.56/22.36 | | | | | | (137) ~ (all_52_11 = e1) % 151.56/22.36 | | | | | | % 151.56/22.36 | | | | | | REDUCE: (98), (134) imply: % 151.56/22.36 | | | | | | (138) ~ (all_52_14 = e1) % 151.56/22.36 | | | | | | % 151.56/22.36 | | | | | | REDUCE: (122), (134) imply: % 151.56/22.36 | | | | | | (139) ~ (e1 = e0) % 151.56/22.36 | | | | | | % 151.56/22.36 | | | | | | BETA: splitting (10) gives: % 151.56/22.36 | | | | | | % 151.56/22.36 | | | | | | Case 1: % 151.56/22.36 | | | | | | | % 151.56/22.36 | | | | | | | (140) all_54_14 = e3 % 151.56/22.36 | | | | | | | % 151.56/22.36 | | | | | | | REF_CLOSE: (43), (55), (140) are inconsistent by sub-proof #729. % 151.56/22.36 | | | | | | | % 151.56/22.36 | | | | | | Case 2: % 151.56/22.36 | | | | | | | % 151.56/22.36 | | | | | | | (141) all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0 % 151.56/22.36 | | | | | | | % 151.56/22.36 | | | | | | | BETA: splitting (141) gives: % 151.56/22.36 | | | | | | | % 151.56/22.36 | | | | | | | Case 1: % 151.56/22.36 | | | | | | | | % 151.56/22.36 | | | | | | | | (142) all_54_14 = e2 % 151.56/22.36 | | | | | | | | % 151.56/22.36 | | | | | | | | COMBINE_EQS: (43), (142) imply: % 151.56/22.36 | | | | | | | | (143) all_52_11 = e2 % 151.56/22.36 | | | | | | | | % 151.56/22.36 | | | | | | | | SIMP: (143) implies: % 151.56/22.36 | | | | | | | | (144) all_52_11 = e2 % 151.56/22.36 | | | | | | | | % 151.56/22.36 | | | | | | | | COMBINE_EQS: (106), (144) imply: % 151.56/22.36 | | | | | | | | (145) all_58_14 = e2 % 151.56/22.36 | | | | | | | | % 151.56/22.36 | | | | | | | | REDUCE: (78), (144) imply: % 151.56/22.36 | | | | | | | | (146) ~ (all_52_8 = e2) % 151.56/22.36 | | | | | | | | % 151.56/22.36 | | | | | | | | REDUCE: (59), (144) imply: % 151.56/22.36 | | | | | | | | (147) op(e0, e1) = e2 % 151.56/22.36 | | | | | | | | % 151.56/22.36 | | | | | | | | BETA: splitting (89) gives: % 151.56/22.36 | | | | | | | | % 151.56/22.36 | | | | | | | | Case 1: % 151.56/22.36 | | | | | | | | | % 151.56/22.36 | | | | | | | | | (148) all_58_12 = e1 % 151.56/22.36 | | | | | | | | | % 151.56/22.36 | | | | | | | | | REF_CLOSE: (39), (139), (148) are inconsistent by sub-proof % 151.56/22.36 | | | | | | | | | #475. % 151.56/22.36 | | | | | | | | | % 151.56/22.36 | | | | | | | | Case 2: % 151.56/22.36 | | | | | | | | | % 151.56/22.36 | | | | | | | | | (149) all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1 % 151.56/22.36 | | | | | | | | | % 151.56/22.36 | | | | | | | | | BETA: splitting (149) gives: % 151.56/22.36 | | | | | | | | | % 151.56/22.36 | | | | | | | | | Case 1: % 151.56/22.36 | | | | | | | | | | % 151.56/22.36 | | | | | | | | | | (150) all_58_13 = e1 % 151.56/22.36 | | | | | | | | | | % 151.56/22.36 | | | | | | | | | | COMBINE_EQS: (45), (150) imply: % 151.56/22.36 | | | | | | | | | | (151) all_52_7 = e1 % 151.56/22.36 | | | | | | | | | | % 151.56/22.36 | | | | | | | | | | SIMP: (151) implies: % 151.56/22.36 | | | | | | | | | | (152) all_52_7 = e1 % 151.56/22.36 | | | | | | | | | | % 151.56/22.36 | | | | | | | | | | REDUCE: (21), (152) imply: % 151.56/22.36 | | | | | | | | | | (153) ~ (all_52_4 = e1) % 151.56/22.36 | | | | | | | | | | % 151.56/22.36 | | | | | | | | | | REDUCE: (74), (152) imply: % 151.56/22.36 | | | | | | | | | | (154) ~ (all_52_6 = e1) % 151.56/22.36 | | | | | | | | | | % 151.56/22.36 | | | | | | | | | | REDUCE: (32), (152) imply: % 151.56/22.36 | | | | | | | | | | (155) ~ (all_8_2 = e1) % 151.56/22.36 | | | | | | | | | | % 151.56/22.36 | | | | | | | | | | SIMP: (155) implies: % 151.56/22.36 | | | | | | | | | | (156) ~ (all_8_2 = e1) % 151.56/22.36 | | | | | | | | | | % 151.56/22.36 | | | | | | | | | | REDUCE: (41), (152) imply: % 151.56/22.36 | | | | | | | | | | (157) op(e0, e2) = e1 % 151.56/22.36 | | | | | | | | | | % 151.56/22.36 | | | | | | | | | | BETA: splitting (56) gives: % 151.56/22.36 | | | | | | | | | | % 151.56/22.36 | | | | | | | | | | Case 1: % 151.56/22.36 | | | | | | | | | | | % 151.56/22.36 | | | | | | | | | | | (158) ~ (all_56_11 = e3) % 151.56/22.36 | | | | | | | | | | | % 151.56/22.36 | | | | | | | | | | | REDUCE: (1), (158) imply: % 151.56/22.36 | | | | | | | | | | | (159) ~ (all_8_2 = e3) % 151.56/22.36 | | | | | | | | | | | % 151.56/22.36 | | | | | | | | | | | BETA: splitting (105) gives: % 151.56/22.36 | | | | | | | | | | | % 151.56/22.36 | | | | | | | | | | | Case 1: % 151.56/22.36 | | | | | | | | | | | | % 151.56/22.36 | | | | | | | | | | | | (160) all_54_5 = e3 % 151.56/22.36 | | | | | | | | | | | | % 151.56/22.36 | | | | | | | | | | | | REF_CLOSE: (23), (159), (160) are inconsistent by sub-proof % 151.56/22.36 | | | | | | | | | | | | #737. % 151.56/22.36 | | | | | | | | | | | | % 151.56/22.36 | | | | | | | | | | | Case 2: % 151.56/22.36 | | | | | | | | | | | | % 151.56/22.36 | | | | | | | | | | | | (161) ~ (all_54_5 = e3) % 151.56/22.36 | | | | | | | | | | | | (162) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 151.56/22.36 | | | | | | | | | | | | % 151.56/22.36 | | | | | | | | | | | | BETA: splitting (162) gives: % 151.56/22.36 | | | | | | | | | | | | % 151.56/22.36 | | | | | | | | | | | | Case 1: % 151.56/22.36 | | | | | | | | | | | | | % 151.56/22.36 | | | | | | | | | | | | | (163) all_54_5 = e2 % 151.56/22.36 | | | | | | | | | | | | | % 151.56/22.36 | | | | | | | | | | | | | COMBINE_EQS: (23), (163) imply: % 151.56/22.36 | | | | | | | | | | | | | (164) all_8_2 = e2 % 151.56/22.36 | | | | | | | | | | | | | % 151.56/22.36 | | | | | | | | | | | | | SIMP: (164) implies: % 151.56/22.36 | | | | | | | | | | | | | (165) all_8_2 = e2 % 151.56/22.36 | | | | | | | | | | | | | % 151.56/22.36 | | | | | | | | | | | | | REDUCE: (53), (165) imply: % 151.56/22.36 | | | | | | | | | | | | | (166) ~ (all_52_1 = e2) % 151.56/22.36 | | | | | | | | | | | | | % 151.56/22.36 | | | | | | | | | | | | | REDUCE: (102), (165) imply: % 151.56/22.36 | | | | | | | | | | | | | (167) ~ (all_52_4 = e2) % 151.56/22.36 | | | | | | | | | | | | | % 151.56/22.36 | | | | | | | | | | | | | REDUCE: (20), (165) imply: % 151.56/22.36 | | | | | | | | | | | | | (168) ~ (all_52_9 = e2) % 151.56/22.36 | | | | | | | | | | | | | % 151.56/22.36 | | | | | | | | | | | | | REDUCE: (13), (165) imply: % 151.56/22.36 | | | | | | | | | | | | | (169) ~ (all_52_13 = e2) % 151.56/22.36 | | | | | | | | | | | | | % 151.56/22.36 | | | | | | | | | | | | | REDUCE: (103), (165) imply: % 151.56/22.36 | | | | | | | | | | | | | (170) op(e2, e2) = all_8_1 % 151.56/22.36 | | | | | | | | | | | | | % 151.56/22.36 | | | | | | | | | | | | | REDUCE: (47), (165) imply: % 151.56/22.36 | | | | | | | | | | | | | (171) op(e2, e2) = all_56_10 % 151.56/22.36 | | | | | | | | | | | | | % 151.56/22.36 | | | | | | | | | | | | | REDUCE: (91), (165) imply: % 151.56/22.36 | | | | | | | | | | | | | (172) op(e2, e2) = e2 % 151.56/22.36 | | | | | | | | | | | | | % 151.56/22.36 | | | | | | | | | | | | | GROUND_INST: instantiating (54) with all_8_1, all_56_10, e2, % 151.56/22.36 | | | | | | | | | | | | | e2, simplifying with (170), (171) gives: % 151.56/22.36 | | | | | | | | | | | | | (173) all_56_10 = all_8_1 % 151.56/22.36 | | | | | | | | | | | | | % 151.56/22.36 | | | | | | | | | | | | | GROUND_INST: instantiating (54) with e2, all_56_10, e2, e2, % 151.56/22.36 | | | | | | | | | | | | | simplifying with (171), (172) gives: % 151.56/22.36 | | | | | | | | | | | | | (174) all_56_10 = e2 % 151.56/22.36 | | | | | | | | | | | | | % 151.56/22.36 | | | | | | | | | | | | | COMBINE_EQS: (173), (174) imply: % 151.56/22.36 | | | | | | | | | | | | | (175) all_8_1 = e2 % 151.56/22.36 | | | | | | | | | | | | | % 151.56/22.36 | | | | | | | | | | | | | REDUCE: (7), (175) imply: % 151.56/22.36 | | | | | | | | | | | | | (176) op(e2, e2) = all_8_0 % 151.56/22.36 | | | | | | | | | | | | | % 151.56/22.36 | | | | | | | | | | | | | GROUND_INST: instantiating (54) with e2, all_8_0, e2, e2, % 151.56/22.36 | | | | | | | | | | | | | simplifying with (172), (176) gives: % 151.56/22.36 | | | | | | | | | | | | | (177) all_8_0 = e2 % 151.56/22.36 | | | | | | | | | | | | | % 151.56/22.36 | | | | | | | | | | | | | REDUCE: (17), (177) imply: % 151.56/22.36 | | | | | | | | | | | | | (178) ~ (e2 = e1) % 151.56/22.36 | | | | | | | | | | | | | % 151.56/22.36 | | | | | | | | | | | | | BETA: splitting (66) gives: % 151.56/22.36 | | | | | | | | | | | | | % 151.56/22.36 | | | | | | | | | | | | | Case 1: % 151.56/22.36 | | | | | | | | | | | | | | % 151.56/22.36 | | | | | | | | | | | | | | (179) ~ (all_56_1 = e2) % 151.56/22.36 | | | | | | | | | | | | | | % 151.56/22.36 | | | | | | | | | | | | | | REF_CLOSE: (2), (4), (5), (6), (9), (16), (18), (19), (22), % 151.56/22.36 | | | | | | | | | | | | | | (23), (25), (28), (31), (34), (35), (36), (38), % 151.56/22.36 | | | | | | | | | | | | | | (42), (44), (46), (50), (51), (54), (57), (60), % 151.56/22.36 | | | | | | | | | | | | | | (61), (62), (63), (64), (68), (69), (71), (72), % 151.56/22.36 | | | | | | | | | | | | | | (73), (75), (79), (81), (83), (84), (86), (87), % 151.56/22.36 | | | | | | | | | | | | | | (90), (92), (94), (97), (101), (104), (105), % 151.56/22.36 | | | | | | | | | | | | | | (107), (110), (111), (112), (113), (116), (117), % 151.56/22.36 | | | | | | | | | | | | | | (136), (138), (145), (146), (147), (150), (153), % 151.56/22.36 | | | | | | | | | | | | | | (154), (156), (159), (166), (167), (168), (178), % 151.56/22.36 | | | | | | | | | | | | | | (179) are inconsistent by sub-proof #556. % 151.56/22.36 | | | | | | | | | | | | | | % 151.56/22.36 | | | | | | | | | | | | | Case 2: % 151.56/22.36 | | | | | | | | | | | | | | % 151.56/22.36 | | | | | | | | | | | | | | (180) all_56_1 = e2 % 151.56/22.36 | | | | | | | | | | | | | | % 151.56/22.36 | | | | | | | | | | | | | | COMBINE_EQS: (116), (180) imply: % 151.56/22.36 | | | | | | | | | | | | | | (181) all_4_1 = e2 % 151.56/22.36 | | | | | | | | | | | | | | % 151.56/22.36 | | | | | | | | | | | | | | REDUCE: (119), (181) imply: % 151.56/22.36 | | | | | | | | | | | | | | (182) ~ (all_52_2 = e2) % 151.56/22.36 | | | | | | | | | | | | | | % 151.56/22.36 | | | | | | | | | | | | | | REDUCE: (57), (181) imply: % 151.56/22.36 | | | | | | | | | | | | | | (183) op(e0, e2) = all_4_0 % 151.56/22.36 | | | | | | | | | | | | | | % 151.56/22.36 | | | | | | | | | | | | | | BETA: splitting (99) gives: % 151.56/22.36 | | | | | | | | | | | | | | % 151.56/22.36 | | | | | | | | | | | | | | Case 1: % 151.56/22.36 | | | | | | | | | | | | | | | % 151.56/22.36 | | | | | | | | | | | | | | | (184) all_54_8 = e3 % 151.56/22.36 | | | | | | | | | | | | | | | % 151.56/22.36 | | | | | | | | | | | | | | | COMBINE_EQS: (80), (184) imply: % 151.56/22.36 | | | | | | | | | | | | | | | (185) all_52_2 = e3 % 151.56/22.36 | | | | | | | | | | | | | | | % 151.56/22.36 | | | | | | | | | | | | | | | SIMP: (185) implies: % 151.56/22.36 | | | | | | | | | | | | | | | (186) all_52_2 = e3 % 151.56/22.36 | | | | | | | | | | | | | | | % 151.56/22.36 | | | | | | | | | | | | | | | REDUCE: (95), (186) imply: % 151.56/22.36 | | | | | | | | | | | | | | | (187) ~ (all_52_1 = e3) % 151.56/22.36 | | | | | | | | | | | | | | | % 151.56/22.36 | | | | | | | | | | | | | | | REDUCE: (182), (186) imply: % 151.56/22.36 | | | | | | | | | | | | | | | (188) ~ (e3 = e2) % 151.56/22.36 | | | | | | | | | | | | | | | % 151.56/22.36 | | | | | | | | | | | | | | | BETA: splitting (61) gives: % 151.56/22.36 | | | | | | | | | | | | | | | % 151.56/22.36 | | | | | | | | | | | | | | | Case 1: % 151.56/22.36 | | | | | | | | | | | | | | | | % 151.56/22.36 | | | | | | | | | | | | | | | | (189) all_54_4 = e3 % 151.56/22.36 | | | | | | | | | | | | | | | | % 151.56/22.36 | | | | | | | | | | | | | | | | REF_CLOSE: (16), (187), (189) are inconsistent by sub-proof % 151.56/22.36 | | | | | | | | | | | | | | | | #634. % 151.56/22.36 | | | | | | | | | | | | | | | | % 151.56/22.36 | | | | | | | | | | | | | | | Case 2: % 151.56/22.36 | | | | | | | | | | | | | | | | % 151.56/22.36 | | | | | | | | | | | | | | | | (190) all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0 % 151.56/22.36 | | | | | | | | | | | | | | | | % 151.56/22.36 | | | | | | | | | | | | | | | | BETA: splitting (190) gives: % 151.56/22.36 | | | | | | | | | | | | | | | | % 151.56/22.36 | | | | | | | | | | | | | | | | Case 1: % 151.56/22.36 | | | | | | | | | | | | | | | | | % 151.56/22.36 | | | | | | | | | | | | | | | | | (191) all_54_4 = e2 % 151.56/22.36 | | | | | | | | | | | | | | | | | % 151.56/22.36 | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (166), (191) are inconsistent by sub-proof % 151.56/22.36 | | | | | | | | | | | | | | | | | #633. % 151.56/22.36 | | | | | | | | | | | | | | | | | % 151.56/22.36 | | | | | | | | | | | | | | | | Case 2: % 151.56/22.36 | | | | | | | | | | | | | | | | | % 151.56/22.36 | | | | | | | | | | | | | | | | | (192) ~ (all_54_4 = e2) % 151.56/22.36 | | | | | | | | | | | | | | | | | (193) all_54_4 = e1 | all_54_4 = e0 % 151.56/22.36 | | | | | | | | | | | | | | | | | % 151.56/22.36 | | | | | | | | | | | | | | | | | BETA: splitting (193) gives: % 151.56/22.36 | | | | | | | | | | | | | | | | | % 151.56/22.36 | | | | | | | | | | | | | | | | | Case 1: % 151.56/22.36 | | | | | | | | | | | | | | | | | | % 151.56/22.36 | | | | | | | | | | | | | | | | | | (194) all_54_4 = e1 % 151.56/22.36 | | | | | | | | | | | | | | | | | | % 151.56/22.36 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (16), (194) imply: % 151.56/22.36 | | | | | | | | | | | | | | | | | | (195) all_52_1 = e1 % 151.56/22.36 | | | | | | | | | | | | | | | | | | % 151.56/22.36 | | | | | | | | | | | | | | | | | | SIMP: (195) implies: % 151.56/22.36 | | | | | | | | | | | | | | | | | | (196) all_52_1 = e1 % 151.56/22.36 | | | | | | | | | | | | | | | | | | % 151.56/22.36 | | | | | | | | | | | | | | | | | | REDUCE: (60), (196) imply: % 151.56/22.36 | | | | | | | | | | | | | | | | | | (197) ~ (all_52_13 = e1) % 151.56/22.36 | | | | | | | | | | | | | | | | | | % 151.56/22.36 | | | | | | | | | | | | | | | | | | SIMP: (197) implies: % 151.56/22.36 | | | | | | | | | | | | | | | | | | (198) ~ (all_52_13 = e1) % 151.56/22.36 | | | | | | | | | | | | | | | | | | % 151.56/22.36 | | | | | | | | | | | | | | | | | | REDUCE: (166), (196) imply: % 151.56/22.36 | | | | | | | | | | | | | | | | | | (199) ~ (e2 = e1) % 151.56/22.36 | | | | | | | | | | | | | | | | | | % 151.56/22.36 | | | | | | | | | | | | | | | | | | BETA: splitting (28) gives: % 151.56/22.36 | | | | | | | | | | | | | | | | | | % 151.56/22.36 | | | | | | | | | | | | | | | | | | Case 1: % 151.56/22.36 | | | | | | | | | | | | | | | | | | | % 151.56/22.36 | | | | | | | | | | | | | | | | | | | (200) all_58_9 = e1 % 151.56/22.36 | | | | | | | | | | | | | | | | | | | % 151.56/22.36 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (40), (54), (65), (67), (75), (87), (157), % 151.56/22.36 | | | | | | | | | | | | | | | | | | | (169), (178), (183), (188), (200) are inconsistent % 151.56/22.36 | | | | | | | | | | | | | | | | | | | by sub-proof #474. % 151.56/22.36 | | | | | | | | | | | | | | | | | | | % 151.56/22.36 | | | | | | | | | | | | | | | | | | Case 2: % 151.56/22.36 | | | | | | | | | | | | | | | | | | | % 151.56/22.36 | | | | | | | | | | | | | | | | | | | (201) all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1 % 151.56/22.36 | | | | | | | | | | | | | | | | | | | % 151.56/22.36 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (63), (75), (84), (87), (138), (198), (201) are % 151.56/22.36 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #587. % 151.56/22.36 | | | | | | | | | | | | | | | | | | | % 151.56/22.36 | | | | | | | | | | | | | | | | | | End of split % 151.56/22.36 | | | | | | | | | | | | | | | | | | % 151.56/22.36 | | | | | | | | | | | | | | | | | Case 2: % 151.56/22.36 | | | | | | | | | | | | | | | | | | % 151.56/22.36 | | | | | | | | | | | | | | | | | | (202) all_54_4 = e0 % 151.56/22.36 | | | | | | | | | | | | | | | | | | % 151.56/22.36 | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (70), (202) are inconsistent by sub-proof % 151.56/22.36 | | | | | | | | | | | | | | | | | | #614. % 151.56/22.36 | | | | | | | | | | | | | | | | | | % 151.56/22.36 | | | | | | | | | | | | | | | | | End of split % 151.56/22.36 | | | | | | | | | | | | | | | | | % 151.56/22.36 | | | | | | | | | | | | | | | | End of split % 151.56/22.36 | | | | | | | | | | | | | | | | % 151.56/22.36 | | | | | | | | | | | | | | | End of split % 151.56/22.36 | | | | | | | | | | | | | | | % 151.56/22.36 | | | | | | | | | | | | | | Case 2: % 151.56/22.36 | | | | | | | | | | | | | | | % 151.56/22.36 | | | | | | | | | | | | | | | (203) all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0 % 151.56/22.36 | | | | | | | | | | | | | | | % 151.56/22.36 | | | | | | | | | | | | | | | REF_CLOSE: (58), (80), (135), (182), (203) are inconsistent % 151.56/22.36 | | | | | | | | | | | | | | | by sub-proof #663. % 151.56/22.36 | | | | | | | | | | | | | | | % 151.56/22.36 | | | | | | | | | | | | | | End of split % 151.56/22.36 | | | | | | | | | | | | | | % 151.56/22.36 | | | | | | | | | | | | | End of split % 151.56/22.36 | | | | | | | | | | | | | % 151.56/22.36 | | | | | | | | | | | | Case 2: % 151.56/22.36 | | | | | | | | | | | | | % 151.56/22.36 | | | | | | | | | | | | | (204) all_54_5 = e1 | all_54_5 = e0 % 151.56/22.36 | | | | | | | | | | | | | % 151.56/22.36 | | | | | | | | | | | | | REF_CLOSE: (23), (97), (156), (204) are inconsistent by % 151.56/22.36 | | | | | | | | | | | | | sub-proof #645. % 151.56/22.36 | | | | | | | | | | | | | % 151.56/22.36 | | | | | | | | | | | | End of split % 151.56/22.36 | | | | | | | | | | | | % 151.56/22.36 | | | | | | | | | | | End of split % 151.56/22.36 | | | | | | | | | | | % 151.56/22.36 | | | | | | | | | | Case 2: % 151.56/22.36 | | | | | | | | | | | % 151.56/22.36 | | | | | | | | | | | (205) all_56_11 = e3 % 151.56/22.36 | | | | | | | | | | | (206) all_56_9 = e2 % 151.56/22.36 | | | | | | | | | | | % 151.56/22.36 | | | | | | | | | | | COMBINE_EQS: (108), (206) imply: % 151.56/22.36 | | | | | | | | | | | (207) all_52_1 = e2 % 151.56/22.36 | | | | | | | | | | | % 151.56/22.36 | | | | | | | | | | | COMBINE_EQS: (1), (205) imply: % 151.56/22.36 | | | | | | | | | | | (208) all_8_2 = e3 % 151.56/22.36 | | | | | | | | | | | % 151.56/22.36 | | | | | | | | | | | REDUCE: (95), (207) imply: % 151.56/22.36 | | | | | | | | | | | (209) ~ (all_52_2 = e2) % 151.56/22.36 | | | | | | | | | | | % 151.56/22.36 | | | | | | | | | | | SIMP: (209) implies: % 151.56/22.36 | | | | | | | | | | | (210) ~ (all_52_2 = e2) % 151.56/22.36 | | | | | | | | | | | % 151.56/22.36 | | | | | | | | | | | REDUCE: (118), (207) imply: % 151.56/22.36 | | | | | | | | | | | (211) ~ (all_4_1 = e2) % 151.56/22.36 | | | | | | | | | | | % 151.56/22.36 | | | | | | | | | | | SIMP: (211) implies: % 151.56/22.36 | | | | | | | | | | | (212) ~ (all_4_1 = e2) % 151.56/22.36 | | | | | | | | | | | % 151.56/22.36 | | | | | | | | | | | REDUCE: (103), (208) imply: % 151.56/22.36 | | | | | | | | | | | (213) op(e3, e3) = all_8_1 % 151.56/22.36 | | | | | | | | | | | % 151.56/22.36 | | | | | | | | | | | REF_CLOSE: (8), (15), (26), (48), (54), (58), (80), (82), % 151.56/22.36 | | | | | | | | | | | (99), (115), (119), (135), (210), (212), (213) are % 151.56/22.36 | | | | | | | | | | | inconsistent by sub-proof #551. % 151.56/22.36 | | | | | | | | | | | % 151.56/22.36 | | | | | | | | | | End of split % 151.56/22.36 | | | | | | | | | | % 151.56/22.36 | | | | | | | | | Case 2: % 151.56/22.36 | | | | | | | | | | % 151.56/22.36 | | | | | | | | | | (214) all_58_14 = e1 | all_58_15 = e1 % 151.56/22.36 | | | | | | | | | | % 151.56/22.36 | | | | | | | | | | REF_CLOSE: (63), (84), (106), (137), (214) are inconsistent % 151.56/22.36 | | | | | | | | | | by sub-proof #619. % 151.56/22.36 | | | | | | | | | | % 151.56/22.36 | | | | | | | | | End of split % 151.56/22.36 | | | | | | | | | % 151.56/22.36 | | | | | | | | End of split % 151.56/22.36 | | | | | | | | % 151.56/22.36 | | | | | | | Case 2: % 151.56/22.36 | | | | | | | | % 151.56/22.36 | | | | | | | | (215) all_54_14 = e1 | all_54_14 = e0 % 151.56/22.36 | | | | | | | | % 151.56/22.36 | | | | | | | | REF_CLOSE: (27), (43), (137), (215) are inconsistent by % 151.56/22.36 | | | | | | | | sub-proof #714. % 151.56/22.36 | | | | | | | | % 151.56/22.36 | | | | | | | End of split % 151.56/22.36 | | | | | | | % 151.56/22.36 | | | | | | End of split % 151.56/22.36 | | | | | | % 151.56/22.36 | | | | | Case 2: % 151.56/22.36 | | | | | | % 151.56/22.36 | | | | | | (216) all_54_10 = e0 % 151.56/22.36 | | | | | | % 151.56/22.36 | | | | | | COMBINE_EQS: (11), (216) imply: % 151.56/22.36 | | | | | | (217) all_6_2 = e0 % 151.56/22.36 | | | | | | % 151.56/22.36 | | | | | | REDUCE: (122), (217) imply: % 151.56/22.36 | | | | | | (218) $false % 151.56/22.36 | | | | | | % 151.56/22.36 | | | | | | CLOSE: (218) is inconsistent. % 151.56/22.36 | | | | | | % 151.56/22.36 | | | | | End of split % 151.56/22.36 | | | | | % 151.56/22.36 | | | | End of split % 151.56/22.36 | | | | % 151.56/22.36 | | | End of split % 151.56/22.36 | | | % 151.56/22.36 | | Case 2: % 151.56/22.36 | | | % 151.56/22.36 | | | (219) all_56_21 = e3 % 151.56/22.36 | | | (220) all_56_17 = e1 % 151.56/22.36 | | | % 151.56/22.36 | | | COMBINE_EQS: (37), (220) imply: % 151.56/22.36 | | | (221) all_52_2 = e1 % 151.56/22.36 | | | % 151.56/22.36 | | | REF_CLOSE: (3), (10), (12), (24), (26), (29), (43), (54), (77), (110), % 151.56/22.36 | | | (115), (119), (120), (219), (221) are inconsistent by sub-proof % 151.56/22.36 | | | #468. % 151.56/22.36 | | | % 151.56/22.36 | | End of split % 151.56/22.36 | | % 151.56/22.36 | Case 2: % 151.56/22.36 | | % 151.56/22.36 | | (222) all_56_21 = e0 % 151.56/22.36 | | % 151.56/22.36 | | REF_CLOSE: (24), (29), (54), (76), (77), (222) are inconsistent by sub-proof % 151.56/22.36 | | #539. % 151.56/22.36 | | % 151.56/22.36 | End of split % 151.56/22.36 | % 151.56/22.36 End of proof % 151.56/22.36 % 151.56/22.36 Sub-proof #289 shows that the following formulas are inconsistent: % 151.56/22.36 ---------------------------------------------------------------- % 151.56/22.36 (1) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0 % 151.56/22.36 (2) ~ (all_6_1 = e2) % 151.56/22.36 (3) all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2 % 151.56/22.36 (4) all_54_0 = all_10_2 % 151.56/22.36 (5) op(e1, e1) = e0 % 151.56/22.36 (6) op(e0, e0) = all_4_2 % 151.56/22.36 (7) ~ (all_6_1 = e3) % 151.56/22.36 (8) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 151.56/22.36 (9) all_54_15 = all_4_2 % 151.56/22.36 (10) all_56_1 = all_10_2 % 151.56/22.36 (11) all_58_9 = all_52_12 % 151.56/22.36 (12) ~ (all_56_1 = e1) | all_56_5 = e3 % 151.56/22.36 (13) all_58_1 = all_52_4 % 151.56/22.36 (14) all_58_13 = all_52_7 % 151.56/22.36 (15) op(e3, e3) = all_10_2 % 151.56/22.36 (16) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 151.56/22.36 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 151.56/22.36 (17) all_54_3 = all_52_12 % 151.56/22.36 (18) ~ (all_52_7 = all_4_2) % 151.56/22.36 (19) ~ (all_4_2 = e1) % 151.56/22.36 (20) ~ (all_52_6 = e0) % 151.56/22.36 (21) ~ (all_56_1 = e2) | all_56_3 = e3 % 151.56/22.36 (22) all_56_5 = all_52_8 % 151.56/22.36 (23) all_58_3 = all_8_2 % 151.56/22.36 (24) all_56_3 = all_52_4 % 151.56/22.36 (25) op(e3, e0) = all_52_12 % 151.56/22.36 (26) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0 % 151.56/22.36 (27) all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1 % 151.56/22.36 (28) op(e3, all_10_1) = e1 % 151.56/22.36 (29) all_58_7 = all_52_6 % 151.56/22.36 (30) op(e0, e0) = all_6_1 % 151.56/22.36 (31) op(all_10_2, all_10_2) = all_10_1 % 151.56/22.36 (32) all_58_0 = all_10_2 % 151.56/22.36 (33) all_58_1 = e0 | all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0 % 151.56/22.36 (34) ~ (all_52_4 = all_52_12) % 151.56/22.36 (35) ~ (all_52_8 = all_52_12) % 151.56/22.36 (36) ~ (all_8_2 = e0) % 151.56/22.36 (37) op(e3, all_10_2) = all_56_0 % 151.56/22.36 (38) ~ (all_52_4 = all_10_2) % 151.56/22.36 (39) ~ (all_52_12 = all_10_2) % 151.56/22.36 % 151.56/22.36 Begin of proof % 151.56/22.36 | % 151.56/22.36 | GROUND_INST: instantiating (16) with all_4_2, all_6_1, e0, e0, simplifying % 151.56/22.36 | with (6), (30) gives: % 151.56/22.36 | (40) all_6_1 = all_4_2 % 151.56/22.36 | % 151.56/22.36 | REDUCE: (7), (40) imply: % 151.56/22.36 | (41) ~ (all_4_2 = e3) % 151.56/22.36 | % 151.56/22.36 | REDUCE: (2), (40) imply: % 151.56/22.36 | (42) ~ (all_4_2 = e2) % 151.56/22.36 | % 151.56/22.36 | BETA: splitting (26) gives: % 151.56/22.36 | % 151.56/22.36 | Case 1: % 151.56/22.36 | | % 151.56/22.36 | | (43) all_54_15 = e3 % 151.56/22.36 | | % 151.56/22.36 | | COMBINE_EQS: (9), (43) imply: % 151.56/22.36 | | (44) all_4_2 = e3 % 151.56/22.36 | | % 151.56/22.36 | | REDUCE: (41), (44) imply: % 151.56/22.36 | | (45) $false % 151.56/22.36 | | % 151.56/22.36 | | CLOSE: (45) is inconsistent. % 151.56/22.36 | | % 151.56/22.36 | Case 2: % 151.56/22.36 | | % 151.56/22.36 | | (46) ~ (all_54_15 = e3) % 151.56/22.36 | | (47) all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0 % 151.56/22.36 | | % 151.56/22.36 | | BETA: splitting (47) gives: % 151.56/22.36 | | % 151.56/22.36 | | Case 1: % 151.56/22.36 | | | % 151.56/22.36 | | | (48) all_54_15 = e2 % 151.56/22.36 | | | % 151.56/22.36 | | | COMBINE_EQS: (9), (48) imply: % 151.56/22.36 | | | (49) all_4_2 = e2 % 151.56/22.36 | | | % 151.56/22.36 | | | REDUCE: (42), (49) imply: % 151.56/22.36 | | | (50) $false % 151.56/22.36 | | | % 151.56/22.36 | | | CLOSE: (50) is inconsistent. % 151.56/22.36 | | | % 151.56/22.36 | | Case 2: % 151.56/22.36 | | | % 151.56/22.36 | | | (51) all_54_15 = e1 | all_54_15 = e0 % 151.56/22.36 | | | % 151.56/22.36 | | | BETA: splitting (51) gives: % 151.56/22.36 | | | % 151.56/22.36 | | | Case 1: % 151.56/22.36 | | | | % 151.56/22.36 | | | | (52) all_54_15 = e1 % 151.56/22.36 | | | | % 151.56/22.36 | | | | COMBINE_EQS: (9), (52) imply: % 151.56/22.36 | | | | (53) all_4_2 = e1 % 151.56/22.36 | | | | % 151.56/22.36 | | | | REDUCE: (19), (53) imply: % 151.56/22.36 | | | | (54) $false % 151.56/22.36 | | | | % 151.56/22.36 | | | | CLOSE: (54) is inconsistent. % 151.56/22.36 | | | | % 151.56/22.36 | | | Case 2: % 151.56/22.36 | | | | % 151.56/22.36 | | | | (55) all_54_15 = e0 % 151.56/22.36 | | | | % 151.56/22.36 | | | | COMBINE_EQS: (9), (55) imply: % 151.56/22.36 | | | | (56) all_4_2 = e0 % 151.56/22.36 | | | | % 151.56/22.36 | | | | REDUCE: (18), (56) imply: % 151.56/22.36 | | | | (57) ~ (all_52_7 = e0) % 151.56/22.36 | | | | % 151.56/22.36 | | | | REDUCE: (41), (56) imply: % 151.56/22.36 | | | | (58) ~ (e3 = e0) % 151.56/22.36 | | | | % 151.56/22.36 | | | | SIMP: (58) implies: % 151.56/22.36 | | | | (59) ~ (e3 = e0) % 151.56/22.36 | | | | % 151.56/22.36 | | | | BETA: splitting (33) gives: % 151.56/22.36 | | | | % 151.56/22.36 | | | | Case 1: % 151.56/22.36 | | | | | % 151.56/22.36 | | | | | (60) all_58_1 = e0 % 151.56/22.36 | | | | | % 151.56/22.36 | | | | | COMBINE_EQS: (13), (60) imply: % 151.56/22.36 | | | | | (61) all_52_4 = e0 % 151.56/22.36 | | | | | % 151.56/22.36 | | | | | COMBINE_EQS: (24), (61) imply: % 151.56/22.36 | | | | | (62) all_56_3 = e0 % 151.56/22.36 | | | | | % 151.56/22.36 | | | | | REDUCE: (34), (61) imply: % 151.56/22.36 | | | | | (63) ~ (all_52_12 = e0) % 151.56/22.36 | | | | | % 151.56/22.36 | | | | | SIMP: (63) implies: % 151.56/22.36 | | | | | (64) ~ (all_52_12 = e0) % 151.56/22.36 | | | | | % 151.56/22.36 | | | | | REDUCE: (38), (61) imply: % 151.56/22.36 | | | | | (65) ~ (all_10_2 = e0) % 151.56/22.36 | | | | | % 151.56/22.36 | | | | | SIMP: (65) implies: % 151.56/22.36 | | | | | (66) ~ (all_10_2 = e0) % 151.56/22.36 | | | | | % 151.56/22.36 | | | | | BETA: splitting (21) gives: % 151.56/22.36 | | | | | % 151.56/22.36 | | | | | Case 1: % 151.56/22.36 | | | | | | % 151.56/22.36 | | | | | | (67) ~ (all_56_1 = e2) % 151.56/22.36 | | | | | | % 151.56/22.36 | | | | | | REDUCE: (10), (67) imply: % 151.56/22.36 | | | | | | (68) ~ (all_10_2 = e2) % 151.56/22.36 | | | | | | % 151.56/22.36 | | | | | | BETA: splitting (27) gives: % 151.56/22.36 | | | | | | % 151.56/22.36 | | | | | | Case 1: % 151.56/22.36 | | | | | | | % 151.56/22.36 | | | | | | | (69) all_58_0 = e1 % 151.56/22.36 | | | | | | | % 151.56/22.36 | | | | | | | COMBINE_EQS: (32), (69) imply: % 151.56/22.36 | | | | | | | (70) all_10_2 = e1 % 151.56/22.36 | | | | | | | % 151.56/22.36 | | | | | | | COMBINE_EQS: (10), (70) imply: % 151.56/22.36 | | | | | | | (71) all_56_1 = e1 % 151.56/22.36 | | | | | | | % 151.56/22.36 | | | | | | | REDUCE: (39), (70) imply: % 151.56/22.36 | | | | | | | (72) ~ (all_52_12 = e1) % 151.56/22.36 | | | | | | | % 151.56/22.36 | | | | | | | REDUCE: (31), (70) imply: % 151.56/22.36 | | | | | | | (73) op(e1, e1) = all_10_1 % 151.56/22.36 | | | | | | | % 151.56/22.36 | | | | | | | BETA: splitting (12) gives: % 151.56/22.36 | | | | | | | % 151.56/22.36 | | | | | | | Case 1: % 151.56/22.36 | | | | | | | | % 151.56/22.36 | | | | | | | | (74) ~ (all_56_1 = e1) % 151.56/22.36 | | | | | | | | % 151.56/22.36 | | | | | | | | REDUCE: (71), (74) imply: % 151.56/22.36 | | | | | | | | (75) $false % 151.56/22.36 | | | | | | | | % 151.56/22.36 | | | | | | | | CLOSE: (75) is inconsistent. % 151.56/22.36 | | | | | | | | % 151.56/22.36 | | | | | | | Case 2: % 151.56/22.36 | | | | | | | | % 151.56/22.36 | | | | | | | | (76) all_56_5 = e3 % 151.56/22.36 | | | | | | | | % 151.56/22.36 | | | | | | | | COMBINE_EQS: (22), (76) imply: % 151.56/22.36 | | | | | | | | (77) all_52_8 = e3 % 151.56/22.36 | | | | | | | | % 151.56/22.36 | | | | | | | | SIMP: (77) implies: % 151.56/22.36 | | | | | | | | (78) all_52_8 = e3 % 151.56/22.36 | | | | | | | | % 151.56/22.36 | | | | | | | | REDUCE: (35), (78) imply: % 151.56/22.36 | | | | | | | | (79) ~ (all_52_12 = e3) % 151.56/22.36 | | | | | | | | % 151.56/22.36 | | | | | | | | SIMP: (79) implies: % 151.56/22.36 | | | | | | | | (80) ~ (all_52_12 = e3) % 151.56/22.36 | | | | | | | | % 151.56/22.36 | | | | | | | | REF_CLOSE: (1), (3), (5), (11), (16), (17), (25), (28), (64), % 151.56/22.36 | | | | | | | | (72), (73), (80) are inconsistent by sub-proof #290. % 151.56/22.36 | | | | | | | | % 151.56/22.36 | | | | | | | End of split % 151.56/22.36 | | | | | | | % 151.56/22.36 | | | | | | Case 2: % 151.56/22.36 | | | | | | | % 151.56/22.36 | | | | | | | (81) ~ (all_58_0 = e1) % 151.56/22.36 | | | | | | | % 151.56/22.36 | | | | | | | REDUCE: (32), (81) imply: % 151.56/22.36 | | | | | | | (82) ~ (all_10_2 = e1) % 151.56/22.36 | | | | | | | % 151.56/22.36 | | | | | | | REF_CLOSE: (4), (8), (15), (16), (28), (31), (37), (66), (68), % 151.56/22.36 | | | | | | | (82) are inconsistent by sub-proof #304. % 151.56/22.36 | | | | | | | % 151.56/22.36 | | | | | | End of split % 151.56/22.36 | | | | | | % 151.56/22.36 | | | | | Case 2: % 151.56/22.36 | | | | | | % 151.56/22.36 | | | | | | (83) all_56_3 = e3 % 151.56/22.36 | | | | | | % 151.56/22.36 | | | | | | COMBINE_EQS: (62), (83) imply: % 151.56/22.36 | | | | | | (84) e3 = e0 % 151.56/22.36 | | | | | | % 151.56/22.36 | | | | | | REDUCE: (59), (84) imply: % 151.56/22.36 | | | | | | (85) $false % 151.56/22.36 | | | | | | % 151.56/22.36 | | | | | | CLOSE: (85) is inconsistent. % 151.56/22.36 | | | | | | % 151.56/22.36 | | | | | End of split % 151.56/22.36 | | | | | % 151.56/22.36 | | | | Case 2: % 151.56/22.36 | | | | | % 151.56/22.36 | | | | | (86) all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0 % 151.56/22.36 | | | | | % 151.56/22.36 | | | | | REF_CLOSE: (14), (20), (23), (29), (36), (57), (86) are inconsistent % 151.56/22.36 | | | | | by sub-proof #603. % 151.56/22.36 | | | | | % 151.56/22.36 | | | | End of split % 151.56/22.36 | | | | % 151.56/22.36 | | | End of split % 151.56/22.36 | | | % 151.56/22.36 | | End of split % 151.56/22.36 | | % 151.56/22.36 | End of split % 151.56/22.36 | % 151.56/22.36 End of proof % 151.56/22.36 % 151.56/22.36 Sub-proof #290 shows that the following formulas are inconsistent: % 151.56/22.36 ---------------------------------------------------------------- % 151.56/22.36 (1) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0 % 151.56/22.36 (2) all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2 % 151.56/22.36 (3) op(e1, e1) = e0 % 151.56/22.36 (4) op(e1, e1) = all_10_1 % 151.56/22.36 (5) all_58_9 = all_52_12 % 151.56/22.36 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 151.56/22.36 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 151.56/22.36 (7) all_54_3 = all_52_12 % 151.56/22.36 (8) ~ (all_52_12 = e3) % 151.56/22.36 (9) op(e3, e0) = all_52_12 % 151.56/22.36 (10) op(e3, all_10_1) = e1 % 151.56/22.36 (11) ~ (all_52_12 = e1) % 151.56/22.36 (12) ~ (all_52_12 = e0) % 151.56/22.36 % 151.56/22.36 Begin of proof % 151.56/22.36 | % 151.56/22.36 | BETA: splitting (1) gives: % 151.56/22.36 | % 151.56/22.36 | Case 1: % 151.56/22.36 | | % 151.56/22.36 | | (13) all_54_3 = e3 % 151.56/22.36 | | % 151.56/22.36 | | COMBINE_EQS: (7), (13) imply: % 151.56/22.36 | | (14) all_52_12 = e3 % 151.56/22.36 | | % 151.56/22.36 | | REDUCE: (8), (14) imply: % 151.56/22.36 | | (15) $false % 151.56/22.36 | | % 151.56/22.36 | | CLOSE: (15) is inconsistent. % 151.56/22.36 | | % 151.56/22.36 | Case 2: % 151.56/22.36 | | % 151.56/22.36 | | (16) all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0 % 151.56/22.36 | | % 151.56/22.36 | | BETA: splitting (2) gives: % 151.56/22.36 | | % 151.56/22.36 | | Case 1: % 151.56/22.36 | | | % 151.56/22.36 | | | (17) all_58_9 = e2 % 151.56/22.36 | | | % 151.56/22.36 | | | COMBINE_EQS: (5), (17) imply: % 151.56/22.36 | | | (18) all_52_12 = e2 % 151.56/22.36 | | | % 151.56/22.36 | | | REDUCE: (11), (18) imply: % 151.56/22.36 | | | (19) ~ (e2 = e1) % 151.56/22.36 | | | % 151.56/22.36 | | | REDUCE: (9), (18) imply: % 151.56/22.36 | | | (20) op(e3, e0) = e2 % 151.56/22.36 | | | % 151.56/22.36 | | | REF_CLOSE: (3), (4), (6), (10), (19), (20) are inconsistent by sub-proof % 151.56/22.36 | | | #291. % 151.56/22.36 | | | % 151.56/22.36 | | Case 2: % 151.56/22.36 | | | % 151.56/22.36 | | | (21) ~ (all_58_9 = e2) % 151.56/22.36 | | | % 151.56/22.36 | | | REDUCE: (5), (21) imply: % 151.56/22.36 | | | (22) ~ (all_52_12 = e2) % 151.56/22.36 | | | % 151.56/22.36 | | | REF_CLOSE: (7), (11), (12), (16), (22) are inconsistent by sub-proof #326. % 151.56/22.36 | | | % 151.56/22.36 | | End of split % 151.56/22.36 | | % 151.56/22.36 | End of split % 151.56/22.36 | % 151.56/22.36 End of proof % 151.56/22.36 % 151.56/22.36 Sub-proof #291 shows that the following formulas are inconsistent: % 151.56/22.36 ---------------------------------------------------------------- % 151.56/22.36 (1) op(e1, e1) = e0 % 151.56/22.36 (2) op(e1, e1) = all_10_1 % 151.56/22.36 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 151.56/22.36 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 151.56/22.36 (4) ~ (e2 = e1) % 151.56/22.36 (5) op(e3, all_10_1) = e1 % 151.56/22.36 (6) op(e3, e0) = e2 % 151.56/22.36 % 151.56/22.36 Begin of proof % 151.56/22.36 | % 151.56/22.36 | GROUND_INST: instantiating (3) with e0, all_10_1, e1, e1, simplifying with % 151.56/22.36 | (1), (2) gives: % 151.56/22.36 | (7) all_10_1 = e0 % 151.56/22.36 | % 151.56/22.36 | REDUCE: (5), (7) imply: % 151.56/22.36 | (8) op(e3, e0) = e1 % 151.56/22.36 | % 151.56/22.36 | GROUND_INST: instantiating (3) with e2, e1, e0, e3, simplifying with (6), (8) % 151.56/22.36 | gives: % 151.56/22.36 | (9) e2 = e1 % 151.56/22.36 | % 151.56/22.36 | REDUCE: (4), (9) imply: % 151.56/22.36 | (10) $false % 151.56/22.36 | % 151.56/22.36 | CLOSE: (10) is inconsistent. % 151.56/22.36 | % 151.56/22.36 End of proof % 151.56/22.36 % 151.56/22.36 Sub-proof #292 shows that the following formulas are inconsistent: % 151.56/22.36 ---------------------------------------------------------------- % 151.56/22.36 (1) all_56_11 = all_8_2 % 151.56/22.36 (2) all_54_9 = all_52_6 % 151.56/22.36 (3) ~ (all_6_1 = e2) % 151.56/22.36 (4) all_54_0 = all_10_2 % 151.56/22.36 (5) all_56_21 = e3 % 151.56/22.36 (6) ~ (all_52_14 = all_4_2) % 151.56/22.36 (7) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0 % 151.56/22.36 (8) ~ (all_52_12 = all_52_13) % 151.56/22.36 (9) ~ (all_6_1 = e3) % 151.56/22.36 (10) ~ (all_52_6 = all_52_14) % 151.56/22.36 (11) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 151.56/22.36 (12) ~ (all_6_0 = e2) % 151.56/22.36 (13) all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1 % 151.56/22.36 (14) all_56_21 = all_6_2 % 151.56/22.36 (15) all_56_1 = all_10_2 % 151.56/22.36 (16) all_58_5 = all_52_9 % 151.56/22.36 (17) all_56_17 = all_52_2 % 151.56/22.36 (18) all_58_9 = all_52_12 % 151.56/22.36 (19) op(e1, e0) = all_52_14 % 151.56/22.36 (20) op(e3, e3) = all_10_2 % 151.56/22.36 (21) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 151.56/22.36 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 151.56/22.36 (22) all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0 % 151.56/22.36 (23) ~ (all_52_2 = all_52_6) % 151.56/22.36 (24) all_56_7 = all_52_12 % 151.56/22.36 (25) ~ (all_4_2 = e1) % 151.56/22.36 (26) ~ (all_56_1 = e0) | all_56_7 = e3 % 151.56/22.36 (27) op(e1, all_6_1) = all_6_0 % 151.56/22.36 (28) all_58_3 = all_8_2 % 151.56/22.36 (29) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0 % 151.56/22.36 (30) all_56_31 = all_4_2 % 151.56/22.36 (31) all_58_11 = all_52_14 % 151.56/22.36 (32) ~ (all_52_2 = all_52_14) % 151.56/22.36 (33) op(all_6_2, all_6_2) = all_6_1 % 151.56/22.36 (34) all_56_1 = e3 | all_56_11 = e2 | all_56_21 = e1 | all_56_31 = e0 % 151.56/22.36 (35) all_56_17 = e1 % 151.56/22.36 (36) ~ (all_52_13 = all_52_14) % 151.56/22.36 (37) ~ (all_52_6 = all_8_2) % 151.56/22.36 (38) all_58_15 = all_4_2 % 151.56/22.36 (39) all_58_2 = all_52_1 % 151.56/22.36 (40) all_58_10 = all_52_13 % 151.56/22.36 (41) ~ (all_52_12 = all_52_14) % 151.56/22.36 (42) op(e1, all_52_9) = all_56_12 % 151.56/22.37 (43) ~ (all_52_2 = all_6_2) % 151.56/22.37 (44) ~ (all_52_6 = all_6_2) % 151.56/22.37 (45) ~ (all_8_2 = e0) % 151.56/22.37 (46) ~ (all_52_2 = all_10_2) % 151.56/22.37 (47) ~ (all_52_1 = all_10_2) % 151.56/22.37 (48) all_54_11 = all_52_14 % 151.56/22.37 % 151.56/22.37 Begin of proof % 151.56/22.37 | % 151.56/22.37 | COMBINE_EQS: (17), (35) imply: % 151.56/22.37 | (49) all_52_2 = e1 % 151.56/22.37 | % 151.56/22.37 | COMBINE_EQS: (5), (14) imply: % 151.56/22.37 | (50) all_6_2 = e3 % 151.56/22.37 | % 151.56/22.37 | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), % 151.56/22.37 | (13), (15), (16), (18), (19), (20), (21), (22), (23), (24), (25), % 151.56/22.37 | (26), (27), (28), (29), (30), (31), (32), (33), (34), (36), (37), % 151.56/22.37 | (38), (39), (40), (41), (42), (43), (44), (45), (46), (47), (48), % 151.56/22.37 | (49), (50) are inconsistent by sub-proof #293. % 151.56/22.37 | % 151.56/22.37 End of proof % 151.56/22.37 % 151.56/22.37 Sub-proof #293 shows that the following formulas are inconsistent: % 151.56/22.37 ---------------------------------------------------------------- % 151.56/22.37 (1) all_56_11 = all_8_2 % 151.56/22.37 (2) all_54_9 = all_52_6 % 151.56/22.37 (3) ~ (all_6_1 = e2) % 151.56/22.37 (4) all_54_0 = all_10_2 % 151.56/22.37 (5) all_56_21 = e3 % 151.56/22.37 (6) ~ (all_52_14 = all_4_2) % 151.56/22.37 (7) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0 % 151.56/22.37 (8) ~ (all_52_12 = all_52_13) % 151.56/22.37 (9) all_6_2 = e3 % 151.56/22.37 (10) ~ (all_6_1 = e3) % 151.56/22.37 (11) ~ (all_52_6 = all_52_14) % 151.56/22.37 (12) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 151.56/22.37 (13) ~ (all_6_0 = e2) % 151.56/22.37 (14) all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1 % 151.56/22.37 (15) all_56_1 = all_10_2 % 151.56/22.37 (16) all_58_5 = all_52_9 % 151.56/22.37 (17) all_58_9 = all_52_12 % 151.56/22.37 (18) op(e1, e0) = all_52_14 % 151.56/22.37 (19) op(e3, e3) = all_10_2 % 151.56/22.37 (20) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 151.56/22.37 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 151.56/22.37 (21) all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0 % 151.56/22.37 (22) ~ (all_52_2 = all_52_6) % 151.56/22.37 (23) all_56_7 = all_52_12 % 151.56/22.37 (24) ~ (all_4_2 = e1) % 151.56/22.37 (25) ~ (all_56_1 = e0) | all_56_7 = e3 % 151.56/22.37 (26) all_52_2 = e1 % 151.56/22.37 (27) op(e1, all_6_1) = all_6_0 % 151.56/22.37 (28) all_58_3 = all_8_2 % 151.56/22.37 (29) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0 % 151.56/22.37 (30) all_56_31 = all_4_2 % 151.56/22.37 (31) all_58_11 = all_52_14 % 151.56/22.37 (32) ~ (all_52_2 = all_52_14) % 151.56/22.37 (33) op(all_6_2, all_6_2) = all_6_1 % 151.56/22.37 (34) all_56_1 = e3 | all_56_11 = e2 | all_56_21 = e1 | all_56_31 = e0 % 151.56/22.37 (35) ~ (all_52_13 = all_52_14) % 151.56/22.37 (36) ~ (all_52_6 = all_8_2) % 151.56/22.37 (37) all_58_15 = all_4_2 % 151.56/22.37 (38) all_58_2 = all_52_1 % 151.56/22.37 (39) all_58_10 = all_52_13 % 151.56/22.37 (40) ~ (all_52_12 = all_52_14) % 151.56/22.37 (41) op(e1, all_52_9) = all_56_12 % 151.56/22.37 (42) ~ (all_52_2 = all_6_2) % 151.56/22.37 (43) ~ (all_52_6 = all_6_2) % 151.56/22.37 (44) ~ (all_8_2 = e0) % 151.56/22.37 (45) ~ (all_52_2 = all_10_2) % 151.56/22.37 (46) ~ (all_52_1 = all_10_2) % 151.56/22.37 (47) all_54_11 = all_52_14 % 151.56/22.37 % 151.56/22.37 Begin of proof % 151.56/22.37 | % 151.56/22.37 | REDUCE: (22), (26) imply: % 151.56/22.37 | (48) ~ (all_52_6 = e1) % 151.56/22.37 | % 151.56/22.37 | SIMP: (48) implies: % 151.56/22.37 | (49) ~ (all_52_6 = e1) % 151.56/22.37 | % 151.56/22.37 | REDUCE: (26), (32) imply: % 151.56/22.37 | (50) ~ (all_52_14 = e1) % 151.56/22.37 | % 151.56/22.37 | SIMP: (50) implies: % 151.56/22.37 | (51) ~ (all_52_14 = e1) % 151.56/22.37 | % 151.56/22.37 | REDUCE: (26), (45) imply: % 151.56/22.37 | (52) ~ (all_10_2 = e1) % 151.56/22.37 | % 151.56/22.37 | SIMP: (52) implies: % 151.56/22.37 | (53) ~ (all_10_2 = e1) % 151.56/22.37 | % 151.56/22.37 | REDUCE: (9), (26), (42) imply: % 151.56/22.37 | (54) ~ (e3 = e1) % 151.56/22.37 | % 151.56/22.37 | SIMP: (54) implies: % 151.56/22.37 | (55) ~ (e3 = e1) % 151.56/22.37 | % 151.56/22.37 | REDUCE: (9), (43) imply: % 151.56/22.37 | (56) ~ (all_52_6 = e3) % 151.56/22.37 | % 151.56/22.37 | REDUCE: (9), (33) imply: % 151.56/22.37 | (57) op(e3, e3) = all_6_1 % 151.56/22.37 | % 151.56/22.37 | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (10), (11), (12), (13), % 151.56/22.37 | (14), (15), (16), (17), (18), (19), (20), (21), (23), (24), (25), % 151.56/22.37 | (27), (28), (29), (30), (31), (34), (35), (36), (37), (38), (39), % 151.56/22.37 | (40), (41), (44), (46), (47), (49), (51), (53), (55), (56), (57) % 151.56/22.37 | are inconsistent by sub-proof #294. % 151.56/22.37 | % 151.56/22.37 End of proof % 151.56/22.37 % 151.56/22.37 Sub-proof #294 shows that the following formulas are inconsistent: % 151.56/22.37 ---------------------------------------------------------------- % 151.56/22.37 (1) all_56_11 = all_8_2 % 151.56/22.37 (2) all_54_9 = all_52_6 % 151.56/22.37 (3) ~ (all_52_6 = e1) % 151.56/22.37 (4) ~ (all_6_1 = e2) % 151.56/22.37 (5) all_54_0 = all_10_2 % 151.56/22.37 (6) all_56_21 = e3 % 151.56/22.37 (7) ~ (all_52_14 = all_4_2) % 151.56/22.37 (8) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0 % 151.56/22.37 (9) ~ (all_52_12 = all_52_13) % 151.56/22.37 (10) ~ (all_10_2 = e1) % 151.56/22.37 (11) ~ (all_6_1 = e3) % 151.56/22.37 (12) ~ (all_52_6 = all_52_14) % 151.56/22.37 (13) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 151.56/22.37 (14) ~ (all_6_0 = e2) % 151.56/22.37 (15) all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1 % 151.56/22.37 (16) all_56_1 = all_10_2 % 151.56/22.37 (17) ~ (all_52_6 = e3) % 151.56/22.37 (18) all_58_5 = all_52_9 % 151.56/22.37 (19) all_58_9 = all_52_12 % 151.56/22.37 (20) op(e3, e3) = all_6_1 % 151.56/22.37 (21) op(e1, e0) = all_52_14 % 151.56/22.37 (22) op(e3, e3) = all_10_2 % 151.56/22.37 (23) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 151.56/22.37 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 151.56/22.37 (24) all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0 % 151.56/22.37 (25) ~ (all_52_14 = e1) % 151.56/22.37 (26) all_56_7 = all_52_12 % 151.56/22.37 (27) ~ (all_4_2 = e1) % 151.56/22.37 (28) ~ (all_56_1 = e0) | all_56_7 = e3 % 151.56/22.37 (29) op(e1, all_6_1) = all_6_0 % 151.56/22.37 (30) all_58_3 = all_8_2 % 151.56/22.37 (31) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0 % 151.56/22.37 (32) all_56_31 = all_4_2 % 151.56/22.37 (33) all_58_11 = all_52_14 % 151.56/22.37 (34) all_56_1 = e3 | all_56_11 = e2 | all_56_21 = e1 | all_56_31 = e0 % 151.56/22.37 (35) ~ (all_52_13 = all_52_14) % 151.56/22.37 (36) ~ (all_52_6 = all_8_2) % 151.56/22.37 (37) all_58_15 = all_4_2 % 151.56/22.37 (38) all_58_2 = all_52_1 % 151.56/22.37 (39) all_58_10 = all_52_13 % 151.56/22.37 (40) ~ (all_52_12 = all_52_14) % 151.56/22.37 (41) op(e1, all_52_9) = all_56_12 % 151.56/22.37 (42) ~ (e3 = e1) % 151.56/22.37 (43) ~ (all_8_2 = e0) % 151.56/22.37 (44) ~ (all_52_1 = all_10_2) % 151.56/22.37 (45) all_54_11 = all_52_14 % 151.56/22.37 % 151.56/22.37 Begin of proof % 151.56/22.37 | % 151.56/22.37 | GROUND_INST: instantiating (23) with all_10_2, all_6_1, e3, e3, simplifying % 151.56/22.37 | with (20), (22) gives: % 151.56/22.37 | (46) all_10_2 = all_6_1 % 151.56/22.37 | % 151.56/22.37 | COMBINE_EQS: (5), (46) imply: % 151.56/22.37 | (47) all_54_0 = all_6_1 % 151.56/22.37 | % 151.56/22.37 | COMBINE_EQS: (16), (46) imply: % 151.56/22.37 | (48) all_56_1 = all_6_1 % 151.56/22.37 | % 151.56/22.37 | REDUCE: (44), (46) imply: % 151.56/22.37 | (49) ~ (all_52_1 = all_6_1) % 151.56/22.37 | % 151.56/22.37 | REDUCE: (10), (46) imply: % 151.56/22.37 | (50) ~ (all_6_1 = e1) % 151.56/22.37 | % 151.56/22.37 | BETA: splitting (13) gives: % 151.56/22.37 | % 151.56/22.37 | Case 1: % 151.56/22.37 | | % 151.56/22.37 | | (51) all_54_0 = e3 % 151.56/22.37 | | % 151.56/22.37 | | REF_CLOSE: (11), (47), (51) are inconsistent by sub-proof #686. % 151.56/22.37 | | % 151.56/22.37 | Case 2: % 151.56/22.37 | | % 151.56/22.37 | | (52) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 151.56/22.37 | | % 151.56/22.37 | | BETA: splitting (52) gives: % 151.56/22.37 | | % 151.56/22.37 | | Case 1: % 151.56/22.37 | | | % 151.56/22.37 | | | (53) all_54_0 = e2 % 151.56/22.37 | | | % 151.56/22.37 | | | REF_CLOSE: (4), (47), (53) are inconsistent by sub-proof #685. % 151.56/22.37 | | | % 151.56/22.37 | | Case 2: % 151.56/22.37 | | | % 151.56/22.37 | | | (54) all_54_0 = e1 | all_54_0 = e0 % 151.56/22.37 | | | % 151.56/22.37 | | | BETA: splitting (54) gives: % 151.56/22.37 | | | % 151.56/22.37 | | | Case 1: % 151.56/22.37 | | | | % 151.56/22.37 | | | | (55) all_54_0 = e1 % 151.56/22.37 | | | | % 151.56/22.37 | | | | REF_CLOSE: (47), (50), (55) are inconsistent by sub-proof #684. % 151.56/22.37 | | | | % 151.56/22.37 | | | Case 2: % 151.56/22.37 | | | | % 151.56/22.37 | | | | (56) all_54_0 = e0 % 151.56/22.37 | | | | % 151.56/22.37 | | | | COMBINE_EQS: (47), (56) imply: % 151.56/22.37 | | | | (57) all_6_1 = e0 % 151.56/22.37 | | | | % 151.56/22.37 | | | | SIMP: (57) implies: % 151.56/22.37 | | | | (58) all_6_1 = e0 % 151.56/22.37 | | | | % 151.56/22.37 | | | | COMBINE_EQS: (48), (58) imply: % 151.56/22.37 | | | | (59) all_56_1 = e0 % 151.56/22.37 | | | | % 151.56/22.37 | | | | REDUCE: (49), (58) imply: % 151.56/22.37 | | | | (60) ~ (all_52_1 = e0) % 151.56/22.37 | | | | % 151.56/22.37 | | | | REDUCE: (50), (58) imply: % 151.56/22.37 | | | | (61) ~ (e1 = e0) % 151.56/22.37 | | | | % 151.56/22.37 | | | | SIMP: (61) implies: % 151.56/22.37 | | | | (62) ~ (e1 = e0) % 151.56/22.37 | | | | % 151.56/22.37 | | | | REDUCE: (29), (58) imply: % 151.56/22.37 | | | | (63) op(e1, e0) = all_6_0 % 151.56/22.37 | | | | % 151.56/22.37 | | | | BETA: splitting (28) gives: % 151.56/22.37 | | | | % 151.56/22.37 | | | | Case 1: % 151.56/22.37 | | | | | % 151.56/22.37 | | | | | (64) ~ (all_56_1 = e0) % 151.56/22.37 | | | | | % 151.56/22.37 | | | | | REDUCE: (59), (64) imply: % 151.56/22.37 | | | | | (65) $false % 151.56/22.37 | | | | | % 151.56/22.37 | | | | | CLOSE: (65) is inconsistent. % 151.56/22.37 | | | | | % 151.56/22.37 | | | | Case 2: % 151.56/22.37 | | | | | % 151.56/22.37 | | | | | (66) all_56_7 = e3 % 151.56/22.37 | | | | | % 151.56/22.37 | | | | | COMBINE_EQS: (26), (66) imply: % 151.56/22.37 | | | | | (67) all_52_12 = e3 % 151.56/22.37 | | | | | % 151.56/22.37 | | | | | COMBINE_EQS: (19), (67) imply: % 151.56/22.37 | | | | | (68) all_58_9 = e3 % 151.56/22.37 | | | | | % 151.56/22.37 | | | | | REDUCE: (9), (67) imply: % 151.56/22.37 | | | | | (69) ~ (all_52_13 = e3) % 151.56/22.37 | | | | | % 151.56/22.37 | | | | | SIMP: (69) implies: % 151.56/22.37 | | | | | (70) ~ (all_52_13 = e3) % 151.56/22.37 | | | | | % 151.56/22.37 | | | | | REDUCE: (40), (67) imply: % 151.56/22.37 | | | | | (71) ~ (all_52_14 = e3) % 151.56/22.37 | | | | | % 151.56/22.37 | | | | | SIMP: (71) implies: % 151.56/22.37 | | | | | (72) ~ (all_52_14 = e3) % 151.56/22.37 | | | | | % 151.56/22.37 | | | | | REF_CLOSE: (1), (2), (3), (6), (7), (8), (12), (14), (15), (17), (18), % 151.56/22.37 | | | | | (21), (23), (24), (25), (27), (30), (31), (32), (33), (34), % 151.56/22.37 | | | | | (35), (36), (37), (38), (39), (41), (42), (43), (45), (59), % 151.56/22.37 | | | | | (60), (62), (63), (68), (70), (72) are inconsistent by % 151.56/22.37 | | | | | sub-proof #671. % 151.56/22.37 | | | | | % 151.56/22.37 | | | | End of split % 151.56/22.37 | | | | % 151.56/22.37 | | | End of split % 151.56/22.37 | | | % 151.56/22.37 | | End of split % 151.56/22.37 | | % 151.56/22.37 | End of split % 151.56/22.37 | % 151.56/22.37 End of proof % 151.56/22.37 % 151.56/22.37 Sub-proof #295 shows that the following formulas are inconsistent: % 151.56/22.37 ---------------------------------------------------------------- % 151.56/22.37 (1) all_56_11 = e3 % 151.56/22.37 (2) op(e0, e3) = e1 % 151.56/22.37 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 151.56/22.37 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 151.56/22.37 (4) all_56_11 = all_4_1 % 151.56/22.37 (5) op(e0, all_4_1) = all_4_0 % 151.56/22.37 (6) ~ (all_4_0 = e1) % 151.56/22.37 % 151.56/22.37 Begin of proof % 151.56/22.37 | % 151.56/22.37 | COMBINE_EQS: (1), (4) imply: % 151.56/22.37 | (7) all_4_1 = e3 % 151.56/22.37 | % 151.56/22.37 | REDUCE: (5), (7) imply: % 151.56/22.37 | (8) op(e0, e3) = all_4_0 % 151.56/22.37 | % 151.56/22.37 | GROUND_INST: instantiating (3) with e1, all_4_0, e3, e0, simplifying with (2), % 151.56/22.37 | (8) gives: % 151.56/22.37 | (9) all_4_0 = e1 % 151.56/22.37 | % 151.56/22.37 | REDUCE: (6), (9) imply: % 151.56/22.37 | (10) $false % 151.56/22.37 | % 151.56/22.37 | CLOSE: (10) is inconsistent. % 151.56/22.37 | % 151.56/22.37 End of proof % 151.56/22.37 % 151.56/22.37 Sub-proof #296 shows that the following formulas are inconsistent: % 151.56/22.37 ---------------------------------------------------------------- % 151.56/22.37 (1) all_58_4 = e3 % 151.56/22.37 (2) all_58_4 = e2 % 151.56/22.37 (3) ~ (e3 = e2) % 151.56/22.37 % 151.56/22.37 Begin of proof % 151.56/22.37 | % 151.56/22.37 | COMBINE_EQS: (1), (2) imply: % 151.56/22.37 | (4) e3 = e2 % 151.56/22.37 | % 151.56/22.37 | SIMP: (4) implies: % 151.56/22.37 | (5) e3 = e2 % 151.56/22.37 | % 151.56/22.37 | REDUCE: (3), (5) imply: % 151.56/22.37 | (6) $false % 151.56/22.37 | % 151.56/22.37 | CLOSE: (6) is inconsistent. % 151.56/22.37 | % 151.56/22.37 End of proof % 151.56/22.37 % 151.56/22.37 Sub-proof #297 shows that the following formulas are inconsistent: % 151.56/22.37 ---------------------------------------------------------------- % 151.56/22.37 (1) all_58_6 = all_52_2 % 151.56/22.37 (2) all_54_10 = all_6_2 % 151.56/22.37 (3) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0 % 151.56/22.37 (4) ~ (all_6_1 = e2) % 151.56/22.37 (5) ~ (all_52_13 = all_8_2) % 151.56/22.37 (6) ~ (all_8_2 = e1) % 151.56/22.37 (7) all_54_0 = all_10_2 % 151.56/22.37 (8) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0 % 151.56/22.37 (9) all_54_12 = all_52_3 % 151.56/22.37 (10) ~ (all_52_12 = all_52_13) % 151.56/22.37 (11) ~ (all_52_4 = all_52_7) % 151.56/22.37 (12) op(e0, e0) = all_4_2 % 151.56/22.37 (13) all_54_5 = all_8_2 % 151.56/22.37 (14) ~ (all_6_1 = e3) % 151.56/22.37 (15) ~ (all_52_6 = all_52_14) % 151.56/22.37 (16) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 151.56/22.37 (17) all_54_15 = all_4_2 % 151.56/22.37 (18) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 151.56/22.37 (19) ~ (all_52_7 = all_8_2) % 151.56/22.37 (20) all_56_1 = all_10_2 % 151.56/22.37 (21) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0 % 151.56/22.37 (22) ~ (all_56_1 = e1) | all_56_5 = e3 % 151.56/22.37 (23) all_58_1 = all_52_4 % 151.56/22.37 (24) all_58_13 = all_52_7 % 151.56/22.37 (25) op(e3, e3) = all_10_2 % 151.56/22.37 (26) ~ (all_52_8 = all_6_2) % 151.56/22.37 (27) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 151.56/22.37 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 151.56/22.37 (28) ~ (all_52_3 = all_10_2) % 151.56/22.37 (29) all_54_3 = all_52_12 % 151.56/22.37 (30) ~ (all_52_3 = all_52_7) % 151.56/22.37 (31) ~ (all_6_2 = e0) % 151.56/22.37 (32) op(e0, all_4_1) = all_4_0 % 151.56/22.37 (33) all_56_7 = all_52_12 % 151.56/22.37 (34) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0 % 151.56/22.37 (35) ~ (all_52_7 = all_4_2) % 151.56/22.37 (36) ~ (all_4_2 = e1) % 151.56/22.37 (37) all_58_8 = all_6_2 % 151.56/22.37 (38) ~ (all_52_3 = all_4_2) % 151.56/22.37 (39) all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3 % 151.56/22.37 (40) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0 % 151.56/22.37 (41) ~ (all_56_1 = e2) | all_56_3 = e3 % 151.56/22.37 (42) ~ (all_56_1 = e0) | all_56_7 = e3 % 151.56/22.37 (43) all_56_5 = all_52_8 % 151.56/22.37 (44) ~ (all_4_2 = e2) % 151.56/22.37 (45) ~ (all_52_2 = all_52_3) % 151.56/22.37 (46) op(all_4_2, all_4_2) = all_4_1 % 151.56/22.37 (47) all_58_3 = all_8_2 % 151.56/22.37 (48) all_56_3 = all_52_4 % 151.56/22.37 (49) ~ (all_52_6 = all_52_7) % 151.56/22.37 (50) all_58_11 = all_52_14 % 151.56/22.37 (51) all_54_7 = all_52_13 % 151.56/22.37 (52) op(all_6_2, all_6_2) = all_6_1 % 151.56/22.37 (53) ~ (all_52_13 = all_4_2) % 151.56/22.37 (54) op(e3, e0) = all_52_12 % 151.56/22.37 (55) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0 % 151.56/22.37 (56) all_54_13 = all_52_7 % 151.56/22.37 (57) ~ (all_52_13 = all_52_14) % 151.56/22.37 (58) op(e1, e1) = all_6_2 % 151.56/22.37 (59) op(e3, all_10_1) = e1 % 151.56/22.37 (60) ~ (all_6_2 = e2) % 151.56/22.37 (61) ~ (all_4_2 = e3) % 151.56/22.37 (62) all_58_7 = all_52_6 % 151.56/22.37 (63) ~ (all_52_12 = all_4_2) % 151.56/22.37 (64) op(all_10_2, all_10_2) = all_10_1 % 151.56/22.37 (65) op(e1, all_6_2) = all_56_20 % 151.56/22.37 (66) all_58_1 = e0 | all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0 % 151.56/22.37 (67) ~ (all_52_12 = all_52_14) % 151.56/22.37 (68) op(e3, e1) = all_52_8 % 151.56/22.37 (69) ~ (e3 = e1) % 151.56/22.37 (70) ~ (all_52_4 = all_52_12) % 151.56/22.37 (71) op(e0, all_4_2) = all_56_30 % 151.56/22.37 (72) ~ (all_8_2 = e0) % 151.56/22.37 (73) op(e3, all_10_2) = all_56_0 % 151.56/22.37 (74) ~ (all_52_4 = all_8_2) % 151.56/22.37 (75) op(e3, all_52_3) = all_56_24 % 151.56/22.37 (76) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 151.56/22.37 (77) ~ (all_52_12 = all_10_2) % 151.56/22.37 (78) all_58_12 = all_52_3 % 151.56/22.37 (79) all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3 % 151.56/22.37 (80) all_54_11 = all_52_14 % 151.56/22.37 % 151.56/22.37 Begin of proof % 151.56/22.37 | % 151.56/22.37 | BETA: splitting (55) gives: % 151.56/22.37 | % 151.56/22.37 | Case 1: % 151.56/22.37 | | % 151.56/22.37 | | (81) all_54_15 = e3 % 151.56/22.37 | | % 151.56/22.37 | | REF_CLOSE: (17), (61), (81) are inconsistent by sub-proof #740. % 151.56/22.37 | | % 151.56/22.37 | Case 2: % 151.56/22.37 | | % 151.56/22.37 | | (82) all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0 % 151.56/22.37 | | % 151.56/22.37 | | BETA: splitting (82) gives: % 151.56/22.37 | | % 151.56/22.37 | | Case 1: % 151.56/22.37 | | | % 151.56/22.37 | | | (83) all_54_15 = e2 % 151.56/22.37 | | | % 151.56/22.37 | | | REF_CLOSE: (17), (44), (83) are inconsistent by sub-proof #739. % 151.56/22.37 | | | % 151.56/22.37 | | Case 2: % 151.56/22.37 | | | % 151.56/22.37 | | | (84) ~ (all_54_15 = e2) % 151.56/22.37 | | | (85) all_54_15 = e1 | all_54_15 = e0 % 151.56/22.37 | | | % 151.56/22.37 | | | BETA: splitting (85) gives: % 151.56/22.37 | | | % 151.56/22.37 | | | Case 1: % 151.56/22.37 | | | | % 151.56/22.37 | | | | (86) all_54_15 = e1 % 151.56/22.37 | | | | % 151.56/22.37 | | | | REF_CLOSE: (17), (36), (86) are inconsistent by sub-proof #738. % 151.56/22.37 | | | | % 151.56/22.37 | | | Case 2: % 151.56/22.37 | | | | % 151.56/22.37 | | | | (87) all_54_15 = e0 % 151.56/22.37 | | | | % 151.56/22.37 | | | | COMBINE_EQS: (17), (87) imply: % 151.56/22.37 | | | | (88) all_4_2 = e0 % 151.56/22.37 | | | | % 151.56/22.37 | | | | SIMP: (88) implies: % 151.56/22.37 | | | | (89) all_4_2 = e0 % 151.56/22.37 | | | | % 151.56/22.37 | | | | REDUCE: (38), (89) imply: % 151.56/22.37 | | | | (90) ~ (all_52_3 = e0) % 151.56/22.37 | | | | % 151.56/22.37 | | | | REDUCE: (35), (89) imply: % 151.56/22.37 | | | | (91) ~ (all_52_7 = e0) % 151.56/22.37 | | | | % 151.56/22.37 | | | | REDUCE: (63), (89) imply: % 151.56/22.37 | | | | (92) ~ (all_52_12 = e0) % 151.56/22.37 | | | | % 151.56/22.37 | | | | REDUCE: (53), (89) imply: % 151.56/22.37 | | | | (93) ~ (all_52_13 = e0) % 151.56/22.37 | | | | % 151.56/22.37 | | | | REDUCE: (46), (89) imply: % 151.56/22.37 | | | | (94) op(e0, e0) = all_4_1 % 151.56/22.37 | | | | % 151.56/22.37 | | | | REDUCE: (71), (89) imply: % 151.56/22.37 | | | | (95) op(e0, e0) = all_56_30 % 151.56/22.37 | | | | % 151.56/22.37 | | | | REDUCE: (12), (89) imply: % 151.56/22.37 | | | | (96) op(e0, e0) = e0 % 151.56/22.37 | | | | % 151.56/22.37 | | | | GROUND_INST: instantiating (27) with all_4_1, all_56_30, e0, e0, % 151.56/22.37 | | | | simplifying with (94), (95) gives: % 151.56/22.37 | | | | (97) all_56_30 = all_4_1 % 151.56/22.37 | | | | % 151.56/22.37 | | | | GROUND_INST: instantiating (27) with e0, all_56_30, e0, e0, simplifying % 151.56/22.37 | | | | with (95), (96) gives: % 151.56/22.37 | | | | (98) all_56_30 = e0 % 151.56/22.37 | | | | % 151.56/22.37 | | | | COMBINE_EQS: (97), (98) imply: % 151.56/22.37 | | | | (99) all_4_1 = e0 % 151.56/22.37 | | | | % 151.56/22.37 | | | | SIMP: (99) implies: % 151.56/22.37 | | | | (100) all_4_1 = e0 % 151.56/22.37 | | | | % 151.56/22.37 | | | | REDUCE: (32), (100) imply: % 151.56/22.37 | | | | (101) op(e0, e0) = all_4_0 % 151.56/22.37 | | | | % 151.56/22.37 | | | | GROUND_INST: instantiating (27) with e0, all_4_0, e0, e0, simplifying % 151.56/22.37 | | | | with (96), (101) gives: % 151.56/22.37 | | | | (102) all_4_0 = e0 % 151.56/22.37 | | | | % 151.56/22.37 | | | | BETA: splitting (22) gives: % 151.56/22.37 | | | | % 151.56/22.37 | | | | Case 1: % 151.56/22.37 | | | | | % 151.56/22.37 | | | | | (103) ~ (all_56_1 = e1) % 151.56/22.37 | | | | | % 151.56/22.37 | | | | | REDUCE: (20), (103) imply: % 151.56/22.37 | | | | | (104) ~ (all_10_2 = e1) % 151.56/22.37 | | | | | % 151.56/22.37 | | | | | BETA: splitting (42) gives: % 151.56/22.37 | | | | | % 151.56/22.37 | | | | | Case 1: % 151.56/22.37 | | | | | | % 151.56/22.37 | | | | | | (105) ~ (all_56_1 = e0) % 151.56/22.37 | | | | | | % 151.56/22.37 | | | | | | REDUCE: (20), (105) imply: % 151.56/22.37 | | | | | | (106) ~ (all_10_2 = e0) % 151.56/22.37 | | | | | | % 151.56/22.37 | | | | | | BETA: splitting (41) gives: % 151.56/22.37 | | | | | | % 151.56/22.37 | | | | | | Case 1: % 151.56/22.37 | | | | | | | % 151.56/22.37 | | | | | | | (107) ~ (all_56_1 = e2) % 151.56/22.37 | | | | | | | % 151.56/22.37 | | | | | | | REDUCE: (20), (107) imply: % 151.56/22.37 | | | | | | | (108) ~ (all_10_2 = e2) % 151.56/22.37 | | | | | | | % 151.56/22.37 | | | | | | | REF_CLOSE: (7), (16), (25), (27), (59), (64), (73), (104), (106), % 151.56/22.37 | | | | | | | (108) are inconsistent by sub-proof #304. % 151.56/22.37 | | | | | | | % 151.56/22.37 | | | | | | Case 2: % 151.56/22.37 | | | | | | | % 151.56/22.37 | | | | | | | (109) all_56_3 = e3 % 151.56/22.37 | | | | | | | (110) all_56_1 = e2 % 151.56/22.37 | | | | | | | % 151.56/22.37 | | | | | | | COMBINE_EQS: (20), (110) imply: % 151.56/22.37 | | | | | | | (111) all_10_2 = e2 % 151.56/22.37 | | | | | | | % 151.56/22.37 | | | | | | | COMBINE_EQS: (48), (109) imply: % 151.56/22.37 | | | | | | | (112) all_52_4 = e3 % 151.56/22.37 | | | | | | | % 151.56/22.37 | | | | | | | COMBINE_EQS: (23), (112) imply: % 151.56/22.37 | | | | | | | (113) all_58_1 = e3 % 151.56/22.37 | | | | | | | % 151.56/22.37 | | | | | | | REDUCE: (28), (111) imply: % 151.56/22.37 | | | | | | | (114) ~ (all_52_3 = e2) % 151.56/22.37 | | | | | | | % 151.56/22.37 | | | | | | | REDUCE: (11), (112) imply: % 151.56/22.37 | | | | | | | (115) ~ (all_52_7 = e3) % 151.56/22.37 | | | | | | | % 151.56/22.37 | | | | | | | SIMP: (115) implies: % 151.56/22.37 | | | | | | | (116) ~ (all_52_7 = e3) % 151.56/22.37 | | | | | | | % 151.56/22.37 | | | | | | | REDUCE: (70), (112) imply: % 151.56/22.37 | | | | | | | (117) ~ (all_52_12 = e3) % 151.56/22.37 | | | | | | | % 151.56/22.37 | | | | | | | SIMP: (117) implies: % 151.56/22.37 | | | | | | | (118) ~ (all_52_12 = e3) % 151.56/22.37 | | | | | | | % 151.56/22.37 | | | | | | | REDUCE: (74), (112) imply: % 151.56/22.37 | | | | | | | (119) ~ (all_8_2 = e3) % 151.56/22.37 | | | | | | | % 151.56/22.37 | | | | | | | SIMP: (119) implies: % 151.56/22.37 | | | | | | | (120) ~ (all_8_2 = e3) % 151.56/22.37 | | | | | | | % 151.56/22.37 | | | | | | | REDUCE: (77), (111) imply: % 151.56/22.37 | | | | | | | (121) ~ (all_52_12 = e2) % 151.56/22.37 | | | | | | | % 151.56/22.37 | | | | | | | REDUCE: (25), (111) imply: % 151.56/22.37 | | | | | | | (122) op(e3, e3) = e2 % 151.56/22.37 | | | | | | | % 151.56/22.37 | | | | | | | BETA: splitting (3) gives: % 151.56/22.37 | | | | | | | % 151.56/22.37 | | | | | | | Case 1: % 151.56/22.37 | | | | | | | | % 151.56/22.37 | | | | | | | | (123) all_54_3 = e3 % 151.56/22.37 | | | | | | | | % 151.56/22.37 | | | | | | | | REF_CLOSE: (29), (118), (123) are inconsistent by sub-proof % 151.56/22.37 | | | | | | | | #659. % 151.56/22.37 | | | | | | | | % 151.56/22.37 | | | | | | | Case 2: % 151.56/22.37 | | | | | | | | % 151.56/22.37 | | | | | | | | (124) all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0 % 151.56/22.37 | | | | | | | | % 151.56/22.37 | | | | | | | | BETA: splitting (124) gives: % 151.56/22.37 | | | | | | | | % 151.56/22.37 | | | | | | | | Case 1: % 151.56/22.37 | | | | | | | | | % 151.56/22.37 | | | | | | | | | (125) all_54_3 = e2 % 151.56/22.37 | | | | | | | | | % 151.56/22.37 | | | | | | | | | REF_CLOSE: (29), (121), (125) are inconsistent by sub-proof % 151.56/22.37 | | | | | | | | | #658. % 151.56/22.37 | | | | | | | | | % 151.56/22.37 | | | | | | | | Case 2: % 151.56/22.37 | | | | | | | | | % 151.56/22.37 | | | | | | | | | (126) all_54_3 = e1 | all_54_3 = e0 % 151.56/22.37 | | | | | | | | | % 151.56/22.37 | | | | | | | | | BETA: splitting (76) gives: % 151.56/22.37 | | | | | | | | | % 151.56/22.37 | | | | | | | | | Case 1: % 151.56/22.37 | | | | | | | | | | % 151.56/22.37 | | | | | | | | | | (127) all_54_5 = e3 % 151.56/22.37 | | | | | | | | | | % 151.56/22.37 | | | | | | | | | | COMBINE_EQS: (13), (127) imply: % 151.56/22.37 | | | | | | | | | | (128) all_8_2 = e3 % 151.56/22.37 | | | | | | | | | | % 151.56/22.37 | | | | | | | | | | REDUCE: (120), (128) imply: % 151.56/22.37 | | | | | | | | | | (129) $false % 151.56/22.37 | | | | | | | | | | % 151.56/22.37 | | | | | | | | | | CLOSE: (129) is inconsistent. % 151.56/22.37 | | | | | | | | | | % 151.56/22.37 | | | | | | | | | Case 2: % 151.56/22.37 | | | | | | | | | | % 151.56/22.37 | | | | | | | | | | (130) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 151.56/22.37 | | | | | | | | | | % 151.56/22.37 | | | | | | | | | | BETA: splitting (130) gives: % 151.56/22.37 | | | | | | | | | | % 151.56/22.37 | | | | | | | | | | Case 1: % 151.56/22.37 | | | | | | | | | | | % 151.56/22.37 | | | | | | | | | | | (131) all_54_5 = e2 % 151.56/22.37 | | | | | | | | | | | % 151.56/22.37 | | | | | | | | | | | COMBINE_EQS: (13), (131) imply: % 151.56/22.37 | | | | | | | | | | | (132) all_8_2 = e2 % 151.56/22.37 | | | | | | | | | | | % 151.56/22.37 | | | | | | | | | | | COMBINE_EQS: (47), (132) imply: % 151.56/22.37 | | | | | | | | | | | (133) all_58_3 = e2 % 151.56/22.37 | | | | | | | | | | | % 151.56/22.37 | | | | | | | | | | | REDUCE: (19), (132) imply: % 151.56/22.37 | | | | | | | | | | | (134) ~ (all_52_7 = e2) % 151.56/22.37 | | | | | | | | | | | % 151.56/22.37 | | | | | | | | | | | REDUCE: (5), (132) imply: % 151.56/22.37 | | | | | | | | | | | (135) ~ (all_52_13 = e2) % 151.56/22.37 | | | | | | | | | | | % 151.56/22.37 | | | | | | | | | | | REDUCE: (72), (132) imply: % 151.56/22.37 | | | | | | | | | | | (136) ~ (e2 = e0) % 151.56/22.37 | | | | | | | | | | | % 151.56/22.37 | | | | | | | | | | | BETA: splitting (40) gives: % 151.56/22.37 | | | | | | | | | | | % 151.56/22.37 | | | | | | | | | | | Case 1: % 151.56/22.37 | | | | | | | | | | | | % 151.56/22.37 | | | | | | | | | | | | (137) all_54_13 = e3 % 151.56/22.37 | | | | | | | | | | | | % 151.56/22.37 | | | | | | | | | | | | REF_CLOSE: (56), (116), (137) are inconsistent by sub-proof % 151.56/22.37 | | | | | | | | | | | | #668. % 151.56/22.37 | | | | | | | | | | | | % 151.56/22.37 | | | | | | | | | | | Case 2: % 151.56/22.37 | | | | | | | | | | | | % 151.56/22.37 | | | | | | | | | | | | (138) all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0 % 151.56/22.37 | | | | | | | | | | | | % 151.56/22.37 | | | | | | | | | | | | BETA: splitting (138) gives: % 151.56/22.37 | | | | | | | | | | | | % 151.56/22.37 | | | | | | | | | | | | Case 1: % 151.56/22.37 | | | | | | | | | | | | | % 151.56/22.37 | | | | | | | | | | | | | (139) all_54_13 = e2 % 151.56/22.37 | | | | | | | | | | | | | % 151.56/22.37 | | | | | | | | | | | | | REF_CLOSE: (56), (134), (139) are inconsistent by sub-proof % 151.56/22.37 | | | | | | | | | | | | | #513. % 151.56/22.37 | | | | | | | | | | | | | % 151.56/22.37 | | | | | | | | | | | | Case 2: % 151.56/22.37 | | | | | | | | | | | | | % 151.56/22.37 | | | | | | | | | | | | | (140) all_54_13 = e1 | all_54_13 = e0 % 151.56/22.37 | | | | | | | | | | | | | % 151.56/22.37 | | | | | | | | | | | | | BETA: splitting (126) gives: % 151.56/22.37 | | | | | | | | | | | | | % 151.56/22.37 | | | | | | | | | | | | | Case 1: % 151.56/22.37 | | | | | | | | | | | | | | % 151.56/22.37 | | | | | | | | | | | | | | (141) all_54_3 = e1 % 151.56/22.37 | | | | | | | | | | | | | | % 151.56/22.37 | | | | | | | | | | | | | | COMBINE_EQS: (29), (141) imply: % 151.56/22.37 | | | | | | | | | | | | | | (142) all_52_12 = e1 % 151.56/22.37 | | | | | | | | | | | | | | % 151.56/22.37 | | | | | | | | | | | | | | SIMP: (142) implies: % 151.56/22.37 | | | | | | | | | | | | | | (143) all_52_12 = e1 % 151.56/22.37 | | | | | | | | | | | | | | % 151.56/22.37 | | | | | | | | | | | | | | REDUCE: (10), (143) imply: % 151.56/22.37 | | | | | | | | | | | | | | (144) ~ (all_52_13 = e1) % 151.56/22.37 | | | | | | | | | | | | | | % 151.56/22.37 | | | | | | | | | | | | | | SIMP: (144) implies: % 151.56/22.37 | | | | | | | | | | | | | | (145) ~ (all_52_13 = e1) % 151.56/22.37 | | | | | | | | | | | | | | % 151.56/22.37 | | | | | | | | | | | | | | REDUCE: (67), (143) imply: % 151.56/22.37 | | | | | | | | | | | | | | (146) ~ (all_52_14 = e1) % 151.56/22.37 | | | | | | | | | | | | | | % 151.56/22.37 | | | | | | | | | | | | | | SIMP: (146) implies: % 151.56/22.37 | | | | | | | | | | | | | | (147) ~ (all_52_14 = e1) % 151.56/22.37 | | | | | | | | | | | | | | % 151.56/22.37 | | | | | | | | | | | | | | BETA: splitting (21) gives: % 151.56/22.37 | | | | | | | | | | | | | | % 151.56/22.37 | | | | | | | | | | | | | | Case 1: % 151.56/22.37 | | | | | | | | | | | | | | | % 151.56/22.37 | | | | | | | | | | | | | | | (148) all_54_7 = e3 % 151.56/22.37 | | | | | | | | | | | | | | | % 151.56/22.37 | | | | | | | | | | | | | | | COMBINE_EQS: (51), (148) imply: % 151.56/22.37 | | | | | | | | | | | | | | | (149) all_52_13 = e3 % 151.56/22.37 | | | | | | | | | | | | | | | % 151.56/22.37 | | | | | | | | | | | | | | | SIMP: (149) implies: % 151.56/22.37 | | | | | | | | | | | | | | | (150) all_52_13 = e3 % 151.56/22.37 | | | | | | | | | | | | | | | % 151.56/22.37 | | | | | | | | | | | | | | | REDUCE: (57), (150) imply: % 151.56/22.37 | | | | | | | | | | | | | | | (151) ~ (all_52_14 = e3) % 151.56/22.37 | | | | | | | | | | | | | | | % 151.56/22.37 | | | | | | | | | | | | | | | SIMP: (151) implies: % 151.56/22.37 | | | | | | | | | | | | | | | (152) ~ (all_52_14 = e3) % 151.56/22.37 | | | | | | | | | | | | | | | % 151.56/22.37 | | | | | | | | | | | | | | | REDUCE: (93), (150) imply: % 151.56/22.37 | | | | | | | | | | | | | | | (153) ~ (e3 = e0) % 151.56/22.37 | | | | | | | | | | | | | | | % 151.56/22.37 | | | | | | | | | | | | | | | BETA: splitting (8) gives: % 151.56/22.37 | | | | | | | | | | | | | | | % 151.56/22.37 | | | | | | | | | | | | | | | Case 1: % 151.56/22.37 | | | | | | | | | | | | | | | | % 151.56/22.37 | | | | | | | | | | | | | | | | (154) all_54_11 = e3 % 151.56/22.37 | | | | | | | | | | | | | | | | % 151.56/22.37 | | | | | | | | | | | | | | | | COMBINE_EQS: (80), (154) imply: % 151.56/22.37 | | | | | | | | | | | | | | | | (155) all_52_14 = e3 % 151.56/22.37 | | | | | | | | | | | | | | | | % 151.56/22.37 | | | | | | | | | | | | | | | | REDUCE: (152), (155) imply: % 151.56/22.37 | | | | | | | | | | | | | | | | (156) $false % 151.56/22.37 | | | | | | | | | | | | | | | | % 151.56/22.37 | | | | | | | | | | | | | | | | CLOSE: (156) is inconsistent. % 151.56/22.37 | | | | | | | | | | | | | | | | % 151.56/22.37 | | | | | | | | | | | | | | | Case 2: % 151.56/22.37 | | | | | | | | | | | | | | | | % 151.56/22.37 | | | | | | | | | | | | | | | | (157) all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0 % 151.56/22.37 | | | | | | | | | | | | | | | | % 151.56/22.37 | | | | | | | | | | | | | | | | BETA: splitting (66) gives: % 151.56/22.37 | | | | | | | | | | | | | | | | % 151.56/22.37 | | | | | | | | | | | | | | | | Case 1: % 151.56/22.37 | | | | | | | | | | | | | | | | | % 151.56/22.37 | | | | | | | | | | | | | | | | | (158) all_58_1 = e0 % 151.56/22.37 | | | | | | | | | | | | | | | | | % 151.56/22.37 | | | | | | | | | | | | | | | | | COMBINE_EQS: (113), (158) imply: % 151.56/22.37 | | | | | | | | | | | | | | | | | (159) e3 = e0 % 151.56/22.37 | | | | | | | | | | | | | | | | | % 151.56/22.37 | | | | | | | | | | | | | | | | | REDUCE: (153), (159) imply: % 151.56/22.37 | | | | | | | | | | | | | | | | | (160) $false % 151.56/22.37 | | | | | | | | | | | | | | | | | % 151.56/22.37 | | | | | | | | | | | | | | | | | CLOSE: (160) is inconsistent. % 151.56/22.37 | | | | | | | | | | | | | | | | | % 151.56/22.37 | | | | | | | | | | | | | | | | Case 2: % 151.56/22.37 | | | | | | | | | | | | | | | | | % 151.56/22.37 | | | | | | | | | | | | | | | | | (161) all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0 % 151.56/22.37 | | | | | | | | | | | | | | | | | % 151.56/22.37 | | | | | | | | | | | | | | | | | BETA: splitting (161) gives: % 151.56/22.37 | | | | | | | | | | | | | | | | | % 151.56/22.37 | | | | | | | | | | | | | | | | | Case 1: % 151.56/22.37 | | | | | | | | | | | | | | | | | | % 151.56/22.37 | | | | | | | | | | | | | | | | | | (162) all_58_3 = e0 % 151.56/22.37 | | | | | | | | | | | | | | | | | | % 151.56/22.37 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (133), (162) imply: % 151.56/22.37 | | | | | | | | | | | | | | | | | | (163) e2 = e0 % 151.56/22.37 | | | | | | | | | | | | | | | | | | % 151.56/22.37 | | | | | | | | | | | | | | | | | | REDUCE: (136), (163) imply: % 151.56/22.37 | | | | | | | | | | | | | | | | | | (164) $false % 151.56/22.37 | | | | | | | | | | | | | | | | | | % 151.56/22.37 | | | | | | | | | | | | | | | | | | CLOSE: (164) is inconsistent. % 151.56/22.37 | | | | | | | | | | | | | | | | | | % 151.56/22.37 | | | | | | | | | | | | | | | | | Case 2: % 151.56/22.37 | | | | | | | | | | | | | | | | | | % 151.56/22.37 | | | | | | | | | | | | | | | | | | (165) all_58_7 = e0 | all_58_13 = e0 % 151.56/22.37 | | | | | | | | | | | | | | | | | | % 151.56/22.37 | | | | | | | | | | | | | | | | | | BETA: splitting (165) gives: % 151.56/22.37 | | | | | | | | | | | | | | | | | | % 151.56/22.37 | | | | | | | | | | | | | | | | | | Case 1: % 151.56/22.37 | | | | | | | | | | | | | | | | | | | % 151.56/22.37 | | | | | | | | | | | | | | | | | | | (166) all_58_7 = e0 % 151.56/22.37 | | | | | | | | | | | | | | | | | | | % 151.56/22.37 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (62), (166) imply: % 151.56/22.37 | | | | | | | | | | | | | | | | | | | (167) all_52_6 = e0 % 151.56/22.37 | | | | | | | | | | | | | | | | | | | % 151.56/22.37 | | | | | | | | | | | | | | | | | | | REDUCE: (49), (167) imply: % 151.56/22.37 | | | | | | | | | | | | | | | | | | | (168) ~ (all_52_7 = e0) % 151.56/22.37 | | | | | | | | | | | | | | | | | | | % 151.56/22.37 | | | | | | | | | | | | | | | | | | | REDUCE: (15), (167) imply: % 151.56/22.37 | | | | | | | | | | | | | | | | | | | (169) ~ (all_52_14 = e0) % 151.56/22.37 | | | | | | | | | | | | | | | | | | | % 151.56/22.37 | | | | | | | | | | | | | | | | | | | SIMP: (169) implies: % 151.56/22.37 | | | | | | | | | | | | | | | | | | | (170) ~ (all_52_14 = e0) % 151.56/22.37 | | | | | | | | | | | | | | | | | | | % 151.56/22.37 | | | | | | | | | | | | | | | | | | | BETA: splitting (157) gives: % 151.56/22.37 | | | | | | | | | | | | | | | | | | | % 151.56/22.37 | | | | | | | | | | | | | | | | | | | Case 1: % 151.56/22.37 | | | | | | | | | | | | | | | | | | | | % 151.56/22.37 | | | | | | | | | | | | | | | | | | | | (171) all_54_11 = e2 % 151.56/22.37 | | | | | | | | | | | | | | | | | | | | % 151.56/22.37 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (80), (171) imply: % 151.56/22.37 | | | | | | | | | | | | | | | | | | | | (172) all_52_14 = e2 % 151.56/22.37 | | | | | | | | | | | | | | | | | | | | % 151.56/22.37 | | | | | | | | | | | | | | | | | | | | SIMP: (172) implies: % 151.56/22.37 | | | | | | | | | | | | | | | | | | | | (173) all_52_14 = e2 % 151.56/22.37 | | | | | | | | | | | | | | | | | | | | % 151.56/22.37 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (50), (173) imply: % 151.56/22.37 | | | | | | | | | | | | | | | | | | | | (174) all_58_11 = e2 % 151.56/22.37 | | | | | | | | | | | | | | | | | | | | % 151.56/22.37 | | | | | | | | | | | | | | | | | | | | BETA: splitting (140) gives: % 151.56/22.37 | | | | | | | | | | | | | | | | | | | | % 151.56/22.37 | | | | | | | | | | | | | | | | | | | | Case 1: % 151.56/22.37 | | | | | | | | | | | | | | | | | | | | | % 151.56/22.37 | | | | | | | | | | | | | | | | | | | | | (175) all_54_13 = e1 % 151.56/22.37 | | | | | | | | | | | | | | | | | | | | | % 151.56/22.37 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (56), (175) imply: % 151.56/22.37 | | | | | | | | | | | | | | | | | | | | | (176) all_52_7 = e1 % 151.56/22.37 | | | | | | | | | | | | | | | | | | | | | % 151.56/22.37 | | | | | | | | | | | | | | | | | | | | | REDUCE: (30), (176) imply: % 151.56/22.37 | | | | | | | | | | | | | | | | | | | | | (177) ~ (all_52_3 = e1) % 151.56/22.37 | | | | | | | | | | | | | | | | | | | | | % 151.56/22.37 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (79) gives: % 151.56/22.37 | | | | | | | | | | | | | | | | | | | | | % 151.56/22.37 | | | | | | | | | | | | | | | | | | | | | Case 1: % 151.56/22.37 | | | | | | | | | | | | | | | | | | | | | | % 151.56/22.37 | | | | | | | | | | | | | | | | | | | | | | (178) all_58_12 = e3 % 151.56/22.37 | | | | | | | | | | | | | | | | | | | | | | % 151.56/22.37 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (78), (178) imply: % 151.56/22.37 | | | | | | | | | | | | | | | | | | | | | | (179) all_52_3 = e3 % 151.56/22.37 | | | | | | | | | | | | | | | | | | | | | | % 151.56/22.37 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (45), (179) imply: % 151.56/22.37 | | | | | | | | | | | | | | | | | | | | | | (180) ~ (all_52_2 = e3) % 151.56/22.37 | | | | | | | | | | | | | | | | | | | | | | % 151.56/22.37 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (114), (179) imply: % 151.56/22.37 | | | | | | | | | | | | | | | | | | | | | | (181) ~ (e3 = e2) % 151.56/22.37 | | | | | | | | | | | | | | | | | | | | | | % 151.56/22.37 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (75), (179) imply: % 151.56/22.37 | | | | | | | | | | | | | | | | | | | | | | (182) op(e3, e3) = all_56_24 % 151.56/22.37 | | | | | | | | | | | | | | | | | | | | | | % 151.56/22.37 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (39) gives: % 151.56/22.37 | | | | | | | | | | | | | | | | | | | | | | % 151.56/22.37 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 151.56/22.37 | | | | | | | | | | | | | | | | | | | | | | | % 151.56/22.37 | | | | | | | | | | | | | | | | | | | | | | | (183) all_58_6 = e3 % 151.56/22.37 | | | | | | | | | | | | | | | | | | | | | | | % 151.56/22.37 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1), (183) imply: % 151.56/22.37 | | | | | | | | | | | | | | | | | | | | | | | (184) all_52_2 = e3 % 151.56/22.37 | | | | | | | | | | | | | | | | | | | | | | | % 151.56/22.37 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (180), (184) imply: % 151.56/22.37 | | | | | | | | | | | | | | | | | | | | | | | (185) $false % 151.56/22.37 | | | | | | | | | | | | | | | | | | | | | | | % 151.56/22.37 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (185) is inconsistent. % 151.56/22.37 | | | | | | | | | | | | | | | | | | | | | | | % 151.56/22.37 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 151.56/22.37 | | | | | | | | | | | | | | | | | | | | | | | % 151.56/22.37 | | | | | | | | | | | | | | | | | | | | | | | (186) all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3 % 151.56/22.37 | | | | | | | | | | | | | | | | | | | | | | | % 151.56/22.37 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (186) gives: % 151.56/22.37 | | | | | | | | | | | | | | | | | | | | | | | % 151.56/22.37 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 151.56/22.37 | | | | | | | | | | | | | | | | | | | | | | | | % 151.56/22.37 | | | | | | | | | | | | | | | | | | | | | | | | (187) all_58_7 = e3 % 151.56/22.37 | | | | | | | | | | | | | | | | | | | | | | | | % 151.56/22.37 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (153), (166), (187) are inconsistent by sub-proof % 151.56/22.37 | | | | | | | | | | | | | | | | | | | | | | | | #303. % 151.56/22.37 | | | | | | | | | | | | | | | | | | | | | | | | % 151.56/22.37 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 151.56/22.37 | | | | | | | | | | | | | | | | | | | | | | | | % 151.56/22.37 | | | | | | | | | | | | | | | | | | | | | | | | (188) all_58_8 = e3 | all_58_11 = e3 % 151.56/22.37 | | | | | | | | | | | | | | | | | | | | | | | | % 151.56/22.37 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (188) gives: % 151.56/22.37 | | | | | | | | | | | | | | | | | | | | | | | | % 151.56/22.37 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 151.56/22.37 | | | | | | | | | | | | | | | | | | | | | | | | | % 151.56/22.37 | | | | | | | | | | | | | | | | | | | | | | | | | (189) all_58_8 = e3 % 151.56/22.37 | | | | | | | | | | | | | | | | | | | | | | | | | % 151.56/22.37 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (37), (189) imply: % 151.56/22.38 | | | | | | | | | | | | | | | | | | | | | | | | | (190) all_6_2 = e3 % 151.56/22.38 | | | | | | | | | | | | | | | | | | | | | | | | | % 151.56/22.38 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (52), (190) imply: % 151.56/22.38 | | | | | | | | | | | | | | | | | | | | | | | | | (191) op(e3, e3) = all_6_1 % 151.56/22.38 | | | | | | | | | | | | | | | | | | | | | | | | | % 151.56/22.38 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (27), (122), (182), (191) are inconsistent by % 151.56/22.38 | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #302. % 151.56/22.38 | | | | | | | | | | | | | | | | | | | | | | | | | % 151.56/22.38 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 151.56/22.38 | | | | | | | | | | | | | | | | | | | | | | | | | % 151.56/22.38 | | | | | | | | | | | | | | | | | | | | | | | | | (192) all_58_11 = e3 % 151.56/22.38 | | | | | | | | | | | | | | | | | | | | | | | | | % 151.56/22.38 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (174), (181), (192) are inconsistent by sub-proof % 151.56/22.38 | | | | | | | | | | | | | | | | | | | | | | | | | #301. % 151.56/22.38 | | | | | | | | | | | | | | | | | | | | | | | | | % 151.56/22.38 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 151.56/22.38 | | | | | | | | | | | | | | | | | | | | | | | | % 151.56/22.38 | | | | | | | | | | | | | | | | | | | | | | | End of split % 151.56/22.38 | | | | | | | | | | | | | | | | | | | | | | | % 151.56/22.38 | | | | | | | | | | | | | | | | | | | | | | End of split % 151.56/22.38 | | | | | | | | | | | | | | | | | | | | | | % 151.56/22.38 | | | | | | | | | | | | | | | | | | | | | Case 2: % 151.56/22.38 | | | | | | | | | | | | | | | | | | | | | | % 151.56/22.38 | | | | | | | | | | | | | | | | | | | | | | (193) ~ (all_58_12 = e3) % 151.56/22.38 | | | | | | | | | | | | | | | | | | | | | | % 151.56/22.38 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (78), (193) imply: % 151.56/22.38 | | | | | | | | | | | | | | | | | | | | | | (194) ~ (all_52_3 = e3) % 151.56/22.38 | | | | | | | | | | | | | | | | | | | | | | % 151.56/22.38 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (82) gives: % 151.56/22.38 | | | | | | | | | | | | | | | | | | | | | | % 151.56/22.38 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 151.56/22.38 | | | | | | | | | | | | | | | | | | | | | | | % 151.56/22.38 | | | | | | | | | | | | | | | | | | | | | | | (195) all_54_15 = e2 % 151.56/22.38 | | | | | | | | | | | | | | | | | | | | | | | % 151.56/22.38 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (44), (195) are inconsistent by sub-proof % 151.56/22.38 | | | | | | | | | | | | | | | | | | | | | | | #739. % 151.56/22.38 | | | | | | | | | | | | | | | | | | | | | | | % 151.56/22.38 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 151.56/22.38 | | | | | | | | | | | | | | | | | | | | | | | % 151.56/22.38 | | | | | | | | | | | | | | | | | | | | | | | % 151.56/22.38 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (85) gives: % 151.56/22.38 | | | | | | | | | | | | | | | | | | | | | | | % 151.56/22.38 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 151.56/22.38 | | | | | | | | | | | | | | | | | | | | | | | | % 151.56/22.38 | | | | | | | | | | | | | | | | | | | | | | | | (196) all_54_15 = e1 % 151.56/22.38 | | | | | | | | | | | | | | | | | | | | | | | | % 151.56/22.38 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (36), (196) are inconsistent by sub-proof % 151.56/22.38 | | | | | | | | | | | | | | | | | | | | | | | | #738. % 151.56/22.38 | | | | | | | | | | | | | | | | | | | | | | | | % 151.56/22.38 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 151.56/22.38 | | | | | | | | | | | | | | | | | | | | | | | | % 151.56/22.38 | | | | | | | | | | | | | | | | | | | | | | | | % 151.56/22.38 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (34), (90), (114), (177), (194) are % 151.56/22.38 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #300. % 151.56/22.38 | | | | | | | | | | | | | | | | | | | | | | | | % 151.56/22.38 | | | | | | | | | | | | | | | | | | | | | | | End of split % 151.56/22.38 | | | | | | | | | | | | | | | | | | | | | | | % 151.56/22.38 | | | | | | | | | | | | | | | | | | | | | | End of split % 151.56/22.38 | | | | | | | | | | | | | | | | | | | | | | % 151.56/22.38 | | | | | | | | | | | | | | | | | | | | | End of split % 151.56/22.38 | | | | | | | | | | | | | | | | | | | | | % 151.56/22.38 | | | | | | | | | | | | | | | | | | | | Case 2: % 151.56/22.38 | | | | | | | | | | | | | | | | | | | | | % 151.56/22.38 | | | | | | | | | | | | | | | | | | | | | (197) all_54_13 = e0 % 151.56/22.38 | | | | | | | | | | | | | | | | | | | | | % 151.56/22.38 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (56), (197) imply: % 151.56/22.38 | | | | | | | | | | | | | | | | | | | | | (198) all_52_7 = e0 % 151.56/22.38 | | | | | | | | | | | | | | | | | | | | | % 151.56/22.38 | | | | | | | | | | | | | | | | | | | | | REDUCE: (91), (198) imply: % 151.56/22.38 | | | | | | | | | | | | | | | | | | | | | (199) $false % 151.56/22.38 | | | | | | | | | | | | | | | | | | | | | % 151.56/22.38 | | | | | | | | | | | | | | | | | | | | | CLOSE: (199) is inconsistent. % 151.56/22.38 | | | | | | | | | | | | | | | | | | | | | % 151.56/22.38 | | | | | | | | | | | | | | | | | | | | End of split % 151.56/22.38 | | | | | | | | | | | | | | | | | | | | % 151.56/22.38 | | | | | | | | | | | | | | | | | | | Case 2: % 151.56/22.38 | | | | | | | | | | | | | | | | | | | | % 151.56/22.38 | | | | | | | | | | | | | | | | | | | | (200) all_54_11 = e1 | all_54_11 = e0 % 151.56/22.38 | | | | | | | | | | | | | | | | | | | | % 151.56/22.38 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (80), (147), (170), (200) are inconsistent by % 151.56/22.38 | | | | | | | | | | | | | | | | | | | | sub-proof #688. % 151.56/22.38 | | | | | | | | | | | | | | | | | | | | % 151.56/22.38 | | | | | | | | | | | | | | | | | | | End of split % 151.56/22.38 | | | | | | | | | | | | | | | | | | | % 151.56/22.38 | | | | | | | | | | | | | | | | | | Case 2: % 151.56/22.38 | | | | | | | | | | | | | | | | | | | % 151.56/22.38 | | | | | | | | | | | | | | | | | | | (201) all_58_13 = e0 % 151.56/22.38 | | | | | | | | | | | | | | | | | | | % 151.56/22.38 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (24), (201) imply: % 151.56/22.38 | | | | | | | | | | | | | | | | | | | (202) all_52_7 = e0 % 151.56/22.38 | | | | | | | | | | | | | | | | | | | % 151.56/22.38 | | | | | | | | | | | | | | | | | | | REDUCE: (91), (202) imply: % 151.56/22.38 | | | | | | | | | | | | | | | | | | | (203) $false % 151.56/22.38 | | | | | | | | | | | | | | | | | | | % 151.56/22.38 | | | | | | | | | | | | | | | | | | | CLOSE: (203) is inconsistent. % 151.56/22.38 | | | | | | | | | | | | | | | | | | | % 151.56/22.38 | | | | | | | | | | | | | | | | | | End of split % 151.56/22.38 | | | | | | | | | | | | | | | | | | % 151.56/22.38 | | | | | | | | | | | | | | | | | End of split % 151.56/22.38 | | | | | | | | | | | | | | | | | % 151.56/22.38 | | | | | | | | | | | | | | | | End of split % 151.56/22.38 | | | | | | | | | | | | | | | | % 151.56/22.38 | | | | | | | | | | | | | | | End of split % 151.56/22.38 | | | | | | | | | | | | | | | % 151.56/22.38 | | | | | | | | | | | | | | Case 2: % 151.56/22.38 | | | | | | | | | | | | | | | % 151.56/22.38 | | | | | | | | | | | | | | | (204) all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0 % 151.56/22.38 | | | | | | | | | | | | | | | % 151.56/22.38 | | | | | | | | | | | | | | | REF_CLOSE: (51), (93), (135), (145), (204) are inconsistent % 151.56/22.38 | | | | | | | | | | | | | | | by sub-proof #649. % 151.56/22.38 | | | | | | | | | | | | | | | % 151.56/22.38 | | | | | | | | | | | | | | End of split % 151.56/22.38 | | | | | | | | | | | | | | % 151.56/22.38 | | | | | | | | | | | | | Case 2: % 151.56/22.38 | | | | | | | | | | | | | | % 151.56/22.38 | | | | | | | | | | | | | | (205) all_54_3 = e0 % 151.56/22.38 | | | | | | | | | | | | | | % 151.56/22.38 | | | | | | | | | | | | | | REF_CLOSE: (29), (92), (205) are inconsistent by sub-proof % 151.56/22.38 | | | | | | | | | | | | | | #656. % 151.56/22.38 | | | | | | | | | | | | | | % 151.56/22.38 | | | | | | | | | | | | | End of split % 151.56/22.38 | | | | | | | | | | | | | % 151.56/22.38 | | | | | | | | | | | | End of split % 151.56/22.38 | | | | | | | | | | | | % 151.56/22.38 | | | | | | | | | | | End of split % 151.56/22.38 | | | | | | | | | | | % 151.56/22.38 | | | | | | | | | | Case 2: % 151.56/22.38 | | | | | | | | | | | % 151.56/22.38 | | | | | | | | | | | (206) all_54_5 = e1 | all_54_5 = e0 % 151.56/22.38 | | | | | | | | | | | % 151.56/22.38 | | | | | | | | | | | REF_CLOSE: (6), (13), (72), (206) are inconsistent by % 151.56/22.38 | | | | | | | | | | | sub-proof #645. % 151.56/22.38 | | | | | | | | | | | % 151.56/22.38 | | | | | | | | | | End of split % 151.56/22.38 | | | | | | | | | | % 151.56/22.38 | | | | | | | | | End of split % 151.56/22.38 | | | | | | | | | % 151.56/22.38 | | | | | | | | End of split % 151.56/22.38 | | | | | | | | % 151.56/22.38 | | | | | | | End of split % 151.56/22.38 | | | | | | | % 151.56/22.38 | | | | | | End of split % 151.56/22.38 | | | | | | % 151.56/22.38 | | | | | Case 2: % 151.56/22.38 | | | | | | % 151.56/22.38 | | | | | | (207) all_56_7 = e3 % 151.56/22.38 | | | | | | (208) all_56_1 = e0 % 151.56/22.38 | | | | | | % 151.56/22.38 | | | | | | COMBINE_EQS: (20), (208) imply: % 151.56/22.38 | | | | | | (209) all_10_2 = e0 % 151.56/22.38 | | | | | | % 151.56/22.38 | | | | | | COMBINE_EQS: (33), (207) imply: % 151.56/22.38 | | | | | | (210) all_52_12 = e3 % 151.56/22.38 | | | | | | % 151.56/22.38 | | | | | | REDUCE: (64), (209) imply: % 151.56/22.38 | | | | | | (211) op(e0, e0) = all_10_1 % 151.56/22.38 | | | | | | % 151.56/22.38 | | | | | | REDUCE: (73), (209) imply: % 151.56/22.38 | | | | | | (212) op(e3, e0) = all_56_0 % 151.56/22.38 | | | | | | % 151.56/22.38 | | | | | | REDUCE: (54), (210) imply: % 151.56/22.38 | | | | | | (213) op(e3, e0) = e3 % 151.56/22.38 | | | | | | % 151.56/22.38 | | | | | | GROUND_INST: instantiating (27) with e0, all_10_1, e0, e0, % 151.56/22.38 | | | | | | simplifying with (96), (211) gives: % 151.56/22.38 | | | | | | (214) all_10_1 = e0 % 151.56/22.38 | | | | | | % 151.56/22.38 | | | | | | GROUND_INST: instantiating (27) with e3, all_56_0, e0, e3, % 151.56/22.38 | | | | | | simplifying with (212), (213) gives: % 151.56/22.38 | | | | | | (215) all_56_0 = e3 % 151.56/22.38 | | | | | | % 151.56/22.38 | | | | | | REDUCE: (59), (214) imply: % 151.56/22.38 | | | | | | (216) op(e3, e0) = e1 % 151.56/22.38 | | | | | | % 151.56/22.38 | | | | | | GROUND_INST: instantiating (27) with e3, e1, e0, e3, simplifying % 151.56/22.38 | | | | | | with (213), (216) gives: % 151.56/22.38 | | | | | | (217) e3 = e1 % 151.56/22.38 | | | | | | % 151.56/22.38 | | | | | | REDUCE: (69), (217) imply: % 151.56/22.38 | | | | | | (218) $false % 151.56/22.38 | | | | | | % 151.56/22.38 | | | | | | CLOSE: (218) is inconsistent. % 151.56/22.38 | | | | | | % 151.56/22.38 | | | | | End of split % 151.56/22.38 | | | | | % 151.56/22.38 | | | | Case 2: % 151.56/22.38 | | | | | % 151.56/22.38 | | | | | (219) all_56_5 = e3 % 151.56/22.38 | | | | | (220) all_56_1 = e1 % 151.56/22.38 | | | | | % 151.56/22.38 | | | | | COMBINE_EQS: (20), (220) imply: % 151.56/22.38 | | | | | (221) all_10_2 = e1 % 151.56/22.38 | | | | | % 151.56/22.38 | | | | | COMBINE_EQS: (43), (219) imply: % 151.56/22.38 | | | | | (222) all_52_8 = e3 % 151.56/22.38 | | | | | % 151.56/22.38 | | | | | REDUCE: (26), (222) imply: % 151.56/22.38 | | | | | (223) ~ (all_6_2 = e3) % 151.56/22.38 | | | | | % 151.56/22.38 | | | | | SIMP: (223) implies: % 151.56/22.38 | | | | | (224) ~ (all_6_2 = e3) % 151.56/22.38 | | | | | % 151.56/22.38 | | | | | REDUCE: (64), (221) imply: % 151.56/22.38 | | | | | (225) op(e1, e1) = all_10_1 % 151.56/22.38 | | | | | % 151.56/22.38 | | | | | REDUCE: (73), (221) imply: % 151.56/22.38 | | | | | (226) op(e3, e1) = all_56_0 % 151.56/22.38 | | | | | % 151.56/22.38 | | | | | REDUCE: (68), (222) imply: % 151.56/22.38 | | | | | (227) op(e3, e1) = e3 % 151.56/22.38 | | | | | % 151.56/22.38 | | | | | REF_CLOSE: (2), (14), (18), (27), (31), (52), (58), (59), (60), (65), % 151.56/22.38 | | | | | (224), (225), (226), (227) are inconsistent by sub-proof % 151.56/22.38 | | | | | #298. % 151.56/22.38 | | | | | % 151.56/22.38 | | | | End of split % 151.56/22.38 | | | | % 151.56/22.38 | | | End of split % 151.56/22.38 | | | % 151.56/22.38 | | End of split % 151.56/22.38 | | % 151.56/22.38 | End of split % 151.56/22.38 | % 151.56/22.38 End of proof % 151.56/22.38 % 151.56/22.38 Sub-proof #298 shows that the following formulas are inconsistent: % 151.56/22.38 ---------------------------------------------------------------- % 151.56/22.38 (1) all_54_10 = all_6_2 % 151.56/22.38 (2) ~ (all_6_2 = e3) % 151.56/22.38 (3) ~ (all_6_1 = e3) % 151.56/22.38 (4) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 151.56/22.38 (5) op(e1, e1) = all_10_1 % 151.56/22.38 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 151.56/22.38 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 151.56/22.38 (7) ~ (all_6_2 = e0) % 151.56/22.38 (8) op(e3, e1) = all_56_0 % 151.56/22.38 (9) op(all_6_2, all_6_2) = all_6_1 % 151.56/22.38 (10) op(e1, e1) = all_6_2 % 151.56/22.38 (11) op(e3, all_10_1) = e1 % 151.56/22.38 (12) ~ (all_6_2 = e2) % 151.56/22.38 (13) op(e3, e1) = e3 % 151.56/22.38 (14) op(e1, all_6_2) = all_56_20 % 151.56/22.38 % 151.56/22.38 Begin of proof % 151.56/22.38 | % 151.56/22.38 | BETA: splitting (4) gives: % 151.56/22.38 | % 151.56/22.38 | Case 1: % 151.56/22.38 | | % 151.56/22.38 | | (15) all_54_10 = e3 % 151.56/22.38 | | % 151.56/22.38 | | COMBINE_EQS: (1), (15) imply: % 151.56/22.38 | | (16) all_6_2 = e3 % 151.56/22.38 | | % 151.56/22.38 | | REDUCE: (2), (16) imply: % 151.56/22.38 | | (17) $false % 151.56/22.38 | | % 151.56/22.38 | | CLOSE: (17) is inconsistent. % 151.56/22.38 | | % 151.56/22.38 | Case 2: % 151.56/22.38 | | % 151.56/22.38 | | (18) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 151.56/22.38 | | % 151.56/22.38 | | BETA: splitting (18) gives: % 151.56/22.38 | | % 151.56/22.38 | | Case 1: % 151.56/22.38 | | | % 151.56/22.38 | | | (19) all_54_10 = e2 % 151.56/22.38 | | | % 151.56/22.38 | | | COMBINE_EQS: (1), (19) imply: % 151.56/22.38 | | | (20) all_6_2 = e2 % 151.56/22.38 | | | % 151.56/22.38 | | | REDUCE: (12), (20) imply: % 151.56/22.38 | | | (21) $false % 151.56/22.38 | | | % 151.56/22.38 | | | CLOSE: (21) is inconsistent. % 151.56/22.38 | | | % 151.56/22.38 | | Case 2: % 151.56/22.38 | | | % 151.56/22.38 | | | (22) all_54_10 = e1 | all_54_10 = e0 % 151.56/22.38 | | | % 151.56/22.38 | | | BETA: splitting (22) gives: % 151.56/22.38 | | | % 151.56/22.38 | | | Case 1: % 151.56/22.38 | | | | % 151.56/22.38 | | | | (23) all_54_10 = e1 % 151.56/22.38 | | | | % 151.56/22.38 | | | | COMBINE_EQS: (1), (23) imply: % 151.56/22.38 | | | | (24) all_6_2 = e1 % 151.56/22.38 | | | | % 151.56/22.38 | | | | SIMP: (24) implies: % 151.56/22.38 | | | | (25) all_6_2 = e1 % 151.56/22.38 | | | | % 151.56/22.38 | | | | REDUCE: (9), (25) imply: % 151.56/22.38 | | | | (26) op(e1, e1) = all_6_1 % 151.56/22.38 | | | | % 151.56/22.38 | | | | REDUCE: (14), (25) imply: % 151.56/22.38 | | | | (27) op(e1, e1) = all_56_20 % 151.56/22.38 | | | | % 151.56/22.38 | | | | REDUCE: (10), (25) imply: % 151.56/22.38 | | | | (28) op(e1, e1) = e1 % 151.56/22.38 | | | | % 151.56/22.38 | | | | REF_CLOSE: (3), (5), (6), (8), (11), (13), (26), (27), (28) are % 151.56/22.38 | | | | inconsistent by sub-proof #299. % 151.56/22.38 | | | | % 151.56/22.38 | | | Case 2: % 151.56/22.38 | | | | % 151.56/22.38 | | | | (29) all_54_10 = e0 % 151.56/22.38 | | | | % 151.56/22.38 | | | | REF_CLOSE: (1), (7), (29) are inconsistent by sub-proof #705. % 151.56/22.38 | | | | % 151.56/22.38 | | | End of split % 151.56/22.38 | | | % 151.56/22.38 | | End of split % 151.56/22.38 | | % 151.56/22.38 | End of split % 151.56/22.38 | % 151.56/22.38 End of proof % 151.56/22.38 % 151.56/22.38 Sub-proof #299 shows that the following formulas are inconsistent: % 151.56/22.38 ---------------------------------------------------------------- % 151.56/22.38 (1) ~ (all_6_1 = e3) % 151.56/22.38 (2) op(e1, e1) = all_10_1 % 151.56/22.38 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 151.56/22.38 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 151.56/22.38 (4) op(e3, e1) = all_56_0 % 151.56/22.38 (5) op(e1, e1) = all_56_20 % 151.56/22.38 (6) op(e3, all_10_1) = e1 % 151.56/22.38 (7) op(e3, e1) = e3 % 151.56/22.38 (8) op(e1, e1) = all_6_1 % 151.56/22.38 (9) op(e1, e1) = e1 % 151.56/22.38 % 151.56/22.38 Begin of proof % 151.56/22.38 | % 151.56/22.38 | GROUND_INST: instantiating (3) with all_6_1, all_10_1, e1, e1, simplifying % 151.56/22.38 | with (2), (8) gives: % 151.56/22.38 | (10) all_10_1 = all_6_1 % 151.56/22.38 | % 151.56/22.38 | GROUND_INST: instantiating (3) with all_10_1, all_56_20, e1, e1, simplifying % 151.56/22.38 | with (2), (5) gives: % 151.56/22.38 | (11) all_56_20 = all_10_1 % 151.56/22.38 | % 151.56/22.38 | GROUND_INST: instantiating (3) with e1, all_56_20, e1, e1, simplifying with % 151.56/22.38 | (5), (9) gives: % 151.56/22.38 | (12) all_56_20 = e1 % 151.56/22.38 | % 151.56/22.38 | GROUND_INST: instantiating (3) with e3, all_56_0, e1, e3, simplifying with % 151.56/22.38 | (4), (7) gives: % 151.56/22.38 | (13) all_56_0 = e3 % 151.56/22.38 | % 151.56/22.38 | COMBINE_EQS: (11), (12) imply: % 151.56/22.38 | (14) all_10_1 = e1 % 151.56/22.38 | % 151.56/22.38 | SIMP: (14) implies: % 151.56/22.38 | (15) all_10_1 = e1 % 151.56/22.38 | % 151.56/22.38 | COMBINE_EQS: (10), (15) imply: % 151.56/22.38 | (16) all_6_1 = e1 % 151.56/22.38 | % 151.56/22.38 | REDUCE: (1), (16) imply: % 151.56/22.38 | (17) ~ (e3 = e1) % 151.56/22.38 | % 151.56/22.38 | SIMP: (17) implies: % 151.56/22.38 | (18) ~ (e3 = e1) % 151.56/22.38 | % 151.56/22.38 | REDUCE: (6), (15) imply: % 151.56/22.38 | (19) op(e3, e1) = e1 % 151.56/22.38 | % 151.56/22.38 | GROUND_INST: instantiating (3) with e3, e1, e1, e3, simplifying with (7), (19) % 151.56/22.38 | gives: % 151.56/22.38 | (20) e3 = e1 % 151.56/22.38 | % 151.56/22.38 | REDUCE: (18), (20) imply: % 151.56/22.38 | (21) $false % 151.56/22.38 | % 151.56/22.38 | CLOSE: (21) is inconsistent. % 151.56/22.38 | % 151.56/22.38 End of proof % 151.56/22.38 % 151.56/22.38 Sub-proof #300 shows that the following formulas are inconsistent: % 151.56/22.38 ---------------------------------------------------------------- % 151.56/22.38 (1) all_54_12 = all_52_3 % 151.56/22.38 (2) ~ (all_52_3 = e2) % 151.56/22.38 (3) ~ (all_52_3 = e0) % 151.56/22.38 (4) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0 % 151.56/22.38 (5) ~ (all_52_3 = e3) % 151.56/22.38 (6) ~ (all_52_3 = e1) % 151.56/22.38 % 151.56/22.38 Begin of proof % 151.56/22.38 | % 151.56/22.38 | BETA: splitting (4) gives: % 151.56/22.38 | % 151.56/22.38 | Case 1: % 151.56/22.38 | | % 151.56/22.38 | | (7) all_54_12 = e3 % 151.56/22.38 | | % 151.56/22.38 | | REF_CLOSE: (1), (5), (7) are inconsistent by sub-proof #667. % 151.56/22.38 | | % 151.56/22.38 | Case 2: % 151.56/22.38 | | % 151.56/22.38 | | (8) all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0 % 151.56/22.38 | | % 151.56/22.38 | | REF_CLOSE: (1), (2), (3), (6), (8) are inconsistent by sub-proof #615. % 151.56/22.38 | | % 151.56/22.38 | End of split % 151.56/22.38 | % 151.56/22.38 End of proof % 151.56/22.38 % 151.56/22.38 Sub-proof #301 shows that the following formulas are inconsistent: % 151.56/22.38 ---------------------------------------------------------------- % 151.56/22.38 (1) all_58_11 = e3 % 151.56/22.38 (2) all_58_11 = e2 % 151.56/22.38 (3) ~ (e3 = e2) % 151.56/22.38 % 151.56/22.38 Begin of proof % 151.56/22.38 | % 151.56/22.38 | COMBINE_EQS: (1), (2) imply: % 151.56/22.38 | (4) e3 = e2 % 151.56/22.38 | % 151.56/22.38 | SIMP: (4) implies: % 151.56/22.38 | (5) e3 = e2 % 151.56/22.38 | % 151.56/22.38 | REDUCE: (3), (5) imply: % 151.56/22.38 | (6) $false % 151.56/22.38 | % 151.56/22.38 | CLOSE: (6) is inconsistent. % 151.56/22.38 | % 151.56/22.38 End of proof % 151.56/22.38 % 151.56/22.38 Sub-proof #302 shows that the following formulas are inconsistent: % 151.56/22.38 ---------------------------------------------------------------- % 151.56/22.38 (1) ~ (all_6_1 = e2) % 151.56/22.38 (2) op(e3, e3) = e2 % 151.56/22.38 (3) op(e3, e3) = all_6_1 % 151.56/22.38 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 151.56/22.38 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 151.56/22.38 (5) op(e3, e3) = all_56_24 % 151.56/22.38 % 151.56/22.38 Begin of proof % 151.56/22.38 | % 151.56/22.38 | GROUND_INST: instantiating (4) with all_6_1, all_56_24, e3, e3, simplifying % 151.56/22.38 | with (3), (5) gives: % 151.56/22.38 | (6) all_56_24 = all_6_1 % 151.56/22.38 | % 151.56/22.38 | GROUND_INST: instantiating (4) with e2, all_56_24, e3, e3, simplifying with % 151.56/22.38 | (2), (5) gives: % 151.56/22.38 | (7) all_56_24 = e2 % 151.56/22.38 | % 151.56/22.38 | COMBINE_EQS: (6), (7) imply: % 151.56/22.38 | (8) all_6_1 = e2 % 151.56/22.38 | % 151.56/22.38 | SIMP: (8) implies: % 151.56/22.38 | (9) all_6_1 = e2 % 151.56/22.38 | % 151.56/22.38 | REDUCE: (1), (9) imply: % 151.56/22.38 | (10) $false % 151.56/22.38 | % 151.56/22.38 | CLOSE: (10) is inconsistent. % 151.56/22.38 | % 151.56/22.38 End of proof % 151.56/22.38 % 151.56/22.38 Sub-proof #303 shows that the following formulas are inconsistent: % 151.56/22.38 ---------------------------------------------------------------- % 151.56/22.38 (1) all_58_7 = e3 % 151.56/22.38 (2) all_58_7 = e0 % 151.56/22.38 (3) ~ (e3 = e0) % 151.56/22.38 % 151.56/22.38 Begin of proof % 151.56/22.38 | % 151.56/22.38 | COMBINE_EQS: (1), (2) imply: % 151.56/22.38 | (4) e3 = e0 % 151.56/22.38 | % 151.56/22.38 | SIMP: (4) implies: % 151.56/22.38 | (5) e3 = e0 % 151.56/22.38 | % 151.56/22.38 | REDUCE: (3), (5) imply: % 151.56/22.38 | (6) $false % 151.56/22.38 | % 151.56/22.38 | CLOSE: (6) is inconsistent. % 151.56/22.38 | % 151.56/22.38 End of proof % 151.56/22.38 % 151.56/22.38 Sub-proof #304 shows that the following formulas are inconsistent: % 151.56/22.38 ---------------------------------------------------------------- % 151.56/22.38 (1) all_54_0 = all_10_2 % 151.56/22.38 (2) ~ (all_10_2 = e1) % 151.56/22.38 (3) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 151.56/22.38 (4) ~ (all_10_2 = e2) % 151.56/22.38 (5) op(e3, e3) = all_10_2 % 151.56/22.38 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 151.56/22.38 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 151.56/22.38 (7) ~ (all_10_2 = e0) % 151.56/22.38 (8) op(e3, all_10_1) = e1 % 151.56/22.38 (9) op(all_10_2, all_10_2) = all_10_1 % 151.56/22.38 (10) op(e3, all_10_2) = all_56_0 % 151.56/22.38 % 151.56/22.38 Begin of proof % 151.56/22.38 | % 151.56/22.38 | BETA: splitting (3) gives: % 151.56/22.38 | % 151.56/22.38 | Case 1: % 151.56/22.38 | | % 151.56/22.38 | | (11) all_54_0 = e3 % 151.56/22.38 | | % 151.56/22.38 | | COMBINE_EQS: (1), (11) imply: % 151.56/22.38 | | (12) all_10_2 = e3 % 151.56/22.38 | | % 151.56/22.38 | | SIMP: (12) implies: % 151.56/22.38 | | (13) all_10_2 = e3 % 151.56/22.38 | | % 151.56/22.38 | | REDUCE: (9), (13) imply: % 151.56/22.38 | | (14) op(e3, e3) = all_10_1 % 151.56/22.38 | | % 151.56/22.38 | | REDUCE: (10), (13) imply: % 151.56/22.38 | | (15) op(e3, e3) = all_56_0 % 151.56/22.38 | | % 151.56/22.38 | | REDUCE: (5), (13) imply: % 151.56/22.38 | | (16) op(e3, e3) = e3 % 151.56/22.38 | | % 151.56/22.38 | | GROUND_INST: instantiating (6) with all_10_1, all_56_0, e3, e3, simplifying % 151.56/22.38 | | with (14), (15) gives: % 151.56/22.38 | | (17) all_56_0 = all_10_1 % 151.56/22.38 | | % 151.56/22.38 | | GROUND_INST: instantiating (6) with e3, all_56_0, e3, e3, simplifying with % 151.56/22.38 | | (15), (16) gives: % 151.56/22.38 | | (18) all_56_0 = e3 % 151.56/22.38 | | % 151.56/22.38 | | COMBINE_EQS: (17), (18) imply: % 151.56/22.38 | | (19) all_10_1 = e3 % 151.56/22.38 | | % 151.56/22.38 | | REDUCE: (8), (19) imply: % 151.56/22.38 | | (20) op(e3, e3) = e1 % 151.56/22.38 | | % 151.56/22.38 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (20) are inconsistent by % 151.56/22.38 | | sub-proof #305. % 151.56/22.38 | | % 151.56/22.38 | Case 2: % 151.56/22.38 | | % 151.56/22.38 | | (21) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 151.56/22.38 | | % 151.56/22.38 | | REF_CLOSE: (1), (2), (4), (7), (21) are inconsistent by sub-proof #731. % 151.56/22.38 | | % 151.56/22.38 | End of split % 151.56/22.38 | % 151.56/22.38 End of proof % 151.56/22.38 % 151.56/22.38 Sub-proof #305 shows that the following formulas are inconsistent: % 151.56/22.38 ---------------------------------------------------------------- % 151.56/22.38 (1) all_54_0 = all_10_2 % 151.56/22.38 (2) ~ (all_10_2 = e1) % 151.56/22.38 (3) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 151.56/22.38 (4) ~ (all_10_2 = e2) % 151.56/22.38 (5) op(e3, e3) = all_10_2 % 151.56/22.38 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 151.56/22.38 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 151.56/22.38 (7) op(e3, e3) = e1 % 151.56/22.38 (8) ~ (all_10_2 = e0) % 151.56/22.38 % 151.56/22.38 Begin of proof % 151.56/22.38 | % 151.56/22.38 | BETA: splitting (3) gives: % 151.56/22.38 | % 151.56/22.38 | Case 1: % 151.56/22.38 | | % 151.56/22.38 | | (9) all_54_0 = e3 % 151.56/22.38 | | % 151.56/22.38 | | COMBINE_EQS: (1), (9) imply: % 151.56/22.38 | | (10) all_10_2 = e3 % 151.56/22.38 | | % 151.56/22.38 | | SIMP: (10) implies: % 151.56/22.38 | | (11) all_10_2 = e3 % 151.56/22.38 | | % 151.56/22.38 | | REDUCE: (2), (11) imply: % 151.56/22.38 | | (12) ~ (e3 = e1) % 151.56/22.38 | | % 151.56/22.38 | | REF_CLOSE: (5), (6), (7), (11), (12) are inconsistent by sub-proof #306. % 151.56/22.38 | | % 151.56/22.38 | Case 2: % 151.56/22.38 | | % 151.56/22.38 | | (13) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 151.56/22.38 | | % 151.56/22.38 | | REF_CLOSE: (1), (2), (4), (8), (13) are inconsistent by sub-proof #731. % 151.56/22.38 | | % 151.56/22.38 | End of split % 151.56/22.38 | % 151.56/22.38 End of proof % 151.56/22.38 % 151.56/22.38 Sub-proof #306 shows that the following formulas are inconsistent: % 151.56/22.38 ---------------------------------------------------------------- % 151.56/22.38 (1) op(e3, e3) = all_10_2 % 151.56/22.38 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 151.56/22.38 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 151.56/22.38 (3) op(e3, e3) = e1 % 151.56/22.38 (4) ~ (e3 = e1) % 151.56/22.38 (5) all_10_2 = e3 % 151.56/22.38 % 151.56/22.38 Begin of proof % 151.56/22.38 | % 151.56/22.38 | REDUCE: (1), (5) imply: % 151.56/22.38 | (6) op(e3, e3) = e3 % 151.56/22.38 | % 151.56/22.38 | GROUND_INST: instantiating (2) with e1, e3, e3, e3, simplifying with (3), (6) % 151.56/22.38 | gives: % 151.56/22.38 | (7) e3 = e1 % 151.56/22.38 | % 151.56/22.38 | REDUCE: (4), (7) imply: % 151.56/22.38 | (8) $false % 151.56/22.38 | % 151.56/22.38 | CLOSE: (8) is inconsistent. % 151.56/22.38 | % 151.56/22.38 End of proof % 151.56/22.38 % 151.56/22.38 Sub-proof #307 shows that the following formulas are inconsistent: % 151.56/22.38 ---------------------------------------------------------------- % 151.56/22.38 (1) all_56_11 = all_8_2 % 151.56/22.38 (2) op(e0, all_52_13) = all_56_14 % 151.56/22.38 (3) ~ (all_56_11 = e1) | all_56_13 = e2 % 151.56/22.38 (4) ~ (all_52_11 = all_6_2) % 151.56/22.38 (5) ~ (all_52_4 = all_52_8) % 151.56/22.38 (6) all_56_25 = all_52_3 % 151.56/22.38 (7) ~ (all_52_7 = all_52_11) % 151.56/22.38 (8) ~ (all_52_8 = all_52_9) % 151.56/22.38 (9) all_54_9 = all_52_6 % 151.56/22.38 (10) all_58_6 = all_52_2 % 151.56/22.38 (11) ~ (all_52_1 = all_52_9) % 151.56/22.38 (12) ~ (all_56_31 = e1) | all_56_29 = e0 % 151.56/22.38 (13) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0 % 151.56/22.38 (14) all_54_10 = all_6_2 % 151.56/22.38 (15) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0 % 151.56/22.38 (16) ~ (all_6_1 = e2) % 151.56/22.38 (17) ~ (all_52_13 = all_8_2) % 151.56/22.38 (18) ~ (all_56_21 = e2) | all_56_19 = e1 % 151.56/22.38 (19) all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2 % 151.56/22.38 (20) all_54_0 = all_10_2 % 151.56/22.38 (21) all_54_4 = all_52_1 % 151.56/22.38 (22) ~ (all_52_14 = all_4_2) % 151.56/22.38 (23) ~ (all_8_0 = e1) % 151.56/22.38 (24) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0 % 151.56/22.38 (25) all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2 % 151.56/22.38 (26) ~ (all_52_9 = all_8_2) % 151.56/22.38 (27) all_54_12 = all_52_3 % 151.56/22.38 (28) ~ (all_52_12 = all_52_13) % 151.56/22.38 (29) ~ (all_52_4 = all_52_7) % 151.56/22.38 (30) op(e0, e0) = all_4_2 % 151.56/22.38 (31) all_58_6 = e0 | all_58_7 = e0 | all_58_8 = e0 | all_58_11 = e0 % 151.56/22.38 (32) all_58_4 = all_52_8 % 151.56/22.38 (33) all_54_5 = all_8_2 % 151.56/22.38 (34) ~ (all_52_6 = all_52_14) % 151.56/22.38 (35) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 151.56/22.38 (36) all_54_15 = all_4_2 % 151.56/22.38 (37) all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1 % 151.56/22.38 (38) op(e2, e1) = all_52_9 % 151.56/22.38 (39) all_56_21 = all_6_2 % 151.56/22.38 (40) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 151.56/22.38 (41) op(e3, all_52_1) = all_56_8 % 151.56/22.38 (42) ~ (all_52_7 = all_8_2) % 151.56/22.38 (43) all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2 % 151.56/22.38 (44) all_56_1 = all_10_2 % 151.56/22.38 (45) op(e3, all_10_1) = all_10_0 % 151.56/22.38 (46) all_56_27 = all_52_7 % 151.56/22.38 (47) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0 % 151.56/22.38 (48) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0 % 151.56/22.38 (49) all_58_5 = all_52_9 % 151.56/22.38 (50) all_54_1 = all_52_4 % 151.56/22.38 (51) all_56_17 = all_52_2 % 151.56/22.38 (52) all_58_9 = all_52_12 % 151.56/22.38 (53) op(e0, all_52_14) = all_56_22 % 151.56/22.38 (54) op(e0, e2) = all_52_7 % 151.56/22.38 (55) op(e1, e0) = all_52_14 % 151.56/22.38 (56) all_28_1 = all_6_1 % 151.56/22.38 (57) all_54_14 = all_52_11 % 151.56/22.38 (58) ~ (all_22_0 = e0) | ~ (all_22_2 = e1) % 151.56/22.38 (59) ( ~ (all_56_0 = all_56_1) & ~ (all_56_2 = all_56_3) & ~ (all_56_4 = % 151.56/22.38 all_56_5) & ~ (all_56_6 = all_56_7)) | ( ~ (all_56_8 = all_56_9) & % 151.56/22.38 ~ (all_56_10 = all_56_11) & ~ (all_56_12 = all_56_13) & ~ (all_56_14 % 151.56/22.38 = all_56_15)) | ( ~ (all_56_16 = all_56_17) & ~ (all_56_18 = % 151.56/22.38 all_56_19) & ~ (all_56_20 = all_56_21) & ~ (all_56_22 = % 151.56/22.38 all_56_23)) | ( ~ (all_56_24 = all_56_25) & ~ (all_56_26 = % 151.56/22.38 all_56_27) & ~ (all_56_28 = all_56_29) & ~ (all_56_30 = % 151.56/22.38 all_56_31)) % 151.56/22.38 (60) all_58_1 = all_52_4 % 151.56/22.38 (61) all_58_13 = all_52_7 % 151.56/22.38 (62) op(e2, all_8_2) = all_56_10 % 151.56/22.38 (63) op(e3, e3) = all_10_2 % 151.56/22.38 (64) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0 % 151.56/22.38 (65) all_44_2 = all_4_2 % 151.56/22.38 (66) ~ (all_56_21 = e3) | all_56_17 = e1 % 151.56/22.38 (67) all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2 % 151.56/22.38 (68) all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0 % 151.56/22.38 (69) ~ (e1 = e0) % 151.56/22.38 (70) all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1 % 151.56/22.38 (71) ~ (all_52_1 = all_8_2) % 151.56/22.38 (72) all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2 % 151.56/22.38 (73) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 151.56/22.38 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 151.56/22.38 (74) ~ (all_44_0 = e1) | ~ (all_44_1 = e3) | ~ (all_44_2 = e2) % 151.56/22.38 (75) ~ (all_52_3 = all_10_2) % 151.56/22.38 (76) all_28_0 = all_6_0 % 151.56/22.38 (77) all_54_3 = all_52_12 % 151.56/22.38 (78) all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0 % 151.56/22.38 (79) ~ (all_52_3 = all_52_7) % 151.56/22.38 (80) all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) & % 151.56/22.38 (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0)) % 151.56/22.38 (81) ~ (all_56_11 = e3) | all_56_9 = e2 % 151.56/22.38 (82) all_36_0 = all_6_0 % 151.56/22.38 (83) ~ (all_52_2 = all_52_6) % 151.56/22.38 (84) op(e0, all_4_1) = all_4_0 % 151.56/22.38 (85) all_56_7 = all_52_12 % 151.56/22.38 (86) all_22_0 = all_8_0 % 151.56/22.38 (87) all_46_2 = all_6_2 % 151.56/22.38 (88) op(e2, all_52_7) = all_56_26 % 151.56/22.38 (89) op(e1, e2) = all_52_6 % 151.56/22.38 (90) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0 % 151.56/22.38 (91) all_44_0 = all_4_0 % 151.56/22.38 (92) all_28_2 = all_6_2 % 151.56/22.38 (93) all_56_13 = all_52_9 % 151.56/22.38 (94) op(e2, all_52_6) = all_56_18 % 151.56/22.38 (95) op(e0, e1) = all_52_11 % 151.56/22.38 (96) ~ (all_52_1 = all_52_13) % 151.56/22.38 (97) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0 % 151.56/22.38 (98) op(e1, e3) = all_52_2 % 151.56/22.38 (99) all_26_0 = all_4_0 % 151.56/22.38 (100) all_36_1 = all_6_1 % 151.56/22.38 (101) all_58_8 = all_6_2 % 151.56/22.38 (102) all_54_6 = all_52_9 % 151.56/22.38 (103) ~ (all_52_3 = all_4_2) % 151.56/22.38 (104) ~ (all_52_8 = all_10_2) % 151.56/22.38 (105) all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3 % 151.56/22.38 (106) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0 % 151.56/22.38 (107) ~ (all_56_1 = e0) | all_56_7 = e3 % 151.56/22.38 (108) all_46_0 = all_6_0 % 151.56/22.38 (109) ~ (e2 = e1) % 151.56/22.38 (110) ~ (all_52_9 = all_52_13) % 151.56/22.38 (111) ~ (all_52_2 = all_52_3) % 151.56/22.38 (112) all_26_2 = all_4_2 % 151.56/22.38 (113) op(e2, e3) = all_8_0 % 151.56/22.38 (114) op(e1, all_6_1) = all_6_0 % 151.56/22.38 (115) op(all_4_2, all_4_2) = all_4_1 % 151.56/22.38 (116) ~ (all_36_0 = e0) | ~ (all_36_1 = e3) | ~ (all_36_2 = e2) % 151.56/22.38 (117) all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3 % 151.56/22.38 (118) ~ (all_52_3 = all_52_11) % 151.56/22.38 (119) all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1 % 151.56/22.38 (120) all_58_3 = all_8_2 % 151.56/22.38 (121) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0 % 151.56/22.38 (122) ~ (all_52_11 = all_4_2) % 151.56/22.38 (123) all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1 % 151.56/22.38 (124) ~ (all_52_6 = all_52_7) % 151.56/22.38 (125) op(e1, all_52_8) = all_56_4 % 151.56/22.38 (126) all_56_31 = all_4_2 % 151.56/22.38 (127) all_58_11 = all_52_14 % 151.56/22.38 (128) all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3 % 151.56/22.38 (129) all_36_2 = all_6_2 % 151.56/22.38 (130) ~ (all_52_2 = all_52_14) % 151.56/22.38 (131) ~ (all_52_9 = all_52_11) % 151.56/22.38 (132) all_54_7 = all_52_13 % 151.56/22.38 (133) op(all_6_2, all_6_2) = all_6_1 % 151.56/22.38 (134) all_56_1 = e3 | all_56_11 = e2 | all_56_21 = e1 | all_56_31 = e0 % 151.56/22.38 (135) ~ (all_52_13 = all_4_2) % 151.56/22.38 (136) op(e3, e0) = all_52_12 % 151.56/22.38 (137) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0 % 151.56/22.38 (138) ~ (all_52_8 = all_52_11) % 151.56/22.38 (139) all_54_13 = all_52_7 % 151.56/22.38 (140) all_54_2 = all_52_8 % 151.56/22.38 (141) op(all_8_2, all_8_2) = e3 % 151.56/22.38 (142) op(e3, e2) = all_52_4 % 151.56/22.38 (143) ~ (all_28_0 = e2) | ~ (all_28_1 = e3) | ~ (all_28_2 = e0) % 151.56/22.38 (144) ~ (all_52_13 = all_52_14) % 151.56/22.38 (145) all_56_23 = all_52_14 % 151.56/22.38 (146) all_54_8 = all_52_2 % 151.56/22.38 (147) all_46_1 = all_6_1 % 151.56/22.38 (148) op(e1, e1) = all_6_2 % 151.56/22.38 (149) ~ (all_52_6 = all_8_2) % 151.56/22.38 (150) all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1 % 151.56/22.38 (151) op(e0, e3) = all_52_3 % 151.56/22.38 (152) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0 % 151.56/22.38 (153) all_58_15 = all_4_2 % 151.56/22.38 (154) all_56_29 = all_52_11 % 151.56/22.38 (155) all_58_2 = all_52_1 % 151.56/22.38 (156) ~ (all_52_9 = all_6_2) % 151.56/22.38 (157) all_22_2 = all_8_2 % 151.56/22.38 (158) all_58_7 = all_52_6 % 151.56/22.38 (159) all_58_10 = all_52_13 % 151.56/22.38 (160) ~ (all_26_0 = e1) | ~ (all_26_1 = e2) | ~ (all_26_2 = e3) % 151.56/22.38 (161) op(all_10_2, all_10_2) = all_10_1 % 151.56/22.38 (162) ~ (all_56_11 = e0) | all_56_15 = e2 % 151.56/22.38 (163) all_58_0 = all_10_2 % 151.56/22.39 (164) op(e3, all_52_2) = all_56_16 % 151.56/22.39 (165) op(e1, all_6_2) = all_56_20 % 151.56/22.39 (166) all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1 % 151.56/22.39 (167) op(e2, e3) = all_52_1 % 151.56/22.39 (168) all_58_1 = e0 | all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0 % 151.56/22.39 (169) ~ (all_52_12 = all_52_14) % 151.56/22.39 (170) op(e1, all_52_9) = all_56_12 % 151.56/22.39 (171) op(e3, e1) = all_52_8 % 151.56/22.39 (172) ~ (all_56_31 = e2) | all_56_27 = e0 % 151.56/22.39 (173) ~ (e3 = e1) % 151.56/22.39 (174) all_44_1 = all_4_1 % 151.56/22.39 (175) op(e2, e2) = all_8_2 % 151.56/22.39 (176) ~ (all_52_4 = all_52_12) % 151.56/22.39 (177) op(e2, e0) = all_52_13 % 151.56/22.39 (178) ~ (all_52_2 = all_6_2) % 151.56/22.39 (179) ~ (all_52_8 = all_52_12) % 151.56/22.39 (180) ~ (all_52_1 = all_52_2) % 151.56/22.39 (181) ~ (all_56_21 = e0) | all_56_23 = e1 % 151.56/22.39 (182) op(e0, all_4_2) = all_56_30 % 151.56/22.39 (183) ~ (all_52_6 = all_6_2) % 151.56/22.39 (184) op(e3, all_10_2) = all_56_0 % 151.56/22.39 (185) ~ (all_52_14 = all_6_2) % 151.56/22.39 (186) ~ (e2 = e0) % 151.56/22.39 (187) op(e1, all_52_11) = all_56_28 % 151.56/22.39 (188) all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3 % 151.56/22.39 (189) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0 % 151.56/22.39 (190) ~ (all_52_2 = all_10_2) % 151.56/22.39 (191) ~ (all_52_4 = all_10_2) % 151.56/22.39 (192) ~ (all_46_0 = e2) | ~ (all_46_1 = e0) | ~ (all_46_2 = e3) % 151.56/22.39 (193) all_26_1 = all_4_1 % 151.56/22.39 (194) ~ (all_10_0 = e2) % 151.56/22.39 (195) ~ (all_52_4 = all_8_2) % 151.56/22.39 (196) op(all_8_2, all_8_2) = all_8_1 % 151.56/22.39 (197) op(e3, all_52_3) = all_56_24 % 151.56/22.39 (198) ~ (all_52_4 = all_52_6) % 151.56/22.39 (199) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 151.56/22.39 (200) all_58_14 = all_52_11 % 151.56/22.39 (201) all_56_19 = all_52_6 % 151.56/22.39 (202) ~ (all_52_12 = all_10_2) % 151.56/22.39 (203) ~ (all_4_0 = e2) % 151.56/22.39 (204) ~ (all_4_0 = e3) % 151.56/22.39 (205) all_56_9 = all_52_1 % 151.56/22.39 (206) all_56_15 = all_52_13 % 151.56/22.39 (207) ~ (all_52_1 = all_10_2) % 151.56/22.39 (208) all_58_12 = all_52_3 % 151.56/22.39 (209) all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2 % 151.56/22.39 (210) all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3 % 151.56/22.39 (211) all_54_11 = all_52_14 % 151.56/22.39 (212) ~ (all_56_31 = e3) | all_56_25 = e0 % 151.56/22.39 % 151.56/22.39 Begin of proof % 151.56/22.39 | % 151.56/22.39 | GROUND_INST: instantiating (73) with all_52_1, all_8_0, e3, e2, simplifying % 151.56/22.39 | with (113), (167) gives: % 151.56/22.39 | (213) all_52_1 = all_8_0 % 151.56/22.39 | % 151.56/22.39 | COMBINE_EQS: (21), (213) imply: % 151.56/22.39 | (214) all_54_4 = all_8_0 % 151.56/22.39 | % 151.56/22.39 | COMBINE_EQS: (205), (213) imply: % 151.56/22.39 | (215) all_56_9 = all_8_0 % 151.56/22.39 | % 151.56/22.39 | COMBINE_EQS: (155), (213) imply: % 151.56/22.39 | (216) all_58_2 = all_8_0 % 151.56/22.39 | % 151.56/22.39 | REDUCE: (180), (213) imply: % 151.56/22.39 | (217) ~ (all_52_2 = all_8_0) % 151.56/22.39 | % 151.56/22.39 | SIMP: (217) implies: % 151.56/22.39 | (218) ~ (all_52_2 = all_8_0) % 151.56/22.39 | % 151.56/22.39 | REDUCE: (11), (213) imply: % 151.56/22.39 | (219) ~ (all_52_9 = all_8_0) % 151.56/22.39 | % 151.56/22.39 | SIMP: (219) implies: % 151.56/22.39 | (220) ~ (all_52_9 = all_8_0) % 151.56/22.39 | % 151.56/22.39 | REDUCE: (96), (213) imply: % 151.56/22.39 | (221) ~ (all_52_13 = all_8_0) % 151.56/22.39 | % 151.56/22.39 | SIMP: (221) implies: % 151.56/22.39 | (222) ~ (all_52_13 = all_8_0) % 151.56/22.39 | % 151.56/22.39 | REDUCE: (207), (213) imply: % 151.56/22.39 | (223) ~ (all_10_2 = all_8_0) % 151.56/22.39 | % 151.56/22.39 | SIMP: (223) implies: % 151.56/22.39 | (224) ~ (all_10_2 = all_8_0) % 151.56/22.39 | % 151.56/22.39 | REDUCE: (71), (213) imply: % 151.56/22.39 | (225) ~ (all_8_0 = all_8_2) % 151.56/22.39 | % 151.56/22.39 | REDUCE: (41), (213) imply: % 151.56/22.39 | (226) op(e3, all_8_0) = all_56_8 % 151.56/22.39 | % 151.56/22.39 | BETA: splitting (160) gives: % 151.56/22.39 | % 151.56/22.39 | Case 1: % 151.56/22.39 | | % 151.56/22.39 | | (227) ~ (all_26_0 = e1) % 151.56/22.39 | | % 151.56/22.39 | | REDUCE: (99), (227) imply: % 151.56/22.39 | | (228) ~ (all_4_0 = e1) % 151.56/22.39 | | % 151.56/22.39 | | BETA: splitting (143) gives: % 151.56/22.39 | | % 151.56/22.39 | | Case 1: % 151.56/22.39 | | | % 151.56/22.39 | | | (229) ~ (all_28_0 = e2) % 151.56/22.39 | | | % 151.63/22.39 | | | REDUCE: (76), (229) imply: % 151.63/22.39 | | | (230) ~ (all_6_0 = e2) % 151.63/22.39 | | | % 151.63/22.39 | | | BETA: splitting (116) gives: % 151.63/22.39 | | | % 151.63/22.39 | | | Case 1: % 151.63/22.39 | | | | % 151.63/22.39 | | | | (231) ~ (all_36_1 = e3) % 151.63/22.39 | | | | % 151.63/22.39 | | | | REF_CLOSE: (1), (3), (4), (9), (10), (14), (16), (17), (18), (20), (22), % 151.63/22.39 | | | | (23), (24), (26), (30), (33), (34), (35), (39), (40), (42), % 151.63/22.39 | | | | (44), (47), (49), (51), (53), (55), (58), (61), (62), (63), % 151.63/22.39 | | | | (66), (69), (70), (73), (75), (81), (83), (84), (86), (93), % 151.63/22.39 | | | | (94), (97), (100), (101), (105), (109), (110), (114), (115), % 151.63/22.39 | | | | (120), (121), (124), (126), (127), (130), (132), (133), % 151.63/22.39 | | | | (134), (135), (141), (145), (146), (148), (149), (150), % 151.63/22.39 | | | | (151), (153), (156), (157), (158), (159), (162), (163), % 151.63/22.39 | | | | (165), (175), (178), (181), (182), (183), (185), (189), % 151.63/22.39 | | | | (190), (199), (200), (201), (206), (208), (209), (210), % 151.63/22.39 | | | | (211), (214), (215), (216), (218), (220), (222), (224), % 151.63/22.39 | | | | (225), (228), (230), (231) are inconsistent by sub-proof % 151.63/22.39 | | | | #333. % 151.63/22.39 | | | | % 151.63/22.39 | | | Case 2: % 151.63/22.39 | | | | % 151.63/22.39 | | | | (232) all_36_1 = e3 % 151.63/22.39 | | | | (233) ~ (all_36_0 = e0) | ~ (all_36_2 = e2) % 151.63/22.39 | | | | % 151.63/22.39 | | | | COMBINE_EQS: (100), (232) imply: % 151.63/22.39 | | | | (234) all_6_1 = e3 % 151.63/22.39 | | | | % 151.63/22.39 | | | | SIMP: (234) implies: % 151.63/22.39 | | | | (235) all_6_1 = e3 % 151.63/22.39 | | | | % 151.63/22.39 | | | | REDUCE: (133), (235) imply: % 151.63/22.39 | | | | (236) op(all_6_2, all_6_2) = e3 % 151.63/22.39 | | | | % 151.63/22.39 | | | | REDUCE: (114), (235) imply: % 151.63/22.39 | | | | (237) op(e1, e3) = all_6_0 % 151.63/22.39 | | | | % 151.63/22.39 | | | | GROUND_INST: instantiating (73) with all_52_2, all_6_0, e3, e1, % 151.63/22.39 | | | | simplifying with (98), (237) gives: % 151.63/22.39 | | | | (238) all_52_2 = all_6_0 % 151.63/22.39 | | | | % 151.63/22.39 | | | | COMBINE_EQS: (146), (238) imply: % 151.63/22.39 | | | | (239) all_54_8 = all_6_0 % 151.63/22.39 | | | | % 151.63/22.39 | | | | COMBINE_EQS: (51), (238) imply: % 151.63/22.39 | | | | (240) all_56_17 = all_6_0 % 151.63/22.39 | | | | % 151.63/22.39 | | | | COMBINE_EQS: (10), (238) imply: % 151.63/22.39 | | | | (241) all_58_6 = all_6_0 % 151.63/22.39 | | | | % 151.63/22.39 | | | | REDUCE: (111), (238) imply: % 151.63/22.39 | | | | (242) ~ (all_52_3 = all_6_0) % 151.63/22.39 | | | | % 151.63/22.39 | | | | SIMP: (242) implies: % 151.63/22.39 | | | | (243) ~ (all_52_3 = all_6_0) % 151.63/22.39 | | | | % 151.63/22.39 | | | | REDUCE: (83), (238) imply: % 151.63/22.39 | | | | (244) ~ (all_52_6 = all_6_0) % 151.63/22.39 | | | | % 151.63/22.39 | | | | SIMP: (244) implies: % 151.63/22.39 | | | | (245) ~ (all_52_6 = all_6_0) % 151.63/22.39 | | | | % 151.63/22.39 | | | | REDUCE: (130), (238) imply: % 151.63/22.39 | | | | (246) ~ (all_52_14 = all_6_0) % 151.63/22.39 | | | | % 151.63/22.39 | | | | SIMP: (246) implies: % 151.63/22.39 | | | | (247) ~ (all_52_14 = all_6_0) % 151.63/22.39 | | | | % 151.63/22.39 | | | | REDUCE: (190), (238) imply: % 151.63/22.39 | | | | (248) ~ (all_10_2 = all_6_0) % 151.63/22.39 | | | | % 151.63/22.39 | | | | SIMP: (248) implies: % 151.63/22.39 | | | | (249) ~ (all_10_2 = all_6_0) % 151.63/22.39 | | | | % 151.63/22.39 | | | | REDUCE: (218), (238) imply: % 151.63/22.39 | | | | (250) ~ (all_8_0 = all_6_0) % 151.63/22.39 | | | | % 151.63/22.39 | | | | SIMP: (250) implies: % 151.63/22.39 | | | | (251) ~ (all_8_0 = all_6_0) % 151.63/22.39 | | | | % 151.63/22.39 | | | | REDUCE: (178), (238) imply: % 151.63/22.39 | | | | (252) ~ (all_6_0 = all_6_2) % 151.63/22.39 | | | | % 151.63/22.39 | | | | REDUCE: (164), (238) imply: % 151.63/22.39 | | | | (253) op(e3, all_6_0) = all_56_16 % 151.63/22.39 | | | | % 151.63/22.39 | | | | BETA: splitting (12) gives: % 151.63/22.39 | | | | % 151.63/22.39 | | | | Case 1: % 151.63/22.39 | | | | | % 151.63/22.39 | | | | | (254) ~ (all_56_31 = e1) % 151.63/22.39 | | | | | % 151.63/22.39 | | | | | REDUCE: (126), (254) imply: % 151.63/22.39 | | | | | (255) ~ (all_4_2 = e1) % 151.63/22.39 | | | | | % 151.63/22.39 | | | | | BETA: splitting (212) gives: % 151.63/22.39 | | | | | % 151.63/22.39 | | | | | Case 1: % 151.63/22.39 | | | | | | % 151.63/22.39 | | | | | | (256) ~ (all_56_31 = e3) % 151.63/22.39 | | | | | | % 151.63/22.39 | | | | | | REDUCE: (126), (256) imply: % 151.63/22.39 | | | | | | (257) ~ (all_4_2 = e3) % 151.63/22.39 | | | | | | % 151.63/22.39 | | | | | | BETA: splitting (18) gives: % 151.63/22.39 | | | | | | % 151.63/22.39 | | | | | | Case 1: % 151.63/22.39 | | | | | | | % 151.63/22.39 | | | | | | | (258) ~ (all_56_21 = e2) % 151.63/22.39 | | | | | | | % 151.63/22.39 | | | | | | | REDUCE: (39), (258) imply: % 151.63/22.39 | | | | | | | (259) ~ (all_6_2 = e2) % 151.63/22.39 | | | | | | | % 151.63/22.39 | | | | | | | BETA: splitting (66) gives: % 151.63/22.39 | | | | | | | % 151.63/22.39 | | | | | | | Case 1: % 151.63/22.39 | | | | | | | | % 151.63/22.39 | | | | | | | | (260) ~ (all_56_21 = e3) % 151.63/22.39 | | | | | | | | % 151.63/22.39 | | | | | | | | REDUCE: (39), (260) imply: % 151.63/22.39 | | | | | | | | (261) ~ (all_6_2 = e3) % 151.63/22.39 | | | | | | | | % 151.63/22.39 | | | | | | | | REF_CLOSE: (1), (9), (14), (30), (34), (39), (40), (44), (73), % 151.63/22.39 | | | | | | | | (115), (121), (126), (134), (145), (148), (149), % 151.63/22.39 | | | | | | | | (165), (181), (182), (183), (185), (189), (230), % 151.63/22.39 | | | | | | | | (236), (239), (245), (247), (249), (252), (257), % 151.63/22.39 | | | | | | | | (259), (261) are inconsistent by sub-proof #429. % 151.63/22.39 | | | | | | | | % 151.63/22.39 | | | | | | | Case 2: % 151.63/22.39 | | | | | | | | % 151.63/22.39 | | | | | | | | (262) all_56_21 = e3 % 151.63/22.39 | | | | | | | | (263) all_56_17 = e1 % 151.63/22.39 | | | | | | | | % 151.63/22.39 | | | | | | | | COMBINE_EQS: (240), (263) imply: % 151.63/22.39 | | | | | | | | (264) all_6_0 = e1 % 151.63/22.39 | | | | | | | | % 151.63/22.39 | | | | | | | | COMBINE_EQS: (39), (262) imply: % 151.63/22.39 | | | | | | | | (265) all_6_2 = e3 % 151.63/22.39 | | | | | | | | % 151.63/22.39 | | | | | | | | SIMP: (265) implies: % 151.63/22.39 | | | | | | | | (266) all_6_2 = e3 % 151.63/22.39 | | | | | | | | % 151.63/22.39 | | | | | | | | REDUCE: (245), (264) imply: % 151.63/22.39 | | | | | | | | (267) ~ (all_52_6 = e1) % 151.63/22.39 | | | | | | | | % 151.63/22.39 | | | | | | | | REDUCE: (183), (266) imply: % 151.63/22.39 | | | | | | | | (268) ~ (all_52_6 = e3) % 151.63/22.39 | | | | | | | | % 151.63/22.39 | | | | | | | | REDUCE: (247), (264) imply: % 151.63/22.39 | | | | | | | | (269) ~ (all_52_14 = e1) % 151.63/22.39 | | | | | | | | % 151.63/22.39 | | | | | | | | REDUCE: (185), (266) imply: % 151.63/22.39 | | | | | | | | (270) ~ (all_52_14 = e3) % 151.63/22.39 | | | | | | | | % 151.63/22.39 | | | | | | | | REDUCE: (249), (264) imply: % 151.63/22.39 | | | | | | | | (271) ~ (all_10_2 = e1) % 151.63/22.39 | | | | | | | | % 151.63/22.39 | | | | | | | | REDUCE: (236), (266) imply: % 151.63/22.39 | | | | | | | | (272) op(e3, e3) = e3 % 151.63/22.39 | | | | | | | | % 151.63/22.39 | | | | | | | | GROUND_INST: instantiating (73) with all_10_2, e3, e3, e3, % 151.63/22.39 | | | | | | | | simplifying with (63), (272) gives: % 151.63/22.39 | | | | | | | | (273) all_10_2 = e3 % 151.63/22.39 | | | | | | | | % 151.63/22.39 | | | | | | | | REDUCE: (191), (273) imply: % 151.63/22.39 | | | | | | | | (274) ~ (all_52_4 = e3) % 151.63/22.39 | | | | | | | | % 151.63/22.39 | | | | | | | | REDUCE: (202), (273) imply: % 151.63/22.39 | | | | | | | | (275) ~ (all_52_12 = e3) % 151.63/22.39 | | | | | | | | % 151.63/22.39 | | | | | | | | BETA: splitting (188) gives: % 151.63/22.39 | | | | | | | | % 151.63/22.39 | | | | | | | | Case 1: % 151.63/22.39 | | | | | | | | | % 151.63/22.39 | | | | | | | | | (276) all_58_9 = e3 % 151.63/22.39 | | | | | | | | | % 151.63/22.39 | | | | | | | | | COMBINE_EQS: (52), (276) imply: % 151.63/22.39 | | | | | | | | | (277) all_52_12 = e3 % 151.63/22.39 | | | | | | | | | % 151.63/22.39 | | | | | | | | | REDUCE: (275), (277) imply: % 151.63/22.39 | | | | | | | | | (278) $false % 151.63/22.39 | | | | | | | | | % 151.63/22.39 | | | | | | | | | CLOSE: (278) is inconsistent. % 151.63/22.39 | | | | | | | | | % 151.63/22.39 | | | | | | | | Case 2: % 151.63/22.39 | | | | | | | | | % 151.63/22.39 | | | | | | | | | (279) all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3 % 151.63/22.39 | | | | | | | | | % 151.63/22.39 | | | | | | | | | BETA: splitting (279) gives: % 151.63/22.39 | | | | | | | | | % 151.63/22.39 | | | | | | | | | Case 1: % 151.63/22.39 | | | | | | | | | | % 151.63/22.39 | | | | | | | | | | (280) all_58_10 = e3 % 151.63/22.39 | | | | | | | | | | % 151.63/22.39 | | | | | | | | | | COMBINE_EQS: (159), (280) imply: % 151.63/22.39 | | | | | | | | | | (281) all_52_13 = e3 % 151.63/22.39 | | | | | | | | | | % 151.63/22.39 | | | | | | | | | | REDUCE: (222), (281) imply: % 151.63/22.39 | | | | | | | | | | (282) ~ (all_8_0 = e3) % 151.63/22.39 | | | | | | | | | | % 151.63/22.39 | | | | | | | | | | SIMP: (282) implies: % 151.63/22.39 | | | | | | | | | | (283) ~ (all_8_0 = e3) % 151.63/22.39 | | | | | | | | | | % 151.63/22.39 | | | | | | | | | | REDUCE: (17), (281) imply: % 151.63/22.39 | | | | | | | | | | (284) ~ (all_8_2 = e3) % 151.63/22.39 | | | | | | | | | | % 151.63/22.39 | | | | | | | | | | SIMP: (284) implies: % 151.63/22.39 | | | | | | | | | | (285) ~ (all_8_2 = e3) % 151.63/22.39 | | | | | | | | | | % 151.63/22.39 | | | | | | | | | | BETA: splitting (128) gives: % 151.63/22.39 | | | | | | | | | | % 151.63/22.39 | | | | | | | | | | Case 1: % 151.63/22.39 | | | | | | | | | | | % 151.63/22.39 | | | | | | | | | | | (286) all_58_1 = e3 % 151.63/22.39 | | | | | | | | | | | % 151.63/22.39 | | | | | | | | | | | COMBINE_EQS: (60), (286) imply: % 151.63/22.39 | | | | | | | | | | | (287) all_52_4 = e3 % 151.63/22.39 | | | | | | | | | | | % 151.63/22.39 | | | | | | | | | | | REDUCE: (274), (287) imply: % 151.63/22.39 | | | | | | | | | | | (288) $false % 151.63/22.39 | | | | | | | | | | | % 151.63/22.39 | | | | | | | | | | | CLOSE: (288) is inconsistent. % 151.63/22.39 | | | | | | | | | | | % 151.63/22.39 | | | | | | | | | | Case 2: % 151.63/22.39 | | | | | | | | | | | % 151.63/22.39 | | | | | | | | | | | (289) all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3 % 151.63/22.39 | | | | | | | | | | | % 151.63/22.39 | | | | | | | | | | | BETA: splitting (289) gives: % 151.63/22.39 | | | | | | | | | | | % 151.63/22.39 | | | | | | | | | | | Case 1: % 151.63/22.39 | | | | | | | | | | | | % 151.63/22.39 | | | | | | | | | | | | (290) all_58_3 = e3 % 151.63/22.39 | | | | | | | | | | | | % 151.63/22.39 | | | | | | | | | | | | COMBINE_EQS: (120), (290) imply: % 151.63/22.39 | | | | | | | | | | | | (291) all_8_2 = e3 % 151.63/22.39 | | | | | | | | | | | | % 151.63/22.39 | | | | | | | | | | | | REDUCE: (285), (291) imply: % 151.63/22.39 | | | | | | | | | | | | (292) $false % 151.63/22.39 | | | | | | | | | | | | % 151.63/22.39 | | | | | | | | | | | | CLOSE: (292) is inconsistent. % 151.63/22.39 | | | | | | | | | | | | % 151.63/22.39 | | | | | | | | | | | Case 2: % 151.63/22.39 | | | | | | | | | | | | % 151.63/22.39 | | | | | | | | | | | | (293) all_58_7 = e3 | all_58_13 = e3 % 151.63/22.39 | | | | | | | | | | | | % 151.63/22.39 | | | | | | | | | | | | BETA: splitting (293) gives: % 151.63/22.39 | | | | | | | | | | | | % 151.63/22.39 | | | | | | | | | | | | Case 1: % 151.63/22.39 | | | | | | | | | | | | | % 151.63/22.39 | | | | | | | | | | | | | (294) all_58_7 = e3 % 151.63/22.39 | | | | | | | | | | | | | % 151.63/22.39 | | | | | | | | | | | | | COMBINE_EQS: (158), (294) imply: % 151.63/22.39 | | | | | | | | | | | | | (295) all_52_6 = e3 % 151.63/22.39 | | | | | | | | | | | | | % 151.63/22.39 | | | | | | | | | | | | | REDUCE: (268), (295) imply: % 151.63/22.39 | | | | | | | | | | | | | (296) $false % 151.63/22.39 | | | | | | | | | | | | | % 151.63/22.39 | | | | | | | | | | | | | CLOSE: (296) is inconsistent. % 151.63/22.39 | | | | | | | | | | | | | % 151.63/22.39 | | | | | | | | | | | | Case 2: % 151.63/22.39 | | | | | | | | | | | | | % 151.63/22.39 | | | | | | | | | | | | | (297) all_58_13 = e3 % 151.63/22.39 | | | | | | | | | | | | | % 151.63/22.39 | | | | | | | | | | | | | COMBINE_EQS: (61), (297) imply: % 151.63/22.39 | | | | | | | | | | | | | (298) all_52_7 = e3 % 151.63/22.39 | | | | | | | | | | | | | % 151.63/22.39 | | | | | | | | | | | | | BETA: splitting (37) gives: % 151.63/22.39 | | | | | | | | | | | | | % 151.63/22.39 | | | | | | | | | | | | | Case 1: % 151.63/22.39 | | | | | | | | | | | | | | % 151.63/22.39 | | | | | | | | | | | | | | (299) all_58_9 = e1 % 151.63/22.39 | | | | | | | | | | | | | | % 151.63/22.39 | | | | | | | | | | | | | | COMBINE_EQS: (52), (299) imply: % 151.63/22.39 | | | | | | | | | | | | | | (300) all_52_12 = e1 % 151.63/22.39 | | | | | | | | | | | | | | % 151.63/22.39 | | | | | | | | | | | | | | REDUCE: (176), (300) imply: % 151.63/22.39 | | | | | | | | | | | | | | (301) ~ (all_52_4 = e1) % 151.63/22.39 | | | | | | | | | | | | | | % 151.63/22.39 | | | | | | | | | | | | | | REDUCE: (275), (300) imply: % 151.63/22.39 | | | | | | | | | | | | | | (302) ~ (e3 = e1) % 151.63/22.39 | | | | | | | | | | | | | | % 151.63/22.39 | | | | | | | | | | | | | | BETA: splitting (123) gives: % 151.63/22.39 | | | | | | | | | | | | | | % 151.63/22.39 | | | | | | | | | | | | | | Case 1: % 151.63/22.39 | | | | | | | | | | | | | | | % 151.63/22.39 | | | | | | | | | | | | | | | (303) all_58_1 = e1 % 151.63/22.39 | | | | | | | | | | | | | | | % 151.63/22.39 | | | | | | | | | | | | | | | COMBINE_EQS: (60), (303) imply: % 151.63/22.39 | | | | | | | | | | | | | | | (304) all_52_4 = e1 % 151.63/22.39 | | | | | | | | | | | | | | | % 151.63/22.39 | | | | | | | | | | | | | | | REDUCE: (301), (304) imply: % 151.63/22.39 | | | | | | | | | | | | | | | (305) $false % 151.63/22.39 | | | | | | | | | | | | | | | % 151.63/22.39 | | | | | | | | | | | | | | | CLOSE: (305) is inconsistent. % 151.63/22.39 | | | | | | | | | | | | | | | % 151.63/22.39 | | | | | | | | | | | | | | Case 2: % 151.63/22.39 | | | | | | | | | | | | | | | % 151.63/22.39 | | | | | | | | | | | | | | | (306) all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1 % 151.63/22.39 | | | | | | | | | | | | | | | % 151.63/22.39 | | | | | | | | | | | | | | | BETA: splitting (306) gives: % 151.63/22.39 | | | | | | | | | | | | | | | % 151.63/22.39 | | | | | | | | | | | | | | | Case 1: % 151.63/22.39 | | | | | | | | | | | | | | | | % 151.63/22.39 | | | | | | | | | | | | | | | | (307) all_58_3 = e1 % 151.63/22.39 | | | | | | | | | | | | | | | | % 151.63/22.39 | | | | | | | | | | | | | | | | COMBINE_EQS: (120), (307) imply: % 151.63/22.39 | | | | | | | | | | | | | | | | (308) all_8_2 = e1 % 151.63/22.39 | | | | | | | | | | | | | | | | % 151.63/22.39 | | | | | | | | | | | | | | | | COMBINE_EQS: (157), (308) imply: % 151.63/22.39 | | | | | | | | | | | | | | | | (309) all_22_2 = e1 % 151.63/22.39 | | | | | | | | | | | | | | | | % 151.63/22.39 | | | | | | | | | | | | | | | | COMBINE_EQS: (1), (308) imply: % 151.63/22.39 | | | | | | | | | | | | | | | | (310) all_56_11 = e1 % 151.63/22.39 | | | | | | | | | | | | | | | | % 151.63/22.39 | | | | | | | | | | | | | | | | REF_CLOSE: (3), (23), (58), (78), (86), (93), (97), (214), % 151.63/22.39 | | | | | | | | | | | | | | | | (216), (220), (283), (309), (310) are inconsistent % 151.63/22.39 | | | | | | | | | | | | | | | | by sub-proof #332. % 151.63/22.39 | | | | | | | | | | | | | | | | % 151.63/22.39 | | | | | | | | | | | | | | | Case 2: % 151.63/22.39 | | | | | | | | | | | | | | | | % 151.63/22.39 | | | | | | | | | | | | | | | | (311) all_58_7 = e1 | all_58_13 = e1 % 151.63/22.39 | | | | | | | | | | | | | | | | % 151.63/22.39 | | | | | | | | | | | | | | | | REF_CLOSE: (158), (173), (267), (297), (311) are inconsistent % 151.63/22.39 | | | | | | | | | | | | | | | | by sub-proof #448. % 151.63/22.39 | | | | | | | | | | | | | | | | % 151.63/22.39 | | | | | | | | | | | | | | | End of split % 151.63/22.39 | | | | | | | | | | | | | | | % 151.63/22.39 | | | | | | | | | | | | | | End of split % 151.63/22.39 | | | | | | | | | | | | | | % 151.63/22.39 | | | | | | | | | | | | | Case 2: % 151.63/22.39 | | | | | | | | | | | | | | % 151.63/22.39 | | | | | | | | | | | | | | (312) all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1 % 151.63/22.39 | | | | | | | | | | | | | | % 151.63/22.39 | | | | | | | | | | | | | | REF_CLOSE: (127), (153), (173), (255), (269), (280), (312) % 151.63/22.39 | | | | | | | | | | | | | | are inconsistent by sub-proof #446. % 151.63/22.39 | | | | | | | | | | | | | | % 151.63/22.39 | | | | | | | | | | | | | End of split % 151.63/22.39 | | | | | | | | | | | | | % 151.63/22.39 | | | | | | | | | | | | End of split % 151.63/22.39 | | | | | | | | | | | | % 151.63/22.39 | | | | | | | | | | | End of split % 151.63/22.39 | | | | | | | | | | | % 151.63/22.39 | | | | | | | | | | End of split % 151.63/22.39 | | | | | | | | | | % 151.63/22.39 | | | | | | | | | Case 2: % 151.63/22.39 | | | | | | | | | | % 151.63/22.39 | | | | | | | | | | (313) all_58_11 = e3 | all_58_15 = e3 % 151.63/22.39 | | | | | | | | | | % 151.63/22.39 | | | | | | | | | | REF_CLOSE: (127), (153), (257), (270), (313) are inconsistent % 151.63/22.39 | | | | | | | | | | by sub-proof #331. % 151.63/22.39 | | | | | | | | | | % 151.63/22.39 | | | | | | | | | End of split % 151.63/22.39 | | | | | | | | | % 151.63/22.39 | | | | | | | | End of split % 151.63/22.39 | | | | | | | | % 151.63/22.39 | | | | | | | End of split % 151.63/22.39 | | | | | | | % 151.63/22.39 | | | | | | Case 2: % 151.63/22.39 | | | | | | | % 151.63/22.39 | | | | | | | (314) all_56_21 = e2 % 151.63/22.39 | | | | | | | (315) all_56_19 = e1 % 151.63/22.39 | | | | | | | % 151.63/22.39 | | | | | | | REF_CLOSE: (1), (22), (31), (39), (44), (62), (69), (73), (82), % 151.63/22.39 | | | | | | | (101), (126), (127), (129), (134), (158), (175), (183), % 151.63/22.39 | | | | | | | (186), (189), (196), (201), (233), (236), (239), (241), % 151.63/22.39 | | | | | | | (245), (247), (249), (252), (314), (315) are % 151.63/22.39 | | | | | | | inconsistent by sub-proof #412. % 151.63/22.39 | | | | | | | % 151.63/22.39 | | | | | | End of split % 151.63/22.39 | | | | | | % 151.63/22.39 | | | | | Case 2: % 151.63/22.39 | | | | | | % 151.63/22.39 | | | | | | (316) all_56_31 = e3 % 151.63/22.39 | | | | | | (317) all_56_25 = e0 % 151.63/22.39 | | | | | | % 151.63/22.39 | | | | | | COMBINE_EQS: (6), (317) imply: % 151.63/22.39 | | | | | | (318) all_52_3 = e0 % 151.63/22.39 | | | | | | % 151.63/22.39 | | | | | | SIMP: (318) implies: % 151.63/22.39 | | | | | | (319) all_52_3 = e0 % 151.63/22.39 | | | | | | % 151.63/22.39 | | | | | | COMBINE_EQS: (126), (316) imply: % 151.63/22.39 | | | | | | (320) all_4_2 = e3 % 151.63/22.39 | | | | | | % 151.63/22.39 | | | | | | COMBINE_EQS: (153), (320) imply: % 151.63/22.39 | | | | | | (321) all_58_15 = e3 % 151.63/22.39 | | | | | | % 151.63/22.39 | | | | | | COMBINE_EQS: (208), (319) imply: % 151.63/22.39 | | | | | | (322) all_58_12 = e0 % 151.63/22.39 | | | | | | % 151.63/22.39 | | | | | | REDUCE: (79), (319) imply: % 151.63/22.39 | | | | | | (323) ~ (all_52_7 = e0) % 151.63/22.39 | | | | | | % 151.63/22.39 | | | | | | SIMP: (323) implies: % 151.63/22.39 | | | | | | (324) ~ (all_52_7 = e0) % 151.63/22.39 | | | | | | % 151.63/22.39 | | | | | | REDUCE: (118), (319) imply: % 151.63/22.39 | | | | | | (325) ~ (all_52_11 = e0) % 151.63/22.39 | | | | | | % 151.63/22.39 | | | | | | SIMP: (325) implies: % 151.63/22.39 | | | | | | (326) ~ (all_52_11 = e0) % 151.63/22.39 | | | | | | % 151.63/22.39 | | | | | | REDUCE: (243), (319) imply: % 151.63/22.39 | | | | | | (327) ~ (all_6_0 = e0) % 151.63/22.39 | | | | | | % 151.63/22.39 | | | | | | SIMP: (327) implies: % 151.63/22.39 | | | | | | (328) ~ (all_6_0 = e0) % 151.63/22.39 | | | | | | % 151.63/22.39 | | | | | | REDUCE: (115), (320) imply: % 151.63/22.39 | | | | | | (329) op(e3, e3) = all_4_1 % 151.63/22.39 | | | | | | % 151.63/22.39 | | | | | | REDUCE: (197), (319) imply: % 151.63/22.39 | | | | | | (330) op(e3, e0) = all_56_24 % 151.63/22.39 | | | | | | % 151.63/22.39 | | | | | | REDUCE: (182), (320) imply: % 151.63/22.39 | | | | | | (331) op(e0, e3) = all_56_30 % 151.63/22.39 | | | | | | % 151.63/22.39 | | | | | | REDUCE: (151), (319) imply: % 151.63/22.39 | | | | | | (332) op(e0, e3) = e0 % 151.63/22.39 | | | | | | % 151.63/22.39 | | | | | | GROUND_INST: instantiating (73) with e0, all_56_30, e3, e0, % 151.63/22.39 | | | | | | simplifying with (331), (332) gives: % 151.63/22.39 | | | | | | (333) all_56_30 = e0 % 151.63/22.39 | | | | | | % 151.63/22.39 | | | | | | GROUND_INST: instantiating (73) with all_52_12, all_56_24, e0, e3, % 151.63/22.39 | | | | | | simplifying with (136), (330) gives: % 151.63/22.39 | | | | | | (334) all_56_24 = all_52_12 % 151.63/22.39 | | | | | | % 151.63/22.39 | | | | | | GROUND_INST: instantiating (73) with all_10_2, all_4_1, e3, e3, % 151.63/22.39 | | | | | | simplifying with (63), (329) gives: % 151.63/22.39 | | | | | | (335) all_10_2 = all_4_1 % 151.63/22.39 | | | | | | % 151.63/22.39 | | | | | | COMBINE_EQS: (44), (335) imply: % 151.63/22.39 | | | | | | (336) all_56_1 = all_4_1 % 151.63/22.39 | | | | | | % 151.63/22.39 | | | | | | COMBINE_EQS: (163), (335) imply: % 151.63/22.39 | | | | | | (337) all_58_0 = all_4_1 % 151.63/22.39 | | | | | | % 151.63/22.39 | | | | | | REDUCE: (104), (335) imply: % 151.63/22.39 | | | | | | (338) ~ (all_52_8 = all_4_1) % 151.63/22.39 | | | | | | % 151.63/22.39 | | | | | | REDUCE: (202), (335) imply: % 151.63/22.39 | | | | | | (339) ~ (all_52_12 = all_4_1) % 151.63/22.39 | | | | | | % 151.63/22.39 | | | | | | REDUCE: (249), (335) imply: % 151.63/22.39 | | | | | | (340) ~ (all_6_0 = all_4_1) % 151.63/22.39 | | | | | | % 151.63/22.39 | | | | | | SIMP: (340) implies: % 151.63/22.39 | | | | | | (341) ~ (all_6_0 = all_4_1) % 151.63/22.39 | | | | | | % 151.63/22.39 | | | | | | REDUCE: (161), (335) imply: % 151.63/22.39 | | | | | | (342) op(all_4_1, all_4_1) = all_10_1 % 151.63/22.39 | | | | | | % 151.63/22.39 | | | | | | REDUCE: (184), (335) imply: % 151.63/22.39 | | | | | | (343) op(e3, all_4_1) = all_56_0 % 151.63/22.39 | | | | | | % 151.63/22.39 | | | | | | BETA: splitting (18) gives: % 151.63/22.39 | | | | | | % 151.63/22.39 | | | | | | Case 1: % 151.63/22.39 | | | | | | | % 151.63/22.39 | | | | | | | (344) ~ (all_56_21 = e2) % 151.63/22.39 | | | | | | | % 151.63/22.39 | | | | | | | REDUCE: (39), (344) imply: % 151.63/22.39 | | | | | | | (345) ~ (all_6_2 = e2) % 151.63/22.39 | | | | | | | % 151.63/22.39 | | | | | | | BETA: splitting (181) gives: % 151.63/22.39 | | | | | | | % 151.63/22.39 | | | | | | | Case 1: % 151.63/22.39 | | | | | | | | % 151.63/22.39 | | | | | | | | (346) ~ (all_56_21 = e0) % 151.63/22.39 | | | | | | | | % 151.63/22.39 | | | | | | | | REDUCE: (39), (346) imply: % 151.63/22.39 | | | | | | | | (347) ~ (all_6_2 = e0) % 151.63/22.39 | | | | | | | | % 151.63/22.39 | | | | | | | | BETA: splitting (162) gives: % 151.63/22.39 | | | | | | | | % 151.63/22.39 | | | | | | | | Case 1: % 151.63/22.39 | | | | | | | | | % 151.63/22.39 | | | | | | | | | (348) ~ (all_56_11 = e0) % 151.63/22.39 | | | | | | | | | % 151.63/22.39 | | | | | | | | | REDUCE: (1), (348) imply: % 151.63/22.39 | | | | | | | | | (349) ~ (all_8_2 = e0) % 151.63/22.39 | | | | | | | | | % 151.63/22.39 | | | | | | | | | BETA: splitting (66) gives: % 151.63/22.39 | | | | | | | | | % 151.63/22.39 | | | | | | | | | Case 1: % 151.63/22.39 | | | | | | | | | | % 151.63/22.39 | | | | | | | | | | (350) ~ (all_56_21 = e3) % 151.63/22.39 | | | | | | | | | | % 151.63/22.39 | | | | | | | | | | REDUCE: (39), (350) imply: % 151.63/22.39 | | | | | | | | | | (351) ~ (all_6_2 = e3) % 151.63/22.39 | | | | | | | | | | % 151.63/22.39 | | | | | | | | | | REF_CLOSE: (14), (40), (73), (148), (165), (236), (345), % 151.63/22.39 | | | | | | | | | | (347), (351) are inconsistent by sub-proof #459. % 151.63/22.39 | | | | | | | | | | % 151.63/22.39 | | | | | | | | | Case 2: % 151.63/22.39 | | | | | | | | | | % 151.63/22.39 | | | | | | | | | | (352) all_56_21 = e3 % 151.63/22.39 | | | | | | | | | | (353) all_56_17 = e1 % 151.63/22.39 | | | | | | | | | | % 151.63/22.39 | | | | | | | | | | COMBINE_EQS: (240), (353) imply: % 151.63/22.39 | | | | | | | | | | (354) all_6_0 = e1 % 151.63/22.39 | | | | | | | | | | % 151.63/22.39 | | | | | | | | | | SIMP: (354) implies: % 151.63/22.39 | | | | | | | | | | (355) all_6_0 = e1 % 151.63/22.39 | | | | | | | | | | % 151.63/22.39 | | | | | | | | | | COMBINE_EQS: (39), (352) imply: % 151.63/22.39 | | | | | | | | | | (356) all_6_2 = e3 % 151.63/22.39 | | | | | | | | | | % 151.63/22.39 | | | | | | | | | | SIMP: (356) implies: % 151.63/22.39 | | | | | | | | | | (357) all_6_2 = e3 % 151.63/22.39 | | | | | | | | | | % 151.63/22.39 | | | | | | | | | | COMBINE_EQS: (101), (357) imply: % 151.63/22.39 | | | | | | | | | | (358) all_58_8 = e3 % 151.63/22.39 | | | | | | | | | | % 151.63/22.39 | | | | | | | | | | REDUCE: (245), (355) imply: % 151.63/22.39 | | | | | | | | | | (359) ~ (all_52_6 = e1) % 151.63/22.39 | | | | | | | | | | % 151.63/22.39 | | | | | | | | | | REDUCE: (4), (357) imply: % 151.63/22.39 | | | | | | | | | | (360) ~ (all_52_11 = e3) % 151.63/22.39 | | | | | | | | | | % 151.63/22.39 | | | | | | | | | | REDUCE: (247), (355) imply: % 151.63/22.39 | | | | | | | | | | (361) ~ (all_52_14 = e1) % 151.63/22.39 | | | | | | | | | | % 151.63/22.39 | | | | | | | | | | REDUCE: (185), (357) imply: % 151.63/22.39 | | | | | | | | | | (362) ~ (all_52_14 = e3) % 151.63/22.39 | | | | | | | | | | % 151.63/22.39 | | | | | | | | | | REDUCE: (345), (357) imply: % 151.63/22.39 | | | | | | | | | | (363) ~ (e3 = e2) % 151.63/22.39 | | | | | | | | | | % 151.63/22.39 | | | | | | | | | | REDUCE: (236), (357) imply: % 151.63/22.39 | | | | | | | | | | (364) op(e3, e3) = e3 % 151.63/22.39 | | | | | | | | | | % 151.63/22.39 | | | | | | | | | | REDUCE: (253), (355) imply: % 151.63/22.39 | | | | | | | | | | (365) op(e3, e1) = all_56_16 % 151.63/22.39 | | | | | | | | | | % 151.63/22.39 | | | | | | | | | | GROUND_INST: instantiating (73) with all_52_8, all_56_16, e1, % 151.63/22.39 | | | | | | | | | | e3, simplifying with (171), (365) gives: % 151.63/22.39 | | | | | | | | | | (366) all_56_16 = all_52_8 % 151.63/22.39 | | | | | | | | | | % 151.63/22.39 | | | | | | | | | | GROUND_INST: instantiating (73) with all_4_1, e3, e3, e3, % 151.63/22.39 | | | | | | | | | | simplifying with (329), (364) gives: % 151.63/22.39 | | | | | | | | | | (367) all_4_1 = e3 % 151.63/22.39 | | | | | | | | | | % 151.63/22.39 | | | | | | | | | | COMBINE_EQS: (336), (367) imply: % 151.63/22.39 | | | | | | | | | | (368) all_56_1 = e3 % 151.63/22.39 | | | | | | | | | | % 151.63/22.39 | | | | | | | | | | COMBINE_EQS: (337), (367) imply: % 151.63/22.39 | | | | | | | | | | (369) all_58_0 = e3 % 151.63/22.39 | | | | | | | | | | % 151.63/22.39 | | | | | | | | | | REDUCE: (338), (367) imply: % 151.63/22.39 | | | | | | | | | | (370) ~ (all_52_8 = e3) % 151.63/22.39 | | | | | | | | | | % 151.63/22.39 | | | | | | | | | | REDUCE: (339), (367) imply: % 151.63/22.39 | | | | | | | | | | (371) ~ (all_52_12 = e3) % 151.63/22.39 | | | | | | | | | | % 151.63/22.39 | | | | | | | | | | REDUCE: (342), (367) imply: % 151.63/22.39 | | | | | | | | | | (372) op(e3, e3) = all_10_1 % 151.63/22.39 | | | | | | | | | | % 151.63/22.39 | | | | | | | | | | REDUCE: (343), (367) imply: % 151.63/22.39 | | | | | | | | | | (373) op(e3, e3) = all_56_0 % 151.63/22.39 | | | | | | | | | | % 151.63/22.39 | | | | | | | | | | REDUCE: (84), (367) imply: % 151.63/22.39 | | | | | | | | | | (374) op(e0, e3) = all_4_0 % 151.63/22.39 | | | | | | | | | | % 151.63/22.39 | | | | | | | | | | BETA: splitting (67) gives: % 151.63/22.39 | | | | | | | | | | % 151.63/22.39 | | | | | | | | | | Case 1: % 151.63/22.39 | | | | | | | | | | | % 151.63/22.39 | | | | | | | | | | | (375) all_58_0 = e2 % 151.63/22.39 | | | | | | | | | | | % 151.63/22.39 | | | | | | | | | | | COMBINE_EQS: (369), (375) imply: % 151.63/22.39 | | | | | | | | | | | (376) e3 = e2 % 151.63/22.39 | | | | | | | | | | | % 151.63/22.39 | | | | | | | | | | | REDUCE: (363), (376) imply: % 151.63/22.39 | | | | | | | | | | | (377) $false % 151.63/22.39 | | | | | | | | | | | % 151.63/22.39 | | | | | | | | | | | CLOSE: (377) is inconsistent. % 151.63/22.39 | | | | | | | | | | | % 151.63/22.39 | | | | | | | | | | Case 2: % 151.63/22.39 | | | | | | | | | | | % 151.63/22.39 | | | | | | | | | | | (378) all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2 % 151.63/22.39 | | | | | | | | | | | % 151.63/22.39 | | | | | | | | | | | BETA: splitting (378) gives: % 151.63/22.39 | | | | | | | | | | | % 151.63/22.39 | | | | | | | | | | | Case 1: % 151.63/22.39 | | | | | | | | | | | | % 151.63/22.39 | | | | | | | | | | | | (379) all_58_2 = e2 % 151.63/22.39 | | | | | | | | | | | | % 151.63/22.39 | | | | | | | | | | | | COMBINE_EQS: (216), (379) imply: % 151.63/22.39 | | | | | | | | | | | | (380) all_8_0 = e2 % 151.63/22.39 | | | | | | | | | | | | % 151.63/22.39 | | | | | | | | | | | | COMBINE_EQS: (215), (380) imply: % 151.63/22.39 | | | | | | | | | | | | (381) all_56_9 = e2 % 151.63/22.39 | | | | | | | | | | | | % 151.63/22.39 | | | | | | | | | | | | REDUCE: (220), (380) imply: % 151.63/22.39 | | | | | | | | | | | | (382) ~ (all_52_9 = e2) % 151.63/22.39 | | | | | | | | | | | | % 151.63/22.39 | | | | | | | | | | | | REDUCE: (222), (380) imply: % 151.63/22.39 | | | | | | | | | | | | (383) ~ (all_52_13 = e2) % 151.63/22.39 | | | | | | | | | | | | % 151.63/22.39 | | | | | | | | | | | | REDUCE: (225), (380) imply: % 151.63/22.39 | | | | | | | | | | | | (384) ~ (all_8_2 = e2) % 151.63/22.39 | | | | | | | | | | | | % 151.63/22.39 | | | | | | | | | | | | SIMP: (384) implies: % 151.63/22.39 | | | | | | | | | | | | (385) ~ (all_8_2 = e2) % 151.63/22.39 | | | | | | | | | | | | % 151.63/22.39 | | | | | | | | | | | | REDUCE: (226), (380) imply: % 151.63/22.39 | | | | | | | | | | | | (386) op(e3, e2) = all_56_8 % 151.63/22.39 | | | | | | | | | | | | % 151.63/22.39 | | | | | | | | | | | | BETA: splitting (3) gives: % 151.63/22.39 | | | | | | | | | | | | % 151.63/22.39 | | | | | | | | | | | | Case 1: % 151.63/22.39 | | | | | | | | | | | | | % 151.63/22.39 | | | | | | | | | | | | | (387) ~ (all_56_11 = e1) % 151.63/22.39 | | | | | | | | | | | | | % 151.63/22.39 | | | | | | | | | | | | | REDUCE: (1), (387) imply: % 151.63/22.39 | | | | | | | | | | | | | (388) ~ (all_8_2 = e1) % 151.63/22.39 | | | | | | | | | | | | | % 151.63/22.39 | | | | | | | | | | | | | BETA: splitting (199) gives: % 151.63/22.39 | | | | | | | | | | | | | % 151.63/22.39 | | | | | | | | | | | | | Case 1: % 151.63/22.39 | | | | | | | | | | | | | | % 151.63/22.39 | | | | | | | | | | | | | | (389) all_54_5 = e3 % 151.63/22.39 | | | | | | | | | | | | | | % 151.63/22.39 | | | | | | | | | | | | | | COMBINE_EQS: (33), (389) imply: % 151.63/22.39 | | | | | | | | | | | | | | (390) all_8_2 = e3 % 151.63/22.39 | | | | | | | | | | | | | | % 151.63/22.39 | | | | | | | | | | | | | | COMBINE_EQS: (120), (390) imply: % 151.63/22.39 | | | | | | | | | | | | | | (391) all_58_3 = e3 % 151.63/22.39 | | | | | | | | | | | | | | % 151.63/22.39 | | | | | | | | | | | | | | REDUCE: (195), (390) imply: % 151.63/22.39 | | | | | | | | | | | | | | (392) ~ (all_52_4 = e3) % 151.63/22.39 | | | | | | | | | | | | | | % 151.63/22.39 | | | | | | | | | | | | | | REDUCE: (149), (390) imply: % 151.63/22.39 | | | | | | | | | | | | | | (393) ~ (all_52_6 = e3) % 151.63/22.39 | | | | | | | | | | | | | | % 151.63/22.39 | | | | | | | | | | | | | | REDUCE: (42), (390) imply: % 151.63/22.39 | | | | | | | | | | | | | | (394) ~ (all_52_7 = e3) % 151.63/22.39 | | | | | | | | | | | | | | % 151.63/22.39 | | | | | | | | | | | | | | REDUCE: (26), (390) imply: % 151.63/22.39 | | | | | | | | | | | | | | (395) ~ (all_52_9 = e3) % 151.63/22.39 | | | | | | | | | | | | | | % 151.63/22.39 | | | | | | | | | | | | | | REDUCE: (17), (390) imply: % 151.63/22.39 | | | | | | | | | | | | | | (396) ~ (all_52_13 = e3) % 151.63/22.39 | | | | | | | | | | | | | | % 151.63/22.39 | | | | | | | | | | | | | | REF_CLOSE: (2), (5), (7), (8), (9), (13), (14), (15), (19), % 151.63/22.39 | | | | | | | | | | | | | | (24), (25), (29), (32), (34), (37), (38), (39), % 151.63/22.39 | | | | | | | | | | | | | | (40), (43), (45), (46), (47), (48), (49), (50), % 151.63/22.39 | | | | | | | | | | | | | | (52), (53), (54), (55), (57), (59), (60), (61), % 151.63/22.39 | | | | | | | | | | | | | | (64), (66), (68), (73), (77), (78), (80), (88), % 151.63/22.39 | | | | | | | | | | | | | | (89), (93), (94), (95), (101), (102), (106), % 151.63/22.39 | | | | | | | | | | | | | | (109), (110), (119), (120), (121), (123), (124), % 151.63/22.39 | | | | | | | | | | | | | | (127), (132), (138), (139), (140), (142), (144), % 151.63/22.39 | | | | | | | | | | | | | | (145), (148), (152), (153), (154), (158), (159), % 151.63/22.39 | | | | | | | | | | | | | | (165), (166), (168), (169), (170), (176), (177), % 151.63/22.39 | | | | | | | | | | | | | | (179), (187), (194), (198), (200), (201), (203), % 151.63/22.39 | | | | | | | | | | | | | | (204), (206), (209), (211), (228), (236), (255), % 151.63/22.39 | | | | | | | | | | | | | | (317), (321), (322), (324), (326), (332), (334), % 151.63/22.39 | | | | | | | | | | | | | | (345), (347), (349), (353), (358), (359), (360), % 151.63/22.39 | | | | | | | | | | | | | | (361), (362), (364), (366), (368), (369), (370), % 151.63/22.39 | | | | | | | | | | | | | | (371), (372), (373), (374), (379), (381), (382), % 151.63/22.39 | | | | | | | | | | | | | | (383), (386), (391), (392), (393), (394), (395), % 151.63/22.39 | | | | | | | | | | | | | | (396) are inconsistent by sub-proof #323. % 151.63/22.39 | | | | | | | | | | | | | | % 151.63/22.39 | | | | | | | | | | | | | Case 2: % 151.63/22.39 | | | | | | | | | | | | | | % 151.63/22.39 | | | | | | | | | | | | | | (397) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 151.63/22.39 | | | | | | | | | | | | | | % 151.63/22.39 | | | | | | | | | | | | | | REF_CLOSE: (33), (349), (385), (388), (397) are inconsistent % 151.63/22.39 | | | | | | | | | | | | | | by sub-proof #644. % 151.63/22.39 | | | | | | | | | | | | | | % 151.63/22.39 | | | | | | | | | | | | | End of split % 151.63/22.39 | | | | | | | | | | | | | % 151.63/22.39 | | | | | | | | | | | | Case 2: % 151.63/22.39 | | | | | | | | | | | | | % 151.63/22.39 | | | | | | | | | | | | | (398) all_56_13 = e2 % 151.63/22.39 | | | | | | | | | | | | | % 151.63/22.39 | | | | | | | | | | | | | COMBINE_EQS: (93), (398) imply: % 151.63/22.39 | | | | | | | | | | | | | (399) all_52_9 = e2 % 151.63/22.39 | | | | | | | | | | | | | % 151.63/22.39 | | | | | | | | | | | | | REDUCE: (382), (399) imply: % 151.63/22.39 | | | | | | | | | | | | | (400) $false % 151.63/22.39 | | | | | | | | | | | | | % 151.63/22.39 | | | | | | | | | | | | | CLOSE: (400) is inconsistent. % 151.63/22.39 | | | | | | | | | | | | | % 151.63/22.39 | | | | | | | | | | | | End of split % 151.63/22.39 | | | | | | | | | | | | % 151.63/22.39 | | | | | | | | | | | Case 2: % 151.63/22.39 | | | | | | | | | | | | % 151.63/22.39 | | | | | | | | | | | | (401) all_58_6 = e2 | all_58_12 = e2 % 151.63/22.39 | | | | | | | | | | | | % 151.63/22.39 | | | | | | | | | | | | REF_CLOSE: (186), (230), (241), (322), (401) are inconsistent % 151.63/22.39 | | | | | | | | | | | | by sub-proof #422. % 151.63/22.39 | | | | | | | | | | | | % 151.63/22.39 | | | | | | | | | | | End of split % 151.63/22.39 | | | | | | | | | | | % 151.63/22.40 | | | | | | | | | | End of split % 151.63/22.40 | | | | | | | | | | % 151.63/22.40 | | | | | | | | | End of split % 151.63/22.40 | | | | | | | | | % 151.63/22.40 | | | | | | | | Case 2: % 151.63/22.40 | | | | | | | | | % 151.63/22.40 | | | | | | | | | (402) all_56_15 = e2 % 151.63/22.40 | | | | | | | | | (403) all_56_11 = e0 % 151.63/22.40 | | | | | | | | | % 151.63/22.40 | | | | | | | | | COMBINE_EQS: (1), (403) imply: % 151.63/22.40 | | | | | | | | | (404) all_8_2 = e0 % 151.63/22.40 | | | | | | | | | % 151.63/22.40 | | | | | | | | | COMBINE_EQS: (206), (402) imply: % 151.63/22.40 | | | | | | | | | (405) all_52_13 = e2 % 151.63/22.40 | | | | | | | | | % 151.63/22.40 | | | | | | | | | REF_CLOSE: (1), (17), (23), (30), (39), (44), (49), (69), % 151.63/22.40 | | | | | | | | | (70), (73), (97), (109), (115), (120), (126), % 151.63/22.40 | | | | | | | | | (134), (141), (156), (159), (182), (214), (216), % 151.63/22.40 | | | | | | | | | (222), (224), (225), (404), (405) are inconsistent % 151.63/22.40 | | | | | | | | | by sub-proof #336. % 151.63/22.40 | | | | | | | | | % 151.63/22.40 | | | | | | | | End of split % 151.63/22.40 | | | | | | | | % 151.63/22.40 | | | | | | | Case 2: % 151.63/22.40 | | | | | | | | % 151.63/22.40 | | | | | | | | (406) all_56_23 = e1 % 151.63/22.40 | | | | | | | | (407) all_56_21 = e0 % 151.63/22.40 | | | | | | | | % 151.63/22.40 | | | | | | | | REF_CLOSE: (1), (9), (34), (39), (121), (134), (145), (149), % 151.63/22.40 | | | | | | | | (183), (185), (189), (230), (239), (245), (247), % 151.63/22.40 | | | | | | | | (252), (316), (336), (341), (406), (407) are % 151.63/22.40 | | | | | | | | inconsistent by sub-proof #320. % 151.63/22.40 | | | | | | | | % 151.63/22.40 | | | | | | | End of split % 151.63/22.40 | | | | | | | % 151.63/22.40 | | | | | | Case 2: % 151.63/22.40 | | | | | | | % 151.63/22.40 | | | | | | | (408) all_56_21 = e2 % 151.63/22.40 | | | | | | | (409) all_56_19 = e1 % 151.63/22.40 | | | | | | | % 151.63/22.40 | | | | | | | REF_CLOSE: (1), (22), (31), (39), (44), (62), (69), (73), (101), % 151.63/22.40 | | | | | | | (126), (127), (134), (158), (175), (183), (186), (189), % 151.63/22.40 | | | | | | | (196), (201), (236), (239), (241), (245), (247), (249), % 151.63/22.40 | | | | | | | (252), (328), (408), (409) are inconsistent by % 151.63/22.40 | | | | | | | sub-proof #319. % 151.63/22.40 | | | | | | | % 151.63/22.40 | | | | | | End of split % 151.63/22.40 | | | | | | % 151.63/22.40 | | | | | End of split % 151.63/22.40 | | | | | % 151.63/22.40 | | | | Case 2: % 151.63/22.40 | | | | | % 151.63/22.40 | | | | | (410) all_56_31 = e1 % 151.63/22.40 | | | | | (411) all_56_29 = e0 % 151.63/22.40 | | | | | % 151.63/22.40 | | | | | REF_CLOSE: (1), (4), (14), (18), (22), (27), (31), (39), (40), (44), % 151.63/22.40 | | | | | (62), (66), (73), (82), (84), (90), (101), (115), (118), % 151.63/22.40 | | | | | (122), (126), (127), (129), (134), (148), (151), (154), % 151.63/22.40 | | | | | (158), (165), (175), (183), (189), (196), (201), (203), % 151.63/22.40 | | | | | (204), (233), (236), (239), (240), (241), (243), (245), % 151.63/22.40 | | | | | (247), (249), (252), (410), (411) are inconsistent by % 151.63/22.40 | | | | | sub-proof #316. % 151.63/22.40 | | | | | % 151.63/22.40 | | | | End of split % 151.63/22.40 | | | | % 151.63/22.40 | | | End of split % 151.63/22.40 | | | % 151.63/22.40 | | Case 2: % 151.63/22.40 | | | % 151.63/22.40 | | | (412) all_28_0 = e2 % 151.63/22.40 | | | (413) ~ (all_28_1 = e3) | ~ (all_28_2 = e0) % 151.63/22.40 | | | % 151.63/22.40 | | | COMBINE_EQS: (76), (412) imply: % 151.63/22.40 | | | (414) all_6_0 = e2 % 151.63/22.40 | | | % 151.63/22.40 | | | SIMP: (414) implies: % 151.63/22.40 | | | (415) all_6_0 = e2 % 151.63/22.40 | | | % 151.63/22.40 | | | REF_CLOSE: (1), (4), (7), (12), (14), (16), (18), (20), (27), (30), (32), % 151.63/22.40 | | | (33), (34), (35), (36), (37), (39), (40), (44), (51), (52), % 151.63/22.40 | | | (54), (55), (56), (60), (63), (66), (68), (73), (84), (85), % 151.63/22.40 | | | (87), (90), (92), (98), (106), (107), (108), (109), (111), % 151.63/22.40 | | | (114), (115), (118), (124), (125), (126), (127), (133), (137), % 151.63/22.40 | | | (139), (144), (145), (147), (148), (149), (151), (153), (154), % 151.63/22.40 | | | (159), (162), (163), (165), (172), (173), (175), (178), (181), % 151.63/22.40 | | | (182), (183), (190), (192), (195), (199), (201), (203), (204), % 151.63/22.40 | | | (206), (212), (413), (415) are inconsistent by sub-proof #364. % 151.63/22.40 | | | % 151.63/22.40 | | End of split % 151.63/22.40 | | % 151.63/22.40 | Case 2: % 151.63/22.40 | | % 151.63/22.40 | | (416) all_26_0 = e1 % 151.63/22.40 | | (417) ~ (all_26_1 = e2) | ~ (all_26_2 = e3) % 151.63/22.40 | | % 151.63/22.40 | | COMBINE_EQS: (99), (416) imply: % 151.63/22.40 | | (418) all_4_0 = e1 % 151.63/22.40 | | % 151.63/22.40 | | SIMP: (418) implies: % 151.63/22.40 | | (419) all_4_0 = e1 % 151.63/22.40 | | % 151.63/22.40 | | COMBINE_EQS: (91), (419) imply: % 151.63/22.40 | | (420) all_44_0 = e1 % 151.63/22.40 | | % 151.63/22.40 | | REDUCE: (204), (419) imply: % 151.63/22.40 | | (421) ~ (e3 = e1) % 151.63/22.40 | | % 151.63/22.40 | | REDUCE: (203), (419) imply: % 151.63/22.40 | | (422) ~ (e2 = e1) % 151.63/22.40 | | % 151.63/22.40 | | REDUCE: (84), (419) imply: % 151.63/22.40 | | (423) op(e0, all_4_1) = e1 % 151.63/22.40 | | % 151.63/22.40 | | REF_CLOSE: (1), (3), (4), (6), (7), (9), (10), (12), (14), (16), (17), (18), % 151.63/22.40 | | (19), (20), (22), (23), (24), (25), (26), (27), (30), (31), (32), % 151.63/22.40 | | (33), (34), (35), (36), (37), (39), (40), (42), (44), (46), (47), % 151.63/22.40 | | (49), (51), (52), (54), (55), (56), (58), (60), (61), (62), (63), % 151.63/22.40 | | (65), (66), (67), (68), (69), (70), (72), (73), (74), (75), (76), % 151.63/22.40 | | (79), (81), (82), (83), (84), (85), (86), (87), (90), (92), (93), % 151.63/22.40 | | (94), (97), (98), (100), (101), (103), (104), (105), (106), % 151.63/22.40 | | (107), (108), (109), (110), (111), (112), (114), (115), (116), % 151.63/22.40 | | (117), (118), (120), (121), (122), (124), (125), (126), (127), % 151.63/22.40 | | (129), (130), (131), (132), (133), (134), (135), (137), (138), % 151.63/22.40 | | (139), (141), (143), (144), (145), (146), (147), (148), (149), % 151.63/22.40 | | (151), (153), (154), (156), (157), (158), (159), (162), (163), % 151.63/22.40 | | (165), (172), (173), (174), (175), (178), (179), (181), (182), % 151.63/22.40 | | (183), (185), (186), (189), (190), (192), (193), (195), (196), % 151.63/22.40 | | (199), (200), (201), (203), (204), (206), (208), (210), (211), % 151.63/22.40 | | (212), (214), (215), (216), (218), (220), (222), (224), (225), % 151.63/22.40 | | (417), (420), (423) are inconsistent by sub-proof #308. % 151.63/22.40 | | % 151.63/22.40 | End of split % 151.63/22.40 | % 151.63/22.40 End of proof % 151.63/22.40 % 151.63/22.40 Sub-proof #308 shows that the following formulas are inconsistent: % 151.63/22.40 ---------------------------------------------------------------- % 151.63/22.40 (1) all_56_11 = all_8_2 % 151.63/22.40 (2) ~ (all_56_11 = e1) | all_56_13 = e2 % 151.63/22.40 (3) ~ (all_52_11 = all_6_2) % 151.63/22.40 (4) all_56_25 = all_52_3 % 151.63/22.40 (5) ~ (all_52_7 = all_52_11) % 151.63/22.40 (6) all_54_9 = all_52_6 % 151.63/22.40 (7) all_58_6 = all_52_2 % 151.63/22.40 (8) ~ (all_56_31 = e1) | all_56_29 = e0 % 151.63/22.40 (9) all_54_10 = all_6_2 % 151.63/22.40 (10) ~ (all_6_1 = e2) % 151.63/22.40 (11) ~ (all_52_2 = all_8_0) % 151.63/22.40 (12) ~ (all_52_13 = all_8_2) % 151.63/22.40 (13) ~ (all_56_21 = e2) | all_56_19 = e1 % 151.63/22.40 (14) all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2 % 151.63/22.40 (15) all_54_0 = all_10_2 % 151.63/22.40 (16) ~ (all_52_14 = all_4_2) % 151.63/22.40 (17) ~ (all_8_0 = e1) % 151.63/22.40 (18) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0 % 151.63/22.40 (19) all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2 % 151.63/22.40 (20) ~ (all_52_9 = all_8_2) % 151.63/22.40 (21) all_54_12 = all_52_3 % 151.63/22.40 (22) op(e0, e0) = all_4_2 % 151.63/22.40 (23) ~ (all_52_13 = all_8_0) % 151.63/22.40 (24) all_58_6 = e0 | all_58_7 = e0 | all_58_8 = e0 | all_58_11 = e0 % 151.63/22.40 (25) all_58_4 = all_52_8 % 151.63/22.40 (26) all_54_5 = all_8_2 % 151.63/22.40 (27) ~ (all_52_6 = all_52_14) % 151.63/22.40 (28) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 151.63/22.40 (29) all_54_15 = all_4_2 % 151.63/22.40 (30) all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1 % 151.63/22.40 (31) ~ (all_8_0 = all_8_2) % 151.63/22.40 (32) all_56_21 = all_6_2 % 151.63/22.40 (33) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 151.63/22.40 (34) ~ (all_52_7 = all_8_2) % 151.63/22.40 (35) all_56_1 = all_10_2 % 151.63/22.40 (36) all_56_27 = all_52_7 % 151.63/22.40 (37) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0 % 151.63/22.40 (38) all_58_5 = all_52_9 % 151.63/22.40 (39) all_56_17 = all_52_2 % 151.63/22.40 (40) all_58_9 = all_52_12 % 151.63/22.40 (41) op(e0, e2) = all_52_7 % 151.63/22.40 (42) op(e1, e0) = all_52_14 % 151.63/22.40 (43) all_28_1 = all_6_1 % 151.63/22.40 (44) ~ (all_22_0 = e0) | ~ (all_22_2 = e1) % 151.63/22.40 (45) all_58_1 = all_52_4 % 151.63/22.40 (46) all_58_13 = all_52_7 % 151.63/22.40 (47) op(e2, all_8_2) = all_56_10 % 151.63/22.40 (48) op(e3, e3) = all_10_2 % 151.63/22.40 (49) all_44_2 = all_4_2 % 151.63/22.40 (50) ~ (all_56_21 = e3) | all_56_17 = e1 % 151.63/22.40 (51) all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2 % 151.63/22.40 (52) all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0 % 151.63/22.40 (53) ~ (e1 = e0) % 151.63/22.40 (54) all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1 % 151.63/22.40 (55) all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2 % 151.63/22.40 (56) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 151.63/22.40 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 151.63/22.40 (57) ~ (all_44_0 = e1) | ~ (all_44_1 = e3) | ~ (all_44_2 = e2) % 151.63/22.40 (58) ~ (all_10_2 = all_8_0) % 151.63/22.40 (59) ~ (all_52_3 = all_10_2) % 151.63/22.40 (60) all_28_0 = all_6_0 % 151.63/22.40 (61) ~ (all_52_3 = all_52_7) % 151.63/22.40 (62) ~ (all_26_1 = e2) | ~ (all_26_2 = e3) % 151.63/22.40 (63) ~ (all_56_11 = e3) | all_56_9 = e2 % 151.63/22.40 (64) all_36_0 = all_6_0 % 151.63/22.40 (65) ~ (all_52_2 = all_52_6) % 151.63/22.40 (66) op(e0, all_4_1) = all_4_0 % 151.63/22.40 (67) all_56_7 = all_52_12 % 151.63/22.40 (68) all_22_0 = all_8_0 % 151.63/22.40 (69) all_46_2 = all_6_2 % 151.63/22.40 (70) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0 % 151.63/22.40 (71) all_28_2 = all_6_2 % 151.63/22.40 (72) all_56_13 = all_52_9 % 151.63/22.40 (73) op(e2, all_52_6) = all_56_18 % 151.63/22.40 (74) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0 % 151.63/22.40 (75) op(e1, e3) = all_52_2 % 151.63/22.40 (76) op(e0, all_4_1) = e1 % 151.63/22.40 (77) all_36_1 = all_6_1 % 151.63/22.40 (78) all_58_8 = all_6_2 % 151.63/22.40 (79) ~ (all_52_3 = all_4_2) % 151.63/22.40 (80) ~ (all_52_8 = all_10_2) % 151.63/22.40 (81) all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3 % 151.63/22.40 (82) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0 % 151.63/22.40 (83) ~ (all_56_1 = e0) | all_56_7 = e3 % 151.63/22.40 (84) all_46_0 = all_6_0 % 151.63/22.40 (85) ~ (e2 = e1) % 151.63/22.40 (86) ~ (all_52_9 = all_52_13) % 151.63/22.40 (87) ~ (all_52_2 = all_52_3) % 151.63/22.40 (88) all_26_2 = all_4_2 % 151.63/22.40 (89) op(e1, all_6_1) = all_6_0 % 151.63/22.40 (90) all_56_9 = all_8_0 % 151.63/22.40 (91) op(all_4_2, all_4_2) = all_4_1 % 151.63/22.40 (92) ~ (all_36_0 = e0) | ~ (all_36_1 = e3) | ~ (all_36_2 = e2) % 151.63/22.40 (93) all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3 % 151.63/22.40 (94) ~ (all_52_3 = all_52_11) % 151.63/22.40 (95) all_58_3 = all_8_2 % 151.63/22.40 (96) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0 % 151.63/22.40 (97) ~ (all_52_11 = all_4_2) % 151.63/22.40 (98) ~ (all_52_6 = all_52_7) % 151.63/22.40 (99) op(e1, all_52_8) = all_56_4 % 151.63/22.40 (100) all_56_31 = all_4_2 % 151.63/22.40 (101) all_58_11 = all_52_14 % 151.63/22.40 (102) all_36_2 = all_6_2 % 151.63/22.40 (103) ~ (all_52_2 = all_52_14) % 151.63/22.40 (104) ~ (all_52_9 = all_52_11) % 151.63/22.40 (105) all_54_7 = all_52_13 % 151.63/22.40 (106) op(all_6_2, all_6_2) = all_6_1 % 151.63/22.40 (107) all_56_1 = e3 | all_56_11 = e2 | all_56_21 = e1 | all_56_31 = e0 % 151.63/22.40 (108) ~ (all_52_13 = all_4_2) % 151.63/22.40 (109) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0 % 151.63/22.40 (110) ~ (all_52_8 = all_52_11) % 151.63/22.40 (111) all_54_13 = all_52_7 % 151.63/22.40 (112) op(all_8_2, all_8_2) = e3 % 151.63/22.40 (113) ~ (all_28_0 = e2) | ~ (all_28_1 = e3) | ~ (all_28_2 = e0) % 151.63/22.40 (114) ~ (all_52_13 = all_52_14) % 151.63/22.40 (115) all_56_23 = all_52_14 % 151.63/22.40 (116) all_54_8 = all_52_2 % 151.63/22.40 (117) all_46_1 = all_6_1 % 151.63/22.40 (118) op(e1, e1) = all_6_2 % 151.63/22.40 (119) ~ (all_52_6 = all_8_2) % 151.63/22.40 (120) op(e0, e3) = all_52_3 % 151.63/22.40 (121) all_58_15 = all_4_2 % 151.63/22.40 (122) all_56_29 = all_52_11 % 151.63/22.40 (123) ~ (all_52_9 = all_6_2) % 151.63/22.40 (124) all_22_2 = all_8_2 % 151.63/22.40 (125) all_58_7 = all_52_6 % 151.63/22.40 (126) all_58_10 = all_52_13 % 151.63/22.40 (127) all_58_2 = all_8_0 % 151.63/22.40 (128) ~ (all_56_11 = e0) | all_56_15 = e2 % 151.63/22.40 (129) all_58_0 = all_10_2 % 151.63/22.40 (130) op(e1, all_6_2) = all_56_20 % 151.63/22.40 (131) all_54_4 = all_8_0 % 151.63/22.40 (132) ~ (all_56_31 = e2) | all_56_27 = e0 % 151.63/22.40 (133) ~ (e3 = e1) % 151.63/22.40 (134) all_44_1 = all_4_1 % 151.63/22.40 (135) op(e2, e2) = all_8_2 % 151.63/22.40 (136) ~ (all_52_2 = all_6_2) % 151.63/22.40 (137) ~ (all_52_8 = all_52_12) % 151.63/22.40 (138) ~ (all_56_21 = e0) | all_56_23 = e1 % 151.63/22.40 (139) op(e0, all_4_2) = all_56_30 % 151.63/22.40 (140) ~ (all_52_6 = all_6_2) % 151.63/22.40 (141) ~ (all_52_14 = all_6_2) % 151.63/22.40 (142) ~ (e2 = e0) % 151.63/22.40 (143) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0 % 151.63/22.40 (144) ~ (all_52_2 = all_10_2) % 151.63/22.40 (145) ~ (all_46_0 = e2) | ~ (all_46_1 = e0) | ~ (all_46_2 = e3) % 151.63/22.40 (146) all_44_0 = e1 % 151.63/22.40 (147) all_26_1 = all_4_1 % 151.63/22.40 (148) ~ (all_52_4 = all_8_2) % 151.63/22.40 (149) op(all_8_2, all_8_2) = all_8_1 % 151.63/22.40 (150) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 151.63/22.40 (151) all_58_14 = all_52_11 % 151.63/22.40 (152) all_56_19 = all_52_6 % 151.63/22.40 (153) ~ (all_4_0 = e2) % 151.63/22.40 (154) ~ (all_52_9 = all_8_0) % 151.63/22.40 (155) ~ (all_4_0 = e3) % 151.63/22.40 (156) all_56_15 = all_52_13 % 151.63/22.40 (157) all_58_12 = all_52_3 % 151.63/22.40 (158) all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3 % 151.63/22.40 (159) all_54_11 = all_52_14 % 151.63/22.40 (160) ~ (all_56_31 = e3) | all_56_25 = e0 % 151.63/22.40 % 151.63/22.40 Begin of proof % 151.63/22.40 | % 151.63/22.40 | BETA: splitting (113) gives: % 151.63/22.40 | % 151.63/22.40 | Case 1: % 151.63/22.40 | | % 151.63/22.40 | | (161) ~ (all_28_0 = e2) % 151.63/22.40 | | % 151.63/22.40 | | REDUCE: (60), (161) imply: % 151.63/22.40 | | (162) ~ (all_6_0 = e2) % 151.63/22.40 | | % 151.63/22.40 | | BETA: splitting (92) gives: % 151.63/22.40 | | % 151.63/22.40 | | Case 1: % 151.63/22.40 | | | % 151.63/22.40 | | | (163) ~ (all_36_1 = e3) % 151.63/22.40 | | | % 151.63/22.40 | | | REDUCE: (77), (163) imply: % 151.63/22.40 | | | (164) ~ (all_6_1 = e3) % 151.63/22.40 | | | % 151.63/22.40 | | | BETA: splitting (57) gives: % 151.63/22.40 | | | % 151.63/22.40 | | | Case 1: % 151.63/22.40 | | | | % 151.63/22.40 | | | | (165) ~ (all_44_0 = e1) % 151.63/22.40 | | | | % 151.63/22.40 | | | | REDUCE: (146), (165) imply: % 151.63/22.40 | | | | (166) $false % 151.63/22.40 | | | | % 151.63/22.40 | | | | CLOSE: (166) is inconsistent. % 151.63/22.40 | | | | % 151.63/22.40 | | | Case 2: % 151.63/22.40 | | | | % 151.63/22.40 | | | | (167) ~ (all_44_1 = e3) | ~ (all_44_2 = e2) % 151.63/22.40 | | | | % 151.63/22.40 | | | | BETA: splitting (13) gives: % 151.63/22.40 | | | | % 151.63/22.40 | | | | Case 1: % 151.63/22.40 | | | | | % 151.63/22.40 | | | | | (168) ~ (all_56_21 = e2) % 151.63/22.40 | | | | | % 151.63/22.40 | | | | | REDUCE: (32), (168) imply: % 151.63/22.40 | | | | | (169) ~ (all_6_2 = e2) % 151.63/22.40 | | | | | % 151.63/22.40 | | | | | BETA: splitting (128) gives: % 151.63/22.40 | | | | | % 151.63/22.40 | | | | | Case 1: % 151.63/22.40 | | | | | | % 151.63/22.40 | | | | | | (170) ~ (all_56_11 = e0) % 151.63/22.40 | | | | | | % 151.63/22.40 | | | | | | REDUCE: (1), (170) imply: % 151.63/22.40 | | | | | | (171) ~ (all_8_2 = e0) % 151.63/22.40 | | | | | | % 151.63/22.40 | | | | | | BETA: splitting (50) gives: % 151.63/22.40 | | | | | | % 151.63/22.40 | | | | | | Case 1: % 151.63/22.40 | | | | | | | % 151.63/22.40 | | | | | | | (172) ~ (all_56_21 = e3) % 151.63/22.40 | | | | | | | % 151.63/22.40 | | | | | | | REDUCE: (32), (172) imply: % 151.63/22.40 | | | | | | | (173) ~ (all_6_2 = e3) % 151.63/22.40 | | | | | | | % 151.63/22.40 | | | | | | | BETA: splitting (2) gives: % 151.63/22.40 | | | | | | | % 151.63/22.40 | | | | | | | Case 1: % 151.63/22.40 | | | | | | | | % 151.63/22.40 | | | | | | | | (174) ~ (all_56_11 = e1) % 151.63/22.40 | | | | | | | | % 151.63/22.40 | | | | | | | | REDUCE: (1), (174) imply: % 151.63/22.40 | | | | | | | | (175) ~ (all_8_2 = e1) % 151.63/22.40 | | | | | | | | % 151.63/22.40 | | | | | | | | BETA: splitting (63) gives: % 151.63/22.40 | | | | | | | | % 151.63/22.40 | | | | | | | | Case 1: % 151.63/22.40 | | | | | | | | | % 151.63/22.40 | | | | | | | | | (176) ~ (all_56_11 = e3) % 151.63/22.40 | | | | | | | | | % 151.63/22.40 | | | | | | | | | REDUCE: (1), (176) imply: % 151.63/22.40 | | | | | | | | | (177) ~ (all_8_2 = e3) % 151.63/22.40 | | | | | | | | | % 151.63/22.40 | | | | | | | | | REF_CLOSE: (26), (47), (56), (112), (135), (150), (171), % 151.63/22.40 | | | | | | | | | (175), (177) are inconsistent by sub-proof #347. % 151.63/22.40 | | | | | | | | | % 151.63/22.40 | | | | | | | | Case 2: % 151.63/22.40 | | | | | | | | | % 151.63/22.40 | | | | | | | | | (178) all_56_11 = e3 % 151.63/22.40 | | | | | | | | | (179) all_56_9 = e2 % 151.63/22.40 | | | | | | | | | % 151.63/22.40 | | | | | | | | | COMBINE_EQS: (90), (179) imply: % 151.63/22.40 | | | | | | | | | (180) all_8_0 = e2 % 151.63/22.40 | | | | | | | | | % 151.63/22.40 | | | | | | | | | COMBINE_EQS: (1), (178) imply: % 151.63/22.40 | | | | | | | | | (181) all_8_2 = e3 % 151.63/22.40 | | | | | | | | | % 151.63/22.40 | | | | | | | | | REDUCE: (11), (180) imply: % 151.63/22.40 | | | | | | | | | (182) ~ (all_52_2 = e2) % 151.63/22.40 | | | | | | | | | % 151.63/22.40 | | | | | | | | | REDUCE: (119), (181) imply: % 151.63/22.40 | | | | | | | | | (183) ~ (all_52_6 = e3) % 151.63/22.40 | | | | | | | | | % 151.63/22.40 | | | | | | | | | REDUCE: (34), (181) imply: % 151.63/22.40 | | | | | | | | | (184) ~ (all_52_7 = e3) % 151.63/22.40 | | | | | | | | | % 151.63/22.40 | | | | | | | | | REDUCE: (154), (180) imply: % 151.63/22.40 | | | | | | | | | (185) ~ (all_52_9 = e2) % 151.63/22.40 | | | | | | | | | % 151.63/22.40 | | | | | | | | | REDUCE: (23), (180) imply: % 151.63/22.40 | | | | | | | | | (186) ~ (all_52_13 = e2) % 151.63/22.40 | | | | | | | | | % 151.63/22.40 | | | | | | | | | REDUCE: (58), (180) imply: % 151.63/22.40 | | | | | | | | | (187) ~ (all_10_2 = e2) % 151.63/22.40 | | | | | | | | | % 151.63/22.40 | | | | | | | | | REDUCE: (112), (181) imply: % 151.63/22.40 | | | | | | | | | (188) op(e3, e3) = e3 % 151.63/22.40 | | | | | | | | | % 151.63/22.40 | | | | | | | | | REDUCE: (135), (181) imply: % 151.63/22.40 | | | | | | | | | (189) op(e2, e2) = e3 % 151.63/22.40 | | | | | | | | | % 151.63/22.40 | | | | | | | | | GROUND_INST: instantiating (56) with all_10_2, e3, e3, e3, % 151.63/22.40 | | | | | | | | | simplifying with (48), (188) gives: % 151.63/22.40 | | | | | | | | | (190) all_10_2 = e3 % 151.63/22.40 | | | | | | | | | % 151.63/22.40 | | | | | | | | | REDUCE: (144), (190) imply: % 151.63/22.40 | | | | | | | | | (191) ~ (all_52_2 = e3) % 151.63/22.40 | | | | | | | | | % 151.63/22.40 | | | | | | | | | REDUCE: (59), (190) imply: % 151.63/22.40 | | | | | | | | | (192) ~ (all_52_3 = e3) % 151.63/22.40 | | | | | | | | | % 151.63/22.40 | | | | | | | | | REDUCE: (80), (190) imply: % 151.63/22.40 | | | | | | | | | (193) ~ (all_52_8 = e3) % 151.63/22.40 | | | | | | | | | % 151.63/22.40 | | | | | | | | | REDUCE: (187), (190) imply: % 151.63/22.40 | | | | | | | | | (194) ~ (e3 = e2) % 151.63/22.40 | | | | | | | | | % 151.63/22.40 | | | | | | | | | BETA: splitting (81) gives: % 151.63/22.40 | | | | | | | | | % 151.63/22.40 | | | | | | | | | Case 1: % 151.63/22.40 | | | | | | | | | | % 151.63/22.40 | | | | | | | | | | (195) all_58_6 = e3 % 151.63/22.40 | | | | | | | | | | % 151.63/22.40 | | | | | | | | | | COMBINE_EQS: (7), (195) imply: % 151.63/22.40 | | | | | | | | | | (196) all_52_2 = e3 % 151.63/22.40 | | | | | | | | | | % 151.63/22.40 | | | | | | | | | | REDUCE: (191), (196) imply: % 151.63/22.40 | | | | | | | | | | (197) $false % 151.63/22.40 | | | | | | | | | | % 151.63/22.40 | | | | | | | | | | CLOSE: (197) is inconsistent. % 151.63/22.40 | | | | | | | | | | % 151.63/22.40 | | | | | | | | | Case 2: % 151.63/22.40 | | | | | | | | | | % 151.63/22.40 | | | | | | | | | | (198) all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3 % 151.63/22.40 | | | | | | | | | | % 151.63/22.40 | | | | | | | | | | BETA: splitting (198) gives: % 151.63/22.40 | | | | | | | | | | % 151.63/22.40 | | | | | | | | | | Case 1: % 151.63/22.40 | | | | | | | | | | | % 151.63/22.40 | | | | | | | | | | | (199) all_58_7 = e3 % 151.63/22.40 | | | | | | | | | | | % 151.63/22.40 | | | | | | | | | | | COMBINE_EQS: (125), (199) imply: % 151.63/22.40 | | | | | | | | | | | (200) all_52_6 = e3 % 151.63/22.40 | | | | | | | | | | | % 151.63/22.40 | | | | | | | | | | | REDUCE: (183), (200) imply: % 151.63/22.40 | | | | | | | | | | | (201) $false % 151.63/22.40 | | | | | | | | | | | % 151.63/22.40 | | | | | | | | | | | CLOSE: (201) is inconsistent. % 151.63/22.40 | | | | | | | | | | | % 151.63/22.40 | | | | | | | | | | Case 2: % 151.63/22.40 | | | | | | | | | | | % 151.63/22.40 | | | | | | | | | | | (202) all_58_8 = e3 | all_58_11 = e3 % 151.63/22.40 | | | | | | | | | | | % 151.63/22.40 | | | | | | | | | | | BETA: splitting (202) gives: % 151.63/22.40 | | | | | | | | | | | % 151.63/22.40 | | | | | | | | | | | Case 1: % 151.63/22.40 | | | | | | | | | | | | % 151.63/22.40 | | | | | | | | | | | | (203) all_58_8 = e3 % 151.63/22.40 | | | | | | | | | | | | % 151.63/22.40 | | | | | | | | | | | | COMBINE_EQS: (78), (203) imply: % 151.63/22.40 | | | | | | | | | | | | (204) all_6_2 = e3 % 151.63/22.40 | | | | | | | | | | | | % 151.63/22.40 | | | | | | | | | | | | REDUCE: (173), (204) imply: % 151.63/22.40 | | | | | | | | | | | | (205) $false % 151.63/22.40 | | | | | | | | | | | | % 151.63/22.40 | | | | | | | | | | | | CLOSE: (205) is inconsistent. % 151.63/22.40 | | | | | | | | | | | | % 151.63/22.40 | | | | | | | | | | | Case 2: % 151.63/22.40 | | | | | | | | | | | | % 151.63/22.40 | | | | | | | | | | | | (206) all_58_11 = e3 % 151.63/22.40 | | | | | | | | | | | | % 151.63/22.40 | | | | | | | | | | | | COMBINE_EQS: (101), (206) imply: % 151.63/22.40 | | | | | | | | | | | | (207) all_52_14 = e3 % 151.63/22.40 | | | | | | | | | | | | % 151.63/22.40 | | | | | | | | | | | | REDUCE: (16), (207) imply: % 151.63/22.40 | | | | | | | | | | | | (208) ~ (all_4_2 = e3) % 151.63/22.40 | | | | | | | | | | | | % 151.63/22.40 | | | | | | | | | | | | SIMP: (208) implies: % 151.63/22.40 | | | | | | | | | | | | (209) ~ (all_4_2 = e3) % 151.63/22.40 | | | | | | | | | | | | % 151.63/22.40 | | | | | | | | | | | | BETA: splitting (55) gives: % 151.63/22.40 | | | | | | | | | | | | % 151.63/22.40 | | | | | | | | | | | | Case 1: % 151.63/22.40 | | | | | | | | | | | | | % 151.63/22.40 | | | | | | | | | | | | | (210) all_58_6 = e2 % 151.63/22.40 | | | | | | | | | | | | | % 151.63/22.40 | | | | | | | | | | | | | COMBINE_EQS: (7), (210) imply: % 151.63/22.40 | | | | | | | | | | | | | (211) all_52_2 = e2 % 151.63/22.40 | | | | | | | | | | | | | % 151.63/22.40 | | | | | | | | | | | | | REDUCE: (182), (211) imply: % 151.63/22.40 | | | | | | | | | | | | | (212) $false % 151.63/22.40 | | | | | | | | | | | | | % 151.63/22.40 | | | | | | | | | | | | | CLOSE: (212) is inconsistent. % 151.63/22.40 | | | | | | | | | | | | | % 151.63/22.40 | | | | | | | | | | | | Case 2: % 151.63/22.40 | | | | | | | | | | | | | % 151.63/22.40 | | | | | | | | | | | | | (213) all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2 % 151.63/22.40 | | | | | | | | | | | | | % 151.63/22.40 | | | | | | | | | | | | | BETA: splitting (93) gives: % 151.63/22.40 | | | | | | | | | | | | | % 151.63/22.40 | | | | | | | | | | | | | Case 1: % 151.63/22.40 | | | | | | | | | | | | | | % 151.63/22.40 | | | | | | | | | | | | | | (214) all_58_4 = e3 % 151.63/22.40 | | | | | | | | | | | | | | % 151.63/22.40 | | | | | | | | | | | | | | COMBINE_EQS: (25), (214) imply: % 151.63/22.40 | | | | | | | | | | | | | | (215) all_52_8 = e3 % 151.63/22.40 | | | | | | | | | | | | | | % 151.63/22.40 | | | | | | | | | | | | | | REDUCE: (193), (215) imply: % 151.63/22.40 | | | | | | | | | | | | | | (216) $false % 151.63/22.40 | | | | | | | | | | | | | | % 151.63/22.40 | | | | | | | | | | | | | | CLOSE: (216) is inconsistent. % 151.63/22.40 | | | | | | | | | | | | | | % 151.63/22.40 | | | | | | | | | | | | | Case 2: % 151.63/22.40 | | | | | | | | | | | | | | % 151.63/22.40 | | | | | | | | | | | | | | (217) all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3 % 151.63/22.40 | | | | | | | | | | | | | | % 151.63/22.40 | | | | | | | | | | | | | | BETA: splitting (158) gives: % 151.63/22.40 | | | | | | | | | | | | | | % 151.63/22.40 | | | | | | | | | | | | | | Case 1: % 151.63/22.40 | | | | | | | | | | | | | | | % 151.63/22.40 | | | | | | | | | | | | | | | (218) all_58_12 = e3 % 151.63/22.40 | | | | | | | | | | | | | | | % 151.63/22.40 | | | | | | | | | | | | | | | COMBINE_EQS: (157), (218) imply: % 151.63/22.40 | | | | | | | | | | | | | | | (219) all_52_3 = e3 % 151.63/22.40 | | | | | | | | | | | | | | | % 151.63/22.40 | | | | | | | | | | | | | | | REDUCE: (192), (219) imply: % 151.63/22.40 | | | | | | | | | | | | | | | (220) $false % 151.63/22.40 | | | | | | | | | | | | | | | % 151.63/22.40 | | | | | | | | | | | | | | | CLOSE: (220) is inconsistent. % 151.63/22.40 | | | | | | | | | | | | | | | % 151.63/22.40 | | | | | | | | | | | | | | Case 2: % 151.63/22.40 | | | | | | | | | | | | | | | % 151.63/22.40 | | | | | | | | | | | | | | | (221) all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3 % 151.63/22.40 | | | | | | | | | | | | | | | % 151.63/22.40 | | | | | | | | | | | | | | | BETA: splitting (221) gives: % 151.63/22.40 | | | | | | | | | | | | | | | % 151.63/22.40 | | | | | | | | | | | | | | | Case 1: % 151.63/22.40 | | | | | | | | | | | | | | | | % 151.63/22.40 | | | | | | | | | | | | | | | | (222) all_58_13 = e3 % 151.63/22.40 | | | | | | | | | | | | | | | | % 151.63/22.40 | | | | | | | | | | | | | | | | COMBINE_EQS: (46), (222) imply: % 151.63/22.40 | | | | | | | | | | | | | | | | (223) all_52_7 = e3 % 151.63/22.40 | | | | | | | | | | | | | | | | % 151.63/22.40 | | | | | | | | | | | | | | | | REDUCE: (184), (223) imply: % 151.63/22.40 | | | | | | | | | | | | | | | | (224) $false % 151.63/22.40 | | | | | | | | | | | | | | | | % 151.63/22.40 | | | | | | | | | | | | | | | | CLOSE: (224) is inconsistent. % 151.63/22.40 | | | | | | | | | | | | | | | | % 151.63/22.40 | | | | | | | | | | | | | | | Case 2: % 151.63/22.40 | | | | | | | | | | | | | | | | % 151.63/22.40 | | | | | | | | | | | | | | | | (225) all_58_14 = e3 | all_58_15 = e3 % 151.63/22.40 | | | | | | | | | | | | | | | | % 151.63/22.40 | | | | | | | | | | | | | | | | BETA: splitting (225) gives: % 151.63/22.40 | | | | | | | | | | | | | | | | % 151.63/22.40 | | | | | | | | | | | | | | | | Case 1: % 151.63/22.40 | | | | | | | | | | | | | | | | | % 151.63/22.40 | | | | | | | | | | | | | | | | | (226) all_58_14 = e3 % 151.63/22.40 | | | | | | | | | | | | | | | | | % 151.63/22.40 | | | | | | | | | | | | | | | | | COMBINE_EQS: (151), (226) imply: % 151.63/22.40 | | | | | | | | | | | | | | | | | (227) all_52_11 = e3 % 151.63/22.40 | | | | | | | | | | | | | | | | | % 151.63/22.40 | | | | | | | | | | | | | | | | | SIMP: (227) implies: % 151.63/22.40 | | | | | | | | | | | | | | | | | (228) all_52_11 = e3 % 151.63/22.40 | | | | | | | | | | | | | | | | | % 151.63/22.40 | | | | | | | | | | | | | | | | | REDUCE: (104), (228) imply: % 151.63/22.40 | | | | | | | | | | | | | | | | | (229) ~ (all_52_9 = e3) % 151.63/22.40 | | | | | | | | | | | | | | | | | % 151.63/22.40 | | | | | | | | | | | | | | | | | REDUCE: (3), (228) imply: % 151.63/22.40 | | | | | | | | | | | | | | | | | (230) ~ (all_6_2 = e3) % 151.63/22.40 | | | | | | | | | | | | | | | | | % 151.63/22.40 | | | | | | | | | | | | | | | | | BETA: splitting (213) gives: % 151.63/22.40 | | | | | | | | | | | | | | | | | % 151.63/22.40 | | | | | | | | | | | | | | | | | Case 1: % 151.63/22.40 | | | | | | | | | | | | | | | | | | % 151.63/22.40 | | | | | | | | | | | | | | | | | | (231) all_58_7 = e2 % 151.63/22.40 | | | | | | | | | | | | | | | | | | % 151.63/22.40 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (125), (231) imply: % 151.63/22.40 | | | | | | | | | | | | | | | | | | (232) all_52_6 = e2 % 151.63/22.40 | | | | | | | | | | | | | | | | | | % 151.63/22.40 | | | | | | | | | | | | | | | | | | REDUCE: (140), (232) imply: % 151.63/22.40 | | | | | | | | | | | | | | | | | | (233) ~ (all_6_2 = e2) % 151.63/22.40 | | | | | | | | | | | | | | | | | | % 151.63/22.40 | | | | | | | | | | | | | | | | | | REDUCE: (183), (232) imply: % 151.63/22.40 | | | | | | | | | | | | | | | | | | (234) ~ (e3 = e2) % 151.63/22.40 | | | | | | | | | | | | | | | | | | % 151.63/22.40 | | | | | | | | | | | | | | | | | | REDUCE: (73), (232) imply: % 151.63/22.40 | | | | | | | | | | | | | | | | | | (235) op(e2, e2) = all_56_18 % 151.63/22.40 | | | | | | | | | | | | | | | | | | % 151.63/22.40 | | | | | | | | | | | | | | | | | | BETA: splitting (19) gives: % 151.63/22.40 | | | | | | | | | | | | | | | | | | % 151.63/22.40 | | | | | | | | | | | | | | | | | | Case 1: % 151.63/22.40 | | | | | | | | | | | | | | | | | | | % 151.63/22.40 | | | | | | | | | | | | | | | | | | | (236) all_58_4 = e2 % 151.63/22.40 | | | | | | | | | | | | | | | | | | | % 151.63/22.40 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (25), (236) imply: % 151.63/22.40 | | | | | | | | | | | | | | | | | | | (237) all_52_8 = e2 % 151.63/22.40 | | | | | | | | | | | | | | | | | | | % 151.63/22.40 | | | | | | | | | | | | | | | | | | | REDUCE: (137), (237) imply: % 151.63/22.40 | | | | | | | | | | | | | | | | | | | (238) ~ (all_52_12 = e2) % 151.63/22.40 | | | | | | | | | | | | | | | | | | | % 151.63/22.40 | | | | | | | | | | | | | | | | | | | SIMP: (238) implies: % 151.63/22.40 | | | | | | | | | | | | | | | | | | | (239) ~ (all_52_12 = e2) % 151.63/22.40 | | | | | | | | | | | | | | | | | | | % 151.63/22.40 | | | | | | | | | | | | | | | | | | | BETA: splitting (14) gives: % 151.63/22.40 | | | | | | | | | | | | | | | | | | | % 151.63/22.40 | | | | | | | | | | | | | | | | | | | Case 1: % 151.63/22.40 | | | | | | | | | | | | | | | | | | | | % 151.63/22.40 | | | | | | | | | | | | | | | | | | | | (240) all_58_9 = e2 % 151.63/22.40 | | | | | | | | | | | | | | | | | | | | % 151.63/22.40 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (40), (240) imply: % 151.63/22.40 | | | | | | | | | | | | | | | | | | | | (241) all_52_12 = e2 % 151.63/22.40 | | | | | | | | | | | | | | | | | | | | % 151.63/22.40 | | | | | | | | | | | | | | | | | | | | REDUCE: (239), (241) imply: % 151.63/22.40 | | | | | | | | | | | | | | | | | | | | (242) $false % 151.63/22.40 | | | | | | | | | | | | | | | | | | | | % 151.63/22.40 | | | | | | | | | | | | | | | | | | | | CLOSE: (242) is inconsistent. % 151.63/22.40 | | | | | | | | | | | | | | | | | | | | % 151.63/22.40 | | | | | | | | | | | | | | | | | | | Case 2: % 151.63/22.40 | | | | | | | | | | | | | | | | | | | | % 151.63/22.40 | | | | | | | | | | | | | | | | | | | | (243) all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2 % 151.63/22.40 | | | | | | | | | | | | | | | | | | | | % 151.63/22.40 | | | | | | | | | | | | | | | | | | | | BETA: splitting (243) gives: % 151.63/22.40 | | | | | | | | | | | | | | | | | | | | % 151.63/22.40 | | | | | | | | | | | | | | | | | | | | Case 1: % 151.63/22.40 | | | | | | | | | | | | | | | | | | | | | % 151.63/22.40 | | | | | | | | | | | | | | | | | | | | | (244) all_58_10 = e2 % 151.63/22.40 | | | | | | | | | | | | | | | | | | | | | % 151.63/22.40 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (126), (244) imply: % 151.63/22.40 | | | | | | | | | | | | | | | | | | | | | (245) all_52_13 = e2 % 151.63/22.40 | | | | | | | | | | | | | | | | | | | | | % 151.63/22.40 | | | | | | | | | | | | | | | | | | | | | REDUCE: (186), (245) imply: % 151.63/22.40 | | | | | | | | | | | | | | | | | | | | | (246) $false % 151.63/22.40 | | | | | | | | | | | | | | | | | | | | | % 151.63/22.40 | | | | | | | | | | | | | | | | | | | | | CLOSE: (246) is inconsistent. % 151.63/22.40 | | | | | | | | | | | | | | | | | | | | | % 151.63/22.40 | | | | | | | | | | | | | | | | | | | | Case 2: % 151.63/22.40 | | | | | | | | | | | | | | | | | | | | | % 151.63/22.40 | | | | | | | | | | | | | | | | | | | | | (247) all_58_11 = e2 | all_58_15 = e2 % 151.63/22.40 | | | | | | | | | | | | | | | | | | | | | % 151.63/22.40 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (247) gives: % 151.63/22.40 | | | | | | | | | | | | | | | | | | | | | % 151.63/22.40 | | | | | | | | | | | | | | | | | | | | | Case 1: % 151.63/22.40 | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.40 | | | | | | | | | | | | | | | | | | | | | | (248) all_58_11 = e2 % 151.63/22.40 | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.40 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (206), (248) imply: % 151.63/22.40 | | | | | | | | | | | | | | | | | | | | | | (249) e3 = e2 % 151.63/22.40 | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.40 | | | | | | | | | | | | | | | | | | | | | | SIMP: (249) implies: % 151.63/22.40 | | | | | | | | | | | | | | | | | | | | | | (250) e3 = e2 % 151.63/22.40 | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.40 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (226), (250) imply: % 151.63/22.40 | | | | | | | | | | | | | | | | | | | | | | (251) all_58_14 = e2 % 151.63/22.40 | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.40 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (38), (78), (173), (194), (217), (229), (251) are % 151.63/22.40 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #391. % 151.63/22.40 | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.40 | | | | | | | | | | | | | | | | | | | | | Case 2: % 151.63/22.40 | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.40 | | | | | | | | | | | | | | | | | | | | | | (252) all_58_15 = e2 % 151.63/22.40 | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.40 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (121), (252) imply: % 151.63/22.40 | | | | | | | | | | | | | | | | | | | | | | (253) all_4_2 = e2 % 151.63/22.40 | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.40 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (49), (253) imply: % 151.63/22.40 | | | | | | | | | | | | | | | | | | | | | | (254) all_44_2 = e2 % 151.63/22.40 | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.40 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (91), (253) imply: % 151.63/22.40 | | | | | | | | | | | | | | | | | | | | | | (255) op(e2, e2) = all_4_1 % 151.63/22.40 | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.40 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (167) gives: % 151.63/22.40 | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.40 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 151.63/22.40 | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.40 | | | | | | | | | | | | | | | | | | | | | | | (256) ~ (all_44_1 = e3) % 151.63/22.40 | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.40 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (134), (256) imply: % 151.63/22.40 | | | | | | | | | | | | | | | | | | | | | | | (257) ~ (all_4_1 = e3) % 151.63/22.40 | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.40 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (56) with e3, all_56_18, e2, e2, % 151.63/22.40 | | | | | | | | | | | | | | | | | | | | | | | simplifying with (189), (235) gives: % 151.63/22.40 | | | | | | | | | | | | | | | | | | | | | | | (258) all_56_18 = e3 % 151.63/22.40 | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.41 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (56) with all_4_1, all_56_18, e2, % 151.63/22.41 | | | | | | | | | | | | | | | | | | | | | | | e2, simplifying with (235), (255) gives: % 151.63/22.41 | | | | | | | | | | | | | | | | | | | | | | | (259) all_56_18 = all_4_1 % 151.63/22.41 | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.41 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (258), (259) imply: % 151.63/22.41 | | | | | | | | | | | | | | | | | | | | | | | (260) all_4_1 = e3 % 151.63/22.41 | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.41 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (260) implies: % 151.63/22.41 | | | | | | | | | | | | | | | | | | | | | | | (261) all_4_1 = e3 % 151.63/22.41 | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.41 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (257), (261) imply: % 151.63/22.41 | | | | | | | | | | | | | | | | | | | | | | | (262) $false % 151.63/22.41 | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.41 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (262) is inconsistent. % 151.63/22.41 | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.41 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 151.63/22.41 | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.41 | | | | | | | | | | | | | | | | | | | | | | | (263) ~ (all_44_2 = e2) % 151.63/22.41 | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.41 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (254), (263) imply: % 151.63/22.41 | | | | | | | | | | | | | | | | | | | | | | | (264) $false % 151.63/22.41 | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.41 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (264) is inconsistent. % 151.63/22.41 | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.41 | | | | | | | | | | | | | | | | | | | | | | End of split % 151.63/22.41 | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.41 | | | | | | | | | | | | | | | | | | | | | End of split % 151.63/22.41 | | | | | | | | | | | | | | | | | | | | | % 151.63/22.41 | | | | | | | | | | | | | | | | | | | | End of split % 151.63/22.41 | | | | | | | | | | | | | | | | | | | | % 151.63/22.41 | | | | | | | | | | | | | | | | | | | End of split % 151.63/22.41 | | | | | | | | | | | | | | | | | | | % 151.63/22.41 | | | | | | | | | | | | | | | | | | Case 2: % 151.63/22.41 | | | | | | | | | | | | | | | | | | | % 151.63/22.41 | | | | | | | | | | | | | | | | | | | (265) all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2 % 151.63/22.41 | | | | | | | | | | | | | | | | | | | % 151.63/22.41 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (38), (78), (169), (173), (185), (194), (217), % 151.63/22.41 | | | | | | | | | | | | | | | | | | | (229), (265) are inconsistent by sub-proof #315. % 151.63/22.41 | | | | | | | | | | | | | | | | | | | % 151.63/22.41 | | | | | | | | | | | | | | | | | | End of split % 151.63/22.41 | | | | | | | | | | | | | | | | | | % 151.63/22.41 | | | | | | | | | | | | | | | | | Case 2: % 151.63/22.41 | | | | | | | | | | | | | | | | | | % 151.63/22.41 | | | | | | | | | | | | | | | | | | (266) all_58_8 = e2 | all_58_11 = e2 % 151.63/22.41 | | | | | | | | | | | | | | | | | | % 151.63/22.41 | | | | | | | | | | | | | | | | | | BETA: splitting (266) gives: % 151.63/22.41 | | | | | | | | | | | | | | | | | | % 151.63/22.41 | | | | | | | | | | | | | | | | | | Case 1: % 151.63/22.41 | | | | | | | | | | | | | | | | | | | % 151.63/22.41 | | | | | | | | | | | | | | | | | | | (267) all_58_8 = e2 % 151.63/22.41 | | | | | | | | | | | | | | | | | | | % 151.63/22.41 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (78), (267) imply: % 151.63/22.41 | | | | | | | | | | | | | | | | | | | (268) all_6_2 = e2 % 151.63/22.41 | | | | | | | | | | | | | | | | | | | % 151.63/22.41 | | | | | | | | | | | | | | | | | | | REDUCE: (169), (268) imply: % 151.63/22.41 | | | | | | | | | | | | | | | | | | | (269) $false % 151.63/22.41 | | | | | | | | | | | | | | | | | | | % 151.63/22.41 | | | | | | | | | | | | | | | | | | | CLOSE: (269) is inconsistent. % 151.63/22.41 | | | | | | | | | | | | | | | | | | | % 151.63/22.41 | | | | | | | | | | | | | | | | | | Case 2: % 151.63/22.41 | | | | | | | | | | | | | | | | | | | % 151.63/22.41 | | | | | | | | | | | | | | | | | | | (270) all_58_11 = e2 % 151.63/22.41 | | | | | | | | | | | | | | | | | | | % 151.63/22.41 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (206), (270) imply: % 151.63/22.41 | | | | | | | | | | | | | | | | | | | (271) e3 = e2 % 151.63/22.41 | | | | | | | | | | | | | | | | | | | % 151.63/22.41 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (226), (271) imply: % 151.63/22.41 | | | | | | | | | | | | | | | | | | | (272) all_58_14 = e2 % 151.63/22.41 | | | | | | | | | | | | | | | | | | | % 151.63/22.41 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (38), (78), (173), (194), (217), (229), (272) are % 151.63/22.41 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #391. % 151.63/22.41 | | | | | | | | | | | | | | | | | | | % 151.63/22.41 | | | | | | | | | | | | | | | | | | End of split % 151.63/22.41 | | | | | | | | | | | | | | | | | | % 151.63/22.41 | | | | | | | | | | | | | | | | | End of split % 151.63/22.41 | | | | | | | | | | | | | | | | | % 151.63/22.41 | | | | | | | | | | | | | | | | Case 2: % 151.63/22.41 | | | | | | | | | | | | | | | | | % 151.63/22.41 | | | | | | | | | | | | | | | | | (273) all_58_15 = e3 % 151.63/22.41 | | | | | | | | | | | | | | | | | % 151.63/22.41 | | | | | | | | | | | | | | | | | COMBINE_EQS: (121), (273) imply: % 151.63/22.41 | | | | | | | | | | | | | | | | | (274) all_4_2 = e3 % 151.63/22.41 | | | | | | | | | | | | | | | | | % 151.63/22.41 | | | | | | | | | | | | | | | | | REDUCE: (209), (274) imply: % 151.63/22.41 | | | | | | | | | | | | | | | | | (275) $false % 151.63/22.41 | | | | | | | | | | | | | | | | | % 151.63/22.41 | | | | | | | | | | | | | | | | | CLOSE: (275) is inconsistent. % 151.63/22.41 | | | | | | | | | | | | | | | | | % 151.63/22.41 | | | | | | | | | | | | | | | | End of split % 151.63/22.41 | | | | | | | | | | | | | | | | % 151.63/22.41 | | | | | | | | | | | | | | | End of split % 151.63/22.41 | | | | | | | | | | | | | | | % 151.63/22.41 | | | | | | | | | | | | | | End of split % 151.63/22.41 | | | | | | | | | | | | | | % 151.63/22.41 | | | | | | | | | | | | | End of split % 151.63/22.41 | | | | | | | | | | | | | % 151.63/22.41 | | | | | | | | | | | | End of split % 151.63/22.41 | | | | | | | | | | | | % 151.63/22.41 | | | | | | | | | | | End of split % 151.63/22.41 | | | | | | | | | | | % 151.63/22.41 | | | | | | | | | | End of split % 151.63/22.41 | | | | | | | | | | % 151.63/22.41 | | | | | | | | | End of split % 151.63/22.41 | | | | | | | | | % 151.63/22.41 | | | | | | | | End of split % 151.63/22.41 | | | | | | | | % 151.63/22.41 | | | | | | | Case 2: % 151.63/22.41 | | | | | | | | % 151.63/22.41 | | | | | | | | (276) all_56_13 = e2 % 151.63/22.41 | | | | | | | | (277) all_56_11 = e1 % 151.63/22.41 | | | | | | | | % 151.63/22.41 | | | | | | | | REF_CLOSE: (1), (12), (20), (23), (31), (32), (35), (37), (44), % 151.63/22.41 | | | | | | | | (56), (58), (68), (72), (74), (86), (100), (105), % 151.63/22.41 | | | | | | | | (107), (108), (112), (118), (124), (130), (131), % 151.63/22.41 | | | | | | | | (154), (173), (276), (277) are inconsistent by % 151.63/22.41 | | | | | | | | sub-proof #340. % 151.63/22.41 | | | | | | | | % 151.63/22.41 | | | | | | | End of split % 151.63/22.41 | | | | | | | % 151.63/22.41 | | | | | | Case 2: % 151.63/22.41 | | | | | | | % 151.63/22.41 | | | | | | | (278) all_56_21 = e3 % 151.63/22.41 | | | | | | | (279) all_56_17 = e1 % 151.63/22.41 | | | | | | | % 151.63/22.41 | | | | | | | REF_CLOSE: (1), (10), (15), (16), (18), (28), (32), (35), (39), % 151.63/22.41 | | | | | | | (42), (47), (48), (56), (89), (100), (103), (106), % 151.63/22.41 | | | | | | | (107), (112), (135), (136), (141), (144), (159), (162), % 151.63/22.41 | | | | | | | (164), (169), (278), (279) are inconsistent by % 151.63/22.41 | | | | | | | sub-proof #339. % 151.63/22.41 | | | | | | | % 151.63/22.41 | | | | | | End of split % 151.63/22.41 | | | | | | % 151.63/22.41 | | | | | Case 2: % 151.63/22.41 | | | | | | % 151.63/22.41 | | | | | | (280) all_56_15 = e2 % 151.63/22.41 | | | | | | (281) all_56_11 = e0 % 151.63/22.41 | | | | | | % 151.63/22.41 | | | | | | COMBINE_EQS: (1), (281) imply: % 151.63/22.41 | | | | | | (282) all_8_2 = e0 % 151.63/22.41 | | | | | | % 151.63/22.41 | | | | | | COMBINE_EQS: (156), (280) imply: % 151.63/22.41 | | | | | | (283) all_52_13 = e2 % 151.63/22.41 | | | | | | % 151.63/22.41 | | | | | | REF_CLOSE: (1), (12), (17), (22), (23), (31), (32), (35), (38), % 151.63/22.41 | | | | | | (53), (54), (56), (58), (74), (85), (91), (95), (100), % 151.63/22.41 | | | | | | (107), (112), (123), (126), (127), (131), (139), (282), % 151.63/22.41 | | | | | | (283) are inconsistent by sub-proof #336. % 151.63/22.41 | | | | | | % 151.63/22.41 | | | | | End of split % 151.63/22.41 | | | | | % 151.63/22.41 | | | | Case 2: % 151.63/22.41 | | | | | % 151.63/22.41 | | | | | (284) all_56_21 = e2 % 151.63/22.41 | | | | | (285) all_56_19 = e1 % 151.63/22.41 | | | | | % 151.63/22.41 | | | | | COMBINE_EQS: (152), (285) imply: % 151.63/22.41 | | | | | (286) all_52_6 = e1 % 151.63/22.41 | | | | | % 151.63/22.41 | | | | | COMBINE_EQS: (32), (284) imply: % 151.63/22.41 | | | | | (287) all_6_2 = e2 % 151.63/22.41 | | | | | % 151.63/22.41 | | | | | SIMP: (287) implies: % 151.63/22.41 | | | | | (288) all_6_2 = e2 % 151.63/22.41 | | | | | % 151.63/22.41 | | | | | REDUCE: (119), (286) imply: % 151.63/22.41 | | | | | (289) ~ (all_8_2 = e1) % 151.63/22.41 | | | | | % 151.63/22.41 | | | | | SIMP: (289) implies: % 151.63/22.41 | | | | | (290) ~ (all_8_2 = e1) % 151.63/22.41 | | | | | % 151.63/22.41 | | | | | REDUCE: (140), (286), (288) imply: % 151.63/22.41 | | | | | (291) ~ (e2 = e1) % 151.63/22.41 | | | | | % 151.63/22.41 | | | | | REDUCE: (106), (288) imply: % 151.63/22.41 | | | | | (292) op(e2, e2) = all_6_1 % 151.63/22.41 | | | | | % 151.63/22.41 | | | | | REF_CLOSE: (1), (10), (12), (17), (22), (23), (26), (31), (32), (35), % 151.63/22.41 | | | | | (38), (54), (56), (58), (74), (85), (91), (95), (100), % 151.63/22.41 | | | | | (107), (112), (123), (126), (127), (128), (131), (135), % 151.63/22.41 | | | | | (139), (150), (156), (164), (290), (292) are inconsistent % 151.63/22.41 | | | | | by sub-proof #335. % 151.63/22.41 | | | | | % 151.63/22.41 | | | | End of split % 151.63/22.41 | | | | % 151.63/22.41 | | | End of split % 151.63/22.41 | | | % 151.63/22.41 | | Case 2: % 151.63/22.41 | | | % 151.63/22.41 | | | (293) all_36_1 = e3 % 151.63/22.41 | | | (294) ~ (all_36_0 = e0) | ~ (all_36_2 = e2) % 151.63/22.41 | | | % 151.63/22.41 | | | COMBINE_EQS: (77), (293) imply: % 151.63/22.41 | | | (295) all_6_1 = e3 % 151.63/22.41 | | | % 151.63/22.41 | | | REDUCE: (106), (295) imply: % 151.63/22.41 | | | (296) op(all_6_2, all_6_2) = e3 % 151.63/22.41 | | | % 151.63/22.41 | | | REDUCE: (89), (295) imply: % 151.63/22.41 | | | (297) op(e1, e3) = all_6_0 % 151.63/22.41 | | | % 151.63/22.41 | | | GROUND_INST: instantiating (56) with all_52_2, all_6_0, e3, e1, % 151.63/22.41 | | | simplifying with (75), (297) gives: % 151.63/22.41 | | | (298) all_52_2 = all_6_0 % 151.63/22.41 | | | % 151.63/22.41 | | | COMBINE_EQS: (116), (298) imply: % 151.63/22.41 | | | (299) all_54_8 = all_6_0 % 151.63/22.41 | | | % 151.63/22.41 | | | COMBINE_EQS: (39), (298) imply: % 151.63/22.41 | | | (300) all_56_17 = all_6_0 % 151.63/22.41 | | | % 151.63/22.41 | | | COMBINE_EQS: (7), (298) imply: % 151.63/22.41 | | | (301) all_58_6 = all_6_0 % 151.63/22.41 | | | % 151.63/22.41 | | | REDUCE: (87), (298) imply: % 151.63/22.41 | | | (302) ~ (all_52_3 = all_6_0) % 151.63/22.41 | | | % 151.63/22.41 | | | SIMP: (302) implies: % 151.63/22.41 | | | (303) ~ (all_52_3 = all_6_0) % 151.63/22.41 | | | % 151.63/22.41 | | | REDUCE: (65), (298) imply: % 151.63/22.41 | | | (304) ~ (all_52_6 = all_6_0) % 151.63/22.41 | | | % 151.63/22.41 | | | SIMP: (304) implies: % 151.63/22.41 | | | (305) ~ (all_52_6 = all_6_0) % 151.63/22.41 | | | % 151.63/22.41 | | | REDUCE: (103), (298) imply: % 151.63/22.41 | | | (306) ~ (all_52_14 = all_6_0) % 151.63/22.41 | | | % 151.63/22.41 | | | SIMP: (306) implies: % 151.63/22.41 | | | (307) ~ (all_52_14 = all_6_0) % 151.63/22.41 | | | % 151.63/22.41 | | | REDUCE: (144), (298) imply: % 151.63/22.41 | | | (308) ~ (all_10_2 = all_6_0) % 151.63/22.41 | | | % 151.63/22.41 | | | SIMP: (308) implies: % 151.63/22.41 | | | (309) ~ (all_10_2 = all_6_0) % 151.63/22.41 | | | % 151.63/22.41 | | | REDUCE: (11), (298) imply: % 151.63/22.41 | | | (310) ~ (all_8_0 = all_6_0) % 151.63/22.41 | | | % 151.63/22.41 | | | SIMP: (310) implies: % 151.63/22.41 | | | (311) ~ (all_8_0 = all_6_0) % 151.63/22.41 | | | % 151.63/22.41 | | | REDUCE: (136), (298) imply: % 151.63/22.41 | | | (312) ~ (all_6_0 = all_6_2) % 151.63/22.41 | | | % 151.63/22.41 | | | BETA: splitting (8) gives: % 151.63/22.41 | | | % 151.63/22.41 | | | Case 1: % 151.63/22.41 | | | | % 151.63/22.41 | | | | (313) ~ (all_56_31 = e1) % 151.63/22.41 | | | | % 151.63/22.41 | | | | REDUCE: (100), (313) imply: % 151.63/22.41 | | | | (314) ~ (all_4_2 = e1) % 151.63/22.41 | | | | % 151.63/22.41 | | | | BETA: splitting (13) gives: % 151.63/22.41 | | | | % 151.63/22.41 | | | | Case 1: % 151.63/22.41 | | | | | % 151.63/22.41 | | | | | (315) ~ (all_56_21 = e2) % 151.63/22.41 | | | | | % 151.63/22.41 | | | | | REDUCE: (32), (315) imply: % 151.63/22.41 | | | | | (316) ~ (all_6_2 = e2) % 151.63/22.41 | | | | | % 151.63/22.41 | | | | | BETA: splitting (160) gives: % 151.63/22.41 | | | | | % 151.63/22.41 | | | | | Case 1: % 151.63/22.41 | | | | | | % 151.63/22.41 | | | | | | (317) ~ (all_56_31 = e3) % 151.63/22.41 | | | | | | % 151.63/22.41 | | | | | | REDUCE: (100), (317) imply: % 151.63/22.41 | | | | | | (318) ~ (all_4_2 = e3) % 151.63/22.41 | | | | | | % 151.63/22.41 | | | | | | REF_CLOSE: (1), (6), (9), (13), (16), (21), (22), (24), (27), (29), % 151.63/22.41 | | | | | | (32), (33), (35), (36), (47), (48), (50), (56), (59), % 151.63/22.41 | | | | | | (61), (64), (70), (76), (78), (79), (91), (96), (98), % 151.63/22.41 | | | | | | (100), (101), (102), (107), (109), (115), (118), (119), % 151.63/22.41 | | | | | | (120), (125), (130), (132), (135), (138), (139), (140), % 151.63/22.41 | | | | | | (141), (143), (149), (152), (162), (294), (296), (299), % 151.63/22.41 | | | | | | (300), (301), (303), (305), (307), (309), (312), (314), % 151.63/22.41 | | | | | | (318) are inconsistent by sub-proof #310. % 151.63/22.41 | | | | | | % 151.63/22.41 | | | | | Case 2: % 151.63/22.41 | | | | | | % 151.63/22.41 | | | | | | (319) all_56_31 = e3 % 151.63/22.41 | | | | | | (320) all_56_25 = e0 % 151.63/22.41 | | | | | | % 151.63/22.41 | | | | | | COMBINE_EQS: (4), (320) imply: % 151.63/22.41 | | | | | | (321) all_52_3 = e0 % 151.63/22.41 | | | | | | % 151.63/22.41 | | | | | | SIMP: (321) implies: % 151.63/22.41 | | | | | | (322) all_52_3 = e0 % 151.63/22.41 | | | | | | % 151.63/22.41 | | | | | | COMBINE_EQS: (100), (319) imply: % 151.63/22.41 | | | | | | (323) all_4_2 = e3 % 151.63/22.41 | | | | | | % 151.63/22.41 | | | | | | COMBINE_EQS: (88), (323) imply: % 151.63/22.41 | | | | | | (324) all_26_2 = e3 % 151.63/22.41 | | | | | | % 151.63/22.41 | | | | | | COMBINE_EQS: (157), (322) imply: % 151.63/22.41 | | | | | | (325) all_58_12 = e0 % 151.63/22.41 | | | | | | % 151.63/22.41 | | | | | | REDUCE: (303), (322) imply: % 151.63/22.41 | | | | | | (326) ~ (all_6_0 = e0) % 151.63/22.41 | | | | | | % 151.63/22.41 | | | | | | SIMP: (326) implies: % 151.63/22.41 | | | | | | (327) ~ (all_6_0 = e0) % 151.63/22.41 | | | | | | % 151.63/22.41 | | | | | | REDUCE: (91), (323) imply: % 151.63/22.41 | | | | | | (328) op(e3, e3) = all_4_1 % 151.63/22.41 | | | | | | % 151.63/22.41 | | | | | | REDUCE: (139), (323) imply: % 151.63/22.41 | | | | | | (329) op(e0, e3) = all_56_30 % 151.63/22.41 | | | | | | % 151.63/22.41 | | | | | | REDUCE: (120), (322) imply: % 151.63/22.41 | | | | | | (330) op(e0, e3) = e0 % 151.63/22.41 | | | | | | % 151.63/22.41 | | | | | | BETA: splitting (62) gives: % 151.63/22.41 | | | | | | % 151.63/22.41 | | | | | | Case 1: % 151.63/22.41 | | | | | | | % 151.63/22.41 | | | | | | | (331) ~ (all_26_1 = e2) % 151.63/22.41 | | | | | | | % 151.63/22.41 | | | | | | | REDUCE: (147), (331) imply: % 151.63/22.41 | | | | | | | (332) ~ (all_4_1 = e2) % 151.63/22.41 | | | | | | | % 151.63/22.41 | | | | | | | GROUND_INST: instantiating (56) with e0, all_56_30, e3, e0, % 151.63/22.41 | | | | | | | simplifying with (329), (330) gives: % 151.63/22.41 | | | | | | | (333) all_56_30 = e0 % 151.63/22.41 | | | | | | | % 151.63/22.41 | | | | | | | GROUND_INST: instantiating (56) with all_10_2, all_4_1, e3, e3, % 151.63/22.41 | | | | | | | simplifying with (48), (328) gives: % 151.63/22.41 | | | | | | | (334) all_10_2 = all_4_1 % 151.63/22.41 | | | | | | | % 151.63/22.41 | | | | | | | COMBINE_EQS: (129), (334) imply: % 151.63/22.41 | | | | | | | (335) all_58_0 = all_4_1 % 151.63/22.41 | | | | | | | % 151.63/22.41 | | | | | | | REDUCE: (309), (334) imply: % 151.63/22.41 | | | | | | | (336) ~ (all_6_0 = all_4_1) % 151.63/22.41 | | | | | | | % 151.63/22.41 | | | | | | | SIMP: (336) implies: % 151.63/22.41 | | | | | | | (337) ~ (all_6_0 = all_4_1) % 151.63/22.41 | | | | | | | % 151.63/22.41 | | | | | | | BETA: splitting (51) gives: % 151.63/22.41 | | | | | | | % 151.63/22.41 | | | | | | | Case 1: % 151.63/22.41 | | | | | | | | % 151.63/22.41 | | | | | | | | (338) all_58_0 = e2 % 151.63/22.41 | | | | | | | | % 151.63/22.41 | | | | | | | | COMBINE_EQS: (335), (338) imply: % 151.63/22.41 | | | | | | | | (339) all_4_1 = e2 % 151.63/22.41 | | | | | | | | % 151.63/22.41 | | | | | | | | REDUCE: (332), (339) imply: % 151.63/22.41 | | | | | | | | (340) $false % 151.63/22.41 | | | | | | | | % 151.63/22.41 | | | | | | | | CLOSE: (340) is inconsistent. % 151.63/22.41 | | | | | | | | % 151.63/22.41 | | | | | | | Case 2: % 151.63/22.41 | | | | | | | | % 151.63/22.41 | | | | | | | | (341) all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2 % 151.63/22.41 | | | | | | | | % 151.63/22.41 | | | | | | | | BETA: splitting (341) gives: % 151.63/22.41 | | | | | | | | % 151.63/22.41 | | | | | | | | Case 1: % 151.63/22.41 | | | | | | | | | % 151.63/22.41 | | | | | | | | | (342) all_58_2 = e2 % 151.63/22.41 | | | | | | | | | % 151.63/22.41 | | | | | | | | | COMBINE_EQS: (127), (342) imply: % 151.63/22.41 | | | | | | | | | (343) all_8_0 = e2 % 151.63/22.41 | | | | | | | | | % 151.63/22.41 | | | | | | | | | REDUCE: (154), (343) imply: % 151.63/22.41 | | | | | | | | | (344) ~ (all_52_9 = e2) % 151.63/22.41 | | | | | | | | | % 151.63/22.41 | | | | | | | | | REDUCE: (23), (343) imply: % 151.63/22.41 | | | | | | | | | (345) ~ (all_52_13 = e2) % 151.63/22.41 | | | | | | | | | % 151.63/22.41 | | | | | | | | | REDUCE: (31), (343) imply: % 151.63/22.41 | | | | | | | | | (346) ~ (all_8_2 = e2) % 151.63/22.41 | | | | | | | | | % 151.63/22.41 | | | | | | | | | SIMP: (346) implies: % 151.63/22.41 | | | | | | | | | (347) ~ (all_8_2 = e2) % 151.63/22.41 | | | | | | | | | % 151.63/22.41 | | | | | | | | | REDUCE: (311), (343) imply: % 151.63/22.41 | | | | | | | | | (348) ~ (all_6_0 = e2) % 151.63/22.41 | | | | | | | | | % 151.63/22.41 | | | | | | | | | BETA: splitting (128) gives: % 151.63/22.41 | | | | | | | | | % 151.63/22.41 | | | | | | | | | Case 1: % 151.63/22.41 | | | | | | | | | | % 151.63/22.41 | | | | | | | | | | (349) ~ (all_56_11 = e0) % 151.63/22.41 | | | | | | | | | | % 151.63/22.41 | | | | | | | | | | REDUCE: (1), (349) imply: % 151.63/22.41 | | | | | | | | | | (350) ~ (all_8_2 = e0) % 151.63/22.41 | | | | | | | | | | % 151.63/22.41 | | | | | | | | | | BETA: splitting (2) gives: % 151.63/22.41 | | | | | | | | | | % 151.63/22.41 | | | | | | | | | | Case 1: % 151.63/22.41 | | | | | | | | | | | % 151.63/22.41 | | | | | | | | | | | (351) ~ (all_56_11 = e1) % 151.63/22.41 | | | | | | | | | | | % 151.63/22.41 | | | | | | | | | | | REDUCE: (1), (351) imply: % 151.63/22.41 | | | | | | | | | | | (352) ~ (all_8_2 = e1) % 151.63/22.41 | | | | | | | | | | | % 151.63/22.41 | | | | | | | | | | | BETA: splitting (150) gives: % 151.63/22.41 | | | | | | | | | | | % 151.63/22.41 | | | | | | | | | | | Case 1: % 151.63/22.41 | | | | | | | | | | | | % 151.63/22.41 | | | | | | | | | | | | (353) all_54_5 = e3 % 151.63/22.41 | | | | | | | | | | | | % 151.63/22.41 | | | | | | | | | | | | COMBINE_EQS: (26), (353) imply: % 151.63/22.41 | | | | | | | | | | | | (354) all_8_2 = e3 % 151.63/22.41 | | | | | | | | | | | | % 151.63/22.41 | | | | | | | | | | | | SIMP: (354) implies: % 151.63/22.41 | | | | | | | | | | | | (355) all_8_2 = e3 % 151.63/22.41 | | | | | | | | | | | | % 151.63/22.41 | | | | | | | | | | | | REDUCE: (112), (355) imply: % 151.63/22.41 | | | | | | | | | | | | (356) op(e3, e3) = e3 % 151.63/22.41 | | | | | | | | | | | | % 151.63/22.41 | | | | | | | | | | | | GROUND_INST: instantiating (56) with all_4_1, e3, e3, e3, % 151.63/22.41 | | | | | | | | | | | | simplifying with (328), (356) gives: % 151.63/22.41 | | | | | | | | | | | | (357) all_4_1 = e3 % 151.63/22.41 | | | | | | | | | | | | % 151.63/22.41 | | | | | | | | | | | | REDUCE: (337), (357) imply: % 151.63/22.41 | | | | | | | | | | | | (358) ~ (all_6_0 = e3) % 151.63/22.41 | | | | | | | | | | | | % 151.63/22.41 | | | | | | | | | | | | REDUCE: (76), (357) imply: % 151.63/22.41 | | | | | | | | | | | | (359) op(e0, e3) = e1 % 151.63/22.41 | | | | | | | | | | | | % 151.63/22.41 | | | | | | | | | | | | BETA: splitting (143) gives: % 151.63/22.41 | | | | | | | | | | | | % 151.63/22.41 | | | | | | | | | | | | Case 1: % 151.63/22.41 | | | | | | | | | | | | | % 151.63/22.41 | | | | | | | | | | | | | (360) all_54_8 = e3 % 151.63/22.41 | | | | | | | | | | | | | % 151.63/22.41 | | | | | | | | | | | | | REF_CLOSE: (299), (358), (360) are inconsistent by sub-proof % 151.63/22.41 | | | | | | | | | | | | | #420. % 151.63/22.41 | | | | | | | | | | | | | % 151.63/22.41 | | | | | | | | | | | | Case 2: % 151.63/22.41 | | | | | | | | | | | | | % 151.63/22.41 | | | | | | | | | | | | | (361) all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0 % 151.63/22.41 | | | | | | | | | | | | | % 151.63/22.41 | | | | | | | | | | | | | BETA: splitting (361) gives: % 151.63/22.41 | | | | | | | | | | | | | % 151.63/22.41 | | | | | | | | | | | | | Case 1: % 151.63/22.41 | | | | | | | | | | | | | | % 151.63/22.41 | | | | | | | | | | | | | | (362) all_54_8 = e2 % 151.63/22.41 | | | | | | | | | | | | | | % 151.63/22.41 | | | | | | | | | | | | | | REF_CLOSE: (162), (299), (362) are inconsistent by sub-proof % 151.63/22.41 | | | | | | | | | | | | | | #453. % 151.63/22.41 | | | | | | | | | | | | | | % 151.63/22.41 | | | | | | | | | | | | | Case 2: % 151.63/22.41 | | | | | | | | | | | | | | % 151.63/22.41 | | | | | | | | | | | | | | (363) all_54_8 = e1 | all_54_8 = e0 % 151.63/22.41 | | | | | | | | | | | | | | % 151.63/22.41 | | | | | | | | | | | | | | BETA: splitting (363) gives: % 151.63/22.41 | | | | | | | | | | | | | | % 151.63/22.41 | | | | | | | | | | | | | | Case 1: % 151.63/22.41 | | | | | | | | | | | | | | | % 151.63/22.41 | | | | | | | | | | | | | | | (364) all_54_8 = e1 % 151.63/22.41 | | | | | | | | | | | | | | | % 151.63/22.41 | | | | | | | | | | | | | | | COMBINE_EQS: (299), (364) imply: % 151.63/22.41 | | | | | | | | | | | | | | | (365) all_6_0 = e1 % 151.63/22.41 | | | | | | | | | | | | | | | % 151.63/22.41 | | | | | | | | | | | | | | | SIMP: (365) implies: % 151.63/22.41 | | | | | | | | | | | | | | | (366) all_6_0 = e1 % 151.63/22.41 | | | | | | | | | | | | | | | % 151.63/22.41 | | | | | | | | | | | | | | | COMBINE_EQS: (300), (366) imply: % 151.63/22.41 | | | | | | | | | | | | | | | (367) all_56_17 = e1 % 151.63/22.41 | | | | | | | | | | | | | | | % 151.63/22.41 | | | | | | | | | | | | | | | REDUCE: (307), (366) imply: % 151.63/22.41 | | | | | | | | | | | | | | | (368) ~ (all_52_14 = e1) % 151.63/22.41 | | | | | | | | | | | | | | | % 151.63/22.41 | | | | | | | | | | | | | | | BETA: splitting (138) gives: % 151.63/22.41 | | | | | | | | | | | | | | | % 151.63/22.41 | | | | | | | | | | | | | | | Case 1: % 151.63/22.41 | | | | | | | | | | | | | | | | % 151.63/22.41 | | | | | | | | | | | | | | | | (369) ~ (all_56_21 = e0) % 151.63/22.41 | | | | | | | | | | | | | | | | % 151.63/22.41 | | | | | | | | | | | | | | | | REDUCE: (32), (369) imply: % 151.63/22.41 | | | | | | | | | | | | | | | | (370) ~ (all_6_2 = e0) % 151.63/22.41 | | | | | | | | | | | | | | | | % 151.63/22.41 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (56) with e0, e1, e3, e0, % 151.63/22.41 | | | | | | | | | | | | | | | | simplifying with (330), (359) gives: % 151.63/22.41 | | | | | | | | | | | | | | | | (371) e1 = e0 % 151.63/22.41 | | | | | | | | | | | | | | | | % 151.63/22.41 | | | | | | | | | | | | | | | | COMBINE_EQS: (367), (371) imply: % 151.63/22.41 | | | | | | | | | | | | | | | | (372) all_56_17 = e0 % 151.63/22.41 | | | | | | | | | | | | | | | | % 151.63/22.41 | | | | | | | | | | | | | | | | REF_CLOSE: (9), (32), (33), (50), (53), (56), (118), (130), % 151.63/22.41 | | | | | | | | | | | | | | | | (296), (316), (370), (372) are inconsistent by % 151.63/22.41 | | | | | | | | | | | | | | | | sub-proof #441. % 151.63/22.41 | | | | | | | | | | | | | | | | % 151.63/22.41 | | | | | | | | | | | | | | | Case 2: % 151.63/22.41 | | | | | | | | | | | | | | | | % 151.63/22.41 | | | | | | | | | | | | | | | | (373) all_56_23 = e1 % 151.63/22.41 | | | | | | | | | | | | | | | | % 151.63/22.41 | | | | | | | | | | | | | | | | REF_CLOSE: (115), (368), (373) are inconsistent by sub-proof % 151.63/22.41 | | | | | | | | | | | | | | | | #309. % 151.63/22.41 | | | | | | | | | | | | | | | | % 151.63/22.41 | | | | | | | | | | | | | | | End of split % 151.63/22.41 | | | | | | | | | | | | | | | % 151.63/22.41 | | | | | | | | | | | | | | Case 2: % 151.63/22.41 | | | | | | | | | | | | | | | % 151.63/22.41 | | | | | | | | | | | | | | | (374) all_54_8 = e0 % 151.63/22.41 | | | | | | | | | | | | | | | % 151.63/22.41 | | | | | | | | | | | | | | | REF_CLOSE: (299), (327), (374) are inconsistent by sub-proof % 151.63/22.41 | | | | | | | | | | | | | | | #452. % 151.63/22.41 | | | | | | | | | | | | | | | % 151.63/22.41 | | | | | | | | | | | | | | End of split % 151.63/22.41 | | | | | | | | | | | | | | % 151.63/22.41 | | | | | | | | | | | | | End of split % 151.63/22.41 | | | | | | | | | | | | | % 151.63/22.41 | | | | | | | | | | | | End of split % 151.63/22.41 | | | | | | | | | | | | % 151.63/22.41 | | | | | | | | | | | Case 2: % 151.63/22.41 | | | | | | | | | | | | % 151.63/22.41 | | | | | | | | | | | | (375) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 151.63/22.41 | | | | | | | | | | | | % 151.63/22.41 | | | | | | | | | | | | REF_CLOSE: (26), (347), (350), (352), (375) are inconsistent % 151.63/22.41 | | | | | | | | | | | | by sub-proof #644. % 151.63/22.41 | | | | | | | | | | | | % 151.63/22.41 | | | | | | | | | | | End of split % 151.63/22.41 | | | | | | | | | | | % 151.63/22.41 | | | | | | | | | | Case 2: % 151.63/22.41 | | | | | | | | | | | % 151.63/22.41 | | | | | | | | | | | (376) all_56_13 = e2 % 151.63/22.41 | | | | | | | | | | | % 151.63/22.41 | | | | | | | | | | | COMBINE_EQS: (72), (376) imply: % 151.63/22.41 | | | | | | | | | | | (377) all_52_9 = e2 % 151.63/22.41 | | | | | | | | | | | % 151.63/22.41 | | | | | | | | | | | REDUCE: (344), (377) imply: % 151.63/22.41 | | | | | | | | | | | (378) $false % 151.63/22.41 | | | | | | | | | | | % 151.63/22.41 | | | | | | | | | | | CLOSE: (378) is inconsistent. % 151.63/22.41 | | | | | | | | | | | % 151.63/22.41 | | | | | | | | | | End of split % 151.63/22.41 | | | | | | | | | | % 151.63/22.41 | | | | | | | | | Case 2: % 151.63/22.41 | | | | | | | | | | % 151.63/22.41 | | | | | | | | | | (379) all_56_15 = e2 % 151.63/22.41 | | | | | | | | | | % 151.63/22.41 | | | | | | | | | | COMBINE_EQS: (156), (379) imply: % 151.63/22.41 | | | | | | | | | | (380) all_52_13 = e2 % 151.63/22.41 | | | | | | | | | | % 151.63/22.41 | | | | | | | | | | REDUCE: (345), (380) imply: % 151.63/22.41 | | | | | | | | | | (381) $false % 151.63/22.41 | | | | | | | | | | % 151.63/22.41 | | | | | | | | | | CLOSE: (381) is inconsistent. % 151.63/22.41 | | | | | | | | | | % 151.63/22.41 | | | | | | | | | End of split % 151.63/22.41 | | | | | | | | | % 151.63/22.41 | | | | | | | | Case 2: % 151.63/22.41 | | | | | | | | | % 151.63/22.41 | | | | | | | | | (382) all_58_6 = e2 | all_58_12 = e2 % 151.63/22.41 | | | | | | | | | % 151.63/22.41 | | | | | | | | | REF_CLOSE: (142), (162), (301), (325), (382) are inconsistent % 151.63/22.41 | | | | | | | | | by sub-proof #422. % 151.63/22.41 | | | | | | | | | % 151.63/22.41 | | | | | | | | End of split % 151.63/22.41 | | | | | | | | % 151.63/22.41 | | | | | | | End of split % 151.63/22.41 | | | | | | | % 151.63/22.41 | | | | | | Case 2: % 151.63/22.41 | | | | | | | % 151.63/22.41 | | | | | | | (383) ~ (all_26_2 = e3) % 151.63/22.41 | | | | | | | % 151.63/22.41 | | | | | | | REDUCE: (324), (383) imply: % 151.63/22.41 | | | | | | | (384) $false % 151.63/22.41 | | | | | | | % 151.63/22.41 | | | | | | | CLOSE: (384) is inconsistent. % 151.63/22.41 | | | | | | | % 151.63/22.41 | | | | | | End of split % 151.63/22.41 | | | | | | % 151.63/22.41 | | | | | End of split % 151.63/22.41 | | | | | % 151.63/22.41 | | | | Case 2: % 151.63/22.41 | | | | | % 151.63/22.41 | | | | | (385) all_56_21 = e2 % 151.63/22.41 | | | | | (386) all_56_19 = e1 % 151.63/22.41 | | | | | % 151.63/22.41 | | | | | REF_CLOSE: (1), (16), (24), (32), (35), (47), (53), (56), (64), (78), % 151.63/22.41 | | | | | (100), (101), (102), (107), (125), (135), (140), (142), % 151.63/22.41 | | | | | (143), (149), (152), (294), (296), (299), (301), (305), % 151.63/22.41 | | | | | (307), (309), (312), (385), (386) are inconsistent by % 151.63/22.41 | | | | | sub-proof #412. % 151.63/22.41 | | | | | % 151.63/22.41 | | | | End of split % 151.63/22.41 | | | | % 151.63/22.41 | | | Case 2: % 151.63/22.41 | | | | % 151.63/22.41 | | | | (387) all_56_31 = e1 % 151.63/22.41 | | | | (388) all_56_29 = e0 % 151.63/22.41 | | | | % 151.63/22.41 | | | | COMBINE_EQS: (122), (388) imply: % 151.63/22.41 | | | | (389) all_52_11 = e0 % 151.63/22.41 | | | | % 151.63/22.41 | | | | SIMP: (389) implies: % 151.63/22.41 | | | | (390) all_52_11 = e0 % 151.63/22.41 | | | | % 151.63/22.41 | | | | COMBINE_EQS: (100), (387) imply: % 151.63/22.41 | | | | (391) all_4_2 = e1 % 151.63/22.41 | | | | % 151.63/22.41 | | | | REDUCE: (94), (390) imply: % 151.63/22.41 | | | | (392) ~ (all_52_3 = e0) % 151.63/22.41 | | | | % 151.63/22.41 | | | | REDUCE: (3), (390) imply: % 151.63/22.41 | | | | (393) ~ (all_6_2 = e0) % 151.63/22.41 | | | | % 151.63/22.41 | | | | SIMP: (393) implies: % 151.63/22.41 | | | | (394) ~ (all_6_2 = e0) % 151.63/22.41 | | | | % 151.63/22.41 | | | | REDUCE: (97), (390), (391) imply: % 151.63/22.41 | | | | (395) ~ (e1 = e0) % 151.63/22.41 | | | | % 151.63/22.41 | | | | REDUCE: (91), (391) imply: % 151.63/22.41 | | | | (396) op(e1, e1) = all_4_1 % 151.63/22.41 | | | | % 151.63/22.41 | | | | REF_CLOSE: (1), (9), (13), (16), (21), (24), (32), (33), (35), (47), % 151.63/22.41 | | | | (50), (53), (56), (64), (66), (70), (78), (100), (101), % 151.63/22.41 | | | | (102), (107), (118), (120), (125), (130), (135), (140), % 151.63/22.41 | | | | (143), (149), (152), (153), (155), (294), (296), (299), % 151.63/22.41 | | | | (300), (301), (303), (305), (307), (309), (312), (392), % 151.63/22.41 | | | | (394), (396) are inconsistent by sub-proof #317. % 151.63/22.41 | | | | % 151.63/22.41 | | | End of split % 151.63/22.41 | | | % 151.63/22.41 | | End of split % 151.63/22.41 | | % 151.63/22.41 | Case 2: % 151.63/22.41 | | % 151.63/22.41 | | (397) all_28_0 = e2 % 151.63/22.41 | | (398) ~ (all_28_1 = e3) | ~ (all_28_2 = e0) % 151.63/22.41 | | % 151.63/22.41 | | COMBINE_EQS: (60), (397) imply: % 151.63/22.41 | | (399) all_6_0 = e2 % 151.63/22.41 | | % 151.63/22.41 | | REF_CLOSE: (1), (3), (5), (8), (9), (10), (13), (15), (21), (22), (25), % 151.63/22.41 | | (26), (27), (28), (29), (30), (32), (33), (35), (39), (40), (41), % 151.63/22.41 | | (42), (43), (45), (48), (50), (52), (56), (66), (67), (69), (70), % 151.63/22.41 | | (71), (75), (82), (83), (84), (85), (87), (89), (91), (94), (98), % 151.63/22.41 | | (99), (100), (101), (106), (109), (111), (114), (115), (117), % 151.63/22.41 | | (118), (119), (120), (121), (122), (126), (128), (129), (130), % 151.63/22.41 | | (132), (133), (135), (136), (138), (139), (140), (144), (145), % 151.63/22.41 | | (148), (150), (152), (153), (155), (156), (160), (398), (399) are % 151.63/22.41 | | inconsistent by sub-proof #364. % 151.63/22.41 | | % 151.63/22.41 | End of split % 151.63/22.41 | % 151.63/22.41 End of proof % 151.63/22.41 % 151.63/22.41 Sub-proof #309 shows that the following formulas are inconsistent: % 151.63/22.41 ---------------------------------------------------------------- % 151.63/22.41 (1) all_56_23 = all_52_14 % 151.63/22.41 (2) all_56_23 = e1 % 151.63/22.41 (3) ~ (all_52_14 = e1) % 151.63/22.41 % 151.63/22.41 Begin of proof % 151.63/22.41 | % 151.63/22.41 | COMBINE_EQS: (1), (2) imply: % 151.63/22.41 | (4) all_52_14 = e1 % 151.63/22.41 | % 151.63/22.41 | SIMP: (4) implies: % 151.63/22.41 | (5) all_52_14 = e1 % 151.63/22.41 | % 151.63/22.41 | REDUCE: (3), (5) imply: % 151.63/22.41 | (6) $false % 151.63/22.41 | % 151.63/22.41 | CLOSE: (6) is inconsistent. % 151.63/22.41 | % 151.63/22.41 End of proof % 151.63/22.41 % 151.63/22.41 Sub-proof #310 shows that the following formulas are inconsistent: % 151.63/22.41 ---------------------------------------------------------------- % 151.63/22.41 (1) all_56_11 = all_8_2 % 151.63/22.41 (2) ~ (all_52_3 = all_6_0) % 151.63/22.41 (3) all_54_9 = all_52_6 % 151.63/22.41 (4) all_54_10 = all_6_2 % 151.63/22.41 (5) ~ (all_56_21 = e2) | all_56_19 = e1 % 151.63/22.41 (6) ~ (all_52_14 = all_4_2) % 151.63/22.41 (7) all_54_12 = all_52_3 % 151.63/22.41 (8) op(e0, e0) = all_4_2 % 151.63/22.41 (9) all_58_6 = e0 | all_58_7 = e0 | all_58_8 = e0 | all_58_11 = e0 % 151.63/22.41 (10) ~ (all_52_6 = all_52_14) % 151.63/22.41 (11) ~ (all_6_0 = e2) % 151.63/22.41 (12) all_54_15 = all_4_2 % 151.63/22.41 (13) all_56_21 = all_6_2 % 151.63/22.41 (14) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 151.63/22.41 (15) all_56_1 = all_10_2 % 151.63/22.41 (16) all_56_27 = all_52_7 % 151.63/22.41 (17) op(e2, all_8_2) = all_56_10 % 151.63/22.41 (18) op(e3, e3) = all_10_2 % 151.63/22.41 (19) ~ (all_52_6 = all_6_0) % 151.63/22.41 (20) ~ (all_56_21 = e3) | all_56_17 = e1 % 151.63/22.41 (21) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 151.63/22.41 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 151.63/22.41 (22) ~ (all_52_3 = all_10_2) % 151.63/22.41 (23) ~ (all_52_3 = all_52_7) % 151.63/22.41 (24) all_36_0 = all_6_0 % 151.63/22.41 (25) ~ (all_6_0 = all_6_2) % 151.63/22.41 (26) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0 % 151.63/22.41 (27) op(e0, all_4_1) = e1 % 151.63/22.41 (28) ~ (all_4_2 = e1) % 151.63/22.41 (29) all_54_8 = all_6_0 % 151.63/22.41 (30) all_58_8 = all_6_2 % 151.63/22.41 (31) ~ (all_52_3 = all_4_2) % 151.63/22.41 (32) ~ (all_52_14 = all_6_0) % 151.63/22.41 (33) op(all_4_2, all_4_2) = all_4_1 % 151.63/22.41 (34) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0 % 151.63/22.41 (35) ~ (all_52_6 = all_52_7) % 151.63/22.41 (36) all_56_31 = all_4_2 % 151.63/22.41 (37) all_58_11 = all_52_14 % 151.63/22.41 (38) all_36_2 = all_6_2 % 151.63/22.41 (39) all_56_1 = e3 | all_56_11 = e2 | all_56_21 = e1 | all_56_31 = e0 % 151.63/22.41 (40) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0 % 151.63/22.41 (41) all_56_23 = all_52_14 % 151.63/22.41 (42) all_58_6 = all_6_0 % 151.63/22.41 (43) op(e1, e1) = all_6_2 % 151.63/22.41 (44) ~ (all_52_6 = all_8_2) % 151.63/22.41 (45) op(e0, e3) = all_52_3 % 151.63/22.41 (46) ~ (all_4_2 = e3) % 151.63/22.41 (47) all_58_7 = all_52_6 % 151.63/22.41 (48) op(e1, all_6_2) = all_56_20 % 151.63/22.41 (49) all_56_17 = all_6_0 % 151.63/22.41 (50) ~ (all_56_31 = e2) | all_56_27 = e0 % 151.63/22.41 (51) op(e2, e2) = all_8_2 % 151.63/22.41 (52) ~ (all_36_0 = e0) | ~ (all_36_2 = e2) % 151.63/22.41 (53) ~ (all_56_21 = e0) | all_56_23 = e1 % 151.63/22.41 (54) op(e0, all_4_2) = all_56_30 % 151.63/22.41 (55) ~ (all_52_6 = all_6_2) % 151.63/22.41 (56) op(all_6_2, all_6_2) = e3 % 151.63/22.41 (57) ~ (all_52_14 = all_6_2) % 151.63/22.41 (58) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0 % 151.63/22.41 (59) ~ (all_10_2 = all_6_0) % 151.63/22.41 (60) op(all_8_2, all_8_2) = all_8_1 % 151.63/22.41 (61) all_56_19 = all_52_6 % 151.63/22.41 % 151.63/22.41 Begin of proof % 151.63/22.41 | % 151.63/22.41 | BETA: splitting (53) gives: % 151.63/22.41 | % 151.63/22.41 | Case 1: % 151.63/22.41 | | % 151.63/22.41 | | (62) ~ (all_56_21 = e0) % 151.63/22.41 | | % 151.63/22.41 | | REDUCE: (13), (62) imply: % 151.63/22.41 | | (63) ~ (all_6_2 = e0) % 151.63/22.41 | | % 151.63/22.41 | | BETA: splitting (50) gives: % 151.63/22.41 | | % 151.63/22.41 | | Case 1: % 151.63/22.41 | | | % 151.63/22.41 | | | (64) ~ (all_56_31 = e2) % 151.63/22.41 | | | % 151.63/22.41 | | | REDUCE: (36), (64) imply: % 151.63/22.41 | | | (65) ~ (all_4_2 = e2) % 151.63/22.41 | | | % 151.63/22.41 | | | REF_CLOSE: (8), (12), (21), (27), (28), (33), (40), (46), (54), (65) are % 151.63/22.41 | | | inconsistent by sub-proof #363. % 151.63/22.41 | | | % 151.63/22.41 | | Case 2: % 151.63/22.41 | | | % 151.63/22.41 | | | (66) all_56_31 = e2 % 151.63/22.41 | | | (67) all_56_27 = e0 % 151.63/22.41 | | | % 151.63/22.41 | | | COMBINE_EQS: (16), (67) imply: % 151.63/22.41 | | | (68) all_52_7 = e0 % 151.63/22.41 | | | % 151.63/22.41 | | | SIMP: (68) implies: % 151.63/22.41 | | | (69) all_52_7 = e0 % 151.63/22.41 | | | % 151.63/22.41 | | | COMBINE_EQS: (36), (66) imply: % 151.63/22.41 | | | (70) all_4_2 = e2 % 151.63/22.41 | | | % 151.63/22.41 | | | REDUCE: (23), (69) imply: % 151.63/22.41 | | | (71) ~ (all_52_3 = e0) % 151.63/22.41 | | | % 151.63/22.41 | | | REDUCE: (31), (70) imply: % 151.63/22.41 | | | (72) ~ (all_52_3 = e2) % 151.63/22.41 | | | % 151.63/22.41 | | | REDUCE: (35), (69) imply: % 151.63/22.41 | | | (73) ~ (all_52_6 = e0) % 151.63/22.41 | | | % 151.63/22.41 | | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (9), (13), (14), (15), (17), % 151.63/22.41 | | | (18), (19), (20), (21), (22), (24), (25), (26), (29), (30), % 151.63/22.41 | | | (32), (36), (37), (38), (39), (42), (43), (45), (47), (48), % 151.63/22.41 | | | (49), (51), (52), (55), (56), (58), (59), (60), (61), (63), % 151.63/22.41 | | | (71), (72), (73) are inconsistent by sub-proof #311. % 151.63/22.41 | | | % 151.63/22.41 | | End of split % 151.63/22.41 | | % 151.63/22.41 | Case 2: % 151.63/22.41 | | % 151.63/22.41 | | (74) all_56_23 = e1 % 151.63/22.41 | | (75) all_56_21 = e0 % 151.63/22.41 | | % 151.63/22.41 | | REF_CLOSE: (1), (3), (8), (10), (11), (13), (15), (19), (21), (25), (29), % 151.63/22.41 | | (32), (33), (34), (36), (39), (41), (44), (46), (54), (55), (56), % 151.63/22.41 | | (57), (58), (59), (74), (75) are inconsistent by sub-proof #430. % 151.63/22.41 | | % 151.63/22.41 | End of split % 151.63/22.41 | % 151.63/22.41 End of proof % 151.63/22.41 % 151.63/22.41 Sub-proof #311 shows that the following formulas are inconsistent: % 151.63/22.41 ---------------------------------------------------------------- % 151.63/22.41 (1) all_56_11 = all_8_2 % 151.63/22.41 (2) ~ (all_52_3 = all_6_0) % 151.63/22.41 (3) all_54_10 = all_6_2 % 151.63/22.41 (4) ~ (all_56_21 = e2) | all_56_19 = e1 % 151.63/22.41 (5) ~ (all_52_14 = all_4_2) % 151.63/22.41 (6) all_54_12 = all_52_3 % 151.63/22.41 (7) all_58_6 = e0 | all_58_7 = e0 | all_58_8 = e0 | all_58_11 = e0 % 151.63/22.41 (8) ~ (all_52_3 = e2) % 151.63/22.41 (9) all_56_21 = all_6_2 % 151.63/22.41 (10) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 151.63/22.41 (11) all_56_1 = all_10_2 % 151.63/22.41 (12) op(e2, all_8_2) = all_56_10 % 151.63/22.41 (13) op(e3, e3) = all_10_2 % 151.63/22.41 (14) ~ (all_52_6 = all_6_0) % 151.63/22.41 (15) ~ (all_56_21 = e3) | all_56_17 = e1 % 151.63/22.42 (16) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 151.63/22.42 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 151.63/22.42 (17) ~ (all_52_3 = all_10_2) % 151.63/22.42 (18) ~ (all_6_2 = e0) % 151.63/22.42 (19) all_36_0 = all_6_0 % 151.63/22.42 (20) ~ (all_52_3 = e0) % 151.63/22.42 (21) ~ (all_6_0 = all_6_2) % 151.63/22.42 (22) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0 % 151.63/22.42 (23) all_54_8 = all_6_0 % 151.63/22.42 (24) all_58_8 = all_6_2 % 151.63/22.42 (25) ~ (all_52_6 = e0) % 151.63/22.42 (26) ~ (all_52_14 = all_6_0) % 151.63/22.42 (27) all_56_31 = all_4_2 % 151.63/22.42 (28) all_58_11 = all_52_14 % 151.63/22.42 (29) all_36_2 = all_6_2 % 151.63/22.42 (30) all_56_1 = e3 | all_56_11 = e2 | all_56_21 = e1 | all_56_31 = e0 % 151.63/22.42 (31) all_58_6 = all_6_0 % 151.63/22.42 (32) op(e1, e1) = all_6_2 % 151.63/22.42 (33) op(e0, e3) = all_52_3 % 151.63/22.42 (34) all_58_7 = all_52_6 % 151.63/22.42 (35) op(e1, all_6_2) = all_56_20 % 151.63/22.42 (36) all_56_17 = all_6_0 % 151.63/22.42 (37) op(e2, e2) = all_8_2 % 151.63/22.42 (38) ~ (all_36_0 = e0) | ~ (all_36_2 = e2) % 151.63/22.42 (39) ~ (all_52_6 = all_6_2) % 151.63/22.42 (40) op(all_6_2, all_6_2) = e3 % 151.63/22.42 (41) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0 % 151.63/22.42 (42) ~ (all_10_2 = all_6_0) % 151.63/22.42 (43) op(all_8_2, all_8_2) = all_8_1 % 151.63/22.42 (44) all_56_19 = all_52_6 % 151.63/22.42 % 151.63/22.42 Begin of proof % 151.63/22.42 | % 151.63/22.42 | BETA: splitting (4) gives: % 151.63/22.42 | % 151.63/22.42 | Case 1: % 151.63/22.42 | | % 151.63/22.42 | | (45) ~ (all_56_21 = e2) % 151.63/22.42 | | % 151.63/22.42 | | REDUCE: (9), (45) imply: % 151.63/22.42 | | (46) ~ (all_6_2 = e2) % 151.63/22.42 | | % 151.63/22.42 | | BETA: splitting (15) gives: % 151.63/22.42 | | % 151.63/22.42 | | Case 1: % 151.63/22.42 | | | % 151.63/22.42 | | | (47) ~ (all_56_21 = e3) % 151.63/22.42 | | | % 151.63/22.42 | | | REDUCE: (9), (47) imply: % 151.63/22.42 | | | (48) ~ (all_6_2 = e3) % 151.63/22.42 | | | % 151.63/22.42 | | | REF_CLOSE: (3), (10), (16), (18), (32), (35), (40), (46), (48) are % 151.63/22.42 | | | inconsistent by sub-proof #459. % 151.63/22.42 | | | % 151.63/22.42 | | Case 2: % 151.63/22.42 | | | % 151.63/22.42 | | | (49) all_56_21 = e3 % 151.63/22.42 | | | (50) all_56_17 = e1 % 151.63/22.42 | | | % 151.63/22.42 | | | COMBINE_EQS: (36), (50) imply: % 151.63/22.42 | | | (51) all_6_0 = e1 % 151.63/22.42 | | | % 151.63/22.42 | | | SIMP: (51) implies: % 151.63/22.42 | | | (52) all_6_0 = e1 % 151.63/22.42 | | | % 151.63/22.42 | | | COMBINE_EQS: (9), (49) imply: % 151.63/22.42 | | | (53) all_6_2 = e3 % 151.63/22.42 | | | % 151.63/22.42 | | | SIMP: (53) implies: % 151.63/22.42 | | | (54) all_6_2 = e3 % 151.63/22.42 | | | % 151.63/22.42 | | | REDUCE: (2), (52) imply: % 151.63/22.42 | | | (55) ~ (all_52_3 = e1) % 151.63/22.42 | | | % 151.63/22.42 | | | REDUCE: (40), (54) imply: % 151.63/22.42 | | | (56) op(e3, e3) = e3 % 151.63/22.42 | | | % 151.63/22.42 | | | REF_CLOSE: (6), (8), (13), (16), (17), (20), (22), (33), (55), (56) are % 151.63/22.42 | | | inconsistent by sub-proof #313. % 151.63/22.42 | | | % 151.63/22.42 | | End of split % 151.63/22.42 | | % 151.63/22.42 | Case 2: % 151.63/22.42 | | % 151.63/22.42 | | (57) all_56_21 = e2 % 151.63/22.42 | | (58) all_56_19 = e1 % 151.63/22.42 | | % 151.63/22.42 | | REF_CLOSE: (1), (5), (7), (9), (11), (12), (14), (16), (18), (19), (21), % 151.63/22.42 | | (23), (24), (25), (26), (27), (28), (29), (30), (31), (34), (37), % 151.63/22.42 | | (38), (39), (40), (41), (42), (43), (44), (57), (58) are % 151.63/22.42 | | inconsistent by sub-proof #312. % 151.63/22.42 | | % 151.63/22.42 | End of split % 151.63/22.42 | % 151.63/22.42 End of proof % 151.63/22.42 % 151.63/22.42 Sub-proof #312 shows that the following formulas are inconsistent: % 151.63/22.42 ---------------------------------------------------------------- % 151.63/22.42 (1) all_56_11 = all_8_2 % 151.63/22.42 (2) ~ (all_52_14 = all_4_2) % 151.63/22.42 (3) all_58_6 = e0 | all_58_7 = e0 | all_58_8 = e0 | all_58_11 = e0 % 151.63/22.42 (4) all_56_21 = all_6_2 % 151.63/22.42 (5) all_56_1 = all_10_2 % 151.63/22.42 (6) op(e2, all_8_2) = all_56_10 % 151.63/22.42 (7) ~ (all_52_6 = all_6_0) % 151.63/22.42 (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 151.63/22.42 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 151.63/22.42 (9) ~ (all_6_2 = e0) % 151.63/22.42 (10) all_36_0 = all_6_0 % 151.63/22.42 (11) ~ (all_6_0 = all_6_2) % 151.63/22.42 (12) all_54_8 = all_6_0 % 151.63/22.42 (13) all_58_8 = all_6_2 % 151.63/22.42 (14) all_56_21 = e2 % 151.63/22.42 (15) ~ (all_52_6 = e0) % 151.63/22.42 (16) all_56_19 = e1 % 151.63/22.42 (17) ~ (all_52_14 = all_6_0) % 151.63/22.42 (18) all_56_31 = all_4_2 % 151.63/22.42 (19) all_58_11 = all_52_14 % 151.63/22.42 (20) all_36_2 = all_6_2 % 151.63/22.42 (21) all_56_1 = e3 | all_56_11 = e2 | all_56_21 = e1 | all_56_31 = e0 % 151.63/22.42 (22) all_58_6 = all_6_0 % 151.63/22.42 (23) all_58_7 = all_52_6 % 151.63/22.42 (24) op(e2, e2) = all_8_2 % 151.63/22.42 (25) ~ (all_36_0 = e0) | ~ (all_36_2 = e2) % 151.63/22.42 (26) ~ (all_52_6 = all_6_2) % 151.63/22.42 (27) op(all_6_2, all_6_2) = e3 % 151.63/22.42 (28) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0 % 151.63/22.42 (29) ~ (all_10_2 = all_6_0) % 151.63/22.42 (30) op(all_8_2, all_8_2) = all_8_1 % 151.63/22.42 (31) all_56_19 = all_52_6 % 151.63/22.42 % 151.63/22.42 Begin of proof % 151.63/22.42 | % 151.63/22.42 | COMBINE_EQS: (16), (31) imply: % 151.63/22.42 | (32) all_52_6 = e1 % 151.63/22.42 | % 151.63/22.42 | SIMP: (32) implies: % 151.63/22.42 | (33) all_52_6 = e1 % 151.63/22.42 | % 151.63/22.42 | COMBINE_EQS: (4), (14) imply: % 151.63/22.42 | (34) all_6_2 = e2 % 151.63/22.42 | % 151.63/22.42 | SIMP: (34) implies: % 151.63/22.42 | (35) all_6_2 = e2 % 151.63/22.42 | % 151.63/22.42 | COMBINE_EQS: (20), (35) imply: % 151.63/22.42 | (36) all_36_2 = e2 % 151.63/22.42 | % 151.63/22.42 | COMBINE_EQS: (13), (35) imply: % 151.63/22.42 | (37) all_58_8 = e2 % 151.63/22.42 | % 151.63/22.42 | COMBINE_EQS: (23), (33) imply: % 151.63/22.42 | (38) all_58_7 = e1 % 151.63/22.42 | % 151.63/22.42 | REDUCE: (7), (33) imply: % 151.63/22.42 | (39) ~ (all_6_0 = e1) % 151.63/22.42 | % 151.63/22.42 | SIMP: (39) implies: % 151.63/22.42 | (40) ~ (all_6_0 = e1) % 151.63/22.42 | % 151.63/22.42 | REDUCE: (26), (33), (35) imply: % 151.63/22.42 | (41) ~ (e2 = e1) % 151.63/22.42 | % 151.63/22.42 | SIMP: (41) implies: % 151.63/22.42 | (42) ~ (e2 = e1) % 151.63/22.42 | % 151.63/22.42 | REDUCE: (15), (33) imply: % 151.63/22.42 | (43) ~ (e1 = e0) % 151.63/22.42 | % 151.63/22.42 | REDUCE: (11), (35) imply: % 151.63/22.42 | (44) ~ (all_6_0 = e2) % 151.63/22.42 | % 151.63/22.42 | REDUCE: (9), (35) imply: % 151.63/22.42 | (45) ~ (e2 = e0) % 151.63/22.42 | % 151.63/22.42 | REDUCE: (27), (35) imply: % 151.63/22.42 | (46) op(e2, e2) = e3 % 151.63/22.42 | % 151.63/22.42 | REF_CLOSE: (1), (2), (3), (5), (6), (8), (10), (12), (14), (17), (18), (19), % 151.63/22.42 | (21), (22), (24), (25), (28), (29), (30), (36), (37), (38), (40), % 151.63/22.42 | (42), (43), (44), (45), (46) are inconsistent by sub-proof #433. % 151.63/22.42 | % 151.63/22.42 End of proof % 151.63/22.42 % 151.63/22.42 Sub-proof #313 shows that the following formulas are inconsistent: % 151.63/22.42 ---------------------------------------------------------------- % 151.63/22.42 (1) all_54_12 = all_52_3 % 151.63/22.42 (2) op(e3, e3) = e3 % 151.63/22.42 (3) ~ (all_52_3 = e2) % 151.63/22.42 (4) op(e3, e3) = all_10_2 % 151.63/22.42 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 151.63/22.42 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 151.63/22.42 (6) ~ (all_52_3 = all_10_2) % 151.63/22.42 (7) ~ (all_52_3 = e0) % 151.63/22.42 (8) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0 % 151.63/22.42 (9) op(e0, e3) = all_52_3 % 151.63/22.42 (10) ~ (all_52_3 = e1) % 151.63/22.42 % 151.63/22.42 Begin of proof % 151.63/22.42 | % 151.63/22.42 | BETA: splitting (8) gives: % 151.63/22.42 | % 151.63/22.42 | Case 1: % 151.63/22.42 | | % 151.63/22.42 | | (11) all_54_12 = e3 % 151.63/22.42 | | % 151.63/22.42 | | COMBINE_EQS: (1), (11) imply: % 151.63/22.42 | | (12) all_52_3 = e3 % 151.63/22.42 | | % 151.63/22.42 | | SIMP: (12) implies: % 151.63/22.42 | | (13) all_52_3 = e3 % 151.63/22.42 | | % 151.63/22.42 | | REDUCE: (9), (13) imply: % 151.63/22.42 | | (14) op(e0, e3) = e3 % 151.63/22.42 | | % 151.63/22.42 | | REF_CLOSE: (2), (4), (5), (6), (9), (14) are inconsistent by sub-proof #314. % 151.63/22.42 | | % 151.63/22.42 | Case 2: % 151.63/22.42 | | % 151.63/22.42 | | (15) all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0 % 151.63/22.42 | | % 151.63/22.42 | | REF_CLOSE: (1), (3), (7), (10), (15) are inconsistent by sub-proof #615. % 151.63/22.42 | | % 151.63/22.42 | End of split % 151.63/22.42 | % 151.63/22.42 End of proof % 151.63/22.42 % 151.63/22.42 Sub-proof #314 shows that the following formulas are inconsistent: % 151.63/22.42 ---------------------------------------------------------------- % 151.63/22.42 (1) op(e3, e3) = e3 % 151.63/22.42 (2) op(e3, e3) = all_10_2 % 151.63/22.42 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 151.63/22.42 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 151.63/22.42 (4) ~ (all_52_3 = all_10_2) % 151.63/22.42 (5) op(e0, e3) = e3 % 151.63/22.42 (6) op(e0, e3) = all_52_3 % 151.63/22.42 % 151.63/22.42 Begin of proof % 151.63/22.42 | % 151.63/22.42 | GROUND_INST: instantiating (3) with all_52_3, e3, e3, e0, simplifying with % 151.63/22.42 | (5), (6) gives: % 151.63/22.42 | (7) all_52_3 = e3 % 151.63/22.42 | % 151.63/22.42 | GROUND_INST: instantiating (3) with all_10_2, e3, e3, e3, simplifying with % 151.63/22.42 | (1), (2) gives: % 151.63/22.42 | (8) all_10_2 = e3 % 151.63/22.42 | % 151.63/22.42 | REDUCE: (4), (7), (8) imply: % 151.63/22.42 | (9) $false % 151.63/22.42 | % 151.63/22.42 | CLOSE: (9) is inconsistent. % 151.63/22.42 | % 151.63/22.42 End of proof % 151.63/22.42 % 151.63/22.42 Sub-proof #315 shows that the following formulas are inconsistent: % 151.63/22.42 ---------------------------------------------------------------- % 151.63/22.42 (1) ~ (all_52_9 = e2) % 151.63/22.42 (2) ~ (all_6_2 = e3) % 151.63/22.42 (3) ~ (e3 = e2) % 151.63/22.42 (4) all_58_5 = all_52_9 % 151.63/22.42 (5) all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2 % 151.63/22.42 (6) ~ (all_52_9 = e3) % 151.63/22.42 (7) all_58_8 = all_6_2 % 151.63/22.42 (8) all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3 % 151.63/22.42 (9) ~ (all_6_2 = e2) % 151.63/22.42 % 151.63/22.42 Begin of proof % 151.63/22.42 | % 151.63/22.42 | BETA: splitting (5) gives: % 151.63/22.42 | % 151.63/22.42 | Case 1: % 151.63/22.42 | | % 151.63/22.42 | | (10) all_58_5 = e2 % 151.63/22.42 | | % 151.63/22.42 | | COMBINE_EQS: (4), (10) imply: % 151.63/22.42 | | (11) all_52_9 = e2 % 151.63/22.42 | | % 151.63/22.42 | | REDUCE: (1), (11) imply: % 151.63/22.42 | | (12) $false % 151.63/22.42 | | % 151.63/22.42 | | CLOSE: (12) is inconsistent. % 151.63/22.42 | | % 151.63/22.42 | Case 2: % 151.63/22.42 | | % 151.63/22.42 | | (13) all_58_8 = e2 | all_58_14 = e2 % 151.63/22.42 | | % 151.63/22.42 | | BETA: splitting (13) gives: % 151.63/22.42 | | % 151.63/22.42 | | Case 1: % 151.63/22.42 | | | % 151.63/22.42 | | | (14) all_58_8 = e2 % 151.63/22.42 | | | % 151.63/22.42 | | | COMBINE_EQS: (7), (14) imply: % 151.63/22.42 | | | (15) all_6_2 = e2 % 151.63/22.42 | | | % 151.63/22.42 | | | REDUCE: (9), (15) imply: % 151.63/22.42 | | | (16) $false % 151.63/22.42 | | | % 151.63/22.42 | | | CLOSE: (16) is inconsistent. % 151.63/22.42 | | | % 151.63/22.42 | | Case 2: % 151.63/22.42 | | | % 151.63/22.42 | | | (17) all_58_14 = e2 % 151.63/22.42 | | | % 151.63/22.42 | | | REF_CLOSE: (2), (3), (4), (6), (7), (8), (17) are inconsistent by % 151.63/22.42 | | | sub-proof #391. % 151.63/22.42 | | | % 151.63/22.42 | | End of split % 151.63/22.42 | | % 151.63/22.42 | End of split % 151.63/22.42 | % 151.63/22.42 End of proof % 151.63/22.42 % 151.63/22.42 Sub-proof #316 shows that the following formulas are inconsistent: % 151.63/22.42 ---------------------------------------------------------------- % 151.63/22.42 (1) all_56_11 = all_8_2 % 151.63/22.42 (2) ~ (all_52_3 = all_6_0) % 151.63/22.42 (3) ~ (all_52_11 = all_6_2) % 151.63/22.42 (4) all_56_31 = e1 % 151.63/22.42 (5) all_54_10 = all_6_2 % 151.63/22.42 (6) ~ (all_56_21 = e2) | all_56_19 = e1 % 151.63/22.42 (7) ~ (all_52_14 = all_4_2) % 151.63/22.42 (8) all_54_12 = all_52_3 % 151.63/22.42 (9) all_58_6 = e0 | all_58_7 = e0 | all_58_8 = e0 | all_58_11 = e0 % 151.63/22.42 (10) all_56_21 = all_6_2 % 151.63/22.42 (11) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 151.63/22.42 (12) all_56_1 = all_10_2 % 151.63/22.42 (13) op(e2, all_8_2) = all_56_10 % 151.63/22.42 (14) ~ (all_52_6 = all_6_0) % 151.63/22.42 (15) ~ (all_56_21 = e3) | all_56_17 = e1 % 151.63/22.42 (16) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 151.63/22.42 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 151.63/22.42 (17) all_36_0 = all_6_0 % 151.63/22.42 (18) op(e0, all_4_1) = all_4_0 % 151.63/22.42 (19) ~ (all_6_0 = all_6_2) % 151.63/22.42 (20) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0 % 151.63/22.42 (21) all_54_8 = all_6_0 % 151.63/22.42 (22) all_58_8 = all_6_2 % 151.63/22.42 (23) ~ (all_52_14 = all_6_0) % 151.63/22.42 (24) op(all_4_2, all_4_2) = all_4_1 % 151.63/22.42 (25) all_56_29 = e0 % 151.63/22.42 (26) ~ (all_52_3 = all_52_11) % 151.63/22.42 (27) ~ (all_52_11 = all_4_2) % 151.63/22.42 (28) all_56_31 = all_4_2 % 151.63/22.42 (29) all_58_11 = all_52_14 % 151.63/22.42 (30) all_36_2 = all_6_2 % 151.63/22.42 (31) all_56_1 = e3 | all_56_11 = e2 | all_56_21 = e1 | all_56_31 = e0 % 151.63/22.42 (32) all_58_6 = all_6_0 % 151.63/22.42 (33) op(e1, e1) = all_6_2 % 151.63/22.42 (34) op(e0, e3) = all_52_3 % 151.63/22.42 (35) all_56_29 = all_52_11 % 151.63/22.42 (36) all_58_7 = all_52_6 % 151.63/22.42 (37) op(e1, all_6_2) = all_56_20 % 151.63/22.42 (38) all_56_17 = all_6_0 % 151.63/22.42 (39) op(e2, e2) = all_8_2 % 151.63/22.42 (40) ~ (all_36_0 = e0) | ~ (all_36_2 = e2) % 151.63/22.42 (41) ~ (all_52_6 = all_6_2) % 151.63/22.42 (42) op(all_6_2, all_6_2) = e3 % 151.63/22.42 (43) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0 % 151.63/22.42 (44) ~ (all_10_2 = all_6_0) % 151.63/22.42 (45) op(all_8_2, all_8_2) = all_8_1 % 151.63/22.42 (46) all_56_19 = all_52_6 % 151.63/22.42 (47) ~ (all_4_0 = e2) % 151.63/22.42 (48) ~ (all_4_0 = e3) % 151.63/22.42 % 151.63/22.42 Begin of proof % 151.63/22.42 | % 151.63/22.42 | COMBINE_EQS: (25), (35) imply: % 151.63/22.42 | (49) all_52_11 = e0 % 151.63/22.42 | % 151.63/22.42 | SIMP: (49) implies: % 151.63/22.42 | (50) all_52_11 = e0 % 151.63/22.42 | % 151.63/22.42 | COMBINE_EQS: (4), (28) imply: % 151.63/22.42 | (51) all_4_2 = e1 % 151.63/22.42 | % 151.63/22.42 | REDUCE: (26), (50) imply: % 151.63/22.42 | (52) ~ (all_52_3 = e0) % 151.63/22.42 | % 151.63/22.42 | REDUCE: (3), (50) imply: % 151.63/22.42 | (53) ~ (all_6_2 = e0) % 151.63/22.42 | % 151.63/22.42 | SIMP: (53) implies: % 151.63/22.42 | (54) ~ (all_6_2 = e0) % 151.63/22.42 | % 151.63/22.42 | REDUCE: (27), (50), (51) imply: % 151.63/22.42 | (55) ~ (e1 = e0) % 151.63/22.42 | % 151.63/22.42 | SIMP: (55) implies: % 151.63/22.42 | (56) ~ (e1 = e0) % 151.63/22.42 | % 151.63/22.42 | REDUCE: (24), (51) imply: % 151.63/22.42 | (57) op(e1, e1) = all_4_1 % 151.63/22.42 | % 151.63/22.42 | REF_CLOSE: (1), (2), (5), (6), (7), (8), (9), (10), (11), (12), (13), (14), % 151.63/22.42 | (15), (16), (17), (18), (19), (20), (21), (22), (23), (28), (29), % 151.63/22.42 | (30), (31), (32), (33), (34), (36), (37), (38), (39), (40), (41), % 151.63/22.42 | (42), (43), (44), (45), (46), (47), (48), (52), (54), (56), (57) % 151.63/22.42 | are inconsistent by sub-proof #317. % 151.63/22.42 | % 151.63/22.42 End of proof % 151.63/22.42 % 151.63/22.42 Sub-proof #317 shows that the following formulas are inconsistent: % 151.63/22.42 ---------------------------------------------------------------- % 151.63/22.42 (1) all_56_11 = all_8_2 % 151.63/22.42 (2) ~ (all_52_3 = all_6_0) % 151.63/22.42 (3) all_54_10 = all_6_2 % 151.63/22.42 (4) ~ (all_56_21 = e2) | all_56_19 = e1 % 151.63/22.42 (5) ~ (all_52_14 = all_4_2) % 151.63/22.42 (6) all_54_12 = all_52_3 % 151.63/22.42 (7) all_58_6 = e0 | all_58_7 = e0 | all_58_8 = e0 | all_58_11 = e0 % 151.63/22.42 (8) all_56_21 = all_6_2 % 151.63/22.42 (9) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 151.63/22.42 (10) all_56_1 = all_10_2 % 151.63/22.42 (11) op(e2, all_8_2) = all_56_10 % 151.63/22.42 (12) ~ (all_52_6 = all_6_0) % 151.63/22.42 (13) ~ (all_56_21 = e3) | all_56_17 = e1 % 151.63/22.42 (14) ~ (e1 = e0) % 151.63/22.42 (15) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 151.63/22.42 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 151.63/22.42 (16) ~ (all_6_2 = e0) % 151.63/22.42 (17) all_36_0 = all_6_0 % 151.63/22.42 (18) op(e0, all_4_1) = all_4_0 % 151.63/22.42 (19) ~ (all_52_3 = e0) % 151.63/22.42 (20) ~ (all_6_0 = all_6_2) % 151.63/22.42 (21) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0 % 151.63/22.42 (22) all_54_8 = all_6_0 % 151.63/22.42 (23) all_58_8 = all_6_2 % 151.63/22.42 (24) ~ (all_52_14 = all_6_0) % 151.63/22.42 (25) all_56_31 = all_4_2 % 151.63/22.42 (26) all_58_11 = all_52_14 % 151.63/22.42 (27) all_36_2 = all_6_2 % 151.63/22.42 (28) all_56_1 = e3 | all_56_11 = e2 | all_56_21 = e1 | all_56_31 = e0 % 151.63/22.42 (29) all_58_6 = all_6_0 % 151.63/22.42 (30) op(e1, e1) = all_6_2 % 151.63/22.42 (31) op(e0, e3) = all_52_3 % 151.63/22.42 (32) all_58_7 = all_52_6 % 151.63/22.42 (33) op(e1, e1) = all_4_1 % 151.63/22.42 (34) op(e1, all_6_2) = all_56_20 % 151.63/22.42 (35) all_56_17 = all_6_0 % 151.63/22.42 (36) op(e2, e2) = all_8_2 % 151.63/22.42 (37) ~ (all_36_0 = e0) | ~ (all_36_2 = e2) % 151.63/22.42 (38) ~ (all_52_6 = all_6_2) % 151.63/22.42 (39) op(all_6_2, all_6_2) = e3 % 151.63/22.42 (40) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0 % 151.63/22.42 (41) ~ (all_10_2 = all_6_0) % 151.63/22.42 (42) op(all_8_2, all_8_2) = all_8_1 % 151.63/22.42 (43) all_56_19 = all_52_6 % 151.63/22.42 (44) ~ (all_4_0 = e2) % 151.63/22.42 (45) ~ (all_4_0 = e3) % 151.63/22.42 % 151.63/22.42 Begin of proof % 151.63/22.42 | % 151.63/22.42 | GROUND_INST: instantiating (15) with all_6_2, all_4_1, e1, e1, simplifying % 151.63/22.42 | with (30), (33) gives: % 151.63/22.42 | (46) all_6_2 = all_4_1 % 151.63/22.42 | % 151.63/22.42 | COMBINE_EQS: (27), (46) imply: % 151.63/22.42 | (47) all_36_2 = all_4_1 % 151.63/22.42 | % 151.63/22.42 | COMBINE_EQS: (3), (46) imply: % 151.63/22.42 | (48) all_54_10 = all_4_1 % 151.63/22.42 | % 151.63/22.42 | COMBINE_EQS: (8), (46) imply: % 151.63/22.42 | (49) all_56_21 = all_4_1 % 151.63/22.42 | % 151.63/22.42 | COMBINE_EQS: (23), (46) imply: % 151.63/22.42 | (50) all_58_8 = all_4_1 % 151.63/22.42 | % 151.63/22.42 | REDUCE: (38), (46) imply: % 151.63/22.42 | (51) ~ (all_52_6 = all_4_1) % 151.63/22.42 | % 151.63/22.42 | REDUCE: (20), (46) imply: % 151.63/22.42 | (52) ~ (all_6_0 = all_4_1) % 151.63/22.42 | % 151.63/22.42 | REDUCE: (16), (46) imply: % 151.63/22.42 | (53) ~ (all_4_1 = e0) % 151.63/22.42 | % 151.63/22.42 | REDUCE: (39), (46) imply: % 151.63/22.42 | (54) op(all_4_1, all_4_1) = e3 % 151.63/22.42 | % 151.63/22.42 | REDUCE: (34), (46) imply: % 151.63/22.42 | (55) op(e1, all_4_1) = all_56_20 % 151.63/22.42 | % 151.63/22.42 | BETA: splitting (4) gives: % 151.63/22.42 | % 151.63/22.42 | Case 1: % 151.63/22.42 | | % 151.63/22.42 | | (56) ~ (all_56_21 = e2) % 151.63/22.42 | | % 151.63/22.42 | | REDUCE: (49), (56) imply: % 151.63/22.42 | | (57) ~ (all_4_1 = e2) % 151.63/22.42 | | % 151.63/22.42 | | REF_CLOSE: (2), (6), (9), (13), (15), (18), (19), (21), (31), (33), (35), % 151.63/22.42 | | (44), (45), (48), (49), (53), (54), (55), (57) are inconsistent % 151.63/22.42 | | by sub-proof #437. % 151.63/22.42 | | % 151.63/22.42 | Case 2: % 151.63/22.42 | | % 151.63/22.42 | | (58) all_56_21 = e2 % 151.63/22.42 | | (59) all_56_19 = e1 % 151.63/22.42 | | % 151.63/22.42 | | COMBINE_EQS: (43), (59) imply: % 151.63/22.42 | | (60) all_52_6 = e1 % 151.63/22.42 | | % 151.63/22.42 | | COMBINE_EQS: (49), (58) imply: % 151.63/22.42 | | (61) all_4_1 = e2 % 151.63/22.42 | | % 151.63/22.42 | | COMBINE_EQS: (47), (61) imply: % 151.63/22.42 | | (62) all_36_2 = e2 % 151.63/22.42 | | % 151.63/22.42 | | REF_CLOSE: (1), (5), (7), (10), (11), (12), (14), (15), (17), (22), (24), % 151.63/22.42 | | (25), (26), (28), (29), (32), (36), (37), (40), (41), (42), (50), % 151.63/22.42 | | (51), (52), (53), (54), (58), (60), (61), (62) are inconsistent % 151.63/22.42 | | by sub-proof #318. % 151.63/22.42 | | % 151.63/22.42 | End of split % 151.63/22.42 | % 151.63/22.42 End of proof % 151.63/22.42 % 151.63/22.42 Sub-proof #318 shows that the following formulas are inconsistent: % 151.63/22.42 ---------------------------------------------------------------- % 151.63/22.42 (1) all_56_11 = all_8_2 % 151.63/22.42 (2) all_52_6 = e1 % 151.63/22.42 (3) op(all_4_1, all_4_1) = e3 % 151.63/22.42 (4) ~ (all_4_1 = e0) % 151.63/22.42 (5) ~ (all_52_14 = all_4_2) % 151.63/22.42 (6) all_58_6 = e0 | all_58_7 = e0 | all_58_8 = e0 | all_58_11 = e0 % 151.63/22.42 (7) all_4_1 = e2 % 151.63/22.42 (8) all_56_1 = all_10_2 % 151.63/22.42 (9) op(e2, all_8_2) = all_56_10 % 151.63/22.42 (10) ~ (all_52_6 = all_4_1) % 151.63/22.42 (11) ~ (all_52_6 = all_6_0) % 151.63/22.42 (12) ~ (e1 = e0) % 151.63/22.42 (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 151.63/22.42 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 151.63/22.42 (14) all_36_0 = all_6_0 % 151.63/22.42 (15) all_54_8 = all_6_0 % 151.63/22.42 (16) all_56_21 = e2 % 151.63/22.42 (17) ~ (all_52_14 = all_6_0) % 151.63/22.42 (18) all_56_31 = all_4_2 % 151.63/22.42 (19) all_58_11 = all_52_14 % 151.63/22.42 (20) all_36_2 = e2 % 151.63/22.42 (21) all_56_1 = e3 | all_56_11 = e2 | all_56_21 = e1 | all_56_31 = e0 % 151.63/22.42 (22) all_58_6 = all_6_0 % 151.63/22.42 (23) all_58_7 = all_52_6 % 151.63/22.42 (24) ~ (all_6_0 = all_4_1) % 151.63/22.42 (25) all_58_8 = all_4_1 % 151.63/22.42 (26) op(e2, e2) = all_8_2 % 151.63/22.42 (27) ~ (all_36_0 = e0) | ~ (all_36_2 = e2) % 151.63/22.42 (28) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0 % 151.63/22.42 (29) ~ (all_10_2 = all_6_0) % 151.63/22.42 (30) op(all_8_2, all_8_2) = all_8_1 % 151.63/22.42 % 151.63/22.42 Begin of proof % 151.63/22.42 | % 151.63/22.42 | COMBINE_EQS: (7), (25) imply: % 151.63/22.42 | (31) all_58_8 = e2 % 151.63/22.42 | % 151.63/22.42 | COMBINE_EQS: (2), (23) imply: % 151.63/22.42 | (32) all_58_7 = e1 % 151.63/22.42 | % 151.63/22.42 | REDUCE: (2), (11) imply: % 151.63/22.42 | (33) ~ (all_6_0 = e1) % 151.63/22.42 | % 151.63/22.42 | SIMP: (33) implies: % 151.63/22.42 | (34) ~ (all_6_0 = e1) % 151.63/22.42 | % 151.63/22.42 | REDUCE: (2), (7), (10) imply: % 151.63/22.42 | (35) ~ (e2 = e1) % 151.63/22.42 | % 151.63/22.42 | SIMP: (35) implies: % 151.63/22.42 | (36) ~ (e2 = e1) % 151.63/22.42 | % 151.63/22.42 | REDUCE: (7), (24) imply: % 151.63/22.42 | (37) ~ (all_6_0 = e2) % 151.63/22.42 | % 151.63/22.42 | REDUCE: (4), (7) imply: % 151.63/22.42 | (38) ~ (e2 = e0) % 151.63/22.42 | % 151.63/22.42 | REDUCE: (3), (7) imply: % 151.63/22.42 | (39) op(e2, e2) = e3 % 151.63/22.42 | % 151.63/22.42 | REF_CLOSE: (1), (5), (6), (8), (9), (12), (13), (14), (15), (16), (17), (18), % 151.63/22.42 | (19), (20), (21), (22), (26), (27), (28), (29), (30), (31), (32), % 151.63/22.42 | (34), (36), (37), (38), (39) are inconsistent by sub-proof #433. % 151.63/22.42 | % 151.63/22.42 End of proof % 151.63/22.42 % 151.63/22.42 Sub-proof #319 shows that the following formulas are inconsistent: % 151.63/22.42 ---------------------------------------------------------------- % 151.63/22.42 (1) all_56_11 = all_8_2 % 151.63/22.42 (2) ~ (all_52_14 = all_4_2) % 151.63/22.42 (3) all_58_6 = e0 | all_58_7 = e0 | all_58_8 = e0 | all_58_11 = e0 % 151.63/22.42 (4) all_56_21 = all_6_2 % 151.63/22.42 (5) all_56_1 = all_10_2 % 151.63/22.42 (6) op(e2, all_8_2) = all_56_10 % 151.63/22.42 (7) ~ (all_52_6 = all_6_0) % 151.63/22.42 (8) ~ (e1 = e0) % 151.63/22.42 (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 151.63/22.42 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 151.63/22.42 (10) ~ (all_6_0 = all_6_2) % 151.63/22.42 (11) all_54_8 = all_6_0 % 151.63/22.42 (12) all_58_8 = all_6_2 % 151.63/22.42 (13) all_56_21 = e2 % 151.63/22.42 (14) all_56_19 = e1 % 151.63/22.42 (15) ~ (all_52_14 = all_6_0) % 151.63/22.42 (16) all_56_31 = all_4_2 % 151.63/22.42 (17) all_58_11 = all_52_14 % 151.63/22.42 (18) all_56_1 = e3 | all_56_11 = e2 | all_56_21 = e1 | all_56_31 = e0 % 151.63/22.42 (19) all_58_6 = all_6_0 % 151.63/22.42 (20) ~ (all_6_0 = e0) % 151.63/22.42 (21) all_58_7 = all_52_6 % 151.63/22.42 (22) op(e2, e2) = all_8_2 % 151.63/22.42 (23) ~ (all_52_6 = all_6_2) % 151.63/22.42 (24) op(all_6_2, all_6_2) = e3 % 151.63/22.42 (25) ~ (e2 = e0) % 151.63/22.42 (26) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0 % 151.63/22.42 (27) ~ (all_10_2 = all_6_0) % 151.63/22.42 (28) op(all_8_2, all_8_2) = all_8_1 % 151.63/22.42 (29) all_56_19 = all_52_6 % 151.63/22.42 % 151.63/22.42 Begin of proof % 151.63/22.42 | % 151.63/22.42 | COMBINE_EQS: (14), (29) imply: % 151.63/22.42 | (30) all_52_6 = e1 % 151.63/22.42 | % 151.63/22.42 | SIMP: (30) implies: % 151.63/22.42 | (31) all_52_6 = e1 % 151.63/22.42 | % 151.63/22.42 | COMBINE_EQS: (4), (13) imply: % 151.63/22.42 | (32) all_6_2 = e2 % 151.63/22.42 | % 151.63/22.42 | SIMP: (32) implies: % 151.63/22.42 | (33) all_6_2 = e2 % 151.63/22.42 | % 151.63/22.42 | COMBINE_EQS: (12), (33) imply: % 151.63/22.42 | (34) all_58_8 = e2 % 151.63/22.42 | % 151.63/22.42 | COMBINE_EQS: (21), (31) imply: % 151.63/22.42 | (35) all_58_7 = e1 % 151.63/22.42 | % 151.63/22.42 | REDUCE: (7), (31) imply: % 151.63/22.42 | (36) ~ (all_6_0 = e1) % 151.63/22.42 | % 151.63/22.42 | SIMP: (36) implies: % 151.63/22.42 | (37) ~ (all_6_0 = e1) % 151.63/22.42 | % 151.63/22.42 | REDUCE: (23), (31), (33) imply: % 151.63/22.42 | (38) ~ (e2 = e1) % 151.63/22.42 | % 151.63/22.42 | SIMP: (38) implies: % 151.63/22.42 | (39) ~ (e2 = e1) % 151.63/22.42 | % 151.63/22.42 | REDUCE: (10), (33) imply: % 151.63/22.42 | (40) ~ (all_6_0 = e2) % 151.63/22.42 | % 151.63/22.42 | REDUCE: (24), (33) imply: % 151.63/22.43 | (41) op(e2, e2) = e3 % 151.63/22.43 | % 151.63/22.43 | REF_CLOSE: (1), (2), (3), (5), (6), (8), (9), (11), (13), (15), (16), (17), % 151.63/22.43 | (18), (19), (20), (22), (25), (26), (27), (28), (34), (35), (37), % 151.63/22.43 | (39), (40), (41) are inconsistent by sub-proof #434. % 151.63/22.43 | % 151.63/22.43 End of proof % 151.63/22.43 % 151.63/22.43 Sub-proof #320 shows that the following formulas are inconsistent: % 151.63/22.43 ---------------------------------------------------------------- % 151.63/22.43 (1) all_56_11 = all_8_2 % 151.63/22.43 (2) all_54_9 = all_52_6 % 151.63/22.43 (3) all_56_31 = e3 % 151.63/22.43 (4) ~ (all_52_6 = all_52_14) % 151.63/22.43 (5) ~ (all_6_0 = e2) % 151.63/22.43 (6) all_56_21 = all_6_2 % 151.63/22.43 (7) all_56_21 = e0 % 151.63/22.43 (8) all_56_1 = all_4_1 % 151.63/22.43 (9) all_56_23 = e1 % 151.63/22.43 (10) ~ (all_52_6 = all_6_0) % 151.63/22.43 (11) ~ (all_6_0 = all_6_2) % 151.63/22.43 (12) all_54_8 = all_6_0 % 151.63/22.43 (13) ~ (all_52_14 = all_6_0) % 151.63/22.43 (14) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0 % 151.63/22.43 (15) all_56_1 = e3 | all_56_11 = e2 | all_56_21 = e1 | all_56_31 = e0 % 151.63/22.43 (16) all_56_23 = all_52_14 % 151.63/22.43 (17) ~ (all_52_6 = all_8_2) % 151.63/22.43 (18) ~ (all_6_0 = all_4_1) % 151.63/22.43 (19) ~ (all_52_6 = all_6_2) % 151.63/22.43 (20) ~ (all_52_14 = all_6_2) % 151.63/22.43 (21) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0 % 151.63/22.43 % 151.63/22.43 Begin of proof % 151.63/22.43 | % 151.63/22.43 | COMBINE_EQS: (6), (7) imply: % 151.63/22.43 | (22) all_6_2 = e0 % 151.63/22.43 | % 151.63/22.43 | SIMP: (22) implies: % 151.63/22.43 | (23) all_6_2 = e0 % 151.63/22.43 | % 151.63/22.43 | COMBINE_EQS: (9), (16) imply: % 151.63/22.43 | (24) all_52_14 = e1 % 151.63/22.43 | % 151.63/22.43 | SIMP: (24) implies: % 151.63/22.43 | (25) all_52_14 = e1 % 151.63/22.43 | % 151.63/22.43 | REDUCE: (4), (25) imply: % 151.63/22.43 | (26) ~ (all_52_6 = e1) % 151.63/22.43 | % 151.63/22.43 | REDUCE: (19), (23) imply: % 151.63/22.43 | (27) ~ (all_52_6 = e0) % 151.63/22.43 | % 151.63/22.43 | REDUCE: (13), (25) imply: % 151.63/22.43 | (28) ~ (all_6_0 = e1) % 151.63/22.43 | % 151.63/22.43 | SIMP: (28) implies: % 151.63/22.43 | (29) ~ (all_6_0 = e1) % 151.63/22.43 | % 151.63/22.43 | REDUCE: (20), (23), (25) imply: % 151.63/22.43 | (30) ~ (e1 = e0) % 151.63/22.43 | % 151.63/22.43 | REDUCE: (11), (23) imply: % 151.63/22.43 | (31) ~ (all_6_0 = e0) % 151.63/22.43 | % 151.63/22.43 | REF_CLOSE: (1), (2), (3), (5), (7), (8), (10), (12), (14), (15), (17), (18), % 151.63/22.43 | (21), (26), (27), (29), (30), (31) are inconsistent by sub-proof % 151.63/22.43 | #321. % 151.63/22.43 | % 151.63/22.43 End of proof % 151.63/22.43 % 151.63/22.43 Sub-proof #321 shows that the following formulas are inconsistent: % 151.63/22.43 ---------------------------------------------------------------- % 151.63/22.43 (1) all_56_11 = all_8_2 % 151.63/22.43 (2) all_54_9 = all_52_6 % 151.63/22.43 (3) ~ (all_52_6 = e1) % 151.63/22.43 (4) all_56_31 = e3 % 151.63/22.43 (5) ~ (all_6_0 = e2) % 151.63/22.43 (6) all_56_21 = e0 % 151.63/22.43 (7) all_56_1 = all_4_1 % 151.63/22.43 (8) ~ (all_6_0 = e1) % 151.63/22.43 (9) ~ (all_52_6 = all_6_0) % 151.63/22.43 (10) ~ (e1 = e0) % 151.63/22.43 (11) all_54_8 = all_6_0 % 151.63/22.43 (12) ~ (all_52_6 = e0) % 151.63/22.43 (13) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0 % 151.63/22.43 (14) all_56_1 = e3 | all_56_11 = e2 | all_56_21 = e1 | all_56_31 = e0 % 151.63/22.43 (15) ~ (all_52_6 = all_8_2) % 151.63/22.43 (16) ~ (all_6_0 = e0) % 151.63/22.43 (17) ~ (all_6_0 = all_4_1) % 151.63/22.43 (18) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0 % 151.63/22.43 % 151.63/22.43 Begin of proof % 151.63/22.43 | % 151.63/22.43 | BETA: splitting (18) gives: % 151.63/22.43 | % 151.63/22.43 | Case 1: % 151.63/22.43 | | % 151.63/22.43 | | (19) all_54_8 = e3 % 151.63/22.43 | | % 151.63/22.43 | | COMBINE_EQS: (11), (19) imply: % 151.63/22.43 | | (20) all_6_0 = e3 % 151.63/22.43 | | % 151.63/22.43 | | SIMP: (20) implies: % 151.63/22.43 | | (21) all_6_0 = e3 % 151.63/22.43 | | % 151.63/22.43 | | REDUCE: (9), (21) imply: % 151.63/22.43 | | (22) ~ (all_52_6 = e3) % 151.63/22.43 | | % 151.63/22.43 | | REDUCE: (17), (21) imply: % 151.63/22.43 | | (23) ~ (all_4_1 = e3) % 151.63/22.43 | | % 151.63/22.43 | | SIMP: (23) implies: % 151.63/22.43 | | (24) ~ (all_4_1 = e3) % 151.63/22.43 | | % 151.63/22.43 | | REDUCE: (16), (21) imply: % 151.63/22.43 | | (25) ~ (e3 = e0) % 151.63/22.43 | | % 151.63/22.43 | | BETA: splitting (14) gives: % 151.63/22.43 | | % 151.63/22.43 | | Case 1: % 151.63/22.43 | | | % 151.63/22.43 | | | (26) all_56_1 = e3 % 151.63/22.43 | | | % 151.63/22.43 | | | COMBINE_EQS: (7), (26) imply: % 151.63/22.43 | | | (27) all_4_1 = e3 % 151.63/22.43 | | | % 151.63/22.43 | | | REDUCE: (24), (27) imply: % 151.63/22.43 | | | (28) $false % 151.63/22.43 | | | % 151.63/22.43 | | | CLOSE: (28) is inconsistent. % 151.63/22.43 | | | % 151.63/22.43 | | Case 2: % 151.63/22.43 | | | % 151.63/22.43 | | | (29) all_56_11 = e2 | all_56_21 = e1 | all_56_31 = e0 % 151.63/22.43 | | | % 151.63/22.43 | | | BETA: splitting (13) gives: % 151.63/22.43 | | | % 151.63/22.43 | | | Case 1: % 151.63/22.43 | | | | % 151.63/22.43 | | | | (30) all_54_9 = e3 % 151.63/22.43 | | | | % 151.63/22.43 | | | | COMBINE_EQS: (2), (30) imply: % 151.63/22.43 | | | | (31) all_52_6 = e3 % 151.63/22.43 | | | | % 151.63/22.43 | | | | REDUCE: (22), (31) imply: % 151.63/22.43 | | | | (32) $false % 151.63/22.43 | | | | % 151.63/22.43 | | | | CLOSE: (32) is inconsistent. % 151.63/22.43 | | | | % 151.63/22.43 | | | Case 2: % 151.63/22.43 | | | | % 151.63/22.43 | | | | (33) all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0 % 151.63/22.43 | | | | % 151.63/22.43 | | | | BETA: splitting (29) gives: % 151.63/22.43 | | | | % 151.63/22.43 | | | | Case 1: % 151.63/22.43 | | | | | % 151.63/22.43 | | | | | (34) all_56_11 = e2 % 151.63/22.43 | | | | | % 151.63/22.43 | | | | | COMBINE_EQS: (1), (34) imply: % 151.63/22.43 | | | | | (35) all_8_2 = e2 % 151.63/22.43 | | | | | % 151.63/22.43 | | | | | REDUCE: (15), (35) imply: % 151.63/22.43 | | | | | (36) ~ (all_52_6 = e2) % 151.63/22.43 | | | | | % 151.63/22.43 | | | | | REF_CLOSE: (2), (3), (12), (33), (36) are inconsistent by sub-proof % 151.63/22.43 | | | | | #677. % 151.63/22.43 | | | | | % 151.63/22.43 | | | | Case 2: % 151.63/22.43 | | | | | % 151.63/22.43 | | | | | (37) all_56_21 = e1 | all_56_31 = e0 % 151.63/22.43 | | | | | % 151.63/22.43 | | | | | REF_CLOSE: (4), (6), (10), (25), (37) are inconsistent by sub-proof % 151.63/22.43 | | | | | #322. % 151.63/22.43 | | | | | % 151.63/22.43 | | | | End of split % 151.63/22.43 | | | | % 151.63/22.43 | | | End of split % 151.63/22.43 | | | % 151.63/22.43 | | End of split % 151.63/22.43 | | % 151.63/22.43 | Case 2: % 151.63/22.43 | | % 151.63/22.43 | | (38) all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0 % 151.63/22.43 | | % 151.63/22.43 | | REF_CLOSE: (5), (8), (11), (16), (38) are inconsistent by sub-proof #451. % 151.63/22.43 | | % 151.63/22.43 | End of split % 151.63/22.43 | % 151.63/22.43 End of proof % 151.63/22.43 % 151.63/22.43 Sub-proof #322 shows that the following formulas are inconsistent: % 151.63/22.43 ---------------------------------------------------------------- % 151.63/22.43 (1) ~ (e3 = e0) % 151.63/22.43 (2) all_56_31 = e3 % 151.63/22.43 (3) all_56_21 = e0 % 151.63/22.43 (4) ~ (e1 = e0) % 151.63/22.43 (5) all_56_21 = e1 | all_56_31 = e0 % 151.63/22.43 % 151.63/22.43 Begin of proof % 151.63/22.43 | % 151.63/22.43 | BETA: splitting (5) gives: % 151.63/22.43 | % 151.63/22.43 | Case 1: % 151.63/22.43 | | % 151.63/22.43 | | (6) all_56_21 = e1 % 151.63/22.43 | | % 151.63/22.43 | | COMBINE_EQS: (3), (6) imply: % 151.63/22.43 | | (7) e1 = e0 % 151.63/22.43 | | % 151.63/22.43 | | REDUCE: (4), (7) imply: % 151.63/22.43 | | (8) $false % 151.63/22.43 | | % 151.63/22.43 | | CLOSE: (8) is inconsistent. % 151.63/22.43 | | % 151.63/22.43 | Case 2: % 151.63/22.43 | | % 151.63/22.43 | | (9) all_56_31 = e0 % 151.63/22.43 | | % 151.63/22.43 | | REF_CLOSE: (1), (2), (9) are inconsistent by sub-proof #543. % 151.63/22.43 | | % 151.63/22.43 | End of split % 151.63/22.43 | % 151.63/22.43 End of proof % 151.63/22.43 % 151.63/22.43 Sub-proof #323 shows that the following formulas are inconsistent: % 151.63/22.43 ---------------------------------------------------------------- % 151.63/22.43 (1) op(e0, all_52_13) = all_56_14 % 151.63/22.43 (2) ~ (all_52_4 = all_52_8) % 151.63/22.43 (3) ~ (all_52_7 = all_52_11) % 151.63/22.43 (4) ~ (all_52_8 = all_52_9) % 151.63/22.43 (5) all_54_9 = all_52_6 % 151.63/22.43 (6) ~ (all_52_6 = e1) % 151.63/22.43 (7) ~ (all_52_9 = e2) % 151.63/22.43 (8) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0 % 151.63/22.43 (9) all_54_10 = all_6_2 % 151.63/22.43 (10) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0 % 151.63/22.43 (11) op(e3, e2) = all_56_8 % 151.63/22.43 (12) all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2 % 151.63/22.43 (13) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0 % 151.63/22.43 (14) all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2 % 151.63/22.43 (15) op(e3, e3) = e3 % 151.63/22.43 (16) ~ (all_52_4 = all_52_7) % 151.63/22.43 (17) all_58_4 = all_52_8 % 151.63/22.43 (18) ~ (all_52_6 = all_52_14) % 151.63/22.43 (19) ~ (all_52_11 = e0) % 151.63/22.43 (20) all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1 % 151.63/22.43 (21) op(e2, e1) = all_52_9 % 151.63/22.43 (22) all_56_21 = all_6_2 % 151.63/22.43 (23) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 151.63/22.43 (24) all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2 % 151.63/22.43 (25) op(e3, all_10_1) = all_10_0 % 151.63/22.43 (26) all_56_27 = all_52_7 % 151.63/22.43 (27) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0 % 151.63/22.43 (28) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0 % 151.63/22.43 (29) ~ (all_52_6 = e3) % 151.63/22.43 (30) all_58_5 = all_52_9 % 151.63/22.43 (31) all_54_1 = all_52_4 % 151.63/22.43 (32) ~ (all_52_13 = e2) % 151.63/22.43 (33) all_58_9 = all_52_12 % 151.63/22.43 (34) all_58_12 = e0 % 151.63/22.43 (35) op(e0, all_52_14) = all_56_22 % 151.63/22.43 (36) op(e0, e2) = all_52_7 % 151.63/22.43 (37) op(e1, e0) = all_52_14 % 151.63/22.43 (38) all_54_14 = all_52_11 % 151.63/22.43 (39) ( ~ (all_56_0 = all_56_1) & ~ (all_56_2 = all_56_3) & ~ (all_56_4 = % 151.63/22.43 all_56_5) & ~ (all_56_6 = all_56_7)) | ( ~ (all_56_8 = all_56_9) & % 151.63/22.43 ~ (all_56_10 = all_56_11) & ~ (all_56_12 = all_56_13) & ~ (all_56_14 % 151.63/22.43 = all_56_15)) | ( ~ (all_56_16 = all_56_17) & ~ (all_56_18 = % 151.63/22.43 all_56_19) & ~ (all_56_20 = all_56_21) & ~ (all_56_22 = % 151.63/22.43 all_56_23)) | ( ~ (all_56_24 = all_56_25) & ~ (all_56_26 = % 151.63/22.43 all_56_27) & ~ (all_56_28 = all_56_29) & ~ (all_56_30 = % 151.63/22.43 all_56_31)) % 151.63/22.43 (40) all_56_16 = all_52_8 % 151.63/22.43 (41) all_58_1 = all_52_4 % 151.63/22.43 (42) all_58_13 = all_52_7 % 151.63/22.43 (43) all_58_3 = e3 % 151.63/22.43 (44) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0 % 151.63/22.43 (45) ~ (all_56_21 = e3) | all_56_17 = e1 % 151.63/22.43 (46) all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0 % 151.63/22.43 (47) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 151.63/22.43 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 151.63/22.43 (48) ~ (all_52_11 = e3) % 151.63/22.43 (49) all_56_25 = e0 % 151.63/22.43 (50) all_54_3 = all_52_12 % 151.63/22.43 (51) all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0 % 151.63/22.43 (52) ~ (all_52_14 = e1) % 151.63/22.43 (53) all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) & % 151.63/22.43 (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0)) % 151.63/22.43 (54) ~ (all_6_2 = e0) % 151.63/22.43 (55) ~ (all_52_12 = e3) % 151.63/22.43 (56) op(e2, all_52_7) = all_56_26 % 151.63/22.43 (57) op(e1, e2) = all_52_6 % 151.63/22.43 (58) all_56_13 = all_52_9 % 151.63/22.43 (59) op(e2, all_52_6) = all_56_18 % 151.63/22.43 (60) op(e0, e1) = all_52_11 % 151.63/22.43 (61) all_58_2 = e2 % 151.63/22.43 (62) op(e3, e3) = all_56_0 % 151.63/22.43 (63) ~ (all_52_14 = e3) % 151.63/22.43 (64) ~ (all_4_2 = e1) % 151.63/22.43 (65) ~ (all_52_9 = e3) % 151.63/22.43 (66) all_58_8 = all_6_2 % 151.63/22.43 (67) op(e0, e3) = all_4_0 % 151.63/22.43 (68) all_54_6 = all_52_9 % 151.63/22.43 (69) ~ (all_4_0 = e1) % 151.63/22.43 (70) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0 % 151.63/22.43 (71) all_58_15 = e3 % 151.63/22.43 (72) all_56_9 = e2 % 151.63/22.43 (73) ~ (e2 = e1) % 151.63/22.43 (74) ~ (all_52_9 = all_52_13) % 151.63/22.43 (75) all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1 % 151.63/22.43 (76) all_58_3 = all_8_2 % 151.63/22.43 (77) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0 % 151.63/22.43 (78) all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1 % 151.63/22.43 (79) ~ (all_52_6 = all_52_7) % 151.63/22.43 (80) ~ (all_52_8 = e3) % 151.63/22.43 (81) all_58_11 = all_52_14 % 151.63/22.43 (82) all_56_24 = all_52_12 % 151.63/22.43 (83) all_54_7 = all_52_13 % 151.63/22.43 (84) ~ (all_52_8 = all_52_11) % 151.63/22.43 (85) all_54_13 = all_52_7 % 151.63/22.43 (86) all_54_2 = all_52_8 % 151.63/22.43 (87) all_56_17 = e1 % 151.63/22.43 (88) op(e3, e2) = all_52_4 % 151.63/22.43 (89) ~ (all_52_13 = all_52_14) % 151.63/22.43 (90) all_56_23 = all_52_14 % 151.63/22.43 (91) op(e1, e1) = all_6_2 % 151.63/22.43 (92) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0 % 151.63/22.43 (93) all_58_15 = all_4_2 % 151.63/22.43 (94) all_56_29 = all_52_11 % 151.63/22.43 (95) ~ (all_52_13 = e3) % 151.63/22.43 (96) ~ (all_52_7 = e3) % 151.63/22.43 (97) ~ (all_6_2 = e2) % 151.63/22.43 (98) all_58_7 = all_52_6 % 151.63/22.43 (99) all_58_10 = all_52_13 % 151.63/22.43 (100) op(e1, all_6_2) = all_56_20 % 151.63/22.43 (101) all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1 % 151.63/22.43 (102) ~ (all_52_4 = e3) % 151.63/22.43 (103) all_58_1 = e0 | all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0 % 151.63/22.43 (104) ~ (all_52_12 = all_52_14) % 151.63/22.43 (105) op(e1, all_52_9) = all_56_12 % 151.63/22.43 (106) ~ (all_52_4 = all_52_12) % 151.63/22.43 (107) op(e2, e0) = all_52_13 % 151.63/22.43 (108) ~ (all_52_8 = all_52_12) % 151.63/22.43 (109) all_58_8 = e3 % 151.63/22.43 (110) ~ (all_8_2 = e0) % 151.63/22.43 (111) op(all_6_2, all_6_2) = e3 % 151.63/22.43 (112) op(e1, all_52_11) = all_56_28 % 151.63/22.43 (113) all_58_0 = e3 % 151.63/22.43 (114) ~ (all_52_7 = e0) % 151.63/22.43 (115) op(e3, e3) = all_10_1 % 151.63/22.43 (116) ~ (all_10_0 = e2) % 151.63/22.43 (117) all_56_1 = e3 % 151.63/22.43 (118) ~ (all_52_4 = all_52_6) % 151.63/22.43 (119) all_58_14 = all_52_11 % 151.63/22.43 (120) all_56_19 = all_52_6 % 151.63/22.43 (121) ~ (all_4_0 = e2) % 151.63/22.43 (122) ~ (all_4_0 = e3) % 151.63/22.43 (123) all_56_15 = all_52_13 % 151.63/22.43 (124) all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2 % 151.63/22.43 (125) all_54_11 = all_52_14 % 151.63/22.43 (126) op(e0, e3) = e0 % 151.63/22.43 % 151.63/22.43 Begin of proof % 151.63/22.43 | % 151.63/22.43 | GROUND_INST: instantiating (47) with e0, all_4_0, e3, e0, simplifying with % 151.63/22.43 | (67), (126) gives: % 151.63/22.43 | (127) all_4_0 = e0 % 151.63/22.43 | % 151.63/22.43 | GROUND_INST: instantiating (47) with all_52_4, all_56_8, e2, e3, simplifying % 151.63/22.43 | with (11), (88) gives: % 151.63/22.43 | (128) all_56_8 = all_52_4 % 151.63/22.43 | % 151.63/22.43 | GROUND_INST: instantiating (47) with e3, all_56_0, e3, e3, simplifying with % 151.63/22.43 | (15), (62) gives: % 151.63/22.43 | (129) all_56_0 = e3 % 151.63/22.43 | % 151.63/22.43 | GROUND_INST: instantiating (47) with all_10_1, all_56_0, e3, e3, simplifying % 151.63/22.43 | with (62), (115) gives: % 151.63/22.43 | (130) all_56_0 = all_10_1 % 151.63/22.43 | % 151.63/22.43 | COMBINE_EQS: (129), (130) imply: % 151.63/22.43 | (131) all_10_1 = e3 % 151.63/22.43 | % 151.63/22.43 | REDUCE: (122), (127) imply: % 151.63/22.43 | (132) ~ (e3 = e0) % 151.63/22.43 | % 151.63/22.43 | SIMP: (132) implies: % 151.63/22.43 | (133) ~ (e3 = e0) % 151.63/22.43 | % 151.63/22.43 | REDUCE: (121), (127) imply: % 151.63/22.43 | (134) ~ (e2 = e0) % 151.63/22.43 | % 151.63/22.43 | SIMP: (134) implies: % 151.63/22.43 | (135) ~ (e2 = e0) % 151.63/22.43 | % 151.63/22.43 | REDUCE: (69), (127) imply: % 151.63/22.43 | (136) ~ (e1 = e0) % 151.63/22.43 | % 151.63/22.43 | SIMP: (136) implies: % 151.63/22.43 | (137) ~ (e1 = e0) % 151.63/22.43 | % 151.63/22.43 | REDUCE: (25), (131) imply: % 151.63/22.43 | (138) op(e3, e3) = all_10_0 % 151.63/22.43 | % 151.63/22.43 | GROUND_INST: instantiating (47) with e3, all_10_0, e3, e3, simplifying with % 151.63/22.43 | (15), (138) gives: % 151.63/22.43 | (139) all_10_0 = e3 % 151.63/22.43 | % 151.63/22.43 | REDUCE: (116), (139) imply: % 151.63/22.43 | (140) ~ (e3 = e2) % 151.63/22.43 | % 151.63/22.43 | BETA: splitting (70) gives: % 151.63/22.43 | % 151.63/22.43 | Case 1: % 151.63/22.43 | | % 151.63/22.43 | | (141) all_54_13 = e3 % 151.63/22.43 | | % 151.63/22.43 | | REF_CLOSE: (85), (96), (141) are inconsistent by sub-proof #668. % 151.63/22.43 | | % 151.63/22.43 | Case 2: % 151.63/22.43 | | % 151.63/22.43 | | (142) all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0 % 151.63/22.43 | | % 151.63/22.43 | | BETA: splitting (13) gives: % 151.63/22.43 | | % 151.63/22.43 | | Case 1: % 151.63/22.43 | | | % 151.63/22.43 | | | (143) all_54_11 = e3 % 151.63/22.43 | | | % 151.63/22.43 | | | REF_CLOSE: (63), (125), (143) are inconsistent by sub-proof #416. % 151.63/22.43 | | | % 151.63/22.43 | | Case 2: % 151.63/22.43 | | | % 151.63/22.43 | | | (144) all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0 % 151.63/22.43 | | | % 151.63/22.43 | | | BETA: splitting (28) gives: % 151.63/22.43 | | | % 151.63/22.43 | | | Case 1: % 151.63/22.43 | | | | % 151.63/22.43 | | | | (145) all_54_6 = e3 % 151.63/22.43 | | | | % 151.63/22.43 | | | | REF_CLOSE: (65), (68), (145) are inconsistent by sub-proof #402. % 151.63/22.43 | | | | % 151.63/22.43 | | | Case 2: % 151.63/22.43 | | | | % 151.63/22.43 | | | | (146) all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0 % 151.63/22.43 | | | | % 151.63/22.43 | | | | BETA: splitting (8) gives: % 151.63/22.43 | | | | % 151.63/22.43 | | | | Case 1: % 151.63/22.43 | | | | | % 151.63/22.43 | | | | | (147) all_54_14 = e3 % 151.63/22.43 | | | | | % 151.63/22.43 | | | | | REF_CLOSE: (38), (48), (147) are inconsistent by sub-proof #729. % 151.63/22.43 | | | | | % 151.63/22.43 | | | | Case 2: % 151.63/22.43 | | | | | % 151.63/22.43 | | | | | (148) ~ (all_54_14 = e3) % 151.63/22.43 | | | | | (149) all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0 % 151.63/22.43 | | | | | % 151.63/22.43 | | | | | BETA: splitting (27) gives: % 151.63/22.43 | | | | | % 151.63/22.43 | | | | | Case 1: % 151.63/22.43 | | | | | | % 151.63/22.43 | | | | | | (150) all_54_7 = e3 % 151.63/22.43 | | | | | | % 151.63/22.43 | | | | | | REF_CLOSE: (83), (95), (150) are inconsistent by sub-proof #601. % 151.63/22.43 | | | | | | % 151.63/22.43 | | | | | Case 2: % 151.63/22.43 | | | | | | % 151.63/22.43 | | | | | | (151) ~ (all_54_7 = e3) % 151.63/22.43 | | | | | | (152) all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0 % 151.63/22.43 | | | | | | % 151.63/22.43 | | | | | | BETA: splitting (77) gives: % 151.63/22.43 | | | | | | % 151.63/22.43 | | | | | | Case 1: % 151.63/22.43 | | | | | | | % 151.63/22.43 | | | | | | | (153) all_54_9 = e3 % 151.63/22.43 | | | | | | | % 151.63/22.43 | | | | | | | COMBINE_EQS: (5), (153) imply: % 151.63/22.43 | | | | | | | (154) all_52_6 = e3 % 151.63/22.43 | | | | | | | % 151.63/22.43 | | | | | | | REDUCE: (29), (154) imply: % 151.63/22.43 | | | | | | | (155) $false % 151.63/22.43 | | | | | | | % 151.63/22.43 | | | | | | | CLOSE: (155) is inconsistent. % 151.63/22.43 | | | | | | | % 151.63/22.43 | | | | | | Case 2: % 151.63/22.43 | | | | | | | % 151.63/22.43 | | | | | | | (156) ~ (all_54_9 = e3) % 151.63/22.43 | | | | | | | (157) all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0 % 151.63/22.43 | | | | | | | % 151.63/22.43 | | | | | | | BETA: splitting (10) gives: % 151.63/22.43 | | | | | | | % 151.63/22.43 | | | | | | | Case 1: % 151.63/22.43 | | | | | | | | % 151.63/22.43 | | | | | | | | (158) all_54_3 = e3 % 151.63/22.43 | | | | | | | | % 151.63/22.43 | | | | | | | | REF_CLOSE: (50), (55), (158) are inconsistent by sub-proof #659. % 151.63/22.43 | | | | | | | | % 151.63/22.43 | | | | | | | Case 2: % 151.63/22.43 | | | | | | | | % 151.63/22.43 | | | | | | | | (159) ~ (all_54_3 = e3) % 151.63/22.43 | | | | | | | | (160) all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0 % 151.63/22.43 | | | | | | | | % 151.63/22.43 | | | | | | | | BETA: splitting (44) gives: % 151.63/22.43 | | | | | | | | % 151.63/22.43 | | | | | | | | Case 1: % 151.63/22.43 | | | | | | | | | % 151.63/22.43 | | | | | | | | | (161) all_54_2 = e3 % 151.63/22.43 | | | | | | | | | % 151.63/22.43 | | | | | | | | | REF_CLOSE: (80), (86), (161) are inconsistent by sub-proof % 151.63/22.43 | | | | | | | | | #728. % 151.63/22.43 | | | | | | | | | % 151.63/22.43 | | | | | | | | Case 2: % 151.63/22.43 | | | | | | | | | % 151.63/22.43 | | | | | | | | | (162) all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0 % 151.63/22.43 | | | | | | | | | % 151.63/22.43 | | | | | | | | | BETA: splitting (92) gives: % 151.63/22.43 | | | | | | | | | % 151.63/22.43 | | | | | | | | | Case 1: % 151.63/22.43 | | | | | | | | | | % 151.63/22.43 | | | | | | | | | | (163) all_54_1 = e3 % 151.63/22.43 | | | | | | | | | | % 151.63/22.43 | | | | | | | | | | REF_CLOSE: (31), (102), (163) are inconsistent by sub-proof % 151.63/22.43 | | | | | | | | | | #722. % 151.63/22.43 | | | | | | | | | | % 151.63/22.43 | | | | | | | | | Case 2: % 151.63/22.43 | | | | | | | | | | % 151.63/22.43 | | | | | | | | | | (164) all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0 % 151.63/22.43 | | | | | | | | | | % 151.63/22.43 | | | | | | | | | | BETA: splitting (53) gives: % 151.63/22.43 | | | | | | | | | | % 151.63/22.43 | | | | | | | | | | Case 1: % 151.63/22.43 | | | | | | | | | | | % 151.63/22.43 | | | | | | | | | | | (165) all_58_15 = e0 % 151.63/22.43 | | | | | | | | | | | % 151.63/22.43 | | | | | | | | | | | COMBINE_EQS: (71), (165) imply: % 151.63/22.43 | | | | | | | | | | | (166) e3 = e0 % 151.63/22.43 | | | | | | | | | | | % 151.63/22.43 | | | | | | | | | | | REDUCE: (133), (166) imply: % 151.63/22.43 | | | | | | | | | | | (167) $false % 151.63/22.43 | | | | | | | | | | | % 151.63/22.43 | | | | | | | | | | | CLOSE: (167) is inconsistent. % 151.63/22.43 | | | | | | | | | | | % 151.63/22.43 | | | | | | | | | | Case 2: % 151.63/22.43 | | | | | | | | | | | % 151.63/22.43 | | | | | | | | | | | (168) ~ (all_58_15 = e0) % 151.63/22.43 | | | | | | | | | | | (169) (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) % 151.63/22.43 | | | | | | | | | | | & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = % 151.63/22.43 | | | | | | | | | | | e0) % 151.63/22.43 | | | | | | | | | | | % 151.63/22.43 | | | | | | | | | | | ALPHA: (169) implies: % 151.63/22.43 | | | | | | | | | | | (170) all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0 % 151.63/22.43 | | | | | | | | | | | % 151.63/22.43 | | | | | | | | | | | BETA: splitting (12) gives: % 151.63/22.43 | | | | | | | | | | | % 151.63/22.43 | | | | | | | | | | | Case 1: % 151.63/22.43 | | | | | | | | | | | | % 151.63/22.43 | | | | | | | | | | | | (171) all_58_9 = e2 % 151.63/22.43 | | | | | | | | | | | | % 151.63/22.43 | | | | | | | | | | | | COMBINE_EQS: (33), (171) imply: % 151.63/22.43 | | | | | | | | | | | | (172) all_52_12 = e2 % 151.63/22.43 | | | | | | | | | | | | % 151.63/22.43 | | | | | | | | | | | | REDUCE: (106), (172) imply: % 151.63/22.43 | | | | | | | | | | | | (173) ~ (all_52_4 = e2) % 151.63/22.43 | | | | | | | | | | | | % 151.63/22.43 | | | | | | | | | | | | REDUCE: (108), (172) imply: % 151.63/22.43 | | | | | | | | | | | | (174) ~ (all_52_8 = e2) % 151.63/22.43 | | | | | | | | | | | | % 151.63/22.43 | | | | | | | | | | | | REDUCE: (104), (172) imply: % 151.63/22.43 | | | | | | | | | | | | (175) ~ (all_52_14 = e2) % 151.63/22.43 | | | | | | | | | | | | % 151.63/22.43 | | | | | | | | | | | | SIMP: (175) implies: % 151.63/22.43 | | | | | | | | | | | | (176) ~ (all_52_14 = e2) % 151.63/22.43 | | | | | | | | | | | | % 151.63/22.43 | | | | | | | | | | | | REDUCE: (55), (172) imply: % 151.63/22.43 | | | | | | | | | | | | (177) ~ (e3 = e2) % 151.63/22.43 | | | | | | | | | | | | % 151.63/22.43 | | | | | | | | | | | | BETA: splitting (20) gives: % 151.63/22.43 | | | | | | | | | | | | % 151.63/22.43 | | | | | | | | | | | | Case 1: % 151.63/22.43 | | | | | | | | | | | | | % 151.63/22.43 | | | | | | | | | | | | | (178) all_58_9 = e1 % 151.63/22.43 | | | | | | | | | | | | | % 151.63/22.43 | | | | | | | | | | | | | COMBINE_EQS: (171), (178) imply: % 151.63/22.43 | | | | | | | | | | | | | (179) e2 = e1 % 151.63/22.43 | | | | | | | | | | | | | % 151.63/22.43 | | | | | | | | | | | | | REDUCE: (73), (179) imply: % 151.63/22.43 | | | | | | | | | | | | | (180) $false % 151.63/22.43 | | | | | | | | | | | | | % 151.63/22.43 | | | | | | | | | | | | | CLOSE: (180) is inconsistent. % 151.63/22.43 | | | | | | | | | | | | | % 151.63/22.43 | | | | | | | | | | | | Case 2: % 151.63/22.43 | | | | | | | | | | | | | % 151.63/22.43 | | | | | | | | | | | | | (181) all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1 % 151.63/22.43 | | | | | | | | | | | | | % 151.63/22.43 | | | | | | | | | | | | | BETA: splitting (14) gives: % 151.63/22.43 | | | | | | | | | | | | | % 151.63/22.43 | | | | | | | | | | | | | Case 1: % 151.63/22.43 | | | | | | | | | | | | | | % 151.63/22.43 | | | | | | | | | | | | | | (182) all_58_4 = e2 % 151.63/22.43 | | | | | | | | | | | | | | % 151.63/22.43 | | | | | | | | | | | | | | COMBINE_EQS: (17), (182) imply: % 151.63/22.43 | | | | | | | | | | | | | | (183) all_52_8 = e2 % 151.63/22.43 | | | | | | | | | | | | | | % 151.63/22.43 | | | | | | | | | | | | | | REDUCE: (174), (183) imply: % 151.63/22.43 | | | | | | | | | | | | | | (184) $false % 151.63/22.43 | | | | | | | | | | | | | | % 151.63/22.43 | | | | | | | | | | | | | | CLOSE: (184) is inconsistent. % 151.63/22.43 | | | | | | | | | | | | | | % 151.63/22.43 | | | | | | | | | | | | | Case 2: % 151.63/22.43 | | | | | | | | | | | | | | % 151.63/22.43 | | | | | | | | | | | | | | (185) all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2 % 151.63/22.43 | | | | | | | | | | | | | | % 151.63/22.43 | | | | | | | | | | | | | | BETA: splitting (181) gives: % 151.63/22.43 | | | | | | | | | | | | | | % 151.63/22.43 | | | | | | | | | | | | | | Case 1: % 151.63/22.43 | | | | | | | | | | | | | | | % 151.63/22.43 | | | | | | | | | | | | | | | (186) all_58_10 = e1 % 151.63/22.43 | | | | | | | | | | | | | | | % 151.63/22.43 | | | | | | | | | | | | | | | COMBINE_EQS: (99), (186) imply: % 151.63/22.43 | | | | | | | | | | | | | | | (187) all_52_13 = e1 % 151.63/22.43 | | | | | | | | | | | | | | | % 151.63/22.43 | | | | | | | | | | | | | | | REDUCE: (74), (187) imply: % 151.63/22.43 | | | | | | | | | | | | | | | (188) ~ (all_52_9 = e1) % 151.63/22.43 | | | | | | | | | | | | | | | % 151.63/22.43 | | | | | | | | | | | | | | | REDUCE: (89), (187) imply: % 151.63/22.43 | | | | | | | | | | | | | | | (189) ~ (all_52_14 = e1) % 151.63/22.43 | | | | | | | | | | | | | | | % 151.63/22.43 | | | | | | | | | | | | | | | BETA: splitting (185) gives: % 151.63/22.43 | | | | | | | | | | | | | | | % 151.63/22.43 | | | | | | | | | | | | | | | Case 1: % 151.63/22.43 | | | | | | | | | | | | | | | | % 151.63/22.43 | | | | | | | | | | | | | | | | (190) all_58_5 = e2 % 151.63/22.43 | | | | | | | | | | | | | | | | % 151.63/22.43 | | | | | | | | | | | | | | | | COMBINE_EQS: (30), (190) imply: % 151.63/22.43 | | | | | | | | | | | | | | | | (191) all_52_9 = e2 % 151.63/22.43 | | | | | | | | | | | | | | | | % 151.63/22.43 | | | | | | | | | | | | | | | | REDUCE: (7), (191) imply: % 151.63/22.43 | | | | | | | | | | | | | | | | (192) $false % 151.63/22.43 | | | | | | | | | | | | | | | | % 151.63/22.43 | | | | | | | | | | | | | | | | CLOSE: (192) is inconsistent. % 151.63/22.43 | | | | | | | | | | | | | | | | % 151.63/22.43 | | | | | | | | | | | | | | | Case 2: % 151.63/22.43 | | | | | | | | | | | | | | | | % 151.63/22.43 | | | | | | | | | | | | | | | | (193) ~ (all_58_5 = e2) % 151.63/22.43 | | | | | | | | | | | | | | | | (194) all_58_8 = e2 | all_58_14 = e2 % 151.63/22.43 | | | | | | | | | | | | | | | | % 151.63/22.43 | | | | | | | | | | | | | | | | BETA: splitting (51) gives: % 151.63/22.43 | | | | | | | | | | | | | | | | % 151.63/22.43 | | | | | | | | | | | | | | | | Case 1: % 151.63/22.43 | | | | | | | | | | | | | | | | | % 151.63/22.43 | | | | | | | | | | | | | | | | | (195) all_58_2 = e0 % 151.63/22.43 | | | | | | | | | | | | | | | | | % 151.63/22.43 | | | | | | | | | | | | | | | | | COMBINE_EQS: (61), (195) imply: % 151.63/22.43 | | | | | | | | | | | | | | | | | (196) e2 = e0 % 151.63/22.43 | | | | | | | | | | | | | | | | | % 151.63/22.43 | | | | | | | | | | | | | | | | | REDUCE: (135), (196) imply: % 151.63/22.43 | | | | | | | | | | | | | | | | | (197) $false % 151.63/22.43 | | | | | | | | | | | | | | | | | % 151.63/22.43 | | | | | | | | | | | | | | | | | CLOSE: (197) is inconsistent. % 151.63/22.43 | | | | | | | | | | | | | | | | | % 151.63/22.43 | | | | | | | | | | | | | | | | Case 2: % 151.63/22.43 | | | | | | | | | | | | | | | | | % 151.63/22.43 | | | | | | | | | | | | | | | | | (198) all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0 % 151.63/22.43 | | | | | | | | | | | | | | | | | % 151.63/22.43 | | | | | | | | | | | | | | | | | BETA: splitting (198) gives: % 151.63/22.43 | | | | | | | | | | | | | | | | | % 151.63/22.43 | | | | | | | | | | | | | | | | | Case 1: % 151.63/22.43 | | | | | | | | | | | | | | | | | | % 151.63/22.43 | | | | | | | | | | | | | | | | | | (199) all_58_3 = e0 % 151.63/22.43 | | | | | | | | | | | | | | | | | | % 151.63/22.43 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (43), (199) imply: % 151.63/22.43 | | | | | | | | | | | | | | | | | | (200) e3 = e0 % 151.63/22.43 | | | | | | | | | | | | | | | | | | % 151.63/22.43 | | | | | | | | | | | | | | | | | | REDUCE: (133), (200) imply: % 151.63/22.43 | | | | | | | | | | | | | | | | | | (201) $false % 151.63/22.43 | | | | | | | | | | | | | | | | | | % 151.63/22.43 | | | | | | | | | | | | | | | | | | CLOSE: (201) is inconsistent. % 151.63/22.43 | | | | | | | | | | | | | | | | | | % 151.63/22.43 | | | | | | | | | | | | | | | | | Case 2: % 151.63/22.43 | | | | | | | | | | | | | | | | | | % 151.63/22.43 | | | | | | | | | | | | | | | | | | (202) all_58_5 = e0 | all_58_10 = e0 % 151.63/22.43 | | | | | | | | | | | | | | | | | | % 151.63/22.43 | | | | | | | | | | | | | | | | | | BETA: splitting (202) gives: % 151.63/22.43 | | | | | | | | | | | | | | | | | | % 151.63/22.43 | | | | | | | | | | | | | | | | | | Case 1: % 151.63/22.43 | | | | | | | | | | | | | | | | | | | % 151.63/22.43 | | | | | | | | | | | | | | | | | | | (203) all_58_5 = e0 % 151.63/22.43 | | | | | | | | | | | | | | | | | | | % 151.63/22.43 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (30), (203) imply: % 151.63/22.43 | | | | | | | | | | | | | | | | | | | (204) all_52_9 = e0 % 151.63/22.43 | | | | | | | | | | | | | | | | | | | % 151.63/22.43 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (58), (204) imply: % 151.63/22.43 | | | | | | | | | | | | | | | | | | | (205) all_56_13 = e0 % 151.63/22.43 | | | | | | | | | | | | | | | | | | | % 151.63/22.43 | | | | | | | | | | | | | | | | | | | REDUCE: (105), (204) imply: % 151.63/22.43 | | | | | | | | | | | | | | | | | | | (206) op(e1, e0) = all_56_12 % 151.63/22.43 | | | | | | | | | | | | | | | | | | | % 151.63/22.43 | | | | | | | | | | | | | | | | | | | BETA: splitting (194) gives: % 151.63/22.43 | | | | | | | | | | | | | | | | | | | % 151.63/22.43 | | | | | | | | | | | | | | | | | | | Case 1: % 151.63/22.43 | | | | | | | | | | | | | | | | | | | | % 151.63/22.43 | | | | | | | | | | | | | | | | | | | | (207) all_58_8 = e2 % 151.63/22.43 | | | | | | | | | | | | | | | | | | | | % 151.63/22.43 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (109), (207) imply: % 151.63/22.43 | | | | | | | | | | | | | | | | | | | | (208) e3 = e2 % 151.63/22.43 | | | | | | | | | | | | | | | | | | | | % 151.63/22.43 | | | | | | | | | | | | | | | | | | | | REDUCE: (140), (208) imply: % 151.63/22.43 | | | | | | | | | | | | | | | | | | | | (209) $false % 151.63/22.43 | | | | | | | | | | | | | | | | | | | | % 151.63/22.43 | | | | | | | | | | | | | | | | | | | | CLOSE: (209) is inconsistent. % 151.63/22.43 | | | | | | | | | | | | | | | | | | | | % 151.63/22.43 | | | | | | | | | | | | | | | | | | | Case 2: % 151.63/22.43 | | | | | | | | | | | | | | | | | | | | % 151.63/22.43 | | | | | | | | | | | | | | | | | | | | (210) all_58_14 = e2 % 151.63/22.43 | | | | | | | | | | | | | | | | | | | | % 151.63/22.43 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (119), (210) imply: % 151.63/22.43 | | | | | | | | | | | | | | | | | | | | (211) all_52_11 = e2 % 151.63/22.43 | | | | | | | | | | | | | | | | | | | | % 151.63/22.43 | | | | | | | | | | | | | | | | | | | | SIMP: (211) implies: % 151.63/22.43 | | | | | | | | | | | | | | | | | | | | (212) all_52_11 = e2 % 151.63/22.43 | | | | | | | | | | | | | | | | | | | | % 151.63/22.43 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (94), (212) imply: % 151.63/22.43 | | | | | | | | | | | | | | | | | | | | (213) all_56_29 = e2 % 151.63/22.43 | | | | | | | | | | | | | | | | | | | | % 151.63/22.43 | | | | | | | | | | | | | | | | | | | | REDUCE: (3), (212) imply: % 151.63/22.43 | | | | | | | | | | | | | | | | | | | | (214) ~ (all_52_7 = e2) % 151.63/22.43 | | | | | | | | | | | | | | | | | | | | % 151.63/22.43 | | | | | | | | | | | | | | | | | | | | REDUCE: (112), (212) imply: % 151.63/22.43 | | | | | | | | | | | | | | | | | | | | (215) op(e1, e2) = all_56_28 % 151.63/22.43 | | | | | | | | | | | | | | | | | | | | % 151.63/22.43 | | | | | | | | | | | | | | | | | | | | BETA: splitting (75) gives: % 151.63/22.43 | | | | | | | | | | | | | | | | | | | | % 151.63/22.43 | | | | | | | | | | | | | | | | | | | | Case 1: % 151.63/22.43 | | | | | | | | | | | | | | | | | | | | | % 151.63/22.43 | | | | | | | | | | | | | | | | | | | | | (216) all_58_4 = e1 % 151.63/22.43 | | | | | | | | | | | | | | | | | | | | | % 151.63/22.43 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (17), (216) imply: % 151.63/22.43 | | | | | | | | | | | | | | | | | | | | | (217) all_52_8 = e1 % 151.63/22.43 | | | | | | | | | | | | | | | | | | | | | % 151.63/22.43 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (40), (217) imply: % 151.63/22.43 | | | | | | | | | | | | | | | | | | | | | (218) all_56_16 = e1 % 151.63/22.43 | | | | | | | | | | | | | | | | | | | | | % 151.63/22.43 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (144) gives: % 151.63/22.43 | | | | | | | | | | | | | | | | | | | | | % 151.63/22.43 | | | | | | | | | | | | | | | | | | | | | Case 1: % 151.63/22.43 | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.43 | | | | | | | | | | | | | | | | | | | | | | (219) all_54_11 = e2 % 151.63/22.43 | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.43 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (125), (219) imply: % 151.63/22.43 | | | | | | | | | | | | | | | | | | | | | | (220) all_52_14 = e2 % 151.63/22.43 | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.43 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (176), (220) imply: % 151.63/22.43 | | | | | | | | | | | | | | | | | | | | | | (221) $false % 151.63/22.43 | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.43 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (221) is inconsistent. % 151.63/22.43 | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.43 | | | | | | | | | | | | | | | | | | | | | Case 2: % 151.63/22.43 | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.43 | | | | | | | | | | | | | | | | | | | | | | (222) all_54_11 = e1 | all_54_11 = e0 % 151.63/22.43 | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.43 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (222) gives: % 151.63/22.43 | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.43 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 151.63/22.43 | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.43 | | | | | | | | | | | | | | | | | | | | | | | (223) all_54_11 = e1 % 151.63/22.43 | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.43 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (125), (223) imply: % 151.63/22.43 | | | | | | | | | | | | | | | | | | | | | | | (224) all_52_14 = e1 % 151.63/22.43 | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.43 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (52), (224) imply: % 151.63/22.43 | | | | | | | | | | | | | | | | | | | | | | | (225) $false % 151.63/22.43 | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.43 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (225) is inconsistent. % 151.63/22.43 | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.43 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 151.63/22.43 | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.43 | | | | | | | | | | | | | | | | | | | | | | | (226) all_54_11 = e0 % 151.63/22.43 | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.43 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (125), (226) imply: % 151.63/22.43 | | | | | | | | | | | | | | | | | | | | | | | (227) all_52_14 = e0 % 151.63/22.43 | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.43 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (18), (227) imply: % 151.63/22.43 | | | | | | | | | | | | | | | | | | | | | | | (228) ~ (all_52_6 = e0) % 151.63/22.43 | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.43 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (37), (227) imply: % 151.63/22.43 | | | | | | | | | | | | | | | | | | | | | | | (229) op(e1, e0) = e0 % 151.63/22.43 | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.43 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (103) gives: % 151.63/22.43 | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.43 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 151.63/22.43 | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.43 | | | | | | | | | | | | | | | | | | | | | | | | (230) all_58_1 = e0 % 151.63/22.43 | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.43 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (41), (230) imply: % 151.63/22.43 | | | | | | | | | | | | | | | | | | | | | | | | (231) all_52_4 = e0 % 151.63/22.43 | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.43 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (24) gives: % 151.63/22.43 | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.43 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 151.63/22.43 | | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.43 | | | | | | | | | | | | | | | | | | | | | | | | | (232) all_58_1 = e2 % 151.63/22.43 | | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.43 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (135), (230), (232) are inconsistent by sub-proof % 151.63/22.43 | | | | | | | | | | | | | | | | | | | | | | | | | #330. % 151.63/22.43 | | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.43 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 151.63/22.43 | | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.43 | | | | | | | | | | | | | | | | | | | | | | | | | (233) all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2 % 151.63/22.43 | | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.43 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (233) gives: % 151.63/22.43 | | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.43 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 151.63/22.43 | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.43 | | | | | | | | | | | | | | | | | | | | | | | | | | (234) all_58_3 = e2 % 151.63/22.43 | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.43 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (43), (234) imply: % 151.63/22.43 | | | | | | | | | | | | | | | | | | | | | | | | | | (235) e3 = e2 % 151.63/22.43 | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.43 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (140), (235) imply: % 151.63/22.43 | | | | | | | | | | | | | | | | | | | | | | | | | | (236) $false % 151.63/22.43 | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.43 | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (236) is inconsistent. % 151.63/22.43 | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.43 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 151.63/22.43 | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.43 | | | | | | | | | | | | | | | | | | | | | | | | | | (237) all_58_7 = e2 | all_58_13 = e2 % 151.63/22.43 | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.43 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (237) gives: % 151.63/22.43 | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.43 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 151.63/22.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | (238) all_58_7 = e2 % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (98), (238) imply: % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | (239) all_52_6 = e2 % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (57), (239) imply: % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | (240) op(e1, e2) = e2 % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (47) with e0, all_56_12, e0, e1, % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (206), (229) gives: % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | (241) all_56_12 = e0 % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (47) with e2, all_56_28, e2, e1, % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (215), (240) gives: % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | (242) all_56_28 = e2 % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (39) gives: % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (243) ( ~ (all_56_0 = all_56_1) & ~ (all_56_2 = % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_3) & ~ (all_56_4 = all_56_5) & ~ % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_6 = all_56_7)) | ( ~ (all_56_8 = % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_9) & ~ (all_56_10 = all_56_11) & ~ % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = all_56_13) & ~ (all_56_14 = % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15)) % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (243) gives: % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (244) ~ (all_56_0 = all_56_1) & ~ (all_56_2 = % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_3) & ~ (all_56_4 = all_56_5) & ~ % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_6 = all_56_7) % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (244) implies: % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (245) ~ (all_56_0 = all_56_1) % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (117), (129), (245) imply: % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (246) $false % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (246) is inconsistent. % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (247) ~ (all_56_8 = all_56_9) & ~ (all_56_10 = % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_11) & ~ (all_56_12 = all_56_13) & ~ % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = all_56_15) % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (247) implies: % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (248) ~ (all_56_12 = all_56_13) % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (205), (241), (248) imply: % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (249) $false % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (249) is inconsistent. % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (250) ( ~ (all_56_16 = all_56_17) & ~ (all_56_18 = % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19) & ~ (all_56_20 = all_56_21) & ~ % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_22 = all_56_23)) | ( ~ (all_56_24 = % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_25) & ~ (all_56_26 = all_56_27) & ~ % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_28 = all_56_29) & ~ (all_56_30 = % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31)) % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (250) gives: % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (251) ~ (all_56_16 = all_56_17) & ~ (all_56_18 = % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19) & ~ (all_56_20 = all_56_21) & ~ % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_22 = all_56_23) % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (251) implies: % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (252) ~ (all_56_16 = all_56_17) % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (87), (218), (252) imply: % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (253) $false % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (253) is inconsistent. % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (254) ~ (all_56_24 = all_56_25) & ~ (all_56_26 = % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_27) & ~ (all_56_28 = all_56_29) & ~ % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_30 = all_56_31) % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (254) implies: % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (255) ~ (all_56_28 = all_56_29) % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (213), (242), (255) imply: % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (256) $false % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (256) is inconsistent. % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | (257) all_58_13 = e2 % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (42), (257) imply: % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | (258) all_52_7 = e2 % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (214), (258) imply: % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | (259) $false % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (259) is inconsistent. % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | (260) all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0 % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (42), (76), (98), (110), (114), (228), (260) are % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #603. % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | End of split % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | End of split % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | End of split % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | Case 2: % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | (261) ~ (all_58_4 = e1) % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | REDUCE: (17), (261) imply: % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | (262) ~ (all_52_8 = e1) % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (68), (86), (146), (162), (174), (188), % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | (262) are inconsistent by sub-proof #329. % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | End of split % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | End of split % 151.63/22.44 | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | Case 2: % 151.63/22.44 | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | (263) all_58_10 = e0 % 151.63/22.44 | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (186), (263) imply: % 151.63/22.44 | | | | | | | | | | | | | | | | | | | (264) e1 = e0 % 151.63/22.44 | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (87), (264) imply: % 151.63/22.44 | | | | | | | | | | | | | | | | | | | (265) all_56_17 = e0 % 151.63/22.44 | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (22), (23), (45), (47), (54), (91), (97), % 151.63/22.44 | | | | | | | | | | | | | | | | | | | (100), (111), (137), (265) are inconsistent by % 151.63/22.44 | | | | | | | | | | | | | | | | | | | sub-proof #441. % 151.63/22.44 | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | End of split % 151.63/22.44 | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | End of split % 151.63/22.44 | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | End of split % 151.63/22.44 | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | End of split % 151.63/22.44 | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | Case 2: % 151.63/22.44 | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | (266) all_58_11 = e1 | all_58_15 = e1 % 151.63/22.44 | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | REF_CLOSE: (52), (64), (81), (93), (266) are inconsistent by % 151.63/22.44 | | | | | | | | | | | | | | | sub-proof #672. % 151.63/22.44 | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | End of split % 151.63/22.44 | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | End of split % 151.63/22.44 | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | End of split % 151.63/22.44 | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | Case 2: % 151.63/22.44 | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | (267) all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2 % 151.63/22.44 | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | BETA: splitting (267) gives: % 151.63/22.44 | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | Case 1: % 151.63/22.44 | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | (268) all_58_10 = e2 % 151.63/22.44 | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | COMBINE_EQS: (99), (268) imply: % 151.63/22.44 | | | | | | | | | | | | | (269) all_52_13 = e2 % 151.63/22.44 | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | REDUCE: (32), (269) imply: % 151.63/22.44 | | | | | | | | | | | | | (270) $false % 151.63/22.44 | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | CLOSE: (270) is inconsistent. % 151.63/22.44 | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | Case 2: % 151.63/22.44 | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | (271) all_58_11 = e2 | all_58_15 = e2 % 151.63/22.44 | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | BETA: splitting (271) gives: % 151.63/22.44 | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | Case 1: % 151.63/22.44 | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | (272) all_58_11 = e2 % 151.63/22.44 | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | COMBINE_EQS: (81), (272) imply: % 151.63/22.44 | | | | | | | | | | | | | | (273) all_52_14 = e2 % 151.63/22.44 | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | COMBINE_EQS: (90), (273) imply: % 151.63/22.44 | | | | | | | | | | | | | | (274) all_56_23 = e2 % 151.63/22.44 | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | REDUCE: (18), (273) imply: % 151.63/22.44 | | | | | | | | | | | | | | (275) ~ (all_52_6 = e2) % 151.63/22.44 | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | REDUCE: (35), (273) imply: % 151.63/22.44 | | | | | | | | | | | | | | (276) op(e0, e2) = all_56_22 % 151.63/22.44 | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | BETA: splitting (157) gives: % 151.63/22.44 | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | Case 1: % 151.63/22.44 | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | (277) all_54_9 = e2 % 151.63/22.44 | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | COMBINE_EQS: (5), (277) imply: % 151.63/22.44 | | | | | | | | | | | | | | | (278) all_52_6 = e2 % 151.63/22.44 | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | SIMP: (278) implies: % 151.63/22.44 | | | | | | | | | | | | | | | (279) all_52_6 = e2 % 151.63/22.44 | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | REDUCE: (275), (279) imply: % 151.63/22.44 | | | | | | | | | | | | | | | (280) $false % 151.63/22.44 | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | CLOSE: (280) is inconsistent. % 151.63/22.44 | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | Case 2: % 151.63/22.44 | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | (281) ~ (all_54_9 = e2) % 151.63/22.44 | | | | | | | | | | | | | | | (282) all_54_9 = e1 | all_54_9 = e0 % 151.63/22.44 | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | BETA: splitting (282) gives: % 151.63/22.44 | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | Case 1: % 151.63/22.44 | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | (283) all_54_9 = e1 % 151.63/22.44 | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (283) are inconsistent by sub-proof % 151.63/22.44 | | | | | | | | | | | | | | | | #679. % 151.63/22.44 | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | Case 2: % 151.63/22.44 | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | (284) all_54_9 = e0 % 151.63/22.44 | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | COMBINE_EQS: (5), (284) imply: % 151.63/22.44 | | | | | | | | | | | | | | | | (285) all_52_6 = e0 % 151.63/22.44 | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | SIMP: (285) implies: % 151.63/22.44 | | | | | | | | | | | | | | | | (286) all_52_6 = e0 % 151.63/22.44 | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | COMBINE_EQS: (120), (286) imply: % 151.63/22.44 | | | | | | | | | | | | | | | | (287) all_56_19 = e0 % 151.63/22.44 | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | REDUCE: (118), (286) imply: % 151.63/22.44 | | | | | | | | | | | | | | | | (288) ~ (all_52_4 = e0) % 151.63/22.44 | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | REDUCE: (79), (286) imply: % 151.63/22.44 | | | | | | | | | | | | | | | | (289) ~ (all_52_7 = e0) % 151.63/22.44 | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | REDUCE: (59), (286) imply: % 151.63/22.44 | | | | | | | | | | | | | | | | (290) op(e2, e0) = all_56_18 % 151.63/22.44 | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (47) with all_52_7, all_56_22, e2, % 151.63/22.44 | | | | | | | | | | | | | | | | e0, simplifying with (36), (276) gives: % 151.63/22.44 | | | | | | | | | | | | | | | | (291) all_56_22 = all_52_7 % 151.63/22.44 | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (47) with all_52_13, all_56_18, e0, % 151.63/22.44 | | | | | | | | | | | | | | | | e2, simplifying with (107), (290) gives: % 151.63/22.44 | | | | | | | | | | | | | | | | (292) all_56_18 = all_52_13 % 151.63/22.44 | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | BETA: splitting (14) gives: % 151.63/22.44 | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | Case 1: % 151.63/22.44 | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | (293) all_58_4 = e2 % 151.63/22.44 | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | COMBINE_EQS: (17), (293) imply: % 151.63/22.44 | | | | | | | | | | | | | | | | | (294) all_52_8 = e2 % 151.63/22.44 | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | REDUCE: (84), (294) imply: % 151.63/22.44 | | | | | | | | | | | | | | | | | (295) ~ (all_52_11 = e2) % 151.63/22.44 | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | SIMP: (295) implies: % 151.63/22.44 | | | | | | | | | | | | | | | | | (296) ~ (all_52_11 = e2) % 151.63/22.44 | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | REDUCE: (108), (294) imply: % 151.63/22.44 | | | | | | | | | | | | | | | | | (297) ~ (all_52_12 = e2) % 151.63/22.44 | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | SIMP: (297) implies: % 151.63/22.44 | | | | | | | | | | | | | | | | | (298) ~ (all_52_12 = e2) % 151.63/22.44 | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | BETA: splitting (124) gives: % 151.63/22.44 | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | Case 1: % 151.63/22.44 | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | (299) all_58_12 = e2 % 151.63/22.44 | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | REF_CLOSE: (34), (135), (299) are inconsistent by sub-proof % 151.63/22.44 | | | | | | | | | | | | | | | | | | #423. % 151.63/22.44 | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | Case 2: % 151.63/22.44 | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | (300) all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2 % 151.63/22.44 | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | BETA: splitting (300) gives: % 151.63/22.44 | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | Case 1: % 151.63/22.44 | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | (301) all_58_13 = e2 % 151.63/22.44 | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (42), (301) imply: % 151.63/22.44 | | | | | | | | | | | | | | | | | | | (302) all_52_7 = e2 % 151.63/22.44 | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | SIMP: (302) implies: % 151.63/22.44 | | | | | | | | | | | | | | | | | | | (303) all_52_7 = e2 % 151.63/22.44 | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (291), (303) imply: % 151.63/22.44 | | | | | | | | | | | | | | | | | | | (304) all_56_22 = e2 % 151.63/22.44 | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | REDUCE: (16), (303) imply: % 151.63/22.44 | | | | | | | | | | | | | | | | | | | (305) ~ (all_52_4 = e2) % 151.63/22.44 | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | BETA: splitting (78) gives: % 151.63/22.44 | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | Case 1: % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | (306) all_58_1 = e1 % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (41), (306) imply: % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | (307) all_52_4 = e1 % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | REDUCE: (106), (307) imply: % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | (308) ~ (all_52_12 = e1) % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | SIMP: (308) implies: % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | (309) ~ (all_52_12 = e1) % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | BETA: splitting (101) gives: % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | Case 1: % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | (310) all_58_12 = e1 % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (22), (23), (34), (45), (47), (54), (87), % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | (91), (97), (100), (111), (137), (310) are % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #328. % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | Case 2: % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | (311) all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1 % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (20) gives: % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | Case 1: % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | (312) all_58_9 = e1 % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (33), (312) imply: % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | (313) all_52_12 = e1 % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (309), (313) imply: % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | (314) $false % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (314) is inconsistent. % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | Case 2: % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | (315) ~ (all_58_9 = e1) % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | (316) all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1 % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (170) gives: % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | (317) all_58_9 = e0 % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (33), (317) imply: % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | (318) all_52_12 = e0 % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (82), (318) imply: % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | (319) all_56_24 = e0 % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (39) gives: % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | (320) ( ~ (all_56_0 = all_56_1) & ~ (all_56_2 = % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | all_56_3) & ~ (all_56_4 = all_56_5) & ~ % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_6 = all_56_7)) | ( ~ (all_56_8 = % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | all_56_9) & ~ (all_56_10 = all_56_11) & ~ % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = all_56_13) & ~ (all_56_14 = % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | all_56_15)) % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (320) gives: % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | (321) ~ (all_56_0 = all_56_1) & ~ (all_56_2 = % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_3) & ~ (all_56_4 = all_56_5) & ~ % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_6 = all_56_7) % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (321) implies: % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | (322) ~ (all_56_0 = all_56_1) % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (117), (129), (322) imply: % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | (323) $false % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (323) is inconsistent. % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | (324) ~ (all_56_8 = all_56_9) & ~ (all_56_10 = % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_11) & ~ (all_56_12 = all_56_13) & ~ % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = all_56_15) % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (324) implies: % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | (325) ~ (all_56_14 = all_56_15) % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (123), (325) imply: % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | (326) ~ (all_56_14 = all_52_13) % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (316) gives: % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | (327) all_58_10 = e1 % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (99), (327) imply: % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | (328) all_52_13 = e1 % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (326), (328) imply: % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | (329) ~ (all_56_14 = e1) % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (95), (328) imply: % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | (330) ~ (e3 = e1) % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (330) implies: % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | (331) ~ (e3 = e1) % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (32), (328) imply: % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | (332) ~ (e2 = e1) % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1), (328) imply: % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | (333) op(e0, e1) = all_56_14 % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (311) gives: % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | (334) all_58_13 = e1 % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (301), (334) imply: % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | (335) e2 = e1 % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (73), (335) imply: % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | (336) $false % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (336) is inconsistent. % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | (337) all_58_14 = e1 | all_58_15 = e1 % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (337) gives: % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (338) all_58_14 = e1 % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (119), (338) imply: % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (339) all_52_11 = e1 % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (339) implies: % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (340) all_52_11 = e1 % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (60), (340) imply: % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (341) op(e0, e1) = e1 % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (47) with e1, all_56_14, e1, e0, % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (333), (341) gives: % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (342) all_56_14 = e1 % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (329), (342) imply: % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (343) $false % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (343) is inconsistent. % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (344) all_58_15 = e1 % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (71), (331), (344) are inconsistent by sub-proof % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | #327. % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | (345) all_58_11 = e1 | all_58_15 = e1 % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (52), (64), (81), (93), (345) are inconsistent by % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #672. % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | (346) ( ~ (all_56_16 = all_56_17) & ~ (all_56_18 = % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | all_56_19) & ~ (all_56_20 = all_56_21) & ~ % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_22 = all_56_23)) | ( ~ (all_56_24 = % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | all_56_25) & ~ (all_56_26 = all_56_27) & ~ % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_28 = all_56_29) & ~ (all_56_30 = % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | all_56_31)) % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (346) gives: % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | (347) ~ (all_56_16 = all_56_17) & ~ (all_56_18 = % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19) & ~ (all_56_20 = all_56_21) & ~ % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_22 = all_56_23) % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (347) implies: % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | (348) ~ (all_56_22 = all_56_23) % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (274), (304), (348) imply: % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | (349) $false % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (349) is inconsistent. % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | (350) ~ (all_56_24 = all_56_25) & ~ (all_56_26 = % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_27) & ~ (all_56_28 = all_56_29) & ~ % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_30 = all_56_31) % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (350) implies: % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | (351) ~ (all_56_24 = all_56_25) % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (49), (319), (351) imply: % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | (352) $false % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (352) is inconsistent. % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | End of split % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | (353) ~ (all_58_9 = e0) % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (33), (353) imply: % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | (354) ~ (all_52_12 = e0) % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (50), (160), (298), (309), (354) are inconsistent % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #326. % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | End of split % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | End of split % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | End of split % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | Case 2: % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | (355) ~ (all_58_1 = e1) % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | REDUCE: (41), (355) imply: % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | (356) ~ (all_52_4 = e1) % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (31), (164), (288), (305), (356) are inconsistent % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | by sub-proof #718. % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | End of split % 151.63/22.44 | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | Case 2: % 151.63/22.44 | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | (357) ~ (all_58_13 = e2) % 151.63/22.44 | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | REDUCE: (42), (357) imply: % 151.63/22.44 | | | | | | | | | | | | | | | | | | | (358) ~ (all_52_7 = e2) % 151.63/22.44 | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | BETA: splitting (149) gives: % 151.63/22.44 | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | Case 1: % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | (359) all_54_14 = e2 % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (38), (296), (359) are inconsistent by sub-proof % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | #581. % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | Case 2: % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | (360) all_54_14 = e1 | all_54_14 = e0 % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | BETA: splitting (360) gives: % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | Case 1: % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | (361) all_54_14 = e1 % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (38), (361) imply: % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | (362) all_52_11 = e1 % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | SIMP: (362) implies: % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | (363) all_52_11 = e1 % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | REDUCE: (3), (363) imply: % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | (364) ~ (all_52_7 = e1) % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (85), (114), (142), (358), (364) are inconsistent % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | by sub-proof #710. % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | Case 2: % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | (365) all_54_14 = e0 % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (19), (38), (365) are inconsistent by sub-proof % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | #715. % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | End of split % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | End of split % 151.63/22.44 | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | End of split % 151.63/22.44 | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | End of split % 151.63/22.44 | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | Case 2: % 151.63/22.44 | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | (366) all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2 % 151.63/22.44 | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | BETA: splitting (366) gives: % 151.63/22.44 | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | Case 1: % 151.63/22.44 | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | (367) all_58_5 = e2 % 151.63/22.44 | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (30), (367) imply: % 151.63/22.44 | | | | | | | | | | | | | | | | | | (368) all_52_9 = e2 % 151.63/22.44 | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | REDUCE: (7), (368) imply: % 151.63/22.44 | | | | | | | | | | | | | | | | | | (369) $false % 151.63/22.44 | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | CLOSE: (369) is inconsistent. % 151.63/22.44 | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | Case 2: % 151.63/22.44 | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | (370) ~ (all_58_5 = e2) % 151.63/22.44 | | | | | | | | | | | | | | | | | | (371) all_58_8 = e2 | all_58_14 = e2 % 151.63/22.44 | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | BETA: splitting (24) gives: % 151.63/22.44 | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | Case 1: % 151.63/22.44 | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | (372) all_58_1 = e2 % 151.63/22.44 | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (41), (372) imply: % 151.63/22.44 | | | | | | | | | | | | | | | | | | | (373) all_52_4 = e2 % 151.63/22.44 | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (128), (373) imply: % 151.63/22.44 | | | | | | | | | | | | | | | | | | | (374) all_56_8 = e2 % 151.63/22.44 | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | REDUCE: (2), (373) imply: % 151.63/22.44 | | | | | | | | | | | | | | | | | | | (375) ~ (all_52_8 = e2) % 151.63/22.44 | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | SIMP: (375) implies: % 151.63/22.44 | | | | | | | | | | | | | | | | | | | (376) ~ (all_52_8 = e2) % 151.63/22.44 | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | REDUCE: (106), (373) imply: % 151.63/22.44 | | | | | | | | | | | | | | | | | | | (377) ~ (all_52_12 = e2) % 151.63/22.44 | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | SIMP: (377) implies: % 151.63/22.44 | | | | | | | | | | | | | | | | | | | (378) ~ (all_52_12 = e2) % 151.63/22.44 | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | BETA: splitting (101) gives: % 151.63/22.44 | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | Case 1: % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | (379) all_58_12 = e1 % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (22), (23), (34), (45), (47), (54), (87), % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | (91), (97), (100), (111), (137), (379) are % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #328. % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | Case 2: % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | (380) all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1 % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | BETA: splitting (380) gives: % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | Case 1: % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | (381) all_58_13 = e1 % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (42), (381) imply: % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | (382) all_52_7 = e1 % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | SIMP: (382) implies: % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | (383) all_52_7 = e1 % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (26), (383) imply: % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | (384) all_56_27 = e1 % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | REDUCE: (56), (383) imply: % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | (385) op(e2, e1) = all_56_26 % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (47) with all_52_9, all_56_26, e1, % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | e2, simplifying with (21), (385) gives: % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | (386) all_56_26 = all_52_9 % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (20) gives: % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | Case 1: % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | (387) all_58_9 = e1 % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (33), (387) imply: % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | (388) all_52_12 = e1 % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (9), (17), (22), (23), (32), (33), (39), % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | (45), (46), (47), (54), (68), (72), (74), (83), % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | (87), (91), (97), (100), (111), (113), (117), % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | (129), (133), (135), (137), (146), (152), (287), % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | (292), (372), (374), (384), (386), (388) are % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #324. % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | Case 2: % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | (389) all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1 % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (160) gives: % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | (390) all_54_3 = e2 % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (50), (390) imply: % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | (391) all_52_12 = e2 % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (378), (391) imply: % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | (392) $false % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (392) is inconsistent. % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | (393) all_54_3 = e1 | all_54_3 = e0 % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (393) gives: % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | (394) all_54_3 = e1 % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (50), (394) imply: % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | (395) all_52_12 = e1 % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (9), (17), (22), (23), (32), (33), (39), % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | (45), (46), (47), (54), (68), (72), (74), (83), % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | (87), (91), (97), (100), (111), (113), (117), % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | (129), (133), (135), (137), (146), (152), (287), % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | (292), (372), (374), (384), (386), (395) are % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #324. % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | (396) all_54_3 = e0 % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (50), (396) imply: % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | (397) all_52_12 = e0 % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (82), (397) imply: % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | (398) all_56_24 = e0 % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (389) gives: % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | (399) all_58_10 = e1 % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (99), (399) imply: % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | (400) all_52_13 = e1 % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (74), (400) imply: % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | (401) ~ (all_52_9 = e1) % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (75) gives: % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | (402) all_58_4 = e1 % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (17), (402) imply: % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | (403) all_52_8 = e1 % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (40), (403) imply: % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | (404) all_56_16 = e1 % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (39) gives: % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | (405) ( ~ (all_56_0 = all_56_1) & ~ (all_56_2 = % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_3) & ~ (all_56_4 = all_56_5) & ~ % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_6 = all_56_7)) | ( ~ (all_56_8 = % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_9) & ~ (all_56_10 = all_56_11) & ~ % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = all_56_13) & ~ (all_56_14 = % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15)) % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (72), (117), (129), (374), (405) are inconsistent % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #325. % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | (406) ( ~ (all_56_16 = all_56_17) & ~ (all_56_18 = % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19) & ~ (all_56_20 = all_56_21) & ~ % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_22 = all_56_23)) | ( ~ (all_56_24 = % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_25) & ~ (all_56_26 = all_56_27) & ~ % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_28 = all_56_29) & ~ (all_56_30 = % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31)) % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (406) gives: % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (407) ~ (all_56_16 = all_56_17) & ~ (all_56_18 = % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19) & ~ (all_56_20 = all_56_21) & ~ % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_22 = all_56_23) % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (407) implies: % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (408) ~ (all_56_16 = all_56_17) % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (87), (404), (408) imply: % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (409) $false % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (409) is inconsistent. % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (410) ~ (all_56_24 = all_56_25) & ~ (all_56_26 = % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_27) & ~ (all_56_28 = all_56_29) & ~ % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_30 = all_56_31) % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (410) implies: % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (411) ~ (all_56_24 = all_56_25) % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (49), (398), (411) imply: % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (412) $false % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (412) is inconsistent. % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | (413) ~ (all_58_4 = e1) % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (17), (413) imply: % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | (414) ~ (all_52_8 = e1) % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (68), (86), (146), (162), (376), (401), % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | (414) are inconsistent by sub-proof #329. % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | (415) all_58_11 = e1 | all_58_15 = e1 % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (52), (64), (81), (93), (415) are inconsistent by % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #672. % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | End of split % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | End of split % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | End of split % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | Case 2: % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | (416) all_58_14 = e1 | all_58_15 = e1 % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (64), (66), (73), (93), (97), (371), (416) are % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #400. % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | End of split % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | End of split % 151.63/22.44 | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | Case 2: % 151.63/22.44 | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | (417) ~ (all_58_1 = e2) % 151.63/22.44 | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | REDUCE: (41), (417) imply: % 151.63/22.44 | | | | | | | | | | | | | | | | | | | (418) ~ (all_52_4 = e2) % 151.63/22.44 | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | BETA: splitting (101) gives: % 151.63/22.44 | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | Case 1: % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | (419) all_58_12 = e1 % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (22), (23), (34), (45), (47), (54), (87), % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | (91), (97), (100), (111), (137), (419) are % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #328. % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | Case 2: % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | (420) all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1 % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | BETA: splitting (420) gives: % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | Case 1: % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | (421) all_58_13 = e1 % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (42), (421) imply: % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | (422) all_52_7 = e1 % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | SIMP: (422) implies: % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | (423) all_52_7 = e1 % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | REDUCE: (16), (423) imply: % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | (424) ~ (all_52_4 = e1) % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (31), (164), (288), (418), (424) are inconsistent % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | by sub-proof #718. % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | Case 2: % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | (425) all_58_14 = e1 | all_58_15 = e1 % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (64), (66), (73), (93), (97), (371), (425) are % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #400. % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | End of split % 151.63/22.44 | | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | | End of split % 151.63/22.44 | | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | | End of split % 151.63/22.44 | | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | | End of split % 151.63/22.44 | | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | | End of split % 151.63/22.44 | | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | | End of split % 151.63/22.44 | | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | End of split % 151.63/22.44 | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | Case 2: % 151.63/22.44 | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | (426) all_58_15 = e2 % 151.63/22.44 | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | COMBINE_EQS: (71), (426) imply: % 151.63/22.44 | | | | | | | | | | | | | | (427) e3 = e2 % 151.63/22.44 | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | REDUCE: (140), (427) imply: % 151.63/22.44 | | | | | | | | | | | | | | (428) $false % 151.63/22.44 | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | | CLOSE: (428) is inconsistent. % 151.63/22.44 | | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | | End of split % 151.63/22.44 | | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | | End of split % 151.63/22.44 | | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | | End of split % 151.63/22.44 | | | | | | | | | | | % 151.63/22.44 | | | | | | | | | | End of split % 151.63/22.44 | | | | | | | | | | % 151.63/22.44 | | | | | | | | | End of split % 151.63/22.44 | | | | | | | | | % 151.63/22.44 | | | | | | | | End of split % 151.63/22.44 | | | | | | | | % 151.63/22.44 | | | | | | | End of split % 151.63/22.44 | | | | | | | % 151.63/22.44 | | | | | | End of split % 151.63/22.44 | | | | | | % 151.63/22.44 | | | | | End of split % 151.63/22.44 | | | | | % 151.63/22.44 | | | | End of split % 151.63/22.44 | | | | % 151.63/22.44 | | | End of split % 151.63/22.44 | | | % 151.63/22.44 | | End of split % 151.63/22.44 | | % 151.63/22.44 | End of split % 151.63/22.44 | % 151.63/22.44 End of proof % 151.63/22.44 % 151.63/22.44 Sub-proof #324 shows that the following formulas are inconsistent: % 151.63/22.44 ---------------------------------------------------------------- % 151.63/22.44 (1) ~ (all_52_8 = all_52_9) % 151.63/22.44 (2) all_56_27 = e1 % 151.63/22.44 (3) ~ (e3 = e0) % 151.63/22.44 (4) ~ (all_52_9 = e2) % 151.63/22.44 (5) all_54_10 = all_6_2 % 151.63/22.44 (6) all_56_8 = e2 % 151.63/22.44 (7) all_58_4 = all_52_8 % 151.63/22.44 (8) all_56_21 = all_6_2 % 151.63/22.44 (9) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 151.63/22.44 (10) all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0 % 151.63/22.44 (11) ~ (all_52_13 = e2) % 151.63/22.44 (12) all_58_9 = all_52_12 % 151.63/22.44 (13) ( ~ (all_56_0 = all_56_1) & ~ (all_56_2 = all_56_3) & ~ (all_56_4 = % 151.63/22.44 all_56_5) & ~ (all_56_6 = all_56_7)) | ( ~ (all_56_8 = all_56_9) & % 151.63/22.44 ~ (all_56_10 = all_56_11) & ~ (all_56_12 = all_56_13) & ~ (all_56_14 % 151.63/22.44 = all_56_15)) | ( ~ (all_56_16 = all_56_17) & ~ (all_56_18 = % 151.63/22.44 all_56_19) & ~ (all_56_20 = all_56_21) & ~ (all_56_22 = % 151.63/22.44 all_56_23)) | ( ~ (all_56_24 = all_56_25) & ~ (all_56_26 = % 151.63/22.44 all_56_27) & ~ (all_56_28 = all_56_29) & ~ (all_56_30 = % 151.63/22.44 all_56_31)) % 151.63/22.44 (14) ~ (all_56_21 = e3) | all_56_17 = e1 % 151.63/22.44 (15) all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0 % 151.63/22.44 (16) ~ (e1 = e0) % 151.63/22.44 (17) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 151.63/22.44 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 151.63/22.44 (18) ~ (all_6_2 = e0) % 151.63/22.44 (19) all_56_18 = all_52_13 % 151.63/22.44 (20) all_54_6 = all_52_9 % 151.63/22.44 (21) all_56_9 = e2 % 151.63/22.44 (22) ~ (all_52_9 = all_52_13) % 151.63/22.44 (23) all_56_19 = e0 % 151.63/22.45 (24) all_56_0 = e3 % 151.63/22.45 (25) all_56_26 = all_52_9 % 151.63/22.45 (26) all_54_7 = all_52_13 % 151.63/22.45 (27) all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0 % 151.63/22.45 (28) all_56_17 = e1 % 151.63/22.45 (29) op(e1, e1) = all_6_2 % 151.63/22.45 (30) ~ (all_6_2 = e2) % 151.63/22.45 (31) op(e1, all_6_2) = all_56_20 % 151.63/22.45 (32) all_52_12 = e1 % 151.63/22.45 (33) all_58_1 = e2 % 151.63/22.45 (34) op(all_6_2, all_6_2) = e3 % 151.63/22.45 (35) ~ (e2 = e0) % 151.63/22.45 (36) all_58_0 = e3 % 151.63/22.45 (37) all_56_1 = e3 % 151.63/22.45 % 151.63/22.45 Begin of proof % 151.63/22.45 | % 151.63/22.45 | COMBINE_EQS: (12), (32) imply: % 151.63/22.45 | (38) all_58_9 = e1 % 151.63/22.45 | % 151.63/22.45 | BETA: splitting (15) gives: % 151.63/22.45 | % 151.63/22.45 | Case 1: % 151.63/22.45 | | % 151.63/22.45 | | (39) all_58_0 = e0 % 151.63/22.45 | | % 151.63/22.45 | | COMBINE_EQS: (36), (39) imply: % 151.63/22.45 | | (40) e3 = e0 % 151.63/22.45 | | % 151.63/22.45 | | REDUCE: (3), (40) imply: % 151.63/22.45 | | (41) $false % 151.63/22.45 | | % 151.63/22.45 | | CLOSE: (41) is inconsistent. % 151.63/22.45 | | % 151.63/22.45 | Case 2: % 151.63/22.45 | | % 151.63/22.45 | | (42) all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0 % 151.63/22.45 | | % 151.63/22.45 | | BETA: splitting (42) gives: % 151.63/22.45 | | % 151.63/22.45 | | Case 1: % 151.63/22.45 | | | % 151.63/22.45 | | | (43) all_58_1 = e0 % 151.63/22.45 | | | % 151.63/22.45 | | | COMBINE_EQS: (33), (43) imply: % 151.63/22.45 | | | (44) e2 = e0 % 151.63/22.45 | | | % 151.63/22.45 | | | REDUCE: (35), (44) imply: % 151.63/22.45 | | | (45) $false % 151.63/22.45 | | | % 151.63/22.45 | | | CLOSE: (45) is inconsistent. % 151.63/22.45 | | | % 151.63/22.45 | | Case 2: % 151.63/22.45 | | | % 151.63/22.45 | | | (46) all_58_4 = e0 | all_58_9 = e0 % 151.63/22.45 | | | % 151.63/22.45 | | | BETA: splitting (46) gives: % 151.63/22.45 | | | % 151.63/22.45 | | | Case 1: % 151.63/22.45 | | | | % 151.63/22.45 | | | | (47) all_58_4 = e0 % 151.63/22.45 | | | | % 151.63/22.45 | | | | COMBINE_EQS: (7), (47) imply: % 151.63/22.45 | | | | (48) all_52_8 = e0 % 151.63/22.45 | | | | % 151.63/22.45 | | | | REDUCE: (1), (48) imply: % 151.63/22.45 | | | | (49) ~ (all_52_9 = e0) % 151.63/22.45 | | | | % 151.63/22.45 | | | | SIMP: (49) implies: % 151.63/22.45 | | | | (50) ~ (all_52_9 = e0) % 151.63/22.45 | | | | % 151.63/22.45 | | | | BETA: splitting (27) gives: % 151.63/22.45 | | | | % 151.63/22.45 | | | | Case 1: % 151.63/22.45 | | | | | % 151.63/22.45 | | | | | (51) all_54_6 = e2 % 151.63/22.45 | | | | | % 151.63/22.45 | | | | | REF_CLOSE: (4), (20), (51) are inconsistent by sub-proof #610. % 151.63/22.45 | | | | | % 151.63/22.45 | | | | Case 2: % 151.63/22.45 | | | | | % 151.63/22.45 | | | | | (52) all_54_6 = e1 | all_54_6 = e0 % 151.63/22.45 | | | | | % 151.63/22.45 | | | | | BETA: splitting (52) gives: % 151.63/22.45 | | | | | % 151.63/22.45 | | | | | Case 1: % 151.63/22.45 | | | | | | % 151.63/22.45 | | | | | | (53) all_54_6 = e1 % 151.63/22.45 | | | | | | % 151.63/22.45 | | | | | | COMBINE_EQS: (20), (53) imply: % 151.63/22.45 | | | | | | (54) all_52_9 = e1 % 151.63/22.45 | | | | | | % 151.63/22.45 | | | | | | SIMP: (54) implies: % 151.63/22.45 | | | | | | (55) all_52_9 = e1 % 151.63/22.45 | | | | | | % 151.63/22.45 | | | | | | COMBINE_EQS: (25), (55) imply: % 151.63/22.45 | | | | | | (56) all_56_26 = e1 % 151.63/22.45 | | | | | | % 151.63/22.45 | | | | | | REDUCE: (22), (55) imply: % 151.63/22.45 | | | | | | (57) ~ (all_52_13 = e1) % 151.63/22.45 | | | | | | % 151.63/22.45 | | | | | | SIMP: (57) implies: % 151.63/22.45 | | | | | | (58) ~ (all_52_13 = e1) % 151.63/22.45 | | | | | | % 151.63/22.45 | | | | | | BETA: splitting (13) gives: % 151.63/22.45 | | | | | | % 151.63/22.45 | | | | | | Case 1: % 151.63/22.45 | | | | | | | % 151.63/22.45 | | | | | | | (59) ( ~ (all_56_0 = all_56_1) & ~ (all_56_2 = all_56_3) & ~ % 151.63/22.45 | | | | | | | (all_56_4 = all_56_5) & ~ (all_56_6 = all_56_7)) | ( ~ % 151.63/22.45 | | | | | | | (all_56_8 = all_56_9) & ~ (all_56_10 = all_56_11) & ~ % 151.63/22.45 | | | | | | | (all_56_12 = all_56_13) & ~ (all_56_14 = all_56_15)) % 151.63/22.45 | | | | | | | % 151.63/22.45 | | | | | | | REF_CLOSE: (6), (21), (24), (37), (59) are inconsistent by % 151.63/22.45 | | | | | | | sub-proof #325. % 151.63/22.45 | | | | | | | % 151.63/22.45 | | | | | | Case 2: % 151.63/22.45 | | | | | | | % 151.63/22.45 | | | | | | | (60) ( ~ (all_56_16 = all_56_17) & ~ (all_56_18 = all_56_19) & % 151.63/22.45 | | | | | | | ~ (all_56_20 = all_56_21) & ~ (all_56_22 = all_56_23)) % 151.63/22.45 | | | | | | | | ( ~ (all_56_24 = all_56_25) & ~ (all_56_26 = all_56_27) % 151.63/22.45 | | | | | | | & ~ (all_56_28 = all_56_29) & ~ (all_56_30 = % 151.63/22.45 | | | | | | | all_56_31)) % 151.63/22.45 | | | | | | | % 151.63/22.45 | | | | | | | BETA: splitting (60) gives: % 151.63/22.45 | | | | | | | % 151.63/22.45 | | | | | | | Case 1: % 151.63/22.45 | | | | | | | | % 151.63/22.45 | | | | | | | | (61) ~ (all_56_16 = all_56_17) & ~ (all_56_18 = all_56_19) % 151.63/22.45 | | | | | | | | & ~ (all_56_20 = all_56_21) & ~ (all_56_22 = % 151.63/22.45 | | | | | | | | all_56_23) % 151.63/22.45 | | | | | | | | % 151.63/22.45 | | | | | | | | ALPHA: (61) implies: % 151.63/22.45 | | | | | | | | (62) ~ (all_56_18 = all_56_19) % 151.63/22.45 | | | | | | | | % 151.63/22.45 | | | | | | | | REDUCE: (19), (23), (62) imply: % 151.63/22.45 | | | | | | | | (63) ~ (all_52_13 = e0) % 151.63/22.45 | | | | | | | | % 151.63/22.45 | | | | | | | | REF_CLOSE: (10), (11), (26), (58), (63) are inconsistent by % 151.63/22.45 | | | | | | | | sub-proof #649. % 151.63/22.45 | | | | | | | | % 151.63/22.45 | | | | | | | Case 2: % 151.63/22.45 | | | | | | | | % 151.63/22.45 | | | | | | | | (64) ~ (all_56_24 = all_56_25) & ~ (all_56_26 = all_56_27) % 151.63/22.45 | | | | | | | | & ~ (all_56_28 = all_56_29) & ~ (all_56_30 = % 151.63/22.45 | | | | | | | | all_56_31) % 151.63/22.45 | | | | | | | | % 151.63/22.45 | | | | | | | | ALPHA: (64) implies: % 151.63/22.45 | | | | | | | | (65) ~ (all_56_26 = all_56_27) % 151.63/22.45 | | | | | | | | % 151.63/22.45 | | | | | | | | REDUCE: (2), (56), (65) imply: % 151.63/22.45 | | | | | | | | (66) $false % 151.63/22.45 | | | | | | | | % 151.63/22.45 | | | | | | | | CLOSE: (66) is inconsistent. % 151.63/22.45 | | | | | | | | % 151.63/22.45 | | | | | | | End of split % 151.63/22.45 | | | | | | | % 151.63/22.45 | | | | | | End of split % 151.63/22.45 | | | | | | % 151.63/22.45 | | | | | Case 2: % 151.63/22.45 | | | | | | % 151.63/22.45 | | | | | | (67) all_54_6 = e0 % 151.63/22.45 | | | | | | % 151.63/22.45 | | | | | | REF_CLOSE: (20), (50), (67) are inconsistent by sub-proof #609. % 151.63/22.45 | | | | | | % 151.63/22.45 | | | | | End of split % 151.63/22.45 | | | | | % 151.63/22.45 | | | | End of split % 151.63/22.45 | | | | % 151.63/22.45 | | | Case 2: % 151.63/22.45 | | | | % 151.63/22.45 | | | | (68) all_58_9 = e0 % 151.63/22.45 | | | | % 151.63/22.45 | | | | COMBINE_EQS: (38), (68) imply: % 151.63/22.45 | | | | (69) e1 = e0 % 151.63/22.45 | | | | % 151.63/22.45 | | | | COMBINE_EQS: (28), (69) imply: % 151.63/22.45 | | | | (70) all_56_17 = e0 % 151.63/22.45 | | | | % 151.63/22.45 | | | | REF_CLOSE: (5), (8), (9), (14), (16), (17), (18), (29), (30), (31), % 151.63/22.45 | | | | (34), (70) are inconsistent by sub-proof #441. % 151.63/22.45 | | | | % 151.63/22.45 | | | End of split % 151.63/22.45 | | | % 151.63/22.45 | | End of split % 151.63/22.45 | | % 151.63/22.45 | End of split % 151.63/22.45 | % 151.63/22.45 End of proof % 151.63/22.45 % 151.63/22.45 Sub-proof #325 shows that the following formulas are inconsistent: % 151.63/22.45 ---------------------------------------------------------------- % 151.63/22.45 (1) all_56_8 = e2 % 151.63/22.45 (2) all_56_9 = e2 % 151.63/22.45 (3) all_56_0 = e3 % 151.63/22.45 (4) ( ~ (all_56_0 = all_56_1) & ~ (all_56_2 = all_56_3) & ~ (all_56_4 = % 151.63/22.45 all_56_5) & ~ (all_56_6 = all_56_7)) | ( ~ (all_56_8 = all_56_9) & % 151.63/22.45 ~ (all_56_10 = all_56_11) & ~ (all_56_12 = all_56_13) & ~ (all_56_14 % 151.63/22.45 = all_56_15)) % 151.63/22.45 (5) all_56_1 = e3 % 151.63/22.45 % 151.63/22.45 Begin of proof % 151.63/22.45 | % 151.63/22.45 | BETA: splitting (4) gives: % 151.63/22.45 | % 151.63/22.45 | Case 1: % 151.63/22.45 | | % 151.63/22.45 | | (6) ~ (all_56_0 = all_56_1) & ~ (all_56_2 = all_56_3) & ~ (all_56_4 = % 151.63/22.45 | | all_56_5) & ~ (all_56_6 = all_56_7) % 151.63/22.45 | | % 151.63/22.45 | | ALPHA: (6) implies: % 151.63/22.45 | | (7) ~ (all_56_0 = all_56_1) % 151.63/22.45 | | % 151.63/22.45 | | REDUCE: (3), (5), (7) imply: % 151.63/22.45 | | (8) $false % 151.63/22.45 | | % 151.63/22.45 | | CLOSE: (8) is inconsistent. % 151.63/22.45 | | % 151.63/22.45 | Case 2: % 151.63/22.45 | | % 151.63/22.45 | | (9) ~ (all_56_8 = all_56_9) & ~ (all_56_10 = all_56_11) & ~ (all_56_12 % 151.63/22.45 | | = all_56_13) & ~ (all_56_14 = all_56_15) % 151.63/22.45 | | % 151.63/22.45 | | ALPHA: (9) implies: % 151.63/22.45 | | (10) ~ (all_56_8 = all_56_9) % 151.63/22.45 | | % 151.63/22.45 | | REDUCE: (1), (2), (10) imply: % 151.63/22.45 | | (11) $false % 151.63/22.45 | | % 151.63/22.45 | | CLOSE: (11) is inconsistent. % 151.63/22.45 | | % 151.63/22.45 | End of split % 151.63/22.45 | % 151.63/22.45 End of proof % 151.63/22.45 % 151.63/22.45 Sub-proof #326 shows that the following formulas are inconsistent: % 151.63/22.45 ---------------------------------------------------------------- % 151.63/22.45 (1) ~ (all_52_12 = e2) % 151.63/22.45 (2) all_54_3 = all_52_12 % 151.63/22.45 (3) all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0 % 151.63/22.45 (4) ~ (all_52_12 = e1) % 151.63/22.45 (5) ~ (all_52_12 = e0) % 151.63/22.45 % 151.63/22.45 Begin of proof % 151.63/22.45 | % 151.63/22.45 | BETA: splitting (3) gives: % 151.63/22.45 | % 151.63/22.45 | Case 1: % 151.63/22.45 | | % 151.63/22.45 | | (6) all_54_3 = e2 % 151.63/22.45 | | % 151.63/22.45 | | REF_CLOSE: (1), (2), (6) are inconsistent by sub-proof #658. % 151.63/22.45 | | % 151.63/22.45 | Case 2: % 151.63/22.45 | | % 151.63/22.45 | | (7) all_54_3 = e1 | all_54_3 = e0 % 151.63/22.45 | | % 151.63/22.45 | | REF_CLOSE: (2), (4), (5), (7) are inconsistent by sub-proof #655. % 151.63/22.45 | | % 151.63/22.45 | End of split % 151.63/22.45 | % 151.63/22.45 End of proof % 151.63/22.45 % 151.63/22.45 Sub-proof #327 shows that the following formulas are inconsistent: % 151.63/22.45 ---------------------------------------------------------------- % 151.63/22.45 (1) all_58_15 = e3 % 151.63/22.45 (2) all_58_15 = e1 % 151.63/22.45 (3) ~ (e3 = e1) % 151.63/22.45 % 151.63/22.45 Begin of proof % 151.63/22.45 | % 151.63/22.45 | COMBINE_EQS: (1), (2) imply: % 151.63/22.45 | (4) e3 = e1 % 151.63/22.45 | % 151.63/22.45 | SIMP: (4) implies: % 151.63/22.45 | (5) e3 = e1 % 151.63/22.45 | % 151.63/22.45 | REDUCE: (3), (5) imply: % 151.63/22.45 | (6) $false % 151.63/22.45 | % 151.63/22.45 | CLOSE: (6) is inconsistent. % 151.63/22.45 | % 151.63/22.45 End of proof % 151.63/22.45 % 151.63/22.45 Sub-proof #328 shows that the following formulas are inconsistent: % 151.63/22.45 ---------------------------------------------------------------- % 151.63/22.45 (1) all_54_10 = all_6_2 % 151.63/22.45 (2) all_56_21 = all_6_2 % 151.63/22.45 (3) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 151.63/22.45 (4) all_58_12 = e0 % 151.63/22.45 (5) ~ (all_56_21 = e3) | all_56_17 = e1 % 151.63/22.45 (6) ~ (e1 = e0) % 151.63/22.45 (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 151.63/22.45 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 151.63/22.45 (8) ~ (all_6_2 = e0) % 151.63/22.45 (9) all_56_17 = e1 % 151.63/22.45 (10) op(e1, e1) = all_6_2 % 151.63/22.45 (11) ~ (all_6_2 = e2) % 151.63/22.45 (12) op(e1, all_6_2) = all_56_20 % 151.63/22.45 (13) all_58_12 = e1 % 151.63/22.45 (14) op(all_6_2, all_6_2) = e3 % 151.63/22.45 % 151.63/22.45 Begin of proof % 151.63/22.45 | % 151.63/22.45 | COMBINE_EQS: (4), (13) imply: % 151.63/22.45 | (15) e1 = e0 % 151.63/22.45 | % 151.63/22.45 | SIMP: (15) implies: % 151.63/22.45 | (16) e1 = e0 % 151.63/22.45 | % 151.63/22.45 | COMBINE_EQS: (9), (16) imply: % 151.63/22.45 | (17) all_56_17 = e0 % 151.63/22.45 | % 151.63/22.45 | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (10), (11), (12), (14), (17) are % 151.63/22.45 | inconsistent by sub-proof #441. % 151.63/22.45 | % 151.63/22.45 End of proof % 151.63/22.45 % 151.63/22.45 Sub-proof #329 shows that the following formulas are inconsistent: % 151.63/22.45 ---------------------------------------------------------------- % 151.63/22.45 (1) ~ (all_52_8 = all_52_9) % 151.63/22.45 (2) ~ (all_52_9 = e2) % 151.63/22.45 (3) ~ (all_52_8 = e2) % 151.63/22.45 (4) all_54_6 = all_52_9 % 151.63/22.45 (5) all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0 % 151.63/22.45 (6) ~ (all_52_8 = e1) % 151.63/22.45 (7) all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0 % 151.63/22.45 (8) ~ (all_52_9 = e1) % 151.63/22.45 (9) all_54_2 = all_52_8 % 151.63/22.45 % 151.63/22.45 Begin of proof % 151.63/22.45 | % 151.63/22.45 | BETA: splitting (5) gives: % 151.63/22.45 | % 151.63/22.45 | Case 1: % 151.63/22.45 | | % 151.63/22.45 | | (10) all_54_2 = e2 % 151.63/22.45 | | % 151.63/22.45 | | REF_CLOSE: (3), (9), (10) are inconsistent by sub-proof #727. % 151.63/22.45 | | % 151.63/22.45 | Case 2: % 151.63/22.45 | | % 151.63/22.45 | | (11) all_54_2 = e1 | all_54_2 = e0 % 151.63/22.45 | | % 151.63/22.45 | | BETA: splitting (11) gives: % 151.63/22.45 | | % 151.63/22.45 | | Case 1: % 151.63/22.45 | | | % 151.63/22.45 | | | (12) all_54_2 = e1 % 151.63/22.45 | | | % 151.63/22.45 | | | REF_CLOSE: (6), (9), (12) are inconsistent by sub-proof #726. % 151.63/22.45 | | | % 151.63/22.45 | | Case 2: % 151.63/22.45 | | | % 151.63/22.45 | | | (13) all_54_2 = e0 % 151.63/22.45 | | | % 151.63/22.45 | | | COMBINE_EQS: (9), (13) imply: % 151.63/22.45 | | | (14) all_52_8 = e0 % 151.63/22.45 | | | % 151.63/22.45 | | | SIMP: (14) implies: % 151.63/22.45 | | | (15) all_52_8 = e0 % 151.63/22.45 | | | % 151.63/22.45 | | | REDUCE: (1), (15) imply: % 151.63/22.45 | | | (16) ~ (all_52_9 = e0) % 151.63/22.45 | | | % 151.63/22.45 | | | SIMP: (16) implies: % 151.63/22.45 | | | (17) ~ (all_52_9 = e0) % 151.63/22.45 | | | % 151.63/22.45 | | | REF_CLOSE: (2), (4), (7), (8), (17) are inconsistent by sub-proof #608. % 151.63/22.45 | | | % 151.63/22.45 | | End of split % 151.63/22.45 | | % 151.63/22.45 | End of split % 151.63/22.45 | % 151.63/22.45 End of proof % 151.63/22.45 % 151.63/22.45 Sub-proof #330 shows that the following formulas are inconsistent: % 151.63/22.45 ---------------------------------------------------------------- % 151.63/22.45 (1) all_58_1 = e2 % 151.63/22.45 (2) all_58_1 = e0 % 151.63/22.45 (3) ~ (e2 = e0) % 151.63/22.45 % 151.63/22.45 Begin of proof % 151.63/22.45 | % 151.63/22.45 | COMBINE_EQS: (1), (2) imply: % 151.63/22.45 | (4) e2 = e0 % 151.63/22.45 | % 151.63/22.45 | SIMP: (4) implies: % 151.63/22.45 | (5) e2 = e0 % 151.63/22.45 | % 151.63/22.45 | REDUCE: (3), (5) imply: % 151.63/22.45 | (6) $false % 151.63/22.45 | % 151.63/22.45 | CLOSE: (6) is inconsistent. % 151.63/22.45 | % 151.63/22.45 End of proof % 151.63/22.45 % 151.63/22.45 Sub-proof #331 shows that the following formulas are inconsistent: % 151.63/22.45 ---------------------------------------------------------------- % 151.63/22.45 (1) all_58_11 = e3 | all_58_15 = e3 % 151.63/22.45 (2) ~ (all_52_14 = e3) % 151.63/22.45 (3) all_58_11 = all_52_14 % 151.63/22.45 (4) all_58_15 = all_4_2 % 151.63/22.45 (5) ~ (all_4_2 = e3) % 151.63/22.45 % 151.63/22.45 Begin of proof % 151.63/22.45 | % 151.63/22.45 | BETA: splitting (1) gives: % 151.63/22.45 | % 151.63/22.45 | Case 1: % 151.63/22.45 | | % 151.63/22.45 | | (6) all_58_11 = e3 % 151.63/22.45 | | % 151.63/22.45 | | COMBINE_EQS: (3), (6) imply: % 151.63/22.45 | | (7) all_52_14 = e3 % 151.63/22.45 | | % 151.63/22.45 | | REDUCE: (2), (7) imply: % 151.63/22.45 | | (8) $false % 151.63/22.45 | | % 151.63/22.45 | | CLOSE: (8) is inconsistent. % 151.63/22.45 | | % 151.63/22.45 | Case 2: % 151.63/22.45 | | % 151.63/22.45 | | (9) all_58_15 = e3 % 151.63/22.45 | | % 151.63/22.45 | | COMBINE_EQS: (4), (9) imply: % 151.63/22.45 | | (10) all_4_2 = e3 % 151.63/22.45 | | % 151.63/22.45 | | REDUCE: (5), (10) imply: % 151.63/22.45 | | (11) $false % 151.63/22.45 | | % 151.63/22.45 | | CLOSE: (11) is inconsistent. % 151.63/22.45 | | % 151.63/22.45 | End of split % 151.63/22.45 | % 151.63/22.45 End of proof % 151.63/22.45 % 151.63/22.45 Sub-proof #332 shows that the following formulas are inconsistent: % 151.63/22.45 ---------------------------------------------------------------- % 151.63/22.45 (1) ~ (all_56_11 = e1) | all_56_13 = e2 % 151.63/22.45 (2) ~ (all_8_0 = e1) % 151.63/22.45 (3) all_22_2 = e1 % 151.63/22.45 (4) ~ (all_22_0 = e0) | ~ (all_22_2 = e1) % 151.63/22.45 (5) all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0 % 151.63/22.45 (6) all_22_0 = all_8_0 % 151.63/22.45 (7) all_56_13 = all_52_9 % 151.63/22.45 (8) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0 % 151.63/22.45 (9) all_56_11 = e1 % 151.63/22.45 (10) ~ (all_8_0 = e3) % 151.63/22.45 (11) all_58_2 = all_8_0 % 151.63/22.45 (12) all_54_4 = all_8_0 % 151.63/22.45 (13) ~ (all_52_9 = all_8_0) % 151.63/22.45 % 151.63/22.45 Begin of proof % 151.63/22.45 | % 151.63/22.45 | BETA: splitting (1) gives: % 151.63/22.45 | % 151.63/22.45 | Case 1: % 151.63/22.45 | | % 151.63/22.45 | | (14) ~ (all_56_11 = e1) % 151.63/22.45 | | % 151.63/22.45 | | REDUCE: (9), (14) imply: % 151.63/22.45 | | (15) $false % 151.63/22.45 | | % 151.63/22.45 | | CLOSE: (15) is inconsistent. % 151.63/22.45 | | % 151.63/22.45 | Case 2: % 151.63/22.45 | | % 151.63/22.45 | | (16) all_56_13 = e2 % 151.63/22.45 | | % 151.63/22.45 | | COMBINE_EQS: (7), (16) imply: % 151.63/22.45 | | (17) all_52_9 = e2 % 151.63/22.45 | | % 151.63/22.45 | | SIMP: (17) implies: % 151.63/22.45 | | (18) all_52_9 = e2 % 151.63/22.45 | | % 151.63/22.45 | | REDUCE: (13), (18) imply: % 151.63/22.45 | | (19) ~ (all_8_0 = e2) % 151.63/22.45 | | % 151.63/22.45 | | SIMP: (19) implies: % 151.63/22.45 | | (20) ~ (all_8_0 = e2) % 151.63/22.45 | | % 151.63/22.45 | | BETA: splitting (8) gives: % 151.63/22.45 | | % 151.63/22.45 | | Case 1: % 151.63/22.45 | | | % 151.63/22.45 | | | (21) all_54_4 = e3 % 151.63/22.45 | | | % 151.63/22.45 | | | COMBINE_EQS: (12), (21) imply: % 151.63/22.45 | | | (22) all_8_0 = e3 % 151.63/22.45 | | | % 151.63/22.45 | | | SIMP: (22) implies: % 151.63/22.45 | | | (23) all_8_0 = e3 % 151.63/22.45 | | | % 151.63/22.45 | | | REDUCE: (10), (23) imply: % 151.63/22.45 | | | (24) $false % 151.63/22.45 | | | % 151.63/22.45 | | | CLOSE: (24) is inconsistent. % 151.63/22.45 | | | % 151.63/22.45 | | Case 2: % 151.63/22.45 | | | % 151.63/22.45 | | | (25) all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0 % 151.63/22.45 | | | % 151.63/22.45 | | | BETA: splitting (5) gives: % 151.63/22.45 | | | % 151.63/22.45 | | | Case 1: % 151.63/22.45 | | | | % 151.63/22.45 | | | | (26) all_58_2 = e0 % 151.63/22.45 | | | | % 151.63/22.45 | | | | COMBINE_EQS: (11), (26) imply: % 151.63/22.45 | | | | (27) all_8_0 = e0 % 151.63/22.45 | | | | % 151.63/22.45 | | | | COMBINE_EQS: (6), (27) imply: % 151.63/22.45 | | | | (28) all_22_0 = e0 % 151.63/22.45 | | | | % 151.63/22.45 | | | | BETA: splitting (4) gives: % 151.63/22.45 | | | | % 151.63/22.45 | | | | Case 1: % 151.63/22.45 | | | | | % 151.63/22.45 | | | | | (29) ~ (all_22_2 = e1) % 151.63/22.45 | | | | | % 151.63/22.45 | | | | | REDUCE: (3), (29) imply: % 151.63/22.45 | | | | | (30) $false % 151.63/22.45 | | | | | % 151.63/22.45 | | | | | CLOSE: (30) is inconsistent. % 151.63/22.45 | | | | | % 151.63/22.45 | | | | Case 2: % 151.63/22.45 | | | | | % 151.63/22.45 | | | | | (31) ~ (all_22_0 = e0) % 151.63/22.45 | | | | | % 151.63/22.45 | | | | | REDUCE: (28), (31) imply: % 151.63/22.45 | | | | | (32) $false % 151.63/22.45 | | | | | % 151.63/22.45 | | | | | CLOSE: (32) is inconsistent. % 151.63/22.45 | | | | | % 151.63/22.45 | | | | End of split % 151.63/22.45 | | | | % 151.63/22.45 | | | Case 2: % 151.63/22.45 | | | | % 151.63/22.45 | | | | (33) ~ (all_58_2 = e0) % 151.63/22.45 | | | | % 151.63/22.45 | | | | REDUCE: (11), (33) imply: % 151.63/22.45 | | | | (34) ~ (all_8_0 = e0) % 151.63/22.45 | | | | % 151.63/22.45 | | | | REF_CLOSE: (2), (12), (20), (25), (34) are inconsistent by sub-proof % 151.63/22.45 | | | | #342. % 151.63/22.45 | | | | % 151.63/22.45 | | | End of split % 151.63/22.45 | | | % 151.63/22.45 | | End of split % 151.63/22.45 | | % 151.63/22.45 | End of split % 151.63/22.45 | % 151.63/22.45 End of proof % 151.63/22.45 % 151.63/22.45 Sub-proof #333 shows that the following formulas are inconsistent: % 151.63/22.45 ---------------------------------------------------------------- % 151.63/22.45 (1) all_56_11 = all_8_2 % 151.63/22.45 (2) ~ (all_56_11 = e1) | all_56_13 = e2 % 151.63/22.45 (3) ~ (all_52_11 = all_6_2) % 151.63/22.45 (4) all_54_9 = all_52_6 % 151.63/22.45 (5) all_58_6 = all_52_2 % 151.63/22.45 (6) all_54_10 = all_6_2 % 151.63/22.45 (7) ~ (all_6_1 = e2) % 151.63/22.45 (8) ~ (all_52_2 = all_8_0) % 151.63/22.45 (9) ~ (all_52_13 = all_8_2) % 151.63/22.45 (10) ~ (all_56_21 = e2) | all_56_19 = e1 % 151.63/22.45 (11) all_54_0 = all_10_2 % 151.63/22.45 (12) ~ (all_52_14 = all_4_2) % 151.63/22.45 (13) ~ (all_8_0 = e1) % 151.63/22.45 (14) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0 % 151.63/22.45 (15) ~ (all_52_9 = all_8_2) % 151.63/22.45 (16) op(e0, e0) = all_4_2 % 151.63/22.45 (17) ~ (all_52_13 = all_8_0) % 151.63/22.45 (18) all_54_5 = all_8_2 % 151.63/22.45 (19) ~ (all_52_6 = all_52_14) % 151.63/22.45 (20) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 151.63/22.45 (21) ~ (all_6_0 = e2) % 151.63/22.45 (22) ~ (all_8_0 = all_8_2) % 151.63/22.45 (23) all_56_21 = all_6_2 % 151.63/22.45 (24) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 151.63/22.45 (25) ~ (all_52_7 = all_8_2) % 151.63/22.45 (26) all_56_1 = all_10_2 % 151.63/22.45 (27) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0 % 151.63/22.45 (28) all_58_5 = all_52_9 % 151.63/22.45 (29) all_56_17 = all_52_2 % 151.63/22.45 (30) op(e0, all_52_14) = all_56_22 % 151.63/22.45 (31) ~ (all_36_1 = e3) % 151.63/22.45 (32) op(e1, e0) = all_52_14 % 151.63/22.45 (33) ~ (all_22_0 = e0) | ~ (all_22_2 = e1) % 151.63/22.45 (34) all_58_13 = all_52_7 % 151.63/22.45 (35) op(e2, all_8_2) = all_56_10 % 151.63/22.45 (36) op(e3, e3) = all_10_2 % 151.63/22.45 (37) ~ (all_56_21 = e3) | all_56_17 = e1 % 151.63/22.45 (38) ~ (e1 = e0) % 151.63/22.45 (39) all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1 % 151.63/22.45 (40) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 151.63/22.45 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 151.63/22.45 (41) ~ (all_10_2 = all_8_0) % 151.63/22.45 (42) ~ (all_52_3 = all_10_2) % 151.63/22.45 (43) ~ (all_56_11 = e3) | all_56_9 = e2 % 151.63/22.45 (44) ~ (all_52_2 = all_52_6) % 151.63/22.45 (45) op(e0, all_4_1) = all_4_0 % 151.63/22.45 (46) all_22_0 = all_8_0 % 151.63/22.45 (47) all_56_13 = all_52_9 % 151.63/22.45 (48) op(e2, all_52_6) = all_56_18 % 151.63/22.45 (49) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0 % 151.63/22.45 (50) all_36_1 = all_6_1 % 151.63/22.45 (51) all_58_8 = all_6_2 % 151.63/22.45 (52) ~ (all_4_0 = e1) % 151.63/22.45 (53) all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3 % 151.63/22.45 (54) ~ (e2 = e1) % 151.63/22.45 (55) ~ (all_52_9 = all_52_13) % 151.63/22.45 (56) op(e1, all_6_1) = all_6_0 % 151.63/22.45 (57) all_56_9 = all_8_0 % 151.63/22.45 (58) op(all_4_2, all_4_2) = all_4_1 % 151.63/22.45 (59) all_58_3 = all_8_2 % 151.63/22.45 (60) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0 % 151.63/22.45 (61) ~ (all_52_6 = all_52_7) % 151.63/22.45 (62) all_56_31 = all_4_2 % 151.63/22.45 (63) all_58_11 = all_52_14 % 151.63/22.45 (64) ~ (all_52_2 = all_52_14) % 151.63/22.45 (65) all_54_7 = all_52_13 % 151.63/22.45 (66) op(all_6_2, all_6_2) = all_6_1 % 151.63/22.45 (67) all_56_1 = e3 | all_56_11 = e2 | all_56_21 = e1 | all_56_31 = e0 % 151.63/22.45 (68) ~ (all_52_13 = all_4_2) % 151.63/22.45 (69) op(all_8_2, all_8_2) = e3 % 151.63/22.45 (70) all_56_23 = all_52_14 % 151.63/22.45 (71) all_54_8 = all_52_2 % 151.63/22.45 (72) op(e1, e1) = all_6_2 % 151.63/22.45 (73) ~ (all_52_6 = all_8_2) % 151.63/22.45 (74) all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1 % 151.63/22.45 (75) op(e0, e3) = all_52_3 % 151.63/22.45 (76) all_58_15 = all_4_2 % 151.63/22.45 (77) ~ (all_52_9 = all_6_2) % 151.63/22.45 (78) all_22_2 = all_8_2 % 151.63/22.45 (79) all_58_7 = all_52_6 % 151.63/22.45 (80) all_58_10 = all_52_13 % 151.63/22.45 (81) all_58_2 = all_8_0 % 151.63/22.45 (82) ~ (all_56_11 = e0) | all_56_15 = e2 % 151.63/22.45 (83) all_58_0 = all_10_2 % 151.63/22.45 (84) op(e1, all_6_2) = all_56_20 % 151.63/22.45 (85) all_54_4 = all_8_0 % 151.63/22.45 (86) op(e2, e2) = all_8_2 % 151.63/22.45 (87) ~ (all_52_2 = all_6_2) % 151.63/22.45 (88) ~ (all_56_21 = e0) | all_56_23 = e1 % 151.63/22.45 (89) op(e0, all_4_2) = all_56_30 % 151.63/22.45 (90) ~ (all_52_6 = all_6_2) % 151.63/22.45 (91) ~ (all_52_14 = all_6_2) % 151.63/22.45 (92) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0 % 151.63/22.45 (93) ~ (all_52_2 = all_10_2) % 151.63/22.45 (94) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 151.63/22.45 (95) all_58_14 = all_52_11 % 151.63/22.45 (96) all_56_19 = all_52_6 % 151.63/22.45 (97) ~ (all_52_9 = all_8_0) % 151.63/22.45 (98) all_56_15 = all_52_13 % 151.63/22.45 (99) all_58_12 = all_52_3 % 151.63/22.45 (100) all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2 % 151.63/22.45 (101) all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3 % 151.63/22.45 (102) all_54_11 = all_52_14 % 151.63/22.45 % 151.63/22.45 Begin of proof % 151.63/22.45 | % 151.63/22.45 | REDUCE: (31), (50) imply: % 151.63/22.45 | (103) ~ (all_6_1 = e3) % 151.63/22.45 | % 151.63/22.45 | BETA: splitting (10) gives: % 151.63/22.45 | % 151.63/22.45 | Case 1: % 151.63/22.45 | | % 151.63/22.45 | | (104) ~ (all_56_21 = e2) % 151.63/22.45 | | % 151.63/22.45 | | REDUCE: (23), (104) imply: % 151.63/22.45 | | (105) ~ (all_6_2 = e2) % 151.63/22.45 | | % 151.63/22.45 | | BETA: splitting (82) gives: % 151.63/22.45 | | % 151.63/22.45 | | Case 1: % 151.63/22.45 | | | % 151.63/22.45 | | | (106) ~ (all_56_11 = e0) % 151.63/22.45 | | | % 151.63/22.45 | | | REDUCE: (1), (106) imply: % 151.63/22.45 | | | (107) ~ (all_8_2 = e0) % 151.63/22.45 | | | % 151.63/22.45 | | | BETA: splitting (37) gives: % 151.63/22.45 | | | % 151.63/22.45 | | | Case 1: % 151.63/22.45 | | | | % 151.63/22.45 | | | | (108) ~ (all_56_21 = e3) % 151.63/22.45 | | | | % 151.63/22.45 | | | | REDUCE: (23), (108) imply: % 151.63/22.45 | | | | (109) ~ (all_6_2 = e3) % 151.63/22.45 | | | | % 151.63/22.45 | | | | BETA: splitting (2) gives: % 151.63/22.45 | | | | % 151.63/22.45 | | | | Case 1: % 151.63/22.45 | | | | | % 151.63/22.45 | | | | | (110) ~ (all_56_11 = e1) % 151.63/22.45 | | | | | % 151.63/22.45 | | | | | REDUCE: (1), (110) imply: % 151.63/22.45 | | | | | (111) ~ (all_8_2 = e1) % 151.63/22.45 | | | | | % 151.63/22.45 | | | | | BETA: splitting (43) gives: % 151.63/22.45 | | | | | % 151.63/22.45 | | | | | Case 1: % 151.63/22.45 | | | | | | % 151.63/22.45 | | | | | | (112) ~ (all_56_11 = e3) % 151.63/22.45 | | | | | | % 151.63/22.45 | | | | | | REDUCE: (1), (112) imply: % 151.63/22.45 | | | | | | (113) ~ (all_8_2 = e3) % 151.63/22.45 | | | | | | % 151.63/22.45 | | | | | | REF_CLOSE: (18), (35), (40), (69), (86), (94), (107), (111), (113) % 151.63/22.45 | | | | | | are inconsistent by sub-proof #347. % 151.63/22.45 | | | | | | % 151.63/22.45 | | | | | Case 2: % 151.63/22.45 | | | | | | % 151.63/22.45 | | | | | | (114) all_56_11 = e3 % 151.63/22.45 | | | | | | (115) all_56_9 = e2 % 151.63/22.45 | | | | | | % 151.63/22.45 | | | | | | COMBINE_EQS: (57), (115) imply: % 151.63/22.45 | | | | | | (116) all_8_0 = e2 % 151.63/22.45 | | | | | | % 151.63/22.45 | | | | | | COMBINE_EQS: (1), (114) imply: % 151.63/22.45 | | | | | | (117) all_8_2 = e3 % 151.63/22.45 | | | | | | % 151.63/22.45 | | | | | | COMBINE_EQS: (81), (116) imply: % 151.63/22.45 | | | | | | (118) all_58_2 = e2 % 151.63/22.45 | | | | | | % 151.63/22.45 | | | | | | REDUCE: (8), (116) imply: % 151.63/22.45 | | | | | | (119) ~ (all_52_2 = e2) % 151.63/22.45 | | | | | | % 151.63/22.45 | | | | | | REDUCE: (73), (117) imply: % 151.63/22.45 | | | | | | (120) ~ (all_52_6 = e3) % 151.63/22.45 | | | | | | % 151.63/22.45 | | | | | | REDUCE: (25), (117) imply: % 151.63/22.45 | | | | | | (121) ~ (all_52_7 = e3) % 151.63/22.45 | | | | | | % 151.63/22.45 | | | | | | REDUCE: (111), (117) imply: % 151.63/22.45 | | | | | | (122) ~ (e3 = e1) % 151.63/22.45 | | | | | | % 151.63/22.45 | | | | | | REDUCE: (107), (117) imply: % 151.63/22.45 | | | | | | (123) ~ (e3 = e0) % 151.63/22.45 | | | | | | % 151.63/22.45 | | | | | | REDUCE: (69), (117) imply: % 151.63/22.45 | | | | | | (124) op(e3, e3) = e3 % 151.63/22.45 | | | | | | % 151.63/22.45 | | | | | | REDUCE: (86), (117) imply: % 151.63/22.45 | | | | | | (125) op(e2, e2) = e3 % 151.63/22.45 | | | | | | % 151.63/22.45 | | | | | | GROUND_INST: instantiating (40) with all_10_2, e3, e3, e3, % 151.63/22.45 | | | | | | simplifying with (36), (124) gives: % 151.63/22.45 | | | | | | (126) all_10_2 = e3 % 151.63/22.45 | | | | | | % 151.63/22.45 | | | | | | COMBINE_EQS: (83), (126) imply: % 151.63/22.45 | | | | | | (127) all_58_0 = e3 % 151.63/22.45 | | | | | | % 151.63/22.45 | | | | | | REDUCE: (93), (126) imply: % 151.63/22.45 | | | | | | (128) ~ (all_52_2 = e3) % 151.63/22.45 | | | | | | % 151.63/22.45 | | | | | | REDUCE: (42), (126) imply: % 151.63/22.45 | | | | | | (129) ~ (all_52_3 = e3) % 151.63/22.45 | | | | | | % 151.63/22.45 | | | | | | BETA: splitting (53) gives: % 151.63/22.45 | | | | | | % 151.63/22.45 | | | | | | Case 1: % 151.63/22.45 | | | | | | | % 151.63/22.45 | | | | | | | (130) all_58_6 = e3 % 151.63/22.45 | | | | | | | % 151.63/22.45 | | | | | | | REF_CLOSE: (5), (128), (130) are inconsistent by sub-proof #346. % 151.63/22.45 | | | | | | | % 151.63/22.45 | | | | | | Case 2: % 151.63/22.45 | | | | | | | % 151.63/22.45 | | | | | | | (131) all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3 % 151.63/22.45 | | | | | | | % 151.63/22.45 | | | | | | | BETA: splitting (131) gives: % 151.63/22.45 | | | | | | | % 151.63/22.45 | | | | | | | Case 1: % 151.63/22.45 | | | | | | | | % 151.63/22.45 | | | | | | | | (132) all_58_7 = e3 % 151.63/22.45 | | | | | | | | % 151.63/22.45 | | | | | | | | COMBINE_EQS: (79), (132) imply: % 151.63/22.45 | | | | | | | | (133) all_52_6 = e3 % 151.63/22.45 | | | | | | | | % 151.63/22.45 | | | | | | | | REDUCE: (120), (133) imply: % 151.63/22.45 | | | | | | | | (134) $false % 151.63/22.45 | | | | | | | | % 151.63/22.45 | | | | | | | | CLOSE: (134) is inconsistent. % 151.63/22.45 | | | | | | | | % 151.63/22.45 | | | | | | | Case 2: % 151.63/22.45 | | | | | | | | % 151.63/22.45 | | | | | | | | (135) all_58_8 = e3 | all_58_11 = e3 % 151.63/22.45 | | | | | | | | % 151.63/22.45 | | | | | | | | BETA: splitting (135) gives: % 151.63/22.45 | | | | | | | | % 151.63/22.45 | | | | | | | | Case 1: % 151.63/22.45 | | | | | | | | | % 151.63/22.45 | | | | | | | | | (136) all_58_8 = e3 % 151.63/22.45 | | | | | | | | | % 151.63/22.45 | | | | | | | | | COMBINE_EQS: (51), (136) imply: % 151.63/22.45 | | | | | | | | | (137) all_6_2 = e3 % 151.63/22.45 | | | | | | | | | % 151.63/22.45 | | | | | | | | | REDUCE: (109), (137) imply: % 151.63/22.45 | | | | | | | | | (138) $false % 151.63/22.45 | | | | | | | | | % 151.63/22.45 | | | | | | | | | CLOSE: (138) is inconsistent. % 151.63/22.45 | | | | | | | | | % 151.63/22.45 | | | | | | | | Case 2: % 151.63/22.45 | | | | | | | | | % 151.63/22.45 | | | | | | | | | (139) all_58_11 = e3 % 151.63/22.45 | | | | | | | | | % 151.63/22.45 | | | | | | | | | COMBINE_EQS: (63), (139) imply: % 151.63/22.45 | | | | | | | | | (140) all_52_14 = e3 % 151.63/22.45 | | | | | | | | | % 151.63/22.45 | | | | | | | | | COMBINE_EQS: (70), (140) imply: % 151.63/22.45 | | | | | | | | | (141) all_56_23 = e3 % 151.63/22.45 | | | | | | | | | % 151.63/22.45 | | | | | | | | | REDUCE: (91), (140) imply: % 151.63/22.45 | | | | | | | | | (142) ~ (all_6_2 = e3) % 151.63/22.45 | | | | | | | | | % 151.63/22.45 | | | | | | | | | REDUCE: (12), (140) imply: % 151.63/22.45 | | | | | | | | | (143) ~ (all_4_2 = e3) % 151.63/22.45 | | | | | | | | | % 151.63/22.45 | | | | | | | | | SIMP: (143) implies: % 151.63/22.45 | | | | | | | | | (144) ~ (all_4_2 = e3) % 151.63/22.45 | | | | | | | | | % 151.63/22.45 | | | | | | | | | REDUCE: (30), (140) imply: % 151.63/22.45 | | | | | | | | | (145) op(e0, e3) = all_56_22 % 151.63/22.45 | | | | | | | | | % 151.63/22.45 | | | | | | | | | BETA: splitting (88) gives: % 151.63/22.45 | | | | | | | | | % 151.63/22.45 | | | | | | | | | Case 1: % 151.63/22.45 | | | | | | | | | | % 151.63/22.45 | | | | | | | | | | (146) ~ (all_56_21 = e0) % 151.63/22.45 | | | | | | | | | | % 151.63/22.45 | | | | | | | | | | REDUCE: (23), (146) imply: % 151.63/22.45 | | | | | | | | | | (147) ~ (all_6_2 = e0) % 151.63/22.45 | | | | | | | | | | % 151.63/22.45 | | | | | | | | | | BETA: splitting (24) gives: % 151.63/22.45 | | | | | | | | | | % 151.63/22.45 | | | | | | | | | | Case 1: % 151.63/22.45 | | | | | | | | | | | % 151.63/22.45 | | | | | | | | | | | (148) all_54_10 = e3 % 151.63/22.45 | | | | | | | | | | | % 151.63/22.45 | | | | | | | | | | | COMBINE_EQS: (6), (148) imply: % 151.63/22.45 | | | | | | | | | | | (149) all_6_2 = e3 % 151.63/22.45 | | | | | | | | | | | % 151.63/22.45 | | | | | | | | | | | REDUCE: (109), (149) imply: % 151.63/22.45 | | | | | | | | | | | (150) $false % 151.63/22.45 | | | | | | | | | | | % 151.63/22.45 | | | | | | | | | | | CLOSE: (150) is inconsistent. % 151.63/22.45 | | | | | | | | | | | % 151.63/22.45 | | | | | | | | | | Case 2: % 151.63/22.45 | | | | | | | | | | | % 151.63/22.45 | | | | | | | | | | | (151) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 151.63/22.45 | | | | | | | | | | | % 151.63/22.45 | | | | | | | | | | | BETA: splitting (151) gives: % 151.63/22.45 | | | | | | | | | | | % 151.63/22.45 | | | | | | | | | | | Case 1: % 151.63/22.45 | | | | | | | | | | | | % 151.63/22.45 | | | | | | | | | | | | (152) all_54_10 = e2 % 151.63/22.45 | | | | | | | | | | | | % 151.63/22.45 | | | | | | | | | | | | COMBINE_EQS: (6), (152) imply: % 151.63/22.45 | | | | | | | | | | | | (153) all_6_2 = e2 % 151.63/22.45 | | | | | | | | | | | | % 151.63/22.45 | | | | | | | | | | | | REDUCE: (105), (153) imply: % 151.63/22.45 | | | | | | | | | | | | (154) $false % 151.63/22.45 | | | | | | | | | | | | % 151.63/22.45 | | | | | | | | | | | | CLOSE: (154) is inconsistent. % 151.63/22.45 | | | | | | | | | | | | % 151.63/22.45 | | | | | | | | | | | Case 2: % 151.63/22.45 | | | | | | | | | | | | % 151.63/22.45 | | | | | | | | | | | | (155) ~ (all_54_10 = e2) % 151.63/22.45 | | | | | | | | | | | | (156) all_54_10 = e1 | all_54_10 = e0 % 151.63/22.45 | | | | | | | | | | | | % 151.63/22.45 | | | | | | | | | | | | BETA: splitting (101) gives: % 151.63/22.45 | | | | | | | | | | | | % 151.63/22.45 | | | | | | | | | | | | Case 1: % 151.63/22.45 | | | | | | | | | | | | | % 151.63/22.45 | | | | | | | | | | | | | (157) all_58_12 = e3 % 151.63/22.45 | | | | | | | | | | | | | % 151.63/22.45 | | | | | | | | | | | | | COMBINE_EQS: (99), (157) imply: % 151.63/22.45 | | | | | | | | | | | | | (158) all_52_3 = e3 % 151.63/22.45 | | | | | | | | | | | | | % 151.63/22.45 | | | | | | | | | | | | | REDUCE: (129), (158) imply: % 151.63/22.45 | | | | | | | | | | | | | (159) $false % 151.63/22.45 | | | | | | | | | | | | | % 151.63/22.45 | | | | | | | | | | | | | CLOSE: (159) is inconsistent. % 151.63/22.45 | | | | | | | | | | | | | % 151.63/22.45 | | | | | | | | | | | | Case 2: % 151.63/22.45 | | | | | | | | | | | | | % 151.63/22.45 | | | | | | | | | | | | | (160) all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3 % 151.63/22.45 | | | | | | | | | | | | | % 151.63/22.45 | | | | | | | | | | | | | BETA: splitting (160) gives: % 151.63/22.45 | | | | | | | | | | | | | % 151.63/22.45 | | | | | | | | | | | | | Case 1: % 151.63/22.45 | | | | | | | | | | | | | | % 151.63/22.45 | | | | | | | | | | | | | | (161) all_58_13 = e3 % 151.63/22.45 | | | | | | | | | | | | | | % 151.63/22.45 | | | | | | | | | | | | | | REF_CLOSE: (34), (121), (161) are inconsistent by sub-proof % 151.63/22.45 | | | | | | | | | | | | | | #444. % 151.63/22.45 | | | | | | | | | | | | | | % 151.63/22.45 | | | | | | | | | | | | | Case 2: % 151.63/22.45 | | | | | | | | | | | | | | % 151.63/22.45 | | | | | | | | | | | | | | (162) all_58_14 = e3 | all_58_15 = e3 % 151.63/22.45 | | | | | | | | | | | | | | % 151.63/22.45 | | | | | | | | | | | | | | BETA: splitting (162) gives: % 151.63/22.45 | | | | | | | | | | | | | | % 151.63/22.45 | | | | | | | | | | | | | | Case 1: % 151.63/22.45 | | | | | | | | | | | | | | | % 151.63/22.45 | | | | | | | | | | | | | | | (163) all_58_14 = e3 % 151.63/22.45 | | | | | | | | | | | | | | | % 151.63/22.45 | | | | | | | | | | | | | | | COMBINE_EQS: (95), (163) imply: % 151.63/22.45 | | | | | | | | | | | | | | | (164) all_52_11 = e3 % 151.63/22.45 | | | | | | | | | | | | | | | % 151.63/22.45 | | | | | | | | | | | | | | | SIMP: (164) implies: % 151.63/22.45 | | | | | | | | | | | | | | | (165) all_52_11 = e3 % 151.63/22.45 | | | | | | | | | | | | | | | % 151.63/22.45 | | | | | | | | | | | | | | | BETA: splitting (156) gives: % 151.63/22.45 | | | | | | | | | | | | | | | % 151.63/22.45 | | | | | | | | | | | | | | | Case 1: % 151.63/22.45 | | | | | | | | | | | | | | | | % 151.63/22.45 | | | | | | | | | | | | | | | | (166) all_54_10 = e1 % 151.63/22.45 | | | | | | | | | | | | | | | | % 151.63/22.45 | | | | | | | | | | | | | | | | COMBINE_EQS: (6), (166) imply: % 151.63/22.45 | | | | | | | | | | | | | | | | (167) all_6_2 = e1 % 151.63/22.46 | | | | | | | | | | | | | | | | % 151.63/22.46 | | | | | | | | | | | | | | | | SIMP: (167) implies: % 151.63/22.46 | | | | | | | | | | | | | | | | (168) all_6_2 = e1 % 151.63/22.46 | | | | | | | | | | | | | | | | % 151.63/22.46 | | | | | | | | | | | | | | | | REDUCE: (87), (168) imply: % 151.63/22.46 | | | | | | | | | | | | | | | | (169) ~ (all_52_2 = e1) % 151.63/22.46 | | | | | | | | | | | | | | | | % 151.63/22.46 | | | | | | | | | | | | | | | | REDUCE: (90), (168) imply: % 151.63/22.46 | | | | | | | | | | | | | | | | (170) ~ (all_52_6 = e1) % 151.63/22.46 | | | | | | | | | | | | | | | | % 151.63/22.46 | | | | | | | | | | | | | | | | REDUCE: (109), (168) imply: % 151.63/22.46 | | | | | | | | | | | | | | | | (171) ~ (e3 = e1) % 151.63/22.46 | | | | | | | | | | | | | | | | % 151.63/22.46 | | | | | | | | | | | | | | | | REDUCE: (105), (168) imply: % 151.63/22.46 | | | | | | | | | | | | | | | | (172) ~ (e2 = e1) % 151.63/22.46 | | | | | | | | | | | | | | | | % 151.63/22.46 | | | | | | | | | | | | | | | | BETA: splitting (92) gives: % 151.63/22.46 | | | | | | | | | | | | | | | | % 151.63/22.46 | | | | | | | | | | | | | | | | Case 1: % 151.63/22.46 | | | | | | | | | | | | | | | | | % 151.63/22.46 | | | | | | | | | | | | | | | | | (173) all_54_8 = e3 % 151.63/22.46 | | | | | | | | | | | | | | | | | % 151.63/22.46 | | | | | | | | | | | | | | | | | REF_CLOSE: (71), (128), (173) are inconsistent by sub-proof % 151.63/22.46 | | | | | | | | | | | | | | | | | #345. % 151.63/22.46 | | | | | | | | | | | | | | | | | % 151.63/22.46 | | | | | | | | | | | | | | | | Case 2: % 151.63/22.46 | | | | | | | | | | | | | | | | | % 151.63/22.46 | | | | | | | | | | | | | | | | | (174) all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0 % 151.63/22.46 | | | | | | | | | | | | | | | | | % 151.63/22.46 | | | | | | | | | | | | | | | | | BETA: splitting (174) gives: % 151.63/22.46 | | | | | | | | | | | | | | | | | % 151.63/22.46 | | | | | | | | | | | | | | | | | Case 1: % 151.63/22.46 | | | | | | | | | | | | | | | | | | % 151.63/22.46 | | | | | | | | | | | | | | | | | | (175) all_54_8 = e2 % 151.63/22.46 | | | | | | | | | | | | | | | | | | % 151.63/22.46 | | | | | | | | | | | | | | | | | | REF_CLOSE: (71), (119), (175) are inconsistent by sub-proof % 151.63/22.46 | | | | | | | | | | | | | | | | | | #666. % 151.63/22.46 | | | | | | | | | | | | | | | | | | % 151.63/22.46 | | | | | | | | | | | | | | | | | Case 2: % 151.63/22.46 | | | | | | | | | | | | | | | | | | % 151.63/22.46 | | | | | | | | | | | | | | | | | | (176) all_54_8 = e1 | all_54_8 = e0 % 151.63/22.46 | | | | | | | | | | | | | | | | | | % 151.63/22.46 | | | | | | | | | | | | | | | | | | BETA: splitting (176) gives: % 151.63/22.46 | | | | | | | | | | | | | | | | | | % 151.63/22.46 | | | | | | | | | | | | | | | | | | Case 1: % 151.63/22.46 | | | | | | | | | | | | | | | | | | | % 151.63/22.46 | | | | | | | | | | | | | | | | | | | (177) all_54_8 = e1 % 151.63/22.46 | | | | | | | | | | | | | | | | | | | % 151.63/22.46 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (71), (169), (177) are inconsistent by sub-proof % 151.63/22.46 | | | | | | | | | | | | | | | | | | | #665. % 151.63/22.46 | | | | | | | | | | | | | | | | | | | % 151.63/22.46 | | | | | | | | | | | | | | | | | | Case 2: % 151.63/22.46 | | | | | | | | | | | | | | | | | | | % 151.63/22.46 | | | | | | | | | | | | | | | | | | | (178) all_54_8 = e0 % 151.63/22.46 | | | | | | | | | | | | | | | | | | | % 151.63/22.46 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (71), (178) imply: % 151.63/22.46 | | | | | | | | | | | | | | | | | | | (179) all_52_2 = e0 % 151.63/22.46 | | | | | | | | | | | | | | | | | | | % 151.63/22.46 | | | | | | | | | | | | | | | | | | | SIMP: (179) implies: % 151.63/22.46 | | | | | | | | | | | | | | | | | | | (180) all_52_2 = e0 % 151.63/22.46 | | | | | | | | | | | | | | | | | | | % 151.63/22.46 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5), (180) imply: % 151.63/22.46 | | | | | | | | | | | | | | | | | | | (181) all_58_6 = e0 % 151.63/22.46 | | | | | | | | | | | | | | | | | | | % 151.63/22.46 | | | | | | | | | | | | | | | | | | | REDUCE: (44), (180) imply: % 151.63/22.46 | | | | | | | | | | | | | | | | | | | (182) ~ (all_52_6 = e0) % 151.63/22.46 | | | | | | | | | | | | | | | | | | | % 151.63/22.46 | | | | | | | | | | | | | | | | | | | SIMP: (182) implies: % 151.63/22.46 | | | | | | | | | | | | | | | | | | | (183) ~ (all_52_6 = e0) % 151.63/22.46 | | | | | | | | | | | | | | | | | | | % 151.63/22.46 | | | | | | | | | | | | | | | | | | | REDUCE: (169), (180) imply: % 151.63/22.46 | | | | | | | | | | | | | | | | | | | (184) ~ (e1 = e0) % 151.63/22.46 | | | | | | | | | | | | | | | | | | | % 151.63/22.46 | | | | | | | | | | | | | | | | | | | BETA: splitting (60) gives: % 151.63/22.46 | | | | | | | | | | | | | | | | | | | % 151.63/22.46 | | | | | | | | | | | | | | | | | | | Case 1: % 151.63/22.46 | | | | | | | | | | | | | | | | | | | | % 151.63/22.46 | | | | | | | | | | | | | | | | | | | | (185) all_54_9 = e3 % 151.63/22.46 | | | | | | | | | | | | | | | | | | | | % 151.63/22.46 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4), (185) imply: % 151.63/22.46 | | | | | | | | | | | | | | | | | | | | (186) all_52_6 = e3 % 151.63/22.46 | | | | | | | | | | | | | | | | | | | | % 151.63/22.46 | | | | | | | | | | | | | | | | | | | | REDUCE: (120), (186) imply: % 151.63/22.46 | | | | | | | | | | | | | | | | | | | | (187) $false % 151.63/22.46 | | | | | | | | | | | | | | | | | | | | % 151.63/22.46 | | | | | | | | | | | | | | | | | | | | CLOSE: (187) is inconsistent. % 151.63/22.46 | | | | | | | | | | | | | | | | | | | | % 151.63/22.46 | | | | | | | | | | | | | | | | | | | Case 2: % 151.63/22.46 | | | | | | | | | | | | | | | | | | | | % 151.63/22.46 | | | | | | | | | | | | | | | | | | | | (188) ~ (all_54_9 = e3) % 151.63/22.46 | | | | | | | | | | | | | | | | | | | | (189) all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0 % 151.63/22.46 | | | | | | | | | | | | | | | | | | | | % 151.63/22.46 | | | | | | | | | | | | | | | | | | | | BETA: splitting (74) gives: % 151.63/22.46 | | | | | | | | | | | | | | | | | | | | % 151.63/22.46 | | | | | | | | | | | | | | | | | | | | Case 1: % 151.63/22.46 | | | | | | | | | | | | | | | | | | | | | % 151.63/22.46 | | | | | | | | | | | | | | | | | | | | | (190) all_58_0 = e1 % 151.63/22.46 | | | | | | | | | | | | | | | | | | | | | % 151.63/22.46 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (127), (190) imply: % 151.63/22.46 | | | | | | | | | | | | | | | | | | | | | (191) e3 = e1 % 151.63/22.46 | | | | | | | | | | | | | | | | | | | | | % 151.63/22.46 | | | | | | | | | | | | | | | | | | | | | REDUCE: (122), (191) imply: % 151.63/22.46 | | | | | | | | | | | | | | | | | | | | | (192) $false % 151.63/22.46 | | | | | | | | | | | | | | | | | | | | | % 151.63/22.46 | | | | | | | | | | | | | | | | | | | | | CLOSE: (192) is inconsistent. % 151.63/22.46 | | | | | | | | | | | | | | | | | | | | | % 151.63/22.46 | | | | | | | | | | | | | | | | | | | | Case 2: % 151.63/22.46 | | | | | | | | | | | | | | | | | | | | | % 151.63/22.46 | | | | | | | | | | | | | | | | | | | | | (193) all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1 % 151.63/22.46 | | | | | | | | | | | | | | | | | | | | | % 151.63/22.46 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (193) gives: % 151.63/22.46 | | | | | | | | | | | | | | | | | | | | | % 151.63/22.46 | | | | | | | | | | | | | | | | | | | | | Case 1: % 151.63/22.46 | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.46 | | | | | | | | | | | | | | | | | | | | | | (194) all_58_2 = e1 % 151.63/22.46 | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.46 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (118), (194) imply: % 151.63/22.46 | | | | | | | | | | | | | | | | | | | | | | (195) e2 = e1 % 151.63/22.46 | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.46 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (54), (195) imply: % 151.63/22.46 | | | | | | | | | | | | | | | | | | | | | | (196) $false % 151.63/22.46 | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.46 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (196) is inconsistent. % 151.63/22.46 | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.46 | | | | | | | | | | | | | | | | | | | | | Case 2: % 151.63/22.46 | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.46 | | | | | | | | | | | | | | | | | | | | | | (197) all_58_6 = e1 | all_58_12 = e1 % 151.63/22.46 | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.46 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (197) gives: % 151.63/22.46 | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.46 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 151.63/22.46 | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.46 | | | | | | | | | | | | | | | | | | | | | | | (198) all_58_6 = e1 % 151.63/22.46 | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.46 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (38), (181), (198) are inconsistent by sub-proof % 151.63/22.46 | | | | | | | | | | | | | | | | | | | | | | | #344. % 151.63/22.46 | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.46 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 151.63/22.46 | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.46 | | | | | | | | | | | | | | | | | | | | | | | (199) all_58_12 = e1 % 151.63/22.46 | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.46 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (99), (199) imply: % 151.63/22.46 | | | | | | | | | | | | | | | | | | | | | | | (200) all_52_3 = e1 % 151.63/22.46 | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.46 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (75), (200) imply: % 151.63/22.46 | | | | | | | | | | | | | | | | | | | | | | | (201) op(e0, e3) = e1 % 151.63/22.46 | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.46 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (189) gives: % 151.63/22.46 | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.46 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 151.63/22.46 | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.46 | | | | | | | | | | | | | | | | | | | | | | | | (202) all_54_9 = e2 % 151.63/22.46 | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.46 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4), (202) imply: % 151.63/22.46 | | | | | | | | | | | | | | | | | | | | | | | | (203) all_52_6 = e2 % 151.63/22.46 | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.46 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (203) implies: % 151.63/22.46 | | | | | | | | | | | | | | | | | | | | | | | | (204) all_52_6 = e2 % 151.63/22.46 | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.46 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (61), (204) imply: % 151.63/22.46 | | | | | | | | | | | | | | | | | | | | | | | | (205) ~ (all_52_7 = e2) % 151.63/22.46 | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.46 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (205) implies: % 151.63/22.46 | | | | | | | | | | | | | | | | | | | | | | | | (206) ~ (all_52_7 = e2) % 151.63/22.46 | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.46 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (120), (204) imply: % 151.63/22.46 | | | | | | | | | | | | | | | | | | | | | | | | (207) ~ (e3 = e2) % 151.63/22.46 | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.46 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (207) implies: % 151.63/22.46 | | | | | | | | | | | | | | | | | | | | | | | | (208) ~ (e3 = e2) % 151.63/22.46 | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.46 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (48), (204) imply: % 151.63/22.46 | | | | | | | | | | | | | | | | | | | | | | | | (209) op(e2, e2) = all_56_18 % 151.63/22.46 | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.46 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (100) gives: % 151.63/22.46 | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.46 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 151.63/22.46 | | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.46 | | | | | | | | | | | | | | | | | | | | | | | | | (210) all_58_12 = e2 % 151.63/22.46 | | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.46 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (54), (199), (210) are inconsistent by sub-proof % 151.63/22.46 | | | | | | | | | | | | | | | | | | | | | | | | | #622. % 151.63/22.46 | | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.46 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 151.63/22.46 | | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.46 | | | | | | | | | | | | | | | | | | | | | | | | | (211) all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2 % 151.63/22.46 | | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.46 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (211) gives: % 151.63/22.46 | | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.46 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 151.63/22.46 | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.46 | | | | | | | | | | | | | | | | | | | | | | | | | | (212) all_58_13 = e2 % 151.63/22.46 | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.46 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (34), (212) imply: % 151.63/22.46 | | | | | | | | | | | | | | | | | | | | | | | | | | (213) all_52_7 = e2 % 151.63/22.46 | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.46 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (206), (213) imply: % 151.63/22.46 | | | | | | | | | | | | | | | | | | | | | | | | | | (214) $false % 151.63/22.46 | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.46 | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (214) is inconsistent. % 151.63/22.46 | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.46 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 151.63/22.46 | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.46 | | | | | | | | | | | | | | | | | | | | | | | | | | (215) all_58_14 = e2 | all_58_15 = e2 % 151.63/22.46 | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.46 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (215) gives: % 151.63/22.46 | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.46 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 151.63/22.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | (216) all_58_14 = e2 % 151.63/22.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (163), (216) imply: % 151.63/22.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | (217) e3 = e2 % 151.63/22.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (208), (217) imply: % 151.63/22.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | (218) $false % 151.63/22.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (218) is inconsistent. % 151.63/22.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.46 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 151.63/22.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | (219) all_58_15 = e2 % 151.63/22.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (76), (219) imply: % 151.63/22.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | (220) all_4_2 = e2 % 151.63/22.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (58), (220) imply: % 151.63/22.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | (221) op(e2, e2) = all_4_1 % 151.63/22.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (40) with e1, all_56_22, e3, e0, % 151.63/22.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (145), (201) gives: % 151.63/22.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | (222) all_56_22 = e1 % 151.63/22.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (40) with e3, all_56_18, e2, e2, % 151.63/22.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (125), (209) gives: % 151.63/22.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | (223) all_56_18 = e3 % 151.63/22.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (40) with all_4_1, all_56_18, e2, % 151.63/22.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2, simplifying with (209), (221) gives: % 151.63/22.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | (224) all_56_18 = all_4_1 % 151.63/22.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (223), (224) imply: % 151.63/22.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | (225) all_4_1 = e3 % 151.63/22.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (225) implies: % 151.63/22.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | (226) all_4_1 = e3 % 151.63/22.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (45), (226) imply: % 151.63/22.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | (227) op(e0, e3) = all_4_0 % 151.63/22.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (40) with e1, all_4_0, e3, e0, % 151.63/22.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (201), (227) gives: % 151.63/22.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | (228) all_4_0 = e1 % 151.63/22.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (52), (228) imply: % 151.63/22.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | (229) $false % 151.63/22.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (229) is inconsistent. % 151.63/22.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.46 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 151.63/22.46 | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.46 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 151.63/22.46 | | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.46 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 151.63/22.46 | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.46 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 151.63/22.46 | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.46 | | | | | | | | | | | | | | | | | | | | | | | | (230) all_54_9 = e1 | all_54_9 = e0 % 151.63/22.46 | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.46 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (170), (183), (230) are inconsistent by % 151.63/22.46 | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #678. % 151.63/22.46 | | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.46 | | | | | | | | | | | | | | | | | | | | | | | End of split % 151.63/22.46 | | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.46 | | | | | | | | | | | | | | | | | | | | | | End of split % 151.63/22.46 | | | | | | | | | | | | | | | | | | | | | | % 151.63/22.46 | | | | | | | | | | | | | | | | | | | | | End of split % 151.63/22.46 | | | | | | | | | | | | | | | | | | | | | % 151.63/22.46 | | | | | | | | | | | | | | | | | | | | End of split % 151.63/22.46 | | | | | | | | | | | | | | | | | | | | % 151.63/22.46 | | | | | | | | | | | | | | | | | | | End of split % 151.63/22.46 | | | | | | | | | | | | | | | | | | | % 151.63/22.46 | | | | | | | | | | | | | | | | | | End of split % 151.63/22.46 | | | | | | | | | | | | | | | | | | % 151.63/22.46 | | | | | | | | | | | | | | | | | End of split % 151.63/22.46 | | | | | | | | | | | | | | | | | % 151.63/22.46 | | | | | | | | | | | | | | | | End of split % 151.63/22.46 | | | | | | | | | | | | | | | | % 151.63/22.46 | | | | | | | | | | | | | | | Case 2: % 151.63/22.46 | | | | | | | | | | | | | | | | % 151.63/22.46 | | | | | | | | | | | | | | | | (231) all_54_10 = e0 % 151.63/22.46 | | | | | | | | | | | | | | | | % 151.63/22.46 | | | | | | | | | | | | | | | | REF_CLOSE: (6), (147), (231) are inconsistent by sub-proof % 151.63/22.46 | | | | | | | | | | | | | | | | #705. % 151.63/22.46 | | | | | | | | | | | | | | | | % 151.63/22.46 | | | | | | | | | | | | | | | End of split % 151.63/22.46 | | | | | | | | | | | | | | | % 151.63/22.46 | | | | | | | | | | | | | | Case 2: % 151.63/22.46 | | | | | | | | | | | | | | | % 151.63/22.46 | | | | | | | | | | | | | | | (232) all_58_15 = e3 % 151.63/22.46 | | | | | | | | | | | | | | | % 151.63/22.46 | | | | | | | | | | | | | | | COMBINE_EQS: (76), (232) imply: % 151.63/22.46 | | | | | | | | | | | | | | | (233) all_4_2 = e3 % 151.63/22.46 | | | | | | | | | | | | | | | % 151.63/22.46 | | | | | | | | | | | | | | | REDUCE: (144), (233) imply: % 151.63/22.46 | | | | | | | | | | | | | | | (234) $false % 151.63/22.46 | | | | | | | | | | | | | | | % 151.63/22.46 | | | | | | | | | | | | | | | CLOSE: (234) is inconsistent. % 151.63/22.46 | | | | | | | | | | | | | | | % 151.63/22.46 | | | | | | | | | | | | | | End of split % 151.63/22.46 | | | | | | | | | | | | | | % 151.63/22.46 | | | | | | | | | | | | | End of split % 151.63/22.46 | | | | | | | | | | | | | % 151.63/22.46 | | | | | | | | | | | | End of split % 151.63/22.46 | | | | | | | | | | | | % 151.63/22.46 | | | | | | | | | | | End of split % 151.63/22.46 | | | | | | | | | | | % 151.63/22.46 | | | | | | | | | | End of split % 151.63/22.46 | | | | | | | | | | % 151.63/22.46 | | | | | | | | | Case 2: % 151.63/22.46 | | | | | | | | | | % 151.63/22.46 | | | | | | | | | | (235) all_56_23 = e1 % 151.63/22.46 | | | | | | | | | | (236) all_56_21 = e0 % 151.63/22.46 | | | | | | | | | | % 151.63/22.46 | | | | | | | | | | COMBINE_EQS: (23), (236) imply: % 151.63/22.46 | | | | | | | | | | (237) all_6_2 = e0 % 151.63/22.46 | | | | | | | | | | % 151.63/22.46 | | | | | | | | | | SIMP: (237) implies: % 151.63/22.46 | | | | | | | | | | (238) all_6_2 = e0 % 151.63/22.46 | | | | | | | | | | % 151.63/22.46 | | | | | | | | | | COMBINE_EQS: (141), (235) imply: % 151.63/22.46 | | | | | | | | | | (239) e3 = e1 % 151.63/22.46 | | | | | | | | | | % 151.63/22.46 | | | | | | | | | | SIMP: (239) implies: % 151.63/22.46 | | | | | | | | | | (240) e3 = e1 % 151.63/22.46 | | | | | | | | | | % 151.63/22.46 | | | | | | | | | | COMBINE_EQS: (139), (240) imply: % 151.63/22.46 | | | | | | | | | | (241) all_58_11 = e1 % 151.63/22.46 | | | | | | | | | | % 151.63/22.46 | | | | | | | | | | COMBINE_EQS: (51), (238) imply: % 151.63/22.46 | | | | | | | | | | (242) all_58_8 = e0 % 151.63/22.46 | | | | | | | | | | % 151.63/22.46 | | | | | | | | | | REF_CLOSE: (122), (123), (135), (241), (242) are inconsistent % 151.63/22.46 | | | | | | | | | | by sub-proof #343. % 151.63/22.46 | | | | | | | | | | % 151.63/22.46 | | | | | | | | | End of split % 151.63/22.46 | | | | | | | | | % 151.63/22.46 | | | | | | | | End of split % 151.63/22.46 | | | | | | | | % 151.63/22.46 | | | | | | | End of split % 151.63/22.46 | | | | | | | % 151.63/22.46 | | | | | | End of split % 151.63/22.46 | | | | | | % 151.63/22.46 | | | | | End of split % 151.63/22.46 | | | | | % 151.63/22.46 | | | | Case 2: % 151.63/22.46 | | | | | % 151.63/22.46 | | | | | (243) all_56_13 = e2 % 151.63/22.46 | | | | | (244) all_56_11 = e1 % 151.63/22.46 | | | | | % 151.63/22.46 | | | | | REF_CLOSE: (1), (9), (15), (17), (22), (23), (26), (27), (33), (40), % 151.63/22.46 | | | | | (41), (46), (47), (49), (55), (62), (65), (67), (68), (69), % 151.63/22.46 | | | | | (72), (78), (84), (85), (97), (109), (243), (244) are % 151.63/22.46 | | | | | inconsistent by sub-proof #340. % 151.63/22.46 | | | | | % 151.63/22.46 | | | | End of split % 151.63/22.46 | | | | % 151.63/22.46 | | | Case 2: % 151.63/22.46 | | | | % 151.63/22.46 | | | | (245) all_56_21 = e3 % 151.63/22.46 | | | | (246) all_56_17 = e1 % 151.63/22.46 | | | | % 151.63/22.46 | | | | REF_CLOSE: (1), (7), (11), (12), (14), (20), (21), (23), (26), (29), % 151.63/22.46 | | | | (32), (35), (36), (40), (56), (62), (64), (66), (67), (69), % 151.63/22.46 | | | | (86), (87), (91), (93), (102), (103), (105), (245), (246) are % 151.63/22.46 | | | | inconsistent by sub-proof #339. % 151.63/22.46 | | | | % 151.63/22.46 | | | End of split % 151.63/22.46 | | | % 151.63/22.46 | | Case 2: % 151.63/22.46 | | | % 151.63/22.46 | | | (247) all_56_15 = e2 % 151.63/22.46 | | | (248) all_56_11 = e0 % 151.63/22.46 | | | % 151.63/22.46 | | | COMBINE_EQS: (1), (248) imply: % 151.63/22.46 | | | (249) all_8_2 = e0 % 151.63/22.46 | | | % 151.63/22.46 | | | COMBINE_EQS: (98), (247) imply: % 151.63/22.46 | | | (250) all_52_13 = e2 % 151.63/22.46 | | | % 151.63/22.46 | | | REF_CLOSE: (1), (9), (13), (16), (17), (22), (23), (26), (28), (38), (39), % 151.63/22.46 | | | (40), (41), (49), (54), (58), (59), (62), (67), (69), (77), % 151.63/22.46 | | | (80), (81), (85), (89), (249), (250) are inconsistent by % 151.63/22.46 | | | sub-proof #336. % 151.63/22.46 | | | % 151.63/22.46 | | End of split % 151.63/22.46 | | % 151.63/22.46 | Case 2: % 151.63/22.46 | | % 151.63/22.46 | | (251) all_56_21 = e2 % 151.63/22.46 | | (252) all_56_19 = e1 % 151.63/22.46 | | % 151.63/22.46 | | COMBINE_EQS: (96), (252) imply: % 151.63/22.46 | | (253) all_52_6 = e1 % 151.63/22.46 | | % 151.63/22.46 | | SIMP: (253) implies: % 151.63/22.46 | | (254) all_52_6 = e1 % 151.63/22.46 | | % 151.63/22.46 | | COMBINE_EQS: (23), (251) imply: % 151.63/22.46 | | (255) all_6_2 = e2 % 151.63/22.46 | | % 151.63/22.46 | | SIMP: (255) implies: % 151.63/22.46 | | (256) all_6_2 = e2 % 151.63/22.46 | | % 151.63/22.46 | | REF_CLOSE: (1), (7), (9), (13), (16), (17), (18), (22), (23), (26), (28), % 151.63/22.46 | | (39), (40), (41), (49), (58), (59), (62), (66), (67), (69), (73), % 151.63/22.46 | | (77), (80), (81), (82), (85), (86), (89), (90), (94), (98), % 151.63/22.46 | | (103), (254), (256) are inconsistent by sub-proof #334. % 151.63/22.46 | | % 151.63/22.46 | End of split % 151.63/22.46 | % 151.63/22.46 End of proof % 151.63/22.46 % 151.63/22.46 Sub-proof #334 shows that the following formulas are inconsistent: % 151.63/22.46 ---------------------------------------------------------------- % 151.63/22.46 (1) all_56_11 = all_8_2 % 151.63/22.46 (2) all_52_6 = e1 % 151.63/22.46 (3) ~ (all_6_1 = e2) % 151.63/22.46 (4) ~ (all_52_13 = all_8_2) % 151.63/22.46 (5) ~ (all_8_0 = e1) % 151.63/22.46 (6) op(e0, e0) = all_4_2 % 151.63/22.46 (7) ~ (all_52_13 = all_8_0) % 151.63/22.46 (8) all_54_5 = all_8_2 % 151.63/22.46 (9) ~ (all_6_1 = e3) % 151.63/22.46 (10) ~ (all_8_0 = all_8_2) % 151.63/22.46 (11) all_56_21 = all_6_2 % 151.63/22.46 (12) all_56_1 = all_10_2 % 151.63/22.46 (13) all_58_5 = all_52_9 % 151.63/22.46 (14) all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1 % 151.63/22.46 (15) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 151.63/22.46 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 151.63/22.46 (16) ~ (all_10_2 = all_8_0) % 151.63/22.46 (17) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0 % 151.63/22.46 (18) op(all_4_2, all_4_2) = all_4_1 % 151.63/22.46 (19) all_58_3 = all_8_2 % 151.63/22.46 (20) all_56_31 = all_4_2 % 151.63/22.46 (21) op(all_6_2, all_6_2) = all_6_1 % 151.63/22.46 (22) all_56_1 = e3 | all_56_11 = e2 | all_56_21 = e1 | all_56_31 = e0 % 151.63/22.46 (23) op(all_8_2, all_8_2) = e3 % 151.63/22.46 (24) ~ (all_52_6 = all_8_2) % 151.63/22.46 (25) all_6_2 = e2 % 151.63/22.46 (26) ~ (all_52_9 = all_6_2) % 151.63/22.46 (27) all_58_10 = all_52_13 % 151.63/22.46 (28) all_58_2 = all_8_0 % 151.63/22.46 (29) ~ (all_56_11 = e0) | all_56_15 = e2 % 151.63/22.46 (30) all_54_4 = all_8_0 % 151.63/22.46 (31) op(e2, e2) = all_8_2 % 151.63/22.46 (32) op(e0, all_4_2) = all_56_30 % 151.63/22.46 (33) ~ (all_52_6 = all_6_2) % 151.63/22.46 (34) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 151.63/22.46 (35) all_56_15 = all_52_13 % 151.63/22.46 % 151.63/22.46 Begin of proof % 151.63/22.46 | % 151.63/22.46 | REDUCE: (2), (24) imply: % 151.63/22.46 | (36) ~ (all_8_2 = e1) % 151.63/22.46 | % 151.63/22.46 | SIMP: (36) implies: % 151.63/22.46 | (37) ~ (all_8_2 = e1) % 151.63/22.46 | % 151.63/22.46 | REDUCE: (2), (25), (33) imply: % 151.63/22.46 | (38) ~ (e2 = e1) % 151.63/22.46 | % 151.63/22.46 | SIMP: (38) implies: % 151.63/22.46 | (39) ~ (e2 = e1) % 151.63/22.46 | % 151.63/22.46 | REDUCE: (21), (25) imply: % 151.63/22.46 | (40) op(e2, e2) = all_6_1 % 151.63/22.46 | % 151.63/22.46 | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13), % 151.63/22.46 | (14), (15), (16), (17), (18), (19), (20), (22), (23), (26), (27), % 151.63/22.46 | (28), (29), (30), (31), (32), (34), (35), (37), (39), (40) are % 151.63/22.46 | inconsistent by sub-proof #335. % 151.63/22.46 | % 151.63/22.46 End of proof % 151.63/22.46 % 151.63/22.46 Sub-proof #335 shows that the following formulas are inconsistent: % 151.63/22.46 ---------------------------------------------------------------- % 151.63/22.46 (1) all_56_11 = all_8_2 % 151.63/22.46 (2) ~ (all_6_1 = e2) % 151.63/22.46 (3) ~ (all_52_13 = all_8_2) % 151.63/22.46 (4) ~ (all_8_2 = e1) % 151.63/22.46 (5) ~ (all_8_0 = e1) % 151.63/22.46 (6) op(e0, e0) = all_4_2 % 151.63/22.46 (7) ~ (all_52_13 = all_8_0) % 151.63/22.46 (8) op(e2, e2) = all_6_1 % 151.63/22.46 (9) all_54_5 = all_8_2 % 151.63/22.46 (10) ~ (all_6_1 = e3) % 151.63/22.46 (11) ~ (all_8_0 = all_8_2) % 151.63/22.46 (12) all_56_21 = all_6_2 % 151.63/22.46 (13) all_56_1 = all_10_2 % 151.63/22.46 (14) all_58_5 = all_52_9 % 151.63/22.46 (15) all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1 % 151.63/22.46 (16) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 151.63/22.46 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 151.63/22.46 (17) ~ (all_10_2 = all_8_0) % 151.63/22.46 (18) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0 % 151.63/22.46 (19) ~ (e2 = e1) % 151.63/22.46 (20) op(all_4_2, all_4_2) = all_4_1 % 151.63/22.46 (21) all_58_3 = all_8_2 % 151.63/22.46 (22) all_56_31 = all_4_2 % 151.63/22.46 (23) all_56_1 = e3 | all_56_11 = e2 | all_56_21 = e1 | all_56_31 = e0 % 151.63/22.46 (24) op(all_8_2, all_8_2) = e3 % 151.63/22.46 (25) ~ (all_52_9 = all_6_2) % 151.63/22.46 (26) all_58_10 = all_52_13 % 151.63/22.46 (27) all_58_2 = all_8_0 % 151.63/22.46 (28) ~ (all_56_11 = e0) | all_56_15 = e2 % 151.63/22.46 (29) all_54_4 = all_8_0 % 151.63/22.46 (30) op(e2, e2) = all_8_2 % 151.63/22.46 (31) op(e0, all_4_2) = all_56_30 % 151.63/22.46 (32) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 151.63/22.46 (33) all_56_15 = all_52_13 % 151.63/22.46 % 151.63/22.46 Begin of proof % 151.63/22.46 | % 151.63/22.46 | GROUND_INST: instantiating (16) with all_8_2, all_6_1, e2, e2, simplifying % 151.63/22.46 | with (8), (30) gives: % 151.63/22.46 | (34) all_8_2 = all_6_1 % 151.63/22.46 | % 151.63/22.46 | COMBINE_EQS: (9), (34) imply: % 151.63/22.46 | (35) all_54_5 = all_6_1 % 151.63/22.46 | % 151.63/22.46 | COMBINE_EQS: (1), (34) imply: % 151.63/22.46 | (36) all_56_11 = all_6_1 % 151.63/22.46 | % 151.63/22.46 | COMBINE_EQS: (21), (34) imply: % 151.63/22.46 | (37) all_58_3 = all_6_1 % 151.63/22.46 | % 151.63/22.46 | REDUCE: (3), (34) imply: % 151.63/22.46 | (38) ~ (all_52_13 = all_6_1) % 151.63/22.46 | % 151.63/22.46 | REDUCE: (11), (34) imply: % 151.63/22.46 | (39) ~ (all_8_0 = all_6_1) % 151.63/22.46 | % 151.63/22.46 | REDUCE: (4), (34) imply: % 151.63/22.46 | (40) ~ (all_6_1 = e1) % 151.63/22.46 | % 151.63/22.46 | REDUCE: (24), (34) imply: % 151.63/22.46 | (41) op(all_6_1, all_6_1) = e3 % 151.63/22.46 | % 151.63/22.46 | BETA: splitting (32) gives: % 151.63/22.46 | % 151.63/22.46 | Case 1: % 151.63/22.46 | | % 151.63/22.46 | | (42) all_54_5 = e3 % 151.63/22.46 | | % 151.63/22.46 | | REF_CLOSE: (10), (35), (42) are inconsistent by sub-proof #509. % 151.63/22.46 | | % 151.63/22.46 | Case 2: % 151.63/22.46 | | % 151.63/22.46 | | (43) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 151.63/22.46 | | % 151.63/22.46 | | BETA: splitting (43) gives: % 151.63/22.46 | | % 151.63/22.46 | | Case 1: % 151.63/22.46 | | | % 151.63/22.46 | | | (44) all_54_5 = e2 % 151.63/22.46 | | | % 151.63/22.46 | | | REF_CLOSE: (2), (35), (44) are inconsistent by sub-proof #466. % 151.63/22.46 | | | % 151.63/22.46 | | Case 2: % 151.63/22.46 | | | % 151.63/22.46 | | | (45) all_54_5 = e1 | all_54_5 = e0 % 151.63/22.46 | | | % 151.63/22.46 | | | BETA: splitting (45) gives: % 151.63/22.46 | | | % 151.63/22.46 | | | Case 1: % 151.63/22.46 | | | | % 151.63/22.46 | | | | (46) all_54_5 = e1 % 151.63/22.46 | | | | % 151.63/22.46 | | | | REF_CLOSE: (35), (40), (46) are inconsistent by sub-proof #465. % 151.63/22.46 | | | | % 151.63/22.46 | | | Case 2: % 151.63/22.46 | | | | % 151.63/22.46 | | | | (47) all_54_5 = e0 % 151.63/22.46 | | | | % 151.63/22.46 | | | | COMBINE_EQS: (35), (47) imply: % 151.63/22.46 | | | | (48) all_6_1 = e0 % 151.63/22.46 | | | | % 151.63/22.46 | | | | SIMP: (48) implies: % 151.63/22.46 | | | | (49) all_6_1 = e0 % 151.63/22.46 | | | | % 151.63/22.46 | | | | COMBINE_EQS: (36), (49) imply: % 151.63/22.46 | | | | (50) all_56_11 = e0 % 151.63/22.46 | | | | % 151.63/22.46 | | | | COMBINE_EQS: (37), (49) imply: % 151.63/22.46 | | | | (51) all_58_3 = e0 % 151.63/22.46 | | | | % 151.63/22.46 | | | | REDUCE: (38), (49) imply: % 151.63/22.46 | | | | (52) ~ (all_52_13 = e0) % 151.63/22.46 | | | | % 151.63/22.46 | | | | REDUCE: (39), (49) imply: % 151.63/22.46 | | | | (53) ~ (all_8_0 = e0) % 151.63/22.46 | | | | % 151.63/22.46 | | | | REDUCE: (40), (49) imply: % 151.63/22.46 | | | | (54) ~ (e1 = e0) % 151.63/22.46 | | | | % 151.63/22.46 | | | | SIMP: (54) implies: % 151.63/22.46 | | | | (55) ~ (e1 = e0) % 151.63/22.46 | | | | % 151.63/22.46 | | | | REDUCE: (41), (49) imply: % 151.63/22.46 | | | | (56) op(e0, e0) = e3 % 151.63/22.46 | | | | % 151.63/22.46 | | | | BETA: splitting (28) gives: % 151.63/22.46 | | | | % 151.63/22.46 | | | | Case 1: % 151.63/22.46 | | | | | % 151.63/22.46 | | | | | (57) ~ (all_56_11 = e0) % 151.63/22.46 | | | | | % 151.63/22.46 | | | | | REDUCE: (50), (57) imply: % 151.63/22.46 | | | | | (58) $false % 151.63/22.46 | | | | | % 151.63/22.46 | | | | | CLOSE: (58) is inconsistent. % 151.63/22.46 | | | | | % 151.63/22.46 | | | | Case 2: % 151.63/22.46 | | | | | % 151.63/22.46 | | | | | (59) all_56_15 = e2 % 151.63/22.46 | | | | | % 151.63/22.46 | | | | | COMBINE_EQS: (33), (59) imply: % 151.63/22.46 | | | | | (60) all_52_13 = e2 % 151.63/22.46 | | | | | % 151.63/22.46 | | | | | COMBINE_EQS: (26), (60) imply: % 151.63/22.46 | | | | | (61) all_58_10 = e2 % 151.63/22.46 | | | | | % 151.63/22.46 | | | | | REDUCE: (7), (60) imply: % 151.63/22.46 | | | | | (62) ~ (all_8_0 = e2) % 151.63/22.46 | | | | | % 151.63/22.46 | | | | | SIMP: (62) implies: % 151.63/22.46 | | | | | (63) ~ (all_8_0 = e2) % 151.63/22.46 | | | | | % 151.63/22.46 | | | | | REDUCE: (52), (60) imply: % 151.63/22.46 | | | | | (64) ~ (e2 = e0) % 151.63/22.46 | | | | | % 151.63/22.46 | | | | | REF_CLOSE: (5), (6), (12), (13), (14), (15), (16), (17), (18), (19), % 151.63/22.46 | | | | | (20), (22), (23), (25), (27), (29), (31), (50), (51), (53), % 151.63/22.46 | | | | | (55), (56), (61), (63), (64) are inconsistent by sub-proof % 151.63/22.46 | | | | | #337. % 151.63/22.46 | | | | | % 151.63/22.46 | | | | End of split % 151.63/22.46 | | | | % 151.63/22.46 | | | End of split % 151.63/22.46 | | | % 151.63/22.46 | | End of split % 151.63/22.46 | | % 151.63/22.46 | End of split % 151.63/22.46 | % 151.63/22.46 End of proof % 151.63/22.46 % 151.63/22.46 Sub-proof #336 shows that the following formulas are inconsistent: % 151.63/22.46 ---------------------------------------------------------------- % 151.63/22.46 (1) all_56_11 = all_8_2 % 151.63/22.46 (2) ~ (all_52_13 = all_8_2) % 151.63/22.46 (3) ~ (all_8_0 = e1) % 151.63/22.46 (4) op(e0, e0) = all_4_2 % 151.63/22.46 (5) ~ (all_52_13 = all_8_0) % 151.63/22.46 (6) ~ (all_8_0 = all_8_2) % 151.63/22.46 (7) all_56_21 = all_6_2 % 151.63/22.46 (8) all_56_1 = all_10_2 % 151.63/22.46 (9) all_58_5 = all_52_9 % 151.63/22.46 (10) all_52_13 = e2 % 151.63/22.46 (11) ~ (e1 = e0) % 151.63/22.46 (12) all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1 % 151.63/22.46 (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 151.63/22.46 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 151.63/22.46 (14) ~ (all_10_2 = all_8_0) % 151.63/22.46 (15) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0 % 151.63/22.46 (16) ~ (e2 = e1) % 151.63/22.46 (17) op(all_4_2, all_4_2) = all_4_1 % 151.63/22.46 (18) all_58_3 = all_8_2 % 151.63/22.46 (19) all_56_31 = all_4_2 % 151.63/22.46 (20) all_56_1 = e3 | all_56_11 = e2 | all_56_21 = e1 | all_56_31 = e0 % 151.63/22.46 (21) op(all_8_2, all_8_2) = e3 % 151.63/22.46 (22) ~ (all_52_9 = all_6_2) % 151.63/22.46 (23) all_58_10 = all_52_13 % 151.63/22.46 (24) all_58_2 = all_8_0 % 151.63/22.46 (25) all_54_4 = all_8_0 % 151.63/22.46 (26) op(e0, all_4_2) = all_56_30 % 151.63/22.46 (27) all_8_2 = e0 % 151.63/22.46 % 151.63/22.46 Begin of proof % 151.63/22.46 | % 151.63/22.46 | COMBINE_EQS: (1), (27) imply: % 151.63/22.46 | (28) all_56_11 = e0 % 151.63/22.46 | % 151.63/22.46 | COMBINE_EQS: (10), (23) imply: % 151.63/22.46 | (29) all_58_10 = e2 % 151.63/22.46 | % 151.63/22.46 | COMBINE_EQS: (18), (27) imply: % 151.63/22.46 | (30) all_58_3 = e0 % 151.63/22.46 | % 151.63/22.46 | REDUCE: (5), (10) imply: % 151.63/22.46 | (31) ~ (all_8_0 = e2) % 151.63/22.46 | % 151.63/22.46 | SIMP: (31) implies: % 151.63/22.46 | (32) ~ (all_8_0 = e2) % 151.63/22.46 | % 151.63/22.46 | REDUCE: (2), (10), (27) imply: % 151.63/22.46 | (33) ~ (e2 = e0) % 151.63/22.46 | % 151.63/22.46 | REDUCE: (6), (27) imply: % 151.63/22.46 | (34) ~ (all_8_0 = e0) % 151.63/22.46 | % 151.63/22.46 | REDUCE: (21), (27) imply: % 151.63/22.46 | (35) op(e0, e0) = e3 % 151.63/22.46 | % 151.63/22.46 | REF_CLOSE: (3), (4), (7), (8), (9), (11), (12), (13), (14), (15), (16), (17), % 151.63/22.46 | (19), (20), (22), (24), (25), (26), (28), (29), (30), (32), (33), % 151.63/22.46 | (34), (35) are inconsistent by sub-proof #337. % 151.63/22.46 | % 151.63/22.46 End of proof % 151.63/22.46 % 151.63/22.46 Sub-proof #337 shows that the following formulas are inconsistent: % 151.63/22.46 ---------------------------------------------------------------- % 151.63/22.46 (1) ~ (all_8_0 = e1) % 151.63/22.46 (2) op(e0, e0) = all_4_2 % 151.63/22.46 (3) all_58_10 = e2 % 151.63/22.46 (4) all_56_21 = all_6_2 % 151.63/22.46 (5) all_56_1 = all_10_2 % 151.63/22.46 (6) all_58_5 = all_52_9 % 151.63/22.46 (7) ~ (e1 = e0) % 151.63/22.46 (8) all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1 % 151.63/22.46 (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 151.63/22.46 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 151.63/22.46 (10) ~ (all_10_2 = all_8_0) % 151.63/22.46 (11) ~ (all_8_0 = e0) % 151.63/22.46 (12) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0 % 151.63/22.46 (13) all_58_3 = e0 % 151.63/22.46 (14) ~ (e2 = e1) % 151.63/22.46 (15) op(all_4_2, all_4_2) = all_4_1 % 151.63/22.46 (16) all_56_31 = all_4_2 % 151.63/22.46 (17) op(e0, e0) = e3 % 151.63/22.46 (18) all_56_1 = e3 | all_56_11 = e2 | all_56_21 = e1 | all_56_31 = e0 % 151.63/22.46 (19) ~ (all_8_0 = e2) % 151.63/22.46 (20) all_56_11 = e0 % 151.63/22.46 (21) ~ (all_52_9 = all_6_2) % 151.63/22.46 (22) all_58_2 = all_8_0 % 151.63/22.46 (23) all_54_4 = all_8_0 % 151.63/22.46 (24) op(e0, all_4_2) = all_56_30 % 151.63/22.46 (25) ~ (e2 = e0) % 151.63/22.46 % 151.63/22.46 Begin of proof % 151.63/22.46 | % 151.63/22.46 | BETA: splitting (8) gives: % 151.63/22.46 | % 151.63/22.46 | Case 1: % 151.63/22.46 | | % 151.63/22.46 | | (26) all_58_2 = e1 % 151.63/22.46 | | % 151.63/22.46 | | COMBINE_EQS: (22), (26) imply: % 151.63/22.46 | | (27) all_8_0 = e1 % 151.63/22.46 | | % 151.63/22.46 | | REDUCE: (1), (27) imply: % 151.63/22.46 | | (28) $false % 151.63/22.46 | | % 151.63/22.46 | | CLOSE: (28) is inconsistent. % 151.63/22.46 | | % 151.63/22.46 | Case 2: % 151.63/22.46 | | % 151.63/22.46 | | (29) ~ (all_58_2 = e1) % 151.63/22.46 | | (30) all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1 % 151.63/22.46 | | % 151.63/22.46 | | BETA: splitting (12) gives: % 151.63/22.46 | | % 151.63/22.46 | | Case 1: % 151.63/22.46 | | | % 151.63/22.46 | | | (31) all_54_4 = e3 % 151.63/22.46 | | | % 151.63/22.46 | | | COMBINE_EQS: (23), (31) imply: % 151.63/22.46 | | | (32) all_8_0 = e3 % 151.63/22.46 | | | % 151.63/22.46 | | | SIMP: (32) implies: % 151.63/22.46 | | | (33) all_8_0 = e3 % 151.63/22.46 | | | % 151.63/22.46 | | | REDUCE: (10), (33) imply: % 151.63/22.46 | | | (34) ~ (all_10_2 = e3) % 151.63/22.46 | | | % 151.63/22.46 | | | REDUCE: (11), (33) imply: % 151.63/22.46 | | | (35) ~ (e3 = e0) % 151.63/22.46 | | | % 151.63/22.46 | | | BETA: splitting (30) gives: % 151.63/22.46 | | | % 151.63/22.46 | | | Case 1: % 151.63/22.46 | | | | % 151.63/22.46 | | | | (36) all_58_3 = e1 % 151.63/22.46 | | | | % 151.63/22.46 | | | | REF_CLOSE: (7), (13), (36) are inconsistent by sub-proof #338. % 151.63/22.46 | | | | % 151.63/22.46 | | | Case 2: % 151.63/22.46 | | | | % 151.63/22.46 | | | | (37) all_58_5 = e1 | all_58_10 = e1 % 151.63/22.46 | | | | % 151.63/22.46 | | | | BETA: splitting (37) gives: % 151.63/22.46 | | | | % 151.63/22.46 | | | | Case 1: % 151.63/22.46 | | | | | % 151.63/22.46 | | | | | (38) all_58_5 = e1 % 151.63/22.46 | | | | | % 151.63/22.46 | | | | | COMBINE_EQS: (6), (38) imply: % 151.63/22.46 | | | | | (39) all_52_9 = e1 % 151.63/22.46 | | | | | % 151.63/22.46 | | | | | REDUCE: (21), (39) imply: % 151.63/22.46 | | | | | (40) ~ (all_6_2 = e1) % 151.63/22.46 | | | | | % 151.63/22.46 | | | | | SIMP: (40) implies: % 151.63/22.46 | | | | | (41) ~ (all_6_2 = e1) % 151.63/22.46 | | | | | % 151.63/22.46 | | | | | BETA: splitting (18) gives: % 151.63/22.46 | | | | | % 151.63/22.46 | | | | | Case 1: % 151.63/22.46 | | | | | | % 151.63/22.46 | | | | | | (42) all_56_1 = e3 % 151.63/22.46 | | | | | | % 151.63/22.46 | | | | | | COMBINE_EQS: (5), (42) imply: % 151.63/22.46 | | | | | | (43) all_10_2 = e3 % 151.63/22.46 | | | | | | % 151.63/22.46 | | | | | | REDUCE: (34), (43) imply: % 151.63/22.47 | | | | | | (44) $false % 151.63/22.47 | | | | | | % 151.63/22.47 | | | | | | CLOSE: (44) is inconsistent. % 151.63/22.47 | | | | | | % 151.63/22.47 | | | | | Case 2: % 151.63/22.47 | | | | | | % 151.63/22.47 | | | | | | (45) all_56_11 = e2 | all_56_21 = e1 | all_56_31 = e0 % 151.63/22.47 | | | | | | % 151.63/22.47 | | | | | | BETA: splitting (45) gives: % 151.63/22.47 | | | | | | % 151.63/22.47 | | | | | | Case 1: % 151.63/22.47 | | | | | | | % 151.63/22.47 | | | | | | | (46) all_56_11 = e2 % 151.63/22.47 | | | | | | | % 151.63/22.47 | | | | | | | REF_CLOSE: (20), (25), (46) are inconsistent by sub-proof #427. % 151.63/22.47 | | | | | | | % 151.63/22.47 | | | | | | Case 2: % 151.63/22.47 | | | | | | | % 151.63/22.47 | | | | | | | (47) all_56_21 = e1 | all_56_31 = e0 % 151.63/22.47 | | | | | | | % 151.63/22.47 | | | | | | | BETA: splitting (47) gives: % 151.63/22.47 | | | | | | | % 151.63/22.47 | | | | | | | Case 1: % 151.63/22.47 | | | | | | | | % 151.63/22.47 | | | | | | | | (48) all_56_21 = e1 % 151.63/22.47 | | | | | | | | % 151.63/22.47 | | | | | | | | COMBINE_EQS: (4), (48) imply: % 151.63/22.47 | | | | | | | | (49) all_6_2 = e1 % 151.63/22.47 | | | | | | | | % 151.63/22.47 | | | | | | | | REDUCE: (41), (49) imply: % 151.63/22.47 | | | | | | | | (50) $false % 151.63/22.47 | | | | | | | | % 151.63/22.47 | | | | | | | | CLOSE: (50) is inconsistent. % 151.63/22.47 | | | | | | | | % 151.63/22.47 | | | | | | | Case 2: % 151.63/22.47 | | | | | | | | % 151.63/22.47 | | | | | | | | (51) all_56_31 = e0 % 151.63/22.47 | | | | | | | | % 151.63/22.47 | | | | | | | | COMBINE_EQS: (16), (51) imply: % 151.63/22.47 | | | | | | | | (52) all_4_2 = e0 % 151.63/22.47 | | | | | | | | % 151.63/22.47 | | | | | | | | SIMP: (52) implies: % 151.63/22.47 | | | | | | | | (53) all_4_2 = e0 % 151.63/22.47 | | | | | | | | % 151.63/22.47 | | | | | | | | REDUCE: (15), (53) imply: % 151.63/22.47 | | | | | | | | (54) op(e0, e0) = all_4_1 % 151.63/22.47 | | | | | | | | % 151.63/22.47 | | | | | | | | REDUCE: (24), (53) imply: % 151.63/22.47 | | | | | | | | (55) op(e0, e0) = all_56_30 % 151.63/22.47 | | | | | | | | % 151.63/22.47 | | | | | | | | REDUCE: (2), (53) imply: % 151.63/22.47 | | | | | | | | (56) op(e0, e0) = e0 % 151.63/22.47 | | | | | | | | % 151.63/22.47 | | | | | | | | REF_CLOSE: (9), (17), (35), (54), (55), (56) are inconsistent by % 151.63/22.47 | | | | | | | | sub-proof #454. % 151.63/22.47 | | | | | | | | % 151.63/22.47 | | | | | | | End of split % 151.63/22.47 | | | | | | | % 151.63/22.47 | | | | | | End of split % 151.63/22.47 | | | | | | % 151.63/22.47 | | | | | End of split % 151.63/22.47 | | | | | % 151.63/22.47 | | | | Case 2: % 151.63/22.47 | | | | | % 151.63/22.47 | | | | | (57) all_58_10 = e1 % 151.63/22.47 | | | | | % 151.63/22.47 | | | | | COMBINE_EQS: (3), (57) imply: % 151.63/22.47 | | | | | (58) e2 = e1 % 151.63/22.47 | | | | | % 151.63/22.47 | | | | | REDUCE: (14), (58) imply: % 151.63/22.47 | | | | | (59) $false % 151.63/22.47 | | | | | % 151.63/22.47 | | | | | CLOSE: (59) is inconsistent. % 151.63/22.47 | | | | | % 151.63/22.47 | | | | End of split % 151.63/22.47 | | | | % 151.63/22.47 | | | End of split % 151.63/22.47 | | | % 151.63/22.47 | | Case 2: % 151.63/22.47 | | | % 151.63/22.47 | | | (60) all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0 % 151.63/22.47 | | | % 151.63/22.47 | | | REF_CLOSE: (1), (11), (19), (23), (60) are inconsistent by sub-proof #342. % 151.63/22.47 | | | % 151.63/22.47 | | End of split % 151.63/22.47 | | % 151.63/22.47 | End of split % 151.63/22.47 | % 151.63/22.47 End of proof % 151.63/22.47 % 151.63/22.47 Sub-proof #338 shows that the following formulas are inconsistent: % 151.63/22.47 ---------------------------------------------------------------- % 151.63/22.47 (1) all_58_3 = e1 % 151.63/22.47 (2) all_58_3 = e0 % 151.63/22.47 (3) ~ (e1 = e0) % 151.63/22.47 % 151.63/22.47 Begin of proof % 151.63/22.47 | % 151.63/22.47 | COMBINE_EQS: (1), (2) imply: % 151.63/22.47 | (4) e1 = e0 % 151.63/22.47 | % 151.63/22.47 | SIMP: (4) implies: % 151.63/22.47 | (5) e1 = e0 % 151.63/22.47 | % 151.63/22.47 | REDUCE: (3), (5) imply: % 151.63/22.47 | (6) $false % 151.63/22.47 | % 151.63/22.47 | CLOSE: (6) is inconsistent. % 151.63/22.47 | % 151.63/22.47 End of proof % 151.63/22.47 % 151.63/22.47 Sub-proof #339 shows that the following formulas are inconsistent: % 151.63/22.47 ---------------------------------------------------------------- % 151.63/22.47 (1) all_56_11 = all_8_2 % 151.63/22.47 (2) ~ (all_6_1 = e2) % 151.63/22.47 (3) all_54_0 = all_10_2 % 151.63/22.47 (4) all_56_21 = e3 % 151.63/22.47 (5) ~ (all_52_14 = all_4_2) % 151.63/22.47 (6) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0 % 151.63/22.47 (7) ~ (all_6_1 = e3) % 151.63/22.47 (8) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 151.63/22.47 (9) ~ (all_6_0 = e2) % 151.63/22.47 (10) all_56_21 = all_6_2 % 151.63/22.47 (11) all_56_1 = all_10_2 % 151.63/22.47 (12) all_56_17 = all_52_2 % 151.63/22.47 (13) op(e1, e0) = all_52_14 % 151.63/22.47 (14) op(e2, all_8_2) = all_56_10 % 151.63/22.47 (15) op(e3, e3) = all_10_2 % 151.63/22.47 (16) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 151.63/22.47 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 151.63/22.47 (17) op(e1, all_6_1) = all_6_0 % 151.63/22.47 (18) all_56_31 = all_4_2 % 151.63/22.47 (19) ~ (all_52_2 = all_52_14) % 151.63/22.47 (20) op(all_6_2, all_6_2) = all_6_1 % 151.63/22.47 (21) all_56_1 = e3 | all_56_11 = e2 | all_56_21 = e1 | all_56_31 = e0 % 151.63/22.47 (22) op(all_8_2, all_8_2) = e3 % 151.63/22.47 (23) all_56_17 = e1 % 151.63/22.47 (24) ~ (all_6_2 = e2) % 151.63/22.47 (25) op(e2, e2) = all_8_2 % 151.63/22.47 (26) ~ (all_52_2 = all_6_2) % 151.63/22.47 (27) ~ (all_52_14 = all_6_2) % 151.63/22.47 (28) ~ (all_52_2 = all_10_2) % 151.63/22.47 (29) all_54_11 = all_52_14 % 151.63/22.47 % 151.63/22.47 Begin of proof % 151.63/22.47 | % 151.63/22.47 | COMBINE_EQS: (12), (23) imply: % 151.63/22.47 | (30) all_52_2 = e1 % 151.63/22.47 | % 151.63/22.47 | COMBINE_EQS: (4), (10) imply: % 151.63/22.47 | (31) all_6_2 = e3 % 151.63/22.47 | % 151.63/22.47 | SIMP: (31) implies: % 151.63/22.47 | (32) all_6_2 = e3 % 151.63/22.47 | % 151.63/22.47 | REDUCE: (19), (30) imply: % 151.63/22.47 | (33) ~ (all_52_14 = e1) % 151.63/22.47 | % 151.63/22.47 | SIMP: (33) implies: % 151.63/22.47 | (34) ~ (all_52_14 = e1) % 151.63/22.47 | % 151.63/22.47 | REDUCE: (28), (30) imply: % 151.63/22.47 | (35) ~ (all_10_2 = e1) % 151.63/22.47 | % 151.63/22.47 | SIMP: (35) implies: % 151.63/22.47 | (36) ~ (all_10_2 = e1) % 151.63/22.47 | % 151.63/22.47 | REDUCE: (26), (30), (32) imply: % 151.63/22.47 | (37) ~ (e3 = e1) % 151.63/22.47 | % 151.63/22.47 | SIMP: (37) implies: % 151.63/22.47 | (38) ~ (e3 = e1) % 151.63/22.47 | % 151.63/22.47 | REDUCE: (27), (32) imply: % 151.63/22.47 | (39) ~ (all_52_14 = e3) % 151.63/22.47 | % 151.78/22.47 | REDUCE: (24), (32) imply: % 151.78/22.47 | (40) ~ (e3 = e2) % 151.78/22.47 | % 151.78/22.47 | REDUCE: (20), (32) imply: % 151.78/22.47 | (41) op(e3, e3) = all_6_1 % 151.78/22.47 | % 151.78/22.47 | GROUND_INST: instantiating (16) with all_10_2, all_6_1, e3, e3, simplifying % 151.78/22.47 | with (15), (41) gives: % 151.78/22.47 | (42) all_10_2 = all_6_1 % 151.78/22.47 | % 151.78/22.47 | COMBINE_EQS: (3), (42) imply: % 151.78/22.47 | (43) all_54_0 = all_6_1 % 151.78/22.47 | % 151.78/22.47 | COMBINE_EQS: (11), (42) imply: % 151.78/22.47 | (44) all_56_1 = all_6_1 % 151.78/22.47 | % 151.78/22.47 | REDUCE: (36), (42) imply: % 151.78/22.47 | (45) ~ (all_6_1 = e1) % 151.78/22.47 | % 151.78/22.47 | BETA: splitting (8) gives: % 151.78/22.47 | % 151.78/22.47 | Case 1: % 151.78/22.47 | | % 151.78/22.47 | | (46) all_54_0 = e3 % 151.78/22.47 | | % 151.78/22.47 | | REF_CLOSE: (7), (43), (46) are inconsistent by sub-proof #686. % 151.78/22.47 | | % 151.78/22.47 | Case 2: % 151.78/22.47 | | % 151.78/22.47 | | (47) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 151.78/22.47 | | % 151.78/22.47 | | BETA: splitting (47) gives: % 151.78/22.47 | | % 151.78/22.47 | | Case 1: % 151.78/22.47 | | | % 151.78/22.47 | | | (48) all_54_0 = e2 % 151.78/22.47 | | | % 151.78/22.47 | | | REF_CLOSE: (2), (43), (48) are inconsistent by sub-proof #685. % 151.78/22.47 | | | % 151.78/22.47 | | Case 2: % 151.78/22.47 | | | % 151.78/22.47 | | | (49) all_54_0 = e1 | all_54_0 = e0 % 151.78/22.47 | | | % 151.78/22.47 | | | BETA: splitting (49) gives: % 151.78/22.47 | | | % 151.78/22.47 | | | Case 1: % 151.78/22.47 | | | | % 151.78/22.47 | | | | (50) all_54_0 = e1 % 151.78/22.47 | | | | % 151.78/22.47 | | | | REF_CLOSE: (43), (45), (50) are inconsistent by sub-proof #684. % 151.78/22.47 | | | | % 151.78/22.47 | | | Case 2: % 151.78/22.47 | | | | % 151.78/22.47 | | | | (51) all_54_0 = e0 % 151.78/22.47 | | | | % 151.78/22.47 | | | | COMBINE_EQS: (43), (51) imply: % 151.78/22.47 | | | | (52) all_6_1 = e0 % 151.78/22.47 | | | | % 151.78/22.47 | | | | SIMP: (52) implies: % 151.78/22.47 | | | | (53) all_6_1 = e0 % 151.78/22.47 | | | | % 151.78/22.47 | | | | COMBINE_EQS: (44), (53) imply: % 151.78/22.47 | | | | (54) all_56_1 = e0 % 151.78/22.47 | | | | % 151.78/22.47 | | | | REDUCE: (17), (53) imply: % 151.78/22.47 | | | | (55) op(e1, e0) = all_6_0 % 151.78/22.47 | | | | % 151.78/22.47 | | | | GROUND_INST: instantiating (16) with all_52_14, all_6_0, e0, e1, % 151.78/22.47 | | | | simplifying with (13), (55) gives: % 151.78/22.47 | | | | (56) all_52_14 = all_6_0 % 151.78/22.47 | | | | % 151.78/22.47 | | | | COMBINE_EQS: (29), (56) imply: % 151.78/22.47 | | | | (57) all_54_11 = all_6_0 % 151.78/22.47 | | | | % 151.78/22.47 | | | | REDUCE: (5), (56) imply: % 151.78/22.47 | | | | (58) ~ (all_6_0 = all_4_2) % 151.78/22.47 | | | | % 151.78/22.47 | | | | REDUCE: (39), (56) imply: % 151.78/22.47 | | | | (59) ~ (all_6_0 = e3) % 151.78/22.47 | | | | % 151.78/22.47 | | | | REDUCE: (34), (56) imply: % 151.78/22.47 | | | | (60) ~ (all_6_0 = e1) % 151.78/22.47 | | | | % 151.78/22.47 | | | | BETA: splitting (6) gives: % 151.78/22.47 | | | | % 151.78/22.47 | | | | Case 1: % 151.78/22.47 | | | | | % 151.78/22.47 | | | | | (61) all_54_11 = e3 % 151.78/22.47 | | | | | % 151.78/22.47 | | | | | REF_CLOSE: (57), (59), (61) are inconsistent by sub-proof #683. % 151.78/22.47 | | | | | % 151.78/22.47 | | | | Case 2: % 151.78/22.47 | | | | | % 151.78/22.47 | | | | | (62) ~ (all_54_11 = e3) % 151.78/22.47 | | | | | (63) all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0 % 151.78/22.47 | | | | | % 151.78/22.47 | | | | | BETA: splitting (63) gives: % 151.78/22.47 | | | | | % 151.78/22.47 | | | | | Case 1: % 151.78/22.47 | | | | | | % 151.78/22.47 | | | | | | (64) all_54_11 = e2 % 151.78/22.47 | | | | | | % 151.78/22.47 | | | | | | REF_CLOSE: (9), (57), (64) are inconsistent by sub-proof #682. % 151.78/22.47 | | | | | | % 151.78/22.47 | | | | | Case 2: % 151.78/22.47 | | | | | | % 151.78/22.47 | | | | | | (65) all_54_11 = e1 | all_54_11 = e0 % 151.78/22.47 | | | | | | % 151.78/22.47 | | | | | | BETA: splitting (65) gives: % 151.78/22.47 | | | | | | % 151.78/22.47 | | | | | | Case 1: % 151.78/22.47 | | | | | | | % 151.78/22.47 | | | | | | | (66) all_54_11 = e1 % 151.78/22.47 | | | | | | | % 151.78/22.47 | | | | | | | REF_CLOSE: (57), (60), (66) are inconsistent by sub-proof #681. % 151.78/22.47 | | | | | | | % 151.78/22.47 | | | | | | Case 2: % 151.78/22.47 | | | | | | | % 151.78/22.47 | | | | | | | (67) all_54_11 = e0 % 151.78/22.47 | | | | | | | % 151.78/22.47 | | | | | | | COMBINE_EQS: (57), (67) imply: % 151.78/22.47 | | | | | | | (68) all_6_0 = e0 % 151.78/22.47 | | | | | | | % 151.78/22.47 | | | | | | | SIMP: (68) implies: % 151.78/22.47 | | | | | | | (69) all_6_0 = e0 % 151.78/22.47 | | | | | | | % 151.78/22.47 | | | | | | | REDUCE: (58), (69) imply: % 151.78/22.47 | | | | | | | (70) ~ (all_4_2 = e0) % 151.78/22.47 | | | | | | | % 151.78/22.47 | | | | | | | SIMP: (70) implies: % 151.78/22.47 | | | | | | | (71) ~ (all_4_2 = e0) % 151.78/22.47 | | | | | | | % 151.78/22.47 | | | | | | | REDUCE: (59), (69) imply: % 151.78/22.47 | | | | | | | (72) ~ (e3 = e0) % 151.78/22.47 | | | | | | | % 151.78/22.47 | | | | | | | SIMP: (72) implies: % 151.78/22.47 | | | | | | | (73) ~ (e3 = e0) % 151.78/22.47 | | | | | | | % 151.78/22.47 | | | | | | | BETA: splitting (21) gives: % 151.78/22.47 | | | | | | | % 151.78/22.47 | | | | | | | Case 1: % 151.78/22.47 | | | | | | | | % 151.78/22.47 | | | | | | | | (74) all_56_1 = e3 % 151.78/22.47 | | | | | | | | % 151.78/22.47 | | | | | | | | COMBINE_EQS: (54), (74) imply: % 151.78/22.47 | | | | | | | | (75) e3 = e0 % 151.78/22.47 | | | | | | | | % 151.78/22.47 | | | | | | | | REDUCE: (73), (75) imply: % 151.78/22.47 | | | | | | | | (76) $false % 151.78/22.47 | | | | | | | | % 151.78/22.47 | | | | | | | | CLOSE: (76) is inconsistent. % 151.78/22.47 | | | | | | | | % 151.78/22.47 | | | | | | | Case 2: % 151.78/22.47 | | | | | | | | % 151.78/22.47 | | | | | | | | (77) all_56_11 = e2 | all_56_21 = e1 | all_56_31 = e0 % 151.78/22.47 | | | | | | | | % 151.78/22.47 | | | | | | | | BETA: splitting (77) gives: % 151.78/22.47 | | | | | | | | % 151.78/22.47 | | | | | | | | Case 1: % 151.78/22.47 | | | | | | | | | % 151.78/22.47 | | | | | | | | | (78) all_56_11 = e2 % 151.78/22.47 | | | | | | | | | % 151.78/22.47 | | | | | | | | | COMBINE_EQS: (1), (78) imply: % 151.78/22.47 | | | | | | | | | (79) all_8_2 = e2 % 151.78/22.47 | | | | | | | | | % 151.78/22.47 | | | | | | | | | SIMP: (79) implies: % 151.78/22.47 | | | | | | | | | (80) all_8_2 = e2 % 151.78/22.47 | | | | | | | | | % 151.78/22.47 | | | | | | | | | REDUCE: (25), (80) imply: % 151.78/22.47 | | | | | | | | | (81) op(e2, e2) = e2 % 151.78/22.47 | | | | | | | | | % 151.78/22.47 | | | | | | | | | REF_CLOSE: (14), (16), (22), (25), (40), (81) are inconsistent % 151.78/22.47 | | | | | | | | | by sub-proof #349. % 151.78/22.47 | | | | | | | | | % 151.78/22.47 | | | | | | | | Case 2: % 151.78/22.47 | | | | | | | | | % 151.78/22.47 | | | | | | | | | (82) all_56_21 = e1 | all_56_31 = e0 % 151.78/22.47 | | | | | | | | | % 151.78/22.47 | | | | | | | | | REF_CLOSE: (4), (18), (38), (71), (82) are inconsistent by % 151.78/22.47 | | | | | | | | | sub-proof #674. % 151.78/22.47 | | | | | | | | | % 151.78/22.47 | | | | | | | | End of split % 151.78/22.47 | | | | | | | | % 151.78/22.47 | | | | | | | End of split % 151.78/22.47 | | | | | | | % 151.78/22.47 | | | | | | End of split % 151.78/22.47 | | | | | | % 151.78/22.47 | | | | | End of split % 151.78/22.47 | | | | | % 151.78/22.47 | | | | End of split % 151.78/22.47 | | | | % 151.78/22.47 | | | End of split % 151.78/22.47 | | | % 151.78/22.47 | | End of split % 151.78/22.47 | | % 151.78/22.47 | End of split % 151.78/22.47 | % 151.78/22.47 End of proof % 151.78/22.47 % 151.78/22.47 Sub-proof #340 shows that the following formulas are inconsistent: % 151.78/22.47 ---------------------------------------------------------------- % 151.78/22.47 (1) all_56_11 = all_8_2 % 151.78/22.47 (2) ~ (all_52_13 = all_8_2) % 151.78/22.47 (3) ~ (all_52_9 = all_8_2) % 151.78/22.47 (4) ~ (all_6_2 = e3) % 151.78/22.47 (5) ~ (all_52_13 = all_8_0) % 151.78/22.47 (6) ~ (all_8_0 = all_8_2) % 151.78/22.47 (7) all_56_21 = all_6_2 % 151.78/22.47 (8) all_56_1 = all_10_2 % 151.78/22.47 (9) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0 % 151.78/22.47 (10) ~ (all_22_0 = e0) | ~ (all_22_2 = e1) % 151.78/22.47 (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 151.78/22.47 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 151.78/22.47 (12) ~ (all_10_2 = all_8_0) % 151.78/22.47 (13) all_22_0 = all_8_0 % 151.78/22.47 (14) all_56_13 = all_52_9 % 151.78/22.47 (15) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0 % 151.78/22.47 (16) all_56_11 = e1 % 151.78/22.47 (17) ~ (all_52_9 = all_52_13) % 151.78/22.47 (18) all_56_31 = all_4_2 % 151.78/22.47 (19) all_54_7 = all_52_13 % 151.78/22.47 (20) all_56_1 = e3 | all_56_11 = e2 | all_56_21 = e1 | all_56_31 = e0 % 151.78/22.48 (21) ~ (all_52_13 = all_4_2) % 151.78/22.48 (22) op(all_8_2, all_8_2) = e3 % 151.78/22.48 (23) op(e1, e1) = all_6_2 % 151.78/22.48 (24) all_22_2 = all_8_2 % 151.78/22.48 (25) op(e1, all_6_2) = all_56_20 % 151.78/22.48 (26) all_54_4 = all_8_0 % 151.78/22.48 (27) all_56_13 = e2 % 151.78/22.48 (28) ~ (all_52_9 = all_8_0) % 151.78/22.48 % 151.78/22.48 Begin of proof % 151.78/22.48 | % 151.78/22.48 | COMBINE_EQS: (1), (16) imply: % 151.78/22.48 | (29) all_8_2 = e1 % 151.78/22.48 | % 151.78/22.48 | COMBINE_EQS: (14), (27) imply: % 151.78/22.48 | (30) all_52_9 = e2 % 151.78/22.48 | % 151.78/22.48 | COMBINE_EQS: (24), (29) imply: % 151.78/22.48 | (31) all_22_2 = e1 % 151.78/22.48 | % 151.78/22.48 | REDUCE: (17), (30) imply: % 151.78/22.48 | (32) ~ (all_52_13 = e2) % 151.78/22.48 | % 151.78/22.48 | SIMP: (32) implies: % 151.78/22.48 | (33) ~ (all_52_13 = e2) % 151.78/22.48 | % 151.78/22.48 | REDUCE: (28), (30) imply: % 151.78/22.48 | (34) ~ (all_8_0 = e2) % 151.78/22.48 | % 151.78/22.48 | SIMP: (34) implies: % 151.78/22.48 | (35) ~ (all_8_0 = e2) % 151.78/22.48 | % 151.78/22.48 | REDUCE: (3), (29), (30) imply: % 151.78/22.48 | (36) ~ (e2 = e1) % 151.78/22.48 | % 151.78/22.48 | REDUCE: (2), (29) imply: % 151.78/22.48 | (37) ~ (all_52_13 = e1) % 151.78/22.48 | % 151.78/22.48 | REDUCE: (6), (29) imply: % 151.78/22.48 | (38) ~ (all_8_0 = e1) % 151.78/22.48 | % 151.78/22.48 | REDUCE: (22), (29) imply: % 151.78/22.48 | (39) op(e1, e1) = e3 % 151.78/22.48 | % 151.78/22.48 | REF_CLOSE: (4), (5), (7), (8), (9), (10), (11), (12), (13), (15), (16), (18), % 151.78/22.48 | (19), (20), (21), (23), (25), (26), (31), (33), (35), (36), (37), % 151.78/22.48 | (38), (39) are inconsistent by sub-proof #341. % 151.78/22.48 | % 151.78/22.48 End of proof % 151.78/22.48 % 151.78/22.48 Sub-proof #341 shows that the following formulas are inconsistent: % 151.78/22.48 ---------------------------------------------------------------- % 151.78/22.48 (1) ~ (all_52_13 = e1) % 151.78/22.48 (2) ~ (all_8_0 = e1) % 151.78/22.48 (3) ~ (all_6_2 = e3) % 151.78/22.48 (4) ~ (all_52_13 = all_8_0) % 151.78/22.48 (5) all_56_21 = all_6_2 % 151.78/22.48 (6) all_56_1 = all_10_2 % 151.78/22.48 (7) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0 % 151.78/22.48 (8) ~ (all_52_13 = e2) % 151.78/22.48 (9) all_22_2 = e1 % 151.78/22.48 (10) ~ (all_22_0 = e0) | ~ (all_22_2 = e1) % 151.78/22.48 (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 151.78/22.48 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 151.78/22.48 (12) ~ (all_10_2 = all_8_0) % 151.78/22.48 (13) op(e1, e1) = e3 % 151.78/22.48 (14) all_22_0 = all_8_0 % 151.78/22.48 (15) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0 % 151.78/22.48 (16) all_56_11 = e1 % 151.78/22.48 (17) ~ (e2 = e1) % 151.78/22.48 (18) all_56_31 = all_4_2 % 151.78/22.48 (19) all_54_7 = all_52_13 % 151.78/22.48 (20) all_56_1 = e3 | all_56_11 = e2 | all_56_21 = e1 | all_56_31 = e0 % 151.78/22.48 (21) ~ (all_8_0 = e2) % 151.78/22.48 (22) ~ (all_52_13 = all_4_2) % 151.78/22.48 (23) op(e1, e1) = all_6_2 % 151.78/22.48 (24) op(e1, all_6_2) = all_56_20 % 151.78/22.48 (25) all_54_4 = all_8_0 % 151.78/22.48 % 151.78/22.48 Begin of proof % 151.78/22.48 | % 151.78/22.48 | BETA: splitting (10) gives: % 151.78/22.48 | % 151.78/22.48 | Case 1: % 151.78/22.48 | | % 151.78/22.48 | | (26) ~ (all_22_2 = e1) % 151.78/22.48 | | % 151.78/22.48 | | REDUCE: (9), (26) imply: % 151.78/22.48 | | (27) $false % 151.78/22.48 | | % 151.78/22.48 | | CLOSE: (27) is inconsistent. % 151.78/22.48 | | % 151.78/22.48 | Case 2: % 151.78/22.48 | | % 151.78/22.48 | | (28) ~ (all_22_0 = e0) % 151.78/22.48 | | % 151.78/22.48 | | REDUCE: (14), (28) imply: % 151.78/22.48 | | (29) ~ (all_8_0 = e0) % 151.78/22.48 | | % 151.78/22.48 | | BETA: splitting (15) gives: % 151.78/22.48 | | % 151.78/22.48 | | Case 1: % 151.78/22.48 | | | % 151.78/22.48 | | | (30) all_54_4 = e3 % 151.78/22.48 | | | % 151.78/22.48 | | | COMBINE_EQS: (25), (30) imply: % 151.78/22.48 | | | (31) all_8_0 = e3 % 151.78/22.48 | | | % 151.78/22.48 | | | SIMP: (31) implies: % 151.78/22.48 | | | (32) all_8_0 = e3 % 151.78/22.48 | | | % 151.78/22.48 | | | REDUCE: (4), (32) imply: % 151.78/22.48 | | | (33) ~ (all_52_13 = e3) % 151.78/22.48 | | | % 151.78/22.48 | | | REDUCE: (12), (32) imply: % 151.78/22.48 | | | (34) ~ (all_10_2 = e3) % 151.78/22.48 | | | % 151.78/22.48 | | | BETA: splitting (7) gives: % 151.78/22.48 | | | % 151.78/22.48 | | | Case 1: % 151.78/22.48 | | | | % 151.78/22.48 | | | | (35) all_54_7 = e3 % 151.78/22.48 | | | | % 151.78/22.48 | | | | REF_CLOSE: (19), (33), (35) are inconsistent by sub-proof #601. % 151.78/22.48 | | | | % 151.78/22.48 | | | Case 2: % 151.78/22.48 | | | | % 151.78/22.48 | | | | (36) all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0 % 151.78/22.48 | | | | % 151.78/22.48 | | | | BETA: splitting (36) gives: % 151.78/22.48 | | | | % 151.78/22.48 | | | | Case 1: % 151.78/22.48 | | | | | % 151.78/22.48 | | | | | (37) all_54_7 = e2 % 151.78/22.48 | | | | | % 151.78/22.48 | | | | | REF_CLOSE: (8), (19), (37) are inconsistent by sub-proof #652. % 151.78/22.48 | | | | | % 151.78/22.48 | | | | Case 2: % 151.78/22.48 | | | | | % 151.78/22.48 | | | | | (38) all_54_7 = e1 | all_54_7 = e0 % 151.78/22.48 | | | | | % 151.78/22.48 | | | | | BETA: splitting (38) gives: % 151.78/22.48 | | | | | % 151.78/22.48 | | | | | Case 1: % 151.78/22.48 | | | | | | % 151.78/22.48 | | | | | | (39) all_54_7 = e1 % 151.78/22.48 | | | | | | % 151.78/22.48 | | | | | | REF_CLOSE: (1), (19), (39) are inconsistent by sub-proof #651. % 151.78/22.48 | | | | | | % 151.78/22.48 | | | | | Case 2: % 151.78/22.48 | | | | | | % 151.78/22.48 | | | | | | (40) all_54_7 = e0 % 151.78/22.48 | | | | | | % 151.78/22.48 | | | | | | COMBINE_EQS: (19), (40) imply: % 151.78/22.48 | | | | | | (41) all_52_13 = e0 % 151.78/22.48 | | | | | | % 151.78/22.48 | | | | | | SIMP: (41) implies: % 151.78/22.48 | | | | | | (42) all_52_13 = e0 % 151.78/22.48 | | | | | | % 151.78/22.48 | | | | | | REDUCE: (22), (42) imply: % 151.78/22.48 | | | | | | (43) ~ (all_4_2 = e0) % 151.78/22.48 | | | | | | % 151.78/22.48 | | | | | | SIMP: (43) implies: % 151.78/22.48 | | | | | | (44) ~ (all_4_2 = e0) % 151.78/22.48 | | | | | | % 151.78/22.48 | | | | | | BETA: splitting (20) gives: % 151.78/22.48 | | | | | | % 151.78/22.48 | | | | | | Case 1: % 151.78/22.48 | | | | | | | % 151.78/22.48 | | | | | | | (45) all_56_1 = e3 % 151.78/22.48 | | | | | | | % 151.78/22.48 | | | | | | | COMBINE_EQS: (6), (45) imply: % 151.78/22.48 | | | | | | | (46) all_10_2 = e3 % 151.78/22.48 | | | | | | | % 151.78/22.48 | | | | | | | REDUCE: (34), (46) imply: % 151.78/22.48 | | | | | | | (47) $false % 151.78/22.48 | | | | | | | % 151.78/22.48 | | | | | | | CLOSE: (47) is inconsistent. % 151.78/22.48 | | | | | | | % 151.78/22.48 | | | | | | Case 2: % 151.78/22.48 | | | | | | | % 151.78/22.48 | | | | | | | (48) all_56_11 = e2 | all_56_21 = e1 | all_56_31 = e0 % 151.78/22.48 | | | | | | | % 151.78/22.48 | | | | | | | BETA: splitting (48) gives: % 151.78/22.48 | | | | | | | % 151.78/22.48 | | | | | | | Case 1: % 151.78/22.48 | | | | | | | | % 151.78/22.48 | | | | | | | | (49) all_56_11 = e2 % 151.78/22.48 | | | | | | | | % 151.78/22.48 | | | | | | | | REF_CLOSE: (16), (17), (49) are inconsistent by sub-proof #419. % 151.78/22.48 | | | | | | | | % 151.78/22.48 | | | | | | | Case 2: % 151.78/22.48 | | | | | | | | % 151.78/22.48 | | | | | | | | (50) all_56_21 = e1 | all_56_31 = e0 % 151.78/22.48 | | | | | | | | % 151.78/22.48 | | | | | | | | BETA: splitting (50) gives: % 151.78/22.48 | | | | | | | | % 151.78/22.48 | | | | | | | | Case 1: % 151.78/22.48 | | | | | | | | | % 151.78/22.48 | | | | | | | | | (51) all_56_21 = e1 % 151.78/22.48 | | | | | | | | | % 151.78/22.48 | | | | | | | | | COMBINE_EQS: (5), (51) imply: % 151.78/22.48 | | | | | | | | | (52) all_6_2 = e1 % 151.78/22.48 | | | | | | | | | % 151.78/22.48 | | | | | | | | | REDUCE: (3), (52) imply: % 151.78/22.48 | | | | | | | | | (53) ~ (e3 = e1) % 151.78/22.48 | | | | | | | | | % 151.78/22.48 | | | | | | | | | SIMP: (53) implies: % 151.78/22.48 | | | | | | | | | (54) ~ (e3 = e1) % 151.78/22.48 | | | | | | | | | % 151.78/22.48 | | | | | | | | | REDUCE: (24), (52) imply: % 151.78/22.48 | | | | | | | | | (55) op(e1, e1) = all_56_20 % 151.78/22.48 | | | | | | | | | % 151.78/22.48 | | | | | | | | | REDUCE: (23), (52) imply: % 151.78/22.48 | | | | | | | | | (56) op(e1, e1) = e1 % 151.78/22.48 | | | | | | | | | % 151.78/22.48 | | | | | | | | | REF_CLOSE: (11), (13), (54), (55), (56) are inconsistent by % 151.78/22.48 | | | | | | | | | sub-proof #516. % 151.78/22.48 | | | | | | | | | % 151.78/22.48 | | | | | | | | Case 2: % 151.78/22.48 | | | | | | | | | % 151.78/22.48 | | | | | | | | | (57) all_56_31 = e0 % 151.78/22.48 | | | | | | | | | % 151.78/22.48 | | | | | | | | | REF_CLOSE: (18), (44), (57) are inconsistent by sub-proof % 151.78/22.48 | | | | | | | | | #675. % 151.78/22.48 | | | | | | | | | % 151.78/22.48 | | | | | | | | End of split % 151.78/22.48 | | | | | | | | % 151.78/22.48 | | | | | | | End of split % 151.78/22.48 | | | | | | | % 151.78/22.48 | | | | | | End of split % 151.78/22.48 | | | | | | % 151.78/22.48 | | | | | End of split % 151.78/22.48 | | | | | % 151.78/22.48 | | | | End of split % 151.78/22.48 | | | | % 151.78/22.48 | | | End of split % 151.78/22.48 | | | % 151.78/22.48 | | Case 2: % 151.78/22.48 | | | % 151.78/22.48 | | | (58) all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0 % 151.78/22.48 | | | % 151.78/22.48 | | | REF_CLOSE: (2), (21), (25), (29), (58) are inconsistent by sub-proof #342. % 151.78/22.48 | | | % 151.78/22.48 | | End of split % 151.78/22.48 | | % 151.78/22.48 | End of split % 151.78/22.48 | % 151.78/22.48 End of proof % 151.78/22.48 % 151.78/22.48 Sub-proof #342 shows that the following formulas are inconsistent: % 151.78/22.48 ---------------------------------------------------------------- % 151.78/22.48 (1) all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0 % 151.78/22.48 (2) ~ (all_8_0 = e1) % 151.78/22.48 (3) ~ (all_8_0 = e0) % 151.78/22.48 (4) ~ (all_8_0 = e2) % 151.78/22.48 (5) all_54_4 = all_8_0 % 151.78/22.48 % 151.78/22.48 Begin of proof % 151.78/22.48 | % 151.78/22.48 | BETA: splitting (1) gives: % 151.78/22.48 | % 151.78/22.48 | Case 1: % 151.78/22.48 | | % 151.78/22.48 | | (6) all_54_4 = e2 % 151.78/22.48 | | % 151.78/22.48 | | COMBINE_EQS: (5), (6) imply: % 151.78/22.48 | | (7) all_8_0 = e2 % 151.78/22.48 | | % 151.78/22.48 | | SIMP: (7) implies: % 151.78/22.48 | | (8) all_8_0 = e2 % 151.78/22.48 | | % 151.78/22.48 | | REDUCE: (4), (8) imply: % 151.78/22.48 | | (9) $false % 151.78/22.48 | | % 151.78/22.48 | | CLOSE: (9) is inconsistent. % 151.78/22.48 | | % 151.78/22.48 | Case 2: % 151.78/22.48 | | % 151.81/22.48 | | (10) all_54_4 = e1 | all_54_4 = e0 % 151.81/22.48 | | % 151.81/22.48 | | BETA: splitting (10) gives: % 151.81/22.48 | | % 151.81/22.48 | | Case 1: % 151.81/22.48 | | | % 151.81/22.48 | | | (11) all_54_4 = e1 % 151.81/22.48 | | | % 151.81/22.48 | | | COMBINE_EQS: (5), (11) imply: % 151.81/22.48 | | | (12) all_8_0 = e1 % 151.81/22.48 | | | % 151.81/22.48 | | | SIMP: (12) implies: % 151.81/22.48 | | | (13) all_8_0 = e1 % 151.81/22.48 | | | % 151.81/22.48 | | | REDUCE: (2), (13) imply: % 151.81/22.48 | | | (14) $false % 151.81/22.48 | | | % 151.81/22.48 | | | CLOSE: (14) is inconsistent. % 151.81/22.48 | | | % 151.81/22.48 | | Case 2: % 151.81/22.48 | | | % 151.81/22.48 | | | (15) all_54_4 = e0 % 151.81/22.48 | | | % 151.81/22.48 | | | COMBINE_EQS: (5), (15) imply: % 151.81/22.48 | | | (16) all_8_0 = e0 % 151.81/22.48 | | | % 151.81/22.48 | | | SIMP: (16) implies: % 151.81/22.48 | | | (17) all_8_0 = e0 % 151.81/22.48 | | | % 151.81/22.48 | | | REDUCE: (3), (17) imply: % 151.81/22.48 | | | (18) $false % 151.81/22.48 | | | % 151.81/22.48 | | | CLOSE: (18) is inconsistent. % 151.81/22.48 | | | % 151.81/22.48 | | End of split % 151.81/22.48 | | % 151.81/22.48 | End of split % 151.81/22.48 | % 151.81/22.48 End of proof % 151.81/22.48 % 151.81/22.48 Sub-proof #343 shows that the following formulas are inconsistent: % 151.81/22.48 ---------------------------------------------------------------- % 151.81/22.48 (1) ~ (e3 = e0) % 151.81/22.48 (2) all_58_8 = e3 | all_58_11 = e3 % 151.81/22.48 (3) all_58_11 = e1 % 151.81/22.48 (4) all_58_8 = e0 % 151.81/22.48 (5) ~ (e3 = e1) % 151.81/22.48 % 151.81/22.48 Begin of proof % 151.81/22.48 | % 151.81/22.48 | BETA: splitting (2) gives: % 151.81/22.48 | % 151.81/22.48 | Case 1: % 151.81/22.48 | | % 151.81/22.48 | | (6) all_58_8 = e3 % 151.81/22.48 | | % 151.81/22.48 | | COMBINE_EQS: (4), (6) imply: % 151.81/22.48 | | (7) e3 = e0 % 151.81/22.48 | | % 151.81/22.48 | | SIMP: (7) implies: % 151.81/22.48 | | (8) e3 = e0 % 151.81/22.48 | | % 151.81/22.48 | | REDUCE: (1), (8) imply: % 151.81/22.48 | | (9) $false % 151.81/22.48 | | % 151.81/22.48 | | CLOSE: (9) is inconsistent. % 151.81/22.48 | | % 151.81/22.48 | Case 2: % 151.81/22.48 | | % 151.81/22.48 | | (10) all_58_11 = e3 % 151.81/22.48 | | % 151.81/22.48 | | COMBINE_EQS: (3), (10) imply: % 151.81/22.48 | | (11) e3 = e1 % 151.81/22.48 | | % 151.81/22.48 | | SIMP: (11) implies: % 151.81/22.48 | | (12) e3 = e1 % 151.81/22.48 | | % 151.81/22.48 | | REDUCE: (5), (12) imply: % 151.81/22.48 | | (13) $false % 151.81/22.48 | | % 151.81/22.48 | | CLOSE: (13) is inconsistent. % 151.81/22.48 | | % 151.81/22.48 | End of split % 151.81/22.48 | % 151.81/22.48 End of proof % 151.81/22.48 % 151.81/22.48 Sub-proof #344 shows that the following formulas are inconsistent: % 151.81/22.48 ---------------------------------------------------------------- % 151.81/22.48 (1) all_58_6 = e1 % 151.81/22.48 (2) all_58_6 = e0 % 151.81/22.48 (3) ~ (e1 = e0) % 151.81/22.48 % 151.81/22.48 Begin of proof % 151.81/22.48 | % 151.81/22.48 | COMBINE_EQS: (1), (2) imply: % 151.81/22.48 | (4) e1 = e0 % 151.81/22.48 | % 151.81/22.48 | SIMP: (4) implies: % 151.81/22.48 | (5) e1 = e0 % 151.81/22.48 | % 151.81/22.48 | REDUCE: (3), (5) imply: % 151.81/22.48 | (6) $false % 151.81/22.48 | % 151.81/22.48 | CLOSE: (6) is inconsistent. % 151.81/22.48 | % 151.81/22.48 End of proof % 151.81/22.48 % 151.81/22.48 Sub-proof #345 shows that the following formulas are inconsistent: % 151.81/22.48 ---------------------------------------------------------------- % 151.81/22.48 (1) all_54_8 = all_52_2 % 151.81/22.48 (2) all_54_8 = e3 % 151.81/22.48 (3) ~ (all_52_2 = e3) % 151.81/22.48 % 151.81/22.48 Begin of proof % 151.81/22.48 | % 151.81/22.48 | COMBINE_EQS: (1), (2) imply: % 151.81/22.48 | (4) all_52_2 = e3 % 151.81/22.48 | % 151.81/22.48 | SIMP: (4) implies: % 151.81/22.48 | (5) all_52_2 = e3 % 151.81/22.48 | % 151.81/22.48 | REDUCE: (3), (5) imply: % 151.81/22.48 | (6) $false % 151.81/22.48 | % 151.81/22.48 | CLOSE: (6) is inconsistent. % 151.81/22.48 | % 151.81/22.48 End of proof % 151.81/22.48 % 151.81/22.48 Sub-proof #346 shows that the following formulas are inconsistent: % 151.81/22.48 ---------------------------------------------------------------- % 151.81/22.48 (1) all_58_6 = all_52_2 % 151.81/22.48 (2) all_58_6 = e3 % 151.81/22.48 (3) ~ (all_52_2 = e3) % 151.81/22.48 % 151.81/22.48 Begin of proof % 151.81/22.48 | % 151.81/22.48 | COMBINE_EQS: (1), (2) imply: % 151.81/22.48 | (4) all_52_2 = e3 % 151.81/22.48 | % 151.81/22.48 | SIMP: (4) implies: % 151.81/22.48 | (5) all_52_2 = e3 % 151.81/22.48 | % 151.81/22.48 | REDUCE: (3), (5) imply: % 151.81/22.48 | (6) $false % 151.81/22.48 | % 151.81/22.48 | CLOSE: (6) is inconsistent. % 151.81/22.48 | % 151.81/22.48 End of proof % 151.81/22.48 % 151.81/22.48 Sub-proof #347 shows that the following formulas are inconsistent: % 151.81/22.48 ---------------------------------------------------------------- % 151.81/22.48 (1) ~ (all_8_2 = e1) % 151.81/22.48 (2) all_54_5 = all_8_2 % 151.81/22.48 (3) op(e2, all_8_2) = all_56_10 % 151.81/22.48 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 151.81/22.48 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 151.81/22.48 (5) ~ (all_8_2 = e3) % 151.81/22.48 (6) op(all_8_2, all_8_2) = e3 % 151.81/22.48 (7) op(e2, e2) = all_8_2 % 151.81/22.48 (8) ~ (all_8_2 = e0) % 151.81/22.48 (9) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 151.81/22.48 % 151.81/22.48 Begin of proof % 151.81/22.48 | % 151.81/22.48 | BETA: splitting (9) gives: % 151.81/22.48 | % 151.81/22.48 | Case 1: % 151.81/22.48 | | % 151.81/22.48 | | (10) all_54_5 = e3 % 151.81/22.48 | | % 151.81/22.48 | | REF_CLOSE: (2), (5), (10) are inconsistent by sub-proof #737. % 151.81/22.48 | | % 151.81/22.48 | Case 2: % 151.81/22.48 | | % 151.81/22.48 | | (11) ~ (all_54_5 = e3) % 151.81/22.48 | | (12) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 151.81/22.48 | | % 151.81/22.48 | | BETA: splitting (12) gives: % 151.81/22.48 | | % 151.81/22.48 | | Case 1: % 151.81/22.48 | | | % 151.81/22.48 | | | (13) all_54_5 = e2 % 151.81/22.48 | | | % 151.81/22.48 | | | COMBINE_EQS: (2), (13) imply: % 151.81/22.48 | | | (14) all_8_2 = e2 % 151.81/22.48 | | | % 151.81/22.48 | | | SIMP: (14) implies: % 151.81/22.48 | | | (15) all_8_2 = e2 % 151.81/22.48 | | | % 151.81/22.48 | | | REF_CLOSE: (3), (4), (5), (6), (7), (15) are inconsistent by sub-proof % 151.81/22.48 | | | #348. % 151.81/22.48 | | | % 151.81/22.48 | | Case 2: % 151.81/22.48 | | | % 151.81/22.48 | | | (16) all_54_5 = e1 | all_54_5 = e0 % 151.81/22.48 | | | % 151.81/22.48 | | | REF_CLOSE: (1), (2), (8), (16) are inconsistent by sub-proof #645. % 151.81/22.48 | | | % 151.81/22.48 | | End of split % 151.81/22.48 | | % 151.81/22.48 | End of split % 151.81/22.48 | % 151.81/22.48 End of proof % 151.81/22.48 % 151.81/22.48 Sub-proof #348 shows that the following formulas are inconsistent: % 151.81/22.48 ---------------------------------------------------------------- % 151.81/22.48 (1) all_8_2 = e2 % 151.81/22.48 (2) op(e2, all_8_2) = all_56_10 % 151.81/22.48 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 151.81/22.48 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 151.81/22.48 (4) ~ (all_8_2 = e3) % 151.81/22.48 (5) op(all_8_2, all_8_2) = e3 % 151.81/22.48 (6) op(e2, e2) = all_8_2 % 151.81/22.48 % 151.81/22.48 Begin of proof % 151.81/22.48 | % 151.81/22.48 | REDUCE: (1), (4) imply: % 151.81/22.48 | (7) ~ (e3 = e2) % 151.81/22.48 | % 151.81/22.48 | SIMP: (7) implies: % 151.81/22.48 | (8) ~ (e3 = e2) % 151.81/22.48 | % 151.81/22.48 | REDUCE: (1), (6) imply: % 151.81/22.48 | (9) op(e2, e2) = e2 % 151.81/22.48 | % 151.81/22.48 | REF_CLOSE: (2), (3), (5), (6), (8), (9) are inconsistent by sub-proof #349. % 151.81/22.48 | % 151.81/22.48 End of proof % 151.81/22.48 % 151.81/22.48 Sub-proof #349 shows that the following formulas are inconsistent: % 151.81/22.48 ---------------------------------------------------------------- % 151.81/22.48 (1) op(e2, e2) = e2 % 151.81/22.48 (2) ~ (e3 = e2) % 151.81/22.49 (3) op(e2, all_8_2) = all_56_10 % 151.81/22.49 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 151.81/22.49 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 151.81/22.49 (5) op(all_8_2, all_8_2) = e3 % 151.81/22.49 (6) op(e2, e2) = all_8_2 % 151.81/22.49 % 151.81/22.49 Begin of proof % 151.81/22.49 | % 151.81/22.49 | GROUND_INST: instantiating (4) with all_8_2, e2, e2, e2, simplifying with (1), % 151.81/22.49 | (6) gives: % 151.81/22.49 | (7) all_8_2 = e2 % 151.81/22.49 | % 151.81/22.49 | REDUCE: (5), (7) imply: % 151.81/22.49 | (8) op(e2, e2) = e3 % 151.81/22.49 | % 151.81/22.49 | REDUCE: (3), (7) imply: % 151.81/22.49 | (9) op(e2, e2) = all_56_10 % 151.81/22.49 | % 151.81/22.49 | GROUND_INST: instantiating (4) with e2, all_56_10, e2, e2, simplifying with % 151.81/22.49 | (1), (9) gives: % 151.81/22.49 | (10) all_56_10 = e2 % 151.81/22.49 | % 151.81/22.49 | GROUND_INST: instantiating (4) with e3, all_56_10, e2, e2, simplifying with % 151.81/22.49 | (8), (9) gives: % 151.81/22.49 | (11) all_56_10 = e3 % 151.81/22.49 | % 151.81/22.49 | COMBINE_EQS: (10), (11) imply: % 151.81/22.49 | (12) e3 = e2 % 151.81/22.49 | % 151.81/22.49 | SIMP: (12) implies: % 151.81/22.49 | (13) e3 = e2 % 151.81/22.49 | % 151.81/22.49 | REDUCE: (2), (13) imply: % 151.81/22.49 | (14) $false % 151.81/22.49 | % 151.81/22.49 | CLOSE: (14) is inconsistent. % 151.81/22.49 | % 151.81/22.49 End of proof % 151.81/22.49 % 151.81/22.49 Sub-proof #350 shows that the following formulas are inconsistent: % 151.81/22.49 ---------------------------------------------------------------- % 151.81/22.49 (1) op(e0, e1) = all_56_30 % 151.81/22.49 (2) all_54_0 = all_10_2 % 151.81/22.49 (3) all_54_2 = all_10_0 % 151.81/22.49 (4) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 151.81/22.49 (5) ~ (all_10_0 = e0) % 151.81/22.49 (6) all_56_1 = all_10_2 % 151.81/22.49 (7) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0 % 151.81/22.49 (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 151.81/22.49 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 151.81/22.49 (9) ~ (all_6_2 = e0) % 151.81/22.49 (10) all_56_7 = all_52_12 % 151.81/22.49 (11) op(e0, all_4_1) = e1 % 151.81/22.49 (12) ~ (all_52_12 = all_10_0) % 151.81/22.49 (13) ~ (all_56_1 = e2) | all_56_3 = e3 % 151.81/22.49 (14) ~ (all_56_1 = e0) | all_56_7 = e3 % 151.81/22.49 (15) ~ (all_52_4 = all_10_0) % 151.81/22.49 (16) op(all_10_2, all_10_2) = e1 % 151.81/22.49 (17) all_56_3 = all_52_4 % 151.81/22.49 (18) op(e0, e1) = e0 % 151.81/22.49 (19) ~ (all_10_0 = e1) % 151.81/22.49 (20) op(e1, e1) = all_6_2 % 151.81/22.49 (21) op(e1, e1) = all_4_1 % 151.81/22.49 (22) ~ (all_10_0 = all_10_2) % 151.81/22.49 (23) ~ (all_10_0 = e2) % 151.81/22.49 % 151.81/22.49 Begin of proof % 151.81/22.49 | % 151.81/22.49 | BETA: splitting (7) gives: % 151.81/22.49 | % 151.81/22.49 | Case 1: % 151.81/22.49 | | % 151.81/22.49 | | (24) all_54_2 = e3 % 151.81/22.49 | | % 151.81/22.49 | | COMBINE_EQS: (3), (24) imply: % 151.81/22.49 | | (25) all_10_0 = e3 % 151.81/22.49 | | % 151.81/22.49 | | SIMP: (25) implies: % 151.81/22.49 | | (26) all_10_0 = e3 % 151.81/22.49 | | % 151.81/22.49 | | REDUCE: (15), (26) imply: % 151.81/22.49 | | (27) ~ (all_52_4 = e3) % 151.81/22.49 | | % 151.81/22.49 | | REDUCE: (12), (26) imply: % 151.81/22.49 | | (28) ~ (all_52_12 = e3) % 151.81/22.49 | | % 151.81/22.49 | | REDUCE: (22), (26) imply: % 151.81/22.49 | | (29) ~ (all_10_2 = e3) % 151.81/22.49 | | % 151.81/22.49 | | SIMP: (29) implies: % 151.81/22.49 | | (30) ~ (all_10_2 = e3) % 151.81/22.49 | | % 151.81/22.49 | | BETA: splitting (14) gives: % 151.81/22.49 | | % 151.81/22.49 | | Case 1: % 151.81/22.49 | | | % 151.81/22.49 | | | (31) ~ (all_56_1 = e0) % 151.81/22.49 | | | % 151.81/22.49 | | | REDUCE: (6), (31) imply: % 151.81/22.49 | | | (32) ~ (all_10_2 = e0) % 151.81/22.49 | | | % 151.81/22.49 | | | BETA: splitting (13) gives: % 151.81/22.49 | | | % 151.81/22.49 | | | Case 1: % 151.81/22.49 | | | | % 151.81/22.49 | | | | (33) ~ (all_56_1 = e2) % 151.81/22.49 | | | | % 151.81/22.49 | | | | REDUCE: (6), (33) imply: % 151.81/22.49 | | | | (34) ~ (all_10_2 = e2) % 151.81/22.49 | | | | % 151.81/22.49 | | | | BETA: splitting (4) gives: % 151.81/22.49 | | | | % 151.81/22.49 | | | | Case 1: % 151.81/22.49 | | | | | % 151.81/22.49 | | | | | (35) all_54_0 = e3 % 151.81/22.49 | | | | | % 151.81/22.49 | | | | | REF_CLOSE: (2), (30), (35) are inconsistent by sub-proof #709. % 151.81/22.49 | | | | | % 151.81/22.49 | | | | Case 2: % 151.81/22.49 | | | | | % 151.81/22.49 | | | | | (36) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 151.81/22.49 | | | | | % 151.81/22.49 | | | | | BETA: splitting (36) gives: % 151.81/22.49 | | | | | % 151.81/22.49 | | | | | Case 1: % 151.81/22.49 | | | | | | % 151.81/22.49 | | | | | | (37) all_54_0 = e2 % 151.81/22.49 | | | | | | % 151.81/22.49 | | | | | | REF_CLOSE: (2), (34), (37) are inconsistent by sub-proof #734. % 151.81/22.49 | | | | | | % 151.81/22.49 | | | | | Case 2: % 151.81/22.49 | | | | | | % 151.81/22.49 | | | | | | (38) all_54_0 = e1 | all_54_0 = e0 % 151.81/22.49 | | | | | | % 151.81/22.49 | | | | | | BETA: splitting (38) gives: % 151.81/22.49 | | | | | | % 151.81/22.49 | | | | | | Case 1: % 151.81/22.49 | | | | | | | % 151.81/22.49 | | | | | | | (39) all_54_0 = e1 % 151.81/22.49 | | | | | | | % 151.81/22.49 | | | | | | | COMBINE_EQS: (2), (39) imply: % 151.81/22.49 | | | | | | | (40) all_10_2 = e1 % 151.81/22.49 | | | | | | | % 151.81/22.49 | | | | | | | SIMP: (40) implies: % 151.81/22.49 | | | | | | | (41) all_10_2 = e1 % 151.81/22.49 | | | | | | | % 151.81/22.49 | | | | | | | REDUCE: (16), (41) imply: % 151.81/22.49 | | | | | | | (42) op(e1, e1) = e1 % 151.81/22.49 | | | | | | | % 151.81/22.49 | | | | | | | GROUND_INST: instantiating (8) with e0, all_56_30, e1, e0, % 151.81/22.49 | | | | | | | simplifying with (1), (18) gives: % 151.81/22.49 | | | | | | | (43) all_56_30 = e0 % 151.81/22.49 | | | | | | | % 151.81/22.49 | | | | | | | GROUND_INST: instantiating (8) with all_6_2, e1, e1, e1, % 151.81/22.49 | | | | | | | simplifying with (20), (42) gives: % 151.81/22.49 | | | | | | | (44) all_6_2 = e1 % 151.81/22.49 | | | | | | | % 151.81/22.49 | | | | | | | GROUND_INST: instantiating (8) with all_6_2, all_4_1, e1, e1, % 151.81/22.49 | | | | | | | simplifying with (20), (21) gives: % 151.81/22.49 | | | | | | | (45) all_6_2 = all_4_1 % 151.81/22.49 | | | | | | | % 151.81/22.49 | | | | | | | COMBINE_EQS: (44), (45) imply: % 151.81/22.49 | | | | | | | (46) all_4_1 = e1 % 151.81/22.49 | | | | | | | % 151.81/22.49 | | | | | | | SIMP: (46) implies: % 151.81/22.49 | | | | | | | (47) all_4_1 = e1 % 151.81/22.49 | | | | | | | % 151.81/22.49 | | | | | | | REDUCE: (9), (44) imply: % 151.81/22.49 | | | | | | | (48) ~ (e1 = e0) % 151.81/22.49 | | | | | | | % 151.81/22.49 | | | | | | | REDUCE: (11), (47) imply: % 151.81/22.49 | | | | | | | (49) op(e0, e1) = e1 % 151.81/22.49 | | | | | | | % 151.81/22.49 | | | | | | | REF_CLOSE: (8), (18), (48), (49) are inconsistent by sub-proof % 151.81/22.49 | | | | | | | #351. % 151.81/22.49 | | | | | | | % 151.81/22.49 | | | | | | Case 2: % 151.81/22.49 | | | | | | | % 151.81/22.49 | | | | | | | (50) all_54_0 = e0 % 151.81/22.49 | | | | | | | % 151.81/22.49 | | | | | | | REF_CLOSE: (2), (32), (50) are inconsistent by sub-proof #732. % 151.81/22.49 | | | | | | | % 151.81/22.49 | | | | | | End of split % 151.81/22.49 | | | | | | % 151.81/22.49 | | | | | End of split % 151.81/22.49 | | | | | % 151.81/22.49 | | | | End of split % 151.81/22.49 | | | | % 151.81/22.49 | | | Case 2: % 151.81/22.49 | | | | % 151.81/22.49 | | | | (51) all_56_3 = e3 % 151.81/22.49 | | | | % 151.81/22.49 | | | | REF_CLOSE: (17), (27), (51) are inconsistent by sub-proof #395. % 151.81/22.49 | | | | % 151.81/22.49 | | | End of split % 151.81/22.49 | | | % 151.81/22.49 | | Case 2: % 151.81/22.49 | | | % 151.81/22.49 | | | (52) all_56_7 = e3 % 151.81/22.49 | | | % 151.81/22.49 | | | REF_CLOSE: (10), (28), (52) are inconsistent by sub-proof #691. % 151.81/22.49 | | | % 151.81/22.49 | | End of split % 151.81/22.49 | | % 151.81/22.49 | Case 2: % 151.81/22.49 | | % 151.81/22.49 | | (53) all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0 % 151.81/22.49 | | % 151.81/22.49 | | REF_CLOSE: (3), (5), (19), (23), (53) are inconsistent by sub-proof #382. % 151.81/22.49 | | % 151.81/22.49 | End of split % 151.81/22.49 | % 151.81/22.49 End of proof % 151.81/22.49 % 151.81/22.49 Sub-proof #351 shows that the following formulas are inconsistent: % 151.81/22.49 ---------------------------------------------------------------- % 151.81/22.49 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 151.81/22.49 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 151.81/22.49 (2) op(e0, e1) = e1 % 151.81/22.49 (3) op(e0, e1) = e0 % 151.81/22.49 (4) ~ (e1 = e0) % 151.81/22.49 % 151.81/22.49 Begin of proof % 151.81/22.49 | % 151.81/22.49 | GROUND_INST: instantiating (1) with e0, e1, e1, e0, simplifying with (2), (3) % 151.81/22.49 | gives: % 151.81/22.49 | (5) e1 = e0 % 151.81/22.49 | % 151.81/22.49 | REDUCE: (4), (5) imply: % 151.81/22.49 | (6) $false % 151.81/22.49 | % 151.81/22.49 | CLOSE: (6) is inconsistent. % 151.81/22.49 | % 151.81/22.49 End of proof % 151.81/22.49 % 151.81/22.49 Sub-proof #352 shows that the following formulas are inconsistent: % 151.81/22.49 ---------------------------------------------------------------- % 151.81/22.49 (1) all_56_15 = all_52_13 % 151.81/22.49 (2) all_56_15 = e2 % 151.81/22.49 (3) ~ (all_52_13 = e2) % 151.81/22.49 % 151.81/22.49 Begin of proof % 151.81/22.49 | % 151.81/22.49 | COMBINE_EQS: (1), (2) imply: % 151.81/22.49 | (4) all_52_13 = e2 % 151.81/22.49 | % 151.81/22.49 | SIMP: (4) implies: % 151.81/22.49 | (5) all_52_13 = e2 % 151.81/22.49 | % 151.81/22.49 | REDUCE: (3), (5) imply: % 151.81/22.49 | (6) $false % 151.81/22.49 | % 151.81/22.49 | CLOSE: (6) is inconsistent. % 151.81/22.49 | % 151.81/22.49 End of proof % 151.81/22.49 % 151.81/22.49 Sub-proof #353 shows that the following formulas are inconsistent: % 151.81/22.49 ---------------------------------------------------------------- % 151.81/22.49 (1) all_56_13 = all_52_9 % 151.81/22.49 (2) all_56_13 = e2 % 151.81/22.49 (3) ~ (all_52_9 = e2) % 151.81/22.49 % 151.81/22.49 Begin of proof % 151.81/22.49 | % 151.81/22.49 | COMBINE_EQS: (1), (2) imply: % 151.81/22.49 | (4) all_52_9 = e2 % 151.81/22.49 | % 151.81/22.49 | SIMP: (4) implies: % 151.81/22.49 | (5) all_52_9 = e2 % 151.81/22.49 | % 151.81/22.49 | REDUCE: (3), (5) imply: % 151.81/22.49 | (6) $false % 151.81/22.49 | % 151.81/22.49 | CLOSE: (6) is inconsistent. % 151.81/22.49 | % 151.81/22.49 End of proof % 151.81/22.49 % 151.81/22.49 Sub-proof #354 shows that the following formulas are inconsistent: % 151.81/22.49 ---------------------------------------------------------------- % 151.81/22.49 (1) ~ (e3 = e0) % 151.81/22.49 (2) all_56_5 = all_10_0 % 151.81/22.49 (3) ~ (all_4_1 = e0) % 151.81/22.49 (4) all_54_0 = all_10_2 % 151.81/22.49 (5) all_58_4 = all_10_0 % 151.81/22.49 (6) all_54_2 = all_10_0 % 151.81/22.49 (7) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 151.81/22.49 (8) all_56_1 = all_10_2 % 151.81/22.49 (9) ~ (all_32_0 = e0) | ~ (all_32_2 = e2) % 151.81/22.49 (10) ~ (all_10_0 = all_4_1) % 151.81/22.49 (11) all_56_1 = all_4_1 % 151.81/22.49 (12) ~ (all_56_1 = e1) | all_56_5 = e3 % 151.81/22.49 (13) all_54_0 = all_4_1 % 151.81/22.49 (14) op(e3, e3) = all_10_2 % 151.81/22.49 (15) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0 % 151.81/22.49 (16) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 151.81/22.49 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 151.81/22.49 (17) ~ (all_56_1 = e2) | all_56_3 = e3 % 151.81/22.49 (18) ~ (all_52_4 = all_10_0) % 151.81/22.49 (19) op(all_10_2, all_10_2) = e1 % 151.81/22.49 (20) all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3 % 151.81/22.49 (21) all_56_3 = all_52_4 % 151.81/22.49 (22) ~ (all_4_1 = e1) % 151.81/22.49 (23) ~ (all_10_0 = e1) % 151.81/22.49 (24) all_32_0 = all_10_0 % 151.81/22.49 (25) ~ (all_10_2 = e0) % 151.81/22.49 (26) op(e3, all_10_2) = all_56_0 % 151.81/22.49 (27) ~ (all_10_0 = e2) % 151.81/22.49 (28) all_32_2 = all_10_2 % 151.81/22.49 % 151.81/22.49 Begin of proof % 151.81/22.49 | % 151.81/22.49 | BETA: splitting (20) gives: % 151.81/22.49 | % 151.81/22.49 | Case 1: % 151.81/22.49 | | % 151.81/22.49 | | (29) all_58_4 = e3 % 151.81/22.49 | | % 151.81/22.49 | | COMBINE_EQS: (5), (29) imply: % 151.81/22.49 | | (30) all_10_0 = e3 % 151.81/22.49 | | % 151.81/22.49 | | REDUCE: (18), (30) imply: % 151.81/22.49 | | (31) ~ (all_52_4 = e3) % 151.81/22.49 | | % 151.81/22.49 | | REDUCE: (10), (30) imply: % 151.81/22.49 | | (32) ~ (all_4_1 = e3) % 151.81/22.49 | | % 151.81/22.49 | | SIMP: (32) implies: % 151.81/22.49 | | (33) ~ (all_4_1 = e3) % 151.81/22.49 | | % 151.81/22.49 | | REF_CLOSE: (3), (7), (11), (13), (17), (21), (22), (31), (33) are % 151.81/22.49 | | inconsistent by sub-proof #355. % 151.81/22.49 | | % 151.81/22.49 | Case 2: % 151.81/22.49 | | % 151.81/22.49 | | (34) ~ (all_58_4 = e3) % 151.81/22.49 | | % 151.81/22.49 | | REDUCE: (5), (34) imply: % 151.81/22.49 | | (35) ~ (all_10_0 = e3) % 151.81/22.49 | | % 151.81/22.49 | | BETA: splitting (15) gives: % 151.81/22.49 | | % 151.81/22.49 | | Case 1: % 151.81/22.49 | | | % 151.81/22.49 | | | (36) all_54_2 = e3 % 151.81/22.49 | | | % 151.81/22.49 | | | REF_CLOSE: (6), (35), (36) are inconsistent by sub-proof #408. % 151.81/22.49 | | | % 151.81/22.49 | | Case 2: % 151.81/22.49 | | | % 151.81/22.49 | | | (37) all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0 % 151.81/22.49 | | | % 151.81/22.49 | | | BETA: splitting (37) gives: % 151.81/22.49 | | | % 151.81/22.49 | | | Case 1: % 151.81/22.49 | | | | % 151.81/22.49 | | | | (38) all_54_2 = e2 % 151.81/22.49 | | | | % 151.81/22.49 | | | | REF_CLOSE: (6), (27), (38) are inconsistent by sub-proof #407. % 151.81/22.49 | | | | % 151.81/22.49 | | | Case 2: % 151.81/22.49 | | | | % 151.81/22.49 | | | | (39) all_54_2 = e1 | all_54_2 = e0 % 151.81/22.49 | | | | % 151.81/22.49 | | | | BETA: splitting (39) gives: % 151.81/22.49 | | | | % 151.81/22.49 | | | | Case 1: % 151.81/22.49 | | | | | % 151.81/22.49 | | | | | (40) all_54_2 = e1 % 151.81/22.49 | | | | | % 151.81/22.49 | | | | | REF_CLOSE: (6), (23), (40) are inconsistent by sub-proof #406. % 151.81/22.49 | | | | | % 151.81/22.49 | | | | Case 2: % 151.81/22.49 | | | | | % 151.81/22.49 | | | | | (41) all_54_2 = e0 % 151.81/22.49 | | | | | % 151.81/22.49 | | | | | COMBINE_EQS: (6), (41) imply: % 151.81/22.49 | | | | | (42) all_10_0 = e0 % 151.81/22.49 | | | | | % 151.81/22.49 | | | | | SIMP: (42) implies: % 151.81/22.49 | | | | | (43) all_10_0 = e0 % 151.81/22.49 | | | | | % 151.81/22.49 | | | | | REF_CLOSE: (1), (2), (4), (7), (8), (9), (12), (14), (16), (19), (24), % 151.81/22.49 | | | | | (25), (26), (28), (43) are inconsistent by sub-proof #388. % 151.81/22.49 | | | | | % 151.81/22.49 | | | | End of split % 151.81/22.49 | | | | % 151.81/22.49 | | | End of split % 151.81/22.49 | | | % 151.81/22.49 | | End of split % 151.81/22.49 | | % 151.81/22.49 | End of split % 151.81/22.49 | % 151.81/22.49 End of proof % 151.81/22.49 % 151.81/22.49 Sub-proof #355 shows that the following formulas are inconsistent: % 151.81/22.49 ---------------------------------------------------------------- % 151.81/22.49 (1) ~ (all_4_1 = e0) % 151.81/22.49 (2) ~ (all_4_1 = e3) % 151.81/22.49 (3) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 151.81/22.49 (4) all_56_1 = all_4_1 % 151.81/22.49 (5) all_54_0 = all_4_1 % 151.81/22.49 (6) ~ (all_56_1 = e2) | all_56_3 = e3 % 151.81/22.49 (7) all_56_3 = all_52_4 % 151.81/22.49 (8) ~ (all_4_1 = e1) % 151.81/22.49 (9) ~ (all_52_4 = e3) % 151.81/22.49 % 151.81/22.49 Begin of proof % 151.81/22.49 | % 151.81/22.49 | BETA: splitting (6) gives: % 151.81/22.49 | % 151.81/22.49 | Case 1: % 151.81/22.49 | | % 151.81/22.49 | | (10) ~ (all_56_1 = e2) % 151.81/22.49 | | % 151.81/22.49 | | REDUCE: (4), (10) imply: % 151.81/22.49 | | (11) ~ (all_4_1 = e2) % 151.81/22.49 | | % 151.81/22.49 | | REF_CLOSE: (1), (2), (3), (5), (8), (11) are inconsistent by sub-proof #548. % 151.81/22.49 | | % 151.81/22.49 | Case 2: % 151.81/22.49 | | % 151.81/22.49 | | (12) all_56_3 = e3 % 151.81/22.49 | | % 151.81/22.49 | | REF_CLOSE: (7), (9), (12) are inconsistent by sub-proof #395. % 151.81/22.49 | | % 151.81/22.49 | End of split % 151.81/22.49 | % 151.81/22.49 End of proof % 151.81/22.49 % 151.81/22.49 Sub-proof #356 shows that the following formulas are inconsistent: % 151.81/22.49 ---------------------------------------------------------------- % 151.81/22.49 (1) all_56_11 = all_8_2 % 151.81/22.49 (2) ~ (all_8_1 = e1) % 151.81/22.49 (3) ~ (all_6_1 = e2) % 151.81/22.49 (4) ~ (all_8_2 = e1) % 151.81/22.49 (5) ~ (all_8_1 = e3) % 151.81/22.49 (6) op(e0, e0) = all_4_2 % 151.81/22.49 (7) op(e2, e2) = all_6_1 % 151.81/22.49 (8) all_54_5 = all_8_2 % 151.81/22.49 (9) ~ (all_6_1 = e3) % 151.81/22.49 (10) all_54_15 = all_4_2 % 151.81/22.49 (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 151.81/22.49 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 151.81/22.49 (12) op(e0, all_4_1) = e1 % 151.81/22.50 (13) op(all_4_2, all_4_2) = all_4_1 % 151.81/22.50 (14) ~ (all_52_13 = all_4_2) % 151.81/22.50 (15) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0 % 151.81/22.50 (16) ~ (all_56_11 = e0) | all_56_15 = e2 % 151.81/22.50 (17) op(e2, e2) = all_8_2 % 151.81/22.50 (18) op(e0, all_4_2) = all_56_30 % 151.81/22.50 (19) op(all_8_2, all_8_2) = all_8_1 % 151.81/22.50 (20) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 151.81/22.50 (21) all_56_15 = all_52_13 % 151.81/22.50 % 151.81/22.50 Begin of proof % 151.81/22.50 | % 151.81/22.50 | GROUND_INST: instantiating (11) with all_8_2, all_6_1, e2, e2, simplifying % 151.81/22.50 | with (7), (17) gives: % 151.81/22.50 | (22) all_8_2 = all_6_1 % 151.81/22.50 | % 151.81/22.50 | COMBINE_EQS: (8), (22) imply: % 151.81/22.50 | (23) all_54_5 = all_6_1 % 151.81/22.50 | % 151.81/22.50 | COMBINE_EQS: (1), (22) imply: % 151.81/22.50 | (24) all_56_11 = all_6_1 % 151.81/22.50 | % 151.81/22.50 | REDUCE: (4), (22) imply: % 151.81/22.50 | (25) ~ (all_6_1 = e1) % 151.81/22.50 | % 151.81/22.50 | REDUCE: (19), (22) imply: % 151.81/22.50 | (26) op(all_6_1, all_6_1) = all_8_1 % 151.81/22.50 | % 151.81/22.50 | BETA: splitting (20) gives: % 151.81/22.50 | % 151.81/22.50 | Case 1: % 151.81/22.50 | | % 151.81/22.50 | | (27) all_54_5 = e3 % 151.81/22.50 | | % 151.81/22.50 | | REF_CLOSE: (9), (23), (27) are inconsistent by sub-proof #509. % 151.81/22.50 | | % 151.81/22.50 | Case 2: % 151.81/22.50 | | % 151.81/22.50 | | (28) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 151.81/22.50 | | % 151.81/22.50 | | BETA: splitting (28) gives: % 151.81/22.50 | | % 151.81/22.50 | | Case 1: % 151.81/22.50 | | | % 151.81/22.50 | | | (29) all_54_5 = e2 % 151.81/22.50 | | | % 151.81/22.50 | | | REF_CLOSE: (3), (23), (29) are inconsistent by sub-proof #466. % 151.81/22.50 | | | % 151.81/22.50 | | Case 2: % 151.81/22.50 | | | % 151.81/22.50 | | | (30) all_54_5 = e1 | all_54_5 = e0 % 151.81/22.50 | | | % 151.81/22.50 | | | BETA: splitting (30) gives: % 151.81/22.50 | | | % 151.81/22.50 | | | Case 1: % 151.81/22.50 | | | | % 151.81/22.50 | | | | (31) all_54_5 = e1 % 151.81/22.50 | | | | % 151.81/22.50 | | | | REF_CLOSE: (23), (25), (31) are inconsistent by sub-proof #465. % 151.81/22.50 | | | | % 151.81/22.50 | | | Case 2: % 151.81/22.50 | | | | % 151.81/22.50 | | | | (32) all_54_5 = e0 % 151.81/22.50 | | | | % 151.81/22.50 | | | | COMBINE_EQS: (23), (32) imply: % 151.81/22.50 | | | | (33) all_6_1 = e0 % 151.81/22.50 | | | | % 151.81/22.50 | | | | SIMP: (33) implies: % 151.81/22.50 | | | | (34) all_6_1 = e0 % 151.81/22.50 | | | | % 151.81/22.50 | | | | COMBINE_EQS: (24), (34) imply: % 151.81/22.50 | | | | (35) all_56_11 = e0 % 151.81/22.50 | | | | % 151.81/22.50 | | | | REDUCE: (26), (34) imply: % 151.81/22.50 | | | | (36) op(e0, e0) = all_8_1 % 151.81/22.50 | | | | % 151.81/22.50 | | | | REF_CLOSE: (2), (5), (6), (10), (11), (12), (13), (14), (15), (16), % 151.81/22.50 | | | | (18), (21), (35), (36) are inconsistent by sub-proof #358. % 151.81/22.50 | | | | % 151.81/22.50 | | | End of split % 151.81/22.50 | | | % 151.81/22.50 | | End of split % 151.81/22.50 | | % 151.81/22.50 | End of split % 151.81/22.50 | % 151.81/22.50 End of proof % 151.81/22.50 % 151.81/22.50 Sub-proof #357 shows that the following formulas are inconsistent: % 151.81/22.50 ---------------------------------------------------------------- % 151.81/22.50 (1) all_56_11 = all_8_2 % 151.81/22.50 (2) ~ (all_8_1 = e1) % 151.81/22.50 (3) ~ (all_8_1 = e3) % 151.81/22.50 (4) op(e0, e0) = all_4_2 % 151.81/22.50 (5) all_54_15 = all_4_2 % 151.81/22.50 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 151.81/22.50 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 151.81/22.50 (7) op(e0, all_4_1) = e1 % 151.81/22.50 (8) op(all_4_2, all_4_2) = all_4_1 % 151.81/22.50 (9) ~ (all_52_13 = all_4_2) % 151.81/22.50 (10) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0 % 151.81/22.50 (11) all_56_11 = e0 % 151.81/22.50 (12) ~ (all_56_11 = e0) | all_56_15 = e2 % 151.81/22.50 (13) op(e0, all_4_2) = all_56_30 % 151.81/22.50 (14) op(all_8_2, all_8_2) = all_8_1 % 151.81/22.50 (15) all_56_15 = all_52_13 % 151.81/22.50 % 151.81/22.50 Begin of proof % 151.81/22.50 | % 151.81/22.50 | COMBINE_EQS: (1), (11) imply: % 151.81/22.50 | (16) all_8_2 = e0 % 151.81/22.50 | % 151.81/22.50 | REDUCE: (14), (16) imply: % 151.81/22.50 | (17) op(e0, e0) = all_8_1 % 151.81/22.50 | % 151.81/22.50 | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13), % 151.81/22.50 | (15), (17) are inconsistent by sub-proof #358. % 151.81/22.50 | % 151.81/22.50 End of proof % 151.81/22.50 % 151.81/22.50 Sub-proof #358 shows that the following formulas are inconsistent: % 151.81/22.50 ---------------------------------------------------------------- % 151.81/22.50 (1) ~ (all_8_1 = e1) % 151.81/22.50 (2) ~ (all_8_1 = e3) % 151.81/22.50 (3) op(e0, e0) = all_4_2 % 151.81/22.50 (4) all_54_15 = all_4_2 % 151.81/22.50 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 151.81/22.50 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 151.81/22.50 (6) op(e0, all_4_1) = e1 % 151.81/22.50 (7) op(e0, e0) = all_8_1 % 151.81/22.50 (8) op(all_4_2, all_4_2) = all_4_1 % 151.81/22.50 (9) ~ (all_52_13 = all_4_2) % 151.81/22.50 (10) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0 % 151.81/22.50 (11) all_56_11 = e0 % 151.81/22.50 (12) ~ (all_56_11 = e0) | all_56_15 = e2 % 151.81/22.50 (13) op(e0, all_4_2) = all_56_30 % 151.81/22.50 (14) all_56_15 = all_52_13 % 151.81/22.50 % 151.81/22.50 Begin of proof % 151.81/22.50 | % 151.81/22.50 | BETA: splitting (12) gives: % 151.81/22.50 | % 151.81/22.50 | Case 1: % 151.81/22.50 | | % 151.81/22.50 | | (15) ~ (all_56_11 = e0) % 151.81/22.50 | | % 151.81/22.50 | | REDUCE: (11), (15) imply: % 151.81/22.50 | | (16) $false % 151.81/22.50 | | % 151.81/22.50 | | CLOSE: (16) is inconsistent. % 151.81/22.50 | | % 151.81/22.50 | Case 2: % 151.81/22.50 | | % 151.81/22.50 | | (17) all_56_15 = e2 % 151.81/22.50 | | % 151.81/22.50 | | COMBINE_EQS: (14), (17) imply: % 151.81/22.50 | | (18) all_52_13 = e2 % 151.81/22.50 | | % 151.81/22.50 | | REDUCE: (9), (18) imply: % 151.81/22.50 | | (19) ~ (all_4_2 = e2) % 151.81/22.50 | | % 151.81/22.50 | | SIMP: (19) implies: % 151.81/22.50 | | (20) ~ (all_4_2 = e2) % 151.81/22.50 | | % 151.81/22.50 | | GROUND_INST: instantiating (5) with all_4_2, all_8_1, e0, e0, simplifying % 151.81/22.50 | | with (3), (7) gives: % 151.81/22.50 | | (21) all_8_1 = all_4_2 % 151.81/22.50 | | % 151.81/22.50 | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (8), (10), (13), (20), (21) are % 151.81/22.50 | | inconsistent by sub-proof #359. % 151.81/22.50 | | % 151.81/22.50 | End of split % 151.81/22.50 | % 151.81/22.50 End of proof % 151.81/22.50 % 151.81/22.50 Sub-proof #359 shows that the following formulas are inconsistent: % 151.81/22.50 ---------------------------------------------------------------- % 151.81/22.50 (1) ~ (all_8_1 = e1) % 151.81/22.50 (2) all_8_1 = all_4_2 % 151.81/22.50 (3) ~ (all_8_1 = e3) % 151.81/22.50 (4) all_54_15 = all_4_2 % 151.81/22.50 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 151.81/22.50 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 151.81/22.50 (6) op(e0, all_4_1) = e1 % 151.81/22.50 (7) op(e0, e0) = all_8_1 % 151.81/22.50 (8) ~ (all_4_2 = e2) % 151.81/22.50 (9) op(all_4_2, all_4_2) = all_4_1 % 151.81/22.50 (10) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0 % 151.81/22.50 (11) op(e0, all_4_2) = all_56_30 % 151.81/22.50 % 151.81/22.50 Begin of proof % 151.81/22.50 | % 151.81/22.50 | REDUCE: (2), (3) imply: % 151.81/22.50 | (12) ~ (all_4_2 = e3) % 151.81/22.50 | % 151.81/22.50 | REDUCE: (1), (2) imply: % 151.81/22.50 | (13) ~ (all_4_2 = e1) % 151.81/22.50 | % 151.81/22.50 | REDUCE: (2), (7) imply: % 151.81/22.50 | (14) op(e0, e0) = all_4_2 % 151.81/22.50 | % 151.81/22.50 | REF_CLOSE: (4), (5), (6), (8), (9), (10), (11), (12), (13), (14) are % 151.81/22.50 | inconsistent by sub-proof #363. % 151.81/22.50 | % 151.81/22.50 End of proof % 151.81/22.50 % 151.81/22.50 Sub-proof #360 shows that the following formulas are inconsistent: % 151.81/22.50 ---------------------------------------------------------------- % 151.81/22.50 (1) all_56_11 = all_8_2 % 151.81/22.50 (2) ~ (all_52_11 = all_6_2) % 151.81/22.50 (3) all_58_6 = all_52_2 % 151.81/22.50 (4) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0 % 151.81/22.50 (5) all_54_10 = all_6_2 % 151.81/22.50 (6) ~ (all_6_1 = e2) % 151.81/22.50 (7) ~ (all_56_21 = e2) | all_56_19 = e1 % 151.81/22.50 (8) all_54_0 = all_10_2 % 151.81/22.50 (9) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0 % 151.81/22.50 (10) all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2 % 151.81/22.50 (11) ~ (all_8_1 = e3) % 151.81/22.50 (12) all_58_4 = all_52_8 % 151.81/22.50 (13) all_54_5 = all_8_2 % 151.81/22.50 (14) ~ (all_6_1 = e3) % 151.81/22.50 (15) ~ (all_52_6 = all_52_14) % 151.81/22.50 (16) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 151.81/22.50 (17) ~ (all_52_11 = e0) % 151.81/22.50 (18) all_56_21 = all_6_2 % 151.81/22.50 (19) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 151.81/22.50 (20) ~ (all_52_7 = all_8_2) % 151.81/22.50 (21) all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2 % 151.81/22.50 (22) all_56_1 = all_10_2 % 151.81/22.50 (23) all_56_17 = all_52_2 % 151.81/22.50 (24) all_58_9 = all_52_12 % 151.81/22.50 (25) all_56_3 = all_10_0 % 151.81/22.50 (26) ~ (all_56_1 = e1) | all_56_5 = e3 % 151.81/22.50 (27) all_54_14 = all_52_11 % 151.81/22.50 (28) all_58_13 = all_52_7 % 151.81/22.50 (29) op(e3, e3) = all_10_2 % 151.81/22.50 (30) ~ (all_52_8 = all_6_2) % 151.81/22.50 (31) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0 % 151.81/22.50 (32) all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1 % 151.81/22.50 (33) ~ (all_56_21 = e3) | all_56_17 = e1 % 151.81/22.50 (34) all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2 % 151.81/22.50 (35) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 151.81/22.50 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 151.81/22.50 (36) ~ (all_52_11 = e3) % 151.81/22.50 (37) ~ (all_52_8 = all_10_0) % 151.81/22.50 (38) ~ (all_52_3 = all_52_7) % 151.81/22.50 (39) ~ (all_26_1 = e2) | ~ (all_26_2 = e3) % 151.81/22.50 (40) all_56_7 = all_52_12 % 151.81/22.50 (41) op(e2, all_52_7) = all_56_26 % 151.81/22.50 (42) ~ (all_52_1 = all_52_13) % 151.81/22.50 (43) ~ (all_52_14 = e3) % 151.81/22.50 (44) ~ (all_52_8 = all_10_2) % 151.81/22.50 (45) ~ (all_52_12 = all_10_0) % 151.81/22.50 (46) ~ (all_56_1 = e2) | all_56_3 = e3 % 151.81/22.50 (47) ~ (all_56_1 = e0) | all_56_7 = e3 % 151.81/22.50 (48) all_56_5 = all_52_8 % 151.81/22.50 (49) all_58_3 = all_8_2 % 151.81/22.50 (50) op(e0, e0) = e3 % 151.81/22.50 (51) all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3 % 151.81/22.50 (52) op(all_10_2, all_10_2) = e2 % 151.81/22.50 (53) op(all_6_2, all_6_2) = all_6_1 % 151.81/22.50 (54) ~ (all_52_8 = all_52_11) % 151.81/22.50 (55) all_54_2 = all_52_8 % 151.81/22.50 (56) op(e1, e1) = all_6_2 % 151.81/22.50 (57) ~ (all_52_6 = all_8_2) % 151.81/22.50 (58) ~ (all_10_2 = e0) % 151.81/22.50 (59) all_58_2 = all_52_1 % 151.81/22.50 (60) all_58_7 = all_52_6 % 151.81/22.50 (61) ~ (all_56_11 = e0) | all_56_15 = e2 % 151.81/22.50 (62) all_58_0 = all_10_2 % 151.81/22.50 (63) op(e1, all_6_2) = all_56_20 % 151.81/22.50 (64) all_58_1 = all_10_0 % 151.81/22.50 (65) all_58_1 = e0 | all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0 % 151.81/22.50 (66) ~ (all_52_12 = all_52_14) % 151.81/22.50 (67) op(e2, e2) = all_8_2 % 151.81/22.50 (68) ~ (all_52_2 = all_6_2) % 151.81/22.50 (69) ~ (all_52_8 = all_52_12) % 151.81/22.50 (70) ~ (all_56_21 = e0) | all_56_23 = e1 % 151.81/22.50 (71) ~ (all_52_6 = all_6_2) % 151.81/22.50 (72) ~ (all_52_14 = all_6_2) % 151.81/22.50 (73) ~ (all_10_0 = all_10_2) % 151.81/22.50 (74) ~ (all_52_7 = e0) % 151.81/22.50 (75) ~ (all_52_2 = all_10_2) % 151.81/22.50 (76) all_26_1 = all_4_1 % 151.81/22.50 (77) ~ (all_10_0 = e2) % 151.81/22.50 (78) op(all_8_2, all_8_2) = all_8_1 % 151.81/22.50 (79) ~ (all_52_7 = all_10_0) % 151.81/22.50 (80) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 151.81/22.50 (81) all_56_19 = all_52_6 % 151.81/22.50 (82) ~ (all_52_12 = all_10_2) % 151.81/22.50 (83) all_26_2 = e3 % 151.81/22.50 (84) all_56_15 = all_52_13 % 151.81/22.50 (85) op(e3, e3) = all_4_1 % 151.81/22.50 (86) all_58_12 = all_52_3 % 151.81/22.50 (87) all_54_11 = all_52_14 % 151.81/22.50 % 151.81/22.50 Begin of proof % 151.81/22.50 | % 151.81/22.50 | BETA: splitting (39) gives: % 151.81/22.50 | % 151.81/22.50 | Case 1: % 151.81/22.50 | | % 151.81/22.50 | | (88) ~ (all_26_1 = e2) % 151.81/22.50 | | % 151.81/22.50 | | REDUCE: (76), (88) imply: % 151.81/22.50 | | (89) ~ (all_4_1 = e2) % 151.81/22.50 | | % 151.81/22.50 | | GROUND_INST: instantiating (35) with all_10_2, all_4_1, e3, e3, simplifying % 151.81/22.50 | | with (29), (85) gives: % 151.81/22.50 | | (90) all_10_2 = all_4_1 % 151.81/22.50 | | % 151.81/22.50 | | COMBINE_EQS: (8), (90) imply: % 151.81/22.50 | | (91) all_54_0 = all_4_1 % 151.81/22.50 | | % 151.81/22.50 | | COMBINE_EQS: (62), (90) imply: % 151.81/22.50 | | (92) all_58_0 = all_4_1 % 151.81/22.50 | | % 151.81/22.50 | | REDUCE: (75), (90) imply: % 151.81/22.50 | | (93) ~ (all_52_2 = all_4_1) % 151.81/22.50 | | % 151.81/22.50 | | REDUCE: (44), (90) imply: % 151.81/22.50 | | (94) ~ (all_52_8 = all_4_1) % 151.81/22.50 | | % 151.81/22.50 | | REDUCE: (82), (90) imply: % 151.81/22.50 | | (95) ~ (all_52_12 = all_4_1) % 151.81/22.50 | | % 151.81/22.50 | | REDUCE: (58), (90) imply: % 151.81/22.50 | | (96) ~ (all_4_1 = e0) % 151.81/22.50 | | % 151.81/22.50 | | REDUCE: (52), (90) imply: % 151.81/22.50 | | (97) op(all_4_1, all_4_1) = e2 % 151.81/22.50 | | % 151.81/22.50 | | BETA: splitting (61) gives: % 151.81/22.50 | | % 151.81/22.50 | | Case 1: % 151.81/22.50 | | | % 151.81/22.50 | | | (98) ~ (all_56_11 = e0) % 151.81/22.50 | | | % 151.81/22.50 | | | REDUCE: (1), (98) imply: % 151.81/22.50 | | | (99) ~ (all_8_2 = e0) % 151.81/22.50 | | | % 151.81/22.50 | | | BETA: splitting (70) gives: % 151.81/22.50 | | | % 151.81/22.50 | | | Case 1: % 151.81/22.50 | | | | % 151.81/22.50 | | | | (100) ~ (all_56_21 = e0) % 151.81/22.50 | | | | % 151.81/22.50 | | | | REDUCE: (18), (100) imply: % 151.81/22.50 | | | | (101) ~ (all_6_2 = e0) % 151.81/22.50 | | | | % 151.81/22.50 | | | | BETA: splitting (7) gives: % 151.81/22.50 | | | | % 151.81/22.50 | | | | Case 1: % 151.81/22.50 | | | | | % 151.81/22.50 | | | | | (102) ~ (all_56_21 = e2) % 151.81/22.50 | | | | | % 151.81/22.50 | | | | | REDUCE: (18), (102) imply: % 151.81/22.50 | | | | | (103) ~ (all_6_2 = e2) % 151.81/22.50 | | | | | % 151.81/22.50 | | | | | BETA: splitting (33) gives: % 151.81/22.50 | | | | | % 151.81/22.50 | | | | | Case 1: % 151.81/22.50 | | | | | | % 151.81/22.50 | | | | | | (104) ~ (all_56_21 = e3) % 151.81/22.50 | | | | | | % 151.81/22.50 | | | | | | REDUCE: (18), (104) imply: % 151.81/22.50 | | | | | | (105) ~ (all_6_2 = e3) % 151.81/22.50 | | | | | | % 151.81/22.50 | | | | | | BETA: splitting (19) gives: % 151.81/22.50 | | | | | | % 151.81/22.50 | | | | | | Case 1: % 151.81/22.50 | | | | | | | % 151.81/22.50 | | | | | | | (106) all_54_10 = e3 % 151.81/22.51 | | | | | | | % 151.81/22.51 | | | | | | | COMBINE_EQS: (5), (106) imply: % 151.81/22.51 | | | | | | | (107) all_6_2 = e3 % 151.81/22.51 | | | | | | | % 151.81/22.51 | | | | | | | REDUCE: (105), (107) imply: % 151.81/22.51 | | | | | | | (108) $false % 151.81/22.51 | | | | | | | % 151.81/22.51 | | | | | | | CLOSE: (108) is inconsistent. % 151.81/22.51 | | | | | | | % 151.81/22.51 | | | | | | Case 2: % 151.81/22.51 | | | | | | | % 151.81/22.51 | | | | | | | (109) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 151.81/22.51 | | | | | | | % 151.81/22.51 | | | | | | | BETA: splitting (109) gives: % 151.81/22.51 | | | | | | | % 151.81/22.51 | | | | | | | Case 1: % 151.81/22.51 | | | | | | | | % 151.81/22.51 | | | | | | | | (110) all_54_10 = e2 % 151.81/22.51 | | | | | | | | % 151.81/22.51 | | | | | | | | COMBINE_EQS: (5), (110) imply: % 151.81/22.51 | | | | | | | | (111) all_6_2 = e2 % 151.81/22.51 | | | | | | | | % 151.81/22.51 | | | | | | | | REDUCE: (103), (111) imply: % 151.81/22.51 | | | | | | | | (112) $false % 151.81/22.51 | | | | | | | | % 151.81/22.51 | | | | | | | | CLOSE: (112) is inconsistent. % 151.81/22.51 | | | | | | | | % 151.81/22.51 | | | | | | | Case 2: % 151.81/22.51 | | | | | | | | % 151.81/22.51 | | | | | | | | (113) all_54_10 = e1 | all_54_10 = e0 % 151.81/22.51 | | | | | | | | % 151.81/22.51 | | | | | | | | BETA: splitting (113) gives: % 151.81/22.51 | | | | | | | | % 151.81/22.51 | | | | | | | | Case 1: % 151.81/22.51 | | | | | | | | | % 151.81/22.51 | | | | | | | | | (114) all_54_10 = e1 % 151.81/22.51 | | | | | | | | | % 151.81/22.51 | | | | | | | | | COMBINE_EQS: (5), (114) imply: % 151.81/22.51 | | | | | | | | | (115) all_6_2 = e1 % 151.81/22.51 | | | | | | | | | % 151.81/22.51 | | | | | | | | | REDUCE: (30), (115) imply: % 151.81/22.51 | | | | | | | | | (116) ~ (all_52_8 = e1) % 151.81/22.51 | | | | | | | | | % 151.81/22.51 | | | | | | | | | REDUCE: (2), (115) imply: % 151.81/22.51 | | | | | | | | | (117) ~ (all_52_11 = e1) % 151.81/22.51 | | | | | | | | | % 151.81/22.51 | | | | | | | | | REDUCE: (72), (115) imply: % 151.81/22.51 | | | | | | | | | (118) ~ (all_52_14 = e1) % 151.81/22.51 | | | | | | | | | % 151.81/22.51 | | | | | | | | | REDUCE: (63), (115) imply: % 151.81/22.51 | | | | | | | | | (119) op(e1, e1) = all_56_20 % 151.81/22.51 | | | | | | | | | % 151.81/22.51 | | | | | | | | | REDUCE: (56), (115) imply: % 151.81/22.51 | | | | | | | | | (120) op(e1, e1) = e1 % 151.81/22.51 | | | | | | | | | % 151.81/22.51 | | | | | | | | | BETA: splitting (4) gives: % 151.81/22.51 | | | | | | | | | % 151.81/22.51 | | | | | | | | | Case 1: % 151.81/22.51 | | | | | | | | | | % 151.81/22.51 | | | | | | | | | | (121) all_54_14 = e3 % 151.81/22.51 | | | | | | | | | | % 151.81/22.51 | | | | | | | | | | REF_CLOSE: (27), (36), (121) are inconsistent by sub-proof % 151.81/22.51 | | | | | | | | | | #729. % 151.81/22.51 | | | | | | | | | | % 151.81/22.51 | | | | | | | | | Case 2: % 151.81/22.51 | | | | | | | | | | % 151.81/22.51 | | | | | | | | | | (122) all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0 % 151.81/22.51 | | | | | | | | | | % 151.81/22.51 | | | | | | | | | | BETA: splitting (122) gives: % 151.81/22.51 | | | | | | | | | | % 151.81/22.51 | | | | | | | | | | Case 1: % 151.81/22.51 | | | | | | | | | | | % 151.81/22.51 | | | | | | | | | | | (123) all_54_14 = e2 % 151.81/22.51 | | | | | | | | | | | % 151.81/22.51 | | | | | | | | | | | COMBINE_EQS: (27), (123) imply: % 151.81/22.51 | | | | | | | | | | | (124) all_52_11 = e2 % 151.81/22.51 | | | | | | | | | | | % 151.81/22.51 | | | | | | | | | | | SIMP: (124) implies: % 151.81/22.51 | | | | | | | | | | | (125) all_52_11 = e2 % 151.81/22.51 | | | | | | | | | | | % 151.81/22.51 | | | | | | | | | | | REDUCE: (54), (125) imply: % 151.81/22.51 | | | | | | | | | | | (126) ~ (all_52_8 = e2) % 151.81/22.51 | | | | | | | | | | | % 151.81/22.51 | | | | | | | | | | | BETA: splitting (10) gives: % 151.81/22.51 | | | | | | | | | | | % 151.81/22.51 | | | | | | | | | | | Case 1: % 151.81/22.51 | | | | | | | | | | | | % 151.81/22.51 | | | | | | | | | | | | (127) all_58_0 = e2 % 151.81/22.51 | | | | | | | | | | | | % 151.81/22.51 | | | | | | | | | | | | COMBINE_EQS: (92), (127) imply: % 151.81/22.51 | | | | | | | | | | | | (128) all_4_1 = e2 % 151.81/22.51 | | | | | | | | | | | | % 151.81/22.51 | | | | | | | | | | | | REDUCE: (89), (128) imply: % 151.81/22.51 | | | | | | | | | | | | (129) $false % 151.81/22.51 | | | | | | | | | | | | % 151.81/22.51 | | | | | | | | | | | | CLOSE: (129) is inconsistent. % 151.81/22.51 | | | | | | | | | | | | % 151.81/22.51 | | | | | | | | | | | Case 2: % 151.81/22.51 | | | | | | | | | | | | % 151.81/22.51 | | | | | | | | | | | | (130) all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2 % 151.81/22.51 | | | | | | | | | | | | % 151.81/22.51 | | | | | | | | | | | | BETA: splitting (130) gives: % 151.81/22.51 | | | | | | | | | | | | % 151.81/22.51 | | | | | | | | | | | | Case 1: % 151.81/22.51 | | | | | | | | | | | | | % 151.81/22.51 | | | | | | | | | | | | | (131) all_58_1 = e2 % 151.81/22.51 | | | | | | | | | | | | | % 151.81/22.51 | | | | | | | | | | | | | COMBINE_EQS: (64), (131) imply: % 151.81/22.51 | | | | | | | | | | | | | (132) all_10_0 = e2 % 151.81/22.51 | | | | | | | | | | | | | % 151.81/22.51 | | | | | | | | | | | | | REDUCE: (77), (132) imply: % 151.81/22.51 | | | | | | | | | | | | | (133) $false % 151.81/22.51 | | | | | | | | | | | | | % 151.81/22.51 | | | | | | | | | | | | | CLOSE: (133) is inconsistent. % 151.81/22.51 | | | | | | | | | | | | | % 151.81/22.51 | | | | | | | | | | | | Case 2: % 151.81/22.51 | | | | | | | | | | | | | % 151.81/22.51 | | | | | | | | | | | | | (134) all_58_4 = e2 | all_58_9 = e2 % 151.81/22.51 | | | | | | | | | | | | | % 151.81/22.51 | | | | | | | | | | | | | BETA: splitting (134) gives: % 151.81/22.51 | | | | | | | | | | | | | % 151.81/22.51 | | | | | | | | | | | | | Case 1: % 151.81/22.51 | | | | | | | | | | | | | | % 151.81/22.51 | | | | | | | | | | | | | | (135) all_58_4 = e2 % 151.81/22.51 | | | | | | | | | | | | | | % 151.81/22.51 | | | | | | | | | | | | | | COMBINE_EQS: (12), (135) imply: % 151.81/22.51 | | | | | | | | | | | | | | (136) all_52_8 = e2 % 151.81/22.51 | | | | | | | | | | | | | | % 151.81/22.51 | | | | | | | | | | | | | | REDUCE: (126), (136) imply: % 151.81/22.51 | | | | | | | | | | | | | | (137) $false % 151.81/22.51 | | | | | | | | | | | | | | % 151.81/22.51 | | | | | | | | | | | | | | CLOSE: (137) is inconsistent. % 151.81/22.51 | | | | | | | | | | | | | | % 151.81/22.51 | | | | | | | | | | | | | Case 2: % 151.81/22.51 | | | | | | | | | | | | | | % 151.81/22.51 | | | | | | | | | | | | | | (138) all_58_9 = e2 % 151.81/22.51 | | | | | | | | | | | | | | % 151.81/22.51 | | | | | | | | | | | | | | COMBINE_EQS: (24), (138) imply: % 151.81/22.51 | | | | | | | | | | | | | | (139) all_52_12 = e2 % 151.81/22.51 | | | | | | | | | | | | | | % 151.81/22.51 | | | | | | | | | | | | | | REDUCE: (66), (139) imply: % 151.81/22.51 | | | | | | | | | | | | | | (140) ~ (all_52_14 = e2) % 151.81/22.51 | | | | | | | | | | | | | | % 151.81/22.51 | | | | | | | | | | | | | | SIMP: (140) implies: % 151.81/22.51 | | | | | | | | | | | | | | (141) ~ (all_52_14 = e2) % 151.81/22.51 | | | | | | | | | | | | | | % 151.81/22.51 | | | | | | | | | | | | | | REDUCE: (95), (139) imply: % 151.81/22.51 | | | | | | | | | | | | | | (142) ~ (all_4_1 = e2) % 151.81/22.51 | | | | | | | | | | | | | | % 151.81/22.51 | | | | | | | | | | | | | | BETA: splitting (9) gives: % 151.81/22.51 | | | | | | | | | | | | | | % 151.81/22.51 | | | | | | | | | | | | | | Case 1: % 151.81/22.51 | | | | | | | | | | | | | | | % 151.81/22.51 | | | | | | | | | | | | | | | (143) all_54_11 = e3 % 151.81/22.51 | | | | | | | | | | | | | | | % 151.81/22.51 | | | | | | | | | | | | | | | REF_CLOSE: (43), (87), (143) are inconsistent by sub-proof % 151.81/22.51 | | | | | | | | | | | | | | | #416. % 151.81/22.51 | | | | | | | | | | | | | | | % 151.81/22.51 | | | | | | | | | | | | | | Case 2: % 151.81/22.51 | | | | | | | | | | | | | | | % 151.81/22.51 | | | | | | | | | | | | | | | (144) all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0 % 151.81/22.51 | | | | | | | | | | | | | | | % 151.81/22.51 | | | | | | | | | | | | | | | BETA: splitting (32) gives: % 151.81/22.51 | | | | | | | | | | | | | | | % 151.81/22.51 | | | | | | | | | | | | | | | Case 1: % 151.81/22.51 | | | | | | | | | | | | | | | | % 151.81/22.51 | | | | | | | | | | | | | | | | (145) all_58_0 = e1 % 151.81/22.51 | | | | | | | | | | | | | | | | % 151.81/22.51 | | | | | | | | | | | | | | | | COMBINE_EQS: (92), (145) imply: % 151.81/22.51 | | | | | | | | | | | | | | | | (146) all_4_1 = e1 % 151.81/22.51 | | | | | | | | | | | | | | | | % 151.81/22.51 | | | | | | | | | | | | | | | | REDUCE: (89), (146) imply: % 151.81/22.51 | | | | | | | | | | | | | | | | (147) ~ (e2 = e1) % 151.81/22.51 | | | | | | | | | | | | | | | | % 151.81/22.51 | | | | | | | | | | | | | | | | SIMP: (147) implies: % 151.81/22.51 | | | | | | | | | | | | | | | | (148) ~ (e2 = e1) % 151.81/22.51 | | | | | | | | | | | | | | | | % 151.81/22.51 | | | | | | | | | | | | | | | | REDUCE: (97), (146) imply: % 151.81/22.51 | | | | | | | | | | | | | | | | (149) op(e1, e1) = e2 % 151.81/22.51 | | | | | | | | | | | | | | | | % 151.81/22.51 | | | | | | | | | | | | | | | | REF_CLOSE: (35), (119), (120), (148), (149) are inconsistent % 151.81/22.51 | | | | | | | | | | | | | | | | by sub-proof #494. % 151.81/22.51 | | | | | | | | | | | | | | | | % 151.81/22.51 | | | | | | | | | | | | | | | Case 2: % 151.81/22.51 | | | | | | | | | | | | | | | | % 151.81/22.51 | | | | | | | | | | | | | | | | (150) ~ (all_58_0 = e1) % 151.81/22.51 | | | | | | | | | | | | | | | | % 151.81/22.51 | | | | | | | | | | | | | | | | REDUCE: (92), (150) imply: % 151.81/22.51 | | | | | | | | | | | | | | | | (151) ~ (all_4_1 = e1) % 151.81/22.51 | | | | | | | | | | | | | | | | % 151.81/22.51 | | | | | | | | | | | | | | | | BETA: splitting (144) gives: % 151.81/22.51 | | | | | | | | | | | | | | | | % 151.81/22.51 | | | | | | | | | | | | | | | | Case 1: % 151.81/22.51 | | | | | | | | | | | | | | | | | % 151.81/22.51 | | | | | | | | | | | | | | | | | (152) all_54_11 = e2 % 151.81/22.51 | | | | | | | | | | | | | | | | | % 151.81/22.51 | | | | | | | | | | | | | | | | | REF_CLOSE: (87), (141), (152) are inconsistent by sub-proof % 151.81/22.51 | | | | | | | | | | | | | | | | | #690. % 151.81/22.51 | | | | | | | | | | | | | | | | | % 151.81/22.51 | | | | | | | | | | | | | | | | Case 2: % 151.81/22.51 | | | | | | | | | | | | | | | | | % 151.81/22.51 | | | | | | | | | | | | | | | | | (153) all_54_11 = e1 | all_54_11 = e0 % 151.81/22.51 | | | | | | | | | | | | | | | | | % 151.81/22.51 | | | | | | | | | | | | | | | | | BETA: splitting (16) gives: % 151.81/22.51 | | | | | | | | | | | | | | | | | % 151.81/22.51 | | | | | | | | | | | | | | | | | Case 1: % 151.81/22.51 | | | | | | | | | | | | | | | | | | % 151.81/22.51 | | | | | | | | | | | | | | | | | | (154) all_54_0 = e3 % 151.81/22.51 | | | | | | | | | | | | | | | | | | % 151.81/22.51 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (91), (154) imply: % 151.81/22.51 | | | | | | | | | | | | | | | | | | (155) all_4_1 = e3 % 151.81/22.51 | | | | | | | | | | | | | | | | | | % 151.81/22.51 | | | | | | | | | | | | | | | | | | SIMP: (155) implies: % 151.81/22.51 | | | | | | | | | | | | | | | | | | (156) all_4_1 = e3 % 151.81/22.51 | | | | | | | | | | | | | | | | | | % 151.81/22.51 | | | | | | | | | | | | | | | | | | REDUCE: (94), (156) imply: % 151.81/22.51 | | | | | | | | | | | | | | | | | | (157) ~ (all_52_8 = e3) % 151.81/22.51 | | | | | | | | | | | | | | | | | | % 151.81/22.51 | | | | | | | | | | | | | | | | | | BETA: splitting (153) gives: % 151.81/22.51 | | | | | | | | | | | | | | | | | | % 151.81/22.51 | | | | | | | | | | | | | | | | | | Case 1: % 151.81/22.51 | | | | | | | | | | | | | | | | | | | % 151.81/22.51 | | | | | | | | | | | | | | | | | | | (158) all_54_11 = e1 % 151.81/22.51 | | | | | | | | | | | | | | | | | | | % 151.81/22.51 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (87), (118), (158) are inconsistent by sub-proof % 151.81/22.51 | | | | | | | | | | | | | | | | | | | #689. % 151.81/22.51 | | | | | | | | | | | | | | | | | | | % 151.81/22.51 | | | | | | | | | | | | | | | | | | Case 2: % 151.81/22.51 | | | | | | | | | | | | | | | | | | | % 151.81/22.51 | | | | | | | | | | | | | | | | | | | (159) all_54_11 = e0 % 151.81/22.51 | | | | | | | | | | | | | | | | | | | % 151.81/22.51 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (87), (159) imply: % 151.81/22.51 | | | | | | | | | | | | | | | | | | | (160) all_52_14 = e0 % 151.81/22.51 | | | | | | | | | | | | | | | | | | | % 151.81/22.51 | | | | | | | | | | | | | | | | | | | SIMP: (160) implies: % 151.81/22.51 | | | | | | | | | | | | | | | | | | | (161) all_52_14 = e0 % 151.81/22.51 | | | | | | | | | | | | | | | | | | | % 151.81/22.51 | | | | | | | | | | | | | | | | | | | REDUCE: (15), (161) imply: % 151.81/22.51 | | | | | | | | | | | | | | | | | | | (162) ~ (all_52_6 = e0) % 151.81/22.51 | | | | | | | | | | | | | | | | | | | % 151.81/22.51 | | | | | | | | | | | | | | | | | | | BETA: splitting (65) gives: % 151.81/22.51 | | | | | | | | | | | | | | | | | | | % 151.81/22.51 | | | | | | | | | | | | | | | | | | | Case 1: % 151.81/22.51 | | | | | | | | | | | | | | | | | | | | % 151.81/22.51 | | | | | | | | | | | | | | | | | | | | (163) all_58_1 = e0 % 151.81/22.51 | | | | | | | | | | | | | | | | | | | | % 151.81/22.51 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (64), (163) imply: % 151.81/22.51 | | | | | | | | | | | | | | | | | | | | (164) all_10_0 = e0 % 151.81/22.51 | | | | | | | | | | | | | | | | | | | | % 151.81/22.51 | | | | | | | | | | | | | | | | | | | | REDUCE: (37), (164) imply: % 151.81/22.51 | | | | | | | | | | | | | | | | | | | | (165) ~ (all_52_8 = e0) % 151.81/22.51 | | | | | | | | | | | | | | | | | | | | % 151.81/22.51 | | | | | | | | | | | | | | | | | | | | BETA: splitting (31) gives: % 151.81/22.51 | | | | | | | | | | | | | | | | | | | | % 151.81/22.51 | | | | | | | | | | | | | | | | | | | | Case 1: % 151.81/22.51 | | | | | | | | | | | | | | | | | | | | | % 151.81/22.51 | | | | | | | | | | | | | | | | | | | | | (166) all_54_2 = e3 % 151.81/22.51 | | | | | | | | | | | | | | | | | | | | | % 151.81/22.51 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (55), (157), (166) are inconsistent by sub-proof % 151.81/22.51 | | | | | | | | | | | | | | | | | | | | | #728. % 151.81/22.51 | | | | | | | | | | | | | | | | | | | | | % 151.81/22.51 | | | | | | | | | | | | | | | | | | | | Case 2: % 151.81/22.51 | | | | | | | | | | | | | | | | | | | | | % 151.81/22.51 | | | | | | | | | | | | | | | | | | | | | (167) all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0 % 151.81/22.51 | | | | | | | | | | | | | | | | | | | | | % 151.81/22.51 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (167) gives: % 151.81/22.51 | | | | | | | | | | | | | | | | | | | | | % 151.81/22.51 | | | | | | | | | | | | | | | | | | | | | Case 1: % 151.81/22.51 | | | | | | | | | | | | | | | | | | | | | | % 151.81/22.51 | | | | | | | | | | | | | | | | | | | | | | (168) all_54_2 = e2 % 151.81/22.51 | | | | | | | | | | | | | | | | | | | | | | % 151.81/22.51 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (55), (126), (168) are inconsistent by sub-proof % 151.81/22.51 | | | | | | | | | | | | | | | | | | | | | | #727. % 151.81/22.51 | | | | | | | | | | | | | | | | | | | | | | % 151.81/22.51 | | | | | | | | | | | | | | | | | | | | | Case 2: % 151.81/22.51 | | | | | | | | | | | | | | | | | | | | | | % 151.81/22.51 | | | | | | | | | | | | | | | | | | | | | | (169) all_54_2 = e1 | all_54_2 = e0 % 151.81/22.51 | | | | | | | | | | | | | | | | | | | | | | % 151.81/22.51 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (55), (116), (165), (169) are inconsistent by % 151.81/22.51 | | | | | | | | | | | | | | | | | | | | | | sub-proof #724. % 151.81/22.51 | | | | | | | | | | | | | | | | | | | | | | % 151.81/22.51 | | | | | | | | | | | | | | | | | | | | | End of split % 151.81/22.51 | | | | | | | | | | | | | | | | | | | | | % 151.81/22.51 | | | | | | | | | | | | | | | | | | | | End of split % 151.81/22.51 | | | | | | | | | | | | | | | | | | | | % 151.81/22.51 | | | | | | | | | | | | | | | | | | | Case 2: % 151.81/22.51 | | | | | | | | | | | | | | | | | | | | % 151.81/22.51 | | | | | | | | | | | | | | | | | | | | (170) all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0 % 151.81/22.51 | | | | | | | | | | | | | | | | | | | | % 151.81/22.51 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (28), (49), (60), (74), (99), (162), (170) are % 151.81/22.51 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #603. % 151.81/22.51 | | | | | | | | | | | | | | | | | | | | % 151.81/22.51 | | | | | | | | | | | | | | | | | | | End of split % 151.81/22.51 | | | | | | | | | | | | | | | | | | | % 151.81/22.51 | | | | | | | | | | | | | | | | | | End of split % 151.81/22.51 | | | | | | | | | | | | | | | | | | % 151.81/22.51 | | | | | | | | | | | | | | | | | Case 2: % 151.81/22.51 | | | | | | | | | | | | | | | | | | % 151.81/22.51 | | | | | | | | | | | | | | | | | | (171) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 151.81/22.51 | | | | | | | | | | | | | | | | | | % 151.81/22.51 | | | | | | | | | | | | | | | | | | REF_CLOSE: (89), (91), (96), (151), (171) are inconsistent by % 151.81/22.51 | | | | | | | | | | | | | | | | | | sub-proof #549. % 151.81/22.51 | | | | | | | | | | | | | | | | | | % 151.81/22.51 | | | | | | | | | | | | | | | | | End of split % 151.81/22.51 | | | | | | | | | | | | | | | | | % 151.81/22.51 | | | | | | | | | | | | | | | | End of split % 151.81/22.51 | | | | | | | | | | | | | | | | % 151.81/22.51 | | | | | | | | | | | | | | | End of split % 151.81/22.51 | | | | | | | | | | | | | | | % 151.81/22.51 | | | | | | | | | | | | | | End of split % 151.81/22.51 | | | | | | | | | | | | | | % 151.81/22.51 | | | | | | | | | | | | | End of split % 151.81/22.51 | | | | | | | | | | | | | % 151.81/22.51 | | | | | | | | | | | | End of split % 151.81/22.51 | | | | | | | | | | | | % 151.81/22.51 | | | | | | | | | | | End of split % 151.81/22.51 | | | | | | | | | | | % 151.81/22.51 | | | | | | | | | | Case 2: % 151.81/22.51 | | | | | | | | | | | % 151.81/22.51 | | | | | | | | | | | (172) all_54_14 = e1 | all_54_14 = e0 % 151.81/22.51 | | | | | | | | | | | % 151.81/22.51 | | | | | | | | | | | REF_CLOSE: (17), (27), (117), (172) are inconsistent by % 151.81/22.51 | | | | | | | | | | | sub-proof #714. % 151.81/22.51 | | | | | | | | | | | % 151.81/22.51 | | | | | | | | | | End of split % 151.81/22.51 | | | | | | | | | | % 151.81/22.51 | | | | | | | | | End of split % 151.81/22.51 | | | | | | | | | % 151.81/22.51 | | | | | | | | Case 2: % 151.81/22.51 | | | | | | | | | % 151.81/22.51 | | | | | | | | | (173) all_54_10 = e0 % 151.81/22.51 | | | | | | | | | % 151.81/22.51 | | | | | | | | | COMBINE_EQS: (5), (173) imply: % 151.81/22.51 | | | | | | | | | (174) all_6_2 = e0 % 151.81/22.51 | | | | | | | | | % 151.81/22.51 | | | | | | | | | REDUCE: (101), (174) imply: % 151.81/22.51 | | | | | | | | | (175) $false % 151.81/22.51 | | | | | | | | | % 151.81/22.51 | | | | | | | | | CLOSE: (175) is inconsistent. % 151.81/22.51 | | | | | | | | | % 151.81/22.51 | | | | | | | | End of split % 151.81/22.51 | | | | | | | | % 151.81/22.51 | | | | | | | End of split % 151.81/22.51 | | | | | | | % 151.81/22.51 | | | | | | End of split % 151.81/22.51 | | | | | | % 151.81/22.51 | | | | | Case 2: % 151.81/22.51 | | | | | | % 151.81/22.51 | | | | | | (176) all_56_21 = e3 % 151.81/22.51 | | | | | | (177) all_56_17 = e1 % 151.81/22.51 | | | | | | % 151.81/22.51 | | | | | | COMBINE_EQS: (23), (177) imply: % 151.81/22.51 | | | | | | (178) all_52_2 = e1 % 151.81/22.51 | | | | | | % 151.81/22.51 | | | | | | REF_CLOSE: (2), (4), (6), (14), (16), (18), (27), (35), (53), (85), % 151.81/22.51 | | | | | | (91), (93), (96), (176), (178) are inconsistent by % 151.81/22.51 | | | | | | sub-proof #468. % 151.81/22.51 | | | | | | % 151.81/22.51 | | | | | End of split % 151.81/22.51 | | | | | % 151.81/22.51 | | | | Case 2: % 151.81/22.51 | | | | | % 151.81/22.51 | | | | | (179) all_56_21 = e2 % 151.81/22.51 | | | | | (180) all_56_19 = e1 % 151.81/22.51 | | | | | % 151.81/22.51 | | | | | COMBINE_EQS: (81), (180) imply: % 151.81/22.51 | | | | | (181) all_52_6 = e1 % 151.81/22.51 | | | | | % 151.81/22.51 | | | | | SIMP: (181) implies: % 151.81/22.51 | | | | | (182) all_52_6 = e1 % 151.81/22.51 | | | | | % 151.81/22.51 | | | | | COMBINE_EQS: (18), (179) imply: % 151.81/22.51 | | | | | (183) all_6_2 = e2 % 151.81/22.51 | | | | | % 151.81/22.51 | | | | | SIMP: (183) implies: % 151.81/22.51 | | | | | (184) all_6_2 = e2 % 151.81/22.51 | | | | | % 151.81/22.51 | | | | | REF_CLOSE: (1), (3), (6), (8), (10), (12), (13), (14), (16), (20), % 151.81/22.51 | | | | | (21), (22), (24), (25), (26), (28), (30), (34), (35), (37), % 151.81/22.51 | | | | | (38), (40), (41), (42), (45), (46), (47), (48), (49), (51), % 151.81/22.51 | | | | | (52), (53), (57), (59), (60), (61), (62), (64), (67), (68), % 151.81/22.51 | | | | | (71), (73), (77), (79), (80), (84), (86), (182), (184) are % 151.81/22.51 | | | | | inconsistent by sub-proof #361. % 151.81/22.51 | | | | | % 151.81/22.51 | | | | End of split % 151.81/22.51 | | | | % 151.81/22.51 | | | Case 2: % 151.81/22.51 | | | | % 151.81/22.51 | | | | (185) all_56_21 = e0 % 151.81/22.51 | | | | % 151.81/22.51 | | | | REF_CLOSE: (14), (18), (35), (50), (53), (185) are inconsistent by % 151.81/22.51 | | | | sub-proof #539. % 151.81/22.51 | | | | % 151.81/22.51 | | | End of split % 151.81/22.51 | | | % 151.81/22.51 | | Case 2: % 151.81/22.51 | | | % 151.81/22.51 | | | (186) all_56_11 = e0 % 151.81/22.51 | | | % 151.81/22.51 | | | COMBINE_EQS: (1), (186) imply: % 151.81/22.51 | | | (187) all_8_2 = e0 % 151.81/22.51 | | | % 151.81/22.51 | | | REDUCE: (78), (187) imply: % 151.81/22.51 | | | (188) op(e0, e0) = all_8_1 % 151.81/22.51 | | | % 151.81/22.51 | | | REF_CLOSE: (11), (35), (50), (188) are inconsistent by sub-proof #546. % 151.81/22.51 | | | % 151.81/22.51 | | End of split % 151.81/22.51 | | % 151.81/22.51 | Case 2: % 151.81/22.51 | | % 151.81/22.51 | | (189) ~ (all_26_2 = e3) % 151.81/22.51 | | % 151.81/22.51 | | REDUCE: (83), (189) imply: % 151.81/22.51 | | (190) $false % 151.81/22.51 | | % 151.81/22.51 | | CLOSE: (190) is inconsistent. % 151.81/22.51 | | % 151.81/22.51 | End of split % 151.81/22.51 | % 151.81/22.51 End of proof % 151.81/22.51 % 151.81/22.51 Sub-proof #361 shows that the following formulas are inconsistent: % 151.81/22.51 ---------------------------------------------------------------- % 151.81/22.51 (1) all_56_11 = all_8_2 % 151.81/22.51 (2) all_58_6 = all_52_2 % 151.81/22.51 (3) all_52_6 = e1 % 151.81/22.51 (4) ~ (all_6_1 = e2) % 151.81/22.51 (5) all_54_0 = all_10_2 % 151.81/22.51 (6) all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2 % 151.81/22.51 (7) all_58_4 = all_52_8 % 151.81/22.51 (8) all_54_5 = all_8_2 % 151.81/22.51 (9) ~ (all_6_1 = e3) % 151.81/22.51 (10) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 151.81/22.51 (11) ~ (all_52_7 = all_8_2) % 151.81/22.51 (12) all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2 % 151.81/22.51 (13) all_56_1 = all_10_2 % 151.81/22.51 (14) all_58_9 = all_52_12 % 151.81/22.51 (15) all_56_3 = all_10_0 % 151.81/22.51 (16) ~ (all_56_1 = e1) | all_56_5 = e3 % 151.81/22.51 (17) all_58_13 = all_52_7 % 151.81/22.51 (18) ~ (all_52_8 = all_6_2) % 151.81/22.51 (19) all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2 % 151.81/22.51 (20) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 151.81/22.51 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 151.81/22.51 (21) ~ (all_52_8 = all_10_0) % 151.81/22.51 (22) ~ (all_52_3 = all_52_7) % 151.81/22.51 (23) all_56_7 = all_52_12 % 151.81/22.51 (24) op(e2, all_52_7) = all_56_26 % 151.81/22.51 (25) ~ (all_52_1 = all_52_13) % 151.81/22.51 (26) ~ (all_52_12 = all_10_0) % 151.81/22.51 (27) ~ (all_56_1 = e2) | all_56_3 = e3 % 151.81/22.51 (28) ~ (all_56_1 = e0) | all_56_7 = e3 % 151.81/22.51 (29) all_56_5 = all_52_8 % 151.81/22.51 (30) all_58_3 = all_8_2 % 151.81/22.51 (31) all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3 % 151.81/22.51 (32) op(all_10_2, all_10_2) = e2 % 151.81/22.51 (33) op(all_6_2, all_6_2) = all_6_1 % 151.81/22.51 (34) ~ (all_52_6 = all_8_2) % 151.81/22.51 (35) all_6_2 = e2 % 151.81/22.51 (36) all_58_2 = all_52_1 % 151.81/22.51 (37) all_58_7 = all_52_6 % 151.81/22.51 (38) ~ (all_56_11 = e0) | all_56_15 = e2 % 151.81/22.51 (39) all_58_0 = all_10_2 % 151.81/22.51 (40) all_58_1 = all_10_0 % 151.81/22.51 (41) op(e2, e2) = all_8_2 % 151.81/22.51 (42) ~ (all_52_2 = all_6_2) % 151.81/22.51 (43) ~ (all_52_6 = all_6_2) % 151.81/22.51 (44) ~ (all_10_0 = all_10_2) % 151.81/22.51 (45) ~ (all_10_0 = e2) % 151.81/22.51 (46) ~ (all_52_7 = all_10_0) % 151.81/22.51 (47) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 151.81/22.51 (48) all_56_15 = all_52_13 % 151.81/22.51 (49) all_58_12 = all_52_3 % 151.81/22.51 % 151.81/22.51 Begin of proof % 151.81/22.51 | % 151.81/22.51 | COMBINE_EQS: (3), (37) imply: % 151.81/22.51 | (50) all_58_7 = e1 % 151.81/22.51 | % 151.81/22.51 | REDUCE: (35), (42) imply: % 151.81/22.51 | (51) ~ (all_52_2 = e2) % 151.81/22.51 | % 151.81/22.51 | REDUCE: (3), (34) imply: % 151.81/22.51 | (52) ~ (all_8_2 = e1) % 151.81/22.51 | % 151.81/22.51 | SIMP: (52) implies: % 151.81/22.51 | (53) ~ (all_8_2 = e1) % 151.81/22.51 | % 151.81/22.51 | REDUCE: (3), (35), (43) imply: % 151.81/22.51 | (54) ~ (e2 = e1) % 151.81/22.51 | % 151.81/22.51 | SIMP: (54) implies: % 151.81/22.51 | (55) ~ (e2 = e1) % 151.81/22.51 | % 151.81/22.51 | REDUCE: (18), (35) imply: % 151.81/22.52 | (56) ~ (all_52_8 = e2) % 151.81/22.52 | % 151.81/22.52 | REDUCE: (33), (35) imply: % 151.81/22.52 | (57) op(e2, e2) = all_6_1 % 151.81/22.52 | % 151.81/22.52 | REF_CLOSE: (1), (2), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13), % 151.81/22.52 | (14), (15), (16), (17), (19), (20), (21), (22), (23), (24), (25), % 151.81/22.52 | (26), (27), (28), (29), (30), (31), (32), (36), (38), (39), (40), % 151.81/22.52 | (41), (44), (45), (46), (47), (48), (49), (50), (51), (53), (55), % 151.81/22.52 | (56), (57) are inconsistent by sub-proof #464. % 151.81/22.52 | % 151.81/22.52 End of proof % 151.81/22.52 % 151.81/22.52 Sub-proof #362 shows that the following formulas are inconsistent: % 151.81/22.52 ---------------------------------------------------------------- % 151.81/22.52 (1) all_56_11 = all_8_2 % 151.81/22.52 (2) op(e0, all_52_13) = all_56_14 % 151.81/22.52 (3) ~ (all_56_11 = e1) | all_56_13 = e2 % 151.81/22.52 (4) ~ (all_52_11 = all_6_2) % 151.81/22.52 (5) ~ (all_52_4 = all_52_8) % 151.81/22.52 (6) ~ (all_52_8 = all_52_9) % 151.81/22.52 (7) all_54_9 = all_52_6 % 151.81/22.52 (8) op(e2, all_8_1) = all_8_0 % 151.81/22.52 (9) ~ (all_8_1 = e1) % 151.81/22.52 (10) ~ (all_52_1 = all_52_9) % 151.81/22.52 (11) ~ (e3 = e0) % 151.81/22.52 (12) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0 % 151.81/22.52 (13) all_54_10 = all_6_2 % 151.81/22.52 (14) ~ (all_6_1 = e2) % 151.81/22.52 (15) ~ (all_52_13 = all_8_2) % 151.81/22.52 (16) ~ (all_56_21 = e2) | all_56_19 = e1 % 151.81/22.52 (17) all_54_0 = all_10_2 % 151.81/22.52 (18) all_54_4 = all_52_1 % 151.81/22.52 (19) ~ (all_52_14 = all_4_2) % 151.81/22.52 (20) ~ (all_8_0 = e1) % 151.81/22.52 (21) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0 % 151.81/22.52 (22) all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2 % 151.81/22.52 (23) all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2 % 151.81/22.52 (24) ~ (all_52_9 = all_8_2) % 151.81/22.52 (25) ~ (all_52_12 = all_52_13) % 151.81/22.52 (26) ~ (all_8_1 = e3) % 151.81/22.52 (27) op(e0, e0) = all_4_2 % 151.81/22.52 (28) all_58_4 = all_52_8 % 151.81/22.52 (29) all_54_5 = all_8_2 % 151.81/22.52 (30) ~ (all_6_1 = e3) % 151.81/22.52 (31) ~ (all_52_6 = all_52_14) % 151.81/22.52 (32) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 151.81/22.52 (33) ~ (all_6_0 = e2) % 151.81/22.52 (34) ~ (all_52_11 = e0) % 151.81/22.52 (35) all_54_15 = all_4_2 % 151.81/22.52 (36) all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1 % 151.81/22.52 (37) ~ (all_10_1 = e1) % 151.81/22.52 (38) all_56_21 = all_6_2 % 151.81/22.52 (39) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 151.81/22.52 (40) all_56_1 = all_10_2 % 151.81/22.52 (41) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0 % 151.81/22.52 (42) all_58_5 = all_52_9 % 151.81/22.52 (43) all_54_1 = all_52_4 % 151.81/22.52 (44) all_56_17 = all_52_2 % 151.81/22.52 (45) all_58_9 = all_52_12 % 151.81/22.52 (46) op(e0, all_52_12) = all_56_6 % 151.81/22.52 (47) op(e0, all_52_14) = all_56_22 % 151.81/22.52 (48) op(e1, e0) = all_52_14 % 151.81/22.52 (49) ~ (all_56_1 = e1) | all_56_5 = e3 % 151.81/22.52 (50) all_54_14 = all_52_11 % 151.81/22.52 (51) all_58_1 = all_52_4 % 151.81/22.52 (52) all_58_4 = e0 | all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0 % 151.81/22.52 (53) op(e3, e3) = all_10_2 % 151.81/22.52 (54) ~ (all_52_8 = all_6_2) % 151.81/22.52 (55) all_58_15 = e2 % 151.81/22.52 (56) all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1 % 151.81/22.52 (57) ~ (all_56_21 = e3) | all_56_17 = e1 % 151.81/22.52 (58) all_58_13 = e0 % 151.81/22.52 (59) all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1 % 151.81/22.52 (60) ~ (all_52_1 = all_8_2) % 151.81/22.52 (61) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 151.81/22.52 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 151.81/22.52 (62) ~ (all_52_3 = all_10_2) % 151.81/22.52 (63) all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0 % 151.81/22.52 (64) all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) & % 151.81/22.52 (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0)) % 151.81/22.52 (65) ~ (all_52_2 = all_52_6) % 151.81/22.52 (66) op(e0, all_4_1) = all_4_0 % 151.81/22.52 (67) all_56_7 = all_52_12 % 151.81/22.52 (68) ~ (all_10_1 = e2) % 151.81/22.52 (69) op(e2, all_52_7) = all_56_26 % 151.81/22.52 (70) all_56_13 = all_52_9 % 151.81/22.52 (71) op(e0, e1) = all_52_11 % 151.81/22.52 (72) ~ (all_52_1 = all_52_13) % 151.81/22.52 (73) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0 % 151.81/22.52 (74) ~ (all_4_2 = e1) % 151.81/22.52 (75) all_58_8 = all_6_2 % 151.81/22.52 (76) ~ (all_52_8 = all_10_2) % 151.81/22.52 (77) ~ (all_56_1 = e2) | all_56_3 = e3 % 151.81/22.52 (78) ~ (all_56_1 = e0) | all_56_7 = e3 % 151.81/22.52 (79) all_56_5 = all_52_8 % 151.81/22.52 (80) all_4_2 = e2 % 151.81/22.52 (81) op(e1, all_6_1) = all_6_0 % 151.81/22.52 (82) op(all_4_2, all_4_2) = all_4_1 % 151.81/22.52 (83) all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3 % 151.81/22.52 (84) all_58_3 = all_8_2 % 151.81/22.52 (85) all_56_3 = all_52_4 % 151.81/22.52 (86) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0 % 151.81/22.52 (87) ~ (all_52_11 = all_4_2) % 151.81/22.52 (88) ~ (all_52_1 = all_52_3) % 151.81/22.52 (89) all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1 % 151.81/22.52 (90) all_56_31 = all_4_2 % 151.81/22.52 (91) all_58_11 = all_52_14 % 151.81/22.52 (92) ~ (all_52_2 = all_52_14) % 151.81/22.52 (93) ~ (all_52_9 = all_52_11) % 151.81/22.52 (94) all_54_7 = all_52_13 % 151.81/22.52 (95) op(all_6_2, all_6_2) = all_6_1 % 151.81/22.52 (96) all_56_1 = e3 | all_56_11 = e2 | all_56_21 = e1 | all_56_31 = e0 % 151.81/22.52 (97) ~ (all_52_13 = all_4_2) % 151.81/22.52 (98) ~ (e2 = e0) % 151.81/22.52 (99) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0 % 151.81/22.52 (100) ~ (all_52_13 = all_52_14) % 151.81/22.52 (101) op(e1, e1) = all_6_2 % 151.81/22.52 (102) ~ (all_52_6 = all_8_2) % 151.81/22.52 (103) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0 % 151.81/22.52 (104) all_58_15 = all_4_2 % 151.81/22.52 (105) all_58_2 = all_52_1 % 151.81/22.52 (106) ~ (all_52_9 = all_6_2) % 151.81/22.52 (107) all_58_10 = all_52_13 % 151.81/22.52 (108) ~ (all_52_12 = all_4_2) % 151.81/22.52 (109) op(all_10_2, all_10_2) = all_10_1 % 151.81/22.52 (110) all_58_0 = all_10_2 % 151.81/22.52 (111) all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1 % 151.81/22.52 (112) ~ (all_52_12 = all_52_14) % 151.81/22.52 (113) op(e1, all_52_9) = all_56_12 % 151.81/22.52 (114) op(e2, e2) = all_8_2 % 151.81/22.52 (115) ~ (all_52_4 = all_52_12) % 151.81/22.52 (116) op(e2, e0) = all_52_13 % 151.81/22.52 (117) ~ (all_52_2 = all_6_2) % 151.81/22.52 (118) ~ (all_52_8 = all_52_12) % 151.81/22.52 (119) ~ (all_56_21 = e0) | all_56_23 = e1 % 151.81/22.52 (120) ~ (all_52_6 = all_6_2) % 151.81/22.52 (121) ~ (all_8_2 = e0) % 151.81/22.52 (122) ~ (all_52_14 = all_6_2) % 151.81/22.52 (123) all_52_7 = e0 % 151.81/22.52 (124) ~ (all_52_2 = all_10_2) % 151.81/22.52 (125) ~ (all_52_4 = all_10_2) % 151.81/22.52 (126) ~ (all_52_4 = all_8_2) % 151.81/22.52 (127) op(all_8_2, all_8_2) = all_8_1 % 151.81/22.52 (128) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 151.81/22.52 (129) all_58_14 = all_52_11 % 151.81/22.52 (130) all_56_19 = all_52_6 % 151.81/22.52 (131) ~ (all_52_12 = all_10_2) % 151.81/22.52 (132) ~ (all_4_0 = e3) % 151.81/22.52 (133) ~ (all_52_1 = all_10_2) % 151.81/22.52 (134) all_58_12 = all_52_3 % 151.81/22.52 (135) all_54_11 = all_52_14 % 151.81/22.52 % 151.81/22.52 Begin of proof % 151.81/22.52 | % 151.81/22.52 | SIMP: (98) implies: % 151.81/22.52 | (136) ~ (e2 = e0) % 151.81/22.52 | % 151.81/22.52 | REDUCE: (80), (87) imply: % 151.81/22.52 | (137) ~ (all_52_11 = e2) % 151.81/22.52 | % 151.81/22.52 | REDUCE: (80), (108) imply: % 151.81/22.52 | (138) ~ (all_52_12 = e2) % 151.81/22.52 | % 151.81/22.52 | REDUCE: (80), (97) imply: % 151.81/22.52 | (139) ~ (all_52_13 = e2) % 151.81/22.52 | % 151.81/22.52 | REDUCE: (80), (82) imply: % 151.81/22.52 | (140) op(e2, e2) = all_4_1 % 151.81/22.52 | % 151.81/22.52 | REDUCE: (69), (123) imply: % 151.81/22.52 | (141) op(e2, e0) = all_56_26 % 151.81/22.52 | % 151.81/22.52 | REDUCE: (27), (80) imply: % 151.81/22.52 | (142) op(e0, e0) = e2 % 151.81/22.52 | % 151.81/22.52 | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), % 151.81/22.52 | (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23), % 151.81/22.52 | (24), (25), (26), (27), (28), (29), (30), (31), (32), (33), (34), % 151.81/22.52 | (35), (36), (37), (38), (39), (40), (41), (42), (43), (44), (45), % 151.81/22.52 | (46), (47), (48), (49), (50), (51), (52), (53), (54), (55), (56), % 151.81/22.52 | (57), (58), (59), (60), (61), (62), (63), (64), (65), (66), (67), % 151.81/22.52 | (68), (70), (71), (72), (73), (74), (75), (76), (77), (78), (79), % 151.81/22.52 | (81), (83), (84), (85), (86), (88), (89), (90), (91), (92), (93), % 151.81/22.52 | (94), (95), (96), (97), (99), (100), (101), (102), (103), (104), % 151.81/22.52 | (105), (106), (107), (108), (109), (110), (111), (112), (113), % 151.81/22.52 | (114), (115), (116), (117), (118), (119), (120), (121), (122), % 151.81/22.52 | (124), (125), (126), (127), (128), (129), (130), (131), (132), % 151.81/22.52 | (133), (134), (135), (136), (137), (138), (139), (140), (141), % 151.81/22.52 | (142) are inconsistent by sub-proof #564. % 151.81/22.52 | % 151.81/22.52 End of proof % 151.81/22.52 % 151.81/22.52 Sub-proof #363 shows that the following formulas are inconsistent: % 151.81/22.52 ---------------------------------------------------------------- % 151.81/22.52 (1) op(e0, e0) = all_4_2 % 151.81/22.52 (2) all_54_15 = all_4_2 % 151.81/22.52 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 151.81/22.52 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 151.81/22.52 (4) op(e0, all_4_1) = e1 % 151.81/22.52 (5) ~ (all_4_2 = e1) % 151.81/22.52 (6) ~ (all_4_2 = e2) % 151.81/22.52 (7) op(all_4_2, all_4_2) = all_4_1 % 151.81/22.52 (8) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0 % 151.81/22.52 (9) ~ (all_4_2 = e3) % 151.81/22.52 (10) op(e0, all_4_2) = all_56_30 % 151.81/22.52 % 151.81/22.52 Begin of proof % 151.81/22.52 | % 151.81/22.52 | BETA: splitting (8) gives: % 151.81/22.52 | % 151.81/22.52 | Case 1: % 151.81/22.52 | | % 151.81/22.52 | | (11) all_54_15 = e3 % 151.81/22.52 | | % 151.81/22.52 | | REF_CLOSE: (2), (9), (11) are inconsistent by sub-proof #740. % 151.81/22.52 | | % 151.81/22.52 | Case 2: % 151.81/22.52 | | % 151.81/22.52 | | (12) all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0 % 151.81/22.52 | | % 151.81/22.52 | | BETA: splitting (12) gives: % 151.81/22.52 | | % 151.81/22.52 | | Case 1: % 151.81/22.52 | | | % 151.81/22.52 | | | (13) all_54_15 = e2 % 151.81/22.52 | | | % 151.81/22.52 | | | REF_CLOSE: (2), (6), (13) are inconsistent by sub-proof #739. % 151.81/22.52 | | | % 151.81/22.52 | | Case 2: % 151.81/22.52 | | | % 151.81/22.52 | | | (14) all_54_15 = e1 | all_54_15 = e0 % 151.81/22.52 | | | % 151.81/22.52 | | | BETA: splitting (14) gives: % 151.81/22.52 | | | % 151.81/22.52 | | | Case 1: % 151.81/22.52 | | | | % 151.81/22.52 | | | | (15) all_54_15 = e1 % 151.81/22.52 | | | | % 151.81/22.52 | | | | REF_CLOSE: (2), (5), (15) are inconsistent by sub-proof #738. % 151.81/22.52 | | | | % 151.81/22.52 | | | Case 2: % 151.81/22.52 | | | | % 151.81/22.52 | | | | (16) all_54_15 = e0 % 151.81/22.52 | | | | % 151.81/22.52 | | | | COMBINE_EQS: (2), (16) imply: % 151.81/22.52 | | | | (17) all_4_2 = e0 % 151.81/22.52 | | | | % 151.81/22.52 | | | | SIMP: (17) implies: % 151.81/22.52 | | | | (18) all_4_2 = e0 % 151.81/22.52 | | | | % 151.81/22.52 | | | | REDUCE: (5), (18) imply: % 151.81/22.52 | | | | (19) ~ (e1 = e0) % 151.81/22.52 | | | | % 151.81/22.52 | | | | SIMP: (19) implies: % 151.81/22.52 | | | | (20) ~ (e1 = e0) % 151.81/22.52 | | | | % 151.81/22.52 | | | | REDUCE: (7), (18) imply: % 151.81/22.52 | | | | (21) op(e0, e0) = all_4_1 % 151.81/22.52 | | | | % 151.81/22.52 | | | | REDUCE: (10), (18) imply: % 151.81/22.52 | | | | (22) op(e0, e0) = all_56_30 % 151.81/22.52 | | | | % 151.81/22.52 | | | | REDUCE: (1), (18) imply: % 151.81/22.52 | | | | (23) op(e0, e0) = e0 % 151.81/22.52 | | | | % 151.81/22.52 | | | | GROUND_INST: instantiating (3) with all_4_1, all_56_30, e0, e0, % 151.81/22.52 | | | | simplifying with (21), (22) gives: % 151.81/22.52 | | | | (24) all_56_30 = all_4_1 % 151.81/22.52 | | | | % 151.81/22.52 | | | | GROUND_INST: instantiating (3) with e0, all_56_30, e0, e0, simplifying % 151.81/22.52 | | | | with (22), (23) gives: % 151.81/22.52 | | | | (25) all_56_30 = e0 % 151.81/22.52 | | | | % 151.81/22.52 | | | | COMBINE_EQS: (24), (25) imply: % 151.81/22.52 | | | | (26) all_4_1 = e0 % 151.81/22.52 | | | | % 151.81/22.52 | | | | SIMP: (26) implies: % 151.81/22.52 | | | | (27) all_4_1 = e0 % 151.81/22.52 | | | | % 151.81/22.52 | | | | REDUCE: (4), (27) imply: % 151.81/22.52 | | | | (28) op(e0, e0) = e1 % 151.81/22.52 | | | | % 151.81/22.52 | | | | REF_CLOSE: (3), (20), (21), (22), (23), (28) are inconsistent by % 151.81/22.52 | | | | sub-proof #389. % 151.81/22.52 | | | | % 151.81/22.52 | | | End of split % 151.81/22.52 | | | % 151.81/22.52 | | End of split % 151.81/22.52 | | % 151.81/22.52 | End of split % 151.81/22.52 | % 151.81/22.52 End of proof % 151.81/22.52 % 151.81/22.52 Sub-proof #364 shows that the following formulas are inconsistent: % 151.81/22.52 ---------------------------------------------------------------- % 151.81/22.52 (1) all_56_11 = all_8_2 % 151.81/22.52 (2) ~ (all_52_11 = all_6_2) % 151.81/22.52 (3) ~ (all_52_7 = all_52_11) % 151.81/22.52 (4) ~ (all_56_31 = e1) | all_56_29 = e0 % 151.81/22.52 (5) all_54_10 = all_6_2 % 151.81/22.52 (6) ~ (all_6_1 = e2) % 151.81/22.52 (7) ~ (all_56_21 = e2) | all_56_19 = e1 % 151.81/22.52 (8) all_54_0 = all_10_2 % 151.81/22.52 (9) all_54_12 = all_52_3 % 151.81/22.53 (10) op(e0, e0) = all_4_2 % 151.81/22.53 (11) all_58_4 = all_52_8 % 151.81/22.53 (12) all_54_5 = all_8_2 % 151.81/22.53 (13) ~ (all_52_6 = all_52_14) % 151.81/22.53 (14) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 151.81/22.53 (15) all_6_0 = e2 % 151.81/22.53 (16) all_54_15 = all_4_2 % 151.81/22.53 (17) all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1 % 151.81/22.53 (18) all_56_21 = all_6_2 % 151.81/22.53 (19) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 151.81/22.53 (20) all_56_1 = all_10_2 % 151.81/22.53 (21) all_56_17 = all_52_2 % 151.81/22.53 (22) all_58_9 = all_52_12 % 151.81/22.53 (23) op(e0, e2) = all_52_7 % 151.81/22.53 (24) op(e1, e0) = all_52_14 % 151.81/22.53 (25) all_28_1 = all_6_1 % 151.81/22.53 (26) all_58_1 = all_52_4 % 151.81/22.53 (27) op(e3, e3) = all_10_2 % 151.81/22.53 (28) ~ (all_56_21 = e3) | all_56_17 = e1 % 151.81/22.53 (29) all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0 % 151.81/22.53 (30) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 151.81/22.53 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 151.81/22.53 (31) op(e0, all_4_1) = all_4_0 % 151.81/22.53 (32) all_56_7 = all_52_12 % 151.81/22.53 (33) all_46_2 = all_6_2 % 151.81/22.53 (34) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0 % 151.81/22.53 (35) all_28_2 = all_6_2 % 151.81/22.53 (36) op(e1, e3) = all_52_2 % 151.81/22.53 (37) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0 % 151.81/22.53 (38) ~ (all_56_1 = e0) | all_56_7 = e3 % 151.81/22.53 (39) all_46_0 = all_6_0 % 151.81/22.53 (40) ~ (e2 = e1) % 151.81/22.53 (41) ~ (all_52_2 = all_52_3) % 151.81/22.53 (42) op(e1, all_6_1) = all_6_0 % 151.81/22.53 (43) op(all_4_2, all_4_2) = all_4_1 % 151.81/22.53 (44) ~ (all_52_3 = all_52_11) % 151.81/22.53 (45) ~ (all_52_6 = all_52_7) % 151.81/22.53 (46) op(e1, all_52_8) = all_56_4 % 151.81/22.53 (47) all_56_31 = all_4_2 % 151.81/22.53 (48) all_58_11 = all_52_14 % 151.81/22.53 (49) op(all_6_2, all_6_2) = all_6_1 % 151.81/22.53 (50) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0 % 151.81/22.53 (51) all_54_13 = all_52_7 % 151.81/22.53 (52) ~ (all_52_13 = all_52_14) % 151.81/22.53 (53) ~ (all_28_1 = e3) | ~ (all_28_2 = e0) % 151.81/22.53 (54) all_56_23 = all_52_14 % 151.81/22.53 (55) all_46_1 = all_6_1 % 151.81/22.53 (56) op(e1, e1) = all_6_2 % 151.81/22.53 (57) ~ (all_52_6 = all_8_2) % 151.81/22.53 (58) op(e0, e3) = all_52_3 % 151.81/22.53 (59) all_58_15 = all_4_2 % 151.81/22.53 (60) all_56_29 = all_52_11 % 151.81/22.53 (61) all_58_10 = all_52_13 % 151.81/22.53 (62) ~ (all_56_11 = e0) | all_56_15 = e2 % 151.81/22.53 (63) all_58_0 = all_10_2 % 151.81/22.53 (64) op(e1, all_6_2) = all_56_20 % 151.81/22.53 (65) ~ (all_56_31 = e2) | all_56_27 = e0 % 151.81/22.53 (66) ~ (e3 = e1) % 151.81/22.53 (67) op(e2, e2) = all_8_2 % 151.81/22.53 (68) ~ (all_52_2 = all_6_2) % 151.81/22.53 (69) ~ (all_56_21 = e0) | all_56_23 = e1 % 151.81/22.53 (70) op(e0, all_4_2) = all_56_30 % 151.81/22.53 (71) ~ (all_52_6 = all_6_2) % 151.81/22.53 (72) ~ (all_52_2 = all_10_2) % 151.81/22.53 (73) ~ (all_46_0 = e2) | ~ (all_46_1 = e0) | ~ (all_46_2 = e3) % 151.81/22.53 (74) ~ (all_52_4 = all_8_2) % 151.81/22.53 (75) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 151.81/22.53 (76) all_56_19 = all_52_6 % 151.81/22.53 (77) ~ (all_4_0 = e2) % 151.81/22.53 (78) ~ (all_4_0 = e3) % 151.81/22.53 (79) all_56_15 = all_52_13 % 151.81/22.53 (80) ~ (all_56_31 = e3) | all_56_25 = e0 % 151.81/22.53 % 151.81/22.53 Begin of proof % 151.81/22.53 | % 151.81/22.53 | COMBINE_EQS: (15), (39) imply: % 151.81/22.53 | (81) all_46_0 = e2 % 151.81/22.53 | % 151.81/22.53 | REDUCE: (15), (42) imply: % 151.81/22.53 | (82) op(e1, all_6_1) = e2 % 151.81/22.53 | % 151.81/22.53 | BETA: splitting (73) gives: % 151.81/22.53 | % 151.81/22.53 | Case 1: % 151.81/22.53 | | % 151.81/22.53 | | (83) ~ (all_46_0 = e2) % 151.81/22.53 | | % 151.81/22.53 | | REDUCE: (81), (83) imply: % 151.81/22.53 | | (84) $false % 151.81/22.53 | | % 151.81/22.53 | | CLOSE: (84) is inconsistent. % 151.81/22.53 | | % 151.81/22.53 | Case 2: % 151.81/22.53 | | % 151.81/22.53 | | (85) ~ (all_46_1 = e0) | ~ (all_46_2 = e3) % 151.81/22.53 | | % 151.81/22.53 | | BETA: splitting (4) gives: % 151.81/22.53 | | % 151.81/22.53 | | Case 1: % 151.81/22.53 | | | % 151.81/22.53 | | | (86) ~ (all_56_31 = e1) % 151.81/22.53 | | | % 151.81/22.53 | | | REDUCE: (47), (86) imply: % 151.81/22.53 | | | (87) ~ (all_4_2 = e1) % 151.81/22.53 | | | % 151.89/22.53 | | | REF_CLOSE: (1), (5), (6), (7), (8), (10), (11), (12), (13), (14), (16), % 151.89/22.53 | | | (17), (18), (19), (20), (21), (22), (24), (25), (26), (27), % 151.89/22.53 | | | (28), (29), (30), (31), (32), (33), (35), (36), (38), (40), % 151.89/22.53 | | | (43), (46), (47), (48), (49), (50), (52), (53), (54), (55), % 151.89/22.53 | | | (56), (57), (59), (61), (62), (63), (64), (65), (66), (67), % 151.89/22.53 | | | (68), (69), (70), (71), (72), (74), (75), (76), (79), (80), % 151.89/22.53 | | | (82), (85), (87) are inconsistent by sub-proof #366. % 151.89/22.53 | | | % 151.89/22.53 | | Case 2: % 151.89/22.53 | | | % 151.89/22.53 | | | (88) all_56_31 = e1 % 151.89/22.53 | | | (89) all_56_29 = e0 % 151.89/22.53 | | | % 151.89/22.53 | | | COMBINE_EQS: (60), (89) imply: % 151.89/22.53 | | | (90) all_52_11 = e0 % 151.89/22.53 | | | % 151.89/22.53 | | | SIMP: (90) implies: % 151.89/22.53 | | | (91) all_52_11 = e0 % 151.89/22.53 | | | % 151.89/22.53 | | | COMBINE_EQS: (47), (88) imply: % 151.89/22.53 | | | (92) all_4_2 = e1 % 151.89/22.53 | | | % 151.89/22.53 | | | REDUCE: (44), (91) imply: % 151.89/22.53 | | | (93) ~ (all_52_3 = e0) % 151.89/22.53 | | | % 151.89/22.53 | | | REDUCE: (3), (91) imply: % 151.89/22.53 | | | (94) ~ (all_52_7 = e0) % 151.89/22.53 | | | % 151.89/22.53 | | | REDUCE: (2), (91) imply: % 151.89/22.53 | | | (95) ~ (all_6_2 = e0) % 151.89/22.53 | | | % 151.89/22.53 | | | SIMP: (95) implies: % 151.89/22.53 | | | (96) ~ (all_6_2 = e0) % 151.89/22.53 | | | % 151.89/22.53 | | | REDUCE: (43), (92) imply: % 151.89/22.53 | | | (97) op(e1, e1) = all_4_1 % 151.89/22.53 | | | % 151.89/22.53 | | | GROUND_INST: instantiating (30) with all_6_2, all_4_1, e1, e1, simplifying % 151.89/22.53 | | | with (56), (97) gives: % 151.89/22.53 | | | (98) all_6_2 = all_4_1 % 151.89/22.53 | | | % 151.89/22.53 | | | COMBINE_EQS: (5), (98) imply: % 151.89/22.53 | | | (99) all_54_10 = all_4_1 % 151.89/22.53 | | | % 151.89/22.53 | | | COMBINE_EQS: (18), (98) imply: % 151.89/22.53 | | | (100) all_56_21 = all_4_1 % 151.89/22.53 | | | % 151.89/22.53 | | | BETA: splitting (7) gives: % 151.89/22.53 | | | % 151.89/22.53 | | | Case 1: % 151.89/22.53 | | | | % 151.89/22.53 | | | | (101) ~ (all_56_21 = e2) % 151.89/22.53 | | | | % 151.89/22.53 | | | | REDUCE: (100), (101) imply: % 151.89/22.53 | | | | (102) ~ (all_4_1 = e2) % 151.89/22.53 | | | | % 151.89/22.53 | | | | BETA: splitting (28) gives: % 151.89/22.53 | | | | % 151.89/22.53 | | | | Case 1: % 151.89/22.53 | | | | | % 151.89/22.53 | | | | | (103) ~ (all_56_21 = e3) % 151.89/22.53 | | | | | % 151.89/22.53 | | | | | REDUCE: (100), (103) imply: % 151.89/22.53 | | | | | (104) ~ (all_4_1 = e3) % 151.89/22.53 | | | | | % 151.89/22.53 | | | | | BETA: splitting (19) gives: % 151.89/22.53 | | | | | % 151.89/22.53 | | | | | Case 1: % 151.89/22.53 | | | | | | % 151.89/22.53 | | | | | | (105) all_54_10 = e3 % 151.89/22.53 | | | | | | % 151.89/22.53 | | | | | | COMBINE_EQS: (99), (105) imply: % 151.89/22.53 | | | | | | (106) all_4_1 = e3 % 151.89/22.53 | | | | | | % 151.89/22.53 | | | | | | REDUCE: (104), (106) imply: % 151.89/22.53 | | | | | | (107) $false % 151.89/22.53 | | | | | | % 151.89/22.53 | | | | | | CLOSE: (107) is inconsistent. % 151.89/22.53 | | | | | | % 151.89/22.53 | | | | | Case 2: % 151.89/22.53 | | | | | | % 151.89/22.53 | | | | | | (108) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 151.89/22.53 | | | | | | % 151.89/22.53 | | | | | | BETA: splitting (108) gives: % 151.89/22.53 | | | | | | % 151.89/22.53 | | | | | | Case 1: % 151.89/22.53 | | | | | | | % 151.89/22.53 | | | | | | | (109) all_54_10 = e2 % 151.89/22.53 | | | | | | | % 151.89/22.53 | | | | | | | COMBINE_EQS: (99), (109) imply: % 151.89/22.53 | | | | | | | (110) all_4_1 = e2 % 151.89/22.53 | | | | | | | % 151.89/22.53 | | | | | | | REDUCE: (102), (110) imply: % 151.89/22.53 | | | | | | | (111) $false % 151.89/22.53 | | | | | | | % 151.89/22.53 | | | | | | | CLOSE: (111) is inconsistent. % 151.89/22.53 | | | | | | | % 151.89/22.53 | | | | | | Case 2: % 151.89/22.53 | | | | | | | % 151.89/22.53 | | | | | | | (112) all_54_10 = e1 | all_54_10 = e0 % 151.89/22.53 | | | | | | | % 151.89/22.53 | | | | | | | REF_CLOSE: (5), (6), (30), (49), (56), (64), (82), (96), (112) are % 151.89/22.53 | | | | | | | inconsistent by sub-proof #377. % 151.89/22.53 | | | | | | | % 151.89/22.53 | | | | | | End of split % 151.89/22.53 | | | | | | % 151.89/22.53 | | | | | End of split % 151.89/22.53 | | | | | % 151.89/22.53 | | | | Case 2: % 151.89/22.53 | | | | | % 151.89/22.53 | | | | | (113) all_56_21 = e3 % 151.89/22.53 | | | | | (114) all_56_17 = e1 % 151.89/22.53 | | | | | % 151.89/22.53 | | | | | REF_CLOSE: (9), (21), (30), (31), (34), (41), (58), (77), (78), (93), % 151.89/22.53 | | | | | (100), (113), (114) are inconsistent by sub-proof #365. % 151.89/22.53 | | | | | % 151.89/22.53 | | | | End of split % 151.89/22.53 | | | | % 151.89/22.53 | | | Case 2: % 151.89/22.53 | | | | % 151.89/22.53 | | | | (115) all_56_21 = e2 % 151.89/22.53 | | | | (116) all_56_19 = e1 % 151.89/22.53 | | | | % 151.89/22.53 | | | | REF_CLOSE: (23), (30), (31), (37), (45), (51), (76), (77), (78), (94), % 151.89/22.53 | | | | (100), (115), (116) are inconsistent by sub-proof #500. % 151.89/22.53 | | | | % 151.89/22.53 | | | End of split % 151.89/22.53 | | | % 151.89/22.53 | | End of split % 151.89/22.53 | | % 151.89/22.53 | End of split % 151.89/22.53 | % 151.89/22.53 End of proof % 151.89/22.53 % 151.89/22.53 Sub-proof #365 shows that the following formulas are inconsistent: % 151.89/22.53 ---------------------------------------------------------------- % 151.89/22.53 (1) all_56_21 = e3 % 151.89/22.53 (2) all_54_12 = all_52_3 % 151.89/22.53 (3) all_56_17 = all_52_2 % 151.89/22.53 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 151.89/22.53 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 151.89/22.53 (5) op(e0, all_4_1) = all_4_0 % 151.89/22.53 (6) ~ (all_52_3 = e0) % 151.89/22.53 (7) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0 % 151.89/22.53 (8) all_56_21 = all_4_1 % 151.89/22.53 (9) ~ (all_52_2 = all_52_3) % 151.89/22.53 (10) all_56_17 = e1 % 151.89/22.53 (11) op(e0, e3) = all_52_3 % 151.89/22.53 (12) ~ (all_4_0 = e2) % 151.89/22.53 (13) ~ (all_4_0 = e3) % 151.89/22.53 % 151.89/22.53 Begin of proof % 151.89/22.53 | % 151.89/22.53 | COMBINE_EQS: (3), (10) imply: % 151.89/22.53 | (14) all_52_2 = e1 % 151.89/22.53 | % 151.89/22.53 | COMBINE_EQS: (1), (8) imply: % 151.89/22.53 | (15) all_4_1 = e3 % 151.89/22.53 | % 151.89/22.53 | SIMP: (15) implies: % 151.89/22.53 | (16) all_4_1 = e3 % 151.89/22.53 | % 151.89/22.53 | REF_CLOSE: (2), (4), (5), (6), (7), (9), (11), (12), (13), (14), (16) are % 151.89/22.53 | inconsistent by sub-proof #521. % 151.89/22.53 | % 151.89/22.53 End of proof % 151.89/22.53 % 151.89/22.53 Sub-proof #366 shows that the following formulas are inconsistent: % 151.89/22.53 ---------------------------------------------------------------- % 151.89/22.53 (1) all_56_11 = all_8_2 % 151.89/22.53 (2) all_54_10 = all_6_2 % 151.89/22.53 (3) ~ (all_6_1 = e2) % 151.89/22.53 (4) ~ (all_56_21 = e2) | all_56_19 = e1 % 151.89/22.53 (5) all_54_0 = all_10_2 % 151.89/22.53 (6) op(e0, e0) = all_4_2 % 151.89/22.53 (7) all_58_4 = all_52_8 % 151.89/22.53 (8) all_54_5 = all_8_2 % 151.89/22.53 (9) ~ (all_52_6 = all_52_14) % 151.89/22.53 (10) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 151.89/22.53 (11) all_54_15 = all_4_2 % 151.89/22.53 (12) all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1 % 151.89/22.53 (13) all_56_21 = all_6_2 % 151.89/22.53 (14) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 151.89/22.53 (15) all_56_1 = all_10_2 % 151.89/22.53 (16) all_56_17 = all_52_2 % 151.89/22.53 (17) all_58_9 = all_52_12 % 151.89/22.53 (18) op(e1, e0) = all_52_14 % 151.89/22.53 (19) all_28_1 = all_6_1 % 151.89/22.53 (20) all_58_1 = all_52_4 % 151.89/22.53 (21) op(e3, e3) = all_10_2 % 151.89/22.53 (22) ~ (all_56_21 = e3) | all_56_17 = e1 % 151.89/22.53 (23) all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0 % 151.89/22.53 (24) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 151.89/22.53 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 151.89/22.53 (25) op(e0, all_4_1) = all_4_0 % 151.89/22.53 (26) all_56_7 = all_52_12 % 151.89/22.53 (27) all_46_2 = all_6_2 % 151.89/22.53 (28) all_28_2 = all_6_2 % 151.89/22.53 (29) op(e1, e3) = all_52_2 % 151.89/22.53 (30) ~ (all_4_2 = e1) % 151.89/22.53 (31) ~ (all_46_1 = e0) | ~ (all_46_2 = e3) % 151.89/22.53 (32) ~ (all_56_1 = e0) | all_56_7 = e3 % 151.89/22.53 (33) ~ (e2 = e1) % 151.89/22.53 (34) op(all_4_2, all_4_2) = all_4_1 % 151.89/22.53 (35) op(e1, all_52_8) = all_56_4 % 151.89/22.53 (36) all_56_31 = all_4_2 % 151.89/22.53 (37) all_58_11 = all_52_14 % 151.89/22.53 (38) op(e1, all_6_1) = e2 % 151.89/22.53 (39) op(all_6_2, all_6_2) = all_6_1 % 151.89/22.53 (40) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0 % 151.89/22.53 (41) ~ (all_52_13 = all_52_14) % 151.89/22.53 (42) ~ (all_28_1 = e3) | ~ (all_28_2 = e0) % 151.89/22.53 (43) all_56_23 = all_52_14 % 151.89/22.53 (44) all_46_1 = all_6_1 % 151.89/22.53 (45) op(e1, e1) = all_6_2 % 151.89/22.53 (46) ~ (all_52_6 = all_8_2) % 151.89/22.53 (47) all_58_15 = all_4_2 % 151.89/22.53 (48) all_58_10 = all_52_13 % 151.89/22.53 (49) ~ (all_56_11 = e0) | all_56_15 = e2 % 151.89/22.53 (50) all_58_0 = all_10_2 % 151.89/22.53 (51) op(e1, all_6_2) = all_56_20 % 151.89/22.53 (52) ~ (all_56_31 = e2) | all_56_27 = e0 % 151.89/22.53 (53) ~ (e3 = e1) % 151.89/22.53 (54) op(e2, e2) = all_8_2 % 151.89/22.53 (55) ~ (all_52_2 = all_6_2) % 151.89/22.53 (56) ~ (all_56_21 = e0) | all_56_23 = e1 % 151.89/22.53 (57) op(e0, all_4_2) = all_56_30 % 151.89/22.53 (58) ~ (all_52_6 = all_6_2) % 151.89/22.53 (59) ~ (all_52_2 = all_10_2) % 151.89/22.53 (60) ~ (all_52_4 = all_8_2) % 151.89/22.53 (61) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 151.89/22.53 (62) all_56_19 = all_52_6 % 151.89/22.53 (63) all_56_15 = all_52_13 % 151.89/22.53 (64) ~ (all_56_31 = e3) | all_56_25 = e0 % 151.89/22.53 % 151.89/22.53 Begin of proof % 151.89/22.53 | % 151.89/22.53 | BETA: splitting (64) gives: % 151.89/22.53 | % 151.89/22.53 | Case 1: % 151.89/22.53 | | % 151.89/22.53 | | (65) ~ (all_56_31 = e3) % 151.89/22.53 | | % 151.89/22.53 | | REDUCE: (36), (65) imply: % 151.89/22.53 | | (66) ~ (all_4_2 = e3) % 151.89/22.53 | | % 151.89/22.53 | | BETA: splitting (52) gives: % 151.89/22.53 | | % 151.89/22.53 | | Case 1: % 151.89/22.53 | | | % 151.89/22.53 | | | (67) ~ (all_56_31 = e2) % 151.89/22.53 | | | % 151.89/22.53 | | | REDUCE: (36), (67) imply: % 151.89/22.53 | | | (68) ~ (all_4_2 = e2) % 151.89/22.53 | | | % 151.89/22.53 | | | BETA: splitting (40) gives: % 151.89/22.53 | | | % 151.89/22.53 | | | Case 1: % 151.89/22.53 | | | | % 151.89/22.53 | | | | (69) all_54_15 = e3 % 151.89/22.53 | | | | % 151.89/22.53 | | | | REF_CLOSE: (11), (66), (69) are inconsistent by sub-proof #740. % 151.89/22.53 | | | | % 151.89/22.53 | | | Case 2: % 151.89/22.53 | | | | % 151.89/22.53 | | | | (70) all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0 % 151.89/22.53 | | | | % 151.89/22.53 | | | | BETA: splitting (70) gives: % 151.89/22.53 | | | | % 151.89/22.53 | | | | Case 1: % 151.89/22.53 | | | | | % 151.89/22.53 | | | | | (71) all_54_15 = e2 % 151.89/22.53 | | | | | % 151.89/22.53 | | | | | REF_CLOSE: (11), (68), (71) are inconsistent by sub-proof #739. % 151.89/22.53 | | | | | % 151.89/22.53 | | | | Case 2: % 151.89/22.53 | | | | | % 151.89/22.53 | | | | | (72) all_54_15 = e1 | all_54_15 = e0 % 151.89/22.53 | | | | | % 151.89/22.53 | | | | | BETA: splitting (72) gives: % 151.89/22.53 | | | | | % 151.89/22.53 | | | | | Case 1: % 151.89/22.53 | | | | | | % 151.89/22.53 | | | | | | (73) all_54_15 = e1 % 151.89/22.53 | | | | | | % 151.89/22.53 | | | | | | REF_CLOSE: (11), (30), (73) are inconsistent by sub-proof #738. % 151.89/22.53 | | | | | | % 151.89/22.53 | | | | | Case 2: % 151.89/22.53 | | | | | | % 151.89/22.53 | | | | | | (74) all_54_15 = e0 % 151.89/22.53 | | | | | | % 151.89/22.53 | | | | | | COMBINE_EQS: (11), (74) imply: % 151.89/22.53 | | | | | | (75) all_4_2 = e0 % 151.89/22.53 | | | | | | % 151.89/22.53 | | | | | | SIMP: (75) implies: % 151.89/22.53 | | | | | | (76) all_4_2 = e0 % 151.89/22.53 | | | | | | % 151.89/22.53 | | | | | | REDUCE: (34), (76) imply: % 151.89/22.53 | | | | | | (77) op(e0, e0) = all_4_1 % 151.89/22.53 | | | | | | % 151.89/22.53 | | | | | | REDUCE: (57), (76) imply: % 151.89/22.53 | | | | | | (78) op(e0, e0) = all_56_30 % 151.89/22.53 | | | | | | % 151.89/22.53 | | | | | | REDUCE: (6), (76) imply: % 151.89/22.53 | | | | | | (79) op(e0, e0) = e0 % 151.89/22.53 | | | | | | % 151.89/22.53 | | | | | | GROUND_INST: instantiating (24) with all_4_1, all_56_30, e0, e0, % 151.89/22.53 | | | | | | simplifying with (77), (78) gives: % 151.89/22.53 | | | | | | (80) all_56_30 = all_4_1 % 151.89/22.53 | | | | | | % 151.89/22.53 | | | | | | GROUND_INST: instantiating (24) with e0, all_56_30, e0, e0, % 151.89/22.53 | | | | | | simplifying with (78), (79) gives: % 151.89/22.53 | | | | | | (81) all_56_30 = e0 % 151.89/22.53 | | | | | | % 151.89/22.53 | | | | | | COMBINE_EQS: (80), (81) imply: % 151.89/22.53 | | | | | | (82) all_4_1 = e0 % 151.89/22.53 | | | | | | % 151.89/22.53 | | | | | | SIMP: (82) implies: % 151.89/22.53 | | | | | | (83) all_4_1 = e0 % 151.89/22.53 | | | | | | % 151.89/22.53 | | | | | | REDUCE: (25), (83) imply: % 151.89/22.53 | | | | | | (84) op(e0, e0) = all_4_0 % 151.89/22.53 | | | | | | % 151.89/22.54 | | | | | | GROUND_INST: instantiating (24) with e0, all_4_0, e0, e0, % 151.89/22.54 | | | | | | simplifying with (79), (84) gives: % 151.89/22.54 | | | | | | (85) all_4_0 = e0 % 151.89/22.54 | | | | | | % 151.89/22.54 | | | | | | BETA: splitting (4) gives: % 151.89/22.54 | | | | | | % 151.89/22.54 | | | | | | Case 1: % 151.89/22.54 | | | | | | | % 151.89/22.54 | | | | | | | (86) ~ (all_56_21 = e2) % 151.89/22.54 | | | | | | | % 151.89/22.54 | | | | | | | REDUCE: (13), (86) imply: % 151.89/22.54 | | | | | | | (87) ~ (all_6_2 = e2) % 151.89/22.54 | | | | | | | % 151.89/22.54 | | | | | | | BETA: splitting (56) gives: % 151.89/22.54 | | | | | | | % 151.89/22.54 | | | | | | | Case 1: % 151.89/22.54 | | | | | | | | % 151.89/22.54 | | | | | | | | (88) ~ (all_56_21 = e0) % 151.89/22.54 | | | | | | | | % 151.89/22.54 | | | | | | | | REDUCE: (13), (88) imply: % 151.89/22.54 | | | | | | | | (89) ~ (all_6_2 = e0) % 151.89/22.54 | | | | | | | | % 151.89/22.54 | | | | | | | | REF_CLOSE: (2), (3), (5), (10), (13), (14), (16), (21), (22), % 151.89/22.54 | | | | | | | | (24), (27), (29), (31), (33), (38), (39), (44), (45), % 151.89/22.54 | | | | | | | | (51), (59), (87), (89) are inconsistent by sub-proof % 151.89/22.54 | | | | | | | | #372. % 151.89/22.54 | | | | | | | | % 151.89/22.54 | | | | | | | Case 2: % 151.89/22.54 | | | | | | | | % 151.89/22.54 | | | | | | | | (90) all_56_23 = e1 % 151.89/22.54 | | | | | | | | (91) all_56_21 = e0 % 151.89/22.54 | | | | | | | | % 151.89/22.54 | | | | | | | | COMBINE_EQS: (13), (91) imply: % 151.89/22.54 | | | | | | | | (92) all_6_2 = e0 % 151.89/22.54 | | | | | | | | % 151.89/22.54 | | | | | | | | SIMP: (92) implies: % 151.89/22.54 | | | | | | | | (93) all_6_2 = e0 % 151.89/22.54 | | | | | | | | % 151.89/22.54 | | | | | | | | COMBINE_EQS: (43), (90) imply: % 151.89/22.54 | | | | | | | | (94) all_52_14 = e1 % 151.89/22.54 | | | | | | | | % 151.89/22.54 | | | | | | | | SIMP: (94) implies: % 151.89/22.54 | | | | | | | | (95) all_52_14 = e1 % 151.89/22.54 | | | | | | | | % 151.89/22.54 | | | | | | | | REDUCE: (39), (93) imply: % 151.89/22.54 | | | | | | | | (96) op(e0, e0) = all_6_1 % 151.89/22.54 | | | | | | | | % 151.89/22.54 | | | | | | | | REDUCE: (51), (93) imply: % 151.89/22.54 | | | | | | | | (97) op(e1, e0) = all_56_20 % 151.89/22.54 | | | | | | | | % 151.89/22.54 | | | | | | | | REDUCE: (18), (95) imply: % 151.89/22.54 | | | | | | | | (98) op(e1, e0) = e1 % 151.89/22.54 | | | | | | | | % 151.89/22.54 | | | | | | | | GROUND_INST: instantiating (24) with e0, all_6_1, e0, e0, % 151.89/22.54 | | | | | | | | simplifying with (79), (96) gives: % 151.89/22.54 | | | | | | | | (99) all_6_1 = e0 % 151.89/22.54 | | | | | | | | % 151.89/22.54 | | | | | | | | GROUND_INST: instantiating (24) with e1, all_56_20, e0, e1, % 151.89/22.54 | | | | | | | | simplifying with (97), (98) gives: % 151.89/22.54 | | | | | | | | (100) all_56_20 = e1 % 151.89/22.54 | | | | | | | | % 151.89/22.54 | | | | | | | | REDUCE: (38), (99) imply: % 151.89/22.54 | | | | | | | | (101) op(e1, e0) = e2 % 151.89/22.54 | | | | | | | | % 151.89/22.54 | | | | | | | | GROUND_INST: instantiating (24) with e1, e2, e0, e1, simplifying % 151.89/22.54 | | | | | | | | with (98), (101) gives: % 151.89/22.54 | | | | | | | | (102) e2 = e1 % 151.89/22.54 | | | | | | | | % 151.89/22.54 | | | | | | | | REDUCE: (33), (102) imply: % 151.89/22.54 | | | | | | | | (103) $false % 151.89/22.54 | | | | | | | | % 151.89/22.54 | | | | | | | | CLOSE: (103) is inconsistent. % 151.89/22.54 | | | | | | | | % 151.89/22.54 | | | | | | | End of split % 151.89/22.54 | | | | | | | % 151.89/22.54 | | | | | | Case 2: % 151.89/22.54 | | | | | | | % 151.89/22.54 | | | | | | | (104) all_56_21 = e2 % 151.89/22.54 | | | | | | | (105) all_56_19 = e1 % 151.89/22.54 | | | | | | | % 151.89/22.54 | | | | | | | REF_CLOSE: (1), (3), (7), (8), (9), (12), (13), (15), (17), (18), % 151.89/22.54 | | | | | | | (20), (23), (24), (26), (29), (30), (32), (35), (37), % 151.89/22.54 | | | | | | | (38), (39), (41), (46), (47), (48), (49), (50), (53), % 151.89/22.54 | | | | | | | (54), (55), (58), (60), (61), (62), (63), (104), (105) % 151.89/22.54 | | | | | | | are inconsistent by sub-proof #368. % 151.89/22.54 | | | | | | | % 151.89/22.54 | | | | | | End of split % 151.89/22.54 | | | | | | % 151.89/22.54 | | | | | End of split % 151.89/22.54 | | | | | % 151.89/22.54 | | | | End of split % 151.89/22.54 | | | | % 151.89/22.54 | | | End of split % 151.89/22.54 | | | % 151.89/22.54 | | Case 2: % 151.89/22.54 | | | % 151.89/22.54 | | | (106) all_56_31 = e2 % 151.89/22.54 | | | % 151.89/22.54 | | | COMBINE_EQS: (36), (106) imply: % 151.89/22.54 | | | (107) all_4_2 = e2 % 151.89/22.54 | | | % 151.89/22.54 | | | REDUCE: (6), (107) imply: % 151.89/22.54 | | | (108) op(e0, e0) = e2 % 151.89/22.54 | | | % 151.89/22.54 | | | BETA: splitting (56) gives: % 151.89/22.54 | | | % 151.89/22.54 | | | Case 1: % 151.89/22.54 | | | | % 151.89/22.54 | | | | (109) ~ (all_56_21 = e0) % 151.89/22.54 | | | | % 151.89/22.54 | | | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (10), (12), (13), % 151.89/22.54 | | | | (14), (15), (16), (17), (18), (20), (21), (22), (23), (24), % 151.89/22.54 | | | | (26), (27), (29), (30), (31), (32), (33), (35), (37), (38), % 151.89/22.54 | | | | (39), (41), (44), (45), (46), (47), (48), (49), (50), (51), % 151.89/22.54 | | | | (53), (54), (55), (58), (59), (60), (61), (62), (63), (109) % 151.89/22.54 | | | | are inconsistent by sub-proof #367. % 151.89/22.54 | | | | % 151.89/22.54 | | | Case 2: % 151.89/22.54 | | | | % 151.89/22.54 | | | | (110) all_56_21 = e0 % 151.89/22.54 | | | | % 151.89/22.54 | | | | REF_CLOSE: (3), (13), (24), (39), (108), (110) are inconsistent by % 151.89/22.54 | | | | sub-proof #565. % 151.89/22.54 | | | | % 151.89/22.54 | | | End of split % 151.89/22.54 | | | % 151.89/22.54 | | End of split % 151.89/22.54 | | % 151.89/22.54 | Case 2: % 151.89/22.54 | | % 151.89/22.54 | | (111) all_56_31 = e3 % 151.89/22.54 | | % 151.89/22.54 | | COMBINE_EQS: (36), (111) imply: % 151.89/22.54 | | (112) all_4_2 = e3 % 151.89/22.54 | | % 151.89/22.54 | | REDUCE: (6), (112) imply: % 151.89/22.54 | | (113) op(e0, e0) = e3 % 151.89/22.54 | | % 151.89/22.54 | | BETA: splitting (56) gives: % 151.89/22.54 | | % 151.89/22.54 | | Case 1: % 151.89/22.54 | | | % 151.89/22.54 | | | (114) ~ (all_56_21 = e0) % 151.89/22.54 | | | % 151.89/22.54 | | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (10), (12), (13), (14), % 151.89/22.54 | | | (15), (16), (17), (18), (20), (21), (22), (23), (24), (26), % 151.89/22.54 | | | (27), (29), (30), (31), (32), (33), (35), (37), (38), (39), % 151.89/22.54 | | | (41), (44), (45), (46), (47), (48), (49), (50), (51), (53), % 151.89/22.54 | | | (54), (55), (58), (59), (60), (61), (62), (63), (114) are % 151.89/22.54 | | | inconsistent by sub-proof #367. % 151.89/22.54 | | | % 151.89/22.54 | | Case 2: % 151.89/22.54 | | | % 151.89/22.54 | | | (115) all_56_21 = e0 % 151.89/22.54 | | | % 151.89/22.54 | | | COMBINE_EQS: (13), (115) imply: % 151.89/22.54 | | | (116) all_6_2 = e0 % 151.89/22.54 | | | % 151.89/22.54 | | | SIMP: (116) implies: % 151.89/22.54 | | | (117) all_6_2 = e0 % 151.89/22.54 | | | % 151.89/22.54 | | | COMBINE_EQS: (28), (117) imply: % 151.89/22.54 | | | (118) all_28_2 = e0 % 151.89/22.54 | | | % 151.89/22.54 | | | REDUCE: (39), (117) imply: % 151.89/22.54 | | | (119) op(e0, e0) = all_6_1 % 151.89/22.54 | | | % 151.89/22.54 | | | BETA: splitting (42) gives: % 151.89/22.54 | | | % 151.89/22.54 | | | Case 1: % 151.89/22.54 | | | | % 151.89/22.54 | | | | (120) ~ (all_28_1 = e3) % 151.89/22.54 | | | | % 151.89/22.54 | | | | REDUCE: (19), (120) imply: % 151.89/22.54 | | | | (121) ~ (all_6_1 = e3) % 151.89/22.54 | | | | % 151.89/22.54 | | | | REF_CLOSE: (24), (113), (119), (121) are inconsistent by sub-proof #540. % 151.89/22.54 | | | | % 151.89/22.54 | | | Case 2: % 151.89/22.54 | | | | % 151.89/22.54 | | | | (122) ~ (all_28_2 = e0) % 151.89/22.54 | | | | % 151.89/22.54 | | | | REDUCE: (118), (122) imply: % 151.89/22.54 | | | | (123) $false % 151.89/22.54 | | | | % 151.89/22.54 | | | | CLOSE: (123) is inconsistent. % 151.89/22.54 | | | | % 151.89/22.54 | | | End of split % 151.89/22.54 | | | % 151.89/22.54 | | End of split % 151.89/22.54 | | % 151.89/22.54 | End of split % 151.89/22.54 | % 151.89/22.54 End of proof % 151.89/22.54 % 151.89/22.54 Sub-proof #367 shows that the following formulas are inconsistent: % 151.89/22.54 ---------------------------------------------------------------- % 151.89/22.54 (1) all_56_11 = all_8_2 % 151.89/22.54 (2) all_54_10 = all_6_2 % 151.89/22.54 (3) ~ (all_6_1 = e2) % 151.89/22.54 (4) ~ (all_56_21 = e2) | all_56_19 = e1 % 151.89/22.54 (5) all_54_0 = all_10_2 % 151.89/22.54 (6) all_58_4 = all_52_8 % 151.89/22.54 (7) all_54_5 = all_8_2 % 151.89/22.54 (8) ~ (all_52_6 = all_52_14) % 151.89/22.54 (9) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 151.89/22.54 (10) all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1 % 151.89/22.54 (11) all_56_21 = all_6_2 % 151.89/22.54 (12) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 151.89/22.54 (13) all_56_1 = all_10_2 % 151.89/22.54 (14) all_56_17 = all_52_2 % 151.89/22.54 (15) all_58_9 = all_52_12 % 151.89/22.54 (16) ~ (all_56_21 = e0) % 151.89/22.54 (17) op(e1, e0) = all_52_14 % 151.89/22.54 (18) all_58_1 = all_52_4 % 151.89/22.54 (19) op(e3, e3) = all_10_2 % 151.89/22.54 (20) ~ (all_56_21 = e3) | all_56_17 = e1 % 151.89/22.54 (21) all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0 % 151.89/22.54 (22) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 151.89/22.54 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 151.89/22.54 (23) all_56_7 = all_52_12 % 151.89/22.54 (24) all_46_2 = all_6_2 % 151.89/22.54 (25) op(e1, e3) = all_52_2 % 151.89/22.54 (26) ~ (all_4_2 = e1) % 151.89/22.54 (27) ~ (all_46_1 = e0) | ~ (all_46_2 = e3) % 151.89/22.54 (28) ~ (all_56_1 = e0) | all_56_7 = e3 % 151.89/22.54 (29) ~ (e2 = e1) % 151.89/22.54 (30) op(e1, all_52_8) = all_56_4 % 151.89/22.54 (31) all_58_11 = all_52_14 % 151.89/22.54 (32) op(e1, all_6_1) = e2 % 151.89/22.54 (33) op(all_6_2, all_6_2) = all_6_1 % 151.89/22.54 (34) ~ (all_52_13 = all_52_14) % 151.89/22.54 (35) all_46_1 = all_6_1 % 151.89/22.54 (36) op(e1, e1) = all_6_2 % 151.89/22.54 (37) ~ (all_52_6 = all_8_2) % 151.89/22.54 (38) all_58_15 = all_4_2 % 151.89/22.54 (39) all_58_10 = all_52_13 % 151.89/22.54 (40) ~ (all_56_11 = e0) | all_56_15 = e2 % 151.89/22.54 (41) all_58_0 = all_10_2 % 151.89/22.54 (42) op(e1, all_6_2) = all_56_20 % 151.89/22.54 (43) ~ (e3 = e1) % 151.89/22.54 (44) op(e2, e2) = all_8_2 % 151.89/22.54 (45) ~ (all_52_2 = all_6_2) % 151.89/22.54 (46) ~ (all_52_6 = all_6_2) % 151.89/22.54 (47) ~ (all_52_2 = all_10_2) % 151.89/22.54 (48) ~ (all_52_4 = all_8_2) % 151.89/22.54 (49) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 151.89/22.54 (50) all_56_19 = all_52_6 % 151.89/22.54 (51) all_56_15 = all_52_13 % 151.89/22.54 % 151.89/22.54 Begin of proof % 151.89/22.54 | % 151.89/22.54 | REDUCE: (11), (16) imply: % 151.89/22.54 | (52) ~ (all_6_2 = e0) % 151.89/22.54 | % 151.89/22.54 | BETA: splitting (4) gives: % 151.89/22.54 | % 151.89/22.54 | Case 1: % 151.89/22.54 | | % 151.89/22.54 | | (53) ~ (all_56_21 = e2) % 151.89/22.54 | | % 151.89/22.54 | | REDUCE: (11), (53) imply: % 151.89/22.54 | | (54) ~ (all_6_2 = e2) % 151.89/22.54 | | % 151.89/22.54 | | REF_CLOSE: (2), (3), (5), (9), (11), (12), (14), (19), (20), (22), (24), % 151.89/22.54 | | (25), (27), (29), (32), (33), (35), (36), (42), (47), (52), (54) % 151.89/22.54 | | are inconsistent by sub-proof #372. % 151.89/22.54 | | % 151.89/22.54 | Case 2: % 151.89/22.54 | | % 151.89/22.54 | | (55) all_56_21 = e2 % 151.89/22.54 | | (56) all_56_19 = e1 % 151.89/22.54 | | % 151.89/22.54 | | REF_CLOSE: (1), (3), (6), (7), (8), (10), (11), (13), (15), (17), (18), % 151.89/22.54 | | (21), (22), (23), (25), (26), (28), (30), (31), (32), (33), (34), % 151.89/22.54 | | (37), (38), (39), (40), (41), (43), (44), (45), (46), (48), (49), % 151.89/22.54 | | (50), (51), (55), (56) are inconsistent by sub-proof #368. % 151.89/22.54 | | % 151.89/22.54 | End of split % 151.89/22.54 | % 151.89/22.54 End of proof % 151.89/22.54 % 151.89/22.54 Sub-proof #368 shows that the following formulas are inconsistent: % 151.89/22.54 ---------------------------------------------------------------- % 151.89/22.54 (1) all_56_11 = all_8_2 % 151.89/22.54 (2) ~ (all_6_1 = e2) % 151.89/22.54 (3) all_58_4 = all_52_8 % 151.89/22.54 (4) all_54_5 = all_8_2 % 151.89/22.54 (5) ~ (all_52_6 = all_52_14) % 151.89/22.54 (6) all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1 % 151.89/22.54 (7) all_56_21 = all_6_2 % 151.89/22.54 (8) all_56_1 = all_10_2 % 151.89/22.54 (9) all_58_9 = all_52_12 % 151.89/22.54 (10) op(e1, e0) = all_52_14 % 151.89/22.54 (11) all_58_1 = all_52_4 % 151.89/22.54 (12) all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0 % 151.89/22.54 (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 151.89/22.54 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 151.89/22.54 (14) all_56_7 = all_52_12 % 151.89/22.54 (15) op(e1, e3) = all_52_2 % 151.89/22.54 (16) ~ (all_4_2 = e1) % 151.89/22.54 (17) all_56_21 = e2 % 151.89/22.54 (18) ~ (all_56_1 = e0) | all_56_7 = e3 % 151.89/22.54 (19) all_56_19 = e1 % 151.89/22.54 (20) op(e1, all_52_8) = all_56_4 % 151.89/22.54 (21) all_58_11 = all_52_14 % 151.89/22.54 (22) op(e1, all_6_1) = e2 % 151.89/22.54 (23) op(all_6_2, all_6_2) = all_6_1 % 151.89/22.54 (24) ~ (all_52_13 = all_52_14) % 151.89/22.54 (25) ~ (all_52_6 = all_8_2) % 151.89/22.54 (26) all_58_15 = all_4_2 % 151.89/22.54 (27) all_58_10 = all_52_13 % 151.89/22.54 (28) ~ (all_56_11 = e0) | all_56_15 = e2 % 151.89/22.54 (29) all_58_0 = all_10_2 % 151.89/22.54 (30) ~ (e3 = e1) % 151.89/22.54 (31) op(e2, e2) = all_8_2 % 151.89/22.54 (32) ~ (all_52_2 = all_6_2) % 151.89/22.54 (33) ~ (all_52_6 = all_6_2) % 151.89/22.54 (34) ~ (all_52_4 = all_8_2) % 151.89/22.54 (35) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 151.89/22.54 (36) all_56_19 = all_52_6 % 151.89/22.54 (37) all_56_15 = all_52_13 % 151.89/22.54 % 151.89/22.54 Begin of proof % 151.89/22.54 | % 151.89/22.54 | COMBINE_EQS: (19), (36) imply: % 151.89/22.54 | (38) all_52_6 = e1 % 151.89/22.54 | % 151.89/22.54 | COMBINE_EQS: (7), (17) imply: % 151.89/22.54 | (39) all_6_2 = e2 % 151.89/22.54 | % 151.89/22.54 | REDUCE: (32), (39) imply: % 151.89/22.54 | (40) ~ (all_52_2 = e2) % 151.89/22.54 | % 151.89/22.54 | REDUCE: (5), (38) imply: % 151.89/22.54 | (41) ~ (all_52_14 = e1) % 151.89/22.54 | % 151.89/22.54 | SIMP: (41) implies: % 151.89/22.54 | (42) ~ (all_52_14 = e1) % 151.89/22.54 | % 151.89/22.54 | REDUCE: (25), (38) imply: % 151.89/22.54 | (43) ~ (all_8_2 = e1) % 151.89/22.54 | % 151.89/22.54 | SIMP: (43) implies: % 151.89/22.54 | (44) ~ (all_8_2 = e1) % 151.89/22.54 | % 151.89/22.54 | REDUCE: (33), (38), (39) imply: % 151.89/22.54 | (45) ~ (e2 = e1) % 151.89/22.54 | % 151.89/22.54 | SIMP: (45) implies: % 151.89/22.54 | (46) ~ (e2 = e1) % 151.89/22.54 | % 151.89/22.54 | REDUCE: (23), (39) imply: % 151.89/22.54 | (47) op(e2, e2) = all_6_1 % 151.89/22.54 | % 151.89/22.54 | REF_CLOSE: (1), (2), (3), (4), (6), (8), (9), (10), (11), (12), (13), (14), % 151.89/22.54 | (15), (16), (18), (20), (21), (22), (24), (26), (27), (28), (29), % 151.89/22.54 | (30), (31), (34), (35), (37), (40), (42), (44), (46), (47) are % 151.89/22.54 | inconsistent by sub-proof #369. % 151.89/22.54 | % 151.89/22.54 End of proof % 151.89/22.54 % 151.89/22.54 Sub-proof #369 shows that the following formulas are inconsistent: % 151.89/22.54 ---------------------------------------------------------------- % 151.89/22.54 (1) all_56_11 = all_8_2 % 151.89/22.54 (2) ~ (all_6_1 = e2) % 151.89/22.54 (3) ~ (all_8_2 = e1) % 151.89/22.54 (4) all_58_4 = all_52_8 % 151.89/22.54 (5) op(e2, e2) = all_6_1 % 151.89/22.54 (6) all_54_5 = all_8_2 % 151.89/22.54 (7) all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1 % 151.89/22.54 (8) all_56_1 = all_10_2 % 151.89/22.54 (9) all_58_9 = all_52_12 % 151.89/22.54 (10) op(e1, e0) = all_52_14 % 151.89/22.54 (11) all_58_1 = all_52_4 % 151.89/22.54 (12) all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0 % 151.89/22.54 (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 151.89/22.54 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 151.89/22.54 (14) ~ (all_52_14 = e1) % 151.89/22.54 (15) all_56_7 = all_52_12 % 151.89/22.54 (16) op(e1, e3) = all_52_2 % 151.89/22.54 (17) ~ (all_4_2 = e1) % 151.89/22.54 (18) ~ (all_56_1 = e0) | all_56_7 = e3 % 151.89/22.54 (19) ~ (e2 = e1) % 151.89/22.54 (20) op(e1, all_52_8) = all_56_4 % 151.89/22.54 (21) all_58_11 = all_52_14 % 151.89/22.54 (22) op(e1, all_6_1) = e2 % 151.89/22.54 (23) ~ (all_52_2 = e2) % 151.89/22.54 (24) ~ (all_52_13 = all_52_14) % 151.89/22.54 (25) all_58_15 = all_4_2 % 151.89/22.54 (26) all_58_10 = all_52_13 % 151.89/22.54 (27) ~ (all_56_11 = e0) | all_56_15 = e2 % 151.89/22.54 (28) all_58_0 = all_10_2 % 151.89/22.54 (29) ~ (e3 = e1) % 151.89/22.54 (30) op(e2, e2) = all_8_2 % 151.89/22.54 (31) ~ (all_52_4 = all_8_2) % 151.89/22.54 (32) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 151.89/22.54 (33) all_56_15 = all_52_13 % 151.89/22.54 % 151.89/22.54 Begin of proof % 151.89/22.54 | % 151.89/22.54 | GROUND_INST: instantiating (13) with all_8_2, all_6_1, e2, e2, simplifying % 151.89/22.54 | with (5), (30) gives: % 151.89/22.54 | (34) all_8_2 = all_6_1 % 151.89/22.54 | % 151.89/22.54 | COMBINE_EQS: (6), (34) imply: % 151.89/22.54 | (35) all_54_5 = all_6_1 % 151.89/22.54 | % 151.89/22.54 | COMBINE_EQS: (1), (34) imply: % 151.89/22.54 | (36) all_56_11 = all_6_1 % 151.89/22.54 | % 151.89/22.54 | REDUCE: (31), (34) imply: % 151.89/22.54 | (37) ~ (all_52_4 = all_6_1) % 151.89/22.54 | % 151.89/22.54 | REDUCE: (3), (34) imply: % 151.89/22.54 | (38) ~ (all_6_1 = e1) % 151.89/22.54 | % 151.89/22.54 | BETA: splitting (27) gives: % 151.89/22.54 | % 151.89/22.54 | Case 1: % 151.89/22.54 | | % 151.89/22.54 | | (39) ~ (all_56_11 = e0) % 151.89/22.54 | | % 151.89/22.54 | | REDUCE: (36), (39) imply: % 151.89/22.54 | | (40) ~ (all_6_1 = e0) % 151.89/22.54 | | % 151.89/22.54 | | REF_CLOSE: (2), (13), (16), (22), (23), (32), (35), (38), (40) are % 151.89/22.54 | | inconsistent by sub-proof #371. % 151.89/22.54 | | % 151.89/22.54 | Case 2: % 151.89/22.54 | | % 151.89/22.54 | | (41) all_56_15 = e2 % 151.89/22.54 | | (42) all_56_11 = e0 % 151.89/22.54 | | % 151.89/22.54 | | COMBINE_EQS: (36), (42) imply: % 151.89/22.54 | | (43) all_6_1 = e0 % 151.89/22.54 | | % 151.89/22.54 | | COMBINE_EQS: (33), (41) imply: % 151.89/22.54 | | (44) all_52_13 = e2 % 151.89/22.54 | | % 151.89/22.54 | | COMBINE_EQS: (26), (44) imply: % 151.89/22.54 | | (45) all_58_10 = e2 % 151.89/22.54 | | % 151.89/22.54 | | REDUCE: (37), (43) imply: % 151.89/22.54 | | (46) ~ (all_52_4 = e0) % 151.89/22.54 | | % 151.89/22.54 | | REDUCE: (24), (44) imply: % 151.89/22.54 | | (47) ~ (all_52_14 = e2) % 151.89/22.54 | | % 151.89/22.54 | | SIMP: (47) implies: % 151.89/22.54 | | (48) ~ (all_52_14 = e2) % 151.89/22.54 | | % 151.89/22.54 | | REDUCE: (38), (43) imply: % 151.89/22.54 | | (49) ~ (e1 = e0) % 151.89/22.54 | | % 151.89/22.54 | | SIMP: (49) implies: % 151.89/22.54 | | (50) ~ (e1 = e0) % 151.89/22.54 | | % 151.89/22.54 | | REDUCE: (22), (43) imply: % 151.89/22.54 | | (51) op(e1, e0) = e2 % 151.89/22.54 | | % 151.89/22.54 | | BETA: splitting (7) gives: % 151.89/22.54 | | % 151.89/22.54 | | Case 1: % 151.89/22.54 | | | % 151.89/22.54 | | | (52) all_58_9 = e1 % 151.89/22.54 | | | % 151.89/22.54 | | | COMBINE_EQS: (9), (52) imply: % 151.89/22.54 | | | (53) all_52_12 = e1 % 151.89/22.54 | | | % 151.89/22.54 | | | COMBINE_EQS: (15), (53) imply: % 151.89/22.54 | | | (54) all_56_7 = e1 % 151.89/22.54 | | | % 151.89/22.54 | | | BETA: splitting (18) gives: % 151.89/22.54 | | | % 151.89/22.54 | | | Case 1: % 151.89/22.54 | | | | % 151.89/22.54 | | | | (55) ~ (all_56_1 = e0) % 151.89/22.54 | | | | % 151.89/22.54 | | | | REDUCE: (8), (55) imply: % 151.89/22.54 | | | | (56) ~ (all_10_2 = e0) % 151.89/22.54 | | | | % 151.89/22.54 | | | | BETA: splitting (12) gives: % 151.89/22.54 | | | | % 151.89/22.54 | | | | Case 1: % 151.89/22.54 | | | | | % 151.89/22.54 | | | | | (57) all_58_0 = e0 % 151.89/22.54 | | | | | % 151.89/22.54 | | | | | COMBINE_EQS: (28), (57) imply: % 151.89/22.54 | | | | | (58) all_10_2 = e0 % 151.89/22.54 | | | | | % 151.89/22.54 | | | | | REDUCE: (56), (58) imply: % 151.89/22.54 | | | | | (59) $false % 151.89/22.54 | | | | | % 151.89/22.54 | | | | | CLOSE: (59) is inconsistent. % 151.89/22.54 | | | | | % 151.89/22.54 | | | | Case 2: % 151.89/22.54 | | | | | % 151.89/22.54 | | | | | (60) all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0 % 151.89/22.54 | | | | | % 151.89/22.54 | | | | | BETA: splitting (60) gives: % 151.89/22.54 | | | | | % 151.89/22.54 | | | | | Case 1: % 151.89/22.54 | | | | | | % 151.89/22.54 | | | | | | (61) all_58_1 = e0 % 151.89/22.54 | | | | | | % 151.89/22.54 | | | | | | COMBINE_EQS: (11), (61) imply: % 151.92/22.54 | | | | | | (62) all_52_4 = e0 % 151.92/22.54 | | | | | | % 151.92/22.54 | | | | | | REDUCE: (46), (62) imply: % 151.92/22.54 | | | | | | (63) $false % 151.92/22.54 | | | | | | % 151.92/22.54 | | | | | | CLOSE: (63) is inconsistent. % 151.92/22.54 | | | | | | % 151.92/22.54 | | | | | Case 2: % 151.92/22.54 | | | | | | % 151.92/22.54 | | | | | | (64) all_58_4 = e0 | all_58_9 = e0 % 151.92/22.54 | | | | | | % 151.92/22.54 | | | | | | BETA: splitting (64) gives: % 151.92/22.54 | | | | | | % 151.92/22.54 | | | | | | Case 1: % 151.92/22.54 | | | | | | | % 151.92/22.54 | | | | | | | (65) all_58_4 = e0 % 151.92/22.54 | | | | | | | % 151.92/22.54 | | | | | | | COMBINE_EQS: (4), (65) imply: % 151.92/22.54 | | | | | | | (66) all_52_8 = e0 % 151.92/22.54 | | | | | | | % 151.92/22.54 | | | | | | | REDUCE: (20), (66) imply: % 151.92/22.54 | | | | | | | (67) op(e1, e0) = all_56_4 % 151.92/22.54 | | | | | | | % 151.92/22.54 | | | | | | | GROUND_INST: instantiating (13) with all_52_14, all_56_4, e0, e1, % 151.92/22.54 | | | | | | | simplifying with (10), (67) gives: % 151.92/22.54 | | | | | | | (68) all_56_4 = all_52_14 % 151.92/22.54 | | | | | | | % 151.92/22.54 | | | | | | | GROUND_INST: instantiating (13) with e2, all_56_4, e0, e1, % 151.92/22.54 | | | | | | | simplifying with (51), (67) gives: % 151.92/22.54 | | | | | | | (69) all_56_4 = e2 % 151.92/22.54 | | | | | | | % 151.92/22.54 | | | | | | | COMBINE_EQS: (68), (69) imply: % 151.92/22.54 | | | | | | | (70) all_52_14 = e2 % 151.92/22.54 | | | | | | | % 151.92/22.54 | | | | | | | REDUCE: (48), (70) imply: % 151.92/22.54 | | | | | | | (71) $false % 151.92/22.54 | | | | | | | % 151.92/22.54 | | | | | | | CLOSE: (71) is inconsistent. % 151.92/22.54 | | | | | | | % 151.92/22.54 | | | | | | Case 2: % 151.92/22.54 | | | | | | | % 151.92/22.54 | | | | | | | (72) all_58_9 = e0 % 151.92/22.54 | | | | | | | % 151.92/22.54 | | | | | | | COMBINE_EQS: (52), (72) imply: % 151.92/22.54 | | | | | | | (73) e1 = e0 % 151.92/22.54 | | | | | | | % 151.92/22.54 | | | | | | | REDUCE: (50), (73) imply: % 151.92/22.54 | | | | | | | (74) $false % 151.92/22.54 | | | | | | | % 151.92/22.54 | | | | | | | CLOSE: (74) is inconsistent. % 151.92/22.54 | | | | | | | % 151.92/22.54 | | | | | | End of split % 151.92/22.54 | | | | | | % 151.92/22.54 | | | | | End of split % 151.92/22.54 | | | | | % 151.92/22.54 | | | | End of split % 151.92/22.54 | | | | % 151.92/22.54 | | | Case 2: % 151.92/22.54 | | | | % 151.92/22.54 | | | | (75) all_56_7 = e3 % 151.92/22.54 | | | | % 151.92/22.54 | | | | COMBINE_EQS: (54), (75) imply: % 151.92/22.54 | | | | (76) e3 = e1 % 151.92/22.54 | | | | % 151.92/22.54 | | | | REDUCE: (29), (76) imply: % 151.92/22.54 | | | | (77) $false % 151.92/22.54 | | | | % 151.92/22.54 | | | | CLOSE: (77) is inconsistent. % 151.92/22.54 | | | | % 151.92/22.54 | | | End of split % 151.92/22.54 | | | % 151.92/22.54 | | Case 2: % 151.92/22.54 | | | % 151.92/22.55 | | | (78) all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1 % 151.92/22.55 | | | % 151.92/22.55 | | | REF_CLOSE: (14), (17), (19), (21), (25), (45), (78) are inconsistent by % 151.92/22.55 | | | sub-proof #370. % 151.92/22.55 | | | % 151.92/22.55 | | End of split % 151.92/22.55 | | % 151.92/22.55 | End of split % 151.92/22.55 | % 151.92/22.55 End of proof % 151.92/22.55 % 151.92/22.55 Sub-proof #370 shows that the following formulas are inconsistent: % 151.92/22.55 ---------------------------------------------------------------- % 151.92/22.55 (1) all_58_10 = e2 % 151.92/22.55 (2) ~ (all_52_14 = e1) % 151.92/22.55 (3) ~ (all_4_2 = e1) % 151.92/22.55 (4) ~ (e2 = e1) % 151.92/22.55 (5) all_58_11 = all_52_14 % 151.92/22.55 (6) all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1 % 151.92/22.55 (7) all_58_15 = all_4_2 % 151.92/22.55 % 151.92/22.55 Begin of proof % 151.92/22.55 | % 151.92/22.55 | BETA: splitting (6) gives: % 151.92/22.55 | % 151.92/22.55 | Case 1: % 151.92/22.55 | | % 151.92/22.55 | | (8) all_58_10 = e1 % 151.92/22.55 | | % 151.92/22.55 | | COMBINE_EQS: (1), (8) imply: % 151.92/22.55 | | (9) e2 = e1 % 151.92/22.55 | | % 151.92/22.55 | | REDUCE: (4), (9) imply: % 151.92/22.55 | | (10) $false % 151.92/22.55 | | % 151.92/22.55 | | CLOSE: (10) is inconsistent. % 151.92/22.55 | | % 151.92/22.55 | Case 2: % 151.92/22.55 | | % 151.92/22.55 | | (11) all_58_11 = e1 | all_58_15 = e1 % 151.92/22.55 | | % 151.92/22.55 | | REF_CLOSE: (2), (3), (5), (7), (11) are inconsistent by sub-proof #672. % 151.92/22.55 | | % 151.92/22.55 | End of split % 151.92/22.55 | % 151.92/22.55 End of proof % 151.92/22.55 % 151.92/22.55 Sub-proof #371 shows that the following formulas are inconsistent: % 151.92/22.55 ---------------------------------------------------------------- % 151.92/22.55 (1) ~ (all_6_1 = e2) % 151.92/22.55 (2) ~ (all_6_1 = e1) % 151.92/22.55 (3) all_54_5 = all_6_1 % 151.92/22.55 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 151.92/22.55 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 151.92/22.55 (5) op(e1, e3) = all_52_2 % 151.92/22.55 (6) op(e1, all_6_1) = e2 % 151.92/22.55 (7) ~ (all_52_2 = e2) % 151.92/22.55 (8) ~ (all_6_1 = e0) % 151.92/22.55 (9) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 151.92/22.55 % 151.92/22.55 Begin of proof % 151.92/22.55 | % 151.92/22.55 | BETA: splitting (9) gives: % 151.92/22.55 | % 151.92/22.55 | Case 1: % 151.92/22.55 | | % 151.92/22.55 | | (10) all_54_5 = e3 % 151.92/22.55 | | % 151.92/22.55 | | COMBINE_EQS: (3), (10) imply: % 151.92/22.55 | | (11) all_6_1 = e3 % 151.92/22.55 | | % 151.92/22.55 | | REDUCE: (6), (11) imply: % 151.92/22.55 | | (12) op(e1, e3) = e2 % 151.92/22.55 | | % 151.92/22.55 | | GROUND_INST: instantiating (4) with all_52_2, e2, e3, e1, simplifying with % 151.92/22.55 | | (5), (12) gives: % 151.92/22.55 | | (13) all_52_2 = e2 % 151.92/22.55 | | % 151.92/22.55 | | REDUCE: (7), (13) imply: % 151.92/22.55 | | (14) $false % 151.92/22.55 | | % 151.92/22.55 | | CLOSE: (14) is inconsistent. % 151.92/22.55 | | % 151.92/22.55 | Case 2: % 151.92/22.55 | | % 151.92/22.55 | | (15) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 151.92/22.55 | | % 151.92/22.55 | | REF_CLOSE: (1), (2), (3), (8), (15) are inconsistent by sub-proof #508. % 151.92/22.55 | | % 151.92/22.55 | End of split % 151.92/22.55 | % 151.92/22.55 End of proof % 151.92/22.55 % 151.92/22.55 Sub-proof #372 shows that the following formulas are inconsistent: % 151.92/22.55 ---------------------------------------------------------------- % 151.92/22.55 (1) all_54_10 = all_6_2 % 151.92/22.55 (2) ~ (all_6_1 = e2) % 151.92/22.55 (3) all_54_0 = all_10_2 % 151.92/22.55 (4) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 151.92/22.55 (5) all_56_21 = all_6_2 % 151.92/22.55 (6) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 151.92/22.55 (7) all_56_17 = all_52_2 % 151.92/22.55 (8) op(e3, e3) = all_10_2 % 151.92/22.55 (9) ~ (all_56_21 = e3) | all_56_17 = e1 % 151.92/22.55 (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 151.92/22.55 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 151.92/22.55 (11) ~ (all_6_2 = e0) % 151.92/22.55 (12) all_46_2 = all_6_2 % 151.92/22.55 (13) op(e1, e3) = all_52_2 % 151.92/22.55 (14) ~ (all_46_1 = e0) | ~ (all_46_2 = e3) % 151.92/22.55 (15) ~ (e2 = e1) % 151.92/22.55 (16) op(e1, all_6_1) = e2 % 151.92/22.55 (17) op(all_6_2, all_6_2) = all_6_1 % 151.92/22.55 (18) all_46_1 = all_6_1 % 151.92/22.55 (19) op(e1, e1) = all_6_2 % 151.92/22.55 (20) ~ (all_6_2 = e2) % 151.92/22.55 (21) op(e1, all_6_2) = all_56_20 % 151.92/22.55 (22) ~ (all_52_2 = all_10_2) % 151.92/22.55 % 151.92/22.55 Begin of proof % 151.92/22.55 | % 151.92/22.55 | BETA: splitting (9) gives: % 151.92/22.55 | % 151.92/22.55 | Case 1: % 151.92/22.55 | | % 151.92/22.55 | | (23) ~ (all_56_21 = e3) % 151.92/22.55 | | % 151.92/22.55 | | REDUCE: (5), (23) imply: % 151.92/22.55 | | (24) ~ (all_6_2 = e3) % 151.92/22.55 | | % 151.92/22.55 | | REF_CLOSE: (1), (2), (6), (10), (11), (16), (17), (19), (20), (21), (24) are % 151.92/22.55 | | inconsistent by sub-proof #376. % 151.92/22.55 | | % 151.92/22.55 | Case 2: % 151.92/22.55 | | % 151.92/22.55 | | (25) all_56_21 = e3 % 151.92/22.55 | | % 151.92/22.55 | | REF_CLOSE: (2), (3), (4), (5), (7), (8), (9), (10), (12), (13), (14), (15), % 151.92/22.55 | | (16), (17), (18), (21), (22), (25) are inconsistent by sub-proof % 151.92/22.55 | | #373. % 151.92/22.55 | | % 151.92/22.55 | End of split % 151.92/22.55 | % 151.92/22.55 End of proof % 151.92/22.55 % 151.92/22.55 Sub-proof #373 shows that the following formulas are inconsistent: % 151.92/22.55 ---------------------------------------------------------------- % 151.92/22.55 (1) ~ (all_6_1 = e2) % 151.92/22.55 (2) all_54_0 = all_10_2 % 151.92/22.55 (3) all_56_21 = e3 % 151.92/22.55 (4) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 151.92/22.55 (5) all_56_21 = all_6_2 % 151.92/22.55 (6) all_56_17 = all_52_2 % 151.92/22.55 (7) op(e3, e3) = all_10_2 % 151.92/22.55 (8) ~ (all_56_21 = e3) | all_56_17 = e1 % 151.92/22.55 (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 151.92/22.55 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 151.92/22.55 (10) all_46_2 = all_6_2 % 151.92/22.55 (11) op(e1, e3) = all_52_2 % 151.92/22.55 (12) ~ (all_46_1 = e0) | ~ (all_46_2 = e3) % 151.92/22.55 (13) ~ (e2 = e1) % 151.92/22.55 (14) op(e1, all_6_1) = e2 % 151.92/22.55 (15) op(all_6_2, all_6_2) = all_6_1 % 151.92/22.55 (16) all_46_1 = all_6_1 % 151.92/22.55 (17) op(e1, all_6_2) = all_56_20 % 151.92/22.55 (18) ~ (all_52_2 = all_10_2) % 151.92/22.55 % 151.92/22.55 Begin of proof % 151.92/22.55 | % 151.92/22.55 | COMBINE_EQS: (3), (5) imply: % 151.92/22.55 | (19) all_6_2 = e3 % 151.92/22.55 | % 151.92/22.55 | SIMP: (19) implies: % 151.92/22.55 | (20) all_6_2 = e3 % 151.92/22.55 | % 151.92/22.55 | COMBINE_EQS: (10), (20) imply: % 151.92/22.55 | (21) all_46_2 = e3 % 151.92/22.55 | % 151.92/22.55 | REDUCE: (15), (20) imply: % 151.92/22.55 | (22) op(e3, e3) = all_6_1 % 151.92/22.55 | % 151.92/22.55 | REDUCE: (17), (20) imply: % 151.92/22.55 | (23) op(e1, e3) = all_56_20 % 151.92/22.55 | % 151.92/22.55 | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (9), (11), (12), (13), (14), % 151.92/22.55 | (16), (18), (21), (22), (23) are inconsistent by sub-proof #374. % 151.92/22.55 | % 151.92/22.55 End of proof % 151.92/22.55 % 151.92/22.55 Sub-proof #374 shows that the following formulas are inconsistent: % 151.92/22.55 ---------------------------------------------------------------- % 151.92/22.55 (1) ~ (all_6_1 = e2) % 151.92/22.55 (2) all_54_0 = all_10_2 % 151.92/22.55 (3) all_56_21 = e3 % 151.92/22.55 (4) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 151.92/22.55 (5) all_56_17 = all_52_2 % 151.92/22.55 (6) op(e3, e3) = all_6_1 % 151.92/22.55 (7) op(e3, e3) = all_10_2 % 151.92/22.55 (8) ~ (all_56_21 = e3) | all_56_17 = e1 % 151.92/22.55 (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 151.92/22.55 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 151.92/22.55 (10) op(e1, e3) = all_52_2 % 151.92/22.55 (11) ~ (all_46_1 = e0) | ~ (all_46_2 = e3) % 151.92/22.55 (12) all_46_2 = e3 % 151.92/22.55 (13) ~ (e2 = e1) % 151.92/22.55 (14) op(e1, all_6_1) = e2 % 151.92/22.55 (15) all_46_1 = all_6_1 % 151.92/22.55 (16) op(e1, e3) = all_56_20 % 151.92/22.55 (17) ~ (all_52_2 = all_10_2) % 151.92/22.55 % 151.92/22.55 Begin of proof % 151.92/22.55 | % 151.92/22.55 | BETA: splitting (8) gives: % 151.92/22.55 | % 151.92/22.55 | Case 1: % 151.92/22.55 | | % 151.92/22.55 | | (18) ~ (all_56_21 = e3) % 151.92/22.55 | | % 151.92/22.55 | | REDUCE: (3), (18) imply: % 151.92/22.55 | | (19) $false % 151.92/22.55 | | % 151.92/22.55 | | CLOSE: (19) is inconsistent. % 151.92/22.55 | | % 151.92/22.55 | Case 2: % 151.92/22.55 | | % 151.92/22.55 | | (20) all_56_17 = e1 % 151.92/22.55 | | % 151.92/22.55 | | COMBINE_EQS: (5), (20) imply: % 151.92/22.55 | | (21) all_52_2 = e1 % 151.92/22.55 | | % 151.92/22.55 | | REDUCE: (17), (21) imply: % 151.92/22.55 | | (22) ~ (all_10_2 = e1) % 151.92/22.55 | | % 151.92/22.55 | | SIMP: (22) implies: % 151.92/22.55 | | (23) ~ (all_10_2 = e1) % 151.92/22.55 | | % 151.92/22.55 | | REDUCE: (10), (21) imply: % 151.92/22.55 | | (24) op(e1, e3) = e1 % 151.92/22.55 | | % 151.92/22.55 | | REF_CLOSE: (1), (2), (4), (6), (7), (9), (11), (12), (13), (14), (15), (16), % 151.92/22.55 | | (23), (24) are inconsistent by sub-proof #375. % 151.92/22.55 | | % 151.92/22.55 | End of split % 151.92/22.55 | % 151.92/22.55 End of proof % 151.92/22.55 % 151.92/22.55 Sub-proof #375 shows that the following formulas are inconsistent: % 151.92/22.55 ---------------------------------------------------------------- % 151.92/22.55 (1) ~ (all_6_1 = e2) % 151.92/22.55 (2) all_54_0 = all_10_2 % 151.92/22.55 (3) ~ (all_10_2 = e1) % 151.92/22.55 (4) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 151.92/22.55 (5) op(e3, e3) = all_6_1 % 151.92/22.55 (6) op(e3, e3) = all_10_2 % 151.92/22.55 (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 151.92/22.55 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 151.92/22.55 (8) ~ (all_46_1 = e0) | ~ (all_46_2 = e3) % 151.92/22.55 (9) all_46_2 = e3 % 151.92/22.55 (10) ~ (e2 = e1) % 151.92/22.55 (11) op(e1, all_6_1) = e2 % 151.92/22.55 (12) all_46_1 = all_6_1 % 151.92/22.55 (13) op(e1, e3) = all_56_20 % 151.92/22.55 (14) op(e1, e3) = e1 % 151.92/22.55 % 151.92/22.55 Begin of proof % 151.92/22.55 | % 151.92/22.55 | BETA: splitting (8) gives: % 151.92/22.55 | % 151.92/22.55 | Case 1: % 151.92/22.55 | | % 151.92/22.55 | | (15) ~ (all_46_2 = e3) % 151.92/22.55 | | % 151.92/22.55 | | REDUCE: (9), (15) imply: % 151.92/22.55 | | (16) $false % 151.92/22.55 | | % 151.92/22.55 | | CLOSE: (16) is inconsistent. % 151.92/22.55 | | % 151.92/22.55 | Case 2: % 151.92/22.55 | | % 151.92/22.55 | | (17) ~ (all_46_1 = e0) % 151.92/22.55 | | % 151.92/22.55 | | REDUCE: (12), (17) imply: % 151.92/22.55 | | (18) ~ (all_6_1 = e0) % 151.92/22.55 | | % 151.92/22.55 | | GROUND_INST: instantiating (7) with e1, all_56_20, e3, e1, simplifying with % 151.92/22.55 | | (13), (14) gives: % 151.92/22.55 | | (19) all_56_20 = e1 % 151.92/22.55 | | % 151.92/22.55 | | GROUND_INST: instantiating (7) with all_10_2, all_6_1, e3, e3, simplifying % 151.92/22.55 | | with (5), (6) gives: % 151.92/22.55 | | (20) all_10_2 = all_6_1 % 151.92/22.55 | | % 151.92/22.55 | | COMBINE_EQS: (2), (20) imply: % 151.92/22.55 | | (21) all_54_0 = all_6_1 % 151.92/22.55 | | % 151.92/22.55 | | REDUCE: (3), (20) imply: % 151.92/22.55 | | (22) ~ (all_6_1 = e1) % 151.92/22.55 | | % 151.92/22.55 | | BETA: splitting (4) gives: % 151.92/22.55 | | % 151.92/22.55 | | Case 1: % 151.92/22.55 | | | % 151.92/22.55 | | | (23) all_54_0 = e3 % 151.92/22.55 | | | % 151.92/22.55 | | | COMBINE_EQS: (21), (23) imply: % 151.92/22.55 | | | (24) all_6_1 = e3 % 151.92/22.55 | | | % 151.92/22.55 | | | SIMP: (24) implies: % 151.92/22.55 | | | (25) all_6_1 = e3 % 151.92/22.55 | | | % 151.92/22.55 | | | REDUCE: (11), (25) imply: % 151.92/22.55 | | | (26) op(e1, e3) = e2 % 151.92/22.55 | | | % 151.92/22.55 | | | GROUND_INST: instantiating (7) with e1, e2, e3, e1, simplifying with (14), % 151.92/22.55 | | | (26) gives: % 151.92/22.55 | | | (27) e2 = e1 % 151.92/22.55 | | | % 151.92/22.55 | | | REDUCE: (10), (27) imply: % 151.92/22.55 | | | (28) $false % 151.92/22.55 | | | % 151.92/22.55 | | | CLOSE: (28) is inconsistent. % 151.92/22.55 | | | % 151.92/22.55 | | Case 2: % 151.92/22.55 | | | % 151.92/22.55 | | | (29) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 151.92/22.55 | | | % 151.92/22.55 | | | BETA: splitting (29) gives: % 151.92/22.55 | | | % 151.92/22.55 | | | Case 1: % 151.92/22.55 | | | | % 151.92/22.55 | | | | (30) all_54_0 = e2 % 151.92/22.55 | | | | % 151.92/22.55 | | | | REF_CLOSE: (1), (21), (30) are inconsistent by sub-proof #685. % 151.92/22.55 | | | | % 151.92/22.55 | | | Case 2: % 151.92/22.55 | | | | % 151.92/22.55 | | | | (31) all_54_0 = e1 | all_54_0 = e0 % 151.92/22.55 | | | | % 151.92/22.55 | | | | BETA: splitting (31) gives: % 151.92/22.55 | | | | % 151.92/22.55 | | | | Case 1: % 151.92/22.55 | | | | | % 151.92/22.55 | | | | | (32) all_54_0 = e1 % 151.92/22.55 | | | | | % 151.92/22.55 | | | | | REF_CLOSE: (21), (22), (32) are inconsistent by sub-proof #684. % 151.92/22.55 | | | | | % 151.92/22.55 | | | | Case 2: % 151.92/22.55 | | | | | % 151.92/22.55 | | | | | (33) all_54_0 = e0 % 151.92/22.55 | | | | | % 151.92/22.55 | | | | | COMBINE_EQS: (21), (33) imply: % 151.92/22.55 | | | | | (34) all_6_1 = e0 % 151.92/22.55 | | | | | % 151.92/22.55 | | | | | SIMP: (34) implies: % 151.92/22.55 | | | | | (35) all_6_1 = e0 % 151.92/22.55 | | | | | % 151.92/22.55 | | | | | REDUCE: (18), (35) imply: % 151.92/22.55 | | | | | (36) $false % 151.92/22.55 | | | | | % 151.92/22.55 | | | | | CLOSE: (36) is inconsistent. % 151.92/22.55 | | | | | % 151.92/22.55 | | | | End of split % 151.92/22.55 | | | | % 151.92/22.55 | | | End of split % 151.92/22.55 | | | % 151.92/22.55 | | End of split % 151.92/22.55 | | % 151.92/22.55 | End of split % 151.92/22.55 | % 151.92/22.55 End of proof % 151.92/22.55 % 151.92/22.55 Sub-proof #376 shows that the following formulas are inconsistent: % 151.92/22.55 ---------------------------------------------------------------- % 151.92/22.55 (1) all_54_10 = all_6_2 % 151.92/22.55 (2) ~ (all_6_1 = e2) % 151.92/22.55 (3) ~ (all_6_2 = e3) % 151.92/22.55 (4) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 151.92/22.55 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 151.92/22.55 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 151.92/22.55 (6) ~ (all_6_2 = e0) % 151.92/22.55 (7) op(e1, all_6_1) = e2 % 151.92/22.55 (8) op(all_6_2, all_6_2) = all_6_1 % 151.92/22.55 (9) op(e1, e1) = all_6_2 % 151.92/22.55 (10) ~ (all_6_2 = e2) % 151.92/22.55 (11) op(e1, all_6_2) = all_56_20 % 151.92/22.55 % 151.92/22.55 Begin of proof % 151.92/22.55 | % 151.92/22.55 | BETA: splitting (4) gives: % 151.92/22.55 | % 151.92/22.55 | Case 1: % 151.92/22.55 | | % 151.92/22.55 | | (12) all_54_10 = e3 % 151.92/22.55 | | % 151.92/22.55 | | REF_CLOSE: (1), (3), (12) are inconsistent by sub-proof #736. % 151.92/22.55 | | % 151.92/22.55 | Case 2: % 151.92/22.55 | | % 151.92/22.55 | | (13) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 151.92/22.55 | | % 151.92/22.55 | | BETA: splitting (13) gives: % 151.92/22.55 | | % 151.92/22.55 | | Case 1: % 151.92/22.55 | | | % 151.92/22.55 | | | (14) all_54_10 = e2 % 151.92/22.55 | | | % 151.92/22.55 | | | REF_CLOSE: (1), (10), (14) are inconsistent by sub-proof #735. % 151.92/22.55 | | | % 151.92/22.55 | | Case 2: % 151.92/22.55 | | | % 151.92/22.55 | | | (15) all_54_10 = e1 | all_54_10 = e0 % 151.92/22.55 | | | % 151.92/22.55 | | | REF_CLOSE: (1), (2), (5), (6), (7), (8), (9), (11), (15) are inconsistent % 151.92/22.55 | | | by sub-proof #377. % 151.92/22.55 | | | % 151.92/22.55 | | End of split % 151.92/22.55 | | % 151.92/22.55 | End of split % 151.92/22.55 | % 151.92/22.55 End of proof % 151.92/22.55 % 151.92/22.55 Sub-proof #377 shows that the following formulas are inconsistent: % 151.92/22.55 ---------------------------------------------------------------- % 151.92/22.55 (1) all_54_10 = all_6_2 % 151.92/22.55 (2) ~ (all_6_1 = e2) % 151.92/22.55 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 151.92/22.55 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 151.92/22.55 (4) ~ (all_6_2 = e0) % 151.92/22.55 (5) op(e1, all_6_1) = e2 % 151.92/22.55 (6) op(all_6_2, all_6_2) = all_6_1 % 151.92/22.55 (7) op(e1, e1) = all_6_2 % 151.92/22.55 (8) op(e1, all_6_2) = all_56_20 % 151.92/22.55 (9) all_54_10 = e1 | all_54_10 = e0 % 151.92/22.55 % 151.92/22.55 Begin of proof % 151.92/22.55 | % 151.92/22.55 | BETA: splitting (9) gives: % 151.92/22.55 | % 151.92/22.55 | Case 1: % 151.92/22.55 | | % 151.92/22.55 | | (10) all_54_10 = e1 % 151.92/22.55 | | % 151.92/22.55 | | COMBINE_EQS: (1), (10) imply: % 151.92/22.55 | | (11) all_6_2 = e1 % 151.92/22.55 | | % 151.92/22.55 | | SIMP: (11) implies: % 151.92/22.55 | | (12) all_6_2 = e1 % 151.92/22.55 | | % 151.92/22.55 | | REDUCE: (6), (12) imply: % 151.92/22.55 | | (13) op(e1, e1) = all_6_1 % 151.92/22.55 | | % 151.92/22.55 | | REDUCE: (8), (12) imply: % 151.92/22.55 | | (14) op(e1, e1) = all_56_20 % 151.92/22.55 | | % 151.92/22.55 | | REDUCE: (7), (12) imply: % 151.92/22.55 | | (15) op(e1, e1) = e1 % 151.92/22.55 | | % 151.92/22.55 | | GROUND_INST: instantiating (3) with all_6_1, all_56_20, e1, e1, simplifying % 151.92/22.55 | | with (13), (14) gives: % 151.92/22.55 | | (16) all_56_20 = all_6_1 % 151.92/22.55 | | % 151.92/22.55 | | GROUND_INST: instantiating (3) with e1, all_56_20, e1, e1, simplifying with % 151.92/22.55 | | (14), (15) gives: % 151.92/22.55 | | (17) all_56_20 = e1 % 151.92/22.55 | | % 151.92/22.55 | | COMBINE_EQS: (16), (17) imply: % 151.92/22.55 | | (18) all_6_1 = e1 % 151.92/22.55 | | % 151.92/22.55 | | REF_CLOSE: (2), (3), (5), (13), (14), (18) are inconsistent by sub-proof % 151.92/22.55 | | #378. % 151.92/22.55 | | % 151.92/22.55 | Case 2: % 151.92/22.55 | | % 151.92/22.55 | | (19) all_54_10 = e0 % 151.92/22.55 | | % 151.92/22.55 | | REF_CLOSE: (1), (4), (19) are inconsistent by sub-proof #705. % 151.92/22.55 | | % 151.92/22.55 | End of split % 151.92/22.55 | % 151.92/22.55 End of proof % 151.92/22.55 % 151.92/22.55 Sub-proof #378 shows that the following formulas are inconsistent: % 151.92/22.55 ---------------------------------------------------------------- % 151.92/22.55 (1) ~ (all_6_1 = e2) % 151.92/22.55 (2) all_6_1 = e1 % 151.92/22.55 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 151.92/22.55 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 151.92/22.55 (4) op(e1, all_6_1) = e2 % 151.92/22.55 (5) op(e1, e1) = all_56_20 % 151.92/22.55 (6) op(e1, e1) = all_6_1 % 151.92/22.55 % 151.92/22.55 Begin of proof % 151.92/22.55 | % 151.92/22.55 | REDUCE: (1), (2) imply: % 151.92/22.55 | (7) ~ (e2 = e1) % 151.92/22.55 | % 151.92/22.55 | SIMP: (7) implies: % 151.92/22.55 | (8) ~ (e2 = e1) % 151.92/22.55 | % 151.92/22.55 | REDUCE: (2), (4) imply: % 151.92/22.55 | (9) op(e1, e1) = e2 % 151.92/22.55 | % 151.92/22.55 | REDUCE: (2), (6) imply: % 151.92/22.55 | (10) op(e1, e1) = e1 % 151.92/22.55 | % 151.92/22.55 | REF_CLOSE: (3), (5), (8), (9), (10) are inconsistent by sub-proof #494. % 151.92/22.55 | % 151.92/22.55 End of proof % 151.92/22.55 % 151.92/22.55 Sub-proof #379 shows that the following formulas are inconsistent: % 151.92/22.55 ---------------------------------------------------------------- % 151.92/22.55 (1) all_56_11 = all_8_2 % 151.92/22.55 (2) ~ (all_56_11 = e1) | all_56_13 = e2 % 151.92/22.55 (3) op(e2, all_8_1) = all_8_0 % 151.92/22.55 (4) ~ (all_8_1 = e1) % 151.92/22.55 (5) all_54_10 = all_6_2 % 151.92/22.55 (6) ~ (all_52_13 = all_8_2) % 151.92/22.55 (7) all_54_0 = all_10_2 % 151.92/22.55 (8) ~ (all_8_1 = e3) % 151.92/22.55 (9) ~ (e3 = e2) % 151.92/22.55 (10) op(e0, e0) = all_4_2 % 151.92/22.55 (11) all_54_5 = all_8_2 % 151.92/22.55 (12) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 151.92/22.55 (13) all_54_15 = all_4_2 % 151.92/22.55 (14) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 151.92/22.55 (15) op(e2, all_8_2) = all_56_10 % 151.92/22.55 (16) op(e3, e3) = all_10_2 % 151.92/22.55 (17) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 151.92/22.55 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 151.92/22.55 (18) ~ (all_56_11 = e3) | all_56_9 = e2 % 151.92/22.55 (19) all_56_13 = all_52_9 % 151.92/22.55 (20) all_30_2 = all_8_2 % 151.92/22.55 (21) all_8_0 = e3 % 151.92/22.55 (22) ~ (all_52_13 = all_4_2) % 151.92/22.55 (23) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0 % 151.92/22.55 (24) ~ (all_30_1 = e0) | ~ (all_30_2 = e1) % 151.92/22.55 (25) op(e1, e1) = all_6_2 % 151.92/22.55 (26) ~ (all_52_9 = all_6_2) % 151.92/22.55 (27) ~ (all_56_11 = e0) | all_56_15 = e2 % 151.92/22.55 (28) all_30_1 = all_8_1 % 151.92/22.55 (29) op(e2, e2) = all_8_2 % 151.92/22.55 (30) op(e2, e0) = all_52_13 % 151.92/22.55 (31) op(all_8_2, all_8_2) = all_8_1 % 151.92/22.55 (32) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 151.92/22.55 (33) all_56_9 = all_52_1 % 151.92/22.55 (34) all_56_15 = all_52_13 % 151.92/22.55 (35) ~ (all_52_1 = all_10_2) % 151.92/22.55 % 151.92/22.55 Begin of proof % 151.92/22.55 | % 151.92/22.55 | REDUCE: (3), (21) imply: % 151.92/22.55 | (36) op(e2, all_8_1) = e3 % 151.92/22.55 | % 151.92/22.55 | BETA: splitting (27) gives: % 151.92/22.55 | % 151.92/22.55 | Case 1: % 151.92/22.55 | | % 151.92/22.55 | | (37) ~ (all_56_11 = e0) % 151.92/22.55 | | % 151.92/22.55 | | REDUCE: (1), (37) imply: % 151.92/22.55 | | (38) ~ (all_8_2 = e0) % 151.92/22.55 | | % 151.92/22.55 | | BETA: splitting (2) gives: % 151.92/22.55 | | % 151.92/22.55 | | Case 1: % 151.92/22.55 | | | % 151.92/22.55 | | | (39) ~ (all_56_11 = e1) % 151.92/22.55 | | | % 151.92/22.55 | | | REDUCE: (1), (39) imply: % 151.92/22.55 | | | (40) ~ (all_8_2 = e1) % 151.92/22.55 | | | % 151.92/22.55 | | | BETA: splitting (18) gives: % 151.92/22.55 | | | % 151.92/22.55 | | | Case 1: % 151.92/22.55 | | | | % 151.92/22.55 | | | | (41) ~ (all_56_11 = e3) % 151.92/22.55 | | | | % 151.92/22.55 | | | | REDUCE: (1), (41) imply: % 151.92/22.55 | | | | (42) ~ (all_8_2 = e3) % 151.92/22.55 | | | | % 151.92/22.55 | | | | BETA: splitting (32) gives: % 151.92/22.55 | | | | % 151.92/22.55 | | | | Case 1: % 151.92/22.55 | | | | | % 151.92/22.55 | | | | | (43) all_54_5 = e3 % 151.92/22.55 | | | | | % 151.92/22.55 | | | | | REF_CLOSE: (11), (42), (43) are inconsistent by sub-proof #737. % 151.92/22.55 | | | | | % 151.92/22.55 | | | | Case 2: % 151.92/22.55 | | | | | % 151.92/22.55 | | | | | (44) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 151.92/22.55 | | | | | % 151.92/22.55 | | | | | BETA: splitting (44) gives: % 151.92/22.55 | | | | | % 151.92/22.55 | | | | | Case 1: % 151.92/22.55 | | | | | | % 151.92/22.55 | | | | | | (45) all_54_5 = e2 % 151.92/22.55 | | | | | | % 151.92/22.55 | | | | | | COMBINE_EQS: (11), (45) imply: % 151.92/22.55 | | | | | | (46) all_8_2 = e2 % 151.92/22.55 | | | | | | % 151.92/22.55 | | | | | | SIMP: (46) implies: % 151.92/22.55 | | | | | | (47) all_8_2 = e2 % 151.92/22.55 | | | | | | % 151.92/22.55 | | | | | | REDUCE: (29), (47) imply: % 151.92/22.55 | | | | | | (48) op(e2, e2) = e2 % 151.92/22.55 | | | | | | % 151.92/22.55 | | | | | | REDUCE: (31), (47) imply: % 151.92/22.55 | | | | | | (49) op(e2, e2) = all_8_1 % 151.92/22.55 | | | | | | % 151.92/22.55 | | | | | | REDUCE: (15), (47) imply: % 151.92/22.55 | | | | | | (50) op(e2, e2) = all_56_10 % 151.92/22.55 | | | | | | % 151.92/22.55 | | | | | | GROUND_INST: instantiating (17) with e2, all_56_10, e2, e2, % 151.92/22.55 | | | | | | simplifying with (48), (50) gives: % 151.92/22.55 | | | | | | (51) all_56_10 = e2 % 151.92/22.55 | | | | | | % 151.92/22.55 | | | | | | GROUND_INST: instantiating (17) with all_8_1, all_56_10, e2, e2, % 151.92/22.55 | | | | | | simplifying with (49), (50) gives: % 151.92/22.55 | | | | | | (52) all_56_10 = all_8_1 % 151.92/22.55 | | | | | | % 151.92/22.55 | | | | | | COMBINE_EQS: (51), (52) imply: % 151.92/22.55 | | | | | | (53) all_8_1 = e2 % 151.92/22.55 | | | | | | % 151.92/22.55 | | | | | | SIMP: (53) implies: % 151.92/22.55 | | | | | | (54) all_8_1 = e2 % 151.92/22.55 | | | | | | % 151.92/22.55 | | | | | | REDUCE: (8), (54) imply: % 151.92/22.55 | | | | | | (55) ~ (e3 = e2) % 151.92/22.55 | | | | | | % 151.92/22.55 | | | | | | REDUCE: (36), (54) imply: % 151.92/22.55 | | | | | | (56) op(e2, e2) = e3 % 151.92/22.55 | | | | | | % 151.92/22.55 | | | | | | GROUND_INST: instantiating (17) with e2, e3, e2, e2, simplifying % 151.92/22.55 | | | | | | with (48), (56) gives: % 151.92/22.55 | | | | | | (57) e3 = e2 % 151.92/22.55 | | | | | | % 151.92/22.55 | | | | | | REDUCE: (9), (57) imply: % 151.92/22.55 | | | | | | (58) $false % 151.92/22.55 | | | | | | % 151.92/22.55 | | | | | | CLOSE: (58) is inconsistent. % 151.92/22.55 | | | | | | % 151.92/22.55 | | | | | Case 2: % 151.92/22.55 | | | | | | % 151.92/22.55 | | | | | | (59) all_54_5 = e1 | all_54_5 = e0 % 151.92/22.55 | | | | | | % 151.92/22.55 | | | | | | REF_CLOSE: (11), (38), (40), (59) are inconsistent by sub-proof % 151.92/22.55 | | | | | | #645. % 151.92/22.55 | | | | | | % 151.92/22.55 | | | | | End of split % 151.92/22.55 | | | | | % 151.92/22.55 | | | | End of split % 151.92/22.55 | | | | % 151.92/22.55 | | | Case 2: % 151.92/22.55 | | | | % 151.92/22.55 | | | | (60) all_56_11 = e3 % 151.92/22.55 | | | | (61) all_56_9 = e2 % 151.92/22.55 | | | | % 151.92/22.55 | | | | COMBINE_EQS: (33), (61) imply: % 151.92/22.55 | | | | (62) all_52_1 = e2 % 151.92/22.55 | | | | % 151.92/22.55 | | | | COMBINE_EQS: (1), (60) imply: % 151.92/22.55 | | | | (63) all_8_2 = e3 % 151.92/22.55 | | | | % 151.92/22.55 | | | | REDUCE: (35), (62) imply: % 151.92/22.55 | | | | (64) ~ (all_10_2 = e2) % 151.92/22.55 | | | | % 151.92/22.55 | | | | SIMP: (64) implies: % 151.92/22.55 | | | | (65) ~ (all_10_2 = e2) % 151.92/22.55 | | | | % 151.92/22.55 | | | | REDUCE: (6), (63) imply: % 151.92/22.55 | | | | (66) ~ (all_52_13 = e3) % 151.92/22.55 | | | | % 151.92/22.55 | | | | REDUCE: (31), (63) imply: % 151.92/22.55 | | | | (67) op(e3, e3) = all_8_1 % 151.92/22.55 | | | | % 151.92/22.55 | | | | GROUND_INST: instantiating (17) with all_10_2, all_8_1, e3, e3, % 151.92/22.55 | | | | simplifying with (16), (67) gives: % 151.92/22.55 | | | | (68) all_10_2 = all_8_1 % 151.92/22.55 | | | | % 151.92/22.55 | | | | COMBINE_EQS: (7), (68) imply: % 151.92/22.55 | | | | (69) all_54_0 = all_8_1 % 151.92/22.55 | | | | % 151.92/22.55 | | | | REDUCE: (65), (68) imply: % 151.92/22.55 | | | | (70) ~ (all_8_1 = e2) % 151.92/22.55 | | | | % 151.92/22.55 | | | | BETA: splitting (12) gives: % 151.92/22.55 | | | | % 151.92/22.55 | | | | Case 1: % 151.92/22.55 | | | | | % 151.92/22.55 | | | | | (71) all_54_0 = e3 % 151.92/22.55 | | | | | % 151.92/22.55 | | | | | REF_CLOSE: (8), (69), (71) are inconsistent by sub-proof #600. % 151.92/22.55 | | | | | % 151.92/22.55 | | | | Case 2: % 151.92/22.55 | | | | | % 151.92/22.55 | | | | | (72) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 151.92/22.55 | | | | | % 151.92/22.55 | | | | | BETA: splitting (72) gives: % 151.92/22.55 | | | | | % 151.92/22.55 | | | | | Case 1: % 151.92/22.55 | | | | | | % 151.92/22.55 | | | | | | (73) all_54_0 = e2 % 151.92/22.55 | | | | | | % 151.92/22.55 | | | | | | REF_CLOSE: (69), (70), (73) are inconsistent by sub-proof #599. % 151.92/22.55 | | | | | | % 151.92/22.55 | | | | | Case 2: % 151.92/22.55 | | | | | | % 151.92/22.55 | | | | | | (74) all_54_0 = e1 | all_54_0 = e0 % 151.92/22.55 | | | | | | % 151.92/22.55 | | | | | | BETA: splitting (74) gives: % 151.92/22.55 | | | | | | % 151.92/22.55 | | | | | | Case 1: % 151.92/22.55 | | | | | | | % 151.92/22.55 | | | | | | | (75) all_54_0 = e1 % 151.92/22.55 | | | | | | | % 151.92/22.55 | | | | | | | REF_CLOSE: (4), (69), (75) are inconsistent by sub-proof #598. % 151.92/22.55 | | | | | | | % 151.92/22.55 | | | | | | Case 2: % 151.92/22.55 | | | | | | | % 151.92/22.55 | | | | | | | (76) all_54_0 = e0 % 151.92/22.55 | | | | | | | % 151.92/22.55 | | | | | | | COMBINE_EQS: (69), (76) imply: % 151.92/22.55 | | | | | | | (77) all_8_1 = e0 % 151.92/22.55 | | | | | | | % 151.92/22.55 | | | | | | | SIMP: (77) implies: % 151.92/22.55 | | | | | | | (78) all_8_1 = e0 % 151.92/22.55 | | | | | | | % 151.92/22.55 | | | | | | | REDUCE: (36), (78) imply: % 151.92/22.55 | | | | | | | (79) op(e2, e0) = e3 % 151.92/22.55 | | | | | | | % 151.92/22.55 | | | | | | | GROUND_INST: instantiating (17) with all_52_13, e3, e0, e2, % 151.92/22.55 | | | | | | | simplifying with (30), (79) gives: % 151.92/22.55 | | | | | | | (80) all_52_13 = e3 % 151.92/22.55 | | | | | | | % 151.92/22.55 | | | | | | | REDUCE: (66), (80) imply: % 151.92/22.55 | | | | | | | (81) $false % 151.92/22.55 | | | | | | | % 151.92/22.55 | | | | | | | CLOSE: (81) is inconsistent. % 151.92/22.55 | | | | | | | % 151.92/22.55 | | | | | | End of split % 151.92/22.55 | | | | | | % 151.92/22.55 | | | | | End of split % 151.92/22.55 | | | | | % 151.92/22.55 | | | | End of split % 151.92/22.55 | | | | % 151.92/22.55 | | | End of split % 151.92/22.55 | | | % 151.92/22.55 | | Case 2: % 151.92/22.55 | | | % 151.92/22.55 | | | (82) all_56_13 = e2 % 151.92/22.55 | | | (83) all_56_11 = e1 % 151.92/22.55 | | | % 151.92/22.55 | | | COMBINE_EQS: (1), (83) imply: % 151.92/22.55 | | | (84) all_8_2 = e1 % 151.92/22.55 | | | % 151.92/22.55 | | | COMBINE_EQS: (19), (82) imply: % 151.92/22.55 | | | (85) all_52_9 = e2 % 151.92/22.55 | | | % 151.92/22.55 | | | COMBINE_EQS: (20), (84) imply: % 151.92/22.56 | | | (86) all_30_2 = e1 % 151.92/22.56 | | | % 151.92/22.56 | | | REDUCE: (26), (85) imply: % 151.92/22.56 | | | (87) ~ (all_6_2 = e2) % 151.92/22.56 | | | % 151.92/22.56 | | | SIMP: (87) implies: % 151.92/22.56 | | | (88) ~ (all_6_2 = e2) % 151.92/22.56 | | | % 151.92/22.56 | | | REDUCE: (31), (84) imply: % 151.92/22.56 | | | (89) op(e1, e1) = all_8_1 % 151.92/22.56 | | | % 151.92/22.56 | | | BETA: splitting (24) gives: % 151.92/22.56 | | | % 151.92/22.56 | | | Case 1: % 151.92/22.56 | | | | % 151.92/22.56 | | | | (90) ~ (all_30_2 = e1) % 151.92/22.56 | | | | % 151.92/22.56 | | | | REDUCE: (86), (90) imply: % 151.92/22.56 | | | | (91) $false % 151.92/22.56 | | | | % 151.92/22.56 | | | | CLOSE: (91) is inconsistent. % 151.92/22.56 | | | | % 151.92/22.56 | | | Case 2: % 151.92/22.56 | | | | % 151.92/22.56 | | | | (92) ~ (all_30_1 = e0) % 151.92/22.56 | | | | % 151.92/22.56 | | | | REDUCE: (28), (92) imply: % 151.92/22.56 | | | | (93) ~ (all_8_1 = e0) % 151.92/22.56 | | | | % 151.92/22.56 | | | | GROUND_INST: instantiating (17) with all_6_2, all_8_1, e1, e1, % 151.92/22.56 | | | | simplifying with (25), (89) gives: % 151.92/22.56 | | | | (94) all_8_1 = all_6_2 % 151.92/22.56 | | | | % 151.92/22.56 | | | | REDUCE: (8), (94) imply: % 151.92/22.56 | | | | (95) ~ (all_6_2 = e3) % 151.92/22.56 | | | | % 151.92/22.56 | | | | REDUCE: (4), (94) imply: % 151.92/22.56 | | | | (96) ~ (all_6_2 = e1) % 151.92/22.56 | | | | % 151.92/22.56 | | | | REDUCE: (93), (94) imply: % 151.92/22.56 | | | | (97) ~ (all_6_2 = e0) % 151.92/22.56 | | | | % 151.92/22.56 | | | | REF_CLOSE: (5), (14), (88), (95), (96), (97) are inconsistent by % 151.92/22.56 | | | | sub-proof #573. % 151.92/22.56 | | | | % 151.92/22.56 | | | End of split % 151.92/22.56 | | | % 151.92/22.56 | | End of split % 151.92/22.56 | | % 151.92/22.56 | Case 2: % 151.92/22.56 | | % 151.92/22.56 | | (98) all_56_15 = e2 % 151.92/22.56 | | (99) all_56_11 = e0 % 151.92/22.56 | | % 151.92/22.56 | | COMBINE_EQS: (1), (99) imply: % 151.92/22.56 | | (100) all_8_2 = e0 % 151.92/22.56 | | % 151.92/22.56 | | COMBINE_EQS: (34), (98) imply: % 151.92/22.56 | | (101) all_52_13 = e2 % 151.92/22.56 | | % 151.92/22.56 | | REDUCE: (22), (101) imply: % 151.92/22.56 | | (102) ~ (all_4_2 = e2) % 151.92/22.56 | | % 151.92/22.56 | | SIMP: (102) implies: % 151.92/22.56 | | (103) ~ (all_4_2 = e2) % 151.92/22.56 | | % 151.92/22.56 | | REDUCE: (31), (100) imply: % 151.92/22.56 | | (104) op(e0, e0) = all_8_1 % 151.92/22.56 | | % 151.92/22.56 | | REDUCE: (15), (100) imply: % 151.92/22.56 | | (105) op(e2, e0) = all_56_10 % 151.92/22.56 | | % 151.92/22.56 | | REDUCE: (30), (101) imply: % 151.92/22.56 | | (106) op(e2, e0) = e2 % 151.92/22.56 | | % 151.92/22.56 | | GROUND_INST: instantiating (17) with all_4_2, all_8_1, e0, e0, simplifying % 151.92/22.56 | | with (10), (104) gives: % 151.92/22.56 | | (107) all_8_1 = all_4_2 % 151.92/22.56 | | % 151.92/22.56 | | GROUND_INST: instantiating (17) with e2, all_56_10, e0, e2, simplifying with % 151.92/22.56 | | (105), (106) gives: % 151.92/22.56 | | (108) all_56_10 = e2 % 151.92/22.56 | | % 151.92/22.56 | | REDUCE: (8), (107) imply: % 151.92/22.56 | | (109) ~ (all_4_2 = e3) % 151.92/22.56 | | % 151.92/22.56 | | REDUCE: (4), (107) imply: % 151.92/22.56 | | (110) ~ (all_4_2 = e1) % 151.92/22.56 | | % 151.92/22.56 | | REDUCE: (36), (107) imply: % 151.92/22.56 | | (111) op(e2, all_4_2) = e3 % 151.92/22.56 | | % 151.92/22.56 | | BETA: splitting (23) gives: % 151.92/22.56 | | % 151.92/22.56 | | Case 1: % 151.92/22.56 | | | % 151.92/22.56 | | | (112) all_54_15 = e3 % 151.92/22.56 | | | % 151.92/22.56 | | | REF_CLOSE: (13), (109), (112) are inconsistent by sub-proof #740. % 151.92/22.56 | | | % 151.92/22.56 | | Case 2: % 151.92/22.56 | | | % 151.92/22.56 | | | (113) all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0 % 151.92/22.56 | | | % 151.92/22.56 | | | BETA: splitting (113) gives: % 151.92/22.56 | | | % 151.92/22.56 | | | Case 1: % 151.92/22.56 | | | | % 151.92/22.56 | | | | (114) all_54_15 = e2 % 151.92/22.56 | | | | % 151.92/22.56 | | | | REF_CLOSE: (13), (103), (114) are inconsistent by sub-proof #739. % 151.92/22.56 | | | | % 151.92/22.56 | | | Case 2: % 151.92/22.56 | | | | % 151.92/22.56 | | | | (115) all_54_15 = e1 | all_54_15 = e0 % 151.92/22.56 | | | | % 151.92/22.56 | | | | BETA: splitting (115) gives: % 151.92/22.56 | | | | % 151.92/22.56 | | | | Case 1: % 151.92/22.56 | | | | | % 151.92/22.56 | | | | | (116) all_54_15 = e1 % 151.92/22.56 | | | | | % 151.92/22.56 | | | | | REF_CLOSE: (13), (110), (116) are inconsistent by sub-proof #738. % 151.92/22.56 | | | | | % 151.92/22.56 | | | | Case 2: % 151.92/22.56 | | | | | % 151.92/22.56 | | | | | (117) all_54_15 = e0 % 151.92/22.56 | | | | | % 151.92/22.56 | | | | | COMBINE_EQS: (13), (117) imply: % 151.92/22.56 | | | | | (118) all_4_2 = e0 % 151.92/22.56 | | | | | % 151.92/22.56 | | | | | SIMP: (118) implies: % 151.92/22.56 | | | | | (119) all_4_2 = e0 % 151.92/22.56 | | | | | % 151.92/22.56 | | | | | REDUCE: (111), (119) imply: % 151.92/22.56 | | | | | (120) op(e2, e0) = e3 % 151.92/22.56 | | | | | % 151.92/22.56 | | | | | GROUND_INST: instantiating (17) with e2, e3, e0, e2, simplifying with % 151.92/22.56 | | | | | (106), (120) gives: % 151.92/22.56 | | | | | (121) e3 = e2 % 151.92/22.56 | | | | | % 151.92/22.56 | | | | | REDUCE: (9), (121) imply: % 151.92/22.56 | | | | | (122) $false % 151.92/22.56 | | | | | % 151.92/22.56 | | | | | CLOSE: (122) is inconsistent. % 151.92/22.56 | | | | | % 151.92/22.56 | | | | End of split % 151.92/22.56 | | | | % 151.92/22.56 | | | End of split % 151.92/22.56 | | | % 151.92/22.56 | | End of split % 151.92/22.56 | | % 151.92/22.56 | End of split % 151.92/22.56 | % 151.92/22.56 End of proof % 151.92/22.56 % 151.92/22.56 Sub-proof #380 shows that the following formulas are inconsistent: % 151.92/22.56 ---------------------------------------------------------------- % 151.92/22.56 (1) all_56_11 = all_8_2 % 151.92/22.56 (2) op(e0, all_52_13) = all_56_14 % 151.92/22.56 (3) ~ (all_56_11 = e1) | all_56_13 = e2 % 151.92/22.56 (4) ~ (all_52_11 = all_6_2) % 151.92/22.56 (5) op(e2, all_8_1) = all_8_0 % 151.92/22.56 (6) ~ (all_8_1 = e1) % 151.92/22.56 (7) ~ (all_52_1 = all_52_9) % 151.92/22.56 (8) ~ (e3 = e0) % 151.92/22.56 (9) ~ (all_56_31 = e1) | all_56_29 = e0 % 151.92/22.56 (10) all_56_5 = all_10_0 % 151.92/22.56 (11) all_54_0 = all_10_2 % 151.92/22.56 (12) all_54_4 = all_52_1 % 151.92/22.56 (13) ~ (all_8_0 = e1) % 151.92/22.56 (14) all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2 % 151.92/22.56 (15) all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2 % 151.92/22.56 (16) ~ (all_52_9 = all_8_2) % 151.92/22.56 (17) all_58_4 = all_10_0 % 151.92/22.56 (18) all_54_2 = all_10_0 % 151.92/22.56 (19) all_54_5 = all_8_2 % 151.92/22.56 (20) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 151.92/22.56 (21) all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1 % 151.92/22.56 (22) all_56_21 = all_6_2 % 151.92/22.56 (23) op(e3, all_52_1) = all_56_8 % 151.92/22.56 (24) all_56_1 = all_10_2 % 151.92/22.56 (25) ~ (all_32_0 = e0) | ~ (all_32_2 = e2) % 151.92/22.56 (26) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0 % 151.92/22.56 (27) all_58_5 = all_52_9 % 151.92/22.56 (28) all_58_9 = all_52_12 % 151.92/22.56 (29) ~ (all_56_1 = e1) | all_56_5 = e3 % 151.92/22.56 (30) all_58_1 = all_52_4 % 151.92/22.56 (31) all_58_13 = all_52_7 % 151.92/22.56 (32) all_58_4 = e0 | all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0 % 151.92/22.56 (33) op(e2, all_8_2) = all_56_10 % 151.92/22.56 (34) op(e3, e3) = all_10_2 % 151.92/22.56 (35) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0 % 151.92/22.56 (36) ~ (all_56_21 = e3) | all_56_17 = e1 % 151.92/22.56 (37) ~ (all_52_1 = all_8_2) % 151.92/22.56 (38) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 151.92/22.56 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 151.92/22.56 (39) ~ (all_52_3 = all_10_2) % 151.92/22.56 (40) ~ (all_52_11 = all_10_0) % 151.92/22.56 (41) ~ (all_56_11 = e3) | all_56_9 = e2 % 151.92/22.56 (42) op(e0, all_4_1) = all_4_0 % 151.92/22.56 (43) all_56_7 = all_52_12 % 151.92/22.56 (44) all_56_13 = all_52_9 % 151.92/22.56 (45) op(e0, e1) = all_52_11 % 151.92/22.56 (46) ~ (all_52_1 = all_52_13) % 151.92/22.56 (47) ~ (all_52_7 = all_4_2) % 151.92/22.56 (48) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0 % 151.92/22.56 (49) all_58_8 = all_6_2 % 151.92/22.56 (50) all_54_6 = all_52_9 % 151.92/22.56 (51) ~ (all_52_12 = all_10_0) % 151.92/22.56 (52) ~ (all_56_1 = e2) | all_56_3 = e3 % 151.92/22.56 (53) ~ (all_56_1 = e0) | all_56_7 = e3 % 151.92/22.56 (54) ~ (all_52_4 = all_10_0) % 151.92/22.56 (55) ~ (all_52_9 = all_52_13) % 151.92/22.56 (56) op(all_4_2, all_4_2) = all_4_1 % 151.92/22.56 (57) op(all_10_2, all_10_2) = e1 % 151.92/22.56 (58) all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3 % 151.92/22.56 (59) all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1 % 151.92/22.56 (60) all_58_3 = all_8_2 % 151.92/22.56 (61) all_56_3 = all_52_4 % 151.92/22.56 (62) ~ (all_52_1 = all_52_3) % 151.92/22.56 (63) all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1 % 151.92/22.56 (64) all_56_31 = all_4_2 % 151.92/22.56 (65) all_58_11 = all_52_14 % 151.92/22.56 (66) ~ (all_8_0 = e3) % 151.92/22.56 (67) ~ (all_10_0 = all_6_2) % 151.92/22.56 (68) ~ (all_52_9 = all_52_11) % 151.92/22.56 (69) ~ (all_10_0 = e1) % 151.92/22.56 (70) ~ (all_52_9 = all_10_0) % 151.92/22.56 (71) all_32_0 = all_10_0 % 151.92/22.56 (72) op(e1, e1) = all_6_2 % 151.92/22.56 (73) all_58_15 = all_4_2 % 151.92/22.56 (74) all_56_29 = all_52_11 % 151.92/22.56 (75) ~ (all_6_2 = e2) % 151.92/22.56 (76) all_58_2 = all_52_1 % 151.92/22.56 (77) all_58_7 = all_52_6 % 151.92/22.56 (78) all_58_10 = all_52_13 % 151.92/22.56 (79) all_58_0 = all_10_2 % 151.92/22.56 (80) op(e1, all_6_2) = all_56_20 % 151.92/22.56 (81) all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1 % 151.92/22.56 (82) op(e2, e2) = all_8_2 % 151.92/22.56 (83) ~ (all_52_6 = all_6_2) % 151.92/22.56 (84) ~ (all_8_2 = e0) % 151.92/22.56 (85) op(e3, all_10_2) = all_56_0 % 151.92/22.56 (86) ~ (all_52_14 = all_6_2) % 151.92/22.56 (87) ~ (e2 = e0) % 151.92/22.56 (88) ~ (all_10_0 = all_10_2) % 151.92/22.56 (89) ~ (all_52_4 = all_10_2) % 151.92/22.56 (90) all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3 % 151.92/22.56 (91) ~ (all_10_0 = e2) % 151.92/22.56 (92) ~ (all_52_4 = all_8_2) % 151.92/22.56 (93) op(all_8_2, all_8_2) = all_8_1 % 151.92/22.56 (94) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 151.92/22.56 (95) all_58_14 = all_52_11 % 151.92/22.56 (96) ~ (all_52_12 = all_10_2) % 151.92/22.56 (97) ~ (all_4_0 = e2) % 151.92/22.56 (98) all_56_9 = all_52_1 % 151.92/22.56 (99) all_32_2 = all_10_2 % 151.92/22.56 (100) ~ (all_52_1 = all_10_2) % 151.92/22.56 (101) all_58_12 = all_52_3 % 151.92/22.56 (102) all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3 % 151.92/22.56 % 151.92/22.56 Begin of proof % 151.92/22.56 | % 151.92/22.56 | BETA: splitting (9) gives: % 151.92/22.56 | % 151.92/22.56 | Case 1: % 151.92/22.56 | | % 151.92/22.56 | | (103) ~ (all_56_31 = e1) % 151.92/22.56 | | % 151.92/22.56 | | REDUCE: (64), (103) imply: % 151.92/22.56 | | (104) ~ (all_4_2 = e1) % 151.92/22.56 | | % 151.92/22.56 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (10), (11), (12), (13), % 151.92/22.56 | | (14), (15), (16), (17), (18), (19), (20), (21), (22), (23), (24), % 151.92/22.56 | | (25), (26), (27), (28), (29), (30), (31), (32), (33), (34), (35), % 151.92/22.56 | | (36), (37), (38), (39), (40), (41), (42), (43), (44), (45), (46), % 151.92/22.56 | | (47), (48), (49), (50), (51), (52), (53), (54), (55), (56), (57), % 151.92/22.56 | | (58), (59), (61), (62), (65), (66), (67), (68), (69), (70), (71), % 151.92/22.56 | | (72), (73), (75), (76), (78), (79), (81), (82), (84), (85), (86), % 151.92/22.56 | | (87), (88), (90), (91), (92), (93), (94), (95), (96), (97), (98), % 151.92/22.56 | | (99), (100), (101), (102), (104) are inconsistent by sub-proof % 151.92/22.56 | | #390. % 151.92/22.56 | | % 151.92/22.56 | Case 2: % 151.92/22.56 | | % 151.92/22.56 | | (105) all_56_31 = e1 % 151.92/22.56 | | (106) all_56_29 = e0 % 151.92/22.56 | | % 151.92/22.56 | | COMBINE_EQS: (74), (106) imply: % 151.92/22.56 | | (107) all_52_11 = e0 % 151.92/22.56 | | % 151.92/22.56 | | REF_CLOSE: (6), (11), (18), (20), (24), (30), (31), (35), (38), (40), (43), % 151.92/22.56 | | (47), (51), (52), (53), (54), (56), (57), (60), (61), (63), (64), % 151.92/22.56 | | (69), (72), (77), (80), (83), (88), (89), (91), (93), (105), % 151.92/22.56 | | (107) are inconsistent by sub-proof #381. % 151.92/22.56 | | % 151.92/22.56 | End of split % 151.92/22.56 | % 151.92/22.56 End of proof % 151.92/22.56 % 151.92/22.56 Sub-proof #381 shows that the following formulas are inconsistent: % 151.92/22.56 ---------------------------------------------------------------- % 151.92/22.56 (1) all_56_31 = e1 % 151.92/22.56 (2) ~ (all_8_1 = e1) % 151.92/22.56 (3) all_54_0 = all_10_2 % 151.92/22.56 (4) all_54_2 = all_10_0 % 151.92/22.56 (5) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 151.92/22.56 (6) all_52_11 = e0 % 151.92/22.56 (7) all_56_1 = all_10_2 % 151.92/22.56 (8) all_58_1 = all_52_4 % 151.92/22.56 (9) all_58_13 = all_52_7 % 151.92/22.56 (10) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0 % 151.92/22.56 (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 151.92/22.56 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 151.92/22.56 (12) ~ (all_52_11 = all_10_0) % 151.92/22.56 (13) all_56_7 = all_52_12 % 151.92/22.56 (14) ~ (all_52_7 = all_4_2) % 151.92/22.56 (15) ~ (all_52_12 = all_10_0) % 151.92/22.56 (16) ~ (all_56_1 = e2) | all_56_3 = e3 % 151.92/22.56 (17) ~ (all_56_1 = e0) | all_56_7 = e3 % 151.92/22.56 (18) ~ (all_52_4 = all_10_0) % 151.92/22.56 (19) op(all_4_2, all_4_2) = all_4_1 % 151.92/22.56 (20) op(all_10_2, all_10_2) = e1 % 151.92/22.56 (21) all_58_3 = all_8_2 % 151.92/22.56 (22) all_56_3 = all_52_4 % 151.92/22.56 (23) all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1 % 151.92/22.56 (24) all_56_31 = all_4_2 % 151.92/22.56 (25) ~ (all_10_0 = e1) % 151.92/22.56 (26) op(e1, e1) = all_6_2 % 151.92/22.56 (27) all_58_7 = all_52_6 % 151.92/22.56 (28) op(e1, all_6_2) = all_56_20 % 151.92/22.56 (29) ~ (all_52_6 = all_6_2) % 151.92/22.56 (30) ~ (all_10_0 = all_10_2) % 151.92/22.56 (31) ~ (all_52_4 = all_10_2) % 151.92/22.56 (32) ~ (all_10_0 = e2) % 151.92/22.56 (33) op(all_8_2, all_8_2) = all_8_1 % 151.92/22.56 % 151.92/22.56 Begin of proof % 151.92/22.56 | % 151.92/22.56 | COMBINE_EQS: (1), (24) imply: % 151.92/22.56 | (34) all_4_2 = e1 % 151.92/22.56 | % 151.92/22.56 | REDUCE: (14), (34) imply: % 151.92/22.56 | (35) ~ (all_52_7 = e1) % 151.92/22.56 | % 151.92/22.56 | REDUCE: (6), (12) imply: % 151.92/22.56 | (36) ~ (all_10_0 = e0) % 151.92/22.56 | % 151.92/22.56 | SIMP: (36) implies: % 151.92/22.56 | (37) ~ (all_10_0 = e0) % 151.92/22.56 | % 151.92/22.56 | REDUCE: (19), (34) imply: % 151.92/22.56 | (38) op(e1, e1) = all_4_1 % 151.92/22.56 | % 151.92/22.56 | BETA: splitting (10) gives: % 151.92/22.56 | % 151.92/22.56 | Case 1: % 151.92/22.56 | | % 151.92/22.56 | | (39) all_54_2 = e3 % 151.92/22.56 | | % 151.92/22.56 | | COMBINE_EQS: (4), (39) imply: % 151.92/22.56 | | (40) all_10_0 = e3 % 151.92/22.56 | | % 151.92/22.56 | | SIMP: (40) implies: % 151.92/22.56 | | (41) all_10_0 = e3 % 151.92/22.56 | | % 151.92/22.56 | | REDUCE: (18), (41) imply: % 151.92/22.56 | | (42) ~ (all_52_4 = e3) % 151.92/22.56 | | % 151.92/22.56 | | REDUCE: (15), (41) imply: % 151.92/22.56 | | (43) ~ (all_52_12 = e3) % 151.92/22.56 | | % 151.92/22.56 | | REDUCE: (30), (41) imply: % 151.92/22.56 | | (44) ~ (all_10_2 = e3) % 151.92/22.56 | | % 151.92/22.56 | | SIMP: (44) implies: % 151.92/22.56 | | (45) ~ (all_10_2 = e3) % 151.92/22.56 | | % 151.92/22.56 | | BETA: splitting (17) gives: % 151.92/22.56 | | % 151.92/22.56 | | Case 1: % 151.92/22.56 | | | % 151.92/22.56 | | | (46) ~ (all_56_1 = e0) % 151.92/22.56 | | | % 151.92/22.56 | | | REDUCE: (7), (46) imply: % 151.92/22.56 | | | (47) ~ (all_10_2 = e0) % 151.92/22.56 | | | % 151.92/22.56 | | | BETA: splitting (16) gives: % 151.92/22.56 | | | % 151.92/22.56 | | | Case 1: % 151.92/22.56 | | | | % 151.92/22.56 | | | | (48) ~ (all_56_1 = e2) % 151.92/22.56 | | | | % 151.92/22.56 | | | | REDUCE: (7), (48) imply: % 151.92/22.56 | | | | (49) ~ (all_10_2 = e2) % 151.92/22.56 | | | | % 151.92/22.56 | | | | BETA: splitting (5) gives: % 151.92/22.56 | | | | % 151.92/22.56 | | | | Case 1: % 151.92/22.56 | | | | | % 151.92/22.56 | | | | | (50) all_54_0 = e3 % 151.92/22.56 | | | | | % 151.92/22.56 | | | | | REF_CLOSE: (3), (45), (50) are inconsistent by sub-proof #709. % 151.92/22.56 | | | | | % 151.92/22.56 | | | | Case 2: % 151.92/22.56 | | | | | % 151.92/22.56 | | | | | (51) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 151.92/22.56 | | | | | % 151.92/22.56 | | | | | BETA: splitting (51) gives: % 151.92/22.56 | | | | | % 151.92/22.56 | | | | | Case 1: % 151.92/22.56 | | | | | | % 151.92/22.56 | | | | | | (52) all_54_0 = e2 % 151.92/22.56 | | | | | | % 151.92/22.56 | | | | | | REF_CLOSE: (3), (49), (52) are inconsistent by sub-proof #734. % 151.92/22.56 | | | | | | % 151.92/22.56 | | | | | Case 2: % 151.92/22.56 | | | | | | % 151.92/22.56 | | | | | | (53) all_54_0 = e1 | all_54_0 = e0 % 151.92/22.56 | | | | | | % 151.92/22.56 | | | | | | BETA: splitting (53) gives: % 151.92/22.56 | | | | | | % 151.92/22.56 | | | | | | Case 1: % 151.92/22.56 | | | | | | | % 151.92/22.56 | | | | | | | (54) all_54_0 = e1 % 151.92/22.56 | | | | | | | % 151.92/22.56 | | | | | | | COMBINE_EQS: (3), (54) imply: % 151.92/22.56 | | | | | | | (55) all_10_2 = e1 % 151.92/22.56 | | | | | | | % 151.92/22.56 | | | | | | | SIMP: (55) implies: % 151.92/22.56 | | | | | | | (56) all_10_2 = e1 % 151.92/22.56 | | | | | | | % 151.92/22.56 | | | | | | | REDUCE: (31), (56) imply: % 151.92/22.56 | | | | | | | (57) ~ (all_52_4 = e1) % 151.92/22.56 | | | | | | | % 151.92/22.56 | | | | | | | REDUCE: (20), (56) imply: % 151.92/22.56 | | | | | | | (58) op(e1, e1) = e1 % 151.92/22.56 | | | | | | | % 151.92/22.56 | | | | | | | GROUND_INST: instantiating (11) with all_6_2, e1, e1, e1, % 151.92/22.56 | | | | | | | simplifying with (26), (58) gives: % 151.92/22.56 | | | | | | | (59) all_6_2 = e1 % 151.92/22.56 | | | | | | | % 151.92/22.56 | | | | | | | GROUND_INST: instantiating (11) with all_6_2, all_4_1, e1, e1, % 151.92/22.56 | | | | | | | simplifying with (26), (38) gives: % 151.92/22.56 | | | | | | | (60) all_6_2 = all_4_1 % 151.92/22.56 | | | | | | | % 151.92/22.56 | | | | | | | COMBINE_EQS: (59), (60) imply: % 151.92/22.56 | | | | | | | (61) all_4_1 = e1 % 151.92/22.56 | | | | | | | % 151.92/22.56 | | | | | | | REDUCE: (29), (59) imply: % 151.92/22.56 | | | | | | | (62) ~ (all_52_6 = e1) % 151.92/22.56 | | | | | | | % 151.92/22.56 | | | | | | | REDUCE: (28), (59) imply: % 151.92/22.56 | | | | | | | (63) op(e1, e1) = all_56_20 % 151.92/22.56 | | | | | | | % 151.92/22.56 | | | | | | | REF_CLOSE: (2), (8), (9), (11), (21), (23), (27), (33), (35), % 151.92/22.56 | | | | | | | (57), (58), (62), (63) are inconsistent by sub-proof % 151.92/22.56 | | | | | | | #532. % 151.92/22.56 | | | | | | | % 151.92/22.56 | | | | | | Case 2: % 151.92/22.56 | | | | | | | % 151.92/22.56 | | | | | | | (64) all_54_0 = e0 % 151.92/22.56 | | | | | | | % 151.92/22.56 | | | | | | | REF_CLOSE: (3), (47), (64) are inconsistent by sub-proof #732. % 151.92/22.56 | | | | | | | % 151.92/22.56 | | | | | | End of split % 151.92/22.56 | | | | | | % 151.92/22.56 | | | | | End of split % 151.92/22.56 | | | | | % 151.92/22.56 | | | | End of split % 151.92/22.56 | | | | % 151.92/22.56 | | | Case 2: % 151.92/22.56 | | | | % 151.92/22.56 | | | | (65) all_56_3 = e3 % 151.92/22.56 | | | | % 151.92/22.56 | | | | REF_CLOSE: (22), (42), (65) are inconsistent by sub-proof #395. % 151.92/22.56 | | | | % 151.92/22.56 | | | End of split % 151.92/22.56 | | | % 151.92/22.56 | | Case 2: % 151.92/22.56 | | | % 151.92/22.56 | | | (66) all_56_7 = e3 % 151.92/22.56 | | | % 151.92/22.56 | | | REF_CLOSE: (13), (43), (66) are inconsistent by sub-proof #691. % 151.92/22.56 | | | % 151.92/22.56 | | End of split % 151.92/22.56 | | % 151.92/22.56 | Case 2: % 151.92/22.56 | | % 151.92/22.56 | | (67) all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0 % 151.92/22.56 | | % 151.92/22.56 | | REF_CLOSE: (4), (25), (32), (37), (67) are inconsistent by sub-proof #382. % 151.92/22.56 | | % 151.92/22.56 | End of split % 151.92/22.56 | % 151.92/22.56 End of proof % 151.92/22.56 % 151.92/22.56 Sub-proof #382 shows that the following formulas are inconsistent: % 151.92/22.56 ---------------------------------------------------------------- % 151.92/22.56 (1) all_54_2 = all_10_0 % 151.92/22.56 (2) ~ (all_10_0 = e0) % 151.92/22.56 (3) all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0 % 151.92/22.56 (4) ~ (all_10_0 = e1) % 151.92/22.56 (5) ~ (all_10_0 = e2) % 151.92/22.56 % 151.92/22.56 Begin of proof % 151.92/22.56 | % 151.92/22.56 | BETA: splitting (3) gives: % 151.92/22.56 | % 151.92/22.56 | Case 1: % 151.92/22.56 | | % 151.92/22.56 | | (6) all_54_2 = e2 % 151.92/22.56 | | % 151.92/22.56 | | REF_CLOSE: (1), (5), (6) are inconsistent by sub-proof #407. % 151.92/22.56 | | % 151.92/22.56 | Case 2: % 151.92/22.56 | | % 151.92/22.56 | | (7) all_54_2 = e1 | all_54_2 = e0 % 151.92/22.56 | | % 151.92/22.56 | | BETA: splitting (7) gives: % 151.92/22.56 | | % 151.92/22.56 | | Case 1: % 151.92/22.56 | | | % 151.92/22.56 | | | (8) all_54_2 = e1 % 151.92/22.56 | | | % 151.92/22.56 | | | REF_CLOSE: (1), (4), (8) are inconsistent by sub-proof #406. % 151.92/22.56 | | | % 151.92/22.56 | | Case 2: % 151.92/22.56 | | | % 151.92/22.56 | | | (9) all_54_2 = e0 % 151.92/22.56 | | | % 151.92/22.56 | | | COMBINE_EQS: (1), (9) imply: % 151.92/22.56 | | | (10) all_10_0 = e0 % 151.92/22.56 | | | % 151.92/22.56 | | | SIMP: (10) implies: % 151.92/22.56 | | | (11) all_10_0 = e0 % 151.92/22.56 | | | % 151.92/22.56 | | | REDUCE: (2), (11) imply: % 151.92/22.56 | | | (12) $false % 151.92/22.56 | | | % 151.92/22.56 | | | CLOSE: (12) is inconsistent. % 151.92/22.56 | | | % 151.92/22.56 | | End of split % 151.92/22.56 | | % 151.92/22.56 | End of split % 151.92/22.56 | % 151.92/22.56 End of proof % 151.92/22.56 % 151.92/22.56 Sub-proof #383 shows that the following formulas are inconsistent: % 151.92/22.56 ---------------------------------------------------------------- % 151.92/22.56 (1) all_56_11 = all_8_2 % 151.92/22.56 (2) op(e0, all_52_13) = all_56_14 % 151.92/22.56 (3) ~ (all_56_11 = e1) | all_56_13 = e2 % 151.92/22.56 (4) ~ (all_52_11 = all_6_2) % 151.92/22.56 (5) op(e2, all_8_1) = all_8_0 % 151.92/22.56 (6) ~ (all_8_1 = e1) % 151.92/22.56 (7) ~ (all_52_1 = all_52_9) % 151.92/22.56 (8) ~ (e3 = e0) % 151.92/22.56 (9) all_56_5 = all_10_0 % 151.92/22.56 (10) all_54_0 = all_10_2 % 151.92/22.56 (11) all_54_4 = all_52_1 % 151.92/22.56 (12) ~ (all_8_0 = e1) % 151.92/22.56 (13) all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2 % 151.92/22.56 (14) all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2 % 151.92/22.56 (15) ~ (all_52_9 = all_8_2) % 151.92/22.56 (16) all_58_4 = all_10_0 % 151.92/22.56 (17) ~ (all_52_12 = all_52_13) % 151.92/22.56 (18) all_54_2 = all_10_0 % 151.92/22.56 (19) ~ (all_8_1 = e3) % 151.92/22.56 (20) op(e0, e0) = all_4_2 % 151.92/22.56 (21) all_54_5 = all_8_2 % 151.92/22.56 (22) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 151.92/22.56 (23) all_54_15 = all_4_2 % 151.92/22.56 (24) all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1 % 151.92/22.56 (25) all_56_21 = all_6_2 % 151.92/22.56 (26) op(e3, all_52_1) = all_56_8 % 151.92/22.56 (27) all_56_1 = all_10_2 % 151.92/22.56 (28) ~ (all_32_0 = e0) | ~ (all_32_2 = e2) % 151.92/22.56 (29) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0 % 151.92/22.56 (30) all_58_5 = all_52_9 % 151.92/22.56 (31) all_58_9 = all_52_12 % 151.92/22.56 (32) ~ (all_56_1 = e1) | all_56_5 = e3 % 151.92/22.56 (33) all_58_1 = all_52_4 % 151.92/22.56 (34) all_58_13 = all_52_7 % 151.92/22.56 (35) all_58_4 = e0 | all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0 % 151.92/22.56 (36) op(e2, all_8_2) = all_56_10 % 151.92/22.56 (37) op(e3, e3) = all_10_2 % 151.92/22.56 (38) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0 % 151.92/22.56 (39) ~ (all_56_21 = e3) | all_56_17 = e1 % 151.92/22.56 (40) all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0 % 151.92/22.56 (41) ~ (all_52_1 = all_8_2) % 151.92/22.56 (42) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 151.92/22.56 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 151.92/22.56 (43) ~ (all_52_3 = all_10_2) % 151.92/22.56 (44) ~ (all_52_11 = all_10_0) % 151.92/22.56 (45) ~ (all_56_11 = e3) | all_56_9 = e2 % 151.92/22.56 (46) op(e0, all_4_1) = all_4_0 % 151.92/22.56 (47) all_56_7 = all_52_12 % 151.92/22.56 (48) all_56_13 = all_52_9 % 151.92/22.56 (49) op(e0, e1) = all_52_11 % 151.92/22.56 (50) ~ (all_52_1 = all_52_13) % 151.92/22.56 (51) ~ (all_52_7 = all_4_2) % 151.92/22.56 (52) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0 % 151.92/22.56 (53) ~ (all_4_2 = e1) % 151.92/22.56 (54) all_58_8 = all_6_2 % 151.92/22.56 (55) all_54_6 = all_52_9 % 151.92/22.56 (56) ~ (all_4_0 = e1) % 151.92/22.56 (57) ~ (all_52_12 = all_10_0) % 151.92/22.56 (58) ~ (all_56_1 = e2) | all_56_3 = e3 % 151.92/22.56 (59) ~ (all_56_1 = e0) | all_56_7 = e3 % 151.92/22.56 (60) ~ (all_52_4 = all_10_0) % 151.92/22.56 (61) ~ (all_52_9 = all_52_13) % 151.92/22.56 (62) op(all_4_2, all_4_2) = all_4_1 % 151.92/22.56 (63) op(all_10_2, all_10_2) = e1 % 151.92/22.56 (64) all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3 % 151.92/22.56 (65) all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1 % 151.92/22.56 (66) all_56_3 = all_52_4 % 151.92/22.56 (67) ~ (all_52_1 = all_52_3) % 151.92/22.56 (68) all_58_11 = all_52_14 % 151.92/22.56 (69) ~ (all_8_0 = e3) % 151.92/22.56 (70) ~ (all_10_0 = all_6_2) % 151.92/22.56 (71) ~ (all_52_9 = all_52_11) % 151.92/22.56 (72) ~ (all_10_0 = e1) % 151.92/22.56 (73) ~ (all_52_9 = all_10_0) % 151.92/22.56 (74) all_32_0 = all_10_0 % 151.92/22.56 (75) ~ (all_52_13 = all_4_2) % 151.92/22.56 (76) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0 % 151.92/22.56 (77) op(e1, e1) = all_6_2 % 151.92/22.56 (78) all_58_15 = all_4_2 % 151.92/22.56 (79) ~ (all_6_2 = e2) % 151.92/22.56 (80) all_58_2 = all_52_1 % 151.92/22.56 (81) all_58_10 = all_52_13 % 151.92/22.56 (82) ~ (all_52_12 = all_4_2) % 151.92/22.56 (83) ~ (all_56_11 = e0) | all_56_15 = e2 % 151.92/22.56 (84) all_58_0 = all_10_2 % 151.92/22.56 (85) all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1 % 151.92/22.56 (86) op(e2, e2) = all_8_2 % 151.92/22.56 (87) op(e0, all_4_2) = all_56_30 % 151.92/22.56 (88) op(e3, all_10_2) = all_56_0 % 151.92/22.56 (89) ~ (all_52_14 = all_6_2) % 151.92/22.56 (90) ~ (e2 = e0) % 151.92/22.56 (91) all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0 % 151.92/22.56 (92) ~ (all_10_0 = all_10_2) % 151.92/22.56 (93) ~ (all_52_4 = all_10_2) % 151.92/22.56 (94) all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3 % 151.92/22.56 (95) ~ (all_10_0 = e2) % 151.92/22.56 (96) ~ (all_52_4 = all_8_2) % 151.92/22.56 (97) op(all_8_2, all_8_2) = all_8_1 % 151.92/22.56 (98) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 151.92/22.56 (99) all_58_14 = all_52_11 % 151.92/22.56 (100) ~ (all_52_12 = all_10_2) % 151.92/22.56 (101) ~ (all_4_0 = e2) % 151.92/22.56 (102) ~ (all_4_0 = e3) % 151.92/22.56 (103) all_56_9 = all_52_1 % 151.92/22.56 (104) all_56_15 = all_52_13 % 151.92/22.56 (105) all_32_2 = all_10_2 % 151.92/22.56 (106) ~ (all_52_1 = all_10_2) % 151.92/22.56 (107) all_58_12 = all_52_3 % 151.92/22.56 (108) all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3 % 151.92/22.56 % 151.92/22.56 Begin of proof % 151.92/22.56 | % 151.92/22.56 | BETA: splitting (83) gives: % 151.92/22.56 | % 151.92/22.56 | Case 1: % 151.92/22.56 | | % 151.92/22.56 | | (109) ~ (all_56_11 = e0) % 151.92/22.56 | | % 151.92/22.56 | | REDUCE: (1), (109) imply: % 151.92/22.56 | | (110) ~ (all_8_2 = e0) % 151.92/22.56 | | % 151.92/22.56 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), % 151.92/22.56 | | (13), (14), (15), (16), (18), (21), (22), (24), (25), (26), (27), % 151.92/22.56 | | (28), (29), (30), (31), (32), (33), (34), (35), (36), (37), (38), % 151.92/22.56 | | (39), (41), (42), (43), (44), (45), (46), (47), (48), (49), (50), % 151.92/22.56 | | (51), (52), (53), (54), (55), (57), (58), (59), (60), (61), (62), % 151.92/22.56 | | (63), (64), (65), (66), (67), (68), (69), (70), (71), (72), (73), % 151.92/22.56 | | (74), (77), (78), (79), (80), (81), (84), (85), (86), (88), (89), % 151.92/22.56 | | (90), (92), (94), (95), (96), (97), (98), (99), (100), (101), % 151.92/22.56 | | (103), (105), (106), (107), (108), (110) are inconsistent by % 151.92/22.56 | | sub-proof #390. % 151.92/22.56 | | % 151.92/22.56 | Case 2: % 151.92/22.56 | | % 151.92/22.56 | | (111) all_56_15 = e2 % 151.92/22.56 | | (112) all_56_11 = e0 % 151.92/22.56 | | % 151.92/22.57 | | REF_CLOSE: (1), (6), (9), (10), (14), (16), (17), (18), (19), (20), (22), % 151.92/22.57 | | (23), (27), (28), (31), (32), (33), (37), (38), (40), (42), (46), % 151.92/22.57 | | (56), (58), (60), (62), (63), (66), (72), (74), (75), (76), (82), % 151.92/22.57 | | (84), (87), (88), (91), (92), (93), (95), (96), (97), (100), % 151.92/22.57 | | (102), (104), (105), (111), (112) are inconsistent by sub-proof % 151.92/22.57 | | #384. % 151.92/22.57 | | % 151.92/22.57 | End of split % 151.92/22.57 | % 151.92/22.57 End of proof % 151.92/22.57 % 151.92/22.57 Sub-proof #384 shows that the following formulas are inconsistent: % 151.92/22.57 ---------------------------------------------------------------- % 151.92/22.57 (1) all_56_11 = all_8_2 % 151.92/22.57 (2) ~ (all_8_1 = e1) % 151.92/22.57 (3) all_56_5 = all_10_0 % 151.92/22.57 (4) all_54_0 = all_10_2 % 151.92/22.57 (5) all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2 % 151.92/22.57 (6) all_58_4 = all_10_0 % 151.92/22.57 (7) ~ (all_52_12 = all_52_13) % 151.92/22.57 (8) all_54_2 = all_10_0 % 151.92/22.57 (9) ~ (all_8_1 = e3) % 151.92/22.57 (10) op(e0, e0) = all_4_2 % 151.92/22.57 (11) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 151.92/22.57 (12) all_54_15 = all_4_2 % 151.92/22.57 (13) all_56_1 = all_10_2 % 151.92/22.57 (14) ~ (all_32_0 = e0) | ~ (all_32_2 = e2) % 151.92/22.57 (15) all_58_9 = all_52_12 % 151.92/22.57 (16) ~ (all_56_1 = e1) | all_56_5 = e3 % 151.92/22.57 (17) all_58_1 = all_52_4 % 151.92/22.57 (18) op(e3, e3) = all_10_2 % 151.92/22.57 (19) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0 % 151.92/22.57 (20) all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0 % 151.92/22.57 (21) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 151.92/22.57 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 151.92/22.57 (22) op(e0, all_4_1) = all_4_0 % 151.92/22.57 (23) all_56_15 = e2 % 151.92/22.57 (24) ~ (all_4_0 = e1) % 151.92/22.57 (25) ~ (all_56_1 = e2) | all_56_3 = e3 % 151.92/22.57 (26) ~ (all_52_4 = all_10_0) % 151.92/22.57 (27) op(all_4_2, all_4_2) = all_4_1 % 151.92/22.57 (28) op(all_10_2, all_10_2) = e1 % 151.92/22.57 (29) all_56_3 = all_52_4 % 151.92/22.57 (30) ~ (all_10_0 = e1) % 151.92/22.57 (31) all_32_0 = all_10_0 % 151.92/22.57 (32) ~ (all_52_13 = all_4_2) % 151.92/22.57 (33) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0 % 151.92/22.57 (34) all_56_11 = e0 % 151.92/22.57 (35) ~ (all_52_12 = all_4_2) % 151.92/22.57 (36) all_58_0 = all_10_2 % 151.92/22.57 (37) op(e0, all_4_2) = all_56_30 % 151.92/22.57 (38) op(e3, all_10_2) = all_56_0 % 151.92/22.57 (39) all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0 % 151.92/22.57 (40) ~ (all_10_0 = all_10_2) % 151.92/22.57 (41) ~ (all_52_4 = all_10_2) % 151.92/22.57 (42) ~ (all_10_0 = e2) % 151.92/22.57 (43) ~ (all_52_4 = all_8_2) % 151.92/22.57 (44) op(all_8_2, all_8_2) = all_8_1 % 151.92/22.57 (45) ~ (all_52_12 = all_10_2) % 151.92/22.57 (46) ~ (all_4_0 = e3) % 151.92/22.57 (47) all_56_15 = all_52_13 % 151.92/22.57 (48) all_32_2 = all_10_2 % 151.92/22.57 % 151.92/22.57 Begin of proof % 151.92/22.57 | % 151.92/22.57 | COMBINE_EQS: (1), (34) imply: % 151.92/22.57 | (49) all_8_2 = e0 % 151.92/22.57 | % 151.92/22.57 | COMBINE_EQS: (23), (47) imply: % 151.92/22.57 | (50) all_52_13 = e2 % 151.92/22.57 | % 151.92/22.57 | REDUCE: (43), (49) imply: % 151.92/22.57 | (51) ~ (all_52_4 = e0) % 151.92/22.57 | % 151.92/22.57 | REDUCE: (7), (50) imply: % 151.92/22.57 | (52) ~ (all_52_12 = e2) % 151.92/22.57 | % 151.92/22.57 | REDUCE: (32), (50) imply: % 151.92/22.57 | (53) ~ (all_4_2 = e2) % 151.92/22.57 | % 151.92/22.57 | SIMP: (53) implies: % 151.92/22.57 | (54) ~ (all_4_2 = e2) % 151.92/22.57 | % 151.92/22.57 | REDUCE: (44), (49) imply: % 151.92/22.57 | (55) op(e0, e0) = all_8_1 % 151.92/22.57 | % 151.92/22.57 | REF_CLOSE: (2), (3), (4), (5), (6), (8), (9), (10), (11), (12), (13), (14), % 151.92/22.57 | (15), (16), (17), (18), (19), (20), (21), (22), (24), (25), (26), % 151.92/22.57 | (27), (28), (29), (30), (31), (33), (35), (36), (37), (38), (39), % 151.92/22.57 | (40), (41), (42), (45), (46), (48), (51), (52), (54), (55) are % 151.92/22.57 | inconsistent by sub-proof #385. % 151.92/22.57 | % 151.92/22.57 End of proof % 151.92/22.57 % 151.92/22.57 Sub-proof #385 shows that the following formulas are inconsistent: % 151.92/22.57 ---------------------------------------------------------------- % 151.92/22.57 (1) ~ (all_8_1 = e1) % 151.92/22.57 (2) all_56_5 = all_10_0 % 151.92/22.57 (3) all_54_0 = all_10_2 % 151.92/22.57 (4) all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2 % 151.92/22.57 (5) all_58_4 = all_10_0 % 151.92/22.57 (6) ~ (all_52_12 = e2) % 151.92/22.57 (7) all_54_2 = all_10_0 % 151.92/22.57 (8) ~ (all_8_1 = e3) % 151.92/22.57 (9) op(e0, e0) = all_4_2 % 151.92/22.57 (10) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 151.92/22.57 (11) all_54_15 = all_4_2 % 151.92/22.57 (12) all_56_1 = all_10_2 % 151.92/22.57 (13) ~ (all_32_0 = e0) | ~ (all_32_2 = e2) % 151.92/22.57 (14) all_58_9 = all_52_12 % 151.92/22.57 (15) ~ (all_56_1 = e1) | all_56_5 = e3 % 151.92/22.57 (16) all_58_1 = all_52_4 % 151.92/22.57 (17) op(e3, e3) = all_10_2 % 151.92/22.57 (18) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0 % 151.92/22.57 (19) all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0 % 151.92/22.57 (20) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 151.92/22.57 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 151.92/22.57 (21) op(e0, all_4_1) = all_4_0 % 151.92/22.57 (22) ~ (all_52_4 = e0) % 151.92/22.57 (23) ~ (all_4_0 = e1) % 151.92/22.57 (24) ~ (all_56_1 = e2) | all_56_3 = e3 % 151.92/22.57 (25) op(e0, e0) = all_8_1 % 151.92/22.57 (26) ~ (all_4_2 = e2) % 151.92/22.57 (27) ~ (all_52_4 = all_10_0) % 151.92/22.57 (28) op(all_4_2, all_4_2) = all_4_1 % 151.92/22.57 (29) op(all_10_2, all_10_2) = e1 % 151.92/22.57 (30) all_56_3 = all_52_4 % 151.92/22.57 (31) ~ (all_10_0 = e1) % 151.92/22.57 (32) all_32_0 = all_10_0 % 151.92/22.57 (33) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0 % 151.92/22.57 (34) ~ (all_52_12 = all_4_2) % 151.92/22.57 (35) all_58_0 = all_10_2 % 151.92/22.57 (36) op(e0, all_4_2) = all_56_30 % 151.92/22.57 (37) op(e3, all_10_2) = all_56_0 % 151.92/22.57 (38) all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0 % 151.92/22.57 (39) ~ (all_10_0 = all_10_2) % 151.92/22.57 (40) ~ (all_52_4 = all_10_2) % 151.92/22.57 (41) ~ (all_10_0 = e2) % 151.92/22.57 (42) ~ (all_52_12 = all_10_2) % 151.92/22.57 (43) ~ (all_4_0 = e3) % 151.92/22.57 (44) all_32_2 = all_10_2 % 151.92/22.57 % 151.92/22.57 Begin of proof % 151.92/22.57 | % 151.92/22.57 | GROUND_INST: instantiating (20) with all_4_2, all_8_1, e0, e0, simplifying % 151.92/22.57 | with (9), (25) gives: % 151.92/22.57 | (45) all_8_1 = all_4_2 % 151.92/22.57 | % 151.92/22.57 | REDUCE: (8), (45) imply: % 151.92/22.57 | (46) ~ (all_4_2 = e3) % 151.92/22.57 | % 151.92/22.57 | REDUCE: (1), (45) imply: % 151.92/22.57 | (47) ~ (all_4_2 = e1) % 151.92/22.57 | % 151.92/22.57 | BETA: splitting (33) gives: % 151.92/22.57 | % 151.92/22.57 | Case 1: % 151.92/22.57 | | % 151.92/22.57 | | (48) all_54_15 = e3 % 151.92/22.57 | | % 151.92/22.57 | | REF_CLOSE: (11), (46), (48) are inconsistent by sub-proof #740. % 151.92/22.57 | | % 151.92/22.57 | Case 2: % 151.92/22.57 | | % 151.92/22.57 | | (49) all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0 % 151.92/22.57 | | % 151.92/22.57 | | BETA: splitting (49) gives: % 151.92/22.57 | | % 151.92/22.57 | | Case 1: % 151.92/22.57 | | | % 151.92/22.57 | | | (50) all_54_15 = e2 % 151.92/22.57 | | | % 151.92/22.57 | | | REF_CLOSE: (11), (26), (50) are inconsistent by sub-proof #739. % 151.92/22.57 | | | % 151.92/22.57 | | Case 2: % 151.92/22.57 | | | % 151.92/22.57 | | | (51) all_54_15 = e1 | all_54_15 = e0 % 151.92/22.57 | | | % 151.92/22.57 | | | BETA: splitting (51) gives: % 151.92/22.57 | | | % 151.92/22.57 | | | Case 1: % 151.92/22.57 | | | | % 151.92/22.57 | | | | (52) all_54_15 = e1 % 151.92/22.57 | | | | % 151.92/22.57 | | | | REF_CLOSE: (11), (47), (52) are inconsistent by sub-proof #738. % 151.92/22.57 | | | | % 151.92/22.57 | | | Case 2: % 151.92/22.57 | | | | % 151.92/22.57 | | | | (53) all_54_15 = e0 % 151.92/22.57 | | | | % 151.92/22.57 | | | | COMBINE_EQS: (11), (53) imply: % 151.92/22.57 | | | | (54) all_4_2 = e0 % 151.92/22.57 | | | | % 151.92/22.57 | | | | SIMP: (54) implies: % 151.92/22.57 | | | | (55) all_4_2 = e0 % 151.92/22.57 | | | | % 151.92/22.57 | | | | REDUCE: (34), (55) imply: % 151.92/22.57 | | | | (56) ~ (all_52_12 = e0) % 151.92/22.57 | | | | % 151.92/22.57 | | | | REDUCE: (28), (55) imply: % 151.92/22.57 | | | | (57) op(e0, e0) = all_4_1 % 151.92/22.57 | | | | % 151.92/22.57 | | | | REDUCE: (36), (55) imply: % 151.92/22.57 | | | | (58) op(e0, e0) = all_56_30 % 151.92/22.57 | | | | % 151.92/22.57 | | | | REDUCE: (9), (55) imply: % 151.92/22.57 | | | | (59) op(e0, e0) = e0 % 151.92/22.57 | | | | % 151.92/22.57 | | | | GROUND_INST: instantiating (20) with all_4_1, all_56_30, e0, e0, % 151.92/22.57 | | | | simplifying with (57), (58) gives: % 151.92/22.57 | | | | (60) all_56_30 = all_4_1 % 151.92/22.57 | | | | % 151.92/22.57 | | | | GROUND_INST: instantiating (20) with e0, all_56_30, e0, e0, simplifying % 151.92/22.57 | | | | with (58), (59) gives: % 151.92/22.57 | | | | (61) all_56_30 = e0 % 151.92/22.57 | | | | % 151.92/22.57 | | | | COMBINE_EQS: (60), (61) imply: % 151.92/22.57 | | | | (62) all_4_1 = e0 % 151.92/22.57 | | | | % 151.92/22.57 | | | | SIMP: (62) implies: % 151.92/22.57 | | | | (63) all_4_1 = e0 % 151.92/22.57 | | | | % 151.92/22.57 | | | | REDUCE: (21), (63) imply: % 151.92/22.57 | | | | (64) op(e0, e0) = all_4_0 % 151.92/22.57 | | | | % 151.92/22.57 | | | | GROUND_INST: instantiating (20) with e0, all_4_0, e0, e0, simplifying % 151.92/22.57 | | | | with (59), (64) gives: % 151.92/22.57 | | | | (65) all_4_0 = e0 % 151.92/22.57 | | | | % 151.92/22.57 | | | | REDUCE: (43), (65) imply: % 151.92/22.57 | | | | (66) ~ (e3 = e0) % 151.92/22.57 | | | | % 151.92/22.57 | | | | SIMP: (66) implies: % 151.92/22.57 | | | | (67) ~ (e3 = e0) % 151.92/22.57 | | | | % 151.92/22.57 | | | | REDUCE: (23), (65) imply: % 151.92/22.57 | | | | (68) ~ (e1 = e0) % 151.92/22.57 | | | | % 151.92/22.57 | | | | SIMP: (68) implies: % 151.92/22.57 | | | | (69) ~ (e1 = e0) % 151.92/22.57 | | | | % 151.92/22.57 | | | | BETA: splitting (24) gives: % 151.92/22.57 | | | | % 151.92/22.57 | | | | Case 1: % 151.92/22.57 | | | | | % 151.92/22.57 | | | | | (70) ~ (all_56_1 = e2) % 151.92/22.57 | | | | | % 151.92/22.57 | | | | | REDUCE: (12), (70) imply: % 151.92/22.57 | | | | | (71) ~ (all_10_2 = e2) % 151.92/22.57 | | | | | % 151.92/22.57 | | | | | BETA: splitting (4) gives: % 151.92/22.57 | | | | | % 151.92/22.57 | | | | | Case 1: % 151.92/22.57 | | | | | | % 151.92/22.57 | | | | | | (72) all_58_0 = e2 % 151.92/22.57 | | | | | | % 151.92/22.57 | | | | | | COMBINE_EQS: (35), (72) imply: % 151.92/22.57 | | | | | | (73) all_10_2 = e2 % 151.92/22.57 | | | | | | % 151.92/22.57 | | | | | | REDUCE: (71), (73) imply: % 151.92/22.57 | | | | | | (74) $false % 151.92/22.57 | | | | | | % 151.92/22.57 | | | | | | CLOSE: (74) is inconsistent. % 151.92/22.57 | | | | | | % 151.92/22.57 | | | | | Case 2: % 151.92/22.57 | | | | | | % 151.92/22.57 | | | | | | (75) all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2 % 151.92/22.57 | | | | | | % 151.92/22.57 | | | | | | BETA: splitting (75) gives: % 151.92/22.57 | | | | | | % 151.92/22.57 | | | | | | Case 1: % 151.92/22.57 | | | | | | | % 151.92/22.57 | | | | | | | (76) all_58_1 = e2 % 151.92/22.57 | | | | | | | % 151.92/22.57 | | | | | | | COMBINE_EQS: (16), (76) imply: % 151.92/22.57 | | | | | | | (77) all_52_4 = e2 % 151.92/22.57 | | | | | | | % 151.92/22.57 | | | | | | | REDUCE: (22), (77) imply: % 151.92/22.57 | | | | | | | (78) ~ (e2 = e0) % 151.92/22.57 | | | | | | | % 151.92/22.57 | | | | | | | BETA: splitting (38) gives: % 151.92/22.57 | | | | | | | % 151.92/22.57 | | | | | | | Case 1: % 151.92/22.57 | | | | | | | | % 151.92/22.57 | | | | | | | | (79) all_58_0 = e0 % 151.92/22.57 | | | | | | | | % 151.92/22.57 | | | | | | | | COMBINE_EQS: (35), (79) imply: % 151.92/22.57 | | | | | | | | (80) all_10_2 = e0 % 151.92/22.57 | | | | | | | | % 151.92/22.57 | | | | | | | | REDUCE: (29), (80) imply: % 151.92/22.57 | | | | | | | | (81) op(e0, e0) = e1 % 151.92/22.57 | | | | | | | | % 151.92/22.57 | | | | | | | | REF_CLOSE: (20), (57), (58), (59), (69), (81) are inconsistent % 151.92/22.57 | | | | | | | | by sub-proof #389. % 151.92/22.57 | | | | | | | | % 151.92/22.57 | | | | | | | Case 2: % 151.92/22.57 | | | | | | | | % 151.92/22.57 | | | | | | | | (82) ~ (all_58_0 = e0) % 151.92/22.57 | | | | | | | | % 151.92/22.57 | | | | | | | | REDUCE: (35), (82) imply: % 151.92/22.57 | | | | | | | | (83) ~ (all_10_2 = e0) % 151.92/22.57 | | | | | | | | % 151.92/22.57 | | | | | | | | BETA: splitting (19) gives: % 151.92/22.57 | | | | | | | | % 151.92/22.57 | | | | | | | | Case 1: % 151.92/22.57 | | | | | | | | | % 151.92/22.57 | | | | | | | | | (84) all_58_0 = e0 % 151.92/22.57 | | | | | | | | | % 151.92/22.57 | | | | | | | | | COMBINE_EQS: (35), (84) imply: % 151.92/22.57 | | | | | | | | | (85) all_10_2 = e0 % 151.92/22.57 | | | | | | | | | % 151.92/22.57 | | | | | | | | | REDUCE: (83), (85) imply: % 151.92/22.57 | | | | | | | | | (86) $false % 151.92/22.57 | | | | | | | | | % 151.92/22.57 | | | | | | | | | CLOSE: (86) is inconsistent. % 151.92/22.57 | | | | | | | | | % 151.92/22.57 | | | | | | | | Case 2: % 151.92/22.57 | | | | | | | | | % 151.92/22.57 | | | | | | | | | (87) all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0 % 151.92/22.57 | | | | | | | | | % 151.92/22.57 | | | | | | | | | BETA: splitting (87) gives: % 151.92/22.57 | | | | | | | | | % 151.92/22.57 | | | | | | | | | Case 1: % 151.92/22.57 | | | | | | | | | | % 151.92/22.57 | | | | | | | | | | (88) all_58_1 = e0 % 151.92/22.57 | | | | | | | | | | % 151.92/22.57 | | | | | | | | | | COMBINE_EQS: (76), (88) imply: % 151.92/22.57 | | | | | | | | | | (89) e2 = e0 % 151.92/22.57 | | | | | | | | | | % 151.92/22.57 | | | | | | | | | | REDUCE: (78), (89) imply: % 151.92/22.57 | | | | | | | | | | (90) $false % 151.92/22.57 | | | | | | | | | | % 151.92/22.57 | | | | | | | | | | CLOSE: (90) is inconsistent. % 151.92/22.57 | | | | | | | | | | % 151.92/22.57 | | | | | | | | | Case 2: % 151.92/22.57 | | | | | | | | | | % 151.92/22.57 | | | | | | | | | | (91) all_58_4 = e0 | all_58_9 = e0 % 151.92/22.57 | | | | | | | | | | % 151.92/22.57 | | | | | | | | | | BETA: splitting (91) gives: % 151.92/22.57 | | | | | | | | | | % 151.92/22.57 | | | | | | | | | | Case 1: % 151.92/22.57 | | | | | | | | | | | % 151.92/22.57 | | | | | | | | | | | (92) all_58_4 = e0 % 151.92/22.57 | | | | | | | | | | | % 151.92/22.57 | | | | | | | | | | | COMBINE_EQS: (5), (92) imply: % 151.92/22.57 | | | | | | | | | | | (93) all_10_0 = e0 % 151.92/22.57 | | | | | | | | | | | % 151.92/22.57 | | | | | | | | | | | REF_CLOSE: (2), (3), (10), (12), (13), (15), (17), (20), % 151.92/22.57 | | | | | | | | | | | (29), (32), (37), (44), (67), (83), (93) are % 151.92/22.57 | | | | | | | | | | | inconsistent by sub-proof #388. % 151.92/22.57 | | | | | | | | | | | % 151.92/22.57 | | | | | | | | | | Case 2: % 151.92/22.57 | | | | | | | | | | | % 151.92/22.57 | | | | | | | | | | | (94) all_58_9 = e0 % 151.92/22.57 | | | | | | | | | | | % 151.92/22.57 | | | | | | | | | | | COMBINE_EQS: (14), (94) imply: % 151.92/22.57 | | | | | | | | | | | (95) all_52_12 = e0 % 151.92/22.57 | | | | | | | | | | | % 151.92/22.57 | | | | | | | | | | | REDUCE: (56), (95) imply: % 151.92/22.57 | | | | | | | | | | | (96) $false % 151.92/22.57 | | | | | | | | | | | % 151.92/22.57 | | | | | | | | | | | CLOSE: (96) is inconsistent. % 151.92/22.57 | | | | | | | | | | | % 151.92/22.57 | | | | | | | | | | End of split % 151.92/22.57 | | | | | | | | | | % 151.92/22.57 | | | | | | | | | End of split % 151.92/22.57 | | | | | | | | | % 151.92/22.57 | | | | | | | | End of split % 151.92/22.57 | | | | | | | | % 151.92/22.57 | | | | | | | End of split % 151.92/22.57 | | | | | | | % 151.92/22.57 | | | | | | Case 2: % 151.92/22.57 | | | | | | | % 151.92/22.57 | | | | | | | (97) all_58_4 = e2 | all_58_9 = e2 % 151.92/22.57 | | | | | | | % 151.92/22.57 | | | | | | | REF_CLOSE: (5), (6), (14), (41), (97) are inconsistent by % 151.92/22.57 | | | | | | | sub-proof #387. % 151.92/22.57 | | | | | | | % 151.92/22.57 | | | | | | End of split % 151.92/22.57 | | | | | | % 151.92/22.57 | | | | | End of split % 151.92/22.57 | | | | | % 151.92/22.57 | | | | Case 2: % 151.92/22.57 | | | | | % 151.92/22.57 | | | | | (98) all_56_3 = e3 % 151.92/22.57 | | | | | (99) all_56_1 = e2 % 151.92/22.57 | | | | | % 151.92/22.57 | | | | | COMBINE_EQS: (12), (99) imply: % 151.92/22.57 | | | | | (100) all_10_2 = e2 % 151.92/22.57 | | | | | % 151.92/22.57 | | | | | COMBINE_EQS: (30), (98) imply: % 151.92/22.57 | | | | | (101) all_52_4 = e3 % 151.92/22.57 | | | | | % 151.92/22.57 | | | | | COMBINE_EQS: (16), (101) imply: % 151.92/22.57 | | | | | (102) all_58_1 = e3 % 151.92/22.57 | | | | | % 151.92/22.57 | | | | | REDUCE: (27), (101) imply: % 151.92/22.57 | | | | | (103) ~ (all_10_0 = e3) % 151.92/22.57 | | | | | % 151.92/22.57 | | | | | SIMP: (103) implies: % 151.92/22.57 | | | | | (104) ~ (all_10_0 = e3) % 151.92/22.57 | | | | | % 151.92/22.57 | | | | | REDUCE: (40), (100), (101) imply: % 151.92/22.57 | | | | | (105) ~ (e3 = e2) % 151.92/22.57 | | | | | % 151.92/22.57 | | | | | REF_CLOSE: (4), (5), (6), (7), (13), (14), (18), (31), (32), (35), % 151.92/22.57 | | | | | (39), (41), (44), (102), (104), (105) are inconsistent by % 151.92/22.57 | | | | | sub-proof #386. % 151.92/22.57 | | | | | % 151.92/22.57 | | | | End of split % 151.92/22.57 | | | | % 151.92/22.57 | | | End of split % 151.92/22.57 | | | % 151.92/22.57 | | End of split % 151.92/22.57 | | % 151.92/22.57 | End of split % 151.92/22.57 | % 151.92/22.57 End of proof % 151.92/22.57 % 151.92/22.57 Sub-proof #386 shows that the following formulas are inconsistent: % 151.92/22.57 ---------------------------------------------------------------- % 151.92/22.57 (1) all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2 % 151.92/22.57 (2) all_58_4 = all_10_0 % 151.92/22.57 (3) ~ (all_52_12 = e2) % 151.92/22.57 (4) all_54_2 = all_10_0 % 151.92/22.57 (5) ~ (e3 = e2) % 151.92/22.57 (6) ~ (all_32_0 = e0) | ~ (all_32_2 = e2) % 151.92/22.57 (7) all_58_9 = all_52_12 % 151.92/22.57 (8) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0 % 151.92/22.57 (9) ~ (all_10_0 = e1) % 151.92/22.57 (10) all_32_0 = all_10_0 % 151.92/22.57 (11) all_58_1 = e3 % 151.92/22.57 (12) ~ (all_10_0 = e3) % 151.92/22.57 (13) all_58_0 = all_10_2 % 151.92/22.57 (14) ~ (all_10_0 = all_10_2) % 151.92/22.57 (15) ~ (all_10_0 = e2) % 151.92/22.57 (16) all_32_2 = all_10_2 % 151.92/22.57 % 151.92/22.57 Begin of proof % 151.92/22.57 | % 151.92/22.57 | BETA: splitting (1) gives: % 151.92/22.57 | % 151.92/22.57 | Case 1: % 151.92/22.57 | | % 151.92/22.57 | | (17) all_58_0 = e2 % 151.92/22.57 | | % 151.92/22.57 | | COMBINE_EQS: (13), (17) imply: % 151.92/22.57 | | (18) all_10_2 = e2 % 151.92/22.57 | | % 151.92/22.57 | | COMBINE_EQS: (16), (18) imply: % 151.92/22.57 | | (19) all_32_2 = e2 % 151.92/22.57 | | % 151.92/22.57 | | REF_CLOSE: (4), (6), (8), (9), (10), (12), (15), (19) are inconsistent by % 151.92/22.57 | | sub-proof #404. % 151.92/22.57 | | % 151.92/22.57 | Case 2: % 151.92/22.57 | | % 151.92/22.57 | | (20) all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2 % 151.92/22.57 | | % 151.92/22.57 | | BETA: splitting (20) gives: % 151.92/22.57 | | % 151.92/22.57 | | Case 1: % 151.92/22.57 | | | % 151.92/22.57 | | | (21) all_58_1 = e2 % 151.92/22.57 | | | % 151.92/22.57 | | | COMBINE_EQS: (11), (21) imply: % 151.92/22.57 | | | (22) e3 = e2 % 151.92/22.57 | | | % 151.92/22.57 | | | REDUCE: (5), (22) imply: % 151.92/22.57 | | | (23) $false % 151.92/22.57 | | | % 151.92/22.57 | | | CLOSE: (23) is inconsistent. % 151.92/22.57 | | | % 151.92/22.57 | | Case 2: % 151.92/22.57 | | | % 151.92/22.57 | | | (24) all_58_4 = e2 | all_58_9 = e2 % 151.92/22.57 | | | % 151.92/22.57 | | | REF_CLOSE: (2), (3), (7), (15), (24) are inconsistent by sub-proof #387. % 151.92/22.57 | | | % 151.92/22.57 | | End of split % 151.92/22.57 | | % 151.92/22.57 | End of split % 151.92/22.57 | % 151.92/22.57 End of proof % 151.92/22.57 % 151.92/22.57 Sub-proof #387 shows that the following formulas are inconsistent: % 151.92/22.57 ---------------------------------------------------------------- % 151.92/22.57 (1) all_58_4 = all_10_0 % 151.92/22.57 (2) ~ (all_52_12 = e2) % 151.92/22.57 (3) all_58_9 = all_52_12 % 151.92/22.57 (4) all_58_4 = e2 | all_58_9 = e2 % 151.92/22.57 (5) ~ (all_10_0 = e2) % 151.92/22.57 % 151.92/22.57 Begin of proof % 151.92/22.57 | % 151.92/22.57 | BETA: splitting (4) gives: % 151.92/22.57 | % 151.92/22.57 | Case 1: % 151.92/22.57 | | % 151.92/22.57 | | (6) all_58_4 = e2 % 151.92/22.57 | | % 151.92/22.57 | | COMBINE_EQS: (1), (6) imply: % 151.92/22.57 | | (7) all_10_0 = e2 % 151.92/22.57 | | % 151.92/22.57 | | REDUCE: (5), (7) imply: % 151.92/22.57 | | (8) $false % 151.92/22.57 | | % 151.92/22.57 | | CLOSE: (8) is inconsistent. % 151.92/22.57 | | % 151.92/22.57 | Case 2: % 151.92/22.57 | | % 151.92/22.57 | | (9) all_58_9 = e2 % 151.92/22.57 | | % 151.92/22.57 | | COMBINE_EQS: (3), (9) imply: % 151.92/22.57 | | (10) all_52_12 = e2 % 151.92/22.57 | | % 151.92/22.57 | | REDUCE: (2), (10) imply: % 151.92/22.57 | | (11) $false % 151.92/22.57 | | % 151.92/22.57 | | CLOSE: (11) is inconsistent. % 151.92/22.57 | | % 151.92/22.57 | End of split % 151.92/22.57 | % 151.92/22.57 End of proof % 151.92/22.57 % 151.92/22.57 Sub-proof #388 shows that the following formulas are inconsistent: % 151.92/22.57 ---------------------------------------------------------------- % 151.92/22.57 (1) ~ (e3 = e0) % 151.92/22.57 (2) all_56_5 = all_10_0 % 151.92/22.57 (3) all_54_0 = all_10_2 % 151.92/22.57 (4) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 151.92/22.57 (5) all_10_0 = e0 % 151.92/22.57 (6) all_56_1 = all_10_2 % 151.92/22.57 (7) ~ (all_32_0 = e0) | ~ (all_32_2 = e2) % 151.92/22.57 (8) ~ (all_56_1 = e1) | all_56_5 = e3 % 151.92/22.57 (9) op(e3, e3) = all_10_2 % 151.92/22.57 (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 151.92/22.57 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 151.92/22.57 (11) op(all_10_2, all_10_2) = e1 % 151.92/22.57 (12) all_32_0 = all_10_0 % 151.92/22.57 (13) ~ (all_10_2 = e0) % 151.92/22.57 (14) op(e3, all_10_2) = all_56_0 % 151.92/22.57 (15) all_32_2 = all_10_2 % 151.92/22.57 % 151.92/22.57 Begin of proof % 151.92/22.57 | % 151.92/22.57 | COMBINE_EQS: (5), (12) imply: % 151.92/22.57 | (16) all_32_0 = e0 % 151.92/22.57 | % 151.92/22.57 | COMBINE_EQS: (2), (5) imply: % 151.92/22.57 | (17) all_56_5 = e0 % 151.92/22.57 | % 151.92/22.57 | REF_CLOSE: (1), (3), (4), (6), (7), (8), (9), (10), (11), (13), (14), (15), % 151.92/22.57 | (16), (17) are inconsistent by sub-proof #398. % 151.92/22.57 | % 151.92/22.57 End of proof % 151.92/22.57 % 151.92/22.57 Sub-proof #389 shows that the following formulas are inconsistent: % 151.92/22.57 ---------------------------------------------------------------- % 151.92/22.57 (1) op(e0, e0) = e1 % 151.92/22.57 (2) op(e0, e0) = all_56_30 % 151.92/22.57 (3) op(e0, e0) = all_4_1 % 151.92/22.57 (4) ~ (e1 = e0) % 151.92/22.57 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 151.92/22.57 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 151.92/22.57 (6) op(e0, e0) = e0 % 151.92/22.57 % 151.92/22.57 Begin of proof % 151.92/22.57 | % 151.92/22.57 | GROUND_INST: instantiating (5) with e0, all_4_1, e0, e0, simplifying with (3), % 151.92/22.57 | (6) gives: % 151.92/22.57 | (7) all_4_1 = e0 % 151.92/22.57 | % 151.92/22.57 | GROUND_INST: instantiating (5) with all_4_1, all_56_30, e0, e0, simplifying % 151.92/22.57 | with (2), (3) gives: % 151.92/22.57 | (8) all_56_30 = all_4_1 % 151.92/22.57 | % 151.92/22.57 | GROUND_INST: instantiating (5) with e1, all_56_30, e0, e0, simplifying with % 151.92/22.57 | (1), (2) gives: % 151.92/22.57 | (9) all_56_30 = e1 % 151.92/22.57 | % 151.92/22.57 | COMBINE_EQS: (8), (9) imply: % 151.92/22.57 | (10) all_4_1 = e1 % 151.92/22.57 | % 151.92/22.57 | SIMP: (10) implies: % 151.92/22.57 | (11) all_4_1 = e1 % 151.92/22.57 | % 151.92/22.57 | COMBINE_EQS: (7), (11) imply: % 151.92/22.57 | (12) e1 = e0 % 151.92/22.57 | % 151.92/22.57 | SIMP: (12) implies: % 151.92/22.57 | (13) e1 = e0 % 151.92/22.57 | % 151.92/22.57 | REDUCE: (4), (13) imply: % 151.92/22.57 | (14) $false % 151.92/22.57 | % 151.92/22.57 | CLOSE: (14) is inconsistent. % 151.92/22.57 | % 151.92/22.57 End of proof % 151.92/22.57 % 151.92/22.57 Sub-proof #390 shows that the following formulas are inconsistent: % 151.92/22.57 ---------------------------------------------------------------- % 151.92/22.57 (1) all_56_11 = all_8_2 % 151.92/22.57 (2) op(e0, all_52_13) = all_56_14 % 151.92/22.57 (3) ~ (all_56_11 = e1) | all_56_13 = e2 % 151.92/22.57 (4) ~ (all_52_11 = all_6_2) % 151.92/22.57 (5) op(e2, all_8_1) = all_8_0 % 151.92/22.57 (6) ~ (all_8_1 = e1) % 151.92/22.57 (7) ~ (all_52_1 = all_52_9) % 151.92/22.57 (8) ~ (e3 = e0) % 151.92/22.57 (9) all_56_5 = all_10_0 % 151.92/22.57 (10) all_54_0 = all_10_2 % 151.92/22.57 (11) all_54_4 = all_52_1 % 151.92/22.57 (12) ~ (all_8_0 = e1) % 151.92/22.57 (13) all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2 % 151.92/22.57 (14) all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2 % 151.92/22.57 (15) ~ (all_52_9 = all_8_2) % 151.92/22.57 (16) all_58_4 = all_10_0 % 151.92/22.57 (17) all_54_2 = all_10_0 % 151.92/22.57 (18) all_54_5 = all_8_2 % 151.92/22.57 (19) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 151.92/22.57 (20) all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1 % 151.92/22.57 (21) all_56_21 = all_6_2 % 151.92/22.57 (22) op(e3, all_52_1) = all_56_8 % 151.92/22.57 (23) all_56_1 = all_10_2 % 151.92/22.57 (24) ~ (all_32_0 = e0) | ~ (all_32_2 = e2) % 151.92/22.57 (25) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0 % 151.92/22.57 (26) all_58_5 = all_52_9 % 151.92/22.57 (27) all_58_9 = all_52_12 % 151.92/22.57 (28) ~ (all_56_1 = e1) | all_56_5 = e3 % 151.92/22.57 (29) all_58_1 = all_52_4 % 151.92/22.57 (30) all_58_13 = all_52_7 % 151.92/22.57 (31) all_58_4 = e0 | all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0 % 151.92/22.57 (32) op(e2, all_8_2) = all_56_10 % 151.92/22.57 (33) op(e3, e3) = all_10_2 % 151.92/22.57 (34) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0 % 151.92/22.57 (35) ~ (all_56_21 = e3) | all_56_17 = e1 % 151.92/22.57 (36) ~ (all_52_1 = all_8_2) % 151.92/22.57 (37) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 151.92/22.57 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 151.92/22.57 (38) ~ (all_52_3 = all_10_2) % 151.92/22.57 (39) ~ (all_52_11 = all_10_0) % 151.92/22.57 (40) ~ (all_56_11 = e3) | all_56_9 = e2 % 151.92/22.57 (41) op(e0, all_4_1) = all_4_0 % 151.92/22.57 (42) all_56_7 = all_52_12 % 151.92/22.57 (43) all_56_13 = all_52_9 % 151.92/22.57 (44) op(e0, e1) = all_52_11 % 151.92/22.57 (45) ~ (all_52_1 = all_52_13) % 151.92/22.57 (46) ~ (all_52_7 = all_4_2) % 151.92/22.57 (47) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0 % 151.92/22.57 (48) ~ (all_4_2 = e1) % 151.92/22.57 (49) all_58_8 = all_6_2 % 151.92/22.57 (50) all_54_6 = all_52_9 % 151.92/22.57 (51) ~ (all_52_12 = all_10_0) % 151.92/22.57 (52) ~ (all_56_1 = e2) | all_56_3 = e3 % 151.92/22.57 (53) ~ (all_56_1 = e0) | all_56_7 = e3 % 151.92/22.57 (54) ~ (all_52_4 = all_10_0) % 151.92/22.57 (55) ~ (all_52_9 = all_52_13) % 151.92/22.57 (56) op(all_4_2, all_4_2) = all_4_1 % 151.92/22.57 (57) op(all_10_2, all_10_2) = e1 % 151.92/22.57 (58) all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3 % 151.92/22.57 (59) all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1 % 151.92/22.57 (60) all_56_3 = all_52_4 % 151.92/22.57 (61) ~ (all_52_1 = all_52_3) % 151.92/22.57 (62) all_58_11 = all_52_14 % 151.92/22.57 (63) ~ (all_8_0 = e3) % 151.92/22.57 (64) ~ (all_10_0 = all_6_2) % 151.92/22.57 (65) ~ (all_52_9 = all_52_11) % 151.92/22.57 (66) ~ (all_10_0 = e1) % 151.92/22.57 (67) ~ (all_52_9 = all_10_0) % 151.92/22.57 (68) all_32_0 = all_10_0 % 151.92/22.57 (69) op(e1, e1) = all_6_2 % 151.92/22.57 (70) all_58_15 = all_4_2 % 151.92/22.57 (71) ~ (all_6_2 = e2) % 151.92/22.57 (72) all_58_2 = all_52_1 % 151.92/22.57 (73) all_58_10 = all_52_13 % 151.92/22.57 (74) all_58_0 = all_10_2 % 151.92/22.57 (75) all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1 % 151.92/22.57 (76) op(e2, e2) = all_8_2 % 151.92/22.57 (77) ~ (all_8_2 = e0) % 151.92/22.57 (78) op(e3, all_10_2) = all_56_0 % 151.92/22.57 (79) ~ (all_52_14 = all_6_2) % 151.92/22.57 (80) ~ (e2 = e0) % 151.92/22.57 (81) ~ (all_10_0 = all_10_2) % 151.92/22.57 (82) all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3 % 151.92/22.57 (83) ~ (all_10_0 = e2) % 151.92/22.57 (84) ~ (all_52_4 = all_8_2) % 151.92/22.57 (85) op(all_8_2, all_8_2) = all_8_1 % 151.92/22.57 (86) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 151.92/22.57 (87) all_58_14 = all_52_11 % 151.92/22.57 (88) ~ (all_52_12 = all_10_2) % 151.92/22.57 (89) ~ (all_4_0 = e2) % 151.92/22.57 (90) all_56_9 = all_52_1 % 151.92/22.57 (91) all_32_2 = all_10_2 % 151.92/22.57 (92) ~ (all_52_1 = all_10_2) % 151.92/22.57 (93) all_58_12 = all_52_3 % 151.92/22.57 (94) all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3 % 151.92/22.57 % 151.92/22.57 Begin of proof % 151.92/22.57 | % 151.92/22.57 | BETA: splitting (35) gives: % 151.92/22.57 | % 151.92/22.57 | Case 1: % 151.92/22.57 | | % 151.92/22.57 | | (95) ~ (all_56_21 = e3) % 151.92/22.57 | | % 151.92/22.57 | | REDUCE: (21), (95) imply: % 151.92/22.57 | | (96) ~ (all_6_2 = e3) % 151.92/22.58 | | % 151.92/22.58 | | BETA: splitting (40) gives: % 151.92/22.58 | | % 151.92/22.58 | | Case 1: % 151.92/22.58 | | | % 151.92/22.58 | | | (97) ~ (all_56_11 = e3) % 151.92/22.58 | | | % 151.92/22.58 | | | REDUCE: (1), (97) imply: % 151.92/22.58 | | | (98) ~ (all_8_2 = e3) % 151.92/22.58 | | | % 151.92/22.58 | | | BETA: splitting (3) gives: % 151.92/22.58 | | | % 151.92/22.58 | | | Case 1: % 151.92/22.58 | | | | % 151.92/22.58 | | | | (99) ~ (all_56_11 = e1) % 151.92/22.58 | | | | % 151.92/22.58 | | | | REDUCE: (1), (99) imply: % 151.92/22.58 | | | | (100) ~ (all_8_2 = e1) % 151.92/22.58 | | | | % 151.92/22.58 | | | | BETA: splitting (86) gives: % 151.92/22.58 | | | | % 151.92/22.58 | | | | Case 1: % 151.92/22.58 | | | | | % 151.92/22.58 | | | | | (101) all_54_5 = e3 % 151.92/22.58 | | | | | % 151.92/22.58 | | | | | REF_CLOSE: (18), (98), (101) are inconsistent by sub-proof #737. % 151.92/22.58 | | | | | % 151.92/22.58 | | | | Case 2: % 151.92/22.58 | | | | | % 151.92/22.58 | | | | | (102) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 151.92/22.58 | | | | | % 151.92/22.58 | | | | | BETA: splitting (102) gives: % 151.92/22.58 | | | | | % 151.92/22.58 | | | | | Case 1: % 151.92/22.58 | | | | | | % 151.92/22.58 | | | | | | (103) all_54_5 = e2 % 151.92/22.58 | | | | | | % 151.92/22.58 | | | | | | COMBINE_EQS: (18), (103) imply: % 151.92/22.58 | | | | | | (104) all_8_2 = e2 % 151.92/22.58 | | | | | | % 151.92/22.58 | | | | | | SIMP: (104) implies: % 151.92/22.58 | | | | | | (105) all_8_2 = e2 % 151.92/22.58 | | | | | | % 151.92/22.58 | | | | | | REDUCE: (36), (105) imply: % 151.92/22.58 | | | | | | (106) ~ (all_52_1 = e2) % 151.92/22.58 | | | | | | % 151.92/22.58 | | | | | | REDUCE: (84), (105) imply: % 151.92/22.58 | | | | | | (107) ~ (all_52_4 = e2) % 151.92/22.58 | | | | | | % 151.92/22.58 | | | | | | REDUCE: (15), (105) imply: % 151.92/22.58 | | | | | | (108) ~ (all_52_9 = e2) % 151.92/22.58 | | | | | | % 151.92/22.58 | | | | | | REDUCE: (85), (105) imply: % 151.92/22.58 | | | | | | (109) op(e2, e2) = all_8_1 % 151.92/22.58 | | | | | | % 151.92/22.58 | | | | | | REDUCE: (32), (105) imply: % 151.92/22.58 | | | | | | (110) op(e2, e2) = all_56_10 % 151.92/22.58 | | | | | | % 151.92/22.58 | | | | | | REDUCE: (76), (105) imply: % 151.92/22.58 | | | | | | (111) op(e2, e2) = e2 % 151.92/22.58 | | | | | | % 151.92/22.58 | | | | | | BETA: splitting (13) gives: % 151.92/22.58 | | | | | | % 151.92/22.58 | | | | | | Case 1: % 151.92/22.58 | | | | | | | % 151.92/22.58 | | | | | | | (112) all_58_4 = e2 % 151.92/22.58 | | | | | | | % 151.92/22.58 | | | | | | | COMBINE_EQS: (16), (112) imply: % 151.92/22.58 | | | | | | | (113) all_10_0 = e2 % 151.92/22.58 | | | | | | | % 151.92/22.58 | | | | | | | REDUCE: (83), (113) imply: % 151.92/22.58 | | | | | | | (114) $false % 151.92/22.58 | | | | | | | % 151.92/22.58 | | | | | | | CLOSE: (114) is inconsistent. % 151.92/22.58 | | | | | | | % 151.92/22.58 | | | | | | Case 2: % 151.92/22.58 | | | | | | | % 151.92/22.58 | | | | | | | (115) all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2 % 151.92/22.58 | | | | | | | % 151.92/22.58 | | | | | | | BETA: splitting (115) gives: % 151.92/22.58 | | | | | | | % 151.92/22.58 | | | | | | | Case 1: % 151.92/22.58 | | | | | | | | % 151.92/22.58 | | | | | | | | (116) all_58_5 = e2 % 151.92/22.58 | | | | | | | | % 151.92/22.58 | | | | | | | | COMBINE_EQS: (26), (116) imply: % 151.92/22.58 | | | | | | | | (117) all_52_9 = e2 % 151.92/22.58 | | | | | | | | % 151.92/22.58 | | | | | | | | REDUCE: (108), (117) imply: % 151.92/22.58 | | | | | | | | (118) $false % 151.92/22.58 | | | | | | | | % 151.92/22.58 | | | | | | | | CLOSE: (118) is inconsistent. % 151.92/22.58 | | | | | | | | % 151.92/22.58 | | | | | | | Case 2: % 151.92/22.58 | | | | | | | | % 151.92/22.58 | | | | | | | | (119) all_58_8 = e2 | all_58_14 = e2 % 151.92/22.58 | | | | | | | | % 151.92/22.58 | | | | | | | | BETA: splitting (119) gives: % 151.92/22.58 | | | | | | | | % 151.92/22.58 | | | | | | | | Case 1: % 151.92/22.58 | | | | | | | | | % 151.92/22.58 | | | | | | | | | (120) all_58_8 = e2 % 151.92/22.58 | | | | | | | | | % 151.92/22.58 | | | | | | | | | COMBINE_EQS: (49), (120) imply: % 151.92/22.58 | | | | | | | | | (121) all_6_2 = e2 % 151.92/22.58 | | | | | | | | | % 151.92/22.58 | | | | | | | | | REDUCE: (71), (121) imply: % 151.92/22.58 | | | | | | | | | (122) $false % 151.92/22.58 | | | | | | | | | % 151.92/22.58 | | | | | | | | | CLOSE: (122) is inconsistent. % 151.92/22.58 | | | | | | | | | % 151.92/22.58 | | | | | | | | Case 2: % 151.92/22.58 | | | | | | | | | % 151.92/22.58 | | | | | | | | | (123) all_58_14 = e2 % 151.92/22.58 | | | | | | | | | % 151.92/22.58 | | | | | | | | | COMBINE_EQS: (87), (123) imply: % 151.92/22.58 | | | | | | | | | (124) all_52_11 = e2 % 151.92/22.58 | | | | | | | | | % 151.92/22.58 | | | | | | | | | SIMP: (124) implies: % 151.92/22.58 | | | | | | | | | (125) all_52_11 = e2 % 151.92/22.58 | | | | | | | | | % 151.92/22.58 | | | | | | | | | REDUCE: (39), (125) imply: % 151.92/22.58 | | | | | | | | | (126) ~ (all_10_0 = e2) % 151.92/22.58 | | | | | | | | | % 151.92/22.58 | | | | | | | | | REDUCE: (4), (125) imply: % 151.92/22.58 | | | | | | | | | (127) ~ (all_6_2 = e2) % 151.92/22.58 | | | | | | | | | % 151.92/22.58 | | | | | | | | | REDUCE: (44), (125) imply: % 151.92/22.58 | | | | | | | | | (128) op(e0, e1) = e2 % 151.92/22.58 | | | | | | | | | % 151.92/22.58 | | | | | | | | | GROUND_INST: instantiating (37) with all_8_1, all_56_10, e2, % 151.92/22.58 | | | | | | | | | e2, simplifying with (109), (110) gives: % 151.92/22.58 | | | | | | | | | (129) all_56_10 = all_8_1 % 151.92/22.58 | | | | | | | | | % 151.92/22.58 | | | | | | | | | GROUND_INST: instantiating (37) with e2, all_56_10, e2, e2, % 151.92/22.58 | | | | | | | | | simplifying with (110), (111) gives: % 151.92/22.58 | | | | | | | | | (130) all_56_10 = e2 % 151.92/22.58 | | | | | | | | | % 151.92/22.58 | | | | | | | | | COMBINE_EQS: (129), (130) imply: % 151.92/22.58 | | | | | | | | | (131) all_8_1 = e2 % 151.92/22.58 | | | | | | | | | % 151.92/22.58 | | | | | | | | | SIMP: (131) implies: % 151.92/22.58 | | | | | | | | | (132) all_8_1 = e2 % 151.92/22.58 | | | | | | | | | % 151.92/22.58 | | | | | | | | | REDUCE: (5), (132) imply: % 151.92/22.58 | | | | | | | | | (133) op(e2, e2) = all_8_0 % 151.92/22.58 | | | | | | | | | % 151.92/22.58 | | | | | | | | | GROUND_INST: instantiating (37) with e2, all_8_0, e2, e2, % 151.92/22.58 | | | | | | | | | simplifying with (111), (133) gives: % 151.92/22.58 | | | | | | | | | (134) all_8_0 = e2 % 151.92/22.58 | | | | | | | | | % 151.92/22.58 | | | | | | | | | REDUCE: (63), (134) imply: % 151.92/22.58 | | | | | | | | | (135) ~ (e3 = e2) % 151.92/22.58 | | | | | | | | | % 151.92/22.58 | | | | | | | | | SIMP: (135) implies: % 151.92/22.58 | | | | | | | | | (136) ~ (e3 = e2) % 151.92/22.58 | | | | | | | | | % 151.92/22.58 | | | | | | | | | REDUCE: (12), (134) imply: % 151.92/22.58 | | | | | | | | | (137) ~ (e2 = e1) % 151.92/22.58 | | | | | | | | | % 151.92/22.58 | | | | | | | | | BETA: splitting (52) gives: % 151.92/22.58 | | | | | | | | | % 151.92/22.58 | | | | | | | | | Case 1: % 151.92/22.58 | | | | | | | | | | % 151.92/22.58 | | | | | | | | | | (138) ~ (all_56_1 = e2) % 151.92/22.58 | | | | | | | | | | % 151.92/22.58 | | | | | | | | | | REDUCE: (23), (138) imply: % 151.92/22.58 | | | | | | | | | | (139) ~ (all_10_2 = e2) % 151.92/22.58 | | | | | | | | | | % 151.92/22.58 | | | | | | | | | | BETA: splitting (14) gives: % 151.92/22.58 | | | | | | | | | | % 151.92/22.58 | | | | | | | | | | Case 1: % 151.92/22.58 | | | | | | | | | | | % 151.92/22.58 | | | | | | | | | | | (140) all_58_0 = e2 % 151.92/22.58 | | | | | | | | | | | % 151.92/22.58 | | | | | | | | | | | COMBINE_EQS: (74), (140) imply: % 151.92/22.58 | | | | | | | | | | | (141) all_10_2 = e2 % 151.92/22.58 | | | | | | | | | | | % 151.92/22.58 | | | | | | | | | | | REDUCE: (139), (141) imply: % 151.92/22.58 | | | | | | | | | | | (142) $false % 151.92/22.58 | | | | | | | | | | | % 151.92/22.58 | | | | | | | | | | | CLOSE: (142) is inconsistent. % 151.92/22.58 | | | | | | | | | | | % 151.92/22.58 | | | | | | | | | | Case 2: % 151.92/22.58 | | | | | | | | | | | % 151.92/22.58 | | | | | | | | | | | (143) all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2 % 151.92/22.58 | | | | | | | | | | | % 151.92/22.58 | | | | | | | | | | | BETA: splitting (143) gives: % 151.92/22.58 | | | | | | | | | | | % 151.92/22.58 | | | | | | | | | | | Case 1: % 151.92/22.58 | | | | | | | | | | | | % 151.92/22.58 | | | | | | | | | | | | (144) all_58_1 = e2 % 151.92/22.58 | | | | | | | | | | | | % 151.92/22.58 | | | | | | | | | | | | COMBINE_EQS: (29), (144) imply: % 151.92/22.58 | | | | | | | | | | | | (145) all_52_4 = e2 % 151.92/22.58 | | | | | | | | | | | | % 151.92/22.58 | | | | | | | | | | | | REDUCE: (107), (145) imply: % 151.92/22.58 | | | | | | | | | | | | (146) $false % 151.92/22.58 | | | | | | | | | | | | % 151.92/22.58 | | | | | | | | | | | | CLOSE: (146) is inconsistent. % 151.92/22.58 | | | | | | | | | | | | % 151.92/22.58 | | | | | | | | | | | Case 2: % 151.92/22.58 | | | | | | | | | | | | % 151.92/22.58 | | | | | | | | | | | | (147) all_58_4 = e2 | all_58_9 = e2 % 151.92/22.58 | | | | | | | | | | | | % 151.92/22.58 | | | | | | | | | | | | BETA: splitting (147) gives: % 151.92/22.58 | | | | | | | | | | | | % 151.92/22.58 | | | | | | | | | | | | Case 1: % 151.92/22.58 | | | | | | | | | | | | | % 151.92/22.58 | | | | | | | | | | | | | (148) all_58_4 = e2 % 151.92/22.58 | | | | | | | | | | | | | % 151.92/22.58 | | | | | | | | | | | | | COMBINE_EQS: (16), (148) imply: % 151.92/22.58 | | | | | | | | | | | | | (149) all_10_0 = e2 % 151.92/22.58 | | | | | | | | | | | | | % 151.92/22.58 | | | | | | | | | | | | | REDUCE: (83), (149) imply: % 151.92/22.58 | | | | | | | | | | | | | (150) $false % 151.92/22.58 | | | | | | | | | | | | | % 151.92/22.58 | | | | | | | | | | | | | CLOSE: (150) is inconsistent. % 151.92/22.58 | | | | | | | | | | | | | % 151.92/22.58 | | | | | | | | | | | | Case 2: % 151.92/22.58 | | | | | | | | | | | | | % 151.92/22.58 | | | | | | | | | | | | | (151) all_58_9 = e2 % 151.92/22.58 | | | | | | | | | | | | | % 151.92/22.58 | | | | | | | | | | | | | COMBINE_EQS: (27), (151) imply: % 151.92/22.58 | | | | | | | | | | | | | (152) all_52_12 = e2 % 151.92/22.58 | | | | | | | | | | | | | % 151.92/22.58 | | | | | | | | | | | | | COMBINE_EQS: (42), (152) imply: % 151.92/22.58 | | | | | | | | | | | | | (153) all_56_7 = e2 % 151.92/22.58 | | | | | | | | | | | | | % 151.92/22.58 | | | | | | | | | | | | | REDUCE: (88), (152) imply: % 151.92/22.58 | | | | | | | | | | | | | (154) ~ (all_10_2 = e2) % 151.92/22.58 | | | | | | | | | | | | | % 151.92/22.58 | | | | | | | | | | | | | BETA: splitting (53) gives: % 151.92/22.58 | | | | | | | | | | | | | % 151.92/22.58 | | | | | | | | | | | | | Case 1: % 151.92/22.58 | | | | | | | | | | | | | | % 151.92/22.58 | | | | | | | | | | | | | | (155) ~ (all_56_1 = e0) % 151.92/22.58 | | | | | | | | | | | | | | % 151.92/22.58 | | | | | | | | | | | | | | REDUCE: (23), (155) imply: % 151.92/22.58 | | | | | | | | | | | | | | (156) ~ (all_10_2 = e0) % 151.92/22.58 | | | | | | | | | | | | | | % 151.92/22.58 | | | | | | | | | | | | | | BETA: splitting (28) gives: % 151.92/22.58 | | | | | | | | | | | | | | % 151.92/22.58 | | | | | | | | | | | | | | Case 1: % 151.92/22.58 | | | | | | | | | | | | | | | % 151.92/22.58 | | | | | | | | | | | | | | | (157) ~ (all_56_1 = e1) % 151.92/22.58 | | | | | | | | | | | | | | | % 151.92/22.58 | | | | | | | | | | | | | | | REDUCE: (23), (157) imply: % 151.92/22.58 | | | | | | | | | | | | | | | (158) ~ (all_10_2 = e1) % 151.92/22.58 | | | | | | | | | | | | | | | % 151.92/22.58 | | | | | | | | | | | | | | | REF_CLOSE: (10), (17), (19), (23), (24), (33), (34), (37), % 151.92/22.58 | | | | | | | | | | | | | | | (52), (54), (57), (60), (66), (68), (78), (81), % 151.92/22.58 | | | | | | | | | | | | | | | (91), (156), (158) are inconsistent by sub-proof % 151.92/22.58 | | | | | | | | | | | | | | | #403. % 151.92/22.58 | | | | | | | | | | | | | | | % 151.92/22.58 | | | | | | | | | | | | | | Case 2: % 151.92/22.58 | | | | | | | | | | | | | | | % 151.92/22.58 | | | | | | | | | | | | | | | (159) all_56_5 = e3 % 151.92/22.58 | | | | | | | | | | | | | | | (160) all_56_1 = e1 % 151.92/22.58 | | | | | | | | | | | | | | | % 151.92/22.58 | | | | | | | | | | | | | | | COMBINE_EQS: (23), (160) imply: % 151.92/22.58 | | | | | | | | | | | | | | | (161) all_10_2 = e1 % 151.92/22.58 | | | | | | | | | | | | | | | % 151.92/22.58 | | | | | | | | | | | | | | | COMBINE_EQS: (9), (159) imply: % 151.92/22.58 | | | | | | | | | | | | | | | (162) all_10_0 = e3 % 151.92/22.58 | | | | | | | | | | | | | | | % 151.92/22.58 | | | | | | | | | | | | | | | COMBINE_EQS: (16), (162) imply: % 151.92/22.58 | | | | | | | | | | | | | | | (163) all_58_4 = e3 % 151.92/22.58 | | | | | | | | | | | | | | | % 151.92/22.58 | | | | | | | | | | | | | | | REDUCE: (38), (161) imply: % 151.92/22.58 | | | | | | | | | | | | | | | (164) ~ (all_52_3 = e1) % 151.92/22.58 | | | | | | | | | | | | | | | % 151.92/22.58 | | | | | | | | | | | | | | | REDUCE: (67), (162) imply: % 151.92/22.58 | | | | | | | | | | | | | | | (165) ~ (all_52_9 = e3) % 151.92/22.58 | | | | | | | | | | | | | | | % 151.92/22.58 | | | | | | | | | | | | | | | REDUCE: (139), (161) imply: % 151.92/22.58 | | | | | | | | | | | | | | | (166) ~ (e2 = e1) % 151.92/22.58 | | | | | | | | | | | | | | | % 151.92/22.58 | | | | | | | | | | | | | | | REDUCE: (57), (161) imply: % 151.92/22.58 | | | | | | | | | | | | | | | (167) op(e1, e1) = e1 % 151.92/22.58 | | | | | | | | | | | | | | | % 151.92/22.58 | | | | | | | | | | | | | | | REDUCE: (33), (161) imply: % 151.92/22.58 | | | | | | | | | | | | | | | (168) op(e3, e3) = e1 % 151.92/22.58 | | | | | | | | | | | | | | | % 151.92/22.58 | | | | | | | | | | | | | | | BETA: splitting (75) gives: % 151.92/22.58 | | | | | | | | | | | | | | | % 151.92/22.58 | | | | | | | | | | | | | | | Case 1: % 151.92/22.58 | | | | | | | | | | | | | | | | % 151.92/22.58 | | | | | | | | | | | | | | | | (169) all_58_12 = e1 % 151.92/22.58 | | | | | | | | | | | | | | | | % 151.92/22.58 | | | | | | | | | | | | | | | | COMBINE_EQS: (93), (169) imply: % 151.92/22.58 | | | | | | | | | | | | | | | | (170) all_52_3 = e1 % 151.92/22.58 | | | | | | | | | | | | | | | | % 151.92/22.58 | | | | | | | | | | | | | | | | SIMP: (170) implies: % 151.92/22.58 | | | | | | | | | | | | | | | | (171) all_52_3 = e1 % 151.92/22.58 | | | | | | | | | | | | | | | | % 151.92/22.58 | | | | | | | | | | | | | | | | REDUCE: (164), (171) imply: % 151.92/22.58 | | | | | | | | | | | | | | | | (172) $false % 151.92/22.58 | | | | | | | | | | | | | | | | % 151.92/22.58 | | | | | | | | | | | | | | | | CLOSE: (172) is inconsistent. % 151.92/22.58 | | | | | | | | | | | | | | | | % 151.92/22.58 | | | | | | | | | | | | | | | Case 2: % 151.92/22.58 | | | | | | | | | | | | | | | | % 151.92/22.58 | | | | | | | | | | | | | | | | (173) all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1 % 151.92/22.58 | | | | | | | | | | | | | | | | % 151.92/22.58 | | | | | | | | | | | | | | | | BETA: splitting (173) gives: % 151.92/22.58 | | | | | | | | | | | | | | | | % 151.92/22.58 | | | | | | | | | | | | | | | | Case 1: % 151.92/22.58 | | | | | | | | | | | | | | | | | % 151.92/22.58 | | | | | | | | | | | | | | | | | (174) all_58_13 = e1 % 151.92/22.58 | | | | | | | | | | | | | | | | | % 151.92/22.58 | | | | | | | | | | | | | | | | | COMBINE_EQS: (30), (174) imply: % 151.92/22.58 | | | | | | | | | | | | | | | | | (175) all_52_7 = e1 % 151.92/22.58 | | | | | | | | | | | | | | | | | % 151.92/22.58 | | | | | | | | | | | | | | | | | SIMP: (175) implies: % 151.92/22.58 | | | | | | | | | | | | | | | | | (176) all_52_7 = e1 % 151.92/22.58 | | | | | | | | | | | | | | | | | % 151.92/22.58 | | | | | | | | | | | | | | | | | REDUCE: (46), (176) imply: % 151.92/22.58 | | | | | | | | | | | | | | | | | (177) ~ (all_4_2 = e1) % 151.92/22.58 | | | | | | | | | | | | | | | | | % 151.92/22.58 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (37) with all_6_2, e1, e1, e1, % 151.92/22.58 | | | | | | | | | | | | | | | | | simplifying with (69), (167) gives: % 151.92/22.58 | | | | | | | | | | | | | | | | | (178) all_6_2 = e1 % 151.92/22.58 | | | | | | | | | | | | | | | | | % 151.92/22.58 | | | | | | | | | | | | | | | | | REDUCE: (79), (178) imply: % 151.92/22.58 | | | | | | | | | | | | | | | | | (179) ~ (all_52_14 = e1) % 151.92/22.58 | | | | | | | | | | | | | | | | | % 151.92/22.58 | | | | | | | | | | | | | | | | | BETA: splitting (25) gives: % 151.92/22.58 | | | | | | | | | | | | | | | | | % 151.92/22.58 | | | | | | | | | | | | | | | | | Case 1: % 151.92/22.58 | | | | | | | | | | | | | | | | | | % 151.92/22.58 | | | | | | | | | | | | | | | | | | (180) all_54_6 = e3 % 151.92/22.58 | | | | | | | | | | | | | | | | | | % 151.92/22.58 | | | | | | | | | | | | | | | | | | REF_CLOSE: (50), (165), (180) are inconsistent by sub-proof % 151.92/22.58 | | | | | | | | | | | | | | | | | | #402. % 151.92/22.58 | | | | | | | | | | | | | | | | | | % 151.92/22.58 | | | | | | | | | | | | | | | | | Case 2: % 151.92/22.58 | | | | | | | | | | | | | | | | | | % 151.92/22.58 | | | | | | | | | | | | | | | | | | (181) all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0 % 151.92/22.58 | | | | | | | | | | | | | | | | | | % 151.92/22.58 | | | | | | | | | | | | | | | | | | BETA: splitting (20) gives: % 151.92/22.58 | | | | | | | | | | | | | | | | | | % 151.92/22.58 | | | | | | | | | | | | | | | | | | Case 1: % 151.92/22.58 | | | | | | | | | | | | | | | | | | | % 151.92/22.58 | | | | | | | | | | | | | | | | | | | (182) all_58_9 = e1 % 151.92/22.58 | | | | | | | | | | | | | | | | | | | % 151.92/22.58 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (151), (182) imply: % 151.92/22.58 | | | | | | | | | | | | | | | | | | | (183) e2 = e1 % 151.92/22.58 | | | | | | | | | | | | | | | | | | | % 151.92/22.58 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (123), (183) imply: % 151.92/22.58 | | | | | | | | | | | | | | | | | | | (184) all_58_14 = e1 % 151.92/22.58 | | | | | | | | | | | | | | | | | | | % 151.92/22.58 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (49), (71), (119), (137), (184) are inconsistent % 151.92/22.58 | | | | | | | | | | | | | | | | | | | by sub-proof #401. % 151.92/22.58 | | | | | | | | | | | | | | | | | | | % 151.92/22.58 | | | | | | | | | | | | | | | | | | Case 2: % 151.92/22.58 | | | | | | | | | | | | | | | | | | | % 151.92/22.58 | | | | | | | | | | | | | | | | | | | (185) all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1 % 151.92/22.58 | | | | | | | | | | | | | | | | | | | % 151.92/22.58 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (7), (8), (11), (22), (26), (31), (37), (41), % 151.92/22.58 | | | | | | | | | | | | | | | | | | | (45), (47), (48), (50), (55), (56), (61), (62), % 151.92/22.58 | | | | | | | | | | | | | | | | | | | (70), (72), (73), (82), (89), (93), (94), (106), % 151.92/22.58 | | | | | | | | | | | | | | | | | | | (108), (123), (128), (163), (168), (174), (179), % 151.92/22.58 | | | | | | | | | | | | | | | | | | | (181), (185) are inconsistent by sub-proof #558. % 151.92/22.58 | | | | | | | | | | | | | | | | | | | % 151.92/22.58 | | | | | | | | | | | | | | | | | | End of split % 151.92/22.58 | | | | | | | | | | | | | | | | | | % 151.92/22.58 | | | | | | | | | | | | | | | | | End of split % 151.92/22.58 | | | | | | | | | | | | | | | | | % 151.92/22.58 | | | | | | | | | | | | | | | | Case 2: % 151.92/22.58 | | | | | | | | | | | | | | | | | % 151.92/22.58 | | | | | | | | | | | | | | | | | (186) all_58_14 = e1 | all_58_15 = e1 % 151.92/22.58 | | | | | | | | | | | | | | | | | % 151.92/22.58 | | | | | | | | | | | | | | | | | REF_CLOSE: (48), (49), (70), (71), (119), (137), (186) are % 151.92/22.58 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #400. % 151.92/22.58 | | | | | | | | | | | | | | | | | % 151.92/22.58 | | | | | | | | | | | | | | | | End of split % 151.92/22.58 | | | | | | | | | | | | | | | | % 151.92/22.58 | | | | | | | | | | | | | | | End of split % 151.92/22.58 | | | | | | | | | | | | | | | % 151.92/22.58 | | | | | | | | | | | | | | End of split % 151.92/22.58 | | | | | | | | | | | | | | % 151.92/22.58 | | | | | | | | | | | | | Case 2: % 151.92/22.58 | | | | | | | | | | | | | | % 151.92/22.58 | | | | | | | | | | | | | | (187) all_56_7 = e3 % 151.92/22.58 | | | | | | | | | | | | | | % 151.92/22.58 | | | | | | | | | | | | | | COMBINE_EQS: (153), (187) imply: % 151.92/22.58 | | | | | | | | | | | | | | (188) e3 = e2 % 151.92/22.58 | | | | | | | | | | | | | | % 151.92/22.58 | | | | | | | | | | | | | | REDUCE: (136), (188) imply: % 151.92/22.58 | | | | | | | | | | | | | | (189) $false % 151.92/22.58 | | | | | | | | | | | | | | % 151.92/22.58 | | | | | | | | | | | | | | CLOSE: (189) is inconsistent. % 151.92/22.58 | | | | | | | | | | | | | | % 151.92/22.58 | | | | | | | | | | | | | End of split % 151.92/22.58 | | | | | | | | | | | | | % 151.92/22.58 | | | | | | | | | | | | End of split % 151.92/22.58 | | | | | | | | | | | | % 151.92/22.58 | | | | | | | | | | | End of split % 151.92/22.58 | | | | | | | | | | | % 151.92/22.58 | | | | | | | | | | End of split % 151.92/22.58 | | | | | | | | | | % 151.92/22.58 | | | | | | | | | Case 2: % 151.92/22.58 | | | | | | | | | | % 151.92/22.58 | | | | | | | | | | (190) all_56_1 = e2 % 151.92/22.58 | | | | | | | | | | % 151.92/22.58 | | | | | | | | | | COMBINE_EQS: (23), (190) imply: % 151.92/22.58 | | | | | | | | | | (191) all_10_2 = e2 % 151.92/22.58 | | | | | | | | | | % 151.92/22.58 | | | | | | | | | | REDUCE: (57), (191) imply: % 151.92/22.58 | | | | | | | | | | (192) op(e2, e2) = e1 % 151.92/22.58 | | | | | | | | | | % 151.92/22.58 | | | | | | | | | | REF_CLOSE: (37), (111), (137), (192) are inconsistent by % 151.92/22.58 | | | | | | | | | | sub-proof #479. % 151.92/22.58 | | | | | | | | | | % 151.92/22.58 | | | | | | | | | End of split % 151.92/22.58 | | | | | | | | | % 151.92/22.58 | | | | | | | | End of split % 151.92/22.58 | | | | | | | | % 151.92/22.58 | | | | | | | End of split % 151.92/22.58 | | | | | | | % 151.92/22.58 | | | | | | End of split % 151.92/22.58 | | | | | | % 151.92/22.58 | | | | | Case 2: % 151.92/22.58 | | | | | | % 151.92/22.58 | | | | | | (193) all_54_5 = e1 | all_54_5 = e0 % 151.92/22.58 | | | | | | % 151.92/22.58 | | | | | | REF_CLOSE: (18), (77), (100), (193) are inconsistent by sub-proof % 151.92/22.58 | | | | | | #645. % 151.92/22.58 | | | | | | % 151.92/22.58 | | | | | End of split % 151.92/22.58 | | | | | % 151.92/22.58 | | | | End of split % 151.92/22.58 | | | | % 151.92/22.58 | | | Case 2: % 151.92/22.58 | | | | % 151.92/22.58 | | | | (194) all_56_13 = e2 % 151.92/22.58 | | | | (195) all_56_11 = e1 % 151.92/22.58 | | | | % 151.92/22.58 | | | | COMBINE_EQS: (1), (195) imply: % 151.92/22.58 | | | | (196) all_8_2 = e1 % 151.92/22.58 | | | | % 151.92/22.58 | | | | COMBINE_EQS: (43), (194) imply: % 151.92/22.58 | | | | (197) all_52_9 = e2 % 151.92/22.58 | | | | % 151.92/22.58 | | | | COMBINE_EQS: (26), (197) imply: % 151.92/22.58 | | | | (198) all_58_5 = e2 % 151.92/22.58 | | | | % 151.92/22.58 | | | | REDUCE: (67), (197) imply: % 151.92/22.58 | | | | (199) ~ (all_10_0 = e2) % 151.92/22.58 | | | | % 151.92/22.58 | | | | REDUCE: (15), (196), (197) imply: % 151.92/22.58 | | | | (200) ~ (e2 = e1) % 151.92/22.58 | | | | % 151.92/22.58 | | | | REDUCE: (77), (196) imply: % 151.92/22.58 | | | | (201) ~ (e1 = e0) % 151.92/22.58 | | | | % 151.92/22.58 | | | | REDUCE: (85), (196) imply: % 151.92/22.58 | | | | (202) op(e1, e1) = all_8_1 % 151.92/22.58 | | | | % 151.92/22.58 | | | | GROUND_INST: instantiating (37) with all_6_2, all_8_1, e1, e1, % 151.92/22.58 | | | | simplifying with (69), (202) gives: % 151.92/22.58 | | | | (203) all_8_1 = all_6_2 % 151.92/22.58 | | | | % 151.92/22.58 | | | | REDUCE: (6), (203) imply: % 151.92/22.58 | | | | (204) ~ (all_6_2 = e1) % 151.92/22.58 | | | | % 151.92/22.58 | | | | BETA: splitting (59) gives: % 151.92/22.58 | | | | % 151.92/22.58 | | | | Case 1: % 151.92/22.58 | | | | | % 151.92/22.58 | | | | | (205) all_58_4 = e1 % 151.92/22.58 | | | | | % 151.92/22.58 | | | | | COMBINE_EQS: (16), (205) imply: % 151.92/22.58 | | | | | (206) all_10_0 = e1 % 151.92/22.58 | | | | | % 151.92/22.58 | | | | | REDUCE: (66), (206) imply: % 151.92/22.58 | | | | | (207) $false % 151.92/22.58 | | | | | % 151.92/22.58 | | | | | CLOSE: (207) is inconsistent. % 151.92/22.58 | | | | | % 151.92/22.58 | | | | Case 2: % 151.92/22.58 | | | | | % 151.92/22.58 | | | | | (208) all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1 % 151.92/22.58 | | | | | % 151.92/22.58 | | | | | BETA: splitting (208) gives: % 151.92/22.58 | | | | | % 151.92/22.58 | | | | | Case 1: % 151.92/22.58 | | | | | | % 151.92/22.58 | | | | | | (209) all_58_5 = e1 % 151.92/22.58 | | | | | | % 151.92/22.58 | | | | | | COMBINE_EQS: (198), (209) imply: % 151.92/22.58 | | | | | | (210) e2 = e1 % 151.92/22.58 | | | | | | % 151.92/22.58 | | | | | | REDUCE: (200), (210) imply: % 151.92/22.58 | | | | | | (211) $false % 151.92/22.58 | | | | | | % 151.92/22.58 | | | | | | CLOSE: (211) is inconsistent. % 151.92/22.58 | | | | | | % 151.92/22.58 | | | | | Case 2: % 151.92/22.58 | | | | | | % 151.92/22.58 | | | | | | (212) all_58_8 = e1 | all_58_14 = e1 % 151.92/22.58 | | | | | | % 151.92/22.58 | | | | | | BETA: splitting (212) gives: % 151.92/22.58 | | | | | | % 151.92/22.58 | | | | | | Case 1: % 151.92/22.58 | | | | | | | % 151.92/22.58 | | | | | | | (213) all_58_8 = e1 % 151.92/22.58 | | | | | | | % 151.92/22.58 | | | | | | | COMBINE_EQS: (49), (213) imply: % 151.92/22.58 | | | | | | | (214) all_6_2 = e1 % 151.92/22.58 | | | | | | | % 151.92/22.58 | | | | | | | REDUCE: (204), (214) imply: % 151.92/22.58 | | | | | | | (215) $false % 151.92/22.58 | | | | | | | % 151.92/22.58 | | | | | | | CLOSE: (215) is inconsistent. % 151.92/22.58 | | | | | | | % 151.92/22.58 | | | | | | Case 2: % 151.92/22.58 | | | | | | | % 151.92/22.58 | | | | | | | (216) all_58_14 = e1 % 151.92/22.58 | | | | | | | % 151.92/22.58 | | | | | | | COMBINE_EQS: (87), (216) imply: % 151.92/22.58 | | | | | | | (217) all_52_11 = e1 % 151.92/22.58 | | | | | | | % 151.92/22.58 | | | | | | | SIMP: (217) implies: % 151.92/22.58 | | | | | | | (218) all_52_11 = e1 % 151.92/22.58 | | | | | | | % 151.92/22.58 | | | | | | | REDUCE: (39), (218) imply: % 151.92/22.58 | | | | | | | (219) ~ (all_10_0 = e1) % 151.92/22.58 | | | | | | | % 151.92/22.58 | | | | | | | BETA: splitting (58) gives: % 151.92/22.58 | | | | | | | % 151.92/22.58 | | | | | | | Case 1: % 151.92/22.58 | | | | | | | | % 151.92/22.58 | | | | | | | | (220) all_58_4 = e3 % 151.92/22.58 | | | | | | | | % 151.92/22.58 | | | | | | | | COMBINE_EQS: (16), (220) imply: % 151.92/22.58 | | | | | | | | (221) all_10_0 = e3 % 151.92/22.58 | | | | | | | | % 151.92/22.58 | | | | | | | | COMBINE_EQS: (68), (221) imply: % 151.92/22.58 | | | | | | | | (222) all_32_0 = e3 % 151.92/22.58 | | | | | | | | % 151.92/22.58 | | | | | | | | COMBINE_EQS: (9), (221) imply: % 151.92/22.58 | | | | | | | | (223) all_56_5 = e3 % 151.92/22.58 | | | | | | | | % 151.92/22.58 | | | | | | | | REDUCE: (54), (221) imply: % 151.92/22.58 | | | | | | | | (224) ~ (all_52_4 = e3) % 151.92/22.58 | | | | | | | | % 151.92/22.58 | | | | | | | | REDUCE: (51), (221) imply: % 151.92/22.58 | | | | | | | | (225) ~ (all_52_12 = e3) % 151.92/22.58 | | | | | | | | % 151.92/22.58 | | | | | | | | REDUCE: (81), (221) imply: % 151.92/22.58 | | | | | | | | (226) ~ (all_10_2 = e3) % 151.92/22.58 | | | | | | | | % 151.92/22.58 | | | | | | | | SIMP: (226) implies: % 151.92/22.58 | | | | | | | | (227) ~ (all_10_2 = e3) % 151.92/22.58 | | | | | | | | % 151.92/22.58 | | | | | | | | BETA: splitting (52) gives: % 151.92/22.58 | | | | | | | | % 151.92/22.58 | | | | | | | | Case 1: % 151.92/22.58 | | | | | | | | | % 151.92/22.58 | | | | | | | | | (228) ~ (all_56_1 = e2) % 151.92/22.58 | | | | | | | | | % 151.92/22.58 | | | | | | | | | REDUCE: (23), (228) imply: % 151.92/22.58 | | | | | | | | | (229) ~ (all_10_2 = e2) % 151.92/22.58 | | | | | | | | | % 151.92/22.58 | | | | | | | | | BETA: splitting (53) gives: % 151.92/22.58 | | | | | | | | | % 151.92/22.58 | | | | | | | | | Case 1: % 151.92/22.58 | | | | | | | | | | % 151.92/22.58 | | | | | | | | | | (230) ~ (all_56_1 = e0) % 151.92/22.58 | | | | | | | | | | % 151.92/22.58 | | | | | | | | | | REDUCE: (23), (230) imply: % 151.92/22.58 | | | | | | | | | | (231) ~ (all_10_2 = e0) % 151.92/22.58 | | | | | | | | | | % 151.92/22.58 | | | | | | | | | | BETA: splitting (31) gives: % 151.92/22.58 | | | | | | | | | | % 151.92/22.58 | | | | | | | | | | Case 1: % 151.92/22.58 | | | | | | | | | | | % 151.92/22.58 | | | | | | | | | | | (232) all_58_4 = e0 % 151.92/22.58 | | | | | | | | | | | % 151.92/22.58 | | | | | | | | | | | COMBINE_EQS: (220), (232) imply: % 151.92/22.58 | | | | | | | | | | | (233) e3 = e0 % 151.92/22.58 | | | | | | | | | | | % 151.92/22.58 | | | | | | | | | | | COMBINE_EQS: (222), (233) imply: % 151.92/22.58 | | | | | | | | | | | (234) all_32_0 = e0 % 151.92/22.58 | | | | | | | | | | | % 151.92/22.58 | | | | | | | | | | | COMBINE_EQS: (223), (233) imply: % 151.92/22.58 | | | | | | | | | | | (235) all_56_5 = e0 % 151.92/22.58 | | | | | | | | | | | % 151.92/22.58 | | | | | | | | | | | REF_CLOSE: (8), (10), (19), (23), (24), (28), (33), (37), % 151.92/22.58 | | | | | | | | | | | (57), (78), (91), (231), (234), (235) are % 151.92/22.58 | | | | | | | | | | | inconsistent by sub-proof #398. % 151.92/22.58 | | | | | | | | | | | % 151.92/22.58 | | | | | | | | | | Case 2: % 151.92/22.58 | | | | | | | | | | | % 151.92/22.58 | | | | | | | | | | | (236) all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0 % 151.92/22.58 | | | | | | | | | | | % 151.92/22.58 | | | | | | | | | | | BETA: splitting (19) gives: % 151.92/22.58 | | | | | | | | | | | % 151.92/22.58 | | | | | | | | | | | Case 1: % 151.92/22.58 | | | | | | | | | | | | % 151.92/22.58 | | | | | | | | | | | | (237) all_54_0 = e3 % 151.92/22.58 | | | | | | | | | | | | % 151.92/22.58 | | | | | | | | | | | | REF_CLOSE: (10), (227), (237) are inconsistent by sub-proof % 151.92/22.58 | | | | | | | | | | | | #709. % 151.92/22.58 | | | | | | | | | | | | % 151.92/22.58 | | | | | | | | | | | Case 2: % 151.92/22.58 | | | | | | | | | | | | % 151.92/22.58 | | | | | | | | | | | | (238) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 151.92/22.58 | | | | | | | | | | | | % 151.92/22.58 | | | | | | | | | | | | BETA: splitting (238) gives: % 151.92/22.58 | | | | | | | | | | | | % 151.92/22.58 | | | | | | | | | | | | Case 1: % 151.92/22.58 | | | | | | | | | | | | | % 151.92/22.58 | | | | | | | | | | | | | (239) all_54_0 = e2 % 151.92/22.58 | | | | | | | | | | | | | % 151.92/22.58 | | | | | | | | | | | | | REF_CLOSE: (10), (229), (239) are inconsistent by sub-proof % 151.92/22.58 | | | | | | | | | | | | | #734. % 151.92/22.58 | | | | | | | | | | | | | % 151.92/22.58 | | | | | | | | | | | | Case 2: % 151.92/22.58 | | | | | | | | | | | | | % 151.92/22.58 | | | | | | | | | | | | | (240) all_54_0 = e1 | all_54_0 = e0 % 151.92/22.58 | | | | | | | | | | | | | % 151.92/22.58 | | | | | | | | | | | | | BETA: splitting (236) gives: % 151.92/22.58 | | | | | | | | | | | | | % 151.92/22.58 | | | | | | | | | | | | | Case 1: % 151.92/22.58 | | | | | | | | | | | | | | % 151.92/22.58 | | | | | | | | | | | | | | (241) all_58_5 = e0 % 151.92/22.58 | | | | | | | | | | | | | | % 151.92/22.58 | | | | | | | | | | | | | | COMBINE_EQS: (198), (241) imply: % 151.92/22.58 | | | | | | | | | | | | | | (242) e2 = e0 % 151.92/22.58 | | | | | | | | | | | | | | % 151.92/22.58 | | | | | | | | | | | | | | REDUCE: (80), (242) imply: % 151.92/22.58 | | | | | | | | | | | | | | (243) $false % 151.92/22.58 | | | | | | | | | | | | | | % 151.92/22.58 | | | | | | | | | | | | | | CLOSE: (243) is inconsistent. % 151.92/22.58 | | | | | | | | | | | | | | % 151.92/22.58 | | | | | | | | | | | | | Case 2: % 151.92/22.58 | | | | | | | | | | | | | | % 151.92/22.58 | | | | | | | | | | | | | | (244) all_58_8 = e0 | all_58_14 = e0 % 151.92/22.58 | | | | | | | | | | | | | | % 151.92/22.58 | | | | | | | | | | | | | | BETA: splitting (244) gives: % 151.92/22.58 | | | | | | | | | | | | | | % 151.92/22.58 | | | | | | | | | | | | | | Case 1: % 151.92/22.58 | | | | | | | | | | | | | | | % 151.92/22.58 | | | | | | | | | | | | | | | (245) all_58_8 = e0 % 151.92/22.58 | | | | | | | | | | | | | | | % 151.92/22.58 | | | | | | | | | | | | | | | COMBINE_EQS: (49), (245) imply: % 151.92/22.58 | | | | | | | | | | | | | | | (246) all_6_2 = e0 % 151.92/22.58 | | | | | | | | | | | | | | | % 151.92/22.58 | | | | | | | | | | | | | | | REDUCE: (69), (246) imply: % 151.92/22.58 | | | | | | | | | | | | | | | (247) op(e1, e1) = e0 % 151.92/22.58 | | | | | | | | | | | | | | | % 151.92/22.58 | | | | | | | | | | | | | | | REF_CLOSE: (10), (37), (57), (231), (240), (247) are % 151.92/22.58 | | | | | | | | | | | | | | | inconsistent by sub-proof #397. % 151.92/22.58 | | | | | | | | | | | | | | | % 151.92/22.58 | | | | | | | | | | | | | | Case 2: % 151.92/22.58 | | | | | | | | | | | | | | | % 151.92/22.58 | | | | | | | | | | | | | | | (248) all_58_14 = e0 % 151.92/22.58 | | | | | | | | | | | | | | | % 151.92/22.58 | | | | | | | | | | | | | | | REF_CLOSE: (201), (216), (248) are inconsistent by sub-proof % 151.92/22.58 | | | | | | | | | | | | | | | #396. % 151.92/22.58 | | | | | | | | | | | | | | | % 151.92/22.58 | | | | | | | | | | | | | | End of split % 151.92/22.58 | | | | | | | | | | | | | | % 151.92/22.58 | | | | | | | | | | | | | End of split % 151.92/22.58 | | | | | | | | | | | | | % 151.92/22.58 | | | | | | | | | | | | End of split % 151.92/22.58 | | | | | | | | | | | | % 151.92/22.58 | | | | | | | | | | | End of split % 151.92/22.58 | | | | | | | | | | | % 151.92/22.58 | | | | | | | | | | End of split % 151.92/22.58 | | | | | | | | | | % 151.92/22.58 | | | | | | | | | Case 2: % 151.92/22.58 | | | | | | | | | | % 151.92/22.58 | | | | | | | | | | (249) all_56_7 = e3 % 151.92/22.58 | | | | | | | | | | % 151.92/22.58 | | | | | | | | | | REF_CLOSE: (42), (225), (249) are inconsistent by sub-proof % 151.92/22.58 | | | | | | | | | | #691. % 151.92/22.58 | | | | | | | | | | % 151.92/22.58 | | | | | | | | | End of split % 151.92/22.58 | | | | | | | | | % 151.92/22.58 | | | | | | | | Case 2: % 151.92/22.58 | | | | | | | | | % 151.92/22.58 | | | | | | | | | (250) all_56_3 = e3 % 151.92/22.58 | | | | | | | | | % 151.92/22.58 | | | | | | | | | REF_CLOSE: (60), (224), (250) are inconsistent by sub-proof % 151.92/22.58 | | | | | | | | | #395. % 151.92/22.58 | | | | | | | | | % 151.92/22.58 | | | | | | | | End of split % 151.92/22.58 | | | | | | | | % 151.92/22.58 | | | | | | | Case 2: % 151.92/22.58 | | | | | | | | % 151.92/22.58 | | | | | | | | (251) ~ (all_58_4 = e3) % 151.92/22.58 | | | | | | | | % 151.92/22.58 | | | | | | | | REDUCE: (16), (251) imply: % 151.92/22.58 | | | | | | | | (252) ~ (all_10_0 = e3) % 151.92/22.58 | | | | | | | | % 151.92/22.58 | | | | | | | | REF_CLOSE: (9), (10), (17), (19), (23), (24), (28), (33), (34), % 151.92/22.58 | | | | | | | | (37), (57), (66), (68), (78), (81), (83), (91), (252) % 151.92/22.58 | | | | | | | | are inconsistent by sub-proof #393. % 151.92/22.58 | | | | | | | | % 151.92/22.58 | | | | | | | End of split % 151.92/22.58 | | | | | | | % 151.92/22.58 | | | | | | End of split % 151.92/22.58 | | | | | | % 151.92/22.58 | | | | | End of split % 151.92/22.58 | | | | | % 151.92/22.58 | | | | End of split % 151.92/22.58 | | | | % 151.92/22.58 | | | End of split % 151.92/22.58 | | | % 151.92/22.58 | | Case 2: % 151.92/22.58 | | | % 151.92/22.58 | | | (253) all_56_11 = e3 % 151.92/22.58 | | | (254) all_56_9 = e2 % 151.92/22.58 | | | % 151.92/22.58 | | | COMBINE_EQS: (90), (254) imply: % 151.92/22.58 | | | (255) all_52_1 = e2 % 151.92/22.58 | | | % 151.92/22.58 | | | COMBINE_EQS: (1), (253) imply: % 151.92/22.58 | | | (256) all_8_2 = e3 % 151.92/22.58 | | | % 151.92/22.58 | | | REDUCE: (7), (255) imply: % 151.92/22.58 | | | (257) ~ (all_52_9 = e2) % 151.92/22.58 | | | % 151.92/22.58 | | | SIMP: (257) implies: % 151.92/22.58 | | | (258) ~ (all_52_9 = e2) % 151.92/22.58 | | | % 151.92/22.58 | | | REDUCE: (92), (255) imply: % 151.92/22.58 | | | (259) ~ (all_10_2 = e2) % 151.92/22.58 | | | % 151.92/22.58 | | | SIMP: (259) implies: % 151.92/22.58 | | | (260) ~ (all_10_2 = e2) % 151.92/22.58 | | | % 151.92/22.58 | | | REDUCE: (36), (255), (256) imply: % 151.92/22.58 | | | (261) ~ (e3 = e2) % 151.92/22.58 | | | % 151.92/22.58 | | | SIMP: (261) implies: % 151.92/22.58 | | | (262) ~ (e3 = e2) % 151.92/22.58 | | | % 151.92/22.58 | | | REDUCE: (15), (256) imply: % 151.92/22.58 | | | (263) ~ (all_52_9 = e3) % 151.92/22.58 | | | % 151.92/22.58 | | | REDUCE: (85), (256) imply: % 151.92/22.58 | | | (264) op(e3, e3) = all_8_1 % 151.92/22.58 | | | % 151.92/22.58 | | | BETA: splitting (13) gives: % 151.92/22.58 | | | % 151.92/22.58 | | | Case 1: % 151.92/22.58 | | | | % 151.92/22.58 | | | | (265) all_58_4 = e2 % 151.92/22.58 | | | | % 151.92/22.58 | | | | COMBINE_EQS: (16), (265) imply: % 151.92/22.58 | | | | (266) all_10_0 = e2 % 151.92/22.58 | | | | % 151.92/22.58 | | | | REDUCE: (83), (266) imply: % 151.92/22.58 | | | | (267) $false % 151.92/22.58 | | | | % 151.92/22.58 | | | | CLOSE: (267) is inconsistent. % 151.92/22.58 | | | | % 151.92/22.58 | | | Case 2: % 151.92/22.58 | | | | % 151.92/22.58 | | | | (268) all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2 % 151.92/22.58 | | | | % 151.92/22.58 | | | | BETA: splitting (268) gives: % 151.92/22.58 | | | | % 151.92/22.58 | | | | Case 1: % 151.92/22.58 | | | | | % 151.92/22.58 | | | | | (269) all_58_5 = e2 % 151.92/22.58 | | | | | % 151.92/22.58 | | | | | COMBINE_EQS: (26), (269) imply: % 151.92/22.58 | | | | | (270) all_52_9 = e2 % 151.92/22.58 | | | | | % 151.92/22.58 | | | | | REDUCE: (258), (270) imply: % 151.92/22.58 | | | | | (271) $false % 151.92/22.58 | | | | | % 151.92/22.58 | | | | | CLOSE: (271) is inconsistent. % 151.92/22.58 | | | | | % 151.92/22.58 | | | | Case 2: % 151.92/22.58 | | | | | % 151.92/22.58 | | | | | (272) all_58_8 = e2 | all_58_14 = e2 % 151.92/22.58 | | | | | % 151.92/22.58 | | | | | BETA: splitting (272) gives: % 151.92/22.58 | | | | | % 151.92/22.58 | | | | | Case 1: % 151.92/22.58 | | | | | | % 151.92/22.58 | | | | | | (273) all_58_8 = e2 % 151.92/22.58 | | | | | | % 151.92/22.58 | | | | | | COMBINE_EQS: (49), (273) imply: % 151.92/22.58 | | | | | | (274) all_6_2 = e2 % 151.92/22.58 | | | | | | % 151.92/22.58 | | | | | | REDUCE: (71), (274) imply: % 151.92/22.58 | | | | | | (275) $false % 151.92/22.58 | | | | | | % 151.92/22.58 | | | | | | CLOSE: (275) is inconsistent. % 151.92/22.58 | | | | | | % 151.92/22.58 | | | | | Case 2: % 151.92/22.58 | | | | | | % 151.92/22.58 | | | | | | (276) all_58_14 = e2 % 151.92/22.58 | | | | | | % 151.92/22.58 | | | | | | BETA: splitting (58) gives: % 151.92/22.58 | | | | | | % 151.92/22.58 | | | | | | Case 1: % 151.92/22.58 | | | | | | | % 151.92/22.58 | | | | | | | (277) all_58_4 = e3 % 151.92/22.58 | | | | | | | % 151.92/22.58 | | | | | | | COMBINE_EQS: (16), (277) imply: % 151.92/22.58 | | | | | | | (278) all_10_0 = e3 % 151.92/22.58 | | | | | | | % 151.92/22.58 | | | | | | | REDUCE: (51), (278) imply: % 151.92/22.58 | | | | | | | (279) ~ (all_52_12 = e3) % 151.92/22.58 | | | | | | | % 151.92/22.58 | | | | | | | REDUCE: (81), (278) imply: % 151.92/22.58 | | | | | | | (280) ~ (all_10_2 = e3) % 151.92/22.58 | | | | | | | % 151.92/22.58 | | | | | | | SIMP: (280) implies: % 151.92/22.58 | | | | | | | (281) ~ (all_10_2 = e3) % 151.92/22.58 | | | | | | | % 151.92/22.58 | | | | | | | REF_CLOSE: (6), (10), (19), (23), (33), (37), (42), (53), (260), % 151.92/22.58 | | | | | | | (264), (279), (281) are inconsistent by sub-proof #392. % 151.92/22.58 | | | | | | | % 151.92/22.58 | | | | | | Case 2: % 151.92/22.58 | | | | | | | % 151.92/22.58 | | | | | | | (282) all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3 % 151.92/22.58 | | | | | | | % 151.92/22.58 | | | | | | | REF_CLOSE: (26), (49), (96), (262), (263), (276), (282) are % 151.92/22.58 | | | | | | | inconsistent by sub-proof #391. % 151.92/22.58 | | | | | | | % 151.92/22.58 | | | | | | End of split % 151.92/22.58 | | | | | | % 151.92/22.58 | | | | | End of split % 151.92/22.58 | | | | | % 151.92/22.58 | | | | End of split % 151.92/22.58 | | | | % 151.92/22.58 | | | End of split % 151.92/22.58 | | | % 151.92/22.58 | | End of split % 151.92/22.58 | | % 151.92/22.58 | Case 2: % 151.92/22.58 | | % 151.92/22.58 | | (283) all_56_21 = e3 % 151.92/22.58 | | % 151.92/22.58 | | COMBINE_EQS: (21), (283) imply: % 151.92/22.58 | | (284) all_6_2 = e3 % 151.92/22.58 | | % 151.92/22.58 | | SIMP: (284) implies: % 151.92/22.58 | | (285) all_6_2 = e3 % 151.92/22.58 | | % 151.92/22.58 | | REDUCE: (64), (285) imply: % 151.92/22.58 | | (286) ~ (all_10_0 = e3) % 151.92/22.58 | | % 151.92/22.58 | | REF_CLOSE: (9), (10), (17), (19), (23), (24), (28), (33), (34), (37), (57), % 151.92/22.58 | | (66), (68), (78), (81), (83), (91), (286) are inconsistent by % 151.92/22.58 | | sub-proof #393. % 151.92/22.58 | | % 151.92/22.58 | End of split % 151.92/22.58 | % 151.92/22.58 End of proof % 151.92/22.58 % 151.92/22.58 Sub-proof #391 shows that the following formulas are inconsistent: % 151.92/22.58 ---------------------------------------------------------------- % 151.92/22.58 (1) ~ (all_6_2 = e3) % 151.92/22.58 (2) ~ (e3 = e2) % 151.92/22.58 (3) all_58_5 = all_52_9 % 151.92/22.58 (4) ~ (all_52_9 = e3) % 151.92/22.58 (5) all_58_8 = all_6_2 % 151.92/22.58 (6) all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3 % 151.92/22.58 (7) all_58_14 = e2 % 151.92/22.58 % 151.92/22.58 Begin of proof % 151.92/22.58 | % 151.92/22.58 | BETA: splitting (6) gives: % 151.92/22.58 | % 151.92/22.58 | Case 1: % 151.92/22.58 | | % 151.92/22.58 | | (8) all_58_5 = e3 % 151.92/22.58 | | % 151.92/22.58 | | COMBINE_EQS: (3), (8) imply: % 151.92/22.58 | | (9) all_52_9 = e3 % 151.92/22.58 | | % 151.92/22.58 | | REDUCE: (4), (9) imply: % 151.92/22.58 | | (10) $false % 151.92/22.58 | | % 151.92/22.58 | | CLOSE: (10) is inconsistent. % 151.92/22.58 | | % 151.92/22.58 | Case 2: % 151.92/22.58 | | % 151.92/22.58 | | (11) all_58_8 = e3 | all_58_14 = e3 % 151.92/22.58 | | % 151.92/22.58 | | REF_CLOSE: (1), (2), (5), (7), (11) are inconsistent by sub-proof #591. % 151.92/22.58 | | % 151.92/22.58 | End of split % 151.92/22.58 | % 151.92/22.58 End of proof % 151.92/22.58 % 151.92/22.58 Sub-proof #392 shows that the following formulas are inconsistent: % 151.92/22.58 ---------------------------------------------------------------- % 151.92/22.58 (1) ~ (all_8_1 = e1) % 151.92/22.58 (2) all_54_0 = all_10_2 % 151.92/22.58 (3) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 151.92/22.58 (4) all_56_1 = all_10_2 % 151.92/22.58 (5) ~ (all_10_2 = e2) % 151.92/22.58 (6) op(e3, e3) = all_10_2 % 151.92/22.58 (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 151.92/22.58 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 151.92/22.58 (8) all_56_7 = all_52_12 % 151.92/22.58 (9) ~ (all_52_12 = e3) % 151.92/22.58 (10) ~ (all_56_1 = e0) | all_56_7 = e3 % 151.92/22.58 (11) op(e3, e3) = all_8_1 % 151.92/22.58 (12) ~ (all_10_2 = e3) % 151.92/22.58 % 151.92/22.58 Begin of proof % 151.92/22.58 | % 151.92/22.58 | BETA: splitting (10) gives: % 151.92/22.58 | % 151.92/22.58 | Case 1: % 151.92/22.58 | | % 151.92/22.58 | | (13) ~ (all_56_1 = e0) % 151.92/22.58 | | % 151.92/22.58 | | REDUCE: (4), (13) imply: % 151.92/22.58 | | (14) ~ (all_10_2 = e0) % 151.92/22.58 | | % 151.92/22.58 | | BETA: splitting (3) gives: % 151.92/22.58 | | % 151.92/22.58 | | Case 1: % 151.92/22.58 | | | % 151.92/22.58 | | | (15) all_54_0 = e3 % 151.92/22.58 | | | % 151.92/22.58 | | | REF_CLOSE: (2), (12), (15) are inconsistent by sub-proof #709. % 151.92/22.58 | | | % 151.92/22.58 | | Case 2: % 151.92/22.58 | | | % 151.92/22.58 | | | (16) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 151.92/22.58 | | | % 151.92/22.58 | | | BETA: splitting (16) gives: % 151.92/22.58 | | | % 151.92/22.58 | | | Case 1: % 151.92/22.58 | | | | % 151.92/22.58 | | | | (17) all_54_0 = e2 % 151.92/22.58 | | | | % 151.92/22.58 | | | | REF_CLOSE: (2), (5), (17) are inconsistent by sub-proof #734. % 151.92/22.58 | | | | % 151.92/22.58 | | | Case 2: % 151.92/22.58 | | | | % 151.92/22.58 | | | | (18) all_54_0 = e1 | all_54_0 = e0 % 151.92/22.58 | | | | % 151.92/22.58 | | | | REF_CLOSE: (1), (2), (6), (7), (11), (14), (18) are inconsistent by % 151.92/22.58 | | | | sub-proof #552. % 151.92/22.58 | | | | % 151.92/22.58 | | | End of split % 151.92/22.58 | | | % 151.92/22.58 | | End of split % 151.92/22.58 | | % 151.92/22.58 | Case 2: % 151.92/22.58 | | % 151.92/22.58 | | (19) all_56_7 = e3 % 151.92/22.58 | | % 151.92/22.58 | | COMBINE_EQS: (8), (19) imply: % 151.92/22.58 | | (20) all_52_12 = e3 % 151.92/22.58 | | % 151.92/22.58 | | REDUCE: (9), (20) imply: % 151.92/22.58 | | (21) $false % 151.92/22.58 | | % 151.92/22.58 | | CLOSE: (21) is inconsistent. % 151.92/22.58 | | % 151.92/22.58 | End of split % 151.92/22.58 | % 151.92/22.58 End of proof % 151.92/22.58 % 151.92/22.58 Sub-proof #393 shows that the following formulas are inconsistent: % 151.92/22.58 ---------------------------------------------------------------- % 151.92/22.58 (1) all_56_5 = all_10_0 % 151.92/22.58 (2) all_54_0 = all_10_2 % 151.92/22.58 (3) all_54_2 = all_10_0 % 151.92/22.58 (4) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 151.92/22.58 (5) all_56_1 = all_10_2 % 151.92/22.58 (6) ~ (all_32_0 = e0) | ~ (all_32_2 = e2) % 151.92/22.58 (7) ~ (all_56_1 = e1) | all_56_5 = e3 % 151.92/22.58 (8) op(e3, e3) = all_10_2 % 151.92/22.58 (9) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0 % 151.92/22.58 (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 151.92/22.58 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 151.92/22.58 (11) op(all_10_2, all_10_2) = e1 % 151.92/22.58 (12) ~ (all_10_0 = e1) % 151.92/22.58 (13) all_32_0 = all_10_0 % 151.92/22.58 (14) ~ (all_10_0 = e3) % 151.92/22.58 (15) op(e3, all_10_2) = all_56_0 % 151.92/22.58 (16) ~ (all_10_0 = all_10_2) % 151.92/22.58 (17) ~ (all_10_0 = e2) % 151.92/22.58 (18) all_32_2 = all_10_2 % 151.92/22.58 % 151.92/22.58 Begin of proof % 151.92/22.58 | % 151.92/22.58 | BETA: splitting (7) gives: % 151.92/22.58 | % 151.92/22.58 | Case 1: % 151.92/22.58 | | % 151.92/22.58 | | (19) ~ (all_56_1 = e1) % 151.92/22.58 | | % 151.92/22.58 | | REDUCE: (5), (19) imply: % 151.92/22.58 | | (20) ~ (all_10_2 = e1) % 151.92/22.58 | | % 151.92/22.58 | | REF_CLOSE: (2), (3), (4), (6), (8), (9), (10), (11), (12), (13), (14), (15), % 151.92/22.58 | | (16), (17), (18), (20) are inconsistent by sub-proof #394. % 151.92/22.58 | | % 151.92/22.58 | Case 2: % 151.92/22.58 | | % 151.92/22.58 | | (21) all_56_5 = e3 % 151.92/22.58 | | % 151.92/22.58 | | COMBINE_EQS: (1), (21) imply: % 151.92/22.58 | | (22) all_10_0 = e3 % 151.92/22.58 | | % 151.92/22.58 | | REDUCE: (14), (22) imply: % 151.92/22.58 | | (23) $false % 151.92/22.58 | | % 151.92/22.58 | | CLOSE: (23) is inconsistent. % 151.92/22.58 | | % 151.92/22.58 | End of split % 151.92/22.58 | % 151.92/22.58 End of proof % 151.92/22.58 % 151.92/22.58 Sub-proof #394 shows that the following formulas are inconsistent: % 151.92/22.58 ---------------------------------------------------------------- % 151.92/22.58 (1) all_54_0 = all_10_2 % 151.92/22.58 (2) all_54_2 = all_10_0 % 151.92/22.58 (3) ~ (all_10_2 = e1) % 151.92/22.58 (4) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 151.92/22.58 (5) ~ (all_32_0 = e0) | ~ (all_32_2 = e2) % 151.92/22.58 (6) op(e3, e3) = all_10_2 % 151.92/22.58 (7) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0 % 151.92/22.59 (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 151.92/22.59 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 151.92/22.59 (9) op(all_10_2, all_10_2) = e1 % 151.92/22.59 (10) ~ (all_10_0 = e1) % 151.92/22.59 (11) all_32_0 = all_10_0 % 151.92/22.59 (12) ~ (all_10_0 = e3) % 151.92/22.59 (13) op(e3, all_10_2) = all_56_0 % 151.92/22.59 (14) ~ (all_10_0 = all_10_2) % 151.92/22.59 (15) ~ (all_10_0 = e2) % 151.92/22.59 (16) all_32_2 = all_10_2 % 151.92/22.59 % 151.92/22.59 Begin of proof % 151.92/22.59 | % 151.92/22.59 | BETA: splitting (7) gives: % 151.92/22.59 | % 151.92/22.59 | Case 1: % 151.92/22.59 | | % 151.92/22.59 | | (17) all_54_2 = e3 % 151.92/22.59 | | % 151.92/22.59 | | REF_CLOSE: (2), (12), (17) are inconsistent by sub-proof #408. % 151.92/22.59 | | % 151.92/22.59 | Case 2: % 151.92/22.59 | | % 151.92/22.59 | | (18) all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0 % 151.92/22.59 | | % 151.92/22.59 | | BETA: splitting (18) gives: % 151.92/22.59 | | % 151.92/22.59 | | Case 1: % 151.92/22.59 | | | % 151.92/22.59 | | | (19) all_54_2 = e2 % 151.92/22.59 | | | % 151.92/22.59 | | | REF_CLOSE: (2), (15), (19) are inconsistent by sub-proof #407. % 151.92/22.59 | | | % 151.92/22.59 | | Case 2: % 151.92/22.59 | | | % 151.92/22.59 | | | (20) all_54_2 = e1 | all_54_2 = e0 % 151.92/22.59 | | | % 151.92/22.59 | | | BETA: splitting (20) gives: % 151.92/22.59 | | | % 151.92/22.59 | | | Case 1: % 151.92/22.59 | | | | % 151.92/22.59 | | | | (21) all_54_2 = e1 % 151.92/22.59 | | | | % 151.92/22.59 | | | | REF_CLOSE: (2), (10), (21) are inconsistent by sub-proof #406. % 151.92/22.59 | | | | % 151.92/22.59 | | | Case 2: % 151.92/22.59 | | | | % 151.92/22.59 | | | | (22) all_54_2 = e0 % 151.92/22.59 | | | | % 151.92/22.59 | | | | COMBINE_EQS: (2), (22) imply: % 151.92/22.59 | | | | (23) all_10_0 = e0 % 151.92/22.59 | | | | % 151.92/22.59 | | | | SIMP: (23) implies: % 151.92/22.59 | | | | (24) all_10_0 = e0 % 151.92/22.59 | | | | % 151.92/22.59 | | | | COMBINE_EQS: (11), (24) imply: % 151.92/22.59 | | | | (25) all_32_0 = e0 % 151.92/22.59 | | | | % 151.92/22.59 | | | | REDUCE: (14), (24) imply: % 151.92/22.59 | | | | (26) ~ (all_10_2 = e0) % 151.92/22.59 | | | | % 151.92/22.59 | | | | SIMP: (26) implies: % 151.92/22.59 | | | | (27) ~ (all_10_2 = e0) % 151.92/22.59 | | | | % 151.92/22.59 | | | | REF_CLOSE: (1), (3), (4), (5), (6), (8), (9), (13), (16), (25), (27) are % 151.92/22.59 | | | | inconsistent by sub-proof #399. % 151.92/22.59 | | | | % 151.92/22.59 | | | End of split % 151.92/22.59 | | | % 151.92/22.59 | | End of split % 151.92/22.59 | | % 151.92/22.59 | End of split % 151.92/22.59 | % 151.92/22.59 End of proof % 151.92/22.59 % 151.92/22.59 Sub-proof #395 shows that the following formulas are inconsistent: % 151.92/22.59 ---------------------------------------------------------------- % 151.92/22.59 (1) all_56_3 = all_52_4 % 151.92/22.59 (2) all_56_3 = e3 % 151.92/22.59 (3) ~ (all_52_4 = e3) % 151.92/22.59 % 151.92/22.59 Begin of proof % 151.92/22.59 | % 151.92/22.59 | COMBINE_EQS: (1), (2) imply: % 151.92/22.59 | (4) all_52_4 = e3 % 151.92/22.59 | % 151.92/22.59 | SIMP: (4) implies: % 151.92/22.59 | (5) all_52_4 = e3 % 151.92/22.59 | % 151.92/22.59 | REDUCE: (3), (5) imply: % 151.92/22.59 | (6) $false % 151.92/22.59 | % 151.92/22.59 | CLOSE: (6) is inconsistent. % 151.92/22.59 | % 151.92/22.59 End of proof % 151.92/22.59 % 151.92/22.59 Sub-proof #396 shows that the following formulas are inconsistent: % 151.92/22.59 ---------------------------------------------------------------- % 151.92/22.59 (1) all_58_14 = e1 % 151.92/22.59 (2) all_58_14 = e0 % 151.92/22.59 (3) ~ (e1 = e0) % 151.92/22.59 % 151.92/22.59 Begin of proof % 151.92/22.59 | % 151.92/22.59 | COMBINE_EQS: (1), (2) imply: % 151.92/22.59 | (4) e1 = e0 % 151.92/22.59 | % 151.92/22.59 | SIMP: (4) implies: % 151.92/22.59 | (5) e1 = e0 % 151.92/22.59 | % 151.92/22.59 | REDUCE: (3), (5) imply: % 151.92/22.59 | (6) $false % 151.92/22.59 | % 151.92/22.59 | CLOSE: (6) is inconsistent. % 151.92/22.59 | % 151.92/22.59 End of proof % 151.92/22.59 % 151.92/22.59 Sub-proof #397 shows that the following formulas are inconsistent: % 151.92/22.59 ---------------------------------------------------------------- % 151.92/22.59 (1) all_54_0 = all_10_2 % 151.92/22.59 (2) op(e1, e1) = e0 % 151.92/22.59 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 151.92/22.59 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 151.92/22.59 (4) op(all_10_2, all_10_2) = e1 % 151.92/22.59 (5) all_54_0 = e1 | all_54_0 = e0 % 151.92/22.59 (6) ~ (all_10_2 = e0) % 151.92/22.59 % 151.92/22.59 Begin of proof % 151.92/22.59 | % 151.92/22.59 | BETA: splitting (5) gives: % 151.92/22.59 | % 151.92/22.59 | Case 1: % 151.92/22.59 | | % 151.92/22.59 | | (7) all_54_0 = e1 % 151.92/22.59 | | % 151.92/22.59 | | COMBINE_EQS: (1), (7) imply: % 151.92/22.59 | | (8) all_10_2 = e1 % 151.92/22.59 | | % 151.92/22.59 | | SIMP: (8) implies: % 151.92/22.59 | | (9) all_10_2 = e1 % 151.92/22.59 | | % 151.92/22.59 | | REDUCE: (6), (9) imply: % 151.92/22.59 | | (10) ~ (e1 = e0) % 151.92/22.59 | | % 151.92/22.59 | | REDUCE: (4), (9) imply: % 151.92/22.59 | | (11) op(e1, e1) = e1 % 151.92/22.59 | | % 151.92/22.59 | | GROUND_INST: instantiating (3) with e0, e1, e1, e1, simplifying with (2), % 151.92/22.59 | | (11) gives: % 151.92/22.59 | | (12) e1 = e0 % 151.92/22.59 | | % 151.92/22.59 | | REDUCE: (10), (12) imply: % 151.92/22.59 | | (13) $false % 151.92/22.59 | | % 151.92/22.59 | | CLOSE: (13) is inconsistent. % 151.92/22.59 | | % 151.92/22.59 | Case 2: % 151.92/22.59 | | % 151.92/22.59 | | (14) all_54_0 = e0 % 151.92/22.59 | | % 151.92/22.59 | | REF_CLOSE: (1), (6), (14) are inconsistent by sub-proof #732. % 151.92/22.59 | | % 151.92/22.59 | End of split % 151.92/22.59 | % 151.92/22.59 End of proof % 151.92/22.59 % 151.92/22.59 Sub-proof #398 shows that the following formulas are inconsistent: % 151.92/22.59 ---------------------------------------------------------------- % 151.92/22.59 (1) ~ (e3 = e0) % 151.92/22.59 (2) all_54_0 = all_10_2 % 151.92/22.59 (3) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 151.92/22.59 (4) all_56_1 = all_10_2 % 151.92/22.59 (5) ~ (all_32_0 = e0) | ~ (all_32_2 = e2) % 151.92/22.59 (6) ~ (all_56_1 = e1) | all_56_5 = e3 % 151.92/22.59 (7) op(e3, e3) = all_10_2 % 151.92/22.59 (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 151.92/22.59 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 151.92/22.59 (9) all_32_0 = e0 % 151.92/22.59 (10) op(all_10_2, all_10_2) = e1 % 151.92/22.59 (11) ~ (all_10_2 = e0) % 151.92/22.59 (12) all_56_5 = e0 % 151.92/22.59 (13) op(e3, all_10_2) = all_56_0 % 151.92/22.59 (14) all_32_2 = all_10_2 % 151.92/22.59 % 151.92/22.59 Begin of proof % 151.92/22.59 | % 151.92/22.59 | BETA: splitting (6) gives: % 151.92/22.59 | % 151.92/22.59 | Case 1: % 151.92/22.59 | | % 151.92/22.59 | | (15) ~ (all_56_1 = e1) % 151.92/22.59 | | % 151.92/22.59 | | REDUCE: (4), (15) imply: % 151.92/22.59 | | (16) ~ (all_10_2 = e1) % 151.92/22.59 | | % 151.92/22.59 | | REF_CLOSE: (2), (3), (5), (7), (8), (9), (10), (11), (13), (14), (16) are % 151.92/22.59 | | inconsistent by sub-proof #399. % 151.92/22.59 | | % 151.92/22.59 | Case 2: % 151.92/22.59 | | % 151.92/22.59 | | (17) all_56_5 = e3 % 151.92/22.59 | | % 151.92/22.59 | | COMBINE_EQS: (12), (17) imply: % 151.92/22.59 | | (18) e3 = e0 % 151.92/22.59 | | % 151.92/22.59 | | SIMP: (18) implies: % 151.92/22.59 | | (19) e3 = e0 % 151.92/22.59 | | % 151.92/22.59 | | REDUCE: (1), (19) imply: % 151.92/22.59 | | (20) $false % 151.92/22.59 | | % 151.92/22.59 | | CLOSE: (20) is inconsistent. % 151.92/22.59 | | % 151.92/22.59 | End of split % 151.92/22.59 | % 151.92/22.59 End of proof % 151.92/22.59 % 151.92/22.59 Sub-proof #399 shows that the following formulas are inconsistent: % 151.92/22.59 ---------------------------------------------------------------- % 151.92/22.59 (1) all_54_0 = all_10_2 % 151.92/22.59 (2) ~ (all_10_2 = e1) % 151.92/22.59 (3) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 151.92/22.59 (4) ~ (all_32_0 = e0) | ~ (all_32_2 = e2) % 151.92/22.59 (5) op(e3, e3) = all_10_2 % 151.92/22.59 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 151.92/22.59 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 151.92/22.59 (7) all_32_0 = e0 % 151.92/22.59 (8) op(all_10_2, all_10_2) = e1 % 151.92/22.59 (9) ~ (all_10_2 = e0) % 151.92/22.59 (10) op(e3, all_10_2) = all_56_0 % 151.92/22.59 (11) all_32_2 = all_10_2 % 151.92/22.59 % 151.92/22.59 Begin of proof % 151.92/22.59 | % 151.92/22.59 | BETA: splitting (4) gives: % 151.92/22.59 | % 151.92/22.59 | Case 1: % 151.92/22.59 | | % 151.92/22.59 | | (12) ~ (all_32_2 = e2) % 151.92/22.59 | | % 151.92/22.59 | | REDUCE: (11), (12) imply: % 151.92/22.59 | | (13) ~ (all_10_2 = e2) % 151.92/22.59 | | % 151.92/22.59 | | REF_CLOSE: (1), (2), (3), (5), (6), (8), (9), (10), (13) are inconsistent by % 151.92/22.59 | | sub-proof #409. % 151.92/22.59 | | % 151.92/22.59 | Case 2: % 151.92/22.59 | | % 151.92/22.59 | | (14) all_32_2 = e2 % 151.92/22.59 | | % 151.92/22.59 | | REF_CLOSE: (4), (7), (14) are inconsistent by sub-proof #405. % 151.92/22.59 | | % 151.92/22.59 | End of split % 151.92/22.59 | % 151.92/22.59 End of proof % 151.92/22.59 % 151.92/22.59 Sub-proof #400 shows that the following formulas are inconsistent: % 151.92/22.59 ---------------------------------------------------------------- % 151.92/22.59 (1) all_58_14 = e1 | all_58_15 = e1 % 151.92/22.59 (2) all_58_8 = e2 | all_58_14 = e2 % 151.92/22.59 (3) ~ (all_4_2 = e1) % 151.92/22.59 (4) all_58_8 = all_6_2 % 151.92/22.59 (5) ~ (e2 = e1) % 151.92/22.59 (6) all_58_15 = all_4_2 % 151.92/22.59 (7) ~ (all_6_2 = e2) % 151.92/22.59 % 151.92/22.59 Begin of proof % 151.92/22.59 | % 151.92/22.59 | BETA: splitting (1) gives: % 151.92/22.59 | % 151.92/22.59 | Case 1: % 151.92/22.59 | | % 151.92/22.59 | | (8) all_58_14 = e1 % 151.92/22.59 | | % 151.92/22.59 | | REF_CLOSE: (2), (4), (5), (7), (8) are inconsistent by sub-proof #401. % 151.92/22.59 | | % 151.92/22.59 | Case 2: % 151.92/22.59 | | % 151.92/22.59 | | (9) all_58_15 = e1 % 151.92/22.59 | | % 151.92/22.59 | | COMBINE_EQS: (6), (9) imply: % 151.92/22.59 | | (10) all_4_2 = e1 % 151.92/22.59 | | % 151.92/22.59 | | REDUCE: (3), (10) imply: % 151.92/22.59 | | (11) $false % 151.92/22.59 | | % 151.92/22.59 | | CLOSE: (11) is inconsistent. % 151.92/22.59 | | % 151.92/22.59 | End of split % 151.92/22.59 | % 151.92/22.59 End of proof % 151.92/22.59 % 151.92/22.59 Sub-proof #401 shows that the following formulas are inconsistent: % 151.92/22.59 ---------------------------------------------------------------- % 151.92/22.59 (1) all_58_8 = e2 | all_58_14 = e2 % 151.92/22.59 (2) all_58_8 = all_6_2 % 151.92/22.59 (3) all_58_14 = e1 % 151.92/22.59 (4) ~ (e2 = e1) % 151.92/22.59 (5) ~ (all_6_2 = e2) % 151.92/22.59 % 151.92/22.59 Begin of proof % 151.92/22.59 | % 151.92/22.59 | BETA: splitting (1) gives: % 151.92/22.59 | % 151.92/22.59 | Case 1: % 151.92/22.59 | | % 151.92/22.59 | | (6) all_58_8 = e2 % 151.92/22.59 | | % 151.92/22.59 | | COMBINE_EQS: (2), (6) imply: % 151.92/22.59 | | (7) all_6_2 = e2 % 151.92/22.59 | | % 151.92/22.59 | | REDUCE: (5), (7) imply: % 151.92/22.59 | | (8) $false % 151.92/22.59 | | % 151.92/22.59 | | CLOSE: (8) is inconsistent. % 151.92/22.59 | | % 151.92/22.59 | Case 2: % 151.92/22.59 | | % 151.92/22.59 | | (9) all_58_14 = e2 % 151.92/22.59 | | % 151.92/22.59 | | COMBINE_EQS: (3), (9) imply: % 151.92/22.59 | | (10) e2 = e1 % 151.92/22.59 | | % 151.92/22.59 | | REDUCE: (4), (10) imply: % 151.92/22.59 | | (11) $false % 151.92/22.59 | | % 151.92/22.59 | | CLOSE: (11) is inconsistent. % 151.92/22.59 | | % 151.92/22.59 | End of split % 151.92/22.59 | % 151.92/22.59 End of proof % 151.92/22.59 % 151.92/22.59 Sub-proof #402 shows that the following formulas are inconsistent: % 151.92/22.59 ---------------------------------------------------------------- % 151.92/22.59 (1) all_54_6 = all_52_9 % 151.92/22.59 (2) all_54_6 = e3 % 151.92/22.59 (3) ~ (all_52_9 = e3) % 151.92/22.59 % 151.92/22.59 Begin of proof % 151.92/22.59 | % 151.92/22.59 | COMBINE_EQS: (1), (2) imply: % 151.92/22.59 | (4) all_52_9 = e3 % 151.92/22.59 | % 151.92/22.59 | SIMP: (4) implies: % 151.92/22.59 | (5) all_52_9 = e3 % 151.92/22.59 | % 151.92/22.59 | REDUCE: (3), (5) imply: % 151.92/22.59 | (6) $false % 151.92/22.59 | % 151.92/22.59 | CLOSE: (6) is inconsistent. % 151.92/22.59 | % 151.92/22.59 End of proof % 151.92/22.59 % 151.92/22.59 Sub-proof #403 shows that the following formulas are inconsistent: % 151.92/22.59 ---------------------------------------------------------------- % 151.92/22.59 (1) all_54_0 = all_10_2 % 151.92/22.59 (2) all_54_2 = all_10_0 % 151.92/22.59 (3) ~ (all_10_2 = e1) % 151.92/22.59 (4) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 151.92/22.59 (5) all_56_1 = all_10_2 % 151.92/22.59 (6) ~ (all_32_0 = e0) | ~ (all_32_2 = e2) % 151.92/22.59 (7) op(e3, e3) = all_10_2 % 151.92/22.59 (8) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0 % 151.92/22.59 (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 151.92/22.59 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 151.92/22.59 (10) ~ (all_56_1 = e2) | all_56_3 = e3 % 151.92/22.59 (11) ~ (all_52_4 = all_10_0) % 151.92/22.59 (12) op(all_10_2, all_10_2) = e1 % 151.92/22.59 (13) all_56_3 = all_52_4 % 151.92/22.59 (14) ~ (all_10_0 = e1) % 151.92/22.59 (15) all_32_0 = all_10_0 % 151.92/22.59 (16) ~ (all_10_2 = e0) % 151.92/22.59 (17) op(e3, all_10_2) = all_56_0 % 151.92/22.59 (18) ~ (all_10_0 = all_10_2) % 151.92/22.59 (19) all_32_2 = all_10_2 % 151.92/22.59 % 151.92/22.59 Begin of proof % 151.92/22.59 | % 151.92/22.59 | BETA: splitting (10) gives: % 151.92/22.59 | % 151.92/22.59 | Case 1: % 151.92/22.59 | | % 151.92/22.59 | | (20) ~ (all_56_1 = e2) % 151.92/22.59 | | % 151.92/22.59 | | REDUCE: (5), (20) imply: % 151.92/22.59 | | (21) ~ (all_10_2 = e2) % 151.92/22.59 | | % 151.92/22.59 | | REF_CLOSE: (1), (3), (4), (7), (9), (12), (16), (17), (21) are inconsistent % 151.92/22.59 | | by sub-proof #409. % 151.92/22.59 | | % 151.92/22.59 | Case 2: % 151.92/22.59 | | % 151.92/22.59 | | (22) all_56_3 = e3 % 151.92/22.59 | | (23) all_56_1 = e2 % 151.92/22.59 | | % 151.92/22.59 | | COMBINE_EQS: (5), (23) imply: % 151.92/22.59 | | (24) all_10_2 = e2 % 151.92/22.59 | | % 151.92/22.59 | | COMBINE_EQS: (13), (22) imply: % 151.92/22.59 | | (25) all_52_4 = e3 % 151.92/22.59 | | % 151.92/22.59 | | COMBINE_EQS: (19), (24) imply: % 151.92/22.59 | | (26) all_32_2 = e2 % 151.92/22.59 | | % 151.92/22.59 | | REDUCE: (11), (25) imply: % 151.92/22.59 | | (27) ~ (all_10_0 = e3) % 151.92/22.59 | | % 151.92/22.59 | | SIMP: (27) implies: % 151.92/22.59 | | (28) ~ (all_10_0 = e3) % 151.92/22.59 | | % 151.92/22.59 | | REDUCE: (18), (24) imply: % 151.92/22.59 | | (29) ~ (all_10_0 = e2) % 151.92/22.59 | | % 151.92/22.59 | | REF_CLOSE: (2), (6), (8), (14), (15), (26), (28), (29) are inconsistent by % 151.92/22.59 | | sub-proof #404. % 151.92/22.59 | | % 151.92/22.59 | End of split % 151.92/22.59 | % 151.92/22.59 End of proof % 151.92/22.59 % 151.92/22.59 Sub-proof #404 shows that the following formulas are inconsistent: % 151.92/22.59 ---------------------------------------------------------------- % 151.92/22.59 (1) all_54_2 = all_10_0 % 151.92/22.59 (2) ~ (all_32_0 = e0) | ~ (all_32_2 = e2) % 151.92/22.59 (3) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0 % 151.92/22.59 (4) ~ (all_10_0 = e1) % 151.92/22.59 (5) all_32_0 = all_10_0 % 151.92/22.59 (6) ~ (all_10_0 = e3) % 151.92/22.59 (7) ~ (all_10_0 = e2) % 151.92/22.59 (8) all_32_2 = e2 % 151.92/22.59 % 151.92/22.59 Begin of proof % 151.92/22.59 | % 151.92/22.59 | BETA: splitting (3) gives: % 151.92/22.59 | % 151.92/22.59 | Case 1: % 151.92/22.59 | | % 151.92/22.59 | | (9) all_54_2 = e3 % 151.92/22.59 | | % 151.92/22.59 | | REF_CLOSE: (1), (6), (9) are inconsistent by sub-proof #408. % 151.92/22.59 | | % 151.92/22.59 | Case 2: % 151.92/22.59 | | % 151.92/22.59 | | (10) all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0 % 151.92/22.59 | | % 151.92/22.59 | | BETA: splitting (10) gives: % 151.92/22.59 | | % 151.92/22.59 | | Case 1: % 151.92/22.59 | | | % 151.92/22.59 | | | (11) all_54_2 = e2 % 151.92/22.59 | | | % 151.92/22.59 | | | REF_CLOSE: (1), (7), (11) are inconsistent by sub-proof #407. % 151.92/22.59 | | | % 151.92/22.59 | | Case 2: % 151.92/22.59 | | | % 151.92/22.59 | | | (12) all_54_2 = e1 | all_54_2 = e0 % 151.92/22.59 | | | % 151.92/22.59 | | | BETA: splitting (12) gives: % 151.92/22.59 | | | % 151.92/22.59 | | | Case 1: % 151.92/22.59 | | | | % 151.92/22.59 | | | | (13) all_54_2 = e1 % 151.92/22.59 | | | | % 151.92/22.59 | | | | REF_CLOSE: (1), (4), (13) are inconsistent by sub-proof #406. % 151.92/22.59 | | | | % 151.92/22.59 | | | Case 2: % 151.92/22.59 | | | | % 151.92/22.59 | | | | (14) all_54_2 = e0 % 151.92/22.59 | | | | % 151.92/22.59 | | | | COMBINE_EQS: (1), (14) imply: % 151.92/22.59 | | | | (15) all_10_0 = e0 % 151.92/22.59 | | | | % 151.92/22.59 | | | | SIMP: (15) implies: % 151.92/22.59 | | | | (16) all_10_0 = e0 % 151.92/22.59 | | | | % 151.92/22.59 | | | | COMBINE_EQS: (5), (16) imply: % 151.92/22.59 | | | | (17) all_32_0 = e0 % 151.92/22.59 | | | | % 151.92/22.59 | | | | REF_CLOSE: (2), (8), (17) are inconsistent by sub-proof #405. % 151.92/22.59 | | | | % 151.92/22.59 | | | End of split % 151.92/22.59 | | | % 151.92/22.59 | | End of split % 151.92/22.59 | | % 151.92/22.59 | End of split % 151.92/22.59 | % 151.92/22.59 End of proof % 151.92/22.59 % 151.92/22.59 Sub-proof #405 shows that the following formulas are inconsistent: % 151.92/22.59 ---------------------------------------------------------------- % 151.92/22.59 (1) ~ (all_32_0 = e0) | ~ (all_32_2 = e2) % 151.92/22.59 (2) all_32_2 = e2 % 151.92/22.59 (3) all_32_0 = e0 % 151.92/22.59 % 151.92/22.59 Begin of proof % 151.92/22.59 | % 151.92/22.59 | BETA: splitting (1) gives: % 151.92/22.59 | % 151.92/22.59 | Case 1: % 151.92/22.59 | | % 151.92/22.59 | | (4) ~ (all_32_2 = e2) % 151.92/22.59 | | % 151.92/22.59 | | REDUCE: (2), (4) imply: % 151.92/22.59 | | (5) $false % 151.92/22.59 | | % 151.92/22.59 | | CLOSE: (5) is inconsistent. % 151.92/22.59 | | % 151.92/22.59 | Case 2: % 151.92/22.59 | | % 151.92/22.59 | | (6) ~ (all_32_0 = e0) % 151.92/22.59 | | % 151.92/22.59 | | REDUCE: (3), (6) imply: % 151.92/22.59 | | (7) $false % 151.92/22.59 | | % 151.92/22.59 | | CLOSE: (7) is inconsistent. % 151.92/22.59 | | % 151.92/22.59 | End of split % 151.92/22.59 | % 151.92/22.59 End of proof % 151.92/22.59 % 151.92/22.59 Sub-proof #406 shows that the following formulas are inconsistent: % 151.92/22.59 ---------------------------------------------------------------- % 151.92/22.59 (1) all_54_2 = all_10_0 % 151.92/22.59 (2) all_54_2 = e1 % 151.92/22.59 (3) ~ (all_10_0 = e1) % 151.92/22.59 % 151.92/22.59 Begin of proof % 151.92/22.59 | % 151.92/22.59 | COMBINE_EQS: (1), (2) imply: % 151.92/22.59 | (4) all_10_0 = e1 % 151.92/22.59 | % 151.92/22.59 | SIMP: (4) implies: % 151.92/22.59 | (5) all_10_0 = e1 % 151.92/22.59 | % 151.92/22.59 | REDUCE: (3), (5) imply: % 151.92/22.59 | (6) $false % 151.92/22.59 | % 151.92/22.59 | CLOSE: (6) is inconsistent. % 151.92/22.59 | % 151.92/22.59 End of proof % 151.92/22.59 % 151.92/22.59 Sub-proof #407 shows that the following formulas are inconsistent: % 151.92/22.59 ---------------------------------------------------------------- % 151.92/22.59 (1) all_54_2 = all_10_0 % 151.92/22.59 (2) all_54_2 = e2 % 151.92/22.59 (3) ~ (all_10_0 = e2) % 151.92/22.59 % 151.92/22.59 Begin of proof % 151.92/22.59 | % 151.92/22.59 | COMBINE_EQS: (1), (2) imply: % 151.92/22.59 | (4) all_10_0 = e2 % 151.92/22.59 | % 151.92/22.59 | SIMP: (4) implies: % 151.92/22.59 | (5) all_10_0 = e2 % 151.92/22.59 | % 151.92/22.59 | REDUCE: (3), (5) imply: % 151.92/22.59 | (6) $false % 151.92/22.59 | % 151.92/22.59 | CLOSE: (6) is inconsistent. % 151.92/22.59 | % 151.92/22.59 End of proof % 151.92/22.59 % 151.92/22.59 Sub-proof #408 shows that the following formulas are inconsistent: % 151.92/22.59 ---------------------------------------------------------------- % 151.92/22.59 (1) all_54_2 = all_10_0 % 151.92/22.59 (2) all_54_2 = e3 % 151.92/22.59 (3) ~ (all_10_0 = e3) % 151.92/22.59 % 151.92/22.59 Begin of proof % 151.92/22.59 | % 151.92/22.59 | COMBINE_EQS: (1), (2) imply: % 151.92/22.59 | (4) all_10_0 = e3 % 151.92/22.59 | % 151.92/22.59 | SIMP: (4) implies: % 151.92/22.59 | (5) all_10_0 = e3 % 151.92/22.59 | % 151.92/22.59 | REDUCE: (3), (5) imply: % 151.92/22.59 | (6) $false % 151.92/22.59 | % 151.92/22.59 | CLOSE: (6) is inconsistent. % 151.92/22.59 | % 151.92/22.59 End of proof % 151.92/22.59 % 151.92/22.59 Sub-proof #409 shows that the following formulas are inconsistent: % 151.92/22.59 ---------------------------------------------------------------- % 151.92/22.59 (1) all_54_0 = all_10_2 % 151.92/22.59 (2) ~ (all_10_2 = e1) % 151.92/22.59 (3) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 151.92/22.59 (4) ~ (all_10_2 = e2) % 151.92/22.59 (5) op(e3, e3) = all_10_2 % 151.92/22.59 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 151.92/22.59 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 151.92/22.59 (7) op(all_10_2, all_10_2) = e1 % 151.92/22.59 (8) ~ (all_10_2 = e0) % 151.92/22.59 (9) op(e3, all_10_2) = all_56_0 % 151.92/22.59 % 151.92/22.59 Begin of proof % 151.92/22.59 | % 151.92/22.59 | BETA: splitting (3) gives: % 151.92/22.59 | % 151.92/22.59 | Case 1: % 151.92/22.59 | | % 151.92/22.59 | | (10) all_54_0 = e3 % 151.92/22.59 | | % 151.92/22.59 | | COMBINE_EQS: (1), (10) imply: % 151.92/22.59 | | (11) all_10_2 = e3 % 151.92/22.59 | | % 151.92/22.59 | | SIMP: (11) implies: % 151.92/22.59 | | (12) all_10_2 = e3 % 151.92/22.59 | | % 151.92/22.59 | | REDUCE: (2), (12) imply: % 151.92/22.59 | | (13) ~ (e3 = e1) % 151.92/22.59 | | % 151.92/22.59 | | REDUCE: (7), (12) imply: % 151.92/22.59 | | (14) op(e3, e3) = e1 % 151.92/22.59 | | % 151.92/22.59 | | REDUCE: (9), (12) imply: % 151.92/22.59 | | (15) op(e3, e3) = all_56_0 % 151.92/22.59 | | % 151.92/22.59 | | REDUCE: (5), (12) imply: % 151.92/22.59 | | (16) op(e3, e3) = e3 % 151.92/22.59 | | % 151.92/22.59 | | REF_CLOSE: (6), (13), (14), (15), (16) are inconsistent by sub-proof #410. % 151.92/22.59 | | % 151.92/22.59 | Case 2: % 151.92/22.59 | | % 151.92/22.59 | | (17) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 151.92/22.59 | | % 151.92/22.59 | | REF_CLOSE: (1), (2), (4), (8), (17) are inconsistent by sub-proof #731. % 151.92/22.59 | | % 151.92/22.59 | End of split % 151.92/22.59 | % 151.92/22.59 End of proof % 151.92/22.59 % 151.92/22.59 Sub-proof #410 shows that the following formulas are inconsistent: % 151.92/22.59 ---------------------------------------------------------------- % 151.92/22.59 (1) op(e3, e3) = e3 % 151.92/22.59 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 151.92/22.59 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 151.92/22.59 (3) op(e3, e3) = all_56_0 % 151.92/22.59 (4) op(e3, e3) = e1 % 151.92/22.59 (5) ~ (e3 = e1) % 151.92/22.59 % 151.92/22.59 Begin of proof % 151.92/22.59 | % 151.92/22.59 | GROUND_INST: instantiating (2) with e3, all_56_0, e3, e3, simplifying with % 151.92/22.59 | (1), (3) gives: % 151.92/22.59 | (6) all_56_0 = e3 % 151.92/22.59 | % 151.92/22.59 | GROUND_INST: instantiating (2) with e1, all_56_0, e3, e3, simplifying with % 151.92/22.59 | (3), (4) gives: % 151.92/22.59 | (7) all_56_0 = e1 % 151.92/22.59 | % 151.92/22.59 | COMBINE_EQS: (6), (7) imply: % 151.92/22.59 | (8) e3 = e1 % 151.92/22.59 | % 151.92/22.59 | SIMP: (8) implies: % 151.92/22.59 | (9) e3 = e1 % 151.92/22.59 | % 151.92/22.59 | REDUCE: (5), (9) imply: % 151.92/22.59 | (10) $false % 151.92/22.59 | % 151.92/22.59 | CLOSE: (10) is inconsistent. % 151.92/22.59 | % 151.92/22.59 End of proof % 151.92/22.59 % 151.92/22.59 Sub-proof #411 shows that the following formulas are inconsistent: % 151.92/22.59 ---------------------------------------------------------------- % 151.92/22.59 (1) all_56_11 = all_8_2 % 151.92/22.59 (2) ~ (all_52_3 = all_6_0) % 151.92/22.59 (3) ~ (all_56_11 = e1) | all_56_13 = e2 % 151.92/22.59 (4) ~ (all_52_11 = all_6_2) % 151.92/22.59 (5) ~ (all_52_4 = all_52_8) % 151.92/22.59 (6) all_56_25 = all_52_3 % 151.92/22.59 (7) all_54_9 = all_52_6 % 151.92/22.59 (8) ~ (all_52_1 = all_52_9) % 151.92/22.59 (9) ~ (all_56_31 = e1) | all_56_29 = e0 % 151.92/22.59 (10) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0 % 151.92/22.59 (11) all_54_10 = all_6_2 % 151.92/22.59 (12) ~ (all_56_21 = e2) | all_56_19 = e1 % 151.92/22.59 (13) all_54_0 = all_10_2 % 151.92/22.59 (14) all_54_4 = all_52_1 % 151.92/22.59 (15) ~ (all_52_14 = all_4_2) % 151.92/22.59 (16) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0 % 151.92/22.59 (17) all_54_12 = all_52_3 % 151.92/22.59 (18) op(e0, e0) = all_4_2 % 151.92/22.59 (19) all_58_6 = e0 | all_58_7 = e0 | all_58_8 = e0 | all_58_11 = e0 % 151.92/22.59 (20) all_54_5 = all_8_2 % 151.92/22.59 (21) ~ (all_52_6 = all_52_14) % 151.92/22.59 (22) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 151.92/22.59 (23) ~ (all_6_0 = e2) % 151.92/22.59 (24) all_56_21 = all_6_2 % 151.92/22.59 (25) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 151.92/22.59 (26) all_56_1 = all_10_2 % 151.92/22.59 (27) all_54_1 = all_52_4 % 151.92/22.59 (28) ~ (all_52_1 = all_6_0) % 151.92/22.59 (29) ~ (all_56_1 = e1) | all_56_5 = e3 % 151.92/22.59 (30) all_54_14 = all_52_11 % 151.92/22.59 (31) op(e3, e2) = all_10_0 % 151.92/22.59 (32) all_58_1 = all_52_4 % 151.92/22.59 (33) all_58_13 = all_52_7 % 151.92/22.59 (34) op(e2, all_8_2) = all_56_10 % 151.92/22.59 (35) op(e3, e3) = all_10_2 % 151.92/22.59 (36) ~ (all_52_6 = all_6_0) % 151.92/22.59 (37) ~ (all_56_21 = e3) | all_56_17 = e1 % 151.92/22.59 (38) all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2 % 151.92/22.59 (39) ~ (e1 = e0) % 151.92/22.59 (40) all_38_0 = all_10_0 % 151.92/22.59 (41) ~ (all_52_1 = all_8_2) % 151.92/22.59 (42) all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2 % 151.92/22.59 (43) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 151.92/22.59 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 151.92/22.59 (44) ~ (all_52_3 = all_10_2) % 151.92/22.59 (45) ~ (all_52_3 = all_52_7) % 151.92/22.59 (46) ~ (all_56_11 = e3) | all_56_9 = e2 % 151.92/22.59 (47) all_36_0 = all_6_0 % 151.92/22.59 (48) op(e0, all_4_1) = all_4_0 % 151.92/22.59 (49) all_56_7 = all_52_12 % 151.92/22.59 (50) ~ (all_6_0 = all_6_2) % 151.92/22.59 (51) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0 % 151.92/22.59 (52) all_56_13 = all_52_9 % 151.92/22.59 (53) op(e2, all_52_6) = all_56_18 % 151.92/22.59 (54) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0 % 151.92/22.59 (55) all_54_8 = all_6_0 % 151.92/22.59 (56) all_58_8 = all_6_2 % 151.92/22.59 (57) ~ (all_52_3 = all_4_2) % 151.92/22.59 (58) ~ (all_56_1 = e2) | all_56_3 = e3 % 151.92/22.59 (59) ~ (all_56_1 = e0) | all_56_7 = e3 % 151.92/22.59 (60) ~ (all_52_14 = all_6_0) % 151.92/22.59 (61) all_56_5 = all_52_8 % 151.92/22.59 (62) op(all_4_2, all_4_2) = all_4_1 % 151.92/22.59 (63) ~ (all_52_3 = all_52_11) % 151.92/22.59 (64) all_58_3 = all_8_2 % 151.92/22.59 (65) all_56_3 = all_52_4 % 151.92/22.59 (66) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0 % 151.92/22.59 (67) ~ (all_52_11 = all_4_2) % 151.92/22.59 (68) ~ (all_52_1 = all_52_3) % 151.92/22.59 (69) all_56_31 = all_4_2 % 151.92/22.59 (70) all_58_11 = all_52_14 % 151.92/22.59 (71) op(all_10_2, all_10_2) = e2 % 151.92/22.59 (72) all_36_2 = all_6_2 % 151.92/22.59 (73) ~ (all_52_9 = all_52_11) % 151.92/22.59 (74) all_56_1 = e3 | all_56_11 = e2 | all_56_21 = e1 | all_56_31 = e0 % 151.92/22.59 (75) ~ (all_10_0 = e1) % 151.92/22.59 (76) op(e3, e2) = all_52_4 % 151.92/22.59 (77) ~ (all_52_13 = all_52_14) % 151.92/22.59 (78) all_56_23 = all_52_14 % 151.92/22.59 (79) all_58_6 = all_6_0 % 151.92/22.59 (80) ~ (all_38_0 = e0) | ~ (all_38_2 = e1) % 151.92/22.59 (81) all_38_2 = all_10_2 % 151.92/22.59 (82) op(e1, e1) = all_6_2 % 151.92/22.59 (83) ~ (all_52_6 = all_8_2) % 151.92/22.59 (84) op(e0, e3) = all_52_3 % 151.92/22.59 (85) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0 % 151.92/22.59 (86) all_56_29 = all_52_11 % 151.92/22.59 (87) all_58_2 = all_52_1 % 151.92/22.59 (88) all_58_7 = all_52_6 % 151.92/22.59 (89) op(all_10_2, all_10_2) = all_10_1 % 151.92/22.59 (90) ~ (all_56_11 = e0) | all_56_15 = e2 % 151.92/22.59 (91) all_58_0 = all_10_2 % 151.92/22.59 (92) op(e1, all_6_2) = all_56_20 % 151.92/22.59 (93) all_58_1 = e0 | all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0 % 151.92/22.59 (94) all_56_17 = all_6_0 % 151.92/22.59 (95) op(e2, e2) = all_8_2 % 151.92/22.59 (96) ~ (all_36_0 = e0) | ~ (all_36_2 = e2) % 151.92/22.59 (97) ~ (all_52_4 = all_52_12) % 151.92/22.59 (98) ~ (all_56_21 = e0) | all_56_23 = e1 % 151.92/22.59 (99) op(e0, all_4_2) = all_56_30 % 151.92/22.59 (100) ~ (all_52_6 = all_6_2) % 151.92/22.59 (101) op(all_6_2, all_6_2) = e3 % 151.92/22.59 (102) op(e3, all_10_2) = all_56_0 % 151.92/22.59 (103) ~ (all_52_14 = all_6_2) % 151.92/22.59 (104) ~ (e2 = e0) % 151.92/22.59 (105) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0 % 151.92/22.59 (106) ~ (all_10_2 = all_6_0) % 151.92/22.59 (107) ~ (all_52_4 = all_10_2) % 151.92/22.59 (108) ~ (all_10_0 = e2) % 151.92/22.59 (109) ~ (all_52_4 = all_8_2) % 151.92/22.59 (110) op(all_8_2, all_8_2) = all_8_1 % 151.92/22.59 (111) ~ (all_52_4 = all_52_6) % 151.92/22.59 (112) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 151.92/22.59 (113) all_56_19 = all_52_6 % 151.92/22.59 (114) ~ (all_4_0 = e2) % 151.92/22.59 (115) ~ (all_4_0 = e3) % 151.92/22.59 (116) all_56_9 = all_52_1 % 151.92/22.59 (117) all_56_15 = all_52_13 % 151.92/22.59 (118) ~ (all_52_1 = all_10_2) % 151.92/22.59 (119) all_58_12 = all_52_3 % 151.92/22.59 (120) all_54_11 = all_52_14 % 151.92/22.59 (121) ~ (all_56_31 = e3) | all_56_25 = e0 % 151.92/22.59 % 151.92/22.59 Begin of proof % 151.92/22.59 | % 151.92/22.59 | GROUND_INST: instantiating (43) with all_52_4, all_10_0, e2, e3, simplifying % 151.92/22.59 | with (31), (76) gives: % 151.92/22.59 | (122) all_52_4 = all_10_0 % 151.92/22.59 | % 151.92/22.59 | COMBINE_EQS: (27), (122) imply: % 151.92/22.59 | (123) all_54_1 = all_10_0 % 151.92/22.59 | % 151.92/22.59 | COMBINE_EQS: (65), (122) imply: % 151.92/22.59 | (124) all_56_3 = all_10_0 % 151.92/22.59 | % 151.92/22.59 | COMBINE_EQS: (32), (122) imply: % 151.92/22.59 | (125) all_58_1 = all_10_0 % 151.92/22.59 | % 151.92/22.59 | REDUCE: (111), (122) imply: % 151.92/22.59 | (126) ~ (all_52_6 = all_10_0) % 151.92/22.59 | % 151.92/22.59 | SIMP: (126) implies: % 151.92/22.59 | (127) ~ (all_52_6 = all_10_0) % 151.92/22.59 | % 151.92/22.59 | REDUCE: (5), (122) imply: % 151.92/22.59 | (128) ~ (all_52_8 = all_10_0) % 151.92/22.59 | % 151.92/22.59 | SIMP: (128) implies: % 151.92/22.59 | (129) ~ (all_52_8 = all_10_0) % 151.92/22.59 | % 151.92/22.59 | REDUCE: (97), (122) imply: % 151.92/22.59 | (130) ~ (all_52_12 = all_10_0) % 151.92/22.59 | % 151.92/22.59 | SIMP: (130) implies: % 151.92/22.59 | (131) ~ (all_52_12 = all_10_0) % 151.92/22.59 | % 151.92/22.59 | REDUCE: (107), (122) imply: % 151.92/22.59 | (132) ~ (all_10_0 = all_10_2) % 151.92/22.59 | % 151.92/22.59 | REDUCE: (109), (122) imply: % 151.92/22.59 | (133) ~ (all_10_0 = all_8_2) % 151.92/22.59 | % 151.92/22.59 | BETA: splitting (12) gives: % 151.92/22.59 | % 151.92/22.59 | Case 1: % 151.92/22.59 | | % 151.92/22.59 | | (134) ~ (all_56_21 = e2) % 151.92/22.59 | | % 151.92/22.59 | | REDUCE: (24), (134) imply: % 151.92/22.59 | | (135) ~ (all_6_2 = e2) % 151.92/22.59 | | % 151.92/22.59 | | BETA: splitting (9) gives: % 151.92/22.59 | | % 151.92/22.59 | | Case 1: % 151.92/22.59 | | | % 151.92/22.59 | | | (136) ~ (all_56_31 = e1) % 151.92/22.59 | | | % 151.92/22.59 | | | REDUCE: (69), (136) imply: % 151.92/22.59 | | | (137) ~ (all_4_2 = e1) % 151.92/22.59 | | | % 151.92/22.60 | | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (10), (11), (13), (14), % 151.92/22.60 | | | (15), (16), (18), (20), (21), (22), (23), (24), (25), (26), % 151.92/22.60 | | | (28), (29), (30), (33), (35), (36), (37), (38), (40), (41), % 151.92/22.60 | | | (42), (43), (44), (45), (46), (49), (50), (52), (53), (54), % 151.92/22.60 | | | (55), (56), (57), (58), (59), (60), (61), (62), (63), (64), % 151.92/22.60 | | | (66), (67), (68), (69), (70), (71), (73), (74), (75), (77), % 151.92/22.60 | | | (78), (79), (80), (81), (82), (83), (85), (87), (88), (89), % 151.92/22.60 | | | (90), (91), (92), (93), (94), (95), (98), (99), (100), (101), % 151.92/22.60 | | | (102), (103), (105), (106), (108), (110), (112), (116), (117), % 151.92/22.60 | | | (118), (119), (120), (121), (123), (124), (125), (127), (129), % 151.92/22.60 | | | (131), (132), (133), (135), (137) are inconsistent by sub-proof % 151.92/22.60 | | | #413. % 151.92/22.60 | | | % 151.92/22.60 | | Case 2: % 151.92/22.60 | | | % 151.92/22.60 | | | (138) all_56_31 = e1 % 151.92/22.60 | | | (139) all_56_29 = e0 % 151.92/22.60 | | | % 151.92/22.60 | | | COMBINE_EQS: (86), (139) imply: % 151.92/22.60 | | | (140) all_52_11 = e0 % 151.92/22.60 | | | % 151.92/22.60 | | | REF_CLOSE: (2), (4), (11), (17), (24), (25), (37), (43), (48), (51), (62), % 151.92/22.60 | | | (63), (69), (82), (84), (92), (94), (101), (114), (115), (135), % 151.92/22.60 | | | (138), (140) are inconsistent by sub-proof #436. % 151.92/22.60 | | | % 151.92/22.60 | | End of split % 151.92/22.60 | | % 151.92/22.60 | Case 2: % 151.92/22.60 | | % 151.92/22.60 | | (141) all_56_21 = e2 % 151.92/22.60 | | (142) all_56_19 = e1 % 151.92/22.60 | | % 151.92/22.60 | | REF_CLOSE: (1), (15), (19), (24), (26), (34), (36), (39), (43), (47), (50), % 151.92/22.60 | | (55), (56), (60), (69), (70), (72), (74), (79), (88), (95), (96), % 151.92/22.60 | | (100), (101), (104), (105), (106), (110), (113), (141), (142) are % 151.92/22.60 | | inconsistent by sub-proof #412. % 151.92/22.60 | | % 151.92/22.60 | End of split % 151.92/22.60 | % 151.92/22.60 End of proof % 151.92/22.60 % 151.92/22.60 Sub-proof #412 shows that the following formulas are inconsistent: % 151.92/22.60 ---------------------------------------------------------------- % 151.92/22.60 (1) all_56_11 = all_8_2 % 151.92/22.60 (2) ~ (all_52_14 = all_4_2) % 151.92/22.60 (3) all_58_6 = e0 | all_58_7 = e0 | all_58_8 = e0 | all_58_11 = e0 % 151.92/22.60 (4) all_56_21 = all_6_2 % 151.92/22.60 (5) all_56_1 = all_10_2 % 151.92/22.60 (6) op(e2, all_8_2) = all_56_10 % 151.92/22.60 (7) ~ (all_52_6 = all_6_0) % 151.92/22.60 (8) ~ (e1 = e0) % 151.92/22.60 (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 151.92/22.60 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 151.92/22.60 (10) all_36_0 = all_6_0 % 151.92/22.60 (11) ~ (all_6_0 = all_6_2) % 151.92/22.60 (12) all_54_8 = all_6_0 % 151.92/22.60 (13) all_58_8 = all_6_2 % 151.92/22.60 (14) all_56_21 = e2 % 151.92/22.60 (15) all_56_19 = e1 % 151.92/22.60 (16) ~ (all_52_14 = all_6_0) % 151.92/22.60 (17) all_56_31 = all_4_2 % 151.92/22.60 (18) all_58_11 = all_52_14 % 151.92/22.60 (19) all_36_2 = all_6_2 % 151.92/22.60 (20) all_56_1 = e3 | all_56_11 = e2 | all_56_21 = e1 | all_56_31 = e0 % 151.92/22.60 (21) all_58_6 = all_6_0 % 151.92/22.60 (22) all_58_7 = all_52_6 % 151.92/22.60 (23) op(e2, e2) = all_8_2 % 151.92/22.60 (24) ~ (all_36_0 = e0) | ~ (all_36_2 = e2) % 151.92/22.60 (25) ~ (all_52_6 = all_6_2) % 151.92/22.60 (26) op(all_6_2, all_6_2) = e3 % 151.92/22.60 (27) ~ (e2 = e0) % 151.92/22.60 (28) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0 % 151.92/22.60 (29) ~ (all_10_2 = all_6_0) % 151.92/22.60 (30) op(all_8_2, all_8_2) = all_8_1 % 151.92/22.60 (31) all_56_19 = all_52_6 % 151.92/22.60 % 151.92/22.60 Begin of proof % 151.92/22.60 | % 151.92/22.60 | COMBINE_EQS: (15), (31) imply: % 151.92/22.60 | (32) all_52_6 = e1 % 151.92/22.60 | % 151.92/22.60 | COMBINE_EQS: (4), (14) imply: % 151.92/22.60 | (33) all_6_2 = e2 % 151.92/22.60 | % 151.92/22.60 | COMBINE_EQS: (19), (33) imply: % 151.92/22.60 | (34) all_36_2 = e2 % 151.92/22.60 | % 151.92/22.60 | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (9), (10), (11), (12), (13), % 151.92/22.60 | (14), (16), (17), (18), (20), (21), (22), (23), (24), (25), (26), % 151.92/22.60 | (27), (28), (29), (30), (32), (33), (34) are inconsistent by % 151.92/22.60 | sub-proof #432. % 151.92/22.60 | % 151.92/22.60 End of proof % 151.92/22.60 % 151.92/22.60 Sub-proof #413 shows that the following formulas are inconsistent: % 151.92/22.60 ---------------------------------------------------------------- % 151.92/22.60 (1) all_56_11 = all_8_2 % 151.92/22.60 (2) ~ (all_52_3 = all_6_0) % 151.92/22.60 (3) ~ (all_56_11 = e1) | all_56_13 = e2 % 151.92/22.60 (4) ~ (all_52_11 = all_6_2) % 151.92/22.60 (5) all_56_25 = all_52_3 % 151.92/22.60 (6) all_54_9 = all_52_6 % 151.92/22.60 (7) ~ (all_52_1 = all_52_9) % 151.92/22.60 (8) ~ (all_10_0 = all_8_2) % 151.92/22.60 (9) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0 % 151.92/22.60 (10) all_54_10 = all_6_2 % 151.92/22.60 (11) all_54_0 = all_10_2 % 151.92/22.60 (12) all_54_4 = all_52_1 % 151.92/22.60 (13) ~ (all_52_14 = all_4_2) % 151.92/22.60 (14) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0 % 151.92/22.60 (15) op(e0, e0) = all_4_2 % 151.92/22.60 (16) all_54_5 = all_8_2 % 151.92/22.60 (17) ~ (all_52_6 = all_52_14) % 151.92/22.60 (18) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 151.92/22.60 (19) ~ (all_6_0 = e2) % 151.92/22.60 (20) all_54_1 = all_10_0 % 151.92/22.60 (21) all_56_21 = all_6_2 % 151.92/22.60 (22) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 151.92/22.60 (23) all_56_1 = all_10_2 % 151.92/22.60 (24) all_56_3 = all_10_0 % 151.92/22.60 (25) ~ (all_52_1 = all_6_0) % 151.92/22.60 (26) ~ (all_56_1 = e1) | all_56_5 = e3 % 151.92/22.60 (27) all_54_14 = all_52_11 % 151.92/22.60 (28) all_58_13 = all_52_7 % 151.92/22.60 (29) op(e3, e3) = all_10_2 % 151.92/22.60 (30) ~ (all_52_6 = all_6_0) % 151.92/22.60 (31) ~ (all_56_21 = e3) | all_56_17 = e1 % 151.92/22.60 (32) all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2 % 151.92/22.60 (33) all_38_0 = all_10_0 % 151.92/22.60 (34) ~ (all_52_1 = all_8_2) % 151.92/22.60 (35) all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2 % 151.92/22.60 (36) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 151.92/22.60 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 151.92/22.60 (37) ~ (all_52_8 = all_10_0) % 151.92/22.60 (38) ~ (all_52_3 = all_10_2) % 151.92/22.60 (39) ~ (all_52_3 = all_52_7) % 151.92/22.60 (40) ~ (all_56_11 = e3) | all_56_9 = e2 % 151.92/22.60 (41) all_56_7 = all_52_12 % 151.92/22.60 (42) ~ (all_6_0 = all_6_2) % 151.92/22.60 (43) all_56_13 = all_52_9 % 151.92/22.60 (44) op(e2, all_52_6) = all_56_18 % 151.92/22.60 (45) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0 % 151.92/22.60 (46) ~ (all_4_2 = e1) % 151.92/22.60 (47) all_54_8 = all_6_0 % 151.92/22.60 (48) all_58_8 = all_6_2 % 151.92/22.60 (49) ~ (all_52_3 = all_4_2) % 151.92/22.60 (50) ~ (all_52_12 = all_10_0) % 151.92/22.60 (51) ~ (all_56_1 = e2) | all_56_3 = e3 % 151.92/22.60 (52) ~ (all_56_1 = e0) | all_56_7 = e3 % 151.92/22.60 (53) ~ (all_52_6 = all_10_0) % 151.92/22.60 (54) ~ (all_52_14 = all_6_0) % 151.92/22.60 (55) all_56_5 = all_52_8 % 151.92/22.60 (56) op(all_4_2, all_4_2) = all_4_1 % 151.92/22.60 (57) ~ (all_52_3 = all_52_11) % 151.92/22.60 (58) all_58_3 = all_8_2 % 151.92/22.60 (59) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0 % 151.92/22.60 (60) ~ (all_52_11 = all_4_2) % 151.92/22.60 (61) ~ (all_52_1 = all_52_3) % 151.92/22.60 (62) all_56_31 = all_4_2 % 151.92/22.60 (63) all_58_11 = all_52_14 % 151.92/22.60 (64) op(all_10_2, all_10_2) = e2 % 151.92/22.60 (65) ~ (all_52_9 = all_52_11) % 151.92/22.60 (66) all_56_1 = e3 | all_56_11 = e2 | all_56_21 = e1 | all_56_31 = e0 % 151.92/22.60 (67) ~ (all_10_0 = e1) % 151.92/22.60 (68) ~ (all_52_13 = all_52_14) % 151.92/22.60 (69) all_56_23 = all_52_14 % 151.92/22.60 (70) all_58_6 = all_6_0 % 151.92/22.60 (71) ~ (all_38_0 = e0) | ~ (all_38_2 = e1) % 151.92/22.60 (72) all_38_2 = all_10_2 % 151.92/22.60 (73) op(e1, e1) = all_6_2 % 151.92/22.60 (74) ~ (all_52_6 = all_8_2) % 151.92/22.60 (75) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0 % 151.92/22.60 (76) ~ (all_6_2 = e2) % 151.92/22.60 (77) all_58_2 = all_52_1 % 151.92/22.60 (78) all_58_7 = all_52_6 % 151.92/22.60 (79) op(all_10_2, all_10_2) = all_10_1 % 151.92/22.60 (80) ~ (all_56_11 = e0) | all_56_15 = e2 % 151.92/22.60 (81) all_58_0 = all_10_2 % 151.92/22.60 (82) op(e1, all_6_2) = all_56_20 % 151.92/22.60 (83) all_58_1 = all_10_0 % 151.92/22.60 (84) all_58_1 = e0 | all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0 % 151.92/22.60 (85) all_56_17 = all_6_0 % 151.92/22.60 (86) op(e2, e2) = all_8_2 % 151.92/22.60 (87) ~ (all_56_21 = e0) | all_56_23 = e1 % 151.92/22.60 (88) op(e0, all_4_2) = all_56_30 % 151.92/22.60 (89) ~ (all_52_6 = all_6_2) % 151.92/22.60 (90) op(all_6_2, all_6_2) = e3 % 151.92/22.60 (91) op(e3, all_10_2) = all_56_0 % 151.92/22.60 (92) ~ (all_52_14 = all_6_2) % 151.92/22.60 (93) ~ (all_10_0 = all_10_2) % 151.92/22.60 (94) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0 % 151.92/22.60 (95) ~ (all_10_2 = all_6_0) % 151.92/22.60 (96) ~ (all_10_0 = e2) % 151.92/22.60 (97) op(all_8_2, all_8_2) = all_8_1 % 151.92/22.60 (98) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 151.92/22.60 (99) all_56_9 = all_52_1 % 151.92/22.60 (100) all_56_15 = all_52_13 % 151.92/22.60 (101) ~ (all_52_1 = all_10_2) % 151.92/22.60 (102) all_58_12 = all_52_3 % 151.92/22.60 (103) all_54_11 = all_52_14 % 151.92/22.60 (104) ~ (all_56_31 = e3) | all_56_25 = e0 % 151.92/22.60 % 151.92/22.60 Begin of proof % 151.92/22.60 | % 151.92/22.60 | BETA: splitting (80) gives: % 151.92/22.60 | % 151.92/22.60 | Case 1: % 151.92/22.60 | | % 151.92/22.60 | | (105) ~ (all_56_11 = e0) % 151.92/22.60 | | % 151.92/22.60 | | REDUCE: (1), (105) imply: % 151.92/22.60 | | (106) ~ (all_8_2 = e0) % 151.92/22.60 | | % 151.92/22.60 | | BETA: splitting (31) gives: % 151.92/22.60 | | % 151.92/22.60 | | Case 1: % 151.92/22.60 | | | % 151.92/22.60 | | | (107) ~ (all_56_21 = e3) % 151.92/22.60 | | | % 151.92/22.60 | | | REDUCE: (21), (107) imply: % 151.92/22.60 | | | (108) ~ (all_6_2 = e3) % 151.92/22.60 | | | % 151.92/22.60 | | | BETA: splitting (104) gives: % 151.92/22.60 | | | % 151.92/22.60 | | | Case 1: % 151.92/22.60 | | | | % 151.92/22.60 | | | | (109) ~ (all_56_31 = e3) % 151.92/22.60 | | | | % 151.92/22.60 | | | | REDUCE: (62), (109) imply: % 151.92/22.60 | | | | (110) ~ (all_4_2 = e3) % 151.92/22.60 | | | | % 151.92/22.60 | | | | REF_CLOSE: (1), (6), (10), (15), (17), (19), (21), (22), (23), (30), % 151.92/22.60 | | | | (36), (42), (47), (54), (56), (59), (62), (66), (69), (73), % 151.92/22.60 | | | | (74), (76), (82), (87), (88), (89), (90), (92), (94), (95), % 151.92/22.60 | | | | (108), (110) are inconsistent by sub-proof #429. % 151.92/22.60 | | | | % 151.92/22.60 | | | Case 2: % 151.92/22.60 | | | | % 151.92/22.60 | | | | (111) all_56_31 = e3 % 151.92/22.60 | | | | (112) all_56_25 = e0 % 151.92/22.60 | | | | % 151.92/22.60 | | | | COMBINE_EQS: (5), (112) imply: % 151.92/22.60 | | | | (113) all_52_3 = e0 % 151.92/22.60 | | | | % 151.92/22.60 | | | | SIMP: (113) implies: % 151.92/22.60 | | | | (114) all_52_3 = e0 % 151.92/22.60 | | | | % 151.92/22.60 | | | | COMBINE_EQS: (62), (111) imply: % 151.92/22.60 | | | | (115) all_4_2 = e3 % 151.92/22.60 | | | | % 151.92/22.60 | | | | COMBINE_EQS: (102), (114) imply: % 151.92/22.60 | | | | (116) all_58_12 = e0 % 151.92/22.60 | | | | % 151.92/22.60 | | | | REDUCE: (61), (114) imply: % 151.92/22.60 | | | | (117) ~ (all_52_1 = e0) % 151.92/22.60 | | | | % 151.92/22.60 | | | | REDUCE: (39), (114) imply: % 151.92/22.60 | | | | (118) ~ (all_52_7 = e0) % 151.92/22.60 | | | | % 151.92/22.60 | | | | SIMP: (118) implies: % 151.92/22.60 | | | | (119) ~ (all_52_7 = e0) % 151.92/22.60 | | | | % 151.92/22.60 | | | | REDUCE: (57), (114) imply: % 151.92/22.60 | | | | (120) ~ (all_52_11 = e0) % 151.92/22.60 | | | | % 151.92/22.60 | | | | SIMP: (120) implies: % 151.92/22.60 | | | | (121) ~ (all_52_11 = e0) % 151.92/22.60 | | | | % 151.92/22.60 | | | | REDUCE: (38), (114) imply: % 151.92/22.60 | | | | (122) ~ (all_10_2 = e0) % 151.92/22.60 | | | | % 151.92/22.60 | | | | SIMP: (122) implies: % 151.92/22.60 | | | | (123) ~ (all_10_2 = e0) % 151.92/22.60 | | | | % 151.92/22.60 | | | | REDUCE: (2), (114) imply: % 151.92/22.60 | | | | (124) ~ (all_6_0 = e0) % 151.92/22.60 | | | | % 151.92/22.60 | | | | SIMP: (124) implies: % 151.92/22.60 | | | | (125) ~ (all_6_0 = e0) % 151.92/22.60 | | | | % 151.92/22.60 | | | | REDUCE: (49), (114), (115) imply: % 151.92/22.60 | | | | (126) ~ (e3 = e0) % 151.92/22.60 | | | | % 151.92/22.60 | | | | SIMP: (126) implies: % 151.92/22.60 | | | | (127) ~ (e3 = e0) % 151.92/22.60 | | | | % 151.92/22.60 | | | | REDUCE: (60), (115) imply: % 151.92/22.60 | | | | (128) ~ (all_52_11 = e3) % 151.92/22.60 | | | | % 151.92/22.60 | | | | REDUCE: (46), (115) imply: % 151.92/22.60 | | | | (129) ~ (e3 = e1) % 151.92/22.60 | | | | % 151.92/22.60 | | | | REDUCE: (56), (115) imply: % 151.92/22.60 | | | | (130) op(e3, e3) = all_4_1 % 151.92/22.60 | | | | % 151.92/22.60 | | | | GROUND_INST: instantiating (36) with all_10_2, all_4_1, e3, e3, % 151.92/22.60 | | | | simplifying with (29), (130) gives: % 151.92/22.60 | | | | (131) all_10_2 = all_4_1 % 151.92/22.60 | | | | % 151.92/22.60 | | | | COMBINE_EQS: (11), (131) imply: % 151.92/22.60 | | | | (132) all_54_0 = all_4_1 % 151.92/22.60 | | | | % 151.92/22.60 | | | | COMBINE_EQS: (23), (131) imply: % 151.92/22.60 | | | | (133) all_56_1 = all_4_1 % 151.92/22.60 | | | | % 151.92/22.60 | | | | COMBINE_EQS: (81), (131) imply: % 151.92/22.60 | | | | (134) all_58_0 = all_4_1 % 151.92/22.60 | | | | % 151.92/22.60 | | | | REDUCE: (101), (131) imply: % 151.92/22.60 | | | | (135) ~ (all_52_1 = all_4_1) % 151.92/22.60 | | | | % 151.92/22.60 | | | | REDUCE: (95), (131) imply: % 151.92/22.60 | | | | (136) ~ (all_6_0 = all_4_1) % 151.92/22.60 | | | | % 151.92/22.60 | | | | SIMP: (136) implies: % 151.92/22.60 | | | | (137) ~ (all_6_0 = all_4_1) % 151.92/22.60 | | | | % 151.92/22.60 | | | | REDUCE: (123), (131) imply: % 151.92/22.60 | | | | (138) ~ (all_4_1 = e0) % 151.92/22.60 | | | | % 151.92/22.60 | | | | BETA: splitting (3) gives: % 151.92/22.60 | | | | % 151.92/22.60 | | | | Case 1: % 151.92/22.60 | | | | | % 151.92/22.60 | | | | | (139) ~ (all_56_11 = e1) % 151.92/22.60 | | | | | % 151.92/22.60 | | | | | REDUCE: (1), (139) imply: % 151.92/22.60 | | | | | (140) ~ (all_8_2 = e1) % 151.92/22.60 | | | | | % 151.92/22.60 | | | | | COMBINE_EQS: (72), (131) imply: % 151.92/22.60 | | | | | (141) all_38_2 = all_4_1 % 151.92/22.60 | | | | | % 151.92/22.60 | | | | | REDUCE: (93), (131) imply: % 151.92/22.60 | | | | | (142) ~ (all_10_0 = all_4_1) % 151.92/22.60 | | | | | % 151.92/22.60 | | | | | REDUCE: (64), (131) imply: % 151.92/22.60 | | | | | (143) op(all_4_1, all_4_1) = e2 % 151.92/22.60 | | | | | % 151.92/22.60 | | | | | REDUCE: (91), (131) imply: % 151.92/22.60 | | | | | (144) op(e3, all_4_1) = all_56_0 % 151.92/22.60 | | | | | % 151.92/22.60 | | | | | BETA: splitting (40) gives: % 151.92/22.60 | | | | | % 151.92/22.60 | | | | | Case 1: % 151.92/22.60 | | | | | | % 151.92/22.60 | | | | | | (145) ~ (all_56_11 = e3) % 151.92/22.60 | | | | | | % 151.92/22.60 | | | | | | REDUCE: (1), (145) imply: % 151.92/22.60 | | | | | | (146) ~ (all_8_2 = e3) % 151.92/22.60 | | | | | | % 151.92/22.60 | | | | | | BETA: splitting (98) gives: % 151.92/22.60 | | | | | | % 151.92/22.60 | | | | | | Case 1: % 151.92/22.60 | | | | | | | % 151.92/22.60 | | | | | | | (147) all_54_5 = e3 % 151.92/22.60 | | | | | | | % 151.92/22.60 | | | | | | | COMBINE_EQS: (16), (147) imply: % 151.92/22.60 | | | | | | | (148) all_8_2 = e3 % 151.92/22.60 | | | | | | | % 151.92/22.60 | | | | | | | REDUCE: (146), (148) imply: % 151.92/22.60 | | | | | | | (149) $false % 151.92/22.60 | | | | | | | % 151.92/22.60 | | | | | | | CLOSE: (149) is inconsistent. % 151.92/22.60 | | | | | | | % 151.92/22.60 | | | | | | Case 2: % 151.92/22.60 | | | | | | | % 151.92/22.60 | | | | | | | (150) ~ (all_54_5 = e3) % 151.92/22.60 | | | | | | | (151) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 151.92/22.60 | | | | | | | % 151.92/22.60 | | | | | | | BETA: splitting (151) gives: % 151.92/22.60 | | | | | | | % 151.92/22.60 | | | | | | | Case 1: % 151.92/22.60 | | | | | | | | % 151.92/22.60 | | | | | | | | (152) all_54_5 = e2 % 151.92/22.60 | | | | | | | | % 151.92/22.60 | | | | | | | | COMBINE_EQS: (16), (152) imply: % 151.92/22.60 | | | | | | | | (153) all_8_2 = e2 % 151.92/22.60 | | | | | | | | % 151.92/22.60 | | | | | | | | COMBINE_EQS: (1), (153) imply: % 151.92/22.60 | | | | | | | | (154) all_56_11 = e2 % 151.92/22.60 | | | | | | | | % 151.92/22.60 | | | | | | | | COMBINE_EQS: (58), (153) imply: % 151.92/22.60 | | | | | | | | (155) all_58_3 = e2 % 151.92/22.60 | | | | | | | | % 151.92/22.60 | | | | | | | | REDUCE: (34), (153) imply: % 151.92/22.60 | | | | | | | | (156) ~ (all_52_1 = e2) % 151.92/22.60 | | | | | | | | % 151.92/22.60 | | | | | | | | REDUCE: (146), (153) imply: % 151.92/22.60 | | | | | | | | (157) ~ (e3 = e2) % 151.92/22.60 | | | | | | | | % 151.92/22.60 | | | | | | | | SIMP: (157) implies: % 151.92/22.60 | | | | | | | | (158) ~ (e3 = e2) % 151.92/22.60 | | | | | | | | % 151.92/22.60 | | | | | | | | REDUCE: (106), (153) imply: % 151.92/22.60 | | | | | | | | (159) ~ (e2 = e0) % 151.92/22.60 | | | | | | | | % 151.92/22.60 | | | | | | | | BETA: splitting (32) gives: % 151.92/22.60 | | | | | | | | % 151.92/22.60 | | | | | | | | Case 1: % 151.92/22.60 | | | | | | | | | % 151.92/22.60 | | | | | | | | | (160) all_58_0 = e2 % 151.92/22.60 | | | | | | | | | % 151.92/22.60 | | | | | | | | | COMBINE_EQS: (134), (160) imply: % 151.92/22.60 | | | | | | | | | (161) all_4_1 = e2 % 151.92/22.60 | | | | | | | | | % 151.92/22.60 | | | | | | | | | COMBINE_EQS: (133), (161) imply: % 151.92/22.60 | | | | | | | | | (162) all_56_1 = e2 % 151.92/22.60 | | | | | | | | | % 151.92/22.60 | | | | | | | | | BETA: splitting (51) gives: % 151.92/22.60 | | | | | | | | | % 151.92/22.60 | | | | | | | | | Case 1: % 151.92/22.60 | | | | | | | | | | % 151.92/22.60 | | | | | | | | | | (163) ~ (all_56_1 = e2) % 151.92/22.60 | | | | | | | | | | % 151.92/22.60 | | | | | | | | | | REDUCE: (162), (163) imply: % 151.92/22.60 | | | | | | | | | | (164) $false % 151.92/22.60 | | | | | | | | | | % 151.92/22.60 | | | | | | | | | | CLOSE: (164) is inconsistent. % 151.92/22.60 | | | | | | | | | | % 151.92/22.60 | | | | | | | | | Case 2: % 151.92/22.60 | | | | | | | | | | % 151.92/22.60 | | | | | | | | | | (165) all_56_3 = e3 % 151.92/22.60 | | | | | | | | | | % 151.92/22.60 | | | | | | | | | | COMBINE_EQS: (24), (165) imply: % 151.92/22.60 | | | | | | | | | | (166) all_10_0 = e3 % 151.92/22.60 | | | | | | | | | | % 151.92/22.60 | | | | | | | | | | SIMP: (166) implies: % 151.92/22.60 | | | | | | | | | | (167) all_10_0 = e3 % 151.92/22.60 | | | | | | | | | | % 151.92/22.60 | | | | | | | | | | COMBINE_EQS: (83), (167) imply: % 151.92/22.60 | | | | | | | | | | (168) all_58_1 = e3 % 151.92/22.60 | | | | | | | | | | % 151.92/22.60 | | | | | | | | | | REF_CLOSE: (10), (21), (22), (28), (36), (66), (73), (76), % 151.92/22.60 | | | | | | | | | | (78), (82), (84), (89), (90), (108), (111), (119), % 151.92/22.60 | | | | | | | | | | (127), (129), (154), (155), (158), (159), (162), % 151.92/22.60 | | | | | | | | | | (168) are inconsistent by sub-proof #424. % 151.92/22.60 | | | | | | | | | | % 151.92/22.60 | | | | | | | | | End of split % 151.92/22.60 | | | | | | | | | % 151.92/22.60 | | | | | | | | Case 2: % 151.92/22.60 | | | | | | | | | % 151.92/22.60 | | | | | | | | | (169) all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2 % 151.92/22.60 | | | | | | | | | % 151.92/22.60 | | | | | | | | | REF_CLOSE: (19), (70), (77), (116), (156), (159), (169) are % 151.92/22.60 | | | | | | | | | inconsistent by sub-proof #421. % 151.92/22.60 | | | | | | | | | % 151.92/22.60 | | | | | | | | End of split % 151.92/22.60 | | | | | | | | % 151.92/22.60 | | | | | | | Case 2: % 151.92/22.60 | | | | | | | | % 151.92/22.60 | | | | | | | | (170) all_54_5 = e1 | all_54_5 = e0 % 151.92/22.60 | | | | | | | | % 151.92/22.60 | | | | | | | | REF_CLOSE: (16), (106), (140), (170) are inconsistent by % 151.92/22.60 | | | | | | | | sub-proof #645. % 151.92/22.60 | | | | | | | | % 151.92/22.60 | | | | | | | End of split % 151.92/22.60 | | | | | | | % 151.92/22.60 | | | | | | End of split % 151.92/22.60 | | | | | | % 151.92/22.60 | | | | | Case 2: % 151.92/22.60 | | | | | | % 151.92/22.60 | | | | | | (171) all_56_11 = e3 % 151.92/22.60 | | | | | | (172) all_56_9 = e2 % 151.92/22.60 | | | | | | % 151.92/22.60 | | | | | | COMBINE_EQS: (99), (172) imply: % 151.92/22.60 | | | | | | (173) all_52_1 = e2 % 151.92/22.60 | | | | | | % 151.92/22.60 | | | | | | COMBINE_EQS: (1), (171) imply: % 151.92/22.60 | | | | | | (174) all_8_2 = e3 % 151.92/22.60 | | | | | | % 151.92/22.60 | | | | | | REDUCE: (135), (173) imply: % 151.92/22.60 | | | | | | (175) ~ (all_4_1 = e2) % 151.92/22.60 | | | | | | % 151.92/22.60 | | | | | | SIMP: (175) implies: % 151.92/22.60 | | | | | | (176) ~ (all_4_1 = e2) % 151.92/22.60 | | | | | | % 151.92/22.60 | | | | | | REDUCE: (8), (174) imply: % 151.92/22.60 | | | | | | (177) ~ (all_10_0 = e3) % 151.92/22.60 | | | | | | % 151.92/22.60 | | | | | | REDUCE: (97), (174) imply: % 151.92/22.60 | | | | | | (178) op(e3, e3) = all_8_1 % 151.92/22.60 | | | | | | % 151.92/22.60 | | | | | | REF_CLOSE: (18), (20), (33), (36), (67), (71), (75), (96), (130), % 151.92/22.60 | | | | | | (132), (141), (142), (143), (144), (176), (177), (178) % 151.92/22.60 | | | | | | are inconsistent by sub-proof #470. % 151.92/22.60 | | | | | | % 151.92/22.60 | | | | | End of split % 151.92/22.60 | | | | | % 151.92/22.60 | | | | Case 2: % 151.92/22.60 | | | | | % 151.92/22.60 | | | | | (179) all_56_13 = e2 % 151.92/22.60 | | | | | (180) all_56_11 = e1 % 151.92/22.60 | | | | | % 151.92/22.60 | | | | | COMBINE_EQS: (1), (180) imply: % 151.92/22.60 | | | | | (181) all_8_2 = e1 % 151.92/22.60 | | | | | % 151.92/22.60 | | | | | COMBINE_EQS: (43), (179) imply: % 151.92/22.60 | | | | | (182) all_52_9 = e2 % 151.92/22.60 | | | | | % 151.92/22.60 | | | | | REF_CLOSE: (1), (4), (7), (9), (12), (18), (19), (21), (25), (27), % 151.92/22.60 | | | | | (32), (34), (45), (47), (65), (66), (94), (111), (117), % 151.92/22.60 | | | | | (121), (125), (128), (132), (133), (134), (135), (137), % 151.92/22.60 | | | | | (138), (181), (182) are inconsistent by sub-proof #417. % 151.92/22.60 | | | | | % 151.92/22.60 | | | | End of split % 151.92/22.60 | | | | % 151.92/22.60 | | | End of split % 151.92/22.60 | | | % 151.92/22.60 | | Case 2: % 151.92/22.60 | | | % 151.92/22.60 | | | (183) all_56_21 = e3 % 151.92/22.60 | | | (184) all_56_17 = e1 % 151.92/22.60 | | | % 151.92/22.60 | | | COMBINE_EQS: (85), (184) imply: % 151.92/22.60 | | | (185) all_6_0 = e1 % 151.92/22.60 | | | % 151.92/22.60 | | | COMBINE_EQS: (21), (183) imply: % 151.92/22.60 | | | (186) all_6_2 = e3 % 151.92/22.60 | | | % 151.92/22.60 | | | SIMP: (186) implies: % 151.92/22.60 | | | (187) all_6_2 = e3 % 151.92/22.60 | | | % 151.92/22.60 | | | REDUCE: (30), (185) imply: % 151.92/22.60 | | | (188) ~ (all_52_6 = e1) % 151.92/22.60 | | | % 151.92/22.60 | | | REDUCE: (89), (187) imply: % 151.92/22.60 | | | (189) ~ (all_52_6 = e3) % 151.92/22.60 | | | % 151.92/22.60 | | | REDUCE: (54), (185) imply: % 151.92/22.60 | | | (190) ~ (all_52_14 = e1) % 151.92/22.60 | | | % 151.92/22.60 | | | REDUCE: (92), (187) imply: % 151.92/22.60 | | | (191) ~ (all_52_14 = e3) % 151.92/22.60 | | | % 151.92/22.60 | | | REDUCE: (95), (185) imply: % 151.92/22.60 | | | (192) ~ (all_10_2 = e1) % 151.92/22.60 | | | % 151.92/22.60 | | | REDUCE: (90), (187) imply: % 151.92/22.60 | | | (193) op(e3, e3) = e3 % 151.92/22.60 | | | % 151.92/22.60 | | | GROUND_INST: instantiating (36) with all_10_2, e3, e3, e3, simplifying % 151.92/22.60 | | | with (29), (193) gives: % 151.92/22.60 | | | (194) all_10_2 = e3 % 151.92/22.60 | | | % 151.92/22.60 | | | REDUCE: (93), (194) imply: % 151.92/22.60 | | | (195) ~ (all_10_0 = e3) % 151.92/22.60 | | | % 151.92/22.60 | | | REDUCE: (192), (194) imply: % 151.92/22.60 | | | (196) ~ (e3 = e1) % 151.92/22.60 | | | % 151.92/22.60 | | | REDUCE: (64), (194) imply: % 151.92/22.60 | | | (197) op(e3, e3) = e2 % 151.92/22.60 | | | % 151.92/22.60 | | | BETA: splitting (75) gives: % 151.92/22.60 | | | % 151.92/22.60 | | | Case 1: % 151.92/22.60 | | | | % 151.92/22.60 | | | | (198) all_54_1 = e3 % 151.92/22.60 | | | | % 151.92/22.60 | | | | REF_CLOSE: (20), (195), (198) are inconsistent by sub-proof #493. % 151.92/22.60 | | | | % 151.92/22.60 | | | Case 2: % 151.92/22.60 | | | | % 151.92/22.60 | | | | (199) all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0 % 151.92/22.60 | | | | % 151.92/22.60 | | | | BETA: splitting (199) gives: % 151.92/22.60 | | | | % 151.92/22.60 | | | | Case 1: % 151.92/22.60 | | | | | % 151.92/22.60 | | | | | (200) all_54_1 = e2 % 151.92/22.60 | | | | | % 151.92/22.60 | | | | | REF_CLOSE: (20), (96), (200) are inconsistent by sub-proof #492. % 151.92/22.60 | | | | | % 151.92/22.60 | | | | Case 2: % 151.92/22.60 | | | | | % 151.92/22.60 | | | | | (201) all_54_1 = e1 | all_54_1 = e0 % 151.92/22.60 | | | | | % 151.92/22.60 | | | | | BETA: splitting (201) gives: % 151.92/22.60 | | | | | % 151.92/22.60 | | | | | Case 1: % 151.92/22.60 | | | | | | % 151.92/22.60 | | | | | | (202) all_54_1 = e1 % 151.92/22.60 | | | | | | % 151.92/22.60 | | | | | | REF_CLOSE: (20), (67), (202) are inconsistent by sub-proof #491. % 151.92/22.60 | | | | | | % 151.92/22.60 | | | | | Case 2: % 151.92/22.60 | | | | | | % 151.92/22.60 | | | | | | (203) all_54_1 = e0 % 151.92/22.60 | | | | | | % 151.92/22.60 | | | | | | COMBINE_EQS: (20), (203) imply: % 151.92/22.60 | | | | | | (204) all_10_0 = e0 % 151.92/22.60 | | | | | | % 151.92/22.60 | | | | | | SIMP: (204) implies: % 151.92/22.60 | | | | | | (205) all_10_0 = e0 % 151.92/22.60 | | | | | | % 151.92/22.60 | | | | | | REDUCE: (53), (205) imply: % 151.92/22.60 | | | | | | (206) ~ (all_52_6 = e0) % 151.92/22.60 | | | | | | % 151.92/22.60 | | | | | | BETA: splitting (59) gives: % 151.92/22.60 | | | | | | % 151.92/22.60 | | | | | | Case 1: % 151.92/22.60 | | | | | | | % 151.92/22.60 | | | | | | | (207) all_54_9 = e3 % 151.92/22.60 | | | | | | | % 151.92/22.60 | | | | | | | COMBINE_EQS: (6), (207) imply: % 151.92/22.60 | | | | | | | (208) all_52_6 = e3 % 151.92/22.60 | | | | | | | % 151.92/22.60 | | | | | | | REDUCE: (189), (208) imply: % 151.92/22.60 | | | | | | | (209) $false % 151.92/22.60 | | | | | | | % 151.92/22.60 | | | | | | | CLOSE: (209) is inconsistent. % 151.92/22.60 | | | | | | | % 151.92/22.60 | | | | | | Case 2: % 151.92/22.60 | | | | | | | % 151.92/22.60 | | | | | | | (210) ~ (all_54_9 = e3) % 151.92/22.60 | | | | | | | (211) all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0 % 151.92/22.60 | | | | | | | % 151.92/22.60 | | | | | | | BETA: splitting (211) gives: % 151.92/22.60 | | | | | | | % 151.92/22.60 | | | | | | | Case 1: % 151.92/22.60 | | | | | | | | % 151.92/22.60 | | | | | | | | (212) all_54_9 = e2 % 151.92/22.60 | | | | | | | | % 151.92/22.60 | | | | | | | | COMBINE_EQS: (6), (212) imply: % 151.92/22.60 | | | | | | | | (213) all_52_6 = e2 % 151.92/22.60 | | | | | | | | % 151.92/22.60 | | | | | | | | REDUCE: (17), (213) imply: % 151.92/22.60 | | | | | | | | (214) ~ (all_52_14 = e2) % 151.92/22.60 | | | | | | | | % 151.92/22.60 | | | | | | | | SIMP: (214) implies: % 151.92/22.60 | | | | | | | | (215) ~ (all_52_14 = e2) % 151.92/22.60 | | | | | | | | % 151.92/22.60 | | | | | | | | REDUCE: (74), (213) imply: % 151.92/22.60 | | | | | | | | (216) ~ (all_8_2 = e2) % 151.92/22.60 | | | | | | | | % 151.92/22.60 | | | | | | | | SIMP: (216) implies: % 151.92/22.60 | | | | | | | | (217) ~ (all_8_2 = e2) % 151.92/22.60 | | | | | | | | % 151.92/22.60 | | | | | | | | REDUCE: (189), (213) imply: % 151.92/22.60 | | | | | | | | (218) ~ (e3 = e2) % 151.92/22.60 | | | | | | | | % 151.92/22.60 | | | | | | | | SIMP: (218) implies: % 151.92/22.60 | | | | | | | | (219) ~ (e3 = e2) % 151.92/22.60 | | | | | | | | % 151.92/22.60 | | | | | | | | REF_CLOSE: (1), (13), (14), (23), (29), (36), (62), (66), (79), % 151.92/22.60 | | | | | | | | (91), (103), (183), (190), (191), (196), (197), % 151.92/22.60 | | | | | | | | (215), (217), (219) are inconsistent by sub-proof % 151.92/22.60 | | | | | | | | #414. % 151.92/22.60 | | | | | | | | % 151.92/22.60 | | | | | | | Case 2: % 151.92/22.60 | | | | | | | | % 151.92/22.60 | | | | | | | | (220) all_54_9 = e1 | all_54_9 = e0 % 151.92/22.60 | | | | | | | | % 151.92/22.60 | | | | | | | | REF_CLOSE: (6), (188), (206), (220) are inconsistent by % 151.92/22.60 | | | | | | | | sub-proof #678. % 151.92/22.60 | | | | | | | | % 151.92/22.60 | | | | | | | End of split % 151.92/22.60 | | | | | | | % 151.92/22.60 | | | | | | End of split % 151.92/22.60 | | | | | | % 151.92/22.60 | | | | | End of split % 151.92/22.60 | | | | | % 151.92/22.60 | | | | End of split % 151.92/22.60 | | | | % 151.92/22.60 | | | End of split % 151.92/22.60 | | | % 151.92/22.60 | | End of split % 151.92/22.60 | | % 151.92/22.60 | Case 2: % 151.92/22.60 | | % 151.92/22.60 | | (221) all_56_15 = e2 % 151.92/22.60 | | (222) all_56_11 = e0 % 151.92/22.60 | | % 151.92/22.60 | | COMBINE_EQS: (1), (222) imply: % 151.92/22.60 | | (223) all_8_2 = e0 % 151.92/22.60 | | % 151.92/22.60 | | COMBINE_EQS: (100), (221) imply: % 151.92/22.60 | | (224) all_52_13 = e2 % 151.92/22.60 | | % 151.92/22.60 | | REDUCE: (68), (224) imply: % 151.92/22.60 | | (225) ~ (all_52_14 = e2) % 151.92/22.60 | | % 151.92/22.60 | | SIMP: (225) implies: % 151.92/22.60 | | (226) ~ (all_52_14 = e2) % 151.92/22.60 | | % 151.92/22.60 | | REDUCE: (8), (223) imply: % 151.92/22.60 | | (227) ~ (all_10_0 = e0) % 151.92/22.60 | | % 151.92/22.60 | | REDUCE: (86), (223) imply: % 151.92/22.60 | | (228) op(e2, e2) = e0 % 151.92/22.60 | | % 151.92/22.60 | | BETA: splitting (75) gives: % 151.92/22.60 | | % 151.92/22.60 | | Case 1: % 151.92/22.60 | | | % 151.92/22.60 | | | (229) all_54_1 = e3 % 151.92/22.60 | | | % 151.92/22.60 | | | COMBINE_EQS: (20), (229) imply: % 151.92/22.60 | | | (230) all_10_0 = e3 % 151.92/22.60 | | | % 151.92/22.60 | | | SIMP: (230) implies: % 151.92/22.60 | | | (231) all_10_0 = e3 % 151.92/22.60 | | | % 151.92/22.60 | | | REDUCE: (37), (231) imply: % 151.92/22.60 | | | (232) ~ (all_52_8 = e3) % 151.92/22.60 | | | % 151.92/22.60 | | | REDUCE: (50), (231) imply: % 151.92/22.60 | | | (233) ~ (all_52_12 = e3) % 151.92/22.60 | | | % 151.92/22.60 | | | REDUCE: (93), (231) imply: % 151.92/22.60 | | | (234) ~ (all_10_2 = e3) % 151.92/22.60 | | | % 151.92/22.60 | | | SIMP: (234) implies: % 151.92/22.60 | | | (235) ~ (all_10_2 = e3) % 151.92/22.60 | | | % 151.92/22.60 | | | BETA: splitting (26) gives: % 151.92/22.60 | | | % 151.92/22.60 | | | Case 1: % 151.92/22.60 | | | | % 151.92/22.60 | | | | (236) ~ (all_56_1 = e1) % 151.92/22.60 | | | | % 151.92/22.60 | | | | REDUCE: (23), (236) imply: % 151.92/22.60 | | | | (237) ~ (all_10_2 = e1) % 151.92/22.60 | | | | % 151.92/22.60 | | | | BETA: splitting (35) gives: % 151.92/22.60 | | | | % 151.92/22.60 | | | | Case 1: % 151.92/22.60 | | | | | % 151.92/22.60 | | | | | (238) all_58_6 = e2 % 151.92/22.60 | | | | | % 151.92/22.60 | | | | | REF_CLOSE: (19), (70), (238) are inconsistent by sub-proof #461. % 151.92/22.60 | | | | | % 151.92/22.60 | | | | Case 2: % 151.92/22.60 | | | | | % 151.92/22.60 | | | | | (239) all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2 % 151.92/22.60 | | | | | % 151.92/22.60 | | | | | REF_CLOSE: (11), (18), (23), (36), (41), (44), (48), (52), (63), (64), % 151.92/22.60 | | | | | (76), (78), (226), (228), (233), (235), (237), (239) are % 151.92/22.60 | | | | | inconsistent by sub-proof #482. % 151.92/22.60 | | | | | % 151.92/22.60 | | | | End of split % 151.92/22.60 | | | | % 151.92/22.60 | | | Case 2: % 151.92/22.60 | | | | % 151.92/22.60 | | | | (240) all_56_5 = e3 % 151.92/22.60 | | | | % 151.92/22.60 | | | | REF_CLOSE: (55), (232), (240) are inconsistent by sub-proof #481. % 151.92/22.60 | | | | % 151.92/22.60 | | | End of split % 151.92/22.60 | | | % 151.92/22.60 | | Case 2: % 151.92/22.60 | | | % 151.92/22.60 | | | (241) all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0 % 151.92/22.60 | | | % 151.92/22.60 | | | REF_CLOSE: (20), (67), (96), (227), (241) are inconsistent by sub-proof % 151.92/22.60 | | | #490. % 151.92/22.60 | | | % 151.92/22.60 | | End of split % 151.92/22.60 | | % 151.92/22.60 | End of split % 151.92/22.60 | % 151.92/22.60 End of proof % 151.92/22.60 % 151.92/22.60 Sub-proof #414 shows that the following formulas are inconsistent: % 151.92/22.60 ---------------------------------------------------------------- % 151.92/22.60 (1) all_56_11 = all_8_2 % 151.92/22.60 (2) all_56_21 = e3 % 151.92/22.60 (3) ~ (all_52_14 = all_4_2) % 151.92/22.60 (4) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0 % 151.92/22.60 (5) ~ (e3 = e2) % 151.92/22.60 (6) ~ (all_8_2 = e2) % 151.92/22.60 (7) ~ (all_52_14 = e2) % 151.92/22.60 (8) op(e3, e3) = e2 % 151.92/22.60 (9) all_56_1 = all_10_2 % 151.92/22.60 (10) op(e3, e3) = all_10_2 % 151.92/22.60 (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 151.92/22.60 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 151.92/22.60 (12) ~ (all_52_14 = e1) % 151.92/22.60 (13) ~ (all_52_14 = e3) % 151.92/22.60 (14) all_56_31 = all_4_2 % 151.92/22.60 (15) all_56_1 = e3 | all_56_11 = e2 | all_56_21 = e1 | all_56_31 = e0 % 151.92/22.60 (16) op(all_10_2, all_10_2) = all_10_1 % 151.92/22.60 (17) ~ (e3 = e1) % 151.92/22.60 (18) op(e3, all_10_2) = all_56_0 % 151.92/22.60 (19) all_54_11 = all_52_14 % 151.92/22.60 % 151.92/22.60 Begin of proof % 151.92/22.60 | % 151.92/22.60 | BETA: splitting (4) gives: % 151.92/22.60 | % 151.92/22.60 | Case 1: % 151.92/22.60 | | % 151.92/22.60 | | (20) all_54_11 = e3 % 151.92/22.60 | | % 151.92/22.60 | | REF_CLOSE: (13), (19), (20) are inconsistent by sub-proof #416. % 151.92/22.60 | | % 151.92/22.60 | Case 2: % 151.92/22.60 | | % 151.92/22.61 | | (21) all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0 % 151.92/22.61 | | % 151.92/22.61 | | BETA: splitting (21) gives: % 151.92/22.61 | | % 151.92/22.61 | | Case 1: % 151.92/22.61 | | | % 151.92/22.61 | | | (22) all_54_11 = e2 % 151.92/22.61 | | | % 151.92/22.61 | | | REF_CLOSE: (7), (19), (22) are inconsistent by sub-proof #690. % 151.92/22.61 | | | % 151.92/22.61 | | Case 2: % 151.92/22.61 | | | % 151.92/22.61 | | | (23) all_54_11 = e1 | all_54_11 = e0 % 151.92/22.61 | | | % 151.92/22.61 | | | BETA: splitting (23) gives: % 151.92/22.61 | | | % 151.92/22.61 | | | Case 1: % 151.92/22.61 | | | | % 151.92/22.61 | | | | (24) all_54_11 = e1 % 151.92/22.61 | | | | % 151.92/22.61 | | | | REF_CLOSE: (12), (19), (24) are inconsistent by sub-proof #689. % 151.92/22.61 | | | | % 151.92/22.61 | | | Case 2: % 151.92/22.61 | | | | % 151.92/22.61 | | | | (25) all_54_11 = e0 % 151.92/22.61 | | | | % 151.92/22.61 | | | | COMBINE_EQS: (19), (25) imply: % 151.92/22.61 | | | | (26) all_52_14 = e0 % 151.92/22.61 | | | | % 151.92/22.61 | | | | SIMP: (26) implies: % 151.92/22.61 | | | | (27) all_52_14 = e0 % 151.92/22.61 | | | | % 151.92/22.61 | | | | REDUCE: (3), (27) imply: % 151.92/22.61 | | | | (28) ~ (all_4_2 = e0) % 151.92/22.61 | | | | % 151.92/22.61 | | | | SIMP: (28) implies: % 151.92/22.61 | | | | (29) ~ (all_4_2 = e0) % 151.92/22.61 | | | | % 151.92/22.61 | | | | BETA: splitting (15) gives: % 151.92/22.61 | | | | % 151.92/22.61 | | | | Case 1: % 151.92/22.61 | | | | | % 151.92/22.61 | | | | | (30) all_56_1 = e3 % 151.92/22.61 | | | | | % 151.92/22.61 | | | | | COMBINE_EQS: (9), (30) imply: % 151.92/22.61 | | | | | (31) all_10_2 = e3 % 151.92/22.61 | | | | | % 151.92/22.61 | | | | | REDUCE: (16), (31) imply: % 151.92/22.61 | | | | | (32) op(e3, e3) = all_10_1 % 151.92/22.61 | | | | | % 151.92/22.61 | | | | | REDUCE: (18), (31) imply: % 151.92/22.61 | | | | | (33) op(e3, e3) = all_56_0 % 151.92/22.61 | | | | | % 151.92/22.61 | | | | | REDUCE: (10), (31) imply: % 151.92/22.61 | | | | | (34) op(e3, e3) = e3 % 151.92/22.61 | | | | | % 151.92/22.61 | | | | | REF_CLOSE: (5), (8), (11), (32), (33), (34) are inconsistent by % 151.92/22.61 | | | | | sub-proof #415. % 151.92/22.61 | | | | | % 151.92/22.61 | | | | Case 2: % 151.92/22.61 | | | | | % 151.92/22.61 | | | | | (35) all_56_11 = e2 | all_56_21 = e1 | all_56_31 = e0 % 151.92/22.61 | | | | | % 151.92/22.61 | | | | | BETA: splitting (35) gives: % 151.92/22.61 | | | | | % 151.92/22.61 | | | | | Case 1: % 151.92/22.61 | | | | | | % 151.92/22.61 | | | | | | (36) all_56_11 = e2 % 151.92/22.61 | | | | | | % 151.92/22.61 | | | | | | COMBINE_EQS: (1), (36) imply: % 151.92/22.61 | | | | | | (37) all_8_2 = e2 % 151.92/22.61 | | | | | | % 151.92/22.61 | | | | | | REDUCE: (6), (37) imply: % 151.92/22.61 | | | | | | (38) $false % 151.92/22.61 | | | | | | % 151.92/22.61 | | | | | | CLOSE: (38) is inconsistent. % 151.92/22.61 | | | | | | % 151.92/22.61 | | | | | Case 2: % 151.92/22.61 | | | | | | % 151.92/22.61 | | | | | | (39) all_56_21 = e1 | all_56_31 = e0 % 151.92/22.61 | | | | | | % 151.92/22.61 | | | | | | BETA: splitting (39) gives: % 151.92/22.61 | | | | | | % 151.92/22.61 | | | | | | Case 1: % 151.92/22.61 | | | | | | | % 151.92/22.61 | | | | | | | (40) all_56_21 = e1 % 151.92/22.61 | | | | | | | % 151.92/22.61 | | | | | | | REF_CLOSE: (2), (17), (40) are inconsistent by sub-proof #676. % 151.92/22.61 | | | | | | | % 151.92/22.61 | | | | | | Case 2: % 151.92/22.61 | | | | | | | % 151.92/22.61 | | | | | | | (41) all_56_31 = e0 % 151.92/22.61 | | | | | | | % 151.92/22.61 | | | | | | | REF_CLOSE: (14), (29), (41) are inconsistent by sub-proof #675. % 151.92/22.61 | | | | | | | % 151.92/22.61 | | | | | | End of split % 151.92/22.61 | | | | | | % 151.92/22.61 | | | | | End of split % 151.92/22.61 | | | | | % 151.92/22.61 | | | | End of split % 151.92/22.61 | | | | % 151.92/22.61 | | | End of split % 151.92/22.61 | | | % 151.92/22.61 | | End of split % 151.92/22.61 | | % 151.92/22.61 | End of split % 151.92/22.61 | % 151.92/22.61 End of proof % 151.92/22.61 % 151.92/22.61 Sub-proof #415 shows that the following formulas are inconsistent: % 151.92/22.61 ---------------------------------------------------------------- % 151.92/22.61 (1) op(e3, e3) = e3 % 151.92/22.61 (2) ~ (e3 = e2) % 151.92/22.61 (3) op(e3, e3) = e2 % 151.92/22.61 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 151.92/22.61 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 151.92/22.61 (5) op(e3, e3) = all_56_0 % 151.92/22.61 (6) op(e3, e3) = all_10_1 % 151.92/22.61 % 151.92/22.61 Begin of proof % 151.92/22.61 | % 151.92/22.61 | GROUND_INST: instantiating (4) with e3, all_10_1, e3, e3, simplifying with % 151.92/22.61 | (1), (6) gives: % 151.92/22.61 | (7) all_10_1 = e3 % 151.92/22.61 | % 151.92/22.61 | GROUND_INST: instantiating (4) with all_10_1, all_56_0, e3, e3, simplifying % 151.92/22.61 | with (5), (6) gives: % 151.92/22.61 | (8) all_56_0 = all_10_1 % 151.92/22.61 | % 151.92/22.61 | GROUND_INST: instantiating (4) with e2, all_56_0, e3, e3, simplifying with % 151.92/22.61 | (3), (5) gives: % 151.92/22.61 | (9) all_56_0 = e2 % 151.92/22.61 | % 151.92/22.61 | COMBINE_EQS: (8), (9) imply: % 151.92/22.61 | (10) all_10_1 = e2 % 151.92/22.61 | % 151.92/22.61 | SIMP: (10) implies: % 151.92/22.61 | (11) all_10_1 = e2 % 151.92/22.61 | % 151.92/22.61 | COMBINE_EQS: (7), (11) imply: % 151.92/22.61 | (12) e3 = e2 % 151.92/22.61 | % 151.92/22.61 | REDUCE: (2), (12) imply: % 151.92/22.61 | (13) $false % 151.92/22.61 | % 151.92/22.61 | CLOSE: (13) is inconsistent. % 151.92/22.61 | % 151.92/22.61 End of proof % 151.92/22.61 % 151.92/22.61 Sub-proof #416 shows that the following formulas are inconsistent: % 151.92/22.61 ---------------------------------------------------------------- % 151.92/22.61 (1) all_54_11 = all_52_14 % 151.92/22.61 (2) all_54_11 = e3 % 151.92/22.61 (3) ~ (all_52_14 = e3) % 151.92/22.61 % 151.92/22.61 Begin of proof % 151.92/22.61 | % 151.92/22.61 | COMBINE_EQS: (1), (2) imply: % 151.92/22.61 | (4) all_52_14 = e3 % 151.92/22.61 | % 151.92/22.61 | SIMP: (4) implies: % 151.92/22.61 | (5) all_52_14 = e3 % 151.92/22.61 | % 151.92/22.61 | REDUCE: (3), (5) imply: % 151.92/22.61 | (6) $false % 151.92/22.61 | % 151.92/22.61 | CLOSE: (6) is inconsistent. % 151.92/22.61 | % 151.92/22.61 End of proof % 151.92/22.61 % 151.92/22.61 Sub-proof #417 shows that the following formulas are inconsistent: % 151.92/22.61 ---------------------------------------------------------------- % 151.92/22.61 (1) all_56_11 = all_8_2 % 151.92/22.61 (2) ~ (all_52_11 = all_6_2) % 151.92/22.61 (3) ~ (all_52_1 = all_52_9) % 151.92/22.61 (4) all_52_9 = e2 % 151.92/22.61 (5) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0 % 151.92/22.61 (6) ~ (all_4_1 = e0) % 151.92/22.61 (7) all_8_2 = e1 % 151.92/22.61 (8) all_56_31 = e3 % 151.92/22.61 (9) all_54_4 = all_52_1 % 151.92/22.61 (10) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 151.92/22.61 (11) ~ (all_6_0 = e2) % 151.92/22.61 (12) ~ (all_52_11 = e0) % 151.92/22.61 (13) all_56_21 = all_6_2 % 151.92/22.61 (14) all_56_1 = all_4_1 % 151.92/22.61 (15) ~ (all_52_1 = all_4_1) % 151.92/22.61 (16) ~ (all_52_1 = all_6_0) % 151.92/22.61 (17) all_54_14 = all_52_11 % 151.92/22.61 (18) all_54_0 = all_4_1 % 151.92/22.61 (19) all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2 % 151.92/22.61 (20) ~ (all_52_1 = all_8_2) % 151.92/22.61 (21) ~ (all_52_11 = e3) % 151.92/22.61 (22) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0 % 151.92/22.61 (23) all_54_8 = all_6_0 % 151.92/22.61 (24) all_58_0 = all_4_1 % 151.92/22.61 (25) ~ (all_52_1 = e0) % 151.92/22.61 (26) ~ (all_52_9 = all_52_11) % 151.92/22.61 (27) all_56_1 = e3 | all_56_11 = e2 | all_56_21 = e1 | all_56_31 = e0 % 151.92/22.61 (28) ~ (all_6_0 = e0) % 151.92/22.61 (29) ~ (all_6_0 = all_4_1) % 151.92/22.61 (30) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0 % 151.92/22.61 % 151.92/22.61 Begin of proof % 151.92/22.61 | % 151.92/22.61 | COMBINE_EQS: (1), (7) imply: % 151.92/22.61 | (31) all_56_11 = e1 % 151.92/22.61 | % 151.92/22.61 | REDUCE: (3), (4) imply: % 151.92/22.61 | (32) ~ (all_52_1 = e2) % 151.92/22.61 | % 151.92/22.61 | REDUCE: (7), (20) imply: % 151.92/22.61 | (33) ~ (all_52_1 = e1) % 151.92/22.61 | % 151.92/22.61 | REDUCE: (4), (26) imply: % 151.92/22.61 | (34) ~ (all_52_11 = e2) % 151.92/22.61 | % 151.92/22.61 | SIMP: (34) implies: % 151.92/22.61 | (35) ~ (all_52_11 = e2) % 151.92/22.61 | % 151.92/22.61 | BETA: splitting (5) gives: % 151.92/22.61 | % 151.92/22.61 | Case 1: % 151.92/22.61 | | % 151.92/22.61 | | (36) all_54_14 = e3 % 151.92/22.61 | | % 151.92/22.61 | | COMBINE_EQS: (17), (36) imply: % 151.92/22.61 | | (37) all_52_11 = e3 % 151.92/22.61 | | % 151.92/22.61 | | REDUCE: (21), (37) imply: % 151.92/22.61 | | (38) $false % 151.92/22.61 | | % 151.92/22.61 | | CLOSE: (38) is inconsistent. % 151.92/22.61 | | % 151.92/22.61 | Case 2: % 151.92/22.61 | | % 151.92/22.61 | | (39) all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0 % 151.92/22.61 | | % 151.92/22.61 | | BETA: splitting (22) gives: % 151.92/22.61 | | % 151.92/22.61 | | Case 1: % 151.92/22.61 | | | % 151.92/22.61 | | | (40) all_54_4 = e3 % 151.92/22.61 | | | % 151.92/22.61 | | | COMBINE_EQS: (9), (40) imply: % 151.92/22.61 | | | (41) all_52_1 = e3 % 151.92/22.61 | | | % 151.92/22.61 | | | SIMP: (41) implies: % 151.92/22.61 | | | (42) all_52_1 = e3 % 151.92/22.61 | | | % 151.92/22.61 | | | REDUCE: (16), (42) imply: % 151.92/22.61 | | | (43) ~ (all_6_0 = e3) % 151.92/22.61 | | | % 151.92/22.61 | | | SIMP: (43) implies: % 151.92/22.61 | | | (44) ~ (all_6_0 = e3) % 151.92/22.61 | | | % 151.92/22.61 | | | REDUCE: (15), (42) imply: % 151.92/22.61 | | | (45) ~ (all_4_1 = e3) % 151.92/22.61 | | | % 151.92/22.61 | | | SIMP: (45) implies: % 151.92/22.61 | | | (46) ~ (all_4_1 = e3) % 151.92/22.61 | | | % 151.92/22.61 | | | REDUCE: (25), (42) imply: % 151.92/22.61 | | | (47) ~ (e3 = e0) % 151.92/22.61 | | | % 151.92/22.61 | | | BETA: splitting (39) gives: % 151.92/22.61 | | | % 151.92/22.61 | | | Case 1: % 151.92/22.61 | | | | % 151.92/22.61 | | | | (48) all_54_14 = e2 % 151.92/22.61 | | | | % 151.92/22.61 | | | | REF_CLOSE: (17), (35), (48) are inconsistent by sub-proof #581. % 151.92/22.61 | | | | % 151.92/22.61 | | | Case 2: % 151.92/22.61 | | | | % 151.92/22.61 | | | | (49) ~ (all_54_14 = e2) % 151.92/22.61 | | | | (50) all_54_14 = e1 | all_54_14 = e0 % 151.92/22.61 | | | | % 151.92/22.61 | | | | BETA: splitting (30) gives: % 151.92/22.61 | | | | % 151.92/22.61 | | | | Case 1: % 151.92/22.61 | | | | | % 151.92/22.61 | | | | | (51) all_54_8 = e3 % 151.92/22.61 | | | | | % 151.92/22.61 | | | | | REF_CLOSE: (23), (44), (51) are inconsistent by sub-proof #420. % 151.92/22.61 | | | | | % 151.92/22.61 | | | | Case 2: % 151.92/22.61 | | | | | % 151.92/22.61 | | | | | (52) all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0 % 151.92/22.61 | | | | | % 151.92/22.61 | | | | | BETA: splitting (50) gives: % 151.92/22.61 | | | | | % 151.92/22.61 | | | | | Case 1: % 151.92/22.61 | | | | | | % 151.92/22.61 | | | | | | (53) all_54_14 = e1 % 151.92/22.61 | | | | | | % 151.92/22.61 | | | | | | COMBINE_EQS: (17), (53) imply: % 151.92/22.61 | | | | | | (54) all_52_11 = e1 % 151.92/22.61 | | | | | | % 151.92/22.61 | | | | | | SIMP: (54) implies: % 151.92/22.61 | | | | | | (55) all_52_11 = e1 % 151.92/22.61 | | | | | | % 151.92/22.61 | | | | | | REDUCE: (2), (55) imply: % 151.92/22.61 | | | | | | (56) ~ (all_6_2 = e1) % 151.92/22.61 | | | | | | % 151.92/22.61 | | | | | | SIMP: (56) implies: % 151.92/22.61 | | | | | | (57) ~ (all_6_2 = e1) % 151.92/22.61 | | | | | | % 151.92/22.61 | | | | | | REDUCE: (35), (55) imply: % 151.92/22.61 | | | | | | (58) ~ (e2 = e1) % 151.92/22.61 | | | | | | % 151.92/22.61 | | | | | | SIMP: (58) implies: % 151.92/22.61 | | | | | | (59) ~ (e2 = e1) % 151.92/22.61 | | | | | | % 151.92/22.61 | | | | | | BETA: splitting (19) gives: % 151.92/22.61 | | | | | | % 151.92/22.61 | | | | | | Case 1: % 151.92/22.61 | | | | | | | % 151.92/22.61 | | | | | | | (60) all_58_0 = e2 % 151.92/22.61 | | | | | | | % 151.92/22.61 | | | | | | | COMBINE_EQS: (24), (60) imply: % 151.92/22.61 | | | | | | | (61) all_4_1 = e2 % 151.92/22.61 | | | | | | | % 151.92/22.61 | | | | | | | COMBINE_EQS: (14), (61) imply: % 151.92/22.61 | | | | | | | (62) all_56_1 = e2 % 151.92/22.61 | | | | | | | % 151.92/22.61 | | | | | | | REDUCE: (46), (61) imply: % 151.92/22.61 | | | | | | | (63) ~ (e3 = e2) % 151.92/22.61 | | | | | | | % 151.92/22.61 | | | | | | | SIMP: (63) implies: % 151.92/22.61 | | | | | | | (64) ~ (e3 = e2) % 151.92/22.61 | | | | | | | % 151.92/22.61 | | | | | | | BETA: splitting (27) gives: % 151.92/22.61 | | | | | | | % 151.92/22.61 | | | | | | | Case 1: % 151.92/22.61 | | | | | | | | % 151.92/22.61 | | | | | | | | (65) all_56_1 = e3 % 151.92/22.61 | | | | | | | | % 151.92/22.61 | | | | | | | | REF_CLOSE: (62), (64), (65) are inconsistent by sub-proof #428. % 151.92/22.61 | | | | | | | | % 151.92/22.61 | | | | | | | Case 2: % 151.92/22.61 | | | | | | | | % 151.92/22.61 | | | | | | | | (66) all_56_11 = e2 | all_56_21 = e1 | all_56_31 = e0 % 151.92/22.61 | | | | | | | | % 151.92/22.61 | | | | | | | | REF_CLOSE: (8), (13), (31), (47), (57), (59), (66) are % 151.92/22.61 | | | | | | | | inconsistent by sub-proof #418. % 151.92/22.61 | | | | | | | | % 151.92/22.61 | | | | | | | End of split % 151.92/22.61 | | | | | | | % 151.92/22.61 | | | | | | Case 2: % 151.92/22.61 | | | | | | | % 151.92/22.61 | | | | | | | (67) ~ (all_58_0 = e2) % 151.92/22.61 | | | | | | | % 151.92/22.61 | | | | | | | REDUCE: (24), (67) imply: % 151.92/22.61 | | | | | | | (68) ~ (all_4_1 = e2) % 151.92/22.61 | | | | | | | % 151.92/22.61 | | | | | | | BETA: splitting (10) gives: % 151.92/22.61 | | | | | | | % 151.92/22.61 | | | | | | | Case 1: % 151.92/22.61 | | | | | | | | % 151.92/22.61 | | | | | | | | (69) all_54_0 = e3 % 151.92/22.61 | | | | | | | | % 151.92/22.61 | | | | | | | | REF_CLOSE: (18), (46), (69) are inconsistent by sub-proof #554. % 151.92/22.61 | | | | | | | | % 151.92/22.61 | | | | | | | Case 2: % 151.92/22.61 | | | | | | | | % 151.92/22.61 | | | | | | | | (70) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 151.92/22.61 | | | | | | | | % 151.92/22.61 | | | | | | | | BETA: splitting (70) gives: % 151.92/22.61 | | | | | | | | % 151.92/22.61 | | | | | | | | Case 1: % 151.92/22.61 | | | | | | | | | % 151.92/22.61 | | | | | | | | | (71) all_54_0 = e2 % 151.92/22.61 | | | | | | | | | % 151.92/22.61 | | | | | | | | | REF_CLOSE: (18), (68), (71) are inconsistent by sub-proof % 151.92/22.61 | | | | | | | | | #553. % 151.92/22.61 | | | | | | | | | % 151.92/22.61 | | | | | | | | Case 2: % 151.92/22.61 | | | | | | | | | % 151.92/22.61 | | | | | | | | | (72) all_54_0 = e1 | all_54_0 = e0 % 151.92/22.61 | | | | | | | | | % 151.92/22.61 | | | | | | | | | BETA: splitting (52) gives: % 151.92/22.61 | | | | | | | | | % 151.92/22.61 | | | | | | | | | Case 1: % 151.92/22.61 | | | | | | | | | | % 151.92/22.61 | | | | | | | | | | (73) all_54_8 = e2 % 151.92/22.61 | | | | | | | | | | % 151.92/22.61 | | | | | | | | | | COMBINE_EQS: (23), (73) imply: % 151.92/22.61 | | | | | | | | | | (74) all_6_0 = e2 % 151.92/22.61 | | | | | | | | | | % 151.92/22.61 | | | | | | | | | | REDUCE: (11), (74) imply: % 151.92/22.61 | | | | | | | | | | (75) $false % 151.92/22.61 | | | | | | | | | | % 151.92/22.61 | | | | | | | | | | CLOSE: (75) is inconsistent. % 151.92/22.61 | | | | | | | | | | % 151.92/22.61 | | | | | | | | | Case 2: % 151.92/22.61 | | | | | | | | | | % 151.92/22.61 | | | | | | | | | | (76) all_54_8 = e1 | all_54_8 = e0 % 151.92/22.61 | | | | | | | | | | % 151.92/22.61 | | | | | | | | | | BETA: splitting (76) gives: % 151.92/22.61 | | | | | | | | | | % 151.92/22.61 | | | | | | | | | | Case 1: % 151.92/22.61 | | | | | | | | | | | % 151.92/22.61 | | | | | | | | | | | (77) all_54_8 = e1 % 151.92/22.61 | | | | | | | | | | | % 151.92/22.61 | | | | | | | | | | | COMBINE_EQS: (23), (77) imply: % 151.92/22.61 | | | | | | | | | | | (78) all_6_0 = e1 % 151.92/22.61 | | | | | | | | | | | % 151.92/22.61 | | | | | | | | | | | REDUCE: (29), (78) imply: % 151.92/22.61 | | | | | | | | | | | (79) ~ (all_4_1 = e1) % 151.92/22.61 | | | | | | | | | | | % 151.92/22.61 | | | | | | | | | | | SIMP: (79) implies: % 151.92/22.61 | | | | | | | | | | | (80) ~ (all_4_1 = e1) % 151.92/22.61 | | | | | | | | | | | % 151.92/22.61 | | | | | | | | | | | REF_CLOSE: (6), (18), (72), (80) are inconsistent by % 151.92/22.61 | | | | | | | | | | | sub-proof #550. % 151.92/22.61 | | | | | | | | | | | % 151.92/22.61 | | | | | | | | | | Case 2: % 151.92/22.61 | | | | | | | | | | | % 151.92/22.61 | | | | | | | | | | | (81) all_54_8 = e0 % 151.92/22.61 | | | | | | | | | | | % 151.92/22.61 | | | | | | | | | | | COMBINE_EQS: (23), (81) imply: % 151.92/22.61 | | | | | | | | | | | (82) all_6_0 = e0 % 151.92/22.61 | | | | | | | | | | | % 151.92/22.61 | | | | | | | | | | | REDUCE: (28), (82) imply: % 151.92/22.61 | | | | | | | | | | | (83) $false % 151.92/22.61 | | | | | | | | | | | % 151.92/22.61 | | | | | | | | | | | CLOSE: (83) is inconsistent. % 151.92/22.61 | | | | | | | | | | | % 151.92/22.61 | | | | | | | | | | End of split % 151.92/22.61 | | | | | | | | | | % 151.92/22.61 | | | | | | | | | End of split % 151.92/22.61 | | | | | | | | | % 151.92/22.61 | | | | | | | | End of split % 151.92/22.61 | | | | | | | | % 151.92/22.61 | | | | | | | End of split % 151.92/22.61 | | | | | | | % 151.92/22.61 | | | | | | End of split % 151.92/22.61 | | | | | | % 151.92/22.61 | | | | | Case 2: % 151.92/22.61 | | | | | | % 151.92/22.61 | | | | | | (84) all_54_14 = e0 % 151.92/22.61 | | | | | | % 151.92/22.61 | | | | | | REF_CLOSE: (12), (17), (84) are inconsistent by sub-proof #715. % 151.92/22.61 | | | | | | % 151.92/22.61 | | | | | End of split % 151.92/22.61 | | | | | % 151.92/22.61 | | | | End of split % 151.92/22.61 | | | | % 151.92/22.61 | | | End of split % 151.92/22.61 | | | % 151.92/22.61 | | Case 2: % 151.92/22.61 | | | % 151.92/22.61 | | | (85) all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0 % 151.92/22.61 | | | % 151.92/22.61 | | | REF_CLOSE: (9), (25), (32), (33), (85) are inconsistent by sub-proof #560. % 151.92/22.61 | | | % 151.92/22.61 | | End of split % 151.92/22.61 | | % 151.92/22.61 | End of split % 151.92/22.61 | % 151.92/22.61 End of proof % 151.92/22.61 % 151.92/22.61 Sub-proof #418 shows that the following formulas are inconsistent: % 151.92/22.61 ---------------------------------------------------------------- % 151.92/22.61 (1) ~ (e3 = e0) % 151.92/22.61 (2) all_56_31 = e3 % 151.92/22.61 (3) all_56_21 = all_6_2 % 151.92/22.61 (4) all_56_11 = e2 | all_56_21 = e1 | all_56_31 = e0 % 151.92/22.61 (5) all_56_11 = e1 % 151.92/22.61 (6) ~ (e2 = e1) % 151.92/22.61 (7) ~ (all_6_2 = e1) % 151.92/22.61 % 151.92/22.61 Begin of proof % 151.92/22.61 | % 151.92/22.61 | BETA: splitting (4) gives: % 151.92/22.61 | % 151.92/22.61 | Case 1: % 151.92/22.61 | | % 151.92/22.61 | | (8) all_56_11 = e2 % 151.92/22.61 | | % 151.92/22.61 | | REF_CLOSE: (5), (6), (8) are inconsistent by sub-proof #419. % 151.92/22.61 | | % 151.92/22.61 | Case 2: % 151.92/22.61 | | % 151.92/22.61 | | (9) all_56_21 = e1 | all_56_31 = e0 % 151.92/22.61 | | % 151.92/22.61 | | BETA: splitting (9) gives: % 151.92/22.61 | | % 151.92/22.61 | | Case 1: % 151.92/22.61 | | | % 151.92/22.61 | | | (10) all_56_21 = e1 % 151.92/22.61 | | | % 151.92/22.61 | | | COMBINE_EQS: (3), (10) imply: % 151.92/22.61 | | | (11) all_6_2 = e1 % 151.92/22.61 | | | % 151.92/22.61 | | | REDUCE: (7), (11) imply: % 151.92/22.61 | | | (12) $false % 151.92/22.61 | | | % 151.92/22.61 | | | CLOSE: (12) is inconsistent. % 151.92/22.61 | | | % 151.92/22.61 | | Case 2: % 151.92/22.61 | | | % 151.92/22.61 | | | (13) all_56_31 = e0 % 151.92/22.61 | | | % 151.92/22.61 | | | REF_CLOSE: (1), (2), (13) are inconsistent by sub-proof #543. % 151.92/22.61 | | | % 151.92/22.61 | | End of split % 151.92/22.61 | | % 151.92/22.61 | End of split % 151.92/22.61 | % 151.92/22.61 End of proof % 151.92/22.61 % 151.92/22.61 Sub-proof #419 shows that the following formulas are inconsistent: % 151.92/22.61 ---------------------------------------------------------------- % 151.92/22.61 (1) all_56_11 = e2 % 151.92/22.61 (2) all_56_11 = e1 % 151.92/22.61 (3) ~ (e2 = e1) % 151.92/22.61 % 151.92/22.61 Begin of proof % 151.92/22.61 | % 151.92/22.61 | COMBINE_EQS: (1), (2) imply: % 151.92/22.61 | (4) e2 = e1 % 151.92/22.61 | % 151.92/22.61 | SIMP: (4) implies: % 151.92/22.61 | (5) e2 = e1 % 151.92/22.61 | % 151.92/22.61 | REDUCE: (3), (5) imply: % 151.92/22.61 | (6) $false % 151.92/22.61 | % 151.92/22.61 | CLOSE: (6) is inconsistent. % 151.92/22.61 | % 151.92/22.61 End of proof % 151.92/22.61 % 151.92/22.61 Sub-proof #420 shows that the following formulas are inconsistent: % 151.92/22.61 ---------------------------------------------------------------- % 151.92/22.61 (1) all_54_8 = all_6_0 % 151.92/22.61 (2) all_54_8 = e3 % 151.92/22.61 (3) ~ (all_6_0 = e3) % 151.92/22.61 % 151.92/22.61 Begin of proof % 151.92/22.61 | % 151.92/22.61 | COMBINE_EQS: (1), (2) imply: % 151.92/22.61 | (4) all_6_0 = e3 % 151.92/22.61 | % 151.92/22.61 | SIMP: (4) implies: % 151.92/22.61 | (5) all_6_0 = e3 % 151.92/22.61 | % 151.92/22.61 | REDUCE: (3), (5) imply: % 151.92/22.61 | (6) $false % 151.92/22.61 | % 151.92/22.61 | CLOSE: (6) is inconsistent. % 151.92/22.61 | % 151.92/22.61 End of proof % 151.92/22.61 % 151.92/22.61 Sub-proof #421 shows that the following formulas are inconsistent: % 151.92/22.61 ---------------------------------------------------------------- % 151.92/22.61 (1) ~ (all_6_0 = e2) % 151.92/22.61 (2) all_58_12 = e0 % 151.92/22.61 (3) all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2 % 151.92/22.61 (4) all_58_6 = all_6_0 % 151.92/22.61 (5) all_58_2 = all_52_1 % 151.92/22.61 (6) ~ (e2 = e0) % 151.92/22.61 (7) ~ (all_52_1 = e2) % 151.92/22.61 % 151.92/22.61 Begin of proof % 151.92/22.61 | % 151.92/22.61 | BETA: splitting (3) gives: % 151.92/22.61 | % 151.92/22.61 | Case 1: % 151.92/22.61 | | % 151.92/22.61 | | (8) all_58_2 = e2 % 151.92/22.61 | | % 151.92/22.61 | | COMBINE_EQS: (5), (8) imply: % 151.92/22.61 | | (9) all_52_1 = e2 % 151.92/22.61 | | % 151.92/22.61 | | REDUCE: (7), (9) imply: % 151.92/22.61 | | (10) $false % 151.92/22.61 | | % 151.92/22.61 | | CLOSE: (10) is inconsistent. % 151.92/22.61 | | % 151.92/22.61 | Case 2: % 151.92/22.61 | | % 151.92/22.61 | | (11) all_58_6 = e2 | all_58_12 = e2 % 151.92/22.61 | | % 151.92/22.61 | | REF_CLOSE: (1), (2), (4), (6), (11) are inconsistent by sub-proof #422. % 151.92/22.61 | | % 151.92/22.61 | End of split % 151.92/22.61 | % 151.92/22.61 End of proof % 151.92/22.61 % 151.92/22.61 Sub-proof #422 shows that the following formulas are inconsistent: % 151.92/22.61 ---------------------------------------------------------------- % 151.92/22.61 (1) ~ (all_6_0 = e2) % 151.92/22.61 (2) all_58_12 = e0 % 151.92/22.61 (3) all_58_6 = e2 | all_58_12 = e2 % 151.92/22.61 (4) all_58_6 = all_6_0 % 151.92/22.61 (5) ~ (e2 = e0) % 151.92/22.61 % 151.92/22.61 Begin of proof % 151.92/22.61 | % 151.92/22.61 | BETA: splitting (3) gives: % 151.92/22.61 | % 151.92/22.61 | Case 1: % 151.92/22.61 | | % 151.92/22.61 | | (6) all_58_6 = e2 % 151.92/22.61 | | % 151.92/22.61 | | COMBINE_EQS: (4), (6) imply: % 151.92/22.61 | | (7) all_6_0 = e2 % 151.92/22.61 | | % 151.92/22.61 | | REDUCE: (1), (7) imply: % 151.92/22.61 | | (8) $false % 151.92/22.61 | | % 151.92/22.61 | | CLOSE: (8) is inconsistent. % 151.92/22.61 | | % 151.92/22.61 | Case 2: % 151.92/22.61 | | % 151.92/22.61 | | (9) all_58_12 = e2 % 151.92/22.61 | | % 151.92/22.61 | | REF_CLOSE: (2), (5), (9) are inconsistent by sub-proof #423. % 151.92/22.61 | | % 151.92/22.61 | End of split % 151.92/22.61 | % 151.92/22.61 End of proof % 151.92/22.61 % 151.92/22.61 Sub-proof #423 shows that the following formulas are inconsistent: % 151.92/22.61 ---------------------------------------------------------------- % 151.92/22.61 (1) all_58_12 = e2 % 151.92/22.61 (2) all_58_12 = e0 % 151.92/22.61 (3) ~ (e2 = e0) % 151.92/22.61 % 151.92/22.61 Begin of proof % 151.92/22.61 | % 151.92/22.61 | COMBINE_EQS: (1), (2) imply: % 151.92/22.61 | (4) e2 = e0 % 151.92/22.61 | % 151.92/22.61 | SIMP: (4) implies: % 151.92/22.61 | (5) e2 = e0 % 151.92/22.61 | % 151.92/22.61 | REDUCE: (3), (5) imply: % 151.92/22.61 | (6) $false % 151.92/22.61 | % 151.92/22.61 | CLOSE: (6) is inconsistent. % 151.92/22.61 | % 151.92/22.61 End of proof % 151.92/22.61 % 151.92/22.61 Sub-proof #424 shows that the following formulas are inconsistent: % 151.92/22.61 ---------------------------------------------------------------- % 151.92/22.61 (1) ~ (e3 = e0) % 151.92/22.61 (2) all_54_10 = all_6_2 % 151.92/22.61 (3) all_56_31 = e3 % 151.92/22.61 (4) ~ (all_6_2 = e3) % 151.92/22.61 (5) ~ (e3 = e2) % 151.92/22.61 (6) all_56_21 = all_6_2 % 151.92/22.61 (7) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 151.92/22.61 (8) all_58_13 = all_52_7 % 151.92/22.61 (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 151.92/22.61 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 151.92/22.61 (10) all_56_11 = e2 % 151.92/22.61 (11) all_56_1 = e3 | all_56_11 = e2 | all_56_21 = e1 | all_56_31 = e0 % 151.92/22.61 (12) op(e1, e1) = all_6_2 % 151.92/22.61 (13) ~ (all_6_2 = e2) % 151.92/22.61 (14) all_58_1 = e3 % 151.92/22.61 (15) all_58_7 = all_52_6 % 151.92/22.61 (16) op(e1, all_6_2) = all_56_20 % 151.92/22.61 (17) all_58_3 = e2 % 151.92/22.61 (18) all_58_1 = e0 | all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0 % 151.92/22.61 (19) ~ (e3 = e1) % 151.92/22.61 (20) all_56_1 = e2 % 151.92/22.61 (21) ~ (all_52_6 = all_6_2) % 151.92/22.61 (22) op(all_6_2, all_6_2) = e3 % 151.92/22.61 (23) ~ (e2 = e0) % 151.92/22.61 (24) ~ (all_52_7 = e0) % 151.92/22.61 % 151.92/22.61 Begin of proof % 151.92/22.61 | % 151.92/22.61 | BETA: splitting (18) gives: % 151.92/22.61 | % 151.92/22.61 | Case 1: % 151.92/22.61 | | % 151.92/22.61 | | (25) all_58_1 = e0 % 151.92/22.61 | | % 151.92/22.61 | | COMBINE_EQS: (14), (25) imply: % 151.92/22.61 | | (26) e3 = e0 % 151.92/22.61 | | % 151.92/22.61 | | REDUCE: (1), (26) imply: % 151.92/22.61 | | (27) $false % 151.92/22.61 | | % 151.92/22.61 | | CLOSE: (27) is inconsistent. % 151.92/22.61 | | % 151.92/22.61 | Case 2: % 151.92/22.61 | | % 151.92/22.61 | | (28) ~ (all_58_1 = e0) % 151.92/22.61 | | (29) all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0 % 151.92/22.61 | | % 151.92/22.61 | | BETA: splitting (29) gives: % 151.92/22.61 | | % 151.92/22.61 | | Case 1: % 151.92/22.61 | | | % 151.92/22.61 | | | (30) all_58_3 = e0 % 151.92/22.61 | | | % 151.92/22.61 | | | COMBINE_EQS: (17), (30) imply: % 151.92/22.61 | | | (31) e2 = e0 % 151.92/22.61 | | | % 151.92/22.61 | | | COMBINE_EQS: (10), (31) imply: % 151.92/22.61 | | | (32) all_56_11 = e0 % 151.92/22.61 | | | % 151.92/22.61 | | | REF_CLOSE: (1), (3), (5), (6), (9), (11), (12), (16), (19), (20), (22), % 151.92/22.61 | | | (23), (32) are inconsistent by sub-proof #425. % 151.92/22.61 | | | % 151.92/22.61 | | Case 2: % 151.92/22.61 | | | % 151.92/22.61 | | | (33) all_58_7 = e0 | all_58_13 = e0 % 151.92/22.61 | | | % 151.92/22.61 | | | BETA: splitting (33) gives: % 151.92/22.61 | | | % 151.92/22.61 | | | Case 1: % 151.92/22.61 | | | | % 151.92/22.61 | | | | (34) all_58_7 = e0 % 151.92/22.61 | | | | % 151.92/22.61 | | | | COMBINE_EQS: (15), (34) imply: % 151.92/22.61 | | | | (35) all_52_6 = e0 % 151.92/22.61 | | | | % 151.92/22.61 | | | | REDUCE: (21), (35) imply: % 151.92/22.61 | | | | (36) ~ (all_6_2 = e0) % 151.92/22.61 | | | | % 151.92/22.61 | | | | SIMP: (36) implies: % 151.92/22.61 | | | | (37) ~ (all_6_2 = e0) % 151.92/22.61 | | | | % 151.92/22.61 | | | | REF_CLOSE: (2), (4), (7), (9), (12), (13), (16), (22), (37) are % 151.92/22.61 | | | | inconsistent by sub-proof #459. % 151.92/22.61 | | | | % 151.92/22.61 | | | Case 2: % 151.92/22.61 | | | | % 151.92/22.61 | | | | (38) all_58_13 = e0 % 151.92/22.61 | | | | % 151.92/22.61 | | | | REF_CLOSE: (8), (24), (38) are inconsistent by sub-proof #605. % 151.92/22.61 | | | | % 151.92/22.61 | | | End of split % 151.92/22.61 | | | % 151.92/22.61 | | End of split % 151.92/22.61 | | % 151.92/22.61 | End of split % 151.92/22.61 | % 151.92/22.61 End of proof % 151.92/22.61 % 151.92/22.61 Sub-proof #425 shows that the following formulas are inconsistent: % 151.92/22.61 ---------------------------------------------------------------- % 151.92/22.61 (1) ~ (e3 = e0) % 151.92/22.61 (2) all_56_31 = e3 % 151.92/22.61 (3) ~ (e3 = e2) % 151.92/22.61 (4) all_56_21 = all_6_2 % 151.92/22.61 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 151.92/22.61 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 151.92/22.61 (6) all_56_1 = e3 | all_56_11 = e2 | all_56_21 = e1 | all_56_31 = e0 % 151.92/22.61 (7) all_56_11 = e0 % 151.92/22.61 (8) op(e1, e1) = all_6_2 % 151.92/22.61 (9) op(e1, all_6_2) = all_56_20 % 151.92/22.61 (10) ~ (e3 = e1) % 151.92/22.61 (11) all_56_1 = e2 % 151.92/22.61 (12) op(all_6_2, all_6_2) = e3 % 151.92/22.61 (13) ~ (e2 = e0) % 151.92/22.61 % 151.92/22.61 Begin of proof % 151.92/22.61 | % 151.92/22.61 | BETA: splitting (6) gives: % 151.92/22.61 | % 151.92/22.61 | Case 1: % 151.92/22.61 | | % 151.92/22.61 | | (14) all_56_1 = e3 % 151.92/22.61 | | % 151.92/22.61 | | REF_CLOSE: (3), (11), (14) are inconsistent by sub-proof #428. % 151.92/22.61 | | % 151.92/22.61 | Case 2: % 151.92/22.61 | | % 151.92/22.61 | | (15) all_56_11 = e2 | all_56_21 = e1 | all_56_31 = e0 % 151.92/22.61 | | % 151.92/22.61 | | BETA: splitting (15) gives: % 151.92/22.61 | | % 151.92/22.61 | | Case 1: % 151.92/22.61 | | | % 151.92/22.61 | | | (16) all_56_11 = e2 % 151.92/22.61 | | | % 151.92/22.61 | | | REF_CLOSE: (7), (13), (16) are inconsistent by sub-proof #427. % 151.92/22.61 | | | % 151.92/22.61 | | Case 2: % 151.92/22.61 | | | % 151.92/22.61 | | | (17) all_56_21 = e1 | all_56_31 = e0 % 151.92/22.61 | | | % 151.92/22.61 | | | REF_CLOSE: (1), (2), (4), (5), (8), (9), (10), (12), (17) are inconsistent % 151.92/22.61 | | | by sub-proof #426. % 151.92/22.61 | | | % 151.92/22.61 | | End of split % 151.92/22.61 | | % 151.92/22.61 | End of split % 151.92/22.61 | % 151.92/22.61 End of proof % 151.92/22.61 % 151.92/22.61 Sub-proof #426 shows that the following formulas are inconsistent: % 151.92/22.61 ---------------------------------------------------------------- % 151.92/22.61 (1) ~ (e3 = e0) % 151.92/22.61 (2) all_56_31 = e3 % 151.92/22.61 (3) all_56_21 = all_6_2 % 151.92/22.61 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 151.92/22.61 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 151.92/22.61 (5) op(e1, e1) = all_6_2 % 151.92/22.61 (6) all_56_21 = e1 | all_56_31 = e0 % 151.92/22.61 (7) op(e1, all_6_2) = all_56_20 % 151.92/22.61 (8) ~ (e3 = e1) % 151.92/22.61 (9) op(all_6_2, all_6_2) = e3 % 151.92/22.61 % 151.92/22.61 Begin of proof % 151.92/22.61 | % 151.92/22.61 | BETA: splitting (6) gives: % 151.92/22.61 | % 151.92/22.61 | Case 1: % 151.92/22.61 | | % 151.92/22.61 | | (10) all_56_21 = e1 % 151.92/22.61 | | % 151.92/22.61 | | COMBINE_EQS: (3), (10) imply: % 151.92/22.61 | | (11) all_6_2 = e1 % 151.92/22.61 | | % 151.92/22.61 | | REF_CLOSE: (4), (5), (7), (8), (9), (11) are inconsistent by sub-proof #460. % 151.92/22.61 | | % 151.92/22.61 | Case 2: % 151.92/22.61 | | % 151.92/22.61 | | (12) all_56_31 = e0 % 151.92/22.61 | | % 151.92/22.61 | | REF_CLOSE: (1), (2), (12) are inconsistent by sub-proof #543. % 151.92/22.61 | | % 151.92/22.61 | End of split % 151.92/22.61 | % 151.92/22.61 End of proof % 151.92/22.61 % 151.92/22.61 Sub-proof #427 shows that the following formulas are inconsistent: % 151.92/22.61 ---------------------------------------------------------------- % 152.07/22.61 (1) all_56_11 = e2 % 152.07/22.61 (2) all_56_11 = e0 % 152.07/22.61 (3) ~ (e2 = e0) % 152.07/22.61 % 152.07/22.61 Begin of proof % 152.07/22.61 | % 152.07/22.61 | COMBINE_EQS: (1), (2) imply: % 152.07/22.61 | (4) e2 = e0 % 152.07/22.61 | % 152.07/22.61 | SIMP: (4) implies: % 152.07/22.61 | (5) e2 = e0 % 152.07/22.61 | % 152.07/22.61 | REDUCE: (3), (5) imply: % 152.07/22.61 | (6) $false % 152.07/22.61 | % 152.07/22.61 | CLOSE: (6) is inconsistent. % 152.07/22.61 | % 152.07/22.61 End of proof % 152.07/22.61 % 152.07/22.61 Sub-proof #428 shows that the following formulas are inconsistent: % 152.07/22.61 ---------------------------------------------------------------- % 152.07/22.61 (1) all_56_1 = e3 % 152.07/22.61 (2) all_56_1 = e2 % 152.07/22.61 (3) ~ (e3 = e2) % 152.07/22.61 % 152.07/22.61 Begin of proof % 152.07/22.61 | % 152.07/22.61 | COMBINE_EQS: (1), (2) imply: % 152.07/22.61 | (4) e3 = e2 % 152.07/22.61 | % 152.07/22.61 | SIMP: (4) implies: % 152.07/22.61 | (5) e3 = e2 % 152.07/22.61 | % 152.07/22.61 | REDUCE: (3), (5) imply: % 152.07/22.61 | (6) $false % 152.07/22.61 | % 152.07/22.61 | CLOSE: (6) is inconsistent. % 152.07/22.61 | % 152.07/22.61 End of proof % 152.07/22.61 % 152.07/22.61 Sub-proof #429 shows that the following formulas are inconsistent: % 152.07/22.61 ---------------------------------------------------------------- % 152.07/22.61 (1) all_56_11 = all_8_2 % 152.07/22.61 (2) all_54_9 = all_52_6 % 152.07/22.61 (3) all_54_10 = all_6_2 % 152.07/22.61 (4) ~ (all_6_2 = e3) % 152.07/22.61 (5) op(e0, e0) = all_4_2 % 152.07/22.61 (6) ~ (all_52_6 = all_52_14) % 152.07/22.61 (7) ~ (all_6_0 = e2) % 152.07/22.61 (8) all_56_21 = all_6_2 % 152.07/22.61 (9) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 152.07/22.61 (10) all_56_1 = all_10_2 % 152.07/22.61 (11) ~ (all_52_6 = all_6_0) % 152.07/22.61 (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 152.07/22.61 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 152.07/22.61 (13) ~ (all_6_0 = all_6_2) % 152.07/22.61 (14) all_54_8 = all_6_0 % 152.07/22.61 (15) ~ (all_52_14 = all_6_0) % 152.07/22.61 (16) op(all_4_2, all_4_2) = all_4_1 % 152.07/22.61 (17) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0 % 152.07/22.61 (18) all_56_31 = all_4_2 % 152.07/22.61 (19) all_56_1 = e3 | all_56_11 = e2 | all_56_21 = e1 | all_56_31 = e0 % 152.07/22.61 (20) all_56_23 = all_52_14 % 152.07/22.61 (21) op(e1, e1) = all_6_2 % 152.07/22.61 (22) ~ (all_52_6 = all_8_2) % 152.07/22.61 (23) ~ (all_6_2 = e2) % 152.07/22.61 (24) ~ (all_4_2 = e3) % 152.07/22.61 (25) op(e1, all_6_2) = all_56_20 % 152.07/22.61 (26) ~ (all_56_21 = e0) | all_56_23 = e1 % 152.07/22.61 (27) op(e0, all_4_2) = all_56_30 % 152.07/22.61 (28) ~ (all_52_6 = all_6_2) % 152.07/22.61 (29) op(all_6_2, all_6_2) = e3 % 152.07/22.61 (30) ~ (all_52_14 = all_6_2) % 152.07/22.61 (31) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0 % 152.07/22.61 (32) ~ (all_10_2 = all_6_0) % 152.07/22.61 % 152.07/22.61 Begin of proof % 152.07/22.61 | % 152.07/22.61 | BETA: splitting (26) gives: % 152.07/22.61 | % 152.07/22.61 | Case 1: % 152.07/22.61 | | % 152.07/22.61 | | (33) ~ (all_56_21 = e0) % 152.07/22.61 | | % 152.07/22.61 | | REDUCE: (8), (33) imply: % 152.07/22.61 | | (34) ~ (all_6_2 = e0) % 152.07/22.61 | | % 152.07/22.61 | | REF_CLOSE: (3), (4), (9), (12), (21), (23), (25), (29), (34) are % 152.07/22.61 | | inconsistent by sub-proof #459. % 152.07/22.61 | | % 152.07/22.61 | Case 2: % 152.07/22.61 | | % 152.07/22.61 | | (35) all_56_23 = e1 % 152.07/22.61 | | (36) all_56_21 = e0 % 152.07/22.61 | | % 152.07/22.61 | | REF_CLOSE: (1), (2), (5), (6), (7), (8), (10), (11), (12), (13), (14), (15), % 152.07/22.61 | | (16), (17), (18), (19), (20), (22), (24), (27), (28), (29), (30), % 152.07/22.61 | | (31), (32), (35), (36) are inconsistent by sub-proof #430. % 152.07/22.61 | | % 152.07/22.61 | End of split % 152.07/22.61 | % 152.07/22.61 End of proof % 152.07/22.61 % 152.07/22.61 Sub-proof #430 shows that the following formulas are inconsistent: % 152.07/22.61 ---------------------------------------------------------------- % 152.07/22.61 (1) all_56_11 = all_8_2 % 152.07/22.61 (2) all_54_9 = all_52_6 % 152.07/22.61 (3) op(e0, e0) = all_4_2 % 152.07/22.61 (4) ~ (all_52_6 = all_52_14) % 152.07/22.61 (5) ~ (all_6_0 = e2) % 152.07/22.61 (6) all_56_21 = all_6_2 % 152.07/22.61 (7) all_56_1 = all_10_2 % 152.07/22.61 (8) all_56_21 = e0 % 152.07/22.61 (9) all_56_23 = e1 % 152.07/22.61 (10) ~ (all_52_6 = all_6_0) % 152.07/22.61 (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 152.07/22.61 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 152.07/22.61 (12) ~ (all_6_0 = all_6_2) % 152.07/22.61 (13) all_54_8 = all_6_0 % 152.07/22.61 (14) ~ (all_52_14 = all_6_0) % 152.07/22.61 (15) op(all_4_2, all_4_2) = all_4_1 % 152.07/22.61 (16) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0 % 152.07/22.61 (17) all_56_31 = all_4_2 % 152.07/22.61 (18) all_56_1 = e3 | all_56_11 = e2 | all_56_21 = e1 | all_56_31 = e0 % 152.07/22.61 (19) all_56_23 = all_52_14 % 152.07/22.61 (20) ~ (all_52_6 = all_8_2) % 152.07/22.61 (21) ~ (all_4_2 = e3) % 152.07/22.61 (22) op(e0, all_4_2) = all_56_30 % 152.07/22.61 (23) ~ (all_52_6 = all_6_2) % 152.07/22.62 (24) op(all_6_2, all_6_2) = e3 % 152.07/22.62 (25) ~ (all_52_14 = all_6_2) % 152.07/22.62 (26) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0 % 152.07/22.62 (27) ~ (all_10_2 = all_6_0) % 152.07/22.62 % 152.07/22.62 Begin of proof % 152.07/22.62 | % 152.07/22.62 | COMBINE_EQS: (6), (8) imply: % 152.07/22.62 | (28) all_6_2 = e0 % 152.07/22.62 | % 152.07/22.62 | SIMP: (28) implies: % 152.07/22.62 | (29) all_6_2 = e0 % 152.07/22.62 | % 152.07/22.62 | COMBINE_EQS: (9), (19) imply: % 152.07/22.62 | (30) all_52_14 = e1 % 152.07/22.62 | % 152.07/22.62 | SIMP: (30) implies: % 152.07/22.62 | (31) all_52_14 = e1 % 152.07/22.62 | % 152.07/22.62 | REDUCE: (4), (31) imply: % 152.07/22.62 | (32) ~ (all_52_6 = e1) % 152.07/22.62 | % 152.07/22.62 | REDUCE: (23), (29) imply: % 152.07/22.62 | (33) ~ (all_52_6 = e0) % 152.07/22.62 | % 152.07/22.62 | REDUCE: (14), (31) imply: % 152.07/22.62 | (34) ~ (all_6_0 = e1) % 152.07/22.62 | % 152.07/22.62 | SIMP: (34) implies: % 152.07/22.62 | (35) ~ (all_6_0 = e1) % 152.07/22.62 | % 152.07/22.62 | REDUCE: (25), (29), (31) imply: % 152.07/22.62 | (36) ~ (e1 = e0) % 152.07/22.62 | % 152.07/22.62 | REDUCE: (12), (29) imply: % 152.07/22.62 | (37) ~ (all_6_0 = e0) % 152.07/22.62 | % 152.07/22.62 | REDUCE: (24), (29) imply: % 152.07/22.62 | (38) op(e0, e0) = e3 % 152.07/22.62 | % 152.07/22.62 | REF_CLOSE: (1), (2), (3), (5), (7), (8), (10), (11), (13), (15), (16), (17), % 152.07/22.62 | (18), (20), (21), (22), (26), (27), (32), (33), (35), (36), (37), % 152.07/22.62 | (38) are inconsistent by sub-proof #450. % 152.07/22.62 | % 152.07/22.62 End of proof % 152.07/22.62 % 152.07/22.62 Sub-proof #431 shows that the following formulas are inconsistent: % 152.07/22.62 ---------------------------------------------------------------- % 152.07/22.62 (1) all_56_11 = all_8_2 % 152.07/22.62 (2) all_52_6 = e1 % 152.07/22.62 (3) ~ (all_52_14 = all_4_2) % 152.07/22.62 (4) all_58_6 = e0 | all_58_7 = e0 | all_58_8 = e0 | all_58_11 = e0 % 152.07/22.62 (5) all_56_21 = all_6_2 % 152.07/22.62 (6) all_56_1 = all_10_2 % 152.07/22.62 (7) op(e2, all_8_2) = all_56_10 % 152.07/22.62 (8) ~ (all_52_6 = all_6_0) % 152.07/22.62 (9) ~ (e1 = e0) % 152.07/22.62 (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 152.07/22.62 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 152.07/22.62 (11) all_36_0 = all_6_0 % 152.07/22.62 (12) ~ (all_6_0 = all_6_2) % 152.07/22.62 (13) all_54_8 = all_6_0 % 152.07/22.62 (14) all_58_8 = all_6_2 % 152.07/22.62 (15) all_56_21 = e2 % 152.07/22.62 (16) ~ (all_52_14 = all_6_0) % 152.07/22.62 (17) all_56_31 = all_4_2 % 152.07/22.62 (18) all_58_11 = all_52_14 % 152.07/22.62 (19) all_36_2 = all_6_2 % 152.07/22.62 (20) all_56_1 = e3 | all_56_11 = e2 | all_56_21 = e1 | all_56_31 = e0 % 152.07/22.62 (21) all_58_6 = all_6_0 % 152.07/22.62 (22) all_58_7 = all_52_6 % 152.07/22.62 (23) op(e2, e2) = all_8_2 % 152.07/22.62 (24) ~ (all_36_0 = e0) | ~ (all_36_2 = e2) % 152.07/22.62 (25) ~ (all_52_6 = all_6_2) % 152.07/22.62 (26) op(all_6_2, all_6_2) = e3 % 152.07/22.62 (27) ~ (e2 = e0) % 152.07/22.62 (28) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0 % 152.07/22.62 (29) ~ (all_10_2 = all_6_0) % 152.07/22.62 (30) op(all_8_2, all_8_2) = all_8_1 % 152.07/22.62 % 152.07/22.62 Begin of proof % 152.07/22.62 | % 152.07/22.62 | COMBINE_EQS: (5), (15) imply: % 152.07/22.62 | (31) all_6_2 = e2 % 152.07/22.62 | % 152.07/22.62 | SIMP: (31) implies: % 152.07/22.62 | (32) all_6_2 = e2 % 152.07/22.62 | % 152.07/22.62 | COMBINE_EQS: (19), (32) imply: % 152.07/22.62 | (33) all_36_2 = e2 % 152.07/22.62 | % 152.07/22.62 | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (9), (10), (11), (12), (13), % 152.07/22.62 | (14), (15), (16), (17), (18), (20), (21), (22), (23), (24), (25), % 152.07/22.62 | (26), (27), (28), (29), (30), (32), (33) are inconsistent by % 152.07/22.62 | sub-proof #432. % 152.07/22.62 | % 152.07/22.62 End of proof % 152.07/22.62 % 152.07/22.62 Sub-proof #432 shows that the following formulas are inconsistent: % 152.07/22.62 ---------------------------------------------------------------- % 152.07/22.62 (1) all_56_11 = all_8_2 % 152.07/22.62 (2) all_52_6 = e1 % 152.07/22.62 (3) ~ (all_52_14 = all_4_2) % 152.07/22.62 (4) all_58_6 = e0 | all_58_7 = e0 | all_58_8 = e0 | all_58_11 = e0 % 152.07/22.62 (5) all_56_1 = all_10_2 % 152.07/22.62 (6) op(e2, all_8_2) = all_56_10 % 152.07/22.62 (7) ~ (all_52_6 = all_6_0) % 152.07/22.62 (8) ~ (e1 = e0) % 152.07/22.62 (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 152.07/22.62 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 152.07/22.62 (10) all_36_0 = all_6_0 % 152.07/22.62 (11) ~ (all_6_0 = all_6_2) % 152.07/22.62 (12) all_54_8 = all_6_0 % 152.07/22.62 (13) all_58_8 = all_6_2 % 152.07/22.62 (14) all_56_21 = e2 % 152.07/22.62 (15) ~ (all_52_14 = all_6_0) % 152.07/22.62 (16) all_56_31 = all_4_2 % 152.07/22.62 (17) all_58_11 = all_52_14 % 152.07/22.62 (18) all_36_2 = e2 % 152.07/22.62 (19) all_56_1 = e3 | all_56_11 = e2 | all_56_21 = e1 | all_56_31 = e0 % 152.07/22.62 (20) all_58_6 = all_6_0 % 152.07/22.62 (21) all_6_2 = e2 % 152.07/22.62 (22) all_58_7 = all_52_6 % 152.07/22.62 (23) op(e2, e2) = all_8_2 % 152.07/22.62 (24) ~ (all_36_0 = e0) | ~ (all_36_2 = e2) % 152.07/22.62 (25) ~ (all_52_6 = all_6_2) % 152.07/22.62 (26) op(all_6_2, all_6_2) = e3 % 152.07/22.62 (27) ~ (e2 = e0) % 152.07/22.62 (28) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0 % 152.07/22.62 (29) ~ (all_10_2 = all_6_0) % 152.07/22.62 (30) op(all_8_2, all_8_2) = all_8_1 % 152.07/22.62 % 152.07/22.62 Begin of proof % 152.07/22.62 | % 152.07/22.62 | COMBINE_EQS: (13), (21) imply: % 152.07/22.62 | (31) all_58_8 = e2 % 152.07/22.62 | % 152.07/22.62 | COMBINE_EQS: (2), (22) imply: % 152.07/22.62 | (32) all_58_7 = e1 % 152.07/22.62 | % 152.07/22.62 | REDUCE: (2), (7) imply: % 152.07/22.62 | (33) ~ (all_6_0 = e1) % 152.07/22.62 | % 152.07/22.62 | SIMP: (33) implies: % 152.07/22.62 | (34) ~ (all_6_0 = e1) % 152.07/22.62 | % 152.07/22.62 | REDUCE: (2), (21), (25) imply: % 152.07/22.62 | (35) ~ (e2 = e1) % 152.07/22.62 | % 152.07/22.62 | SIMP: (35) implies: % 152.07/22.62 | (36) ~ (e2 = e1) % 152.07/22.62 | % 152.07/22.62 | REDUCE: (11), (21) imply: % 152.07/22.62 | (37) ~ (all_6_0 = e2) % 152.07/22.62 | % 152.07/22.62 | REDUCE: (21), (26) imply: % 152.07/22.62 | (38) op(e2, e2) = e3 % 152.07/22.62 | % 152.07/22.62 | REF_CLOSE: (1), (3), (4), (5), (6), (8), (9), (10), (12), (14), (15), (16), % 152.07/22.62 | (17), (18), (19), (20), (23), (24), (27), (28), (29), (30), (31), % 152.07/22.62 | (32), (34), (36), (37), (38) are inconsistent by sub-proof #433. % 152.07/22.62 | % 152.07/22.62 End of proof % 152.07/22.62 % 152.07/22.62 Sub-proof #433 shows that the following formulas are inconsistent: % 152.07/22.62 ---------------------------------------------------------------- % 152.07/22.62 (1) all_56_11 = all_8_2 % 152.07/22.62 (2) ~ (all_52_14 = all_4_2) % 152.07/22.62 (3) all_58_6 = e0 | all_58_7 = e0 | all_58_8 = e0 | all_58_11 = e0 % 152.07/22.62 (4) ~ (all_6_0 = e2) % 152.07/22.62 (5) all_56_1 = all_10_2 % 152.07/22.62 (6) ~ (all_6_0 = e1) % 152.07/22.62 (7) op(e2, all_8_2) = all_56_10 % 152.07/22.62 (8) ~ (e1 = e0) % 152.07/22.62 (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 152.07/22.62 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 152.07/22.62 (10) all_36_0 = all_6_0 % 152.07/22.62 (11) all_54_8 = all_6_0 % 152.07/22.62 (12) all_56_21 = e2 % 152.07/22.62 (13) ~ (all_52_14 = all_6_0) % 152.07/22.62 (14) ~ (e2 = e1) % 152.07/22.62 (15) op(e2, e2) = e3 % 152.07/22.62 (16) all_56_31 = all_4_2 % 152.07/22.62 (17) all_58_11 = all_52_14 % 152.07/22.62 (18) all_36_2 = e2 % 152.07/22.62 (19) all_58_8 = e2 % 152.07/22.62 (20) all_56_1 = e3 | all_56_11 = e2 | all_56_21 = e1 | all_56_31 = e0 % 152.07/22.62 (21) all_58_6 = all_6_0 % 152.07/22.62 (22) op(e2, e2) = all_8_2 % 152.07/22.62 (23) ~ (all_36_0 = e0) | ~ (all_36_2 = e2) % 152.07/22.62 (24) ~ (e2 = e0) % 152.07/22.62 (25) all_58_7 = e1 % 152.07/22.62 (26) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0 % 152.07/22.62 (27) ~ (all_10_2 = all_6_0) % 152.07/22.62 (28) op(all_8_2, all_8_2) = all_8_1 % 152.07/22.62 % 152.07/22.62 Begin of proof % 152.07/22.62 | % 152.07/22.62 | BETA: splitting (23) gives: % 152.07/22.62 | % 152.07/22.62 | Case 1: % 152.07/22.62 | | % 152.07/22.62 | | (29) ~ (all_36_2 = e2) % 152.07/22.62 | | % 152.07/22.62 | | REDUCE: (18), (29) imply: % 152.07/22.62 | | (30) $false % 152.07/22.62 | | % 152.07/22.62 | | CLOSE: (30) is inconsistent. % 152.07/22.62 | | % 152.07/22.62 | Case 2: % 152.07/22.62 | | % 152.07/22.62 | | (31) ~ (all_36_0 = e0) % 152.07/22.62 | | % 152.07/22.62 | | REDUCE: (10), (31) imply: % 152.07/22.62 | | (32) ~ (all_6_0 = e0) % 152.07/22.62 | | % 152.07/22.62 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (11), (12), (13), % 152.07/22.62 | | (14), (15), (16), (17), (19), (20), (21), (22), (24), (25), (26), % 152.07/22.62 | | (27), (28), (32) are inconsistent by sub-proof #434. % 152.07/22.62 | | % 152.07/22.62 | End of split % 152.07/22.62 | % 152.07/22.62 End of proof % 152.07/22.62 % 152.07/22.62 Sub-proof #434 shows that the following formulas are inconsistent: % 152.07/22.62 ---------------------------------------------------------------- % 152.07/22.62 (1) all_56_11 = all_8_2 % 152.07/22.62 (2) ~ (all_52_14 = all_4_2) % 152.07/22.62 (3) all_58_6 = e0 | all_58_7 = e0 | all_58_8 = e0 | all_58_11 = e0 % 152.07/22.62 (4) ~ (all_6_0 = e2) % 152.07/22.62 (5) all_56_1 = all_10_2 % 152.07/22.62 (6) ~ (all_6_0 = e1) % 152.07/22.62 (7) op(e2, all_8_2) = all_56_10 % 152.07/22.62 (8) ~ (e1 = e0) % 152.07/22.62 (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 152.07/22.62 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 152.07/22.62 (10) all_54_8 = all_6_0 % 152.07/22.62 (11) all_56_21 = e2 % 152.07/22.62 (12) ~ (all_52_14 = all_6_0) % 152.07/22.62 (13) ~ (e2 = e1) % 152.07/22.62 (14) op(e2, e2) = e3 % 152.07/22.62 (15) all_56_31 = all_4_2 % 152.07/22.62 (16) all_58_11 = all_52_14 % 152.07/22.62 (17) all_58_8 = e2 % 152.07/22.62 (18) all_56_1 = e3 | all_56_11 = e2 | all_56_21 = e1 | all_56_31 = e0 % 152.07/22.62 (19) all_58_6 = all_6_0 % 152.07/22.62 (20) ~ (all_6_0 = e0) % 152.07/22.62 (21) op(e2, e2) = all_8_2 % 152.07/22.62 (22) ~ (e2 = e0) % 152.07/22.62 (23) all_58_7 = e1 % 152.07/22.62 (24) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0 % 152.07/22.62 (25) ~ (all_10_2 = all_6_0) % 152.07/22.62 (26) op(all_8_2, all_8_2) = all_8_1 % 152.07/22.62 % 152.07/22.62 Begin of proof % 152.07/22.62 | % 152.07/22.62 | BETA: splitting (3) gives: % 152.07/22.62 | % 152.07/22.62 | Case 1: % 152.07/22.62 | | % 152.07/22.62 | | (27) all_58_6 = e0 % 152.07/22.62 | | % 152.07/22.62 | | COMBINE_EQS: (19), (27) imply: % 152.07/22.62 | | (28) all_6_0 = e0 % 152.07/22.62 | | % 152.07/22.62 | | REDUCE: (20), (28) imply: % 152.07/22.62 | | (29) $false % 152.07/22.62 | | % 152.07/22.62 | | CLOSE: (29) is inconsistent. % 152.07/22.62 | | % 152.07/22.62 | Case 2: % 152.07/22.62 | | % 152.07/22.62 | | (30) all_58_7 = e0 | all_58_8 = e0 | all_58_11 = e0 % 152.07/22.62 | | % 152.07/22.62 | | BETA: splitting (30) gives: % 152.07/22.62 | | % 152.07/22.62 | | Case 1: % 152.07/22.62 | | | % 152.07/22.62 | | | (31) all_58_7 = e0 % 152.07/22.62 | | | % 152.07/22.62 | | | COMBINE_EQS: (23), (31) imply: % 152.07/22.62 | | | (32) e1 = e0 % 152.07/22.62 | | | % 152.07/22.62 | | | REDUCE: (8), (32) imply: % 152.07/22.62 | | | (33) $false % 152.07/22.62 | | | % 152.07/22.62 | | | CLOSE: (33) is inconsistent. % 152.07/22.62 | | | % 152.07/22.62 | | Case 2: % 152.07/22.62 | | | % 152.07/22.62 | | | (34) all_58_8 = e0 | all_58_11 = e0 % 152.07/22.62 | | | % 152.07/22.62 | | | BETA: splitting (34) gives: % 152.07/22.62 | | | % 152.07/22.62 | | | Case 1: % 152.07/22.62 | | | | % 152.07/22.62 | | | | (35) all_58_8 = e0 % 152.07/22.62 | | | | % 152.07/22.62 | | | | COMBINE_EQS: (17), (35) imply: % 152.07/22.62 | | | | (36) e2 = e0 % 152.07/22.62 | | | | % 152.07/22.62 | | | | REDUCE: (22), (36) imply: % 152.07/22.62 | | | | (37) $false % 152.07/22.62 | | | | % 152.07/22.62 | | | | CLOSE: (37) is inconsistent. % 152.07/22.62 | | | | % 152.07/22.62 | | | Case 2: % 152.07/22.62 | | | | % 152.07/22.62 | | | | (38) all_58_11 = e0 % 152.07/22.62 | | | | % 152.07/22.62 | | | | COMBINE_EQS: (16), (38) imply: % 152.07/22.62 | | | | (39) all_52_14 = e0 % 152.07/22.62 | | | | % 152.07/22.62 | | | | REDUCE: (12), (39) imply: % 152.07/22.62 | | | | (40) ~ (all_6_0 = e0) % 152.07/22.62 | | | | % 152.07/22.62 | | | | REDUCE: (2), (39) imply: % 152.07/22.62 | | | | (41) ~ (all_4_2 = e0) % 152.07/22.62 | | | | % 152.07/22.62 | | | | SIMP: (41) implies: % 152.07/22.62 | | | | (42) ~ (all_4_2 = e0) % 152.07/22.62 | | | | % 152.07/22.62 | | | | BETA: splitting (24) gives: % 152.07/22.62 | | | | % 152.07/22.62 | | | | Case 1: % 152.07/22.62 | | | | | % 152.07/22.62 | | | | | (43) all_54_8 = e3 % 152.07/22.62 | | | | | % 152.07/22.62 | | | | | COMBINE_EQS: (10), (43) imply: % 152.07/22.62 | | | | | (44) all_6_0 = e3 % 152.07/22.62 | | | | | % 152.07/22.62 | | | | | SIMP: (44) implies: % 152.07/22.62 | | | | | (45) all_6_0 = e3 % 152.07/22.62 | | | | | % 152.07/22.62 | | | | | REDUCE: (25), (45) imply: % 152.07/22.62 | | | | | (46) ~ (all_10_2 = e3) % 152.07/22.62 | | | | | % 152.07/22.62 | | | | | REDUCE: (4), (45) imply: % 152.07/22.62 | | | | | (47) ~ (e3 = e2) % 152.07/22.62 | | | | | % 152.07/22.62 | | | | | BETA: splitting (18) gives: % 152.07/22.62 | | | | | % 152.07/22.62 | | | | | Case 1: % 152.07/22.62 | | | | | | % 152.07/22.62 | | | | | | (48) all_56_1 = e3 % 152.07/22.62 | | | | | | % 152.07/22.62 | | | | | | COMBINE_EQS: (5), (48) imply: % 152.07/22.62 | | | | | | (49) all_10_2 = e3 % 152.07/22.62 | | | | | | % 152.07/22.62 | | | | | | REDUCE: (46), (49) imply: % 152.07/22.62 | | | | | | (50) $false % 152.07/22.62 | | | | | | % 152.07/22.62 | | | | | | CLOSE: (50) is inconsistent. % 152.07/22.62 | | | | | | % 152.07/22.62 | | | | | Case 2: % 152.07/22.62 | | | | | | % 152.07/22.62 | | | | | | (51) all_56_11 = e2 | all_56_21 = e1 | all_56_31 = e0 % 152.07/22.62 | | | | | | % 152.07/22.62 | | | | | | BETA: splitting (51) gives: % 152.07/22.62 | | | | | | % 152.07/22.62 | | | | | | Case 1: % 152.07/22.62 | | | | | | | % 152.07/22.62 | | | | | | | (52) all_56_11 = e2 % 152.07/22.62 | | | | | | | % 152.07/22.62 | | | | | | | COMBINE_EQS: (1), (52) imply: % 152.07/22.62 | | | | | | | (53) all_8_2 = e2 % 152.07/22.62 | | | | | | | % 152.07/22.62 | | | | | | | REDUCE: (26), (53) imply: % 152.07/22.62 | | | | | | | (54) op(e2, e2) = all_8_1 % 152.07/22.62 | | | | | | | % 152.07/22.62 | | | | | | | REDUCE: (7), (53) imply: % 152.07/22.62 | | | | | | | (55) op(e2, e2) = all_56_10 % 152.07/22.62 | | | | | | | % 152.07/22.62 | | | | | | | REDUCE: (21), (53) imply: % 152.07/22.62 | | | | | | | (56) op(e2, e2) = e2 % 152.07/22.62 | | | | | | | % 152.07/22.62 | | | | | | | GROUND_INST: instantiating (9) with e2, all_8_1, e2, e2, % 152.07/22.62 | | | | | | | simplifying with (54), (56) gives: % 152.07/22.62 | | | | | | | (57) all_8_1 = e2 % 152.07/22.62 | | | | | | | % 152.07/22.62 | | | | | | | GROUND_INST: instantiating (9) with all_8_1, all_56_10, e2, e2, % 152.07/22.62 | | | | | | | simplifying with (54), (55) gives: % 152.07/22.62 | | | | | | | (58) all_56_10 = all_8_1 % 152.07/22.62 | | | | | | | % 152.07/22.62 | | | | | | | GROUND_INST: instantiating (9) with e3, all_56_10, e2, e2, % 152.07/22.62 | | | | | | | simplifying with (14), (55) gives: % 152.07/22.62 | | | | | | | (59) all_56_10 = e3 % 152.07/22.62 | | | | | | | % 152.07/22.62 | | | | | | | COMBINE_EQS: (58), (59) imply: % 152.07/22.62 | | | | | | | (60) all_8_1 = e3 % 152.07/22.62 | | | | | | | % 152.07/22.62 | | | | | | | SIMP: (60) implies: % 152.07/22.62 | | | | | | | (61) all_8_1 = e3 % 152.07/22.62 | | | | | | | % 152.07/22.62 | | | | | | | COMBINE_EQS: (57), (61) imply: % 152.07/22.62 | | | | | | | (62) e3 = e2 % 152.07/22.62 | | | | | | | % 152.07/22.62 | | | | | | | SIMP: (62) implies: % 152.07/22.62 | | | | | | | (63) e3 = e2 % 152.07/22.62 | | | | | | | % 152.07/22.62 | | | | | | | REDUCE: (47), (63) imply: % 152.07/22.62 | | | | | | | (64) $false % 152.07/22.62 | | | | | | | % 152.07/22.62 | | | | | | | CLOSE: (64) is inconsistent. % 152.07/22.62 | | | | | | | % 152.07/22.62 | | | | | | Case 2: % 152.07/22.62 | | | | | | | % 152.07/22.62 | | | | | | | (65) all_56_21 = e1 | all_56_31 = e0 % 152.07/22.62 | | | | | | | % 152.07/22.62 | | | | | | | REF_CLOSE: (11), (13), (15), (42), (65) are inconsistent by % 152.07/22.62 | | | | | | | sub-proof #435. % 152.07/22.62 | | | | | | | % 152.07/22.62 | | | | | | End of split % 152.07/22.62 | | | | | | % 152.07/22.62 | | | | | End of split % 152.07/22.62 | | | | | % 152.07/22.62 | | | | Case 2: % 152.07/22.62 | | | | | % 152.07/22.62 | | | | | (66) all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0 % 152.07/22.62 | | | | | % 152.07/22.62 | | | | | REF_CLOSE: (4), (6), (10), (20), (66) are inconsistent by sub-proof % 152.07/22.62 | | | | | #451. % 152.07/22.62 | | | | | % 152.07/22.62 | | | | End of split % 152.07/22.62 | | | | % 152.07/22.62 | | | End of split % 152.07/22.62 | | | % 152.07/22.62 | | End of split % 152.07/22.62 | | % 152.07/22.62 | End of split % 152.07/22.62 | % 152.07/22.62 End of proof % 152.07/22.62 % 152.07/22.62 Sub-proof #435 shows that the following formulas are inconsistent: % 152.07/22.62 ---------------------------------------------------------------- % 152.07/22.62 (1) all_56_21 = e2 % 152.07/22.62 (2) ~ (e2 = e1) % 152.07/22.62 (3) ~ (all_4_2 = e0) % 152.07/22.62 (4) all_56_31 = all_4_2 % 152.07/22.62 (5) all_56_21 = e1 | all_56_31 = e0 % 152.07/22.62 % 152.07/22.62 Begin of proof % 152.07/22.62 | % 152.07/22.62 | BETA: splitting (5) gives: % 152.07/22.62 | % 152.07/22.62 | Case 1: % 152.07/22.62 | | % 152.07/22.62 | | (6) all_56_21 = e1 % 152.07/22.62 | | % 152.07/22.62 | | COMBINE_EQS: (1), (6) imply: % 152.07/22.62 | | (7) e2 = e1 % 152.07/22.62 | | % 152.07/22.62 | | REDUCE: (2), (7) imply: % 152.07/22.62 | | (8) $false % 152.07/22.62 | | % 152.07/22.62 | | CLOSE: (8) is inconsistent. % 152.07/22.62 | | % 152.07/22.62 | Case 2: % 152.07/22.62 | | % 152.07/22.62 | | (9) all_56_31 = e0 % 152.07/22.62 | | % 152.07/22.62 | | REF_CLOSE: (3), (4), (9) are inconsistent by sub-proof #675. % 152.07/22.62 | | % 152.07/22.62 | End of split % 152.07/22.62 | % 152.07/22.62 End of proof % 152.07/22.62 % 152.07/22.62 Sub-proof #436 shows that the following formulas are inconsistent: % 152.07/22.62 ---------------------------------------------------------------- % 152.07/22.62 (1) ~ (all_52_3 = all_6_0) % 152.07/22.62 (2) ~ (all_52_11 = all_6_2) % 152.07/22.62 (3) all_56_31 = e1 % 152.07/22.62 (4) all_54_10 = all_6_2 % 152.07/22.62 (5) all_54_12 = all_52_3 % 152.07/22.62 (6) all_52_11 = e0 % 152.07/22.62 (7) all_56_21 = all_6_2 % 152.07/22.62 (8) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 152.07/22.62 (9) ~ (all_56_21 = e3) | all_56_17 = e1 % 152.07/22.62 (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 152.07/22.62 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 152.07/22.62 (11) op(e0, all_4_1) = all_4_0 % 152.07/22.62 (12) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0 % 152.07/22.62 (13) op(all_4_2, all_4_2) = all_4_1 % 152.07/22.62 (14) ~ (all_52_3 = all_52_11) % 152.07/22.62 (15) all_56_31 = all_4_2 % 152.07/22.62 (16) op(e1, e1) = all_6_2 % 152.07/22.62 (17) op(e0, e3) = all_52_3 % 152.07/22.62 (18) ~ (all_6_2 = e2) % 152.07/22.62 (19) op(e1, all_6_2) = all_56_20 % 152.07/22.62 (20) all_56_17 = all_6_0 % 152.07/22.62 (21) op(all_6_2, all_6_2) = e3 % 152.07/22.62 (22) ~ (all_4_0 = e2) % 152.07/22.62 (23) ~ (all_4_0 = e3) % 152.07/22.62 % 152.07/22.62 Begin of proof % 152.07/22.62 | % 152.07/22.62 | COMBINE_EQS: (3), (15) imply: % 152.07/22.62 | (24) all_4_2 = e1 % 152.07/22.62 | % 152.07/22.62 | REDUCE: (6), (14) imply: % 152.07/22.62 | (25) ~ (all_52_3 = e0) % 152.07/22.62 | % 152.07/22.62 | REDUCE: (2), (6) imply: % 152.07/22.62 | (26) ~ (all_6_2 = e0) % 152.07/22.62 | % 152.07/22.62 | SIMP: (26) implies: % 152.07/22.62 | (27) ~ (all_6_2 = e0) % 152.07/22.62 | % 152.07/22.62 | REDUCE: (13), (24) imply: % 152.07/22.62 | (28) op(e1, e1) = all_4_1 % 152.07/22.62 | % 152.07/22.62 | GROUND_INST: instantiating (10) with all_6_2, all_4_1, e1, e1, simplifying % 152.07/22.62 | with (16), (28) gives: % 152.07/22.62 | (29) all_6_2 = all_4_1 % 152.07/22.62 | % 152.07/22.62 | COMBINE_EQS: (4), (29) imply: % 152.07/22.62 | (30) all_54_10 = all_4_1 % 152.07/22.62 | % 152.07/22.62 | COMBINE_EQS: (7), (29) imply: % 152.07/22.62 | (31) all_56_21 = all_4_1 % 152.07/22.62 | % 152.07/22.62 | REDUCE: (18), (29) imply: % 152.07/22.62 | (32) ~ (all_4_1 = e2) % 152.07/22.62 | % 152.07/22.62 | REDUCE: (27), (29) imply: % 152.07/22.62 | (33) ~ (all_4_1 = e0) % 152.07/22.62 | % 152.07/22.62 | REDUCE: (21), (29) imply: % 152.07/22.62 | (34) op(all_4_1, all_4_1) = e3 % 152.07/22.62 | % 152.07/22.62 | REDUCE: (19), (29) imply: % 152.07/22.62 | (35) op(e1, all_4_1) = all_56_20 % 152.07/22.62 | % 152.07/22.62 | REF_CLOSE: (1), (5), (8), (9), (10), (11), (12), (17), (20), (22), (23), (25), % 152.07/22.62 | (28), (30), (31), (32), (33), (34), (35) are inconsistent by % 152.07/22.62 | sub-proof #437. % 152.07/22.62 | % 152.07/22.62 End of proof % 152.07/22.62 % 152.07/22.62 Sub-proof #437 shows that the following formulas are inconsistent: % 152.07/22.62 ---------------------------------------------------------------- % 152.07/22.62 (1) ~ (all_52_3 = all_6_0) % 152.07/22.62 (2) op(all_4_1, all_4_1) = e3 % 152.07/22.62 (3) ~ (all_4_1 = e0) % 152.07/22.62 (4) all_54_12 = all_52_3 % 152.07/22.62 (5) op(e1, all_4_1) = all_56_20 % 152.07/22.62 (6) ~ (all_4_1 = e2) % 152.07/22.62 (7) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 152.07/22.62 (8) ~ (all_56_21 = e3) | all_56_17 = e1 % 152.07/22.62 (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 152.07/22.62 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 152.07/22.62 (10) op(e0, all_4_1) = all_4_0 % 152.07/22.62 (11) ~ (all_52_3 = e0) % 152.07/22.62 (12) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0 % 152.07/22.62 (13) all_56_21 = all_4_1 % 152.07/22.62 (14) all_54_10 = all_4_1 % 152.07/22.62 (15) op(e0, e3) = all_52_3 % 152.07/22.62 (16) op(e1, e1) = all_4_1 % 152.07/22.62 (17) all_56_17 = all_6_0 % 152.07/22.62 (18) ~ (all_4_0 = e2) % 152.07/22.62 (19) ~ (all_4_0 = e3) % 152.07/22.62 % 152.07/22.62 Begin of proof % 152.07/22.62 | % 152.07/22.62 | BETA: splitting (8) gives: % 152.07/22.62 | % 152.07/22.62 | Case 1: % 152.07/22.62 | | % 152.07/22.62 | | (20) ~ (all_56_21 = e3) % 152.07/22.62 | | % 152.07/22.62 | | REDUCE: (13), (20) imply: % 152.07/22.62 | | (21) ~ (all_4_1 = e3) % 152.07/22.62 | | % 152.07/22.62 | | REF_CLOSE: (2), (3), (5), (6), (7), (9), (14), (16), (21) are inconsistent % 152.07/22.62 | | by sub-proof #439. % 152.07/22.62 | | % 152.07/22.62 | Case 2: % 152.07/22.62 | | % 152.07/22.62 | | (22) all_56_21 = e3 % 152.07/22.62 | | (23) all_56_17 = e1 % 152.07/22.62 | | % 152.07/22.62 | | COMBINE_EQS: (17), (23) imply: % 152.07/22.62 | | (24) all_6_0 = e1 % 152.07/22.62 | | % 152.07/22.62 | | SIMP: (24) implies: % 152.07/22.62 | | (25) all_6_0 = e1 % 152.07/22.62 | | % 152.07/22.62 | | REF_CLOSE: (1), (4), (9), (10), (11), (12), (13), (15), (18), (19), (22), % 152.07/22.62 | | (25) are inconsistent by sub-proof #438. % 152.07/22.62 | | % 152.07/22.62 | End of split % 152.07/22.62 | % 152.07/22.62 End of proof % 152.07/22.62 % 152.07/22.62 Sub-proof #438 shows that the following formulas are inconsistent: % 152.07/22.62 ---------------------------------------------------------------- % 152.07/22.62 (1) ~ (all_52_3 = all_6_0) % 152.07/22.62 (2) all_56_21 = e3 % 152.07/22.62 (3) all_54_12 = all_52_3 % 152.07/22.62 (4) all_6_0 = e1 % 152.07/22.62 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 152.07/22.62 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 152.07/22.62 (6) op(e0, all_4_1) = all_4_0 % 152.07/22.62 (7) ~ (all_52_3 = e0) % 152.07/22.62 (8) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0 % 152.07/22.62 (9) all_56_21 = all_4_1 % 152.07/22.62 (10) op(e0, e3) = all_52_3 % 152.07/22.62 (11) ~ (all_4_0 = e2) % 152.07/22.62 (12) ~ (all_4_0 = e3) % 152.07/22.62 % 152.07/22.62 Begin of proof % 152.07/22.62 | % 152.07/22.62 | COMBINE_EQS: (2), (9) imply: % 152.07/22.62 | (13) all_4_1 = e3 % 152.07/22.62 | % 152.07/22.62 | SIMP: (13) implies: % 152.07/22.62 | (14) all_4_1 = e3 % 152.07/22.62 | % 152.07/22.62 | REDUCE: (1), (4) imply: % 152.07/22.62 | (15) ~ (all_52_3 = e1) % 152.07/22.62 | % 152.07/22.62 | REDUCE: (6), (14) imply: % 152.07/22.62 | (16) op(e0, e3) = all_4_0 % 152.07/22.62 | % 152.07/22.62 | REF_CLOSE: (3), (5), (7), (8), (10), (11), (12), (15), (16) are inconsistent % 152.07/22.62 | by sub-proof #522. % 152.07/22.62 | % 152.07/22.62 End of proof % 152.07/22.62 % 152.07/22.62 Sub-proof #439 shows that the following formulas are inconsistent: % 152.07/22.62 ---------------------------------------------------------------- % 152.07/22.62 (1) op(all_4_1, all_4_1) = e3 % 152.07/22.62 (2) ~ (all_4_1 = e0) % 152.07/22.62 (3) ~ (all_4_1 = e3) % 152.07/22.62 (4) op(e1, all_4_1) = all_56_20 % 152.07/22.62 (5) ~ (all_4_1 = e2) % 152.07/22.62 (6) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 152.07/22.62 (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 152.07/22.62 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 152.07/22.62 (8) all_54_10 = all_4_1 % 152.07/22.62 (9) op(e1, e1) = all_4_1 % 152.07/22.62 % 152.07/22.62 Begin of proof % 152.07/22.62 | % 152.07/22.62 | BETA: splitting (6) gives: % 152.07/22.62 | % 152.07/22.62 | Case 1: % 152.07/22.62 | | % 152.07/22.62 | | (10) all_54_10 = e3 % 152.07/22.62 | | % 152.07/22.62 | | COMBINE_EQS: (8), (10) imply: % 152.07/22.62 | | (11) all_4_1 = e3 % 152.07/22.62 | | % 152.07/22.62 | | REDUCE: (3), (11) imply: % 152.07/22.62 | | (12) $false % 152.07/22.62 | | % 152.07/22.62 | | CLOSE: (12) is inconsistent. % 152.07/22.62 | | % 152.07/22.62 | Case 2: % 152.07/22.62 | | % 152.07/22.62 | | (13) ~ (all_54_10 = e3) % 152.07/22.62 | | (14) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 152.07/22.62 | | % 152.07/22.62 | | BETA: splitting (14) gives: % 152.07/22.62 | | % 152.07/22.62 | | Case 1: % 152.07/22.62 | | | % 152.07/22.62 | | | (15) all_54_10 = e2 % 152.07/22.62 | | | % 152.07/22.62 | | | COMBINE_EQS: (8), (15) imply: % 152.07/22.62 | | | (16) all_4_1 = e2 % 152.07/22.62 | | | % 152.07/22.62 | | | REDUCE: (5), (16) imply: % 152.07/22.62 | | | (17) $false % 152.07/22.62 | | | % 152.07/22.62 | | | CLOSE: (17) is inconsistent. % 152.07/22.62 | | | % 152.07/22.62 | | Case 2: % 152.07/22.62 | | | % 152.07/22.62 | | | (18) all_54_10 = e1 | all_54_10 = e0 % 152.07/22.62 | | | % 152.07/22.62 | | | BETA: splitting (18) gives: % 152.07/22.62 | | | % 152.07/22.62 | | | Case 1: % 152.07/22.62 | | | | % 152.07/22.62 | | | | (19) all_54_10 = e1 % 152.07/22.62 | | | | % 152.07/22.62 | | | | COMBINE_EQS: (8), (19) imply: % 152.07/22.62 | | | | (20) all_4_1 = e1 % 152.07/22.62 | | | | % 152.07/22.62 | | | | REF_CLOSE: (1), (3), (4), (7), (9), (20) are inconsistent by sub-proof % 152.07/22.62 | | | | #440. % 152.07/22.62 | | | | % 152.07/22.62 | | | Case 2: % 152.07/22.62 | | | | % 152.07/22.62 | | | | (21) all_54_10 = e0 % 152.07/22.62 | | | | % 152.07/22.62 | | | | COMBINE_EQS: (8), (21) imply: % 152.07/22.62 | | | | (22) all_4_1 = e0 % 152.07/22.62 | | | | % 152.07/22.62 | | | | REDUCE: (2), (22) imply: % 152.07/22.62 | | | | (23) $false % 152.07/22.62 | | | | % 152.07/22.62 | | | | CLOSE: (23) is inconsistent. % 152.07/22.62 | | | | % 152.07/22.62 | | | End of split % 152.07/22.62 | | | % 152.07/22.62 | | End of split % 152.07/22.62 | | % 152.07/22.62 | End of split % 152.07/22.62 | % 152.07/22.62 End of proof % 152.07/22.62 % 152.07/22.62 Sub-proof #440 shows that the following formulas are inconsistent: % 152.07/22.62 ---------------------------------------------------------------- % 152.07/22.62 (1) op(all_4_1, all_4_1) = e3 % 152.07/22.62 (2) ~ (all_4_1 = e3) % 152.07/22.62 (3) op(e1, all_4_1) = all_56_20 % 152.07/22.62 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 152.07/22.62 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 152.07/22.62 (5) all_4_1 = e1 % 152.07/22.62 (6) op(e1, e1) = all_4_1 % 152.07/22.62 % 152.07/22.62 Begin of proof % 152.07/22.62 | % 152.07/22.62 | REDUCE: (2), (5) imply: % 152.07/22.62 | (7) ~ (e3 = e1) % 152.07/22.62 | % 152.07/22.62 | SIMP: (7) implies: % 152.07/22.62 | (8) ~ (e3 = e1) % 152.07/22.62 | % 152.07/22.62 | REDUCE: (1), (5) imply: % 152.07/22.62 | (9) op(e1, e1) = e3 % 152.07/22.62 | % 152.07/22.62 | REDUCE: (3), (5) imply: % 152.07/22.63 | (10) op(e1, e1) = all_56_20 % 152.07/22.63 | % 152.07/22.63 | REDUCE: (5), (6) imply: % 152.07/22.63 | (11) op(e1, e1) = e1 % 152.07/22.63 | % 152.07/22.63 | REF_CLOSE: (4), (8), (9), (10), (11) are inconsistent by sub-proof #516. % 152.07/22.63 | % 152.07/22.63 End of proof % 152.07/22.63 % 152.07/22.63 Sub-proof #441 shows that the following formulas are inconsistent: % 152.07/22.63 ---------------------------------------------------------------- % 152.07/22.63 (1) all_54_10 = all_6_2 % 152.07/22.63 (2) all_56_21 = all_6_2 % 152.07/22.63 (3) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 152.07/22.63 (4) all_56_17 = e0 % 152.07/22.63 (5) ~ (all_56_21 = e3) | all_56_17 = e1 % 152.07/22.63 (6) ~ (e1 = e0) % 152.07/22.63 (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 152.07/22.63 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 152.07/22.63 (8) ~ (all_6_2 = e0) % 152.07/22.63 (9) op(e1, e1) = all_6_2 % 152.07/22.63 (10) ~ (all_6_2 = e2) % 152.07/22.63 (11) op(e1, all_6_2) = all_56_20 % 152.07/22.63 (12) op(all_6_2, all_6_2) = e3 % 152.07/22.63 % 152.07/22.63 Begin of proof % 152.07/22.63 | % 152.07/22.63 | BETA: splitting (5) gives: % 152.07/22.63 | % 152.07/22.63 | Case 1: % 152.07/22.63 | | % 152.07/22.63 | | (13) ~ (all_56_21 = e3) % 152.07/22.63 | | % 152.07/22.63 | | REDUCE: (2), (13) imply: % 152.07/22.63 | | (14) ~ (all_6_2 = e3) % 152.07/22.63 | | % 152.07/22.63 | | REF_CLOSE: (1), (3), (7), (8), (9), (10), (11), (12), (14) are inconsistent % 152.07/22.63 | | by sub-proof #459. % 152.07/22.63 | | % 152.07/22.63 | Case 2: % 152.07/22.63 | | % 152.07/22.63 | | (15) all_56_17 = e1 % 152.07/22.63 | | % 152.07/22.63 | | COMBINE_EQS: (4), (15) imply: % 152.07/22.63 | | (16) e1 = e0 % 152.07/22.63 | | % 152.07/22.63 | | REDUCE: (6), (16) imply: % 152.07/22.63 | | (17) $false % 152.07/22.63 | | % 152.07/22.63 | | CLOSE: (17) is inconsistent. % 152.07/22.63 | | % 152.07/22.63 | End of split % 152.07/22.63 | % 152.07/22.63 End of proof % 152.07/22.63 % 152.07/22.63 Sub-proof #442 shows that the following formulas are inconsistent: % 152.07/22.63 ---------------------------------------------------------------- % 152.07/22.63 (1) all_56_11 = all_8_2 % 152.07/22.63 (2) ~ (all_56_11 = e1) | all_56_13 = e2 % 152.07/22.63 (3) ~ (all_52_11 = all_6_2) % 152.07/22.63 (4) ~ (all_52_4 = all_52_8) % 152.07/22.63 (5) ~ (all_52_8 = all_52_9) % 152.07/22.63 (6) all_54_9 = all_52_6 % 152.07/22.63 (7) op(e2, all_8_1) = all_8_0 % 152.07/22.63 (8) ~ (all_8_1 = e1) % 152.07/22.63 (9) ~ (all_52_1 = all_52_9) % 152.07/22.63 (10) all_54_10 = all_6_2 % 152.07/22.63 (11) all_54_0 = all_10_2 % 152.07/22.63 (12) ~ (all_8_0 = e1) % 152.07/22.63 (13) all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2 % 152.07/22.63 (14) ~ (all_52_9 = all_8_2) % 152.07/22.63 (15) ~ (all_52_12 = all_52_13) % 152.07/22.63 (16) ~ (all_8_1 = e3) % 152.07/22.63 (17) ~ (e3 = e2) % 152.07/22.63 (18) op(e0, e0) = all_4_2 % 152.07/22.63 (19) all_58_4 = all_52_8 % 152.07/22.63 (20) all_54_5 = all_8_2 % 152.07/22.63 (21) ~ (all_52_6 = all_52_14) % 152.07/22.63 (22) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 152.07/22.63 (23) ~ (all_6_0 = e2) % 152.07/22.63 (24) all_54_15 = all_4_2 % 152.07/22.63 (25) all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1 % 152.07/22.63 (26) ~ (all_10_1 = e1) % 152.07/22.63 (27) all_56_21 = all_6_2 % 152.07/22.63 (28) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 152.07/22.63 (29) ~ (all_52_7 = all_8_2) % 152.07/22.63 (30) all_56_1 = all_10_2 % 152.07/22.63 (31) op(e3, all_10_1) = all_10_0 % 152.07/22.63 (32) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0 % 152.07/22.63 (33) all_58_5 = all_52_9 % 152.07/22.63 (34) all_54_1 = all_52_4 % 152.07/22.63 (35) all_58_9 = all_52_12 % 152.07/22.63 (36) ~ (all_52_1 = all_6_0) % 152.07/22.63 (37) ~ (all_56_1 = e1) | all_56_5 = e3 % 152.07/22.63 (38) all_58_1 = all_52_4 % 152.07/22.63 (39) all_58_13 = all_52_7 % 152.07/22.63 (40) op(e3, e3) = all_10_2 % 152.07/22.63 (41) ~ (all_52_8 = all_6_2) % 152.07/22.63 (42) ~ (all_52_6 = all_6_0) % 152.07/22.63 (43) all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1 % 152.07/22.63 (44) ~ (all_56_21 = e3) | all_56_17 = e1 % 152.07/22.63 (45) all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2 % 152.07/22.63 (46) ~ (all_52_1 = all_8_2) % 152.07/22.63 (47) all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2 % 152.07/22.63 (48) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 152.07/22.63 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 152.07/22.63 (49) ~ (all_52_3 = all_10_2) % 152.07/22.63 (50) ~ (all_56_11 = e3) | all_56_9 = e2 % 152.07/22.63 (51) all_56_7 = all_52_12 % 152.07/22.63 (52) ~ (all_10_1 = e2) % 152.07/22.63 (53) ~ (all_6_0 = all_6_2) % 152.07/22.63 (54) all_56_13 = all_52_9 % 152.07/22.63 (55) ~ (all_52_1 = all_52_13) % 152.07/22.63 (56) ~ (all_4_2 = e1) % 152.07/22.63 (57) all_54_8 = all_6_0 % 152.07/22.63 (58) all_58_8 = all_6_2 % 152.07/22.63 (59) ~ (all_52_8 = all_10_2) % 152.07/22.63 (60) ~ (all_56_1 = e2) | all_56_3 = e3 % 152.07/22.63 (61) ~ (all_56_1 = e0) | all_56_7 = e3 % 152.07/22.63 (62) ~ (all_52_14 = all_6_0) % 152.07/22.63 (63) all_56_5 = all_52_8 % 152.07/22.63 (64) op(all_4_2, all_4_2) = all_4_1 % 152.07/22.63 (65) all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3 % 152.07/22.63 (66) all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1 % 152.07/22.63 (67) all_58_3 = all_8_2 % 152.07/22.63 (68) all_56_3 = all_52_4 % 152.07/22.63 (69) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0 % 152.07/22.63 (70) all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1 % 152.07/22.63 (71) all_56_31 = all_4_2 % 152.07/22.63 (72) all_58_11 = all_52_14 % 152.07/22.63 (73) all_54_7 = all_52_13 % 152.07/22.63 (74) all_56_1 = e3 | all_56_11 = e2 | all_56_21 = e1 | all_56_31 = e0 % 152.07/22.63 (75) ~ (all_10_0 = e1) % 152.07/22.63 (76) ~ (all_52_13 = all_4_2) % 152.07/22.63 (77) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0 % 152.07/22.63 (78) all_56_23 = all_52_14 % 152.07/22.63 (79) all_58_6 = all_6_0 % 152.07/22.63 (80) op(e1, e1) = all_6_2 % 152.07/22.63 (81) ~ (all_52_6 = all_8_2) % 152.07/22.63 (82) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0 % 152.07/22.63 (83) all_58_15 = all_4_2 % 152.07/22.63 (84) ~ (all_6_2 = e2) % 152.07/22.63 (85) all_58_2 = all_52_1 % 152.07/22.63 (86) ~ (all_52_9 = all_6_2) % 152.07/22.63 (87) all_58_7 = all_52_6 % 152.07/22.63 (88) all_58_10 = all_52_13 % 152.07/22.63 (89) ~ (all_52_12 = all_4_2) % 152.07/22.63 (90) op(all_10_2, all_10_2) = all_10_1 % 152.07/22.63 (91) all_58_0 = all_10_2 % 152.07/22.63 (92) op(e1, all_6_2) = all_56_20 % 152.07/22.63 (93) all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1 % 152.07/22.63 (94) all_56_17 = all_6_0 % 152.07/22.63 (95) op(e2, e2) = all_8_2 % 152.07/22.63 (96) ~ (all_52_4 = all_52_12) % 152.07/22.63 (97) op(e2, e0) = all_52_13 % 152.07/22.63 (98) ~ (all_52_8 = all_52_12) % 152.07/22.63 (99) ~ (all_56_21 = e0) | all_56_23 = e1 % 152.07/22.63 (100) op(e0, all_4_2) = all_56_30 % 152.07/22.63 (101) ~ (all_52_6 = all_6_2) % 152.07/22.63 (102) ~ (all_8_2 = e0) % 152.07/22.63 (103) op(all_6_2, all_6_2) = e3 % 152.07/22.63 (104) op(e3, all_10_2) = all_56_0 % 152.07/22.63 (105) ~ (all_52_14 = all_6_2) % 152.07/22.63 (106) op(e1, all_52_11) = all_56_28 % 152.07/22.63 (107) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0 % 152.07/22.63 (108) ~ (all_10_2 = all_6_0) % 152.07/22.63 (109) ~ (all_52_4 = all_10_2) % 152.07/22.63 (110) all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3 % 152.07/22.63 (111) ~ (all_52_4 = all_8_2) % 152.07/22.63 (112) op(all_8_2, all_8_2) = all_8_1 % 152.07/22.63 (113) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 152.07/22.63 (114) all_58_14 = all_52_11 % 152.07/22.63 (115) all_56_9 = all_52_1 % 152.07/22.63 (116) ~ (all_52_1 = all_10_2) % 152.07/22.63 (117) all_58_12 = all_52_3 % 152.07/22.63 (118) all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3 % 152.07/22.63 % 152.07/22.63 Begin of proof % 152.07/22.63 | % 152.07/22.63 | BETA: splitting (44) gives: % 152.07/22.63 | % 152.07/22.63 | Case 1: % 152.07/22.63 | | % 152.07/22.63 | | (119) ~ (all_56_21 = e3) % 152.07/22.63 | | % 152.07/22.63 | | REDUCE: (27), (119) imply: % 152.07/22.63 | | (120) ~ (all_6_2 = e3) % 152.07/22.63 | | % 152.07/22.63 | | BETA: splitting (50) gives: % 152.07/22.63 | | % 152.07/22.63 | | Case 1: % 152.07/22.63 | | | % 152.07/22.63 | | | (121) ~ (all_56_11 = e3) % 152.07/22.63 | | | % 152.07/22.63 | | | REDUCE: (1), (121) imply: % 152.07/22.63 | | | (122) ~ (all_8_2 = e3) % 152.07/22.63 | | | % 152.07/22.63 | | | BETA: splitting (37) gives: % 152.07/22.63 | | | % 152.07/22.63 | | | Case 1: % 152.07/22.63 | | | | % 152.07/22.63 | | | | (123) ~ (all_56_1 = e1) % 152.07/22.63 | | | | % 152.07/22.63 | | | | REDUCE: (30), (123) imply: % 152.07/22.63 | | | | (124) ~ (all_10_2 = e1) % 152.07/22.63 | | | | % 152.07/22.63 | | | | BETA: splitting (60) gives: % 152.07/22.63 | | | | % 152.07/22.63 | | | | Case 1: % 152.07/22.63 | | | | | % 152.07/22.63 | | | | | (125) ~ (all_56_1 = e2) % 152.07/22.63 | | | | | % 152.07/22.63 | | | | | REDUCE: (30), (125) imply: % 152.07/22.63 | | | | | (126) ~ (all_10_2 = e2) % 152.07/22.63 | | | | | % 152.07/22.63 | | | | | BETA: splitting (2) gives: % 152.07/22.63 | | | | | % 152.07/22.63 | | | | | Case 1: % 152.07/22.63 | | | | | | % 152.07/22.63 | | | | | | (127) ~ (all_56_11 = e1) % 152.07/22.63 | | | | | | % 152.07/22.63 | | | | | | REDUCE: (1), (127) imply: % 152.07/22.63 | | | | | | (128) ~ (all_8_2 = e1) % 152.07/22.63 | | | | | | % 152.07/22.63 | | | | | | REF_CLOSE: (10), (20), (23), (27), (28), (47), (48), (58), (72), % 152.07/22.63 | | | | | | (78), (79), (80), (81), (84), (87), (92), (99), (102), % 152.07/22.63 | | | | | | (103), (105), (113), (120), (122), (128) are inconsistent % 152.07/22.63 | | | | | | by sub-proof #458. % 152.07/22.63 | | | | | | % 152.07/22.63 | | | | | Case 2: % 152.07/22.63 | | | | | | % 152.07/22.63 | | | | | | (129) all_56_13 = e2 % 152.07/22.63 | | | | | | (130) all_56_11 = e1 % 152.07/22.63 | | | | | | % 152.07/22.63 | | | | | | COMBINE_EQS: (1), (130) imply: % 152.07/22.63 | | | | | | (131) all_8_2 = e1 % 152.07/22.63 | | | | | | % 152.07/22.63 | | | | | | COMBINE_EQS: (54), (129) imply: % 152.07/22.63 | | | | | | (132) all_52_9 = e2 % 152.07/22.63 | | | | | | % 152.07/22.63 | | | | | | COMBINE_EQS: (33), (132) imply: % 152.07/22.63 | | | | | | (133) all_58_5 = e2 % 152.07/22.63 | | | | | | % 152.07/22.63 | | | | | | REDUCE: (9), (132) imply: % 152.07/22.63 | | | | | | (134) ~ (all_52_1 = e2) % 152.07/22.63 | | | | | | % 152.07/22.63 | | | | | | REDUCE: (29), (131) imply: % 152.07/22.63 | | | | | | (135) ~ (all_52_7 = e1) % 152.07/22.63 | | | | | | % 152.07/22.63 | | | | | | REDUCE: (14), (131), (132) imply: % 152.07/22.63 | | | | | | (136) ~ (e2 = e1) % 152.07/22.63 | | | | | | % 152.07/22.63 | | | | | | REDUCE: (122), (131) imply: % 152.07/22.63 | | | | | | (137) ~ (e3 = e1) % 152.07/22.63 | | | | | | % 152.07/22.63 | | | | | | SIMP: (137) implies: % 152.07/22.63 | | | | | | (138) ~ (e3 = e1) % 152.07/22.63 | | | | | | % 152.07/22.63 | | | | | | BETA: splitting (45) gives: % 152.07/22.63 | | | | | | % 152.07/22.63 | | | | | | Case 1: % 152.07/22.63 | | | | | | | % 152.07/22.63 | | | | | | | (139) all_58_0 = e2 % 152.07/22.63 | | | | | | | % 152.07/22.63 | | | | | | | COMBINE_EQS: (91), (139) imply: % 152.07/22.63 | | | | | | | (140) all_10_2 = e2 % 152.07/22.63 | | | | | | | % 152.07/22.63 | | | | | | | REDUCE: (126), (140) imply: % 152.07/22.63 | | | | | | | (141) $false % 152.07/22.63 | | | | | | | % 152.07/22.63 | | | | | | | CLOSE: (141) is inconsistent. % 152.07/22.63 | | | | | | | % 152.07/22.63 | | | | | | Case 2: % 152.07/22.63 | | | | | | | % 152.07/22.63 | | | | | | | (142) all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2 % 152.07/22.63 | | | | | | | % 152.07/22.63 | | | | | | | BETA: splitting (142) gives: % 152.07/22.63 | | | | | | | % 152.07/22.63 | | | | | | | Case 1: % 152.07/22.63 | | | | | | | | % 152.07/22.63 | | | | | | | | (143) all_58_2 = e2 % 152.07/22.63 | | | | | | | | % 152.07/22.63 | | | | | | | | COMBINE_EQS: (85), (143) imply: % 152.07/22.63 | | | | | | | | (144) all_52_1 = e2 % 152.07/22.63 | | | | | | | | % 152.07/22.63 | | | | | | | | REDUCE: (134), (144) imply: % 152.07/22.63 | | | | | | | | (145) $false % 152.07/22.63 | | | | | | | | % 152.07/22.63 | | | | | | | | CLOSE: (145) is inconsistent. % 152.07/22.63 | | | | | | | | % 152.07/22.63 | | | | | | | Case 2: % 152.07/22.63 | | | | | | | | % 152.07/22.63 | | | | | | | | (146) all_58_6 = e2 | all_58_12 = e2 % 152.07/22.63 | | | | | | | | % 152.07/22.63 | | | | | | | | BETA: splitting (146) gives: % 152.07/22.63 | | | | | | | | % 152.07/22.63 | | | | | | | | Case 1: % 152.07/22.63 | | | | | | | | | % 152.07/22.63 | | | | | | | | | (147) all_58_6 = e2 % 152.07/22.63 | | | | | | | | | % 152.07/22.63 | | | | | | | | | REF_CLOSE: (23), (79), (147) are inconsistent by sub-proof % 152.07/22.63 | | | | | | | | | #461. % 152.07/22.63 | | | | | | | | | % 152.07/22.63 | | | | | | | | Case 2: % 152.07/22.63 | | | | | | | | | % 152.07/22.63 | | | | | | | | | (148) all_58_12 = e2 % 152.07/22.63 | | | | | | | | | % 152.07/22.63 | | | | | | | | | COMBINE_EQS: (117), (148) imply: % 152.07/22.63 | | | | | | | | | (149) all_52_3 = e2 % 152.07/22.63 | | | | | | | | | % 152.07/22.63 | | | | | | | | | SIMP: (149) implies: % 152.07/22.63 | | | | | | | | | (150) all_52_3 = e2 % 152.07/22.63 | | | | | | | | | % 152.07/22.63 | | | | | | | | | REDUCE: (49), (150) imply: % 152.07/22.63 | | | | | | | | | (151) ~ (all_10_2 = e2) % 152.07/22.63 | | | | | | | | | % 152.07/22.63 | | | | | | | | | REF_CLOSE: (11), (17), (19), (22), (30), (39), (51), (56), % 152.07/22.63 | | | | | | | | | (58), (59), (61), (65), (83), (93), (98), (120), % 152.07/22.63 | | | | | | | | | (124), (126), (133), (135), (136), (138), (148) are % 152.07/22.63 | | | | | | | | | inconsistent by sub-proof #455. % 152.07/22.63 | | | | | | | | | % 152.07/22.63 | | | | | | | | End of split % 152.07/22.63 | | | | | | | | % 152.07/22.63 | | | | | | | End of split % 152.07/22.63 | | | | | | | % 152.07/22.63 | | | | | | End of split % 152.07/22.63 | | | | | | % 152.07/22.63 | | | | | End of split % 152.07/22.63 | | | | | % 152.07/22.63 | | | | Case 2: % 152.07/22.63 | | | | | % 152.07/22.63 | | | | | (152) all_56_3 = e3 % 152.07/22.63 | | | | | (153) all_56_1 = e2 % 152.07/22.63 | | | | | % 152.07/22.63 | | | | | COMBINE_EQS: (30), (153) imply: % 152.07/22.63 | | | | | (154) all_10_2 = e2 % 152.07/22.63 | | | | | % 152.07/22.63 | | | | | COMBINE_EQS: (68), (152) imply: % 152.07/22.63 | | | | | (155) all_52_4 = e3 % 152.07/22.63 | | | | | % 152.07/22.63 | | | | | REDUCE: (111), (155) imply: % 152.07/22.63 | | | | | (156) ~ (all_8_2 = e3) % 152.07/22.63 | | | | | % 152.07/22.63 | | | | | REDUCE: (108), (154) imply: % 152.07/22.63 | | | | | (157) ~ (all_6_0 = e2) % 152.07/22.63 | | | | | % 152.07/22.63 | | | | | REDUCE: (90), (154) imply: % 152.07/22.63 | | | | | (158) op(e2, e2) = all_10_1 % 152.07/22.63 | | | | | % 152.07/22.63 | | | | | GROUND_INST: instantiating (48) with all_8_2, all_10_1, e2, e2, % 152.07/22.63 | | | | | simplifying with (95), (158) gives: % 152.07/22.63 | | | | | (159) all_10_1 = all_8_2 % 152.07/22.63 | | | | | % 152.07/22.63 | | | | | REDUCE: (26), (159) imply: % 152.07/22.63 | | | | | (160) ~ (all_8_2 = e1) % 152.07/22.63 | | | | | % 152.07/22.63 | | | | | REF_CLOSE: (10), (20), (23), (27), (28), (47), (48), (58), (72), (78), % 152.07/22.63 | | | | | (79), (80), (81), (84), (87), (92), (99), (102), (103), % 152.07/22.63 | | | | | (105), (113), (120), (122), (160) are inconsistent by % 152.07/22.63 | | | | | sub-proof #458. % 152.07/22.63 | | | | | % 152.07/22.63 | | | | End of split % 152.07/22.63 | | | | % 152.07/22.63 | | | Case 2: % 152.07/22.63 | | | | % 152.07/22.63 | | | | (161) all_56_5 = e3 % 152.07/22.63 | | | | (162) all_56_1 = e1 % 152.07/22.63 | | | | % 152.07/22.63 | | | | COMBINE_EQS: (30), (162) imply: % 152.07/22.63 | | | | (163) all_10_2 = e1 % 152.07/22.63 | | | | % 152.07/22.63 | | | | COMBINE_EQS: (63), (161) imply: % 152.07/22.63 | | | | (164) all_52_8 = e3 % 152.07/22.63 | | | | % 152.07/22.63 | | | | REDUCE: (5), (164) imply: % 152.07/22.63 | | | | (165) ~ (all_52_9 = e3) % 152.07/22.63 | | | | % 152.07/22.63 | | | | SIMP: (165) implies: % 152.07/22.63 | | | | (166) ~ (all_52_9 = e3) % 152.07/22.63 | | | | % 152.07/22.63 | | | | REDUCE: (41), (164) imply: % 152.07/22.63 | | | | (167) ~ (all_6_2 = e3) % 152.07/22.63 | | | | % 152.07/22.63 | | | | REDUCE: (90), (163) imply: % 152.07/22.63 | | | | (168) op(e1, e1) = all_10_1 % 152.07/22.63 | | | | % 152.07/22.63 | | | | GROUND_INST: instantiating (48) with all_6_2, all_10_1, e1, e1, % 152.07/22.63 | | | | simplifying with (80), (168) gives: % 152.07/22.63 | | | | (169) all_10_1 = all_6_2 % 152.07/22.63 | | | | % 152.07/22.63 | | | | REDUCE: (26), (169) imply: % 152.07/22.63 | | | | (170) ~ (all_6_2 = e1) % 152.07/22.63 | | | | % 152.07/22.63 | | | | BETA: splitting (28) gives: % 152.07/22.63 | | | | % 152.07/22.63 | | | | Case 1: % 152.07/22.63 | | | | | % 152.07/22.63 | | | | | (171) all_54_10 = e3 % 152.07/22.63 | | | | | % 152.07/22.63 | | | | | REF_CLOSE: (10), (120), (171) are inconsistent by sub-proof #736. % 152.07/22.63 | | | | | % 152.07/22.63 | | | | Case 2: % 152.07/22.63 | | | | | % 152.07/22.63 | | | | | (172) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 152.07/22.63 | | | | | % 152.07/22.63 | | | | | BETA: splitting (172) gives: % 152.07/22.63 | | | | | % 152.07/22.63 | | | | | Case 1: % 152.07/22.63 | | | | | | % 152.07/22.63 | | | | | | (173) all_54_10 = e2 % 152.07/22.63 | | | | | | % 152.07/22.63 | | | | | | REF_CLOSE: (10), (84), (173) are inconsistent by sub-proof #735. % 152.07/22.63 | | | | | | % 152.07/22.63 | | | | | Case 2: % 152.07/22.63 | | | | | | % 152.07/22.63 | | | | | | (174) all_54_10 = e1 | all_54_10 = e0 % 152.07/22.63 | | | | | | % 152.07/22.63 | | | | | | BETA: splitting (174) gives: % 152.07/22.63 | | | | | | % 152.07/22.63 | | | | | | Case 1: % 152.07/22.63 | | | | | | | % 152.07/22.63 | | | | | | | (175) all_54_10 = e1 % 152.07/22.63 | | | | | | | % 152.07/22.63 | | | | | | | REF_CLOSE: (10), (170), (175) are inconsistent by sub-proof #606. % 152.07/22.63 | | | | | | | % 152.07/22.63 | | | | | | Case 2: % 152.07/22.63 | | | | | | | % 152.07/22.63 | | | | | | | (176) all_54_10 = e0 % 152.07/22.63 | | | | | | | % 152.07/22.63 | | | | | | | COMBINE_EQS: (10), (176) imply: % 152.07/22.63 | | | | | | | (177) all_6_2 = e0 % 152.07/22.63 | | | | | | | % 152.07/22.63 | | | | | | | SIMP: (177) implies: % 152.07/22.63 | | | | | | | (178) all_6_2 = e0 % 152.07/22.63 | | | | | | | % 152.07/22.63 | | | | | | | COMBINE_EQS: (27), (178) imply: % 152.07/22.63 | | | | | | | (179) all_56_21 = e0 % 152.07/22.63 | | | | | | | % 152.07/22.63 | | | | | | | REDUCE: (101), (178) imply: % 152.07/22.63 | | | | | | | (180) ~ (all_52_6 = e0) % 152.07/22.63 | | | | | | | % 152.07/22.63 | | | | | | | REDUCE: (105), (178) imply: % 152.07/22.63 | | | | | | | (181) ~ (all_52_14 = e0) % 152.07/22.63 | | | | | | | % 152.07/22.63 | | | | | | | REDUCE: (53), (178) imply: % 152.07/22.63 | | | | | | | (182) ~ (all_6_0 = e0) % 152.07/22.63 | | | | | | | % 152.07/22.63 | | | | | | | REDUCE: (103), (178) imply: % 152.07/22.63 | | | | | | | (183) op(e0, e0) = e3 % 152.07/22.63 | | | | | | | % 152.07/22.63 | | | | | | | BETA: splitting (99) gives: % 152.07/22.63 | | | | | | | % 152.07/22.63 | | | | | | | Case 1: % 152.07/22.63 | | | | | | | | % 152.07/22.63 | | | | | | | | (184) ~ (all_56_21 = e0) % 152.07/22.63 | | | | | | | | % 152.07/22.63 | | | | | | | | REDUCE: (179), (184) imply: % 152.07/22.63 | | | | | | | | (185) $false % 152.07/22.63 | | | | | | | | % 152.07/22.63 | | | | | | | | CLOSE: (185) is inconsistent. % 152.07/22.63 | | | | | | | | % 152.07/22.63 | | | | | | | Case 2: % 152.07/22.63 | | | | | | | | % 152.07/22.63 | | | | | | | | (186) all_56_23 = e1 % 152.07/22.63 | | | | | | | | % 152.07/22.63 | | | | | | | | COMBINE_EQS: (78), (186) imply: % 152.07/22.63 | | | | | | | | (187) all_52_14 = e1 % 152.07/22.63 | | | | | | | | % 152.07/22.63 | | | | | | | | SIMP: (187) implies: % 152.07/22.63 | | | | | | | | (188) all_52_14 = e1 % 152.07/22.63 | | | | | | | | % 152.07/22.63 | | | | | | | | REDUCE: (21), (188) imply: % 152.07/22.63 | | | | | | | | (189) ~ (all_52_6 = e1) % 152.07/22.63 | | | | | | | | % 152.07/22.63 | | | | | | | | REDUCE: (62), (188) imply: % 152.07/22.63 | | | | | | | | (190) ~ (all_6_0 = e1) % 152.07/22.63 | | | | | | | | % 152.07/22.63 | | | | | | | | SIMP: (190) implies: % 152.07/22.63 | | | | | | | | (191) ~ (all_6_0 = e1) % 152.07/22.63 | | | | | | | | % 152.07/22.63 | | | | | | | | REDUCE: (181), (188) imply: % 152.07/22.63 | | | | | | | | (192) ~ (e1 = e0) % 152.07/22.63 | | | | | | | | % 152.07/22.63 | | | | | | | | BETA: splitting (107) gives: % 152.07/22.63 | | | | | | | | % 152.07/22.63 | | | | | | | | Case 1: % 152.07/22.63 | | | | | | | | | % 152.07/22.63 | | | | | | | | | (193) all_54_8 = e3 % 152.07/22.63 | | | | | | | | | % 152.07/22.63 | | | | | | | | | COMBINE_EQS: (57), (193) imply: % 152.07/22.63 | | | | | | | | | (194) all_6_0 = e3 % 152.07/22.63 | | | | | | | | | % 152.07/22.63 | | | | | | | | | SIMP: (194) implies: % 152.07/22.63 | | | | | | | | | (195) all_6_0 = e3 % 152.07/22.63 | | | | | | | | | % 152.07/22.63 | | | | | | | | | REDUCE: (36), (195) imply: % 152.07/22.63 | | | | | | | | | (196) ~ (all_52_1 = e3) % 152.07/22.63 | | | | | | | | | % 152.07/22.63 | | | | | | | | | BETA: splitting (110) gives: % 152.07/22.63 | | | | | | | | | % 152.07/22.63 | | | | | | | | | Case 1: % 152.07/22.63 | | | | | | | | | | % 152.07/22.63 | | | | | | | | | | (197) all_58_2 = e3 % 152.07/22.63 | | | | | | | | | | % 152.07/22.63 | | | | | | | | | | COMBINE_EQS: (85), (197) imply: % 152.07/22.63 | | | | | | | | | | (198) all_52_1 = e3 % 152.07/22.63 | | | | | | | | | | % 152.07/22.63 | | | | | | | | | | REDUCE: (196), (198) imply: % 152.07/22.63 | | | | | | | | | | (199) $false % 152.07/22.63 | | | | | | | | | | % 152.07/22.63 | | | | | | | | | | CLOSE: (199) is inconsistent. % 152.07/22.63 | | | | | | | | | | % 152.07/22.63 | | | | | | | | | Case 2: % 152.07/22.63 | | | | | | | | | | % 152.07/22.63 | | | | | | | | | | (200) all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3 % 152.07/22.63 | | | | | | | | | | % 152.07/22.63 | | | | | | | | | | BETA: splitting (200) gives: % 152.07/22.63 | | | | | | | | | | % 152.07/22.63 | | | | | | | | | | Case 1: % 152.07/22.63 | | | | | | | | | | | % 152.07/22.63 | | | | | | | | | | | (201) all_58_3 = e3 % 152.07/22.63 | | | | | | | | | | | % 152.07/22.63 | | | | | | | | | | | COMBINE_EQS: (67), (201) imply: % 152.07/22.63 | | | | | | | | | | | (202) all_8_2 = e3 % 152.07/22.63 | | | | | | | | | | | % 152.07/22.63 | | | | | | | | | | | REDUCE: (122), (202) imply: % 152.07/22.63 | | | | | | | | | | | (203) $false % 152.07/22.63 | | | | | | | | | | | % 152.07/22.63 | | | | | | | | | | | CLOSE: (203) is inconsistent. % 152.07/22.63 | | | | | | | | | | | % 152.07/22.63 | | | | | | | | | | Case 2: % 152.07/22.63 | | | | | | | | | | | % 152.07/22.63 | | | | | | | | | | | (204) all_58_5 = e3 | all_58_10 = e3 % 152.07/22.63 | | | | | | | | | | | % 152.07/22.63 | | | | | | | | | | | BETA: splitting (204) gives: % 152.07/22.63 | | | | | | | | | | | % 152.07/22.63 | | | | | | | | | | | Case 1: % 152.07/22.63 | | | | | | | | | | | | % 152.07/22.63 | | | | | | | | | | | | (205) all_58_5 = e3 % 152.07/22.63 | | | | | | | | | | | | % 152.07/22.63 | | | | | | | | | | | | COMBINE_EQS: (33), (205) imply: % 152.07/22.63 | | | | | | | | | | | | (206) all_52_9 = e3 % 152.07/22.63 | | | | | | | | | | | | % 152.07/22.63 | | | | | | | | | | | | REDUCE: (166), (206) imply: % 152.07/22.63 | | | | | | | | | | | | (207) $false % 152.07/22.63 | | | | | | | | | | | | % 152.07/22.63 | | | | | | | | | | | | CLOSE: (207) is inconsistent. % 152.07/22.63 | | | | | | | | | | | | % 152.07/22.63 | | | | | | | | | | | Case 2: % 152.07/22.63 | | | | | | | | | | | | % 152.07/22.63 | | | | | | | | | | | | (208) all_58_10 = e3 % 152.07/22.63 | | | | | | | | | | | | % 152.07/22.63 | | | | | | | | | | | | COMBINE_EQS: (88), (208) imply: % 152.07/22.63 | | | | | | | | | | | | (209) all_52_13 = e3 % 152.07/22.63 | | | | | | | | | | | | % 152.07/22.63 | | | | | | | | | | | | REDUCE: (76), (209) imply: % 152.07/22.63 | | | | | | | | | | | | (210) ~ (all_4_2 = e3) % 152.07/22.63 | | | | | | | | | | | | % 152.07/22.63 | | | | | | | | | | | | SIMP: (210) implies: % 152.07/22.63 | | | | | | | | | | | | (211) ~ (all_4_2 = e3) % 152.07/22.63 | | | | | | | | | | | | % 152.07/22.63 | | | | | | | | | | | | REF_CLOSE: (1), (6), (18), (23), (30), (42), (48), (57), % 152.07/22.63 | | | | | | | | | | | | (64), (69), (71), (74), (81), (100), (107), (108), % 152.07/22.63 | | | | | | | | | | | | (179), (180), (182), (183), (189), (191), (192), % 152.07/22.63 | | | | | | | | | | | | (211) are inconsistent by sub-proof #450. % 152.07/22.63 | | | | | | | | | | | | % 152.07/22.63 | | | | | | | | | | | End of split % 152.07/22.63 | | | | | | | | | | | % 152.07/22.63 | | | | | | | | | | End of split % 152.07/22.63 | | | | | | | | | | % 152.07/22.63 | | | | | | | | | End of split % 152.07/22.63 | | | | | | | | | % 152.07/22.63 | | | | | | | | Case 2: % 152.07/22.63 | | | | | | | | | % 152.07/22.63 | | | | | | | | | (212) all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0 % 152.07/22.63 | | | | | | | | | % 152.07/22.63 | | | | | | | | | REF_CLOSE: (23), (57), (182), (191), (212) are inconsistent by % 152.07/22.63 | | | | | | | | | sub-proof #451. % 152.07/22.63 | | | | | | | | | % 152.07/22.63 | | | | | | | | End of split % 152.07/22.63 | | | | | | | | % 152.07/22.63 | | | | | | | End of split % 152.07/22.63 | | | | | | | % 152.07/22.63 | | | | | | End of split % 152.07/22.63 | | | | | | % 152.07/22.63 | | | | | End of split % 152.07/22.63 | | | | | % 152.07/22.63 | | | | End of split % 152.07/22.63 | | | | % 152.07/22.63 | | | End of split % 152.07/22.63 | | | % 152.07/22.63 | | Case 2: % 152.07/22.63 | | | % 152.07/22.63 | | | (213) all_56_11 = e3 % 152.07/22.63 | | | (214) all_56_9 = e2 % 152.07/22.63 | | | % 152.07/22.63 | | | COMBINE_EQS: (115), (214) imply: % 152.07/22.63 | | | (215) all_52_1 = e2 % 152.07/22.63 | | | % 152.07/22.63 | | | COMBINE_EQS: (1), (213) imply: % 152.07/22.63 | | | (216) all_8_2 = e3 % 152.07/22.63 | | | % 152.07/22.63 | | | REDUCE: (9), (215) imply: % 152.07/22.63 | | | (217) ~ (all_52_9 = e2) % 152.07/22.63 | | | % 152.07/22.63 | | | SIMP: (217) implies: % 152.07/22.63 | | | (218) ~ (all_52_9 = e2) % 152.07/22.63 | | | % 152.07/22.63 | | | REDUCE: (55), (215) imply: % 152.07/22.63 | | | (219) ~ (all_52_13 = e2) % 152.07/22.63 | | | % 152.07/22.63 | | | SIMP: (219) implies: % 152.07/22.63 | | | (220) ~ (all_52_13 = e2) % 152.07/22.63 | | | % 152.07/22.63 | | | REDUCE: (116), (215) imply: % 152.07/22.63 | | | (221) ~ (all_10_2 = e2) % 152.07/22.63 | | | % 152.07/22.63 | | | SIMP: (221) implies: % 152.07/22.63 | | | (222) ~ (all_10_2 = e2) % 152.07/22.63 | | | % 152.07/22.63 | | | REDUCE: (46), (215), (216) imply: % 152.07/22.63 | | | (223) ~ (e3 = e2) % 152.07/22.63 | | | % 152.07/22.63 | | | REDUCE: (14), (216) imply: % 152.07/22.63 | | | (224) ~ (all_52_9 = e3) % 152.07/22.63 | | | % 152.07/22.63 | | | REDUCE: (112), (216) imply: % 152.07/22.63 | | | (225) op(e3, e3) = all_8_1 % 152.07/22.63 | | | % 152.07/22.63 | | | REF_CLOSE: (4), (7), (8), (11), (12), (13), (15), (16), (17), (18), (19), % 152.07/22.63 | | | (22), (24), (26), (30), (32), (33), (34), (38), (40), (43), % 152.07/22.63 | | | (48), (51), (52), (58), (61), (65), (73), (76), (77), (82), % 152.07/22.63 | | | (84), (89), (90), (91), (96), (97), (98), (109), (120), (218), % 152.07/22.63 | | | (220), (222), (224), (225) are inconsistent by sub-proof #588. % 152.07/22.63 | | | % 152.07/22.63 | | End of split % 152.07/22.63 | | % 152.07/22.63 | Case 2: % 152.07/22.63 | | % 152.07/22.63 | | (226) all_56_21 = e3 % 152.07/22.63 | | (227) all_56_17 = e1 % 152.07/22.63 | | % 152.07/22.63 | | COMBINE_EQS: (94), (227) imply: % 152.07/22.63 | | (228) all_6_0 = e1 % 152.07/22.63 | | % 152.07/22.63 | | SIMP: (228) implies: % 152.07/22.63 | | (229) all_6_0 = e1 % 152.07/22.63 | | % 152.07/22.63 | | COMBINE_EQS: (27), (226) imply: % 152.07/22.63 | | (230) all_6_2 = e3 % 152.07/22.63 | | % 152.07/22.63 | | SIMP: (230) implies: % 152.07/22.63 | | (231) all_6_2 = e3 % 152.07/22.63 | | % 152.07/22.63 | | COMBINE_EQS: (58), (231) imply: % 152.07/22.63 | | (232) all_58_8 = e3 % 152.07/22.63 | | % 152.07/22.63 | | REDUCE: (42), (229) imply: % 152.07/22.63 | | (233) ~ (all_52_6 = e1) % 152.07/22.63 | | % 152.07/22.63 | | REDUCE: (86), (231) imply: % 152.07/22.63 | | (234) ~ (all_52_9 = e3) % 152.07/22.63 | | % 152.07/22.63 | | REDUCE: (3), (231) imply: % 152.07/22.63 | | (235) ~ (all_52_11 = e3) % 152.07/22.63 | | % 152.07/22.63 | | REDUCE: (62), (229) imply: % 152.07/22.63 | | (236) ~ (all_52_14 = e1) % 152.07/22.63 | | % 152.07/22.63 | | REDUCE: (103), (231) imply: % 152.07/22.63 | | (237) op(e3, e3) = e3 % 152.07/22.63 | | % 152.07/22.63 | | REDUCE: (80), (231) imply: % 152.07/22.63 | | (238) op(e1, e1) = e3 % 152.07/22.63 | | % 152.07/22.63 | | GROUND_INST: instantiating (48) with all_10_2, e3, e3, e3, simplifying with % 152.07/22.63 | | (40), (237) gives: % 152.07/22.63 | | (239) all_10_2 = e3 % 152.07/22.63 | | % 152.07/22.63 | | REDUCE: (116), (239) imply: % 152.07/22.63 | | (240) ~ (all_52_1 = e3) % 152.07/22.63 | | % 152.07/22.63 | | REDUCE: (49), (239) imply: % 152.07/22.63 | | (241) ~ (all_52_3 = e3) % 152.07/22.63 | | % 152.07/22.63 | | REDUCE: (90), (239) imply: % 152.07/22.63 | | (242) op(e3, e3) = all_10_1 % 152.07/22.63 | | % 152.07/22.63 | | REDUCE: (104), (239) imply: % 152.07/22.63 | | (243) op(e3, e3) = all_56_0 % 152.07/22.63 | | % 152.07/22.63 | | GROUND_INST: instantiating (48) with e3, all_56_0, e3, e3, simplifying with % 152.07/22.63 | | (237), (243) gives: % 152.07/22.63 | | (244) all_56_0 = e3 % 152.07/22.63 | | % 152.07/22.63 | | GROUND_INST: instantiating (48) with all_10_1, all_56_0, e3, e3, simplifying % 152.07/22.63 | | with (242), (243) gives: % 152.07/22.63 | | (245) all_56_0 = all_10_1 % 152.07/22.63 | | % 152.07/22.63 | | COMBINE_EQS: (244), (245) imply: % 152.07/22.63 | | (246) all_10_1 = e3 % 152.07/22.63 | | % 152.07/22.63 | | SIMP: (246) implies: % 152.07/22.63 | | (247) all_10_1 = e3 % 152.07/22.63 | | % 152.07/22.63 | | REDUCE: (31), (247) imply: % 152.07/22.63 | | (248) op(e3, e3) = all_10_0 % 152.07/22.63 | | % 152.07/22.63 | | GROUND_INST: instantiating (48) with e3, all_10_0, e3, e3, simplifying with % 152.07/22.63 | | (237), (248) gives: % 152.07/22.63 | | (249) all_10_0 = e3 % 152.07/22.63 | | % 152.07/22.63 | | REDUCE: (75), (249) imply: % 152.07/22.63 | | (250) ~ (e3 = e1) % 152.07/22.63 | | % 152.07/22.63 | | BETA: splitting (50) gives: % 152.07/22.63 | | % 152.07/22.63 | | Case 1: % 152.07/22.63 | | | % 152.07/22.63 | | | (251) ~ (all_56_11 = e3) % 152.07/22.63 | | | % 152.07/22.63 | | | REDUCE: (1), (251) imply: % 152.07/22.63 | | | (252) ~ (all_8_2 = e3) % 152.07/22.63 | | | % 152.07/22.63 | | | BETA: splitting (110) gives: % 152.07/22.63 | | | % 152.07/22.63 | | | Case 1: % 152.07/22.63 | | | | % 152.07/22.63 | | | | (253) all_58_2 = e3 % 152.07/22.63 | | | | % 152.07/22.63 | | | | COMBINE_EQS: (85), (253) imply: % 152.07/22.63 | | | | (254) all_52_1 = e3 % 152.07/22.63 | | | | % 152.07/22.63 | | | | REDUCE: (240), (254) imply: % 152.07/22.63 | | | | (255) $false % 152.07/22.63 | | | | % 152.07/22.63 | | | | CLOSE: (255) is inconsistent. % 152.07/22.63 | | | | % 152.07/22.63 | | | Case 2: % 152.07/22.63 | | | | % 152.07/22.63 | | | | (256) all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3 % 152.07/22.63 | | | | % 152.07/22.63 | | | | BETA: splitting (256) gives: % 152.07/22.63 | | | | % 152.07/22.63 | | | | Case 1: % 152.07/22.63 | | | | | % 152.07/22.63 | | | | | (257) all_58_3 = e3 % 152.07/22.63 | | | | | % 152.07/22.63 | | | | | COMBINE_EQS: (67), (257) imply: % 152.07/22.63 | | | | | (258) all_8_2 = e3 % 152.07/22.63 | | | | | % 152.07/22.63 | | | | | REDUCE: (252), (258) imply: % 152.07/22.63 | | | | | (259) $false % 152.07/22.63 | | | | | % 152.07/22.63 | | | | | CLOSE: (259) is inconsistent. % 152.07/22.63 | | | | | % 152.07/22.63 | | | | Case 2: % 152.07/22.63 | | | | | % 152.07/22.63 | | | | | (260) all_58_5 = e3 | all_58_10 = e3 % 152.07/22.63 | | | | | % 152.07/22.63 | | | | | BETA: splitting (260) gives: % 152.07/22.63 | | | | | % 152.07/22.63 | | | | | Case 1: % 152.07/22.63 | | | | | | % 152.07/22.63 | | | | | | (261) all_58_5 = e3 % 152.07/22.63 | | | | | | % 152.07/22.63 | | | | | | COMBINE_EQS: (33), (261) imply: % 152.07/22.63 | | | | | | (262) all_52_9 = e3 % 152.07/22.63 | | | | | | % 152.07/22.63 | | | | | | REDUCE: (234), (262) imply: % 152.07/22.63 | | | | | | (263) $false % 152.07/22.63 | | | | | | % 152.07/22.63 | | | | | | CLOSE: (263) is inconsistent. % 152.07/22.63 | | | | | | % 152.07/22.63 | | | | | Case 2: % 152.07/22.63 | | | | | | % 152.07/22.63 | | | | | | (264) all_58_10 = e3 % 152.07/22.63 | | | | | | % 152.07/22.63 | | | | | | COMBINE_EQS: (88), (264) imply: % 152.07/22.63 | | | | | | (265) all_52_13 = e3 % 152.07/22.63 | | | | | | % 152.07/22.63 | | | | | | REDUCE: (15), (265) imply: % 152.07/22.63 | | | | | | (266) ~ (all_52_12 = e3) % 152.07/22.63 | | | | | | % 152.07/22.63 | | | | | | REDUCE: (76), (265) imply: % 152.07/22.63 | | | | | | (267) ~ (all_4_2 = e3) % 152.07/22.63 | | | | | | % 152.07/22.63 | | | | | | SIMP: (267) implies: % 152.07/22.63 | | | | | | (268) ~ (all_4_2 = e3) % 152.07/22.63 | | | | | | % 152.07/22.63 | | | | | | REF_CLOSE: (1), (2), (14), (16), (19), (25), (29), (33), (35), (38), % 152.07/22.63 | | | | | | (39), (48), (54), (56), (66), (67), (70), (72), (83), % 152.07/22.63 | | | | | | (87), (96), (98), (106), (112), (114), (117), (118), % 152.07/22.63 | | | | | | (232), (233), (235), (236), (238), (241), (250), (264), % 152.07/22.63 | | | | | | (266), (268) are inconsistent by sub-proof #445. % 152.07/22.63 | | | | | | % 152.07/22.63 | | | | | End of split % 152.07/22.63 | | | | | % 152.07/22.63 | | | | End of split % 152.07/22.63 | | | | % 152.07/22.63 | | | End of split % 152.07/22.63 | | | % 152.07/22.63 | | Case 2: % 152.07/22.63 | | | % 152.07/22.63 | | | (269) all_56_11 = e3 % 152.07/22.63 | | | % 152.07/22.63 | | | COMBINE_EQS: (1), (269) imply: % 152.07/22.63 | | | (270) all_8_2 = e3 % 152.07/22.63 | | | % 152.07/22.63 | | | REDUCE: (29), (270) imply: % 152.07/22.63 | | | (271) ~ (all_52_7 = e3) % 152.07/22.63 | | | % 152.07/22.63 | | | REDUCE: (112), (270) imply: % 152.07/22.63 | | | (272) op(e3, e3) = all_8_1 % 152.07/22.63 | | | % 152.07/22.63 | | | BETA: splitting (118) gives: % 152.07/22.63 | | | % 152.07/22.63 | | | Case 1: % 152.07/22.63 | | | | % 152.07/22.63 | | | | (273) all_58_12 = e3 % 152.07/22.63 | | | | % 152.07/22.63 | | | | REF_CLOSE: (117), (241), (273) are inconsistent by sub-proof #449. % 152.07/22.63 | | | | % 152.07/22.63 | | | Case 2: % 152.07/22.63 | | | | % 152.07/22.64 | | | | (274) all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3 % 152.07/22.64 | | | | % 152.07/22.64 | | | | BETA: splitting (274) gives: % 152.07/22.64 | | | | % 152.07/22.64 | | | | Case 1: % 152.07/22.64 | | | | | % 152.07/22.64 | | | | | (275) all_58_13 = e3 % 152.07/22.64 | | | | | % 152.07/22.64 | | | | | REF_CLOSE: (39), (271), (275) are inconsistent by sub-proof #444. % 152.07/22.64 | | | | | % 152.07/22.64 | | | | Case 2: % 152.07/22.64 | | | | | % 152.07/22.64 | | | | | (276) all_58_14 = e3 | all_58_15 = e3 % 152.07/22.64 | | | | | % 152.07/22.64 | | | | | BETA: splitting (276) gives: % 152.07/22.64 | | | | | % 152.07/22.64 | | | | | Case 1: % 152.07/22.64 | | | | | | % 152.07/22.64 | | | | | | (277) all_58_14 = e3 % 152.07/22.64 | | | | | | % 152.07/22.64 | | | | | | REF_CLOSE: (114), (235), (277) are inconsistent by sub-proof #447. % 152.07/22.64 | | | | | | % 152.07/22.64 | | | | | Case 2: % 152.07/22.64 | | | | | | % 152.07/22.64 | | | | | | (278) all_58_15 = e3 % 152.07/22.64 | | | | | | % 152.07/22.64 | | | | | | COMBINE_EQS: (83), (278) imply: % 152.07/22.64 | | | | | | (279) all_4_2 = e3 % 152.07/22.64 | | | | | | % 152.07/22.64 | | | | | | REDUCE: (64), (279) imply: % 152.07/22.64 | | | | | | (280) op(e3, e3) = all_4_1 % 152.07/22.64 | | | | | | % 152.07/22.64 | | | | | | REF_CLOSE: (16), (48), (237), (272), (280) are inconsistent by % 152.07/22.64 | | | | | | sub-proof #443. % 152.07/22.64 | | | | | | % 152.07/22.64 | | | | | End of split % 152.07/22.64 | | | | | % 152.07/22.64 | | | | End of split % 152.07/22.64 | | | | % 152.07/22.64 | | | End of split % 152.07/22.64 | | | % 152.07/22.64 | | End of split % 152.07/22.64 | | % 152.07/22.64 | End of split % 152.07/22.64 | % 152.07/22.64 End of proof % 152.07/22.64 % 152.07/22.64 Sub-proof #443 shows that the following formulas are inconsistent: % 152.07/22.64 ---------------------------------------------------------------- % 152.07/22.64 (1) op(e3, e3) = e3 % 152.07/22.64 (2) ~ (all_8_1 = e3) % 152.07/22.64 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 152.07/22.64 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 152.07/22.64 (4) op(e3, e3) = all_8_1 % 152.07/22.64 (5) op(e3, e3) = all_4_1 % 152.07/22.64 % 152.07/22.64 Begin of proof % 152.07/22.64 | % 152.07/22.64 | GROUND_INST: instantiating (3) with e3, all_8_1, e3, e3, simplifying with (1), % 152.07/22.64 | (4) gives: % 152.07/22.64 | (6) all_8_1 = e3 % 152.07/22.64 | % 152.07/22.64 | GROUND_INST: instantiating (3) with all_4_1, all_8_1, e3, e3, simplifying with % 152.07/22.64 | (4), (5) gives: % 152.07/22.64 | (7) all_8_1 = all_4_1 % 152.07/22.64 | % 152.07/22.64 | COMBINE_EQS: (6), (7) imply: % 152.07/22.64 | (8) all_4_1 = e3 % 152.07/22.64 | % 152.07/22.64 | REDUCE: (2), (6) imply: % 152.07/22.64 | (9) $false % 152.07/22.64 | % 152.07/22.64 | CLOSE: (9) is inconsistent. % 152.07/22.64 | % 152.07/22.64 End of proof % 152.07/22.64 % 152.07/22.64 Sub-proof #444 shows that the following formulas are inconsistent: % 152.07/22.64 ---------------------------------------------------------------- % 152.07/22.64 (1) all_58_13 = all_52_7 % 152.07/22.64 (2) all_58_13 = e3 % 152.07/22.64 (3) ~ (all_52_7 = e3) % 152.07/22.64 % 152.07/22.64 Begin of proof % 152.07/22.64 | % 152.07/22.64 | COMBINE_EQS: (1), (2) imply: % 152.07/22.64 | (4) all_52_7 = e3 % 152.07/22.64 | % 152.07/22.64 | SIMP: (4) implies: % 152.07/22.64 | (5) all_52_7 = e3 % 152.07/22.64 | % 152.07/22.64 | REDUCE: (3), (5) imply: % 152.07/22.64 | (6) $false % 152.07/22.64 | % 152.07/22.64 | CLOSE: (6) is inconsistent. % 152.07/22.64 | % 152.07/22.64 End of proof % 152.07/22.64 % 152.07/22.64 Sub-proof #445 shows that the following formulas are inconsistent: % 152.07/22.64 ---------------------------------------------------------------- % 152.07/22.64 (1) all_56_11 = all_8_2 % 152.07/22.64 (2) ~ (all_56_11 = e1) | all_56_13 = e2 % 152.07/22.64 (3) ~ (all_52_6 = e1) % 152.07/22.64 (4) ~ (all_52_9 = all_8_2) % 152.07/22.64 (5) ~ (all_8_1 = e3) % 152.07/22.64 (6) all_58_4 = all_52_8 % 152.07/22.64 (7) all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1 % 152.07/22.64 (8) ~ (all_52_7 = all_8_2) % 152.07/22.64 (9) all_58_5 = all_52_9 % 152.07/22.64 (10) all_58_9 = all_52_12 % 152.07/22.64 (11) all_58_1 = all_52_4 % 152.07/22.64 (12) all_58_13 = all_52_7 % 152.07/22.64 (13) all_58_10 = e3 % 152.07/22.64 (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 152.07/22.64 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 152.07/22.64 (15) ~ (all_52_11 = e3) % 152.07/22.64 (16) ~ (all_52_14 = e1) % 152.07/22.64 (17) op(e1, e1) = e3 % 152.07/22.64 (18) ~ (all_52_12 = e3) % 152.07/22.64 (19) all_56_13 = all_52_9 % 152.07/22.64 (20) ~ (all_4_2 = e1) % 152.07/22.64 (21) ~ (all_52_3 = e3) % 152.07/22.64 (22) all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1 % 152.07/22.64 (23) all_58_3 = all_8_2 % 152.07/22.64 (24) all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1 % 152.07/22.64 (25) all_58_11 = all_52_14 % 152.07/22.64 (26) all_58_15 = all_4_2 % 152.07/22.64 (27) ~ (all_4_2 = e3) % 152.07/22.64 (28) all_58_7 = all_52_6 % 152.07/22.64 (29) ~ (e3 = e1) % 152.07/22.64 (30) ~ (all_52_4 = all_52_12) % 152.07/22.64 (31) ~ (all_52_8 = all_52_12) % 152.07/22.64 (32) all_58_8 = e3 % 152.07/22.64 (33) op(e1, all_52_11) = all_56_28 % 152.07/22.64 (34) op(all_8_2, all_8_2) = all_8_1 % 152.07/22.64 (35) all_58_14 = all_52_11 % 152.07/22.64 (36) all_58_12 = all_52_3 % 152.07/22.64 (37) all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3 % 152.07/22.64 % 152.07/22.64 Begin of proof % 152.07/22.64 | % 152.07/22.64 | BETA: splitting (7) gives: % 152.07/22.64 | % 152.07/22.64 | Case 1: % 152.07/22.64 | | % 152.07/22.64 | | (38) all_58_9 = e1 % 152.07/22.64 | | % 152.07/22.64 | | COMBINE_EQS: (10), (38) imply: % 152.07/22.64 | | (39) all_52_12 = e1 % 152.07/22.64 | | % 152.07/22.64 | | REDUCE: (30), (39) imply: % 152.07/22.64 | | (40) ~ (all_52_4 = e1) % 152.07/22.64 | | % 152.07/22.64 | | REDUCE: (31), (39) imply: % 152.07/22.64 | | (41) ~ (all_52_8 = e1) % 152.07/22.64 | | % 152.07/22.64 | | REDUCE: (18), (39) imply: % 152.07/22.64 | | (42) ~ (e3 = e1) % 152.07/22.64 | | % 152.07/22.64 | | BETA: splitting (37) gives: % 152.07/22.64 | | % 152.07/22.64 | | Case 1: % 152.07/22.64 | | | % 152.07/22.64 | | | (43) all_58_12 = e3 % 152.07/22.64 | | | % 152.07/22.64 | | | REF_CLOSE: (21), (36), (43) are inconsistent by sub-proof #449. % 152.07/22.64 | | | % 152.07/22.64 | | Case 2: % 152.07/22.64 | | | % 152.07/22.64 | | | (44) all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3 % 152.07/22.64 | | | % 152.07/22.64 | | | BETA: splitting (44) gives: % 152.07/22.64 | | | % 152.07/22.64 | | | Case 1: % 152.07/22.64 | | | | % 152.07/22.64 | | | | (45) all_58_13 = e3 % 152.07/22.64 | | | | % 152.07/22.64 | | | | COMBINE_EQS: (12), (45) imply: % 152.07/22.64 | | | | (46) all_52_7 = e3 % 152.07/22.64 | | | | % 152.07/22.64 | | | | SIMP: (46) implies: % 152.07/22.64 | | | | (47) all_52_7 = e3 % 152.07/22.64 | | | | % 152.07/22.64 | | | | REDUCE: (8), (47) imply: % 152.07/22.64 | | | | (48) ~ (all_8_2 = e3) % 152.07/22.64 | | | | % 152.07/22.64 | | | | SIMP: (48) implies: % 152.07/22.64 | | | | (49) ~ (all_8_2 = e3) % 152.07/22.64 | | | | % 152.07/22.64 | | | | BETA: splitting (24) gives: % 152.07/22.64 | | | | % 152.07/22.64 | | | | Case 1: % 152.07/22.64 | | | | | % 152.07/22.64 | | | | | (50) all_58_1 = e1 % 152.07/22.64 | | | | | % 152.07/22.64 | | | | | COMBINE_EQS: (11), (50) imply: % 152.07/22.64 | | | | | (51) all_52_4 = e1 % 152.07/22.64 | | | | | % 152.07/22.64 | | | | | REDUCE: (40), (51) imply: % 152.07/22.64 | | | | | (52) $false % 152.07/22.64 | | | | | % 152.07/22.64 | | | | | CLOSE: (52) is inconsistent. % 152.07/22.64 | | | | | % 152.07/22.64 | | | | Case 2: % 152.07/22.64 | | | | | % 152.07/22.64 | | | | | (53) all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1 % 152.07/22.64 | | | | | % 152.07/22.64 | | | | | BETA: splitting (53) gives: % 152.07/22.64 | | | | | % 152.07/22.64 | | | | | Case 1: % 152.07/22.64 | | | | | | % 152.07/22.64 | | | | | | (54) all_58_3 = e1 % 152.07/22.64 | | | | | | % 152.07/22.64 | | | | | | COMBINE_EQS: (23), (54) imply: % 152.07/22.64 | | | | | | (55) all_8_2 = e1 % 152.07/22.64 | | | | | | % 152.07/22.64 | | | | | | COMBINE_EQS: (1), (55) imply: % 152.07/22.64 | | | | | | (56) all_56_11 = e1 % 152.07/22.64 | | | | | | % 152.07/22.64 | | | | | | REDUCE: (4), (55) imply: % 152.07/22.64 | | | | | | (57) ~ (all_52_9 = e1) % 152.07/22.64 | | | | | | % 152.07/22.64 | | | | | | REDUCE: (34), (55) imply: % 152.07/22.64 | | | | | | (58) op(e1, e1) = all_8_1 % 152.07/22.64 | | | | | | % 152.07/22.64 | | | | | | BETA: splitting (2) gives: % 152.07/22.64 | | | | | | % 152.07/22.64 | | | | | | Case 1: % 152.07/22.64 | | | | | | | % 152.07/22.64 | | | | | | | (59) ~ (all_56_11 = e1) % 152.07/22.64 | | | | | | | % 152.07/22.64 | | | | | | | REDUCE: (56), (59) imply: % 152.07/22.64 | | | | | | | (60) $false % 152.07/22.64 | | | | | | | % 152.07/22.64 | | | | | | | CLOSE: (60) is inconsistent. % 152.07/22.64 | | | | | | | % 152.07/22.64 | | | | | | Case 2: % 152.07/22.64 | | | | | | | % 152.07/22.64 | | | | | | | (61) all_56_13 = e2 % 152.07/22.64 | | | | | | | % 152.07/22.64 | | | | | | | COMBINE_EQS: (19), (61) imply: % 152.07/22.64 | | | | | | | (62) all_52_9 = e2 % 152.07/22.64 | | | | | | | % 152.07/22.64 | | | | | | | COMBINE_EQS: (9), (62) imply: % 152.07/22.64 | | | | | | | (63) all_58_5 = e2 % 152.07/22.64 | | | | | | | % 152.07/22.64 | | | | | | | REDUCE: (57), (62) imply: % 152.07/22.64 | | | | | | | (64) ~ (e2 = e1) % 152.07/22.64 | | | | | | | % 152.07/22.64 | | | | | | | BETA: splitting (22) gives: % 152.07/22.64 | | | | | | | % 152.07/22.64 | | | | | | | Case 1: % 152.07/22.64 | | | | | | | | % 152.07/22.64 | | | | | | | | (65) all_58_4 = e1 % 152.07/22.64 | | | | | | | | % 152.07/22.64 | | | | | | | | COMBINE_EQS: (6), (65) imply: % 152.07/22.64 | | | | | | | | (66) all_52_8 = e1 % 152.07/22.64 | | | | | | | | % 152.07/22.64 | | | | | | | | REDUCE: (41), (66) imply: % 152.07/22.64 | | | | | | | | (67) $false % 152.07/22.64 | | | | | | | | % 152.07/22.64 | | | | | | | | CLOSE: (67) is inconsistent. % 152.07/22.64 | | | | | | | | % 152.07/22.64 | | | | | | | Case 2: % 152.07/22.64 | | | | | | | | % 152.07/22.64 | | | | | | | | (68) all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1 % 152.07/22.64 | | | | | | | | % 152.07/22.64 | | | | | | | | BETA: splitting (68) gives: % 152.07/22.64 | | | | | | | | % 152.07/22.64 | | | | | | | | Case 1: % 152.07/22.64 | | | | | | | | | % 152.07/22.64 | | | | | | | | | (69) all_58_5 = e1 % 152.07/22.64 | | | | | | | | | % 152.07/22.64 | | | | | | | | | COMBINE_EQS: (63), (69) imply: % 152.07/22.64 | | | | | | | | | (70) e2 = e1 % 152.07/22.64 | | | | | | | | | % 152.07/22.64 | | | | | | | | | REDUCE: (64), (70) imply: % 152.07/22.64 | | | | | | | | | (71) $false % 152.07/22.64 | | | | | | | | | % 152.07/22.64 | | | | | | | | | CLOSE: (71) is inconsistent. % 152.07/22.64 | | | | | | | | | % 152.07/22.64 | | | | | | | | Case 2: % 152.07/22.64 | | | | | | | | | % 152.07/22.64 | | | | | | | | | (72) all_58_8 = e1 | all_58_14 = e1 % 152.07/22.64 | | | | | | | | | % 152.07/22.64 | | | | | | | | | BETA: splitting (72) gives: % 152.07/22.64 | | | | | | | | | % 152.07/22.64 | | | | | | | | | Case 1: % 152.07/22.64 | | | | | | | | | | % 152.07/22.64 | | | | | | | | | | (73) all_58_8 = e1 % 152.07/22.64 | | | | | | | | | | % 152.07/22.64 | | | | | | | | | | COMBINE_EQS: (32), (73) imply: % 152.07/22.64 | | | | | | | | | | (74) e3 = e1 % 152.07/22.64 | | | | | | | | | | % 152.07/22.64 | | | | | | | | | | REDUCE: (29), (74) imply: % 152.07/22.64 | | | | | | | | | | (75) $false % 152.07/22.64 | | | | | | | | | | % 152.07/22.64 | | | | | | | | | | CLOSE: (75) is inconsistent. % 152.07/22.64 | | | | | | | | | | % 152.07/22.64 | | | | | | | | | Case 2: % 152.07/22.64 | | | | | | | | | | % 152.07/22.64 | | | | | | | | | | (76) all_58_14 = e1 % 152.07/22.64 | | | | | | | | | | % 152.07/22.64 | | | | | | | | | | COMBINE_EQS: (35), (76) imply: % 152.07/22.64 | | | | | | | | | | (77) all_52_11 = e1 % 152.07/22.64 | | | | | | | | | | % 152.07/22.64 | | | | | | | | | | REDUCE: (33), (77) imply: % 152.07/22.64 | | | | | | | | | | (78) op(e1, e1) = all_56_28 % 152.07/22.64 | | | | | | | | | | % 152.07/22.64 | | | | | | | | | | GROUND_INST: instantiating (14) with e3, all_56_28, e1, e1, % 152.07/22.64 | | | | | | | | | | simplifying with (17), (78) gives: % 152.07/22.64 | | | | | | | | | | (79) all_56_28 = e3 % 152.07/22.64 | | | | | | | | | | % 152.07/22.64 | | | | | | | | | | GROUND_INST: instantiating (14) with all_8_1, all_56_28, e1, % 152.07/22.64 | | | | | | | | | | e1, simplifying with (58), (78) gives: % 152.07/22.64 | | | | | | | | | | (80) all_56_28 = all_8_1 % 152.07/22.64 | | | | | | | | | | % 152.07/22.64 | | | | | | | | | | COMBINE_EQS: (79), (80) imply: % 152.07/22.64 | | | | | | | | | | (81) all_8_1 = e3 % 152.07/22.64 | | | | | | | | | | % 152.07/22.64 | | | | | | | | | | REDUCE: (5), (81) imply: % 152.07/22.64 | | | | | | | | | | (82) $false % 152.07/22.64 | | | | | | | | | | % 152.07/22.64 | | | | | | | | | | CLOSE: (82) is inconsistent. % 152.07/22.64 | | | | | | | | | | % 152.07/22.64 | | | | | | | | | End of split % 152.07/22.64 | | | | | | | | | % 152.07/22.64 | | | | | | | | End of split % 152.07/22.64 | | | | | | | | % 152.07/22.64 | | | | | | | End of split % 152.07/22.64 | | | | | | | % 152.07/22.64 | | | | | | End of split % 152.07/22.64 | | | | | | % 152.07/22.64 | | | | | Case 2: % 152.07/22.64 | | | | | | % 152.07/22.64 | | | | | | (83) all_58_7 = e1 | all_58_13 = e1 % 152.07/22.64 | | | | | | % 152.07/22.64 | | | | | | REF_CLOSE: (3), (28), (29), (45), (83) are inconsistent by sub-proof % 152.07/22.64 | | | | | | #448. % 152.07/22.64 | | | | | | % 152.07/22.64 | | | | | End of split % 152.07/22.64 | | | | | % 152.07/22.64 | | | | End of split % 152.07/22.64 | | | | % 152.07/22.64 | | | Case 2: % 152.07/22.64 | | | | % 152.07/22.64 | | | | (84) all_58_14 = e3 | all_58_15 = e3 % 152.07/22.64 | | | | % 152.07/22.64 | | | | BETA: splitting (84) gives: % 152.07/22.64 | | | | % 152.07/22.64 | | | | Case 1: % 152.07/22.64 | | | | | % 152.07/22.64 | | | | | (85) all_58_14 = e3 % 152.07/22.64 | | | | | % 152.07/22.64 | | | | | REF_CLOSE: (15), (35), (85) are inconsistent by sub-proof #447. % 152.07/22.64 | | | | | % 152.07/22.64 | | | | Case 2: % 152.07/22.64 | | | | | % 152.07/22.64 | | | | | (86) all_58_15 = e3 % 152.07/22.64 | | | | | % 152.07/22.64 | | | | | COMBINE_EQS: (26), (86) imply: % 152.07/22.64 | | | | | (87) all_4_2 = e3 % 152.07/22.64 | | | | | % 152.07/22.64 | | | | | REDUCE: (27), (87) imply: % 152.07/22.64 | | | | | (88) $false % 152.07/22.64 | | | | | % 152.07/22.64 | | | | | CLOSE: (88) is inconsistent. % 152.07/22.64 | | | | | % 152.07/22.64 | | | | End of split % 152.07/22.64 | | | | % 152.07/22.64 | | | End of split % 152.07/22.64 | | | % 152.07/22.64 | | End of split % 152.07/22.64 | | % 152.07/22.64 | Case 2: % 152.07/22.64 | | % 152.07/22.64 | | (89) all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1 % 152.07/22.64 | | % 152.07/22.64 | | REF_CLOSE: (13), (16), (20), (25), (26), (29), (89) are inconsistent by % 152.07/22.64 | | sub-proof #446. % 152.07/22.64 | | % 152.07/22.64 | End of split % 152.07/22.64 | % 152.07/22.64 End of proof % 152.07/22.64 % 152.07/22.64 Sub-proof #446 shows that the following formulas are inconsistent: % 152.07/22.64 ---------------------------------------------------------------- % 152.07/22.64 (1) all_58_10 = e3 % 152.07/22.64 (2) ~ (all_52_14 = e1) % 152.07/22.64 (3) ~ (all_4_2 = e1) % 152.07/22.64 (4) all_58_11 = all_52_14 % 152.07/22.64 (5) all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1 % 152.07/22.64 (6) all_58_15 = all_4_2 % 152.07/22.64 (7) ~ (e3 = e1) % 152.07/22.64 % 152.07/22.64 Begin of proof % 152.07/22.64 | % 152.07/22.64 | BETA: splitting (5) gives: % 152.07/22.64 | % 152.07/22.64 | Case 1: % 152.07/22.64 | | % 152.07/22.64 | | (8) all_58_10 = e1 % 152.07/22.64 | | % 152.07/22.64 | | COMBINE_EQS: (1), (8) imply: % 152.07/22.64 | | (9) e3 = e1 % 152.07/22.64 | | % 152.07/22.64 | | REDUCE: (7), (9) imply: % 152.07/22.64 | | (10) $false % 152.07/22.64 | | % 152.07/22.64 | | CLOSE: (10) is inconsistent. % 152.07/22.64 | | % 152.07/22.64 | Case 2: % 152.07/22.64 | | % 152.07/22.64 | | (11) all_58_11 = e1 | all_58_15 = e1 % 152.07/22.64 | | % 152.07/22.64 | | REF_CLOSE: (2), (3), (4), (6), (11) are inconsistent by sub-proof #672. % 152.07/22.64 | | % 152.07/22.64 | End of split % 152.07/22.64 | % 152.07/22.64 End of proof % 152.07/22.64 % 152.07/22.64 Sub-proof #447 shows that the following formulas are inconsistent: % 152.07/22.64 ---------------------------------------------------------------- % 152.07/22.64 (1) all_58_14 = all_52_11 % 152.07/22.64 (2) all_58_14 = e3 % 152.07/22.64 (3) ~ (all_52_11 = e3) % 152.07/22.64 % 152.07/22.64 Begin of proof % 152.07/22.64 | % 152.07/22.64 | COMBINE_EQS: (1), (2) imply: % 152.07/22.64 | (4) all_52_11 = e3 % 152.07/22.64 | % 152.07/22.64 | SIMP: (4) implies: % 152.07/22.64 | (5) all_52_11 = e3 % 152.07/22.64 | % 152.07/22.64 | REDUCE: (3), (5) imply: % 152.07/22.64 | (6) $false % 152.07/22.64 | % 152.07/22.64 | CLOSE: (6) is inconsistent. % 152.07/22.64 | % 152.07/22.64 End of proof % 152.07/22.64 % 152.07/22.64 Sub-proof #448 shows that the following formulas are inconsistent: % 152.07/22.64 ---------------------------------------------------------------- % 152.07/22.64 (1) ~ (all_52_6 = e1) % 152.07/22.64 (2) all_58_7 = e1 | all_58_13 = e1 % 152.07/22.64 (3) all_58_7 = all_52_6 % 152.07/22.64 (4) ~ (e3 = e1) % 152.07/22.64 (5) all_58_13 = e3 % 152.07/22.64 % 152.07/22.64 Begin of proof % 152.07/22.64 | % 152.07/22.64 | BETA: splitting (2) gives: % 152.07/22.64 | % 152.07/22.64 | Case 1: % 152.07/22.64 | | % 152.07/22.64 | | (6) all_58_7 = e1 % 152.07/22.64 | | % 152.07/22.64 | | COMBINE_EQS: (3), (6) imply: % 152.07/22.64 | | (7) all_52_6 = e1 % 152.07/22.64 | | % 152.07/22.64 | | REDUCE: (1), (7) imply: % 152.07/22.64 | | (8) $false % 152.07/22.64 | | % 152.07/22.64 | | CLOSE: (8) is inconsistent. % 152.07/22.64 | | % 152.07/22.64 | Case 2: % 152.07/22.64 | | % 152.07/22.64 | | (9) all_58_13 = e1 % 152.07/22.64 | | % 152.07/22.64 | | REF_CLOSE: (4), (5), (9) are inconsistent by sub-proof #561. % 152.07/22.64 | | % 152.07/22.64 | End of split % 152.07/22.64 | % 152.07/22.64 End of proof % 152.07/22.64 % 152.07/22.64 Sub-proof #449 shows that the following formulas are inconsistent: % 152.07/22.64 ---------------------------------------------------------------- % 152.07/22.64 (1) all_58_12 = all_52_3 % 152.07/22.64 (2) all_58_12 = e3 % 152.07/22.64 (3) ~ (all_52_3 = e3) % 152.07/22.64 % 152.07/22.64 Begin of proof % 152.07/22.64 | % 152.07/22.64 | COMBINE_EQS: (1), (2) imply: % 152.07/22.64 | (4) all_52_3 = e3 % 152.07/22.64 | % 152.07/22.64 | SIMP: (4) implies: % 152.07/22.64 | (5) all_52_3 = e3 % 152.07/22.64 | % 152.07/22.64 | REDUCE: (3), (5) imply: % 152.07/22.64 | (6) $false % 152.07/22.64 | % 152.07/22.64 | CLOSE: (6) is inconsistent. % 152.07/22.64 | % 152.07/22.64 End of proof % 152.07/22.64 % 152.07/22.64 Sub-proof #450 shows that the following formulas are inconsistent: % 152.07/22.64 ---------------------------------------------------------------- % 152.07/22.64 (1) all_56_11 = all_8_2 % 152.07/22.64 (2) all_54_9 = all_52_6 % 152.07/22.64 (3) ~ (all_52_6 = e1) % 152.07/22.64 (4) op(e0, e0) = all_4_2 % 152.07/22.64 (5) ~ (all_6_0 = e2) % 152.07/22.64 (6) all_56_1 = all_10_2 % 152.07/22.64 (7) all_56_21 = e0 % 152.07/22.64 (8) ~ (all_6_0 = e1) % 152.07/22.64 (9) ~ (all_52_6 = all_6_0) % 152.07/22.64 (10) ~ (e1 = e0) % 152.07/22.64 (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 152.07/22.64 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 152.07/22.64 (12) all_54_8 = all_6_0 % 152.07/22.64 (13) ~ (all_52_6 = e0) % 152.07/22.64 (14) op(all_4_2, all_4_2) = all_4_1 % 152.07/22.64 (15) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0 % 152.07/22.64 (16) all_56_31 = all_4_2 % 152.07/22.64 (17) op(e0, e0) = e3 % 152.07/22.64 (18) all_56_1 = e3 | all_56_11 = e2 | all_56_21 = e1 | all_56_31 = e0 % 152.07/22.64 (19) ~ (all_52_6 = all_8_2) % 152.07/22.64 (20) ~ (all_4_2 = e3) % 152.07/22.64 (21) ~ (all_6_0 = e0) % 152.07/22.64 (22) op(e0, all_4_2) = all_56_30 % 152.07/22.64 (23) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0 % 152.07/22.64 (24) ~ (all_10_2 = all_6_0) % 152.07/22.64 % 152.07/22.64 Begin of proof % 152.07/22.64 | % 152.07/22.64 | BETA: splitting (23) gives: % 152.07/22.64 | % 152.07/22.64 | Case 1: % 152.07/22.64 | | % 152.07/22.64 | | (25) all_54_8 = e3 % 152.07/22.64 | | % 152.07/22.64 | | COMBINE_EQS: (12), (25) imply: % 152.07/22.64 | | (26) all_6_0 = e3 % 152.07/22.64 | | % 152.07/22.64 | | SIMP: (26) implies: % 152.07/22.64 | | (27) all_6_0 = e3 % 152.07/22.64 | | % 152.07/22.64 | | REDUCE: (9), (27) imply: % 152.07/22.64 | | (28) ~ (all_52_6 = e3) % 152.07/22.64 | | % 152.07/22.64 | | REDUCE: (24), (27) imply: % 152.07/22.64 | | (29) ~ (all_10_2 = e3) % 152.07/22.64 | | % 152.07/22.64 | | BETA: splitting (15) gives: % 152.07/22.64 | | % 152.07/22.64 | | Case 1: % 152.07/22.64 | | | % 152.07/22.64 | | | (30) all_54_9 = e3 % 152.07/22.64 | | | % 152.07/22.64 | | | REF_CLOSE: (2), (28), (30) are inconsistent by sub-proof #680. % 152.07/22.64 | | | % 152.07/22.64 | | Case 2: % 152.07/22.64 | | | % 152.07/22.64 | | | (31) all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0 % 152.07/22.64 | | | % 152.07/22.64 | | | BETA: splitting (31) gives: % 152.07/22.64 | | | % 152.07/22.64 | | | Case 1: % 152.07/22.64 | | | | % 152.07/22.64 | | | | (32) all_54_9 = e2 % 152.07/22.64 | | | | % 152.07/22.64 | | | | COMBINE_EQS: (2), (32) imply: % 152.07/22.64 | | | | (33) all_52_6 = e2 % 152.07/22.64 | | | | % 152.07/22.64 | | | | SIMP: (33) implies: % 152.07/22.64 | | | | (34) all_52_6 = e2 % 152.07/22.64 | | | | % 152.07/22.64 | | | | REDUCE: (19), (34) imply: % 152.07/22.64 | | | | (35) ~ (all_8_2 = e2) % 152.07/22.64 | | | | % 152.07/22.64 | | | | SIMP: (35) implies: % 152.07/22.64 | | | | (36) ~ (all_8_2 = e2) % 152.07/22.64 | | | | % 152.07/22.64 | | | | BETA: splitting (18) gives: % 152.07/22.64 | | | | % 152.07/22.64 | | | | Case 1: % 152.07/22.64 | | | | | % 152.07/22.64 | | | | | (37) all_56_1 = e3 % 152.07/22.64 | | | | | % 152.07/22.64 | | | | | COMBINE_EQS: (6), (37) imply: % 152.07/22.64 | | | | | (38) all_10_2 = e3 % 152.07/22.64 | | | | | % 152.07/22.64 | | | | | REDUCE: (29), (38) imply: % 152.07/22.64 | | | | | (39) $false % 152.07/22.64 | | | | | % 152.07/22.64 | | | | | CLOSE: (39) is inconsistent. % 152.07/22.64 | | | | | % 152.07/22.64 | | | | Case 2: % 152.07/22.64 | | | | | % 152.07/22.64 | | | | | (40) all_56_11 = e2 | all_56_21 = e1 | all_56_31 = e0 % 152.07/22.64 | | | | | % 152.07/22.64 | | | | | BETA: splitting (40) gives: % 152.07/22.64 | | | | | % 152.07/22.64 | | | | | Case 1: % 152.07/22.64 | | | | | | % 152.07/22.64 | | | | | | (41) all_56_11 = e2 % 152.07/22.64 | | | | | | % 152.07/22.64 | | | | | | COMBINE_EQS: (1), (41) imply: % 152.07/22.64 | | | | | | (42) all_8_2 = e2 % 152.07/22.64 | | | | | | % 152.07/22.64 | | | | | | REDUCE: (36), (42) imply: % 152.07/22.64 | | | | | | (43) $false % 152.07/22.64 | | | | | | % 152.07/22.64 | | | | | | CLOSE: (43) is inconsistent. % 152.07/22.64 | | | | | | % 152.07/22.64 | | | | | Case 2: % 152.07/22.64 | | | | | | % 152.07/22.64 | | | | | | (44) all_56_21 = e1 | all_56_31 = e0 % 152.07/22.64 | | | | | | % 152.07/22.64 | | | | | | BETA: splitting (44) gives: % 152.07/22.64 | | | | | | % 152.07/22.64 | | | | | | Case 1: % 152.07/22.64 | | | | | | | % 152.07/22.64 | | | | | | | (45) all_56_21 = e1 % 152.07/22.64 | | | | | | | % 152.07/22.64 | | | | | | | COMBINE_EQS: (7), (45) imply: % 152.07/22.64 | | | | | | | (46) e1 = e0 % 152.07/22.64 | | | | | | | % 152.07/22.64 | | | | | | | REDUCE: (10), (46) imply: % 152.07/22.64 | | | | | | | (47) $false % 152.07/22.64 | | | | | | | % 152.07/22.64 | | | | | | | CLOSE: (47) is inconsistent. % 152.07/22.64 | | | | | | | % 152.07/22.64 | | | | | | Case 2: % 152.07/22.64 | | | | | | | % 152.07/22.64 | | | | | | | (48) all_56_31 = e0 % 152.07/22.64 | | | | | | | % 152.07/22.64 | | | | | | | COMBINE_EQS: (16), (48) imply: % 152.07/22.64 | | | | | | | (49) all_4_2 = e0 % 152.07/22.64 | | | | | | | % 152.07/22.64 | | | | | | | SIMP: (49) implies: % 152.07/22.64 | | | | | | | (50) all_4_2 = e0 % 152.07/22.64 | | | | | | | % 152.07/22.64 | | | | | | | REDUCE: (20), (50) imply: % 152.07/22.64 | | | | | | | (51) ~ (e3 = e0) % 152.07/22.64 | | | | | | | % 152.07/22.64 | | | | | | | SIMP: (51) implies: % 152.07/22.64 | | | | | | | (52) ~ (e3 = e0) % 152.07/22.64 | | | | | | | % 152.07/22.64 | | | | | | | REDUCE: (14), (50) imply: % 152.07/22.64 | | | | | | | (53) op(e0, e0) = all_4_1 % 152.07/22.64 | | | | | | | % 152.07/22.64 | | | | | | | REDUCE: (22), (50) imply: % 152.07/22.64 | | | | | | | (54) op(e0, e0) = all_56_30 % 152.07/22.64 | | | | | | | % 152.07/22.64 | | | | | | | REDUCE: (4), (50) imply: % 152.07/22.64 | | | | | | | (55) op(e0, e0) = e0 % 152.07/22.64 | | | | | | | % 152.07/22.64 | | | | | | | REF_CLOSE: (11), (17), (52), (53), (54), (55) are inconsistent by % 152.07/22.64 | | | | | | | sub-proof #454. % 152.07/22.64 | | | | | | | % 152.07/22.64 | | | | | | End of split % 152.07/22.64 | | | | | | % 152.07/22.64 | | | | | End of split % 152.07/22.64 | | | | | % 152.07/22.64 | | | | End of split % 152.07/22.64 | | | | % 152.07/22.64 | | | Case 2: % 152.07/22.64 | | | | % 152.07/22.64 | | | | (56) all_54_9 = e1 | all_54_9 = e0 % 152.07/22.64 | | | | % 152.07/22.64 | | | | REF_CLOSE: (2), (3), (13), (56) are inconsistent by sub-proof #678. % 152.07/22.64 | | | | % 152.07/22.64 | | | End of split % 152.07/22.64 | | | % 152.07/22.64 | | End of split % 152.07/22.64 | | % 152.07/22.64 | Case 2: % 152.07/22.64 | | % 152.07/22.64 | | (57) all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0 % 152.07/22.64 | | % 152.07/22.64 | | REF_CLOSE: (5), (8), (12), (21), (57) are inconsistent by sub-proof #451. % 152.07/22.64 | | % 152.07/22.64 | End of split % 152.07/22.64 | % 152.07/22.64 End of proof % 152.07/22.64 % 152.07/22.64 Sub-proof #451 shows that the following formulas are inconsistent: % 152.07/22.64 ---------------------------------------------------------------- % 152.07/22.64 (1) all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0 % 152.07/22.64 (2) ~ (all_6_0 = e2) % 152.07/22.64 (3) ~ (all_6_0 = e1) % 152.07/22.64 (4) all_54_8 = all_6_0 % 152.07/22.64 (5) ~ (all_6_0 = e0) % 152.07/22.64 % 152.07/22.64 Begin of proof % 152.07/22.64 | % 152.07/22.64 | BETA: splitting (1) gives: % 152.07/22.64 | % 152.07/22.64 | Case 1: % 152.07/22.64 | | % 152.07/22.64 | | (6) all_54_8 = e2 % 152.07/22.64 | | % 152.07/22.64 | | REF_CLOSE: (2), (4), (6) are inconsistent by sub-proof #453. % 152.07/22.64 | | % 152.07/22.64 | Case 2: % 152.07/22.64 | | % 152.07/22.64 | | (7) all_54_8 = e1 | all_54_8 = e0 % 152.07/22.64 | | % 152.07/22.64 | | BETA: splitting (7) gives: % 152.07/22.64 | | % 152.07/22.64 | | Case 1: % 152.07/22.64 | | | % 152.07/22.64 | | | (8) all_54_8 = e1 % 152.07/22.64 | | | % 152.07/22.64 | | | COMBINE_EQS: (4), (8) imply: % 152.07/22.64 | | | (9) all_6_0 = e1 % 152.07/22.64 | | | % 152.07/22.64 | | | SIMP: (9) implies: % 152.07/22.64 | | | (10) all_6_0 = e1 % 152.07/22.64 | | | % 152.07/22.64 | | | REDUCE: (3), (10) imply: % 152.07/22.64 | | | (11) $false % 152.07/22.64 | | | % 152.07/22.64 | | | CLOSE: (11) is inconsistent. % 152.07/22.64 | | | % 152.07/22.64 | | Case 2: % 152.07/22.64 | | | % 152.07/22.64 | | | (12) all_54_8 = e0 % 152.07/22.64 | | | % 152.07/22.64 | | | REF_CLOSE: (4), (5), (12) are inconsistent by sub-proof #452. % 152.07/22.64 | | | % 152.07/22.64 | | End of split % 152.07/22.64 | | % 152.07/22.64 | End of split % 152.07/22.64 | % 152.07/22.64 End of proof % 152.07/22.64 % 152.07/22.64 Sub-proof #452 shows that the following formulas are inconsistent: % 152.07/22.64 ---------------------------------------------------------------- % 152.07/22.64 (1) all_54_8 = all_6_0 % 152.07/22.64 (2) all_54_8 = e0 % 152.07/22.64 (3) ~ (all_6_0 = e0) % 152.07/22.64 % 152.07/22.64 Begin of proof % 152.07/22.64 | % 152.07/22.64 | COMBINE_EQS: (1), (2) imply: % 152.07/22.64 | (4) all_6_0 = e0 % 152.07/22.64 | % 152.07/22.64 | SIMP: (4) implies: % 152.07/22.64 | (5) all_6_0 = e0 % 152.07/22.64 | % 152.07/22.64 | REDUCE: (3), (5) imply: % 152.07/22.64 | (6) $false % 152.07/22.64 | % 152.07/22.64 | CLOSE: (6) is inconsistent. % 152.07/22.64 | % 152.07/22.64 End of proof % 152.07/22.64 % 152.07/22.64 Sub-proof #453 shows that the following formulas are inconsistent: % 152.07/22.64 ---------------------------------------------------------------- % 152.07/22.64 (1) all_54_8 = all_6_0 % 152.07/22.64 (2) all_54_8 = e2 % 152.07/22.64 (3) ~ (all_6_0 = e2) % 152.07/22.64 % 152.07/22.64 Begin of proof % 152.07/22.64 | % 152.07/22.64 | COMBINE_EQS: (1), (2) imply: % 152.07/22.64 | (4) all_6_0 = e2 % 152.07/22.64 | % 152.07/22.64 | SIMP: (4) implies: % 152.07/22.64 | (5) all_6_0 = e2 % 152.07/22.64 | % 152.07/22.64 | REDUCE: (3), (5) imply: % 152.07/22.64 | (6) $false % 152.07/22.64 | % 152.07/22.64 | CLOSE: (6) is inconsistent. % 152.07/22.64 | % 152.07/22.64 End of proof % 152.07/22.64 % 152.07/22.64 Sub-proof #454 shows that the following formulas are inconsistent: % 152.07/22.64 ---------------------------------------------------------------- % 152.07/22.64 (1) ~ (e3 = e0) % 152.07/22.64 (2) op(e0, e0) = all_56_30 % 152.07/22.64 (3) op(e0, e0) = all_4_1 % 152.07/22.64 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 152.07/22.64 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 152.07/22.64 (5) op(e0, e0) = e3 % 152.07/22.64 (6) op(e0, e0) = e0 % 152.07/22.64 % 152.07/22.64 Begin of proof % 152.07/22.64 | % 152.07/22.64 | GROUND_INST: instantiating (4) with e0, all_4_1, e0, e0, simplifying with (3), % 152.07/22.64 | (6) gives: % 152.07/22.64 | (7) all_4_1 = e0 % 152.07/22.64 | % 152.07/22.64 | GROUND_INST: instantiating (4) with all_4_1, all_56_30, e0, e0, simplifying % 152.07/22.64 | with (2), (3) gives: % 152.07/22.64 | (8) all_56_30 = all_4_1 % 152.07/22.64 | % 152.07/22.64 | GROUND_INST: instantiating (4) with e3, all_56_30, e0, e0, simplifying with % 152.07/22.64 | (2), (5) gives: % 152.07/22.64 | (9) all_56_30 = e3 % 152.07/22.64 | % 152.07/22.64 | COMBINE_EQS: (8), (9) imply: % 152.07/22.64 | (10) all_4_1 = e3 % 152.07/22.64 | % 152.07/22.64 | SIMP: (10) implies: % 152.07/22.64 | (11) all_4_1 = e3 % 152.07/22.64 | % 152.07/22.64 | COMBINE_EQS: (7), (11) imply: % 152.07/22.64 | (12) e3 = e0 % 152.07/22.64 | % 152.07/22.64 | SIMP: (12) implies: % 152.07/22.64 | (13) e3 = e0 % 152.07/22.64 | % 152.07/22.64 | REDUCE: (1), (13) imply: % 152.07/22.64 | (14) $false % 152.07/22.64 | % 152.07/22.64 | CLOSE: (14) is inconsistent. % 152.07/22.64 | % 152.07/22.64 End of proof % 152.07/22.64 % 152.07/22.64 Sub-proof #455 shows that the following formulas are inconsistent: % 152.07/22.64 ---------------------------------------------------------------- % 152.07/22.64 (1) all_54_0 = all_10_2 % 152.07/22.64 (2) ~ (all_6_2 = e3) % 152.07/22.64 (3) ~ (e3 = e2) % 152.07/22.64 (4) all_58_4 = all_52_8 % 152.07/22.64 (5) ~ (all_10_2 = e1) % 152.07/22.64 (6) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 152.07/22.64 (7) all_56_1 = all_10_2 % 152.07/22.64 (8) ~ (all_10_2 = e2) % 152.07/22.64 (9) all_58_13 = all_52_7 % 152.07/22.64 (10) all_58_12 = e2 % 152.07/22.64 (11) all_56_7 = all_52_12 % 152.07/22.64 (12) ~ (all_4_2 = e1) % 152.07/22.64 (13) all_58_8 = all_6_2 % 152.07/22.64 (14) ~ (all_52_8 = all_10_2) % 152.07/22.64 (15) ~ (all_56_1 = e0) | all_56_7 = e3 % 152.07/22.64 (16) all_58_5 = e2 % 152.07/22.64 (17) ~ (e2 = e1) % 152.07/22.64 (18) all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3 % 152.07/22.64 (19) ~ (all_52_7 = e1) % 152.07/22.64 (20) all_58_15 = all_4_2 % 152.07/22.64 (21) all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1 % 152.07/22.64 (22) ~ (e3 = e1) % 152.07/22.64 (23) ~ (all_52_8 = all_52_12) % 152.07/22.64 % 152.07/22.64 Begin of proof % 152.07/22.64 | % 152.07/22.64 | BETA: splitting (21) gives: % 152.07/22.64 | % 152.07/22.64 | Case 1: % 152.07/22.64 | | % 152.07/22.64 | | (24) all_58_12 = e1 % 152.07/22.64 | | % 152.07/22.64 | | COMBINE_EQS: (10), (24) imply: % 152.07/22.64 | | (25) e2 = e1 % 152.07/22.64 | | % 152.07/22.64 | | REDUCE: (17), (25) imply: % 152.07/22.64 | | (26) $false % 152.07/22.64 | | % 152.07/22.64 | | CLOSE: (26) is inconsistent. % 152.07/22.64 | | % 152.07/22.64 | Case 2: % 152.07/22.64 | | % 152.07/22.64 | | (27) all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1 % 152.07/22.64 | | % 152.07/22.64 | | BETA: splitting (27) gives: % 152.07/22.64 | | % 152.07/22.64 | | Case 1: % 152.07/22.64 | | | % 152.07/22.64 | | | (28) all_58_13 = e1 % 152.07/22.64 | | | % 152.07/22.64 | | | REF_CLOSE: (9), (19), (28) are inconsistent by sub-proof #704. % 152.07/22.64 | | | % 152.07/22.64 | | Case 2: % 152.07/22.64 | | | % 152.07/22.64 | | | (29) all_58_14 = e1 | all_58_15 = e1 % 152.07/22.64 | | | % 152.07/22.64 | | | BETA: splitting (18) gives: % 152.07/22.64 | | | % 152.07/22.64 | | | Case 1: % 152.07/22.64 | | | | % 152.07/22.64 | | | | (30) all_58_4 = e3 % 152.07/22.64 | | | | % 152.07/22.64 | | | | COMBINE_EQS: (4), (30) imply: % 152.07/22.64 | | | | (31) all_52_8 = e3 % 152.07/22.64 | | | | % 152.07/22.64 | | | | REDUCE: (23), (31) imply: % 152.07/22.64 | | | | (32) ~ (all_52_12 = e3) % 152.07/22.64 | | | | % 152.07/22.64 | | | | SIMP: (32) implies: % 152.07/22.64 | | | | (33) ~ (all_52_12 = e3) % 152.07/22.64 | | | | % 152.07/22.64 | | | | REDUCE: (14), (31) imply: % 152.07/22.64 | | | | (34) ~ (all_10_2 = e3) % 152.07/22.64 | | | | % 152.07/22.64 | | | | SIMP: (34) implies: % 152.07/22.64 | | | | (35) ~ (all_10_2 = e3) % 152.07/22.64 | | | | % 152.07/22.64 | | | | REF_CLOSE: (1), (5), (6), (7), (8), (11), (15), (33), (35) are % 152.07/22.64 | | | | inconsistent by sub-proof #707. % 152.07/22.64 | | | | % 152.07/22.64 | | | Case 2: % 152.07/22.64 | | | | % 152.07/22.64 | | | | (36) all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3 % 152.07/22.64 | | | | % 152.07/22.64 | | | | BETA: splitting (36) gives: % 152.07/22.64 | | | | % 152.07/22.64 | | | | Case 1: % 152.07/22.64 | | | | | % 152.07/22.64 | | | | | (37) all_58_5 = e3 % 152.07/22.64 | | | | | % 152.07/22.64 | | | | | REF_CLOSE: (3), (16), (37) are inconsistent by sub-proof #457. % 152.07/22.64 | | | | | % 152.07/22.64 | | | | Case 2: % 152.07/22.64 | | | | | % 152.07/22.64 | | | | | (38) all_58_8 = e3 | all_58_14 = e3 % 152.07/22.64 | | | | | % 152.07/22.64 | | | | | BETA: splitting (38) gives: % 152.07/22.64 | | | | | % 152.07/22.64 | | | | | Case 1: % 152.07/22.64 | | | | | | % 152.07/22.64 | | | | | | (39) all_58_8 = e3 % 152.07/22.64 | | | | | | % 152.07/22.64 | | | | | | COMBINE_EQS: (13), (39) imply: % 152.07/22.64 | | | | | | (40) all_6_2 = e3 % 152.07/22.64 | | | | | | % 152.07/22.64 | | | | | | REDUCE: (2), (40) imply: % 152.07/22.64 | | | | | | (41) $false % 152.07/22.64 | | | | | | % 152.07/22.64 | | | | | | CLOSE: (41) is inconsistent. % 152.07/22.64 | | | | | | % 152.07/22.64 | | | | | Case 2: % 152.07/22.64 | | | | | | % 152.07/22.64 | | | | | | (42) all_58_14 = e3 % 152.07/22.64 | | | | | | % 152.07/22.64 | | | | | | REF_CLOSE: (12), (20), (22), (29), (42) are inconsistent by % 152.07/22.64 | | | | | | sub-proof #456. % 152.07/22.64 | | | | | | % 152.07/22.64 | | | | | End of split % 152.07/22.64 | | | | | % 152.07/22.64 | | | | End of split % 152.07/22.64 | | | | % 152.07/22.64 | | | End of split % 152.07/22.64 | | | % 152.07/22.64 | | End of split % 152.07/22.64 | | % 152.07/22.64 | End of split % 152.07/22.64 | % 152.07/22.64 End of proof % 152.07/22.64 % 152.07/22.64 Sub-proof #456 shows that the following formulas are inconsistent: % 152.07/22.64 ---------------------------------------------------------------- % 152.07/22.64 (1) all_58_14 = e1 | all_58_15 = e1 % 152.07/22.64 (2) all_58_14 = e3 % 152.07/22.64 (3) ~ (all_4_2 = e1) % 152.07/22.64 (4) all_58_15 = all_4_2 % 152.07/22.64 (5) ~ (e3 = e1) % 152.07/22.64 % 152.07/22.64 Begin of proof % 152.07/22.64 | % 152.07/22.64 | BETA: splitting (1) gives: % 152.07/22.64 | % 152.07/22.64 | Case 1: % 152.07/22.64 | | % 152.07/22.64 | | (6) all_58_14 = e1 % 152.07/22.64 | | % 152.07/22.64 | | COMBINE_EQS: (2), (6) imply: % 152.07/22.64 | | (7) e3 = e1 % 152.07/22.64 | | % 152.07/22.64 | | REDUCE: (5), (7) imply: % 152.07/22.64 | | (8) $false % 152.07/22.64 | | % 152.07/22.64 | | CLOSE: (8) is inconsistent. % 152.07/22.64 | | % 152.07/22.64 | Case 2: % 152.07/22.64 | | % 152.07/22.64 | | (9) all_58_15 = e1 % 152.07/22.64 | | % 152.07/22.64 | | COMBINE_EQS: (4), (9) imply: % 152.07/22.64 | | (10) all_4_2 = e1 % 152.07/22.64 | | % 152.07/22.64 | | REDUCE: (3), (10) imply: % 152.07/22.64 | | (11) $false % 152.07/22.64 | | % 152.07/22.64 | | CLOSE: (11) is inconsistent. % 152.07/22.64 | | % 152.07/22.64 | End of split % 152.07/22.64 | % 152.07/22.64 End of proof % 152.07/22.64 % 152.07/22.64 Sub-proof #457 shows that the following formulas are inconsistent: % 152.07/22.64 ---------------------------------------------------------------- % 152.07/22.64 (1) all_58_5 = e3 % 152.07/22.64 (2) all_58_5 = e2 % 152.07/22.64 (3) ~ (e3 = e2) % 152.07/22.64 % 152.07/22.64 Begin of proof % 152.07/22.64 | % 152.07/22.64 | COMBINE_EQS: (1), (2) imply: % 152.07/22.64 | (4) e3 = e2 % 152.07/22.64 | % 152.07/22.64 | SIMP: (4) implies: % 152.07/22.64 | (5) e3 = e2 % 152.07/22.64 | % 152.07/22.64 | REDUCE: (3), (5) imply: % 152.07/22.64 | (6) $false % 152.07/22.64 | % 152.07/22.64 | CLOSE: (6) is inconsistent. % 152.07/22.64 | % 152.07/22.64 End of proof % 152.07/22.64 % 152.07/22.64 Sub-proof #458 shows that the following formulas are inconsistent: % 152.07/22.64 ---------------------------------------------------------------- % 152.07/22.64 (1) all_54_10 = all_6_2 % 152.07/22.64 (2) ~ (all_8_2 = e1) % 152.07/22.64 (3) ~ (all_6_2 = e3) % 152.07/22.64 (4) all_54_5 = all_8_2 % 152.07/22.64 (5) ~ (all_6_0 = e2) % 152.07/22.64 (6) all_56_21 = all_6_2 % 152.07/22.64 (7) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 152.07/22.64 (8) all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2 % 152.07/22.64 (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 152.07/22.64 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 152.07/22.64 (10) all_58_8 = all_6_2 % 152.07/22.64 (11) ~ (all_8_2 = e3) % 152.07/22.64 (12) all_58_11 = all_52_14 % 152.07/22.64 (13) all_56_23 = all_52_14 % 152.07/22.64 (14) all_58_6 = all_6_0 % 152.07/22.64 (15) op(e1, e1) = all_6_2 % 152.07/22.64 (16) ~ (all_52_6 = all_8_2) % 152.07/22.64 (17) ~ (all_6_2 = e2) % 152.07/22.64 (18) all_58_7 = all_52_6 % 152.07/22.64 (19) op(e1, all_6_2) = all_56_20 % 152.07/22.64 (20) ~ (all_56_21 = e0) | all_56_23 = e1 % 152.07/22.64 (21) ~ (all_8_2 = e0) % 152.07/22.65 (22) op(all_6_2, all_6_2) = e3 % 152.07/22.65 (23) ~ (all_52_14 = all_6_2) % 152.07/22.65 (24) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 152.07/22.65 % 152.07/22.65 Begin of proof % 152.07/22.65 | % 152.07/22.65 | BETA: splitting (24) gives: % 152.07/22.65 | % 152.07/22.65 | Case 1: % 152.07/22.65 | | % 152.07/22.65 | | (25) all_54_5 = e3 % 152.07/22.65 | | % 152.07/22.65 | | REF_CLOSE: (4), (11), (25) are inconsistent by sub-proof #737. % 152.07/22.65 | | % 152.07/22.65 | Case 2: % 152.07/22.65 | | % 152.07/22.65 | | (26) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 152.07/22.65 | | % 152.07/22.65 | | BETA: splitting (26) gives: % 152.07/22.65 | | % 152.07/22.65 | | Case 1: % 152.07/22.65 | | | % 152.07/22.65 | | | (27) all_54_5 = e2 % 152.07/22.65 | | | % 152.07/22.65 | | | COMBINE_EQS: (4), (27) imply: % 152.07/22.65 | | | (28) all_8_2 = e2 % 152.07/22.65 | | | % 152.07/22.65 | | | SIMP: (28) implies: % 152.07/22.65 | | | (29) all_8_2 = e2 % 152.07/22.65 | | | % 152.07/22.65 | | | REDUCE: (16), (29) imply: % 152.07/22.65 | | | (30) ~ (all_52_6 = e2) % 152.07/22.65 | | | % 152.07/22.65 | | | REDUCE: (2), (29) imply: % 152.07/22.65 | | | (31) ~ (e2 = e1) % 152.07/22.65 | | | % 152.07/22.65 | | | BETA: splitting (8) gives: % 152.07/22.65 | | | % 152.07/22.65 | | | Case 1: % 152.07/22.65 | | | | % 152.07/22.65 | | | | (32) all_58_6 = e2 % 152.07/22.65 | | | | % 152.07/22.65 | | | | REF_CLOSE: (5), (14), (32) are inconsistent by sub-proof #461. % 152.07/22.65 | | | | % 152.07/22.65 | | | Case 2: % 152.07/22.65 | | | | % 152.07/22.65 | | | | (33) all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2 % 152.07/22.65 | | | | % 152.07/22.65 | | | | BETA: splitting (33) gives: % 152.07/22.65 | | | | % 152.07/22.65 | | | | Case 1: % 152.07/22.65 | | | | | % 152.07/22.65 | | | | | (34) all_58_7 = e2 % 152.07/22.65 | | | | | % 152.07/22.65 | | | | | COMBINE_EQS: (18), (34) imply: % 152.07/22.65 | | | | | (35) all_52_6 = e2 % 152.07/22.65 | | | | | % 152.07/22.65 | | | | | REDUCE: (30), (35) imply: % 152.07/22.65 | | | | | (36) $false % 152.07/22.65 | | | | | % 152.07/22.65 | | | | | CLOSE: (36) is inconsistent. % 152.07/22.65 | | | | | % 152.07/22.65 | | | | Case 2: % 152.07/22.65 | | | | | % 152.07/22.65 | | | | | (37) all_58_8 = e2 | all_58_11 = e2 % 152.07/22.65 | | | | | % 152.07/22.65 | | | | | BETA: splitting (37) gives: % 152.07/22.65 | | | | | % 152.07/22.65 | | | | | Case 1: % 152.07/22.65 | | | | | | % 152.07/22.65 | | | | | | (38) all_58_8 = e2 % 152.07/22.65 | | | | | | % 152.07/22.65 | | | | | | COMBINE_EQS: (10), (38) imply: % 152.07/22.65 | | | | | | (39) all_6_2 = e2 % 152.07/22.65 | | | | | | % 152.07/22.65 | | | | | | REDUCE: (17), (39) imply: % 152.07/22.65 | | | | | | (40) $false % 152.07/22.65 | | | | | | % 152.07/22.65 | | | | | | CLOSE: (40) is inconsistent. % 152.07/22.65 | | | | | | % 152.07/22.65 | | | | | Case 2: % 152.07/22.65 | | | | | | % 152.07/22.65 | | | | | | (41) all_58_11 = e2 % 152.07/22.65 | | | | | | % 152.07/22.65 | | | | | | COMBINE_EQS: (12), (41) imply: % 152.07/22.65 | | | | | | (42) all_52_14 = e2 % 152.07/22.65 | | | | | | % 152.07/22.65 | | | | | | COMBINE_EQS: (13), (42) imply: % 152.07/22.65 | | | | | | (43) all_56_23 = e2 % 152.07/22.65 | | | | | | % 152.07/22.65 | | | | | | REDUCE: (23), (42) imply: % 152.07/22.65 | | | | | | (44) ~ (all_6_2 = e2) % 152.07/22.65 | | | | | | % 152.07/22.65 | | | | | | BETA: splitting (20) gives: % 152.07/22.65 | | | | | | % 152.07/22.65 | | | | | | Case 1: % 152.07/22.65 | | | | | | | % 152.07/22.65 | | | | | | | (45) ~ (all_56_21 = e0) % 152.07/22.65 | | | | | | | % 152.07/22.65 | | | | | | | REDUCE: (6), (45) imply: % 152.07/22.65 | | | | | | | (46) ~ (all_6_2 = e0) % 152.07/22.65 | | | | | | | % 152.07/22.65 | | | | | | | REF_CLOSE: (1), (3), (7), (9), (15), (17), (19), (22), (46) are % 152.07/22.65 | | | | | | | inconsistent by sub-proof #459. % 152.07/22.65 | | | | | | | % 152.07/22.65 | | | | | | Case 2: % 152.07/22.65 | | | | | | | % 152.07/22.65 | | | | | | | (47) all_56_23 = e1 % 152.07/22.65 | | | | | | | % 152.07/22.65 | | | | | | | COMBINE_EQS: (43), (47) imply: % 152.07/22.65 | | | | | | | (48) e2 = e1 % 152.07/22.65 | | | | | | | % 152.07/22.65 | | | | | | | SIMP: (48) implies: % 152.07/22.65 | | | | | | | (49) e2 = e1 % 152.07/22.65 | | | | | | | % 152.07/22.65 | | | | | | | REDUCE: (31), (49) imply: % 152.07/22.65 | | | | | | | (50) $false % 152.07/22.65 | | | | | | | % 152.07/22.65 | | | | | | | CLOSE: (50) is inconsistent. % 152.07/22.65 | | | | | | | % 152.07/22.65 | | | | | | End of split % 152.07/22.65 | | | | | | % 152.07/22.65 | | | | | End of split % 152.07/22.65 | | | | | % 152.07/22.65 | | | | End of split % 152.07/22.65 | | | | % 152.07/22.65 | | | End of split % 152.07/22.65 | | | % 152.07/22.65 | | Case 2: % 152.07/22.65 | | | % 152.07/22.65 | | | (51) all_54_5 = e1 | all_54_5 = e0 % 152.07/22.65 | | | % 152.07/22.65 | | | REF_CLOSE: (2), (4), (21), (51) are inconsistent by sub-proof #645. % 152.07/22.65 | | | % 152.07/22.65 | | End of split % 152.07/22.65 | | % 152.07/22.65 | End of split % 152.07/22.65 | % 152.07/22.65 End of proof % 152.07/22.65 % 152.07/22.65 Sub-proof #459 shows that the following formulas are inconsistent: % 152.07/22.65 ---------------------------------------------------------------- % 152.07/22.65 (1) all_54_10 = all_6_2 % 152.07/22.65 (2) ~ (all_6_2 = e3) % 152.07/22.65 (3) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 152.07/22.65 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 152.07/22.65 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 152.07/22.65 (5) ~ (all_6_2 = e0) % 152.07/22.65 (6) op(e1, e1) = all_6_2 % 152.07/22.65 (7) ~ (all_6_2 = e2) % 152.07/22.65 (8) op(e1, all_6_2) = all_56_20 % 152.07/22.65 (9) op(all_6_2, all_6_2) = e3 % 152.07/22.65 % 152.07/22.65 Begin of proof % 152.07/22.65 | % 152.07/22.65 | BETA: splitting (3) gives: % 152.07/22.65 | % 152.07/22.65 | Case 1: % 152.07/22.65 | | % 152.07/22.65 | | (10) all_54_10 = e3 % 152.07/22.65 | | % 152.07/22.65 | | REF_CLOSE: (1), (2), (10) are inconsistent by sub-proof #736. % 152.07/22.65 | | % 152.07/22.65 | Case 2: % 152.07/22.65 | | % 152.07/22.65 | | (11) ~ (all_54_10 = e3) % 152.07/22.65 | | (12) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 152.07/22.65 | | % 152.07/22.65 | | BETA: splitting (12) gives: % 152.07/22.65 | | % 152.07/22.65 | | Case 1: % 152.07/22.65 | | | % 152.07/22.65 | | | (13) all_54_10 = e2 % 152.07/22.65 | | | % 152.07/22.65 | | | REF_CLOSE: (1), (7), (13) are inconsistent by sub-proof #735. % 152.07/22.65 | | | % 152.07/22.65 | | Case 2: % 152.07/22.65 | | | % 152.07/22.65 | | | (14) all_54_10 = e1 | all_54_10 = e0 % 152.07/22.65 | | | % 152.07/22.65 | | | BETA: splitting (14) gives: % 152.07/22.65 | | | % 152.07/22.65 | | | Case 1: % 152.07/22.65 | | | | % 152.07/22.65 | | | | (15) all_54_10 = e1 % 152.07/22.65 | | | | % 152.07/22.65 | | | | COMBINE_EQS: (1), (15) imply: % 152.07/22.65 | | | | (16) all_6_2 = e1 % 152.07/22.65 | | | | % 152.07/22.65 | | | | SIMP: (16) implies: % 152.07/22.65 | | | | (17) all_6_2 = e1 % 152.07/22.65 | | | | % 152.07/22.65 | | | | REDUCE: (2), (17) imply: % 152.07/22.65 | | | | (18) ~ (e3 = e1) % 152.07/22.65 | | | | % 152.07/22.65 | | | | SIMP: (18) implies: % 152.07/22.65 | | | | (19) ~ (e3 = e1) % 152.07/22.65 | | | | % 152.07/22.65 | | | | REF_CLOSE: (4), (6), (8), (9), (17), (19) are inconsistent by sub-proof % 152.07/22.65 | | | | #460. % 152.07/22.65 | | | | % 152.07/22.65 | | | Case 2: % 152.07/22.65 | | | | % 152.07/22.65 | | | | (20) all_54_10 = e0 % 152.07/22.65 | | | | % 152.07/22.65 | | | | REF_CLOSE: (1), (5), (20) are inconsistent by sub-proof #705. % 152.07/22.65 | | | | % 152.07/22.65 | | | End of split % 152.07/22.65 | | | % 152.07/22.65 | | End of split % 152.07/22.65 | | % 152.07/22.65 | End of split % 152.07/22.65 | % 152.07/22.65 End of proof % 152.07/22.65 % 152.07/22.65 Sub-proof #460 shows that the following formulas are inconsistent: % 152.07/22.65 ---------------------------------------------------------------- % 152.07/22.65 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 152.07/22.65 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 152.07/22.65 (2) op(e1, e1) = all_6_2 % 152.07/22.65 (3) all_6_2 = e1 % 152.07/22.65 (4) op(e1, all_6_2) = all_56_20 % 152.07/22.65 (5) ~ (e3 = e1) % 152.07/22.65 (6) op(all_6_2, all_6_2) = e3 % 152.07/22.65 % 152.07/22.65 Begin of proof % 152.07/22.65 | % 152.07/22.65 | REDUCE: (3), (6) imply: % 152.07/22.65 | (7) op(e1, e1) = e3 % 152.07/22.65 | % 152.07/22.65 | REDUCE: (3), (4) imply: % 152.07/22.65 | (8) op(e1, e1) = all_56_20 % 152.07/22.65 | % 152.07/22.65 | REDUCE: (2), (3) imply: % 152.07/22.65 | (9) op(e1, e1) = e1 % 152.07/22.65 | % 152.07/22.65 | REF_CLOSE: (1), (5), (7), (8), (9) are inconsistent by sub-proof #516. % 152.07/22.65 | % 152.07/22.65 End of proof % 152.07/22.65 % 152.07/22.65 Sub-proof #461 shows that the following formulas are inconsistent: % 152.07/22.65 ---------------------------------------------------------------- % 152.07/22.65 (1) all_58_6 = all_6_0 % 152.07/22.65 (2) all_58_6 = e2 % 152.07/22.65 (3) ~ (all_6_0 = e2) % 152.07/22.65 % 152.07/22.65 Begin of proof % 152.07/22.65 | % 152.07/22.65 | COMBINE_EQS: (1), (2) imply: % 152.07/22.65 | (4) all_6_0 = e2 % 152.07/22.65 | % 152.07/22.65 | SIMP: (4) implies: % 152.07/22.65 | (5) all_6_0 = e2 % 152.07/22.65 | % 152.07/22.65 | REDUCE: (3), (5) imply: % 152.07/22.65 | (6) $false % 152.07/22.65 | % 152.07/22.65 | CLOSE: (6) is inconsistent. % 152.07/22.65 | % 152.07/22.65 End of proof % 152.07/22.65 % 152.07/22.65 Sub-proof #462 shows that the following formulas are inconsistent: % 152.07/22.65 ---------------------------------------------------------------- % 152.07/22.65 (1) ~ (all_52_11 = all_6_2) % 152.07/22.65 (2) all_56_31 = e1 % 152.07/22.65 (3) ~ (all_52_7 = all_52_11) % 152.07/22.65 (4) op(e1, all_6_1) = e3 % 152.07/22.65 (5) all_54_10 = all_6_2 % 152.07/22.65 (6) ~ (all_56_21 = e2) | all_56_19 = e1 % 152.07/22.65 (7) all_54_12 = all_52_3 % 152.07/22.65 (8) ~ (all_6_1 = e3) % 152.07/22.65 (9) all_52_11 = e0 % 152.07/22.65 (10) all_56_21 = all_6_2 % 152.07/22.65 (11) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 152.07/22.65 (12) all_56_17 = all_52_2 % 152.07/22.65 (13) op(e0, e2) = all_52_7 % 152.07/22.65 (14) ~ (all_56_21 = e3) | all_56_17 = e1 % 152.07/22.65 (15) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 152.07/22.65 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 152.07/22.65 (16) op(e0, all_4_1) = all_4_0 % 152.07/22.65 (17) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0 % 152.07/22.65 (18) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0 % 152.07/22.65 (19) ~ (all_52_2 = all_52_3) % 152.07/22.65 (20) op(all_4_2, all_4_2) = all_4_1 % 152.07/22.65 (21) ~ (all_52_3 = all_52_11) % 152.07/22.65 (22) ~ (all_52_6 = all_52_7) % 152.07/22.65 (23) all_56_31 = all_4_2 % 152.07/22.65 (24) op(all_6_2, all_6_2) = all_6_1 % 152.07/22.65 (25) all_54_13 = all_52_7 % 152.07/22.65 (26) op(e1, e1) = all_6_2 % 152.07/22.65 (27) op(e0, e3) = all_52_3 % 152.07/22.65 (28) op(e1, all_6_2) = all_56_20 % 152.07/22.65 (29) all_56_19 = all_52_6 % 152.07/22.65 (30) ~ (all_4_0 = e2) % 152.07/22.65 (31) ~ (all_4_0 = e3) % 152.07/22.65 % 152.07/22.65 Begin of proof % 152.07/22.65 | % 152.07/22.65 | COMBINE_EQS: (2), (23) imply: % 152.07/22.65 | (32) all_4_2 = e1 % 152.07/22.65 | % 152.07/22.65 | REDUCE: (9), (21) imply: % 152.07/22.65 | (33) ~ (all_52_3 = e0) % 152.07/22.65 | % 152.07/22.65 | REDUCE: (3), (9) imply: % 152.07/22.65 | (34) ~ (all_52_7 = e0) % 152.07/22.65 | % 152.07/22.65 | REDUCE: (1), (9) imply: % 152.07/22.65 | (35) ~ (all_6_2 = e0) % 152.07/22.65 | % 152.07/22.65 | SIMP: (35) implies: % 152.07/22.65 | (36) ~ (all_6_2 = e0) % 152.07/22.65 | % 152.07/22.65 | REDUCE: (20), (32) imply: % 152.07/22.65 | (37) op(e1, e1) = all_4_1 % 152.07/22.65 | % 152.07/22.65 | REF_CLOSE: (4), (5), (6), (7), (8), (10), (11), (12), (13), (14), (15), (16), % 152.07/22.65 | (17), (18), (19), (22), (24), (25), (26), (27), (28), (29), (30), % 152.07/22.65 | (31), (33), (34), (36), (37) are inconsistent by sub-proof #499. % 152.07/22.65 | % 152.07/22.65 End of proof % 152.07/22.65 % 152.07/22.65 Sub-proof #463 shows that the following formulas are inconsistent: % 152.07/22.65 ---------------------------------------------------------------- % 152.07/22.65 (1) all_56_11 = all_8_2 % 152.07/22.65 (2) op(e0, all_52_13) = all_56_14 % 152.07/22.65 (3) ~ (all_56_11 = e1) | all_56_13 = e2 % 152.07/22.65 (4) ~ (all_52_11 = all_6_2) % 152.07/22.65 (5) all_56_31 = e1 % 152.07/22.65 (6) ~ (all_52_7 = all_52_11) % 152.07/22.65 (7) ~ (all_8_1 = e1) % 152.07/22.65 (8) ~ (all_52_1 = all_52_9) % 152.07/22.65 (9) all_54_10 = all_6_2 % 152.07/22.65 (10) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0 % 152.07/22.65 (11) ~ (all_52_13 = all_8_2) % 152.07/22.65 (12) ~ (all_56_21 = e2) | all_56_19 = e1 % 152.07/22.65 (13) all_54_0 = all_10_2 % 152.07/22.65 (14) all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2 % 152.07/22.65 (15) ~ (all_52_9 = all_8_2) % 152.07/22.65 (16) all_54_12 = all_52_3 % 152.07/22.65 (17) ~ (all_52_12 = all_52_13) % 152.07/22.65 (18) ~ (e3 = e2) % 152.07/22.65 (19) op(e0, e0) = all_4_2 % 152.07/22.65 (20) all_58_4 = all_52_8 % 152.07/22.65 (21) all_54_5 = all_8_2 % 152.07/22.65 (22) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 152.07/22.65 (23) all_52_11 = e0 % 152.07/22.65 (24) ~ (all_10_1 = e1) % 152.07/22.65 (25) all_56_21 = all_6_2 % 152.07/22.65 (26) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 152.07/22.65 (27) all_56_1 = all_10_2 % 152.07/22.65 (28) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0 % 152.07/22.65 (29) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0 % 152.07/22.65 (30) all_58_5 = all_52_9 % 152.07/22.65 (31) all_56_17 = all_52_2 % 152.07/22.65 (32) all_58_9 = all_52_12 % 152.07/22.65 (33) op(e0, e2) = all_52_7 % 152.07/22.65 (34) ~ (all_56_1 = e1) | all_56_5 = e3 % 152.07/22.65 (35) all_58_1 = all_52_4 % 152.07/22.65 (36) all_58_13 = all_52_7 % 152.07/22.65 (37) ~ (all_52_8 = all_6_2) % 152.07/22.65 (38) all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1 % 152.07/22.65 (39) ~ (all_56_21 = e3) | all_56_17 = e1 % 152.07/22.65 (40) all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1 % 152.07/22.65 (41) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 152.07/22.65 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 152.07/22.65 (42) all_54_3 = all_52_12 % 152.07/22.65 (43) all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0 % 152.07/22.65 (44) ~ (all_56_11 = e3) | all_56_9 = e2 % 152.07/22.65 (45) op(e0, all_4_1) = all_4_0 % 152.07/22.65 (46) all_56_7 = all_52_12 % 152.07/22.65 (47) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0 % 152.07/22.65 (48) all_56_13 = all_52_9 % 152.07/22.65 (49) ~ (all_52_7 = all_4_2) % 152.07/22.65 (50) all_58_8 = all_6_2 % 152.07/22.65 (51) ~ (all_6_0 = e3) % 152.07/22.65 (52) all_54_6 = all_52_9 % 152.07/22.65 (53) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0 % 152.07/22.65 (54) ~ (all_56_1 = e2) | all_56_3 = e3 % 152.07/22.65 (55) ~ (all_56_1 = e0) | all_56_7 = e3 % 152.07/22.65 (56) ~ (all_52_9 = all_52_13) % 152.07/22.65 (57) ~ (all_52_2 = all_52_3) % 152.07/22.65 (58) op(e1, all_6_1) = all_6_0 % 152.07/22.65 (59) op(all_4_2, all_4_2) = all_4_1 % 152.07/22.65 (60) all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3 % 152.07/22.65 (61) ~ (all_52_3 = all_52_11) % 152.07/22.65 (62) all_58_3 = all_8_2 % 152.07/22.65 (63) all_56_3 = all_52_4 % 152.07/22.65 (64) all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1 % 152.07/22.65 (65) ~ (all_52_6 = all_52_7) % 152.07/22.65 (66) all_56_31 = all_4_2 % 152.07/22.65 (67) ~ (all_52_9 = all_52_11) % 152.07/22.65 (68) all_54_7 = all_52_13 % 152.07/22.65 (69) op(all_6_2, all_6_2) = all_6_1 % 152.07/22.65 (70) ~ (all_52_13 = all_4_2) % 152.07/22.65 (71) all_54_13 = all_52_7 % 152.07/22.65 (72) op(e1, e1) = all_6_2 % 152.07/22.65 (73) op(e0, e3) = all_52_3 % 152.07/22.65 (74) all_58_2 = all_52_1 % 152.07/22.65 (75) ~ (all_52_9 = all_6_2) % 152.07/22.65 (76) all_58_7 = all_52_6 % 152.07/22.65 (77) all_58_10 = all_52_13 % 152.07/22.65 (78) ~ (all_52_12 = all_4_2) % 152.07/22.65 (79) op(all_10_2, all_10_2) = all_10_1 % 152.07/22.65 (80) ~ (all_56_11 = e0) | all_56_15 = e2 % 152.07/22.65 (81) all_58_0 = all_10_2 % 152.07/22.65 (82) op(e1, all_6_2) = all_56_20 % 152.07/22.65 (83) ~ (all_52_4 = all_52_12) % 152.07/22.65 (84) ~ (all_52_8 = all_52_12) % 152.07/22.65 (85) ~ (all_52_6 = all_6_2) % 152.07/22.65 (86) ~ (all_52_4 = all_10_2) % 152.07/22.65 (87) ~ (all_52_4 = all_8_2) % 152.07/22.65 (88) op(all_8_2, all_8_2) = all_8_1 % 152.07/22.65 (89) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 152.07/22.65 (90) all_58_14 = all_52_11 % 152.07/22.65 (91) all_56_19 = all_52_6 % 152.07/22.65 (92) ~ (all_52_12 = all_10_2) % 152.07/22.65 (93) ~ (all_4_0 = e2) % 152.07/22.65 (94) ~ (all_4_0 = e3) % 152.07/22.65 (95) all_56_9 = all_52_1 % 152.07/22.65 (96) ~ (all_52_1 = all_10_2) % 152.07/22.65 % 152.07/22.65 Begin of proof % 152.07/22.65 | % 152.07/22.65 | COMBINE_EQS: (5), (66) imply: % 152.07/22.65 | (97) all_4_2 = e1 % 152.07/22.65 | % 152.07/22.65 | COMBINE_EQS: (23), (90) imply: % 152.07/22.65 | (98) all_58_14 = e0 % 152.07/22.65 | % 152.07/22.65 | REDUCE: (23), (61) imply: % 152.07/22.65 | (99) ~ (all_52_3 = e0) % 152.07/22.65 | % 152.07/22.65 | REDUCE: (6), (23) imply: % 152.07/22.65 | (100) ~ (all_52_7 = e0) % 152.07/22.65 | % 152.07/22.65 | REDUCE: (49), (97) imply: % 152.07/22.65 | (101) ~ (all_52_7 = e1) % 152.07/22.65 | % 152.07/22.65 | REDUCE: (23), (67) imply: % 152.07/22.65 | (102) ~ (all_52_9 = e0) % 152.07/22.65 | % 152.07/22.65 | REDUCE: (4), (23) imply: % 152.07/22.65 | (103) ~ (all_6_2 = e0) % 152.07/22.65 | % 152.07/22.65 | SIMP: (103) implies: % 152.07/22.65 | (104) ~ (all_6_2 = e0) % 152.07/22.65 | % 152.07/22.65 | REDUCE: (78), (97) imply: % 152.07/22.65 | (105) ~ (all_52_12 = e1) % 152.07/22.65 | % 152.07/22.65 | REDUCE: (70), (97) imply: % 152.07/22.65 | (106) ~ (all_52_13 = e1) % 152.07/22.65 | % 152.07/22.65 | REDUCE: (59), (97) imply: % 152.07/22.65 | (107) op(e1, e1) = all_4_1 % 152.07/22.65 | % 152.07/22.65 | REDUCE: (19), (97) imply: % 152.07/22.65 | (108) op(e0, e0) = e1 % 152.07/22.65 | % 152.07/22.65 | REF_CLOSE: (1), (2), (3), (7), (8), (9), (10), (11), (12), (13), (14), (15), % 152.07/22.65 | (16), (17), (18), (20), (21), (22), (24), (25), (26), (27), (28), % 152.07/22.65 | (29), (30), (31), (32), (33), (34), (35), (36), (37), (38), (39), % 152.07/22.65 | (40), (41), (42), (43), (44), (45), (46), (47), (48), (50), (51), % 152.07/22.65 | (52), (53), (54), (55), (56), (57), (58), (60), (62), (63), (64), % 152.07/22.65 | (65), (68), (69), (71), (72), (73), (74), (75), (76), (77), (79), % 152.07/22.65 | (80), (81), (82), (83), (84), (85), (86), (87), (88), (89), (91), % 152.07/22.65 | (92), (93), (94), (95), (96), (98), (99), (100), (101), (102), % 152.07/22.65 | (104), (105), (106), (107), (108) are inconsistent by sub-proof % 152.07/22.65 | #517. % 152.07/22.65 | % 152.07/22.65 End of proof % 152.07/22.65 % 152.07/22.65 Sub-proof #464 shows that the following formulas are inconsistent: % 152.07/22.65 ---------------------------------------------------------------- % 152.07/22.65 (1) all_56_11 = all_8_2 % 152.07/22.65 (2) all_58_6 = all_52_2 % 152.07/22.65 (3) ~ (all_52_8 = e2) % 152.07/22.65 (4) ~ (all_6_1 = e2) % 152.07/22.65 (5) ~ (all_8_2 = e1) % 152.07/22.65 (6) all_54_0 = all_10_2 % 152.07/22.65 (7) all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2 % 152.07/22.65 (8) all_58_4 = all_52_8 % 152.07/22.65 (9) op(e2, e2) = all_6_1 % 152.07/22.65 (10) all_54_5 = all_8_2 % 152.07/22.65 (11) ~ (all_6_1 = e3) % 152.07/22.65 (12) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 152.07/22.65 (13) ~ (all_52_7 = all_8_2) % 152.07/22.65 (14) all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2 % 152.07/22.65 (15) all_56_1 = all_10_2 % 152.07/22.65 (16) all_58_9 = all_52_12 % 152.07/22.65 (17) all_56_3 = all_10_0 % 152.07/22.65 (18) ~ (all_56_1 = e1) | all_56_5 = e3 % 152.07/22.65 (19) all_58_13 = all_52_7 % 152.07/22.65 (20) all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2 % 152.07/22.65 (21) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 152.07/22.65 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 152.07/22.65 (22) ~ (all_52_8 = all_10_0) % 152.07/22.65 (23) ~ (all_52_3 = all_52_7) % 152.07/22.65 (24) all_56_7 = all_52_12 % 152.07/22.65 (25) op(e2, all_52_7) = all_56_26 % 152.07/22.65 (26) ~ (all_52_1 = all_52_13) % 152.07/22.65 (27) ~ (all_52_12 = all_10_0) % 152.07/22.65 (28) ~ (all_56_1 = e2) | all_56_3 = e3 % 152.07/22.65 (29) ~ (all_56_1 = e0) | all_56_7 = e3 % 152.07/22.65 (30) all_56_5 = all_52_8 % 152.07/22.65 (31) ~ (e2 = e1) % 152.07/22.65 (32) all_58_3 = all_8_2 % 152.07/22.65 (33) all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3 % 152.07/22.65 (34) op(all_10_2, all_10_2) = e2 % 152.07/22.65 (35) ~ (all_52_2 = e2) % 152.07/22.65 (36) all_58_2 = all_52_1 % 152.07/22.65 (37) ~ (all_56_11 = e0) | all_56_15 = e2 % 152.07/22.65 (38) all_58_0 = all_10_2 % 152.07/22.65 (39) all_58_1 = all_10_0 % 152.07/22.65 (40) op(e2, e2) = all_8_2 % 152.07/22.65 (41) all_58_7 = e1 % 152.07/22.65 (42) ~ (all_10_0 = all_10_2) % 152.07/22.65 (43) ~ (all_10_0 = e2) % 152.07/22.65 (44) ~ (all_52_7 = all_10_0) % 152.07/22.65 (45) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 152.07/22.65 (46) all_56_15 = all_52_13 % 152.07/22.65 (47) all_58_12 = all_52_3 % 152.07/22.65 % 152.07/22.65 Begin of proof % 152.07/22.65 | % 152.07/22.65 | GROUND_INST: instantiating (21) with all_8_2, all_6_1, e2, e2, simplifying % 152.07/22.65 | with (9), (40) gives: % 152.07/22.65 | (48) all_8_2 = all_6_1 % 152.07/22.65 | % 152.07/22.65 | COMBINE_EQS: (10), (48) imply: % 152.07/22.65 | (49) all_54_5 = all_6_1 % 152.07/22.65 | % 152.07/22.65 | COMBINE_EQS: (1), (48) imply: % 152.07/22.65 | (50) all_56_11 = all_6_1 % 152.07/22.65 | % 152.07/22.65 | COMBINE_EQS: (32), (48) imply: % 152.07/22.65 | (51) all_58_3 = all_6_1 % 152.07/22.65 | % 152.07/22.65 | REDUCE: (13), (48) imply: % 152.07/22.65 | (52) ~ (all_52_7 = all_6_1) % 152.07/22.65 | % 152.07/22.65 | REDUCE: (5), (48) imply: % 152.07/22.65 | (53) ~ (all_6_1 = e1) % 152.07/22.65 | % 152.07/22.65 | BETA: splitting (14) gives: % 152.07/22.65 | % 152.07/22.65 | Case 1: % 152.07/22.65 | | % 152.07/22.65 | | (54) all_58_1 = e2 % 152.07/22.65 | | % 152.07/22.65 | | COMBINE_EQS: (39), (54) imply: % 152.07/22.65 | | (55) all_10_0 = e2 % 152.07/22.65 | | % 152.07/22.65 | | REDUCE: (43), (55) imply: % 152.07/22.65 | | (56) $false % 152.07/22.65 | | % 152.07/22.65 | | CLOSE: (56) is inconsistent. % 152.07/22.65 | | % 152.07/22.65 | Case 2: % 152.07/22.65 | | % 152.07/22.65 | | (57) all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2 % 152.07/22.65 | | % 152.07/22.65 | | BETA: splitting (57) gives: % 152.07/22.65 | | % 152.07/22.65 | | Case 1: % 152.07/22.65 | | | % 152.07/22.65 | | | (58) all_58_3 = e2 % 152.07/22.65 | | | % 152.07/22.65 | | | COMBINE_EQS: (51), (58) imply: % 152.07/22.65 | | | (59) all_6_1 = e2 % 152.07/22.65 | | | % 152.07/22.65 | | | REDUCE: (4), (59) imply: % 152.07/22.65 | | | (60) $false % 152.07/22.65 | | | % 152.07/22.65 | | | CLOSE: (60) is inconsistent. % 152.07/22.65 | | | % 152.07/22.65 | | Case 2: % 152.07/22.65 | | | % 152.07/22.65 | | | (61) all_58_7 = e2 | all_58_13 = e2 % 152.07/22.65 | | | % 152.07/22.65 | | | BETA: splitting (61) gives: % 152.07/22.65 | | | % 152.07/22.65 | | | Case 1: % 152.07/22.65 | | | | % 152.07/22.65 | | | | (62) all_58_7 = e2 % 152.07/22.65 | | | | % 152.07/22.65 | | | | COMBINE_EQS: (41), (62) imply: % 152.07/22.65 | | | | (63) e2 = e1 % 152.07/22.65 | | | | % 152.07/22.65 | | | | SIMP: (63) implies: % 152.07/22.65 | | | | (64) e2 = e1 % 152.07/22.65 | | | | % 152.07/22.65 | | | | REDUCE: (31), (64) imply: % 152.07/22.65 | | | | (65) $false % 152.07/22.65 | | | | % 152.07/22.65 | | | | CLOSE: (65) is inconsistent. % 152.07/22.65 | | | | % 152.07/22.65 | | | Case 2: % 152.07/22.65 | | | | % 152.07/22.65 | | | | (66) all_58_13 = e2 % 152.07/22.65 | | | | % 152.07/22.65 | | | | COMBINE_EQS: (19), (66) imply: % 152.07/22.65 | | | | (67) all_52_7 = e2 % 152.07/22.65 | | | | % 152.07/22.65 | | | | REDUCE: (23), (67) imply: % 152.07/22.65 | | | | (68) ~ (all_52_3 = e2) % 152.07/22.65 | | | | % 152.07/22.65 | | | | REDUCE: (44), (67) imply: % 152.07/22.65 | | | | (69) ~ (all_10_0 = e2) % 152.07/22.65 | | | | % 152.07/22.65 | | | | REDUCE: (52), (67) imply: % 152.07/22.65 | | | | (70) ~ (all_6_1 = e2) % 152.07/22.65 | | | | % 152.07/22.65 | | | | REDUCE: (25), (67) imply: % 152.07/22.65 | | | | (71) op(e2, e2) = all_56_26 % 152.07/22.65 | | | | % 152.07/22.65 | | | | BETA: splitting (45) gives: % 152.07/22.65 | | | | % 152.07/22.65 | | | | Case 1: % 152.07/22.65 | | | | | % 152.07/22.65 | | | | | (72) all_54_5 = e3 % 152.07/22.65 | | | | | % 152.07/22.65 | | | | | REF_CLOSE: (11), (49), (72) are inconsistent by sub-proof #509. % 152.07/22.65 | | | | | % 152.07/22.65 | | | | Case 2: % 152.07/22.65 | | | | | % 152.07/22.65 | | | | | (73) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 152.07/22.65 | | | | | % 152.07/22.65 | | | | | BETA: splitting (33) gives: % 152.07/22.65 | | | | | % 152.07/22.65 | | | | | Case 1: % 152.07/22.65 | | | | | | % 152.07/22.65 | | | | | | (74) all_58_1 = e3 % 152.07/22.65 | | | | | | % 152.07/22.65 | | | | | | COMBINE_EQS: (39), (74) imply: % 152.07/22.65 | | | | | | (75) all_10_0 = e3 % 152.07/22.65 | | | | | | % 152.07/22.65 | | | | | | REDUCE: (22), (75) imply: % 152.07/22.65 | | | | | | (76) ~ (all_52_8 = e3) % 152.07/22.65 | | | | | | % 152.07/22.65 | | | | | | REDUCE: (27), (75) imply: % 152.07/22.65 | | | | | | (77) ~ (all_52_12 = e3) % 152.07/22.65 | | | | | | % 152.07/22.65 | | | | | | REDUCE: (42), (75) imply: % 152.07/22.65 | | | | | | (78) ~ (all_10_2 = e3) % 152.07/22.65 | | | | | | % 152.07/22.65 | | | | | | SIMP: (78) implies: % 152.07/22.65 | | | | | | (79) ~ (all_10_2 = e3) % 152.07/22.65 | | | | | | % 152.07/22.65 | | | | | | REDUCE: (43), (75) imply: % 152.07/22.65 | | | | | | (80) ~ (e3 = e2) % 152.07/22.65 | | | | | | % 152.07/22.65 | | | | | | BETA: splitting (73) gives: % 152.07/22.65 | | | | | | % 152.07/22.65 | | | | | | Case 1: % 152.07/22.65 | | | | | | | % 152.07/22.65 | | | | | | | (81) all_54_5 = e2 % 152.07/22.65 | | | | | | | % 152.07/22.65 | | | | | | | REF_CLOSE: (4), (49), (81) are inconsistent by sub-proof #466. % 152.07/22.65 | | | | | | | % 152.07/22.65 | | | | | | Case 2: % 152.07/22.65 | | | | | | | % 152.07/22.65 | | | | | | | (82) ~ (all_54_5 = e2) % 152.07/22.65 | | | | | | | (83) all_54_5 = e1 | all_54_5 = e0 % 152.07/22.65 | | | | | | | % 152.07/22.65 | | | | | | | BETA: splitting (18) gives: % 152.07/22.65 | | | | | | | % 152.07/22.65 | | | | | | | Case 1: % 152.07/22.65 | | | | | | | | % 152.07/22.65 | | | | | | | | (84) ~ (all_56_1 = e1) % 152.07/22.65 | | | | | | | | % 152.07/22.65 | | | | | | | | REDUCE: (15), (84) imply: % 152.07/22.65 | | | | | | | | (85) ~ (all_10_2 = e1) % 152.07/22.65 | | | | | | | | % 152.07/22.65 | | | | | | | | BETA: splitting (83) gives: % 152.07/22.65 | | | | | | | | % 152.07/22.65 | | | | | | | | Case 1: % 152.07/22.65 | | | | | | | | | % 152.07/22.65 | | | | | | | | | (86) all_54_5 = e1 % 152.07/22.65 | | | | | | | | | % 152.07/22.65 | | | | | | | | | REF_CLOSE: (49), (53), (86) are inconsistent by sub-proof % 152.07/22.65 | | | | | | | | | #465. % 152.07/22.65 | | | | | | | | | % 152.07/22.65 | | | | | | | | Case 2: % 152.07/22.65 | | | | | | | | | % 152.07/22.65 | | | | | | | | | (87) all_54_5 = e0 % 152.07/22.65 | | | | | | | | | % 152.07/22.65 | | | | | | | | | COMBINE_EQS: (49), (87) imply: % 152.07/22.65 | | | | | | | | | (88) all_6_1 = e0 % 152.07/22.65 | | | | | | | | | % 152.07/22.65 | | | | | | | | | SIMP: (88) implies: % 152.07/22.65 | | | | | | | | | (89) all_6_1 = e0 % 152.07/22.65 | | | | | | | | | % 152.07/22.65 | | | | | | | | | REDUCE: (4), (89) imply: % 152.07/22.65 | | | | | | | | | (90) ~ (e2 = e0) % 152.07/22.65 | | | | | | | | | % 152.07/22.65 | | | | | | | | | SIMP: (90) implies: % 152.07/22.65 | | | | | | | | | (91) ~ (e2 = e0) % 152.07/22.65 | | | | | | | | | % 152.07/22.65 | | | | | | | | | REDUCE: (9), (89) imply: % 152.07/22.65 | | | | | | | | | (92) op(e2, e2) = e0 % 152.07/22.65 | | | | | | | | | % 152.07/22.65 | | | | | | | | | BETA: splitting (29) gives: % 152.07/22.65 | | | | | | | | | % 152.07/22.65 | | | | | | | | | Case 1: % 152.07/22.65 | | | | | | | | | | % 152.07/22.65 | | | | | | | | | | (93) ~ (all_56_1 = e0) % 152.07/22.65 | | | | | | | | | | % 152.07/22.65 | | | | | | | | | | REDUCE: (15), (93) imply: % 152.07/22.65 | | | | | | | | | | (94) ~ (all_10_2 = e0) % 152.07/22.65 | | | | | | | | | | % 152.07/22.65 | | | | | | | | | | BETA: splitting (7) gives: % 152.07/22.65 | | | | | | | | | | % 152.07/22.65 | | | | | | | | | | Case 1: % 152.07/22.65 | | | | | | | | | | | % 152.07/22.65 | | | | | | | | | | | (95) all_58_0 = e2 % 152.07/22.65 | | | | | | | | | | | % 152.07/22.65 | | | | | | | | | | | COMBINE_EQS: (38), (95) imply: % 152.07/22.65 | | | | | | | | | | | (96) all_10_2 = e2 % 152.07/22.65 | | | | | | | | | | | % 152.07/22.65 | | | | | | | | | | | REDUCE: (34), (96) imply: % 152.07/22.65 | | | | | | | | | | | (97) op(e2, e2) = e2 % 152.07/22.65 | | | | | | | | | | | % 152.07/22.65 | | | | | | | | | | | GROUND_INST: instantiating (21) with e2, all_56_26, e2, e2, % 152.07/22.65 | | | | | | | | | | | simplifying with (71), (97) gives: % 152.07/22.65 | | | | | | | | | | | (98) all_56_26 = e2 % 152.07/22.65 | | | | | | | | | | | % 152.07/22.65 | | | | | | | | | | | GROUND_INST: instantiating (21) with e0, all_56_26, e2, e2, % 152.07/22.65 | | | | | | | | | | | simplifying with (71), (92) gives: % 152.07/22.65 | | | | | | | | | | | (99) all_56_26 = e0 % 152.07/22.65 | | | | | | | | | | | % 152.07/22.65 | | | | | | | | | | | COMBINE_EQS: (98), (99) imply: % 152.07/22.65 | | | | | | | | | | | (100) e2 = e0 % 152.07/22.65 | | | | | | | | | | | % 152.07/22.65 | | | | | | | | | | | SIMP: (100) implies: % 152.07/22.65 | | | | | | | | | | | (101) e2 = e0 % 152.07/22.65 | | | | | | | | | | | % 152.07/22.65 | | | | | | | | | | | REDUCE: (91), (101) imply: % 152.07/22.65 | | | | | | | | | | | (102) $false % 152.07/22.65 | | | | | | | | | | | % 152.07/22.65 | | | | | | | | | | | CLOSE: (102) is inconsistent. % 152.07/22.65 | | | | | | | | | | | % 152.07/22.65 | | | | | | | | | | Case 2: % 152.07/22.65 | | | | | | | | | | | % 152.07/22.65 | | | | | | | | | | | (103) ~ (all_58_0 = e2) % 152.07/22.65 | | | | | | | | | | | % 152.07/22.65 | | | | | | | | | | | REDUCE: (38), (103) imply: % 152.07/22.65 | | | | | | | | | | | (104) ~ (all_10_2 = e2) % 152.07/22.65 | | | | | | | | | | | % 152.07/22.65 | | | | | | | | | | | REF_CLOSE: (6), (12), (15), (24), (29), (77), (79), (85), % 152.07/22.65 | | | | | | | | | | | (104) are inconsistent by sub-proof #707. % 152.07/22.65 | | | | | | | | | | | % 152.07/22.65 | | | | | | | | | | End of split % 152.07/22.65 | | | | | | | | | | % 152.07/22.65 | | | | | | | | | Case 2: % 152.07/22.65 | | | | | | | | | | % 152.07/22.65 | | | | | | | | | | (105) all_56_7 = e3 % 152.07/22.65 | | | | | | | | | | (106) all_56_1 = e0 % 152.07/22.65 | | | | | | | | | | % 152.07/22.65 | | | | | | | | | | COMBINE_EQS: (15), (106) imply: % 152.07/22.65 | | | | | | | | | | (107) all_10_2 = e0 % 152.07/22.65 | | | | | | | | | | % 152.07/22.65 | | | | | | | | | | COMBINE_EQS: (24), (105) imply: % 152.07/22.65 | | | | | | | | | | (108) all_52_12 = e3 % 152.07/22.65 | | | | | | | | | | % 152.07/22.65 | | | | | | | | | | SIMP: (108) implies: % 152.07/22.65 | | | | | | | | | | (109) all_52_12 = e3 % 152.07/22.65 | | | | | | | | | | % 152.07/22.65 | | | | | | | | | | COMBINE_EQS: (16), (109) imply: % 152.07/22.65 | | | | | | | | | | (110) all_58_9 = e3 % 152.07/22.65 | | | | | | | | | | % 152.07/22.65 | | | | | | | | | | COMBINE_EQS: (38), (107) imply: % 152.07/22.65 | | | | | | | | | | (111) all_58_0 = e0 % 152.07/22.65 | | | | | | | | | | % 152.07/22.65 | | | | | | | | | | BETA: splitting (7) gives: % 152.07/22.65 | | | | | | | | | | % 152.07/22.65 | | | | | | | | | | Case 1: % 152.07/22.65 | | | | | | | | | | | % 152.07/22.65 | | | | | | | | | | | (112) all_58_0 = e2 % 152.07/22.65 | | | | | | | | | | | % 152.07/22.65 | | | | | | | | | | | COMBINE_EQS: (111), (112) imply: % 152.07/22.66 | | | | | | | | | | | (113) e2 = e0 % 152.07/22.66 | | | | | | | | | | | % 152.07/22.66 | | | | | | | | | | | SIMP: (113) implies: % 152.07/22.66 | | | | | | | | | | | (114) e2 = e0 % 152.07/22.66 | | | | | | | | | | | % 152.07/22.66 | | | | | | | | | | | REDUCE: (91), (114) imply: % 152.07/22.66 | | | | | | | | | | | (115) $false % 152.07/22.66 | | | | | | | | | | | % 152.07/22.66 | | | | | | | | | | | CLOSE: (115) is inconsistent. % 152.07/22.66 | | | | | | | | | | | % 152.07/22.66 | | | | | | | | | | Case 2: % 152.07/22.66 | | | | | | | | | | | % 152.07/22.66 | | | | | | | | | | | (116) all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2 % 152.07/22.66 | | | | | | | | | | | % 152.07/22.66 | | | | | | | | | | | BETA: splitting (116) gives: % 152.07/22.66 | | | | | | | | | | | % 152.07/22.66 | | | | | | | | | | | Case 1: % 152.07/22.66 | | | | | | | | | | | | % 152.07/22.66 | | | | | | | | | | | | (117) all_58_1 = e2 % 152.07/22.66 | | | | | | | | | | | | % 152.07/22.66 | | | | | | | | | | | | COMBINE_EQS: (39), (117) imply: % 152.07/22.66 | | | | | | | | | | | | (118) all_10_0 = e2 % 152.07/22.66 | | | | | | | | | | | | % 152.07/22.66 | | | | | | | | | | | | REDUCE: (43), (118) imply: % 152.07/22.66 | | | | | | | | | | | | (119) $false % 152.07/22.66 | | | | | | | | | | | | % 152.07/22.66 | | | | | | | | | | | | CLOSE: (119) is inconsistent. % 152.07/22.66 | | | | | | | | | | | | % 152.07/22.66 | | | | | | | | | | | Case 2: % 152.07/22.66 | | | | | | | | | | | | % 152.07/22.66 | | | | | | | | | | | | (120) all_58_4 = e2 | all_58_9 = e2 % 152.07/22.66 | | | | | | | | | | | | % 152.07/22.66 | | | | | | | | | | | | BETA: splitting (120) gives: % 152.07/22.66 | | | | | | | | | | | | % 152.07/22.66 | | | | | | | | | | | | Case 1: % 152.07/22.66 | | | | | | | | | | | | | % 152.07/22.66 | | | | | | | | | | | | | (121) all_58_4 = e2 % 152.07/22.66 | | | | | | | | | | | | | % 152.07/22.66 | | | | | | | | | | | | | COMBINE_EQS: (8), (121) imply: % 152.07/22.66 | | | | | | | | | | | | | (122) all_52_8 = e2 % 152.07/22.66 | | | | | | | | | | | | | % 152.07/22.66 | | | | | | | | | | | | | REDUCE: (3), (122) imply: % 152.07/22.66 | | | | | | | | | | | | | (123) $false % 152.07/22.66 | | | | | | | | | | | | | % 152.07/22.66 | | | | | | | | | | | | | CLOSE: (123) is inconsistent. % 152.07/22.66 | | | | | | | | | | | | | % 152.07/22.66 | | | | | | | | | | | | Case 2: % 152.07/22.66 | | | | | | | | | | | | | % 152.07/22.66 | | | | | | | | | | | | | (124) all_58_9 = e2 % 152.07/22.66 | | | | | | | | | | | | | % 152.07/22.66 | | | | | | | | | | | | | COMBINE_EQS: (110), (124) imply: % 152.07/22.66 | | | | | | | | | | | | | (125) e3 = e2 % 152.07/22.66 | | | | | | | | | | | | | % 152.07/22.66 | | | | | | | | | | | | | REDUCE: (80), (125) imply: % 152.07/22.66 | | | | | | | | | | | | | (126) $false % 152.07/22.66 | | | | | | | | | | | | | % 152.07/22.66 | | | | | | | | | | | | | CLOSE: (126) is inconsistent. % 152.07/22.66 | | | | | | | | | | | | | % 152.07/22.66 | | | | | | | | | | | | End of split % 152.07/22.66 | | | | | | | | | | | | % 152.07/22.66 | | | | | | | | | | | End of split % 152.07/22.66 | | | | | | | | | | | % 152.07/22.66 | | | | | | | | | | End of split % 152.07/22.66 | | | | | | | | | | % 152.07/22.66 | | | | | | | | | End of split % 152.07/22.66 | | | | | | | | | % 152.07/22.66 | | | | | | | | End of split % 152.07/22.66 | | | | | | | | % 152.07/22.66 | | | | | | | Case 2: % 152.07/22.66 | | | | | | | | % 152.07/22.66 | | | | | | | | (127) all_56_5 = e3 % 152.07/22.66 | | | | | | | | % 152.07/22.66 | | | | | | | | REF_CLOSE: (30), (76), (127) are inconsistent by sub-proof #481. % 152.07/22.66 | | | | | | | | % 152.07/22.66 | | | | | | | End of split % 152.07/22.66 | | | | | | | % 152.07/22.66 | | | | | | End of split % 152.07/22.66 | | | | | | % 152.07/22.66 | | | | | Case 2: % 152.07/22.66 | | | | | | % 152.07/22.66 | | | | | | (128) ~ (all_58_1 = e3) % 152.07/22.66 | | | | | | % 152.07/22.66 | | | | | | REDUCE: (39), (128) imply: % 152.07/22.66 | | | | | | (129) ~ (all_10_0 = e3) % 152.07/22.66 | | | | | | % 152.07/22.66 | | | | | | BETA: splitting (28) gives: % 152.07/22.66 | | | | | | % 152.07/22.66 | | | | | | Case 1: % 152.07/22.66 | | | | | | | % 152.07/22.66 | | | | | | | (130) ~ (all_56_1 = e2) % 152.07/22.66 | | | | | | | % 152.07/22.66 | | | | | | | REDUCE: (15), (130) imply: % 152.07/22.66 | | | | | | | (131) ~ (all_10_2 = e2) % 152.07/22.66 | | | | | | | % 152.07/22.66 | | | | | | | BETA: splitting (73) gives: % 152.07/22.66 | | | | | | | % 152.07/22.66 | | | | | | | Case 1: % 152.07/22.66 | | | | | | | | % 152.07/22.66 | | | | | | | | (132) all_54_5 = e2 % 152.07/22.66 | | | | | | | | % 152.07/22.66 | | | | | | | | REF_CLOSE: (4), (49), (132) are inconsistent by sub-proof #466. % 152.07/22.66 | | | | | | | | % 152.07/22.66 | | | | | | | Case 2: % 152.07/22.66 | | | | | | | | % 152.07/22.66 | | | | | | | | (133) all_54_5 = e1 | all_54_5 = e0 % 152.07/22.66 | | | | | | | | % 152.07/22.66 | | | | | | | | BETA: splitting (133) gives: % 152.07/22.66 | | | | | | | | % 152.07/22.66 | | | | | | | | Case 1: % 152.07/22.66 | | | | | | | | | % 152.07/22.66 | | | | | | | | | (134) all_54_5 = e1 % 152.07/22.66 | | | | | | | | | % 152.07/22.66 | | | | | | | | | REF_CLOSE: (49), (53), (134) are inconsistent by sub-proof % 152.07/22.66 | | | | | | | | | #465. % 152.07/22.66 | | | | | | | | | % 152.07/22.66 | | | | | | | | Case 2: % 152.07/22.66 | | | | | | | | | % 152.07/22.66 | | | | | | | | | (135) all_54_5 = e0 % 152.07/22.66 | | | | | | | | | % 152.07/22.66 | | | | | | | | | COMBINE_EQS: (49), (135) imply: % 152.07/22.66 | | | | | | | | | (136) all_6_1 = e0 % 152.07/22.66 | | | | | | | | | % 152.07/22.66 | | | | | | | | | SIMP: (136) implies: % 152.07/22.66 | | | | | | | | | (137) all_6_1 = e0 % 152.07/22.66 | | | | | | | | | % 152.07/22.66 | | | | | | | | | COMBINE_EQS: (50), (137) imply: % 152.07/22.66 | | | | | | | | | (138) all_56_11 = e0 % 152.07/22.66 | | | | | | | | | % 152.07/22.66 | | | | | | | | | REF_CLOSE: (2), (20), (26), (35), (36), (37), (38), (46), % 152.07/22.66 | | | | | | | | | (47), (68), (131), (138) are inconsistent by % 152.07/22.66 | | | | | | | | | sub-proof #596. % 152.07/22.66 | | | | | | | | | % 152.07/22.66 | | | | | | | | End of split % 152.07/22.66 | | | | | | | | % 152.07/22.66 | | | | | | | End of split % 152.07/22.66 | | | | | | | % 152.07/22.66 | | | | | | Case 2: % 152.07/22.66 | | | | | | | % 152.07/22.66 | | | | | | | (139) all_56_3 = e3 % 152.07/22.66 | | | | | | | % 152.07/22.66 | | | | | | | COMBINE_EQS: (17), (139) imply: % 152.07/22.66 | | | | | | | (140) all_10_0 = e3 % 152.07/22.66 | | | | | | | % 152.07/22.66 | | | | | | | REDUCE: (129), (140) imply: % 152.07/22.66 | | | | | | | (141) $false % 152.07/22.66 | | | | | | | % 152.07/22.66 | | | | | | | CLOSE: (141) is inconsistent. % 152.07/22.66 | | | | | | | % 152.07/22.66 | | | | | | End of split % 152.07/22.66 | | | | | | % 152.07/22.66 | | | | | End of split % 152.07/22.66 | | | | | % 152.07/22.66 | | | | End of split % 152.07/22.66 | | | | % 152.07/22.66 | | | End of split % 152.07/22.66 | | | % 152.07/22.66 | | End of split % 152.07/22.66 | | % 152.07/22.66 | End of split % 152.07/22.66 | % 152.07/22.66 End of proof % 152.07/22.66 % 152.07/22.66 Sub-proof #465 shows that the following formulas are inconsistent: % 152.07/22.66 ---------------------------------------------------------------- % 152.07/22.66 (1) all_54_5 = all_6_1 % 152.07/22.66 (2) all_54_5 = e1 % 152.07/22.66 (3) ~ (all_6_1 = e1) % 152.07/22.66 % 152.07/22.66 Begin of proof % 152.07/22.66 | % 152.07/22.66 | COMBINE_EQS: (1), (2) imply: % 152.07/22.66 | (4) all_6_1 = e1 % 152.07/22.66 | % 152.07/22.66 | SIMP: (4) implies: % 152.07/22.66 | (5) all_6_1 = e1 % 152.07/22.66 | % 152.07/22.66 | REDUCE: (3), (5) imply: % 152.07/22.66 | (6) $false % 152.07/22.66 | % 152.07/22.66 | CLOSE: (6) is inconsistent. % 152.07/22.66 | % 152.07/22.66 End of proof % 152.07/22.66 % 152.07/22.66 Sub-proof #466 shows that the following formulas are inconsistent: % 152.07/22.66 ---------------------------------------------------------------- % 152.07/22.66 (1) all_54_5 = all_6_1 % 152.07/22.66 (2) all_54_5 = e2 % 152.07/22.66 (3) ~ (all_6_1 = e2) % 152.07/22.66 % 152.07/22.66 Begin of proof % 152.07/22.66 | % 152.07/22.66 | COMBINE_EQS: (1), (2) imply: % 152.07/22.66 | (4) all_6_1 = e2 % 152.07/22.66 | % 152.07/22.66 | SIMP: (4) implies: % 152.07/22.66 | (5) all_6_1 = e2 % 152.07/22.66 | % 152.07/22.66 | REDUCE: (3), (5) imply: % 152.07/22.66 | (6) $false % 152.07/22.66 | % 152.07/22.66 | CLOSE: (6) is inconsistent. % 152.07/22.66 | % 152.07/22.66 End of proof % 152.07/22.66 % 152.07/22.66 Sub-proof #467 shows that the following formulas are inconsistent: % 152.07/22.66 ---------------------------------------------------------------- % 152.07/22.66 (1) all_56_11 = all_8_2 % 152.07/22.66 (2) ~ (all_52_11 = all_6_2) % 152.07/22.66 (3) op(e2, all_8_1) = all_8_0 % 152.07/22.66 (4) all_58_6 = all_52_2 % 152.07/22.66 (5) ~ (all_10_0 = all_8_2) % 152.07/22.66 (6) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0 % 152.07/22.66 (7) all_54_10 = all_6_2 % 152.07/22.66 (8) ~ (all_6_1 = e2) % 152.07/22.66 (9) ~ (all_52_13 = all_8_2) % 152.07/22.66 (10) all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2 % 152.07/22.66 (11) all_54_0 = all_10_2 % 152.07/22.66 (12) ~ (all_8_0 = e1) % 152.07/22.66 (13) all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2 % 152.07/22.66 (14) ~ (all_8_1 = e3) % 152.07/22.66 (15) all_58_4 = all_52_8 % 152.07/22.66 (16) all_54_5 = all_8_2 % 152.07/22.66 (17) ~ (all_6_1 = e3) % 152.07/22.66 (18) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 152.07/22.66 (19) ~ (all_52_11 = e0) % 152.07/22.66 (20) all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1 % 152.07/22.66 (21) all_54_1 = all_10_0 % 152.07/22.66 (22) all_56_21 = all_6_2 % 152.07/22.66 (23) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 152.07/22.66 (24) ~ (all_52_7 = all_8_2) % 152.07/22.66 (25) all_56_1 = all_10_2 % 152.07/22.66 (26) all_56_17 = all_52_2 % 152.07/22.66 (27) all_58_9 = all_52_12 % 152.07/22.66 (28) all_58_12 = e0 % 152.07/22.66 (29) op(e0, all_52_14) = all_56_22 % 152.07/22.66 (30) op(e0, e2) = all_52_7 % 152.07/22.66 (31) ~ (all_56_1 = e1) | all_56_5 = e3 % 152.07/22.66 (32) all_54_14 = all_52_11 % 152.07/22.66 (33) all_58_13 = all_52_7 % 152.07/22.66 (34) op(e2, all_8_2) = all_56_10 % 152.07/22.66 (35) op(e3, e3) = all_10_2 % 152.07/22.66 (36) ~ (all_56_21 = e3) | all_56_17 = e1 % 152.07/22.66 (37) all_38_0 = all_10_0 % 152.07/22.66 (38) ~ (all_52_1 = all_8_2) % 152.07/22.66 (39) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 152.07/22.66 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 152.07/22.66 (40) ~ (all_52_11 = e3) % 152.07/22.66 (41) ~ (all_56_11 = e3) | all_56_9 = e2 % 152.07/22.66 (42) op(e0, all_4_1) = all_4_0 % 152.07/22.66 (43) ~ (all_52_1 = all_52_13) % 152.07/22.66 (44) ~ (all_4_2 = e1) % 152.07/22.66 (45) ~ (all_4_0 = e1) % 152.07/22.66 (46) all_58_15 = e3 % 152.07/22.66 (47) op(e1, all_6_1) = all_6_0 % 152.07/22.66 (48) all_58_11 = all_52_14 % 152.07/22.66 (49) op(e0, e0) = e3 % 152.07/22.66 (50) ~ (all_8_0 = e3) % 152.07/22.66 (51) op(all_10_2, all_10_2) = e2 % 152.07/22.66 (52) op(all_6_2, all_6_2) = all_6_1 % 152.07/22.66 (53) ~ (all_52_8 = all_52_11) % 152.07/22.66 (54) ~ (all_38_0 = e0) | ~ (all_38_2 = e1) % 152.07/22.66 (55) all_38_2 = all_10_2 % 152.07/22.66 (56) op(e1, e1) = all_6_2 % 152.07/22.66 (57) all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1 % 152.07/22.66 (58) ~ (all_10_2 = e0) % 152.07/22.66 (59) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0 % 152.07/22.66 (60) all_58_15 = all_4_2 % 152.07/22.66 (61) ~ (all_6_2 = e2) % 152.07/22.66 (62) all_58_2 = all_52_1 % 152.07/22.66 (63) all_58_10 = all_52_13 % 152.07/22.66 (64) ~ (all_56_11 = e0) | all_56_15 = e2 % 152.07/22.66 (65) all_58_0 = all_10_2 % 152.07/22.66 (66) op(e1, all_6_2) = all_56_20 % 152.07/22.66 (67) all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1 % 152.07/22.66 (68) all_58_1 = all_10_0 % 152.07/22.66 (69) op(e2, e2) = all_8_2 % 152.07/22.66 (70) ~ (all_52_2 = all_6_2) % 152.07/22.66 (71) ~ (all_56_21 = e0) | all_56_23 = e1 % 152.07/22.66 (72) op(e3, all_10_2) = all_56_0 % 152.07/22.66 (73) ~ (all_52_14 = all_6_2) % 152.07/22.66 (74) ~ (all_10_0 = all_10_2) % 152.07/22.66 (75) ~ (all_52_7 = e0) % 152.07/22.66 (76) ~ (all_52_2 = all_10_2) % 152.07/22.66 (77) ~ (all_10_0 = e2) % 152.07/22.66 (78) op(all_8_2, all_8_2) = all_8_1 % 152.07/22.66 (79) ~ (all_52_7 = all_10_0) % 152.07/22.66 (80) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 152.07/22.66 (81) all_58_14 = all_52_11 % 152.07/22.66 (82) ~ (all_52_12 = all_10_2) % 152.07/22.66 (83) all_56_9 = all_52_1 % 152.07/22.66 (84) ~ (all_52_1 = all_10_2) % 152.07/22.66 (85) op(e3, e3) = all_4_1 % 152.07/22.66 % 152.07/22.66 Begin of proof % 152.07/22.66 | % 152.07/22.66 | GROUND_INST: instantiating (39) with all_10_2, all_4_1, e3, e3, simplifying % 152.07/22.66 | with (35), (85) gives: % 152.07/22.66 | (86) all_10_2 = all_4_1 % 152.07/22.66 | % 152.07/22.66 | COMBINE_EQS: (55), (86) imply: % 152.07/22.66 | (87) all_38_2 = all_4_1 % 152.07/22.66 | % 152.07/22.66 | COMBINE_EQS: (11), (86) imply: % 152.07/22.66 | (88) all_54_0 = all_4_1 % 152.07/22.66 | % 152.07/22.66 | COMBINE_EQS: (25), (86) imply: % 152.07/22.66 | (89) all_56_1 = all_4_1 % 152.07/22.66 | % 152.07/22.66 | COMBINE_EQS: (65), (86) imply: % 152.07/22.66 | (90) all_58_0 = all_4_1 % 152.07/22.66 | % 152.07/22.66 | REDUCE: (84), (86) imply: % 152.07/22.66 | (91) ~ (all_52_1 = all_4_1) % 152.07/22.66 | % 152.07/22.66 | REDUCE: (76), (86) imply: % 152.07/22.66 | (92) ~ (all_52_2 = all_4_1) % 152.07/22.66 | % 152.07/22.66 | REDUCE: (82), (86) imply: % 152.07/22.66 | (93) ~ (all_52_12 = all_4_1) % 152.07/22.66 | % 152.07/22.66 | REDUCE: (74), (86) imply: % 152.07/22.66 | (94) ~ (all_10_0 = all_4_1) % 152.07/22.66 | % 152.07/22.66 | REDUCE: (58), (86) imply: % 152.07/22.66 | (95) ~ (all_4_1 = e0) % 152.07/22.66 | % 152.07/22.66 | REDUCE: (51), (86) imply: % 152.07/22.66 | (96) op(all_4_1, all_4_1) = e2 % 152.07/22.66 | % 152.07/22.66 | REDUCE: (72), (86) imply: % 152.07/22.66 | (97) op(e3, all_4_1) = all_56_0 % 152.07/22.66 | % 152.07/22.66 | BETA: splitting (71) gives: % 152.07/22.66 | % 152.07/22.66 | Case 1: % 152.07/22.66 | | % 152.07/22.66 | | (98) ~ (all_56_21 = e0) % 152.07/22.66 | | % 152.07/22.66 | | REDUCE: (22), (98) imply: % 152.07/22.66 | | (99) ~ (all_6_2 = e0) % 152.07/22.66 | | % 152.07/22.66 | | BETA: splitting (64) gives: % 152.07/22.66 | | % 152.07/22.66 | | Case 1: % 152.07/22.66 | | | % 152.07/22.66 | | | (100) ~ (all_56_11 = e0) % 152.07/22.66 | | | % 152.07/22.66 | | | REDUCE: (1), (100) imply: % 152.07/22.66 | | | (101) ~ (all_8_2 = e0) % 152.07/22.66 | | | % 152.07/22.66 | | | BETA: splitting (36) gives: % 152.07/22.66 | | | % 152.07/22.66 | | | Case 1: % 152.07/22.66 | | | | % 152.07/22.66 | | | | (102) ~ (all_56_21 = e3) % 152.07/22.66 | | | | % 152.07/22.66 | | | | REDUCE: (22), (102) imply: % 152.07/22.66 | | | | (103) ~ (all_6_2 = e3) % 152.07/22.66 | | | | % 152.07/22.66 | | | | BETA: splitting (23) gives: % 152.07/22.66 | | | | % 152.07/22.66 | | | | Case 1: % 152.07/22.66 | | | | | % 152.07/22.66 | | | | | (104) all_54_10 = e3 % 152.07/22.66 | | | | | % 152.07/22.66 | | | | | COMBINE_EQS: (7), (104) imply: % 152.07/22.66 | | | | | (105) all_6_2 = e3 % 152.07/22.66 | | | | | % 152.07/22.66 | | | | | REDUCE: (103), (105) imply: % 152.07/22.66 | | | | | (106) $false % 152.07/22.66 | | | | | % 152.07/22.66 | | | | | CLOSE: (106) is inconsistent. % 152.07/22.66 | | | | | % 152.07/22.66 | | | | Case 2: % 152.07/22.66 | | | | | % 152.07/22.66 | | | | | (107) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 152.07/22.66 | | | | | % 152.07/22.66 | | | | | BETA: splitting (107) gives: % 152.07/22.66 | | | | | % 152.07/22.66 | | | | | Case 1: % 152.07/22.66 | | | | | | % 152.07/22.66 | | | | | | (108) all_54_10 = e2 % 152.07/22.66 | | | | | | % 152.07/22.66 | | | | | | COMBINE_EQS: (7), (108) imply: % 152.07/22.66 | | | | | | (109) all_6_2 = e2 % 152.07/22.66 | | | | | | % 152.07/22.66 | | | | | | REDUCE: (61), (109) imply: % 152.07/22.66 | | | | | | (110) $false % 152.07/22.66 | | | | | | % 152.07/22.66 | | | | | | CLOSE: (110) is inconsistent. % 152.07/22.66 | | | | | | % 152.07/22.66 | | | | | Case 2: % 152.07/22.66 | | | | | | % 152.07/22.66 | | | | | | (111) all_54_10 = e1 | all_54_10 = e0 % 152.07/22.66 | | | | | | % 152.07/22.66 | | | | | | BETA: splitting (111) gives: % 152.07/22.66 | | | | | | % 152.07/22.66 | | | | | | Case 1: % 152.07/22.66 | | | | | | | % 152.07/22.66 | | | | | | | (112) all_54_10 = e1 % 152.07/22.66 | | | | | | | % 152.07/22.66 | | | | | | | COMBINE_EQS: (7), (112) imply: % 152.07/22.66 | | | | | | | (113) all_6_2 = e1 % 152.07/22.66 | | | | | | | % 152.07/22.66 | | | | | | | REDUCE: (70), (113) imply: % 152.07/22.66 | | | | | | | (114) ~ (all_52_2 = e1) % 152.07/22.66 | | | | | | | % 152.07/22.66 | | | | | | | REDUCE: (2), (113) imply: % 152.07/22.66 | | | | | | | (115) ~ (all_52_11 = e1) % 152.07/22.66 | | | | | | | % 152.07/22.66 | | | | | | | REDUCE: (73), (113) imply: % 152.07/22.66 | | | | | | | (116) ~ (all_52_14 = e1) % 152.07/22.66 | | | | | | | % 152.07/22.66 | | | | | | | REDUCE: (99), (113) imply: % 152.07/22.66 | | | | | | | (117) ~ (e1 = e0) % 152.07/22.66 | | | | | | | % 152.07/22.66 | | | | | | | REDUCE: (52), (113) imply: % 152.07/22.66 | | | | | | | (118) op(e1, e1) = all_6_1 % 152.07/22.66 | | | | | | | % 152.07/22.66 | | | | | | | REDUCE: (66), (113) imply: % 152.07/22.66 | | | | | | | (119) op(e1, e1) = all_56_20 % 152.07/22.66 | | | | | | | % 152.07/22.66 | | | | | | | REDUCE: (56), (113) imply: % 152.07/22.66 | | | | | | | (120) op(e1, e1) = e1 % 152.07/22.66 | | | | | | | % 152.07/22.66 | | | | | | | BETA: splitting (6) gives: % 152.07/22.66 | | | | | | | % 152.07/22.66 | | | | | | | Case 1: % 152.07/22.66 | | | | | | | | % 152.07/22.66 | | | | | | | | (121) all_54_14 = e3 % 152.07/22.66 | | | | | | | | % 152.07/22.66 | | | | | | | | REF_CLOSE: (32), (40), (121) are inconsistent by sub-proof #729. % 152.07/22.66 | | | | | | | | % 152.07/22.66 | | | | | | | Case 2: % 152.07/22.66 | | | | | | | | % 152.07/22.66 | | | | | | | | (122) all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0 % 152.07/22.66 | | | | | | | | % 152.07/22.66 | | | | | | | | BETA: splitting (122) gives: % 152.07/22.66 | | | | | | | | % 152.07/22.66 | | | | | | | | Case 1: % 152.07/22.66 | | | | | | | | | % 152.07/22.66 | | | | | | | | | (123) all_54_14 = e2 % 152.07/22.66 | | | | | | | | | % 152.07/22.66 | | | | | | | | | COMBINE_EQS: (32), (123) imply: % 152.07/22.66 | | | | | | | | | (124) all_52_11 = e2 % 152.07/22.66 | | | | | | | | | % 152.07/22.66 | | | | | | | | | SIMP: (124) implies: % 152.07/22.66 | | | | | | | | | (125) all_52_11 = e2 % 152.07/22.66 | | | | | | | | | % 152.07/22.66 | | | | | | | | | REDUCE: (53), (125) imply: % 152.07/22.66 | | | | | | | | | (126) ~ (all_52_8 = e2) % 152.07/22.66 | | | | | | | | | % 152.07/22.66 | | | | | | | | | BETA: splitting (67) gives: % 152.07/22.66 | | | | | | | | | % 152.07/22.66 | | | | | | | | | Case 1: % 152.07/22.66 | | | | | | | | | | % 152.07/22.66 | | | | | | | | | | (127) all_58_12 = e1 % 152.07/22.66 | | | | | | | | | | % 152.07/22.66 | | | | | | | | | | REF_CLOSE: (28), (117), (127) are inconsistent by sub-proof % 152.07/22.66 | | | | | | | | | | #475. % 152.07/22.66 | | | | | | | | | | % 152.07/22.66 | | | | | | | | | Case 2: % 152.07/22.66 | | | | | | | | | | % 152.07/22.66 | | | | | | | | | | (128) all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1 % 152.07/22.66 | | | | | | | | | | % 152.07/22.66 | | | | | | | | | | BETA: splitting (128) gives: % 152.07/22.66 | | | | | | | | | | % 152.07/22.66 | | | | | | | | | | Case 1: % 152.07/22.66 | | | | | | | | | | | % 152.07/22.66 | | | | | | | | | | | (129) all_58_13 = e1 % 152.07/22.66 | | | | | | | | | | | % 152.07/22.66 | | | | | | | | | | | COMBINE_EQS: (33), (129) imply: % 152.07/22.66 | | | | | | | | | | | (130) all_52_7 = e1 % 152.07/22.66 | | | | | | | | | | | % 152.07/22.66 | | | | | | | | | | | SIMP: (130) implies: % 152.07/22.66 | | | | | | | | | | | (131) all_52_7 = e1 % 152.07/22.66 | | | | | | | | | | | % 152.07/22.66 | | | | | | | | | | | REDUCE: (79), (131) imply: % 152.07/22.66 | | | | | | | | | | | (132) ~ (all_10_0 = e1) % 152.07/22.66 | | | | | | | | | | | % 152.07/22.66 | | | | | | | | | | | SIMP: (132) implies: % 152.07/22.66 | | | | | | | | | | | (133) ~ (all_10_0 = e1) % 152.07/22.66 | | | | | | | | | | | % 152.07/22.66 | | | | | | | | | | | REDUCE: (24), (131) imply: % 152.07/22.66 | | | | | | | | | | | (134) ~ (all_8_2 = e1) % 152.07/22.66 | | | | | | | | | | | % 152.07/22.66 | | | | | | | | | | | SIMP: (134) implies: % 152.07/22.66 | | | | | | | | | | | (135) ~ (all_8_2 = e1) % 152.07/22.66 | | | | | | | | | | | % 152.07/22.66 | | | | | | | | | | | REDUCE: (30), (131) imply: % 152.07/22.66 | | | | | | | | | | | (136) op(e0, e2) = e1 % 152.07/22.66 | | | | | | | | | | | % 152.07/22.66 | | | | | | | | | | | GROUND_INST: instantiating (39) with all_6_1, all_56_20, e1, % 152.07/22.66 | | | | | | | | | | | e1, simplifying with (118), (119) gives: % 152.07/22.66 | | | | | | | | | | | (137) all_56_20 = all_6_1 % 152.07/22.66 | | | | | | | | | | | % 152.07/22.66 | | | | | | | | | | | GROUND_INST: instantiating (39) with e1, all_56_20, e1, e1, % 152.07/22.66 | | | | | | | | | | | simplifying with (119), (120) gives: % 152.07/22.66 | | | | | | | | | | | (138) all_56_20 = e1 % 152.07/22.66 | | | | | | | | | | | % 152.07/22.66 | | | | | | | | | | | COMBINE_EQS: (137), (138) imply: % 152.07/22.66 | | | | | | | | | | | (139) all_6_1 = e1 % 152.07/22.66 | | | | | | | | | | | % 152.07/22.66 | | | | | | | | | | | REDUCE: (47), (139) imply: % 152.07/22.66 | | | | | | | | | | | (140) op(e1, e1) = all_6_0 % 152.07/22.66 | | | | | | | | | | | % 152.07/22.66 | | | | | | | | | | | GROUND_INST: instantiating (39) with e1, all_6_0, e1, e1, % 152.07/22.66 | | | | | | | | | | | simplifying with (120), (140) gives: % 152.07/22.66 | | | | | | | | | | | (141) all_6_0 = e1 % 152.07/22.66 | | | | | | | | | | | % 152.07/22.66 | | | | | | | | | | | BETA: splitting (41) gives: % 152.07/22.66 | | | | | | | | | | | % 152.07/22.66 | | | | | | | | | | | Case 1: % 152.07/22.66 | | | | | | | | | | | | % 152.07/22.66 | | | | | | | | | | | | (142) ~ (all_56_11 = e3) % 152.07/22.66 | | | | | | | | | | | | % 152.07/22.66 | | | | | | | | | | | | REDUCE: (1), (142) imply: % 152.07/22.66 | | | | | | | | | | | | (143) ~ (all_8_2 = e3) % 152.07/22.66 | | | | | | | | | | | | % 152.07/22.66 | | | | | | | | | | | | BETA: splitting (80) gives: % 152.07/22.66 | | | | | | | | | | | | % 152.07/22.66 | | | | | | | | | | | | Case 1: % 152.07/22.66 | | | | | | | | | | | | | % 152.07/22.66 | | | | | | | | | | | | | (144) all_54_5 = e3 % 152.07/22.66 | | | | | | | | | | | | | % 152.07/22.66 | | | | | | | | | | | | | REF_CLOSE: (16), (143), (144) are inconsistent by sub-proof % 152.07/22.66 | | | | | | | | | | | | | #737. % 152.07/22.66 | | | | | | | | | | | | | % 152.07/22.66 | | | | | | | | | | | | Case 2: % 152.07/22.66 | | | | | | | | | | | | | % 152.07/22.66 | | | | | | | | | | | | | (145) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 152.07/22.66 | | | | | | | | | | | | | % 152.07/22.66 | | | | | | | | | | | | | BETA: splitting (145) gives: % 152.07/22.66 | | | | | | | | | | | | | % 152.07/22.66 | | | | | | | | | | | | | Case 1: % 152.07/22.66 | | | | | | | | | | | | | | % 152.07/22.66 | | | | | | | | | | | | | | (146) all_54_5 = e2 % 152.07/22.66 | | | | | | | | | | | | | | % 152.07/22.66 | | | | | | | | | | | | | | COMBINE_EQS: (16), (146) imply: % 152.07/22.66 | | | | | | | | | | | | | | (147) all_8_2 = e2 % 152.07/22.66 | | | | | | | | | | | | | | % 152.07/22.66 | | | | | | | | | | | | | | SIMP: (147) implies: % 152.07/22.66 | | | | | | | | | | | | | | (148) all_8_2 = e2 % 152.07/22.66 | | | | | | | | | | | | | | % 152.07/22.66 | | | | | | | | | | | | | | REDUCE: (38), (148) imply: % 152.07/22.66 | | | | | | | | | | | | | | (149) ~ (all_52_1 = e2) % 152.07/22.66 | | | | | | | | | | | | | | % 152.07/22.66 | | | | | | | | | | | | | | REDUCE: (9), (148) imply: % 152.07/22.66 | | | | | | | | | | | | | | (150) ~ (all_52_13 = e2) % 152.07/22.66 | | | | | | | | | | | | | | % 152.07/22.66 | | | | | | | | | | | | | | REDUCE: (78), (148) imply: % 152.07/22.66 | | | | | | | | | | | | | | (151) op(e2, e2) = all_8_1 % 152.07/22.66 | | | | | | | | | | | | | | % 152.07/22.66 | | | | | | | | | | | | | | REDUCE: (34), (148) imply: % 152.07/22.66 | | | | | | | | | | | | | | (152) op(e2, e2) = all_56_10 % 152.07/22.66 | | | | | | | | | | | | | | % 152.07/22.66 | | | | | | | | | | | | | | REDUCE: (69), (148) imply: % 152.07/22.66 | | | | | | | | | | | | | | (153) op(e2, e2) = e2 % 152.07/22.66 | | | | | | | | | | | | | | % 152.07/22.66 | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_8_1, all_56_10, e2, % 152.07/22.66 | | | | | | | | | | | | | | e2, simplifying with (151), (152) gives: % 152.07/22.66 | | | | | | | | | | | | | | (154) all_56_10 = all_8_1 % 152.07/22.66 | | | | | | | | | | | | | | % 152.07/22.66 | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with e2, all_56_10, e2, e2, % 152.07/22.66 | | | | | | | | | | | | | | simplifying with (152), (153) gives: % 152.07/22.66 | | | | | | | | | | | | | | (155) all_56_10 = e2 % 152.07/22.66 | | | | | | | | | | | | | | % 152.07/22.66 | | | | | | | | | | | | | | COMBINE_EQS: (154), (155) imply: % 152.07/22.66 | | | | | | | | | | | | | | (156) all_8_1 = e2 % 152.07/22.66 | | | | | | | | | | | | | | % 152.07/22.66 | | | | | | | | | | | | | | REDUCE: (3), (156) imply: % 152.07/22.66 | | | | | | | | | | | | | | (157) op(e2, e2) = all_8_0 % 152.07/22.66 | | | | | | | | | | | | | | % 152.07/22.66 | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with e2, all_8_0, e2, e2, % 152.07/22.66 | | | | | | | | | | | | | | simplifying with (153), (157) gives: % 152.07/22.66 | | | | | | | | | | | | | | (158) all_8_0 = e2 % 152.07/22.66 | | | | | | | | | | | | | | % 152.07/22.66 | | | | | | | | | | | | | | REDUCE: (50), (158) imply: % 152.07/22.66 | | | | | | | | | | | | | | (159) ~ (e3 = e2) % 152.07/22.66 | | | | | | | | | | | | | | % 152.07/22.66 | | | | | | | | | | | | | | SIMP: (159) implies: % 152.07/22.66 | | | | | | | | | | | | | | (160) ~ (e3 = e2) % 152.07/22.66 | | | | | | | | | | | | | | % 152.07/22.66 | | | | | | | | | | | | | | REDUCE: (12), (158) imply: % 152.07/22.66 | | | | | | | | | | | | | | (161) ~ (e2 = e1) % 152.07/22.66 | | | | | | | | | | | | | | % 152.07/22.66 | | | | | | | | | | | | | | BETA: splitting (31) gives: % 152.07/22.66 | | | | | | | | | | | | | | % 152.07/22.66 | | | | | | | | | | | | | | Case 1: % 152.07/22.66 | | | | | | | | | | | | | | | % 152.07/22.66 | | | | | | | | | | | | | | | (162) ~ (all_56_1 = e1) % 152.07/22.66 | | | | | | | | | | | | | | | % 152.07/22.66 | | | | | | | | | | | | | | | REDUCE: (89), (162) imply: % 152.07/22.66 | | | | | | | | | | | | | | | (163) ~ (all_4_1 = e1) % 152.07/22.66 | | | | | | | | | | | | | | | % 152.07/22.66 | | | | | | | | | | | | | | | BETA: splitting (57) gives: % 152.07/22.66 | | | | | | | | | | | | | | | % 152.07/22.66 | | | | | | | | | | | | | | | Case 1: % 152.07/22.66 | | | | | | | | | | | | | | | | % 152.07/22.66 | | | | | | | | | | | | | | | | (164) all_58_0 = e1 % 152.07/22.66 | | | | | | | | | | | | | | | | % 152.07/22.66 | | | | | | | | | | | | | | | | COMBINE_EQS: (90), (164) imply: % 152.07/22.66 | | | | | | | | | | | | | | | | (165) all_4_1 = e1 % 152.07/22.66 | | | | | | | | | | | | | | | | % 152.07/22.66 | | | | | | | | | | | | | | | | REDUCE: (163), (165) imply: % 152.07/22.66 | | | | | | | | | | | | | | | | (166) $false % 152.07/22.66 | | | | | | | | | | | | | | | | % 152.07/22.66 | | | | | | | | | | | | | | | | CLOSE: (166) is inconsistent. % 152.07/22.66 | | | | | | | | | | | | | | | | % 152.07/22.66 | | | | | | | | | | | | | | | Case 2: % 152.07/22.66 | | | | | | | | | | | | | | | | % 152.07/22.66 | | | | | | | | | | | | | | | | (167) all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1 % 152.07/22.66 | | | | | | | | | | | | | | | | % 152.07/22.66 | | | | | | | | | | | | | | | | BETA: splitting (167) gives: % 152.07/22.66 | | | | | | | | | | | | | | | | % 152.07/22.66 | | | | | | | | | | | | | | | | Case 1: % 152.07/22.66 | | | | | | | | | | | | | | | | | % 152.07/22.66 | | | | | | | | | | | | | | | | | (168) all_58_2 = e1 % 152.07/22.66 | | | | | | | | | | | | | | | | | % 152.07/22.66 | | | | | | | | | | | | | | | | | COMBINE_EQS: (62), (168) imply: % 152.07/22.66 | | | | | | | | | | | | | | | | | (169) all_52_1 = e1 % 152.07/22.66 | | | | | | | | | | | | | | | | | % 152.07/22.66 | | | | | | | | | | | | | | | | | REDUCE: (43), (169) imply: % 152.07/22.66 | | | | | | | | | | | | | | | | | (170) ~ (all_52_13 = e1) % 152.07/22.66 | | | | | | | | | | | | | | | | | % 152.07/22.66 | | | | | | | | | | | | | | | | | SIMP: (170) implies: % 152.07/22.66 | | | | | | | | | | | | | | | | | (171) ~ (all_52_13 = e1) % 152.07/22.66 | | | | | | | | | | | | | | | | | % 152.07/22.66 | | | | | | | | | | | | | | | | | REDUCE: (149), (169) imply: % 152.07/22.66 | | | | | | | | | | | | | | | | | (172) ~ (e2 = e1) % 152.07/22.66 | | | | | | | | | | | | | | | | | % 152.07/22.66 | | | | | | | | | | | | | | | | | BETA: splitting (20) gives: % 152.07/22.66 | | | | | | | | | | | | | | | | | % 152.07/22.66 | | | | | | | | | | | | | | | | | Case 1: % 152.07/22.66 | | | | | | | | | | | | | | | | | | % 152.07/22.66 | | | | | | | | | | | | | | | | | | (173) all_58_9 = e1 % 152.07/22.66 | | | | | | | | | | | | | | | | | | % 152.07/22.66 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (27), (173) imply: % 152.07/22.66 | | | | | | | | | | | | | | | | | | (174) all_52_12 = e1 % 152.07/22.66 | | | | | | | | | | | | | | | | | | % 152.07/22.66 | | | | | | | | | | | | | | | | | | REDUCE: (93), (174) imply: % 152.07/22.66 | | | | | | | | | | | | | | | | | | (175) ~ (all_4_1 = e1) % 152.07/22.66 | | | | | | | | | | | | | | | | | | % 152.07/22.66 | | | | | | | | | | | | | | | | | | BETA: splitting (13) gives: % 152.07/22.66 | | | | | | | | | | | | | | | | | | % 152.07/22.66 | | | | | | | | | | | | | | | | | | Case 1: % 152.07/22.66 | | | | | | | | | | | | | | | | | | | % 152.07/22.66 | | | | | | | | | | | | | | | | | | | (176) all_58_0 = e2 % 152.07/22.66 | | | | | | | | | | | | | | | | | | | % 152.07/22.66 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (90), (176) imply: % 152.07/22.66 | | | | | | | | | | | | | | | | | | | (177) all_4_1 = e2 % 152.07/22.66 | | | | | | | | | | | | | | | | | | | % 152.07/22.66 | | | | | | | | | | | | | | | | | | | REDUCE: (42), (177) imply: % 152.07/22.66 | | | | | | | | | | | | | | | | | | | (178) op(e0, e2) = all_4_0 % 152.07/22.66 | | | | | | | | | | | | | | | | | | | % 152.07/22.66 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10), (29), (39), (45), (46), (48), (63), (136), % 152.07/22.66 | | | | | | | | | | | | | | | | | | | (150), (160), (161), (173), (178) are inconsistent % 152.07/22.66 | | | | | | | | | | | | | | | | | | | by sub-proof #474. % 152.07/22.66 | | | | | | | | | | | | | | | | | | | % 152.07/22.66 | | | | | | | | | | | | | | | | | | Case 2: % 152.07/22.66 | | | | | | | | | | | | | | | | | | | % 152.07/22.66 | | | | | | | | | | | | | | | | | | | (179) all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2 % 152.07/22.66 | | | | | | | | | | | | | | | | | | | % 152.07/22.66 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (68), (77), (126), (161), (173), (179) are % 152.07/22.66 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #473. % 152.07/22.66 | | | | | | | | | | | | | | | | | | | % 152.07/22.66 | | | | | | | | | | | | | | | | | | End of split % 152.07/22.66 | | | | | | | | | | | | | | | | | | % 152.07/22.66 | | | | | | | | | | | | | | | | | Case 2: % 152.07/22.66 | | | | | | | | | | | | | | | | | | % 152.07/22.66 | | | | | | | | | | | | | | | | | | (180) all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1 % 152.07/22.66 | | | | | | | | | | | | | | | | | | % 152.07/22.66 | | | | | | | | | | | | | | | | | | REF_CLOSE: (44), (48), (60), (63), (116), (171), (180) are % 152.07/22.66 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #587. % 152.07/22.66 | | | | | | | | | | | | | | | | | | % 152.07/22.66 | | | | | | | | | | | | | | | | | End of split % 152.07/22.66 | | | | | | | | | | | | | | | | | % 152.07/22.66 | | | | | | | | | | | | | | | | Case 2: % 152.07/22.66 | | | | | | | | | | | | | | | | | % 152.07/22.66 | | | | | | | | | | | | | | | | | (181) all_58_6 = e1 | all_58_12 = e1 % 152.07/22.66 | | | | | | | | | | | | | | | | | % 152.07/22.66 | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (28), (44), (60), (81), (114), (115), (117), % 152.07/22.66 | | | | | | | | | | | | | | | | | (128), (129), (181) are inconsistent by sub-proof % 152.07/22.66 | | | | | | | | | | | | | | | | | #471. % 152.07/22.66 | | | | | | | | | | | | | | | | | % 152.07/22.66 | | | | | | | | | | | | | | | | End of split % 152.07/22.66 | | | | | | | | | | | | | | | | % 152.07/22.66 | | | | | | | | | | | | | | | End of split % 152.07/22.66 | | | | | | | | | | | | | | | % 152.07/22.66 | | | | | | | | | | | | | | Case 2: % 152.07/22.66 | | | | | | | | | | | | | | | % 152.07/22.66 | | | | | | | | | | | | | | | (182) all_56_1 = e1 % 152.07/22.66 | | | | | | | | | | | | | | | % 152.07/22.66 | | | | | | | | | | | | | | | COMBINE_EQS: (89), (182) imply: % 152.07/22.66 | | | | | | | | | | | | | | | (183) all_4_1 = e1 % 152.07/22.66 | | | | | | | | | | | | | | | % 152.07/22.66 | | | | | | | | | | | | | | | REDUCE: (96), (183) imply: % 152.07/22.66 | | | | | | | | | | | | | | | (184) op(e1, e1) = e2 % 152.07/22.66 | | | | | | | | | | | | | | | % 152.07/22.66 | | | | | | | | | | | | | | | REF_CLOSE: (39), (119), (120), (161), (184) are inconsistent % 152.07/22.66 | | | | | | | | | | | | | | | by sub-proof #494. % 152.07/22.66 | | | | | | | | | | | | | | | % 152.07/22.66 | | | | | | | | | | | | | | End of split % 152.07/22.66 | | | | | | | | | | | | | | % 152.07/22.66 | | | | | | | | | | | | | Case 2: % 152.07/22.66 | | | | | | | | | | | | | | % 152.07/22.66 | | | | | | | | | | | | | | (185) all_54_5 = e1 | all_54_5 = e0 % 152.07/22.66 | | | | | | | | | | | | | | % 152.07/22.66 | | | | | | | | | | | | | | REF_CLOSE: (16), (101), (135), (185) are inconsistent by % 152.07/22.66 | | | | | | | | | | | | | | sub-proof #645. % 152.07/22.66 | | | | | | | | | | | | | | % 152.07/22.66 | | | | | | | | | | | | | End of split % 152.07/22.66 | | | | | | | | | | | | | % 152.07/22.66 | | | | | | | | | | | | End of split % 152.07/22.66 | | | | | | | | | | | | % 152.07/22.66 | | | | | | | | | | | Case 2: % 152.07/22.66 | | | | | | | | | | | | % 152.07/22.66 | | | | | | | | | | | | (186) all_56_11 = e3 % 152.07/22.66 | | | | | | | | | | | | (187) all_56_9 = e2 % 152.07/22.66 | | | | | | | | | | | | % 152.07/22.66 | | | | | | | | | | | | COMBINE_EQS: (83), (187) imply: % 152.07/22.66 | | | | | | | | | | | | (188) all_52_1 = e2 % 152.07/22.66 | | | | | | | | | | | | % 152.07/22.66 | | | | | | | | | | | | COMBINE_EQS: (1), (186) imply: % 152.07/22.66 | | | | | | | | | | | | (189) all_8_2 = e3 % 152.07/22.66 | | | | | | | | | | | | % 152.07/22.66 | | | | | | | | | | | | REDUCE: (91), (188) imply: % 152.07/22.66 | | | | | | | | | | | | (190) ~ (all_4_1 = e2) % 152.07/22.66 | | | | | | | | | | | | % 152.07/22.66 | | | | | | | | | | | | SIMP: (190) implies: % 152.07/22.66 | | | | | | | | | | | | (191) ~ (all_4_1 = e2) % 152.07/22.66 | | | | | | | | | | | | % 152.07/22.66 | | | | | | | | | | | | REDUCE: (5), (189) imply: % 152.07/22.66 | | | | | | | | | | | | (192) ~ (all_10_0 = e3) % 152.07/22.66 | | | | | | | | | | | | % 152.07/22.66 | | | | | | | | | | | | REDUCE: (78), (189) imply: % 152.07/22.66 | | | | | | | | | | | | (193) op(e3, e3) = all_8_1 % 152.07/22.66 | | | | | | | | | | | | % 152.07/22.66 | | | | | | | | | | | | REF_CLOSE: (18), (21), (37), (39), (54), (59), (77), (85), % 152.07/22.66 | | | | | | | | | | | | (87), (88), (94), (96), (97), (133), (191), (192), % 152.07/22.66 | | | | | | | | | | | | (193) are inconsistent by sub-proof #470. % 152.07/22.66 | | | | | | | | | | | | % 152.07/22.66 | | | | | | | | | | | End of split % 152.07/22.66 | | | | | | | | | | | % 152.07/22.66 | | | | | | | | | | Case 2: % 152.07/22.66 | | | | | | | | | | | % 152.07/22.66 | | | | | | | | | | | (194) all_58_14 = e1 | all_58_15 = e1 % 152.07/22.66 | | | | | | | | | | | % 152.07/22.66 | | | | | | | | | | | REF_CLOSE: (44), (60), (81), (115), (194) are inconsistent by % 152.07/22.66 | | | | | | | | | | | sub-proof #619. % 152.07/22.66 | | | | | | | | | | | % 152.07/22.66 | | | | | | | | | | End of split % 152.07/22.66 | | | | | | | | | | % 152.07/22.66 | | | | | | | | | End of split % 152.07/22.66 | | | | | | | | | % 152.07/22.66 | | | | | | | | Case 2: % 152.07/22.66 | | | | | | | | | % 152.07/22.66 | | | | | | | | | (195) all_54_14 = e1 | all_54_14 = e0 % 152.07/22.66 | | | | | | | | | % 152.07/22.66 | | | | | | | | | REF_CLOSE: (19), (32), (115), (195) are inconsistent by % 152.07/22.66 | | | | | | | | | sub-proof #714. % 152.07/22.66 | | | | | | | | | % 152.07/22.66 | | | | | | | | End of split % 152.07/22.66 | | | | | | | | % 152.07/22.66 | | | | | | | End of split % 152.07/22.66 | | | | | | | % 152.07/22.66 | | | | | | Case 2: % 152.07/22.66 | | | | | | | % 152.07/22.66 | | | | | | | (196) all_54_10 = e0 % 152.07/22.66 | | | | | | | % 152.07/22.66 | | | | | | | COMBINE_EQS: (7), (196) imply: % 152.07/22.66 | | | | | | | (197) all_6_2 = e0 % 152.07/22.66 | | | | | | | % 152.07/22.66 | | | | | | | REDUCE: (99), (197) imply: % 152.07/22.66 | | | | | | | (198) $false % 152.07/22.66 | | | | | | | % 152.07/22.66 | | | | | | | CLOSE: (198) is inconsistent. % 152.07/22.66 | | | | | | | % 152.07/22.66 | | | | | | End of split % 152.07/22.66 | | | | | | % 152.07/22.66 | | | | | End of split % 152.07/22.66 | | | | | % 152.07/22.66 | | | | End of split % 152.07/22.66 | | | | % 152.07/22.66 | | | Case 2: % 152.07/22.66 | | | | % 152.07/22.66 | | | | (199) all_56_21 = e3 % 152.07/22.66 | | | | (200) all_56_17 = e1 % 152.07/22.66 | | | | % 152.07/22.66 | | | | COMBINE_EQS: (26), (200) imply: % 152.07/22.66 | | | | (201) all_52_2 = e1 % 152.07/22.66 | | | | % 152.07/22.66 | | | | REF_CLOSE: (2), (6), (8), (17), (18), (22), (32), (39), (52), (85), % 152.07/22.66 | | | | (88), (92), (95), (199), (201) are inconsistent by sub-proof % 152.07/22.66 | | | | #468. % 152.07/22.66 | | | | % 152.07/22.66 | | | End of split % 152.07/22.66 | | | % 152.07/22.66 | | Case 2: % 152.07/22.66 | | | % 152.07/22.66 | | | (202) all_56_11 = e0 % 152.07/22.66 | | | % 152.07/22.66 | | | COMBINE_EQS: (1), (202) imply: % 152.07/22.66 | | | (203) all_8_2 = e0 % 152.07/22.66 | | | % 152.07/22.66 | | | REDUCE: (78), (203) imply: % 152.07/22.66 | | | (204) op(e0, e0) = all_8_1 % 152.07/22.66 | | | % 152.07/22.66 | | | REF_CLOSE: (14), (39), (49), (204) are inconsistent by sub-proof #546. % 152.07/22.66 | | | % 152.07/22.66 | | End of split % 152.07/22.66 | | % 152.07/22.66 | Case 2: % 152.07/22.66 | | % 152.07/22.66 | | (205) all_56_21 = e0 % 152.07/22.66 | | % 152.07/22.66 | | REF_CLOSE: (17), (22), (39), (49), (52), (205) are inconsistent by sub-proof % 152.07/22.66 | | #539. % 152.07/22.66 | | % 152.07/22.66 | End of split % 152.07/22.66 | % 152.07/22.66 End of proof % 152.07/22.66 % 152.07/22.66 Sub-proof #468 shows that the following formulas are inconsistent: % 152.07/22.66 ---------------------------------------------------------------- % 152.07/22.66 (1) ~ (all_52_11 = all_6_2) % 152.07/22.66 (2) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0 % 152.07/22.66 (3) ~ (all_4_1 = e0) % 152.07/22.66 (4) ~ (all_52_2 = all_4_1) % 152.07/22.66 (5) ~ (all_6_1 = e2) % 152.07/22.66 (6) all_56_21 = e3 % 152.07/22.66 (7) ~ (all_6_1 = e3) % 152.07/22.66 (8) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 152.07/22.66 (9) all_56_21 = all_6_2 % 152.07/22.66 (10) all_54_14 = all_52_11 % 152.07/22.66 (11) all_54_0 = all_4_1 % 152.07/22.66 (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 152.07/22.66 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 152.07/22.66 (13) all_52_2 = e1 % 152.07/22.66 (14) op(all_6_2, all_6_2) = all_6_1 % 152.07/22.66 (15) op(e3, e3) = all_4_1 % 152.07/22.66 % 152.07/22.66 Begin of proof % 152.07/22.66 | % 152.07/22.66 | COMBINE_EQS: (6), (9) imply: % 152.07/22.66 | (16) all_6_2 = e3 % 152.07/22.66 | % 152.07/22.66 | SIMP: (16) implies: % 152.07/22.66 | (17) all_6_2 = e3 % 152.07/22.66 | % 152.07/22.66 | REDUCE: (4), (13) imply: % 152.07/22.66 | (18) ~ (all_4_1 = e1) % 152.07/22.66 | % 152.07/22.66 | SIMP: (18) implies: % 152.07/22.66 | (19) ~ (all_4_1 = e1) % 152.07/22.66 | % 152.07/22.66 | REF_CLOSE: (1), (2), (3), (5), (7), (8), (10), (11), (12), (14), (15), (17), % 152.07/22.66 | (19) are inconsistent by sub-proof #469. % 152.07/22.66 | % 152.07/22.66 End of proof % 152.07/22.66 % 152.07/22.66 Sub-proof #469 shows that the following formulas are inconsistent: % 152.07/22.66 ---------------------------------------------------------------- % 152.07/22.66 (1) ~ (all_52_11 = all_6_2) % 152.07/22.66 (2) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0 % 152.07/22.66 (3) ~ (all_4_1 = e0) % 152.07/22.66 (4) ~ (all_6_1 = e2) % 152.07/22.66 (5) all_6_2 = e3 % 152.07/22.66 (6) ~ (all_6_1 = e3) % 152.07/22.66 (7) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 152.07/22.66 (8) all_54_14 = all_52_11 % 152.07/22.66 (9) all_54_0 = all_4_1 % 152.07/22.66 (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 152.07/22.66 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 152.07/22.66 (11) ~ (all_4_1 = e1) % 152.07/22.66 (12) op(all_6_2, all_6_2) = all_6_1 % 152.07/22.66 (13) op(e3, e3) = all_4_1 % 152.07/22.66 % 152.07/22.66 Begin of proof % 152.07/22.66 | % 152.07/22.66 | REDUCE: (1), (5) imply: % 152.07/22.66 | (14) ~ (all_52_11 = e3) % 152.07/22.66 | % 152.07/22.66 | REDUCE: (5), (12) imply: % 152.07/22.66 | (15) op(e3, e3) = all_6_1 % 152.07/22.66 | % 152.07/22.66 | BETA: splitting (2) gives: % 152.07/22.66 | % 152.07/22.66 | Case 1: % 152.07/22.66 | | % 152.07/22.66 | | (16) all_54_14 = e3 % 152.07/22.66 | | % 152.07/22.66 | | COMBINE_EQS: (8), (16) imply: % 152.07/22.66 | | (17) all_52_11 = e3 % 152.07/22.66 | | % 152.07/22.66 | | REDUCE: (14), (17) imply: % 152.07/22.66 | | (18) $false % 152.07/22.66 | | % 152.07/22.66 | | CLOSE: (18) is inconsistent. % 152.07/22.66 | | % 152.07/22.66 | Case 2: % 152.07/22.66 | | % 152.07/22.66 | | % 152.07/22.66 | | GROUND_INST: instantiating (10) with all_4_1, all_6_1, e3, e3, simplifying % 152.07/22.66 | | with (13), (15) gives: % 152.07/22.66 | | (19) all_6_1 = all_4_1 % 152.07/22.66 | | % 152.07/22.66 | | REDUCE: (6), (19) imply: % 152.07/22.67 | | (20) ~ (all_4_1 = e3) % 152.07/22.67 | | % 152.07/22.67 | | REDUCE: (4), (19) imply: % 152.07/22.67 | | (21) ~ (all_4_1 = e2) % 152.07/22.67 | | % 152.07/22.67 | | REF_CLOSE: (3), (7), (9), (11), (20), (21) are inconsistent by sub-proof % 152.07/22.67 | | #548. % 152.07/22.67 | | % 152.07/22.67 | End of split % 152.07/22.67 | % 152.07/22.67 End of proof % 152.07/22.67 % 152.07/22.67 Sub-proof #470 shows that the following formulas are inconsistent: % 152.07/22.67 ---------------------------------------------------------------- % 152.07/22.67 (1) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 152.07/22.67 (2) all_38_2 = all_4_1 % 152.07/22.67 (3) all_54_1 = all_10_0 % 152.07/22.67 (4) ~ (all_4_1 = e2) % 152.07/22.67 (5) ~ (all_10_0 = all_4_1) % 152.07/22.67 (6) all_54_0 = all_4_1 % 152.07/22.67 (7) all_38_0 = all_10_0 % 152.07/22.67 (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 152.07/22.67 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 152.07/22.67 (9) ~ (all_10_0 = e1) % 152.07/22.67 (10) ~ (all_38_0 = e0) | ~ (all_38_2 = e1) % 152.07/22.67 (11) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0 % 152.07/22.67 (12) op(e3, e3) = all_8_1 % 152.07/22.67 (13) ~ (all_10_0 = e3) % 152.07/22.67 (14) op(all_4_1, all_4_1) = e2 % 152.07/22.67 (15) ~ (all_10_0 = e2) % 152.18/22.67 (16) op(e3, all_4_1) = all_56_0 % 152.18/22.67 (17) op(e3, e3) = all_4_1 % 152.18/22.67 % 152.18/22.67 Begin of proof % 152.18/22.67 | % 152.18/22.67 | BETA: splitting (11) gives: % 152.18/22.67 | % 152.18/22.67 | Case 1: % 152.18/22.67 | | % 152.18/22.67 | | (18) all_54_1 = e3 % 152.18/22.67 | | % 152.18/22.67 | | REF_CLOSE: (3), (13), (18) are inconsistent by sub-proof #493. % 152.18/22.67 | | % 152.18/22.67 | Case 2: % 152.18/22.67 | | % 152.18/22.67 | | (19) all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0 % 152.18/22.67 | | % 152.18/22.67 | | BETA: splitting (19) gives: % 152.18/22.67 | | % 152.18/22.67 | | Case 1: % 152.18/22.67 | | | % 152.18/22.67 | | | (20) all_54_1 = e2 % 152.18/22.67 | | | % 152.18/22.67 | | | REF_CLOSE: (3), (15), (20) are inconsistent by sub-proof #492. % 152.18/22.67 | | | % 152.18/22.67 | | Case 2: % 152.18/22.67 | | | % 152.18/22.67 | | | (21) all_54_1 = e1 | all_54_1 = e0 % 152.18/22.67 | | | % 152.18/22.67 | | | BETA: splitting (21) gives: % 152.18/22.67 | | | % 152.18/22.67 | | | Case 1: % 152.18/22.67 | | | | % 152.18/22.67 | | | | (22) all_54_1 = e1 % 152.18/22.67 | | | | % 152.18/22.67 | | | | REF_CLOSE: (3), (9), (22) are inconsistent by sub-proof #491. % 152.18/22.67 | | | | % 152.18/22.67 | | | Case 2: % 152.18/22.67 | | | | % 152.18/22.67 | | | | (23) all_54_1 = e0 % 152.18/22.67 | | | | % 152.18/22.67 | | | | COMBINE_EQS: (3), (23) imply: % 152.18/22.67 | | | | (24) all_10_0 = e0 % 152.18/22.67 | | | | % 152.18/22.67 | | | | SIMP: (24) implies: % 152.18/22.67 | | | | (25) all_10_0 = e0 % 152.18/22.67 | | | | % 152.18/22.67 | | | | COMBINE_EQS: (7), (25) imply: % 152.18/22.67 | | | | (26) all_38_0 = e0 % 152.18/22.67 | | | | % 152.18/22.67 | | | | REDUCE: (5), (25) imply: % 152.18/22.67 | | | | (27) ~ (all_4_1 = e0) % 152.18/22.67 | | | | % 152.18/22.67 | | | | SIMP: (27) implies: % 152.18/22.67 | | | | (28) ~ (all_4_1 = e0) % 152.18/22.67 | | | | % 152.18/22.67 | | | | BETA: splitting (10) gives: % 152.18/22.67 | | | | % 152.18/22.67 | | | | Case 1: % 152.18/22.67 | | | | | % 152.18/22.67 | | | | | (29) ~ (all_38_2 = e1) % 152.18/22.67 | | | | | % 152.18/22.67 | | | | | REDUCE: (2), (29) imply: % 152.18/22.67 | | | | | (30) ~ (all_4_1 = e1) % 152.18/22.67 | | | | | % 152.18/22.67 | | | | | BETA: splitting (1) gives: % 152.18/22.67 | | | | | % 152.18/22.67 | | | | | Case 1: % 152.18/22.67 | | | | | | % 152.18/22.67 | | | | | | (31) all_54_0 = e3 % 152.18/22.67 | | | | | | % 152.18/22.67 | | | | | | COMBINE_EQS: (6), (31) imply: % 152.18/22.67 | | | | | | (32) all_4_1 = e3 % 152.18/22.67 | | | | | | % 152.18/22.67 | | | | | | SIMP: (32) implies: % 152.18/22.67 | | | | | | (33) all_4_1 = e3 % 152.18/22.67 | | | | | | % 152.18/22.67 | | | | | | REDUCE: (4), (33) imply: % 152.18/22.67 | | | | | | (34) ~ (e3 = e2) % 152.18/22.67 | | | | | | % 152.18/22.67 | | | | | | REDUCE: (14), (33) imply: % 152.18/22.67 | | | | | | (35) op(e3, e3) = e2 % 152.18/22.67 | | | | | | % 152.18/22.67 | | | | | | REDUCE: (16), (33) imply: % 152.18/22.67 | | | | | | (36) op(e3, e3) = all_56_0 % 152.18/22.67 | | | | | | % 152.18/22.67 | | | | | | REDUCE: (17), (33) imply: % 152.18/22.67 | | | | | | (37) op(e3, e3) = e3 % 152.18/22.67 | | | | | | % 152.18/22.67 | | | | | | GROUND_INST: instantiating (8) with all_4_1, all_8_1, e3, e3, % 152.18/22.67 | | | | | | simplifying with (12), (17) gives: % 152.18/22.67 | | | | | | (38) all_8_1 = all_4_1 % 152.18/22.67 | | | | | | % 152.18/22.67 | | | | | | GROUND_INST: instantiating (8) with all_8_1, all_56_0, e3, e3, % 152.18/22.67 | | | | | | simplifying with (12), (36) gives: % 152.18/22.67 | | | | | | (39) all_56_0 = all_8_1 % 152.18/22.67 | | | | | | % 152.18/22.67 | | | | | | GROUND_INST: instantiating (8) with e2, all_56_0, e3, e3, % 152.18/22.67 | | | | | | simplifying with (35), (36) gives: % 152.18/22.67 | | | | | | (40) all_56_0 = e2 % 152.18/22.67 | | | | | | % 152.18/22.67 | | | | | | COMBINE_EQS: (39), (40) imply: % 152.18/22.67 | | | | | | (41) all_8_1 = e2 % 152.18/22.67 | | | | | | % 152.18/22.67 | | | | | | SIMP: (41) implies: % 152.18/22.67 | | | | | | (42) all_8_1 = e2 % 152.18/22.67 | | | | | | % 152.18/22.67 | | | | | | COMBINE_EQS: (38), (42) imply: % 152.18/22.67 | | | | | | (43) all_4_1 = e2 % 152.18/22.67 | | | | | | % 152.18/22.67 | | | | | | SIMP: (43) implies: % 152.18/22.67 | | | | | | (44) all_4_1 = e2 % 152.18/22.67 | | | | | | % 152.18/22.67 | | | | | | COMBINE_EQS: (33), (44) imply: % 152.18/22.67 | | | | | | (45) e3 = e2 % 152.18/22.67 | | | | | | % 152.18/22.67 | | | | | | SIMP: (45) implies: % 152.18/22.67 | | | | | | (46) e3 = e2 % 152.18/22.67 | | | | | | % 152.18/22.67 | | | | | | REDUCE: (34), (46) imply: % 152.18/22.67 | | | | | | (47) $false % 152.18/22.67 | | | | | | % 152.18/22.67 | | | | | | CLOSE: (47) is inconsistent. % 152.18/22.67 | | | | | | % 152.18/22.67 | | | | | Case 2: % 152.18/22.67 | | | | | | % 152.18/22.67 | | | | | | (48) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 152.18/22.67 | | | | | | % 152.18/22.67 | | | | | | REF_CLOSE: (4), (6), (28), (30), (48) are inconsistent by sub-proof % 152.18/22.67 | | | | | | #549. % 152.18/22.67 | | | | | | % 152.18/22.67 | | | | | End of split % 152.18/22.67 | | | | | % 152.18/22.67 | | | | Case 2: % 152.18/22.67 | | | | | % 152.18/22.67 | | | | | (49) all_38_2 = e1 % 152.18/22.67 | | | | | % 152.18/22.67 | | | | | REF_CLOSE: (10), (26), (49) are inconsistent by sub-proof #487. % 152.18/22.67 | | | | | % 152.18/22.67 | | | | End of split % 152.18/22.67 | | | | % 152.18/22.67 | | | End of split % 152.18/22.67 | | | % 152.18/22.67 | | End of split % 152.18/22.67 | | % 152.18/22.67 | End of split % 152.18/22.67 | % 152.18/22.67 End of proof % 152.18/22.67 % 152.18/22.67 Sub-proof #471 shows that the following formulas are inconsistent: % 152.18/22.67 ---------------------------------------------------------------- % 152.18/22.67 (1) all_58_6 = all_52_2 % 152.18/22.67 (2) all_58_12 = e0 % 152.18/22.67 (3) all_58_6 = e1 | all_58_12 = e1 % 152.18/22.67 (4) ~ (e1 = e0) % 152.18/22.67 (5) all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1 % 152.18/22.67 (6) ~ (all_4_2 = e1) % 152.18/22.67 (7) ~ (all_52_11 = e1) % 152.18/22.67 (8) ~ (all_52_2 = e1) % 152.18/22.67 (9) all_58_15 = all_4_2 % 152.18/22.67 (10) all_58_14 = all_52_11 % 152.18/22.67 (11) all_58_13 = e1 % 152.18/22.67 % 152.18/22.67 Begin of proof % 152.18/22.67 | % 152.18/22.67 | BETA: splitting (3) gives: % 152.18/22.67 | % 152.18/22.67 | Case 1: % 152.18/22.67 | | % 152.18/22.67 | | (12) all_58_6 = e1 % 152.18/22.67 | | % 152.18/22.67 | | REF_CLOSE: (1), (8), (12) are inconsistent by sub-proof #472. % 152.18/22.67 | | % 152.18/22.67 | Case 2: % 152.18/22.67 | | % 152.18/22.67 | | (13) all_58_12 = e1 % 152.18/22.67 | | % 152.18/22.67 | | COMBINE_EQS: (2), (13) imply: % 152.18/22.67 | | (14) e1 = e0 % 152.18/22.67 | | % 152.18/22.67 | | COMBINE_EQS: (11), (14) imply: % 152.18/22.67 | | (15) all_58_13 = e0 % 152.18/22.67 | | % 152.18/22.67 | | REF_CLOSE: (4), (5), (6), (7), (9), (10), (15) are inconsistent by sub-proof % 152.18/22.67 | | #575. % 152.18/22.67 | | % 152.18/22.67 | End of split % 152.18/22.67 | % 152.18/22.67 End of proof % 152.18/22.67 % 152.18/22.67 Sub-proof #472 shows that the following formulas are inconsistent: % 152.18/22.67 ---------------------------------------------------------------- % 152.18/22.67 (1) all_58_6 = all_52_2 % 152.18/22.67 (2) all_58_6 = e1 % 152.18/22.67 (3) ~ (all_52_2 = e1) % 152.18/22.67 % 152.18/22.67 Begin of proof % 152.18/22.67 | % 152.18/22.67 | COMBINE_EQS: (1), (2) imply: % 152.18/22.67 | (4) all_52_2 = e1 % 152.18/22.67 | % 152.18/22.67 | SIMP: (4) implies: % 152.18/22.67 | (5) all_52_2 = e1 % 152.18/22.67 | % 152.18/22.67 | REDUCE: (3), (5) imply: % 152.18/22.67 | (6) $false % 152.18/22.67 | % 152.18/22.67 | CLOSE: (6) is inconsistent. % 152.18/22.67 | % 152.18/22.67 End of proof % 152.18/22.67 % 152.18/22.67 Sub-proof #473 shows that the following formulas are inconsistent: % 152.18/22.67 ---------------------------------------------------------------- % 152.18/22.67 (1) ~ (all_52_8 = e2) % 152.18/22.67 (2) all_58_4 = all_52_8 % 152.18/22.67 (3) ~ (e2 = e1) % 152.18/22.67 (4) all_58_9 = e1 % 152.18/22.67 (5) all_58_1 = all_10_0 % 152.18/22.67 (6) all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2 % 152.18/22.67 (7) ~ (all_10_0 = e2) % 152.18/22.67 % 152.18/22.67 Begin of proof % 152.18/22.67 | % 152.18/22.67 | BETA: splitting (6) gives: % 152.18/22.67 | % 152.18/22.67 | Case 1: % 152.18/22.67 | | % 152.18/22.67 | | (8) all_58_1 = e2 % 152.18/22.67 | | % 152.18/22.67 | | COMBINE_EQS: (5), (8) imply: % 152.18/22.67 | | (9) all_10_0 = e2 % 152.18/22.67 | | % 152.18/22.67 | | REDUCE: (7), (9) imply: % 152.18/22.67 | | (10) $false % 152.18/22.67 | | % 152.18/22.67 | | CLOSE: (10) is inconsistent. % 152.18/22.67 | | % 152.18/22.67 | Case 2: % 152.18/22.67 | | % 152.18/22.67 | | (11) all_58_4 = e2 | all_58_9 = e2 % 152.18/22.67 | | % 152.18/22.67 | | REF_CLOSE: (1), (2), (3), (4), (11) are inconsistent by sub-proof #562. % 152.18/22.67 | | % 152.18/22.67 | End of split % 152.18/22.67 | % 152.18/22.67 End of proof % 152.18/22.67 % 152.18/22.67 Sub-proof #474 shows that the following formulas are inconsistent: % 152.18/22.67 ---------------------------------------------------------------- % 152.18/22.67 (1) op(e0, e2) = all_4_0 % 152.18/22.67 (2) all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2 % 152.18/22.67 (3) op(e0, e2) = e1 % 152.18/22.67 (4) ~ (e3 = e2) % 152.18/22.67 (5) ~ (all_52_13 = e2) % 152.18/22.67 (6) op(e0, all_52_14) = all_56_22 % 152.18/22.67 (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 152.18/22.67 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 152.18/22.67 (8) ~ (all_4_0 = e1) % 152.18/22.67 (9) all_58_15 = e3 % 152.18/22.67 (10) ~ (e2 = e1) % 152.18/22.67 (11) all_58_11 = all_52_14 % 152.18/22.67 (12) all_58_10 = all_52_13 % 152.18/22.67 (13) all_58_9 = e1 % 152.18/22.67 % 152.18/22.67 Begin of proof % 152.18/22.67 | % 152.18/22.67 | BETA: splitting (2) gives: % 152.18/22.67 | % 152.18/22.67 | Case 1: % 152.18/22.67 | | % 152.18/22.67 | | (14) all_58_9 = e2 % 152.18/22.67 | | % 152.18/22.67 | | REF_CLOSE: (10), (13), (14) are inconsistent by sub-proof #563. % 152.18/22.67 | | % 152.18/22.67 | Case 2: % 152.18/22.67 | | % 152.18/22.67 | | (15) all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2 % 152.18/22.67 | | % 152.18/22.67 | | BETA: splitting (15) gives: % 152.18/22.67 | | % 152.18/22.67 | | Case 1: % 152.18/22.67 | | | % 152.18/22.67 | | | (16) all_58_10 = e2 % 152.18/22.67 | | | % 152.18/22.67 | | | COMBINE_EQS: (12), (16) imply: % 152.18/22.67 | | | (17) all_52_13 = e2 % 152.18/22.67 | | | % 152.18/22.67 | | | REDUCE: (5), (17) imply: % 152.18/22.67 | | | (18) $false % 152.18/22.67 | | | % 152.18/22.67 | | | CLOSE: (18) is inconsistent. % 152.18/22.67 | | | % 152.18/22.67 | | Case 2: % 152.18/22.67 | | | % 152.18/22.67 | | | (19) all_58_11 = e2 | all_58_15 = e2 % 152.18/22.67 | | | % 152.18/22.67 | | | BETA: splitting (19) gives: % 152.18/22.67 | | | % 152.18/22.67 | | | Case 1: % 152.18/22.67 | | | | % 152.18/22.67 | | | | (20) all_58_11 = e2 % 152.18/22.67 | | | | % 152.18/22.67 | | | | COMBINE_EQS: (11), (20) imply: % 152.18/22.67 | | | | (21) all_52_14 = e2 % 152.18/22.67 | | | | % 152.18/22.67 | | | | REDUCE: (6), (21) imply: % 152.18/22.67 | | | | (22) op(e0, e2) = all_56_22 % 152.18/22.67 | | | | % 152.18/22.67 | | | | GROUND_INST: instantiating (7) with e1, all_56_22, e2, e0, simplifying % 152.18/22.67 | | | | with (3), (22) gives: % 152.18/22.67 | | | | (23) all_56_22 = e1 % 152.18/22.67 | | | | % 152.18/22.67 | | | | GROUND_INST: instantiating (7) with all_4_0, all_56_22, e2, e0, % 152.18/22.67 | | | | simplifying with (1), (22) gives: % 152.18/22.67 | | | | (24) all_56_22 = all_4_0 % 152.18/22.67 | | | | % 152.18/22.67 | | | | COMBINE_EQS: (23), (24) imply: % 152.18/22.67 | | | | (25) all_4_0 = e1 % 152.18/22.67 | | | | % 152.18/22.67 | | | | REDUCE: (8), (25) imply: % 152.18/22.67 | | | | (26) $false % 152.18/22.67 | | | | % 152.18/22.67 | | | | CLOSE: (26) is inconsistent. % 152.18/22.67 | | | | % 152.18/22.67 | | | Case 2: % 152.18/22.67 | | | | % 152.18/22.67 | | | | (27) all_58_15 = e2 % 152.18/22.67 | | | | % 152.18/22.67 | | | | COMBINE_EQS: (9), (27) imply: % 152.18/22.67 | | | | (28) e3 = e2 % 152.18/22.67 | | | | % 152.18/22.67 | | | | REDUCE: (4), (28) imply: % 152.18/22.67 | | | | (29) $false % 152.18/22.67 | | | | % 152.18/22.67 | | | | CLOSE: (29) is inconsistent. % 152.18/22.67 | | | | % 152.18/22.67 | | | End of split % 152.18/22.67 | | | % 152.18/22.67 | | End of split % 152.18/22.67 | | % 152.18/22.67 | End of split % 152.18/22.67 | % 152.18/22.67 End of proof % 152.18/22.67 % 152.18/22.67 Sub-proof #475 shows that the following formulas are inconsistent: % 152.18/22.67 ---------------------------------------------------------------- % 152.18/22.67 (1) all_58_12 = e1 % 152.18/22.67 (2) all_58_12 = e0 % 152.18/22.67 (3) ~ (e1 = e0) % 152.18/22.67 % 152.18/22.67 Begin of proof % 152.18/22.67 | % 152.18/22.67 | COMBINE_EQS: (1), (2) imply: % 152.18/22.67 | (4) e1 = e0 % 152.18/22.67 | % 152.18/22.67 | SIMP: (4) implies: % 152.18/22.67 | (5) e1 = e0 % 152.18/22.67 | % 152.18/22.67 | REDUCE: (3), (5) imply: % 152.18/22.67 | (6) $false % 152.18/22.67 | % 152.18/22.67 | CLOSE: (6) is inconsistent. % 152.18/22.67 | % 152.18/22.67 End of proof % 152.18/22.67 % 152.18/22.67 Sub-proof #476 shows that the following formulas are inconsistent: % 152.18/22.67 ---------------------------------------------------------------- % 152.18/22.67 (1) all_56_11 = all_8_2 % 152.18/22.67 (2) ~ (all_56_11 = e1) | all_56_13 = e2 % 152.18/22.67 (3) ~ (all_52_11 = all_6_2) % 152.18/22.67 (4) ~ (all_52_4 = all_52_8) % 152.18/22.67 (5) ~ (all_52_7 = all_52_11) % 152.18/22.67 (6) all_54_9 = all_52_6 % 152.18/22.67 (7) op(e2, all_8_1) = all_8_0 % 152.18/22.67 (8) all_58_6 = all_52_2 % 152.18/22.67 (9) ~ (all_8_1 = e1) % 152.18/22.67 (10) ~ (all_10_0 = all_8_2) % 152.18/22.67 (11) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0 % 152.18/22.67 (12) all_54_10 = all_6_2 % 152.18/22.67 (13) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0 % 152.18/22.67 (14) ~ (all_6_1 = e2) % 152.18/22.67 (15) ~ (all_52_13 = all_8_2) % 152.18/22.67 (16) ~ (all_56_21 = e2) | all_56_19 = e1 % 152.18/22.67 (17) all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2 % 152.18/22.67 (18) all_54_0 = all_10_2 % 152.18/22.67 (19) ~ (all_52_14 = all_4_2) % 152.18/22.67 (20) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0 % 152.18/22.67 (21) all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2 % 152.18/22.67 (22) ~ (all_52_9 = all_8_2) % 152.18/22.67 (23) all_54_12 = all_52_3 % 152.18/22.67 (24) ~ (all_52_12 = all_52_13) % 152.18/22.67 (25) ~ (all_52_4 = all_52_7) % 152.18/22.67 (26) ~ (all_8_1 = e3) % 152.18/22.67 (27) op(e0, e0) = all_4_2 % 152.18/22.67 (28) all_58_4 = all_52_8 % 152.18/22.67 (29) all_54_5 = all_8_2 % 152.18/22.67 (30) ~ (all_6_1 = e3) % 152.18/22.67 (31) ~ (all_52_6 = all_52_14) % 152.18/22.67 (32) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 152.18/22.67 (33) ~ (all_6_0 = e2) % 152.18/22.67 (34) all_54_15 = all_4_2 % 152.18/22.67 (35) all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1 % 152.18/22.67 (36) all_54_1 = all_10_0 % 152.18/22.67 (37) ~ (all_10_1 = e1) % 152.18/22.67 (38) all_56_21 = all_6_2 % 152.18/22.67 (39) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 152.18/22.67 (40) ~ (all_52_7 = all_8_2) % 152.18/22.67 (41) all_56_1 = all_10_2 % 152.18/22.67 (42) all_56_27 = all_52_7 % 152.18/22.67 (43) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0 % 152.18/22.67 (44) all_58_5 = all_52_9 % 152.18/22.67 (45) all_54_1 = all_52_4 % 152.18/22.67 (46) all_56_17 = all_52_2 % 152.18/22.67 (47) all_58_9 = all_52_12 % 152.18/22.67 (48) all_56_3 = all_10_0 % 152.18/22.67 (49) op(e1, e0) = all_52_14 % 152.18/22.67 (50) ~ (all_56_1 = e1) | all_56_5 = e3 % 152.18/22.67 (51) all_54_14 = all_52_11 % 152.18/22.67 (52) ( ~ (all_56_0 = all_56_1) & ~ (all_56_2 = all_56_3) & ~ (all_56_4 = % 152.18/22.67 all_56_5) & ~ (all_56_6 = all_56_7)) | ( ~ (all_56_8 = all_56_9) & % 152.18/22.67 ~ (all_56_10 = all_56_11) & ~ (all_56_12 = all_56_13) & ~ (all_56_14 % 152.18/22.67 = all_56_15)) | ( ~ (all_56_16 = all_56_17) & ~ (all_56_18 = % 152.18/22.67 all_56_19) & ~ (all_56_20 = all_56_21) & ~ (all_56_22 = % 152.18/22.67 all_56_23)) | ( ~ (all_56_24 = all_56_25) & ~ (all_56_26 = % 152.18/22.67 all_56_27) & ~ (all_56_28 = all_56_29) & ~ (all_56_30 = % 152.18/22.67 all_56_31)) % 152.18/22.67 (53) all_58_1 = all_52_4 % 152.18/22.67 (54) all_58_13 = all_52_7 % 152.18/22.67 (55) all_58_4 = e0 | all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0 % 152.18/22.67 (56) op(e2, all_8_2) = all_56_10 % 152.18/22.67 (57) op(e3, e3) = all_10_2 % 152.18/22.67 (58) ~ (all_52_8 = all_6_2) % 152.18/22.67 (59) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0 % 152.18/22.67 (60) all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1 % 152.18/22.67 (61) ~ (all_56_21 = e3) | all_56_17 = e1 % 152.18/22.67 (62) all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2 % 152.18/22.67 (63) all_38_0 = all_10_0 % 152.18/22.67 (64) all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1 % 152.18/22.67 (65) ~ (all_52_1 = all_8_2) % 152.18/22.67 (66) all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2 % 152.18/22.67 (67) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 152.18/22.67 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 152.18/22.67 (68) ~ (all_52_8 = all_10_0) % 152.18/22.67 (69) ~ (all_52_3 = all_10_2) % 152.18/22.67 (70) all_54_3 = all_52_12 % 152.18/22.67 (71) all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0 % 152.18/22.67 (72) ~ (all_52_3 = all_52_7) % 152.18/22.67 (73) ~ (all_56_11 = e3) | all_56_9 = e2 % 152.18/22.67 (74) ~ (all_52_2 = all_52_6) % 152.18/22.67 (75) op(e0, all_4_1) = all_4_0 % 152.18/22.67 (76) all_56_7 = all_52_12 % 152.18/22.67 (77) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0 % 152.18/22.67 (78) all_56_13 = all_52_9 % 152.18/22.67 (79) op(e2, all_52_6) = all_56_18 % 152.18/22.67 (80) ~ (all_52_1 = all_52_13) % 152.18/22.67 (81) ~ (all_52_7 = all_4_2) % 152.18/22.67 (82) ~ (all_4_2 = e1) % 152.18/22.67 (83) all_58_8 = all_6_2 % 152.18/22.67 (84) ~ (all_6_0 = e3) % 152.18/22.67 (85) ~ (all_52_3 = all_4_2) % 152.18/22.67 (86) ~ (all_52_8 = all_10_2) % 152.18/22.67 (87) ~ (all_52_12 = all_10_0) % 152.18/22.67 (88) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0 % 152.18/22.67 (89) ~ (all_56_1 = e2) | all_56_3 = e3 % 152.18/22.67 (90) ~ (all_56_1 = e0) | all_56_7 = e3 % 152.18/22.67 (91) all_56_5 = all_52_8 % 152.18/22.67 (92) ~ (all_52_9 = all_52_13) % 152.18/22.67 (93) ~ (all_52_2 = all_52_3) % 152.18/22.67 (94) op(e1, all_6_1) = all_6_0 % 152.18/22.67 (95) op(all_4_2, all_4_2) = all_4_1 % 152.18/22.67 (96) all_58_3 = all_8_2 % 152.18/22.67 (97) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0 % 152.18/22.67 (98) ~ (all_52_11 = all_4_2) % 152.18/22.67 (99) ~ (all_52_1 = all_52_3) % 152.18/22.67 (100) all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1 % 152.18/22.67 (101) ~ (all_52_6 = all_52_7) % 152.18/22.67 (102) all_56_31 = all_4_2 % 152.18/22.67 (103) all_58_11 = all_52_14 % 152.18/22.67 (104) ~ (all_8_0 = e3) % 152.18/22.67 (105) op(all_10_2, all_10_2) = e2 % 152.18/22.67 (106) ~ (all_52_2 = all_52_14) % 152.18/22.67 (107) all_54_7 = all_52_13 % 152.18/22.67 (108) op(all_6_2, all_6_2) = all_6_1 % 152.18/22.67 (109) all_56_1 = e3 | all_56_11 = e2 | all_56_21 = e1 | all_56_31 = e0 % 152.18/22.67 (110) ~ (all_10_0 = e1) % 152.18/22.67 (111) ~ (all_52_13 = all_4_2) % 152.18/22.67 (112) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0 % 152.18/22.67 (113) ~ (all_52_8 = all_52_11) % 152.18/22.67 (114) all_54_13 = all_52_7 % 152.18/22.67 (115) all_54_2 = all_52_8 % 152.18/22.67 (116) ~ (all_52_13 = all_52_14) % 152.18/22.67 (117) all_56_23 = all_52_14 % 152.18/22.67 (118) all_54_8 = all_52_2 % 152.18/22.67 (119) ~ (all_38_0 = e0) | ~ (all_38_2 = e1) % 152.18/22.67 (120) all_38_2 = all_10_2 % 152.18/22.67 (121) op(e1, e1) = all_6_2 % 152.18/22.67 (122) ~ (all_52_6 = all_8_2) % 152.18/22.67 (123) all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1 % 152.18/22.67 (124) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0 % 152.18/22.67 (125) all_58_15 = all_4_2 % 152.18/22.67 (126) op(e2, all_10_0) = all_56_2 % 152.18/22.67 (127) ~ (all_6_2 = e2) % 152.18/22.67 (128) all_58_2 = all_52_1 % 152.18/22.67 (129) ~ (all_4_2 = e3) % 152.18/22.67 (130) ~ (all_52_9 = all_6_2) % 152.18/22.67 (131) all_58_7 = all_52_6 % 152.18/22.67 (132) all_58_10 = all_52_13 % 152.18/22.67 (133) ~ (all_52_12 = all_4_2) % 152.18/22.67 (134) op(all_10_2, all_10_2) = all_10_1 % 152.18/22.67 (135) ~ (all_56_11 = e0) | all_56_15 = e2 % 152.18/22.67 (136) all_58_0 = all_10_2 % 152.18/22.67 (137) op(e1, all_6_2) = all_56_20 % 152.18/22.67 (138) all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1 % 152.18/22.67 (139) all_58_1 = all_10_0 % 152.18/22.67 (140) all_58_1 = e0 | all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0 % 152.18/22.67 (141) ~ (all_52_12 = all_52_14) % 152.18/22.67 (142) op(e1, all_52_9) = all_56_12 % 152.18/22.67 (143) ~ (all_56_31 = e2) | all_56_27 = e0 % 152.18/22.67 (144) op(e2, e2) = all_8_2 % 152.18/22.67 (145) ~ (all_52_4 = all_52_12) % 152.18/22.67 (146) op(e2, e0) = all_52_13 % 152.18/22.67 (147) ~ (all_52_2 = all_6_2) % 152.18/22.67 (148) ~ (all_52_8 = all_52_12) % 152.18/22.67 (149) ~ (all_56_21 = e0) | all_56_23 = e1 % 152.18/22.67 (150) op(e0, all_4_2) = all_56_30 % 152.18/22.67 (151) ~ (all_52_6 = all_6_2) % 152.18/22.67 (152) op(e3, all_10_2) = all_56_0 % 152.18/22.67 (153) ~ (all_52_14 = all_6_2) % 152.18/22.67 (154) all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0 % 152.18/22.67 (155) ~ (all_10_0 = all_10_2) % 152.18/22.67 (156) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0 % 152.18/22.67 (157) ~ (all_52_2 = all_10_2) % 152.18/22.67 (158) ~ (all_52_4 = all_10_2) % 152.18/22.67 (159) ~ (all_10_0 = e2) % 152.18/22.67 (160) ~ (all_52_4 = all_8_2) % 152.18/22.67 (161) op(all_8_2, all_8_2) = all_8_1 % 152.18/22.67 (162) ~ (all_52_7 = all_10_0) % 152.18/22.67 (163) ~ (all_52_4 = all_52_6) % 152.18/22.67 (164) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 152.18/22.67 (165) all_58_14 = all_52_11 % 152.18/22.67 (166) all_56_19 = all_52_6 % 152.18/22.67 (167) ~ (all_52_12 = all_10_2) % 152.18/22.67 (168) ~ (all_4_0 = e3) % 152.18/22.67 (169) all_56_9 = all_52_1 % 152.18/22.67 (170) all_56_15 = all_52_13 % 152.18/22.67 (171) ~ (all_52_1 = all_10_2) % 152.18/22.67 (172) all_58_12 = all_52_3 % 152.18/22.67 (173) all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2 % 152.18/22.67 (174) all_54_11 = all_52_14 % 152.18/22.67 % 152.18/22.67 Begin of proof % 152.18/22.67 | % 152.18/22.67 | BETA: splitting (143) gives: % 152.18/22.67 | % 152.18/22.67 | Case 1: % 152.18/22.67 | | % 152.18/22.67 | | (175) ~ (all_56_31 = e2) % 152.18/22.67 | | % 152.18/22.67 | | REDUCE: (102), (175) imply: % 152.18/22.67 | | (176) ~ (all_4_2 = e2) % 152.18/22.67 | | % 152.18/22.67 | | BETA: splitting (112) gives: % 152.18/22.67 | | % 152.18/22.67 | | Case 1: % 152.18/22.67 | | | % 152.18/22.67 | | | (177) all_54_15 = e3 % 152.18/22.67 | | | % 152.18/22.67 | | | REF_CLOSE: (34), (129), (177) are inconsistent by sub-proof #740. % 152.18/22.67 | | | % 152.18/22.67 | | Case 2: % 152.18/22.67 | | | % 152.18/22.67 | | | (178) ~ (all_54_15 = e3) % 152.18/22.67 | | | (179) all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0 % 152.18/22.67 | | | % 152.18/22.67 | | | BETA: splitting (179) gives: % 152.18/22.67 | | | % 152.18/22.67 | | | Case 1: % 152.18/22.67 | | | | % 152.18/22.67 | | | | (180) all_54_15 = e2 % 152.18/22.67 | | | | % 152.18/22.67 | | | | REF_CLOSE: (34), (176), (180) are inconsistent by sub-proof #739. % 152.18/22.67 | | | | % 152.18/22.67 | | | Case 2: % 152.18/22.67 | | | | % 152.18/22.67 | | | | (181) ~ (all_54_15 = e2) % 152.18/22.67 | | | | (182) all_54_15 = e1 | all_54_15 = e0 % 152.18/22.67 | | | | % 152.18/22.67 | | | | BETA: splitting (182) gives: % 152.18/22.67 | | | | % 152.18/22.67 | | | | Case 1: % 152.18/22.67 | | | | | % 152.18/22.67 | | | | | (183) all_54_15 = e1 % 152.18/22.67 | | | | | % 152.18/22.67 | | | | | REF_CLOSE: (34), (82), (183) are inconsistent by sub-proof #738. % 152.18/22.67 | | | | | % 152.18/22.67 | | | | Case 2: % 152.18/22.67 | | | | | % 152.18/22.67 | | | | | (184) all_54_15 = e0 % 152.18/22.67 | | | | | % 152.18/22.67 | | | | | COMBINE_EQS: (34), (184) imply: % 152.18/22.67 | | | | | (185) all_4_2 = e0 % 152.18/22.67 | | | | | % 152.18/22.67 | | | | | SIMP: (185) implies: % 152.18/22.67 | | | | | (186) all_4_2 = e0 % 152.18/22.67 | | | | | % 152.18/22.67 | | | | | COMBINE_EQS: (102), (186) imply: % 152.18/22.67 | | | | | (187) all_56_31 = e0 % 152.18/22.67 | | | | | % 152.18/22.67 | | | | | REDUCE: (85), (186) imply: % 152.18/22.67 | | | | | (188) ~ (all_52_3 = e0) % 152.18/22.67 | | | | | % 152.18/22.67 | | | | | REDUCE: (81), (186) imply: % 152.18/22.67 | | | | | (189) ~ (all_52_7 = e0) % 152.18/22.67 | | | | | % 152.18/22.67 | | | | | REDUCE: (98), (186) imply: % 152.18/22.67 | | | | | (190) ~ (all_52_11 = e0) % 152.18/22.67 | | | | | % 152.18/22.67 | | | | | REDUCE: (133), (186) imply: % 152.18/22.67 | | | | | (191) ~ (all_52_12 = e0) % 152.18/22.67 | | | | | % 152.18/22.67 | | | | | REDUCE: (111), (186) imply: % 152.18/22.67 | | | | | (192) ~ (all_52_13 = e0) % 152.18/22.67 | | | | | % 152.18/22.67 | | | | | REDUCE: (19), (186) imply: % 152.18/22.67 | | | | | (193) ~ (all_52_14 = e0) % 152.18/22.67 | | | | | % 152.18/22.67 | | | | | REDUCE: (95), (186) imply: % 152.18/22.67 | | | | | (194) op(e0, e0) = all_4_1 % 152.18/22.67 | | | | | % 152.18/22.67 | | | | | REDUCE: (150), (186) imply: % 152.18/22.67 | | | | | (195) op(e0, e0) = all_56_30 % 152.18/22.67 | | | | | % 152.18/22.67 | | | | | REDUCE: (27), (186) imply: % 152.18/22.67 | | | | | (196) op(e0, e0) = e0 % 152.18/22.67 | | | | | % 152.18/22.67 | | | | | GROUND_INST: instantiating (67) with all_4_1, all_56_30, e0, e0, % 152.18/22.67 | | | | | simplifying with (194), (195) gives: % 152.18/22.67 | | | | | (197) all_56_30 = all_4_1 % 152.18/22.67 | | | | | % 152.18/22.67 | | | | | GROUND_INST: instantiating (67) with e0, all_56_30, e0, e0, % 152.18/22.67 | | | | | simplifying with (195), (196) gives: % 152.18/22.67 | | | | | (198) all_56_30 = e0 % 152.18/22.67 | | | | | % 152.18/22.67 | | | | | COMBINE_EQS: (197), (198) imply: % 152.18/22.67 | | | | | (199) all_4_1 = e0 % 152.18/22.67 | | | | | % 152.18/22.67 | | | | | SIMP: (199) implies: % 152.18/22.67 | | | | | (200) all_4_1 = e0 % 152.18/22.67 | | | | | % 152.18/22.67 | | | | | REDUCE: (75), (200) imply: % 152.18/22.67 | | | | | (201) op(e0, e0) = all_4_0 % 152.18/22.67 | | | | | % 152.18/22.67 | | | | | GROUND_INST: instantiating (67) with e0, all_4_0, e0, e0, simplifying % 152.18/22.67 | | | | | with (196), (201) gives: % 152.18/22.67 | | | | | (202) all_4_0 = e0 % 152.18/22.67 | | | | | % 152.18/22.67 | | | | | REDUCE: (168), (202) imply: % 152.18/22.67 | | | | | (203) ~ (e3 = e0) % 152.18/22.67 | | | | | % 152.18/22.67 | | | | | SIMP: (203) implies: % 152.18/22.67 | | | | | (204) ~ (e3 = e0) % 152.18/22.67 | | | | | % 152.18/22.67 | | | | | BETA: splitting (135) gives: % 152.18/22.67 | | | | | % 152.18/22.67 | | | | | Case 1: % 152.18/22.67 | | | | | | % 152.18/22.67 | | | | | | (205) ~ (all_56_11 = e0) % 152.18/22.67 | | | | | | % 152.18/22.67 | | | | | | REDUCE: (1), (205) imply: % 152.18/22.67 | | | | | | (206) ~ (all_8_2 = e0) % 152.18/22.67 | | | | | | % 152.18/22.67 | | | | | | BETA: splitting (2) gives: % 152.18/22.67 | | | | | | % 152.18/22.67 | | | | | | Case 1: % 152.18/22.67 | | | | | | | % 152.18/22.67 | | | | | | | (207) ~ (all_56_11 = e1) % 152.18/22.67 | | | | | | | % 152.18/22.67 | | | | | | | REDUCE: (1), (207) imply: % 152.18/22.67 | | | | | | | (208) ~ (all_8_2 = e1) % 152.18/22.67 | | | | | | | % 152.18/22.67 | | | | | | | BETA: splitting (149) gives: % 152.18/22.67 | | | | | | | % 152.18/22.67 | | | | | | | Case 1: % 152.18/22.67 | | | | | | | | % 152.18/22.67 | | | | | | | | (209) ~ (all_56_21 = e0) % 152.18/22.67 | | | | | | | | % 152.18/22.67 | | | | | | | | REDUCE: (38), (209) imply: % 152.18/22.67 | | | | | | | | (210) ~ (all_6_2 = e0) % 152.18/22.67 | | | | | | | | % 152.18/22.67 | | | | | | | | BETA: splitting (61) gives: % 152.18/22.67 | | | | | | | | % 152.18/22.67 | | | | | | | | Case 1: % 152.18/22.67 | | | | | | | | | % 152.18/22.67 | | | | | | | | | (211) ~ (all_56_21 = e3) % 152.18/22.67 | | | | | | | | | % 152.18/22.67 | | | | | | | | | REDUCE: (38), (211) imply: % 152.18/22.67 | | | | | | | | | (212) ~ (all_6_2 = e3) % 152.18/22.67 | | | | | | | | | % 152.18/22.67 | | | | | | | | | BETA: splitting (39) gives: % 152.18/22.67 | | | | | | | | | % 152.18/22.67 | | | | | | | | | Case 1: % 152.18/22.67 | | | | | | | | | | % 152.18/22.67 | | | | | | | | | | (213) all_54_10 = e3 % 152.18/22.67 | | | | | | | | | | % 152.18/22.67 | | | | | | | | | | COMBINE_EQS: (12), (213) imply: % 152.18/22.67 | | | | | | | | | | (214) all_6_2 = e3 % 152.18/22.67 | | | | | | | | | | % 152.18/22.67 | | | | | | | | | | REDUCE: (212), (214) imply: % 152.18/22.68 | | | | | | | | | | (215) $false % 152.18/22.68 | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | CLOSE: (215) is inconsistent. % 152.18/22.68 | | | | | | | | | | % 152.18/22.68 | | | | | | | | | Case 2: % 152.18/22.68 | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | (216) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 152.18/22.68 | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | BETA: splitting (216) gives: % 152.18/22.68 | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | Case 1: % 152.18/22.68 | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | | (217) all_54_10 = e2 % 152.18/22.68 | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | | COMBINE_EQS: (12), (217) imply: % 152.18/22.68 | | | | | | | | | | | (218) all_6_2 = e2 % 152.18/22.68 | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | | REDUCE: (127), (218) imply: % 152.18/22.68 | | | | | | | | | | | (219) $false % 152.18/22.68 | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | | CLOSE: (219) is inconsistent. % 152.18/22.68 | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | Case 2: % 152.18/22.68 | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | | (220) all_54_10 = e1 | all_54_10 = e0 % 152.18/22.68 | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | | BETA: splitting (220) gives: % 152.18/22.68 | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | | Case 1: % 152.18/22.68 | | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | | | (221) all_54_10 = e1 % 152.18/22.68 | | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | | | COMBINE_EQS: (12), (221) imply: % 152.18/22.68 | | | | | | | | | | | | (222) all_6_2 = e1 % 152.18/22.68 | | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | | | REDUCE: (58), (222) imply: % 152.18/22.68 | | | | | | | | | | | | (223) ~ (all_52_8 = e1) % 152.18/22.68 | | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | | | REDUCE: (130), (222) imply: % 152.18/22.68 | | | | | | | | | | | | (224) ~ (all_52_9 = e1) % 152.18/22.68 | | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | | | REDUCE: (153), (222) imply: % 152.18/22.68 | | | | | | | | | | | | (225) ~ (all_52_14 = e1) % 152.18/22.68 | | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | | | REDUCE: (108), (222) imply: % 152.18/22.68 | | | | | | | | | | | | (226) op(e1, e1) = all_6_1 % 152.18/22.68 | | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | | | REDUCE: (137), (222) imply: % 152.18/22.68 | | | | | | | | | | | | (227) op(e1, e1) = all_56_20 % 152.18/22.68 | | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | | | REDUCE: (121), (222) imply: % 152.18/22.68 | | | | | | | | | | | | (228) op(e1, e1) = e1 % 152.18/22.68 | | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | | | GROUND_INST: instantiating (67) with all_6_1, all_56_20, e1, % 152.18/22.68 | | | | | | | | | | | | e1, simplifying with (226), (227) gives: % 152.18/22.68 | | | | | | | | | | | | (229) all_56_20 = all_6_1 % 152.18/22.68 | | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | | | GROUND_INST: instantiating (67) with e1, all_56_20, e1, e1, % 152.18/22.68 | | | | | | | | | | | | simplifying with (227), (228) gives: % 152.18/22.68 | | | | | | | | | | | | (230) all_56_20 = e1 % 152.18/22.68 | | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | | | COMBINE_EQS: (229), (230) imply: % 152.18/22.68 | | | | | | | | | | | | (231) all_6_1 = e1 % 152.18/22.68 | | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | | | REDUCE: (94), (231) imply: % 152.18/22.68 | | | | | | | | | | | | (232) op(e1, e1) = all_6_0 % 152.18/22.68 | | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | | | GROUND_INST: instantiating (67) with e1, all_6_0, e1, e1, % 152.18/22.68 | | | | | | | | | | | | simplifying with (228), (232) gives: % 152.18/22.68 | | | | | | | | | | | | (233) all_6_0 = e1 % 152.18/22.68 | | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | | | REDUCE: (84), (233) imply: % 152.18/22.68 | | | | | | | | | | | | (234) ~ (e3 = e1) % 152.18/22.68 | | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | | | SIMP: (234) implies: % 152.18/22.68 | | | | | | | | | | | | (235) ~ (e3 = e1) % 152.18/22.68 | | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | | | REDUCE: (33), (233) imply: % 152.18/22.68 | | | | | | | | | | | | (236) ~ (e2 = e1) % 152.18/22.68 | | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | | | SIMP: (236) implies: % 152.18/22.68 | | | | | | | | | | | | (237) ~ (e2 = e1) % 152.18/22.68 | | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | | | BETA: splitting (50) gives: % 152.18/22.68 | | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | | | Case 1: % 152.18/22.68 | | | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | | | | (238) ~ (all_56_1 = e1) % 152.18/22.68 | | | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | | | | REDUCE: (41), (238) imply: % 152.18/22.68 | | | | | | | | | | | | | (239) ~ (all_10_2 = e1) % 152.18/22.68 | | | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | | | | BETA: splitting (123) gives: % 152.18/22.68 | | | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | | | | Case 1: % 152.18/22.68 | | | | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | | | | | (240) all_58_0 = e1 % 152.18/22.68 | | | | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | | | | | COMBINE_EQS: (136), (240) imply: % 152.18/22.68 | | | | | | | | | | | | | | (241) all_10_2 = e1 % 152.18/22.68 | | | | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | | | | | REDUCE: (239), (241) imply: % 152.18/22.68 | | | | | | | | | | | | | | (242) $false % 152.18/22.68 | | | | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | | | | | CLOSE: (242) is inconsistent. % 152.18/22.68 | | | | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | | | | Case 2: % 152.18/22.68 | | | | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | | | | | (243) ~ (all_58_0 = e1) % 152.18/22.68 | | | | | | | | | | | | | | (244) all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1 % 152.18/22.68 | | | | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | | | | | BETA: splitting (60) gives: % 152.18/22.68 | | | | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | | | | | Case 1: % 152.18/22.68 | | | | | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | | | | | | (245) all_58_0 = e1 % 152.18/22.68 | | | | | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | | | | | | COMBINE_EQS: (136), (245) imply: % 152.18/22.68 | | | | | | | | | | | | | | | (246) all_10_2 = e1 % 152.18/22.68 | | | | | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | | | | | | REDUCE: (239), (246) imply: % 152.18/22.68 | | | | | | | | | | | | | | | (247) $false % 152.18/22.68 | | | | | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | | | | | | CLOSE: (247) is inconsistent. % 152.18/22.68 | | | | | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | | | | | Case 2: % 152.18/22.68 | | | | | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | | | | | | (248) all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1 % 152.18/22.68 | | | | | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | | | | | | BETA: splitting (248) gives: % 152.18/22.68 | | | | | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | | | | | | Case 1: % 152.18/22.68 | | | | | | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | | | | | | | (249) all_58_1 = e1 % 152.18/22.68 | | | | | | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | | | | | | | COMBINE_EQS: (139), (249) imply: % 152.18/22.68 | | | | | | | | | | | | | | | | (250) all_10_0 = e1 % 152.18/22.68 | | | | | | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | | | | | | | REDUCE: (110), (250) imply: % 152.18/22.68 | | | | | | | | | | | | | | | | (251) $false % 152.18/22.68 | | | | | | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | | | | | | | CLOSE: (251) is inconsistent. % 152.18/22.68 | | | | | | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | | | | | | Case 2: % 152.18/22.68 | | | | | | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | | | | | | | (252) all_58_4 = e1 | all_58_9 = e1 % 152.18/22.68 | | | | | | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | | | | | | | BETA: splitting (244) gives: % 152.18/22.68 | | | | | | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | | | | | | | Case 1: % 152.18/22.68 | | | | | | | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | | | | | | | | (253) all_58_2 = e1 % 152.18/22.68 | | | | | | | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | | | | | | | | COMBINE_EQS: (128), (253) imply: % 152.18/22.68 | | | | | | | | | | | | | | | | | (254) all_52_1 = e1 % 152.18/22.68 | | | | | | | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | | | | | | | | COMBINE_EQS: (169), (254) imply: % 152.18/22.68 | | | | | | | | | | | | | | | | | (255) all_56_9 = e1 % 152.18/22.68 | | | | | | | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | | | | | | | | REDUCE: (80), (254) imply: % 152.18/22.68 | | | | | | | | | | | | | | | | | (256) ~ (all_52_13 = e1) % 152.18/22.68 | | | | | | | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | | | | | | | | SIMP: (256) implies: % 152.18/22.68 | | | | | | | | | | | | | | | | | (257) ~ (all_52_13 = e1) % 152.18/22.68 | | | | | | | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | | | | | | | | REDUCE: (65), (254) imply: % 152.18/22.68 | | | | | | | | | | | | | | | | | (258) ~ (all_8_2 = e1) % 152.18/22.68 | | | | | | | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | | | | | | | | BETA: splitting (73) gives: % 152.18/22.68 | | | | | | | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | | | | | | | | Case 1: % 152.18/22.68 | | | | | | | | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | | | | | | | | | (259) ~ (all_56_11 = e3) % 152.18/22.68 | | | | | | | | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | | | | | | | | | REDUCE: (1), (259) imply: % 152.18/22.68 | | | | | | | | | | | | | | | | | | (260) ~ (all_8_2 = e3) % 152.18/22.68 | | | | | | | | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | | | | | | | | | BETA: splitting (35) gives: % 152.18/22.68 | | | | | | | | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | | | | | | | | | Case 1: % 152.18/22.68 | | | | | | | | | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | | | | | | | | | | (261) all_58_9 = e1 % 152.18/22.68 | | | | | | | | | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (47), (261) imply: % 152.18/22.68 | | | | | | | | | | | | | | | | | | | (262) all_52_12 = e1 % 152.18/22.68 | | | | | | | | | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (76), (262) imply: % 152.18/22.68 | | | | | | | | | | | | | | | | | | | (263) all_56_7 = e1 % 152.18/22.68 | | | | | | | | | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | | | | | | | | | | REDUCE: (167), (262) imply: % 152.18/22.68 | | | | | | | | | | | | | | | | | | | (264) ~ (all_10_2 = e1) % 152.18/22.68 | | | | | | | | | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | | | | | | | | | | REDUCE: (191), (262) imply: % 152.18/22.68 | | | | | | | | | | | | | | | | | | | (265) ~ (e1 = e0) % 152.18/22.68 | | | | | | | | | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | | | | | | | | | | BETA: splitting (90) gives: % 152.18/22.68 | | | | | | | | | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | | | | | | | | | | Case 1: % 152.18/22.68 | | | | | | | | | | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | | | | | | | | | | | (266) ~ (all_56_1 = e0) % 152.18/22.68 | | | | | | | | | | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | | | | | | | | | | | REDUCE: (41), (266) imply: % 152.18/22.68 | | | | | | | | | | | | | | | | | | | | (267) ~ (all_10_2 = e0) % 152.18/22.68 | | | | | | | | | | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | | | | | | | | | | | BETA: splitting (164) gives: % 152.18/22.68 | | | | | | | | | | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | | | | | | | | | | | Case 1: % 152.18/22.68 | | | | | | | | | | | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | | | | | | | | | | | | (268) all_54_5 = e3 % 152.18/22.68 | | | | | | | | | | | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (29), (260), (268) are inconsistent by sub-proof % 152.18/22.68 | | | | | | | | | | | | | | | | | | | | | #737. % 152.18/22.68 | | | | | | | | | | | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | | | | | | | | | | | Case 2: % 152.18/22.68 | | | | | | | | | | | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | | | | | | | | | | | | (269) ~ (all_54_5 = e3) % 152.18/22.68 | | | | | | | | | | | | | | | | | | | | | (270) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 152.18/22.68 | | | | | | | | | | | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (154) gives: % 152.18/22.68 | | | | | | | | | | | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.18/22.68 | | | | | | | | | | | | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | | | | | | | | | | | | | (271) all_58_0 = e0 % 152.18/22.68 | | | | | | | | | | | | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (136), (271) imply: % 152.18/22.68 | | | | | | | | | | | | | | | | | | | | | | (272) all_10_2 = e0 % 152.18/22.68 | | | | | | | | | | | | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (267), (272) imply: % 152.18/22.68 | | | | | | | | | | | | | | | | | | | | | | (273) $false % 152.18/22.68 | | | | | | | | | | | | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (273) is inconsistent. % 152.18/22.68 | | | | | | | | | | | | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.18/22.68 | | | | | | | | | | | | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | | | | | | | | | | | | | (274) all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0 % 152.18/22.68 | | | | | | | | | | | | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (274) gives: % 152.18/22.68 | | | | | | | | | | | | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.18/22.68 | | | | | | | | | | | | | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | | | | | | | | | | | | | | (275) all_58_2 = e0 % 152.18/22.68 | | | | | | | | | | | | | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (253), (275) imply: % 152.18/22.68 | | | | | | | | | | | | | | | | | | | | | | | (276) e1 = e0 % 152.18/22.68 | | | | | | | | | | | | | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (265), (276) imply: % 152.18/22.68 | | | | | | | | | | | | | | | | | | | | | | | (277) $false % 152.18/22.68 | | | | | | | | | | | | | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (277) is inconsistent. % 152.18/22.68 | | | | | | | | | | | | | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.18/22.68 | | | | | | | | | | | | | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | | | | | | | | | | | | | | (278) all_58_6 = e0 | all_58_12 = e0 % 152.18/22.68 | | | | | | | | | | | | | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (278) gives: % 152.18/22.68 | | | | | | | | | | | | | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.18/22.68 | | | | | | | | | | | | | | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | | | | | | | | | | | | | | | (279) all_58_6 = e0 % 152.18/22.68 | | | | | | | | | | | | | | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (8), (279) imply: % 152.18/22.68 | | | | | | | | | | | | | | | | | | | | | | | | (280) all_52_2 = e0 % 152.18/22.68 | | | | | | | | | | | | | | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (280) implies: % 152.18/22.68 | | | | | | | | | | | | | | | | | | | | | | | | (281) all_52_2 = e0 % 152.18/22.68 | | | | | | | | | | | | | | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (93), (281) imply: % 152.18/22.68 | | | | | | | | | | | | | | | | | | | | | | | | (282) ~ (all_52_3 = e0) % 152.18/22.68 | | | | | | | | | | | | | | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (74), (281) imply: % 152.18/22.68 | | | | | | | | | | | | | | | | | | | | | | | | (283) ~ (all_52_6 = e0) % 152.18/22.68 | | | | | | | | | | | | | | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (283) implies: % 152.18/22.68 | | | | | | | | | | | | | | | | | | | | | | | | (284) ~ (all_52_6 = e0) % 152.18/22.68 | | | | | | | | | | | | | | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (106), (281) imply: % 152.18/22.68 | | | | | | | | | | | | | | | | | | | | | | | | (285) ~ (all_52_14 = e0) % 152.18/22.68 | | | | | | | | | | | | | | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (140) gives: % 152.18/22.68 | | | | | | | | | | | | | | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.18/22.68 | | | | | | | | | | | | | | | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | | | | | | | | | | | | | | | | (286) all_58_1 = e0 % 152.18/22.68 | | | | | | | | | | | | | | | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (139), (286) imply: % 152.18/22.68 | | | | | | | | | | | | | | | | | | | | | | | | | (287) all_10_0 = e0 % 152.18/22.68 | | | | | | | | | | | | | | | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (48), (287) imply: % 152.18/22.68 | | | | | | | | | | | | | | | | | | | | | | | | | (288) all_56_3 = e0 % 152.18/22.68 | | | | | | | | | | | | | | | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (89) gives: % 152.18/22.68 | | | | | | | | | | | | | | | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.18/22.68 | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | | | | | | | | | | | | | | | | | (289) ~ (all_56_1 = e2) % 152.18/22.68 | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (41), (289) imply: % 152.18/22.68 | | | | | | | | | | | | | | | | | | | | | | | | | | (290) ~ (all_10_2 = e2) % 152.18/22.68 | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (3), (4), (5), (6), (8), (11), (12), (13), % 152.18/22.68 | | | | | | | | | | | | | | | | | | | | | | | | | | (14), (15), (16), (17), (18), (19), (20), (23), % 152.18/22.68 | | | | | | | | | | | | | | | | | | | | | | | | | | (24), (25), (27), (28), (29), (30), (31), (32), % 152.18/22.68 | | | | | | | | | | | | | | | | | | | | | | | | | | (33), (34), (35), (37), (38), (39), (40), (41), % 152.18/22.68 | | | | | | | | | | | | | | | | | | | | | | | | | | (43), (44), (45), (46), (47), (49), (51), (52), % 152.18/22.68 | | | | | | | | | | | | | | | | | | | | | | | | | | (53), (54), (56), (57), (59), (60), (61), (62), % 152.18/22.68 | | | | | | | | | | | | | | | | | | | | | | | | | | (65), (66), (67), (69), (70), (71), (72), (74), % 152.18/22.68 | | | | | | | | | | | | | | | | | | | | | | | | | | (76), (77), (82), (86), (88), (90), (93), (94), % 152.18/22.68 | | | | | | | | | | | | | | | | | | | | | | | | | | (96), (97), (100), (101), (102), (103), (106), % 152.18/22.68 | | | | | | | | | | | | | | | | | | | | | | | | | | (107), (108), (109), (112), (113), (114), (115), % 152.18/22.68 | | | | | | | | | | | | | | | | | | | | | | | | | | (116), (117), (118), (121), (122), (124), (125), % 152.18/22.68 | | | | | | | | | | | | | | | | | | | | | | | | | | (128), (129), (132), (133), (134), (136), (137), % 152.18/22.68 | | | | | | | | | | | | | | | | | | | | | | | | | | (138), (141), (142), (144), (145), (147), (148), % 152.18/22.68 | | | | | | | | | | | | | | | | | | | | | | | | | | (149), (151), (152), (153), (156), (157), (158), % 152.18/22.68 | | | | | | | | | | | | | | | | | | | | | | | | | | (160), (161), (163), (164), (165), (166), (167), % 152.18/22.68 | | | | | | | | | | | | | | | | | | | | | | | | | | (171), (172), (173), (174), (176), (187), (188), % 152.18/22.68 | | | | | | | | | | | | | | | | | | | | | | | | | | (189), (190), (191), (192), (193), (198), (206), % 152.18/22.68 | | | | | | | | | | | | | | | | | | | | | | | | | | (208), (239), (260), (270), (290) are inconsistent % 152.18/22.68 | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #641. % 152.18/22.68 | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.18/22.68 | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | | | | | | | | | | | | | | | | | (291) all_56_3 = e3 % 152.18/22.68 | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (288), (291) imply: % 152.18/22.68 | | | | | | | | | | | | | | | | | | | | | | | | | | (292) e3 = e0 % 152.18/22.68 | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (204), (292) imply: % 152.18/22.68 | | | | | | | | | | | | | | | | | | | | | | | | | | (293) $false % 152.18/22.68 | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (293) is inconsistent. % 152.18/22.68 | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.18/22.68 | | | | | | | | | | | | | | | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.18/22.68 | | | | | | | | | | | | | | | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | | | | | | | | | | | | | | | | (294) all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0 % 152.18/22.68 | | | | | | | | | | | | | | | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (54), (96), (131), (189), (206), (284), (294) are % 152.18/22.68 | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #603. % 152.18/22.68 | | | | | | | | | | | | | | | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.18/22.68 | | | | | | | | | | | | | | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.18/22.68 | | | | | | | | | | | | | | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | | | | | | | | | | | | | | | (295) all_58_12 = e0 % 152.18/22.68 | | | | | | | | | | | | | | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (172), (295) imply: % 152.18/22.68 | | | | | | | | | | | | | | | | | | | | | | | | (296) all_52_3 = e0 % 152.18/22.68 | | | | | | | | | | | | | | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (188), (296) imply: % 152.18/22.68 | | | | | | | | | | | | | | | | | | | | | | | | (297) $false % 152.18/22.68 | | | | | | | | | | | | | | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (297) is inconsistent. % 152.18/22.68 | | | | | | | | | | | | | | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.18/22.68 | | | | | | | | | | | | | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | | | | | | | | | | | | | End of split % 152.18/22.68 | | | | | | | | | | | | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | | | | | | | | | | | | End of split % 152.18/22.68 | | | | | | | | | | | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | | | | | | | | | | | End of split % 152.18/22.68 | | | | | | | | | | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | | | | | | | | | | Case 2: % 152.18/22.68 | | | | | | | | | | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | | | | | | | | | | | (298) all_56_7 = e3 % 152.18/22.68 | | | | | | | | | | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (235), (263), (298) are inconsistent by sub-proof % 152.18/22.68 | | | | | | | | | | | | | | | | | | | | #497. % 152.18/22.68 | | | | | | | | | | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | | | | | | | | | | End of split % 152.18/22.68 | | | | | | | | | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | | | | | | | | | Case 2: % 152.18/22.68 | | | | | | | | | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | | | | | | | | | | (299) all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1 % 152.18/22.68 | | | | | | | | | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (82), (103), (125), (132), (225), (257), (299) are % 152.18/22.68 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #587. % 152.18/22.68 | | | | | | | | | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | | | | | | | | | End of split % 152.18/22.68 | | | | | | | | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | | | | | | | | Case 2: % 152.18/22.68 | | | | | | | | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | | | | | | | | | (300) all_56_9 = e2 % 152.18/22.68 | | | | | | | | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | | | | | | | | | REF_CLOSE: (237), (255), (300) are inconsistent by sub-proof % 152.18/22.68 | | | | | | | | | | | | | | | | | | #496. % 152.18/22.68 | | | | | | | | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | | | | | | | | End of split % 152.18/22.68 | | | | | | | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | | | | | | | Case 2: % 152.18/22.68 | | | | | | | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | | | | | | | | (301) ~ (all_58_2 = e1) % 152.18/22.68 | | | | | | | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | | | | | | | | REDUCE: (128), (301) imply: % 152.18/22.68 | | | | | | | | | | | | | | | | | (302) ~ (all_52_1 = e1) % 152.18/22.68 | | | | | | | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | | | | | | | | BETA: splitting (64) gives: % 152.18/22.68 | | | | | | | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | | | | | | | | Case 1: % 152.18/22.68 | | | | | | | | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | | | | | | | | | (303) all_58_2 = e1 % 152.18/22.68 | | | | | | | | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (128), (303) imply: % 152.18/22.68 | | | | | | | | | | | | | | | | | | (304) all_52_1 = e1 % 152.18/22.68 | | | | | | | | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | | | | | | | | | REDUCE: (302), (304) imply: % 152.18/22.68 | | | | | | | | | | | | | | | | | | (305) $false % 152.18/22.68 | | | | | | | | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | | | | | | | | | CLOSE: (305) is inconsistent. % 152.18/22.68 | | | | | | | | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | | | | | | | | Case 2: % 152.18/22.68 | | | | | | | | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | | | | | | | | | (306) all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1 % 152.18/22.68 | | | | | | | | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | | | | | | | | | BETA: splitting (252) gives: % 152.18/22.68 | | | | | | | | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | | | | | | | | | Case 1: % 152.18/22.68 | | | | | | | | | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | | | | | | | | | | (307) all_58_4 = e1 % 152.18/22.68 | | | | | | | | | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (28), (307) imply: % 152.18/22.68 | | | | | | | | | | | | | | | | | | | (308) all_52_8 = e1 % 152.18/22.68 | | | | | | | | | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | | | | | | | | | | REDUCE: (223), (308) imply: % 152.18/22.68 | | | | | | | | | | | | | | | | | | | (309) $false % 152.18/22.68 | | | | | | | | | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | | | | | | | | | | CLOSE: (309) is inconsistent. % 152.18/22.68 | | | | | | | | | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | | | | | | | | | Case 2: % 152.18/22.68 | | | | | | | | | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | | | | | | | | | | (310) all_58_9 = e1 % 152.18/22.68 | | | | | | | | | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (47), (310) imply: % 152.18/22.68 | | | | | | | | | | | | | | | | | | | (311) all_52_12 = e1 % 152.18/22.68 | | | | | | | | | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | | | | | | | | | | REDUCE: (24), (311) imply: % 152.18/22.68 | | | | | | | | | | | | | | | | | | | (312) ~ (all_52_13 = e1) % 152.18/22.68 | | | | | | | | | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | | | | | | | | | | SIMP: (312) implies: % 152.18/22.68 | | | | | | | | | | | | | | | | | | | (313) ~ (all_52_13 = e1) % 152.18/22.68 | | | | | | | | | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (44), (96), (132), (208), (224), (306), (313) are % 152.18/22.68 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #495. % 152.18/22.68 | | | | | | | | | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | | | | | | | | | End of split % 152.18/22.68 | | | | | | | | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | | | | | | | | End of split % 152.18/22.68 | | | | | | | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | | | | | | | End of split % 152.18/22.68 | | | | | | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | | | | | | End of split % 152.18/22.68 | | | | | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | | | | | End of split % 152.18/22.68 | | | | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | | | | End of split % 152.18/22.68 | | | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | | | Case 2: % 152.18/22.68 | | | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | | | | (314) all_56_1 = e1 % 152.18/22.68 | | | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | | | | COMBINE_EQS: (41), (314) imply: % 152.18/22.68 | | | | | | | | | | | | | (315) all_10_2 = e1 % 152.18/22.68 | | | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | | | | REDUCE: (105), (315) imply: % 152.18/22.68 | | | | | | | | | | | | | (316) op(e1, e1) = e2 % 152.18/22.68 | | | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | | | | REF_CLOSE: (67), (227), (228), (237), (316) are inconsistent % 152.18/22.68 | | | | | | | | | | | | | by sub-proof #494. % 152.18/22.68 | | | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | | | End of split % 152.18/22.68 | | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | | Case 2: % 152.18/22.68 | | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | | | (317) all_54_10 = e0 % 152.18/22.68 | | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | | | COMBINE_EQS: (12), (317) imply: % 152.18/22.68 | | | | | | | | | | | | (318) all_6_2 = e0 % 152.18/22.68 | | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | | | REDUCE: (210), (318) imply: % 152.18/22.68 | | | | | | | | | | | | (319) $false % 152.18/22.68 | | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | | | CLOSE: (319) is inconsistent. % 152.18/22.68 | | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | | End of split % 152.18/22.68 | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | End of split % 152.18/22.68 | | | | | | | | | | % 152.18/22.68 | | | | | | | | | End of split % 152.18/22.68 | | | | | | | | | % 152.18/22.68 | | | | | | | | Case 2: % 152.18/22.68 | | | | | | | | | % 152.18/22.68 | | | | | | | | | (320) all_56_21 = e3 % 152.18/22.68 | | | | | | | | | (321) all_56_17 = e1 % 152.18/22.68 | | | | | | | | | % 152.18/22.68 | | | | | | | | | COMBINE_EQS: (46), (321) imply: % 152.18/22.68 | | | | | | | | | (322) all_52_2 = e1 % 152.18/22.68 | | | | | | | | | % 152.18/22.68 | | | | | | | | | COMBINE_EQS: (38), (320) imply: % 152.18/22.68 | | | | | | | | | (323) all_6_2 = e3 % 152.18/22.68 | | | | | | | | | % 152.18/22.68 | | | | | | | | | SIMP: (323) implies: % 152.18/22.68 | | | | | | | | | (324) all_6_2 = e3 % 152.18/22.68 | | | | | | | | | % 152.18/22.68 | | | | | | | | | REF_CLOSE: (14), (18), (30), (32), (36), (41), (57), (67), % 152.18/22.68 | | | | | | | | | (76), (87), (90), (108), (110), (124), (155), % 152.18/22.68 | | | | | | | | | (157), (159), (322), (324) are inconsistent by % 152.18/22.68 | | | | | | | | | sub-proof #488. % 152.18/22.68 | | | | | | | | | % 152.18/22.68 | | | | | | | | End of split % 152.18/22.68 | | | | | | | | % 152.18/22.68 | | | | | | | Case 2: % 152.18/22.68 | | | | | | | | % 152.18/22.68 | | | | | | | | (325) all_56_21 = e0 % 152.18/22.68 | | | | | | | | % 152.18/22.68 | | | | | | | | COMBINE_EQS: (38), (325) imply: % 152.18/22.68 | | | | | | | | (326) all_6_2 = e0 % 152.18/22.68 | | | | | | | | % 152.18/22.68 | | | | | | | | SIMP: (326) implies: % 152.18/22.68 | | | | | | | | (327) all_6_2 = e0 % 152.18/22.68 | | | | | | | | % 152.18/22.68 | | | | | | | | REDUCE: (147), (327) imply: % 152.18/22.68 | | | | | | | | (328) ~ (all_52_2 = e0) % 152.18/22.68 | | | | | | | | % 152.18/22.68 | | | | | | | | REDUCE: (151), (327) imply: % 152.18/22.68 | | | | | | | | (329) ~ (all_52_6 = e0) % 152.18/22.68 | | | | | | | | % 152.18/22.68 | | | | | | | | REDUCE: (127), (327) imply: % 152.18/22.68 | | | | | | | | (330) ~ (e2 = e0) % 152.18/22.68 | | | | | | | | % 152.18/22.68 | | | | | | | | SIMP: (330) implies: % 152.18/22.68 | | | | | | | | (331) ~ (e2 = e0) % 152.18/22.68 | | | | | | | | % 152.18/22.68 | | | | | | | | BETA: splitting (71) gives: % 152.18/22.68 | | | | | | | | % 152.18/22.68 | | | | | | | | Case 1: % 152.18/22.68 | | | | | | | | | % 152.18/22.68 | | | | | | | | | (332) all_58_2 = e0 % 152.18/22.68 | | | | | | | | | % 152.18/22.68 | | | | | | | | | COMBINE_EQS: (128), (332) imply: % 152.18/22.68 | | | | | | | | | (333) all_52_1 = e0 % 152.18/22.68 | | | | | | | | | % 152.18/22.68 | | | | | | | | | COMBINE_EQS: (169), (333) imply: % 152.18/22.68 | | | | | | | | | (334) all_56_9 = e0 % 152.18/22.68 | | | | | | | | | % 152.18/22.68 | | | | | | | | | REDUCE: (99), (333) imply: % 152.18/22.68 | | | | | | | | | (335) ~ (all_52_3 = e0) % 152.18/22.68 | | | | | | | | | % 152.18/22.68 | | | | | | | | | REDUCE: (80), (333) imply: % 152.18/22.68 | | | | | | | | | (336) ~ (all_52_13 = e0) % 152.18/22.68 | | | | | | | | | % 152.18/22.68 | | | | | | | | | REDUCE: (65), (333) imply: % 152.18/22.68 | | | | | | | | | (337) ~ (all_8_2 = e0) % 152.18/22.68 | | | | | | | | | % 152.18/22.68 | | | | | | | | | BETA: splitting (73) gives: % 152.18/22.68 | | | | | | | | | % 152.18/22.68 | | | | | | | | | Case 1: % 152.18/22.68 | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | (338) ~ (all_56_11 = e3) % 152.18/22.68 | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | REDUCE: (1), (338) imply: % 152.18/22.68 | | | | | | | | | | (339) ~ (all_8_2 = e3) % 152.18/22.68 | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | BETA: splitting (140) gives: % 152.18/22.68 | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | Case 1: % 152.18/22.68 | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | | (340) all_58_1 = e0 % 152.18/22.68 | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | | COMBINE_EQS: (139), (340) imply: % 152.18/22.68 | | | | | | | | | | | (341) all_10_0 = e0 % 152.18/22.68 | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | | COMBINE_EQS: (63), (341) imply: % 152.18/22.68 | | | | | | | | | | | (342) all_38_0 = e0 % 152.18/22.68 | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | | COMBINE_EQS: (48), (341) imply: % 152.18/22.68 | | | | | | | | | | | (343) all_56_3 = e0 % 152.18/22.68 | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | | BETA: splitting (89) gives: % 152.18/22.68 | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | | Case 1: % 152.18/22.68 | | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | | | (344) ~ (all_56_1 = e2) % 152.18/22.68 | | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | | | REDUCE: (41), (344) imply: % 152.18/22.68 | | | | | | | | | | | | (345) ~ (all_10_2 = e2) % 152.18/22.68 | | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | | | BETA: splitting (119) gives: % 152.18/22.68 | | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | | | Case 1: % 152.18/22.68 | | | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | | | | (346) ~ (all_38_2 = e1) % 152.18/22.68 | | | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | | | | REDUCE: (120), (346) imply: % 152.18/22.68 | | | | | | | | | | | | | (347) ~ (all_10_2 = e1) % 152.18/22.68 | | | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | | | | REF_CLOSE: (1), (3), (4), (5), (6), (8), (11), (12), (13), % 152.18/22.68 | | | | | | | | | | | | | (14), (15), (16), (17), (18), (19), (20), (23), % 152.18/22.68 | | | | | | | | | | | | | (24), (25), (27), (28), (29), (30), (31), (32), % 152.18/22.68 | | | | | | | | | | | | | (33), (34), (35), (37), (38), (39), (40), (41), % 152.18/22.68 | | | | | | | | | | | | | (43), (44), (45), (46), (47), (49), (51), (52), % 152.18/22.68 | | | | | | | | | | | | | (53), (54), (56), (57), (59), (60), (61), (62), % 152.18/22.68 | | | | | | | | | | | | | (65), (66), (67), (69), (70), (71), (72), (74), % 152.18/22.68 | | | | | | | | | | | | | (76), (77), (82), (86), (88), (90), (93), (94), % 152.18/22.68 | | | | | | | | | | | | | (96), (97), (100), (101), (102), (103), (106), % 152.18/22.68 | | | | | | | | | | | | | (107), (108), (109), (112), (113), (114), (115), % 152.18/22.68 | | | | | | | | | | | | | (116), (117), (118), (121), (122), (124), (125), % 152.18/22.68 | | | | | | | | | | | | | (128), (129), (132), (133), (134), (136), (137), % 152.18/22.68 | | | | | | | | | | | | | (138), (141), (142), (144), (145), (147), (148), % 152.18/22.68 | | | | | | | | | | | | | (149), (151), (152), (153), (156), (157), (158), % 152.18/22.68 | | | | | | | | | | | | | (160), (161), (163), (164), (165), (166), (167), % 152.18/22.68 | | | | | | | | | | | | | (171), (172), (173), (174), (176), (187), (188), % 152.18/22.68 | | | | | | | | | | | | | (189), (190), (191), (192), (193), (198), (206), % 152.18/22.68 | | | | | | | | | | | | | (208), (339), (345), (347) are inconsistent by % 152.18/22.68 | | | | | | | | | | | | | sub-proof #640. % 152.18/22.68 | | | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | | | Case 2: % 152.18/22.68 | | | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | | | | (348) all_38_2 = e1 % 152.18/22.68 | | | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | | | | REF_CLOSE: (119), (342), (348) are inconsistent by sub-proof % 152.18/22.68 | | | | | | | | | | | | | #487. % 152.18/22.68 | | | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | | | End of split % 152.18/22.68 | | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | | Case 2: % 152.18/22.68 | | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | | | (349) all_56_3 = e3 % 152.18/22.68 | | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | | | COMBINE_EQS: (343), (349) imply: % 152.18/22.68 | | | | | | | | | | | | (350) e3 = e0 % 152.18/22.68 | | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | | | REDUCE: (204), (350) imply: % 152.18/22.68 | | | | | | | | | | | | (351) $false % 152.18/22.68 | | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | | | CLOSE: (351) is inconsistent. % 152.18/22.68 | | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | | End of split % 152.18/22.68 | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | Case 2: % 152.18/22.68 | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | | (352) all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0 % 152.18/22.68 | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | | REF_CLOSE: (54), (96), (131), (189), (206), (329), (352) are % 152.18/22.68 | | | | | | | | | | | inconsistent by sub-proof #603. % 152.18/22.68 | | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | End of split % 152.18/22.68 | | | | | | | | | | % 152.18/22.68 | | | | | | | | | Case 2: % 152.18/22.68 | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | (353) all_56_9 = e2 % 152.18/22.68 | | | | | | | | | | % 152.18/22.68 | | | | | | | | | | REF_CLOSE: (331), (334), (353) are inconsistent by sub-proof % 152.18/22.68 | | | | | | | | | | #486. % 152.18/22.68 | | | | | | | | | | % 152.18/22.68 | | | | | | | | | End of split % 152.18/22.68 | | | | | | | | | % 152.18/22.68 | | | | | | | | Case 2: % 152.18/22.68 | | | | | | | | | % 152.18/22.68 | | | | | | | | | (354) ~ (all_58_2 = e0) % 152.18/22.68 | | | | | | | | | % 152.18/22.68 | | | | | | | | | REF_CLOSE: (8), (53), (54), (96), (128), (131), (136), (140), % 152.18/22.68 | | | | | | | | | (154), (158), (172), (188), (189), (206), (328), % 152.18/22.68 | | | | | | | | | (329), (354) are inconsistent by sub-proof #602. % 152.18/22.68 | | | | | | | | | % 152.18/22.68 | | | | | | | | End of split % 152.18/22.68 | | | | | | | | % 152.18/22.68 | | | | | | | End of split % 152.18/22.68 | | | | | | | % 152.18/22.68 | | | | | | Case 2: % 152.18/22.68 | | | | | | | % 152.18/22.68 | | | | | | | (355) all_56_13 = e2 % 152.18/22.68 | | | | | | | (356) all_56_11 = e1 % 152.18/22.68 | | | | | | | % 152.18/22.68 | | | | | | | COMBINE_EQS: (1), (356) imply: % 152.18/22.68 | | | | | | | (357) all_8_2 = e1 % 152.18/22.68 | | | | | | | % 152.18/22.68 | | | | | | | COMBINE_EQS: (78), (355) imply: % 152.18/22.68 | | | | | | | (358) all_52_9 = e2 % 152.18/22.68 | | | | | | | % 152.18/22.68 | | | | | | | COMBINE_EQS: (44), (358) imply: % 152.18/22.68 | | | | | | | (359) all_58_5 = e2 % 152.18/22.68 | | | | | | | % 152.18/22.68 | | | | | | | REDUCE: (92), (358) imply: % 152.18/22.68 | | | | | | | (360) ~ (all_52_13 = e2) % 152.18/22.68 | | | | | | | % 152.18/22.68 | | | | | | | SIMP: (360) implies: % 152.18/22.68 | | | | | | | (361) ~ (all_52_13 = e2) % 152.18/22.68 | | | | | | | % 152.18/22.68 | | | | | | | REDUCE: (130), (358) imply: % 152.18/22.68 | | | | | | | (362) ~ (all_6_2 = e2) % 152.18/22.68 | | | | | | | % 152.18/22.68 | | | | | | | REDUCE: (15), (357) imply: % 152.18/22.68 | | | | | | | (363) ~ (all_52_13 = e1) % 152.18/22.68 | | | | | | | % 152.18/22.68 | | | | | | | REDUCE: (161), (357) imply: % 152.18/22.68 | | | | | | | (364) op(e1, e1) = all_8_1 % 152.18/22.68 | | | | | | | % 152.18/22.68 | | | | | | | BETA: splitting (43) gives: % 152.18/22.68 | | | | | | | % 152.18/22.68 | | | | | | | Case 1: % 152.18/22.68 | | | | | | | | % 152.18/22.68 | | | | | | | | (365) all_54_7 = e3 % 152.18/22.68 | | | | | | | | % 152.18/22.68 | | | | | | | | COMBINE_EQS: (107), (365) imply: % 152.18/22.68 | | | | | | | | (366) all_52_13 = e3 % 152.18/22.68 | | | | | | | | % 152.18/22.68 | | | | | | | | SIMP: (366) implies: % 152.18/22.68 | | | | | | | | (367) all_52_13 = e3 % 152.18/22.68 | | | | | | | | % 152.18/22.68 | | | | | | | | REDUCE: (146), (367) imply: % 152.18/22.68 | | | | | | | | (368) op(e2, e0) = e3 % 152.18/22.68 | | | | | | | | % 152.18/22.68 | | | | | | | | REF_CLOSE: (3), (7), (9), (12), (26), (28), (39), (54), (55), % 152.18/22.68 | | | | | | | | (67), (68), (83), (96), (104), (121), (126), (127), % 152.18/22.68 | | | | | | | | (131), (139), (140), (151), (159), (165), (189), % 152.18/22.68 | | | | | | | | (206), (359), (364), (368) are inconsistent by % 152.18/22.68 | | | | | | | | sub-proof #485. % 152.18/22.68 | | | | | | | | % 152.18/22.68 | | | | | | | Case 2: % 152.18/22.68 | | | | | | | | % 152.18/22.68 | | | | | | | | (369) all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0 % 152.18/22.68 | | | | | | | | % 152.18/22.68 | | | | | | | | REF_CLOSE: (107), (192), (361), (363), (369) are inconsistent by % 152.18/22.68 | | | | | | | | sub-proof #649. % 152.18/22.68 | | | | | | | | % 152.18/22.68 | | | | | | | End of split % 152.18/22.68 | | | | | | | % 152.18/22.68 | | | | | | End of split % 152.18/22.68 | | | | | | % 152.18/22.68 | | | | | Case 2: % 152.18/22.68 | | | | | | % 152.18/22.68 | | | | | | (370) all_56_15 = e2 % 152.18/22.68 | | | | | | (371) all_56_11 = e0 % 152.18/22.68 | | | | | | % 152.18/22.68 | | | | | | REF_CLOSE: (1), (8), (10), (18), (32), (36), (41), (50), (66), (67), % 152.18/22.68 | | | | | | (68), (76), (79), (83), (87), (90), (91), (103), (105), % 152.18/22.68 | | | | | | (110), (116), (124), (127), (131), (144), (155), (157), % 152.18/22.68 | | | | | | (159), (170), (370), (371) are inconsistent by sub-proof % 152.18/22.68 | | | | | | #480. % 152.18/22.68 | | | | | | % 152.18/22.68 | | | | | End of split % 152.18/22.68 | | | | | % 152.18/22.68 | | | | End of split % 152.18/22.68 | | | | % 152.18/22.68 | | | End of split % 152.18/22.68 | | | % 152.18/22.68 | | End of split % 152.18/22.68 | | % 152.18/22.68 | Case 2: % 152.18/22.68 | | % 152.18/22.68 | | (372) all_56_31 = e2 % 152.18/22.68 | | (373) all_56_27 = e0 % 152.18/22.68 | | % 152.18/22.68 | | COMBINE_EQS: (42), (373) imply: % 152.18/22.68 | | (374) all_52_7 = e0 % 152.18/22.68 | | % 152.18/22.68 | | SIMP: (374) implies: % 152.18/22.68 | | (375) all_52_7 = e0 % 152.18/22.68 | | % 152.18/22.68 | | COMBINE_EQS: (102), (372) imply: % 152.18/22.68 | | (376) all_4_2 = e2 % 152.18/22.68 | | % 152.18/22.68 | | REDUCE: (162), (375) imply: % 152.18/22.68 | | (377) ~ (all_10_0 = e0) % 152.18/22.68 | | % 152.18/22.68 | | SIMP: (377) implies: % 152.18/22.68 | | (378) ~ (all_10_0 = e0) % 152.18/22.68 | | % 152.18/22.68 | | REDUCE: (40), (375) imply: % 152.18/22.68 | | (379) ~ (all_8_2 = e0) % 152.18/22.68 | | % 152.18/22.68 | | SIMP: (379) implies: % 152.18/22.68 | | (380) ~ (all_8_2 = e0) % 152.18/22.68 | | % 152.18/22.68 | | REDUCE: (98), (376) imply: % 152.18/22.68 | | (381) ~ (all_52_11 = e2) % 152.18/22.68 | | % 152.18/22.68 | | BETA: splitting (124) gives: % 152.18/22.68 | | % 152.18/22.68 | | Case 1: % 152.18/22.68 | | | % 152.18/22.68 | | | (382) all_54_1 = e3 % 152.18/22.68 | | | % 152.18/22.68 | | | COMBINE_EQS: (36), (382) imply: % 152.18/22.68 | | | (383) all_10_0 = e3 % 152.18/22.68 | | | % 152.18/22.68 | | | SIMP: (383) implies: % 152.18/22.68 | | | (384) all_10_0 = e3 % 152.18/22.68 | | | % 152.18/22.68 | | | REDUCE: (68), (384) imply: % 152.18/22.68 | | | (385) ~ (all_52_8 = e3) % 152.18/22.68 | | | % 152.18/22.68 | | | REDUCE: (155), (384) imply: % 152.18/22.68 | | | (386) ~ (all_10_2 = e3) % 152.18/22.68 | | | % 152.18/22.68 | | | SIMP: (386) implies: % 152.18/22.68 | | | (387) ~ (all_10_2 = e3) % 152.18/22.68 | | | % 152.18/22.68 | | | REDUCE: (10), (384) imply: % 152.18/22.68 | | | (388) ~ (all_8_2 = e3) % 152.18/22.68 | | | % 152.18/22.68 | | | SIMP: (388) implies: % 152.18/22.68 | | | (389) ~ (all_8_2 = e3) % 152.18/22.68 | | | % 152.18/22.68 | | | BETA: splitting (50) gives: % 152.18/22.68 | | | % 152.18/22.68 | | | Case 1: % 152.18/22.68 | | | | % 152.18/22.68 | | | | (390) ~ (all_56_1 = e1) % 152.18/22.68 | | | | % 152.18/22.68 | | | | REDUCE: (41), (390) imply: % 152.18/22.68 | | | | (391) ~ (all_10_2 = e1) % 152.18/22.68 | | | | % 152.18/22.68 | | | | BETA: splitting (90) gives: % 152.18/22.68 | | | | % 152.18/22.68 | | | | Case 1: % 152.18/22.68 | | | | | % 152.18/22.68 | | | | | (392) ~ (all_56_1 = e0) % 152.18/22.68 | | | | | % 152.18/22.68 | | | | | REDUCE: (41), (392) imply: % 152.18/22.68 | | | | | (393) ~ (all_10_2 = e0) % 152.18/22.68 | | | | | % 152.18/22.68 | | | | | BETA: splitting (32) gives: % 152.18/22.68 | | | | | % 152.18/22.68 | | | | | Case 1: % 152.18/22.68 | | | | | | % 152.18/22.68 | | | | | | (394) all_54_0 = e3 % 152.18/22.68 | | | | | | % 152.18/22.68 | | | | | | REF_CLOSE: (18), (387), (394) are inconsistent by sub-proof #709. % 152.18/22.68 | | | | | | % 152.18/22.68 | | | | | Case 2: % 152.18/22.68 | | | | | | % 152.18/22.68 | | | | | | (395) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 152.18/22.68 | | | | | | % 152.18/22.68 | | | | | | BETA: splitting (395) gives: % 152.18/22.68 | | | | | | % 152.18/22.68 | | | | | | Case 1: % 152.18/22.68 | | | | | | | % 152.18/22.68 | | | | | | | (396) all_54_0 = e2 % 152.18/22.68 | | | | | | | % 152.18/22.68 | | | | | | | COMBINE_EQS: (18), (396) imply: % 152.18/22.68 | | | | | | | (397) all_10_2 = e2 % 152.18/22.68 | | | | | | | % 152.18/22.68 | | | | | | | SIMP: (397) implies: % 152.18/22.68 | | | | | | | (398) all_10_2 = e2 % 152.18/22.68 | | | | | | | % 152.18/22.68 | | | | | | | REDUCE: (86), (398) imply: % 152.18/22.68 | | | | | | | (399) ~ (all_52_8 = e2) % 152.18/22.68 | | | | | | | % 152.18/22.68 | | | | | | | REDUCE: (105), (398) imply: % 152.18/22.68 | | | | | | | (400) op(e2, e2) = e2 % 152.18/22.68 | | | | | | | % 152.18/22.68 | | | | | | | BETA: splitting (21) gives: % 152.18/22.68 | | | | | | | % 152.18/22.68 | | | | | | | Case 1: % 152.18/22.68 | | | | | | | | % 152.18/22.68 | | | | | | | | (401) all_58_4 = e2 % 152.18/22.68 | | | | | | | | % 152.18/22.68 | | | | | | | | COMBINE_EQS: (28), (401) imply: % 152.18/22.68 | | | | | | | | (402) all_52_8 = e2 % 152.18/22.68 | | | | | | | | % 152.18/22.68 | | | | | | | | REDUCE: (399), (402) imply: % 152.18/22.68 | | | | | | | | (403) $false % 152.18/22.68 | | | | | | | | % 152.18/22.68 | | | | | | | | CLOSE: (403) is inconsistent. % 152.18/22.68 | | | | | | | | % 152.18/22.68 | | | | | | | Case 2: % 152.18/22.68 | | | | | | | | % 152.18/22.68 | | | | | | | | (404) all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2 % 152.18/22.68 | | | | | | | | % 152.18/22.68 | | | | | | | | REF_CLOSE: (22), (29), (44), (67), (83), (127), (144), (164), % 152.18/22.68 | | | | | | | | (165), (380), (381), (389), (400), (404) are % 152.18/22.68 | | | | | | | | inconsistent by sub-proof #477. % 152.18/22.68 | | | | | | | | % 152.18/22.68 | | | | | | | End of split % 152.18/22.68 | | | | | | | % 152.18/22.68 | | | | | | Case 2: % 152.18/22.68 | | | | | | | % 152.18/22.68 | | | | | | | (405) all_54_0 = e1 | all_54_0 = e0 % 152.18/22.68 | | | | | | | % 152.18/22.68 | | | | | | | REF_CLOSE: (18), (391), (393), (405) are inconsistent by sub-proof % 152.18/22.68 | | | | | | | #483. % 152.18/22.68 | | | | | | | % 152.18/22.68 | | | | | | End of split % 152.18/22.68 | | | | | | % 152.18/22.68 | | | | | End of split % 152.18/22.68 | | | | | % 152.18/22.68 | | | | Case 2: % 152.18/22.68 | | | | | % 152.18/22.68 | | | | | (406) all_56_1 = e0 % 152.18/22.68 | | | | | % 152.18/22.68 | | | | | REF_CLOSE: (36), (76), (87), (90), (110), (124), (159), (378), (406) % 152.18/22.68 | | | | | are inconsistent by sub-proof #489. % 152.18/22.68 | | | | | % 152.18/22.68 | | | | End of split % 152.18/22.68 | | | | % 152.18/22.68 | | | Case 2: % 152.18/22.68 | | | | % 152.18/22.68 | | | | (407) all_56_5 = e3 % 152.18/22.68 | | | | % 152.18/22.68 | | | | REF_CLOSE: (91), (385), (407) are inconsistent by sub-proof #481. % 152.18/22.68 | | | | % 152.18/22.68 | | | End of split % 152.18/22.68 | | | % 152.18/22.68 | | Case 2: % 152.18/22.68 | | | % 152.18/22.68 | | | (408) all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0 % 152.18/22.68 | | | % 152.18/22.68 | | | REF_CLOSE: (36), (110), (159), (378), (408) are inconsistent by sub-proof % 152.18/22.68 | | | #490. % 152.18/22.68 | | | % 152.18/22.68 | | End of split % 152.18/22.68 | | % 152.18/22.68 | End of split % 152.18/22.68 | % 152.18/22.68 End of proof % 152.18/22.68 % 152.18/22.68 Sub-proof #477 shows that the following formulas are inconsistent: % 152.18/22.68 ---------------------------------------------------------------- % 152.18/22.68 (1) op(e2, e2) = e2 % 152.18/22.68 (2) ~ (all_52_9 = all_8_2) % 152.18/22.68 (3) all_54_5 = all_8_2 % 152.18/22.68 (4) all_58_5 = all_52_9 % 152.18/22.68 (5) all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2 % 152.18/22.68 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 152.18/22.68 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 152.18/22.68 (7) ~ (all_52_11 = e2) % 152.18/22.68 (8) all_58_8 = all_6_2 % 152.18/22.68 (9) ~ (all_8_2 = e3) % 152.18/22.68 (10) ~ (all_6_2 = e2) % 152.18/22.68 (11) op(e2, e2) = all_8_2 % 152.18/22.68 (12) ~ (all_8_2 = e0) % 152.18/22.68 (13) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 152.18/22.68 (14) all_58_14 = all_52_11 % 152.18/22.68 % 152.18/22.68 Begin of proof % 152.18/22.68 | % 152.18/22.68 | BETA: splitting (5) gives: % 152.18/22.68 | % 152.18/22.68 | Case 1: % 152.18/22.68 | | % 152.18/22.68 | | (15) all_58_5 = e2 % 152.18/22.68 | | % 152.18/22.68 | | COMBINE_EQS: (4), (15) imply: % 152.18/22.68 | | (16) all_52_9 = e2 % 152.18/22.68 | | % 152.18/22.68 | | REDUCE: (2), (16) imply: % 152.18/22.68 | | (17) ~ (all_8_2 = e2) % 152.18/22.68 | | % 152.18/22.68 | | SIMP: (17) implies: % 152.18/22.68 | | (18) ~ (all_8_2 = e2) % 152.18/22.68 | | % 152.18/22.68 | | BETA: splitting (13) gives: % 152.18/22.68 | | % 152.18/22.68 | | Case 1: % 152.18/22.68 | | | % 152.18/22.68 | | | (19) all_54_5 = e3 % 152.18/22.68 | | | % 152.18/22.68 | | | REF_CLOSE: (3), (9), (19) are inconsistent by sub-proof #737. % 152.18/22.68 | | | % 152.18/22.68 | | Case 2: % 152.18/22.68 | | | % 152.18/22.68 | | | (20) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 152.18/22.68 | | | % 152.18/22.68 | | | BETA: splitting (20) gives: % 152.18/22.68 | | | % 152.18/22.68 | | | Case 1: % 152.18/22.68 | | | | % 152.18/22.68 | | | | (21) all_54_5 = e2 % 152.18/22.68 | | | | % 152.18/22.68 | | | | REF_CLOSE: (3), (18), (21) are inconsistent by sub-proof #648. % 152.18/22.68 | | | | % 152.18/22.68 | | | Case 2: % 152.18/22.68 | | | | % 152.18/22.68 | | | | (22) ~ (all_54_5 = e2) % 152.18/22.69 | | | | (23) all_54_5 = e1 | all_54_5 = e0 % 152.18/22.69 | | | | % 152.18/22.69 | | | | BETA: splitting (23) gives: % 152.18/22.69 | | | | % 152.18/22.69 | | | | Case 1: % 152.18/22.69 | | | | | % 152.18/22.69 | | | | | (24) all_54_5 = e1 % 152.18/22.69 | | | | | % 152.18/22.69 | | | | | COMBINE_EQS: (3), (24) imply: % 152.18/22.69 | | | | | (25) all_8_2 = e1 % 152.18/22.69 | | | | | % 152.18/22.69 | | | | | SIMP: (25) implies: % 152.18/22.69 | | | | | (26) all_8_2 = e1 % 152.18/22.69 | | | | | % 152.18/22.69 | | | | | REDUCE: (18), (26) imply: % 152.18/22.69 | | | | | (27) ~ (e2 = e1) % 152.18/22.69 | | | | | % 152.18/22.69 | | | | | SIMP: (27) implies: % 152.18/22.69 | | | | | (28) ~ (e2 = e1) % 152.18/22.69 | | | | | % 152.18/22.69 | | | | | REDUCE: (11), (26) imply: % 152.18/22.69 | | | | | (29) op(e2, e2) = e1 % 152.18/22.69 | | | | | % 152.18/22.69 | | | | | REF_CLOSE: (1), (6), (28), (29) are inconsistent by sub-proof #479. % 152.18/22.69 | | | | | % 152.18/22.69 | | | | Case 2: % 152.18/22.69 | | | | | % 152.18/22.69 | | | | | (30) all_54_5 = e0 % 152.18/22.69 | | | | | % 152.18/22.69 | | | | | REF_CLOSE: (3), (12), (30) are inconsistent by sub-proof #646. % 152.18/22.69 | | | | | % 152.18/22.69 | | | | End of split % 152.18/22.69 | | | | % 152.18/22.69 | | | End of split % 152.18/22.69 | | | % 152.18/22.69 | | End of split % 152.18/22.69 | | % 152.18/22.69 | Case 2: % 152.18/22.69 | | % 152.18/22.69 | | (31) all_58_8 = e2 | all_58_14 = e2 % 152.18/22.69 | | % 152.18/22.69 | | REF_CLOSE: (7), (8), (10), (14), (31) are inconsistent by sub-proof #478. % 152.18/22.69 | | % 152.18/22.69 | End of split % 152.18/22.69 | % 152.18/22.69 End of proof % 152.18/22.69 % 152.18/22.69 Sub-proof #478 shows that the following formulas are inconsistent: % 152.18/22.69 ---------------------------------------------------------------- % 152.18/22.69 (1) all_58_8 = e2 | all_58_14 = e2 % 152.18/22.69 (2) ~ (all_52_11 = e2) % 152.18/22.69 (3) all_58_8 = all_6_2 % 152.18/22.69 (4) ~ (all_6_2 = e2) % 152.18/22.69 (5) all_58_14 = all_52_11 % 152.18/22.69 % 152.18/22.69 Begin of proof % 152.18/22.69 | % 152.18/22.69 | BETA: splitting (1) gives: % 152.18/22.69 | % 152.18/22.69 | Case 1: % 152.18/22.69 | | % 152.18/22.69 | | (6) all_58_8 = e2 % 152.18/22.69 | | % 152.18/22.69 | | COMBINE_EQS: (3), (6) imply: % 152.18/22.69 | | (7) all_6_2 = e2 % 152.18/22.69 | | % 152.18/22.69 | | REDUCE: (4), (7) imply: % 152.18/22.69 | | (8) $false % 152.18/22.69 | | % 152.18/22.69 | | CLOSE: (8) is inconsistent. % 152.18/22.69 | | % 152.18/22.69 | Case 2: % 152.18/22.69 | | % 152.18/22.69 | | (9) all_58_14 = e2 % 152.18/22.69 | | % 152.18/22.69 | | REF_CLOSE: (2), (5), (9) are inconsistent by sub-proof #629. % 152.18/22.69 | | % 152.18/22.69 | End of split % 152.18/22.69 | % 152.18/22.69 End of proof % 152.18/22.69 % 152.18/22.69 Sub-proof #479 shows that the following formulas are inconsistent: % 152.18/22.69 ---------------------------------------------------------------- % 152.18/22.69 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 152.18/22.69 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 152.18/22.69 (2) op(e2, e2) = e2 % 152.18/22.69 (3) op(e2, e2) = e1 % 152.18/22.69 (4) ~ (e2 = e1) % 152.18/22.69 % 152.18/22.69 Begin of proof % 152.18/22.69 | % 152.18/22.69 | GROUND_INST: instantiating (1) with e1, e2, e2, e2, simplifying with (2), (3) % 152.18/22.69 | gives: % 152.18/22.69 | (5) e2 = e1 % 152.18/22.69 | % 152.18/22.69 | REDUCE: (4), (5) imply: % 152.18/22.69 | (6) $false % 152.18/22.69 | % 152.18/22.69 | CLOSE: (6) is inconsistent. % 152.18/22.69 | % 152.18/22.69 End of proof % 152.18/22.69 % 152.18/22.69 Sub-proof #480 shows that the following formulas are inconsistent: % 152.18/22.69 ---------------------------------------------------------------- % 152.18/22.69 (1) all_56_11 = all_8_2 % 152.18/22.69 (2) all_58_6 = all_52_2 % 152.18/22.69 (3) ~ (all_10_0 = all_8_2) % 152.18/22.69 (4) all_54_0 = all_10_2 % 152.18/22.69 (5) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 152.18/22.69 (6) all_54_1 = all_10_0 % 152.18/22.69 (7) all_56_1 = all_10_2 % 152.18/22.69 (8) ~ (all_56_1 = e1) | all_56_5 = e3 % 152.18/22.69 (9) all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2 % 152.18/22.69 (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 152.18/22.69 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 152.18/22.69 (11) ~ (all_52_8 = all_10_0) % 152.18/22.69 (12) all_56_15 = e2 % 152.18/22.69 (13) all_56_7 = all_52_12 % 152.18/22.69 (14) op(e2, all_52_6) = all_56_18 % 152.18/22.69 (15) all_58_8 = all_6_2 % 152.18/22.69 (16) ~ (all_52_12 = all_10_0) % 152.18/22.69 (17) ~ (all_56_1 = e0) | all_56_7 = e3 % 152.18/22.69 (18) all_56_5 = all_52_8 % 152.18/22.69 (19) all_58_11 = all_52_14 % 152.18/22.69 (20) op(all_10_2, all_10_2) = e2 % 152.18/22.69 (21) ~ (all_10_0 = e1) % 152.18/22.69 (22) all_56_11 = e0 % 152.18/22.69 (23) ~ (all_52_13 = all_52_14) % 152.18/22.69 (24) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0 % 152.18/22.69 (25) ~ (all_6_2 = e2) % 152.18/22.69 (26) all_58_7 = all_52_6 % 152.18/22.69 (27) op(e2, e2) = all_8_2 % 152.18/22.69 (28) ~ (all_10_0 = all_10_2) % 152.18/22.69 (29) ~ (all_52_2 = all_10_2) % 152.18/22.69 (30) ~ (all_10_0 = e2) % 152.18/22.69 (31) all_56_15 = all_52_13 % 152.18/22.69 % 152.18/22.69 Begin of proof % 152.18/22.69 | % 152.18/22.69 | COMBINE_EQS: (1), (22) imply: % 152.18/22.69 | (32) all_8_2 = e0 % 152.18/22.69 | % 152.18/22.69 | COMBINE_EQS: (12), (31) imply: % 152.18/22.69 | (33) all_52_13 = e2 % 152.18/22.69 | % 152.18/22.69 | REDUCE: (23), (33) imply: % 152.18/22.69 | (34) ~ (all_52_14 = e2) % 152.18/22.69 | % 152.18/22.69 | SIMP: (34) implies: % 152.18/22.69 | (35) ~ (all_52_14 = e2) % 152.18/22.69 | % 152.18/22.69 | REDUCE: (3), (32) imply: % 152.18/22.69 | (36) ~ (all_10_0 = e0) % 152.18/22.69 | % 152.18/22.69 | REDUCE: (27), (32) imply: % 152.18/22.69 | (37) op(e2, e2) = e0 % 152.18/22.69 | % 152.18/22.69 | BETA: splitting (24) gives: % 152.18/22.69 | % 152.18/22.69 | Case 1: % 152.18/22.69 | | % 152.18/22.69 | | (38) all_54_1 = e3 % 152.18/22.69 | | % 152.18/22.69 | | COMBINE_EQS: (6), (38) imply: % 152.18/22.69 | | (39) all_10_0 = e3 % 152.18/22.69 | | % 152.18/22.69 | | SIMP: (39) implies: % 152.18/22.69 | | (40) all_10_0 = e3 % 152.18/22.69 | | % 152.18/22.69 | | REDUCE: (11), (40) imply: % 152.18/22.69 | | (41) ~ (all_52_8 = e3) % 152.18/22.69 | | % 152.18/22.69 | | REDUCE: (16), (40) imply: % 152.18/22.69 | | (42) ~ (all_52_12 = e3) % 152.18/22.69 | | % 152.18/22.69 | | REDUCE: (28), (40) imply: % 152.18/22.69 | | (43) ~ (all_10_2 = e3) % 152.18/22.69 | | % 152.18/22.69 | | SIMP: (43) implies: % 152.18/22.69 | | (44) ~ (all_10_2 = e3) % 152.18/22.69 | | % 152.18/22.69 | | BETA: splitting (8) gives: % 152.18/22.69 | | % 152.18/22.69 | | Case 1: % 152.18/22.69 | | | % 152.18/22.69 | | | (45) ~ (all_56_1 = e1) % 152.18/22.69 | | | % 152.18/22.69 | | | REDUCE: (7), (45) imply: % 152.18/22.69 | | | (46) ~ (all_10_2 = e1) % 152.18/22.69 | | | % 152.18/22.69 | | | BETA: splitting (17) gives: % 152.18/22.69 | | | % 152.18/22.69 | | | Case 1: % 152.18/22.69 | | | | % 152.18/22.69 | | | | (47) ~ (all_56_1 = e0) % 152.18/22.69 | | | | % 152.18/22.69 | | | | REDUCE: (7), (47) imply: % 152.18/22.69 | | | | (48) ~ (all_10_2 = e0) % 152.18/22.69 | | | | % 152.18/22.69 | | | | BETA: splitting (5) gives: % 152.18/22.69 | | | | % 152.18/22.69 | | | | Case 1: % 152.18/22.69 | | | | | % 152.18/22.69 | | | | | (49) all_54_0 = e3 % 152.18/22.69 | | | | | % 152.18/22.69 | | | | | REF_CLOSE: (4), (44), (49) are inconsistent by sub-proof #709. % 152.18/22.69 | | | | | % 152.18/22.69 | | | | Case 2: % 152.18/22.69 | | | | | % 152.18/22.69 | | | | | (50) ~ (all_54_0 = e3) % 152.18/22.69 | | | | | (51) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 152.18/22.69 | | | | | % 152.18/22.69 | | | | | BETA: splitting (51) gives: % 152.18/22.69 | | | | | % 152.18/22.69 | | | | | Case 1: % 152.18/22.69 | | | | | | % 152.18/22.69 | | | | | | (52) all_54_0 = e2 % 152.18/22.69 | | | | | | % 152.18/22.69 | | | | | | COMBINE_EQS: (4), (52) imply: % 152.18/22.69 | | | | | | (53) all_10_2 = e2 % 152.18/22.69 | | | | | | % 152.18/22.69 | | | | | | SIMP: (53) implies: % 152.18/22.69 | | | | | | (54) all_10_2 = e2 % 152.18/22.69 | | | | | | % 152.18/22.69 | | | | | | REDUCE: (29), (54) imply: % 152.18/22.69 | | | | | | (55) ~ (all_52_2 = e2) % 152.18/22.69 | | | | | | % 152.18/22.69 | | | | | | BETA: splitting (9) gives: % 152.18/22.69 | | | | | | % 152.18/22.69 | | | | | | Case 1: % 152.18/22.69 | | | | | | | % 152.18/22.69 | | | | | | | (56) all_58_6 = e2 % 152.18/22.69 | | | | | | | % 152.18/22.69 | | | | | | | COMBINE_EQS: (2), (56) imply: % 152.18/22.69 | | | | | | | (57) all_52_2 = e2 % 152.18/22.69 | | | | | | | % 152.18/22.69 | | | | | | | REDUCE: (55), (57) imply: % 152.18/22.69 | | | | | | | (58) $false % 152.18/22.69 | | | | | | | % 152.18/22.69 | | | | | | | CLOSE: (58) is inconsistent. % 152.18/22.69 | | | | | | | % 152.18/22.69 | | | | | | Case 2: % 152.18/22.69 | | | | | | | % 152.18/22.69 | | | | | | | (59) all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2 % 152.18/22.69 | | | | | | | % 152.18/22.69 | | | | | | | REF_CLOSE: (4), (5), (7), (10), (13), (14), (15), (17), (19), % 152.18/22.69 | | | | | | | (20), (25), (26), (35), (37), (42), (44), (46), (59) % 152.18/22.69 | | | | | | | are inconsistent by sub-proof #482. % 152.18/22.69 | | | | | | | % 152.18/22.69 | | | | | | End of split % 152.18/22.69 | | | | | | % 152.18/22.69 | | | | | Case 2: % 152.18/22.69 | | | | | | % 152.18/22.69 | | | | | | (60) all_54_0 = e1 | all_54_0 = e0 % 152.18/22.69 | | | | | | % 152.18/22.69 | | | | | | REF_CLOSE: (4), (46), (48), (60) are inconsistent by sub-proof #483. % 152.18/22.69 | | | | | | % 152.18/22.69 | | | | | End of split % 152.18/22.69 | | | | | % 152.18/22.69 | | | | End of split % 152.18/22.69 | | | | % 152.18/22.69 | | | Case 2: % 152.18/22.69 | | | | % 152.18/22.69 | | | | (61) all_56_1 = e0 % 152.18/22.69 | | | | % 152.18/22.69 | | | | REF_CLOSE: (6), (13), (16), (17), (21), (24), (30), (36), (61) are % 152.18/22.69 | | | | inconsistent by sub-proof #489. % 152.18/22.69 | | | | % 152.18/22.69 | | | End of split % 152.18/22.69 | | | % 152.18/22.69 | | Case 2: % 152.18/22.69 | | | % 152.18/22.69 | | | (62) all_56_5 = e3 % 152.18/22.69 | | | % 152.18/22.69 | | | REF_CLOSE: (18), (41), (62) are inconsistent by sub-proof #481. % 152.18/22.69 | | | % 152.18/22.69 | | End of split % 152.18/22.69 | | % 152.18/22.69 | Case 2: % 152.18/22.69 | | % 152.18/22.69 | | (63) all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0 % 152.18/22.69 | | % 152.18/22.69 | | REF_CLOSE: (6), (21), (30), (36), (63) are inconsistent by sub-proof #490. % 152.18/22.69 | | % 152.18/22.69 | End of split % 152.18/22.69 | % 152.18/22.69 End of proof % 152.18/22.69 % 152.18/22.69 Sub-proof #481 shows that the following formulas are inconsistent: % 152.18/22.69 ---------------------------------------------------------------- % 152.18/22.69 (1) all_56_5 = all_52_8 % 152.18/22.69 (2) all_56_5 = e3 % 152.18/22.69 (3) ~ (all_52_8 = e3) % 152.18/22.69 % 152.18/22.69 Begin of proof % 152.18/22.69 | % 152.18/22.69 | COMBINE_EQS: (1), (2) imply: % 152.18/22.69 | (4) all_52_8 = e3 % 152.18/22.69 | % 152.18/22.69 | SIMP: (4) implies: % 152.18/22.69 | (5) all_52_8 = e3 % 152.18/22.69 | % 152.18/22.69 | REDUCE: (3), (5) imply: % 152.18/22.69 | (6) $false % 152.18/22.69 | % 152.18/22.69 | CLOSE: (6) is inconsistent. % 152.18/22.69 | % 152.18/22.69 End of proof % 152.18/22.69 % 152.18/22.69 Sub-proof #482 shows that the following formulas are inconsistent: % 152.18/22.69 ---------------------------------------------------------------- % 152.18/22.69 (1) all_54_0 = all_10_2 % 152.18/22.69 (2) ~ (all_10_2 = e1) % 152.18/22.69 (3) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 152.18/22.69 (4) ~ (all_52_14 = e2) % 152.18/22.69 (5) all_56_1 = all_10_2 % 152.18/22.69 (6) op(e2, e2) = e0 % 152.18/22.69 (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 152.18/22.69 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 152.18/22.69 (8) all_56_7 = all_52_12 % 152.18/22.69 (9) ~ (all_52_12 = e3) % 152.18/22.69 (10) op(e2, all_52_6) = all_56_18 % 152.18/22.69 (11) all_58_8 = all_6_2 % 152.18/22.69 (12) ~ (all_56_1 = e0) | all_56_7 = e3 % 152.18/22.69 (13) all_58_11 = all_52_14 % 152.18/22.69 (14) op(all_10_2, all_10_2) = e2 % 152.18/22.69 (15) ~ (all_6_2 = e2) % 152.18/22.69 (16) all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2 % 152.18/22.69 (17) all_58_7 = all_52_6 % 152.18/22.69 (18) ~ (all_10_2 = e3) % 152.18/22.69 % 152.18/22.69 Begin of proof % 152.18/22.69 | % 152.18/22.69 | BETA: splitting (16) gives: % 152.18/22.69 | % 152.18/22.69 | Case 1: % 152.18/22.69 | | % 152.18/22.69 | | (19) all_58_7 = e2 % 152.18/22.69 | | % 152.18/22.69 | | COMBINE_EQS: (17), (19) imply: % 152.18/22.69 | | (20) all_52_6 = e2 % 152.18/22.69 | | % 152.18/22.69 | | REDUCE: (10), (20) imply: % 152.18/22.69 | | (21) op(e2, e2) = all_56_18 % 152.18/22.69 | | % 152.18/22.69 | | BETA: splitting (12) gives: % 152.18/22.69 | | % 152.18/22.69 | | Case 1: % 152.18/22.69 | | | % 152.18/22.69 | | | (22) ~ (all_56_1 = e0) % 152.18/22.69 | | | % 152.18/22.69 | | | REDUCE: (5), (22) imply: % 152.18/22.69 | | | (23) ~ (all_10_2 = e0) % 152.18/22.69 | | | % 152.18/22.69 | | | BETA: splitting (3) gives: % 152.18/22.69 | | | % 152.18/22.69 | | | Case 1: % 152.18/22.69 | | | | % 152.18/22.69 | | | | (24) all_54_0 = e3 % 152.18/22.69 | | | | % 152.18/22.69 | | | | REF_CLOSE: (1), (18), (24) are inconsistent by sub-proof #709. % 152.18/22.69 | | | | % 152.18/22.69 | | | Case 2: % 152.18/22.69 | | | | % 152.18/22.69 | | | | (25) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 152.18/22.69 | | | | % 152.18/22.69 | | | | BETA: splitting (25) gives: % 152.18/22.69 | | | | % 152.18/22.69 | | | | Case 1: % 152.18/22.69 | | | | | % 152.18/22.69 | | | | | (26) all_54_0 = e2 % 152.18/22.69 | | | | | % 152.18/22.69 | | | | | COMBINE_EQS: (1), (26) imply: % 152.18/22.69 | | | | | (27) all_10_2 = e2 % 152.18/22.69 | | | | | % 152.18/22.69 | | | | | SIMP: (27) implies: % 152.18/22.69 | | | | | (28) all_10_2 = e2 % 152.18/22.69 | | | | | % 152.18/22.69 | | | | | REDUCE: (23), (28) imply: % 152.18/22.69 | | | | | (29) ~ (e2 = e0) % 152.18/22.69 | | | | | % 152.18/22.69 | | | | | REDUCE: (14), (28) imply: % 152.18/22.69 | | | | | (30) op(e2, e2) = e2 % 152.18/22.69 | | | | | % 152.18/22.69 | | | | | REF_CLOSE: (6), (7), (21), (29), (30) are inconsistent by sub-proof % 152.18/22.69 | | | | | #484. % 152.18/22.69 | | | | | % 152.18/22.69 | | | | Case 2: % 152.18/22.69 | | | | | % 152.18/22.69 | | | | | (31) all_54_0 = e1 | all_54_0 = e0 % 152.18/22.69 | | | | | % 152.18/22.69 | | | | | REF_CLOSE: (1), (2), (23), (31) are inconsistent by sub-proof #483. % 152.18/22.69 | | | | | % 152.18/22.69 | | | | End of split % 152.18/22.69 | | | | % 152.18/22.69 | | | End of split % 152.18/22.69 | | | % 152.18/22.69 | | Case 2: % 152.18/22.69 | | | % 152.18/22.69 | | | (32) all_56_7 = e3 % 152.18/22.69 | | | % 152.18/22.69 | | | COMBINE_EQS: (8), (32) imply: % 152.18/22.69 | | | (33) all_52_12 = e3 % 152.18/22.69 | | | % 152.18/22.69 | | | REDUCE: (9), (33) imply: % 152.18/22.69 | | | (34) $false % 152.18/22.69 | | | % 152.18/22.69 | | | CLOSE: (34) is inconsistent. % 152.18/22.69 | | | % 152.18/22.69 | | End of split % 152.18/22.69 | | % 152.18/22.69 | Case 2: % 152.18/22.69 | | % 152.18/22.69 | | (35) all_58_8 = e2 | all_58_11 = e2 % 152.18/22.69 | | % 152.18/22.69 | | REF_CLOSE: (4), (11), (13), (15), (35) are inconsistent by sub-proof #511. % 152.18/22.69 | | % 152.18/22.69 | End of split % 152.18/22.69 | % 152.18/22.69 End of proof % 152.18/22.69 % 152.18/22.69 Sub-proof #483 shows that the following formulas are inconsistent: % 152.18/22.69 ---------------------------------------------------------------- % 152.18/22.69 (1) all_54_0 = e1 | all_54_0 = e0 % 152.18/22.69 (2) all_54_0 = all_10_2 % 152.18/22.69 (3) ~ (all_10_2 = e1) % 152.18/22.69 (4) ~ (all_10_2 = e0) % 152.18/22.69 % 152.18/22.69 Begin of proof % 152.18/22.69 | % 152.18/22.69 | BETA: splitting (1) gives: % 152.18/22.69 | % 152.18/22.69 | Case 1: % 152.18/22.69 | | % 152.18/22.69 | | (5) all_54_0 = e1 % 152.18/22.69 | | % 152.18/22.69 | | REF_CLOSE: (2), (3), (5) are inconsistent by sub-proof #733. % 152.18/22.69 | | % 152.18/22.69 | Case 2: % 152.18/22.69 | | % 152.18/22.69 | | (6) all_54_0 = e0 % 152.18/22.69 | | % 152.18/22.69 | | REF_CLOSE: (2), (4), (6) are inconsistent by sub-proof #732. % 152.18/22.69 | | % 152.18/22.69 | End of split % 152.18/22.69 | % 152.18/22.69 End of proof % 152.18/22.69 % 152.18/22.69 Sub-proof #484 shows that the following formulas are inconsistent: % 152.18/22.69 ---------------------------------------------------------------- % 152.18/22.69 (1) op(e2, e2) = e2 % 152.18/22.69 (2) op(e2, e2) = e0 % 152.18/22.69 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 152.18/22.69 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 152.18/22.69 (4) op(e2, e2) = all_56_18 % 152.18/22.69 (5) ~ (e2 = e0) % 152.18/22.69 % 152.18/22.69 Begin of proof % 152.18/22.69 | % 152.18/22.69 | GROUND_INST: instantiating (3) with e2, all_56_18, e2, e2, simplifying with % 152.18/22.69 | (1), (4) gives: % 152.18/22.69 | (6) all_56_18 = e2 % 152.18/22.69 | % 152.18/22.69 | GROUND_INST: instantiating (3) with e0, all_56_18, e2, e2, simplifying with % 152.18/22.69 | (2), (4) gives: % 152.18/22.69 | (7) all_56_18 = e0 % 152.18/22.69 | % 152.18/22.69 | COMBINE_EQS: (6), (7) imply: % 152.18/22.69 | (8) e2 = e0 % 152.18/22.69 | % 152.18/22.69 | REDUCE: (5), (8) imply: % 152.18/22.69 | (9) $false % 152.18/22.69 | % 152.18/22.69 | CLOSE: (9) is inconsistent. % 152.18/22.69 | % 152.18/22.69 End of proof % 152.18/22.69 % 152.18/22.69 Sub-proof #485 shows that the following formulas are inconsistent: % 152.18/22.69 ---------------------------------------------------------------- % 152.18/22.69 (1) ~ (all_52_11 = all_6_2) % 152.18/22.69 (2) op(e2, all_8_1) = all_8_0 % 152.18/22.69 (3) ~ (all_8_1 = e1) % 152.18/22.69 (4) all_54_10 = all_6_2 % 152.18/22.69 (5) op(e2, e0) = e3 % 152.18/22.69 (6) ~ (all_8_1 = e3) % 152.18/22.69 (7) all_58_4 = all_52_8 % 152.18/22.69 (8) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 152.18/22.69 (9) all_58_13 = all_52_7 % 152.18/22.69 (10) all_58_4 = e0 | all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0 % 152.18/22.69 (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 152.18/22.69 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 152.18/22.69 (12) ~ (all_52_8 = all_10_0) % 152.18/22.69 (13) all_58_8 = all_6_2 % 152.18/22.69 (14) all_58_5 = e2 % 152.18/22.69 (15) all_58_3 = all_8_2 % 152.18/22.69 (16) ~ (all_8_0 = e3) % 152.18/22.69 (17) op(e1, e1) = all_8_1 % 152.18/22.69 (18) op(e1, e1) = all_6_2 % 152.18/22.69 (19) op(e2, all_10_0) = all_56_2 % 152.18/22.69 (20) ~ (all_6_2 = e2) % 152.18/22.69 (21) all_58_7 = all_52_6 % 152.18/22.69 (22) all_58_1 = all_10_0 % 152.18/22.69 (23) all_58_1 = e0 | all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0 % 152.18/22.69 (24) ~ (all_52_6 = all_6_2) % 152.18/22.69 (25) ~ (all_8_2 = e0) % 152.18/22.69 (26) ~ (all_52_7 = e0) % 152.18/22.69 (27) ~ (all_10_0 = e2) % 152.18/22.69 (28) all_58_14 = all_52_11 % 152.18/22.69 % 152.18/22.69 Begin of proof % 152.18/22.69 | % 152.18/22.69 | GROUND_INST: instantiating (11) with all_6_2, all_8_1, e1, e1, simplifying % 152.18/22.69 | with (17), (18) gives: % 152.18/22.69 | (29) all_8_1 = all_6_2 % 152.18/22.69 | % 152.18/22.69 | REDUCE: (6), (29) imply: % 152.18/22.69 | (30) ~ (all_6_2 = e3) % 152.18/22.69 | % 152.18/22.69 | REDUCE: (3), (29) imply: % 152.18/22.69 | (31) ~ (all_6_2 = e1) % 152.18/22.69 | % 152.18/22.69 | REDUCE: (2), (29) imply: % 152.18/22.69 | (32) op(e2, all_6_2) = all_8_0 % 152.18/22.69 | % 152.18/22.69 | BETA: splitting (8) gives: % 152.18/22.69 | % 152.18/22.69 | Case 1: % 152.18/22.69 | | % 152.18/22.69 | | (33) all_54_10 = e3 % 152.18/22.69 | | % 152.18/22.69 | | REF_CLOSE: (4), (30), (33) are inconsistent by sub-proof #736. % 152.18/22.69 | | % 152.18/22.69 | Case 2: % 152.18/22.69 | | % 152.18/22.69 | | (34) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 152.18/22.69 | | % 152.18/22.69 | | BETA: splitting (34) gives: % 152.18/22.69 | | % 152.18/22.69 | | Case 1: % 152.18/22.69 | | | % 152.18/22.69 | | | (35) all_54_10 = e2 % 152.18/22.69 | | | % 152.18/22.69 | | | REF_CLOSE: (4), (20), (35) are inconsistent by sub-proof #735. % 152.18/22.69 | | | % 152.18/22.69 | | Case 2: % 152.18/22.69 | | | % 152.18/22.69 | | | (36) all_54_10 = e1 | all_54_10 = e0 % 152.18/22.69 | | | % 152.18/22.69 | | | BETA: splitting (36) gives: % 152.18/22.69 | | | % 152.18/22.69 | | | Case 1: % 152.18/22.69 | | | | % 152.18/22.69 | | | | (37) all_54_10 = e1 % 152.18/22.69 | | | | % 152.18/22.69 | | | | REF_CLOSE: (4), (31), (37) are inconsistent by sub-proof #606. % 152.18/22.69 | | | | % 152.18/22.69 | | | Case 2: % 152.18/22.69 | | | | % 152.18/22.69 | | | | (38) all_54_10 = e0 % 152.18/22.69 | | | | % 152.18/22.69 | | | | COMBINE_EQS: (4), (38) imply: % 152.18/22.69 | | | | (39) all_6_2 = e0 % 152.18/22.69 | | | | % 152.18/22.69 | | | | SIMP: (39) implies: % 152.18/22.69 | | | | (40) all_6_2 = e0 % 152.18/22.69 | | | | % 152.18/22.69 | | | | REDUCE: (24), (40) imply: % 152.18/22.69 | | | | (41) ~ (all_52_6 = e0) % 152.18/22.69 | | | | % 152.18/22.69 | | | | REDUCE: (1), (40) imply: % 152.18/22.69 | | | | (42) ~ (all_52_11 = e0) % 152.18/22.69 | | | | % 152.18/22.69 | | | | BETA: splitting (23) gives: % 152.18/22.69 | | | | % 152.18/22.69 | | | | Case 1: % 152.18/22.69 | | | | | % 152.18/22.69 | | | | | (43) all_58_1 = e0 % 152.18/22.69 | | | | | % 152.18/22.69 | | | | | COMBINE_EQS: (22), (43) imply: % 152.18/22.69 | | | | | (44) all_10_0 = e0 % 152.18/22.69 | | | | | % 152.18/22.69 | | | | | REDUCE: (12), (44) imply: % 152.18/22.69 | | | | | (45) ~ (all_52_8 = e0) % 152.18/22.69 | | | | | % 152.18/22.69 | | | | | REDUCE: (27), (44) imply: % 152.18/22.69 | | | | | (46) ~ (e2 = e0) % 152.18/22.69 | | | | | % 152.18/22.69 | | | | | SIMP: (46) implies: % 152.18/22.69 | | | | | (47) ~ (e2 = e0) % 152.18/22.69 | | | | | % 152.18/22.69 | | | | | REDUCE: (19), (44) imply: % 152.18/22.69 | | | | | (48) op(e2, e0) = all_56_2 % 152.18/22.69 | | | | | % 152.18/22.69 | | | | | REF_CLOSE: (5), (7), (10), (11), (13), (14), (16), (28), (32), (42), % 152.18/22.69 | | | | | (45), (47), (48) are inconsistent by sub-proof #638. % 152.18/22.69 | | | | | % 152.18/22.69 | | | | Case 2: % 152.18/22.69 | | | | | % 152.18/22.69 | | | | | (49) all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0 % 152.18/22.69 | | | | | % 152.18/22.69 | | | | | REF_CLOSE: (9), (15), (21), (25), (26), (41), (49) are inconsistent by % 152.18/22.69 | | | | | sub-proof #603. % 152.18/22.69 | | | | | % 152.18/22.69 | | | | End of split % 152.18/22.69 | | | | % 152.18/22.69 | | | End of split % 152.18/22.69 | | | % 152.18/22.69 | | End of split % 152.18/22.69 | | % 152.18/22.69 | End of split % 152.18/22.69 | % 152.18/22.69 End of proof % 152.18/22.69 % 152.18/22.69 Sub-proof #486 shows that the following formulas are inconsistent: % 152.18/22.69 ---------------------------------------------------------------- % 152.18/22.69 (1) all_56_9 = e2 % 152.18/22.69 (2) all_56_9 = e0 % 152.18/22.69 (3) ~ (e2 = e0) % 152.18/22.69 % 152.18/22.69 Begin of proof % 152.18/22.69 | % 152.18/22.69 | COMBINE_EQS: (1), (2) imply: % 152.18/22.69 | (4) e2 = e0 % 152.18/22.69 | % 152.18/22.69 | SIMP: (4) implies: % 152.18/22.69 | (5) e2 = e0 % 152.18/22.69 | % 152.18/22.69 | REDUCE: (3), (5) imply: % 152.18/22.69 | (6) $false % 152.18/22.69 | % 152.18/22.69 | CLOSE: (6) is inconsistent. % 152.18/22.69 | % 152.18/22.69 End of proof % 152.18/22.69 % 152.18/22.69 Sub-proof #487 shows that the following formulas are inconsistent: % 152.18/22.69 ---------------------------------------------------------------- % 152.18/22.69 (1) ~ (all_38_0 = e0) | ~ (all_38_2 = e1) % 152.18/22.69 (2) all_38_2 = e1 % 152.18/22.69 (3) all_38_0 = e0 % 152.18/22.69 % 152.18/22.69 Begin of proof % 152.18/22.69 | % 152.18/22.69 | BETA: splitting (1) gives: % 152.18/22.69 | % 152.18/22.69 | Case 1: % 152.18/22.69 | | % 152.18/22.69 | | (4) ~ (all_38_2 = e1) % 152.18/22.69 | | % 152.18/22.69 | | REDUCE: (2), (4) imply: % 152.18/22.69 | | (5) $false % 152.18/22.69 | | % 152.18/22.69 | | CLOSE: (5) is inconsistent. % 152.18/22.69 | | % 152.18/22.69 | Case 2: % 152.18/22.69 | | % 152.18/22.69 | | (6) ~ (all_38_0 = e0) % 152.18/22.69 | | % 152.18/22.69 | | REDUCE: (3), (6) imply: % 152.18/22.69 | | (7) $false % 152.18/22.69 | | % 152.18/22.69 | | CLOSE: (7) is inconsistent. % 152.18/22.69 | | % 152.18/22.69 | End of split % 152.18/22.69 | % 152.18/22.69 End of proof % 152.18/22.69 % 152.18/22.69 Sub-proof #488 shows that the following formulas are inconsistent: % 152.18/22.69 ---------------------------------------------------------------- % 152.18/22.69 (1) ~ (all_6_1 = e2) % 152.18/22.69 (2) all_54_0 = all_10_2 % 152.18/22.69 (3) all_6_2 = e3 % 152.18/22.69 (4) ~ (all_6_1 = e3) % 152.18/22.69 (5) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 152.18/22.69 (6) all_54_1 = all_10_0 % 152.18/22.69 (7) all_56_1 = all_10_2 % 152.18/22.69 (8) op(e3, e3) = all_10_2 % 152.18/22.69 (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 152.18/22.69 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 152.18/22.69 (10) all_56_7 = all_52_12 % 152.18/22.69 (11) ~ (all_52_12 = all_10_0) % 152.18/22.69 (12) ~ (all_56_1 = e0) | all_56_7 = e3 % 152.18/22.69 (13) all_52_2 = e1 % 152.18/22.69 (14) op(all_6_2, all_6_2) = all_6_1 % 152.18/22.69 (15) ~ (all_10_0 = e1) % 152.18/22.69 (16) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0 % 152.18/22.69 (17) ~ (all_10_0 = all_10_2) % 152.18/22.69 (18) ~ (all_52_2 = all_10_2) % 152.18/22.69 (19) ~ (all_10_0 = e2) % 152.18/22.69 % 152.18/22.69 Begin of proof % 152.18/22.69 | % 152.18/22.69 | REDUCE: (13), (18) imply: % 152.18/22.69 | (20) ~ (all_10_2 = e1) % 152.18/22.69 | % 152.18/22.69 | SIMP: (20) implies: % 152.18/22.69 | (21) ~ (all_10_2 = e1) % 152.18/22.69 | % 152.18/22.69 | REDUCE: (3), (14) imply: % 152.18/22.69 | (22) op(e3, e3) = all_6_1 % 152.18/22.69 | % 152.18/22.69 | GROUND_INST: instantiating (9) with all_10_2, all_6_1, e3, e3, simplifying % 152.18/22.69 | with (8), (22) gives: % 152.18/22.69 | (23) all_10_2 = all_6_1 % 152.18/22.69 | % 152.18/22.69 | COMBINE_EQS: (2), (23) imply: % 152.18/22.69 | (24) all_54_0 = all_6_1 % 152.18/22.69 | % 152.18/22.69 | COMBINE_EQS: (7), (23) imply: % 152.18/22.69 | (25) all_56_1 = all_6_1 % 152.18/22.69 | % 152.18/22.69 | REDUCE: (17), (23) imply: % 152.18/22.69 | (26) ~ (all_10_0 = all_6_1) % 152.18/22.69 | % 152.18/22.69 | REDUCE: (21), (23) imply: % 152.18/22.69 | (27) ~ (all_6_1 = e1) % 152.18/22.69 | % 152.18/22.69 | BETA: splitting (5) gives: % 152.18/22.69 | % 152.18/22.69 | Case 1: % 152.18/22.69 | | % 152.18/22.69 | | (28) all_54_0 = e3 % 152.18/22.69 | | % 152.18/22.69 | | REF_CLOSE: (4), (24), (28) are inconsistent by sub-proof #686. % 152.18/22.69 | | % 152.18/22.69 | Case 2: % 152.18/22.69 | | % 152.18/22.69 | | (29) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 152.18/22.69 | | % 152.18/22.69 | | BETA: splitting (29) gives: % 152.18/22.69 | | % 152.18/22.69 | | Case 1: % 152.18/22.69 | | | % 152.18/22.69 | | | (30) all_54_0 = e2 % 152.18/22.69 | | | % 152.18/22.69 | | | REF_CLOSE: (1), (24), (30) are inconsistent by sub-proof #685. % 152.18/22.69 | | | % 152.18/22.69 | | Case 2: % 152.18/22.69 | | | % 152.18/22.69 | | | (31) all_54_0 = e1 | all_54_0 = e0 % 152.18/22.69 | | | % 152.18/22.69 | | | BETA: splitting (31) gives: % 152.18/22.69 | | | % 152.18/22.69 | | | Case 1: % 152.18/22.69 | | | | % 152.18/22.69 | | | | (32) all_54_0 = e1 % 152.18/22.69 | | | | % 152.18/22.69 | | | | REF_CLOSE: (24), (27), (32) are inconsistent by sub-proof #684. % 152.18/22.69 | | | | % 152.18/22.69 | | | Case 2: % 152.18/22.69 | | | | % 152.18/22.69 | | | | (33) all_54_0 = e0 % 152.18/22.69 | | | | % 152.18/22.69 | | | | COMBINE_EQS: (24), (33) imply: % 152.18/22.69 | | | | (34) all_6_1 = e0 % 152.18/22.69 | | | | % 152.18/22.69 | | | | SIMP: (34) implies: % 152.18/22.69 | | | | (35) all_6_1 = e0 % 152.18/22.69 | | | | % 152.18/22.69 | | | | COMBINE_EQS: (25), (35) imply: % 152.18/22.69 | | | | (36) all_56_1 = e0 % 152.18/22.69 | | | | % 152.18/22.69 | | | | REDUCE: (26), (35) imply: % 152.18/22.69 | | | | (37) ~ (all_10_0 = e0) % 152.18/22.69 | | | | % 152.18/22.69 | | | | REF_CLOSE: (6), (10), (11), (12), (15), (16), (19), (36), (37) are % 152.18/22.69 | | | | inconsistent by sub-proof #489. % 152.18/22.69 | | | | % 152.18/22.69 | | | End of split % 152.18/22.69 | | | % 152.18/22.69 | | End of split % 152.18/22.69 | | % 152.18/22.69 | End of split % 152.18/22.69 | % 152.18/22.69 End of proof % 152.18/22.69 % 152.18/22.69 Sub-proof #489 shows that the following formulas are inconsistent: % 152.18/22.69 ---------------------------------------------------------------- % 152.18/22.69 (1) all_54_1 = all_10_0 % 152.18/22.69 (2) ~ (all_10_0 = e0) % 152.18/22.69 (3) all_56_7 = all_52_12 % 152.18/22.69 (4) ~ (all_52_12 = all_10_0) % 152.18/22.69 (5) ~ (all_56_1 = e0) | all_56_7 = e3 % 152.18/22.69 (6) all_56_1 = e0 % 152.18/22.69 (7) ~ (all_10_0 = e1) % 152.18/22.69 (8) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0 % 152.18/22.69 (9) ~ (all_10_0 = e2) % 152.18/22.69 % 152.18/22.69 Begin of proof % 152.18/22.69 | % 152.18/22.69 | BETA: splitting (5) gives: % 152.18/22.69 | % 152.18/22.69 | Case 1: % 152.18/22.69 | | % 152.18/22.69 | | (10) ~ (all_56_1 = e0) % 152.18/22.69 | | % 152.18/22.69 | | REDUCE: (6), (10) imply: % 152.18/22.69 | | (11) $false % 152.18/22.69 | | % 152.18/22.69 | | CLOSE: (11) is inconsistent. % 152.18/22.69 | | % 152.18/22.69 | Case 2: % 152.18/22.69 | | % 152.18/22.69 | | (12) all_56_7 = e3 % 152.18/22.69 | | % 152.18/22.69 | | COMBINE_EQS: (3), (12) imply: % 152.18/22.69 | | (13) all_52_12 = e3 % 152.18/22.69 | | % 152.18/22.69 | | REDUCE: (4), (13) imply: % 152.18/22.69 | | (14) ~ (all_10_0 = e3) % 152.18/22.69 | | % 152.18/22.69 | | SIMP: (14) implies: % 152.18/22.69 | | (15) ~ (all_10_0 = e3) % 152.18/22.69 | | % 152.18/22.69 | | BETA: splitting (8) gives: % 152.18/22.69 | | % 152.18/22.69 | | Case 1: % 152.18/22.69 | | | % 152.18/22.69 | | | (16) all_54_1 = e3 % 152.18/22.69 | | | % 152.18/22.69 | | | REF_CLOSE: (1), (15), (16) are inconsistent by sub-proof #493. % 152.18/22.69 | | | % 152.18/22.69 | | Case 2: % 152.18/22.69 | | | % 152.18/22.69 | | | (17) all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0 % 152.18/22.69 | | | % 152.18/22.69 | | | REF_CLOSE: (1), (2), (7), (9), (17) are inconsistent by sub-proof #490. % 152.18/22.69 | | | % 152.18/22.69 | | End of split % 152.18/22.69 | | % 152.18/22.69 | End of split % 152.18/22.69 | % 152.18/22.69 End of proof % 152.18/22.69 % 152.18/22.69 Sub-proof #490 shows that the following formulas are inconsistent: % 152.18/22.69 ---------------------------------------------------------------- % 152.18/22.69 (1) all_54_1 = all_10_0 % 152.18/22.69 (2) ~ (all_10_0 = e0) % 152.18/22.69 (3) all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0 % 152.18/22.69 (4) ~ (all_10_0 = e1) % 152.18/22.69 (5) ~ (all_10_0 = e2) % 152.18/22.69 % 152.18/22.69 Begin of proof % 152.18/22.69 | % 152.18/22.69 | BETA: splitting (3) gives: % 152.18/22.69 | % 152.18/22.69 | Case 1: % 152.18/22.69 | | % 152.18/22.69 | | (6) all_54_1 = e2 % 152.18/22.69 | | % 152.18/22.69 | | REF_CLOSE: (1), (5), (6) are inconsistent by sub-proof #492. % 152.18/22.69 | | % 152.18/22.69 | Case 2: % 152.18/22.69 | | % 152.18/22.69 | | (7) all_54_1 = e1 | all_54_1 = e0 % 152.18/22.69 | | % 152.18/22.69 | | BETA: splitting (7) gives: % 152.18/22.69 | | % 152.18/22.69 | | Case 1: % 152.18/22.69 | | | % 152.18/22.69 | | | (8) all_54_1 = e1 % 152.18/22.69 | | | % 152.18/22.69 | | | REF_CLOSE: (1), (4), (8) are inconsistent by sub-proof #491. % 152.18/22.69 | | | % 152.18/22.69 | | Case 2: % 152.18/22.69 | | | % 152.18/22.69 | | | (9) all_54_1 = e0 % 152.18/22.69 | | | % 152.18/22.69 | | | COMBINE_EQS: (1), (9) imply: % 152.18/22.69 | | | (10) all_10_0 = e0 % 152.18/22.69 | | | % 152.18/22.69 | | | SIMP: (10) implies: % 152.18/22.69 | | | (11) all_10_0 = e0 % 152.18/22.69 | | | % 152.18/22.69 | | | REDUCE: (2), (11) imply: % 152.18/22.69 | | | (12) $false % 152.18/22.69 | | | % 152.18/22.69 | | | CLOSE: (12) is inconsistent. % 152.18/22.69 | | | % 152.18/22.69 | | End of split % 152.18/22.69 | | % 152.18/22.69 | End of split % 152.18/22.69 | % 152.18/22.69 End of proof % 152.18/22.69 % 152.18/22.69 Sub-proof #491 shows that the following formulas are inconsistent: % 152.18/22.69 ---------------------------------------------------------------- % 152.18/22.69 (1) all_54_1 = all_10_0 % 152.18/22.69 (2) all_54_1 = e1 % 152.18/22.69 (3) ~ (all_10_0 = e1) % 152.18/22.69 % 152.18/22.69 Begin of proof % 152.18/22.69 | % 152.18/22.69 | COMBINE_EQS: (1), (2) imply: % 152.18/22.69 | (4) all_10_0 = e1 % 152.18/22.69 | % 152.18/22.69 | SIMP: (4) implies: % 152.18/22.69 | (5) all_10_0 = e1 % 152.18/22.69 | % 152.18/22.69 | REDUCE: (3), (5) imply: % 152.18/22.69 | (6) $false % 152.18/22.69 | % 152.18/22.69 | CLOSE: (6) is inconsistent. % 152.18/22.69 | % 152.18/22.69 End of proof % 152.18/22.69 % 152.18/22.69 Sub-proof #492 shows that the following formulas are inconsistent: % 152.18/22.69 ---------------------------------------------------------------- % 152.18/22.69 (1) all_54_1 = all_10_0 % 152.18/22.69 (2) all_54_1 = e2 % 152.18/22.69 (3) ~ (all_10_0 = e2) % 152.18/22.69 % 152.18/22.69 Begin of proof % 152.18/22.69 | % 152.18/22.69 | COMBINE_EQS: (1), (2) imply: % 152.18/22.69 | (4) all_10_0 = e2 % 152.18/22.69 | % 152.18/22.69 | SIMP: (4) implies: % 152.18/22.69 | (5) all_10_0 = e2 % 152.18/22.69 | % 152.18/22.69 | REDUCE: (3), (5) imply: % 152.18/22.69 | (6) $false % 152.18/22.69 | % 152.18/22.69 | CLOSE: (6) is inconsistent. % 152.18/22.69 | % 152.18/22.69 End of proof % 152.18/22.69 % 152.18/22.69 Sub-proof #493 shows that the following formulas are inconsistent: % 152.18/22.69 ---------------------------------------------------------------- % 152.18/22.69 (1) all_54_1 = all_10_0 % 152.18/22.69 (2) all_54_1 = e3 % 152.18/22.69 (3) ~ (all_10_0 = e3) % 152.18/22.69 % 152.18/22.69 Begin of proof % 152.18/22.69 | % 152.18/22.69 | COMBINE_EQS: (1), (2) imply: % 152.18/22.69 | (4) all_10_0 = e3 % 152.18/22.69 | % 152.18/22.69 | SIMP: (4) implies: % 152.18/22.69 | (5) all_10_0 = e3 % 152.18/22.69 | % 152.18/22.69 | REDUCE: (3), (5) imply: % 152.18/22.69 | (6) $false % 152.18/22.69 | % 152.18/22.69 | CLOSE: (6) is inconsistent. % 152.18/22.69 | % 152.18/22.69 End of proof % 152.18/22.69 % 152.18/22.69 Sub-proof #494 shows that the following formulas are inconsistent: % 152.18/22.69 ---------------------------------------------------------------- % 152.18/22.69 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 152.18/22.69 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 152.18/22.69 (2) ~ (e2 = e1) % 152.18/22.69 (3) op(e1, e1) = all_56_20 % 152.18/22.69 (4) op(e1, e1) = e2 % 152.18/22.69 (5) op(e1, e1) = e1 % 152.18/22.69 % 152.18/22.69 Begin of proof % 152.18/22.69 | % 152.18/22.69 | GROUND_INST: instantiating (1) with e2, all_56_20, e1, e1, simplifying with % 152.18/22.69 | (3), (4) gives: % 152.18/22.69 | (6) all_56_20 = e2 % 152.18/22.69 | % 152.18/22.69 | GROUND_INST: instantiating (1) with e1, all_56_20, e1, e1, simplifying with % 152.18/22.69 | (3), (5) gives: % 152.18/22.69 | (7) all_56_20 = e1 % 152.18/22.69 | % 152.18/22.69 | COMBINE_EQS: (6), (7) imply: % 152.18/22.69 | (8) e2 = e1 % 152.18/22.69 | % 152.18/22.69 | SIMP: (8) implies: % 152.18/22.69 | (9) e2 = e1 % 152.18/22.69 | % 152.18/22.69 | REDUCE: (2), (9) imply: % 152.18/22.69 | (10) $false % 152.18/22.69 | % 152.18/22.69 | CLOSE: (10) is inconsistent. % 152.18/22.69 | % 152.18/22.69 End of proof % 152.18/22.69 % 152.18/22.69 Sub-proof #495 shows that the following formulas are inconsistent: % 152.18/22.69 ---------------------------------------------------------------- % 152.18/22.69 (1) ~ (all_52_13 = e1) % 152.18/22.69 (2) ~ (all_8_2 = e1) % 152.18/22.69 (3) all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1 % 152.18/22.70 (4) all_58_5 = all_52_9 % 152.18/22.70 (5) all_58_3 = all_8_2 % 152.18/22.70 (6) ~ (all_52_9 = e1) % 152.18/22.70 (7) all_58_10 = all_52_13 % 152.18/22.70 % 152.18/22.70 Begin of proof % 152.18/22.70 | % 152.18/22.70 | BETA: splitting (3) gives: % 152.18/22.70 | % 152.18/22.70 | Case 1: % 152.18/22.70 | | % 152.18/22.70 | | (8) all_58_3 = e1 % 152.18/22.70 | | % 152.18/22.70 | | COMBINE_EQS: (5), (8) imply: % 152.18/22.70 | | (9) all_8_2 = e1 % 152.18/22.70 | | % 152.18/22.70 | | REDUCE: (2), (9) imply: % 152.18/22.70 | | (10) $false % 152.18/22.70 | | % 152.18/22.70 | | CLOSE: (10) is inconsistent. % 152.18/22.70 | | % 152.18/22.70 | Case 2: % 152.18/22.70 | | % 152.18/22.70 | | (11) all_58_5 = e1 | all_58_10 = e1 % 152.18/22.70 | | % 152.18/22.70 | | REF_CLOSE: (1), (4), (6), (7), (11) are inconsistent by sub-proof #529. % 152.18/22.70 | | % 152.18/22.70 | End of split % 152.18/22.70 | % 152.18/22.70 End of proof % 152.18/22.70 % 152.18/22.70 Sub-proof #496 shows that the following formulas are inconsistent: % 152.18/22.70 ---------------------------------------------------------------- % 152.18/22.70 (1) all_56_9 = e2 % 152.18/22.70 (2) all_56_9 = e1 % 152.18/22.70 (3) ~ (e2 = e1) % 152.18/22.70 % 152.18/22.70 Begin of proof % 152.18/22.70 | % 152.18/22.70 | COMBINE_EQS: (1), (2) imply: % 152.18/22.70 | (4) e2 = e1 % 152.18/22.70 | % 152.18/22.70 | SIMP: (4) implies: % 152.18/22.70 | (5) e2 = e1 % 152.18/22.70 | % 152.18/22.70 | REDUCE: (3), (5) imply: % 152.18/22.70 | (6) $false % 152.18/22.70 | % 152.18/22.70 | CLOSE: (6) is inconsistent. % 152.18/22.70 | % 152.18/22.70 End of proof % 152.18/22.70 % 152.18/22.70 Sub-proof #497 shows that the following formulas are inconsistent: % 152.18/22.70 ---------------------------------------------------------------- % 152.18/22.70 (1) all_56_7 = e3 % 152.18/22.70 (2) all_56_7 = e1 % 152.18/22.70 (3) ~ (e3 = e1) % 152.18/22.70 % 152.18/22.70 Begin of proof % 152.18/22.70 | % 152.18/22.70 | COMBINE_EQS: (1), (2) imply: % 152.18/22.70 | (4) e3 = e1 % 152.18/22.70 | % 152.18/22.70 | SIMP: (4) implies: % 152.18/22.70 | (5) e3 = e1 % 152.18/22.70 | % 152.18/22.70 | REDUCE: (3), (5) imply: % 152.18/22.70 | (6) $false % 152.18/22.70 | % 152.18/22.70 | CLOSE: (6) is inconsistent. % 152.18/22.70 | % 152.18/22.70 End of proof % 152.18/22.70 % 152.18/22.70 Sub-proof #498 shows that the following formulas are inconsistent: % 152.18/22.70 ---------------------------------------------------------------- % 152.18/22.70 (1) all_56_11 = all_8_2 % 152.18/22.70 (2) op(e0, all_52_13) = all_56_14 % 152.18/22.70 (3) ~ (all_52_11 = all_6_2) % 152.18/22.70 (4) ~ (all_52_4 = all_52_8) % 152.18/22.70 (5) all_56_25 = all_52_3 % 152.18/22.70 (6) ~ (all_52_7 = all_52_11) % 152.18/22.70 (7) ~ (all_52_8 = all_52_9) % 152.18/22.70 (8) all_54_9 = all_52_6 % 152.18/22.70 (9) op(e2, all_8_1) = all_8_0 % 152.18/22.70 (10) all_58_6 = all_52_2 % 152.18/22.70 (11) ~ (all_8_1 = e1) % 152.18/22.70 (12) ~ (all_52_1 = all_52_9) % 152.18/22.70 (13) ~ (all_56_31 = e1) | all_56_29 = e0 % 152.18/22.70 (14) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0 % 152.18/22.70 (15) op(e1, all_6_1) = e3 % 152.18/22.70 (16) all_54_10 = all_6_2 % 152.18/22.70 (17) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0 % 152.18/22.70 (18) ~ (all_6_1 = e2) % 152.18/22.70 (19) ~ (all_56_21 = e2) | all_56_19 = e1 % 152.18/22.70 (20) all_40_2 = all_6_2 % 152.18/22.70 (21) all_54_0 = all_10_2 % 152.18/22.70 (22) all_54_4 = all_52_1 % 152.18/22.70 (23) ~ (all_52_14 = all_4_2) % 152.18/22.70 (24) ~ (all_8_0 = e1) % 152.18/22.70 (25) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0 % 152.18/22.70 (26) all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2 % 152.18/22.70 (27) ~ (all_52_9 = all_8_2) % 152.18/22.70 (28) all_54_12 = all_52_3 % 152.18/22.70 (29) ~ (all_52_12 = all_52_13) % 152.18/22.70 (30) ~ (all_52_4 = all_52_7) % 152.18/22.70 (31) ~ (all_8_1 = e3) % 152.18/22.70 (32) ~ (e3 = e2) % 152.18/22.70 (33) op(e0, e0) = all_4_2 % 152.18/22.70 (34) all_58_6 = e0 | all_58_7 = e0 | all_58_8 = e0 | all_58_11 = e0 % 152.18/22.70 (35) all_58_4 = all_52_8 % 152.18/22.70 (36) all_54_5 = all_8_2 % 152.18/22.70 (37) ~ (all_6_1 = e3) % 152.18/22.70 (38) ~ (all_52_6 = all_52_14) % 152.18/22.70 (39) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 152.18/22.70 (40) ~ (all_6_0 = e2) % 152.18/22.70 (41) all_54_15 = all_4_2 % 152.18/22.70 (42) all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1 % 152.18/22.70 (43) ~ (all_10_1 = e1) % 152.18/22.70 (44) all_56_21 = all_6_2 % 152.18/22.70 (45) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 152.18/22.70 (46) op(e3, all_52_1) = all_56_8 % 152.18/22.70 (47) ~ (all_52_7 = all_8_2) % 152.18/22.70 (48) all_56_1 = all_10_2 % 152.18/22.70 (49) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0 % 152.18/22.70 (50) all_58_5 = all_52_9 % 152.18/22.70 (51) all_54_1 = all_52_4 % 152.18/22.70 (52) all_56_17 = all_52_2 % 152.18/22.70 (53) all_58_9 = all_52_12 % 152.18/22.70 (54) op(e0, e2) = all_52_7 % 152.18/22.70 (55) op(e1, e0) = all_52_14 % 152.18/22.70 (56) ~ (all_56_1 = e1) | all_56_5 = e3 % 152.18/22.70 (57) all_54_14 = all_52_11 % 152.18/22.70 (58) all_58_1 = all_52_4 % 152.18/22.70 (59) all_58_13 = all_52_7 % 152.18/22.70 (60) all_58_4 = e0 | all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0 % 152.18/22.70 (61) op(e2, all_8_2) = all_56_10 % 152.18/22.70 (62) op(e3, e3) = all_10_2 % 152.18/22.70 (63) ~ (all_52_8 = all_6_2) % 152.18/22.70 (64) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0 % 152.18/22.70 (65) all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1 % 152.18/22.70 (66) ~ (all_56_21 = e3) | all_56_17 = e1 % 152.18/22.70 (67) all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2 % 152.18/22.70 (68) ~ (e1 = e0) % 152.18/22.70 (69) ~ (all_52_1 = all_8_2) % 152.18/22.70 (70) all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2 % 152.18/22.70 (71) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 152.18/22.70 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 152.18/22.70 (72) ~ (all_52_3 = all_10_2) % 152.18/22.70 (73) all_54_3 = all_52_12 % 152.18/22.70 (74) all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0 % 152.18/22.70 (75) ~ (all_52_3 = all_52_7) % 152.18/22.70 (76) ~ (all_56_11 = e3) | all_56_9 = e2 % 152.18/22.70 (77) ~ (all_52_2 = all_52_6) % 152.18/22.70 (78) op(e0, all_4_1) = all_4_0 % 152.18/22.70 (79) all_56_7 = all_52_12 % 152.18/22.70 (80) ~ (all_10_1 = e2) % 152.18/22.70 (81) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0 % 152.18/22.70 (82) op(e0, e1) = all_52_11 % 152.18/22.70 (83) ~ (all_52_1 = all_52_13) % 152.18/22.70 (84) ~ (all_52_7 = all_4_2) % 152.18/22.70 (85) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0 % 152.18/22.70 (86) all_58_8 = all_6_2 % 152.18/22.70 (87) all_54_6 = all_52_9 % 152.18/22.70 (88) ~ (all_52_3 = all_4_2) % 152.18/22.70 (89) ~ (all_52_8 = all_10_2) % 152.18/22.70 (90) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0 % 152.18/22.70 (91) ~ (all_56_1 = e2) | all_56_3 = e3 % 152.18/22.70 (92) ~ (all_56_1 = e0) | all_56_7 = e3 % 152.18/22.70 (93) all_56_5 = all_52_8 % 152.18/22.70 (94) ~ (all_52_9 = all_52_13) % 152.18/22.70 (95) ~ (all_52_2 = all_52_3) % 152.18/22.70 (96) op(e1, all_6_1) = all_6_0 % 152.18/22.70 (97) op(all_4_2, all_4_2) = all_4_1 % 152.18/22.70 (98) ~ (all_52_3 = all_52_11) % 152.18/22.70 (99) all_58_3 = all_8_2 % 152.18/22.70 (100) all_56_3 = all_52_4 % 152.18/22.70 (101) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0 % 152.18/22.70 (102) ~ (all_52_11 = all_4_2) % 152.18/22.70 (103) ~ (all_52_1 = all_52_3) % 152.18/22.70 (104) ~ (all_52_6 = all_52_7) % 152.18/22.70 (105) all_56_31 = all_4_2 % 152.18/22.70 (106) all_58_11 = all_52_14 % 152.18/22.70 (107) all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3 % 152.18/22.70 (108) ~ (all_52_2 = all_52_14) % 152.18/22.70 (109) op(all_6_2, all_6_2) = all_6_1 % 152.18/22.70 (110) all_56_1 = e3 | all_56_11 = e2 | all_56_21 = e1 | all_56_31 = e0 % 152.18/22.70 (111) ~ (all_52_13 = all_4_2) % 152.18/22.70 (112) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0 % 152.18/22.70 (113) ~ (all_52_8 = all_52_11) % 152.18/22.70 (114) all_54_13 = all_52_7 % 152.18/22.70 (115) all_54_2 = all_52_8 % 152.18/22.70 (116) ~ (all_52_13 = all_52_14) % 152.18/22.70 (117) all_56_23 = all_52_14 % 152.18/22.70 (118) all_54_8 = all_52_2 % 152.18/22.70 (119) op(e1, e1) = all_6_2 % 152.18/22.70 (120) ~ (all_52_6 = all_8_2) % 152.18/22.70 (121) op(e0, e3) = all_52_3 % 152.18/22.70 (122) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0 % 152.18/22.70 (123) all_58_15 = all_4_2 % 152.18/22.70 (124) all_56_29 = all_52_11 % 152.18/22.70 (125) all_58_2 = all_52_1 % 152.18/22.70 (126) all_58_7 = all_52_6 % 152.18/22.70 (127) all_58_10 = all_52_13 % 152.18/22.70 (128) all_40_1 = all_6_1 % 152.18/22.70 (129) ~ (all_52_12 = all_4_2) % 152.18/22.70 (130) op(all_10_2, all_10_2) = all_10_1 % 152.18/22.70 (131) ~ (all_56_11 = e0) | all_56_15 = e2 % 152.18/22.70 (132) all_58_0 = all_10_2 % 152.18/22.70 (133) op(e1, all_6_2) = all_56_20 % 152.18/22.70 (134) all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1 % 152.18/22.70 (135) all_58_1 = e0 | all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0 % 152.18/22.70 (136) ~ (all_52_12 = all_52_14) % 152.18/22.70 (137) op(e1, all_52_9) = all_56_12 % 152.18/22.70 (138) ~ (e3 = e1) % 152.18/22.70 (139) op(e2, e2) = all_8_2 % 152.18/22.70 (140) ~ (all_52_4 = all_52_12) % 152.18/22.70 (141) ~ (all_52_2 = all_6_2) % 152.18/22.70 (142) ~ (all_52_8 = all_52_12) % 152.18/22.70 (143) ~ (all_52_1 = all_52_2) % 152.18/22.70 (144) ~ (all_56_21 = e0) | all_56_23 = e1 % 152.18/22.70 (145) ~ (all_52_6 = all_6_2) % 152.18/22.70 (146) ~ (all_40_1 = e0) | ~ (all_40_2 = e2) % 152.18/22.70 (147) ~ (all_52_14 = all_6_2) % 152.18/22.70 (148) all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0 % 152.18/22.70 (149) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0 % 152.18/22.70 (150) ~ (all_52_2 = all_10_2) % 152.18/22.70 (151) ~ (all_52_4 = all_10_2) % 152.18/22.70 (152) all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3 % 152.18/22.70 (153) ~ (all_52_4 = all_8_2) % 152.18/22.70 (154) op(all_8_2, all_8_2) = all_8_1 % 152.18/22.70 (155) ~ (all_52_4 = all_52_6) % 152.18/22.70 (156) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 152.18/22.70 (157) all_58_14 = all_52_11 % 152.18/22.70 (158) all_56_19 = all_52_6 % 152.18/22.70 (159) ~ (all_52_12 = all_10_2) % 152.18/22.70 (160) ~ (all_4_0 = e2) % 152.18/22.70 (161) ~ (all_4_0 = e3) % 152.18/22.70 (162) all_56_9 = all_52_1 % 152.18/22.70 (163) all_56_15 = all_52_13 % 152.18/22.70 (164) ~ (all_52_1 = all_10_2) % 152.18/22.70 (165) all_58_12 = all_52_3 % 152.18/22.70 (166) all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3 % 152.18/22.70 (167) all_54_11 = all_52_14 % 152.18/22.70 (168) ~ (all_56_31 = e3) | all_56_25 = e0 % 152.18/22.70 % 152.18/22.70 Begin of proof % 152.18/22.70 | % 152.18/22.70 | BETA: splitting (13) gives: % 152.18/22.70 | % 152.18/22.70 | Case 1: % 152.18/22.70 | | % 152.18/22.70 | | (169) ~ (all_56_31 = e1) % 152.18/22.70 | | % 152.18/22.70 | | REDUCE: (105), (169) imply: % 152.18/22.70 | | (170) ~ (all_4_2 = e1) % 152.18/22.70 | | % 152.18/22.70 | | BETA: splitting (168) gives: % 152.18/22.70 | | % 152.18/22.70 | | Case 1: % 152.18/22.70 | | | % 152.18/22.70 | | | (171) ~ (all_56_31 = e3) % 152.18/22.70 | | | % 152.18/22.70 | | | REDUCE: (105), (171) imply: % 152.18/22.70 | | | (172) ~ (all_4_2 = e3) % 152.18/22.70 | | | % 152.18/22.70 | | | REF_CLOSE: (1), (8), (10), (15), (16), (17), (18), (19), (20), (21), (23), % 152.18/22.70 | | | (25), (27), (29), (30), (33), (34), (35), (36), (37), (38), % 152.18/22.70 | | | (39), (40), (41), (42), (43), (44), (45), (48), (50), (51), % 152.18/22.70 | | | (52), (53), (55), (60), (62), (66), (67), (69), (70), (71), % 152.18/22.70 | | | (73), (74), (77), (79), (84), (86), (88), (89), (90), (91), % 152.18/22.70 | | | (92), (96), (99), (100), (101), (102), (104), (105), (106), % 152.18/22.70 | | | (108), (109), (110), (111), (112), (114), (116), (117), (119), % 152.18/22.70 | | | (120), (122), (123), (125), (126), (127), (128), (129), (130), % 152.18/22.70 | | | (131), (132), (133), (136), (137), (138), (139), (140), (141), % 152.18/22.70 | | | (144), (145), (146), (147), (148), (150), (151), (153), (155), % 152.18/22.70 | | | (156), (157), (158), (159), (163), (164), (165), (167), (170), % 152.18/22.70 | | | (172) are inconsistent by sub-proof #504. % 152.18/22.70 | | | % 152.18/22.70 | | Case 2: % 152.18/22.70 | | | % 152.18/22.70 | | | (173) all_56_31 = e3 % 152.18/22.70 | | | (174) all_56_25 = e0 % 152.18/22.70 | | | % 152.18/22.70 | | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (11), (12), (14), (16), % 152.18/22.70 | | | (18), (19), (21), (22), (23), (24), (25), (26), (27), (30), % 152.18/22.70 | | | (31), (32), (33), (35), (36), (37), (38), (39), (42), (44), % 152.18/22.70 | | | (45), (46), (47), (48), (49), (50), (51), (52), (53), (56), % 152.18/22.70 | | | (57), (58), (59), (60), (61), (62), (63), (64), (65), (66), % 152.18/22.70 | | | (68), (69), (71), (72), (75), (76), (77), (78), (80), (82), % 152.18/22.70 | | | (83), (84), (85), (87), (88), (91), (93), (94), (95), (97), % 152.18/22.70 | | | (98), (99), (101), (102), (103), (104), (105), (106), (107), % 152.18/22.70 | | | (109), (110), (113), (115), (118), (120), (122), (123), (125), % 152.18/22.70 | | | (126), (127), (130), (131), (132), (134), (135), (136), (139), % 152.18/22.70 | | | (140), (141), (142), (143), (144), (145), (147), (149), (150), % 152.18/22.70 | | | (152), (153), (154), (155), (156), (157), (158), (160), (162), % 152.18/22.70 | | | (164), (165), (166), (167), (170), (173), (174) are % 152.18/22.70 | | | inconsistent by sub-proof #503. % 152.18/22.70 | | | % 152.18/22.70 | | End of split % 152.18/22.70 | | % 152.18/22.70 | Case 2: % 152.18/22.70 | | % 152.18/22.70 | | (175) all_56_31 = e1 % 152.18/22.70 | | (176) all_56_29 = e0 % 152.18/22.70 | | % 152.18/22.70 | | COMBINE_EQS: (124), (176) imply: % 152.18/22.70 | | (177) all_52_11 = e0 % 152.18/22.70 | | % 152.18/22.70 | | COMBINE_EQS: (105), (175) imply: % 152.18/22.70 | | (178) all_4_2 = e1 % 152.18/22.70 | | % 152.18/22.70 | | REDUCE: (98), (177) imply: % 152.18/22.70 | | (179) ~ (all_52_3 = e0) % 152.18/22.70 | | % 152.18/22.70 | | REDUCE: (6), (177) imply: % 152.18/22.70 | | (180) ~ (all_52_7 = e0) % 152.18/22.70 | | % 152.18/22.70 | | REDUCE: (3), (177) imply: % 152.18/22.70 | | (181) ~ (all_6_2 = e0) % 152.18/22.70 | | % 152.18/22.70 | | SIMP: (181) implies: % 152.18/22.70 | | (182) ~ (all_6_2 = e0) % 152.18/22.70 | | % 152.18/22.70 | | REDUCE: (97), (178) imply: % 152.18/22.70 | | (183) op(e1, e1) = all_4_1 % 152.18/22.70 | | % 152.18/22.70 | | REF_CLOSE: (15), (16), (19), (28), (37), (44), (45), (52), (54), (66), (71), % 152.18/22.70 | | (78), (81), (90), (95), (104), (109), (114), (119), (121), (133), % 152.18/22.70 | | (158), (160), (161), (179), (180), (182), (183) are inconsistent % 152.18/22.70 | | by sub-proof #499. % 152.18/22.70 | | % 152.18/22.70 | End of split % 152.18/22.70 | % 152.18/22.70 End of proof % 152.18/22.70 % 152.18/22.70 Sub-proof #499 shows that the following formulas are inconsistent: % 152.18/22.70 ---------------------------------------------------------------- % 152.18/22.70 (1) op(e1, all_6_1) = e3 % 152.18/22.70 (2) all_54_10 = all_6_2 % 152.18/22.70 (3) ~ (all_56_21 = e2) | all_56_19 = e1 % 152.18/22.70 (4) all_54_12 = all_52_3 % 152.18/22.70 (5) ~ (all_6_1 = e3) % 152.18/22.70 (6) all_56_21 = all_6_2 % 152.18/22.70 (7) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 152.18/22.70 (8) all_56_17 = all_52_2 % 152.18/22.70 (9) op(e0, e2) = all_52_7 % 152.18/22.70 (10) ~ (all_56_21 = e3) | all_56_17 = e1 % 152.18/22.70 (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 152.18/22.70 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 152.18/22.70 (12) ~ (all_6_2 = e0) % 152.18/22.70 (13) op(e0, all_4_1) = all_4_0 % 152.18/22.70 (14) ~ (all_52_3 = e0) % 152.18/22.70 (15) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0 % 152.18/22.70 (16) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0 % 152.18/22.70 (17) ~ (all_52_2 = all_52_3) % 152.18/22.70 (18) ~ (all_52_6 = all_52_7) % 152.18/22.70 (19) op(all_6_2, all_6_2) = all_6_1 % 152.18/22.70 (20) all_54_13 = all_52_7 % 152.18/22.70 (21) op(e1, e1) = all_6_2 % 152.18/22.70 (22) op(e0, e3) = all_52_3 % 152.18/22.70 (23) op(e1, e1) = all_4_1 % 152.18/22.70 (24) op(e1, all_6_2) = all_56_20 % 152.18/22.70 (25) ~ (all_52_7 = e0) % 152.18/22.70 (26) all_56_19 = all_52_6 % 152.18/22.70 (27) ~ (all_4_0 = e2) % 152.18/22.70 (28) ~ (all_4_0 = e3) % 152.18/22.70 % 152.18/22.70 Begin of proof % 152.18/22.70 | % 152.18/22.70 | GROUND_INST: instantiating (11) with all_6_2, all_4_1, e1, e1, simplifying % 152.18/22.70 | with (21), (23) gives: % 152.18/22.70 | (29) all_6_2 = all_4_1 % 152.18/22.70 | % 152.18/22.70 | COMBINE_EQS: (2), (29) imply: % 152.18/22.70 | (30) all_54_10 = all_4_1 % 152.18/22.70 | % 152.18/22.70 | COMBINE_EQS: (6), (29) imply: % 152.18/22.70 | (31) all_56_21 = all_4_1 % 152.18/22.70 | % 152.18/22.70 | REDUCE: (12), (29) imply: % 152.18/22.70 | (32) ~ (all_4_1 = e0) % 152.18/22.70 | % 152.18/22.70 | REDUCE: (19), (29) imply: % 152.18/22.70 | (33) op(all_4_1, all_4_1) = all_6_1 % 152.18/22.70 | % 152.18/22.70 | REDUCE: (24), (29) imply: % 152.18/22.70 | (34) op(e1, all_4_1) = all_56_20 % 152.18/22.70 | % 152.18/22.70 | BETA: splitting (3) gives: % 152.18/22.70 | % 152.18/22.70 | Case 1: % 152.18/22.70 | | % 152.18/22.70 | | (35) ~ (all_56_21 = e2) % 152.18/22.70 | | % 152.18/22.70 | | REDUCE: (31), (35) imply: % 152.18/22.70 | | (36) ~ (all_4_1 = e2) % 152.18/22.70 | | % 152.18/22.70 | | BETA: splitting (10) gives: % 152.18/22.70 | | % 152.18/22.70 | | Case 1: % 152.18/22.70 | | | % 152.18/22.70 | | | (37) ~ (all_56_21 = e3) % 152.18/22.70 | | | % 152.18/22.70 | | | REDUCE: (31), (37) imply: % 152.18/22.70 | | | (38) ~ (all_4_1 = e3) % 152.18/22.70 | | | % 152.18/22.70 | | | REF_CLOSE: (1), (5), (7), (11), (23), (30), (32), (33), (34), (36), (38) % 152.18/22.70 | | | are inconsistent by sub-proof #502. % 152.18/22.70 | | | % 152.18/22.70 | | Case 2: % 152.18/22.70 | | | % 152.18/22.70 | | | (39) all_56_21 = e3 % 152.18/22.70 | | | (40) all_56_17 = e1 % 152.18/22.70 | | | % 152.18/22.70 | | | REF_CLOSE: (4), (8), (11), (13), (14), (15), (17), (22), (27), (28), (31), % 152.18/22.70 | | | (39), (40) are inconsistent by sub-proof #520. % 152.18/22.70 | | | % 152.18/22.70 | | End of split % 152.18/22.70 | | % 152.18/22.70 | Case 2: % 152.18/22.70 | | % 152.18/22.70 | | (41) all_56_21 = e2 % 152.18/22.70 | | (42) all_56_19 = e1 % 152.18/22.70 | | % 152.18/22.70 | | REF_CLOSE: (9), (11), (13), (16), (18), (20), (25), (26), (27), (28), (31), % 152.18/22.70 | | (41), (42) are inconsistent by sub-proof #500. % 152.18/22.70 | | % 152.18/22.70 | End of split % 152.18/22.70 | % 152.18/22.70 End of proof % 152.18/22.70 % 152.18/22.70 Sub-proof #500 shows that the following formulas are inconsistent: % 152.18/22.70 ---------------------------------------------------------------- % 152.18/22.70 (1) op(e0, e2) = all_52_7 % 152.18/22.70 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 152.18/22.70 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 152.18/22.70 (3) op(e0, all_4_1) = all_4_0 % 152.18/22.70 (4) all_56_21 = all_4_1 % 152.18/22.70 (5) all_56_21 = e2 % 152.18/22.70 (6) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0 % 152.18/22.70 (7) all_56_19 = e1 % 152.18/22.70 (8) ~ (all_52_6 = all_52_7) % 152.18/22.70 (9) all_54_13 = all_52_7 % 152.18/22.70 (10) ~ (all_52_7 = e0) % 152.18/22.70 (11) all_56_19 = all_52_6 % 152.18/22.70 (12) ~ (all_4_0 = e2) % 152.18/22.70 (13) ~ (all_4_0 = e3) % 152.18/22.70 % 152.18/22.70 Begin of proof % 152.18/22.70 | % 152.18/22.70 | COMBINE_EQS: (7), (11) imply: % 152.18/22.70 | (14) all_52_6 = e1 % 152.18/22.70 | % 152.18/22.70 | SIMP: (14) implies: % 152.18/22.70 | (15) all_52_6 = e1 % 152.18/22.70 | % 152.18/22.70 | COMBINE_EQS: (4), (5) imply: % 152.18/22.70 | (16) all_4_1 = e2 % 152.18/22.70 | % 152.18/22.70 | SIMP: (16) implies: % 152.18/22.70 | (17) all_4_1 = e2 % 152.18/22.70 | % 152.18/22.70 | REF_CLOSE: (1), (2), (3), (6), (8), (9), (10), (12), (13), (15), (17) are % 152.18/22.70 | inconsistent by sub-proof #501. % 152.18/22.70 | % 152.18/22.70 End of proof % 152.18/22.70 % 152.18/22.70 Sub-proof #501 shows that the following formulas are inconsistent: % 152.18/22.70 ---------------------------------------------------------------- % 152.18/22.70 (1) all_52_6 = e1 % 152.18/22.70 (2) all_4_1 = e2 % 152.18/22.70 (3) op(e0, e2) = all_52_7 % 152.18/22.70 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 152.18/22.70 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 152.18/22.70 (5) op(e0, all_4_1) = all_4_0 % 152.18/22.70 (6) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0 % 152.18/22.70 (7) ~ (all_52_6 = all_52_7) % 152.18/22.70 (8) all_54_13 = all_52_7 % 152.18/22.70 (9) ~ (all_52_7 = e0) % 152.18/22.70 (10) ~ (all_4_0 = e2) % 152.18/22.70 (11) ~ (all_4_0 = e3) % 152.18/22.70 % 152.18/22.70 Begin of proof % 152.18/22.70 | % 152.18/22.70 | REDUCE: (1), (7) imply: % 152.18/22.70 | (12) ~ (all_52_7 = e1) % 152.18/22.70 | % 152.18/22.70 | SIMP: (12) implies: % 152.18/22.70 | (13) ~ (all_52_7 = e1) % 152.18/22.70 | % 152.18/22.70 | REDUCE: (2), (5) imply: % 152.18/22.70 | (14) op(e0, e2) = all_4_0 % 152.18/22.70 | % 152.18/22.70 | REF_CLOSE: (3), (4), (6), (8), (9), (10), (11), (13), (14) are inconsistent by % 152.18/22.70 | sub-proof #518. % 152.18/22.70 | % 152.18/22.70 End of proof % 152.18/22.70 % 152.18/22.70 Sub-proof #502 shows that the following formulas are inconsistent: % 152.18/22.70 ---------------------------------------------------------------- % 152.18/22.70 (1) op(e1, all_6_1) = e3 % 152.18/22.70 (2) ~ (all_4_1 = e0) % 152.18/22.70 (3) ~ (all_4_1 = e3) % 152.18/22.70 (4) op(e1, all_4_1) = all_56_20 % 152.18/22.70 (5) ~ (all_6_1 = e3) % 152.18/22.70 (6) ~ (all_4_1 = e2) % 152.18/22.70 (7) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 152.18/22.70 (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 152.18/22.70 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 152.18/22.70 (9) op(all_4_1, all_4_1) = all_6_1 % 152.18/22.70 (10) all_54_10 = all_4_1 % 152.18/22.70 (11) op(e1, e1) = all_4_1 % 152.18/22.70 % 152.18/22.70 Begin of proof % 152.18/22.70 | % 152.18/22.70 | BETA: splitting (7) gives: % 152.18/22.70 | % 152.18/22.70 | Case 1: % 152.18/22.70 | | % 152.18/22.70 | | (12) all_54_10 = e3 % 152.18/22.70 | | % 152.18/22.70 | | COMBINE_EQS: (10), (12) imply: % 152.18/22.70 | | (13) all_4_1 = e3 % 152.18/22.70 | | % 152.18/22.70 | | REDUCE: (3), (13) imply: % 152.18/22.70 | | (14) $false % 152.18/22.70 | | % 152.18/22.70 | | CLOSE: (14) is inconsistent. % 152.18/22.70 | | % 152.18/22.70 | Case 2: % 152.18/22.70 | | % 152.18/22.70 | | (15) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 152.18/22.70 | | % 152.18/22.70 | | BETA: splitting (15) gives: % 152.18/22.70 | | % 152.18/22.70 | | Case 1: % 152.18/22.70 | | | % 152.18/22.70 | | | (16) all_54_10 = e2 % 152.18/22.70 | | | % 152.18/22.70 | | | COMBINE_EQS: (10), (16) imply: % 152.18/22.70 | | | (17) all_4_1 = e2 % 152.18/22.70 | | | % 152.18/22.70 | | | REDUCE: (6), (17) imply: % 152.18/22.70 | | | (18) $false % 152.18/22.70 | | | % 152.18/22.70 | | | CLOSE: (18) is inconsistent. % 152.18/22.70 | | | % 152.18/22.70 | | Case 2: % 152.18/22.70 | | | % 152.18/22.70 | | | (19) all_54_10 = e1 | all_54_10 = e0 % 152.18/22.70 | | | % 152.18/22.70 | | | BETA: splitting (19) gives: % 152.18/22.70 | | | % 152.18/22.70 | | | Case 1: % 152.18/22.70 | | | | % 152.18/22.70 | | | | (20) all_54_10 = e1 % 152.18/22.70 | | | | % 152.18/22.70 | | | | COMBINE_EQS: (10), (20) imply: % 152.18/22.70 | | | | (21) all_4_1 = e1 % 152.18/22.70 | | | | % 152.18/22.70 | | | | REDUCE: (9), (21) imply: % 152.18/22.70 | | | | (22) op(e1, e1) = all_6_1 % 152.18/22.70 | | | | % 152.18/22.70 | | | | REDUCE: (4), (21) imply: % 152.18/22.70 | | | | (23) op(e1, e1) = all_56_20 % 152.18/22.70 | | | | % 152.18/22.70 | | | | REDUCE: (11), (21) imply: % 152.18/22.70 | | | | (24) op(e1, e1) = e1 % 152.18/22.70 | | | | % 152.18/22.70 | | | | GROUND_INST: instantiating (8) with all_6_1, all_56_20, e1, e1, % 152.18/22.70 | | | | simplifying with (22), (23) gives: % 152.18/22.70 | | | | (25) all_56_20 = all_6_1 % 152.18/22.70 | | | | % 152.18/22.70 | | | | GROUND_INST: instantiating (8) with e1, all_56_20, e1, e1, simplifying % 152.18/22.70 | | | | with (23), (24) gives: % 152.18/22.70 | | | | (26) all_56_20 = e1 % 152.18/22.70 | | | | % 152.18/22.70 | | | | REF_CLOSE: (1), (5), (8), (22), (23), (25), (26) are inconsistent by % 152.18/22.70 | | | | sub-proof #515. % 152.18/22.70 | | | | % 152.18/22.70 | | | Case 2: % 152.18/22.70 | | | | % 152.18/22.70 | | | | (27) all_54_10 = e0 % 152.18/22.70 | | | | % 152.18/22.70 | | | | COMBINE_EQS: (10), (27) imply: % 152.18/22.70 | | | | (28) all_4_1 = e0 % 152.18/22.70 | | | | % 152.18/22.70 | | | | REDUCE: (2), (28) imply: % 152.18/22.70 | | | | (29) $false % 152.18/22.70 | | | | % 152.18/22.70 | | | | CLOSE: (29) is inconsistent. % 152.18/22.70 | | | | % 152.18/22.70 | | | End of split % 152.18/22.70 | | | % 152.18/22.70 | | End of split % 152.18/22.70 | | % 152.18/22.70 | End of split % 152.18/22.70 | % 152.18/22.70 End of proof % 152.18/22.70 % 152.18/22.70 Sub-proof #503 shows that the following formulas are inconsistent: % 152.18/22.70 ---------------------------------------------------------------- % 152.18/22.70 (1) all_56_11 = all_8_2 % 152.18/22.70 (2) op(e0, all_52_13) = all_56_14 % 152.18/22.70 (3) ~ (all_52_11 = all_6_2) % 152.18/22.70 (4) ~ (all_52_4 = all_52_8) % 152.18/22.70 (5) all_56_25 = all_52_3 % 152.18/22.70 (6) ~ (all_52_8 = all_52_9) % 152.18/22.70 (7) all_54_9 = all_52_6 % 152.18/22.70 (8) op(e2, all_8_1) = all_8_0 % 152.18/22.70 (9) ~ (all_8_1 = e1) % 152.18/22.70 (10) ~ (all_52_1 = all_52_9) % 152.18/22.70 (11) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0 % 152.18/22.70 (12) all_54_10 = all_6_2 % 152.18/22.70 (13) ~ (all_6_1 = e2) % 152.18/22.70 (14) ~ (all_56_21 = e2) | all_56_19 = e1 % 152.18/22.70 (15) all_54_0 = all_10_2 % 152.18/22.70 (16) all_56_31 = e3 % 152.18/22.70 (17) all_54_4 = all_52_1 % 152.18/22.70 (18) ~ (all_52_14 = all_4_2) % 152.18/22.70 (19) ~ (all_8_0 = e1) % 152.18/22.70 (20) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0 % 152.18/22.70 (21) all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2 % 152.18/22.70 (22) ~ (all_52_9 = all_8_2) % 152.18/22.70 (23) ~ (all_52_4 = all_52_7) % 152.18/22.70 (24) ~ (all_8_1 = e3) % 152.18/22.70 (25) ~ (e3 = e2) % 152.18/22.70 (26) op(e0, e0) = all_4_2 % 152.18/22.70 (27) all_58_4 = all_52_8 % 152.18/22.70 (28) all_54_5 = all_8_2 % 152.18/22.71 (29) ~ (all_6_1 = e3) % 152.18/22.71 (30) ~ (all_52_6 = all_52_14) % 152.18/22.71 (31) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 152.18/22.71 (32) all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1 % 152.18/22.71 (33) all_56_21 = all_6_2 % 152.18/22.71 (34) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 152.18/22.71 (35) op(e3, all_52_1) = all_56_8 % 152.18/22.71 (36) ~ (all_52_7 = all_8_2) % 152.18/22.71 (37) all_56_1 = all_10_2 % 152.18/22.71 (38) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0 % 152.18/22.71 (39) all_58_5 = all_52_9 % 152.18/22.71 (40) all_54_1 = all_52_4 % 152.18/22.71 (41) all_56_17 = all_52_2 % 152.18/22.71 (42) all_58_9 = all_52_12 % 152.18/22.71 (43) ~ (all_56_1 = e1) | all_56_5 = e3 % 152.18/22.71 (44) all_54_14 = all_52_11 % 152.18/22.71 (45) all_58_1 = all_52_4 % 152.18/22.71 (46) all_58_13 = all_52_7 % 152.18/22.71 (47) all_58_4 = e0 | all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0 % 152.18/22.71 (48) op(e2, all_8_2) = all_56_10 % 152.18/22.71 (49) op(e3, e3) = all_10_2 % 152.18/22.71 (50) ~ (all_52_8 = all_6_2) % 152.18/22.71 (51) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0 % 152.18/22.71 (52) all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1 % 152.18/22.71 (53) ~ (all_56_21 = e3) | all_56_17 = e1 % 152.18/22.71 (54) ~ (e1 = e0) % 152.18/22.71 (55) ~ (all_52_1 = all_8_2) % 152.18/22.71 (56) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 152.18/22.71 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 152.18/22.71 (57) ~ (all_52_3 = all_10_2) % 152.18/22.71 (58) all_56_25 = e0 % 152.18/22.71 (59) ~ (all_52_3 = all_52_7) % 152.18/22.71 (60) ~ (all_56_11 = e3) | all_56_9 = e2 % 152.18/22.71 (61) ~ (all_52_2 = all_52_6) % 152.18/22.71 (62) op(e0, all_4_1) = all_4_0 % 152.18/22.71 (63) ~ (all_10_1 = e2) % 152.18/22.71 (64) op(e0, e1) = all_52_11 % 152.18/22.71 (65) ~ (all_52_1 = all_52_13) % 152.18/22.71 (66) ~ (all_52_7 = all_4_2) % 152.18/22.71 (67) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0 % 152.18/22.71 (68) ~ (all_4_2 = e1) % 152.18/22.71 (69) all_54_6 = all_52_9 % 152.18/22.71 (70) ~ (all_52_3 = all_4_2) % 152.18/22.71 (71) ~ (all_56_1 = e2) | all_56_3 = e3 % 152.18/22.71 (72) all_56_5 = all_52_8 % 152.18/22.71 (73) ~ (all_52_9 = all_52_13) % 152.18/22.71 (74) ~ (all_52_2 = all_52_3) % 152.18/22.71 (75) op(all_4_2, all_4_2) = all_4_1 % 152.18/22.71 (76) ~ (all_52_3 = all_52_11) % 152.18/22.71 (77) all_58_3 = all_8_2 % 152.18/22.71 (78) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0 % 152.18/22.71 (79) ~ (all_52_11 = all_4_2) % 152.18/22.71 (80) ~ (all_52_1 = all_52_3) % 152.18/22.71 (81) ~ (all_52_6 = all_52_7) % 152.18/22.71 (82) all_56_31 = all_4_2 % 152.18/22.71 (83) all_58_11 = all_52_14 % 152.18/22.71 (84) all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3 % 152.18/22.71 (85) op(all_6_2, all_6_2) = all_6_1 % 152.18/22.71 (86) all_56_1 = e3 | all_56_11 = e2 | all_56_21 = e1 | all_56_31 = e0 % 152.18/22.71 (87) ~ (all_52_8 = all_52_11) % 152.18/22.71 (88) all_54_2 = all_52_8 % 152.18/22.71 (89) all_54_8 = all_52_2 % 152.18/22.71 (90) ~ (all_52_6 = all_8_2) % 152.18/22.71 (91) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0 % 152.18/22.71 (92) all_58_15 = all_4_2 % 152.18/22.71 (93) all_58_2 = all_52_1 % 152.18/22.71 (94) all_58_7 = all_52_6 % 152.18/22.71 (95) all_58_10 = all_52_13 % 152.18/22.71 (96) op(all_10_2, all_10_2) = all_10_1 % 152.18/22.71 (97) ~ (all_56_11 = e0) | all_56_15 = e2 % 152.18/22.71 (98) all_58_0 = all_10_2 % 152.18/22.71 (99) all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1 % 152.18/22.71 (100) all_58_1 = e0 | all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0 % 152.18/22.71 (101) ~ (all_52_12 = all_52_14) % 152.18/22.71 (102) op(e2, e2) = all_8_2 % 152.18/22.71 (103) ~ (all_52_4 = all_52_12) % 152.18/22.71 (104) ~ (all_52_2 = all_6_2) % 152.18/22.71 (105) ~ (all_52_8 = all_52_12) % 152.18/22.71 (106) ~ (all_52_1 = all_52_2) % 152.18/22.71 (107) ~ (all_56_21 = e0) | all_56_23 = e1 % 152.18/22.71 (108) ~ (all_52_6 = all_6_2) % 152.18/22.71 (109) ~ (all_52_14 = all_6_2) % 152.18/22.71 (110) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0 % 152.18/22.71 (111) ~ (all_52_2 = all_10_2) % 152.18/22.71 (112) all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3 % 152.18/22.71 (113) ~ (all_52_4 = all_8_2) % 152.18/22.71 (114) op(all_8_2, all_8_2) = all_8_1 % 152.18/22.71 (115) ~ (all_52_4 = all_52_6) % 152.18/22.71 (116) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 152.18/22.71 (117) all_58_14 = all_52_11 % 152.18/22.71 (118) all_56_19 = all_52_6 % 152.18/22.71 (119) ~ (all_4_0 = e2) % 152.18/22.71 (120) all_56_9 = all_52_1 % 152.18/22.71 (121) ~ (all_52_1 = all_10_2) % 152.18/22.71 (122) all_58_12 = all_52_3 % 152.18/22.71 (123) all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3 % 152.18/22.71 (124) all_54_11 = all_52_14 % 152.18/22.71 % 152.18/22.71 Begin of proof % 152.18/22.71 | % 152.18/22.71 | COMBINE_EQS: (5), (58) imply: % 152.18/22.71 | (125) all_52_3 = e0 % 152.18/22.71 | % 152.18/22.71 | SIMP: (125) implies: % 152.18/22.71 | (126) all_52_3 = e0 % 152.18/22.71 | % 152.18/22.71 | COMBINE_EQS: (16), (82) imply: % 152.18/22.71 | (127) all_4_2 = e3 % 152.18/22.71 | % 152.18/22.71 | COMBINE_EQS: (122), (126) imply: % 152.18/22.71 | (128) all_58_12 = e0 % 152.18/22.71 | % 152.18/22.71 | REDUCE: (74), (126) imply: % 152.18/22.71 | (129) ~ (all_52_2 = e0) % 152.18/22.71 | % 152.18/22.71 | REDUCE: (59), (126) imply: % 152.18/22.71 | (130) ~ (all_52_7 = e0) % 152.18/22.71 | % 152.18/22.71 | SIMP: (130) implies: % 152.18/22.71 | (131) ~ (all_52_7 = e0) % 152.18/22.71 | % 152.18/22.71 | REDUCE: (76), (126) imply: % 152.18/22.71 | (132) ~ (all_52_11 = e0) % 152.18/22.71 | % 152.18/22.71 | SIMP: (132) implies: % 152.18/22.71 | (133) ~ (all_52_11 = e0) % 152.18/22.71 | % 152.18/22.71 | REDUCE: (57), (126) imply: % 152.18/22.71 | (134) ~ (all_10_2 = e0) % 152.18/22.71 | % 152.18/22.71 | SIMP: (134) implies: % 152.18/22.71 | (135) ~ (all_10_2 = e0) % 152.18/22.71 | % 152.18/22.71 | REDUCE: (70), (126), (127) imply: % 152.18/22.71 | (136) ~ (e3 = e0) % 152.18/22.71 | % 152.18/22.71 | SIMP: (136) implies: % 152.18/22.71 | (137) ~ (e3 = e0) % 152.18/22.71 | % 152.18/22.71 | REDUCE: (66), (127) imply: % 152.18/22.71 | (138) ~ (all_52_7 = e3) % 152.18/22.71 | % 152.18/22.71 | REDUCE: (79), (127) imply: % 152.18/22.71 | (139) ~ (all_52_11 = e3) % 152.18/22.71 | % 152.18/22.71 | REDUCE: (18), (127) imply: % 152.18/22.71 | (140) ~ (all_52_14 = e3) % 152.18/22.71 | % 152.18/22.71 | REDUCE: (68), (127) imply: % 152.18/22.71 | (141) ~ (e3 = e1) % 152.18/22.71 | % 152.18/22.71 | REDUCE: (75), (127) imply: % 152.18/22.71 | (142) op(e3, e3) = all_4_1 % 152.18/22.71 | % 152.18/22.71 | REDUCE: (26), (127) imply: % 152.18/22.71 | (143) op(e0, e0) = e3 % 152.18/22.71 | % 152.18/22.71 | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (9), (10), (11), (12), (13), % 152.18/22.71 | (14), (15), (16), (17), (19), (20), (21), (22), (23), (24), (25), % 152.18/22.71 | (27), (28), (29), (30), (31), (32), (33), (34), (35), (36), (37), % 152.18/22.71 | (38), (39), (40), (41), (42), (43), (44), (45), (46), (47), (48), % 152.18/22.71 | (49), (50), (51), (52), (53), (54), (55), (56), (60), (61), (62), % 152.18/22.71 | (63), (64), (65), (67), (68), (69), (71), (72), (73), (75), (77), % 152.18/22.71 | (78), (80), (81), (83), (84), (85), (86), (87), (88), (89), (90), % 152.18/22.71 | (91), (92), (93), (94), (95), (96), (97), (98), (99), (100), (101), % 152.18/22.71 | (102), (103), (104), (105), (106), (107), (108), (109), (110), % 152.18/22.71 | (111), (112), (113), (114), (115), (116), (117), (118), (119), % 152.18/22.71 | (120), (121), (122), (123), (124), (128), (129), (131), (133), % 152.18/22.71 | (135), (137), (138), (139), (140), (141), (142), (143) are % 152.18/22.71 | inconsistent by sub-proof #538. % 152.18/22.71 | % 152.18/22.71 End of proof % 152.18/22.71 % 152.18/22.71 Sub-proof #504 shows that the following formulas are inconsistent: % 152.18/22.71 ---------------------------------------------------------------- % 152.18/22.71 (1) all_56_11 = all_8_2 % 152.18/22.71 (2) all_54_9 = all_52_6 % 152.18/22.71 (3) all_58_6 = all_52_2 % 152.18/22.71 (4) op(e1, all_6_1) = e3 % 152.18/22.71 (5) all_54_10 = all_6_2 % 152.18/22.71 (6) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0 % 152.18/22.71 (7) ~ (all_6_1 = e2) % 152.18/22.71 (8) ~ (all_56_21 = e2) | all_56_19 = e1 % 152.18/22.71 (9) all_40_2 = all_6_2 % 152.18/22.71 (10) all_54_0 = all_10_2 % 152.18/22.71 (11) ~ (all_52_14 = all_4_2) % 152.18/22.71 (12) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0 % 152.18/22.71 (13) ~ (all_52_9 = all_8_2) % 152.18/22.71 (14) ~ (all_52_12 = all_52_13) % 152.18/22.71 (15) ~ (all_52_4 = all_52_7) % 152.18/22.71 (16) op(e0, e0) = all_4_2 % 152.18/22.71 (17) all_58_6 = e0 | all_58_7 = e0 | all_58_8 = e0 | all_58_11 = e0 % 152.18/22.71 (18) all_58_4 = all_52_8 % 152.18/22.71 (19) all_54_5 = all_8_2 % 152.18/22.71 (20) ~ (all_6_1 = e3) % 152.18/22.71 (21) ~ (all_52_6 = all_52_14) % 152.18/22.71 (22) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 152.18/22.71 (23) ~ (all_6_0 = e2) % 152.18/22.71 (24) all_54_15 = all_4_2 % 152.18/22.71 (25) all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1 % 152.18/22.71 (26) ~ (all_10_1 = e1) % 152.18/22.71 (27) all_56_21 = all_6_2 % 152.18/22.71 (28) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 152.18/22.71 (29) all_56_1 = all_10_2 % 152.18/22.71 (30) all_58_5 = all_52_9 % 152.18/22.71 (31) all_54_1 = all_52_4 % 152.18/22.71 (32) all_56_17 = all_52_2 % 152.18/22.71 (33) all_58_9 = all_52_12 % 152.18/22.71 (34) op(e1, e0) = all_52_14 % 152.18/22.71 (35) all_58_4 = e0 | all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0 % 152.18/22.71 (36) op(e3, e3) = all_10_2 % 152.18/22.71 (37) ~ (all_56_21 = e3) | all_56_17 = e1 % 152.18/22.71 (38) all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2 % 152.18/22.71 (39) ~ (all_52_1 = all_8_2) % 152.18/22.71 (40) all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2 % 152.18/22.71 (41) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 152.18/22.71 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 152.18/22.71 (42) all_54_3 = all_52_12 % 152.18/22.71 (43) all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0 % 152.18/22.71 (44) ~ (all_52_2 = all_52_6) % 152.18/22.71 (45) all_56_7 = all_52_12 % 152.18/22.71 (46) ~ (all_52_7 = all_4_2) % 152.18/22.71 (47) ~ (all_4_2 = e1) % 152.18/22.71 (48) all_58_8 = all_6_2 % 152.18/22.71 (49) ~ (all_52_3 = all_4_2) % 152.18/22.71 (50) ~ (all_52_8 = all_10_2) % 152.18/22.71 (51) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0 % 152.18/22.71 (52) ~ (all_56_1 = e2) | all_56_3 = e3 % 152.18/22.71 (53) ~ (all_56_1 = e0) | all_56_7 = e3 % 152.18/22.71 (54) op(e1, all_6_1) = all_6_0 % 152.18/22.71 (55) all_58_3 = all_8_2 % 152.18/22.71 (56) all_56_3 = all_52_4 % 152.18/22.71 (57) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0 % 152.18/22.71 (58) ~ (all_52_11 = all_4_2) % 152.18/22.71 (59) ~ (all_52_6 = all_52_7) % 152.18/22.71 (60) all_56_31 = all_4_2 % 152.18/22.71 (61) all_58_11 = all_52_14 % 152.18/22.71 (62) ~ (all_52_2 = all_52_14) % 152.18/22.71 (63) op(all_6_2, all_6_2) = all_6_1 % 152.18/22.71 (64) all_56_1 = e3 | all_56_11 = e2 | all_56_21 = e1 | all_56_31 = e0 % 152.18/22.71 (65) ~ (all_52_13 = all_4_2) % 152.18/22.71 (66) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0 % 152.18/22.71 (67) all_54_13 = all_52_7 % 152.18/22.71 (68) ~ (all_52_13 = all_52_14) % 152.18/22.71 (69) all_56_23 = all_52_14 % 152.18/22.71 (70) op(e1, e1) = all_6_2 % 152.18/22.71 (71) ~ (all_52_6 = all_8_2) % 152.18/22.71 (72) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0 % 152.18/22.71 (73) all_58_15 = all_4_2 % 152.18/22.71 (74) all_58_2 = all_52_1 % 152.18/22.71 (75) ~ (all_4_2 = e3) % 152.18/22.71 (76) all_58_7 = all_52_6 % 152.18/22.71 (77) all_58_10 = all_52_13 % 152.18/22.71 (78) all_40_1 = all_6_1 % 152.18/22.71 (79) ~ (all_52_12 = all_4_2) % 152.18/22.71 (80) op(all_10_2, all_10_2) = all_10_1 % 152.18/22.71 (81) ~ (all_56_11 = e0) | all_56_15 = e2 % 152.18/22.71 (82) all_58_0 = all_10_2 % 152.18/22.71 (83) op(e1, all_6_2) = all_56_20 % 152.18/22.71 (84) ~ (all_52_12 = all_52_14) % 152.18/22.71 (85) op(e1, all_52_9) = all_56_12 % 152.18/22.71 (86) ~ (e3 = e1) % 152.18/22.71 (87) op(e2, e2) = all_8_2 % 152.18/22.71 (88) ~ (all_52_4 = all_52_12) % 152.18/22.71 (89) ~ (all_52_2 = all_6_2) % 152.18/22.71 (90) ~ (all_56_21 = e0) | all_56_23 = e1 % 152.18/22.71 (91) ~ (all_52_6 = all_6_2) % 152.18/22.71 (92) ~ (all_40_1 = e0) | ~ (all_40_2 = e2) % 152.18/22.71 (93) ~ (all_52_14 = all_6_2) % 152.18/22.71 (94) all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0 % 152.18/22.71 (95) ~ (all_52_2 = all_10_2) % 152.18/22.71 (96) ~ (all_52_4 = all_10_2) % 152.18/22.71 (97) ~ (all_52_4 = all_8_2) % 152.18/22.71 (98) ~ (all_52_4 = all_52_6) % 152.18/22.71 (99) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 152.18/22.71 (100) all_58_14 = all_52_11 % 152.18/22.71 (101) all_56_19 = all_52_6 % 152.18/22.71 (102) ~ (all_52_12 = all_10_2) % 152.18/22.71 (103) all_56_15 = all_52_13 % 152.18/22.71 (104) ~ (all_52_1 = all_10_2) % 152.18/22.71 (105) all_58_12 = all_52_3 % 152.18/22.71 (106) all_54_11 = all_52_14 % 152.18/22.71 % 152.18/22.71 Begin of proof % 152.18/22.71 | % 152.18/22.71 | BETA: splitting (90) gives: % 152.18/22.71 | % 152.18/22.71 | Case 1: % 152.18/22.71 | | % 152.18/22.71 | | (107) ~ (all_56_21 = e0) % 152.18/22.71 | | % 152.18/22.71 | | REDUCE: (27), (107) imply: % 152.18/22.71 | | (108) ~ (all_6_2 = e0) % 152.18/22.71 | | % 152.18/22.71 | | BETA: splitting (8) gives: % 152.18/22.71 | | % 152.18/22.71 | | Case 1: % 152.18/22.71 | | | % 152.18/22.71 | | | (109) ~ (all_56_21 = e2) % 152.18/22.71 | | | % 152.18/22.71 | | | REDUCE: (27), (109) imply: % 152.18/22.71 | | | (110) ~ (all_6_2 = e2) % 152.18/22.71 | | | % 152.18/22.71 | | | BETA: splitting (81) gives: % 152.18/22.71 | | | % 152.18/22.71 | | | Case 1: % 152.18/22.71 | | | | % 152.18/22.71 | | | | (111) ~ (all_56_11 = e0) % 152.18/22.71 | | | | % 152.18/22.71 | | | | REDUCE: (1), (111) imply: % 152.18/22.71 | | | | (112) ~ (all_8_2 = e0) % 152.18/22.71 | | | | % 152.18/22.71 | | | | BETA: splitting (37) gives: % 152.18/22.71 | | | | % 152.18/22.71 | | | | Case 1: % 152.18/22.71 | | | | | % 152.18/22.71 | | | | | (113) ~ (all_56_21 = e3) % 152.18/22.71 | | | | | % 152.18/22.71 | | | | | REDUCE: (27), (113) imply: % 152.18/22.71 | | | | | (114) ~ (all_6_2 = e3) % 152.18/22.71 | | | | | % 152.18/22.71 | | | | | REF_CLOSE: (4), (5), (20), (28), (41), (63), (70), (83), (108), (110), % 152.18/22.71 | | | | | (114) are inconsistent by sub-proof #514. % 152.18/22.71 | | | | | % 152.18/22.71 | | | | Case 2: % 152.18/22.71 | | | | | % 152.18/22.71 | | | | | (115) all_56_21 = e3 % 152.18/22.71 | | | | | (116) all_56_17 = e1 % 152.18/22.71 | | | | | % 152.18/22.71 | | | | | REF_CLOSE: (1), (2), (7), (10), (11), (12), (14), (16), (20), (21), % 152.18/22.71 | | | | | (22), (23), (25), (26), (27), (29), (30), (32), (33), (34), % 152.18/22.71 | | | | | (36), (41), (43), (44), (45), (53), (54), (55), (57), (60), % 152.18/22.71 | | | | | (61), (62), (63), (64), (68), (71), (73), (74), (77), (80), % 152.18/22.71 | | | | | (84), (85), (89), (91), (95), (104), (106), (112), (115), % 152.18/22.71 | | | | | (116) are inconsistent by sub-proof #669. % 152.18/22.71 | | | | | % 152.18/22.71 | | | | End of split % 152.18/22.71 | | | | % 152.18/22.71 | | | Case 2: % 152.18/22.71 | | | | % 152.18/22.71 | | | | (117) all_56_15 = e2 % 152.18/22.71 | | | | (118) all_56_11 = e0 % 152.18/22.71 | | | | % 152.18/22.71 | | | | COMBINE_EQS: (1), (118) imply: % 152.18/22.71 | | | | (119) all_8_2 = e0 % 152.18/22.71 | | | | % 152.18/22.71 | | | | COMBINE_EQS: (103), (117) imply: % 152.18/22.71 | | | | (120) all_52_13 = e2 % 152.18/22.71 | | | | % 152.18/22.71 | | | | REDUCE: (39), (119) imply: % 152.18/22.71 | | | | (121) ~ (all_52_1 = e0) % 152.18/22.71 | | | | % 152.18/22.71 | | | | REDUCE: (97), (119) imply: % 152.18/22.71 | | | | (122) ~ (all_52_4 = e0) % 152.18/22.71 | | | | % 152.18/22.71 | | | | REDUCE: (13), (119) imply: % 152.18/22.71 | | | | (123) ~ (all_52_9 = e0) % 152.18/22.71 | | | | % 152.18/22.71 | | | | REDUCE: (14), (120) imply: % 152.18/22.71 | | | | (124) ~ (all_52_12 = e2) % 152.18/22.71 | | | | % 152.18/22.71 | | | | REDUCE: (68), (120) imply: % 152.18/22.71 | | | | (125) ~ (all_52_14 = e2) % 152.18/22.71 | | | | % 152.18/22.71 | | | | SIMP: (125) implies: % 152.18/22.71 | | | | (126) ~ (all_52_14 = e2) % 152.18/22.71 | | | | % 152.18/22.71 | | | | REDUCE: (65), (120) imply: % 152.18/22.71 | | | | (127) ~ (all_4_2 = e2) % 152.18/22.71 | | | | % 152.18/22.71 | | | | SIMP: (127) implies: % 152.18/22.71 | | | | (128) ~ (all_4_2 = e2) % 152.18/22.71 | | | | % 152.18/22.71 | | | | BETA: splitting (66) gives: % 152.18/22.71 | | | | % 152.18/22.71 | | | | Case 1: % 152.18/22.71 | | | | | % 152.18/22.71 | | | | | (129) all_54_15 = e3 % 152.18/22.71 | | | | | % 152.18/22.71 | | | | | REF_CLOSE: (24), (75), (129) are inconsistent by sub-proof #740. % 152.18/22.71 | | | | | % 152.18/22.71 | | | | Case 2: % 152.18/22.71 | | | | | % 152.18/22.71 | | | | | (130) all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0 % 152.18/22.71 | | | | | % 152.18/22.71 | | | | | BETA: splitting (130) gives: % 152.18/22.71 | | | | | % 152.18/22.71 | | | | | Case 1: % 152.18/22.71 | | | | | | % 152.18/22.71 | | | | | | (131) all_54_15 = e2 % 152.18/22.71 | | | | | | % 152.18/22.71 | | | | | | REF_CLOSE: (24), (128), (131) are inconsistent by sub-proof #739. % 152.18/22.71 | | | | | | % 152.18/22.71 | | | | | Case 2: % 152.18/22.71 | | | | | | % 152.18/22.71 | | | | | | (132) ~ (all_54_15 = e2) % 152.18/22.71 | | | | | | (133) all_54_15 = e1 | all_54_15 = e0 % 152.18/22.71 | | | | | | % 152.18/22.71 | | | | | | BETA: splitting (133) gives: % 152.18/22.71 | | | | | | % 152.18/22.71 | | | | | | Case 1: % 152.18/22.71 | | | | | | | % 152.18/22.71 | | | | | | | (134) all_54_15 = e1 % 152.18/22.71 | | | | | | | % 152.18/22.71 | | | | | | | REF_CLOSE: (24), (47), (134) are inconsistent by sub-proof #738. % 152.18/22.71 | | | | | | | % 152.18/22.71 | | | | | | Case 2: % 152.18/22.71 | | | | | | | % 152.18/22.71 | | | | | | | (135) all_54_15 = e0 % 152.18/22.71 | | | | | | | % 152.18/22.71 | | | | | | | COMBINE_EQS: (24), (135) imply: % 152.18/22.71 | | | | | | | (136) all_4_2 = e0 % 152.18/22.71 | | | | | | | % 152.18/22.71 | | | | | | | SIMP: (136) implies: % 152.18/22.71 | | | | | | | (137) all_4_2 = e0 % 152.18/22.71 | | | | | | | % 152.18/22.71 | | | | | | | REDUCE: (49), (137) imply: % 152.18/22.71 | | | | | | | (138) ~ (all_52_3 = e0) % 152.18/22.71 | | | | | | | % 152.18/22.71 | | | | | | | REDUCE: (46), (137) imply: % 152.18/22.71 | | | | | | | (139) ~ (all_52_7 = e0) % 152.18/22.71 | | | | | | | % 152.18/22.71 | | | | | | | REDUCE: (58), (137) imply: % 152.18/22.71 | | | | | | | (140) ~ (all_52_11 = e0) % 152.18/22.71 | | | | | | | % 152.18/22.71 | | | | | | | REDUCE: (79), (137) imply: % 152.18/22.71 | | | | | | | (141) ~ (all_52_12 = e0) % 152.18/22.71 | | | | | | | % 152.18/22.71 | | | | | | | REDUCE: (128), (137) imply: % 152.18/22.71 | | | | | | | (142) ~ (e2 = e0) % 152.18/22.71 | | | | | | | % 152.18/22.71 | | | | | | | SIMP: (142) implies: % 152.18/22.71 | | | | | | | (143) ~ (e2 = e0) % 152.18/22.71 | | | | | | | % 152.18/22.71 | | | | | | | REDUCE: (47), (137) imply: % 152.18/22.71 | | | | | | | (144) ~ (e1 = e0) % 152.18/22.71 | | | | | | | % 152.18/22.71 | | | | | | | SIMP: (144) implies: % 152.18/22.71 | | | | | | | (145) ~ (e1 = e0) % 152.18/22.71 | | | | | | | % 152.18/22.71 | | | | | | | REF_CLOSE: (3), (4), (5), (6), (10), (12), (15), (17), (18), (20), % 152.18/22.71 | | | | | | | (22), (27), (28), (29), (30), (31), (32), (35), (37), % 152.18/22.71 | | | | | | | (38), (40), (41), (42), (45), (48), (50), (51), (52), % 152.18/22.71 | | | | | | | (53), (56), (59), (61), (62), (63), (67), (70), (72), % 152.18/22.71 | | | | | | | (74), (76), (82), (83), (84), (88), (89), (93), (94), % 152.18/22.71 | | | | | | | (96), (98), (100), (102), (105), (106), (108), (110), % 152.18/22.71 | | | | | | | (121), (122), (123), (124), (126), (138), (139), (140), % 152.18/22.71 | | | | | | | (141), (143), (145) are inconsistent by sub-proof #510. % 152.18/22.71 | | | | | | | % 152.18/22.71 | | | | | | End of split % 152.18/22.71 | | | | | | % 152.18/22.71 | | | | | End of split % 152.18/22.71 | | | | | % 152.18/22.71 | | | | End of split % 152.18/22.71 | | | | % 152.18/22.71 | | | End of split % 152.18/22.71 | | | % 152.18/22.71 | | Case 2: % 152.18/22.71 | | | % 152.18/22.71 | | | (146) all_56_21 = e2 % 152.18/22.71 | | | (147) all_56_19 = e1 % 152.18/22.71 | | | % 152.18/22.71 | | | COMBINE_EQS: (101), (147) imply: % 152.18/22.71 | | | (148) all_52_6 = e1 % 152.18/22.71 | | | % 152.18/22.71 | | | SIMP: (148) implies: % 152.18/22.71 | | | (149) all_52_6 = e1 % 152.18/22.71 | | | % 152.18/22.71 | | | COMBINE_EQS: (27), (146) imply: % 152.18/22.71 | | | (150) all_6_2 = e2 % 152.18/22.71 | | | % 152.18/22.71 | | | SIMP: (150) implies: % 152.18/22.71 | | | (151) all_6_2 = e2 % 152.18/22.71 | | | % 152.18/22.71 | | | REF_CLOSE: (7), (9), (19), (20), (41), (63), (71), (78), (87), (92), (99), % 152.18/22.71 | | | (149), (151) are inconsistent by sub-proof #506. % 152.18/22.71 | | | % 152.18/22.71 | | End of split % 152.18/22.71 | | % 152.18/22.71 | Case 2: % 152.18/22.71 | | % 152.18/22.71 | | (152) all_56_23 = e1 % 152.18/22.71 | | (153) all_56_21 = e0 % 152.18/22.71 | | % 152.18/22.71 | | COMBINE_EQS: (27), (153) imply: % 152.18/22.71 | | (154) all_6_2 = e0 % 152.18/22.71 | | % 152.18/22.71 | | SIMP: (154) implies: % 152.18/22.71 | | (155) all_6_2 = e0 % 152.18/22.71 | | % 152.18/22.71 | | COMBINE_EQS: (69), (152) imply: % 152.18/22.71 | | (156) all_52_14 = e1 % 152.18/22.71 | | % 152.18/22.71 | | SIMP: (156) implies: % 152.18/22.71 | | (157) all_52_14 = e1 % 152.18/22.71 | | % 152.18/22.71 | | REDUCE: (11), (157) imply: % 152.18/22.71 | | (158) ~ (all_4_2 = e1) % 152.18/22.71 | | % 152.18/22.71 | | REDUCE: (63), (155) imply: % 152.18/22.71 | | (159) op(e0, e0) = all_6_1 % 152.18/22.71 | | % 152.18/22.71 | | REDUCE: (83), (155) imply: % 152.18/22.71 | | (160) op(e1, e0) = all_56_20 % 152.18/22.71 | | % 152.18/22.71 | | REDUCE: (34), (157) imply: % 152.18/22.71 | | (161) op(e1, e0) = e1 % 152.18/22.71 | | % 152.18/22.71 | | REF_CLOSE: (4), (7), (16), (20), (24), (41), (47), (66), (86), (159), (160), % 152.18/22.71 | | (161) are inconsistent by sub-proof #505. % 152.18/22.71 | | % 152.18/22.71 | End of split % 152.18/22.71 | % 152.18/22.71 End of proof % 152.18/22.71 % 152.18/22.71 Sub-proof #505 shows that the following formulas are inconsistent: % 152.18/22.71 ---------------------------------------------------------------- % 152.18/22.71 (1) op(e1, e0) = e1 % 152.18/22.71 (2) op(e1, all_6_1) = e3 % 152.18/22.71 (3) ~ (all_6_1 = e2) % 152.18/22.71 (4) op(e0, e0) = all_4_2 % 152.18/22.71 (5) ~ (all_6_1 = e3) % 152.18/22.71 (6) all_54_15 = all_4_2 % 152.18/22.71 (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 152.18/22.71 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 152.18/22.71 (8) ~ (all_4_2 = e1) % 152.18/22.71 (9) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0 % 152.18/22.71 (10) op(e0, e0) = all_6_1 % 152.18/22.71 (11) ~ (e3 = e1) % 152.18/22.71 (12) op(e1, e0) = all_56_20 % 152.18/22.71 % 152.18/22.71 Begin of proof % 152.18/22.71 | % 152.18/22.71 | GROUND_INST: instantiating (7) with all_4_2, all_6_1, e0, e0, simplifying with % 152.18/22.71 | (4), (10) gives: % 152.18/22.71 | (13) all_6_1 = all_4_2 % 152.18/22.71 | % 152.18/22.71 | GROUND_INST: instantiating (7) with e1, all_56_20, e0, e1, simplifying with % 152.18/22.71 | (1), (12) gives: % 152.18/22.71 | (14) all_56_20 = e1 % 152.18/22.71 | % 152.18/22.71 | REDUCE: (5), (13) imply: % 152.18/22.71 | (15) ~ (all_4_2 = e3) % 152.18/22.71 | % 152.18/22.71 | REDUCE: (3), (13) imply: % 152.18/22.71 | (16) ~ (all_4_2 = e2) % 152.18/22.71 | % 152.18/22.71 | REDUCE: (2), (13) imply: % 152.18/22.71 | (17) op(e1, all_4_2) = e3 % 152.18/22.71 | % 152.18/22.71 | BETA: splitting (9) gives: % 152.18/22.71 | % 152.18/22.71 | Case 1: % 152.18/22.71 | | % 152.18/22.71 | | (18) all_54_15 = e3 % 152.18/22.71 | | % 152.18/22.71 | | REF_CLOSE: (6), (15), (18) are inconsistent by sub-proof #740. % 152.18/22.71 | | % 152.18/22.71 | Case 2: % 152.18/22.71 | | % 152.18/22.71 | | (19) all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0 % 152.18/22.71 | | % 152.18/22.71 | | BETA: splitting (19) gives: % 152.18/22.71 | | % 152.18/22.71 | | Case 1: % 152.18/22.71 | | | % 152.18/22.71 | | | (20) all_54_15 = e2 % 152.18/22.71 | | | % 152.18/22.71 | | | REF_CLOSE: (6), (16), (20) are inconsistent by sub-proof #739. % 152.18/22.71 | | | % 152.18/22.71 | | Case 2: % 152.18/22.71 | | | % 152.18/22.71 | | | (21) all_54_15 = e1 | all_54_15 = e0 % 152.18/22.71 | | | % 152.18/22.71 | | | BETA: splitting (21) gives: % 152.18/22.71 | | | % 152.18/22.71 | | | Case 1: % 152.18/22.71 | | | | % 152.18/22.71 | | | | (22) all_54_15 = e1 % 152.18/22.71 | | | | % 152.18/22.71 | | | | REF_CLOSE: (6), (8), (22) are inconsistent by sub-proof #738. % 152.18/22.71 | | | | % 152.18/22.71 | | | Case 2: % 152.18/22.71 | | | | % 152.18/22.71 | | | | (23) all_54_15 = e0 % 152.18/22.71 | | | | % 152.18/22.71 | | | | COMBINE_EQS: (6), (23) imply: % 152.18/22.71 | | | | (24) all_4_2 = e0 % 152.18/22.71 | | | | % 152.18/22.71 | | | | SIMP: (24) implies: % 152.18/22.71 | | | | (25) all_4_2 = e0 % 152.18/22.71 | | | | % 152.18/22.71 | | | | REDUCE: (17), (25) imply: % 152.18/22.71 | | | | (26) op(e1, e0) = e3 % 152.18/22.71 | | | | % 152.18/22.71 | | | | GROUND_INST: instantiating (7) with e1, e3, e0, e1, simplifying with % 152.18/22.71 | | | | (1), (26) gives: % 152.18/22.71 | | | | (27) e3 = e1 % 152.18/22.71 | | | | % 152.18/22.71 | | | | REDUCE: (11), (27) imply: % 152.18/22.71 | | | | (28) $false % 152.18/22.71 | | | | % 152.18/22.71 | | | | CLOSE: (28) is inconsistent. % 152.18/22.71 | | | | % 152.18/22.71 | | | End of split % 152.18/22.71 | | | % 152.18/22.71 | | End of split % 152.18/22.71 | | % 152.18/22.71 | End of split % 152.18/22.71 | % 152.18/22.71 End of proof % 152.18/22.71 % 152.18/22.71 Sub-proof #506 shows that the following formulas are inconsistent: % 152.18/22.71 ---------------------------------------------------------------- % 152.18/22.71 (1) all_52_6 = e1 % 152.18/22.71 (2) ~ (all_6_1 = e2) % 152.18/22.71 (3) all_40_2 = all_6_2 % 152.18/22.71 (4) all_54_5 = all_8_2 % 152.18/22.71 (5) ~ (all_6_1 = e3) % 152.18/22.71 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 152.18/22.71 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 152.18/22.71 (7) op(all_6_2, all_6_2) = all_6_1 % 152.18/22.71 (8) ~ (all_52_6 = all_8_2) % 152.18/22.71 (9) all_6_2 = e2 % 152.18/22.71 (10) all_40_1 = all_6_1 % 152.18/22.71 (11) op(e2, e2) = all_8_2 % 152.18/22.71 (12) ~ (all_40_1 = e0) | ~ (all_40_2 = e2) % 152.18/22.71 (13) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 152.18/22.71 % 152.18/22.71 Begin of proof % 152.18/22.71 | % 152.18/22.71 | COMBINE_EQS: (3), (9) imply: % 152.18/22.71 | (14) all_40_2 = e2 % 152.18/22.71 | % 152.18/22.71 | REDUCE: (1), (8) imply: % 152.18/22.71 | (15) ~ (all_8_2 = e1) % 152.18/22.71 | % 152.18/22.71 | SIMP: (15) implies: % 152.18/22.71 | (16) ~ (all_8_2 = e1) % 152.18/22.71 | % 152.18/22.71 | REDUCE: (7), (9) imply: % 152.18/22.71 | (17) op(e2, e2) = all_6_1 % 152.18/22.71 | % 152.18/22.71 | REF_CLOSE: (2), (4), (5), (6), (10), (11), (12), (13), (14), (16), (17) are % 152.18/22.71 | inconsistent by sub-proof #507. % 152.18/22.71 | % 152.18/22.71 End of proof % 152.18/22.71 % 152.18/22.71 Sub-proof #507 shows that the following formulas are inconsistent: % 152.18/22.71 ---------------------------------------------------------------- % 152.18/22.71 (1) ~ (all_6_1 = e2) % 152.18/22.71 (2) ~ (all_8_2 = e1) % 152.18/22.71 (3) all_40_2 = e2 % 152.18/22.71 (4) op(e2, e2) = all_6_1 % 152.18/22.71 (5) all_54_5 = all_8_2 % 152.18/22.71 (6) ~ (all_6_1 = e3) % 152.18/22.72 (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 152.18/22.72 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 152.18/22.72 (8) all_40_1 = all_6_1 % 152.18/22.72 (9) op(e2, e2) = all_8_2 % 152.18/22.72 (10) ~ (all_40_1 = e0) | ~ (all_40_2 = e2) % 152.18/22.72 (11) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 152.18/22.72 % 152.18/22.72 Begin of proof % 152.18/22.72 | % 152.18/22.72 | BETA: splitting (10) gives: % 152.18/22.72 | % 152.18/22.72 | Case 1: % 152.18/22.72 | | % 152.18/22.72 | | (12) ~ (all_40_2 = e2) % 152.18/22.72 | | % 152.18/22.72 | | REDUCE: (3), (12) imply: % 152.18/22.72 | | (13) $false % 152.18/22.72 | | % 152.18/22.72 | | CLOSE: (13) is inconsistent. % 152.18/22.72 | | % 152.18/22.72 | Case 2: % 152.18/22.72 | | % 152.18/22.72 | | (14) ~ (all_40_1 = e0) % 152.18/22.72 | | % 152.18/22.72 | | REDUCE: (8), (14) imply: % 152.18/22.72 | | (15) ~ (all_6_1 = e0) % 152.18/22.72 | | % 152.18/22.72 | | GROUND_INST: instantiating (7) with all_8_2, all_6_1, e2, e2, simplifying % 152.18/22.72 | | with (4), (9) gives: % 152.18/22.72 | | (16) all_8_2 = all_6_1 % 152.18/22.72 | | % 152.18/22.72 | | COMBINE_EQS: (5), (16) imply: % 152.18/22.72 | | (17) all_54_5 = all_6_1 % 152.18/22.72 | | % 152.18/22.72 | | REDUCE: (2), (16) imply: % 152.18/22.72 | | (18) ~ (all_6_1 = e1) % 152.18/22.72 | | % 152.18/22.72 | | BETA: splitting (11) gives: % 152.18/22.72 | | % 152.18/22.72 | | Case 1: % 152.18/22.72 | | | % 152.18/22.72 | | | (19) all_54_5 = e3 % 152.18/22.72 | | | % 152.18/22.72 | | | REF_CLOSE: (6), (17), (19) are inconsistent by sub-proof #509. % 152.18/22.72 | | | % 152.18/22.72 | | Case 2: % 152.18/22.72 | | | % 152.18/22.72 | | | (20) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 152.18/22.72 | | | % 152.18/22.72 | | | REF_CLOSE: (1), (15), (17), (18), (20) are inconsistent by sub-proof #508. % 152.18/22.72 | | | % 152.18/22.72 | | End of split % 152.18/22.72 | | % 152.18/22.72 | End of split % 152.18/22.72 | % 152.18/22.72 End of proof % 152.18/22.72 % 152.18/22.72 Sub-proof #508 shows that the following formulas are inconsistent: % 152.18/22.72 ---------------------------------------------------------------- % 152.18/22.72 (1) ~ (all_6_1 = e2) % 152.18/22.72 (2) ~ (all_6_1 = e1) % 152.18/22.72 (3) all_54_5 = all_6_1 % 152.18/22.72 (4) ~ (all_6_1 = e0) % 152.18/22.72 (5) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 152.18/22.72 % 152.18/22.72 Begin of proof % 152.18/22.72 | % 152.18/22.72 | BETA: splitting (5) gives: % 152.18/22.72 | % 152.18/22.72 | Case 1: % 152.18/22.72 | | % 152.18/22.72 | | (6) all_54_5 = e2 % 152.18/22.72 | | % 152.18/22.72 | | COMBINE_EQS: (3), (6) imply: % 152.18/22.72 | | (7) all_6_1 = e2 % 152.18/22.72 | | % 152.18/22.72 | | REDUCE: (1), (7) imply: % 152.18/22.72 | | (8) $false % 152.18/22.72 | | % 152.18/22.72 | | CLOSE: (8) is inconsistent. % 152.18/22.72 | | % 152.18/22.72 | Case 2: % 152.18/22.72 | | % 152.18/22.72 | | (9) all_54_5 = e1 | all_54_5 = e0 % 152.18/22.72 | | % 152.18/22.72 | | BETA: splitting (9) gives: % 152.18/22.72 | | % 152.18/22.72 | | Case 1: % 152.18/22.72 | | | % 152.18/22.72 | | | (10) all_54_5 = e1 % 152.18/22.72 | | | % 152.18/22.72 | | | COMBINE_EQS: (3), (10) imply: % 152.18/22.72 | | | (11) all_6_1 = e1 % 152.18/22.72 | | | % 152.18/22.72 | | | REDUCE: (2), (11) imply: % 152.18/22.72 | | | (12) $false % 152.18/22.72 | | | % 152.18/22.72 | | | CLOSE: (12) is inconsistent. % 152.18/22.72 | | | % 152.18/22.72 | | Case 2: % 152.18/22.72 | | | % 152.18/22.72 | | | (13) all_54_5 = e0 % 152.18/22.72 | | | % 152.18/22.72 | | | COMBINE_EQS: (3), (13) imply: % 152.18/22.72 | | | (14) all_6_1 = e0 % 152.18/22.72 | | | % 152.18/22.72 | | | REDUCE: (4), (14) imply: % 152.18/22.72 | | | (15) $false % 152.18/22.72 | | | % 152.18/22.72 | | | CLOSE: (15) is inconsistent. % 152.18/22.72 | | | % 152.18/22.72 | | End of split % 152.18/22.72 | | % 152.18/22.72 | End of split % 152.18/22.72 | % 152.18/22.72 End of proof % 152.18/22.72 % 152.18/22.72 Sub-proof #509 shows that the following formulas are inconsistent: % 152.18/22.72 ---------------------------------------------------------------- % 152.18/22.72 (1) all_54_5 = all_6_1 % 152.18/22.72 (2) all_54_5 = e3 % 152.18/22.72 (3) ~ (all_6_1 = e3) % 152.18/22.72 % 152.18/22.72 Begin of proof % 152.18/22.72 | % 152.18/22.72 | COMBINE_EQS: (1), (2) imply: % 152.18/22.72 | (4) all_6_1 = e3 % 152.18/22.72 | % 152.18/22.72 | SIMP: (4) implies: % 152.18/22.72 | (5) all_6_1 = e3 % 152.18/22.72 | % 152.18/22.72 | REDUCE: (3), (5) imply: % 152.18/22.72 | (6) $false % 152.18/22.72 | % 152.18/22.72 | CLOSE: (6) is inconsistent. % 152.18/22.72 | % 152.18/22.72 End of proof % 152.18/22.72 % 152.18/22.72 Sub-proof #510 shows that the following formulas are inconsistent: % 152.18/22.72 ---------------------------------------------------------------- % 152.18/22.72 (1) all_58_6 = all_52_2 % 152.18/22.72 (2) op(e1, all_6_1) = e3 % 152.18/22.72 (3) all_54_10 = all_6_2 % 152.18/22.72 (4) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0 % 152.18/22.72 (5) all_54_0 = all_10_2 % 152.18/22.72 (6) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0 % 152.18/22.72 (7) ~ (all_52_4 = all_52_7) % 152.18/22.72 (8) ~ (all_52_12 = e2) % 152.18/22.72 (9) all_58_6 = e0 | all_58_7 = e0 | all_58_8 = e0 | all_58_11 = e0 % 152.18/22.72 (10) all_58_4 = all_52_8 % 152.18/22.72 (11) ~ (all_6_1 = e3) % 152.18/22.72 (12) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 152.18/22.72 (13) ~ (all_52_11 = e0) % 152.18/22.72 (14) all_56_21 = all_6_2 % 152.18/22.72 (15) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 152.18/22.72 (16) ~ (all_52_14 = e2) % 152.18/22.72 (17) all_56_1 = all_10_2 % 152.18/22.72 (18) all_58_5 = all_52_9 % 152.18/22.72 (19) all_54_1 = all_52_4 % 152.18/22.72 (20) all_56_17 = all_52_2 % 152.18/22.72 (21) all_58_4 = e0 | all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0 % 152.18/22.72 (22) ~ (all_56_21 = e3) | all_56_17 = e1 % 152.18/22.72 (23) all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2 % 152.18/22.72 (24) ~ (e1 = e0) % 152.18/22.72 (25) all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2 % 152.18/22.72 (26) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 152.18/22.72 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 152.18/22.72 (27) all_54_3 = all_52_12 % 152.18/22.72 (28) ~ (all_6_2 = e0) % 152.18/22.72 (29) ~ (all_52_3 = e0) % 152.18/22.72 (30) all_56_7 = all_52_12 % 152.18/22.72 (31) ~ (all_52_4 = e0) % 152.18/22.72 (32) ~ (all_52_9 = e0) % 152.18/22.72 (33) all_58_8 = all_6_2 % 152.18/22.72 (34) ~ (all_52_8 = all_10_2) % 152.18/22.72 (35) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0 % 152.18/22.72 (36) ~ (all_56_1 = e2) | all_56_3 = e3 % 152.18/22.72 (37) ~ (all_56_1 = e0) | all_56_7 = e3 % 152.18/22.72 (38) ~ (all_52_1 = e0) % 152.18/22.72 (39) all_56_3 = all_52_4 % 152.18/22.72 (40) ~ (all_52_6 = all_52_7) % 152.18/22.72 (41) all_58_11 = all_52_14 % 152.18/22.72 (42) ~ (all_52_2 = all_52_14) % 152.18/22.72 (43) op(all_6_2, all_6_2) = all_6_1 % 152.18/22.72 (44) all_54_13 = all_52_7 % 152.18/22.72 (45) op(e1, e1) = all_6_2 % 152.18/22.72 (46) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0 % 152.18/22.72 (47) ~ (all_6_2 = e2) % 152.18/22.72 (48) all_58_2 = all_52_1 % 152.18/22.72 (49) all_58_7 = all_52_6 % 152.18/22.72 (50) all_58_0 = all_10_2 % 152.18/22.72 (51) op(e1, all_6_2) = all_56_20 % 152.18/22.72 (52) ~ (all_52_12 = all_52_14) % 152.18/22.72 (53) ~ (all_52_12 = e0) % 152.18/22.72 (54) ~ (all_52_4 = all_52_12) % 152.18/22.72 (55) ~ (all_52_2 = all_6_2) % 152.18/22.72 (56) ~ (all_52_14 = all_6_2) % 152.18/22.72 (57) ~ (e2 = e0) % 152.18/22.72 (58) all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0 % 152.18/22.72 (59) ~ (all_52_7 = e0) % 152.18/22.72 (60) ~ (all_52_4 = all_10_2) % 152.18/22.72 (61) ~ (all_52_4 = all_52_6) % 152.18/22.72 (62) all_58_14 = all_52_11 % 152.18/22.72 (63) ~ (all_52_12 = all_10_2) % 152.18/22.72 (64) all_58_12 = all_52_3 % 152.18/22.72 (65) all_54_11 = all_52_14 % 152.18/22.72 % 152.18/22.72 Begin of proof % 152.18/22.72 | % 152.18/22.72 | BETA: splitting (9) gives: % 152.18/22.72 | % 152.18/22.72 | Case 1: % 152.18/22.72 | | % 152.18/22.72 | | (66) all_58_6 = e0 % 152.18/22.72 | | % 152.18/22.72 | | COMBINE_EQS: (1), (66) imply: % 152.18/22.72 | | (67) all_52_2 = e0 % 152.18/22.72 | | % 152.18/22.72 | | SIMP: (67) implies: % 152.18/22.72 | | (68) all_52_2 = e0 % 152.18/22.72 | | % 152.18/22.72 | | COMBINE_EQS: (20), (68) imply: % 152.18/22.72 | | (69) all_56_17 = e0 % 152.18/22.72 | | % 152.18/22.72 | | REDUCE: (42), (68) imply: % 152.18/22.72 | | (70) ~ (all_52_14 = e0) % 152.18/22.72 | | % 152.18/22.72 | | SIMP: (70) implies: % 152.18/22.72 | | (71) ~ (all_52_14 = e0) % 152.18/22.72 | | % 152.18/22.72 | | REDUCE: (55), (68) imply: % 152.18/22.72 | | (72) ~ (all_6_2 = e0) % 152.18/22.72 | | % 152.18/22.72 | | BETA: splitting (22) gives: % 152.18/22.72 | | % 152.18/22.72 | | Case 1: % 152.18/22.72 | | | % 152.18/22.72 | | | (73) ~ (all_56_21 = e3) % 152.18/22.72 | | | % 152.18/22.72 | | | REDUCE: (14), (73) imply: % 152.18/22.72 | | | (74) ~ (all_6_2 = e3) % 152.18/22.72 | | | % 152.18/22.72 | | | BETA: splitting (15) gives: % 152.18/22.72 | | | % 152.18/22.72 | | | Case 1: % 152.18/22.72 | | | | % 152.18/22.72 | | | | (75) all_54_10 = e3 % 152.18/22.72 | | | | % 152.18/22.72 | | | | REF_CLOSE: (3), (74), (75) are inconsistent by sub-proof #736. % 152.18/22.72 | | | | % 152.18/22.72 | | | Case 2: % 152.18/22.72 | | | | % 152.18/22.72 | | | | (76) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 152.18/22.72 | | | | % 152.18/22.72 | | | | BETA: splitting (25) gives: % 152.18/22.72 | | | | % 152.18/22.72 | | | | Case 1: % 152.18/22.72 | | | | | % 152.18/22.72 | | | | | (77) all_58_6 = e2 % 152.18/22.72 | | | | | % 152.18/22.72 | | | | | COMBINE_EQS: (66), (77) imply: % 152.18/22.72 | | | | | (78) e2 = e0 % 152.18/22.72 | | | | | % 152.18/22.72 | | | | | REDUCE: (57), (78) imply: % 152.18/22.72 | | | | | (79) $false % 152.18/22.72 | | | | | % 152.18/22.72 | | | | | CLOSE: (79) is inconsistent. % 152.18/22.72 | | | | | % 152.18/22.72 | | | | Case 2: % 152.18/22.72 | | | | | % 152.18/22.72 | | | | | (80) all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2 % 152.18/22.72 | | | | | % 152.18/22.72 | | | | | BETA: splitting (76) gives: % 152.18/22.72 | | | | | % 152.18/22.72 | | | | | Case 1: % 152.18/22.72 | | | | | | % 152.18/22.72 | | | | | | (81) all_54_10 = e2 % 152.18/22.72 | | | | | | % 152.18/22.72 | | | | | | REF_CLOSE: (3), (47), (81) are inconsistent by sub-proof #735. % 152.18/22.72 | | | | | | % 152.18/22.72 | | | | | Case 2: % 152.18/22.72 | | | | | | % 152.18/22.72 | | | | | | (82) ~ (all_54_10 = e2) % 152.18/22.72 | | | | | | (83) all_54_10 = e1 | all_54_10 = e0 % 152.18/22.72 | | | | | | % 152.18/22.72 | | | | | | BETA: splitting (83) gives: % 152.18/22.72 | | | | | | % 152.18/22.72 | | | | | | Case 1: % 152.18/22.72 | | | | | | | % 152.18/22.72 | | | | | | | (84) all_54_10 = e1 % 152.18/22.72 | | | | | | | % 152.18/22.72 | | | | | | | COMBINE_EQS: (3), (84) imply: % 152.18/22.72 | | | | | | | (85) all_6_2 = e1 % 152.18/22.72 | | | | | | | % 152.18/22.72 | | | | | | | SIMP: (85) implies: % 152.18/22.72 | | | | | | | (86) all_6_2 = e1 % 152.18/22.72 | | | | | | | % 152.18/22.72 | | | | | | | REDUCE: (56), (86) imply: % 152.18/22.72 | | | | | | | (87) ~ (all_52_14 = e1) % 152.18/22.72 | | | | | | | % 152.18/22.72 | | | | | | | REDUCE: (43), (86) imply: % 152.18/22.72 | | | | | | | (88) op(e1, e1) = all_6_1 % 152.18/22.72 | | | | | | | % 152.18/22.72 | | | | | | | REDUCE: (51), (86) imply: % 152.18/22.72 | | | | | | | (89) op(e1, e1) = all_56_20 % 152.18/22.72 | | | | | | | % 152.18/22.72 | | | | | | | REDUCE: (45), (86) imply: % 152.18/22.72 | | | | | | | (90) op(e1, e1) = e1 % 152.18/22.72 | | | | | | | % 152.18/22.72 | | | | | | | BETA: splitting (6) gives: % 152.18/22.72 | | | | | | | % 152.18/22.72 | | | | | | | Case 1: % 152.18/22.72 | | | | | | | | % 152.18/22.72 | | | | | | | | (91) all_54_11 = e3 % 152.18/22.72 | | | | | | | | % 152.18/22.72 | | | | | | | | COMBINE_EQS: (65), (91) imply: % 152.18/22.72 | | | | | | | | (92) all_52_14 = e3 % 152.18/22.72 | | | | | | | | % 152.18/22.72 | | | | | | | | REDUCE: (52), (92) imply: % 152.18/22.72 | | | | | | | | (93) ~ (all_52_12 = e3) % 152.18/22.72 | | | | | | | | % 152.18/22.72 | | | | | | | | BETA: splitting (4) gives: % 152.18/22.72 | | | | | | | | % 152.18/22.72 | | | | | | | | Case 1: % 152.18/22.72 | | | | | | | | | % 152.18/22.72 | | | | | | | | | (94) all_54_3 = e3 % 152.18/22.72 | | | | | | | | | % 152.18/22.72 | | | | | | | | | REF_CLOSE: (27), (93), (94) are inconsistent by sub-proof % 152.18/22.72 | | | | | | | | | #659. % 152.18/22.72 | | | | | | | | | % 152.18/22.72 | | | | | | | | Case 2: % 152.18/22.72 | | | | | | | | | % 152.18/22.72 | | | | | | | | | (95) all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0 % 152.18/22.72 | | | | | | | | | % 152.18/22.72 | | | | | | | | | BETA: splitting (95) gives: % 152.18/22.72 | | | | | | | | | % 152.18/22.72 | | | | | | | | | Case 1: % 152.18/22.72 | | | | | | | | | | % 152.18/22.72 | | | | | | | | | | (96) all_54_3 = e2 % 152.18/22.72 | | | | | | | | | | % 152.18/22.72 | | | | | | | | | | REF_CLOSE: (8), (27), (96) are inconsistent by sub-proof % 152.18/22.72 | | | | | | | | | | #658. % 152.18/22.72 | | | | | | | | | | % 152.18/22.72 | | | | | | | | | Case 2: % 152.18/22.72 | | | | | | | | | | % 152.18/22.72 | | | | | | | | | | (97) all_54_3 = e1 | all_54_3 = e0 % 152.18/22.72 | | | | | | | | | | % 152.18/22.72 | | | | | | | | | | BETA: splitting (80) gives: % 152.18/22.72 | | | | | | | | | | % 152.18/22.72 | | | | | | | | | | Case 1: % 152.18/22.72 | | | | | | | | | | | % 152.18/22.72 | | | | | | | | | | | (98) all_58_7 = e2 % 152.18/22.72 | | | | | | | | | | | % 152.18/22.72 | | | | | | | | | | | COMBINE_EQS: (49), (98) imply: % 152.18/22.72 | | | | | | | | | | | (99) all_52_6 = e2 % 152.18/22.72 | | | | | | | | | | | % 152.18/22.72 | | | | | | | | | | | REDUCE: (61), (99) imply: % 152.18/22.72 | | | | | | | | | | | (100) ~ (all_52_4 = e2) % 152.18/22.72 | | | | | | | | | | | % 152.18/22.72 | | | | | | | | | | | REDUCE: (40), (99) imply: % 152.18/22.72 | | | | | | | | | | | (101) ~ (all_52_7 = e2) % 152.18/22.72 | | | | | | | | | | | % 152.18/22.72 | | | | | | | | | | | SIMP: (101) implies: % 152.18/22.72 | | | | | | | | | | | (102) ~ (all_52_7 = e2) % 152.18/22.72 | | | | | | | | | | | % 152.18/22.72 | | | | | | | | | | | BETA: splitting (97) gives: % 152.18/22.72 | | | | | | | | | | | % 152.18/22.72 | | | | | | | | | | | Case 1: % 152.18/22.72 | | | | | | | | | | | | % 152.18/22.72 | | | | | | | | | | | | (103) all_54_3 = e1 % 152.18/22.72 | | | | | | | | | | | | % 152.18/22.72 | | | | | | | | | | | | COMBINE_EQS: (27), (103) imply: % 152.18/22.72 | | | | | | | | | | | | (104) all_52_12 = e1 % 152.18/22.72 | | | | | | | | | | | | % 152.18/22.72 | | | | | | | | | | | | SIMP: (104) implies: % 152.18/22.72 | | | | | | | | | | | | (105) all_52_12 = e1 % 152.18/22.72 | | | | | | | | | | | | % 152.18/22.72 | | | | | | | | | | | | REDUCE: (54), (105) imply: % 152.18/22.72 | | | | | | | | | | | | (106) ~ (all_52_4 = e1) % 152.18/22.72 | | | | | | | | | | | | % 152.18/22.72 | | | | | | | | | | | | REDUCE: (63), (105) imply: % 152.18/22.72 | | | | | | | | | | | | (107) ~ (all_10_2 = e1) % 152.18/22.72 | | | | | | | | | | | | % 152.18/22.72 | | | | | | | | | | | | SIMP: (107) implies: % 152.18/22.72 | | | | | | | | | | | | (108) ~ (all_10_2 = e1) % 152.18/22.72 | | | | | | | | | | | | % 152.18/22.72 | | | | | | | | | | | | BETA: splitting (23) gives: % 152.18/22.72 | | | | | | | | | | | | % 152.18/22.72 | | | | | | | | | | | | Case 1: % 152.18/22.72 | | | | | | | | | | | | | % 152.18/22.72 | | | | | | | | | | | | | (109) all_58_0 = e2 % 152.18/22.72 | | | | | | | | | | | | | % 152.18/22.72 | | | | | | | | | | | | | COMBINE_EQS: (50), (109) imply: % 152.18/22.72 | | | | | | | | | | | | | (110) all_10_2 = e2 % 152.18/22.72 | | | | | | | | | | | | | % 152.18/22.72 | | | | | | | | | | | | | COMBINE_EQS: (17), (110) imply: % 152.18/22.72 | | | | | | | | | | | | | (111) all_56_1 = e2 % 152.18/22.72 | | | | | | | | | | | | | % 152.18/22.72 | | | | | | | | | | | | | BETA: splitting (36) gives: % 152.18/22.72 | | | | | | | | | | | | | % 152.18/22.72 | | | | | | | | | | | | | Case 1: % 152.18/22.72 | | | | | | | | | | | | | | % 152.18/22.72 | | | | | | | | | | | | | | (112) ~ (all_56_1 = e2) % 152.18/22.72 | | | | | | | | | | | | | | % 152.18/22.72 | | | | | | | | | | | | | | REDUCE: (111), (112) imply: % 152.18/22.72 | | | | | | | | | | | | | | (113) $false % 152.18/22.72 | | | | | | | | | | | | | | % 152.18/22.72 | | | | | | | | | | | | | | CLOSE: (113) is inconsistent. % 152.18/22.72 | | | | | | | | | | | | | | % 152.18/22.72 | | | | | | | | | | | | | Case 2: % 152.18/22.72 | | | | | | | | | | | | | | % 152.18/22.72 | | | | | | | | | | | | | | (114) all_56_3 = e3 % 152.18/22.72 | | | | | | | | | | | | | | % 152.18/22.72 | | | | | | | | | | | | | | COMBINE_EQS: (39), (114) imply: % 152.18/22.72 | | | | | | | | | | | | | | (115) all_52_4 = e3 % 152.18/22.72 | | | | | | | | | | | | | | % 152.18/22.72 | | | | | | | | | | | | | | REDUCE: (7), (115) imply: % 152.18/22.72 | | | | | | | | | | | | | | (116) ~ (all_52_7 = e3) % 152.18/22.72 | | | | | | | | | | | | | | % 152.18/22.72 | | | | | | | | | | | | | | SIMP: (116) implies: % 152.18/22.72 | | | | | | | | | | | | | | (117) ~ (all_52_7 = e3) % 152.18/22.72 | | | | | | | | | | | | | | % 152.18/22.72 | | | | | | | | | | | | | | REF_CLOSE: (2), (11), (26), (35), (44), (59), (88), (89), % 152.18/22.72 | | | | | | | | | | | | | | (90), (102), (117) are inconsistent by sub-proof % 152.18/22.72 | | | | | | | | | | | | | | #512. % 152.18/22.72 | | | | | | | | | | | | | | % 152.18/22.72 | | | | | | | | | | | | | End of split % 152.18/22.72 | | | | | | | | | | | | | % 152.18/22.72 | | | | | | | | | | | | Case 2: % 152.18/22.72 | | | | | | | | | | | | | % 152.18/22.72 | | | | | | | | | | | | | (118) ~ (all_58_0 = e2) % 152.18/22.72 | | | | | | | | | | | | | % 152.18/22.72 | | | | | | | | | | | | | REDUCE: (50), (118) imply: % 152.18/22.72 | | | | | | | | | | | | | (119) ~ (all_10_2 = e2) % 152.18/22.72 | | | | | | | | | | | | | % 152.18/22.72 | | | | | | | | | | | | | REF_CLOSE: (5), (12), (17), (19), (30), (31), (37), (46), % 152.18/22.72 | | | | | | | | | | | | | (54), (60), (100), (106), (108), (119) are % 152.18/22.72 | | | | | | | | | | | | | inconsistent by sub-proof #706. % 152.18/22.72 | | | | | | | | | | | | | % 152.18/22.72 | | | | | | | | | | | | End of split % 152.18/22.72 | | | | | | | | | | | | % 152.18/22.72 | | | | | | | | | | | Case 2: % 152.18/22.72 | | | | | | | | | | | | % 152.18/22.72 | | | | | | | | | | | | (120) all_54_3 = e0 % 152.18/22.72 | | | | | | | | | | | | % 152.18/22.72 | | | | | | | | | | | | REF_CLOSE: (27), (53), (120) are inconsistent by sub-proof % 152.18/22.72 | | | | | | | | | | | | #656. % 152.18/22.72 | | | | | | | | | | | | % 152.18/22.72 | | | | | | | | | | | End of split % 152.18/22.72 | | | | | | | | | | | % 152.18/22.72 | | | | | | | | | | Case 2: % 152.18/22.72 | | | | | | | | | | | % 152.18/22.72 | | | | | | | | | | | (121) all_58_8 = e2 | all_58_11 = e2 % 152.18/22.72 | | | | | | | | | | | % 152.18/22.72 | | | | | | | | | | | REF_CLOSE: (16), (33), (41), (47), (121) are inconsistent by % 152.18/22.72 | | | | | | | | | | | sub-proof #511. % 152.18/22.72 | | | | | | | | | | | % 152.18/22.72 | | | | | | | | | | End of split % 152.18/22.72 | | | | | | | | | | % 152.18/22.72 | | | | | | | | | End of split % 152.18/22.72 | | | | | | | | | % 152.18/22.72 | | | | | | | | End of split % 152.18/22.72 | | | | | | | | % 152.18/22.72 | | | | | | | Case 2: % 152.18/22.72 | | | | | | | | % 152.18/22.72 | | | | | | | | (122) all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0 % 152.18/22.72 | | | | | | | | % 152.18/22.72 | | | | | | | | REF_CLOSE: (16), (65), (71), (87), (122) are inconsistent by % 152.18/22.72 | | | | | | | | sub-proof #687. % 152.18/22.72 | | | | | | | | % 152.18/22.72 | | | | | | | End of split % 152.18/22.72 | | | | | | | % 152.18/22.72 | | | | | | Case 2: % 152.18/22.72 | | | | | | | % 152.18/22.72 | | | | | | | (123) all_54_10 = e0 % 152.18/22.72 | | | | | | | % 152.18/22.72 | | | | | | | REF_CLOSE: (3), (28), (123) are inconsistent by sub-proof #705. % 152.18/22.72 | | | | | | | % 152.18/22.72 | | | | | | End of split % 152.18/22.72 | | | | | | % 152.18/22.72 | | | | | End of split % 152.18/22.72 | | | | | % 152.18/22.72 | | | | End of split % 152.18/22.72 | | | | % 152.18/22.72 | | | End of split % 152.18/22.72 | | | % 152.18/22.72 | | Case 2: % 152.18/22.72 | | | % 152.18/22.72 | | | (124) all_56_17 = e1 % 152.18/22.72 | | | % 152.18/22.72 | | | COMBINE_EQS: (69), (124) imply: % 152.18/22.72 | | | (125) e1 = e0 % 152.18/22.72 | | | % 152.18/22.72 | | | SIMP: (125) implies: % 152.18/22.72 | | | (126) e1 = e0 % 152.18/22.72 | | | % 152.18/22.72 | | | REDUCE: (24), (126) imply: % 152.18/22.72 | | | (127) $false % 152.18/22.72 | | | % 152.18/22.72 | | | CLOSE: (127) is inconsistent. % 152.18/22.72 | | | % 152.18/22.72 | | End of split % 152.18/22.72 | | % 152.18/22.72 | Case 2: % 152.18/22.72 | | % 152.18/22.72 | | (128) ~ (all_58_6 = e0) % 152.18/22.72 | | % 152.18/22.72 | | REF_CLOSE: (1), (10), (13), (18), (21), (28), (29), (32), (33), (34), (38), % 152.18/22.72 | | (48), (50), (58), (62), (64), (128) are inconsistent by sub-proof % 152.18/22.72 | | #623. % 152.18/22.72 | | % 152.18/22.72 | End of split % 152.18/22.72 | % 152.18/22.72 End of proof % 152.18/22.72 % 152.18/22.72 Sub-proof #511 shows that the following formulas are inconsistent: % 152.18/22.72 ---------------------------------------------------------------- % 152.18/22.72 (1) ~ (all_52_14 = e2) % 152.18/22.72 (2) all_58_8 = e2 | all_58_11 = e2 % 152.18/22.72 (3) all_58_8 = all_6_2 % 152.18/22.72 (4) all_58_11 = all_52_14 % 152.18/22.72 (5) ~ (all_6_2 = e2) % 152.18/22.72 % 152.18/22.72 Begin of proof % 152.18/22.72 | % 152.18/22.72 | BETA: splitting (2) gives: % 152.18/22.72 | % 152.18/22.72 | Case 1: % 152.18/22.72 | | % 152.18/22.72 | | (6) all_58_8 = e2 % 152.18/22.72 | | % 152.18/22.72 | | COMBINE_EQS: (3), (6) imply: % 152.18/22.72 | | (7) all_6_2 = e2 % 152.18/22.72 | | % 152.18/22.72 | | REDUCE: (5), (7) imply: % 152.18/22.72 | | (8) $false % 152.18/22.72 | | % 152.18/22.72 | | CLOSE: (8) is inconsistent. % 152.18/22.72 | | % 152.18/22.72 | Case 2: % 152.18/22.72 | | % 152.18/22.72 | | (9) all_58_11 = e2 % 152.18/22.72 | | % 152.18/22.72 | | COMBINE_EQS: (4), (9) imply: % 152.18/22.72 | | (10) all_52_14 = e2 % 152.18/22.72 | | % 152.18/22.72 | | REDUCE: (1), (10) imply: % 152.18/22.72 | | (11) $false % 152.18/22.72 | | % 152.18/22.72 | | CLOSE: (11) is inconsistent. % 152.18/22.72 | | % 152.18/22.72 | End of split % 152.18/22.72 | % 152.18/22.72 End of proof % 152.18/22.72 % 152.18/22.72 Sub-proof #512 shows that the following formulas are inconsistent: % 152.18/22.72 ---------------------------------------------------------------- % 152.18/22.72 (1) ~ (all_52_7 = e2) % 152.18/22.72 (2) op(e1, all_6_1) = e3 % 152.18/22.72 (3) ~ (all_6_1 = e3) % 152.18/22.72 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 152.18/22.72 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 152.18/22.72 (5) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0 % 152.18/22.72 (6) op(e1, e1) = all_56_20 % 152.18/22.72 (7) all_54_13 = all_52_7 % 152.18/22.72 (8) ~ (all_52_7 = e3) % 152.18/22.72 (9) ~ (all_52_7 = e0) % 152.18/22.72 (10) op(e1, e1) = all_6_1 % 152.18/22.72 (11) op(e1, e1) = e1 % 152.18/22.72 % 152.18/22.72 Begin of proof % 152.18/22.72 | % 152.18/22.72 | BETA: splitting (5) gives: % 152.18/22.72 | % 152.18/22.72 | Case 1: % 152.18/22.72 | | % 152.18/22.72 | | (12) all_54_13 = e3 % 152.18/22.72 | | % 152.18/22.72 | | REF_CLOSE: (7), (8), (12) are inconsistent by sub-proof #668. % 152.18/22.72 | | % 152.18/22.72 | Case 2: % 152.18/22.72 | | % 152.18/22.72 | | (13) all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0 % 152.18/22.72 | | % 152.18/22.72 | | BETA: splitting (13) gives: % 152.18/22.72 | | % 152.18/22.72 | | Case 1: % 152.18/22.72 | | | % 152.18/22.72 | | | (14) all_54_13 = e2 % 152.18/22.72 | | | % 152.18/22.72 | | | REF_CLOSE: (1), (7), (14) are inconsistent by sub-proof #513. % 152.18/22.72 | | | % 152.18/22.72 | | Case 2: % 152.18/22.72 | | | % 152.18/22.72 | | | (15) all_54_13 = e1 | all_54_13 = e0 % 152.18/22.72 | | | % 152.18/22.72 | | | BETA: splitting (15) gives: % 152.18/22.72 | | | % 152.18/22.72 | | | Case 1: % 152.18/22.72 | | | | % 152.18/22.72 | | | | % 152.18/22.72 | | | | GROUND_INST: instantiating (4) with all_6_1, all_56_20, e1, e1, % 152.18/22.72 | | | | simplifying with (6), (10) gives: % 152.18/22.72 | | | | (16) all_56_20 = all_6_1 % 152.18/22.72 | | | | % 152.18/22.72 | | | | GROUND_INST: instantiating (4) with e1, all_56_20, e1, e1, simplifying % 152.18/22.72 | | | | with (6), (11) gives: % 152.18/22.72 | | | | (17) all_56_20 = e1 % 152.18/22.72 | | | | % 152.18/22.72 | | | | REF_CLOSE: (2), (3), (4), (6), (10), (16), (17) are inconsistent by % 152.18/22.72 | | | | sub-proof #515. % 152.18/22.72 | | | | % 152.18/22.72 | | | Case 2: % 152.18/22.72 | | | | % 152.18/22.72 | | | | (18) all_54_13 = e0 % 152.18/22.72 | | | | % 152.18/22.72 | | | | REF_CLOSE: (7), (9), (18) are inconsistent by sub-proof #712. % 152.18/22.72 | | | | % 152.18/22.72 | | | End of split % 152.18/22.72 | | | % 152.18/22.72 | | End of split % 152.18/22.72 | | % 152.18/22.72 | End of split % 152.18/22.72 | % 152.18/22.72 End of proof % 152.18/22.72 % 152.18/22.72 Sub-proof #513 shows that the following formulas are inconsistent: % 152.18/22.72 ---------------------------------------------------------------- % 152.18/22.72 (1) all_54_13 = all_52_7 % 152.18/22.72 (2) all_54_13 = e2 % 152.18/22.72 (3) ~ (all_52_7 = e2) % 152.18/22.72 % 152.18/22.72 Begin of proof % 152.18/22.72 | % 152.18/22.72 | COMBINE_EQS: (1), (2) imply: % 152.18/22.72 | (4) all_52_7 = e2 % 152.18/22.72 | % 152.18/22.72 | SIMP: (4) implies: % 152.18/22.72 | (5) all_52_7 = e2 % 152.18/22.72 | % 152.18/22.72 | REDUCE: (3), (5) imply: % 152.18/22.72 | (6) $false % 152.18/22.72 | % 152.18/22.72 | CLOSE: (6) is inconsistent. % 152.18/22.72 | % 152.18/22.72 End of proof % 152.18/22.72 % 152.18/22.72 Sub-proof #514 shows that the following formulas are inconsistent: % 152.18/22.72 ---------------------------------------------------------------- % 152.18/22.72 (1) op(e1, all_6_1) = e3 % 152.18/22.72 (2) all_54_10 = all_6_2 % 152.18/22.72 (3) ~ (all_6_2 = e3) % 152.18/22.72 (4) ~ (all_6_1 = e3) % 152.18/22.72 (5) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 152.18/22.72 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 152.18/22.72 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 152.18/22.72 (7) ~ (all_6_2 = e0) % 152.18/22.72 (8) op(all_6_2, all_6_2) = all_6_1 % 152.18/22.72 (9) op(e1, e1) = all_6_2 % 152.18/22.72 (10) ~ (all_6_2 = e2) % 152.18/22.72 (11) op(e1, all_6_2) = all_56_20 % 152.18/22.72 % 152.18/22.72 Begin of proof % 152.18/22.72 | % 152.18/22.72 | BETA: splitting (5) gives: % 152.18/22.72 | % 152.18/22.72 | Case 1: % 152.18/22.72 | | % 152.18/22.72 | | (12) all_54_10 = e3 % 152.18/22.72 | | % 152.18/22.72 | | REF_CLOSE: (2), (3), (12) are inconsistent by sub-proof #736. % 152.18/22.72 | | % 152.18/22.72 | Case 2: % 152.18/22.72 | | % 152.18/22.72 | | (13) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 152.18/22.72 | | % 152.18/22.72 | | BETA: splitting (13) gives: % 152.18/22.72 | | % 152.18/22.72 | | Case 1: % 152.18/22.72 | | | % 152.18/22.72 | | | (14) all_54_10 = e2 % 152.18/22.72 | | | % 152.18/22.72 | | | REF_CLOSE: (2), (10), (14) are inconsistent by sub-proof #735. % 152.18/22.72 | | | % 152.18/22.72 | | Case 2: % 152.18/22.72 | | | % 152.18/22.72 | | | (15) all_54_10 = e1 | all_54_10 = e0 % 152.18/22.72 | | | % 152.18/22.72 | | | BETA: splitting (15) gives: % 152.18/22.72 | | | % 152.18/22.72 | | | Case 1: % 152.18/22.72 | | | | % 152.18/22.72 | | | | (16) all_54_10 = e1 % 152.18/22.72 | | | | % 152.18/22.72 | | | | COMBINE_EQS: (2), (16) imply: % 152.18/22.72 | | | | (17) all_6_2 = e1 % 152.18/22.72 | | | | % 152.18/22.72 | | | | SIMP: (17) implies: % 152.18/22.72 | | | | (18) all_6_2 = e1 % 152.18/22.72 | | | | % 152.18/22.72 | | | | REDUCE: (8), (18) imply: % 152.18/22.72 | | | | (19) op(e1, e1) = all_6_1 % 152.18/22.72 | | | | % 152.18/22.72 | | | | REDUCE: (11), (18) imply: % 152.18/22.72 | | | | (20) op(e1, e1) = all_56_20 % 152.18/22.72 | | | | % 152.18/22.72 | | | | REDUCE: (9), (18) imply: % 152.18/22.72 | | | | (21) op(e1, e1) = e1 % 152.18/22.72 | | | | % 152.18/22.72 | | | | GROUND_INST: instantiating (6) with all_6_1, all_56_20, e1, e1, % 152.18/22.72 | | | | simplifying with (19), (20) gives: % 152.18/22.72 | | | | (22) all_56_20 = all_6_1 % 152.18/22.72 | | | | % 152.18/22.72 | | | | GROUND_INST: instantiating (6) with e1, all_56_20, e1, e1, simplifying % 152.18/22.72 | | | | with (20), (21) gives: % 152.18/22.72 | | | | (23) all_56_20 = e1 % 152.18/22.72 | | | | % 152.18/22.72 | | | | REF_CLOSE: (1), (4), (6), (19), (20), (22), (23) are inconsistent by % 152.18/22.72 | | | | sub-proof #515. % 152.18/22.72 | | | | % 152.18/22.72 | | | Case 2: % 152.18/22.72 | | | | % 152.18/22.72 | | | | (24) all_54_10 = e0 % 152.18/22.72 | | | | % 152.18/22.72 | | | | REF_CLOSE: (2), (7), (24) are inconsistent by sub-proof #705. % 152.18/22.72 | | | | % 152.18/22.72 | | | End of split % 152.18/22.72 | | | % 152.18/22.72 | | End of split % 152.18/22.72 | | % 152.18/22.72 | End of split % 152.18/22.72 | % 152.18/22.72 End of proof % 152.18/22.72 % 152.18/22.72 Sub-proof #515 shows that the following formulas are inconsistent: % 152.18/22.72 ---------------------------------------------------------------- % 152.18/22.72 (1) op(e1, all_6_1) = e3 % 152.18/22.72 (2) ~ (all_6_1 = e3) % 152.18/22.72 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 152.18/22.72 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 152.18/22.72 (4) op(e1, e1) = all_56_20 % 152.18/22.72 (5) all_56_20 = all_6_1 % 152.18/22.72 (6) all_56_20 = e1 % 152.18/22.72 (7) op(e1, e1) = all_6_1 % 152.18/22.72 % 152.18/22.72 Begin of proof % 152.18/22.72 | % 152.18/22.72 | COMBINE_EQS: (5), (6) imply: % 152.18/22.72 | (8) all_6_1 = e1 % 152.18/22.72 | % 152.18/22.72 | SIMP: (8) implies: % 152.18/22.72 | (9) all_6_1 = e1 % 152.18/22.72 | % 152.18/22.72 | REDUCE: (2), (9) imply: % 152.18/22.72 | (10) ~ (e3 = e1) % 152.18/22.72 | % 152.18/22.72 | SIMP: (10) implies: % 152.18/22.72 | (11) ~ (e3 = e1) % 152.18/22.72 | % 152.18/22.72 | REDUCE: (1), (9) imply: % 152.18/22.72 | (12) op(e1, e1) = e3 % 152.18/22.72 | % 152.18/22.72 | REDUCE: (7), (9) imply: % 152.18/22.72 | (13) op(e1, e1) = e1 % 152.18/22.72 | % 152.18/22.72 | REF_CLOSE: (3), (4), (11), (12), (13) are inconsistent by sub-proof #516. % 152.18/22.72 | % 152.18/22.72 End of proof % 152.18/22.72 % 152.18/22.72 Sub-proof #516 shows that the following formulas are inconsistent: % 152.18/22.72 ---------------------------------------------------------------- % 152.18/22.72 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 152.18/22.72 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 152.18/22.72 (2) op(e1, e1) = e3 % 152.18/22.72 (3) op(e1, e1) = all_56_20 % 152.18/22.72 (4) ~ (e3 = e1) % 152.18/22.72 (5) op(e1, e1) = e1 % 152.18/22.72 % 152.18/22.72 Begin of proof % 152.18/22.72 | % 152.18/22.72 | GROUND_INST: instantiating (1) with e3, all_56_20, e1, e1, simplifying with % 152.18/22.72 | (2), (3) gives: % 152.18/22.72 | (6) all_56_20 = e3 % 152.18/22.72 | % 152.18/22.72 | GROUND_INST: instantiating (1) with e1, all_56_20, e1, e1, simplifying with % 152.18/22.72 | (3), (5) gives: % 152.18/22.72 | (7) all_56_20 = e1 % 152.18/22.72 | % 152.18/22.72 | COMBINE_EQS: (6), (7) imply: % 152.18/22.72 | (8) e3 = e1 % 152.18/22.72 | % 152.18/22.72 | REDUCE: (4), (8) imply: % 152.18/22.72 | (9) $false % 152.18/22.72 | % 152.18/22.72 | CLOSE: (9) is inconsistent. % 152.18/22.72 | % 152.18/22.72 End of proof % 152.18/22.72 % 152.18/22.72 Sub-proof #517 shows that the following formulas are inconsistent: % 152.18/22.72 ---------------------------------------------------------------- % 152.18/22.72 (1) all_56_11 = all_8_2 % 152.18/22.72 (2) op(e0, all_52_13) = all_56_14 % 152.18/22.72 (3) ~ (all_56_11 = e1) | all_56_13 = e2 % 152.18/22.72 (4) op(e0, e0) = e1 % 152.18/22.72 (5) ~ (all_8_1 = e1) % 152.18/22.72 (6) ~ (all_52_1 = all_52_9) % 152.18/22.72 (7) ~ (all_52_13 = e1) % 152.18/22.72 (8) all_54_10 = all_6_2 % 152.18/22.72 (9) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0 % 152.18/22.72 (10) ~ (all_52_13 = all_8_2) % 152.18/22.72 (11) ~ (all_56_21 = e2) | all_56_19 = e1 % 152.18/22.72 (12) all_54_0 = all_10_2 % 152.18/22.72 (13) all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2 % 152.18/22.72 (14) ~ (all_52_9 = all_8_2) % 152.18/22.72 (15) all_54_12 = all_52_3 % 152.18/22.72 (16) ~ (all_52_12 = all_52_13) % 152.18/22.72 (17) ~ (e3 = e2) % 152.18/22.72 (18) all_58_4 = all_52_8 % 152.18/22.72 (19) all_54_5 = all_8_2 % 152.18/22.72 (20) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 152.18/22.72 (21) ~ (all_10_1 = e1) % 152.18/22.72 (22) all_56_21 = all_6_2 % 152.18/22.72 (23) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 152.18/22.72 (24) all_56_1 = all_10_2 % 152.18/22.72 (25) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0 % 152.18/22.72 (26) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0 % 152.18/22.72 (27) all_58_5 = all_52_9 % 152.18/22.72 (28) all_56_17 = all_52_2 % 152.18/22.72 (29) all_58_9 = all_52_12 % 152.18/22.72 (30) op(e0, e2) = all_52_7 % 152.18/22.72 (31) ~ (all_56_1 = e1) | all_56_5 = e3 % 152.18/22.72 (32) all_58_1 = all_52_4 % 152.18/22.72 (33) all_58_13 = all_52_7 % 152.18/22.72 (34) ~ (all_52_8 = all_6_2) % 152.18/22.72 (35) all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1 % 152.18/22.72 (36) ~ (all_56_21 = e3) | all_56_17 = e1 % 152.18/22.72 (37) all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1 % 152.18/22.72 (38) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 152.18/22.72 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 152.18/22.72 (39) all_54_3 = all_52_12 % 152.18/22.72 (40) all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0 % 152.18/22.72 (41) ~ (all_6_2 = e0) % 152.18/22.72 (42) ~ (all_56_11 = e3) | all_56_9 = e2 % 152.18/22.72 (43) op(e0, all_4_1) = all_4_0 % 152.18/22.72 (44) ~ (all_52_3 = e0) % 152.18/22.72 (45) all_56_7 = all_52_12 % 152.18/22.72 (46) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0 % 152.18/22.72 (47) all_56_13 = all_52_9 % 152.18/22.72 (48) ~ (all_52_9 = e0) % 152.18/22.72 (49) all_58_8 = all_6_2 % 152.18/22.72 (50) ~ (all_6_0 = e3) % 152.18/22.72 (51) all_54_6 = all_52_9 % 152.18/22.72 (52) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0 % 152.18/22.72 (53) ~ (all_56_1 = e2) | all_56_3 = e3 % 152.18/22.72 (54) ~ (all_56_1 = e0) | all_56_7 = e3 % 152.18/22.72 (55) ~ (all_52_9 = all_52_13) % 152.18/22.72 (56) ~ (all_52_2 = all_52_3) % 152.18/22.72 (57) op(e1, all_6_1) = all_6_0 % 152.18/22.72 (58) all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3 % 152.18/22.72 (59) all_58_3 = all_8_2 % 152.18/22.72 (60) all_56_3 = all_52_4 % 152.18/22.72 (61) all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1 % 152.18/22.72 (62) ~ (all_52_6 = all_52_7) % 152.18/22.72 (63) all_54_7 = all_52_13 % 152.18/22.72 (64) op(all_6_2, all_6_2) = all_6_1 % 152.18/22.72 (65) ~ (all_52_7 = e1) % 152.18/22.72 (66) all_58_14 = e0 % 152.18/22.72 (67) all_54_13 = all_52_7 % 152.18/22.72 (68) op(e1, e1) = all_6_2 % 152.18/22.72 (69) op(e0, e3) = all_52_3 % 152.18/22.72 (70) all_58_2 = all_52_1 % 152.18/22.72 (71) ~ (all_52_9 = all_6_2) % 152.18/22.72 (72) all_58_7 = all_52_6 % 152.18/22.73 (73) all_58_10 = all_52_13 % 152.18/22.73 (74) op(all_10_2, all_10_2) = all_10_1 % 152.18/22.73 (75) ~ (all_56_11 = e0) | all_56_15 = e2 % 152.18/22.73 (76) op(e1, e1) = all_4_1 % 152.18/22.73 (77) all_58_0 = all_10_2 % 152.18/22.73 (78) op(e1, all_6_2) = all_56_20 % 152.18/22.73 (79) ~ (all_52_12 = e1) % 152.18/22.73 (80) ~ (all_52_4 = all_52_12) % 152.18/22.73 (81) ~ (all_52_8 = all_52_12) % 152.18/22.73 (82) ~ (all_52_6 = all_6_2) % 152.18/22.73 (83) ~ (all_52_7 = e0) % 152.18/22.73 (84) ~ (all_52_4 = all_10_2) % 152.18/22.73 (85) ~ (all_52_4 = all_8_2) % 152.18/22.73 (86) op(all_8_2, all_8_2) = all_8_1 % 152.18/22.73 (87) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 152.18/22.73 (88) all_56_19 = all_52_6 % 152.18/22.73 (89) ~ (all_52_12 = all_10_2) % 152.18/22.73 (90) ~ (all_4_0 = e2) % 152.18/22.73 (91) ~ (all_4_0 = e3) % 152.18/22.73 (92) all_56_9 = all_52_1 % 152.18/22.73 (93) ~ (all_52_1 = all_10_2) % 152.18/22.73 % 152.18/22.73 Begin of proof % 152.18/22.73 | % 152.18/22.73 | GROUND_INST: instantiating (38) with all_6_2, all_4_1, e1, e1, simplifying % 152.18/22.73 | with (68), (76) gives: % 152.18/22.73 | (94) all_6_2 = all_4_1 % 152.18/22.73 | % 152.18/22.73 | COMBINE_EQS: (8), (94) imply: % 152.18/22.73 | (95) all_54_10 = all_4_1 % 152.18/22.73 | % 152.18/22.73 | COMBINE_EQS: (22), (94) imply: % 152.18/22.73 | (96) all_56_21 = all_4_1 % 152.18/22.73 | % 152.18/22.73 | COMBINE_EQS: (49), (94) imply: % 152.18/22.73 | (97) all_58_8 = all_4_1 % 152.18/22.73 | % 152.18/22.73 | REDUCE: (82), (94) imply: % 152.18/22.73 | (98) ~ (all_52_6 = all_4_1) % 152.18/22.73 | % 152.18/22.73 | REDUCE: (34), (94) imply: % 152.18/22.73 | (99) ~ (all_52_8 = all_4_1) % 152.18/22.73 | % 152.18/22.73 | REDUCE: (71), (94) imply: % 152.18/22.73 | (100) ~ (all_52_9 = all_4_1) % 152.18/22.73 | % 152.18/22.73 | REDUCE: (41), (94) imply: % 152.18/22.73 | (101) ~ (all_4_1 = e0) % 152.18/22.73 | % 152.18/22.73 | REDUCE: (64), (94) imply: % 152.18/22.73 | (102) op(all_4_1, all_4_1) = all_6_1 % 152.18/22.73 | % 152.18/22.73 | REDUCE: (78), (94) imply: % 152.18/22.73 | (103) op(e1, all_4_1) = all_56_20 % 152.18/22.73 | % 152.18/22.73 | BETA: splitting (11) gives: % 152.18/22.73 | % 152.18/22.73 | Case 1: % 152.18/22.73 | | % 152.18/22.73 | | (104) ~ (all_56_21 = e2) % 152.18/22.73 | | % 152.18/22.73 | | REDUCE: (96), (104) imply: % 152.18/22.73 | | (105) ~ (all_4_1 = e2) % 152.18/22.73 | | % 152.18/22.73 | | BETA: splitting (75) gives: % 152.18/22.73 | | % 152.18/22.73 | | Case 1: % 152.18/22.73 | | | % 152.18/22.73 | | | (106) ~ (all_56_11 = e0) % 152.18/22.73 | | | % 152.18/22.73 | | | REDUCE: (1), (106) imply: % 152.18/22.73 | | | (107) ~ (all_8_2 = e0) % 152.18/22.73 | | | % 152.18/22.73 | | | BETA: splitting (36) gives: % 152.18/22.73 | | | % 152.18/22.73 | | | Case 1: % 152.18/22.73 | | | | % 152.18/22.73 | | | | (108) ~ (all_56_21 = e3) % 152.18/22.73 | | | | % 152.18/22.73 | | | | REDUCE: (96), (108) imply: % 152.18/22.73 | | | | (109) ~ (all_4_1 = e3) % 152.18/22.73 | | | | % 152.18/22.73 | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (9), (10), (12), (13), % 152.18/22.73 | | | | (14), (16), (17), (18), (19), (20), (21), (23), (24), (25), % 152.18/22.73 | | | | (26), (27), (29), (31), (32), (33), (35), (37), (38), (39), % 152.18/22.73 | | | | (40), (42), (45), (47), (48), (50), (51), (53), (54), (55), % 152.18/22.73 | | | | (57), (58), (59), (60), (61), (63), (65), (66), (70), (72), % 152.18/22.73 | | | | (73), (74), (76), (77), (79), (80), (81), (84), (85), (86), % 152.18/22.73 | | | | (87), (89), (92), (93), (95), (97), (98), (99), (100), (101), % 152.18/22.73 | | | | (102), (103), (105), (107), (109) are inconsistent by % 152.18/22.73 | | | | sub-proof #525. % 152.18/22.73 | | | | % 152.18/22.73 | | | Case 2: % 152.18/22.73 | | | | % 152.18/22.73 | | | | (110) all_56_21 = e3 % 152.18/22.73 | | | | (111) all_56_17 = e1 % 152.18/22.73 | | | | % 152.18/22.73 | | | | REF_CLOSE: (15), (28), (38), (43), (44), (46), (56), (69), (90), (91), % 152.18/22.73 | | | | (96), (110), (111) are inconsistent by sub-proof #520. % 152.18/22.73 | | | | % 152.18/22.73 | | | End of split % 152.18/22.73 | | | % 152.18/22.73 | | Case 2: % 152.18/22.73 | | | % 152.18/22.73 | | | (112) all_56_11 = e0 % 152.18/22.73 | | | % 152.18/22.73 | | | COMBINE_EQS: (1), (112) imply: % 152.18/22.73 | | | (113) all_8_2 = e0 % 152.18/22.73 | | | % 152.18/22.73 | | | REDUCE: (86), (113) imply: % 152.18/22.73 | | | (114) op(e0, e0) = all_8_1 % 152.18/22.73 | | | % 152.18/22.73 | | | REF_CLOSE: (4), (5), (38), (114) are inconsistent by sub-proof #519. % 152.18/22.73 | | | % 152.18/22.73 | | End of split % 152.18/22.73 | | % 152.18/22.73 | Case 2: % 152.18/22.73 | | % 152.18/22.73 | | (115) all_56_21 = e2 % 152.18/22.73 | | (116) all_56_19 = e1 % 152.18/22.73 | | % 152.18/22.73 | | COMBINE_EQS: (88), (116) imply: % 152.18/22.73 | | (117) all_52_6 = e1 % 152.18/22.73 | | % 152.18/22.73 | | SIMP: (117) implies: % 152.18/22.73 | | (118) all_52_6 = e1 % 152.18/22.73 | | % 152.18/22.73 | | COMBINE_EQS: (96), (115) imply: % 152.18/22.73 | | (119) all_4_1 = e2 % 152.18/22.73 | | % 152.18/22.73 | | SIMP: (119) implies: % 152.18/22.73 | | (120) all_4_1 = e2 % 152.18/22.73 | | % 152.18/22.73 | | REDUCE: (62), (118) imply: % 152.18/22.73 | | (121) ~ (all_52_7 = e1) % 152.18/22.73 | | % 152.18/22.73 | | REDUCE: (43), (120) imply: % 152.18/22.73 | | (122) op(e0, e2) = all_4_0 % 152.18/22.73 | | % 152.18/22.73 | | REF_CLOSE: (30), (38), (52), (65), (67), (83), (90), (91), (122) are % 152.18/22.73 | | inconsistent by sub-proof #518. % 152.18/22.73 | | % 152.18/22.73 | End of split % 152.18/22.73 | % 152.18/22.73 End of proof % 152.18/22.73 % 152.18/22.73 Sub-proof #518 shows that the following formulas are inconsistent: % 152.18/22.73 ---------------------------------------------------------------- % 152.18/22.73 (1) op(e0, e2) = all_4_0 % 152.18/22.73 (2) op(e0, e2) = all_52_7 % 152.18/22.73 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 152.18/22.73 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 152.18/22.73 (4) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0 % 152.18/22.73 (5) ~ (all_52_7 = e1) % 152.18/22.73 (6) all_54_13 = all_52_7 % 152.18/22.73 (7) ~ (all_52_7 = e0) % 152.18/22.73 (8) ~ (all_4_0 = e2) % 152.18/22.73 (9) ~ (all_4_0 = e3) % 152.18/22.73 % 152.18/22.73 Begin of proof % 152.18/22.73 | % 152.18/22.73 | GROUND_INST: instantiating (3) with all_52_7, all_4_0, e2, e0, simplifying % 152.18/22.73 | with (1), (2) gives: % 152.18/22.73 | (10) all_52_7 = all_4_0 % 152.18/22.73 | % 152.18/22.73 | COMBINE_EQS: (6), (10) imply: % 152.18/22.73 | (11) all_54_13 = all_4_0 % 152.18/22.73 | % 152.18/22.73 | BETA: splitting (4) gives: % 152.18/22.73 | % 152.18/22.73 | Case 1: % 152.18/22.73 | | % 152.18/22.73 | | (12) all_54_13 = e3 % 152.18/22.73 | | % 152.18/22.73 | | COMBINE_EQS: (11), (12) imply: % 152.18/22.73 | | (13) all_4_0 = e3 % 152.18/22.73 | | % 152.18/22.73 | | SIMP: (13) implies: % 152.18/22.73 | | (14) all_4_0 = e3 % 152.18/22.73 | | % 152.18/22.73 | | REDUCE: (9), (14) imply: % 152.18/22.73 | | (15) $false % 152.18/22.73 | | % 152.18/22.73 | | CLOSE: (15) is inconsistent. % 152.18/22.73 | | % 152.18/22.73 | Case 2: % 152.18/22.73 | | % 152.18/22.73 | | (16) all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0 % 152.18/22.73 | | % 152.18/22.73 | | BETA: splitting (16) gives: % 152.18/22.73 | | % 152.18/22.73 | | Case 1: % 152.18/22.73 | | | % 152.18/22.73 | | | (17) all_54_13 = e2 % 152.18/22.73 | | | % 152.18/22.73 | | | COMBINE_EQS: (11), (17) imply: % 152.18/22.73 | | | (18) all_4_0 = e2 % 152.18/22.73 | | | % 152.18/22.73 | | | REDUCE: (8), (18) imply: % 152.18/22.73 | | | (19) $false % 152.18/22.73 | | | % 152.18/22.73 | | | CLOSE: (19) is inconsistent. % 152.18/22.73 | | | % 152.18/22.73 | | Case 2: % 152.18/22.73 | | | % 152.18/22.73 | | | (20) all_54_13 = e1 | all_54_13 = e0 % 152.18/22.73 | | | % 152.18/22.73 | | | REF_CLOSE: (5), (6), (7), (20) are inconsistent by sub-proof #711. % 152.18/22.73 | | | % 152.18/22.73 | | End of split % 152.18/22.73 | | % 152.18/22.73 | End of split % 152.18/22.73 | % 152.18/22.73 End of proof % 152.18/22.73 % 152.18/22.73 Sub-proof #519 shows that the following formulas are inconsistent: % 152.18/22.73 ---------------------------------------------------------------- % 152.18/22.73 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 152.18/22.73 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 152.18/22.73 (2) op(e0, e0) = all_8_1 % 152.18/22.73 (3) op(e0, e0) = e1 % 152.18/22.73 (4) ~ (all_8_1 = e1) % 152.18/22.73 % 152.18/22.73 Begin of proof % 152.18/22.73 | % 152.18/22.73 | GROUND_INST: instantiating (1) with e1, all_8_1, e0, e0, simplifying with (2), % 152.18/22.73 | (3) gives: % 152.18/22.73 | (5) all_8_1 = e1 % 152.18/22.73 | % 152.18/22.73 | REDUCE: (4), (5) imply: % 152.18/22.73 | (6) $false % 152.18/22.73 | % 152.18/22.73 | CLOSE: (6) is inconsistent. % 152.18/22.73 | % 152.18/22.73 End of proof % 152.18/22.73 % 152.18/22.73 Sub-proof #520 shows that the following formulas are inconsistent: % 152.18/22.73 ---------------------------------------------------------------- % 152.18/22.73 (1) all_56_21 = e3 % 152.18/22.73 (2) all_54_12 = all_52_3 % 152.18/22.73 (3) all_56_17 = all_52_2 % 152.18/22.73 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 152.18/22.73 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 152.18/22.73 (5) op(e0, all_4_1) = all_4_0 % 152.18/22.73 (6) ~ (all_52_3 = e0) % 152.18/22.73 (7) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0 % 152.18/22.73 (8) all_56_21 = all_4_1 % 152.18/22.73 (9) ~ (all_52_2 = all_52_3) % 152.18/22.73 (10) all_56_17 = e1 % 152.18/22.73 (11) op(e0, e3) = all_52_3 % 152.18/22.73 (12) ~ (all_4_0 = e2) % 152.18/22.73 (13) ~ (all_4_0 = e3) % 152.18/22.73 % 152.18/22.73 Begin of proof % 152.18/22.73 | % 152.18/22.73 | COMBINE_EQS: (3), (10) imply: % 152.18/22.73 | (14) all_52_2 = e1 % 152.18/22.73 | % 152.18/22.73 | SIMP: (14) implies: % 152.18/22.73 | (15) all_52_2 = e1 % 152.18/22.73 | % 152.18/22.73 | COMBINE_EQS: (1), (8) imply: % 152.18/22.73 | (16) all_4_1 = e3 % 152.18/22.73 | % 152.18/22.73 | SIMP: (16) implies: % 152.18/22.73 | (17) all_4_1 = e3 % 152.18/22.73 | % 152.18/22.73 | REF_CLOSE: (2), (4), (5), (6), (7), (9), (11), (12), (13), (15), (17) are % 152.18/22.73 | inconsistent by sub-proof #521. % 152.18/22.73 | % 152.18/22.73 End of proof % 152.18/22.73 % 152.18/22.73 Sub-proof #521 shows that the following formulas are inconsistent: % 152.18/22.73 ---------------------------------------------------------------- % 152.18/22.73 (1) all_4_1 = e3 % 152.18/22.73 (2) all_54_12 = all_52_3 % 152.18/22.73 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 152.18/22.73 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 152.18/22.73 (4) op(e0, all_4_1) = all_4_0 % 152.18/22.73 (5) ~ (all_52_3 = e0) % 152.18/22.73 (6) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0 % 152.18/22.73 (7) all_52_2 = e1 % 152.18/22.73 (8) ~ (all_52_2 = all_52_3) % 152.18/22.73 (9) op(e0, e3) = all_52_3 % 152.18/22.73 (10) ~ (all_4_0 = e2) % 152.18/22.73 (11) ~ (all_4_0 = e3) % 152.18/22.73 % 152.18/22.73 Begin of proof % 152.18/22.73 | % 152.18/22.73 | REDUCE: (7), (8) imply: % 152.18/22.73 | (12) ~ (all_52_3 = e1) % 152.18/22.73 | % 152.18/22.73 | SIMP: (12) implies: % 152.18/22.73 | (13) ~ (all_52_3 = e1) % 152.18/22.73 | % 152.18/22.73 | REDUCE: (1), (4) imply: % 152.18/22.73 | (14) op(e0, e3) = all_4_0 % 152.18/22.73 | % 152.18/22.73 | REF_CLOSE: (2), (3), (5), (6), (9), (10), (11), (13), (14) are inconsistent by % 152.18/22.73 | sub-proof #522. % 152.18/22.73 | % 152.18/22.73 End of proof % 152.18/22.73 % 152.18/22.73 Sub-proof #522 shows that the following formulas are inconsistent: % 152.18/22.73 ---------------------------------------------------------------- % 152.18/22.73 (1) all_54_12 = all_52_3 % 152.18/22.73 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 152.18/22.73 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 152.18/22.73 (3) ~ (all_52_3 = e0) % 152.18/22.73 (4) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0 % 152.18/22.73 (5) op(e0, e3) = all_4_0 % 152.18/22.73 (6) op(e0, e3) = all_52_3 % 152.18/22.73 (7) ~ (all_52_3 = e1) % 152.18/22.73 (8) ~ (all_4_0 = e2) % 152.18/22.73 (9) ~ (all_4_0 = e3) % 152.18/22.73 % 152.18/22.73 Begin of proof % 152.18/22.73 | % 152.18/22.73 | GROUND_INST: instantiating (2) with all_52_3, all_4_0, e3, e0, simplifying % 152.18/22.73 | with (5), (6) gives: % 152.18/22.73 | (10) all_52_3 = all_4_0 % 152.18/22.73 | % 152.18/22.73 | COMBINE_EQS: (1), (10) imply: % 152.18/22.73 | (11) all_54_12 = all_4_0 % 152.18/22.73 | % 152.18/22.73 | BETA: splitting (4) gives: % 152.18/22.73 | % 152.18/22.73 | Case 1: % 152.18/22.73 | | % 152.18/22.73 | | (12) all_54_12 = e3 % 152.18/22.73 | | % 152.18/22.73 | | REF_CLOSE: (9), (11), (12) are inconsistent by sub-proof #524. % 152.18/22.73 | | % 152.18/22.73 | Case 2: % 152.18/22.73 | | % 152.18/22.73 | | (13) all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0 % 152.18/22.73 | | % 152.18/22.73 | | REF_CLOSE: (1), (3), (7), (8), (11), (13) are inconsistent by sub-proof % 152.18/22.73 | | #523. % 152.18/22.73 | | % 152.18/22.73 | End of split % 152.18/22.73 | % 152.18/22.73 End of proof % 152.18/22.73 % 152.18/22.73 Sub-proof #523 shows that the following formulas are inconsistent: % 152.18/22.73 ---------------------------------------------------------------- % 152.18/22.73 (1) all_54_12 = all_52_3 % 152.18/22.73 (2) ~ (all_52_3 = e0) % 152.18/22.73 (3) all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0 % 152.18/22.73 (4) all_54_12 = all_4_0 % 152.18/22.73 (5) ~ (all_52_3 = e1) % 152.18/22.73 (6) ~ (all_4_0 = e2) % 152.18/22.73 % 152.18/22.73 Begin of proof % 152.18/22.73 | % 152.18/22.73 | BETA: splitting (3) gives: % 152.18/22.73 | % 152.18/22.73 | Case 1: % 152.18/22.73 | | % 152.18/22.73 | | (7) all_54_12 = e2 % 152.18/22.73 | | % 152.18/22.73 | | COMBINE_EQS: (4), (7) imply: % 152.18/22.73 | | (8) all_4_0 = e2 % 152.18/22.73 | | % 152.18/22.73 | | SIMP: (8) implies: % 152.18/22.73 | | (9) all_4_0 = e2 % 152.18/22.73 | | % 152.18/22.73 | | REDUCE: (6), (9) imply: % 152.18/22.73 | | (10) $false % 152.18/22.73 | | % 152.18/22.73 | | CLOSE: (10) is inconsistent. % 152.18/22.73 | | % 152.18/22.73 | Case 2: % 152.18/22.73 | | % 152.18/22.73 | | (11) all_54_12 = e1 | all_54_12 = e0 % 152.18/22.73 | | % 152.18/22.73 | | REF_CLOSE: (1), (2), (5), (11) are inconsistent by sub-proof #616. % 152.18/22.73 | | % 152.18/22.73 | End of split % 152.18/22.73 | % 152.18/22.73 End of proof % 152.18/22.73 % 152.18/22.73 Sub-proof #524 shows that the following formulas are inconsistent: % 152.18/22.73 ---------------------------------------------------------------- % 152.18/22.73 (1) all_54_12 = all_4_0 % 152.18/22.73 (2) all_54_12 = e3 % 152.18/22.73 (3) ~ (all_4_0 = e3) % 152.18/22.73 % 152.18/22.73 Begin of proof % 152.18/22.73 | % 152.18/22.73 | COMBINE_EQS: (1), (2) imply: % 152.18/22.73 | (4) all_4_0 = e3 % 152.18/22.73 | % 152.18/22.73 | SIMP: (4) implies: % 152.18/22.73 | (5) all_4_0 = e3 % 152.18/22.73 | % 152.18/22.73 | REDUCE: (3), (5) imply: % 152.18/22.73 | (6) $false % 152.18/22.73 | % 152.18/22.73 | CLOSE: (6) is inconsistent. % 152.18/22.73 | % 152.18/22.73 End of proof % 152.18/22.73 % 152.18/22.73 Sub-proof #525 shows that the following formulas are inconsistent: % 152.18/22.73 ---------------------------------------------------------------- % 152.18/22.73 (1) all_56_11 = all_8_2 % 152.18/22.73 (2) op(e0, all_52_13) = all_56_14 % 152.18/22.73 (3) ~ (all_56_11 = e1) | all_56_13 = e2 % 152.18/22.73 (4) op(e0, e0) = e1 % 152.18/22.73 (5) ~ (all_8_1 = e1) % 152.18/22.73 (6) ~ (all_52_1 = all_52_9) % 152.18/22.73 (7) ~ (all_52_13 = e1) % 152.18/22.73 (8) ~ (all_4_1 = e0) % 152.18/22.73 (9) ~ (all_4_1 = e3) % 152.18/22.73 (10) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0 % 152.18/22.73 (11) ~ (all_52_13 = all_8_2) % 152.18/22.73 (12) all_54_0 = all_10_2 % 152.18/22.73 (13) all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2 % 152.18/22.73 (14) ~ (all_52_9 = all_8_2) % 152.18/22.73 (15) ~ (all_52_12 = all_52_13) % 152.18/22.73 (16) ~ (e3 = e2) % 152.18/22.73 (17) all_58_4 = all_52_8 % 152.18/22.73 (18) all_54_5 = all_8_2 % 152.18/22.73 (19) op(e1, all_4_1) = all_56_20 % 152.18/22.73 (20) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 152.18/22.73 (21) ~ (all_10_1 = e1) % 152.18/22.73 (22) ~ (all_4_1 = e2) % 152.18/22.73 (23) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 152.18/22.73 (24) all_56_1 = all_10_2 % 152.18/22.73 (25) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0 % 152.18/22.73 (26) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0 % 152.18/22.73 (27) all_58_5 = all_52_9 % 152.18/22.73 (28) all_58_9 = all_52_12 % 152.18/22.73 (29) ~ (all_52_9 = all_4_1) % 152.18/22.73 (30) ~ (all_56_1 = e1) | all_56_5 = e3 % 152.18/22.73 (31) all_58_1 = all_52_4 % 152.18/22.73 (32) all_58_13 = all_52_7 % 152.18/22.73 (33) ~ (all_52_6 = all_4_1) % 152.18/22.73 (34) all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1 % 152.18/22.73 (35) all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1 % 152.18/22.73 (36) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 152.18/22.73 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 152.18/22.73 (37) all_54_3 = all_52_12 % 152.18/22.73 (38) all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0 % 152.18/22.73 (39) ~ (all_56_11 = e3) | all_56_9 = e2 % 152.18/22.73 (40) all_56_7 = all_52_12 % 152.18/22.73 (41) all_56_13 = all_52_9 % 152.18/22.73 (42) ~ (all_52_9 = e0) % 152.18/22.73 (43) ~ (all_6_0 = e3) % 152.18/22.73 (44) all_54_6 = all_52_9 % 152.18/22.73 (45) ~ (all_56_1 = e2) | all_56_3 = e3 % 152.18/22.73 (46) ~ (all_56_1 = e0) | all_56_7 = e3 % 152.18/22.73 (47) op(all_4_1, all_4_1) = all_6_1 % 152.18/22.73 (48) ~ (all_52_9 = all_52_13) % 152.18/22.73 (49) op(e1, all_6_1) = all_6_0 % 152.18/22.73 (50) all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3 % 152.18/22.73 (51) all_58_3 = all_8_2 % 152.18/22.73 (52) all_56_3 = all_52_4 % 152.18/22.73 (53) all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1 % 152.18/22.73 (54) all_54_7 = all_52_13 % 152.18/22.73 (55) ~ (all_52_7 = e1) % 152.18/22.73 (56) all_58_14 = e0 % 152.18/22.73 (57) all_54_10 = all_4_1 % 152.18/22.73 (58) all_58_2 = all_52_1 % 152.18/22.73 (59) all_58_7 = all_52_6 % 152.18/22.73 (60) all_58_10 = all_52_13 % 152.18/22.73 (61) ~ (all_52_8 = all_4_1) % 152.18/22.73 (62) op(all_10_2, all_10_2) = all_10_1 % 152.18/22.73 (63) op(e1, e1) = all_4_1 % 152.18/22.73 (64) all_58_0 = all_10_2 % 152.18/22.73 (65) ~ (all_52_12 = e1) % 152.18/22.73 (66) all_58_8 = all_4_1 % 152.18/22.73 (67) ~ (all_52_4 = all_52_12) % 152.18/22.73 (68) ~ (all_52_8 = all_52_12) % 152.18/22.73 (69) ~ (all_8_2 = e0) % 152.18/22.73 (70) ~ (all_52_4 = all_10_2) % 152.18/22.73 (71) ~ (all_52_4 = all_8_2) % 152.18/22.73 (72) op(all_8_2, all_8_2) = all_8_1 % 152.18/22.73 (73) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 152.18/22.73 (74) ~ (all_52_12 = all_10_2) % 152.18/22.73 (75) all_56_9 = all_52_1 % 152.18/22.73 (76) ~ (all_52_1 = all_10_2) % 152.18/22.73 % 152.18/22.73 Begin of proof % 152.18/22.73 | % 152.18/22.73 | BETA: splitting (23) gives: % 152.18/22.73 | % 152.18/22.73 | Case 1: % 152.18/22.73 | | % 152.18/22.73 | | (77) all_54_10 = e3 % 152.18/22.73 | | % 152.18/22.73 | | COMBINE_EQS: (57), (77) imply: % 152.18/22.73 | | (78) all_4_1 = e3 % 152.18/22.73 | | % 152.18/22.73 | | REDUCE: (9), (78) imply: % 152.18/22.73 | | (79) $false % 152.18/22.73 | | % 152.18/22.73 | | CLOSE: (79) is inconsistent. % 152.18/22.73 | | % 152.18/22.73 | Case 2: % 152.18/22.73 | | % 152.18/22.73 | | (80) ~ (all_54_10 = e3) % 152.18/22.73 | | (81) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 152.18/22.73 | | % 152.18/22.73 | | BETA: splitting (81) gives: % 152.18/22.73 | | % 152.18/22.73 | | Case 1: % 152.18/22.73 | | | % 152.18/22.73 | | | (82) all_54_10 = e2 % 152.18/22.73 | | | % 152.18/22.73 | | | COMBINE_EQS: (57), (82) imply: % 152.18/22.73 | | | (83) all_4_1 = e2 % 152.18/22.73 | | | % 152.18/22.73 | | | REDUCE: (22), (83) imply: % 152.18/22.73 | | | (84) $false % 152.18/22.73 | | | % 152.18/22.73 | | | CLOSE: (84) is inconsistent. % 152.18/22.73 | | | % 152.18/22.73 | | Case 2: % 152.18/22.73 | | | % 152.18/22.73 | | | (85) ~ (all_54_10 = e2) % 152.18/22.73 | | | (86) all_54_10 = e1 | all_54_10 = e0 % 152.18/22.73 | | | % 152.18/22.73 | | | BETA: splitting (86) gives: % 152.18/22.73 | | | % 152.18/22.73 | | | Case 1: % 152.18/22.73 | | | | % 152.18/22.73 | | | | (87) all_54_10 = e1 % 152.18/22.73 | | | | % 152.18/22.73 | | | | COMBINE_EQS: (57), (87) imply: % 152.18/22.73 | | | | (88) all_4_1 = e1 % 152.18/22.73 | | | | % 152.18/22.73 | | | | REDUCE: (33), (88) imply: % 152.18/22.73 | | | | (89) ~ (all_52_6 = e1) % 152.18/22.73 | | | | % 152.18/22.73 | | | | REDUCE: (61), (88) imply: % 152.18/22.73 | | | | (90) ~ (all_52_8 = e1) % 152.18/22.73 | | | | % 152.18/22.73 | | | | REDUCE: (29), (88) imply: % 152.18/22.73 | | | | (91) ~ (all_52_9 = e1) % 152.18/22.73 | | | | % 152.18/22.73 | | | | REDUCE: (47), (88) imply: % 152.18/22.73 | | | | (92) op(e1, e1) = all_6_1 % 152.18/22.73 | | | | % 152.18/22.73 | | | | REDUCE: (19), (88) imply: % 152.18/22.73 | | | | (93) op(e1, e1) = all_56_20 % 152.18/22.73 | | | | % 152.18/22.73 | | | | REDUCE: (63), (88) imply: % 152.18/22.73 | | | | (94) op(e1, e1) = e1 % 152.18/22.73 | | | | % 152.18/22.73 | | | | GROUND_INST: instantiating (36) with all_6_1, all_56_20, e1, e1, % 152.18/22.73 | | | | simplifying with (92), (93) gives: % 152.18/22.73 | | | | (95) all_56_20 = all_6_1 % 152.18/22.73 | | | | % 152.18/22.73 | | | | GROUND_INST: instantiating (36) with e1, all_56_20, e1, e1, simplifying % 152.18/22.73 | | | | with (93), (94) gives: % 152.18/22.73 | | | | (96) all_56_20 = e1 % 152.18/22.73 | | | | % 152.18/22.73 | | | | COMBINE_EQS: (95), (96) imply: % 152.18/22.73 | | | | (97) all_6_1 = e1 % 152.18/22.73 | | | | % 152.18/22.73 | | | | SIMP: (97) implies: % 152.18/22.73 | | | | (98) all_6_1 = e1 % 152.18/22.73 | | | | % 152.18/22.73 | | | | REDUCE: (49), (98) imply: % 152.18/22.73 | | | | (99) op(e1, e1) = all_6_0 % 152.18/22.73 | | | | % 152.18/22.73 | | | | GROUND_INST: instantiating (36) with e1, all_6_0, e1, e1, simplifying % 152.18/22.73 | | | | with (94), (99) gives: % 152.18/22.73 | | | | (100) all_6_0 = e1 % 152.18/22.73 | | | | % 152.18/22.73 | | | | REDUCE: (43), (100) imply: % 152.18/22.73 | | | | (101) ~ (e3 = e1) % 152.18/22.73 | | | | % 152.18/22.73 | | | | SIMP: (101) implies: % 152.18/22.73 | | | | (102) ~ (e3 = e1) % 152.18/22.73 | | | | % 152.18/22.73 | | | | BETA: splitting (46) gives: % 152.18/22.73 | | | | % 152.18/22.73 | | | | Case 1: % 152.18/22.73 | | | | | % 152.18/22.73 | | | | | (103) ~ (all_56_1 = e0) % 152.18/22.73 | | | | | % 152.18/22.73 | | | | | REDUCE: (24), (103) imply: % 152.18/22.73 | | | | | (104) ~ (all_10_2 = e0) % 152.18/22.73 | | | | | % 152.18/22.73 | | | | | REF_CLOSE: (1), (5), (6), (7), (10), (11), (12), (13), (14), (15), % 152.18/22.73 | | | | | (17), (18), (20), (22), (24), (25), (26), (27), (28), (30), % 152.18/22.73 | | | | | (31), (32), (34), (36), (37), (39), (42), (44), (45), (48), % 152.18/22.73 | | | | | (51), (52), (53), (54), (55), (56), (59), (64), (65), (66), % 152.18/22.73 | | | | | (67), (68), (69), (70), (71), (72), (73), (74), (75), (89), % 152.18/22.73 | | | | | (90), (91), (93), (94), (102), (104) are inconsistent by % 152.18/22.73 | | | | | sub-proof #531. % 152.18/22.73 | | | | | % 152.18/22.73 | | | | Case 2: % 152.18/22.73 | | | | | % 152.18/22.73 | | | | | (105) all_56_7 = e3 % 152.18/22.73 | | | | | (106) all_56_1 = e0 % 152.18/22.73 | | | | | % 152.18/22.73 | | | | | COMBINE_EQS: (24), (106) imply: % 152.18/22.73 | | | | | (107) all_10_2 = e0 % 152.18/22.73 | | | | | % 152.18/22.73 | | | | | COMBINE_EQS: (40), (105) imply: % 152.18/22.73 | | | | | (108) all_52_12 = e3 % 152.18/22.73 | | | | | % 152.18/22.73 | | | | | REDUCE: (76), (107) imply: % 152.18/22.73 | | | | | (109) ~ (all_52_1 = e0) % 152.18/22.73 | | | | | % 152.18/22.73 | | | | | REDUCE: (68), (108) imply: % 152.18/22.73 | | | | | (110) ~ (all_52_8 = e3) % 152.18/22.73 | | | | | % 152.18/22.73 | | | | | REDUCE: (74), (107), (108) imply: % 152.18/22.73 | | | | | (111) ~ (e3 = e0) % 152.18/22.73 | | | | | % 152.18/22.73 | | | | | REDUCE: (62), (107) imply: % 152.18/22.73 | | | | | (112) op(e0, e0) = all_10_1 % 152.18/22.73 | | | | | % 152.18/22.73 | | | | | BETA: splitting (50) gives: % 152.18/22.73 | | | | | % 152.18/22.73 | | | | | Case 1: % 152.18/22.73 | | | | | | % 152.18/22.73 | | | | | | (113) all_58_4 = e3 % 152.18/22.73 | | | | | | % 152.18/22.73 | | | | | | COMBINE_EQS: (17), (113) imply: % 152.18/22.73 | | | | | | (114) all_52_8 = e3 % 152.18/22.73 | | | | | | % 152.18/22.73 | | | | | | REDUCE: (110), (114) imply: % 152.18/22.73 | | | | | | (115) $false % 152.18/22.73 | | | | | | % 152.18/22.73 | | | | | | CLOSE: (115) is inconsistent. % 152.18/22.73 | | | | | | % 152.18/22.73 | | | | | Case 2: % 152.18/22.73 | | | | | | % 152.18/22.73 | | | | | | (116) all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3 % 152.18/22.73 | | | | | | % 152.18/22.73 | | | | | | BETA: splitting (116) gives: % 152.18/22.73 | | | | | | % 152.18/22.73 | | | | | | Case 1: % 152.18/22.73 | | | | | | | % 152.18/22.73 | | | | | | | (117) all_58_5 = e3 % 152.18/22.73 | | | | | | | % 152.18/22.73 | | | | | | | COMBINE_EQS: (27), (117) imply: % 152.18/22.73 | | | | | | | (118) all_52_9 = e3 % 152.18/22.73 | | | | | | | % 152.18/22.73 | | | | | | | COMBINE_EQS: (41), (118) imply: % 152.18/22.73 | | | | | | | (119) all_56_13 = e3 % 152.18/22.73 | | | | | | | % 152.18/22.73 | | | | | | | REDUCE: (14), (118) imply: % 152.18/22.73 | | | | | | | (120) ~ (all_8_2 = e3) % 152.18/22.73 | | | | | | | % 152.18/22.73 | | | | | | | SIMP: (120) implies: % 152.18/22.73 | | | | | | | (121) ~ (all_8_2 = e3) % 152.18/22.73 | | | | | | | % 152.18/22.73 | | | | | | | BETA: splitting (3) gives: % 152.18/22.73 | | | | | | | % 152.18/22.73 | | | | | | | Case 1: % 152.18/22.73 | | | | | | | | % 152.18/22.73 | | | | | | | | (122) ~ (all_56_11 = e1) % 152.18/22.73 | | | | | | | | % 152.18/22.73 | | | | | | | | REDUCE: (1), (122) imply: % 152.18/22.73 | | | | | | | | (123) ~ (all_8_2 = e1) % 152.18/22.73 | | | | | | | | % 152.18/22.73 | | | | | | | | BETA: splitting (73) gives: % 152.18/22.73 | | | | | | | | % 152.18/22.73 | | | | | | | | Case 1: % 152.18/22.73 | | | | | | | | | % 152.18/22.73 | | | | | | | | | (124) all_54_5 = e3 % 152.18/22.73 | | | | | | | | | % 152.18/22.73 | | | | | | | | | REF_CLOSE: (18), (121), (124) are inconsistent by sub-proof % 152.18/22.73 | | | | | | | | | #737. % 152.18/22.73 | | | | | | | | | % 152.18/22.73 | | | | | | | | Case 2: % 152.18/22.73 | | | | | | | | | % 152.18/22.73 | | | | | | | | | (125) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 152.18/22.73 | | | | | | | | | % 152.18/22.73 | | | | | | | | | BETA: splitting (125) gives: % 152.18/22.73 | | | | | | | | | % 152.18/22.73 | | | | | | | | | Case 1: % 152.18/22.73 | | | | | | | | | | % 152.18/22.73 | | | | | | | | | | (126) all_54_5 = e2 % 152.18/22.73 | | | | | | | | | | % 152.18/22.73 | | | | | | | | | | COMBINE_EQS: (18), (126) imply: % 152.18/22.73 | | | | | | | | | | (127) all_8_2 = e2 % 152.18/22.73 | | | | | | | | | | % 152.18/22.73 | | | | | | | | | | SIMP: (127) implies: % 152.18/22.73 | | | | | | | | | | (128) all_8_2 = e2 % 152.18/22.73 | | | | | | | | | | % 152.18/22.73 | | | | | | | | | | COMBINE_EQS: (51), (128) imply: % 152.18/22.73 | | | | | | | | | | (129) all_58_3 = e2 % 152.18/22.73 | | | | | | | | | | % 152.18/22.73 | | | | | | | | | | REDUCE: (123), (128) imply: % 152.18/22.73 | | | | | | | | | | (130) ~ (e2 = e1) % 152.18/22.73 | | | | | | | | | | % 152.18/22.73 | | | | | | | | | | REDUCE: (69), (128) imply: % 152.18/22.73 | | | | | | | | | | (131) ~ (e2 = e0) % 152.18/22.73 | | | | | | | | | | % 152.18/22.73 | | | | | | | | | | BETA: splitting (35) gives: % 152.18/22.73 | | | | | | | | | | % 152.18/22.73 | | | | | | | | | | Case 1: % 152.18/22.73 | | | | | | | | | | | % 152.18/22.73 | | | | | | | | | | | (132) all_58_2 = e1 % 152.18/22.73 | | | | | | | | | | | % 152.18/22.73 | | | | | | | | | | | COMBINE_EQS: (58), (132) imply: % 152.18/22.73 | | | | | | | | | | | (133) all_52_1 = e1 % 152.18/22.73 | | | | | | | | | | | % 152.18/22.73 | | | | | | | | | | | REDUCE: (109), (133) imply: % 152.18/22.73 | | | | | | | | | | | (134) ~ (e1 = e0) % 152.18/22.73 | | | | | | | | | | | % 152.18/22.73 | | | | | | | | | | | BETA: splitting (38) gives: % 152.18/22.73 | | | | | | | | | | | % 152.18/22.73 | | | | | | | | | | | Case 1: % 152.18/22.73 | | | | | | | | | | | | % 152.18/22.73 | | | | | | | | | | | | (135) all_58_2 = e0 % 152.18/22.73 | | | | | | | | | | | | % 152.18/22.73 | | | | | | | | | | | | COMBINE_EQS: (132), (135) imply: % 152.18/22.73 | | | | | | | | | | | | (136) e1 = e0 % 152.18/22.73 | | | | | | | | | | | | % 152.18/22.73 | | | | | | | | | | | | REDUCE: (134), (136) imply: % 152.18/22.73 | | | | | | | | | | | | (137) $false % 152.18/22.73 | | | | | | | | | | | | % 152.18/22.73 | | | | | | | | | | | | CLOSE: (137) is inconsistent. % 152.18/22.73 | | | | | | | | | | | | % 152.18/22.73 | | | | | | | | | | | Case 2: % 152.18/22.73 | | | | | | | | | | | | % 152.18/22.73 | | | | | | | | | | | | (138) all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0 % 152.18/22.73 | | | | | | | | | | | | % 152.18/22.73 | | | | | | | | | | | | BETA: splitting (138) gives: % 152.18/22.73 | | | | | | | | | | | | % 152.18/22.73 | | | | | | | | | | | | Case 1: % 152.18/22.73 | | | | | | | | | | | | | % 152.18/22.73 | | | | | | | | | | | | | (139) all_58_3 = e0 % 152.18/22.73 | | | | | | | | | | | | | % 152.18/22.73 | | | | | | | | | | | | | COMBINE_EQS: (129), (139) imply: % 152.18/22.73 | | | | | | | | | | | | | (140) e2 = e0 % 152.18/22.73 | | | | | | | | | | | | | % 152.18/22.73 | | | | | | | | | | | | | REDUCE: (131), (140) imply: % 152.18/22.73 | | | | | | | | | | | | | (141) $false % 152.18/22.73 | | | | | | | | | | | | | % 152.18/22.73 | | | | | | | | | | | | | CLOSE: (141) is inconsistent. % 152.18/22.73 | | | | | | | | | | | | | % 152.18/22.73 | | | | | | | | | | | | Case 2: % 152.18/22.73 | | | | | | | | | | | | | % 152.18/22.73 | | | | | | | | | | | | | (142) all_58_5 = e0 | all_58_10 = e0 % 152.18/22.73 | | | | | | | | | | | | | % 152.18/22.73 | | | | | | | | | | | | | BETA: splitting (142) gives: % 152.18/22.73 | | | | | | | | | | | | | % 152.18/22.73 | | | | | | | | | | | | | Case 1: % 152.18/22.73 | | | | | | | | | | | | | | % 152.18/22.73 | | | | | | | | | | | | | | (143) all_58_5 = e0 % 152.18/22.73 | | | | | | | | | | | | | | % 152.18/22.73 | | | | | | | | | | | | | | COMBINE_EQS: (117), (143) imply: % 152.18/22.73 | | | | | | | | | | | | | | (144) e3 = e0 % 152.18/22.73 | | | | | | | | | | | | | | % 152.18/22.73 | | | | | | | | | | | | | | REDUCE: (111), (144) imply: % 152.18/22.73 | | | | | | | | | | | | | | (145) $false % 152.18/22.73 | | | | | | | | | | | | | | % 152.18/22.73 | | | | | | | | | | | | | | CLOSE: (145) is inconsistent. % 152.18/22.73 | | | | | | | | | | | | | | % 152.18/22.73 | | | | | | | | | | | | | Case 2: % 152.18/22.73 | | | | | | | | | | | | | | % 152.18/22.73 | | | | | | | | | | | | | | (146) all_58_10 = e0 % 152.18/22.73 | | | | | | | | | | | | | | % 152.18/22.73 | | | | | | | | | | | | | | COMBINE_EQS: (60), (146) imply: % 152.18/22.73 | | | | | | | | | | | | | | (147) all_52_13 = e0 % 152.18/22.73 | | | | | | | | | | | | | | % 152.18/22.73 | | | | | | | | | | | | | | REDUCE: (2), (147) imply: % 152.18/22.73 | | | | | | | | | | | | | | (148) op(e0, e0) = all_56_14 % 152.18/22.73 | | | | | | | | | | | | | | % 152.18/22.73 | | | | | | | | | | | | | | REF_CLOSE: (4), (21), (36), (112), (148) are inconsistent by % 152.18/22.73 | | | | | | | | | | | | | | sub-proof #530. % 152.18/22.73 | | | | | | | | | | | | | | % 152.18/22.73 | | | | | | | | | | | | | End of split % 152.18/22.73 | | | | | | | | | | | | | % 152.18/22.73 | | | | | | | | | | | | End of split % 152.18/22.73 | | | | | | | | | | | | % 152.18/22.73 | | | | | | | | | | | End of split % 152.18/22.73 | | | | | | | | | | | % 152.18/22.73 | | | | | | | | | | Case 2: % 152.18/22.73 | | | | | | | | | | | % 152.18/22.73 | | | | | | | | | | | (149) all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1 % 152.18/22.73 | | | | | | | | | | | % 152.18/22.73 | | | | | | | | | | | REF_CLOSE: (7), (27), (60), (91), (129), (130), (149) are % 152.18/22.73 | | | | | | | | | | | inconsistent by sub-proof #528. % 152.18/22.73 | | | | | | | | | | | % 152.18/22.73 | | | | | | | | | | End of split % 152.18/22.73 | | | | | | | | | | % 152.18/22.73 | | | | | | | | | Case 2: % 152.18/22.73 | | | | | | | | | | % 152.18/22.73 | | | | | | | | | | (150) all_54_5 = e1 | all_54_5 = e0 % 152.18/22.73 | | | | | | | | | | % 152.18/22.73 | | | | | | | | | | REF_CLOSE: (18), (69), (123), (150) are inconsistent by % 152.18/22.73 | | | | | | | | | | sub-proof #645. % 152.18/22.73 | | | | | | | | | | % 152.18/22.73 | | | | | | | | | End of split % 152.18/22.73 | | | | | | | | | % 152.18/22.73 | | | | | | | | End of split % 152.18/22.73 | | | | | | | | % 152.18/22.73 | | | | | | | Case 2: % 152.18/22.73 | | | | | | | | % 152.18/22.73 | | | | | | | | (151) all_56_13 = e2 % 152.18/22.73 | | | | | | | | % 152.18/22.73 | | | | | | | | REF_CLOSE: (16), (119), (151) are inconsistent by sub-proof % 152.18/22.73 | | | | | | | | #527. % 152.18/22.73 | | | | | | | | % 152.18/22.73 | | | | | | | End of split % 152.18/22.73 | | | | | | | % 152.18/22.73 | | | | | | Case 2: % 152.18/22.73 | | | | | | | % 152.18/22.73 | | | | | | | (152) all_58_8 = e3 | all_58_14 = e3 % 152.18/22.73 | | | | | | | % 152.18/22.73 | | | | | | | REF_CLOSE: (9), (56), (66), (111), (152) are inconsistent by % 152.18/22.73 | | | | | | | sub-proof #526. % 152.18/22.73 | | | | | | | % 152.18/22.73 | | | | | | End of split % 152.18/22.73 | | | | | | % 152.18/22.73 | | | | | End of split % 152.18/22.73 | | | | | % 152.18/22.73 | | | | End of split % 152.18/22.73 | | | | % 152.18/22.73 | | | Case 2: % 152.18/22.73 | | | | % 152.18/22.73 | | | | (153) all_54_10 = e0 % 152.18/22.73 | | | | % 152.18/22.73 | | | | COMBINE_EQS: (57), (153) imply: % 152.18/22.73 | | | | (154) all_4_1 = e0 % 152.18/22.73 | | | | % 152.18/22.73 | | | | REDUCE: (8), (154) imply: % 152.18/22.73 | | | | (155) $false % 152.18/22.73 | | | | % 152.18/22.73 | | | | CLOSE: (155) is inconsistent. % 152.18/22.73 | | | | % 152.18/22.73 | | | End of split % 152.18/22.73 | | | % 152.18/22.73 | | End of split % 152.18/22.73 | | % 152.18/22.73 | End of split % 152.18/22.73 | % 152.18/22.73 End of proof % 152.18/22.73 % 152.18/22.73 Sub-proof #526 shows that the following formulas are inconsistent: % 152.18/22.73 ---------------------------------------------------------------- % 152.18/22.73 (1) ~ (e3 = e0) % 152.18/22.73 (2) ~ (all_4_1 = e3) % 152.18/22.74 (3) all_58_8 = e3 | all_58_14 = e3 % 152.18/22.74 (4) all_58_14 = e0 % 152.18/22.74 (5) all_58_8 = all_4_1 % 152.18/22.74 % 152.18/22.74 Begin of proof % 152.18/22.74 | % 152.18/22.74 | BETA: splitting (3) gives: % 152.18/22.74 | % 152.18/22.74 | Case 1: % 152.18/22.74 | | % 152.18/22.74 | | (6) all_58_8 = e3 % 152.18/22.74 | | % 152.18/22.74 | | COMBINE_EQS: (5), (6) imply: % 152.18/22.74 | | (7) all_4_1 = e3 % 152.18/22.74 | | % 152.18/22.74 | | REDUCE: (2), (7) imply: % 152.18/22.74 | | (8) $false % 152.18/22.74 | | % 152.18/22.74 | | CLOSE: (8) is inconsistent. % 152.18/22.74 | | % 152.18/22.74 | Case 2: % 152.18/22.74 | | % 152.18/22.74 | | (9) all_58_14 = e3 % 152.18/22.74 | | % 152.18/22.74 | | COMBINE_EQS: (4), (9) imply: % 152.18/22.74 | | (10) e3 = e0 % 152.18/22.74 | | % 152.18/22.74 | | SIMP: (10) implies: % 152.18/22.74 | | (11) e3 = e0 % 152.18/22.74 | | % 152.18/22.74 | | REDUCE: (1), (11) imply: % 152.18/22.74 | | (12) $false % 152.18/22.74 | | % 152.18/22.74 | | CLOSE: (12) is inconsistent. % 152.18/22.74 | | % 152.18/22.74 | End of split % 152.18/22.74 | % 152.18/22.74 End of proof % 152.18/22.74 % 152.18/22.74 Sub-proof #527 shows that the following formulas are inconsistent: % 152.18/22.74 ---------------------------------------------------------------- % 152.18/22.74 (1) all_56_13 = e3 % 152.18/22.74 (2) all_56_13 = e2 % 152.18/22.74 (3) ~ (e3 = e2) % 152.18/22.74 % 152.18/22.74 Begin of proof % 152.18/22.74 | % 152.18/22.74 | COMBINE_EQS: (1), (2) imply: % 152.18/22.74 | (4) e3 = e2 % 152.18/22.74 | % 152.18/22.74 | SIMP: (4) implies: % 152.18/22.74 | (5) e3 = e2 % 152.18/22.74 | % 152.18/22.74 | REDUCE: (3), (5) imply: % 152.18/22.74 | (6) $false % 152.18/22.74 | % 152.18/22.74 | CLOSE: (6) is inconsistent. % 152.18/22.74 | % 152.18/22.74 End of proof % 152.18/22.74 % 152.18/22.74 Sub-proof #528 shows that the following formulas are inconsistent: % 152.18/22.74 ---------------------------------------------------------------- % 152.18/22.74 (1) ~ (all_52_13 = e1) % 152.18/22.74 (2) all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1 % 152.18/22.74 (3) all_58_5 = all_52_9 % 152.18/22.74 (4) ~ (e2 = e1) % 152.18/22.74 (5) ~ (all_52_9 = e1) % 152.18/22.74 (6) all_58_10 = all_52_13 % 152.18/22.74 (7) all_58_3 = e2 % 152.18/22.74 % 152.18/22.74 Begin of proof % 152.18/22.74 | % 152.18/22.74 | BETA: splitting (2) gives: % 152.18/22.74 | % 152.18/22.74 | Case 1: % 152.18/22.74 | | % 152.18/22.74 | | (8) all_58_3 = e1 % 152.18/22.74 | | % 152.18/22.74 | | COMBINE_EQS: (7), (8) imply: % 152.18/22.74 | | (9) e2 = e1 % 152.18/22.74 | | % 152.18/22.74 | | REDUCE: (4), (9) imply: % 152.18/22.74 | | (10) $false % 152.18/22.74 | | % 152.18/22.74 | | CLOSE: (10) is inconsistent. % 152.18/22.74 | | % 152.18/22.74 | Case 2: % 152.18/22.74 | | % 152.18/22.74 | | (11) all_58_5 = e1 | all_58_10 = e1 % 152.18/22.74 | | % 152.18/22.74 | | REF_CLOSE: (1), (3), (5), (6), (11) are inconsistent by sub-proof #529. % 152.18/22.74 | | % 152.18/22.74 | End of split % 152.18/22.74 | % 152.18/22.74 End of proof % 152.18/22.74 % 152.18/22.74 Sub-proof #529 shows that the following formulas are inconsistent: % 152.18/22.74 ---------------------------------------------------------------- % 152.18/22.74 (1) ~ (all_52_13 = e1) % 152.18/22.74 (2) all_58_5 = e1 | all_58_10 = e1 % 152.18/22.74 (3) all_58_5 = all_52_9 % 152.18/22.74 (4) ~ (all_52_9 = e1) % 152.18/22.74 (5) all_58_10 = all_52_13 % 152.18/22.74 % 152.18/22.74 Begin of proof % 152.18/22.74 | % 152.18/22.74 | BETA: splitting (2) gives: % 152.18/22.74 | % 152.18/22.74 | Case 1: % 152.18/22.74 | | % 152.18/22.74 | | (6) all_58_5 = e1 % 152.18/22.74 | | % 152.18/22.74 | | COMBINE_EQS: (3), (6) imply: % 152.18/22.74 | | (7) all_52_9 = e1 % 152.18/22.74 | | % 152.18/22.74 | | REDUCE: (4), (7) imply: % 152.18/22.74 | | (8) $false % 152.18/22.74 | | % 152.18/22.74 | | CLOSE: (8) is inconsistent. % 152.18/22.74 | | % 152.18/22.74 | Case 2: % 152.18/22.74 | | % 152.18/22.74 | | (9) all_58_10 = e1 % 152.18/22.74 | | % 152.18/22.74 | | COMBINE_EQS: (5), (9) imply: % 152.18/22.74 | | (10) all_52_13 = e1 % 152.18/22.74 | | % 152.18/22.74 | | REDUCE: (1), (10) imply: % 152.18/22.74 | | (11) $false % 152.18/22.74 | | % 152.18/22.74 | | CLOSE: (11) is inconsistent. % 152.18/22.74 | | % 152.18/22.74 | End of split % 152.18/22.74 | % 152.18/22.74 End of proof % 152.18/22.74 % 152.18/22.74 Sub-proof #530 shows that the following formulas are inconsistent: % 152.18/22.74 ---------------------------------------------------------------- % 152.18/22.74 (1) op(e0, e0) = e1 % 152.18/22.74 (2) ~ (all_10_1 = e1) % 152.18/22.74 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 152.18/22.74 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 152.18/22.74 (4) op(e0, e0) = all_10_1 % 152.18/22.74 (5) op(e0, e0) = all_56_14 % 152.18/22.74 % 152.18/22.74 Begin of proof % 152.18/22.74 | % 152.18/22.74 | GROUND_INST: instantiating (3) with e1, all_56_14, e0, e0, simplifying with % 152.18/22.74 | (1), (5) gives: % 152.18/22.74 | (6) all_56_14 = e1 % 152.18/22.74 | % 152.18/22.74 | GROUND_INST: instantiating (3) with all_10_1, all_56_14, e0, e0, simplifying % 152.18/22.74 | with (4), (5) gives: % 152.18/22.74 | (7) all_56_14 = all_10_1 % 152.18/22.74 | % 152.18/22.74 | COMBINE_EQS: (6), (7) imply: % 152.18/22.74 | (8) all_10_1 = e1 % 152.18/22.74 | % 152.18/22.74 | REDUCE: (2), (8) imply: % 152.18/22.74 | (9) $false % 152.18/22.74 | % 152.18/22.74 | CLOSE: (9) is inconsistent. % 152.18/22.74 | % 152.18/22.74 End of proof % 152.18/22.74 % 152.18/22.74 Sub-proof #531 shows that the following formulas are inconsistent: % 152.18/22.74 ---------------------------------------------------------------- % 152.18/22.74 (1) all_56_11 = all_8_2 % 152.18/22.74 (2) ~ (all_52_6 = e1) % 152.18/22.74 (3) ~ (all_8_1 = e1) % 152.18/22.74 (4) ~ (all_52_1 = all_52_9) % 152.18/22.74 (5) ~ (all_52_13 = e1) % 152.18/22.74 (6) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0 % 152.18/22.74 (7) ~ (all_52_13 = all_8_2) % 152.18/22.74 (8) all_54_0 = all_10_2 % 152.18/22.74 (9) all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2 % 152.18/22.74 (10) ~ (all_52_9 = all_8_2) % 152.18/22.74 (11) ~ (all_52_12 = all_52_13) % 152.18/22.74 (12) all_58_4 = all_52_8 % 152.18/22.74 (13) all_54_5 = all_8_2 % 152.18/22.74 (14) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 152.18/22.74 (15) ~ (all_4_1 = e2) % 152.18/22.74 (16) all_56_1 = all_10_2 % 152.18/22.74 (17) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0 % 152.18/22.74 (18) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0 % 152.18/22.74 (19) all_58_5 = all_52_9 % 152.18/22.74 (20) all_58_9 = all_52_12 % 152.18/22.74 (21) ~ (all_56_1 = e1) | all_56_5 = e3 % 152.18/22.74 (22) all_58_1 = all_52_4 % 152.18/22.74 (23) all_58_13 = all_52_7 % 152.18/22.74 (24) all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1 % 152.18/22.74 (25) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 152.18/22.74 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 152.18/22.74 (26) all_54_3 = all_52_12 % 152.18/22.74 (27) ~ (all_56_11 = e3) | all_56_9 = e2 % 152.18/22.74 (28) ~ (all_52_9 = e0) % 152.18/22.74 (29) all_54_6 = all_52_9 % 152.18/22.74 (30) ~ (all_56_1 = e2) | all_56_3 = e3 % 152.18/22.74 (31) ~ (all_52_9 = all_52_13) % 152.18/22.74 (32) all_58_3 = all_8_2 % 152.18/22.74 (33) all_56_3 = all_52_4 % 152.18/22.74 (34) all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1 % 152.18/22.74 (35) all_54_7 = all_52_13 % 152.18/22.74 (36) op(e1, e1) = all_56_20 % 152.18/22.74 (37) ~ (all_52_8 = e1) % 152.18/22.74 (38) ~ (all_52_7 = e1) % 152.18/22.74 (39) ~ (all_52_9 = e1) % 152.18/22.74 (40) all_58_14 = e0 % 152.18/22.74 (41) ~ (all_10_2 = e0) % 152.18/22.74 (42) all_58_7 = all_52_6 % 152.18/22.74 (43) all_58_0 = all_10_2 % 152.18/22.74 (44) ~ (all_52_12 = e1) % 152.18/22.74 (45) ~ (e3 = e1) % 152.18/22.74 (46) all_58_8 = all_4_1 % 152.18/22.74 (47) ~ (all_52_4 = all_52_12) % 152.18/22.74 (48) ~ (all_52_8 = all_52_12) % 152.18/22.74 (49) ~ (all_8_2 = e0) % 152.18/22.74 (50) ~ (all_52_4 = all_10_2) % 152.18/22.74 (51) ~ (all_52_4 = all_8_2) % 152.18/22.74 (52) op(all_8_2, all_8_2) = all_8_1 % 152.18/22.74 (53) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 152.18/22.74 (54) ~ (all_52_12 = all_10_2) % 152.18/22.74 (55) all_56_9 = all_52_1 % 152.18/22.74 (56) op(e1, e1) = e1 % 152.18/22.74 % 152.18/22.74 Begin of proof % 152.18/22.74 | % 152.18/22.74 | BETA: splitting (27) gives: % 152.18/22.74 | % 152.18/22.74 | Case 1: % 152.18/22.74 | | % 152.18/22.74 | | (57) ~ (all_56_11 = e3) % 152.18/22.74 | | % 152.18/22.74 | | REDUCE: (1), (57) imply: % 152.18/22.74 | | (58) ~ (all_8_2 = e3) % 152.18/22.74 | | % 152.18/22.74 | | BETA: splitting (21) gives: % 152.18/22.74 | | % 152.18/22.74 | | Case 1: % 152.18/22.74 | | | % 152.18/22.74 | | | (59) ~ (all_56_1 = e1) % 152.18/22.74 | | | % 152.18/22.74 | | | REDUCE: (16), (59) imply: % 152.18/22.74 | | | (60) ~ (all_10_2 = e1) % 152.18/22.74 | | | % 152.18/22.74 | | | BETA: splitting (24) gives: % 152.18/22.74 | | | % 152.18/22.74 | | | Case 1: % 152.18/22.74 | | | | % 152.18/22.74 | | | | (61) all_58_0 = e1 % 152.18/22.74 | | | | % 152.18/22.74 | | | | COMBINE_EQS: (43), (61) imply: % 152.18/22.74 | | | | (62) all_10_2 = e1 % 152.18/22.74 | | | | % 152.18/22.74 | | | | REDUCE: (60), (62) imply: % 152.18/22.74 | | | | (63) $false % 152.18/22.74 | | | | % 152.18/22.74 | | | | CLOSE: (63) is inconsistent. % 152.18/22.74 | | | | % 152.18/22.74 | | | Case 2: % 152.18/22.74 | | | | % 152.18/22.74 | | | | (64) all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1 % 152.18/22.74 | | | | % 152.18/22.74 | | | | BETA: splitting (64) gives: % 152.18/22.74 | | | | % 152.18/22.74 | | | | Case 1: % 152.18/22.74 | | | | | % 152.18/22.74 | | | | | (65) all_58_1 = e1 % 152.18/22.74 | | | | | % 152.18/22.74 | | | | | COMBINE_EQS: (22), (65) imply: % 152.18/22.74 | | | | | (66) all_52_4 = e1 % 152.18/22.74 | | | | | % 152.18/22.74 | | | | | COMBINE_EQS: (33), (66) imply: % 152.18/22.74 | | | | | (67) all_56_3 = e1 % 152.18/22.74 | | | | | % 152.18/22.74 | | | | | REDUCE: (47), (66) imply: % 152.18/22.74 | | | | | (68) ~ (all_52_12 = e1) % 152.18/22.74 | | | | | % 152.18/22.74 | | | | | REDUCE: (50), (66) imply: % 152.18/22.74 | | | | | (69) ~ (all_10_2 = e1) % 152.18/22.74 | | | | | % 152.18/22.74 | | | | | REDUCE: (51), (66) imply: % 152.18/22.74 | | | | | (70) ~ (all_8_2 = e1) % 152.18/22.74 | | | | | % 152.18/22.74 | | | | | SIMP: (70) implies: % 152.18/22.74 | | | | | (71) ~ (all_8_2 = e1) % 152.18/22.74 | | | | | % 152.18/22.74 | | | | | BETA: splitting (30) gives: % 152.18/22.74 | | | | | % 152.18/22.74 | | | | | Case 1: % 152.18/22.74 | | | | | | % 152.18/22.74 | | | | | | (72) ~ (all_56_1 = e2) % 152.18/22.74 | | | | | | % 152.18/22.74 | | | | | | REDUCE: (16), (72) imply: % 152.18/22.74 | | | | | | (73) ~ (all_10_2 = e2) % 152.18/22.74 | | | | | | % 152.18/22.74 | | | | | | REF_CLOSE: (5), (6), (7), (8), (9), (10), (11), (12), (13), (14), % 152.18/22.74 | | | | | | (15), (17), (18), (19), (26), (28), (29), (31), (35), % 152.18/22.74 | | | | | | (39), (40), (41), (44), (46), (48), (49), (53), (54), % 152.18/22.74 | | | | | | (58), (60), (71), (73) are inconsistent by sub-proof % 152.18/22.74 | | | | | | #536. % 152.18/22.74 | | | | | | % 152.18/22.74 | | | | | Case 2: % 152.18/22.74 | | | | | | % 152.18/22.74 | | | | | | (74) all_56_3 = e3 % 152.18/22.74 | | | | | | % 152.18/22.74 | | | | | | COMBINE_EQS: (67), (74) imply: % 152.18/22.74 | | | | | | (75) e3 = e1 % 152.18/22.74 | | | | | | % 152.18/22.74 | | | | | | REDUCE: (45), (75) imply: % 152.18/22.74 | | | | | | (76) $false % 152.18/22.74 | | | | | | % 152.18/22.74 | | | | | | CLOSE: (76) is inconsistent. % 152.18/22.74 | | | | | | % 152.18/22.74 | | | | | End of split % 152.18/22.74 | | | | | % 152.18/22.74 | | | | Case 2: % 152.18/22.74 | | | | | % 152.18/22.74 | | | | | (77) all_58_4 = e1 | all_58_9 = e1 % 152.18/22.74 | | | | | % 152.18/22.74 | | | | | REF_CLOSE: (12), (20), (37), (44), (77) are inconsistent by sub-proof % 152.18/22.74 | | | | | #578. % 152.18/22.74 | | | | | % 152.18/22.74 | | | | End of split % 152.18/22.74 | | | | % 152.18/22.74 | | | End of split % 152.18/22.74 | | | % 152.18/22.74 | | Case 2: % 152.18/22.74 | | | % 152.18/22.74 | | | (78) all_56_1 = e1 % 152.18/22.74 | | | % 152.18/22.74 | | | COMBINE_EQS: (16), (78) imply: % 152.18/22.74 | | | (79) all_10_2 = e1 % 152.18/22.74 | | | % 152.18/22.74 | | | REDUCE: (50), (79) imply: % 152.18/22.74 | | | (80) ~ (all_52_4 = e1) % 152.18/22.74 | | | % 152.18/22.74 | | | REF_CLOSE: (2), (3), (22), (23), (25), (32), (34), (36), (38), (42), (52), % 152.18/22.74 | | | (56), (80) are inconsistent by sub-proof #532. % 152.18/22.74 | | | % 152.18/22.74 | | End of split % 152.18/22.74 | | % 152.18/22.74 | Case 2: % 152.18/22.74 | | % 152.18/22.74 | | (81) all_56_11 = e3 % 152.18/22.74 | | (82) all_56_9 = e2 % 152.18/22.74 | | % 152.18/22.74 | | COMBINE_EQS: (55), (82) imply: % 152.18/22.74 | | (83) all_52_1 = e2 % 152.18/22.74 | | % 152.18/22.74 | | COMBINE_EQS: (1), (81) imply: % 152.18/22.74 | | (84) all_8_2 = e3 % 152.18/22.74 | | % 152.18/22.74 | | REDUCE: (4), (83) imply: % 152.18/22.74 | | (85) ~ (all_52_9 = e2) % 152.18/22.74 | | % 152.18/22.74 | | SIMP: (85) implies: % 152.18/22.74 | | (86) ~ (all_52_9 = e2) % 152.18/22.74 | | % 152.18/22.74 | | REDUCE: (10), (84) imply: % 152.18/22.74 | | (87) ~ (all_52_9 = e3) % 152.18/22.74 | | % 152.18/22.74 | | BETA: splitting (18) gives: % 152.18/22.74 | | % 152.18/22.74 | | Case 1: % 152.18/22.74 | | | % 152.18/22.74 | | | (88) all_54_6 = e3 % 152.18/22.74 | | | % 152.18/22.74 | | | COMBINE_EQS: (29), (88) imply: % 152.18/22.74 | | | (89) all_52_9 = e3 % 152.18/22.74 | | | % 152.18/22.74 | | | REDUCE: (87), (89) imply: % 152.18/22.74 | | | (90) $false % 152.18/22.74 | | | % 152.18/22.74 | | | CLOSE: (90) is inconsistent. % 152.18/22.74 | | | % 152.18/22.74 | | Case 2: % 152.18/22.74 | | | % 152.18/22.74 | | | (91) all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0 % 152.18/22.74 | | | % 152.18/22.74 | | | REF_CLOSE: (28), (29), (39), (86), (91) are inconsistent by sub-proof % 152.18/22.74 | | | #608. % 152.18/22.74 | | | % 152.18/22.74 | | End of split % 152.18/22.74 | | % 152.18/22.74 | End of split % 152.18/22.74 | % 152.18/22.74 End of proof % 152.18/22.74 % 152.18/22.74 Sub-proof #532 shows that the following formulas are inconsistent: % 152.18/22.74 ---------------------------------------------------------------- % 152.18/22.74 (1) ~ (all_52_6 = e1) % 152.18/22.74 (2) ~ (all_8_1 = e1) % 152.18/22.74 (3) ~ (all_52_4 = e1) % 152.18/22.74 (4) all_58_1 = all_52_4 % 152.18/22.74 (5) all_58_13 = all_52_7 % 152.18/22.74 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 152.18/22.74 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 152.18/22.74 (7) all_58_3 = all_8_2 % 152.18/22.74 (8) all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1 % 152.18/22.74 (9) op(e1, e1) = all_56_20 % 152.18/22.74 (10) ~ (all_52_7 = e1) % 152.18/22.74 (11) all_58_7 = all_52_6 % 152.18/22.74 (12) op(all_8_2, all_8_2) = all_8_1 % 152.18/22.74 (13) op(e1, e1) = e1 % 152.18/22.74 % 152.18/22.74 Begin of proof % 152.18/22.74 | % 152.18/22.74 | BETA: splitting (8) gives: % 152.18/22.74 | % 152.18/22.74 | Case 1: % 152.18/22.74 | | % 152.18/22.74 | | (14) all_58_1 = e1 % 152.18/22.74 | | % 152.18/22.74 | | COMBINE_EQS: (4), (14) imply: % 152.18/22.74 | | (15) all_52_4 = e1 % 152.18/22.74 | | % 152.18/22.74 | | REDUCE: (3), (15) imply: % 152.18/22.74 | | (16) $false % 152.18/22.74 | | % 152.18/22.74 | | CLOSE: (16) is inconsistent. % 152.18/22.74 | | % 152.18/22.74 | Case 2: % 152.18/22.74 | | % 152.18/22.74 | | (17) all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1 % 152.18/22.74 | | % 152.18/22.74 | | REF_CLOSE: (1), (2), (5), (6), (7), (9), (10), (11), (12), (13), (17) are % 152.18/22.74 | | inconsistent by sub-proof #533. % 152.18/22.74 | | % 152.18/22.74 | End of split % 152.18/22.74 | % 152.18/22.74 End of proof % 152.18/22.74 % 152.18/22.74 Sub-proof #533 shows that the following formulas are inconsistent: % 152.18/22.74 ---------------------------------------------------------------- % 152.18/22.74 (1) ~ (all_52_6 = e1) % 152.18/22.74 (2) ~ (all_8_1 = e1) % 152.18/22.74 (3) all_58_13 = all_52_7 % 152.18/22.74 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 152.18/22.74 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 152.18/22.74 (5) all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1 % 152.18/22.74 (6) all_58_3 = all_8_2 % 152.18/22.74 (7) op(e1, e1) = all_56_20 % 152.18/22.74 (8) ~ (all_52_7 = e1) % 152.18/22.74 (9) all_58_7 = all_52_6 % 152.18/22.74 (10) op(all_8_2, all_8_2) = all_8_1 % 152.18/22.74 (11) op(e1, e1) = e1 % 152.18/22.74 % 152.18/22.74 Begin of proof % 152.18/22.74 | % 152.18/22.74 | BETA: splitting (5) gives: % 152.18/22.74 | % 152.18/22.74 | Case 1: % 152.18/22.74 | | % 152.18/22.74 | | (12) all_58_3 = e1 % 152.18/22.74 | | % 152.18/22.74 | | COMBINE_EQS: (6), (12) imply: % 152.18/22.74 | | (13) all_8_2 = e1 % 152.18/22.74 | | % 152.18/22.74 | | REF_CLOSE: (2), (4), (7), (10), (11), (13) are inconsistent by sub-proof % 152.18/22.74 | | #535. % 152.18/22.74 | | % 152.18/22.74 | Case 2: % 152.18/22.74 | | % 152.18/22.74 | | (14) all_58_7 = e1 | all_58_13 = e1 % 152.18/22.74 | | % 152.18/22.74 | | REF_CLOSE: (1), (3), (8), (9), (14) are inconsistent by sub-proof #534. % 152.18/22.74 | | % 152.18/22.74 | End of split % 152.18/22.74 | % 152.18/22.74 End of proof % 152.18/22.74 % 152.18/22.74 Sub-proof #534 shows that the following formulas are inconsistent: % 152.18/22.74 ---------------------------------------------------------------- % 152.18/22.74 (1) ~ (all_52_6 = e1) % 152.18/22.74 (2) all_58_7 = e1 | all_58_13 = e1 % 152.18/22.74 (3) all_58_13 = all_52_7 % 152.18/22.74 (4) ~ (all_52_7 = e1) % 152.18/22.74 (5) all_58_7 = all_52_6 % 152.18/22.74 % 152.18/22.74 Begin of proof % 152.18/22.74 | % 152.18/22.74 | BETA: splitting (2) gives: % 152.18/22.74 | % 152.18/22.74 | Case 1: % 152.18/22.74 | | % 152.18/22.74 | | (6) all_58_7 = e1 % 152.18/22.74 | | % 152.18/22.74 | | COMBINE_EQS: (5), (6) imply: % 152.18/22.74 | | (7) all_52_6 = e1 % 152.18/22.74 | | % 152.18/22.74 | | REDUCE: (1), (7) imply: % 152.18/22.74 | | (8) $false % 152.18/22.74 | | % 152.18/22.74 | | CLOSE: (8) is inconsistent. % 152.18/22.74 | | % 152.18/22.74 | Case 2: % 152.18/22.74 | | % 152.18/22.74 | | (9) all_58_13 = e1 % 152.18/22.74 | | % 152.18/22.74 | | REF_CLOSE: (3), (4), (9) are inconsistent by sub-proof #704. % 152.18/22.74 | | % 152.18/22.74 | End of split % 152.18/22.74 | % 152.18/22.74 End of proof % 152.18/22.74 % 152.18/22.74 Sub-proof #535 shows that the following formulas are inconsistent: % 152.18/22.74 ---------------------------------------------------------------- % 152.18/22.74 (1) ~ (all_8_1 = e1) % 152.18/22.74 (2) all_8_2 = e1 % 152.18/22.74 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 152.18/22.74 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 152.18/22.74 (4) op(e1, e1) = all_56_20 % 152.18/22.74 (5) op(all_8_2, all_8_2) = all_8_1 % 152.18/22.74 (6) op(e1, e1) = e1 % 152.18/22.74 % 152.18/22.74 Begin of proof % 152.18/22.74 | % 152.18/22.74 | REDUCE: (2), (5) imply: % 152.18/22.74 | (7) op(e1, e1) = all_8_1 % 152.18/22.74 | % 152.18/22.74 | GROUND_INST: instantiating (3) with e1, all_56_20, e1, e1, simplifying with % 152.18/22.74 | (4), (6) gives: % 152.18/22.74 | (8) all_56_20 = e1 % 152.18/22.74 | % 152.18/22.74 | GROUND_INST: instantiating (3) with all_8_1, all_56_20, e1, e1, simplifying % 152.18/22.74 | with (4), (7) gives: % 152.18/22.74 | (9) all_56_20 = all_8_1 % 152.18/22.74 | % 152.18/22.74 | COMBINE_EQS: (8), (9) imply: % 152.18/22.74 | (10) all_8_1 = e1 % 152.18/22.74 | % 152.18/22.74 | REDUCE: (1), (10) imply: % 152.18/22.74 | (11) $false % 152.18/22.74 | % 152.18/22.74 | CLOSE: (11) is inconsistent. % 152.18/22.74 | % 152.18/22.74 End of proof % 152.18/22.74 % 152.18/22.74 Sub-proof #536 shows that the following formulas are inconsistent: % 152.18/22.74 ---------------------------------------------------------------- % 152.18/22.74 (1) ~ (all_52_13 = e1) % 152.18/22.74 (2) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0 % 152.18/22.74 (3) ~ (all_52_13 = all_8_2) % 152.18/22.74 (4) ~ (all_8_2 = e1) % 152.18/22.74 (5) all_54_0 = all_10_2 % 152.18/22.74 (6) all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2 % 152.18/22.74 (7) ~ (all_52_9 = all_8_2) % 152.18/22.74 (8) ~ (all_52_12 = all_52_13) % 152.18/22.74 (9) all_58_4 = all_52_8 % 152.18/22.74 (10) all_54_5 = all_8_2 % 152.18/22.74 (11) ~ (all_10_2 = e1) % 152.18/22.74 (12) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 152.18/22.74 (13) ~ (all_4_1 = e2) % 152.18/22.74 (14) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0 % 152.18/22.74 (15) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0 % 152.18/22.74 (16) all_58_5 = all_52_9 % 152.18/22.74 (17) ~ (all_10_2 = e2) % 152.18/22.74 (18) all_54_3 = all_52_12 % 152.18/22.74 (19) ~ (all_52_9 = e0) % 152.18/22.74 (20) all_54_6 = all_52_9 % 152.18/22.74 (21) ~ (all_8_2 = e3) % 152.18/22.74 (22) ~ (all_52_9 = all_52_13) % 152.18/22.74 (23) all_54_7 = all_52_13 % 152.18/22.74 (24) ~ (all_52_9 = e1) % 152.18/22.74 (25) all_58_14 = e0 % 152.18/22.74 (26) ~ (all_10_2 = e0) % 152.18/22.74 (27) ~ (all_52_12 = e1) % 152.18/22.74 (28) all_58_8 = all_4_1 % 152.18/22.74 (29) ~ (all_52_8 = all_52_12) % 152.18/22.74 (30) ~ (all_8_2 = e0) % 152.18/22.74 (31) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 152.18/22.74 (32) ~ (all_52_12 = all_10_2) % 152.18/22.74 % 152.18/22.74 Begin of proof % 152.18/22.74 | % 152.18/22.74 | BETA: splitting (12) gives: % 152.18/22.74 | % 152.18/22.74 | Case 1: % 152.18/22.74 | | % 152.18/22.74 | | (33) all_54_0 = e3 % 152.18/22.74 | | % 152.18/22.74 | | COMBINE_EQS: (5), (33) imply: % 152.18/22.74 | | (34) all_10_2 = e3 % 152.18/22.74 | | % 152.18/22.74 | | REDUCE: (32), (34) imply: % 152.18/22.74 | | (35) ~ (all_52_12 = e3) % 152.18/22.74 | | % 152.18/22.74 | | BETA: splitting (31) gives: % 152.18/22.74 | | % 152.18/22.74 | | Case 1: % 152.18/22.74 | | | % 152.18/22.74 | | | (36) all_54_5 = e3 % 152.18/22.74 | | | % 152.18/22.74 | | | REF_CLOSE: (10), (21), (36) are inconsistent by sub-proof #737. % 152.18/22.74 | | | % 152.18/22.74 | | Case 2: % 152.18/22.74 | | | % 152.18/22.74 | | | (37) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 152.18/22.74 | | | % 152.18/22.74 | | | BETA: splitting (37) gives: % 152.18/22.74 | | | % 152.18/22.74 | | | Case 1: % 152.18/22.74 | | | | % 152.18/22.74 | | | | (38) all_54_5 = e2 % 152.18/22.74 | | | | % 152.18/22.74 | | | | COMBINE_EQS: (10), (38) imply: % 152.18/22.74 | | | | (39) all_8_2 = e2 % 152.18/22.74 | | | | % 152.18/22.74 | | | | SIMP: (39) implies: % 152.18/22.74 | | | | (40) all_8_2 = e2 % 152.18/22.74 | | | | % 152.18/22.74 | | | | REDUCE: (7), (40) imply: % 152.18/22.74 | | | | (41) ~ (all_52_9 = e2) % 152.18/22.74 | | | | % 152.18/22.74 | | | | REDUCE: (3), (40) imply: % 152.18/22.74 | | | | (42) ~ (all_52_13 = e2) % 152.18/22.74 | | | | % 152.18/22.74 | | | | REDUCE: (30), (40) imply: % 152.18/22.74 | | | | (43) ~ (e2 = e0) % 152.18/22.74 | | | | % 152.18/22.74 | | | | BETA: splitting (15) gives: % 152.18/22.74 | | | | % 152.18/22.74 | | | | Case 1: % 152.18/22.74 | | | | | % 152.18/22.74 | | | | | (44) all_54_6 = e3 % 152.18/22.74 | | | | | % 152.18/22.74 | | | | | COMBINE_EQS: (20), (44) imply: % 152.18/22.74 | | | | | (45) all_52_9 = e3 % 152.18/22.74 | | | | | % 152.18/22.74 | | | | | SIMP: (45) implies: % 152.18/22.74 | | | | | (46) all_52_9 = e3 % 152.18/22.74 | | | | | % 152.18/22.74 | | | | | REDUCE: (22), (46) imply: % 152.18/22.74 | | | | | (47) ~ (all_52_13 = e3) % 152.18/22.74 | | | | | % 152.18/22.74 | | | | | SIMP: (47) implies: % 152.18/22.74 | | | | | (48) ~ (all_52_13 = e3) % 152.18/22.74 | | | | | % 152.18/22.74 | | | | | BETA: splitting (14) gives: % 152.18/22.74 | | | | | % 152.18/22.74 | | | | | Case 1: % 152.18/22.74 | | | | | | % 152.18/22.74 | | | | | | (49) all_54_7 = e3 % 152.18/22.74 | | | | | | % 152.18/22.74 | | | | | | REF_CLOSE: (23), (48), (49) are inconsistent by sub-proof #601. % 152.18/22.74 | | | | | | % 152.18/22.74 | | | | | Case 2: % 152.18/22.74 | | | | | | % 152.18/22.74 | | | | | | (50) all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0 % 152.18/22.74 | | | | | | % 152.18/22.74 | | | | | | BETA: splitting (6) gives: % 152.18/22.74 | | | | | | % 152.18/22.74 | | | | | | Case 1: % 152.18/22.74 | | | | | | | % 152.18/22.74 | | | | | | | (51) all_58_4 = e2 % 152.18/22.74 | | | | | | | % 152.18/22.74 | | | | | | | COMBINE_EQS: (9), (51) imply: % 152.18/22.74 | | | | | | | (52) all_52_8 = e2 % 152.18/22.74 | | | | | | | % 152.18/22.74 | | | | | | | REDUCE: (29), (52) imply: % 152.18/22.74 | | | | | | | (53) ~ (all_52_12 = e2) % 152.18/22.74 | | | | | | | % 152.18/22.74 | | | | | | | SIMP: (53) implies: % 152.18/22.74 | | | | | | | (54) ~ (all_52_12 = e2) % 152.18/22.74 | | | | | | | % 152.18/22.74 | | | | | | | BETA: splitting (2) gives: % 152.18/22.74 | | | | | | | % 152.18/22.74 | | | | | | | Case 1: % 152.18/22.74 | | | | | | | | % 152.18/22.74 | | | | | | | | (55) all_54_3 = e3 % 152.18/22.74 | | | | | | | | % 152.18/22.74 | | | | | | | | REF_CLOSE: (18), (35), (55) are inconsistent by sub-proof #659. % 152.18/22.74 | | | | | | | | % 152.18/22.74 | | | | | | | Case 2: % 152.18/22.74 | | | | | | | | % 152.18/22.74 | | | | | | | | (56) all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0 % 152.18/22.74 | | | | | | | | % 152.18/22.74 | | | | | | | | BETA: splitting (56) gives: % 152.18/22.74 | | | | | | | | % 152.18/22.74 | | | | | | | | Case 1: % 152.18/22.74 | | | | | | | | | % 152.18/22.74 | | | | | | | | | (57) all_54_3 = e2 % 152.18/22.74 | | | | | | | | | % 152.18/22.74 | | | | | | | | | REF_CLOSE: (18), (54), (57) are inconsistent by sub-proof % 152.18/22.74 | | | | | | | | | #658. % 152.18/22.74 | | | | | | | | | % 152.18/22.74 | | | | | | | | Case 2: % 152.18/22.74 | | | | | | | | | % 152.18/22.74 | | | | | | | | | (58) all_54_3 = e1 | all_54_3 = e0 % 152.18/22.74 | | | | | | | | | % 152.18/22.74 | | | | | | | | | BETA: splitting (58) gives: % 152.18/22.74 | | | | | | | | | % 152.18/22.74 | | | | | | | | | Case 1: % 152.18/22.74 | | | | | | | | | | % 152.18/22.74 | | | | | | | | | | (59) all_54_3 = e1 % 152.18/22.74 | | | | | | | | | | % 152.18/22.74 | | | | | | | | | | REF_CLOSE: (18), (27), (59) are inconsistent by sub-proof % 152.18/22.74 | | | | | | | | | | #657. % 152.18/22.74 | | | | | | | | | | % 152.18/22.74 | | | | | | | | | Case 2: % 152.18/22.74 | | | | | | | | | | % 152.18/22.74 | | | | | | | | | | (60) all_54_3 = e0 % 152.18/22.74 | | | | | | | | | | % 152.18/22.74 | | | | | | | | | | COMBINE_EQS: (18), (60) imply: % 152.18/22.74 | | | | | | | | | | (61) all_52_12 = e0 % 152.18/22.74 | | | | | | | | | | % 152.18/22.74 | | | | | | | | | | SIMP: (61) implies: % 152.18/22.74 | | | | | | | | | | (62) all_52_12 = e0 % 152.18/22.74 | | | | | | | | | | % 152.18/22.74 | | | | | | | | | | REDUCE: (8), (62) imply: % 152.18/22.74 | | | | | | | | | | (63) ~ (all_52_13 = e0) % 152.18/22.74 | | | | | | | | | | % 152.18/22.74 | | | | | | | | | | SIMP: (63) implies: % 152.18/22.74 | | | | | | | | | | (64) ~ (all_52_13 = e0) % 152.18/22.74 | | | | | | | | | | % 152.18/22.74 | | | | | | | | | | REF_CLOSE: (1), (23), (42), (50), (64) are inconsistent by % 152.18/22.74 | | | | | | | | | | sub-proof #649. % 152.18/22.74 | | | | | | | | | | % 152.18/22.74 | | | | | | | | | End of split % 152.18/22.74 | | | | | | | | | % 152.18/22.74 | | | | | | | | End of split % 152.18/22.74 | | | | | | | | % 152.18/22.74 | | | | | | | End of split % 152.18/22.74 | | | | | | | % 152.18/22.74 | | | | | | Case 2: % 152.18/22.74 | | | | | | | % 152.18/22.74 | | | | | | | (65) all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2 % 152.18/22.74 | | | | | | | % 152.18/22.74 | | | | | | | BETA: splitting (65) gives: % 152.18/22.74 | | | | | | | % 152.18/22.74 | | | | | | | Case 1: % 152.18/22.74 | | | | | | | | % 152.18/22.74 | | | | | | | | (66) all_58_5 = e2 % 152.18/22.74 | | | | | | | | % 152.18/22.74 | | | | | | | | COMBINE_EQS: (16), (66) imply: % 152.18/22.74 | | | | | | | | (67) all_52_9 = e2 % 152.18/22.74 | | | | | | | | % 152.18/22.74 | | | | | | | | REDUCE: (41), (67) imply: % 152.18/22.74 | | | | | | | | (68) $false % 152.18/22.74 | | | | | | | | % 152.18/22.74 | | | | | | | | CLOSE: (68) is inconsistent. % 152.18/22.74 | | | | | | | | % 152.18/22.74 | | | | | | | Case 2: % 152.18/22.74 | | | | | | | | % 152.18/22.74 | | | | | | | | (69) all_58_8 = e2 | all_58_14 = e2 % 152.18/22.74 | | | | | | | | % 152.18/22.74 | | | | | | | | REF_CLOSE: (13), (25), (28), (43), (69) are inconsistent by % 152.18/22.74 | | | | | | | | sub-proof #537. % 152.18/22.74 | | | | | | | | % 152.18/22.74 | | | | | | | End of split % 152.18/22.74 | | | | | | | % 152.18/22.74 | | | | | | End of split % 152.18/22.74 | | | | | | % 152.18/22.74 | | | | | End of split % 152.18/22.74 | | | | | % 152.18/22.74 | | | | Case 2: % 152.18/22.74 | | | | | % 152.18/22.74 | | | | | (70) all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0 % 152.18/22.74 | | | | | % 152.18/22.74 | | | | | REF_CLOSE: (19), (20), (24), (41), (70) are inconsistent by sub-proof % 152.18/22.74 | | | | | #608. % 152.18/22.74 | | | | | % 152.18/22.74 | | | | End of split % 152.18/22.74 | | | | % 152.18/22.74 | | | Case 2: % 152.18/22.74 | | | | % 152.18/22.74 | | | | (71) all_54_5 = e1 | all_54_5 = e0 % 152.18/22.74 | | | | % 152.18/22.74 | | | | REF_CLOSE: (4), (10), (30), (71) are inconsistent by sub-proof #645. % 152.18/22.74 | | | | % 152.18/22.74 | | | End of split % 152.18/22.74 | | | % 152.18/22.74 | | End of split % 152.18/22.74 | | % 152.18/22.74 | Case 2: % 152.18/22.74 | | % 152.18/22.74 | | (72) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 152.18/22.74 | | % 152.18/22.74 | | REF_CLOSE: (5), (11), (17), (26), (72) are inconsistent by sub-proof #731. % 152.18/22.74 | | % 152.18/22.74 | End of split % 152.18/22.74 | % 152.18/22.74 End of proof % 152.18/22.74 % 152.18/22.74 Sub-proof #537 shows that the following formulas are inconsistent: % 152.18/22.74 ---------------------------------------------------------------- % 152.18/22.74 (1) all_58_8 = e2 | all_58_14 = e2 % 152.18/22.74 (2) ~ (all_4_1 = e2) % 152.18/22.74 (3) all_58_14 = e0 % 152.18/22.74 (4) all_58_8 = all_4_1 % 152.18/22.74 (5) ~ (e2 = e0) % 152.18/22.74 % 152.18/22.74 Begin of proof % 152.18/22.74 | % 152.18/22.74 | BETA: splitting (1) gives: % 152.18/22.74 | % 152.18/22.74 | Case 1: % 152.18/22.74 | | % 152.18/22.74 | | (6) all_58_8 = e2 % 152.18/22.74 | | % 152.18/22.74 | | COMBINE_EQS: (4), (6) imply: % 152.18/22.74 | | (7) all_4_1 = e2 % 152.18/22.74 | | % 152.18/22.74 | | REDUCE: (2), (7) imply: % 152.18/22.74 | | (8) $false % 152.18/22.74 | | % 152.18/22.74 | | CLOSE: (8) is inconsistent. % 152.18/22.74 | | % 152.18/22.74 | Case 2: % 152.18/22.74 | | % 152.18/22.74 | | (9) all_58_14 = e2 % 152.18/22.74 | | % 152.18/22.74 | | COMBINE_EQS: (3), (9) imply: % 152.18/22.74 | | (10) e2 = e0 % 152.18/22.74 | | % 152.18/22.74 | | REDUCE: (5), (10) imply: % 152.18/22.74 | | (11) $false % 152.18/22.74 | | % 152.18/22.74 | | CLOSE: (11) is inconsistent. % 152.18/22.74 | | % 152.18/22.74 | End of split % 152.18/22.74 | % 152.18/22.74 End of proof % 152.18/22.74 % 152.18/22.74 Sub-proof #538 shows that the following formulas are inconsistent: % 152.18/22.74 ---------------------------------------------------------------- % 152.18/22.74 (1) all_56_11 = all_8_2 % 152.18/22.74 (2) op(e0, all_52_13) = all_56_14 % 152.18/22.74 (3) ~ (all_52_11 = all_6_2) % 152.18/22.74 (4) ~ (all_52_4 = all_52_8) % 152.18/22.74 (5) ~ (all_52_8 = all_52_9) % 152.18/22.74 (6) all_54_9 = all_52_6 % 152.18/22.74 (7) op(e2, all_8_1) = all_8_0 % 152.18/22.74 (8) ~ (all_8_1 = e1) % 152.18/22.74 (9) ~ (all_52_1 = all_52_9) % 152.18/22.74 (10) ~ (e3 = e0) % 152.18/22.74 (11) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0 % 152.18/22.74 (12) all_54_10 = all_6_2 % 152.18/22.74 (13) ~ (all_6_1 = e2) % 152.18/22.74 (14) ~ (all_56_21 = e2) | all_56_19 = e1 % 152.18/22.74 (15) all_54_0 = all_10_2 % 152.18/22.74 (16) all_56_31 = e3 % 152.18/22.74 (17) all_54_4 = all_52_1 % 152.18/22.74 (18) ~ (all_8_0 = e1) % 152.18/22.74 (19) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0 % 152.18/22.74 (20) all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2 % 152.18/22.74 (21) ~ (all_52_9 = all_8_2) % 152.18/22.74 (22) ~ (all_52_4 = all_52_7) % 152.18/22.74 (23) ~ (all_8_1 = e3) % 152.18/22.74 (24) ~ (e3 = e2) % 152.18/22.74 (25) all_58_4 = all_52_8 % 152.18/22.74 (26) all_54_5 = all_8_2 % 152.18/22.74 (27) ~ (all_6_1 = e3) % 152.18/22.74 (28) ~ (all_52_6 = all_52_14) % 152.18/22.74 (29) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 152.18/22.74 (30) ~ (all_52_11 = e0) % 152.18/22.74 (31) all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1 % 152.18/22.74 (32) all_56_21 = all_6_2 % 152.18/22.74 (33) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 152.18/22.74 (34) op(e3, all_52_1) = all_56_8 % 152.18/22.74 (35) ~ (all_52_7 = all_8_2) % 152.18/22.74 (36) all_56_1 = all_10_2 % 152.18/22.74 (37) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0 % 152.18/22.74 (38) all_58_5 = all_52_9 % 152.18/22.74 (39) all_54_1 = all_52_4 % 152.18/22.74 (40) all_56_17 = all_52_2 % 152.18/22.74 (41) all_58_9 = all_52_12 % 152.18/22.74 (42) all_58_12 = e0 % 152.18/22.74 (43) ~ (all_56_1 = e1) | all_56_5 = e3 % 152.18/22.74 (44) all_54_14 = all_52_11 % 152.18/22.74 (45) all_58_1 = all_52_4 % 152.18/22.74 (46) all_58_13 = all_52_7 % 152.18/22.74 (47) all_58_4 = e0 | all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0 % 152.18/22.74 (48) op(e2, all_8_2) = all_56_10 % 152.18/22.74 (49) op(e3, e3) = all_10_2 % 152.18/22.74 (50) ~ (all_52_8 = all_6_2) % 152.18/22.74 (51) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0 % 152.18/22.74 (52) all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1 % 152.18/22.74 (53) ~ (all_56_21 = e3) | all_56_17 = e1 % 152.18/22.74 (54) ~ (e1 = e0) % 152.18/22.74 (55) ~ (all_52_1 = all_8_2) % 152.18/22.74 (56) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 152.18/22.74 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 152.18/22.74 (57) ~ (all_52_11 = e3) % 152.18/22.74 (58) ~ (all_56_11 = e3) | all_56_9 = e2 % 152.18/22.74 (59) ~ (all_52_2 = all_52_6) % 152.18/22.74 (60) op(e0, all_4_1) = all_4_0 % 152.18/22.74 (61) ~ (all_52_2 = e0) % 152.18/22.74 (62) ~ (all_10_1 = e2) % 152.18/22.74 (63) op(e0, e1) = all_52_11 % 152.18/22.74 (64) ~ (all_52_1 = all_52_13) % 152.18/22.74 (65) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0 % 152.18/22.74 (66) ~ (all_52_14 = e3) % 152.18/22.74 (67) ~ (all_4_2 = e1) % 152.18/22.74 (68) all_54_6 = all_52_9 % 152.18/22.74 (69) ~ (all_56_1 = e2) | all_56_3 = e3 % 152.18/22.74 (70) all_56_5 = all_52_8 % 152.18/22.74 (71) ~ (all_52_9 = all_52_13) % 152.18/22.74 (72) op(all_4_2, all_4_2) = all_4_1 % 152.18/22.74 (73) all_58_3 = all_8_2 % 152.18/22.74 (74) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0 % 152.18/22.74 (75) ~ (all_52_1 = all_52_3) % 152.18/22.74 (76) ~ (all_52_6 = all_52_7) % 152.18/22.74 (77) all_58_11 = all_52_14 % 152.18/22.74 (78) op(e0, e0) = e3 % 152.18/22.75 (79) all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3 % 152.18/22.75 (80) op(all_6_2, all_6_2) = all_6_1 % 152.18/22.75 (81) all_56_1 = e3 | all_56_11 = e2 | all_56_21 = e1 | all_56_31 = e0 % 152.18/22.75 (82) ~ (all_52_8 = all_52_11) % 152.18/22.75 (83) all_54_2 = all_52_8 % 152.18/22.75 (84) all_54_8 = all_52_2 % 152.18/22.75 (85) ~ (all_52_6 = all_8_2) % 152.18/22.75 (86) ~ (all_10_2 = e0) % 152.18/22.75 (87) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0 % 152.18/22.75 (88) all_58_15 = all_4_2 % 152.18/22.75 (89) ~ (all_52_7 = e3) % 152.18/22.75 (90) all_58_2 = all_52_1 % 152.18/22.75 (91) all_58_7 = all_52_6 % 152.18/22.75 (92) all_58_10 = all_52_13 % 152.18/22.75 (93) op(all_10_2, all_10_2) = all_10_1 % 152.18/22.75 (94) ~ (all_56_11 = e0) | all_56_15 = e2 % 152.18/22.75 (95) all_58_0 = all_10_2 % 152.18/22.75 (96) all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1 % 152.18/22.75 (97) all_58_1 = e0 | all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0 % 152.18/22.75 (98) ~ (all_52_12 = all_52_14) % 152.18/22.75 (99) ~ (e3 = e1) % 152.18/22.75 (100) op(e2, e2) = all_8_2 % 152.18/22.75 (101) ~ (all_52_4 = all_52_12) % 152.18/22.75 (102) ~ (all_52_2 = all_6_2) % 152.18/22.75 (103) ~ (all_52_8 = all_52_12) % 152.18/22.75 (104) ~ (all_52_1 = all_52_2) % 152.18/22.75 (105) ~ (all_56_21 = e0) | all_56_23 = e1 % 152.18/22.75 (106) ~ (all_52_6 = all_6_2) % 152.18/22.75 (107) ~ (all_52_14 = all_6_2) % 152.18/22.75 (108) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0 % 152.18/22.75 (109) ~ (all_52_7 = e0) % 152.18/22.75 (110) ~ (all_52_2 = all_10_2) % 152.18/22.75 (111) all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3 % 152.18/22.75 (112) ~ (all_52_4 = all_8_2) % 152.18/22.75 (113) op(all_8_2, all_8_2) = all_8_1 % 152.18/22.75 (114) ~ (all_52_4 = all_52_6) % 152.18/22.75 (115) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 152.18/22.75 (116) all_58_14 = all_52_11 % 152.18/22.75 (117) all_56_19 = all_52_6 % 152.18/22.75 (118) ~ (all_4_0 = e2) % 152.18/22.75 (119) all_56_9 = all_52_1 % 152.18/22.75 (120) ~ (all_52_1 = all_10_2) % 152.18/22.75 (121) op(e3, e3) = all_4_1 % 152.18/22.75 (122) all_58_12 = all_52_3 % 152.18/22.75 (123) all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3 % 152.18/22.75 (124) all_54_11 = all_52_14 % 152.18/22.75 % 152.18/22.75 Begin of proof % 152.18/22.75 | % 152.18/22.75 | GROUND_INST: instantiating (56) with all_10_2, all_4_1, e3, e3, simplifying % 152.18/22.75 | with (49), (121) gives: % 152.18/22.75 | (125) all_10_2 = all_4_1 % 152.18/22.75 | % 152.18/22.75 | COMBINE_EQS: (15), (125) imply: % 152.18/22.75 | (126) all_54_0 = all_4_1 % 152.18/22.75 | % 152.18/22.75 | COMBINE_EQS: (36), (125) imply: % 152.18/22.75 | (127) all_56_1 = all_4_1 % 152.18/22.75 | % 152.18/22.75 | COMBINE_EQS: (95), (125) imply: % 152.18/22.75 | (128) all_58_0 = all_4_1 % 152.18/22.75 | % 152.18/22.75 | REDUCE: (120), (125) imply: % 152.18/22.75 | (129) ~ (all_52_1 = all_4_1) % 152.18/22.75 | % 152.18/22.75 | REDUCE: (110), (125) imply: % 152.18/22.75 | (130) ~ (all_52_2 = all_4_1) % 152.18/22.75 | % 152.18/22.75 | REDUCE: (86), (125) imply: % 152.18/22.75 | (131) ~ (all_4_1 = e0) % 152.18/22.75 | % 152.18/22.75 | REDUCE: (93), (125) imply: % 152.18/22.75 | (132) op(all_4_1, all_4_1) = all_10_1 % 152.18/22.75 | % 152.18/22.75 | BETA: splitting (105) gives: % 152.18/22.75 | % 152.18/22.75 | Case 1: % 152.18/22.75 | | % 152.18/22.75 | | (133) ~ (all_56_21 = e0) % 152.18/22.75 | | % 152.18/22.75 | | REDUCE: (32), (133) imply: % 152.18/22.75 | | (134) ~ (all_6_2 = e0) % 152.18/22.75 | | % 152.18/22.75 | | BETA: splitting (14) gives: % 152.18/22.75 | | % 152.18/22.75 | | Case 1: % 152.18/22.75 | | | % 152.18/22.75 | | | (135) ~ (all_56_21 = e2) % 152.18/22.75 | | | % 152.18/22.75 | | | REDUCE: (32), (135) imply: % 152.18/22.75 | | | (136) ~ (all_6_2 = e2) % 152.18/22.75 | | | % 152.18/22.75 | | | BETA: splitting (94) gives: % 152.18/22.75 | | | % 152.18/22.75 | | | Case 1: % 152.18/22.75 | | | | % 152.18/22.75 | | | | (137) ~ (all_56_11 = e0) % 152.18/22.75 | | | | % 152.18/22.75 | | | | REDUCE: (1), (137) imply: % 152.18/22.75 | | | | (138) ~ (all_8_2 = e0) % 152.18/22.75 | | | | % 152.18/22.75 | | | | BETA: splitting (53) gives: % 152.18/22.75 | | | | % 152.18/22.75 | | | | Case 1: % 152.18/22.75 | | | | | % 152.18/22.75 | | | | | (139) ~ (all_56_21 = e3) % 152.18/22.75 | | | | | % 152.18/22.75 | | | | | REDUCE: (32), (139) imply: % 152.18/22.75 | | | | | (140) ~ (all_6_2 = e3) % 152.18/22.75 | | | | | % 152.18/22.75 | | | | | BETA: splitting (33) gives: % 152.18/22.75 | | | | | % 152.18/22.75 | | | | | Case 1: % 152.18/22.75 | | | | | | % 152.18/22.75 | | | | | | (141) all_54_10 = e3 % 152.18/22.75 | | | | | | % 152.18/22.75 | | | | | | COMBINE_EQS: (12), (141) imply: % 152.18/22.75 | | | | | | (142) all_6_2 = e3 % 152.18/22.75 | | | | | | % 152.18/22.75 | | | | | | REDUCE: (140), (142) imply: % 152.18/22.75 | | | | | | (143) $false % 152.18/22.75 | | | | | | % 152.18/22.75 | | | | | | CLOSE: (143) is inconsistent. % 152.18/22.75 | | | | | | % 152.18/22.75 | | | | | Case 2: % 152.18/22.75 | | | | | | % 152.18/22.75 | | | | | | (144) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 152.18/22.75 | | | | | | % 152.18/22.75 | | | | | | BETA: splitting (144) gives: % 152.18/22.75 | | | | | | % 152.18/22.75 | | | | | | Case 1: % 152.18/22.75 | | | | | | | % 152.18/22.75 | | | | | | | (145) all_54_10 = e2 % 152.18/22.75 | | | | | | | % 152.18/22.75 | | | | | | | COMBINE_EQS: (12), (145) imply: % 152.18/22.75 | | | | | | | (146) all_6_2 = e2 % 152.18/22.75 | | | | | | | % 152.18/22.75 | | | | | | | REDUCE: (136), (146) imply: % 152.18/22.75 | | | | | | | (147) $false % 152.18/22.75 | | | | | | | % 152.18/22.75 | | | | | | | CLOSE: (147) is inconsistent. % 152.18/22.75 | | | | | | | % 152.18/22.75 | | | | | | Case 2: % 152.18/22.75 | | | | | | | % 152.18/22.75 | | | | | | | (148) all_54_10 = e1 | all_54_10 = e0 % 152.18/22.75 | | | | | | | % 152.18/22.75 | | | | | | | BETA: splitting (148) gives: % 152.18/22.75 | | | | | | | % 152.18/22.75 | | | | | | | Case 1: % 152.18/22.75 | | | | | | | | % 152.18/22.75 | | | | | | | | (149) all_54_10 = e1 % 152.18/22.75 | | | | | | | | % 152.18/22.75 | | | | | | | | COMBINE_EQS: (12), (149) imply: % 152.18/22.75 | | | | | | | | (150) all_6_2 = e1 % 152.18/22.75 | | | | | | | | % 152.18/22.75 | | | | | | | | REDUCE: (102), (150) imply: % 152.18/22.75 | | | | | | | | (151) ~ (all_52_2 = e1) % 152.18/22.75 | | | | | | | | % 152.18/22.75 | | | | | | | | REDUCE: (50), (150) imply: % 152.18/22.75 | | | | | | | | (152) ~ (all_52_8 = e1) % 152.18/22.75 | | | | | | | | % 152.18/22.75 | | | | | | | | REDUCE: (3), (150) imply: % 152.18/22.75 | | | | | | | | (153) ~ (all_52_11 = e1) % 152.18/22.75 | | | | | | | | % 152.18/22.75 | | | | | | | | REDUCE: (107), (150) imply: % 152.18/22.75 | | | | | | | | (154) ~ (all_52_14 = e1) % 152.18/22.75 | | | | | | | | % 152.18/22.75 | | | | | | | | BETA: splitting (11) gives: % 152.18/22.75 | | | | | | | | % 152.18/22.75 | | | | | | | | Case 1: % 152.18/22.75 | | | | | | | | | % 152.18/22.75 | | | | | | | | | (155) all_54_14 = e3 % 152.18/22.75 | | | | | | | | | % 152.18/22.75 | | | | | | | | | COMBINE_EQS: (44), (155) imply: % 152.18/22.75 | | | | | | | | | (156) all_52_11 = e3 % 152.18/22.75 | | | | | | | | | % 152.18/22.75 | | | | | | | | | REDUCE: (57), (156) imply: % 152.18/22.75 | | | | | | | | | (157) $false % 152.18/22.75 | | | | | | | | | % 152.18/22.75 | | | | | | | | | CLOSE: (157) is inconsistent. % 152.18/22.75 | | | | | | | | | % 152.18/22.75 | | | | | | | | Case 2: % 152.18/22.75 | | | | | | | | | % 152.18/22.75 | | | | | | | | | (158) all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0 % 152.18/22.75 | | | | | | | | | % 152.18/22.75 | | | | | | | | | BETA: splitting (158) gives: % 152.18/22.75 | | | | | | | | | % 152.18/22.75 | | | | | | | | | Case 1: % 152.18/22.75 | | | | | | | | | | % 152.18/22.75 | | | | | | | | | | (159) all_54_14 = e2 % 152.18/22.75 | | | | | | | | | | % 152.18/22.75 | | | | | | | | | | COMBINE_EQS: (44), (159) imply: % 152.18/22.75 | | | | | | | | | | (160) all_52_11 = e2 % 152.18/22.75 | | | | | | | | | | % 152.18/22.75 | | | | | | | | | | COMBINE_EQS: (116), (160) imply: % 152.18/22.75 | | | | | | | | | | (161) all_58_14 = e2 % 152.18/22.75 | | | | | | | | | | % 152.18/22.75 | | | | | | | | | | REDUCE: (82), (160) imply: % 152.18/22.75 | | | | | | | | | | (162) ~ (all_52_8 = e2) % 152.18/22.75 | | | | | | | | | | % 152.18/22.75 | | | | | | | | | | REDUCE: (63), (160) imply: % 152.18/22.75 | | | | | | | | | | (163) op(e0, e1) = e2 % 152.18/22.75 | | | | | | | | | | % 152.18/22.75 | | | | | | | | | | BETA: splitting (96) gives: % 152.18/22.75 | | | | | | | | | | % 152.18/22.75 | | | | | | | | | | Case 1: % 152.18/22.75 | | | | | | | | | | | % 152.18/22.75 | | | | | | | | | | | (164) all_58_12 = e1 % 152.18/22.75 | | | | | | | | | | | % 152.18/22.75 | | | | | | | | | | | COMBINE_EQS: (42), (164) imply: % 152.18/22.75 | | | | | | | | | | | (165) e1 = e0 % 152.18/22.75 | | | | | | | | | | | % 152.18/22.75 | | | | | | | | | | | REDUCE: (54), (165) imply: % 152.18/22.75 | | | | | | | | | | | (166) $false % 152.18/22.75 | | | | | | | | | | | % 152.18/22.75 | | | | | | | | | | | CLOSE: (166) is inconsistent. % 152.18/22.75 | | | | | | | | | | | % 152.18/22.75 | | | | | | | | | | Case 2: % 152.18/22.75 | | | | | | | | | | | % 152.18/22.75 | | | | | | | | | | | (167) all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1 % 152.18/22.75 | | | | | | | | | | | % 152.18/22.75 | | | | | | | | | | | BETA: splitting (167) gives: % 152.18/22.75 | | | | | | | | | | | % 152.18/22.75 | | | | | | | | | | | Case 1: % 152.18/22.75 | | | | | | | | | | | | % 152.18/22.75 | | | | | | | | | | | | (168) all_58_13 = e1 % 152.18/22.75 | | | | | | | | | | | | % 152.18/22.75 | | | | | | | | | | | | COMBINE_EQS: (46), (168) imply: % 152.18/22.75 | | | | | | | | | | | | (169) all_52_7 = e1 % 152.18/22.75 | | | | | | | | | | | | % 152.18/22.75 | | | | | | | | | | | | SIMP: (169) implies: % 152.18/22.75 | | | | | | | | | | | | (170) all_52_7 = e1 % 152.18/22.75 | | | | | | | | | | | | % 152.18/22.75 | | | | | | | | | | | | REDUCE: (22), (170) imply: % 152.18/22.75 | | | | | | | | | | | | (171) ~ (all_52_4 = e1) % 152.18/22.75 | | | | | | | | | | | | % 152.18/22.75 | | | | | | | | | | | | REDUCE: (76), (170) imply: % 152.18/22.75 | | | | | | | | | | | | (172) ~ (all_52_6 = e1) % 152.18/22.75 | | | | | | | | | | | | % 152.18/22.75 | | | | | | | | | | | | REDUCE: (35), (170) imply: % 152.18/22.75 | | | | | | | | | | | | (173) ~ (all_8_2 = e1) % 152.18/22.75 | | | | | | | | | | | | % 152.18/22.75 | | | | | | | | | | | | SIMP: (173) implies: % 152.18/22.75 | | | | | | | | | | | | (174) ~ (all_8_2 = e1) % 152.18/22.75 | | | | | | | | | | | | % 152.18/22.75 | | | | | | | | | | | | BETA: splitting (58) gives: % 152.18/22.75 | | | | | | | | | | | | % 152.18/22.75 | | | | | | | | | | | | Case 1: % 152.18/22.75 | | | | | | | | | | | | | % 152.18/22.75 | | | | | | | | | | | | | (175) ~ (all_56_11 = e3) % 152.18/22.75 | | | | | | | | | | | | | % 152.18/22.75 | | | | | | | | | | | | | REDUCE: (1), (175) imply: % 152.18/22.75 | | | | | | | | | | | | | (176) ~ (all_8_2 = e3) % 152.18/22.75 | | | | | | | | | | | | | % 152.18/22.75 | | | | | | | | | | | | | BETA: splitting (115) gives: % 152.18/22.75 | | | | | | | | | | | | | % 152.18/22.75 | | | | | | | | | | | | | Case 1: % 152.18/22.75 | | | | | | | | | | | | | | % 152.18/22.75 | | | | | | | | | | | | | | (177) all_54_5 = e3 % 152.18/22.75 | | | | | | | | | | | | | | % 152.18/22.75 | | | | | | | | | | | | | | REF_CLOSE: (26), (176), (177) are inconsistent by sub-proof % 152.18/22.75 | | | | | | | | | | | | | | #737. % 152.18/22.75 | | | | | | | | | | | | | | % 152.18/22.75 | | | | | | | | | | | | | Case 2: % 152.18/22.75 | | | | | | | | | | | | | | % 152.18/22.75 | | | | | | | | | | | | | | (178) ~ (all_54_5 = e3) % 152.18/22.75 | | | | | | | | | | | | | | (179) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 152.18/22.75 | | | | | | | | | | | | | | % 152.18/22.75 | | | | | | | | | | | | | | BETA: splitting (179) gives: % 152.18/22.75 | | | | | | | | | | | | | | % 152.18/22.75 | | | | | | | | | | | | | | Case 1: % 152.18/22.75 | | | | | | | | | | | | | | | % 152.18/22.75 | | | | | | | | | | | | | | | (180) all_54_5 = e2 % 152.18/22.75 | | | | | | | | | | | | | | | % 152.18/22.75 | | | | | | | | | | | | | | | COMBINE_EQS: (26), (180) imply: % 152.18/22.75 | | | | | | | | | | | | | | | (181) all_8_2 = e2 % 152.18/22.75 | | | | | | | | | | | | | | | % 152.18/22.75 | | | | | | | | | | | | | | | SIMP: (181) implies: % 152.18/22.75 | | | | | | | | | | | | | | | (182) all_8_2 = e2 % 152.18/22.75 | | | | | | | | | | | | | | | % 152.18/22.75 | | | | | | | | | | | | | | | REDUCE: (55), (182) imply: % 152.18/22.75 | | | | | | | | | | | | | | | (183) ~ (all_52_1 = e2) % 152.18/22.75 | | | | | | | | | | | | | | | % 152.18/22.75 | | | | | | | | | | | | | | | REDUCE: (112), (182) imply: % 152.18/22.75 | | | | | | | | | | | | | | | (184) ~ (all_52_4 = e2) % 152.18/22.75 | | | | | | | | | | | | | | | % 152.18/22.75 | | | | | | | | | | | | | | | REDUCE: (21), (182) imply: % 152.18/22.75 | | | | | | | | | | | | | | | (185) ~ (all_52_9 = e2) % 152.18/22.75 | | | | | | | | | | | | | | | % 152.18/22.75 | | | | | | | | | | | | | | | REDUCE: (113), (182) imply: % 152.18/22.75 | | | | | | | | | | | | | | | (186) op(e2, e2) = all_8_1 % 152.18/22.75 | | | | | | | | | | | | | | | % 152.18/22.75 | | | | | | | | | | | | | | | REDUCE: (48), (182) imply: % 152.18/22.75 | | | | | | | | | | | | | | | (187) op(e2, e2) = all_56_10 % 152.18/22.75 | | | | | | | | | | | | | | | % 152.18/22.75 | | | | | | | | | | | | | | | REDUCE: (100), (182) imply: % 152.18/22.75 | | | | | | | | | | | | | | | (188) op(e2, e2) = e2 % 152.18/22.75 | | | | | | | | | | | | | | | % 152.18/22.75 | | | | | | | | | | | | | | | GROUND_INST: instantiating (56) with all_8_1, all_56_10, e2, % 152.18/22.75 | | | | | | | | | | | | | | | e2, simplifying with (186), (187) gives: % 152.18/22.75 | | | | | | | | | | | | | | | (189) all_56_10 = all_8_1 % 152.18/22.75 | | | | | | | | | | | | | | | % 152.18/22.75 | | | | | | | | | | | | | | | GROUND_INST: instantiating (56) with e2, all_56_10, e2, e2, % 152.18/22.75 | | | | | | | | | | | | | | | simplifying with (187), (188) gives: % 152.18/22.75 | | | | | | | | | | | | | | | (190) all_56_10 = e2 % 152.18/22.75 | | | | | | | | | | | | | | | % 152.18/22.75 | | | | | | | | | | | | | | | COMBINE_EQS: (189), (190) imply: % 152.18/22.75 | | | | | | | | | | | | | | | (191) all_8_1 = e2 % 152.18/22.75 | | | | | | | | | | | | | | | % 152.18/22.75 | | | | | | | | | | | | | | | REDUCE: (7), (191) imply: % 152.18/22.75 | | | | | | | | | | | | | | | (192) op(e2, e2) = all_8_0 % 152.18/22.75 | | | | | | | | | | | | | | | % 152.18/22.75 | | | | | | | | | | | | | | | GROUND_INST: instantiating (56) with e2, all_8_0, e2, e2, % 152.18/22.75 | | | | | | | | | | | | | | | simplifying with (188), (192) gives: % 152.18/22.75 | | | | | | | | | | | | | | | (193) all_8_0 = e2 % 152.18/22.75 | | | | | | | | | | | | | | | % 152.18/22.75 | | | | | | | | | | | | | | | REDUCE: (18), (193) imply: % 152.18/22.75 | | | | | | | | | | | | | | | (194) ~ (e2 = e1) % 152.18/22.75 | | | | | | | | | | | | | | | % 152.18/22.75 | | | | | | | | | | | | | | | BETA: splitting (69) gives: % 152.18/22.75 | | | | | | | | | | | | | | | % 152.18/22.75 | | | | | | | | | | | | | | | Case 1: % 152.18/22.75 | | | | | | | | | | | | | | | | % 152.18/22.75 | | | | | | | | | | | | | | | | (195) ~ (all_56_1 = e2) % 152.18/22.75 | | | | | | | | | | | | | | | | % 152.18/22.75 | | | | | | | | | | | | | | | | REF_CLOSE: (2), (4), (5), (6), (9), (17), (19), (20), (25), % 152.18/22.75 | | | | | | | | | | | | | | | | (26), (28), (31), (34), (37), (38), (39), (41), % 152.18/22.75 | | | | | | | | | | | | | | | | (43), (45), (47), (51), (52), (56), (60), (64), % 152.18/22.75 | | | | | | | | | | | | | | | | (65), (66), (67), (68), (70), (71), (72), (74), % 152.18/22.75 | | | | | | | | | | | | | | | | (75), (77), (83), (85), (87), (88), (90), (92), % 152.18/22.75 | | | | | | | | | | | | | | | | (98), (101), (103), (111), (114), (115), (118), % 152.18/22.75 | | | | | | | | | | | | | | | | (121), (122), (123), (124), (127), (128), (138), % 152.18/22.75 | | | | | | | | | | | | | | | | (152), (154), (161), (162), (163), (168), (171), % 152.18/22.75 | | | | | | | | | | | | | | | | (172), (174), (176), (183), (184), (185), (194), % 152.18/22.75 | | | | | | | | | | | | | | | | (195) are inconsistent by sub-proof #556. % 152.18/22.75 | | | | | | | | | | | | | | | | % 152.18/22.75 | | | | | | | | | | | | | | | Case 2: % 152.18/22.75 | | | | | | | | | | | | | | | | % 152.18/22.75 | | | | | | | | | | | | | | | | (196) all_56_1 = e2 % 152.18/22.75 | | | | | | | | | | | | | | | | % 152.18/22.75 | | | | | | | | | | | | | | | | COMBINE_EQS: (127), (196) imply: % 152.18/22.75 | | | | | | | | | | | | | | | | (197) all_4_1 = e2 % 152.18/22.75 | | | | | | | | | | | | | | | | % 152.18/22.75 | | | | | | | | | | | | | | | | REF_CLOSE: (56), (62), (132), (188), (197) are inconsistent % 152.18/22.75 | | | | | | | | | | | | | | | | by sub-proof #555. % 152.18/22.75 | | | | | | | | | | | | | | | | % 152.18/22.75 | | | | | | | | | | | | | | | End of split % 152.18/22.75 | | | | | | | | | | | | | | | % 152.30/22.75 | | | | | | | | | | | | | | Case 2: % 152.30/22.75 | | | | | | | | | | | | | | | % 152.30/22.75 | | | | | | | | | | | | | | | (198) all_54_5 = e1 | all_54_5 = e0 % 152.30/22.75 | | | | | | | | | | | | | | | % 152.30/22.75 | | | | | | | | | | | | | | | REF_CLOSE: (26), (138), (174), (198) are inconsistent by % 152.30/22.75 | | | | | | | | | | | | | | | sub-proof #645. % 152.30/22.75 | | | | | | | | | | | | | | | % 152.30/22.75 | | | | | | | | | | | | | | End of split % 152.30/22.75 | | | | | | | | | | | | | | % 152.30/22.75 | | | | | | | | | | | | | End of split % 152.30/22.75 | | | | | | | | | | | | | % 152.30/22.75 | | | | | | | | | | | | Case 2: % 152.30/22.75 | | | | | | | | | | | | | % 152.30/22.75 | | | | | | | | | | | | | (199) all_56_11 = e3 % 152.30/22.75 | | | | | | | | | | | | | (200) all_56_9 = e2 % 152.30/22.75 | | | | | | | | | | | | | % 152.30/22.75 | | | | | | | | | | | | | COMBINE_EQS: (119), (200) imply: % 152.30/22.75 | | | | | | | | | | | | | (201) all_52_1 = e2 % 152.30/22.75 | | | | | | | | | | | | | % 152.30/22.75 | | | | | | | | | | | | | COMBINE_EQS: (1), (199) imply: % 152.30/22.75 | | | | | | | | | | | | | (202) all_8_2 = e3 % 152.30/22.75 | | | | | | | | | | | | | % 152.30/22.75 | | | | | | | | | | | | | REDUCE: (104), (201) imply: % 152.30/22.75 | | | | | | | | | | | | | (203) ~ (all_52_2 = e2) % 152.30/22.75 | | | | | | | | | | | | | % 152.30/22.75 | | | | | | | | | | | | | SIMP: (203) implies: % 152.30/22.75 | | | | | | | | | | | | | (204) ~ (all_52_2 = e2) % 152.30/22.75 | | | | | | | | | | | | | % 152.30/22.75 | | | | | | | | | | | | | REDUCE: (129), (201) imply: % 152.30/22.75 | | | | | | | | | | | | | (205) ~ (all_4_1 = e2) % 152.30/22.75 | | | | | | | | | | | | | % 152.30/22.75 | | | | | | | | | | | | | SIMP: (205) implies: % 152.30/22.75 | | | | | | | | | | | | | (206) ~ (all_4_1 = e2) % 152.30/22.75 | | | | | | | | | | | | | % 152.30/22.75 | | | | | | | | | | | | | REDUCE: (113), (202) imply: % 152.30/22.75 | | | | | | | | | | | | | (207) op(e3, e3) = all_8_1 % 152.30/22.75 | | | | | | | | | | | | | % 152.30/22.75 | | | | | | | | | | | | | REF_CLOSE: (8), (15), (29), (49), (56), (61), (84), (86), % 152.30/22.75 | | | | | | | | | | | | | (108), (126), (130), (151), (204), (206), (207) % 152.30/22.75 | | | | | | | | | | | | | are inconsistent by sub-proof #551. % 152.30/22.75 | | | | | | | | | | | | | % 152.30/22.75 | | | | | | | | | | | | End of split % 152.30/22.75 | | | | | | | | | | | | % 152.30/22.75 | | | | | | | | | | | Case 2: % 152.30/22.75 | | | | | | | | | | | | % 152.30/22.75 | | | | | | | | | | | | (208) all_58_14 = e1 | all_58_15 = e1 % 152.30/22.75 | | | | | | | | | | | | % 152.30/22.75 | | | | | | | | | | | | REF_CLOSE: (67), (88), (116), (153), (208) are inconsistent % 152.30/22.75 | | | | | | | | | | | | by sub-proof #619. % 152.30/22.75 | | | | | | | | | | | | % 152.30/22.75 | | | | | | | | | | | End of split % 152.30/22.75 | | | | | | | | | | | % 152.30/22.75 | | | | | | | | | | End of split % 152.30/22.75 | | | | | | | | | | % 152.30/22.75 | | | | | | | | | Case 2: % 152.30/22.75 | | | | | | | | | | % 152.30/22.75 | | | | | | | | | | (209) all_54_14 = e1 | all_54_14 = e0 % 152.30/22.75 | | | | | | | | | | % 152.30/22.75 | | | | | | | | | | REF_CLOSE: (30), (44), (153), (209) are inconsistent by % 152.30/22.75 | | | | | | | | | | sub-proof #714. % 152.30/22.75 | | | | | | | | | | % 152.30/22.75 | | | | | | | | | End of split % 152.30/22.75 | | | | | | | | | % 152.30/22.75 | | | | | | | | End of split % 152.30/22.75 | | | | | | | | % 152.30/22.75 | | | | | | | Case 2: % 152.30/22.75 | | | | | | | | % 152.30/22.75 | | | | | | | | (210) all_54_10 = e0 % 152.30/22.75 | | | | | | | | % 152.30/22.75 | | | | | | | | COMBINE_EQS: (12), (210) imply: % 152.30/22.75 | | | | | | | | (211) all_6_2 = e0 % 152.30/22.75 | | | | | | | | % 152.30/22.75 | | | | | | | | REDUCE: (134), (211) imply: % 152.30/22.75 | | | | | | | | (212) $false % 152.30/22.75 | | | | | | | | % 152.30/22.75 | | | | | | | | CLOSE: (212) is inconsistent. % 152.30/22.75 | | | | | | | | % 152.30/22.75 | | | | | | | End of split % 152.30/22.75 | | | | | | | % 152.30/22.75 | | | | | | End of split % 152.30/22.75 | | | | | | % 152.30/22.75 | | | | | End of split % 152.30/22.75 | | | | | % 152.30/22.75 | | | | Case 2: % 152.30/22.75 | | | | | % 152.30/22.75 | | | | | (213) all_56_21 = e3 % 152.30/22.75 | | | | | (214) all_56_17 = e1 % 152.30/22.75 | | | | | % 152.30/22.75 | | | | | COMBINE_EQS: (40), (214) imply: % 152.30/22.75 | | | | | (215) all_52_2 = e1 % 152.30/22.75 | | | | | % 152.30/22.75 | | | | | SIMP: (215) implies: % 152.30/22.75 | | | | | (216) all_52_2 = e1 % 152.30/22.75 | | | | | % 152.30/22.75 | | | | | REF_CLOSE: (13), (27), (29), (32), (56), (80), (121), (126), (130), % 152.30/22.75 | | | | | (131), (213), (216) are inconsistent by sub-proof #547. % 152.30/22.75 | | | | | % 152.30/22.75 | | | | End of split % 152.30/22.75 | | | | % 152.30/22.75 | | | Case 2: % 152.30/22.75 | | | | % 152.30/22.75 | | | | (217) all_56_11 = e0 % 152.30/22.75 | | | | % 152.30/22.75 | | | | COMBINE_EQS: (1), (217) imply: % 152.30/22.75 | | | | (218) all_8_2 = e0 % 152.30/22.75 | | | | % 152.30/22.75 | | | | REDUCE: (113), (218) imply: % 152.30/22.75 | | | | (219) op(e0, e0) = all_8_1 % 152.30/22.75 | | | | % 152.30/22.75 | | | | REF_CLOSE: (23), (56), (78), (219) are inconsistent by sub-proof #546. % 152.30/22.75 | | | | % 152.30/22.75 | | | End of split % 152.30/22.75 | | | % 152.30/22.75 | | Case 2: % 152.30/22.75 | | | % 152.30/22.75 | | | (220) all_56_21 = e2 % 152.30/22.75 | | | (221) all_56_19 = e1 % 152.30/22.75 | | | % 152.30/22.75 | | | COMBINE_EQS: (117), (221) imply: % 152.30/22.75 | | | (222) all_52_6 = e1 % 152.30/22.75 | | | % 152.30/22.75 | | | SIMP: (222) implies: % 152.30/22.75 | | | (223) all_52_6 = e1 % 152.30/22.75 | | | % 152.30/22.75 | | | COMBINE_EQS: (32), (220) imply: % 152.30/22.75 | | | (224) all_6_2 = e2 % 152.30/22.75 | | | % 152.30/22.75 | | | SIMP: (224) implies: % 152.30/22.75 | | | (225) all_6_2 = e2 % 152.30/22.75 | | | % 152.30/22.75 | | | REF_CLOSE: (1), (10), (16), (24), (46), (54), (59), (61), (73), (79), % 152.30/22.75 | | | (81), (84), (89), (91), (97), (99), (102), (106), (108), (109), % 152.30/22.75 | | | (127), (130), (134), (220), (223), (225) are inconsistent by % 152.30/22.75 | | | sub-proof #541. % 152.30/22.75 | | | % 152.30/22.75 | | End of split % 152.30/22.75 | | % 152.30/22.75 | Case 2: % 152.30/22.75 | | % 152.30/22.75 | | (226) all_56_21 = e0 % 152.30/22.75 | | % 152.30/22.75 | | REF_CLOSE: (27), (32), (56), (78), (80), (226) are inconsistent by sub-proof % 152.30/22.75 | | #539. % 152.30/22.75 | | % 152.30/22.75 | End of split % 152.30/22.75 | % 152.30/22.75 End of proof % 152.30/22.75 % 152.30/22.75 Sub-proof #539 shows that the following formulas are inconsistent: % 152.30/22.75 ---------------------------------------------------------------- % 152.30/22.75 (1) ~ (all_6_1 = e3) % 152.30/22.75 (2) all_56_21 = all_6_2 % 152.30/22.75 (3) all_56_21 = e0 % 152.30/22.75 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 152.30/22.75 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 152.30/22.75 (5) op(e0, e0) = e3 % 152.30/22.75 (6) op(all_6_2, all_6_2) = all_6_1 % 152.30/22.75 % 152.30/22.75 Begin of proof % 152.30/22.75 | % 152.30/22.75 | COMBINE_EQS: (2), (3) imply: % 152.30/22.75 | (7) all_6_2 = e0 % 152.30/22.75 | % 152.30/22.75 | SIMP: (7) implies: % 152.30/22.75 | (8) all_6_2 = e0 % 152.30/22.75 | % 152.30/22.75 | REDUCE: (6), (8) imply: % 152.30/22.75 | (9) op(e0, e0) = all_6_1 % 152.30/22.75 | % 152.30/22.75 | REF_CLOSE: (1), (4), (5), (9) are inconsistent by sub-proof #540. % 152.30/22.75 | % 152.30/22.75 End of proof % 152.30/22.75 % 152.30/22.75 Sub-proof #540 shows that the following formulas are inconsistent: % 152.30/22.75 ---------------------------------------------------------------- % 152.30/22.75 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 152.30/22.75 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 152.30/22.75 (2) op(e0, e0) = all_6_1 % 152.30/22.75 (3) op(e0, e0) = e3 % 152.30/22.75 (4) ~ (all_6_1 = e3) % 152.30/22.75 % 152.30/22.75 Begin of proof % 152.30/22.75 | % 152.30/22.75 | GROUND_INST: instantiating (1) with e3, all_6_1, e0, e0, simplifying with (2), % 152.30/22.75 | (3) gives: % 152.30/22.75 | (5) all_6_1 = e3 % 152.30/22.75 | % 152.30/22.75 | REDUCE: (4), (5) imply: % 152.30/22.75 | (6) $false % 152.30/22.75 | % 152.30/22.75 | CLOSE: (6) is inconsistent. % 152.30/22.75 | % 152.30/22.75 End of proof % 152.30/22.75 % 152.30/22.75 Sub-proof #541 shows that the following formulas are inconsistent: % 152.30/22.75 ---------------------------------------------------------------- % 152.30/22.75 (1) all_56_11 = all_8_2 % 152.30/22.75 (2) all_52_6 = e1 % 152.30/22.75 (3) ~ (e3 = e0) % 152.30/22.75 (4) ~ (all_52_2 = all_4_1) % 152.30/22.75 (5) all_56_31 = e3 % 152.30/22.75 (6) ~ (e3 = e2) % 152.30/22.75 (7) all_56_1 = all_4_1 % 152.30/22.75 (8) all_58_13 = all_52_7 % 152.30/22.75 (9) ~ (e1 = e0) % 152.30/22.75 (10) ~ (all_6_2 = e0) % 152.30/22.75 (11) ~ (all_52_2 = all_52_6) % 152.30/22.75 (12) ~ (all_52_2 = e0) % 152.30/22.75 (13) all_56_21 = e2 % 152.30/22.75 (14) all_58_3 = all_8_2 % 152.30/22.75 (15) all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3 % 152.30/22.75 (16) all_56_1 = e3 | all_56_11 = e2 | all_56_21 = e1 | all_56_31 = e0 % 152.30/22.75 (17) all_54_8 = all_52_2 % 152.30/22.75 (18) ~ (all_52_7 = e3) % 152.30/22.75 (19) all_6_2 = e2 % 152.30/22.75 (20) all_58_7 = all_52_6 % 152.30/22.75 (21) all_58_1 = e0 | all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0 % 152.30/22.75 (22) ~ (e3 = e1) % 152.30/22.75 (23) ~ (all_52_2 = all_6_2) % 152.30/22.75 (24) ~ (all_52_6 = all_6_2) % 152.30/22.75 (25) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0 % 152.30/22.75 (26) ~ (all_52_7 = e0) % 152.30/22.75 % 152.30/22.75 Begin of proof % 152.30/22.75 | % 152.30/22.75 | COMBINE_EQS: (2), (20) imply: % 152.30/22.75 | (27) all_58_7 = e1 % 152.30/22.75 | % 152.30/22.75 | REDUCE: (2), (11) imply: % 152.30/22.75 | (28) ~ (all_52_2 = e1) % 152.30/22.75 | % 152.30/22.75 | REDUCE: (19), (23) imply: % 152.30/22.75 | (29) ~ (all_52_2 = e2) % 152.30/22.75 | % 152.30/22.75 | REDUCE: (2), (19), (24) imply: % 152.30/22.75 | (30) ~ (e2 = e1) % 152.30/22.75 | % 152.30/22.75 | SIMP: (30) implies: % 152.30/22.75 | (31) ~ (e2 = e1) % 152.30/22.75 | % 152.30/22.75 | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (10), (12), (13), (14), % 152.30/22.75 | (15), (16), (17), (18), (19), (21), (22), (25), (26), (27), (28), % 152.30/22.75 | (29), (31) are inconsistent by sub-proof #542. % 152.30/22.75 | % 152.30/22.75 End of proof % 152.30/22.75 % 152.30/22.75 Sub-proof #542 shows that the following formulas are inconsistent: % 152.30/22.75 ---------------------------------------------------------------- % 152.30/22.75 (1) all_56_11 = all_8_2 % 152.30/22.75 (2) ~ (e3 = e0) % 152.30/22.75 (3) ~ (all_52_2 = all_4_1) % 152.30/22.75 (4) all_56_31 = e3 % 152.30/22.75 (5) ~ (e3 = e2) % 152.30/22.75 (6) all_56_1 = all_4_1 % 152.30/22.75 (7) all_58_13 = all_52_7 % 152.30/22.75 (8) ~ (e1 = e0) % 152.30/22.75 (9) ~ (all_6_2 = e0) % 152.30/22.75 (10) ~ (all_52_2 = e0) % 152.30/22.75 (11) all_56_21 = e2 % 152.30/22.75 (12) ~ (all_52_2 = e1) % 152.30/22.75 (13) ~ (e2 = e1) % 152.30/22.75 (14) all_58_3 = all_8_2 % 152.30/22.75 (15) all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3 % 152.30/22.75 (16) ~ (all_52_2 = e2) % 152.30/22.75 (17) all_56_1 = e3 | all_56_11 = e2 | all_56_21 = e1 | all_56_31 = e0 % 152.30/22.75 (18) all_54_8 = all_52_2 % 152.30/22.75 (19) ~ (all_52_7 = e3) % 152.30/22.75 (20) all_6_2 = e2 % 152.30/22.75 (21) all_58_1 = e0 | all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0 % 152.30/22.75 (22) ~ (e3 = e1) % 152.30/22.75 (23) all_58_7 = e1 % 152.30/22.75 (24) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0 % 152.30/22.75 (25) ~ (all_52_7 = e0) % 152.30/22.75 % 152.30/22.75 Begin of proof % 152.30/22.75 | % 152.30/22.75 | REDUCE: (9), (20) imply: % 152.30/22.75 | (26) ~ (e2 = e0) % 152.30/22.75 | % 152.30/22.75 | BETA: splitting (17) gives: % 152.30/22.75 | % 152.30/22.75 | Case 1: % 152.30/22.75 | | % 152.30/22.75 | | (27) all_56_1 = e3 % 152.30/22.75 | | % 152.30/22.75 | | COMBINE_EQS: (6), (27) imply: % 152.30/22.75 | | (28) all_4_1 = e3 % 152.30/22.75 | | % 152.30/22.75 | | REDUCE: (3), (28) imply: % 152.30/22.75 | | (29) ~ (all_52_2 = e3) % 152.30/22.75 | | % 152.30/22.75 | | REF_CLOSE: (10), (12), (16), (18), (24), (29) are inconsistent by sub-proof % 152.30/22.75 | | #662. % 152.30/22.75 | | % 152.30/22.75 | Case 2: % 152.30/22.75 | | % 152.30/22.75 | | (30) all_56_11 = e2 | all_56_21 = e1 | all_56_31 = e0 % 152.30/22.75 | | % 152.30/22.75 | | BETA: splitting (30) gives: % 152.30/22.75 | | % 152.30/22.75 | | Case 1: % 152.30/22.75 | | | % 152.30/22.75 | | | (31) all_56_11 = e2 % 152.30/22.75 | | | % 152.30/22.75 | | | COMBINE_EQS: (1), (31) imply: % 152.30/22.75 | | | (32) all_8_2 = e2 % 152.30/22.75 | | | % 152.30/22.75 | | | COMBINE_EQS: (14), (32) imply: % 152.30/22.75 | | | (33) all_58_3 = e2 % 152.30/22.75 | | | % 152.30/22.75 | | | REF_CLOSE: (2), (5), (7), (8), (15), (19), (21), (22), (23), (25), (26), % 152.30/22.75 | | | (33) are inconsistent by sub-proof #544. % 152.30/22.75 | | | % 152.30/22.75 | | Case 2: % 152.30/22.75 | | | % 152.30/22.75 | | | (34) all_56_21 = e1 | all_56_31 = e0 % 152.30/22.75 | | | % 152.30/22.75 | | | BETA: splitting (34) gives: % 152.30/22.75 | | | % 152.30/22.75 | | | Case 1: % 152.30/22.75 | | | | % 152.30/22.75 | | | | (35) all_56_21 = e1 % 152.30/22.75 | | | | % 152.30/22.75 | | | | COMBINE_EQS: (11), (35) imply: % 152.30/22.75 | | | | (36) e2 = e1 % 152.30/22.75 | | | | % 152.30/22.75 | | | | SIMP: (36) implies: % 152.30/22.75 | | | | (37) e2 = e1 % 152.30/22.75 | | | | % 152.30/22.75 | | | | REDUCE: (13), (37) imply: % 152.30/22.75 | | | | (38) $false % 152.30/22.75 | | | | % 152.30/22.75 | | | | CLOSE: (38) is inconsistent. % 152.30/22.75 | | | | % 152.30/22.75 | | | Case 2: % 152.30/22.75 | | | | % 152.30/22.75 | | | | (39) all_56_31 = e0 % 152.30/22.75 | | | | % 152.30/22.75 | | | | REF_CLOSE: (2), (4), (39) are inconsistent by sub-proof #543. % 152.30/22.75 | | | | % 152.30/22.75 | | | End of split % 152.30/22.75 | | | % 152.30/22.75 | | End of split % 152.30/22.75 | | % 152.30/22.75 | End of split % 152.30/22.75 | % 152.30/22.75 End of proof % 152.30/22.75 % 152.30/22.75 Sub-proof #543 shows that the following formulas are inconsistent: % 152.30/22.75 ---------------------------------------------------------------- % 152.30/22.75 (1) all_56_31 = e3 % 152.30/22.75 (2) all_56_31 = e0 % 152.30/22.75 (3) ~ (e3 = e0) % 152.30/22.75 % 152.30/22.75 Begin of proof % 152.30/22.75 | % 152.30/22.75 | COMBINE_EQS: (1), (2) imply: % 152.30/22.75 | (4) e3 = e0 % 152.30/22.75 | % 152.30/22.75 | SIMP: (4) implies: % 152.30/22.75 | (5) e3 = e0 % 152.30/22.75 | % 152.30/22.75 | REDUCE: (3), (5) imply: % 152.30/22.75 | (6) $false % 152.30/22.75 | % 152.30/22.75 | CLOSE: (6) is inconsistent. % 152.30/22.75 | % 152.30/22.75 End of proof % 152.30/22.75 % 152.30/22.75 Sub-proof #544 shows that the following formulas are inconsistent: % 152.30/22.75 ---------------------------------------------------------------- % 152.30/22.75 (1) ~ (e3 = e0) % 152.30/22.75 (2) ~ (e3 = e2) % 152.30/22.75 (3) all_58_13 = all_52_7 % 152.30/22.75 (4) ~ (e1 = e0) % 152.30/22.75 (5) all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3 % 152.30/22.75 (6) ~ (all_52_7 = e3) % 152.30/22.75 (7) all_58_3 = e2 % 152.30/22.75 (8) all_58_1 = e0 | all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0 % 152.30/22.75 (9) ~ (e3 = e1) % 152.30/22.75 (10) ~ (e2 = e0) % 152.30/22.75 (11) all_58_7 = e1 % 152.30/22.75 (12) ~ (all_52_7 = e0) % 152.30/22.75 % 152.30/22.75 Begin of proof % 152.30/22.75 | % 152.30/22.75 | BETA: splitting (8) gives: % 152.30/22.75 | % 152.30/22.75 | Case 1: % 152.30/22.75 | | % 152.30/22.75 | | (13) all_58_1 = e0 % 152.30/22.75 | | % 152.30/22.75 | | BETA: splitting (5) gives: % 152.30/22.75 | | % 152.30/22.75 | | Case 1: % 152.30/22.75 | | | % 152.30/22.75 | | | (14) all_58_1 = e3 % 152.30/22.75 | | | % 152.30/22.75 | | | COMBINE_EQS: (13), (14) imply: % 152.30/22.75 | | | (15) e3 = e0 % 152.30/22.75 | | | % 152.30/22.75 | | | SIMP: (15) implies: % 152.30/22.75 | | | (16) e3 = e0 % 152.30/22.75 | | | % 152.30/22.75 | | | REDUCE: (1), (16) imply: % 152.30/22.75 | | | (17) $false % 152.30/22.75 | | | % 152.30/22.75 | | | CLOSE: (17) is inconsistent. % 152.30/22.75 | | | % 152.30/22.75 | | Case 2: % 152.30/22.75 | | | % 152.30/22.75 | | | (18) all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3 % 152.30/22.75 | | | % 152.30/22.75 | | | BETA: splitting (18) gives: % 152.30/22.75 | | | % 152.30/22.75 | | | Case 1: % 152.30/22.75 | | | | % 152.30/22.75 | | | | (19) all_58_3 = e3 % 152.30/22.75 | | | | % 152.30/22.75 | | | | COMBINE_EQS: (7), (19) imply: % 152.30/22.75 | | | | (20) e3 = e2 % 152.30/22.75 | | | | % 152.30/22.75 | | | | SIMP: (20) implies: % 152.30/22.75 | | | | (21) e3 = e2 % 152.30/22.75 | | | | % 152.30/22.75 | | | | REDUCE: (2), (21) imply: % 152.30/22.75 | | | | (22) $false % 152.30/22.75 | | | | % 152.30/22.75 | | | | CLOSE: (22) is inconsistent. % 152.30/22.75 | | | | % 152.30/22.75 | | | Case 2: % 152.30/22.75 | | | | % 152.30/22.75 | | | | (23) all_58_7 = e3 | all_58_13 = e3 % 152.30/22.75 | | | | % 152.30/22.75 | | | | BETA: splitting (23) gives: % 152.30/22.75 | | | | % 152.30/22.75 | | | | Case 1: % 152.30/22.75 | | | | | % 152.30/22.75 | | | | | (24) all_58_7 = e3 % 152.30/22.75 | | | | | % 152.30/22.75 | | | | | COMBINE_EQS: (11), (24) imply: % 152.30/22.75 | | | | | (25) e3 = e1 % 152.30/22.75 | | | | | % 152.30/22.75 | | | | | SIMP: (25) implies: % 152.30/22.75 | | | | | (26) e3 = e1 % 152.30/22.75 | | | | | % 152.30/22.75 | | | | | REDUCE: (9), (26) imply: % 152.30/22.75 | | | | | (27) $false % 152.30/22.75 | | | | | % 152.30/22.75 | | | | | CLOSE: (27) is inconsistent. % 152.30/22.75 | | | | | % 152.30/22.75 | | | | Case 2: % 152.30/22.75 | | | | | % 152.30/22.75 | | | | | (28) all_58_13 = e3 % 152.30/22.75 | | | | | % 152.30/22.75 | | | | | COMBINE_EQS: (3), (28) imply: % 152.30/22.75 | | | | | (29) all_52_7 = e3 % 152.30/22.75 | | | | | % 152.30/22.75 | | | | | REDUCE: (6), (29) imply: % 152.30/22.75 | | | | | (30) $false % 152.30/22.75 | | | | | % 152.30/22.75 | | | | | CLOSE: (30) is inconsistent. % 152.30/22.75 | | | | | % 152.30/22.75 | | | | End of split % 152.30/22.75 | | | | % 152.30/22.75 | | | End of split % 152.30/22.75 | | | % 152.30/22.75 | | End of split % 152.30/22.75 | | % 152.30/22.75 | Case 2: % 152.30/22.75 | | % 152.30/22.75 | | (31) all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0 % 152.30/22.75 | | % 152.30/22.75 | | REF_CLOSE: (3), (4), (7), (10), (11), (12), (31) are inconsistent by % 152.30/22.75 | | sub-proof #545. % 152.30/22.75 | | % 152.30/22.75 | End of split % 152.30/22.75 | % 152.30/22.75 End of proof % 152.30/22.75 % 152.30/22.75 Sub-proof #545 shows that the following formulas are inconsistent: % 152.30/22.75 ---------------------------------------------------------------- % 152.30/22.75 (1) all_58_13 = all_52_7 % 152.30/22.75 (2) ~ (e1 = e0) % 152.30/22.75 (3) all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0 % 152.30/22.75 (4) all_58_3 = e2 % 152.30/22.75 (5) ~ (e2 = e0) % 152.30/22.75 (6) all_58_7 = e1 % 152.30/22.75 (7) ~ (all_52_7 = e0) % 152.30/22.75 % 152.30/22.75 Begin of proof % 152.30/22.75 | % 152.30/22.75 | BETA: splitting (3) gives: % 152.30/22.75 | % 152.30/22.75 | Case 1: % 152.30/22.75 | | % 152.30/22.75 | | (8) all_58_3 = e0 % 152.30/22.75 | | % 152.30/22.75 | | COMBINE_EQS: (4), (8) imply: % 152.30/22.75 | | (9) e2 = e0 % 152.30/22.75 | | % 152.30/22.75 | | REDUCE: (5), (9) imply: % 152.30/22.75 | | (10) $false % 152.30/22.75 | | % 152.30/22.75 | | CLOSE: (10) is inconsistent. % 152.30/22.75 | | % 152.30/22.75 | Case 2: % 152.30/22.75 | | % 152.30/22.75 | | (11) all_58_7 = e0 | all_58_13 = e0 % 152.30/22.75 | | % 152.30/22.75 | | BETA: splitting (11) gives: % 152.30/22.75 | | % 152.30/22.75 | | Case 1: % 152.30/22.75 | | | % 152.30/22.75 | | | (12) all_58_7 = e0 % 152.30/22.75 | | | % 152.30/22.75 | | | COMBINE_EQS: (6), (12) imply: % 152.30/22.75 | | | (13) e1 = e0 % 152.30/22.75 | | | % 152.30/22.75 | | | REDUCE: (2), (13) imply: % 152.30/22.75 | | | (14) $false % 152.30/22.75 | | | % 152.30/22.75 | | | CLOSE: (14) is inconsistent. % 152.30/22.75 | | | % 152.30/22.75 | | Case 2: % 152.30/22.75 | | | % 152.30/22.75 | | | (15) all_58_13 = e0 % 152.30/22.75 | | | % 152.30/22.75 | | | COMBINE_EQS: (1), (15) imply: % 152.30/22.75 | | | (16) all_52_7 = e0 % 152.30/22.75 | | | % 152.30/22.75 | | | REDUCE: (7), (16) imply: % 152.30/22.75 | | | (17) $false % 152.30/22.75 | | | % 152.30/22.75 | | | CLOSE: (17) is inconsistent. % 152.30/22.75 | | | % 152.30/22.75 | | End of split % 152.30/22.75 | | % 152.30/22.75 | End of split % 152.30/22.75 | % 152.30/22.75 End of proof % 152.30/22.75 % 152.30/22.75 Sub-proof #546 shows that the following formulas are inconsistent: % 152.30/22.75 ---------------------------------------------------------------- % 152.30/22.76 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 152.30/22.76 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 152.30/22.76 (2) op(e0, e0) = all_8_1 % 152.30/22.76 (3) op(e0, e0) = e3 % 152.30/22.76 (4) ~ (all_8_1 = e3) % 152.30/22.76 % 152.30/22.76 Begin of proof % 152.30/22.76 | % 152.30/22.76 | GROUND_INST: instantiating (1) with e3, all_8_1, e0, e0, simplifying with (2), % 152.30/22.76 | (3) gives: % 152.30/22.76 | (5) all_8_1 = e3 % 152.30/22.76 | % 152.30/22.76 | REDUCE: (4), (5) imply: % 152.30/22.76 | (6) $false % 152.30/22.76 | % 152.30/22.76 | CLOSE: (6) is inconsistent. % 152.30/22.76 | % 152.30/22.76 End of proof % 152.30/22.76 % 152.30/22.76 Sub-proof #547 shows that the following formulas are inconsistent: % 152.30/22.76 ---------------------------------------------------------------- % 152.30/22.76 (1) ~ (all_4_1 = e0) % 152.30/22.76 (2) ~ (all_52_2 = all_4_1) % 152.30/22.76 (3) ~ (all_6_1 = e2) % 152.30/22.76 (4) all_56_21 = e3 % 152.30/22.76 (5) ~ (all_6_1 = e3) % 152.30/22.76 (6) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 152.30/22.76 (7) all_56_21 = all_6_2 % 152.30/22.76 (8) all_54_0 = all_4_1 % 152.30/22.76 (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 152.30/22.76 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 152.30/22.76 (10) all_52_2 = e1 % 152.30/22.76 (11) op(all_6_2, all_6_2) = all_6_1 % 152.30/22.76 (12) op(e3, e3) = all_4_1 % 152.30/22.76 % 152.30/22.76 Begin of proof % 152.30/22.76 | % 152.30/22.76 | COMBINE_EQS: (4), (7) imply: % 152.30/22.76 | (13) all_6_2 = e3 % 152.30/22.76 | % 152.30/22.76 | SIMP: (13) implies: % 152.30/22.76 | (14) all_6_2 = e3 % 152.30/22.76 | % 152.30/22.76 | REDUCE: (2), (10) imply: % 152.30/22.76 | (15) ~ (all_4_1 = e1) % 152.30/22.76 | % 152.30/22.76 | SIMP: (15) implies: % 152.30/22.76 | (16) ~ (all_4_1 = e1) % 152.30/22.76 | % 152.30/22.76 | REDUCE: (11), (14) imply: % 152.30/22.76 | (17) op(e3, e3) = all_6_1 % 152.30/22.76 | % 152.30/22.76 | GROUND_INST: instantiating (9) with all_4_1, all_6_1, e3, e3, simplifying with % 152.30/22.76 | (12), (17) gives: % 152.30/22.76 | (18) all_6_1 = all_4_1 % 152.30/22.76 | % 152.30/22.76 | REDUCE: (5), (18) imply: % 152.30/22.76 | (19) ~ (all_4_1 = e3) % 152.30/22.76 | % 152.30/22.76 | REDUCE: (3), (18) imply: % 152.30/22.76 | (20) ~ (all_4_1 = e2) % 152.30/22.76 | % 152.30/22.76 | REF_CLOSE: (1), (6), (8), (16), (19), (20) are inconsistent by sub-proof #548. % 152.30/22.76 | % 152.30/22.76 End of proof % 152.30/22.76 % 152.30/22.76 Sub-proof #548 shows that the following formulas are inconsistent: % 152.30/22.76 ---------------------------------------------------------------- % 152.30/22.76 (1) ~ (all_4_1 = e0) % 152.30/22.76 (2) ~ (all_4_1 = e3) % 152.30/22.76 (3) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 152.30/22.76 (4) ~ (all_4_1 = e2) % 152.30/22.76 (5) all_54_0 = all_4_1 % 152.30/22.76 (6) ~ (all_4_1 = e1) % 152.30/22.76 % 152.30/22.76 Begin of proof % 152.30/22.76 | % 152.30/22.76 | BETA: splitting (3) gives: % 152.30/22.76 | % 152.30/22.76 | Case 1: % 152.30/22.76 | | % 152.30/22.76 | | (7) all_54_0 = e3 % 152.30/22.76 | | % 152.30/22.76 | | REF_CLOSE: (2), (5), (7) are inconsistent by sub-proof #554. % 152.30/22.76 | | % 152.30/22.76 | Case 2: % 152.30/22.76 | | % 152.30/22.76 | | (8) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 152.30/22.76 | | % 152.30/22.76 | | REF_CLOSE: (1), (4), (5), (6), (8) are inconsistent by sub-proof #549. % 152.30/22.76 | | % 152.30/22.76 | End of split % 152.30/22.76 | % 152.30/22.76 End of proof % 152.30/22.76 % 152.30/22.76 Sub-proof #549 shows that the following formulas are inconsistent: % 152.30/22.76 ---------------------------------------------------------------- % 152.30/22.76 (1) ~ (all_4_1 = e0) % 152.30/22.76 (2) ~ (all_4_1 = e2) % 152.30/22.76 (3) all_54_0 = all_4_1 % 152.30/22.76 (4) ~ (all_4_1 = e1) % 152.30/22.76 (5) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 152.30/22.76 % 152.30/22.76 Begin of proof % 152.30/22.76 | % 152.30/22.76 | BETA: splitting (5) gives: % 152.30/22.76 | % 152.30/22.76 | Case 1: % 152.30/22.76 | | % 152.30/22.76 | | (6) all_54_0 = e2 % 152.30/22.76 | | % 152.30/22.76 | | REF_CLOSE: (2), (3), (6) are inconsistent by sub-proof #553. % 152.30/22.76 | | % 152.30/22.76 | Case 2: % 152.30/22.76 | | % 152.30/22.76 | | (7) all_54_0 = e1 | all_54_0 = e0 % 152.30/22.76 | | % 152.30/22.76 | | REF_CLOSE: (1), (3), (4), (7) are inconsistent by sub-proof #550. % 152.30/22.76 | | % 152.30/22.76 | End of split % 152.30/22.76 | % 152.30/22.76 End of proof % 152.30/22.76 % 152.30/22.76 Sub-proof #550 shows that the following formulas are inconsistent: % 152.30/22.76 ---------------------------------------------------------------- % 152.30/22.76 (1) all_54_0 = e1 | all_54_0 = e0 % 152.30/22.76 (2) all_54_0 = all_4_1 % 152.30/22.76 (3) ~ (all_4_1 = e1) % 152.30/22.76 (4) ~ (all_4_1 = e0) % 152.30/22.76 % 152.30/22.76 Begin of proof % 152.30/22.76 | % 152.30/22.76 | BETA: splitting (1) gives: % 152.30/22.76 | % 152.30/22.76 | Case 1: % 152.30/22.76 | | % 152.30/22.76 | | (5) all_54_0 = e1 % 152.30/22.76 | | % 152.30/22.76 | | COMBINE_EQS: (2), (5) imply: % 152.30/22.76 | | (6) all_4_1 = e1 % 152.30/22.76 | | % 152.30/22.76 | | SIMP: (6) implies: % 152.30/22.76 | | (7) all_4_1 = e1 % 152.30/22.76 | | % 152.30/22.76 | | REDUCE: (3), (7) imply: % 152.30/22.76 | | (8) $false % 152.30/22.76 | | % 152.30/22.76 | | CLOSE: (8) is inconsistent. % 152.30/22.76 | | % 152.30/22.76 | Case 2: % 152.30/22.76 | | % 152.30/22.76 | | (9) all_54_0 = e0 % 152.30/22.76 | | % 152.30/22.76 | | COMBINE_EQS: (2), (9) imply: % 152.30/22.76 | | (10) all_4_1 = e0 % 152.30/22.76 | | % 152.30/22.76 | | SIMP: (10) implies: % 152.30/22.76 | | (11) all_4_1 = e0 % 152.30/22.76 | | % 152.30/22.76 | | REDUCE: (4), (11) imply: % 152.30/22.76 | | (12) $false % 152.30/22.76 | | % 152.30/22.76 | | CLOSE: (12) is inconsistent. % 152.30/22.76 | | % 152.30/22.76 | End of split % 152.30/22.76 | % 152.30/22.76 End of proof % 152.30/22.76 % 152.30/22.76 Sub-proof #551 shows that the following formulas are inconsistent: % 152.30/22.76 ---------------------------------------------------------------- % 152.30/22.76 (1) ~ (all_8_1 = e1) % 152.30/22.76 (2) ~ (all_52_2 = all_4_1) % 152.30/22.76 (3) all_54_0 = all_10_2 % 152.30/22.76 (4) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 152.30/22.76 (5) ~ (all_4_1 = e2) % 152.30/22.76 (6) all_54_0 = all_4_1 % 152.30/22.76 (7) op(e3, e3) = all_10_2 % 152.30/22.76 (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 152.30/22.76 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 152.30/22.76 (9) ~ (all_52_2 = e0) % 152.30/22.76 (10) ~ (all_52_2 = e1) % 152.30/22.76 (11) ~ (all_52_2 = e2) % 152.30/22.76 (12) all_54_8 = all_52_2 % 152.30/22.76 (13) ~ (all_10_2 = e0) % 152.30/22.76 (14) op(e3, e3) = all_8_1 % 152.30/22.76 (15) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0 % 152.30/22.76 % 152.30/22.76 Begin of proof % 152.30/22.76 | % 152.30/22.76 | BETA: splitting (15) gives: % 152.30/22.76 | % 152.30/22.76 | Case 1: % 152.30/22.76 | | % 152.30/22.76 | | (16) all_54_8 = e3 % 152.30/22.76 | | % 152.30/22.76 | | COMBINE_EQS: (12), (16) imply: % 152.30/22.76 | | (17) all_52_2 = e3 % 152.30/22.76 | | % 152.30/22.76 | | REDUCE: (2), (17) imply: % 152.30/22.76 | | (18) ~ (all_4_1 = e3) % 152.30/22.76 | | % 152.30/22.76 | | SIMP: (18) implies: % 152.30/22.76 | | (19) ~ (all_4_1 = e3) % 152.30/22.76 | | % 152.30/22.76 | | BETA: splitting (4) gives: % 152.30/22.76 | | % 152.30/22.76 | | Case 1: % 152.30/22.76 | | | % 152.30/22.76 | | | (20) all_54_0 = e3 % 152.30/22.76 | | | % 152.30/22.76 | | | REF_CLOSE: (6), (19), (20) are inconsistent by sub-proof #554. % 152.30/22.76 | | | % 152.30/22.76 | | Case 2: % 152.30/22.76 | | | % 152.30/22.76 | | | (21) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 152.30/22.76 | | | % 152.30/22.76 | | | BETA: splitting (21) gives: % 152.30/22.76 | | | % 152.30/22.76 | | | Case 1: % 152.30/22.76 | | | | % 152.30/22.76 | | | | (22) all_54_0 = e2 % 152.30/22.76 | | | | % 152.30/22.76 | | | | REF_CLOSE: (5), (6), (22) are inconsistent by sub-proof #553. % 152.30/22.76 | | | | % 152.30/22.76 | | | Case 2: % 152.30/22.76 | | | | % 152.30/22.76 | | | | (23) all_54_0 = e1 | all_54_0 = e0 % 152.30/22.76 | | | | % 152.30/22.76 | | | | REF_CLOSE: (1), (3), (7), (8), (13), (14), (23) are inconsistent by % 152.30/22.76 | | | | sub-proof #552. % 152.30/22.76 | | | | % 152.30/22.76 | | | End of split % 152.30/22.76 | | | % 152.30/22.76 | | End of split % 152.30/22.76 | | % 152.30/22.76 | Case 2: % 152.30/22.76 | | % 152.30/22.76 | | (24) all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0 % 152.30/22.76 | | % 152.30/22.76 | | REF_CLOSE: (9), (10), (11), (12), (24) are inconsistent by sub-proof #663. % 152.30/22.76 | | % 152.30/22.76 | End of split % 152.30/22.76 | % 152.30/22.76 End of proof % 152.30/22.76 % 152.30/22.76 Sub-proof #552 shows that the following formulas are inconsistent: % 152.30/22.76 ---------------------------------------------------------------- % 152.30/22.76 (1) ~ (all_8_1 = e1) % 152.30/22.76 (2) all_54_0 = all_10_2 % 152.30/22.76 (3) op(e3, e3) = all_10_2 % 152.30/22.76 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 152.30/22.76 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 152.30/22.76 (5) all_54_0 = e1 | all_54_0 = e0 % 152.30/22.76 (6) ~ (all_10_2 = e0) % 152.30/22.76 (7) op(e3, e3) = all_8_1 % 152.30/22.76 % 152.30/22.76 Begin of proof % 152.30/22.76 | % 152.30/22.76 | BETA: splitting (5) gives: % 152.30/22.76 | % 152.30/22.76 | Case 1: % 152.30/22.76 | | % 152.30/22.76 | | (8) all_54_0 = e1 % 152.30/22.76 | | % 152.30/22.76 | | COMBINE_EQS: (2), (8) imply: % 152.30/22.76 | | (9) all_10_2 = e1 % 152.30/22.76 | | % 152.30/22.76 | | SIMP: (9) implies: % 152.30/22.76 | | (10) all_10_2 = e1 % 152.30/22.76 | | % 152.30/22.76 | | REDUCE: (3), (10) imply: % 152.30/22.76 | | (11) op(e3, e3) = e1 % 152.30/22.76 | | % 152.30/22.76 | | GROUND_INST: instantiating (4) with e1, all_8_1, e3, e3, simplifying with % 152.30/22.76 | | (7), (11) gives: % 152.30/22.76 | | (12) all_8_1 = e1 % 152.30/22.76 | | % 152.30/22.76 | | REDUCE: (1), (12) imply: % 152.30/22.76 | | (13) $false % 152.30/22.76 | | % 152.30/22.76 | | CLOSE: (13) is inconsistent. % 152.30/22.76 | | % 152.30/22.76 | Case 2: % 152.30/22.76 | | % 152.30/22.76 | | (14) all_54_0 = e0 % 152.30/22.76 | | % 152.30/22.76 | | REF_CLOSE: (2), (6), (14) are inconsistent by sub-proof #732. % 152.30/22.76 | | % 152.30/22.76 | End of split % 152.30/22.76 | % 152.30/22.76 End of proof % 152.30/22.76 % 152.30/22.76 Sub-proof #553 shows that the following formulas are inconsistent: % 152.30/22.76 ---------------------------------------------------------------- % 152.30/22.76 (1) all_54_0 = all_4_1 % 152.30/22.76 (2) all_54_0 = e2 % 152.30/22.76 (3) ~ (all_4_1 = e2) % 152.30/22.76 % 152.30/22.76 Begin of proof % 152.30/22.76 | % 152.30/22.76 | COMBINE_EQS: (1), (2) imply: % 152.30/22.76 | (4) all_4_1 = e2 % 152.30/22.76 | % 152.30/22.76 | SIMP: (4) implies: % 152.30/22.76 | (5) all_4_1 = e2 % 152.30/22.76 | % 152.30/22.76 | REDUCE: (3), (5) imply: % 152.30/22.76 | (6) $false % 152.30/22.76 | % 152.30/22.76 | CLOSE: (6) is inconsistent. % 152.30/22.76 | % 152.30/22.76 End of proof % 152.30/22.76 % 152.30/22.76 Sub-proof #554 shows that the following formulas are inconsistent: % 152.30/22.76 ---------------------------------------------------------------- % 152.30/22.76 (1) all_54_0 = all_4_1 % 152.30/22.76 (2) all_54_0 = e3 % 152.30/22.76 (3) ~ (all_4_1 = e3) % 152.30/22.76 % 152.30/22.76 Begin of proof % 152.30/22.76 | % 152.30/22.76 | COMBINE_EQS: (1), (2) imply: % 152.30/22.76 | (4) all_4_1 = e3 % 152.30/22.76 | % 152.30/22.76 | SIMP: (4) implies: % 152.30/22.76 | (5) all_4_1 = e3 % 152.30/22.76 | % 152.30/22.76 | REDUCE: (3), (5) imply: % 152.30/22.76 | (6) $false % 152.30/22.76 | % 152.30/22.76 | CLOSE: (6) is inconsistent. % 152.30/22.76 | % 152.30/22.76 End of proof % 152.30/22.76 % 152.30/22.76 Sub-proof #555 shows that the following formulas are inconsistent: % 152.30/22.76 ---------------------------------------------------------------- % 152.30/22.76 (1) op(e2, e2) = e2 % 152.30/22.76 (2) op(all_4_1, all_4_1) = all_10_1 % 152.30/22.76 (3) all_4_1 = e2 % 152.30/22.76 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 152.30/22.76 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 152.30/22.76 (5) ~ (all_10_1 = e2) % 152.30/22.76 % 152.30/22.76 Begin of proof % 152.30/22.76 | % 152.30/22.76 | REDUCE: (2), (3) imply: % 152.30/22.76 | (6) op(e2, e2) = all_10_1 % 152.30/22.76 | % 152.30/22.76 | GROUND_INST: instantiating (4) with e2, all_10_1, e2, e2, simplifying with % 152.30/22.76 | (1), (6) gives: % 152.30/22.76 | (7) all_10_1 = e2 % 152.30/22.76 | % 152.30/22.76 | REDUCE: (5), (7) imply: % 152.30/22.76 | (8) $false % 152.30/22.76 | % 152.30/22.76 | CLOSE: (8) is inconsistent. % 152.30/22.76 | % 152.30/22.76 End of proof % 152.30/22.76 % 152.30/22.76 Sub-proof #556 shows that the following formulas are inconsistent: % 152.30/22.76 ---------------------------------------------------------------- % 152.30/22.76 (1) op(e0, all_52_13) = all_56_14 % 152.30/22.76 (2) ~ (all_52_4 = all_52_8) % 152.30/22.76 (3) ~ (all_52_8 = all_52_9) % 152.30/22.76 (4) all_54_9 = all_52_6 % 152.30/22.76 (5) ~ (all_52_6 = e1) % 152.30/22.76 (6) ~ (all_52_1 = all_52_9) % 152.30/22.76 (7) ~ (all_52_9 = e2) % 152.30/22.76 (8) ~ (all_52_8 = e2) % 152.30/22.76 (9) ~ (all_8_2 = e1) % 152.30/22.76 (10) all_54_4 = all_52_1 % 152.30/22.76 (11) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0 % 152.30/22.76 (12) all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2 % 152.30/22.76 (13) all_58_4 = all_52_8 % 152.30/22.76 (14) all_54_5 = all_8_2 % 152.30/22.76 (15) ~ (all_52_6 = all_52_14) % 152.30/22.76 (16) all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1 % 152.30/22.76 (17) op(e3, all_52_1) = all_56_8 % 152.30/22.76 (18) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0 % 152.30/22.76 (19) all_58_5 = all_52_9 % 152.30/22.76 (20) all_54_1 = all_52_4 % 152.30/22.76 (21) all_58_9 = all_52_12 % 152.30/22.76 (22) all_56_1 = all_4_1 % 152.30/22.76 (23) op(e0, e1) = e2 % 152.30/22.76 (24) ~ (all_52_4 = e1) % 152.30/22.76 (25) ~ (all_56_1 = e1) | all_56_5 = e3 % 152.30/22.76 (26) all_58_1 = all_52_4 % 152.30/22.76 (27) all_58_4 = e0 | all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0 % 152.30/22.76 (28) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0 % 152.30/22.76 (29) all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1 % 152.30/22.76 (30) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 152.30/22.76 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 152.30/22.76 (31) ~ (all_52_14 = e1) % 152.30/22.76 (32) op(e0, all_4_1) = all_4_0 % 152.30/22.76 (33) ~ (all_52_1 = all_52_13) % 152.30/22.76 (34) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0 % 152.30/22.76 (35) ~ (all_52_14 = e3) % 152.30/22.76 (36) ~ (all_4_2 = e1) % 152.30/22.76 (37) all_54_6 = all_52_9 % 152.30/22.76 (38) all_58_0 = all_4_1 % 152.30/22.76 (39) ~ (all_8_2 = e3) % 152.30/22.76 (40) all_56_5 = all_52_8 % 152.30/22.76 (41) ~ (e2 = e1) % 152.30/22.76 (42) ~ (all_52_9 = all_52_13) % 152.30/22.76 (43) op(all_4_2, all_4_2) = all_4_1 % 152.30/22.76 (44) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0 % 152.30/22.76 (45) ~ (all_52_1 = all_52_3) % 152.30/22.76 (46) all_58_11 = all_52_14 % 152.30/22.76 (47) ~ (all_52_8 = e1) % 152.30/22.76 (48) all_58_14 = e2 % 152.30/22.76 (49) ~ (all_52_4 = e2) % 152.30/22.76 (50) all_54_2 = all_52_8 % 152.30/22.76 (51) ~ (all_52_6 = all_8_2) % 152.30/22.76 (52) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0 % 152.30/22.76 (53) all_58_15 = all_4_2 % 152.30/22.76 (54) all_58_2 = all_52_1 % 152.30/22.76 (55) all_58_10 = all_52_13 % 152.30/22.76 (56) ~ (all_52_12 = all_52_14) % 152.30/22.76 (57) ~ (all_52_4 = all_52_12) % 152.30/22.76 (58) ~ (all_56_1 = e2) % 152.30/22.76 (59) ~ (all_52_8 = all_52_12) % 152.30/22.76 (60) ~ (all_8_2 = e0) % 152.30/22.76 (61) all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3 % 152.30/22.76 (62) ~ (all_52_4 = all_52_6) % 152.30/22.76 (63) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 152.30/22.76 (64) ~ (all_52_1 = e2) % 152.30/22.76 (65) ~ (all_4_0 = e2) % 152.30/22.76 (66) all_58_13 = e1 % 152.30/22.76 (67) op(e3, e3) = all_4_1 % 152.30/22.76 (68) all_58_12 = all_52_3 % 152.30/22.76 (69) all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3 % 152.30/22.76 (70) all_54_11 = all_52_14 % 152.30/22.76 % 152.30/22.76 Begin of proof % 152.30/22.76 | % 152.30/22.76 | REDUCE: (22), (58) imply: % 152.30/22.76 | (71) ~ (all_4_1 = e2) % 152.30/22.76 | % 152.30/22.76 | BETA: splitting (12) gives: % 152.30/22.76 | % 152.30/22.76 | Case 1: % 152.30/22.76 | | % 152.30/22.76 | | (72) all_58_0 = e2 % 152.30/22.76 | | % 152.30/22.76 | | COMBINE_EQS: (38), (72) imply: % 152.30/22.76 | | (73) all_4_1 = e2 % 152.30/22.76 | | % 152.30/22.76 | | REDUCE: (71), (73) imply: % 152.30/22.76 | | (74) $false % 152.30/22.76 | | % 152.30/22.76 | | CLOSE: (74) is inconsistent. % 152.30/22.76 | | % 152.30/22.76 | Case 2: % 152.30/22.76 | | % 152.30/22.76 | | (75) all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2 % 152.30/22.76 | | % 152.30/22.76 | | BETA: splitting (75) gives: % 152.30/22.76 | | % 152.30/22.76 | | Case 1: % 152.30/22.76 | | | % 152.30/22.76 | | | (76) all_58_1 = e2 % 152.30/22.76 | | | % 152.30/22.76 | | | COMBINE_EQS: (26), (76) imply: % 152.30/22.76 | | | (77) all_52_4 = e2 % 152.30/22.76 | | | % 152.30/22.76 | | | REDUCE: (49), (77) imply: % 152.30/22.76 | | | (78) $false % 152.30/22.76 | | | % 152.30/22.76 | | | CLOSE: (78) is inconsistent. % 152.30/22.76 | | | % 152.30/22.76 | | Case 2: % 152.30/22.76 | | | % 152.30/22.76 | | | (79) all_58_4 = e2 | all_58_9 = e2 % 152.30/22.76 | | | % 152.30/22.76 | | | BETA: splitting (79) gives: % 152.30/22.76 | | | % 152.30/22.76 | | | Case 1: % 152.30/22.76 | | | | % 152.30/22.76 | | | | (80) all_58_4 = e2 % 152.30/22.76 | | | | % 152.30/22.76 | | | | COMBINE_EQS: (13), (80) imply: % 152.30/22.76 | | | | (81) all_52_8 = e2 % 152.30/22.76 | | | | % 152.30/22.76 | | | | REDUCE: (8), (81) imply: % 152.30/22.76 | | | | (82) $false % 152.30/22.76 | | | | % 152.30/22.76 | | | | CLOSE: (82) is inconsistent. % 152.30/22.76 | | | | % 152.30/22.76 | | | Case 2: % 152.30/22.76 | | | | % 152.30/22.76 | | | | (83) all_58_9 = e2 % 152.30/22.76 | | | | % 152.30/22.76 | | | | COMBINE_EQS: (21), (83) imply: % 152.30/22.76 | | | | (84) all_52_12 = e2 % 152.30/22.76 | | | | % 152.30/22.76 | | | | REDUCE: (56), (84) imply: % 152.30/22.76 | | | | (85) ~ (all_52_14 = e2) % 152.30/22.76 | | | | % 152.30/22.76 | | | | SIMP: (85) implies: % 152.30/22.76 | | | | (86) ~ (all_52_14 = e2) % 152.30/22.76 | | | | % 152.30/22.76 | | | | BETA: splitting (11) gives: % 152.30/22.76 | | | | % 152.30/22.76 | | | | Case 1: % 152.30/22.76 | | | | | % 152.30/22.76 | | | | | (87) all_54_11 = e3 % 152.30/22.76 | | | | | % 152.30/22.76 | | | | | COMBINE_EQS: (70), (87) imply: % 152.30/22.76 | | | | | (88) all_52_14 = e3 % 152.30/22.76 | | | | | % 152.30/22.76 | | | | | REDUCE: (35), (88) imply: % 152.30/22.76 | | | | | (89) $false % 152.30/22.76 | | | | | % 152.30/22.76 | | | | | CLOSE: (89) is inconsistent. % 152.30/22.76 | | | | | % 152.30/22.76 | | | | Case 2: % 152.30/22.76 | | | | | % 152.30/22.76 | | | | | (90) all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0 % 152.30/22.76 | | | | | % 152.30/22.76 | | | | | BETA: splitting (90) gives: % 152.30/22.76 | | | | | % 152.30/22.76 | | | | | Case 1: % 152.30/22.76 | | | | | | % 152.30/22.76 | | | | | | (91) all_54_11 = e2 % 152.30/22.76 | | | | | | % 152.30/22.76 | | | | | | COMBINE_EQS: (70), (91) imply: % 152.30/22.76 | | | | | | (92) all_52_14 = e2 % 152.30/22.76 | | | | | | % 152.30/22.76 | | | | | | REDUCE: (86), (92) imply: % 152.30/22.76 | | | | | | (93) $false % 152.30/22.76 | | | | | | % 152.30/22.76 | | | | | | CLOSE: (93) is inconsistent. % 152.30/22.76 | | | | | | % 152.30/22.76 | | | | | Case 2: % 152.30/22.76 | | | | | | % 152.30/22.76 | | | | | | (94) all_54_11 = e1 | all_54_11 = e0 % 152.30/22.76 | | | | | | % 152.30/22.76 | | | | | | BETA: splitting (94) gives: % 152.30/22.76 | | | | | | % 152.30/22.76 | | | | | | Case 1: % 152.30/22.76 | | | | | | | % 152.30/22.76 | | | | | | | (95) all_54_11 = e1 % 152.30/22.76 | | | | | | | % 152.30/22.76 | | | | | | | COMBINE_EQS: (70), (95) imply: % 152.30/22.76 | | | | | | | (96) all_52_14 = e1 % 152.30/22.76 | | | | | | | % 152.30/22.76 | | | | | | | REDUCE: (31), (96) imply: % 152.30/22.76 | | | | | | | (97) $false % 152.30/22.76 | | | | | | | % 152.30/22.76 | | | | | | | CLOSE: (97) is inconsistent. % 152.30/22.76 | | | | | | | % 152.30/22.76 | | | | | | Case 2: % 152.30/22.76 | | | | | | | % 152.30/22.76 | | | | | | | (98) all_54_11 = e0 % 152.30/22.76 | | | | | | | % 152.30/22.76 | | | | | | | COMBINE_EQS: (70), (98) imply: % 152.30/22.76 | | | | | | | (99) all_52_14 = e0 % 152.30/22.76 | | | | | | | % 152.30/22.76 | | | | | | | REDUCE: (15), (99) imply: % 152.30/22.76 | | | | | | | (100) ~ (all_52_6 = e0) % 152.30/22.76 | | | | | | | % 152.30/22.76 | | | | | | | BETA: splitting (44) gives: % 152.30/22.76 | | | | | | | % 152.30/22.76 | | | | | | | Case 1: % 152.30/22.76 | | | | | | | | % 152.30/22.76 | | | | | | | | (101) all_54_9 = e3 % 152.30/22.76 | | | | | | | | % 152.30/22.76 | | | | | | | | COMBINE_EQS: (4), (101) imply: % 152.30/22.76 | | | | | | | | (102) all_52_6 = e3 % 152.30/22.76 | | | | | | | | % 152.30/22.76 | | | | | | | | SIMP: (102) implies: % 152.30/22.76 | | | | | | | | (103) all_52_6 = e3 % 152.30/22.76 | | | | | | | | % 152.30/22.76 | | | | | | | | REDUCE: (62), (103) imply: % 152.30/22.76 | | | | | | | | (104) ~ (all_52_4 = e3) % 152.30/22.76 | | | | | | | | % 152.30/22.76 | | | | | | | | REDUCE: (5), (103) imply: % 152.30/22.76 | | | | | | | | (105) ~ (e3 = e1) % 152.30/22.76 | | | | | | | | % 152.30/22.76 | | | | | | | | REDUCE: (100), (103) imply: % 152.30/22.76 | | | | | | | | (106) ~ (e3 = e0) % 152.30/22.76 | | | | | | | | % 152.30/22.76 | | | | | | | | BETA: splitting (52) gives: % 152.30/22.76 | | | | | | | | % 152.30/22.76 | | | | | | | | Case 1: % 152.30/22.76 | | | | | | | | | % 152.30/22.76 | | | | | | | | | (107) all_54_1 = e3 % 152.30/22.76 | | | | | | | | | % 152.30/22.76 | | | | | | | | | REF_CLOSE: (20), (104), (107) are inconsistent by sub-proof % 152.30/22.76 | | | | | | | | | #722. % 152.30/22.76 | | | | | | | | | % 152.30/22.76 | | | | | | | | Case 2: % 152.30/22.76 | | | | | | | | | % 152.30/22.76 | | | | | | | | | (108) all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0 % 152.30/22.76 | | | | | | | | | % 152.30/22.76 | | | | | | | | | BETA: splitting (16) gives: % 152.30/22.76 | | | | | | | | | % 152.30/22.76 | | | | | | | | | Case 1: % 152.30/22.76 | | | | | | | | | | % 152.30/22.76 | | | | | | | | | | (109) all_58_9 = e1 % 152.30/22.76 | | | | | | | | | | % 152.30/22.76 | | | | | | | | | | REF_CLOSE: (8), (13), (41), (79), (109) are inconsistent by % 152.30/22.76 | | | | | | | | | | sub-proof #562. % 152.30/22.76 | | | | | | | | | | % 152.30/22.76 | | | | | | | | | Case 2: % 152.30/22.76 | | | | | | | | | | % 152.30/22.76 | | | | | | | | | | (110) ~ (all_58_9 = e1) % 152.30/22.76 | | | | | | | | | | (111) all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1 % 152.30/22.76 | | | | | | | | | | % 152.30/22.76 | | | | | | | | | | BETA: splitting (29) gives: % 152.30/22.76 | | | | | | | | | | % 152.30/22.76 | | | | | | | | | | Case 1: % 152.30/22.76 | | | | | | | | | | | % 152.30/22.76 | | | | | | | | | | | (112) all_58_0 = e1 % 152.30/22.76 | | | | | | | | | | | % 152.30/22.76 | | | | | | | | | | | COMBINE_EQS: (38), (112) imply: % 152.30/22.76 | | | | | | | | | | | (113) all_4_1 = e1 % 152.30/22.76 | | | | | | | | | | | % 152.30/22.76 | | | | | | | | | | | COMBINE_EQS: (22), (113) imply: % 152.30/22.76 | | | | | | | | | | | (114) all_56_1 = e1 % 152.30/22.76 | | | | | | | | | | | % 152.30/22.76 | | | | | | | | | | | REDUCE: (67), (113) imply: % 152.30/22.76 | | | | | | | | | | | (115) op(e3, e3) = e1 % 152.30/22.76 | | | | | | | | | | | % 152.30/22.76 | | | | | | | | | | | BETA: splitting (25) gives: % 152.30/22.76 | | | | | | | | | | | % 152.30/22.76 | | | | | | | | | | | Case 1: % 152.30/22.76 | | | | | | | | | | | | % 152.30/22.76 | | | | | | | | | | | | (116) ~ (all_56_1 = e1) % 152.30/22.76 | | | | | | | | | | | | % 152.30/22.76 | | | | | | | | | | | | REDUCE: (114), (116) imply: % 152.30/22.76 | | | | | | | | | | | | (117) $false % 152.30/22.76 | | | | | | | | | | | | % 152.30/22.76 | | | | | | | | | | | | CLOSE: (117) is inconsistent. % 152.30/22.76 | | | | | | | | | | | | % 152.30/22.76 | | | | | | | | | | | Case 2: % 152.30/22.76 | | | | | | | | | | | | % 152.30/22.76 | | | | | | | | | | | | (118) all_56_5 = e3 % 152.30/22.76 | | | | | | | | | | | | % 152.30/22.76 | | | | | | | | | | | | COMBINE_EQS: (40), (118) imply: % 152.30/22.76 | | | | | | | | | | | | (119) all_52_8 = e3 % 152.30/22.76 | | | | | | | | | | | | % 152.30/22.76 | | | | | | | | | | | | SIMP: (119) implies: % 152.30/22.76 | | | | | | | | | | | | (120) all_52_8 = e3 % 152.30/22.76 | | | | | | | | | | | | % 152.30/22.76 | | | | | | | | | | | | COMBINE_EQS: (13), (120) imply: % 152.30/22.76 | | | | | | | | | | | | (121) all_58_4 = e3 % 152.30/22.76 | | | | | | | | | | | | % 152.30/22.76 | | | | | | | | | | | | REDUCE: (3), (120) imply: % 152.30/22.76 | | | | | | | | | | | | (122) ~ (all_52_9 = e3) % 152.30/22.76 | | | | | | | | | | | | % 152.30/22.76 | | | | | | | | | | | | SIMP: (122) implies: % 152.30/22.76 | | | | | | | | | | | | (123) ~ (all_52_9 = e3) % 152.30/22.76 | | | | | | | | | | | | % 152.30/22.76 | | | | | | | | | | | | BETA: splitting (18) gives: % 152.30/22.76 | | | | | | | | | | | | % 152.30/22.76 | | | | | | | | | | | | Case 1: % 152.30/22.76 | | | | | | | | | | | | | % 152.30/22.76 | | | | | | | | | | | | | (124) all_54_6 = e3 % 152.30/22.76 | | | | | | | | | | | | | % 152.30/22.76 | | | | | | | | | | | | | COMBINE_EQS: (37), (124) imply: % 152.30/22.76 | | | | | | | | | | | | | (125) all_52_9 = e3 % 152.30/22.76 | | | | | | | | | | | | | % 152.30/22.76 | | | | | | | | | | | | | REDUCE: (123), (125) imply: % 152.30/22.76 | | | | | | | | | | | | | (126) $false % 152.30/22.76 | | | | | | | | | | | | | % 152.30/22.76 | | | | | | | | | | | | | CLOSE: (126) is inconsistent. % 152.30/22.76 | | | | | | | | | | | | | % 152.30/22.76 | | | | | | | | | | | | Case 2: % 152.30/22.76 | | | | | | | | | | | | | % 152.30/22.76 | | | | | | | | | | | | | (127) all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0 % 152.30/22.76 | | | | | | | | | | | | | % 152.30/22.76 | | | | | | | | | | | | | REF_CLOSE: (1), (6), (7), (10), (17), (19), (23), (27), (30), % 152.30/22.76 | | | | | | | | | | | | | (31), (32), (33), (34), (36), (37), (42), (43), % 152.30/22.76 | | | | | | | | | | | | | (45), (46), (48), (53), (54), (55), (61), (64), % 152.30/22.76 | | | | | | | | | | | | | (65), (66), (68), (69), (106), (111), (115), % 152.30/22.76 | | | | | | | | | | | | | (121), (127) are inconsistent by sub-proof #558. % 152.30/22.76 | | | | | | | | | | | | | % 152.30/22.76 | | | | | | | | | | | | End of split % 152.30/22.76 | | | | | | | | | | | | % 152.30/22.76 | | | | | | | | | | | End of split % 152.30/22.76 | | | | | | | | | | | % 152.30/22.76 | | | | | | | | | | Case 2: % 152.30/22.76 | | | | | | | | | | | % 152.30/22.76 | | | | | | | | | | | (128) all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1 % 152.30/22.76 | | | | | | | | | | | % 152.30/22.76 | | | | | | | | | | | REF_CLOSE: (2), (8), (13), (20), (24), (26), (27), (28), % 152.30/22.76 | | | | | | | | | | | (41), (47), (49), (50), (83), (105), (108), (128) % 152.30/22.76 | | | | | | | | | | | are inconsistent by sub-proof #557. % 152.30/22.76 | | | | | | | | | | | % 152.30/22.76 | | | | | | | | | | End of split % 152.30/22.76 | | | | | | | | | | % 152.30/22.76 | | | | | | | | | End of split % 152.30/22.76 | | | | | | | | | % 152.30/22.76 | | | | | | | | End of split % 152.30/22.76 | | | | | | | | % 152.30/22.76 | | | | | | | Case 2: % 152.30/22.76 | | | | | | | | % 152.30/22.76 | | | | | | | | (129) all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0 % 152.30/22.76 | | | | | | | | % 152.30/22.76 | | | | | | | | REF_CLOSE: (4), (5), (9), (14), (39), (51), (60), (63), (100), % 152.30/22.76 | | | | | | | | (129) are inconsistent by sub-proof #642. % 152.30/22.76 | | | | | | | | % 152.30/22.76 | | | | | | | End of split % 152.30/22.76 | | | | | | | % 152.30/22.76 | | | | | | End of split % 152.30/22.76 | | | | | | % 152.30/22.76 | | | | | End of split % 152.30/22.76 | | | | | % 152.30/22.76 | | | | End of split % 152.30/22.76 | | | | % 152.30/22.76 | | | End of split % 152.30/22.76 | | | % 152.30/22.76 | | End of split % 152.30/22.76 | | % 152.30/22.76 | End of split % 152.30/22.76 | % 152.30/22.76 End of proof % 152.30/22.76 % 152.30/22.76 Sub-proof #557 shows that the following formulas are inconsistent: % 152.30/22.76 ---------------------------------------------------------------- % 152.30/22.76 (1) ~ (all_52_4 = all_52_8) % 152.30/22.76 (2) ~ (all_52_8 = e2) % 152.30/22.76 (3) all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1 % 152.30/22.76 (4) all_58_4 = all_52_8 % 152.30/22.76 (5) all_54_1 = all_52_4 % 152.30/22.76 (6) ~ (all_52_4 = e1) % 152.30/22.76 (7) all_58_1 = all_52_4 % 152.30/22.76 (8) all_58_4 = e0 | all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0 % 152.30/22.76 (9) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0 % 152.30/22.76 (10) all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0 % 152.30/22.76 (11) all_58_9 = e2 % 152.30/22.76 (12) ~ (e2 = e1) % 152.30/22.76 (13) ~ (all_52_8 = e1) % 152.30/22.76 (14) ~ (all_52_4 = e2) % 152.30/22.76 (15) all_54_2 = all_52_8 % 152.30/22.76 (16) ~ (e3 = e1) % 152.30/22.76 % 152.30/22.76 Begin of proof % 152.30/22.76 | % 152.30/22.76 | BETA: splitting (9) gives: % 152.30/22.76 | % 152.30/22.76 | Case 1: % 152.30/22.76 | | % 152.30/22.76 | | (17) all_54_2 = e3 % 152.30/22.76 | | % 152.30/22.76 | | REF_CLOSE: (3), (4), (5), (6), (7), (10), (11), (12), (14), (15), (16), (17) % 152.30/22.76 | | are inconsistent by sub-proof #700. % 152.30/22.76 | | % 152.30/22.76 | Case 2: % 152.30/22.76 | | % 152.30/22.76 | | (18) all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0 % 152.30/22.76 | | % 152.30/22.76 | | BETA: splitting (8) gives: % 152.30/22.76 | | % 152.30/22.76 | | Case 1: % 152.30/22.76 | | | % 152.30/22.76 | | | (19) all_58_4 = e0 % 152.30/22.76 | | | % 152.30/22.76 | | | COMBINE_EQS: (4), (19) imply: % 152.30/22.76 | | | (20) all_52_8 = e0 % 152.30/22.76 | | | % 152.30/22.76 | | | REDUCE: (1), (20) imply: % 152.30/22.76 | | | (21) ~ (all_52_4 = e0) % 152.30/22.76 | | | % 152.30/22.76 | | | REF_CLOSE: (5), (6), (10), (14), (21) are inconsistent by sub-proof #718. % 152.30/22.76 | | | % 152.30/22.76 | | Case 2: % 152.30/22.76 | | | % 152.30/22.76 | | | (22) ~ (all_58_4 = e0) % 152.30/22.76 | | | % 152.30/22.76 | | | REDUCE: (4), (22) imply: % 152.30/22.76 | | | (23) ~ (all_52_8 = e0) % 152.30/22.76 | | | % 152.30/22.76 | | | REF_CLOSE: (2), (13), (15), (18), (23) are inconsistent by sub-proof #723. % 152.30/22.76 | | | % 152.30/22.76 | | End of split % 152.30/22.76 | | % 152.30/22.76 | End of split % 152.30/22.76 | % 152.30/22.76 End of proof % 152.30/22.76 % 152.30/22.76 Sub-proof #558 shows that the following formulas are inconsistent: % 152.30/22.76 ---------------------------------------------------------------- % 152.30/22.76 (1) op(e0, all_52_13) = all_56_14 % 152.30/22.76 (2) ~ (all_52_1 = all_52_9) % 152.30/22.76 (3) ~ (e3 = e0) % 152.30/22.76 (4) ~ (all_52_9 = e2) % 152.30/22.76 (5) all_54_4 = all_52_1 % 152.30/22.76 (6) op(e3, all_52_1) = all_56_8 % 152.30/22.76 (7) all_58_5 = all_52_9 % 152.30/22.76 (8) op(e0, e1) = e2 % 152.30/22.76 (9) all_58_4 = e0 | all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0 % 152.30/22.76 (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 152.30/22.76 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 152.30/22.76 (11) ~ (all_52_14 = e1) % 152.30/22.76 (12) op(e0, all_4_1) = all_4_0 % 152.30/22.76 (13) ~ (all_52_1 = all_52_13) % 152.30/22.76 (14) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0 % 152.30/22.76 (15) ~ (all_4_2 = e1) % 152.30/22.76 (16) all_54_6 = all_52_9 % 152.30/22.76 (17) ~ (all_52_9 = all_52_13) % 152.30/22.76 (18) op(all_4_2, all_4_2) = all_4_1 % 152.30/22.76 (19) ~ (all_52_1 = all_52_3) % 152.30/22.76 (20) op(e3, e3) = e1 % 152.30/22.76 (21) all_58_11 = all_52_14 % 152.30/22.76 (22) all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1 % 152.30/22.76 (23) all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0 % 152.30/22.76 (24) all_58_14 = e2 % 152.30/22.76 (25) all_58_15 = all_4_2 % 152.30/22.76 (26) all_58_2 = all_52_1 % 152.30/22.76 (27) all_58_10 = all_52_13 % 152.30/22.76 (28) all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3 % 152.30/22.76 (29) ~ (all_52_1 = e2) % 152.30/22.76 (30) ~ (all_4_0 = e2) % 152.30/22.76 (31) all_58_13 = e1 % 152.30/22.76 (32) all_58_4 = e3 % 152.30/22.76 (33) all_58_12 = all_52_3 % 152.30/22.76 (34) all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3 % 152.30/22.76 % 152.30/22.76 Begin of proof % 152.30/22.76 | % 152.30/22.76 | BETA: splitting (22) gives: % 152.30/22.76 | % 152.30/22.76 | Case 1: % 152.30/22.76 | | % 152.30/22.76 | | (35) all_58_10 = e1 % 152.30/22.76 | | % 152.30/22.76 | | COMBINE_EQS: (27), (35) imply: % 152.30/22.76 | | (36) all_52_13 = e1 % 152.30/22.76 | | % 152.30/22.76 | | REDUCE: (13), (36) imply: % 152.30/22.76 | | (37) ~ (all_52_1 = e1) % 152.30/22.76 | | % 152.30/22.76 | | REDUCE: (17), (36) imply: % 152.30/22.76 | | (38) ~ (all_52_9 = e1) % 152.30/22.76 | | % 152.30/22.76 | | REDUCE: (1), (36) imply: % 152.30/22.76 | | (39) op(e0, e1) = all_56_14 % 152.30/22.76 | | % 152.30/22.76 | | BETA: splitting (9) gives: % 152.30/22.76 | | % 152.30/22.76 | | Case 1: % 152.30/22.76 | | | % 152.30/22.76 | | | (40) all_58_4 = e0 % 152.30/22.76 | | | % 152.30/22.76 | | | COMBINE_EQS: (32), (40) imply: % 152.30/22.76 | | | (41) e3 = e0 % 152.30/22.76 | | | % 152.30/22.76 | | | REDUCE: (3), (41) imply: % 152.30/22.76 | | | (42) $false % 152.30/22.76 | | | % 152.30/22.76 | | | CLOSE: (42) is inconsistent. % 152.30/22.76 | | | % 152.30/22.76 | | Case 2: % 152.30/22.76 | | | % 152.30/22.76 | | | (43) all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0 % 152.30/22.76 | | | % 152.30/22.76 | | | BETA: splitting (43) gives: % 152.30/22.76 | | | % 152.30/22.76 | | | Case 1: % 152.30/22.76 | | | | % 152.30/22.76 | | | | (44) all_58_5 = e0 % 152.30/22.76 | | | | % 152.30/22.76 | | | | COMBINE_EQS: (7), (44) imply: % 152.30/22.76 | | | | (45) all_52_9 = e0 % 152.30/22.76 | | | | % 152.30/22.76 | | | | REDUCE: (2), (45) imply: % 152.30/22.76 | | | | (46) ~ (all_52_1 = e0) % 152.30/22.76 | | | | % 152.30/22.76 | | | | BETA: splitting (28) gives: % 152.30/22.76 | | | | % 152.30/22.76 | | | | Case 1: % 152.30/22.76 | | | | | % 152.30/22.76 | | | | | (47) all_58_2 = e3 % 152.30/22.76 | | | | | % 152.30/22.76 | | | | | COMBINE_EQS: (26), (47) imply: % 152.30/22.76 | | | | | (48) all_52_1 = e3 % 152.30/22.76 | | | | | % 152.30/22.76 | | | | | REDUCE: (19), (48) imply: % 152.30/22.76 | | | | | (49) ~ (all_52_3 = e3) % 152.30/22.76 | | | | | % 152.30/22.76 | | | | | SIMP: (49) implies: % 152.30/22.77 | | | | | (50) ~ (all_52_3 = e3) % 152.30/22.77 | | | | | % 152.30/22.77 | | | | | REDUCE: (29), (48) imply: % 152.30/22.77 | | | | | (51) ~ (e3 = e2) % 152.30/22.77 | | | | | % 152.30/22.77 | | | | | REDUCE: (37), (48) imply: % 152.30/22.77 | | | | | (52) ~ (e3 = e1) % 152.30/22.77 | | | | | % 152.30/22.77 | | | | | REDUCE: (6), (48) imply: % 152.30/22.77 | | | | | (53) op(e3, e3) = all_56_8 % 152.30/22.77 | | | | | % 152.30/22.77 | | | | | BETA: splitting (34) gives: % 152.30/22.77 | | | | | % 152.30/22.77 | | | | | Case 1: % 152.30/22.77 | | | | | | % 152.30/22.77 | | | | | | (54) all_58_12 = e3 % 152.30/22.77 | | | | | | % 152.30/22.77 | | | | | | COMBINE_EQS: (33), (54) imply: % 152.30/22.77 | | | | | | (55) all_52_3 = e3 % 152.30/22.77 | | | | | | % 152.30/22.77 | | | | | | REDUCE: (50), (55) imply: % 152.30/22.77 | | | | | | (56) $false % 152.30/22.77 | | | | | | % 152.30/22.77 | | | | | | CLOSE: (56) is inconsistent. % 152.30/22.77 | | | | | | % 152.30/22.77 | | | | | Case 2: % 152.30/22.77 | | | | | | % 152.30/22.77 | | | | | | (57) all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3 % 152.30/22.77 | | | | | | % 152.30/22.77 | | | | | | BETA: splitting (57) gives: % 152.30/22.77 | | | | | | % 152.30/22.77 | | | | | | Case 1: % 152.30/22.77 | | | | | | | % 152.30/22.77 | | | | | | | (58) all_58_13 = e3 % 152.30/22.77 | | | | | | | % 152.30/22.77 | | | | | | | REF_CLOSE: (31), (52), (58) are inconsistent by sub-proof #561. % 152.30/22.77 | | | | | | | % 152.30/22.77 | | | | | | Case 2: % 152.30/22.77 | | | | | | | % 152.30/22.77 | | | | | | | (59) all_58_14 = e3 | all_58_15 = e3 % 152.30/22.77 | | | | | | | % 152.30/22.77 | | | | | | | BETA: splitting (59) gives: % 152.30/22.77 | | | | | | | % 152.30/22.77 | | | | | | | Case 1: % 152.30/22.77 | | | | | | | | % 152.30/22.77 | | | | | | | | (60) all_58_14 = e3 % 152.30/22.77 | | | | | | | | % 152.30/22.77 | | | | | | | | COMBINE_EQS: (24), (60) imply: % 152.30/22.77 | | | | | | | | (61) e3 = e2 % 152.30/22.77 | | | | | | | | % 152.30/22.77 | | | | | | | | SIMP: (61) implies: % 152.30/22.77 | | | | | | | | (62) e3 = e2 % 152.30/22.77 | | | | | | | | % 152.30/22.77 | | | | | | | | REDUCE: (51), (62) imply: % 152.30/22.77 | | | | | | | | (63) $false % 152.30/22.77 | | | | | | | | % 152.30/22.77 | | | | | | | | CLOSE: (63) is inconsistent. % 152.30/22.77 | | | | | | | | % 152.30/22.77 | | | | | | | Case 2: % 152.30/22.77 | | | | | | | | % 152.30/22.77 | | | | | | | | (64) all_58_15 = e3 % 152.30/22.77 | | | | | | | | % 152.30/22.77 | | | | | | | | COMBINE_EQS: (25), (64) imply: % 152.30/22.77 | | | | | | | | (65) all_4_2 = e3 % 152.30/22.77 | | | | | | | | % 152.30/22.77 | | | | | | | | REDUCE: (18), (65) imply: % 152.30/22.77 | | | | | | | | (66) op(e3, e3) = all_4_1 % 152.30/22.77 | | | | | | | | % 152.30/22.77 | | | | | | | | GROUND_INST: instantiating (10) with e2, all_56_14, e1, e0, % 152.30/22.77 | | | | | | | | simplifying with (8), (39) gives: % 152.30/22.77 | | | | | | | | (67) all_56_14 = e2 % 152.30/22.77 | | | | | | | | % 152.30/22.77 | | | | | | | | GROUND_INST: instantiating (10) with e1, all_56_8, e3, e3, % 152.30/22.77 | | | | | | | | simplifying with (20), (53) gives: % 152.30/22.77 | | | | | | | | (68) all_56_8 = e1 % 152.30/22.77 | | | | | | | | % 152.30/22.77 | | | | | | | | GROUND_INST: instantiating (10) with all_4_1, all_56_8, e3, e3, % 152.30/22.77 | | | | | | | | simplifying with (53), (66) gives: % 152.30/22.77 | | | | | | | | (69) all_56_8 = all_4_1 % 152.30/22.77 | | | | | | | | % 152.30/22.77 | | | | | | | | COMBINE_EQS: (68), (69) imply: % 152.30/22.77 | | | | | | | | (70) all_4_1 = e1 % 152.30/22.77 | | | | | | | | % 152.30/22.77 | | | | | | | | REDUCE: (12), (70) imply: % 152.30/22.77 | | | | | | | | (71) op(e0, e1) = all_4_0 % 152.30/22.77 | | | | | | | | % 152.30/22.77 | | | | | | | | GROUND_INST: instantiating (10) with e2, all_4_0, e1, e0, % 152.30/22.77 | | | | | | | | simplifying with (8), (71) gives: % 152.30/22.77 | | | | | | | | (72) all_4_0 = e2 % 152.30/22.77 | | | | | | | | % 152.30/22.77 | | | | | | | | REDUCE: (30), (72) imply: % 152.30/22.77 | | | | | | | | (73) $false % 152.30/22.77 | | | | | | | | % 152.30/22.77 | | | | | | | | CLOSE: (73) is inconsistent. % 152.30/22.77 | | | | | | | | % 152.30/22.77 | | | | | | | End of split % 152.30/22.77 | | | | | | | % 152.30/22.77 | | | | | | End of split % 152.30/22.77 | | | | | | % 152.30/22.77 | | | | | End of split % 152.30/22.77 | | | | | % 152.30/22.77 | | | | Case 2: % 152.30/22.77 | | | | | % 152.30/22.77 | | | | | (74) ~ (all_58_2 = e3) % 152.30/22.77 | | | | | % 152.30/22.77 | | | | | REDUCE: (26), (74) imply: % 152.30/22.77 | | | | | (75) ~ (all_52_1 = e3) % 152.30/22.77 | | | | | % 152.30/22.77 | | | | | REF_CLOSE: (5), (14), (29), (37), (46), (75) are inconsistent by % 152.30/22.77 | | | | | sub-proof #559. % 152.30/22.77 | | | | | % 152.30/22.77 | | | | End of split % 152.30/22.77 | | | | % 152.30/22.77 | | | Case 2: % 152.30/22.77 | | | | % 152.30/22.77 | | | | (76) ~ (all_58_5 = e0) % 152.30/22.77 | | | | % 152.30/22.77 | | | | REDUCE: (7), (76) imply: % 152.30/22.77 | | | | (77) ~ (all_52_9 = e0) % 152.30/22.77 | | | | % 152.30/22.77 | | | | REF_CLOSE: (4), (16), (23), (38), (77) are inconsistent by sub-proof % 152.30/22.77 | | | | #608. % 152.30/22.77 | | | | % 152.30/22.77 | | | End of split % 152.30/22.77 | | | % 152.30/22.77 | | End of split % 152.30/22.77 | | % 152.30/22.77 | Case 2: % 152.30/22.77 | | % 152.30/22.77 | | (78) all_58_11 = e1 | all_58_15 = e1 % 152.30/22.77 | | % 152.30/22.77 | | REF_CLOSE: (11), (15), (21), (25), (78) are inconsistent by sub-proof #672. % 152.30/22.77 | | % 152.30/22.77 | End of split % 152.30/22.77 | % 152.30/22.77 End of proof % 152.30/22.77 % 152.30/22.77 Sub-proof #559 shows that the following formulas are inconsistent: % 152.30/22.77 ---------------------------------------------------------------- % 152.30/22.77 (1) all_54_4 = all_52_1 % 152.30/22.77 (2) ~ (all_52_1 = e3) % 152.30/22.77 (3) ~ (all_52_1 = e1) % 152.30/22.77 (4) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0 % 152.30/22.77 (5) ~ (all_52_1 = e0) % 152.30/22.77 (6) ~ (all_52_1 = e2) % 152.30/22.77 % 152.30/22.77 Begin of proof % 152.30/22.77 | % 152.30/22.77 | BETA: splitting (4) gives: % 152.30/22.77 | % 152.30/22.77 | Case 1: % 152.30/22.77 | | % 152.30/22.77 | | (7) all_54_4 = e3 % 152.30/22.77 | | % 152.30/22.77 | | REF_CLOSE: (1), (2), (7) are inconsistent by sub-proof #634. % 152.30/22.77 | | % 152.30/22.77 | Case 2: % 152.30/22.77 | | % 152.30/22.77 | | (8) all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0 % 152.30/22.77 | | % 152.30/22.77 | | REF_CLOSE: (1), (3), (5), (6), (8) are inconsistent by sub-proof #560. % 152.30/22.77 | | % 152.30/22.77 | End of split % 152.30/22.77 | % 152.30/22.77 End of proof % 152.30/22.77 % 152.30/22.77 Sub-proof #560 shows that the following formulas are inconsistent: % 152.30/22.77 ---------------------------------------------------------------- % 152.30/22.77 (1) all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0 % 152.30/22.77 (2) all_54_4 = all_52_1 % 152.30/22.77 (3) ~ (all_52_1 = e1) % 152.30/22.77 (4) ~ (all_52_1 = e0) % 152.30/22.77 (5) ~ (all_52_1 = e2) % 152.30/22.77 % 152.30/22.77 Begin of proof % 152.30/22.77 | % 152.30/22.77 | BETA: splitting (1) gives: % 152.30/22.77 | % 152.30/22.77 | Case 1: % 152.30/22.77 | | % 152.30/22.77 | | (6) all_54_4 = e2 % 152.30/22.77 | | % 152.30/22.77 | | REF_CLOSE: (2), (5), (6) are inconsistent by sub-proof #633. % 152.30/22.77 | | % 152.30/22.77 | Case 2: % 152.30/22.77 | | % 152.30/22.77 | | (7) all_54_4 = e1 | all_54_4 = e0 % 152.30/22.77 | | % 152.30/22.77 | | REF_CLOSE: (2), (3), (4), (7) are inconsistent by sub-proof #583. % 152.30/22.77 | | % 152.30/22.77 | End of split % 152.30/22.77 | % 152.30/22.77 End of proof % 152.30/22.77 % 152.30/22.77 Sub-proof #561 shows that the following formulas are inconsistent: % 152.30/22.77 ---------------------------------------------------------------- % 152.30/22.77 (1) all_58_13 = e3 % 152.30/22.77 (2) all_58_13 = e1 % 152.30/22.77 (3) ~ (e3 = e1) % 152.30/22.77 % 152.30/22.77 Begin of proof % 152.30/22.77 | % 152.30/22.77 | COMBINE_EQS: (1), (2) imply: % 152.30/22.77 | (4) e3 = e1 % 152.30/22.77 | % 152.30/22.77 | SIMP: (4) implies: % 152.30/22.77 | (5) e3 = e1 % 152.30/22.77 | % 152.30/22.77 | REDUCE: (3), (5) imply: % 152.30/22.77 | (6) $false % 152.30/22.77 | % 152.30/22.77 | CLOSE: (6) is inconsistent. % 152.30/22.77 | % 152.30/22.77 End of proof % 152.30/22.77 % 152.30/22.77 Sub-proof #562 shows that the following formulas are inconsistent: % 152.30/22.77 ---------------------------------------------------------------- % 152.30/22.77 (1) ~ (all_52_8 = e2) % 152.30/22.77 (2) all_58_4 = all_52_8 % 152.30/22.77 (3) all_58_4 = e2 | all_58_9 = e2 % 152.30/22.77 (4) ~ (e2 = e1) % 152.30/22.77 (5) all_58_9 = e1 % 152.30/22.77 % 152.30/22.77 Begin of proof % 152.30/22.77 | % 152.30/22.77 | BETA: splitting (3) gives: % 152.30/22.77 | % 152.30/22.77 | Case 1: % 152.30/22.77 | | % 152.30/22.77 | | (6) all_58_4 = e2 % 152.30/22.77 | | % 152.30/22.77 | | COMBINE_EQS: (2), (6) imply: % 152.30/22.77 | | (7) all_52_8 = e2 % 152.30/22.77 | | % 152.30/22.77 | | REDUCE: (1), (7) imply: % 152.30/22.77 | | (8) $false % 152.30/22.77 | | % 152.30/22.77 | | CLOSE: (8) is inconsistent. % 152.30/22.77 | | % 152.30/22.77 | Case 2: % 152.30/22.77 | | % 152.30/22.77 | | (9) all_58_9 = e2 % 152.30/22.77 | | % 152.30/22.77 | | REF_CLOSE: (4), (5), (9) are inconsistent by sub-proof #563. % 152.30/22.77 | | % 152.30/22.77 | End of split % 152.30/22.77 | % 152.30/22.77 End of proof % 152.30/22.77 % 152.30/22.77 Sub-proof #563 shows that the following formulas are inconsistent: % 152.30/22.77 ---------------------------------------------------------------- % 152.30/22.77 (1) all_58_9 = e2 % 152.30/22.77 (2) all_58_9 = e1 % 152.30/22.77 (3) ~ (e2 = e1) % 152.30/22.77 % 152.30/22.77 Begin of proof % 152.30/22.77 | % 152.30/22.77 | COMBINE_EQS: (1), (2) imply: % 152.30/22.77 | (4) e2 = e1 % 152.30/22.77 | % 152.30/22.77 | SIMP: (4) implies: % 152.30/22.77 | (5) e2 = e1 % 152.30/22.77 | % 152.30/22.77 | REDUCE: (3), (5) imply: % 152.30/22.77 | (6) $false % 152.30/22.77 | % 152.30/22.77 | CLOSE: (6) is inconsistent. % 152.30/22.77 | % 152.30/22.77 End of proof % 152.30/22.77 % 152.30/22.77 Sub-proof #564 shows that the following formulas are inconsistent: % 152.30/22.77 ---------------------------------------------------------------- % 152.30/22.77 (1) all_56_11 = all_8_2 % 152.30/22.77 (2) op(e0, all_52_13) = all_56_14 % 152.30/22.77 (3) ~ (all_56_11 = e1) | all_56_13 = e2 % 152.30/22.77 (4) ~ (all_52_11 = all_6_2) % 152.30/22.77 (5) ~ (all_52_4 = all_52_8) % 152.30/22.77 (6) ~ (all_52_8 = all_52_9) % 152.30/22.77 (7) all_54_9 = all_52_6 % 152.30/22.77 (8) op(e2, all_8_1) = all_8_0 % 152.30/22.77 (9) op(e2, e0) = all_56_26 % 152.30/22.77 (10) ~ (all_8_1 = e1) % 152.30/22.77 (11) ~ (all_52_1 = all_52_9) % 152.30/22.77 (12) ~ (e3 = e0) % 152.30/22.77 (13) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0 % 152.30/22.77 (14) all_54_10 = all_6_2 % 152.30/22.77 (15) ~ (all_6_1 = e2) % 152.30/22.77 (16) ~ (all_52_13 = all_8_2) % 152.30/22.77 (17) ~ (all_56_21 = e2) | all_56_19 = e1 % 152.30/22.77 (18) all_54_0 = all_10_2 % 152.30/22.77 (19) all_54_4 = all_52_1 % 152.30/22.77 (20) ~ (all_52_14 = all_4_2) % 152.30/22.77 (21) ~ (all_8_0 = e1) % 152.30/22.77 (22) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0 % 152.30/22.77 (23) all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2 % 152.30/22.77 (24) all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2 % 152.30/22.77 (25) ~ (all_52_9 = all_8_2) % 152.30/22.77 (26) ~ (all_52_12 = all_52_13) % 152.30/22.77 (27) ~ (all_52_12 = e2) % 152.30/22.77 (28) ~ (all_8_1 = e3) % 152.30/22.77 (29) op(e0, e0) = all_4_2 % 152.30/22.77 (30) all_58_4 = all_52_8 % 152.30/22.77 (31) all_54_5 = all_8_2 % 152.30/22.77 (32) ~ (all_6_1 = e3) % 152.30/22.77 (33) ~ (all_52_6 = all_52_14) % 152.30/22.77 (34) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 152.30/22.77 (35) ~ (all_6_0 = e2) % 152.30/22.77 (36) ~ (all_52_11 = e0) % 152.30/22.77 (37) all_54_15 = all_4_2 % 152.30/22.77 (38) all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1 % 152.30/22.77 (39) ~ (all_10_1 = e1) % 152.30/22.77 (40) all_56_21 = all_6_2 % 152.30/22.77 (41) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 152.30/22.77 (42) all_56_1 = all_10_2 % 152.30/22.77 (43) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0 % 152.30/22.77 (44) all_58_5 = all_52_9 % 152.30/22.77 (45) all_54_1 = all_52_4 % 152.30/22.77 (46) all_56_17 = all_52_2 % 152.30/22.77 (47) ~ (all_52_13 = e2) % 152.30/22.77 (48) all_58_9 = all_52_12 % 152.30/22.77 (49) op(e0, all_52_12) = all_56_6 % 152.30/22.77 (50) op(e0, all_52_14) = all_56_22 % 152.30/22.77 (51) op(e1, e0) = all_52_14 % 152.30/22.77 (52) ~ (all_56_1 = e1) | all_56_5 = e3 % 152.30/22.77 (53) all_54_14 = all_52_11 % 152.30/22.77 (54) all_58_1 = all_52_4 % 152.30/22.77 (55) all_58_4 = e0 | all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0 % 152.30/22.77 (56) op(e3, e3) = all_10_2 % 152.30/22.77 (57) ~ (all_52_8 = all_6_2) % 152.30/22.77 (58) all_58_15 = e2 % 152.30/22.77 (59) all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1 % 152.30/22.77 (60) ~ (all_56_21 = e3) | all_56_17 = e1 % 152.30/22.77 (61) all_58_13 = e0 % 152.30/22.77 (62) all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1 % 152.30/22.77 (63) ~ (all_52_1 = all_8_2) % 152.30/22.77 (64) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 152.30/22.77 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 152.30/22.77 (65) ~ (all_52_3 = all_10_2) % 152.30/22.77 (66) all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0 % 152.30/22.77 (67) all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) & % 152.30/22.77 (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0)) % 152.30/22.77 (68) ~ (all_52_2 = all_52_6) % 152.30/22.77 (69) op(e0, all_4_1) = all_4_0 % 152.30/22.77 (70) all_56_7 = all_52_12 % 152.30/22.77 (71) ~ (all_10_1 = e2) % 152.30/22.77 (72) ~ (all_52_11 = e2) % 152.30/22.77 (73) all_56_13 = all_52_9 % 152.30/22.77 (74) op(e0, e1) = all_52_11 % 152.30/22.77 (75) ~ (all_52_1 = all_52_13) % 152.30/22.77 (76) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0 % 152.30/22.77 (77) ~ (all_4_2 = e1) % 152.30/22.77 (78) all_58_8 = all_6_2 % 152.30/22.77 (79) ~ (all_52_8 = all_10_2) % 152.30/22.77 (80) ~ (all_56_1 = e2) | all_56_3 = e3 % 152.30/22.77 (81) ~ (all_56_1 = e0) | all_56_7 = e3 % 152.30/22.77 (82) all_56_5 = all_52_8 % 152.30/22.77 (83) op(e1, all_6_1) = all_6_0 % 152.30/22.77 (84) op(e0, e0) = e2 % 152.30/22.77 (85) all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3 % 152.30/22.77 (86) all_58_3 = all_8_2 % 152.30/22.77 (87) all_56_3 = all_52_4 % 152.30/22.77 (88) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0 % 152.30/22.77 (89) ~ (all_52_1 = all_52_3) % 152.30/22.77 (90) all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1 % 152.30/22.77 (91) all_56_31 = all_4_2 % 152.30/22.77 (92) all_58_11 = all_52_14 % 152.30/22.77 (93) ~ (all_52_2 = all_52_14) % 152.30/22.77 (94) op(e2, e2) = all_4_1 % 152.30/22.77 (95) ~ (all_52_9 = all_52_11) % 152.30/22.77 (96) all_54_7 = all_52_13 % 152.30/22.77 (97) op(all_6_2, all_6_2) = all_6_1 % 152.30/22.77 (98) all_56_1 = e3 | all_56_11 = e2 | all_56_21 = e1 | all_56_31 = e0 % 152.30/22.77 (99) ~ (all_52_13 = all_4_2) % 152.30/22.77 (100) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0 % 152.30/22.77 (101) ~ (all_52_13 = all_52_14) % 152.30/22.77 (102) op(e1, e1) = all_6_2 % 152.30/22.77 (103) ~ (all_52_6 = all_8_2) % 152.30/22.77 (104) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0 % 152.30/22.77 (105) all_58_15 = all_4_2 % 152.30/22.77 (106) all_58_2 = all_52_1 % 152.30/22.77 (107) ~ (all_52_9 = all_6_2) % 152.30/22.77 (108) all_58_10 = all_52_13 % 152.30/22.77 (109) ~ (all_52_12 = all_4_2) % 152.30/22.77 (110) op(all_10_2, all_10_2) = all_10_1 % 152.30/22.77 (111) all_58_0 = all_10_2 % 152.30/22.77 (112) all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1 % 152.30/22.77 (113) ~ (all_52_12 = all_52_14) % 152.30/22.77 (114) op(e1, all_52_9) = all_56_12 % 152.30/22.77 (115) op(e2, e2) = all_8_2 % 152.30/22.77 (116) ~ (all_52_4 = all_52_12) % 152.30/22.77 (117) op(e2, e0) = all_52_13 % 152.30/22.77 (118) ~ (all_52_2 = all_6_2) % 152.30/22.77 (119) ~ (all_52_8 = all_52_12) % 152.30/22.77 (120) ~ (all_56_21 = e0) | all_56_23 = e1 % 152.30/22.77 (121) ~ (all_52_6 = all_6_2) % 152.30/22.77 (122) ~ (all_8_2 = e0) % 152.30/22.77 (123) ~ (all_52_14 = all_6_2) % 152.30/22.77 (124) ~ (e2 = e0) % 152.30/22.77 (125) ~ (all_52_2 = all_10_2) % 152.30/22.77 (126) ~ (all_52_4 = all_10_2) % 152.30/22.77 (127) ~ (all_52_4 = all_8_2) % 152.30/22.77 (128) op(all_8_2, all_8_2) = all_8_1 % 152.30/22.77 (129) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 152.30/22.77 (130) all_58_14 = all_52_11 % 152.30/22.77 (131) all_56_19 = all_52_6 % 152.30/22.77 (132) ~ (all_52_12 = all_10_2) % 152.30/22.77 (133) ~ (all_4_0 = e3) % 152.30/22.77 (134) ~ (all_52_1 = all_10_2) % 152.30/22.77 (135) all_58_12 = all_52_3 % 152.30/22.77 (136) all_54_11 = all_52_14 % 152.30/22.77 % 152.30/22.77 Begin of proof % 152.30/22.77 | % 152.30/22.77 | GROUND_INST: instantiating (64) with all_52_13, all_56_26, e0, e2, simplifying % 152.30/22.77 | with (9), (117) gives: % 152.30/22.77 | (137) all_56_26 = all_52_13 % 152.30/22.77 | % 152.30/22.77 | GROUND_INST: instantiating (64) with all_8_2, all_4_1, e2, e2, simplifying % 152.30/22.77 | with (94), (115) gives: % 152.30/22.77 | (138) all_8_2 = all_4_1 % 152.30/22.77 | % 152.30/22.77 | COMBINE_EQS: (31), (138) imply: % 152.30/22.77 | (139) all_54_5 = all_4_1 % 152.30/22.77 | % 152.30/22.77 | COMBINE_EQS: (1), (138) imply: % 152.30/22.77 | (140) all_56_11 = all_4_1 % 152.30/22.77 | % 152.30/22.77 | COMBINE_EQS: (86), (138) imply: % 152.30/22.77 | (141) all_58_3 = all_4_1 % 152.30/22.77 | % 152.30/22.77 | REDUCE: (63), (138) imply: % 152.30/22.77 | (142) ~ (all_52_1 = all_4_1) % 152.30/22.77 | % 152.30/22.77 | REDUCE: (127), (138) imply: % 152.30/22.77 | (143) ~ (all_52_4 = all_4_1) % 152.30/22.77 | % 152.30/22.77 | REDUCE: (103), (138) imply: % 152.30/22.77 | (144) ~ (all_52_6 = all_4_1) % 152.30/22.77 | % 152.30/22.77 | REDUCE: (25), (138) imply: % 152.30/22.77 | (145) ~ (all_52_9 = all_4_1) % 152.30/22.77 | % 152.30/22.77 | REDUCE: (16), (138) imply: % 152.30/22.77 | (146) ~ (all_52_13 = all_4_1) % 152.30/22.77 | % 152.30/22.77 | REDUCE: (122), (138) imply: % 152.30/22.77 | (147) ~ (all_4_1 = e0) % 152.30/22.77 | % 152.30/22.77 | REDUCE: (128), (138) imply: % 152.30/22.77 | (148) op(all_4_1, all_4_1) = all_8_1 % 152.30/22.77 | % 152.30/22.77 | BETA: splitting (120) gives: % 152.30/22.77 | % 152.30/22.77 | Case 1: % 152.30/22.77 | | % 152.30/22.77 | | (149) ~ (all_56_21 = e0) % 152.30/22.77 | | % 152.30/22.77 | | REDUCE: (40), (149) imply: % 152.30/22.77 | | (150) ~ (all_6_2 = e0) % 152.30/22.77 | | % 152.30/22.77 | | BETA: splitting (17) gives: % 152.30/22.77 | | % 152.30/22.77 | | Case 1: % 152.30/22.77 | | | % 152.30/22.77 | | | (151) ~ (all_56_21 = e2) % 152.30/22.77 | | | % 152.30/22.77 | | | REDUCE: (40), (151) imply: % 152.30/22.77 | | | (152) ~ (all_6_2 = e2) % 152.30/22.77 | | | % 152.30/22.77 | | | BETA: splitting (3) gives: % 152.30/22.77 | | | % 152.30/22.77 | | | Case 1: % 152.30/22.77 | | | | % 152.30/22.77 | | | | (153) ~ (all_56_11 = e1) % 152.30/22.77 | | | | % 152.30/22.77 | | | | REDUCE: (140), (153) imply: % 152.30/22.77 | | | | (154) ~ (all_4_1 = e1) % 152.30/22.77 | | | | % 152.30/22.77 | | | | BETA: splitting (60) gives: % 152.30/22.77 | | | | % 152.30/22.77 | | | | Case 1: % 152.30/22.77 | | | | | % 152.30/22.77 | | | | | (155) ~ (all_56_21 = e3) % 152.30/22.77 | | | | | % 152.30/22.77 | | | | | REDUCE: (40), (155) imply: % 152.30/22.77 | | | | | (156) ~ (all_6_2 = e3) % 152.30/22.77 | | | | | % 152.30/22.77 | | | | | BETA: splitting (41) gives: % 152.30/22.77 | | | | | % 152.30/22.77 | | | | | Case 1: % 152.30/22.77 | | | | | | % 152.30/22.77 | | | | | | (157) all_54_10 = e3 % 152.30/22.77 | | | | | | % 152.30/22.77 | | | | | | COMBINE_EQS: (14), (157) imply: % 152.30/22.77 | | | | | | (158) all_6_2 = e3 % 152.30/22.77 | | | | | | % 152.30/22.77 | | | | | | REDUCE: (156), (158) imply: % 152.30/22.77 | | | | | | (159) $false % 152.30/22.77 | | | | | | % 152.30/22.77 | | | | | | CLOSE: (159) is inconsistent. % 152.30/22.77 | | | | | | % 152.30/22.77 | | | | | Case 2: % 152.30/22.77 | | | | | | % 152.30/22.77 | | | | | | (160) ~ (all_54_10 = e3) % 152.30/22.77 | | | | | | (161) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 152.30/22.77 | | | | | | % 152.30/22.77 | | | | | | BETA: splitting (161) gives: % 152.30/22.77 | | | | | | % 152.30/22.77 | | | | | | Case 1: % 152.30/22.77 | | | | | | | % 152.30/22.77 | | | | | | | (162) all_54_10 = e2 % 152.30/22.77 | | | | | | | % 152.30/22.77 | | | | | | | COMBINE_EQS: (14), (162) imply: % 152.30/22.77 | | | | | | | (163) all_6_2 = e2 % 152.30/22.77 | | | | | | | % 152.30/22.77 | | | | | | | REDUCE: (152), (163) imply: % 152.30/22.77 | | | | | | | (164) $false % 152.30/22.77 | | | | | | | % 152.30/22.77 | | | | | | | CLOSE: (164) is inconsistent. % 152.30/22.77 | | | | | | | % 152.30/22.77 | | | | | | Case 2: % 152.30/22.77 | | | | | | | % 152.30/22.77 | | | | | | | (165) ~ (all_54_10 = e2) % 152.30/22.77 | | | | | | | (166) all_54_10 = e1 | all_54_10 = e0 % 152.30/22.77 | | | | | | | % 152.30/22.77 | | | | | | | BETA: splitting (166) gives: % 152.30/22.77 | | | | | | | % 152.30/22.77 | | | | | | | Case 1: % 152.30/22.77 | | | | | | | | % 152.30/22.77 | | | | | | | | (167) all_54_10 = e1 % 152.30/22.77 | | | | | | | | % 152.30/22.77 | | | | | | | | COMBINE_EQS: (14), (167) imply: % 152.30/22.77 | | | | | | | | (168) all_6_2 = e1 % 152.30/22.77 | | | | | | | | % 152.30/22.77 | | | | | | | | REDUCE: (57), (168) imply: % 152.30/22.77 | | | | | | | | (169) ~ (all_52_8 = e1) % 152.30/22.77 | | | | | | | | % 152.30/22.77 | | | | | | | | REDUCE: (107), (168) imply: % 152.30/22.77 | | | | | | | | (170) ~ (all_52_9 = e1) % 152.30/22.77 | | | | | | | | % 152.30/22.77 | | | | | | | | REDUCE: (4), (168) imply: % 152.30/22.77 | | | | | | | | (171) ~ (all_52_11 = e1) % 152.30/22.77 | | | | | | | | % 152.30/22.77 | | | | | | | | REDUCE: (123), (168) imply: % 152.30/22.77 | | | | | | | | (172) ~ (all_52_14 = e1) % 152.30/22.77 | | | | | | | | % 152.30/22.77 | | | | | | | | REDUCE: (156), (168) imply: % 152.30/22.77 | | | | | | | | (173) ~ (e3 = e1) % 152.30/22.77 | | | | | | | | % 152.30/22.77 | | | | | | | | SIMP: (173) implies: % 152.30/22.77 | | | | | | | | (174) ~ (e3 = e1) % 152.30/22.77 | | | | | | | | % 152.30/22.77 | | | | | | | | REDUCE: (150), (168) imply: % 152.30/22.77 | | | | | | | | (175) ~ (e1 = e0) % 152.30/22.77 | | | | | | | | % 152.30/22.77 | | | | | | | | BETA: splitting (90) gives: % 152.30/22.77 | | | | | | | | % 152.30/22.77 | | | | | | | | Case 1: % 152.30/22.77 | | | | | | | | | % 152.30/22.77 | | | | | | | | | (176) all_58_1 = e1 % 152.30/22.77 | | | | | | | | | % 152.30/22.77 | | | | | | | | | COMBINE_EQS: (54), (176) imply: % 152.30/22.77 | | | | | | | | | (177) all_52_4 = e1 % 152.30/22.77 | | | | | | | | | % 152.30/22.77 | | | | | | | | | COMBINE_EQS: (87), (177) imply: % 152.30/22.77 | | | | | | | | | (178) all_56_3 = e1 % 152.30/22.77 | | | | | | | | | % 152.30/22.77 | | | | | | | | | REDUCE: (116), (177) imply: % 152.30/22.77 | | | | | | | | | (179) ~ (all_52_12 = e1) % 152.30/22.77 | | | | | | | | | % 152.30/22.77 | | | | | | | | | SIMP: (179) implies: % 152.30/22.77 | | | | | | | | | (180) ~ (all_52_12 = e1) % 152.30/22.77 | | | | | | | | | % 152.30/22.77 | | | | | | | | | REDUCE: (126), (177) imply: % 152.30/22.77 | | | | | | | | | (181) ~ (all_10_2 = e1) % 152.30/22.77 | | | | | | | | | % 152.30/22.77 | | | | | | | | | SIMP: (181) implies: % 152.30/22.77 | | | | | | | | | (182) ~ (all_10_2 = e1) % 152.30/22.77 | | | | | | | | | % 152.30/22.77 | | | | | | | | | BETA: splitting (80) gives: % 152.30/22.77 | | | | | | | | | % 152.30/22.77 | | | | | | | | | Case 1: % 152.30/22.77 | | | | | | | | | | % 152.30/22.77 | | | | | | | | | | (183) ~ (all_56_1 = e2) % 152.30/22.77 | | | | | | | | | | % 152.30/22.77 | | | | | | | | | | REDUCE: (42), (183) imply: % 152.30/22.77 | | | | | | | | | | (184) ~ (all_10_2 = e2) % 152.30/22.77 | | | | | | | | | | % 152.30/22.77 | | | | | | | | | | BETA: splitting (13) gives: % 152.30/22.77 | | | | | | | | | | % 152.30/22.77 | | | | | | | | | | Case 1: % 152.30/22.77 | | | | | | | | | | | % 152.30/22.77 | | | | | | | | | | | (185) all_54_14 = e3 % 152.30/22.77 | | | | | | | | | | | % 152.30/22.77 | | | | | | | | | | | COMBINE_EQS: (53), (185) imply: % 152.30/22.77 | | | | | | | | | | | (186) all_52_11 = e3 % 152.30/22.77 | | | | | | | | | | | % 152.30/22.77 | | | | | | | | | | | SIMP: (186) implies: % 152.30/22.77 | | | | | | | | | | | (187) all_52_11 = e3 % 152.30/22.77 | | | | | | | | | | | % 152.30/22.77 | | | | | | | | | | | REDUCE: (95), (187) imply: % 152.30/22.77 | | | | | | | | | | | (188) ~ (all_52_9 = e3) % 152.30/22.77 | | | | | | | | | | | % 152.30/22.77 | | | | | | | | | | | REDUCE: (74), (187) imply: % 152.30/22.77 | | | | | | | | | | | (189) op(e0, e1) = e3 % 152.30/22.77 | | | | | | | | | | | % 152.30/22.77 | | | | | | | | | | | BETA: splitting (38) gives: % 152.30/22.77 | | | | | | | | | | | % 152.30/22.77 | | | | | | | | | | | Case 1: % 152.30/22.77 | | | | | | | | | | | | % 152.30/22.77 | | | | | | | | | | | | (190) all_58_9 = e1 % 152.30/22.77 | | | | | | | | | | | | % 152.30/22.77 | | | | | | | | | | | | COMBINE_EQS: (48), (190) imply: % 152.30/22.77 | | | | | | | | | | | | (191) all_52_12 = e1 % 152.30/22.77 | | | | | | | | | | | | % 152.30/22.77 | | | | | | | | | | | | REDUCE: (180), (191) imply: % 152.30/22.77 | | | | | | | | | | | | (192) $false % 152.30/22.77 | | | | | | | | | | | | % 152.30/22.77 | | | | | | | | | | | | CLOSE: (192) is inconsistent. % 152.30/22.77 | | | | | | | | | | | | % 152.30/22.77 | | | | | | | | | | | Case 2: % 152.30/22.77 | | | | | | | | | | | | % 152.30/22.77 | | | | | | | | | | | | (193) all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1 % 152.30/22.77 | | | | | | | | | | | | % 152.30/22.77 | | | | | | | | | | | | BETA: splitting (24) gives: % 152.30/22.77 | | | | | | | | | | | | % 152.30/22.77 | | | | | | | | | | | | Case 1: % 152.30/22.77 | | | | | | | | | | | | | % 152.30/22.77 | | | | | | | | | | | | | (194) all_58_0 = e2 % 152.30/22.77 | | | | | | | | | | | | | % 152.30/22.77 | | | | | | | | | | | | | COMBINE_EQS: (111), (194) imply: % 152.30/22.77 | | | | | | | | | | | | | (195) all_10_2 = e2 % 152.30/22.77 | | | | | | | | | | | | | % 152.30/22.77 | | | | | | | | | | | | | REDUCE: (184), (195) imply: % 152.30/22.77 | | | | | | | | | | | | | (196) $false % 152.30/22.77 | | | | | | | | | | | | | % 152.30/22.77 | | | | | | | | | | | | | CLOSE: (196) is inconsistent. % 152.30/22.77 | | | | | | | | | | | | | % 152.30/22.77 | | | | | | | | | | | | Case 2: % 152.30/22.77 | | | | | | | | | | | | | % 152.30/22.77 | | | | | | | | | | | | | (197) all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2 % 152.30/22.77 | | | | | | | | | | | | | % 152.30/22.77 | | | | | | | | | | | | | BETA: splitting (193) gives: % 152.30/22.77 | | | | | | | | | | | | | % 152.30/22.77 | | | | | | | | | | | | | Case 1: % 152.30/22.77 | | | | | | | | | | | | | | % 152.30/22.77 | | | | | | | | | | | | | | (198) all_58_10 = e1 % 152.30/22.77 | | | | | | | | | | | | | | % 152.30/22.77 | | | | | | | | | | | | | | COMBINE_EQS: (108), (198) imply: % 152.30/22.77 | | | | | | | | | | | | | | (199) all_52_13 = e1 % 152.30/22.77 | | | | | | | | | | | | | | % 152.30/22.77 | | | | | | | | | | | | | | REDUCE: (75), (199) imply: % 152.30/22.77 | | | | | | | | | | | | | | (200) ~ (all_52_1 = e1) % 152.30/22.77 | | | | | | | | | | | | | | % 152.30/22.77 | | | | | | | | | | | | | | REDUCE: (101), (199) imply: % 152.30/22.77 | | | | | | | | | | | | | | (201) ~ (all_52_14 = e1) % 152.30/22.77 | | | | | | | | | | | | | | % 152.30/22.77 | | | | | | | | | | | | | | REDUCE: (47), (199) imply: % 152.30/22.77 | | | | | | | | | | | | | | (202) ~ (e2 = e1) % 152.30/22.77 | | | | | | | | | | | | | | % 152.30/22.77 | | | | | | | | | | | | | | SIMP: (202) implies: % 152.30/22.77 | | | | | | | | | | | | | | (203) ~ (e2 = e1) % 152.30/22.77 | | | | | | | | | | | | | | % 152.30/22.77 | | | | | | | | | | | | | | REDUCE: (2), (199) imply: % 152.30/22.77 | | | | | | | | | | | | | | (204) op(e0, e1) = all_56_14 % 152.30/22.77 | | | | | | | | | | | | | | % 152.30/22.77 | | | | | | | | | | | | | | BETA: splitting (197) gives: % 152.30/22.77 | | | | | | | | | | | | | | % 152.30/22.77 | | | | | | | | | | | | | | Case 1: % 152.30/22.77 | | | | | | | | | | | | | | | % 152.30/22.77 | | | | | | | | | | | | | | | (205) all_58_1 = e2 % 152.30/22.77 | | | | | | | | | | | | | | | % 152.30/22.77 | | | | | | | | | | | | | | | REF_CLOSE: (176), (203), (205) are inconsistent by sub-proof % 152.30/22.77 | | | | | | | | | | | | | | | #594. % 152.30/22.77 | | | | | | | | | | | | | | | % 152.30/22.77 | | | | | | | | | | | | | | Case 2: % 152.30/22.77 | | | | | | | | | | | | | | | % 152.30/22.77 | | | | | | | | | | | | | | | (206) all_58_4 = e2 | all_58_9 = e2 % 152.30/22.77 | | | | | | | | | | | | | | | % 152.30/22.77 | | | | | | | | | | | | | | | BETA: splitting (206) gives: % 152.30/22.77 | | | | | | | | | | | | | | | % 152.30/22.77 | | | | | | | | | | | | | | | Case 1: % 152.30/22.77 | | | | | | | | | | | | | | | | % 152.30/22.77 | | | | | | | | | | | | | | | | (207) all_58_4 = e2 % 152.30/22.77 | | | | | | | | | | | | | | | | % 152.30/22.77 | | | | | | | | | | | | | | | | COMBINE_EQS: (30), (207) imply: % 152.30/22.77 | | | | | | | | | | | | | | | | (208) all_52_8 = e2 % 152.30/22.77 | | | | | | | | | | | | | | | | % 152.30/22.77 | | | | | | | | | | | | | | | | REDUCE: (6), (208) imply: % 152.30/22.77 | | | | | | | | | | | | | | | | (209) ~ (all_52_9 = e2) % 152.30/22.77 | | | | | | | | | | | | | | | | % 152.30/22.77 | | | | | | | | | | | | | | | | SIMP: (209) implies: % 152.30/22.77 | | | | | | | | | | | | | | | | (210) ~ (all_52_9 = e2) % 152.30/22.77 | | | | | | | | | | | | | | | | % 152.30/22.77 | | | | | | | | | | | | | | | | REDUCE: (79), (208) imply: % 152.30/22.77 | | | | | | | | | | | | | | | | (211) ~ (all_10_2 = e2) % 152.30/22.77 | | | | | | | | | | | | | | | | % 152.30/22.77 | | | | | | | | | | | | | | | | BETA: splitting (55) gives: % 152.30/22.77 | | | | | | | | | | | | | | | | % 152.30/22.77 | | | | | | | | | | | | | | | | Case 1: % 152.30/22.77 | | | | | | | | | | | | | | | | | % 152.30/22.77 | | | | | | | | | | | | | | | | | (212) all_58_4 = e0 % 152.30/22.77 | | | | | | | | | | | | | | | | | % 152.30/22.77 | | | | | | | | | | | | | | | | | COMBINE_EQS: (207), (212) imply: % 152.30/22.77 | | | | | | | | | | | | | | | | | (213) e2 = e0 % 152.30/22.77 | | | | | | | | | | | | | | | | | % 152.30/22.77 | | | | | | | | | | | | | | | | | REDUCE: (124), (213) imply: % 152.30/22.77 | | | | | | | | | | | | | | | | | (214) $false % 152.30/22.77 | | | | | | | | | | | | | | | | | % 152.30/22.77 | | | | | | | | | | | | | | | | | CLOSE: (214) is inconsistent. % 152.30/22.77 | | | | | | | | | | | | | | | | | % 152.30/22.77 | | | | | | | | | | | | | | | | Case 2: % 152.30/22.77 | | | | | | | | | | | | | | | | | % 152.30/22.77 | | | | | | | | | | | | | | | | | (215) all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0 % 152.30/22.77 | | | | | | | | | | | | | | | | | % 152.30/22.77 | | | | | | | | | | | | | | | | | BETA: splitting (215) gives: % 152.30/22.77 | | | | | | | | | | | | | | | | | % 152.30/22.77 | | | | | | | | | | | | | | | | | Case 1: % 152.30/22.77 | | | | | | | | | | | | | | | | | | % 152.30/22.77 | | | | | | | | | | | | | | | | | | (216) all_58_5 = e0 % 152.30/22.77 | | | | | | | | | | | | | | | | | | % 152.30/22.77 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (44), (216) imply: % 152.30/22.77 | | | | | | | | | | | | | | | | | | (217) all_52_9 = e0 % 152.30/22.77 | | | | | | | | | | | | | | | | | | % 152.30/22.77 | | | | | | | | | | | | | | | | | | REDUCE: (11), (217) imply: % 152.30/22.77 | | | | | | | | | | | | | | | | | | (218) ~ (all_52_1 = e0) % 152.30/22.77 | | | | | | | | | | | | | | | | | | % 152.30/22.77 | | | | | | | | | | | | | | | | | | REDUCE: (145), (217) imply: % 152.30/22.77 | | | | | | | | | | | | | | | | | | (219) ~ (all_4_1 = e0) % 152.30/22.77 | | | | | | | | | | | | | | | | | | % 152.30/22.77 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (64) with e3, all_56_14, e1, e0, % 152.30/22.77 | | | | | | | | | | | | | | | | | | simplifying with (189), (204) gives: % 152.30/22.77 | | | | | | | | | | | | | | | | | | (220) all_56_14 = e3 % 152.30/22.77 | | | | | | | | | | | | | | | | | | % 152.30/22.77 | | | | | | | | | | | | | | | | | | BETA: splitting (81) gives: % 152.30/22.77 | | | | | | | | | | | | | | | | | | % 152.30/22.77 | | | | | | | | | | | | | | | | | | Case 1: % 152.30/22.77 | | | | | | | | | | | | | | | | | | | % 152.30/22.77 | | | | | | | | | | | | | | | | | | | (221) ~ (all_56_1 = e0) % 152.30/22.77 | | | | | | | | | | | | | | | | | | | % 152.30/22.77 | | | | | | | | | | | | | | | | | | | REDUCE: (42), (221) imply: % 152.30/22.77 | | | | | | | | | | | | | | | | | | | (222) ~ (all_10_2 = e0) % 152.30/22.77 | | | | | | | | | | | | | | | | | | | % 152.30/22.77 | | | | | | | | | | | | | | | | | | | BETA: splitting (34) gives: % 152.30/22.77 | | | | | | | | | | | | | | | | | | | % 152.30/22.77 | | | | | | | | | | | | | | | | | | | Case 1: % 152.30/22.77 | | | | | | | | | | | | | | | | | | | | % 152.30/22.77 | | | | | | | | | | | | | | | | | | | | (223) all_54_0 = e3 % 152.30/22.77 | | | | | | | | | | | | | | | | | | | | % 152.30/22.77 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (18), (223) imply: % 152.30/22.77 | | | | | | | | | | | | | | | | | | | | (224) all_10_2 = e3 % 152.30/22.77 | | | | | | | | | | | | | | | | | | | | % 152.30/22.77 | | | | | | | | | | | | | | | | | | | | SIMP: (224) implies: % 152.30/22.77 | | | | | | | | | | | | | | | | | | | | (225) all_10_2 = e3 % 152.30/22.77 | | | | | | | | | | | | | | | | | | | | % 152.30/22.77 | | | | | | | | | | | | | | | | | | | | REDUCE: (134), (225) imply: % 152.30/22.77 | | | | | | | | | | | | | | | | | | | | (226) ~ (all_52_1 = e3) % 152.30/22.77 | | | | | | | | | | | | | | | | | | | | % 152.30/22.77 | | | | | | | | | | | | | | | | | | | | BETA: splitting (76) gives: % 152.30/22.77 | | | | | | | | | | | | | | | | | | | | % 152.30/22.77 | | | | | | | | | | | | | | | | | | | | Case 1: % 152.30/22.77 | | | | | | | | | | | | | | | | | | | | | % 152.30/22.77 | | | | | | | | | | | | | | | | | | | | | (227) all_54_4 = e3 % 152.30/22.77 | | | | | | | | | | | | | | | | | | | | | % 152.30/22.77 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (19), (227) imply: % 152.30/22.77 | | | | | | | | | | | | | | | | | | | | | (228) all_52_1 = e3 % 152.30/22.77 | | | | | | | | | | | | | | | | | | | | | % 152.30/22.77 | | | | | | | | | | | | | | | | | | | | | REDUCE: (226), (228) imply: % 152.30/22.77 | | | | | | | | | | | | | | | | | | | | | (229) $false % 152.30/22.77 | | | | | | | | | | | | | | | | | | | | | % 152.30/22.77 | | | | | | | | | | | | | | | | | | | | | CLOSE: (229) is inconsistent. % 152.30/22.77 | | | | | | | | | | | | | | | | | | | | | % 152.30/22.77 | | | | | | | | | | | | | | | | | | | | Case 2: % 152.30/22.77 | | | | | | | | | | | | | | | | | | | | | % 152.30/22.77 | | | | | | | | | | | | | | | | | | | | | (230) all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0 % 152.30/22.77 | | | | | | | | | | | | | | | | | | | | | % 152.30/22.77 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (230) gives: % 152.30/22.77 | | | | | | | | | | | | | | | | | | | | | % 152.30/22.77 | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.30/22.77 | | | | | | | | | | | | | | | | | | | | | | % 152.30/22.77 | | | | | | | | | | | | | | | | | | | | | | (231) all_54_4 = e2 % 152.30/22.77 | | | | | | | | | | | | | | | | | | | | | | % 152.30/22.77 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (19), (231) imply: % 152.30/22.77 | | | | | | | | | | | | | | | | | | | | | | (232) all_52_1 = e2 % 152.30/22.77 | | | | | | | | | | | | | | | | | | | | | | % 152.30/22.77 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (142), (232) imply: % 152.30/22.77 | | | | | | | | | | | | | | | | | | | | | | (233) ~ (all_4_1 = e2) % 152.30/22.77 | | | | | | | | | | | | | | | | | | | | | | % 152.30/22.77 | | | | | | | | | | | | | | | | | | | | | | SIMP: (233) implies: % 152.30/22.77 | | | | | | | | | | | | | | | | | | | | | | (234) ~ (all_4_1 = e2) % 152.30/22.77 | | | | | | | | | | | | | | | | | | | | | | % 152.30/22.77 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (129) gives: % 152.30/22.77 | | | | | | | | | | | | | | | | | | | | | | % 152.30/22.77 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.30/22.77 | | | | | | | | | | | | | | | | | | | | | | | % 152.30/22.77 | | | | | | | | | | | | | | | | | | | | | | | (235) all_54_5 = e3 % 152.30/22.77 | | | | | | | | | | | | | | | | | | | | | | | % 152.30/22.77 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (139), (235) imply: % 152.30/22.77 | | | | | | | | | | | | | | | | | | | | | | | (236) all_4_1 = e3 % 152.30/22.77 | | | | | | | | | | | | | | | | | | | | | | | % 152.30/22.77 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (234), (236) imply: % 152.30/22.77 | | | | | | | | | | | | | | | | | | | | | | | (237) ~ (e3 = e2) % 152.30/22.77 | | | | | | | | | | | | | | | | | | | | | | | % 152.30/22.77 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (148), (236) imply: % 152.30/22.77 | | | | | | | | | | | | | | | | | | | | | | | (238) op(e3, e3) = all_8_1 % 152.30/22.77 | | | | | | | | | | | | | | | | | | | | | | | % 152.30/22.77 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (8), (10), (18), (21), (23), (26), (28), % 152.30/22.77 | | | | | | | | | | | | | | | | | | | | | | | (29), (30), (34), (37), (39), (42), (43), (44), % 152.30/22.77 | | | | | | | | | | | | | | | | | | | | | | | (45), (47), (54), (56), (59), (64), (70), (71), % 152.30/22.77 | | | | | | | | | | | | | | | | | | | | | | | (78), (81), (85), (96), (99), (100), (104), (109), % 152.30/22.77 | | | | | | | | | | | | | | | | | | | | | | | (110), (111), (116), (117), (119), (126), (152), % 152.30/22.77 | | | | | | | | | | | | | | | | | | | | | | | (156), (184), (188), (210), (237), (238) are % 152.30/22.77 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #588. % 152.30/22.77 | | | | | | | | | | | | | | | | | | | | | | | % 152.30/22.77 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.30/22.77 | | | | | | | | | | | | | | | | | | | | | | | % 152.30/22.77 | | | | | | | | | | | | | | | | | | | | | | | (239) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 152.30/22.77 | | | | | | | | | | | | | | | | | | | | | | | % 152.30/22.77 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (38), (48), (49), (64), (69), (77), (92), (105), % 152.30/22.77 | | | | | | | | | | | | | | | | | | | | | | | (108), (133), (139), (146), (147), (172), (189), % 152.30/22.77 | | | | | | | | | | | | | | | | | | | | | | | (234), (239) are inconsistent by sub-proof #585. % 152.30/22.77 | | | | | | | | | | | | | | | | | | | | | | | % 152.30/22.77 | | | | | | | | | | | | | | | | | | | | | | End of split % 152.30/22.77 | | | | | | | | | | | | | | | | | | | | | | % 152.30/22.77 | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.30/22.77 | | | | | | | | | | | | | | | | | | | | | | % 152.30/22.77 | | | | | | | | | | | | | | | | | | | | | | (240) all_54_4 = e1 | all_54_4 = e0 % 152.30/22.77 | | | | | | | | | | | | | | | | | | | | | | % 152.30/22.77 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (19), (200), (218), (240) are inconsistent by % 152.30/22.77 | | | | | | | | | | | | | | | | | | | | | | sub-proof #583. % 152.30/22.77 | | | | | | | | | | | | | | | | | | | | | | % 152.30/22.77 | | | | | | | | | | | | | | | | | | | | | End of split % 152.30/22.77 | | | | | | | | | | | | | | | | | | | | | % 152.30/22.77 | | | | | | | | | | | | | | | | | | | | End of split % 152.30/22.77 | | | | | | | | | | | | | | | | | | | | % 152.30/22.77 | | | | | | | | | | | | | | | | | | | Case 2: % 152.30/22.77 | | | | | | | | | | | | | | | | | | | | % 152.30/22.77 | | | | | | | | | | | | | | | | | | | | (241) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 152.30/22.77 | | | | | | | | | | | | | | | | | | | | % 152.30/22.77 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (18), (182), (184), (222), (241) are inconsistent % 152.30/22.77 | | | | | | | | | | | | | | | | | | | | by sub-proof #731. % 152.30/22.77 | | | | | | | | | | | | | | | | | | | | % 152.30/22.77 | | | | | | | | | | | | | | | | | | | End of split % 152.30/22.77 | | | | | | | | | | | | | | | | | | | % 152.30/22.77 | | | | | | | | | | | | | | | | | | Case 2: % 152.30/22.77 | | | | | | | | | | | | | | | | | | | % 152.30/22.77 | | | | | | | | | | | | | | | | | | | (242) all_56_7 = e3 % 152.30/22.77 | | | | | | | | | | | | | | | | | | | (243) all_56_1 = e0 % 152.30/22.77 | | | | | | | | | | | | | | | | | | | % 152.30/22.77 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (42), (243) imply: % 152.30/22.77 | | | | | | | | | | | | | | | | | | | (244) all_10_2 = e0 % 152.30/22.77 | | | | | | | | | | | | | | | | | | | % 152.30/22.77 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (70), (242) imply: % 152.30/22.77 | | | | | | | | | | | | | | | | | | | (245) all_52_12 = e3 % 152.30/22.77 | | | | | | | | | | | | | | | | | | | % 152.30/22.77 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (48), (245) imply: % 152.30/22.77 | | | | | | | | | | | | | | | | | | | (246) all_58_9 = e3 % 152.30/22.77 | | | | | | | | | | | | | | | | | | | % 152.30/22.77 | | | | | | | | | | | | | | | | | | | REDUCE: (184), (244) imply: % 152.30/22.77 | | | | | | | | | | | | | | | | | | | (247) ~ (e2 = e0) % 152.30/22.77 | | | | | | | | | | | | | | | | | | | % 152.30/22.77 | | | | | | | | | | | | | | | | | | | REDUCE: (182), (244) imply: % 152.30/22.77 | | | | | | | | | | | | | | | | | | | (248) ~ (e1 = e0) % 152.30/22.77 | | | | | | | | | | | | | | | | | | | % 152.30/22.77 | | | | | | | | | | | | | | | | | | | REDUCE: (110), (244) imply: % 152.30/22.77 | | | | | | | | | | | | | | | | | | | (249) op(e0, e0) = all_10_1 % 152.30/22.77 | | | | | | | | | | | | | | | | | | | % 152.30/22.77 | | | | | | | | | | | | | | | | | | | BETA: splitting (67) gives: % 152.30/22.77 | | | | | | | | | | | | | | | | | | | % 152.30/22.77 | | | | | | | | | | | | | | | | | | | Case 1: % 152.30/22.77 | | | | | | | | | | | | | | | | | | | | % 152.30/22.77 | | | | | | | | | | | | | | | | | | | | (250) all_58_15 = e0 % 152.30/22.77 | | | | | | | | | | | | | | | | | | | | % 152.30/22.77 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (58), (250) imply: % 152.30/22.77 | | | | | | | | | | | | | | | | | | | | (251) e2 = e0 % 152.30/22.77 | | | | | | | | | | | | | | | | | | | | % 152.30/22.77 | | | | | | | | | | | | | | | | | | | | REDUCE: (124), (251) imply: % 152.30/22.77 | | | | | | | | | | | | | | | | | | | | (252) $false % 152.30/22.77 | | | | | | | | | | | | | | | | | | | | % 152.30/22.77 | | | | | | | | | | | | | | | | | | | | CLOSE: (252) is inconsistent. % 152.30/22.77 | | | | | | | | | | | | | | | | | | | | % 152.30/22.77 | | | | | | | | | | | | | | | | | | | Case 2: % 152.30/22.77 | | | | | | | | | | | | | | | | | | | | % 152.30/22.77 | | | | | | | | | | | | | | | | | | | | (253) (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) % 152.30/22.77 | | | | | | | | | | | | | | | | | | | | & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = % 152.30/22.77 | | | | | | | | | | | | | | | | | | | | e0) % 152.30/22.77 | | | | | | | | | | | | | | | | | | | | % 152.30/22.77 | | | | | | | | | | | | | | | | | | | | ALPHA: (253) implies: % 152.30/22.78 | | | | | | | | | | | | | | | | | | | | (254) all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0 % 152.30/22.78 | | | | | | | | | | | | | | | | | | | | % 152.30/22.78 | | | | | | | | | | | | | | | | | | | | BETA: splitting (254) gives: % 152.30/22.78 | | | | | | | | | | | | | | | | | | | | % 152.30/22.78 | | | | | | | | | | | | | | | | | | | | Case 1: % 152.30/22.78 | | | | | | | | | | | | | | | | | | | | | % 152.30/22.78 | | | | | | | | | | | | | | | | | | | | | (255) all_58_9 = e0 % 152.30/22.78 | | | | | | | | | | | | | | | | | | | | | % 152.30/22.78 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (246), (255) imply: % 152.30/22.78 | | | | | | | | | | | | | | | | | | | | | (256) e3 = e0 % 152.30/22.78 | | | | | | | | | | | | | | | | | | | | | % 152.30/22.78 | | | | | | | | | | | | | | | | | | | | | REDUCE: (12), (256) imply: % 152.30/22.78 | | | | | | | | | | | | | | | | | | | | | (257) $false % 152.30/22.78 | | | | | | | | | | | | | | | | | | | | | % 152.30/22.78 | | | | | | | | | | | | | | | | | | | | | CLOSE: (257) is inconsistent. % 152.30/22.78 | | | | | | | | | | | | | | | | | | | | | % 152.30/22.78 | | | | | | | | | | | | | | | | | | | | Case 2: % 152.30/22.78 | | | | | | | | | | | | | | | | | | | | | % 152.30/22.78 | | | | | | | | | | | | | | | | | | | | | (258) all_58_10 = e0 | all_58_11 = e0 % 152.30/22.78 | | | | | | | | | | | | | | | | | | | | | % 152.30/22.78 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (258) gives: % 152.30/22.78 | | | | | | | | | | | | | | | | | | | | | % 152.30/22.78 | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.30/22.78 | | | | | | | | | | | | | | | | | | | | | | % 152.30/22.78 | | | | | | | | | | | | | | | | | | | | | | (259) all_58_10 = e0 % 152.30/22.78 | | | | | | | | | | | | | | | | | | | | | | % 152.30/22.78 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (198), (259) imply: % 152.30/22.78 | | | | | | | | | | | | | | | | | | | | | | (260) e1 = e0 % 152.30/22.78 | | | | | | | | | | | | | | | | | | | | | | % 152.30/22.78 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (175), (260) imply: % 152.30/22.78 | | | | | | | | | | | | | | | | | | | | | | (261) $false % 152.30/22.78 | | | | | | | | | | | | | | | | | | | | | | % 152.30/22.78 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (261) is inconsistent. % 152.30/22.78 | | | | | | | | | | | | | | | | | | | | | | % 152.30/22.78 | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.30/22.78 | | | | | | | | | | | | | | | | | | | | | | % 152.30/22.78 | | | | | | | | | | | | | | | | | | | | | | (262) all_58_11 = e0 % 152.30/22.78 | | | | | | | | | | | | | | | | | | | | | | % 152.30/22.78 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (92), (262) imply: % 152.30/22.78 | | | | | | | | | | | | | | | | | | | | | | (263) all_52_14 = e0 % 152.30/22.78 | | | | | | | | | | | | | | | | | | | | | | % 152.30/22.78 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (50), (263) imply: % 152.30/22.78 | | | | | | | | | | | | | | | | | | | | | | (264) op(e0, e0) = all_56_22 % 152.30/22.78 | | | | | | | | | | | | | | | | | | | | | | % 152.30/22.78 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (64), (71), (84), (249), (264) are inconsistent by % 152.30/22.78 | | | | | | | | | | | | | | | | | | | | | | sub-proof #582. % 152.30/22.78 | | | | | | | | | | | | | | | | | | | | | | % 152.30/22.78 | | | | | | | | | | | | | | | | | | | | | End of split % 152.30/22.78 | | | | | | | | | | | | | | | | | | | | | % 152.30/22.78 | | | | | | | | | | | | | | | | | | | | End of split % 152.30/22.78 | | | | | | | | | | | | | | | | | | | | % 152.30/22.78 | | | | | | | | | | | | | | | | | | | End of split % 152.30/22.78 | | | | | | | | | | | | | | | | | | | % 152.30/22.78 | | | | | | | | | | | | | | | | | | End of split % 152.30/22.78 | | | | | | | | | | | | | | | | | | % 152.30/22.78 | | | | | | | | | | | | | | | | | Case 2: % 152.30/22.78 | | | | | | | | | | | | | | | | | | % 152.30/22.78 | | | | | | | | | | | | | | | | | | (265) all_58_8 = e0 | all_58_14 = e0 % 152.30/22.78 | | | | | | | | | | | | | | | | | | % 152.30/22.78 | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (78), (130), (150), (265) are inconsistent % 152.30/22.78 | | | | | | | | | | | | | | | | | | by sub-proof #627. % 152.30/22.78 | | | | | | | | | | | | | | | | | | % 152.30/22.78 | | | | | | | | | | | | | | | | | End of split % 152.30/22.78 | | | | | | | | | | | | | | | | | % 152.30/22.78 | | | | | | | | | | | | | | | | End of split % 152.30/22.78 | | | | | | | | | | | | | | | | % 152.30/22.78 | | | | | | | | | | | | | | | Case 2: % 152.30/22.78 | | | | | | | | | | | | | | | | % 152.30/22.78 | | | | | | | | | | | | | | | | (266) all_58_9 = e2 % 152.30/22.78 | | | | | | | | | | | | | | | | % 152.30/22.78 | | | | | | | | | | | | | | | | COMBINE_EQS: (48), (266) imply: % 152.30/22.78 | | | | | | | | | | | | | | | | (267) all_52_12 = e2 % 152.30/22.78 | | | | | | | | | | | | | | | | % 152.30/22.78 | | | | | | | | | | | | | | | | REDUCE: (27), (267) imply: % 152.30/22.78 | | | | | | | | | | | | | | | | (268) $false % 152.30/22.78 | | | | | | | | | | | | | | | | % 152.30/22.78 | | | | | | | | | | | | | | | | CLOSE: (268) is inconsistent. % 152.30/22.78 | | | | | | | | | | | | | | | | % 152.30/22.78 | | | | | | | | | | | | | | | End of split % 152.30/22.78 | | | | | | | | | | | | | | | % 152.30/22.78 | | | | | | | | | | | | | | End of split % 152.30/22.78 | | | | | | | | | | | | | | % 152.30/22.78 | | | | | | | | | | | | | Case 2: % 152.30/22.78 | | | | | | | | | | | | | | % 152.30/22.78 | | | | | | | | | | | | | | (269) all_58_11 = e1 | all_58_15 = e1 % 152.30/22.78 | | | | | | | | | | | | | | % 152.30/22.78 | | | | | | | | | | | | | | REF_CLOSE: (77), (92), (105), (172), (269) are inconsistent % 152.30/22.78 | | | | | | | | | | | | | | by sub-proof #672. % 152.30/22.78 | | | | | | | | | | | | | | % 152.30/22.78 | | | | | | | | | | | | | End of split % 152.30/22.78 | | | | | | | | | | | | | % 152.30/22.78 | | | | | | | | | | | | End of split % 152.30/22.78 | | | | | | | | | | | | % 152.30/22.78 | | | | | | | | | | | End of split % 152.30/22.78 | | | | | | | | | | | % 152.30/22.78 | | | | | | | | | | Case 2: % 152.30/22.78 | | | | | | | | | | | % 152.30/22.78 | | | | | | | | | | | (270) all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0 % 152.30/22.78 | | | | | | | | | | | % 152.30/22.78 | | | | | | | | | | | REF_CLOSE: (36), (53), (72), (171), (270) are inconsistent by % 152.30/22.78 | | | | | | | | | | | sub-proof #580. % 152.30/22.78 | | | | | | | | | | | % 152.30/22.78 | | | | | | | | | | End of split % 152.30/22.78 | | | | | | | | | | % 152.30/22.78 | | | | | | | | | Case 2: % 152.30/22.78 | | | | | | | | | | % 152.30/22.78 | | | | | | | | | | (271) all_56_3 = e3 % 152.30/22.78 | | | | | | | | | | % 152.30/22.78 | | | | | | | | | | REF_CLOSE: (174), (178), (271) are inconsistent by sub-proof % 152.30/22.78 | | | | | | | | | | #579. % 152.30/22.78 | | | | | | | | | | % 152.30/22.78 | | | | | | | | | End of split % 152.30/22.78 | | | | | | | | | % 152.30/22.78 | | | | | | | | Case 2: % 152.30/22.78 | | | | | | | | | % 152.30/22.78 | | | | | | | | | (272) ~ (all_58_1 = e1) % 152.30/22.78 | | | | | | | | | % 152.30/22.78 | | | | | | | | | REDUCE: (54), (272) imply: % 152.30/22.78 | | | | | | | | | (273) ~ (all_52_4 = e1) % 152.30/22.78 | | | | | | | | | % 152.30/22.78 | | | | | | | | | BETA: splitting (112) gives: % 152.30/22.78 | | | | | | | | | % 152.30/22.78 | | | | | | | | | Case 1: % 152.30/22.78 | | | | | | | | | | % 152.30/22.78 | | | | | | | | | | (274) all_58_12 = e1 % 152.30/22.78 | | | | | | | | | | % 152.30/22.78 | | | | | | | | | | COMBINE_EQS: (135), (274) imply: % 152.30/22.78 | | | | | | | | | | (275) all_52_3 = e1 % 152.30/22.78 | | | | | | | | | | % 152.30/22.78 | | | | | | | | | | SIMP: (275) implies: % 152.30/22.78 | | | | | | | | | | (276) all_52_3 = e1 % 152.30/22.78 | | | | | | | | | | % 152.30/22.78 | | | | | | | | | | REDUCE: (89), (276) imply: % 152.30/22.78 | | | | | | | | | | (277) ~ (all_52_1 = e1) % 152.30/22.78 | | | | | | | | | | % 152.30/22.78 | | | | | | | | | | REDUCE: (65), (276) imply: % 152.30/22.78 | | | | | | | | | | (278) ~ (all_10_2 = e1) % 152.30/22.78 | | | | | | | | | | % 152.30/22.78 | | | | | | | | | | SIMP: (278) implies: % 152.30/22.78 | | | | | | | | | | (279) ~ (all_10_2 = e1) % 152.30/22.78 | | | | | | | | | | % 152.30/22.78 | | | | | | | | | | REF_CLOSE: (26), (30), (44), (48), (54), (59), (62), (106), % 152.30/22.78 | | | | | | | | | | (108), (111), (141), (154), (169), (170), (273), % 152.30/22.78 | | | | | | | | | | (277), (279) are inconsistent by sub-proof #576. % 152.30/22.78 | | | | | | | | | | % 152.30/22.78 | | | | | | | | | Case 2: % 152.30/22.78 | | | | | | | | | | % 152.30/22.78 | | | | | | | | | | (280) all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1 % 152.30/22.78 | | | | | | | | | | % 152.30/22.78 | | | | | | | | | | REF_CLOSE: (61), (77), (105), (130), (171), (175), (280) are % 152.30/22.78 | | | | | | | | | | inconsistent by sub-proof #575. % 152.30/22.78 | | | | | | | | | | % 152.30/22.78 | | | | | | | | | End of split % 152.30/22.78 | | | | | | | | | % 152.30/22.78 | | | | | | | | End of split % 152.30/22.78 | | | | | | | | % 152.30/22.78 | | | | | | | Case 2: % 152.30/22.78 | | | | | | | | % 152.30/22.78 | | | | | | | | (281) all_54_10 = e0 % 152.30/22.78 | | | | | | | | % 152.30/22.78 | | | | | | | | COMBINE_EQS: (14), (281) imply: % 152.30/22.78 | | | | | | | | (282) all_6_2 = e0 % 152.30/22.78 | | | | | | | | % 152.30/22.78 | | | | | | | | REDUCE: (150), (282) imply: % 152.30/22.78 | | | | | | | | (283) $false % 152.30/22.78 | | | | | | | | % 152.30/22.78 | | | | | | | | CLOSE: (283) is inconsistent. % 152.30/22.78 | | | | | | | | % 152.30/22.78 | | | | | | | End of split % 152.30/22.78 | | | | | | | % 152.30/22.78 | | | | | | End of split % 152.30/22.78 | | | | | | % 152.30/22.78 | | | | | End of split % 152.30/22.78 | | | | | % 152.30/22.78 | | | | Case 2: % 152.30/22.78 | | | | | % 152.30/22.78 | | | | | (284) all_56_21 = e3 % 152.30/22.78 | | | | | (285) all_56_17 = e1 % 152.30/22.78 | | | | | % 152.30/22.78 | | | | | REF_CLOSE: (1), (7), (15), (18), (20), (22), (26), (29), (32), (33), % 152.30/22.78 | | | | | (34), (35), (38), (39), (40), (42), (44), (46), (48), (51), % 152.30/22.78 | | | | | (56), (64), (66), (68), (70), (81), (83), (86), (88), (91), % 152.30/22.78 | | | | | (92), (93), (97), (98), (101), (103), (105), (106), (108), % 152.30/22.78 | | | | | (110), (113), (114), (118), (121), (122), (125), (134), % 152.30/22.78 | | | | | (136), (284), (285) are inconsistent by sub-proof #669. % 152.30/22.78 | | | | | % 152.30/22.78 | | | | End of split % 152.30/22.78 | | | | % 152.30/22.78 | | | Case 2: % 152.30/22.78 | | | | % 152.30/22.78 | | | | (286) all_56_13 = e2 % 152.30/22.78 | | | | (287) all_56_11 = e1 % 152.30/22.78 | | | | % 152.30/22.78 | | | | COMBINE_EQS: (140), (287) imply: % 152.30/22.78 | | | | (288) all_4_1 = e1 % 152.30/22.78 | | | | % 152.30/22.78 | | | | COMBINE_EQS: (73), (286) imply: % 152.30/22.78 | | | | (289) all_52_9 = e2 % 152.30/22.78 | | | | % 152.30/22.78 | | | | COMBINE_EQS: (44), (289) imply: % 152.30/22.78 | | | | (290) all_58_5 = e2 % 152.30/22.78 | | | | % 152.30/22.78 | | | | REDUCE: (143), (288) imply: % 152.30/22.78 | | | | (291) ~ (all_52_4 = e1) % 152.30/22.78 | | | | % 152.30/22.78 | | | | REDUCE: (107), (289) imply: % 152.30/22.78 | | | | (292) ~ (all_6_2 = e2) % 152.30/22.78 | | | | % 152.30/22.78 | | | | REDUCE: (148), (288) imply: % 152.30/22.78 | | | | (293) op(e1, e1) = all_8_1 % 152.30/22.78 | | | | % 152.30/22.78 | | | | REF_CLOSE: (10), (12), (14), (28), (30), (36), (41), (42), (52), (54), % 152.30/22.78 | | | | (55), (57), (59), (64), (78), (82), (102), (111), (124), % 152.30/22.78 | | | | (130), (150), (152), (290), (291), (293) are inconsistent by % 152.30/22.78 | | | | sub-proof #571. % 152.30/22.78 | | | | % 152.30/22.78 | | | End of split % 152.30/22.78 | | | % 152.30/22.78 | | Case 2: % 152.30/22.78 | | | % 152.30/22.78 | | | (294) all_56_21 = e2 % 152.30/22.78 | | | (295) all_56_19 = e1 % 152.30/22.78 | | | % 152.30/22.78 | | | REF_CLOSE: (15), (32), (40), (64), (94), (97), (129), (131), (139), (144), % 152.30/22.78 | | | (147), (294), (295) are inconsistent by sub-proof #566. % 152.30/22.78 | | | % 152.30/22.78 | | End of split % 152.30/22.78 | | % 152.30/22.78 | Case 2: % 152.30/22.78 | | % 152.30/22.78 | | (296) all_56_21 = e0 % 152.30/22.78 | | % 152.30/22.78 | | REF_CLOSE: (15), (40), (64), (84), (97), (296) are inconsistent by sub-proof % 152.30/22.78 | | #565. % 152.30/22.78 | | % 152.30/22.78 | End of split % 152.30/22.78 | % 152.30/22.78 End of proof % 152.30/22.78 % 152.30/22.78 Sub-proof #565 shows that the following formulas are inconsistent: % 152.30/22.78 ---------------------------------------------------------------- % 152.30/22.78 (1) ~ (all_6_1 = e2) % 152.30/22.78 (2) all_56_21 = all_6_2 % 152.30/22.78 (3) all_56_21 = e0 % 152.30/22.78 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 152.30/22.78 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 152.30/22.78 (5) op(e0, e0) = e2 % 152.30/22.78 (6) op(all_6_2, all_6_2) = all_6_1 % 152.30/22.78 % 152.30/22.78 Begin of proof % 152.30/22.78 | % 152.30/22.78 | COMBINE_EQS: (2), (3) imply: % 152.30/22.78 | (7) all_6_2 = e0 % 152.30/22.78 | % 152.30/22.78 | SIMP: (7) implies: % 152.30/22.78 | (8) all_6_2 = e0 % 152.30/22.78 | % 152.30/22.78 | REDUCE: (6), (8) imply: % 152.30/22.78 | (9) op(e0, e0) = all_6_1 % 152.30/22.78 | % 152.30/22.78 | GROUND_INST: instantiating (4) with e2, all_6_1, e0, e0, simplifying with (5), % 152.30/22.78 | (9) gives: % 152.30/22.78 | (10) all_6_1 = e2 % 152.30/22.78 | % 152.30/22.78 | REDUCE: (1), (10) imply: % 152.30/22.78 | (11) $false % 152.30/22.78 | % 152.30/22.78 | CLOSE: (11) is inconsistent. % 152.30/22.78 | % 152.30/22.78 End of proof % 152.30/22.78 % 152.30/22.78 Sub-proof #566 shows that the following formulas are inconsistent: % 152.30/22.78 ---------------------------------------------------------------- % 152.30/22.78 (1) ~ (all_4_1 = e0) % 152.30/22.78 (2) ~ (all_6_1 = e2) % 152.30/22.78 (3) ~ (all_6_1 = e3) % 152.30/22.78 (4) all_56_21 = all_6_2 % 152.30/22.78 (5) ~ (all_52_6 = all_4_1) % 152.30/22.78 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 152.30/22.78 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 152.30/22.78 (7) all_56_21 = e2 % 152.30/22.78 (8) all_56_19 = e1 % 152.30/22.78 (9) op(e2, e2) = all_4_1 % 152.30/22.78 (10) op(all_6_2, all_6_2) = all_6_1 % 152.30/22.78 (11) all_54_5 = all_4_1 % 152.30/22.78 (12) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 152.30/22.78 (13) all_56_19 = all_52_6 % 152.30/22.78 % 152.30/22.78 Begin of proof % 152.30/22.78 | % 152.30/22.78 | COMBINE_EQS: (8), (13) imply: % 152.30/22.78 | (14) all_52_6 = e1 % 152.30/22.78 | % 152.30/22.78 | SIMP: (14) implies: % 152.30/22.78 | (15) all_52_6 = e1 % 152.30/22.78 | % 152.30/22.78 | COMBINE_EQS: (4), (7) imply: % 152.30/22.78 | (16) all_6_2 = e2 % 152.30/22.78 | % 152.30/22.78 | SIMP: (16) implies: % 152.30/22.78 | (17) all_6_2 = e2 % 152.30/22.78 | % 152.30/22.78 | REDUCE: (5), (15) imply: % 152.30/22.78 | (18) ~ (all_4_1 = e1) % 152.30/22.78 | % 152.30/22.78 | SIMP: (18) implies: % 152.30/22.78 | (19) ~ (all_4_1 = e1) % 152.30/22.78 | % 152.30/22.78 | REDUCE: (10), (17) imply: % 152.30/22.78 | (20) op(e2, e2) = all_6_1 % 152.30/22.78 | % 152.30/22.78 | GROUND_INST: instantiating (6) with all_4_1, all_6_1, e2, e2, simplifying with % 152.30/22.78 | (9), (20) gives: % 152.30/22.78 | (21) all_6_1 = all_4_1 % 152.30/22.78 | % 152.30/22.78 | REDUCE: (3), (21) imply: % 152.30/22.78 | (22) ~ (all_4_1 = e3) % 152.30/22.78 | % 152.30/22.78 | REDUCE: (2), (21) imply: % 152.30/22.78 | (23) ~ (all_4_1 = e2) % 152.30/22.78 | % 152.30/22.78 | REF_CLOSE: (1), (11), (12), (19), (22), (23) are inconsistent by sub-proof % 152.30/22.78 | #567. % 152.30/22.78 | % 152.30/22.78 End of proof % 152.30/22.78 % 152.30/22.78 Sub-proof #567 shows that the following formulas are inconsistent: % 152.30/22.78 ---------------------------------------------------------------- % 152.30/22.78 (1) ~ (all_4_1 = e0) % 152.30/22.78 (2) ~ (all_4_1 = e3) % 152.30/22.78 (3) ~ (all_4_1 = e2) % 152.30/22.78 (4) ~ (all_4_1 = e1) % 152.30/22.78 (5) all_54_5 = all_4_1 % 152.30/22.78 (6) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 152.30/22.78 % 152.30/22.78 Begin of proof % 152.30/22.78 | % 152.30/22.78 | BETA: splitting (6) gives: % 152.30/22.78 | % 152.30/22.78 | Case 1: % 152.30/22.78 | | % 152.30/22.78 | | (7) all_54_5 = e3 % 152.30/22.78 | | % 152.30/22.78 | | COMBINE_EQS: (5), (7) imply: % 152.30/22.78 | | (8) all_4_1 = e3 % 152.30/22.78 | | % 152.30/22.78 | | REDUCE: (2), (8) imply: % 152.30/22.78 | | (9) $false % 152.30/22.78 | | % 152.30/22.78 | | CLOSE: (9) is inconsistent. % 152.30/22.78 | | % 152.30/22.78 | Case 2: % 152.30/22.78 | | % 152.30/22.78 | | (10) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 152.30/22.78 | | % 152.30/22.78 | | REF_CLOSE: (1), (3), (4), (5), (10) are inconsistent by sub-proof #568. % 152.30/22.78 | | % 152.30/22.78 | End of split % 152.30/22.78 | % 152.30/22.78 End of proof % 152.30/22.78 % 152.30/22.78 Sub-proof #568 shows that the following formulas are inconsistent: % 152.30/22.78 ---------------------------------------------------------------- % 152.30/22.78 (1) ~ (all_4_1 = e0) % 152.30/22.78 (2) ~ (all_4_1 = e2) % 152.30/22.78 (3) ~ (all_4_1 = e1) % 152.30/22.78 (4) all_54_5 = all_4_1 % 152.30/22.78 (5) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 152.30/22.78 % 152.30/22.78 Begin of proof % 152.30/22.78 | % 152.30/22.78 | BETA: splitting (5) gives: % 152.30/22.78 | % 152.30/22.78 | Case 1: % 152.30/22.78 | | % 152.30/22.78 | | (6) all_54_5 = e2 % 152.30/22.78 | | % 152.30/22.78 | | REF_CLOSE: (2), (4), (6) are inconsistent by sub-proof #570. % 152.30/22.78 | | % 152.30/22.78 | Case 2: % 152.30/22.78 | | % 152.30/22.78 | | (7) all_54_5 = e1 | all_54_5 = e0 % 152.30/22.78 | | % 152.30/22.78 | | REF_CLOSE: (1), (3), (4), (7) are inconsistent by sub-proof #569. % 152.30/22.78 | | % 152.30/22.78 | End of split % 152.30/22.78 | % 152.30/22.78 End of proof % 152.30/22.78 % 152.30/22.78 Sub-proof #569 shows that the following formulas are inconsistent: % 152.30/22.78 ---------------------------------------------------------------- % 152.30/22.78 (1) all_54_5 = e1 | all_54_5 = e0 % 152.30/22.78 (2) all_54_5 = all_4_1 % 152.30/22.78 (3) ~ (all_4_1 = e1) % 152.30/22.78 (4) ~ (all_4_1 = e0) % 152.30/22.78 % 152.30/22.78 Begin of proof % 152.30/22.78 | % 152.30/22.78 | BETA: splitting (1) gives: % 152.30/22.78 | % 152.30/22.78 | Case 1: % 152.30/22.78 | | % 152.30/22.78 | | (5) all_54_5 = e1 % 152.30/22.78 | | % 152.30/22.78 | | COMBINE_EQS: (2), (5) imply: % 152.30/22.78 | | (6) all_4_1 = e1 % 152.30/22.78 | | % 152.30/22.78 | | SIMP: (6) implies: % 152.30/22.78 | | (7) all_4_1 = e1 % 152.30/22.78 | | % 152.30/22.78 | | REDUCE: (3), (7) imply: % 152.30/22.78 | | (8) $false % 152.30/22.78 | | % 152.30/22.78 | | CLOSE: (8) is inconsistent. % 152.30/22.78 | | % 152.30/22.78 | Case 2: % 152.30/22.78 | | % 152.30/22.78 | | (9) all_54_5 = e0 % 152.30/22.78 | | % 152.30/22.78 | | COMBINE_EQS: (2), (9) imply: % 152.30/22.78 | | (10) all_4_1 = e0 % 152.30/22.78 | | % 152.30/22.78 | | SIMP: (10) implies: % 152.30/22.78 | | (11) all_4_1 = e0 % 152.30/22.78 | | % 152.30/22.78 | | REDUCE: (4), (11) imply: % 152.30/22.78 | | (12) $false % 152.30/22.78 | | % 152.30/22.78 | | CLOSE: (12) is inconsistent. % 152.30/22.78 | | % 152.30/22.78 | End of split % 152.30/22.78 | % 152.30/22.78 End of proof % 152.30/22.78 % 152.30/22.78 Sub-proof #570 shows that the following formulas are inconsistent: % 152.30/22.78 ---------------------------------------------------------------- % 152.30/22.78 (1) all_54_5 = all_4_1 % 152.30/22.78 (2) all_54_5 = e2 % 152.30/22.78 (3) ~ (all_4_1 = e2) % 152.30/22.78 % 152.30/22.78 Begin of proof % 152.30/22.78 | % 152.30/22.78 | COMBINE_EQS: (1), (2) imply: % 152.30/22.78 | (4) all_4_1 = e2 % 152.30/22.78 | % 152.30/22.78 | SIMP: (4) implies: % 152.30/22.78 | (5) all_4_1 = e2 % 152.30/22.78 | % 152.30/22.78 | REDUCE: (3), (5) imply: % 152.30/22.78 | (6) $false % 152.30/22.78 | % 152.30/22.78 | CLOSE: (6) is inconsistent. % 152.30/22.78 | % 152.30/22.78 End of proof % 152.30/22.78 % 152.30/22.78 Sub-proof #571 shows that the following formulas are inconsistent: % 152.30/22.78 ---------------------------------------------------------------- % 152.30/22.78 (1) ~ (all_8_1 = e1) % 152.30/22.78 (2) ~ (e3 = e0) % 152.30/22.78 (3) all_54_10 = all_6_2 % 152.30/22.78 (4) ~ (all_8_1 = e3) % 152.30/22.78 (5) all_58_4 = all_52_8 % 152.30/22.78 (6) ~ (all_52_11 = e0) % 152.30/22.78 (7) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 152.30/22.78 (8) all_56_1 = all_10_2 % 152.30/22.78 (9) ~ (all_52_4 = e1) % 152.30/22.78 (10) ~ (all_56_1 = e1) | all_56_5 = e3 % 152.30/22.78 (11) all_58_1 = all_52_4 % 152.30/22.78 (12) all_58_4 = e0 | all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0 % 152.30/22.78 (13) ~ (all_52_8 = all_6_2) % 152.30/22.78 (14) all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1 % 152.30/22.78 (15) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 152.30/22.78 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 152.30/22.78 (16) ~ (all_6_2 = e0) % 152.30/22.78 (17) all_58_8 = all_6_2 % 152.30/22.78 (18) all_56_5 = all_52_8 % 152.30/22.78 (19) all_58_5 = e2 % 152.30/22.78 (20) op(e1, e1) = all_8_1 % 152.30/22.78 (21) op(e1, e1) = all_6_2 % 152.30/22.78 (22) ~ (all_6_2 = e2) % 152.30/22.78 (23) all_58_0 = all_10_2 % 152.30/22.78 (24) ~ (e2 = e0) % 152.30/22.78 (25) all_58_14 = all_52_11 % 152.30/22.78 % 152.30/22.78 Begin of proof % 152.30/22.78 | % 152.30/22.78 | BETA: splitting (12) gives: % 152.30/22.78 | % 152.30/22.78 | Case 1: % 152.30/22.78 | | % 152.30/22.78 | | (26) all_58_4 = e0 % 152.30/22.78 | | % 152.30/22.78 | | COMBINE_EQS: (5), (26) imply: % 152.30/22.78 | | (27) all_52_8 = e0 % 152.30/22.78 | | % 152.30/22.78 | | COMBINE_EQS: (18), (27) imply: % 152.30/22.78 | | (28) all_56_5 = e0 % 152.30/22.78 | | % 152.30/22.78 | | REDUCE: (13), (27) imply: % 152.30/22.78 | | (29) ~ (all_6_2 = e0) % 152.30/22.78 | | % 152.30/22.78 | | BETA: splitting (10) gives: % 152.30/22.78 | | % 152.30/22.78 | | Case 1: % 152.30/22.78 | | | % 152.30/22.78 | | | (30) ~ (all_56_1 = e1) % 152.30/22.78 | | | % 152.30/22.78 | | | REDUCE: (8), (30) imply: % 152.30/22.78 | | | (31) ~ (all_10_2 = e1) % 152.30/22.78 | | | % 152.30/22.78 | | | BETA: splitting (14) gives: % 152.30/22.78 | | | % 152.30/22.78 | | | Case 1: % 152.30/22.78 | | | | % 152.30/22.78 | | | | (32) all_58_0 = e1 % 152.30/22.78 | | | | % 152.30/22.78 | | | | COMBINE_EQS: (23), (32) imply: % 152.30/22.78 | | | | (33) all_10_2 = e1 % 152.30/22.78 | | | | % 152.30/22.78 | | | | REDUCE: (31), (33) imply: % 152.37/22.78 | | | | (34) $false % 152.37/22.78 | | | | % 152.37/22.78 | | | | CLOSE: (34) is inconsistent. % 152.37/22.78 | | | | % 152.37/22.78 | | | Case 2: % 152.37/22.78 | | | | % 152.37/22.78 | | | | (35) all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1 % 152.37/22.78 | | | | % 152.37/22.78 | | | | BETA: splitting (35) gives: % 152.37/22.78 | | | | % 152.37/22.78 | | | | Case 1: % 152.37/22.78 | | | | | % 152.37/22.78 | | | | | (36) all_58_1 = e1 % 152.37/22.78 | | | | | % 152.37/22.78 | | | | | COMBINE_EQS: (11), (36) imply: % 152.37/22.78 | | | | | (37) all_52_4 = e1 % 152.37/22.78 | | | | | % 152.37/22.78 | | | | | REDUCE: (9), (37) imply: % 152.37/22.78 | | | | | (38) $false % 152.37/22.78 | | | | | % 152.37/22.78 | | | | | CLOSE: (38) is inconsistent. % 152.37/22.78 | | | | | % 152.37/22.78 | | | | Case 2: % 152.37/22.78 | | | | | % 152.37/22.78 | | | | | % 152.37/22.78 | | | | | GROUND_INST: instantiating (15) with all_6_2, all_8_1, e1, e1, % 152.37/22.78 | | | | | simplifying with (20), (21) gives: % 152.37/22.78 | | | | | (39) all_8_1 = all_6_2 % 152.37/22.78 | | | | | % 152.37/22.78 | | | | | REDUCE: (4), (39) imply: % 152.37/22.78 | | | | | (40) ~ (all_6_2 = e3) % 152.37/22.78 | | | | | % 152.37/22.78 | | | | | REDUCE: (1), (39) imply: % 152.37/22.78 | | | | | (41) ~ (all_6_2 = e1) % 152.37/22.78 | | | | | % 152.37/22.78 | | | | | REF_CLOSE: (3), (7), (16), (22), (40), (41) are inconsistent by % 152.37/22.78 | | | | | sub-proof #573. % 152.37/22.78 | | | | | % 152.37/22.78 | | | | End of split % 152.37/22.78 | | | | % 152.37/22.78 | | | End of split % 152.37/22.78 | | | % 152.37/22.78 | | Case 2: % 152.37/22.78 | | | % 152.37/22.78 | | | (42) all_56_5 = e3 % 152.37/22.78 | | | % 152.37/22.78 | | | COMBINE_EQS: (28), (42) imply: % 152.37/22.78 | | | (43) e3 = e0 % 152.37/22.78 | | | % 152.37/22.78 | | | REDUCE: (2), (43) imply: % 152.37/22.78 | | | (44) $false % 152.37/22.78 | | | % 152.37/22.78 | | | CLOSE: (44) is inconsistent. % 152.37/22.78 | | | % 152.37/22.78 | | End of split % 152.37/22.78 | | % 152.37/22.78 | Case 2: % 152.37/22.78 | | % 152.37/22.78 | | (45) all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0 % 152.37/22.78 | | % 152.37/22.78 | | REF_CLOSE: (6), (16), (17), (19), (24), (25), (45) are inconsistent by % 152.37/22.78 | | sub-proof #572. % 152.37/22.78 | | % 152.37/22.78 | End of split % 152.37/22.78 | % 152.37/22.78 End of proof % 152.37/22.78 % 152.37/22.78 Sub-proof #572 shows that the following formulas are inconsistent: % 152.37/22.78 ---------------------------------------------------------------- % 152.37/22.78 (1) ~ (all_52_11 = e0) % 152.37/22.78 (2) ~ (all_6_2 = e0) % 152.37/22.78 (3) all_58_8 = all_6_2 % 152.37/22.78 (4) all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0 % 152.37/22.78 (5) all_58_5 = e2 % 152.37/22.78 (6) ~ (e2 = e0) % 152.37/22.78 (7) all_58_14 = all_52_11 % 152.37/22.78 % 152.37/22.78 Begin of proof % 152.37/22.78 | % 152.37/22.78 | BETA: splitting (4) gives: % 152.37/22.78 | % 152.37/22.78 | Case 1: % 152.37/22.78 | | % 152.37/22.78 | | (8) all_58_5 = e0 % 152.37/22.78 | | % 152.37/22.78 | | COMBINE_EQS: (5), (8) imply: % 152.37/22.78 | | (9) e2 = e0 % 152.37/22.78 | | % 152.37/22.78 | | REDUCE: (6), (9) imply: % 152.37/22.78 | | (10) $false % 152.37/22.78 | | % 152.37/22.78 | | CLOSE: (10) is inconsistent. % 152.37/22.78 | | % 152.37/22.78 | Case 2: % 152.37/22.78 | | % 152.37/22.78 | | (11) all_58_8 = e0 | all_58_14 = e0 % 152.37/22.78 | | % 152.37/22.78 | | REF_CLOSE: (1), (2), (3), (7), (11) are inconsistent by sub-proof #627. % 152.37/22.78 | | % 152.37/22.78 | End of split % 152.37/22.78 | % 152.37/22.78 End of proof % 152.37/22.78 % 152.37/22.78 Sub-proof #573 shows that the following formulas are inconsistent: % 152.37/22.78 ---------------------------------------------------------------- % 152.37/22.78 (1) all_54_10 = all_6_2 % 152.37/22.78 (2) ~ (all_6_2 = e3) % 152.37/22.78 (3) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 152.37/22.78 (4) ~ (all_6_2 = e0) % 152.37/22.78 (5) ~ (all_6_2 = e1) % 152.37/22.78 (6) ~ (all_6_2 = e2) % 152.37/22.78 % 152.37/22.78 Begin of proof % 152.37/22.78 | % 152.37/22.78 | BETA: splitting (3) gives: % 152.37/22.78 | % 152.37/22.78 | Case 1: % 152.37/22.78 | | % 152.37/22.78 | | (7) all_54_10 = e3 % 152.37/22.78 | | % 152.37/22.78 | | REF_CLOSE: (1), (2), (7) are inconsistent by sub-proof #736. % 152.37/22.78 | | % 152.37/22.78 | Case 2: % 152.37/22.78 | | % 152.37/22.78 | | (8) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 152.37/22.78 | | % 152.37/22.78 | | REF_CLOSE: (1), (4), (5), (6), (8) are inconsistent by sub-proof #574. % 152.37/22.78 | | % 152.37/22.78 | End of split % 152.37/22.78 | % 152.37/22.78 End of proof % 152.37/22.78 % 152.37/22.78 Sub-proof #574 shows that the following formulas are inconsistent: % 152.37/22.78 ---------------------------------------------------------------- % 152.37/22.78 (1) all_54_10 = all_6_2 % 152.37/22.78 (2) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 152.37/22.78 (3) ~ (all_6_2 = e0) % 152.37/22.78 (4) ~ (all_6_2 = e1) % 152.37/22.78 (5) ~ (all_6_2 = e2) % 152.37/22.78 % 152.37/22.78 Begin of proof % 152.37/22.78 | % 152.37/22.78 | BETA: splitting (2) gives: % 152.37/22.78 | % 152.37/22.78 | Case 1: % 152.37/22.78 | | % 152.37/22.78 | | (6) all_54_10 = e2 % 152.37/22.78 | | % 152.37/22.78 | | REF_CLOSE: (1), (5), (6) are inconsistent by sub-proof #735. % 152.37/22.78 | | % 152.37/22.78 | Case 2: % 152.37/22.78 | | % 152.37/22.78 | | (7) all_54_10 = e1 | all_54_10 = e0 % 152.37/22.78 | | % 152.37/22.78 | | BETA: splitting (7) gives: % 152.37/22.78 | | % 152.37/22.78 | | Case 1: % 152.37/22.78 | | | % 152.37/22.78 | | | (8) all_54_10 = e1 % 152.37/22.78 | | | % 152.37/22.78 | | | REF_CLOSE: (1), (4), (8) are inconsistent by sub-proof #606. % 152.37/22.78 | | | % 152.37/22.78 | | Case 2: % 152.37/22.78 | | | % 152.37/22.78 | | | (9) all_54_10 = e0 % 152.37/22.78 | | | % 152.37/22.78 | | | REF_CLOSE: (1), (3), (9) are inconsistent by sub-proof #705. % 152.37/22.78 | | | % 152.37/22.78 | | End of split % 152.37/22.78 | | % 152.37/22.78 | End of split % 152.37/22.78 | % 152.37/22.78 End of proof % 152.37/22.78 % 152.37/22.78 Sub-proof #575 shows that the following formulas are inconsistent: % 152.37/22.78 ---------------------------------------------------------------- % 152.37/22.78 (1) all_58_13 = e0 % 152.37/22.78 (2) ~ (e1 = e0) % 152.37/22.78 (3) all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1 % 152.37/22.78 (4) ~ (all_4_2 = e1) % 152.37/22.78 (5) ~ (all_52_11 = e1) % 152.37/22.78 (6) all_58_15 = all_4_2 % 152.37/22.78 (7) all_58_14 = all_52_11 % 152.37/22.78 % 152.37/22.78 Begin of proof % 152.37/22.78 | % 152.37/22.78 | BETA: splitting (3) gives: % 152.37/22.78 | % 152.37/22.78 | Case 1: % 152.37/22.78 | | % 152.37/22.78 | | (8) all_58_13 = e1 % 152.37/22.78 | | % 152.37/22.78 | | COMBINE_EQS: (1), (8) imply: % 152.37/22.78 | | (9) e1 = e0 % 152.37/22.78 | | % 152.37/22.78 | | REDUCE: (2), (9) imply: % 152.37/22.78 | | (10) $false % 152.37/22.78 | | % 152.37/22.78 | | CLOSE: (10) is inconsistent. % 152.37/22.78 | | % 152.37/22.78 | Case 2: % 152.37/22.78 | | % 152.37/22.78 | | (11) all_58_14 = e1 | all_58_15 = e1 % 152.37/22.78 | | % 152.37/22.78 | | REF_CLOSE: (4), (5), (6), (7), (11) are inconsistent by sub-proof #619. % 152.37/22.78 | | % 152.37/22.78 | End of split % 152.37/22.78 | % 152.37/22.78 End of proof % 152.37/22.78 % 152.37/22.78 Sub-proof #576 shows that the following formulas are inconsistent: % 152.37/22.78 ---------------------------------------------------------------- % 152.37/22.78 (1) ~ (all_52_12 = all_52_13) % 152.37/22.78 (2) all_58_4 = all_52_8 % 152.37/22.78 (3) ~ (all_10_2 = e1) % 152.37/22.78 (4) ~ (all_52_1 = e1) % 152.37/22.78 (5) all_58_3 = all_4_1 % 152.37/22.78 (6) all_58_5 = all_52_9 % 152.37/22.78 (7) all_58_9 = all_52_12 % 152.37/22.78 (8) ~ (all_52_4 = e1) % 152.37/22.78 (9) all_58_1 = all_52_4 % 152.37/22.78 (10) all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1 % 152.37/22.78 (11) all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1 % 152.37/22.78 (12) ~ (all_4_1 = e1) % 152.37/22.78 (13) ~ (all_52_8 = e1) % 152.37/22.78 (14) ~ (all_52_9 = e1) % 152.37/22.78 (15) all_58_2 = all_52_1 % 152.37/22.78 (16) all_58_10 = all_52_13 % 152.37/22.78 (17) all_58_0 = all_10_2 % 152.37/22.78 % 152.37/22.78 Begin of proof % 152.37/22.78 | % 152.37/22.78 | BETA: splitting (10) gives: % 152.37/22.78 | % 152.37/22.78 | Case 1: % 152.37/22.78 | | % 152.37/22.78 | | (18) all_58_0 = e1 % 152.37/22.78 | | % 152.37/22.78 | | COMBINE_EQS: (17), (18) imply: % 152.37/22.78 | | (19) all_10_2 = e1 % 152.37/22.78 | | % 152.37/22.78 | | REDUCE: (3), (19) imply: % 152.37/22.78 | | (20) $false % 152.37/22.78 | | % 152.37/22.78 | | CLOSE: (20) is inconsistent. % 152.37/22.78 | | % 152.37/22.78 | Case 2: % 152.37/22.78 | | % 152.37/22.78 | | (21) all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1 % 152.37/22.78 | | % 152.37/22.78 | | BETA: splitting (11) gives: % 152.37/22.78 | | % 152.37/22.78 | | Case 1: % 152.37/22.78 | | | % 152.37/22.78 | | | (22) all_58_2 = e1 % 152.37/22.78 | | | % 152.37/22.78 | | | COMBINE_EQS: (15), (22) imply: % 152.37/22.78 | | | (23) all_52_1 = e1 % 152.37/22.78 | | | % 152.37/22.78 | | | REDUCE: (4), (23) imply: % 152.37/22.78 | | | (24) $false % 152.37/22.78 | | | % 152.37/22.78 | | | CLOSE: (24) is inconsistent. % 152.37/22.78 | | | % 152.37/22.78 | | Case 2: % 152.37/22.78 | | | % 152.37/22.78 | | | (25) all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1 % 152.37/22.78 | | | % 152.37/22.78 | | | BETA: splitting (25) gives: % 152.37/22.78 | | | % 152.37/22.78 | | | Case 1: % 152.37/22.78 | | | | % 152.37/22.78 | | | | (26) all_58_3 = e1 % 152.37/22.78 | | | | % 152.37/22.78 | | | | COMBINE_EQS: (5), (26) imply: % 152.37/22.78 | | | | (27) all_4_1 = e1 % 152.37/22.78 | | | | % 152.37/22.78 | | | | REDUCE: (12), (27) imply: % 152.37/22.78 | | | | (28) $false % 152.37/22.78 | | | | % 152.37/22.78 | | | | CLOSE: (28) is inconsistent. % 152.37/22.78 | | | | % 152.37/22.78 | | | Case 2: % 152.37/22.78 | | | | % 152.37/22.78 | | | | (29) all_58_5 = e1 | all_58_10 = e1 % 152.37/22.78 | | | | % 152.37/22.78 | | | | BETA: splitting (29) gives: % 152.37/22.78 | | | | % 152.37/22.78 | | | | Case 1: % 152.37/22.78 | | | | | % 152.37/22.78 | | | | | (30) all_58_5 = e1 % 152.37/22.78 | | | | | % 152.37/22.78 | | | | | COMBINE_EQS: (6), (30) imply: % 152.37/22.78 | | | | | (31) all_52_9 = e1 % 152.37/22.78 | | | | | % 152.37/22.78 | | | | | REDUCE: (14), (31) imply: % 152.37/22.78 | | | | | (32) $false % 152.37/22.78 | | | | | % 152.37/22.78 | | | | | CLOSE: (32) is inconsistent. % 152.37/22.78 | | | | | % 152.37/22.78 | | | | Case 2: % 152.37/22.78 | | | | | % 152.37/22.78 | | | | | (33) all_58_10 = e1 % 152.37/22.78 | | | | | % 152.37/22.78 | | | | | COMBINE_EQS: (16), (33) imply: % 152.37/22.78 | | | | | (34) all_52_13 = e1 % 152.37/22.78 | | | | | % 152.37/22.78 | | | | | REDUCE: (1), (34) imply: % 152.37/22.78 | | | | | (35) ~ (all_52_12 = e1) % 152.37/22.78 | | | | | % 152.37/22.78 | | | | | REF_CLOSE: (2), (7), (8), (9), (13), (21), (35) are inconsistent by % 152.37/22.78 | | | | | sub-proof #577. % 152.37/22.78 | | | | | % 152.37/22.78 | | | | End of split % 152.37/22.78 | | | | % 152.37/22.78 | | | End of split % 152.37/22.78 | | | % 152.37/22.78 | | End of split % 152.37/22.78 | | % 152.37/22.78 | End of split % 152.37/22.78 | % 152.37/22.78 End of proof % 152.37/22.78 % 152.37/22.78 Sub-proof #577 shows that the following formulas are inconsistent: % 152.37/22.78 ---------------------------------------------------------------- % 152.37/22.78 (1) all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1 % 152.37/22.78 (2) all_58_4 = all_52_8 % 152.37/22.78 (3) all_58_9 = all_52_12 % 152.37/22.78 (4) ~ (all_52_4 = e1) % 152.37/22.78 (5) all_58_1 = all_52_4 % 152.37/22.78 (6) ~ (all_52_8 = e1) % 152.37/22.78 (7) ~ (all_52_12 = e1) % 152.37/22.78 % 152.37/22.78 Begin of proof % 152.37/22.78 | % 152.37/22.78 | BETA: splitting (1) gives: % 152.37/22.78 | % 152.37/22.78 | Case 1: % 152.37/22.78 | | % 152.37/22.78 | | (8) all_58_1 = e1 % 152.37/22.78 | | % 152.37/22.78 | | COMBINE_EQS: (5), (8) imply: % 152.37/22.78 | | (9) all_52_4 = e1 % 152.37/22.78 | | % 152.37/22.78 | | REDUCE: (4), (9) imply: % 152.37/22.78 | | (10) $false % 152.37/22.78 | | % 152.37/22.78 | | CLOSE: (10) is inconsistent. % 152.37/22.78 | | % 152.37/22.78 | Case 2: % 152.37/22.78 | | % 152.37/22.78 | | (11) all_58_4 = e1 | all_58_9 = e1 % 152.37/22.78 | | % 152.37/22.78 | | REF_CLOSE: (2), (3), (6), (7), (11) are inconsistent by sub-proof #578. % 152.37/22.78 | | % 152.37/22.78 | End of split % 152.37/22.78 | % 152.37/22.78 End of proof % 152.37/22.78 % 152.37/22.78 Sub-proof #578 shows that the following formulas are inconsistent: % 152.37/22.78 ---------------------------------------------------------------- % 152.37/22.78 (1) all_58_4 = all_52_8 % 152.37/22.78 (2) all_58_9 = all_52_12 % 152.37/22.78 (3) ~ (all_52_8 = e1) % 152.37/22.78 (4) all_58_4 = e1 | all_58_9 = e1 % 152.37/22.78 (5) ~ (all_52_12 = e1) % 152.37/22.78 % 152.37/22.78 Begin of proof % 152.37/22.78 | % 152.37/22.78 | BETA: splitting (4) gives: % 152.37/22.78 | % 152.37/22.78 | Case 1: % 152.37/22.78 | | % 152.37/22.78 | | (6) all_58_4 = e1 % 152.37/22.78 | | % 152.37/22.78 | | COMBINE_EQS: (1), (6) imply: % 152.37/22.78 | | (7) all_52_8 = e1 % 152.37/22.78 | | % 152.37/22.78 | | REDUCE: (3), (7) imply: % 152.37/22.78 | | (8) $false % 152.37/22.78 | | % 152.37/22.78 | | CLOSE: (8) is inconsistent. % 152.37/22.78 | | % 152.37/22.78 | Case 2: % 152.37/22.78 | | % 152.37/22.78 | | (9) all_58_9 = e1 % 152.37/22.78 | | % 152.37/22.78 | | COMBINE_EQS: (2), (9) imply: % 152.37/22.78 | | (10) all_52_12 = e1 % 152.37/22.78 | | % 152.37/22.78 | | REDUCE: (5), (10) imply: % 152.37/22.78 | | (11) $false % 152.37/22.78 | | % 152.37/22.78 | | CLOSE: (11) is inconsistent. % 152.37/22.78 | | % 152.37/22.78 | End of split % 152.37/22.78 | % 152.37/22.78 End of proof % 152.37/22.78 % 152.37/22.78 Sub-proof #579 shows that the following formulas are inconsistent: % 152.37/22.78 ---------------------------------------------------------------- % 152.37/22.78 (1) all_56_3 = e3 % 152.37/22.78 (2) all_56_3 = e1 % 152.37/22.78 (3) ~ (e3 = e1) % 152.37/22.78 % 152.37/22.78 Begin of proof % 152.37/22.78 | % 152.37/22.78 | COMBINE_EQS: (1), (2) imply: % 152.37/22.78 | (4) e3 = e1 % 152.37/22.78 | % 152.37/22.78 | SIMP: (4) implies: % 152.37/22.78 | (5) e3 = e1 % 152.37/22.78 | % 152.37/22.78 | REDUCE: (3), (5) imply: % 152.37/22.78 | (6) $false % 152.37/22.78 | % 152.37/22.78 | CLOSE: (6) is inconsistent. % 152.37/22.78 | % 152.37/22.78 End of proof % 152.37/22.78 % 152.37/22.78 Sub-proof #580 shows that the following formulas are inconsistent: % 152.37/22.78 ---------------------------------------------------------------- % 152.37/22.78 (1) ~ (all_52_11 = e0) % 152.37/22.78 (2) all_54_14 = all_52_11 % 152.37/22.78 (3) ~ (all_52_11 = e2) % 152.37/22.78 (4) all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0 % 152.37/22.78 (5) ~ (all_52_11 = e1) % 152.37/22.78 % 152.37/22.78 Begin of proof % 152.37/22.78 | % 152.37/22.78 | BETA: splitting (4) gives: % 152.37/22.78 | % 152.37/22.78 | Case 1: % 152.37/22.78 | | % 152.37/22.78 | | (6) all_54_14 = e2 % 152.37/22.78 | | % 152.37/22.78 | | REF_CLOSE: (2), (3), (6) are inconsistent by sub-proof #581. % 152.37/22.78 | | % 152.37/22.78 | Case 2: % 152.37/22.78 | | % 152.37/22.78 | | (7) all_54_14 = e1 | all_54_14 = e0 % 152.37/22.78 | | % 152.37/22.78 | | REF_CLOSE: (1), (2), (5), (7) are inconsistent by sub-proof #714. % 152.37/22.78 | | % 152.37/22.78 | End of split % 152.37/22.78 | % 152.37/22.78 End of proof % 152.37/22.78 % 152.37/22.78 Sub-proof #581 shows that the following formulas are inconsistent: % 152.37/22.78 ---------------------------------------------------------------- % 152.37/22.78 (1) all_54_14 = all_52_11 % 152.37/22.78 (2) all_54_14 = e2 % 152.37/22.78 (3) ~ (all_52_11 = e2) % 152.37/22.78 % 152.37/22.78 Begin of proof % 152.37/22.78 | % 152.37/22.78 | COMBINE_EQS: (1), (2) imply: % 152.37/22.78 | (4) all_52_11 = e2 % 152.37/22.78 | % 152.37/22.78 | SIMP: (4) implies: % 152.37/22.78 | (5) all_52_11 = e2 % 152.37/22.78 | % 152.37/22.78 | REDUCE: (3), (5) imply: % 152.37/22.78 | (6) $false % 152.37/22.78 | % 152.37/22.78 | CLOSE: (6) is inconsistent. % 152.37/22.78 | % 152.37/22.78 End of proof % 152.37/22.78 % 152.37/22.78 Sub-proof #582 shows that the following formulas are inconsistent: % 152.37/22.78 ---------------------------------------------------------------- % 152.37/22.78 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 152.37/22.78 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 152.37/22.78 (2) ~ (all_10_1 = e2) % 152.37/22.78 (3) op(e0, e0) = all_10_1 % 152.37/22.78 (4) op(e0, e0) = e2 % 152.37/22.78 (5) op(e0, e0) = all_56_22 % 152.37/22.78 % 152.37/22.78 Begin of proof % 152.37/22.78 | % 152.37/22.78 | GROUND_INST: instantiating (1) with e2, all_56_22, e0, e0, simplifying with % 152.37/22.78 | (4), (5) gives: % 152.37/22.78 | (6) all_56_22 = e2 % 152.37/22.78 | % 152.37/22.78 | GROUND_INST: instantiating (1) with all_10_1, all_56_22, e0, e0, simplifying % 152.37/22.78 | with (3), (5) gives: % 152.37/22.78 | (7) all_56_22 = all_10_1 % 152.37/22.78 | % 152.37/22.78 | COMBINE_EQS: (6), (7) imply: % 152.37/22.78 | (8) all_10_1 = e2 % 152.37/22.78 | % 152.37/22.78 | REDUCE: (2), (8) imply: % 152.37/22.78 | (9) $false % 152.37/22.78 | % 152.37/22.78 | CLOSE: (9) is inconsistent. % 152.37/22.78 | % 152.37/22.78 End of proof % 152.37/22.78 % 152.37/22.78 Sub-proof #583 shows that the following formulas are inconsistent: % 152.37/22.78 ---------------------------------------------------------------- % 152.37/22.78 (1) all_54_4 = e1 | all_54_4 = e0 % 152.37/22.78 (2) all_54_4 = all_52_1 % 152.37/22.78 (3) ~ (all_52_1 = e1) % 152.37/22.78 (4) ~ (all_52_1 = e0) % 152.37/22.78 % 152.37/22.78 Begin of proof % 152.37/22.78 | % 152.37/22.78 | BETA: splitting (1) gives: % 152.37/22.78 | % 152.37/22.78 | Case 1: % 152.37/22.78 | | % 152.37/22.78 | | (5) all_54_4 = e1 % 152.37/22.78 | | % 152.37/22.78 | | REF_CLOSE: (2), (3), (5) are inconsistent by sub-proof #584. % 152.37/22.78 | | % 152.37/22.78 | Case 2: % 152.37/22.78 | | % 152.37/22.78 | | (6) all_54_4 = e0 % 152.37/22.78 | | % 152.37/22.78 | | REF_CLOSE: (2), (4), (6) are inconsistent by sub-proof #614. % 152.37/22.78 | | % 152.37/22.79 | End of split % 152.37/22.79 | % 152.37/22.79 End of proof % 152.37/22.79 % 152.37/22.79 Sub-proof #584 shows that the following formulas are inconsistent: % 152.37/22.79 ---------------------------------------------------------------- % 152.37/22.79 (1) all_54_4 = all_52_1 % 152.37/22.79 (2) all_54_4 = e1 % 152.37/22.79 (3) ~ (all_52_1 = e1) % 152.37/22.79 % 152.37/22.79 Begin of proof % 152.37/22.79 | % 152.37/22.79 | COMBINE_EQS: (1), (2) imply: % 152.37/22.79 | (4) all_52_1 = e1 % 152.37/22.79 | % 152.37/22.79 | SIMP: (4) implies: % 152.37/22.79 | (5) all_52_1 = e1 % 152.37/22.79 | % 152.37/22.79 | REDUCE: (3), (5) imply: % 152.37/22.79 | (6) $false % 152.37/22.79 | % 152.37/22.79 | CLOSE: (6) is inconsistent. % 152.37/22.79 | % 152.37/22.79 End of proof % 152.37/22.79 % 152.37/22.79 Sub-proof #585 shows that the following formulas are inconsistent: % 152.37/22.79 ---------------------------------------------------------------- % 152.37/22.79 (1) ~ (all_4_1 = e0) % 152.37/22.79 (2) all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1 % 152.37/22.79 (3) ~ (all_4_1 = e2) % 152.37/22.79 (4) all_58_9 = all_52_12 % 152.37/22.79 (5) op(e0, all_52_12) = all_56_6 % 152.37/22.79 (6) ~ (all_52_13 = all_4_1) % 152.37/22.79 (7) op(e0, e1) = e3 % 152.37/22.79 (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 152.37/22.79 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 152.37/22.79 (9) ~ (all_52_14 = e1) % 152.37/22.79 (10) op(e0, all_4_1) = all_4_0 % 152.37/22.79 (11) ~ (all_4_2 = e1) % 152.37/22.79 (12) all_58_11 = all_52_14 % 152.37/22.79 (13) all_54_5 = all_4_1 % 152.37/22.79 (14) all_58_15 = all_4_2 % 152.37/22.79 (15) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 152.37/22.79 (16) all_58_10 = all_52_13 % 152.37/22.79 (17) ~ (all_4_0 = e3) % 152.37/22.79 % 152.37/22.79 Begin of proof % 152.37/22.79 | % 152.37/22.79 | BETA: splitting (15) gives: % 152.37/22.79 | % 152.37/22.79 | Case 1: % 152.37/22.79 | | % 152.37/22.79 | | (18) all_54_5 = e2 % 152.37/22.79 | | % 152.37/22.79 | | COMBINE_EQS: (13), (18) imply: % 152.37/22.79 | | (19) all_4_1 = e2 % 152.37/22.79 | | % 152.37/22.79 | | REDUCE: (3), (19) imply: % 152.37/22.79 | | (20) $false % 152.37/22.79 | | % 152.37/22.79 | | CLOSE: (20) is inconsistent. % 152.37/22.79 | | % 152.37/22.79 | Case 2: % 152.37/22.79 | | % 152.37/22.79 | | (21) all_54_5 = e1 | all_54_5 = e0 % 152.37/22.79 | | % 152.37/22.79 | | BETA: splitting (21) gives: % 152.37/22.79 | | % 152.37/22.79 | | Case 1: % 152.37/22.79 | | | % 152.37/22.79 | | | (22) all_54_5 = e1 % 152.37/22.79 | | | % 152.37/22.79 | | | COMBINE_EQS: (13), (22) imply: % 152.37/22.79 | | | (23) all_4_1 = e1 % 152.37/22.79 | | | % 152.37/22.79 | | | REDUCE: (6), (23) imply: % 152.37/22.79 | | | (24) ~ (all_52_13 = e1) % 152.37/22.79 | | | % 152.37/22.79 | | | REF_CLOSE: (2), (4), (5), (7), (8), (9), (10), (11), (12), (14), (16), % 152.37/22.79 | | | (17), (23), (24) are inconsistent by sub-proof #586. % 152.37/22.79 | | | % 152.37/22.79 | | Case 2: % 152.37/22.79 | | | % 152.37/22.79 | | | (25) all_54_5 = e0 % 152.37/22.79 | | | % 152.37/22.79 | | | COMBINE_EQS: (13), (25) imply: % 152.37/22.79 | | | (26) all_4_1 = e0 % 152.37/22.79 | | | % 152.37/22.79 | | | REDUCE: (1), (26) imply: % 152.37/22.79 | | | (27) $false % 152.37/22.79 | | | % 152.37/22.79 | | | CLOSE: (27) is inconsistent. % 152.37/22.79 | | | % 152.37/22.79 | | End of split % 152.37/22.79 | | % 152.37/22.79 | End of split % 152.37/22.79 | % 152.37/22.79 End of proof % 152.37/22.79 % 152.37/22.79 Sub-proof #586 shows that the following formulas are inconsistent: % 152.37/22.79 ---------------------------------------------------------------- % 152.37/22.79 (1) ~ (all_52_13 = e1) % 152.37/22.79 (2) all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1 % 152.37/22.79 (3) all_58_9 = all_52_12 % 152.37/22.79 (4) op(e0, all_52_12) = all_56_6 % 152.37/22.79 (5) op(e0, e1) = e3 % 152.37/22.79 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 152.37/22.79 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 152.37/22.79 (7) ~ (all_52_14 = e1) % 152.37/22.79 (8) op(e0, all_4_1) = all_4_0 % 152.37/22.79 (9) ~ (all_4_2 = e1) % 152.37/22.79 (10) all_58_11 = all_52_14 % 152.37/22.79 (11) all_4_1 = e1 % 152.37/22.79 (12) all_58_15 = all_4_2 % 152.37/22.79 (13) all_58_10 = all_52_13 % 152.37/22.79 (14) ~ (all_4_0 = e3) % 152.37/22.79 % 152.37/22.79 Begin of proof % 152.37/22.79 | % 152.37/22.79 | REDUCE: (8), (11) imply: % 152.37/22.79 | (15) op(e0, e1) = all_4_0 % 152.37/22.79 | % 152.37/22.79 | BETA: splitting (2) gives: % 152.37/22.79 | % 152.37/22.79 | Case 1: % 152.37/22.79 | | % 152.37/22.79 | | (16) all_58_9 = e1 % 152.37/22.79 | | % 152.37/22.79 | | COMBINE_EQS: (3), (16) imply: % 152.37/22.79 | | (17) all_52_12 = e1 % 152.37/22.79 | | % 152.37/22.79 | | REDUCE: (4), (17) imply: % 152.37/22.79 | | (18) op(e0, e1) = all_56_6 % 152.37/22.79 | | % 152.37/22.79 | | GROUND_INST: instantiating (6) with e3, all_56_6, e1, e0, simplifying with % 152.37/22.79 | | (5), (18) gives: % 152.37/22.79 | | (19) all_56_6 = e3 % 152.37/22.79 | | % 152.37/22.79 | | GROUND_INST: instantiating (6) with all_4_0, all_56_6, e1, e0, simplifying % 152.37/22.79 | | with (15), (18) gives: % 152.37/22.79 | | (20) all_56_6 = all_4_0 % 152.37/22.79 | | % 152.37/22.79 | | COMBINE_EQS: (19), (20) imply: % 152.37/22.79 | | (21) all_4_0 = e3 % 152.37/22.79 | | % 152.37/22.79 | | REDUCE: (14), (21) imply: % 152.37/22.79 | | (22) $false % 152.37/22.79 | | % 152.37/22.79 | | CLOSE: (22) is inconsistent. % 152.37/22.79 | | % 152.37/22.79 | Case 2: % 152.37/22.79 | | % 152.37/22.79 | | (23) all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1 % 152.37/22.79 | | % 152.37/22.79 | | REF_CLOSE: (1), (7), (9), (10), (12), (13), (23) are inconsistent by % 152.37/22.79 | | sub-proof #587. % 152.37/22.79 | | % 152.37/22.79 | End of split % 152.37/22.79 | % 152.37/22.79 End of proof % 152.37/22.79 % 152.37/22.79 Sub-proof #587 shows that the following formulas are inconsistent: % 152.37/22.79 ---------------------------------------------------------------- % 152.37/22.79 (1) ~ (all_52_13 = e1) % 152.37/22.79 (2) ~ (all_52_14 = e1) % 152.37/22.79 (3) ~ (all_4_2 = e1) % 152.37/22.79 (4) all_58_11 = all_52_14 % 152.37/22.79 (5) all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1 % 152.37/22.79 (6) all_58_15 = all_4_2 % 152.37/22.79 (7) all_58_10 = all_52_13 % 152.37/22.79 % 152.37/22.79 Begin of proof % 152.37/22.79 | % 152.37/22.79 | BETA: splitting (5) gives: % 152.37/22.79 | % 152.37/22.79 | Case 1: % 152.37/22.79 | | % 152.37/22.79 | | (8) all_58_10 = e1 % 152.37/22.79 | | % 152.37/22.79 | | COMBINE_EQS: (7), (8) imply: % 152.37/22.79 | | (9) all_52_13 = e1 % 152.37/22.79 | | % 152.37/22.79 | | REDUCE: (1), (9) imply: % 152.37/22.79 | | (10) $false % 152.37/22.79 | | % 152.37/22.79 | | CLOSE: (10) is inconsistent. % 152.37/22.79 | | % 152.37/22.79 | Case 2: % 152.37/22.79 | | % 152.37/22.79 | | (11) all_58_11 = e1 | all_58_15 = e1 % 152.37/22.79 | | % 152.37/22.79 | | REF_CLOSE: (2), (3), (4), (6), (11) are inconsistent by sub-proof #672. % 152.37/22.79 | | % 152.37/22.79 | End of split % 152.37/22.79 | % 152.37/22.79 End of proof % 152.37/22.79 % 152.37/22.79 Sub-proof #588 shows that the following formulas are inconsistent: % 152.37/22.79 ---------------------------------------------------------------- % 152.37/22.79 (1) ~ (all_52_4 = all_52_8) % 152.37/22.79 (2) op(e2, all_8_1) = all_8_0 % 152.37/22.79 (3) ~ (all_8_1 = e1) % 152.37/22.79 (4) ~ (all_52_9 = e2) % 152.37/22.79 (5) all_54_0 = all_10_2 % 152.37/22.79 (6) ~ (all_8_0 = e1) % 152.37/22.79 (7) all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2 % 152.37/22.79 (8) ~ (all_52_12 = all_52_13) % 152.37/22.79 (9) ~ (all_6_2 = e3) % 152.37/22.79 (10) ~ (all_8_1 = e3) % 152.37/22.79 (11) ~ (e3 = e2) % 152.37/22.79 (12) op(e0, e0) = all_4_2 % 152.37/22.79 (13) all_58_4 = all_52_8 % 152.37/22.79 (14) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 152.37/22.79 (15) all_54_15 = all_4_2 % 152.37/22.79 (16) ~ (all_10_1 = e1) % 152.37/22.79 (17) all_56_1 = all_10_2 % 152.37/22.79 (18) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0 % 152.37/22.79 (19) all_58_5 = all_52_9 % 152.37/22.79 (20) all_54_1 = all_52_4 % 152.37/22.79 (21) ~ (all_52_13 = e2) % 152.37/22.79 (22) ~ (all_10_2 = e2) % 152.37/22.79 (23) all_58_1 = all_52_4 % 152.37/22.79 (24) op(e3, e3) = all_10_2 % 152.37/22.79 (25) all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1 % 152.37/22.79 (26) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 152.37/22.79 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 152.37/22.79 (27) all_56_7 = all_52_12 % 152.37/22.79 (28) ~ (all_10_1 = e2) % 152.37/22.79 (29) ~ (all_52_9 = e3) % 152.37/22.79 (30) all_58_8 = all_6_2 % 152.37/22.79 (31) ~ (all_56_1 = e0) | all_56_7 = e3 % 152.37/22.79 (32) all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3 % 152.37/22.79 (33) all_54_7 = all_52_13 % 152.37/22.79 (34) ~ (all_52_13 = all_4_2) % 152.37/22.79 (35) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0 % 152.37/22.79 (36) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0 % 152.37/22.79 (37) ~ (all_6_2 = e2) % 152.37/22.79 (38) op(e3, e3) = all_8_1 % 152.37/22.79 (39) ~ (all_52_12 = all_4_2) % 152.37/22.79 (40) op(all_10_2, all_10_2) = all_10_1 % 152.37/22.79 (41) all_58_0 = all_10_2 % 152.37/22.79 (42) ~ (all_52_4 = all_52_12) % 152.37/22.79 (43) op(e2, e0) = all_52_13 % 152.37/22.79 (44) ~ (all_52_8 = all_52_12) % 152.37/22.79 (45) ~ (all_52_4 = all_10_2) % 152.37/22.79 % 152.37/22.79 Begin of proof % 152.37/22.79 | % 152.37/22.79 | GROUND_INST: instantiating (26) with all_10_2, all_8_1, e3, e3, simplifying % 152.37/22.79 | with (24), (38) gives: % 152.37/22.79 | (46) all_10_2 = all_8_1 % 152.37/22.79 | % 152.37/22.79 | COMBINE_EQS: (5), (46) imply: % 152.37/22.79 | (47) all_54_0 = all_8_1 % 152.37/22.79 | % 152.37/22.79 | COMBINE_EQS: (17), (46) imply: % 152.37/22.79 | (48) all_56_1 = all_8_1 % 152.37/22.79 | % 152.37/22.79 | COMBINE_EQS: (41), (46) imply: % 152.37/22.79 | (49) all_58_0 = all_8_1 % 152.37/22.79 | % 152.37/22.79 | REDUCE: (45), (46) imply: % 152.37/22.79 | (50) ~ (all_52_4 = all_8_1) % 152.37/22.79 | % 152.37/22.79 | REDUCE: (22), (46) imply: % 152.37/22.79 | (51) ~ (all_8_1 = e2) % 152.37/22.79 | % 152.37/22.79 | REDUCE: (40), (46) imply: % 152.37/22.79 | (52) op(all_8_1, all_8_1) = all_10_1 % 152.37/22.79 | % 152.37/22.79 | BETA: splitting (14) gives: % 152.37/22.79 | % 152.37/22.79 | Case 1: % 152.37/22.79 | | % 152.37/22.79 | | (53) all_54_0 = e3 % 152.37/22.79 | | % 152.37/22.79 | | REF_CLOSE: (10), (47), (53) are inconsistent by sub-proof #600. % 152.37/22.79 | | % 152.37/22.79 | Case 2: % 152.37/22.79 | | % 152.37/22.79 | | (54) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 152.37/22.79 | | % 152.37/22.79 | | BETA: splitting (54) gives: % 152.37/22.79 | | % 152.37/22.79 | | Case 1: % 152.37/22.79 | | | % 152.37/22.79 | | | (55) all_54_0 = e2 % 152.37/22.79 | | | % 152.37/22.79 | | | REF_CLOSE: (47), (51), (55) are inconsistent by sub-proof #599. % 152.37/22.79 | | | % 152.37/22.79 | | Case 2: % 152.37/22.79 | | | % 152.37/22.79 | | | (56) all_54_0 = e1 | all_54_0 = e0 % 152.37/22.79 | | | % 152.37/22.79 | | | BETA: splitting (56) gives: % 152.37/22.79 | | | % 152.37/22.79 | | | Case 1: % 152.37/22.79 | | | | % 152.37/22.79 | | | | (57) all_54_0 = e1 % 152.37/22.79 | | | | % 152.37/22.79 | | | | REF_CLOSE: (3), (47), (57) are inconsistent by sub-proof #598. % 152.37/22.79 | | | | % 152.37/22.79 | | | Case 2: % 152.37/22.79 | | | | % 152.37/22.79 | | | | (58) all_54_0 = e0 % 152.37/22.79 | | | | % 152.37/22.79 | | | | COMBINE_EQS: (47), (58) imply: % 152.37/22.79 | | | | (59) all_8_1 = e0 % 152.37/22.79 | | | | % 152.37/22.79 | | | | SIMP: (59) implies: % 152.37/22.79 | | | | (60) all_8_1 = e0 % 152.37/22.79 | | | | % 152.37/22.79 | | | | COMBINE_EQS: (48), (60) imply: % 152.37/22.79 | | | | (61) all_56_1 = e0 % 152.37/22.79 | | | | % 152.37/22.79 | | | | COMBINE_EQS: (49), (60) imply: % 152.37/22.79 | | | | (62) all_58_0 = e0 % 152.37/22.79 | | | | % 152.37/22.79 | | | | REDUCE: (50), (60) imply: % 152.37/22.79 | | | | (63) ~ (all_52_4 = e0) % 152.37/22.79 | | | | % 152.37/22.79 | | | | REDUCE: (3), (60) imply: % 152.37/22.79 | | | | (64) ~ (e1 = e0) % 152.37/22.79 | | | | % 152.37/22.79 | | | | SIMP: (64) implies: % 152.37/22.79 | | | | (65) ~ (e1 = e0) % 152.37/22.79 | | | | % 152.37/22.79 | | | | REDUCE: (52), (60) imply: % 152.37/22.79 | | | | (66) op(e0, e0) = all_10_1 % 152.37/22.79 | | | | % 152.37/22.79 | | | | REDUCE: (2), (60) imply: % 152.37/22.79 | | | | (67) op(e2, e0) = all_8_0 % 152.37/22.79 | | | | % 152.37/22.79 | | | | BETA: splitting (31) gives: % 152.37/22.79 | | | | % 152.37/22.79 | | | | Case 1: % 152.37/22.79 | | | | | % 152.37/22.79 | | | | | (68) ~ (all_56_1 = e0) % 152.37/22.79 | | | | | % 152.37/22.79 | | | | | REDUCE: (61), (68) imply: % 152.37/22.79 | | | | | (69) $false % 152.37/22.79 | | | | | % 152.37/22.79 | | | | | CLOSE: (69) is inconsistent. % 152.37/22.79 | | | | | % 152.37/22.79 | | | | Case 2: % 152.37/22.79 | | | | | % 152.37/22.79 | | | | | (70) all_56_7 = e3 % 152.37/22.79 | | | | | % 152.37/22.79 | | | | | COMBINE_EQS: (27), (70) imply: % 152.37/22.79 | | | | | (71) all_52_12 = e3 % 152.37/22.79 | | | | | % 152.37/22.79 | | | | | REDUCE: (42), (71) imply: % 152.37/22.79 | | | | | (72) ~ (all_52_4 = e3) % 152.37/22.79 | | | | | % 152.37/22.79 | | | | | REDUCE: (44), (71) imply: % 152.37/22.79 | | | | | (73) ~ (all_52_8 = e3) % 152.37/22.79 | | | | | % 152.37/22.79 | | | | | REDUCE: (8), (71) imply: % 152.37/22.79 | | | | | (74) ~ (all_52_13 = e3) % 152.37/22.79 | | | | | % 152.37/22.79 | | | | | SIMP: (74) implies: % 152.37/22.79 | | | | | (75) ~ (all_52_13 = e3) % 152.37/22.79 | | | | | % 152.37/22.79 | | | | | REDUCE: (39), (71) imply: % 152.37/22.79 | | | | | (76) ~ (all_4_2 = e3) % 152.37/22.79 | | | | | % 152.37/22.79 | | | | | SIMP: (76) implies: % 152.37/22.79 | | | | | (77) ~ (all_4_2 = e3) % 152.37/22.79 | | | | | % 152.37/22.79 | | | | | BETA: splitting (32) gives: % 152.37/22.79 | | | | | % 152.37/22.79 | | | | | Case 1: % 152.37/22.79 | | | | | | % 152.37/22.79 | | | | | | (78) all_58_4 = e3 % 152.37/22.79 | | | | | | % 152.37/22.79 | | | | | | COMBINE_EQS: (13), (78) imply: % 152.37/22.79 | | | | | | (79) all_52_8 = e3 % 152.37/22.79 | | | | | | % 152.37/22.79 | | | | | | REDUCE: (73), (79) imply: % 152.37/22.79 | | | | | | (80) $false % 152.37/22.79 | | | | | | % 152.37/22.79 | | | | | | CLOSE: (80) is inconsistent. % 152.37/22.79 | | | | | | % 152.37/22.79 | | | | | Case 2: % 152.37/22.79 | | | | | | % 152.37/22.79 | | | | | | (81) all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3 % 152.37/22.79 | | | | | | % 152.37/22.79 | | | | | | BETA: splitting (81) gives: % 152.37/22.79 | | | | | | % 152.37/22.79 | | | | | | Case 1: % 152.37/22.79 | | | | | | | % 152.37/22.79 | | | | | | | (82) all_58_5 = e3 % 152.37/22.79 | | | | | | | % 152.37/22.79 | | | | | | | COMBINE_EQS: (19), (82) imply: % 152.37/22.79 | | | | | | | (83) all_52_9 = e3 % 152.37/22.79 | | | | | | | % 152.37/22.79 | | | | | | | REDUCE: (29), (83) imply: % 152.37/22.79 | | | | | | | (84) $false % 152.37/22.79 | | | | | | | % 152.37/22.79 | | | | | | | CLOSE: (84) is inconsistent. % 152.37/22.79 | | | | | | | % 152.37/22.79 | | | | | | Case 2: % 152.37/22.79 | | | | | | | % 152.37/22.79 | | | | | | | (85) all_58_8 = e3 | all_58_14 = e3 % 152.37/22.79 | | | | | | | % 152.37/22.79 | | | | | | | BETA: splitting (7) gives: % 152.37/22.79 | | | | | | | % 152.37/22.79 | | | | | | | Case 1: % 152.37/22.79 | | | | | | | | % 152.37/22.79 | | | | | | | | (86) all_58_4 = e2 % 152.37/22.79 | | | | | | | | % 152.37/22.79 | | | | | | | | COMBINE_EQS: (13), (86) imply: % 152.37/22.79 | | | | | | | | (87) all_52_8 = e2 % 152.37/22.79 | | | | | | | | % 152.37/22.79 | | | | | | | | REDUCE: (1), (87) imply: % 152.37/22.79 | | | | | | | | (88) ~ (all_52_4 = e2) % 152.37/22.79 | | | | | | | | % 152.37/22.79 | | | | | | | | REF_CLOSE: (6), (12), (15), (16), (18), (20), (21), (23), (25), % 152.37/22.79 | | | | | | | | (26), (28), (33), (34), (35), (36), (43), (62), (63), % 152.37/22.79 | | | | | | | | (65), (66), (67), (72), (75), (77), (88) are % 152.37/22.79 | | | | | | | | inconsistent by sub-proof #592. % 152.37/22.79 | | | | | | | | % 152.37/22.79 | | | | | | | Case 2: % 152.37/22.79 | | | | | | | | % 152.37/22.79 | | | | | | | | (89) all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2 % 152.37/22.79 | | | | | | | | % 152.37/22.79 | | | | | | | | REF_CLOSE: (4), (9), (11), (19), (30), (37), (85), (89) are % 152.37/22.79 | | | | | | | | inconsistent by sub-proof #589. % 152.37/22.79 | | | | | | | | % 152.37/22.79 | | | | | | | End of split % 152.37/22.79 | | | | | | | % 152.37/22.79 | | | | | | End of split % 152.37/22.79 | | | | | | % 152.37/22.79 | | | | | End of split % 152.37/22.79 | | | | | % 152.37/22.79 | | | | End of split % 152.37/22.79 | | | | % 152.37/22.79 | | | End of split % 152.37/22.79 | | | % 152.37/22.79 | | End of split % 152.37/22.79 | | % 152.37/22.79 | End of split % 152.37/22.79 | % 152.37/22.79 End of proof % 152.37/22.79 % 152.37/22.79 Sub-proof #589 shows that the following formulas are inconsistent: % 152.37/22.79 ---------------------------------------------------------------- % 152.37/22.79 (1) ~ (all_52_9 = e2) % 152.37/22.79 (2) ~ (all_6_2 = e3) % 152.37/22.79 (3) ~ (e3 = e2) % 152.37/22.79 (4) all_58_5 = all_52_9 % 152.37/22.79 (5) all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2 % 152.37/22.79 (6) all_58_8 = e3 | all_58_14 = e3 % 152.37/22.79 (7) all_58_8 = all_6_2 % 152.37/22.79 (8) ~ (all_6_2 = e2) % 152.37/22.79 % 152.37/22.79 Begin of proof % 152.37/22.79 | % 152.37/22.79 | BETA: splitting (5) gives: % 152.37/22.79 | % 152.37/22.79 | Case 1: % 152.37/22.79 | | % 152.37/22.79 | | (9) all_58_5 = e2 % 152.37/22.79 | | % 152.37/22.79 | | COMBINE_EQS: (4), (9) imply: % 152.37/22.79 | | (10) all_52_9 = e2 % 152.37/22.79 | | % 152.37/22.79 | | REDUCE: (1), (10) imply: % 152.37/22.79 | | (11) $false % 152.37/22.79 | | % 152.37/22.79 | | CLOSE: (11) is inconsistent. % 152.37/22.79 | | % 152.37/22.79 | Case 2: % 152.37/22.79 | | % 152.37/22.79 | | (12) all_58_8 = e2 | all_58_14 = e2 % 152.37/22.79 | | % 152.37/22.79 | | REF_CLOSE: (2), (3), (6), (7), (8), (12) are inconsistent by sub-proof #590. % 152.37/22.79 | | % 152.37/22.79 | End of split % 152.37/22.79 | % 152.37/22.79 End of proof % 152.37/22.79 % 152.37/22.79 Sub-proof #590 shows that the following formulas are inconsistent: % 152.37/22.79 ---------------------------------------------------------------- % 152.37/22.79 (1) ~ (all_6_2 = e3) % 152.37/22.79 (2) ~ (e3 = e2) % 152.37/22.79 (3) all_58_8 = e2 | all_58_14 = e2 % 152.37/22.79 (4) all_58_8 = e3 | all_58_14 = e3 % 152.37/22.79 (5) all_58_8 = all_6_2 % 152.37/22.79 (6) ~ (all_6_2 = e2) % 152.37/22.79 % 152.37/22.79 Begin of proof % 152.37/22.79 | % 152.37/22.79 | BETA: splitting (3) gives: % 152.37/22.79 | % 152.37/22.79 | Case 1: % 152.37/22.79 | | % 152.37/22.79 | | (7) all_58_8 = e2 % 152.37/22.79 | | % 152.37/22.79 | | COMBINE_EQS: (5), (7) imply: % 152.37/22.79 | | (8) all_6_2 = e2 % 152.37/22.79 | | % 152.37/22.79 | | SIMP: (8) implies: % 152.37/22.79 | | (9) all_6_2 = e2 % 152.37/22.79 | | % 152.37/22.79 | | REDUCE: (6), (9) imply: % 152.37/22.79 | | (10) $false % 152.37/22.79 | | % 152.37/22.79 | | CLOSE: (10) is inconsistent. % 152.37/22.79 | | % 152.37/22.79 | Case 2: % 152.37/22.79 | | % 152.37/22.79 | | (11) all_58_14 = e2 % 152.37/22.79 | | % 152.37/22.79 | | REF_CLOSE: (1), (2), (4), (5), (11) are inconsistent by sub-proof #591. % 152.37/22.79 | | % 152.37/22.79 | End of split % 152.37/22.79 | % 152.37/22.79 End of proof % 152.37/22.79 % 152.37/22.79 Sub-proof #591 shows that the following formulas are inconsistent: % 152.37/22.79 ---------------------------------------------------------------- % 152.37/22.79 (1) ~ (all_6_2 = e3) % 152.37/22.79 (2) ~ (e3 = e2) % 152.37/22.79 (3) all_58_8 = e3 | all_58_14 = e3 % 152.37/22.79 (4) all_58_8 = all_6_2 % 152.37/22.79 (5) all_58_14 = e2 % 152.37/22.79 % 152.37/22.79 Begin of proof % 152.37/22.79 | % 152.37/22.79 | BETA: splitting (3) gives: % 152.37/22.79 | % 152.37/22.79 | Case 1: % 152.37/22.79 | | % 152.37/22.79 | | (6) all_58_8 = e3 % 152.37/22.79 | | % 152.37/22.79 | | COMBINE_EQS: (4), (6) imply: % 152.37/22.79 | | (7) all_6_2 = e3 % 152.37/22.79 | | % 152.37/22.79 | | REDUCE: (1), (7) imply: % 152.37/22.79 | | (8) $false % 152.37/22.79 | | % 152.37/22.79 | | CLOSE: (8) is inconsistent. % 152.37/22.79 | | % 152.37/22.79 | Case 2: % 152.37/22.79 | | % 152.37/22.79 | | (9) all_58_14 = e3 % 152.37/22.79 | | % 152.37/22.79 | | COMBINE_EQS: (5), (9) imply: % 152.37/22.79 | | (10) e3 = e2 % 152.37/22.79 | | % 152.37/22.79 | | REDUCE: (2), (10) imply: % 152.37/22.79 | | (11) $false % 152.37/22.79 | | % 152.37/22.79 | | CLOSE: (11) is inconsistent. % 152.37/22.79 | | % 152.37/22.79 | End of split % 152.37/22.79 | % 152.37/22.79 End of proof % 152.37/22.79 % 152.37/22.79 Sub-proof #592 shows that the following formulas are inconsistent: % 152.37/22.79 ---------------------------------------------------------------- % 152.37/22.79 (1) ~ (all_8_0 = e1) % 152.37/22.79 (2) op(e0, e0) = all_4_2 % 152.37/22.79 (3) all_54_15 = all_4_2 % 152.37/22.79 (4) ~ (all_10_1 = e1) % 152.37/22.79 (5) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0 % 152.37/22.79 (6) all_54_1 = all_52_4 % 152.37/22.79 (7) ~ (all_52_13 = e2) % 152.37/22.79 (8) all_58_1 = all_52_4 % 152.37/22.79 (9) all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1 % 152.37/22.79 (10) ~ (e1 = e0) % 152.37/22.79 (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 152.37/22.79 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 152.37/22.79 (12) ~ (all_10_1 = e2) % 152.37/22.79 (13) ~ (all_52_4 = e0) % 152.37/22.79 (14) all_58_0 = e0 % 152.37/22.79 (15) op(e0, e0) = all_10_1 % 152.37/22.79 (16) all_54_7 = all_52_13 % 152.37/22.79 (17) ~ (all_52_13 = all_4_2) % 152.37/22.79 (18) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0 % 152.37/22.79 (19) ~ (all_52_4 = e2) % 152.37/22.79 (20) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0 % 152.37/22.79 (21) ~ (all_52_13 = e3) % 152.37/22.79 (22) ~ (all_4_2 = e3) % 152.37/22.79 (23) ~ (all_52_4 = e3) % 152.37/22.79 (24) op(e2, e0) = all_52_13 % 152.37/22.79 (25) op(e2, e0) = all_8_0 % 152.37/22.79 % 152.37/22.79 Begin of proof % 152.37/22.79 | % 152.37/22.79 | BETA: splitting (20) gives: % 152.37/22.79 | % 152.37/22.79 | Case 1: % 152.37/22.79 | | % 152.37/22.79 | | (26) all_54_1 = e3 % 152.37/22.79 | | % 152.37/22.79 | | REF_CLOSE: (6), (23), (26) are inconsistent by sub-proof #722. % 152.37/22.79 | | % 152.37/22.79 | Case 2: % 152.37/22.79 | | % 152.37/22.79 | | (27) all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0 % 152.37/22.79 | | % 152.37/22.79 | | BETA: splitting (27) gives: % 152.37/22.79 | | % 152.37/22.79 | | Case 1: % 152.37/22.79 | | | % 152.37/22.79 | | | (28) all_54_1 = e2 % 152.37/22.79 | | | % 152.37/22.79 | | | REF_CLOSE: (6), (19), (28) are inconsistent by sub-proof #721. % 152.37/22.79 | | | % 152.37/22.79 | | Case 2: % 152.37/22.79 | | | % 152.37/22.79 | | | (29) all_54_1 = e1 | all_54_1 = e0 % 152.37/22.79 | | | % 152.37/22.79 | | | BETA: splitting (9) gives: % 152.37/22.79 | | | % 152.37/22.79 | | | Case 1: % 152.37/22.79 | | | | % 152.37/22.79 | | | | (30) all_58_0 = e1 % 152.37/22.79 | | | | % 152.37/22.79 | | | | REF_CLOSE: (10), (14), (30) are inconsistent by sub-proof #730. % 152.37/22.79 | | | | % 152.37/22.79 | | | Case 2: % 152.37/22.79 | | | | % 152.37/22.79 | | | | (31) all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1 % 152.37/22.79 | | | | % 152.37/22.79 | | | | BETA: splitting (31) gives: % 152.37/22.79 | | | | % 152.37/22.79 | | | | Case 1: % 152.37/22.79 | | | | | % 152.37/22.79 | | | | | % 152.37/22.79 | | | | | GROUND_INST: instantiating (11) with all_4_2, all_10_1, e0, e0, % 152.37/22.79 | | | | | simplifying with (2), (15) gives: % 152.37/22.79 | | | | | (32) all_10_1 = all_4_2 % 152.37/22.79 | | | | | % 152.37/22.79 | | | | | GROUND_INST: instantiating (11) with all_52_13, all_8_0, e0, e2, % 152.37/22.79 | | | | | simplifying with (24), (25) gives: % 152.37/22.79 | | | | | (33) all_52_13 = all_8_0 % 152.37/22.79 | | | | | % 152.37/22.79 | | | | | COMBINE_EQS: (16), (33) imply: % 152.37/22.79 | | | | | (34) all_54_7 = all_8_0 % 152.37/22.79 | | | | | % 152.37/22.79 | | | | | REDUCE: (17), (33) imply: % 152.37/22.79 | | | | | (35) ~ (all_8_0 = all_4_2) % 152.37/22.79 | | | | | % 152.37/22.79 | | | | | REDUCE: (21), (33) imply: % 152.37/22.79 | | | | | (36) ~ (all_8_0 = e3) % 152.37/22.79 | | | | | % 152.37/22.79 | | | | | REDUCE: (7), (33) imply: % 152.37/22.79 | | | | | (37) ~ (all_8_0 = e2) % 152.37/22.79 | | | | | % 152.37/22.79 | | | | | REDUCE: (12), (32) imply: % 152.37/22.79 | | | | | (38) ~ (all_4_2 = e2) % 152.37/22.79 | | | | | % 152.37/22.79 | | | | | REDUCE: (4), (32) imply: % 152.37/22.79 | | | | | (39) ~ (all_4_2 = e1) % 152.37/22.79 | | | | | % 152.37/22.79 | | | | | BETA: splitting (18) gives: % 152.37/22.79 | | | | | % 152.37/22.79 | | | | | Case 1: % 152.37/22.79 | | | | | | % 152.37/22.79 | | | | | | (40) all_54_15 = e3 % 152.37/22.79 | | | | | | % 152.37/22.79 | | | | | | COMBINE_EQS: (3), (40) imply: % 152.37/22.79 | | | | | | (41) all_4_2 = e3 % 152.37/22.79 | | | | | | % 152.37/22.79 | | | | | | REDUCE: (22), (41) imply: % 152.37/22.79 | | | | | | (42) $false % 152.37/22.79 | | | | | | % 152.37/22.79 | | | | | | CLOSE: (42) is inconsistent. % 152.37/22.79 | | | | | | % 152.37/22.79 | | | | | Case 2: % 152.37/22.79 | | | | | | % 152.37/22.79 | | | | | | (43) all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0 % 152.37/22.79 | | | | | | % 152.37/22.79 | | | | | | BETA: splitting (5) gives: % 152.37/22.79 | | | | | | % 152.37/22.79 | | | | | | Case 1: % 152.37/22.79 | | | | | | | % 152.37/22.79 | | | | | | | (44) all_54_7 = e3 % 152.37/22.79 | | | | | | | % 152.37/22.79 | | | | | | | COMBINE_EQS: (34), (44) imply: % 152.37/22.79 | | | | | | | (45) all_8_0 = e3 % 152.37/22.79 | | | | | | | % 152.37/22.79 | | | | | | | SIMP: (45) implies: % 152.37/22.79 | | | | | | | (46) all_8_0 = e3 % 152.37/22.79 | | | | | | | % 152.37/22.79 | | | | | | | REDUCE: (36), (46) imply: % 152.37/22.79 | | | | | | | (47) $false % 152.37/22.79 | | | | | | | % 152.37/22.79 | | | | | | | CLOSE: (47) is inconsistent. % 152.37/22.79 | | | | | | | % 152.37/22.79 | | | | | | Case 2: % 152.37/22.79 | | | | | | | % 152.37/22.79 | | | | | | | (48) all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0 % 152.37/22.79 | | | | | | | % 152.37/22.79 | | | | | | | BETA: splitting (48) gives: % 152.37/22.79 | | | | | | | % 152.37/22.79 | | | | | | | Case 1: % 152.37/22.79 | | | | | | | | % 152.37/22.79 | | | | | | | | (49) all_54_7 = e2 % 152.37/22.79 | | | | | | | | % 152.37/22.79 | | | | | | | | COMBINE_EQS: (34), (49) imply: % 152.37/22.79 | | | | | | | | (50) all_8_0 = e2 % 152.37/22.79 | | | | | | | | % 152.37/22.79 | | | | | | | | SIMP: (50) implies: % 152.37/22.79 | | | | | | | | (51) all_8_0 = e2 % 152.37/22.79 | | | | | | | | % 152.37/22.79 | | | | | | | | REDUCE: (37), (51) imply: % 152.37/22.79 | | | | | | | | (52) $false % 152.37/22.79 | | | | | | | | % 152.37/22.79 | | | | | | | | CLOSE: (52) is inconsistent. % 152.37/22.79 | | | | | | | | % 152.37/22.79 | | | | | | | Case 2: % 152.37/22.79 | | | | | | | | % 152.37/22.79 | | | | | | | | (53) all_54_7 = e1 | all_54_7 = e0 % 152.37/22.79 | | | | | | | | % 152.37/22.79 | | | | | | | | BETA: splitting (43) gives: % 152.37/22.79 | | | | | | | | % 152.37/22.79 | | | | | | | | Case 1: % 152.37/22.79 | | | | | | | | | % 152.37/22.79 | | | | | | | | | (54) all_54_15 = e2 % 152.37/22.79 | | | | | | | | | % 152.37/22.79 | | | | | | | | | COMBINE_EQS: (3), (54) imply: % 152.37/22.79 | | | | | | | | | (55) all_4_2 = e2 % 152.37/22.79 | | | | | | | | | % 152.37/22.79 | | | | | | | | | REDUCE: (38), (55) imply: % 152.37/22.79 | | | | | | | | | (56) $false % 152.37/22.79 | | | | | | | | | % 152.37/22.79 | | | | | | | | | CLOSE: (56) is inconsistent. % 152.37/22.79 | | | | | | | | | % 152.37/22.79 | | | | | | | | Case 2: % 152.37/22.79 | | | | | | | | | % 152.37/22.79 | | | | | | | | | (57) all_54_15 = e1 | all_54_15 = e0 % 152.37/22.79 | | | | | | | | | % 152.37/22.79 | | | | | | | | | BETA: splitting (57) gives: % 152.37/22.79 | | | | | | | | | % 152.37/22.79 | | | | | | | | | Case 1: % 152.37/22.79 | | | | | | | | | | % 152.37/22.79 | | | | | | | | | | (58) all_54_15 = e1 % 152.37/22.79 | | | | | | | | | | % 152.37/22.79 | | | | | | | | | | COMBINE_EQS: (3), (58) imply: % 152.37/22.79 | | | | | | | | | | (59) all_4_2 = e1 % 152.37/22.79 | | | | | | | | | | % 152.37/22.79 | | | | | | | | | | REDUCE: (39), (59) imply: % 152.37/22.79 | | | | | | | | | | (60) $false % 152.37/22.79 | | | | | | | | | | % 152.37/22.79 | | | | | | | | | | CLOSE: (60) is inconsistent. % 152.37/22.79 | | | | | | | | | | % 152.37/22.79 | | | | | | | | | Case 2: % 152.37/22.79 | | | | | | | | | | % 152.37/22.79 | | | | | | | | | | (61) all_54_15 = e0 % 152.37/22.79 | | | | | | | | | | % 152.37/22.79 | | | | | | | | | | COMBINE_EQS: (3), (61) imply: % 152.37/22.79 | | | | | | | | | | (62) all_4_2 = e0 % 152.37/22.79 | | | | | | | | | | % 152.37/22.79 | | | | | | | | | | REDUCE: (35), (62) imply: % 152.37/22.79 | | | | | | | | | | (63) ~ (all_8_0 = e0) % 152.37/22.79 | | | | | | | | | | % 152.37/22.79 | | | | | | | | | | BETA: splitting (53) gives: % 152.37/22.79 | | | | | | | | | | % 152.37/22.79 | | | | | | | | | | Case 1: % 152.37/22.79 | | | | | | | | | | | % 152.37/22.79 | | | | | | | | | | | (64) all_54_7 = e1 % 152.37/22.79 | | | | | | | | | | | % 152.37/22.79 | | | | | | | | | | | COMBINE_EQS: (34), (64) imply: % 152.37/22.79 | | | | | | | | | | | (65) all_8_0 = e1 % 152.37/22.79 | | | | | | | | | | | % 152.37/22.79 | | | | | | | | | | | SIMP: (65) implies: % 152.37/22.79 | | | | | | | | | | | (66) all_8_0 = e1 % 152.37/22.79 | | | | | | | | | | | % 152.37/22.79 | | | | | | | | | | | REDUCE: (1), (66) imply: % 152.37/22.79 | | | | | | | | | | | (67) $false % 152.37/22.79 | | | | | | | | | | | % 152.37/22.79 | | | | | | | | | | | CLOSE: (67) is inconsistent. % 152.37/22.79 | | | | | | | | | | | % 152.37/22.79 | | | | | | | | | | Case 2: % 152.37/22.79 | | | | | | | | | | | % 152.37/22.79 | | | | | | | | | | | (68) all_54_7 = e0 % 152.37/22.79 | | | | | | | | | | | % 152.37/22.79 | | | | | | | | | | | COMBINE_EQS: (34), (68) imply: % 152.37/22.79 | | | | | | | | | | | (69) all_8_0 = e0 % 152.37/22.79 | | | | | | | | | | | % 152.37/22.79 | | | | | | | | | | | SIMP: (69) implies: % 152.37/22.79 | | | | | | | | | | | (70) all_8_0 = e0 % 152.37/22.79 | | | | | | | | | | | % 152.37/22.79 | | | | | | | | | | | REDUCE: (63), (70) imply: % 152.37/22.79 | | | | | | | | | | | (71) $false % 152.37/22.79 | | | | | | | | | | | % 152.37/22.79 | | | | | | | | | | | CLOSE: (71) is inconsistent. % 152.37/22.79 | | | | | | | | | | | % 152.37/22.79 | | | | | | | | | | End of split % 152.37/22.79 | | | | | | | | | | % 152.37/22.79 | | | | | | | | | End of split % 152.37/22.79 | | | | | | | | | % 152.37/22.79 | | | | | | | | End of split % 152.37/22.79 | | | | | | | | % 152.37/22.79 | | | | | | | End of split % 152.37/22.79 | | | | | | | % 152.37/22.79 | | | | | | End of split % 152.37/22.79 | | | | | | % 152.37/22.79 | | | | | End of split % 152.37/22.79 | | | | | % 152.37/22.79 | | | | Case 2: % 152.37/22.79 | | | | | % 152.37/22.79 | | | | | (72) ~ (all_58_1 = e1) % 152.37/22.79 | | | | | % 152.37/22.79 | | | | | REF_CLOSE: (6), (8), (13), (29), (72) are inconsistent by sub-proof % 152.37/22.79 | | | | | #593. % 152.37/22.79 | | | | | % 152.37/22.79 | | | | End of split % 152.37/22.79 | | | | % 152.37/22.79 | | | End of split % 152.37/22.79 | | | % 152.37/22.79 | | End of split % 152.37/22.79 | | % 152.37/22.79 | End of split % 152.37/22.79 | % 152.37/22.79 End of proof % 152.37/22.79 % 152.37/22.79 Sub-proof #593 shows that the following formulas are inconsistent: % 152.37/22.79 ---------------------------------------------------------------- % 152.37/22.79 (1) all_54_1 = all_52_4 % 152.37/22.79 (2) all_58_1 = all_52_4 % 152.37/22.79 (3) ~ (all_58_1 = e1) % 152.37/22.79 (4) all_54_1 = e1 | all_54_1 = e0 % 152.37/22.79 (5) ~ (all_52_4 = e0) % 152.37/22.79 % 152.37/22.79 Begin of proof % 152.37/22.79 | % 152.37/22.79 | REDUCE: (2), (3) imply: % 152.37/22.79 | (6) ~ (all_52_4 = e1) % 152.37/22.79 | % 152.37/22.79 | BETA: splitting (4) gives: % 152.37/22.79 | % 152.37/22.79 | Case 1: % 152.37/22.79 | | % 152.37/22.79 | | (7) all_54_1 = e1 % 152.37/22.79 | | % 152.37/22.79 | | REF_CLOSE: (1), (6), (7) are inconsistent by sub-proof #720. % 152.37/22.79 | | % 152.37/22.79 | Case 2: % 152.37/22.79 | | % 152.37/22.79 | | (8) all_54_1 = e0 % 152.37/22.79 | | % 152.37/22.79 | | REF_CLOSE: (1), (5), (8) are inconsistent by sub-proof #719. % 152.37/22.79 | | % 152.37/22.79 | End of split % 152.37/22.79 | % 152.37/22.79 End of proof % 152.37/22.79 % 152.37/22.79 Sub-proof #594 shows that the following formulas are inconsistent: % 152.37/22.79 ---------------------------------------------------------------- % 152.37/22.79 (1) all_58_1 = e2 % 152.37/22.79 (2) all_58_1 = e1 % 152.37/22.79 (3) ~ (e2 = e1) % 152.37/22.79 % 152.37/22.79 Begin of proof % 152.37/22.79 | % 152.37/22.79 | COMBINE_EQS: (1), (2) imply: % 152.37/22.79 | (4) e2 = e1 % 152.37/22.79 | % 152.37/22.79 | SIMP: (4) implies: % 152.37/22.79 | (5) e2 = e1 % 152.37/22.79 | % 152.37/22.79 | REDUCE: (3), (5) imply: % 152.37/22.79 | (6) $false % 152.37/22.79 | % 152.37/22.79 | CLOSE: (6) is inconsistent. % 152.37/22.79 | % 152.37/22.79 End of proof % 152.37/22.79 % 152.37/22.79 Sub-proof #595 shows that the following formulas are inconsistent: % 152.37/22.79 ---------------------------------------------------------------- % 152.37/22.79 (1) all_58_6 = all_52_2 % 152.37/22.79 (2) all_56_11 = e3 % 152.37/22.79 (3) ~ (all_52_3 = e2) % 152.37/22.79 (4) ~ (all_10_2 = e2) % 152.37/22.79 (5) all_58_3 = e3 % 152.37/22.79 (6) all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2 % 152.37/22.79 (7) ~ (all_52_1 = all_52_13) % 152.37/22.79 (8) all_58_3 = e0 % 152.37/22.79 (9) ~ (all_52_2 = e2) % 152.37/22.79 (10) all_58_2 = all_52_1 % 152.37/22.79 (11) ~ (all_56_11 = e0) | all_56_15 = e2 % 152.37/22.79 (12) all_58_0 = all_10_2 % 152.37/22.79 (13) all_56_15 = all_52_13 % 152.37/22.79 (14) all_58_12 = all_52_3 % 152.37/22.79 % 152.37/22.79 Begin of proof % 152.37/22.79 | % 152.37/22.79 | COMBINE_EQS: (5), (8) imply: % 152.37/22.79 | (15) e3 = e0 % 152.37/22.79 | % 152.37/22.79 | COMBINE_EQS: (2), (15) imply: % 152.37/22.79 | (16) all_56_11 = e0 % 152.37/22.79 | % 152.37/22.79 | REF_CLOSE: (1), (3), (4), (6), (7), (9), (10), (11), (12), (13), (14), (16) % 152.37/22.79 | are inconsistent by sub-proof #596. % 152.37/22.79 | % 152.37/22.79 End of proof % 152.37/22.79 % 152.37/22.79 Sub-proof #596 shows that the following formulas are inconsistent: % 152.37/22.79 ---------------------------------------------------------------- % 152.37/22.79 (1) all_58_6 = all_52_2 % 152.37/22.79 (2) ~ (all_52_3 = e2) % 152.37/22.79 (3) ~ (all_10_2 = e2) % 152.37/22.79 (4) all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2 % 152.37/22.79 (5) ~ (all_52_1 = all_52_13) % 152.37/22.79 (6) ~ (all_52_2 = e2) % 152.37/22.79 (7) all_56_11 = e0 % 152.37/22.79 (8) all_58_2 = all_52_1 % 152.37/22.79 (9) ~ (all_56_11 = e0) | all_56_15 = e2 % 152.37/22.79 (10) all_58_0 = all_10_2 % 152.37/22.79 (11) all_56_15 = all_52_13 % 152.37/22.79 (12) all_58_12 = all_52_3 % 152.37/22.79 % 152.37/22.79 Begin of proof % 152.37/22.79 | % 152.37/22.79 | BETA: splitting (9) gives: % 152.37/22.79 | % 152.37/22.79 | Case 1: % 152.37/22.79 | | % 152.37/22.79 | | (13) ~ (all_56_11 = e0) % 152.37/22.79 | | % 152.37/22.79 | | REDUCE: (7), (13) imply: % 152.37/22.79 | | (14) $false % 152.37/22.79 | | % 152.37/22.79 | | CLOSE: (14) is inconsistent. % 152.37/22.79 | | % 152.37/22.79 | Case 2: % 152.37/22.79 | | % 152.37/22.79 | | (15) all_56_15 = e2 % 152.37/22.79 | | % 152.37/22.79 | | COMBINE_EQS: (11), (15) imply: % 152.37/22.79 | | (16) all_52_13 = e2 % 152.37/22.79 | | % 152.37/22.79 | | SIMP: (16) implies: % 152.37/22.79 | | (17) all_52_13 = e2 % 152.37/22.79 | | % 152.37/22.79 | | REDUCE: (5), (17) imply: % 152.37/22.79 | | (18) ~ (all_52_1 = e2) % 152.37/22.79 | | % 152.37/22.79 | | REF_CLOSE: (1), (2), (3), (4), (6), (8), (10), (12), (18) are inconsistent % 152.37/22.79 | | by sub-proof #597. % 152.37/22.79 | | % 152.37/22.79 | End of split % 152.37/22.79 | % 152.37/22.79 End of proof % 152.37/22.79 % 152.37/22.79 Sub-proof #597 shows that the following formulas are inconsistent: % 152.37/22.79 ---------------------------------------------------------------- % 152.37/22.79 (1) all_58_6 = all_52_2 % 152.37/22.79 (2) ~ (all_52_3 = e2) % 152.37/22.79 (3) ~ (all_10_2 = e2) % 152.37/22.79 (4) all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2 % 152.37/22.79 (5) ~ (all_52_2 = e2) % 152.37/22.79 (6) all_58_2 = all_52_1 % 152.37/22.79 (7) all_58_0 = all_10_2 % 152.37/22.79 (8) ~ (all_52_1 = e2) % 152.37/22.79 (9) all_58_12 = all_52_3 % 152.37/22.79 % 152.37/22.79 Begin of proof % 152.37/22.79 | % 152.37/22.79 | BETA: splitting (4) gives: % 152.37/22.79 | % 152.37/22.79 | Case 1: % 152.37/22.79 | | % 152.37/22.79 | | (10) all_58_0 = e2 % 152.37/22.79 | | % 152.37/22.79 | | COMBINE_EQS: (7), (10) imply: % 152.37/22.79 | | (11) all_10_2 = e2 % 152.37/22.79 | | % 152.37/22.79 | | REDUCE: (3), (11) imply: % 152.37/22.79 | | (12) $false % 152.37/22.79 | | % 152.37/22.79 | | CLOSE: (12) is inconsistent. % 152.37/22.79 | | % 152.37/22.79 | Case 2: % 152.37/22.79 | | % 152.37/22.79 | | (13) all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2 % 152.37/22.79 | | % 152.37/22.79 | | REF_CLOSE: (1), (2), (5), (6), (8), (9), (13) are inconsistent by sub-proof % 152.37/22.79 | | #695. % 152.37/22.79 | | % 152.37/22.79 | End of split % 152.37/22.79 | % 152.37/22.79 End of proof % 152.37/22.80 % 152.37/22.80 Sub-proof #598 shows that the following formulas are inconsistent: % 152.37/22.80 ---------------------------------------------------------------- % 152.37/22.80 (1) all_54_0 = all_8_1 % 152.37/22.80 (2) all_54_0 = e1 % 152.37/22.80 (3) ~ (all_8_1 = e1) % 152.37/22.80 % 152.37/22.80 Begin of proof % 152.37/22.80 | % 152.37/22.80 | COMBINE_EQS: (1), (2) imply: % 152.37/22.80 | (4) all_8_1 = e1 % 152.37/22.80 | % 152.37/22.80 | SIMP: (4) implies: % 152.37/22.80 | (5) all_8_1 = e1 % 152.37/22.80 | % 152.37/22.80 | REDUCE: (3), (5) imply: % 152.37/22.80 | (6) $false % 152.37/22.80 | % 152.37/22.80 | CLOSE: (6) is inconsistent. % 152.37/22.80 | % 152.37/22.80 End of proof % 152.37/22.80 % 152.37/22.80 Sub-proof #599 shows that the following formulas are inconsistent: % 152.37/22.80 ---------------------------------------------------------------- % 152.37/22.80 (1) all_54_0 = all_8_1 % 152.37/22.80 (2) all_54_0 = e2 % 152.37/22.80 (3) ~ (all_8_1 = e2) % 152.37/22.80 % 152.37/22.80 Begin of proof % 152.37/22.80 | % 152.37/22.80 | COMBINE_EQS: (1), (2) imply: % 152.37/22.80 | (4) all_8_1 = e2 % 152.37/22.80 | % 152.37/22.80 | SIMP: (4) implies: % 152.37/22.80 | (5) all_8_1 = e2 % 152.37/22.80 | % 152.37/22.80 | REDUCE: (3), (5) imply: % 152.37/22.80 | (6) $false % 152.37/22.80 | % 152.37/22.80 | CLOSE: (6) is inconsistent. % 152.37/22.80 | % 152.37/22.80 End of proof % 152.37/22.80 % 152.37/22.80 Sub-proof #600 shows that the following formulas are inconsistent: % 152.37/22.80 ---------------------------------------------------------------- % 152.37/22.80 (1) all_54_0 = all_8_1 % 152.37/22.80 (2) all_54_0 = e3 % 152.37/22.80 (3) ~ (all_8_1 = e3) % 152.37/22.80 % 152.37/22.80 Begin of proof % 152.37/22.80 | % 152.37/22.80 | COMBINE_EQS: (1), (2) imply: % 152.37/22.80 | (4) all_8_1 = e3 % 152.37/22.80 | % 152.37/22.80 | SIMP: (4) implies: % 152.37/22.80 | (5) all_8_1 = e3 % 152.37/22.80 | % 152.37/22.80 | REDUCE: (3), (5) imply: % 152.37/22.80 | (6) $false % 152.37/22.80 | % 152.37/22.80 | CLOSE: (6) is inconsistent. % 152.37/22.80 | % 152.37/22.80 End of proof % 152.37/22.80 % 152.37/22.80 Sub-proof #601 shows that the following formulas are inconsistent: % 152.37/22.80 ---------------------------------------------------------------- % 152.37/22.80 (1) all_54_7 = all_52_13 % 152.37/22.80 (2) all_54_7 = e3 % 152.37/22.80 (3) ~ (all_52_13 = e3) % 152.37/22.80 % 152.37/22.80 Begin of proof % 152.37/22.80 | % 152.37/22.80 | COMBINE_EQS: (1), (2) imply: % 152.37/22.80 | (4) all_52_13 = e3 % 152.37/22.80 | % 152.37/22.80 | SIMP: (4) implies: % 152.37/22.80 | (5) all_52_13 = e3 % 152.37/22.80 | % 152.37/22.80 | REDUCE: (3), (5) imply: % 152.37/22.80 | (6) $false % 152.37/22.80 | % 152.37/22.80 | CLOSE: (6) is inconsistent. % 152.37/22.80 | % 152.37/22.80 End of proof % 152.37/22.80 % 152.37/22.80 Sub-proof #602 shows that the following formulas are inconsistent: % 152.37/22.80 ---------------------------------------------------------------- % 152.37/22.80 (1) all_58_6 = all_52_2 % 152.37/22.80 (2) ~ (all_58_2 = e0) % 152.37/22.80 (3) all_58_1 = all_52_4 % 152.37/22.80 (4) all_58_13 = all_52_7 % 152.37/22.80 (5) ~ (all_52_3 = e0) % 152.37/22.80 (6) ~ (all_52_2 = e0) % 152.37/22.80 (7) ~ (all_52_6 = e0) % 152.37/22.80 (8) all_58_3 = all_8_2 % 152.37/22.80 (9) all_58_2 = all_52_1 % 152.37/22.80 (10) all_58_7 = all_52_6 % 152.37/22.80 (11) all_58_0 = all_10_2 % 152.37/22.80 (12) all_58_1 = e0 | all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0 % 152.37/22.80 (13) ~ (all_8_2 = e0) % 152.37/22.80 (14) all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0 % 152.37/22.80 (15) ~ (all_52_7 = e0) % 152.37/22.80 (16) ~ (all_52_4 = all_10_2) % 152.37/22.80 (17) all_58_12 = all_52_3 % 152.37/22.80 % 152.37/22.80 Begin of proof % 152.37/22.80 | % 152.37/22.80 | REDUCE: (2), (9) imply: % 152.37/22.80 | (18) ~ (all_52_1 = e0) % 152.37/22.80 | % 152.37/22.80 | BETA: splitting (12) gives: % 152.37/22.80 | % 152.37/22.80 | Case 1: % 152.37/22.80 | | % 152.37/22.80 | | (19) all_58_1 = e0 % 152.37/22.80 | | % 152.37/22.80 | | COMBINE_EQS: (3), (19) imply: % 152.37/22.80 | | (20) all_52_4 = e0 % 152.37/22.80 | | % 152.37/22.80 | | REDUCE: (16), (20) imply: % 152.37/22.80 | | (21) ~ (all_10_2 = e0) % 152.37/22.80 | | % 152.37/22.80 | | REF_CLOSE: (1), (5), (6), (9), (11), (14), (17), (18), (21) are inconsistent % 152.37/22.80 | | by sub-proof #624. % 152.37/22.80 | | % 152.37/22.80 | Case 2: % 152.37/22.80 | | % 152.37/22.80 | | (22) all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0 % 152.37/22.80 | | % 152.37/22.80 | | REF_CLOSE: (4), (7), (8), (10), (13), (15), (22) are inconsistent by % 152.37/22.80 | | sub-proof #603. % 152.37/22.80 | | % 152.37/22.80 | End of split % 152.37/22.80 | % 152.37/22.80 End of proof % 152.37/22.80 % 152.37/22.80 Sub-proof #603 shows that the following formulas are inconsistent: % 152.37/22.80 ---------------------------------------------------------------- % 152.37/22.80 (1) all_58_13 = all_52_7 % 152.37/22.80 (2) ~ (all_52_6 = e0) % 152.37/22.80 (3) all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0 % 152.37/22.80 (4) all_58_3 = all_8_2 % 152.37/22.80 (5) all_58_7 = all_52_6 % 152.37/22.80 (6) ~ (all_8_2 = e0) % 152.37/22.80 (7) ~ (all_52_7 = e0) % 152.37/22.80 % 152.37/22.80 Begin of proof % 152.37/22.80 | % 152.37/22.80 | BETA: splitting (3) gives: % 152.37/22.80 | % 152.37/22.80 | Case 1: % 152.37/22.80 | | % 152.37/22.80 | | (8) all_58_3 = e0 % 152.37/22.80 | | % 152.37/22.80 | | COMBINE_EQS: (4), (8) imply: % 152.37/22.80 | | (9) all_8_2 = e0 % 152.37/22.80 | | % 152.37/22.80 | | REDUCE: (6), (9) imply: % 152.37/22.80 | | (10) $false % 152.37/22.80 | | % 152.37/22.80 | | CLOSE: (10) is inconsistent. % 152.37/22.80 | | % 152.37/22.80 | Case 2: % 152.37/22.80 | | % 152.37/22.80 | | (11) all_58_7 = e0 | all_58_13 = e0 % 152.37/22.80 | | % 152.37/22.80 | | REF_CLOSE: (1), (2), (5), (7), (11) are inconsistent by sub-proof #604. % 152.37/22.80 | | % 152.37/22.80 | End of split % 152.37/22.80 | % 152.37/22.80 End of proof % 152.37/22.80 % 152.37/22.80 Sub-proof #604 shows that the following formulas are inconsistent: % 152.37/22.80 ---------------------------------------------------------------- % 152.37/22.80 (1) all_58_7 = e0 | all_58_13 = e0 % 152.37/22.80 (2) all_58_13 = all_52_7 % 152.37/22.80 (3) ~ (all_52_6 = e0) % 152.37/22.80 (4) all_58_7 = all_52_6 % 152.37/22.80 (5) ~ (all_52_7 = e0) % 152.37/22.80 % 152.37/22.80 Begin of proof % 152.37/22.80 | % 152.37/22.80 | BETA: splitting (1) gives: % 152.37/22.80 | % 152.37/22.80 | Case 1: % 152.37/22.80 | | % 152.37/22.80 | | (6) all_58_7 = e0 % 152.37/22.80 | | % 152.37/22.80 | | COMBINE_EQS: (4), (6) imply: % 152.37/22.80 | | (7) all_52_6 = e0 % 152.37/22.80 | | % 152.37/22.80 | | REDUCE: (3), (7) imply: % 152.37/22.80 | | (8) $false % 152.37/22.80 | | % 152.37/22.80 | | CLOSE: (8) is inconsistent. % 152.37/22.80 | | % 152.37/22.80 | Case 2: % 152.37/22.80 | | % 152.37/22.80 | | (9) all_58_13 = e0 % 152.37/22.80 | | % 152.37/22.80 | | REF_CLOSE: (2), (5), (9) are inconsistent by sub-proof #605. % 152.37/22.80 | | % 152.37/22.80 | End of split % 152.37/22.80 | % 152.37/22.80 End of proof % 152.37/22.80 % 152.37/22.80 Sub-proof #605 shows that the following formulas are inconsistent: % 152.37/22.80 ---------------------------------------------------------------- % 152.37/22.80 (1) all_58_13 = all_52_7 % 152.37/22.80 (2) all_58_13 = e0 % 152.37/22.80 (3) ~ (all_52_7 = e0) % 152.37/22.80 % 152.37/22.80 Begin of proof % 152.37/22.80 | % 152.37/22.80 | COMBINE_EQS: (1), (2) imply: % 152.37/22.80 | (4) all_52_7 = e0 % 152.37/22.80 | % 152.37/22.80 | SIMP: (4) implies: % 152.37/22.80 | (5) all_52_7 = e0 % 152.37/22.80 | % 152.37/22.80 | REDUCE: (3), (5) imply: % 152.37/22.80 | (6) $false % 152.37/22.80 | % 152.37/22.80 | CLOSE: (6) is inconsistent. % 152.37/22.80 | % 152.37/22.80 End of proof % 152.37/22.80 % 152.37/22.80 Sub-proof #606 shows that the following formulas are inconsistent: % 152.37/22.80 ---------------------------------------------------------------- % 152.37/22.80 (1) all_54_10 = all_6_2 % 152.37/22.80 (2) all_54_10 = e1 % 152.37/22.80 (3) ~ (all_6_2 = e1) % 152.37/22.80 % 152.37/22.80 Begin of proof % 152.37/22.80 | % 152.37/22.80 | COMBINE_EQS: (1), (2) imply: % 152.37/22.80 | (4) all_6_2 = e1 % 152.37/22.80 | % 152.37/22.80 | SIMP: (4) implies: % 152.37/22.80 | (5) all_6_2 = e1 % 152.37/22.80 | % 152.37/22.80 | REDUCE: (3), (5) imply: % 152.37/22.80 | (6) $false % 152.37/22.80 | % 152.37/22.80 | CLOSE: (6) is inconsistent. % 152.37/22.80 | % 152.37/22.80 End of proof % 152.37/22.80 % 152.37/22.80 Sub-proof #607 shows that the following formulas are inconsistent: % 152.37/22.80 ---------------------------------------------------------------- % 152.37/22.80 (1) ~ (all_52_4 = all_52_8) % 152.37/22.80 (2) ~ (all_52_8 = all_52_9) % 152.37/22.80 (3) all_54_9 = all_52_6 % 152.37/22.80 (4) all_58_6 = all_52_2 % 152.37/22.80 (5) ~ (all_52_6 = e1) % 152.37/22.80 (6) ~ (all_52_1 = all_52_9) % 152.37/22.80 (7) op(e2, all_52_4) = all_56_2 % 152.37/22.80 (8) ~ (all_52_9 = e2) % 152.37/22.80 (9) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0 % 152.37/22.80 (10) all_54_4 = all_52_1 % 152.37/22.80 (11) all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2 % 152.37/22.80 (12) all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2 % 152.37/22.80 (13) all_54_12 = all_52_3 % 152.37/22.80 (14) ~ (all_52_4 = all_52_7) % 152.37/22.80 (15) ~ (all_52_12 = e2) % 152.37/22.80 (16) all_58_4 = all_52_8 % 152.37/22.80 (17) all_58_10 = e2 % 152.37/22.80 (18) op(e2, e1) = all_52_9 % 152.37/22.80 (19) op(e3, all_52_1) = all_56_8 % 152.37/22.80 (20) all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2 % 152.37/22.80 (21) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0 % 152.37/22.80 (22) all_58_5 = all_52_9 % 152.37/22.80 (23) all_54_1 = all_52_4 % 152.37/22.80 (24) all_56_17 = all_52_2 % 152.37/22.80 (25) all_58_9 = all_52_12 % 152.37/22.80 (26) op(e0, all_52_12) = all_56_6 % 152.37/22.80 (27) ( ~ (all_56_0 = all_56_1) & ~ (all_56_2 = all_56_3) & ~ (all_56_4 = % 152.37/22.80 all_56_5) & ~ (all_56_6 = all_56_7)) | ( ~ (all_56_8 = all_56_9) & % 152.37/22.80 ~ (all_56_10 = all_56_11) & ~ (all_56_12 = all_56_13) & ~ (all_56_14 % 152.37/22.80 = all_56_15)) | ( ~ (all_56_16 = all_56_17) & ~ (all_56_18 = % 152.37/22.80 all_56_19) & ~ (all_56_20 = all_56_21) & ~ (all_56_22 = % 152.37/22.80 all_56_23)) | ( ~ (all_56_24 = all_56_25) & ~ (all_56_26 = % 152.37/22.80 all_56_27) & ~ (all_56_28 = all_56_29) & ~ (all_56_30 = % 152.37/22.80 all_56_31)) % 152.37/22.80 (28) all_56_23 = e1 % 152.37/22.80 (29) all_58_1 = all_52_4 % 152.37/22.80 (30) all_58_13 = all_52_7 % 152.37/22.80 (31) ~ (all_52_8 = e0) % 152.37/22.80 (32) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0 % 152.37/22.80 (33) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 152.37/22.80 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 152.37/22.80 (34) all_54_3 = all_52_12 % 152.37/22.80 (35) ~ (all_52_3 = all_52_7) % 152.37/22.80 (36) ~ (all_52_2 = all_52_6) % 152.37/22.80 (37) ~ (all_52_3 = e0) % 152.37/22.80 (38) all_56_15 = e2 % 152.37/22.80 (39) ~ (all_52_2 = e0) % 152.37/22.80 (40) all_56_7 = all_52_12 % 152.37/22.80 (41) ~ (all_52_4 = e0) % 152.37/22.80 (42) op(e1, e2) = all_52_6 % 152.37/22.80 (43) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0 % 152.37/22.80 (44) all_56_13 = all_52_9 % 152.37/22.80 (45) op(e2, all_52_6) = all_56_18 % 152.37/22.80 (46) op(e0, e1) = all_52_11 % 152.37/22.80 (47) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0 % 152.37/22.80 (48) ~ (all_52_9 = e0) % 152.37/22.80 (49) op(e1, e3) = all_52_2 % 152.37/22.80 (50) ~ (all_4_2 = e1) % 152.37/22.80 (51) all_54_6 = all_52_9 % 152.37/22.80 (52) all_58_8 = e0 % 152.37/22.80 (53) ~ (all_52_6 = e0) % 152.37/22.80 (54) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0 % 152.37/22.80 (55) all_56_5 = all_52_8 % 152.37/22.80 (56) all_58_3 = e0 % 152.37/22.80 (57) ~ (all_52_2 = e1) % 152.37/22.80 (58) ~ (all_52_2 = all_52_3) % 152.37/22.80 (59) op(e0, e1) = all_56_22 % 152.37/22.80 (60) ~ (all_52_1 = e0) % 152.37/22.80 (61) ~ (all_52_3 = all_52_11) % 152.37/22.80 (62) all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1 % 152.37/22.80 (63) all_56_3 = all_52_4 % 152.37/22.80 (64) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0 % 152.37/22.80 (65) ~ (all_52_1 = all_52_3) % 152.37/22.80 (66) all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1 % 152.37/22.80 (67) ~ (all_52_6 = all_52_7) % 152.37/22.80 (68) op(e1, all_52_8) = all_56_4 % 152.37/22.80 (69) all_56_30 = e0 % 152.37/22.80 (70) all_56_31 = e0 % 152.37/22.80 (71) all_54_13 = all_52_7 % 152.37/22.80 (72) all_54_2 = all_52_8 % 152.37/22.80 (73) op(e3, e2) = all_52_4 % 152.37/22.80 (74) all_54_8 = all_52_2 % 152.37/22.80 (75) op(e0, e3) = all_52_3 % 152.37/22.80 (76) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0 % 152.37/22.80 (77) all_58_15 = all_4_2 % 152.37/22.80 (78) all_58_2 = all_52_1 % 152.37/22.80 (79) all_58_7 = all_52_6 % 152.37/22.80 (80) op(e3, all_52_2) = all_56_16 % 152.37/22.80 (81) all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1 % 152.37/22.80 (82) op(e2, e3) = all_52_1 % 152.37/22.80 (83) ~ (all_52_12 = e1) % 152.37/22.80 (84) op(e1, all_52_9) = all_56_12 % 152.37/22.80 (85) op(e3, e1) = all_52_8 % 152.37/22.80 (86) all_56_14 = all_52_7 % 152.37/22.80 (87) ~ (all_52_12 = e0) % 152.37/22.80 (88) ~ (all_52_4 = all_52_12) % 152.37/22.80 (89) ~ (all_52_8 = all_52_12) % 152.37/22.80 (90) ~ (all_52_1 = all_52_2) % 152.37/22.80 (91) all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0 % 152.37/22.80 (92) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0 % 152.37/22.80 (93) ~ (all_52_7 = e0) % 152.37/22.80 (94) all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3 % 152.37/22.80 (95) ~ (all_52_4 = all_52_6) % 152.37/22.80 (96) all_58_14 = all_52_11 % 152.37/22.80 (97) ~ (all_52_1 = e2) % 152.37/22.80 (98) all_56_19 = all_52_6 % 152.37/22.80 (99) all_56_9 = all_52_1 % 152.37/22.80 (100) all_58_12 = all_52_3 % 152.37/22.80 (101) all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2 % 152.37/22.80 % 152.37/22.80 Begin of proof % 152.37/22.80 | % 152.37/22.80 | BETA: splitting (9) gives: % 152.37/22.80 | % 152.37/22.80 | Case 1: % 152.37/22.80 | | % 152.37/22.80 | | (102) all_54_3 = e3 % 152.37/22.80 | | % 152.37/22.80 | | COMBINE_EQS: (34), (102) imply: % 152.37/22.80 | | (103) all_52_12 = e3 % 152.37/22.80 | | % 152.37/22.80 | | SIMP: (103) implies: % 152.37/22.80 | | (104) all_52_12 = e3 % 152.37/22.80 | | % 152.37/22.80 | | COMBINE_EQS: (40), (104) imply: % 152.37/22.80 | | (105) all_56_7 = e3 % 152.37/22.80 | | % 152.37/22.80 | | COMBINE_EQS: (25), (104) imply: % 152.37/22.80 | | (106) all_58_9 = e3 % 152.37/22.80 | | % 152.37/22.80 | | REDUCE: (88), (104) imply: % 152.37/22.80 | | (107) ~ (all_52_4 = e3) % 152.37/22.80 | | % 152.37/22.80 | | REDUCE: (89), (104) imply: % 152.37/22.80 | | (108) ~ (all_52_8 = e3) % 152.37/22.80 | | % 152.37/22.80 | | REDUCE: (26), (104) imply: % 152.37/22.80 | | (109) op(e0, e3) = all_56_6 % 152.37/22.80 | | % 152.37/22.80 | | GROUND_INST: instantiating (33) with all_52_11, all_56_22, e1, e0, % 152.37/22.80 | | simplifying with (46), (59) gives: % 152.37/22.80 | | (110) all_56_22 = all_52_11 % 152.37/22.80 | | % 152.37/22.80 | | GROUND_INST: instantiating (33) with all_52_3, all_56_6, e3, e0, simplifying % 152.37/22.80 | | with (75), (109) gives: % 152.37/22.80 | | (111) all_56_6 = all_52_3 % 152.37/22.80 | | % 152.37/22.80 | | BETA: splitting (76) gives: % 152.37/22.80 | | % 152.37/22.80 | | Case 1: % 152.37/22.80 | | | % 152.37/22.80 | | | (112) all_54_1 = e3 % 152.37/22.80 | | | % 152.37/22.80 | | | REF_CLOSE: (23), (107), (112) are inconsistent by sub-proof #722. % 152.37/22.80 | | | % 152.37/22.80 | | Case 2: % 152.37/22.80 | | | % 152.37/22.80 | | | (113) all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0 % 152.37/22.80 | | | % 152.37/22.80 | | | BETA: splitting (64) gives: % 152.37/22.80 | | | % 152.37/22.80 | | | Case 1: % 152.37/22.80 | | | | % 152.37/22.80 | | | | (114) all_54_9 = e3 % 152.37/22.80 | | | | % 152.37/22.80 | | | | COMBINE_EQS: (3), (114) imply: % 152.37/22.80 | | | | (115) all_52_6 = e3 % 152.37/22.80 | | | | % 152.37/22.80 | | | | COMBINE_EQS: (98), (115) imply: % 152.37/22.80 | | | | (116) all_56_19 = e3 % 152.37/22.80 | | | | % 152.37/22.80 | | | | COMBINE_EQS: (79), (115) imply: % 152.37/22.80 | | | | (117) all_58_7 = e3 % 152.37/22.80 | | | | % 152.37/22.80 | | | | REDUCE: (36), (115) imply: % 152.37/22.80 | | | | (118) ~ (all_52_2 = e3) % 152.37/22.80 | | | | % 152.37/22.80 | | | | REDUCE: (67), (115) imply: % 152.37/22.80 | | | | (119) ~ (all_52_7 = e3) % 152.37/22.80 | | | | % 152.37/22.80 | | | | SIMP: (119) implies: % 152.37/22.80 | | | | (120) ~ (all_52_7 = e3) % 152.37/22.80 | | | | % 152.37/22.80 | | | | REDUCE: (45), (115) imply: % 152.37/22.80 | | | | (121) op(e2, e3) = all_56_18 % 152.37/22.80 | | | | % 152.37/22.80 | | | | BETA: splitting (92) gives: % 152.37/22.80 | | | | % 152.37/22.80 | | | | Case 1: % 152.37/22.80 | | | | | % 152.37/22.80 | | | | | (122) all_54_8 = e3 % 152.37/22.80 | | | | | % 152.37/22.80 | | | | | COMBINE_EQS: (74), (122) imply: % 152.37/22.80 | | | | | (123) all_52_2 = e3 % 152.37/22.80 | | | | | % 152.37/22.80 | | | | | REDUCE: (118), (123) imply: % 152.37/22.80 | | | | | (124) $false % 152.37/22.80 | | | | | % 152.37/22.80 | | | | | CLOSE: (124) is inconsistent. % 152.37/22.80 | | | | | % 152.37/22.80 | | | | Case 2: % 152.37/22.80 | | | | | % 152.37/22.80 | | | | | (125) all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0 % 152.37/22.80 | | | | | % 152.37/22.80 | | | | | BETA: splitting (125) gives: % 152.37/22.80 | | | | | % 152.37/22.80 | | | | | Case 1: % 152.37/22.80 | | | | | | % 152.37/22.80 | | | | | | (126) all_54_8 = e2 % 152.37/22.80 | | | | | | % 152.37/22.80 | | | | | | COMBINE_EQS: (74), (126) imply: % 152.37/22.80 | | | | | | (127) all_52_2 = e2 % 152.37/22.80 | | | | | | % 152.37/22.80 | | | | | | COMBINE_EQS: (24), (127) imply: % 152.37/22.80 | | | | | | (128) all_56_17 = e2 % 152.37/22.80 | | | | | | % 152.37/22.80 | | | | | | REDUCE: (58), (127) imply: % 152.37/22.80 | | | | | | (129) ~ (all_52_3 = e2) % 152.37/22.80 | | | | | | % 152.37/22.80 | | | | | | SIMP: (129) implies: % 152.37/22.80 | | | | | | (130) ~ (all_52_3 = e2) % 152.37/22.80 | | | | | | % 152.37/22.80 | | | | | | REDUCE: (80), (127) imply: % 152.37/22.80 | | | | | | (131) op(e3, e2) = all_56_16 % 152.37/22.80 | | | | | | % 152.37/22.80 | | | | | | GROUND_INST: instantiating (33) with all_52_1, all_56_18, e3, e2, % 152.37/22.80 | | | | | | simplifying with (82), (121) gives: % 152.37/22.80 | | | | | | (132) all_56_18 = all_52_1 % 152.37/22.80 | | | | | | % 152.37/22.80 | | | | | | GROUND_INST: instantiating (33) with all_52_4, all_56_16, e2, e3, % 152.37/22.80 | | | | | | simplifying with (73), (131) gives: % 152.37/22.80 | | | | | | (133) all_56_16 = all_52_4 % 152.37/22.80 | | | | | | % 152.37/22.80 | | | | | | BETA: splitting (32) gives: % 152.37/22.80 | | | | | | % 152.37/22.80 | | | | | | Case 1: % 152.37/22.80 | | | | | | | % 152.37/22.80 | | | | | | | (134) all_54_2 = e3 % 152.37/22.80 | | | | | | | % 152.37/22.80 | | | | | | | COMBINE_EQS: (72), (134) imply: % 152.37/22.80 | | | | | | | (135) all_52_8 = e3 % 152.37/22.80 | | | | | | | % 152.37/22.80 | | | | | | | REDUCE: (108), (135) imply: % 152.37/22.80 | | | | | | | (136) $false % 152.37/22.80 | | | | | | | % 152.37/22.80 | | | | | | | CLOSE: (136) is inconsistent. % 152.37/22.80 | | | | | | | % 152.37/22.80 | | | | | | Case 2: % 152.37/22.80 | | | | | | | % 152.37/22.80 | | | | | | | (137) ~ (all_54_2 = e3) % 152.37/22.80 | | | | | | | (138) all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0 % 152.37/22.80 | | | | | | | % 152.37/22.80 | | | | | | | BETA: splitting (94) gives: % 152.37/22.80 | | | | | | | % 152.37/22.80 | | | | | | | Case 1: % 152.37/22.80 | | | | | | | | % 152.37/22.80 | | | | | | | | (139) all_58_2 = e3 % 152.37/22.80 | | | | | | | | % 152.37/22.80 | | | | | | | | COMBINE_EQS: (78), (139) imply: % 152.37/22.80 | | | | | | | | (140) all_52_1 = e3 % 152.37/22.80 | | | | | | | | % 152.37/22.80 | | | | | | | | COMBINE_EQS: (132), (140) imply: % 152.37/22.80 | | | | | | | | (141) all_56_18 = e3 % 152.37/22.80 | | | | | | | | % 152.37/22.80 | | | | | | | | REDUCE: (65), (140) imply: % 152.37/22.80 | | | | | | | | (142) ~ (all_52_3 = e3) % 152.37/22.80 | | | | | | | | % 152.37/22.80 | | | | | | | | SIMP: (142) implies: % 152.37/22.80 | | | | | | | | (143) ~ (all_52_3 = e3) % 152.37/22.80 | | | | | | | | % 152.37/22.80 | | | | | | | | BETA: splitting (43) gives: % 152.37/22.80 | | | | | | | | % 152.37/22.80 | | | | | | | | Case 1: % 152.37/22.80 | | | | | | | | | % 152.37/22.80 | | | | | | | | | (144) all_54_12 = e3 % 152.37/22.80 | | | | | | | | | % 152.37/22.80 | | | | | | | | | COMBINE_EQS: (13), (144) imply: % 152.37/22.80 | | | | | | | | | (145) all_52_3 = e3 % 152.37/22.80 | | | | | | | | | % 152.37/22.80 | | | | | | | | | REDUCE: (143), (145) imply: % 152.37/22.80 | | | | | | | | | (146) $false % 152.37/22.80 | | | | | | | | | % 152.37/22.80 | | | | | | | | | CLOSE: (146) is inconsistent. % 152.37/22.80 | | | | | | | | | % 152.37/22.80 | | | | | | | | Case 2: % 152.37/22.80 | | | | | | | | | % 152.37/22.80 | | | | | | | | | (147) all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0 % 152.37/22.80 | | | | | | | | | % 152.37/22.80 | | | | | | | | | BETA: splitting (147) gives: % 152.37/22.80 | | | | | | | | | % 152.37/22.80 | | | | | | | | | Case 1: % 152.37/22.80 | | | | | | | | | | % 152.37/22.80 | | | | | | | | | | (148) all_54_12 = e2 % 152.37/22.80 | | | | | | | | | | % 152.37/22.80 | | | | | | | | | | COMBINE_EQS: (13), (148) imply: % 152.37/22.80 | | | | | | | | | | (149) all_52_3 = e2 % 152.37/22.80 | | | | | | | | | | % 152.37/22.80 | | | | | | | | | | REDUCE: (130), (149) imply: % 152.37/22.80 | | | | | | | | | | (150) $false % 152.37/22.80 | | | | | | | | | | % 152.37/22.80 | | | | | | | | | | CLOSE: (150) is inconsistent. % 152.37/22.80 | | | | | | | | | | % 152.37/22.80 | | | | | | | | | Case 2: % 152.37/22.80 | | | | | | | | | | % 152.37/22.80 | | | | | | | | | | (151) ~ (all_54_12 = e2) % 152.37/22.80 | | | | | | | | | | (152) all_54_12 = e1 | all_54_12 = e0 % 152.37/22.80 | | | | | | | | | | % 152.37/22.80 | | | | | | | | | | BETA: splitting (152) gives: % 152.37/22.80 | | | | | | | | | | % 152.37/22.80 | | | | | | | | | | Case 1: % 152.37/22.80 | | | | | | | | | | | % 152.37/22.80 | | | | | | | | | | | (153) all_54_12 = e1 % 152.37/22.80 | | | | | | | | | | | % 152.37/22.80 | | | | | | | | | | | COMBINE_EQS: (13), (153) imply: % 152.37/22.80 | | | | | | | | | | | (154) all_52_3 = e1 % 152.37/22.80 | | | | | | | | | | | % 152.37/22.80 | | | | | | | | | | | COMBINE_EQS: (100), (154) imply: % 152.37/22.80 | | | | | | | | | | | (155) all_58_12 = e1 % 152.37/22.80 | | | | | | | | | | | % 152.37/22.80 | | | | | | | | | | | REDUCE: (35), (154) imply: % 152.37/22.80 | | | | | | | | | | | (156) ~ (all_52_7 = e1) % 152.37/22.80 | | | | | | | | | | | % 152.37/22.80 | | | | | | | | | | | SIMP: (156) implies: % 152.37/22.80 | | | | | | | | | | | (157) ~ (all_52_7 = e1) % 152.37/22.80 | | | | | | | | | | | % 152.37/22.80 | | | | | | | | | | | REDUCE: (61), (154) imply: % 152.37/22.80 | | | | | | | | | | | (158) ~ (all_52_11 = e1) % 152.37/22.80 | | | | | | | | | | | % 152.37/22.80 | | | | | | | | | | | SIMP: (158) implies: % 152.37/22.80 | | | | | | | | | | | (159) ~ (all_52_11 = e1) % 152.37/22.80 | | | | | | | | | | | % 152.37/22.80 | | | | | | | | | | | REDUCE: (130), (154) imply: % 152.37/22.80 | | | | | | | | | | | (160) ~ (e2 = e1) % 152.37/22.80 | | | | | | | | | | | % 152.37/22.80 | | | | | | | | | | | SIMP: (160) implies: % 152.37/22.80 | | | | | | | | | | | (161) ~ (e2 = e1) % 152.37/22.80 | | | | | | | | | | | % 152.37/22.80 | | | | | | | | | | | BETA: splitting (101) gives: % 152.37/22.80 | | | | | | | | | | | % 152.37/22.80 | | | | | | | | | | | Case 1: % 152.37/22.80 | | | | | | | | | | | | % 152.37/22.80 | | | | | | | | | | | | (162) all_58_12 = e2 % 152.37/22.80 | | | | | | | | | | | | % 152.37/22.80 | | | | | | | | | | | | REF_CLOSE: (155), (161), (162) are inconsistent by sub-proof % 152.37/22.80 | | | | | | | | | | | | #622. % 152.37/22.80 | | | | | | | | | | | | % 152.37/22.80 | | | | | | | | | | | Case 2: % 152.37/22.80 | | | | | | | | | | | | % 152.37/22.80 | | | | | | | | | | | | (163) all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2 % 152.37/22.80 | | | | | | | | | | | | % 152.37/22.80 | | | | | | | | | | | | BETA: splitting (163) gives: % 152.37/22.80 | | | | | | | | | | | | % 152.37/22.80 | | | | | | | | | | | | Case 1: % 152.37/22.80 | | | | | | | | | | | | | % 152.37/22.80 | | | | | | | | | | | | | (164) all_58_13 = e2 % 152.37/22.80 | | | | | | | | | | | | | % 152.37/22.80 | | | | | | | | | | | | | COMBINE_EQS: (30), (164) imply: % 152.37/22.80 | | | | | | | | | | | | | (165) all_52_7 = e2 % 152.37/22.80 | | | | | | | | | | | | | % 152.37/22.80 | | | | | | | | | | | | | SIMP: (165) implies: % 152.37/22.80 | | | | | | | | | | | | | (166) all_52_7 = e2 % 152.37/22.80 | | | | | | | | | | | | | % 152.37/22.80 | | | | | | | | | | | | | COMBINE_EQS: (86), (166) imply: % 152.37/22.80 | | | | | | | | | | | | | (167) all_56_14 = e2 % 152.37/22.80 | | | | | | | | | | | | | % 152.37/22.80 | | | | | | | | | | | | | REDUCE: (14), (166) imply: % 152.37/22.80 | | | | | | | | | | | | | (168) ~ (all_52_4 = e2) % 152.37/22.80 | | | | | | | | | | | | | % 152.37/22.80 | | | | | | | | | | | | | BETA: splitting (11) gives: % 152.37/22.80 | | | | | | | | | | | | | % 152.37/22.80 | | | | | | | | | | | | | Case 1: % 152.37/22.80 | | | | | | | | | | | | | | % 152.37/22.80 | | | | | | | | | | | | | | (169) all_58_4 = e2 % 152.37/22.80 | | | | | | | | | | | | | | % 152.37/22.80 | | | | | | | | | | | | | | COMBINE_EQS: (16), (169) imply: % 152.37/22.80 | | | | | | | | | | | | | | (170) all_52_8 = e2 % 152.37/22.80 | | | | | | | | | | | | | | % 152.37/22.80 | | | | | | | | | | | | | | BETA: splitting (66) gives: % 152.37/22.80 | | | | | | | | | | | | | | % 152.37/22.80 | | | | | | | | | | | | | | Case 1: % 152.37/22.80 | | | | | | | | | | | | | | | % 152.37/22.80 | | | | | | | | | | | | | | | (171) all_58_1 = e1 % 152.37/22.80 | | | | | | | | | | | | | | | % 152.37/22.80 | | | | | | | | | | | | | | | COMBINE_EQS: (29), (171) imply: % 152.37/22.80 | | | | | | | | | | | | | | | (172) all_52_4 = e1 % 152.37/22.80 | | | | | | | | | | | | | | | % 152.37/22.80 | | | | | | | | | | | | | | | COMBINE_EQS: (63), (172) imply: % 152.37/22.80 | | | | | | | | | | | | | | | (173) all_56_3 = e1 % 152.37/22.80 | | | | | | | | | | | | | | | % 152.37/22.80 | | | | | | | | | | | | | | | REDUCE: (41), (172) imply: % 152.37/22.80 | | | | | | | | | | | | | | | (174) ~ (e1 = e0) % 152.37/22.80 | | | | | | | | | | | | | | | % 152.37/22.80 | | | | | | | | | | | | | | | REDUCE: (7), (172) imply: % 152.37/22.80 | | | | | | | | | | | | | | | (175) op(e2, e1) = all_56_2 % 152.37/22.80 | | | | | | | | | | | | | | | % 152.37/22.80 | | | | | | | | | | | | | | | BETA: splitting (27) gives: % 152.37/22.80 | | | | | | | | | | | | | | | % 152.37/22.80 | | | | | | | | | | | | | | | Case 1: % 152.37/22.80 | | | | | | | | | | | | | | | | % 152.37/22.80 | | | | | | | | | | | | | | | | (176) ( ~ (all_56_0 = all_56_1) & ~ (all_56_2 = % 152.37/22.80 | | | | | | | | | | | | | | | | all_56_3) & ~ (all_56_4 = all_56_5) & ~ % 152.37/22.80 | | | | | | | | | | | | | | | | (all_56_6 = all_56_7)) | ( ~ (all_56_8 = % 152.37/22.80 | | | | | | | | | | | | | | | | all_56_9) & ~ (all_56_10 = all_56_11) & ~ % 152.37/22.80 | | | | | | | | | | | | | | | | (all_56_12 = all_56_13) & ~ (all_56_14 = % 152.37/22.80 | | | | | | | | | | | | | | | | all_56_15)) % 152.37/22.80 | | | | | | | | | | | | | | | | % 152.37/22.80 | | | | | | | | | | | | | | | | BETA: splitting (176) gives: % 152.37/22.80 | | | | | | | | | | | | | | | | % 152.37/22.80 | | | | | | | | | | | | | | | | Case 1: % 152.37/22.80 | | | | | | | | | | | | | | | | | % 152.37/22.80 | | | | | | | | | | | | | | | | | (177) ~ (all_56_0 = all_56_1) & ~ (all_56_2 = % 152.37/22.80 | | | | | | | | | | | | | | | | | all_56_3) & ~ (all_56_4 = all_56_5) & ~ % 152.37/22.80 | | | | | | | | | | | | | | | | | (all_56_6 = all_56_7) % 152.37/22.80 | | | | | | | | | | | | | | | | | % 152.37/22.80 | | | | | | | | | | | | | | | | | ALPHA: (177) implies: % 152.37/22.80 | | | | | | | | | | | | | | | | | (178) ~ (all_56_2 = all_56_3) % 152.37/22.80 | | | | | | | | | | | | | | | | | % 152.37/22.80 | | | | | | | | | | | | | | | | | REDUCE: (173), (178) imply: % 152.37/22.80 | | | | | | | | | | | | | | | | | (179) ~ (all_56_2 = e1) % 152.37/22.80 | | | | | | | | | | | | | | | | | % 152.37/22.80 | | | | | | | | | | | | | | | | | BETA: splitting (62) gives: % 152.37/22.80 | | | | | | | | | | | | | | | | | % 152.37/22.80 | | | | | | | | | | | | | | | | | Case 1: % 152.37/22.80 | | | | | | | | | | | | | | | | | | % 152.37/22.80 | | | | | | | | | | | | | | | | | | (180) all_58_4 = e1 % 152.37/22.80 | | | | | | | | | | | | | | | | | | % 152.37/22.80 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (169), (180) imply: % 152.37/22.80 | | | | | | | | | | | | | | | | | | (181) e2 = e1 % 152.37/22.80 | | | | | | | | | | | | | | | | | | % 152.37/22.80 | | | | | | | | | | | | | | | | | | REDUCE: (161), (181) imply: % 152.37/22.80 | | | | | | | | | | | | | | | | | | (182) $false % 152.37/22.80 | | | | | | | | | | | | | | | | | | % 152.37/22.80 | | | | | | | | | | | | | | | | | | CLOSE: (182) is inconsistent. % 152.37/22.80 | | | | | | | | | | | | | | | | | | % 152.37/22.80 | | | | | | | | | | | | | | | | | Case 2: % 152.37/22.80 | | | | | | | | | | | | | | | | | | % 152.37/22.80 | | | | | | | | | | | | | | | | | | (183) all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1 % 152.37/22.80 | | | | | | | | | | | | | | | | | | % 152.37/22.80 | | | | | | | | | | | | | | | | | | BETA: splitting (183) gives: % 152.37/22.80 | | | | | | | | | | | | | | | | | | % 152.37/22.80 | | | | | | | | | | | | | | | | | | Case 1: % 152.37/22.80 | | | | | | | | | | | | | | | | | | | % 152.37/22.80 | | | | | | | | | | | | | | | | | | | (184) all_58_5 = e1 % 152.37/22.80 | | | | | | | | | | | | | | | | | | | % 152.37/22.80 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (22), (184) imply: % 152.37/22.80 | | | | | | | | | | | | | | | | | | | (185) all_52_9 = e1 % 152.37/22.80 | | | | | | | | | | | | | | | | | | | % 152.37/22.80 | | | | | | | | | | | | | | | | | | | REDUCE: (18), (185) imply: % 152.37/22.80 | | | | | | | | | | | | | | | | | | | (186) op(e2, e1) = e1 % 152.37/22.80 | | | | | | | | | | | | | | | | | | | % 152.37/22.80 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (33) with e1, all_56_2, e1, e2, % 152.37/22.80 | | | | | | | | | | | | | | | | | | | simplifying with (175), (186) gives: % 152.37/22.80 | | | | | | | | | | | | | | | | | | | (187) all_56_2 = e1 % 152.37/22.80 | | | | | | | | | | | | | | | | | | | % 152.37/22.80 | | | | | | | | | | | | | | | | | | | REDUCE: (179), (187) imply: % 152.37/22.80 | | | | | | | | | | | | | | | | | | | (188) $false % 152.37/22.80 | | | | | | | | | | | | | | | | | | | % 152.37/22.80 | | | | | | | | | | | | | | | | | | | CLOSE: (188) is inconsistent. % 152.37/22.80 | | | | | | | | | | | | | | | | | | | % 152.37/22.80 | | | | | | | | | | | | | | | | | | Case 2: % 152.37/22.80 | | | | | | | | | | | | | | | | | | | % 152.37/22.80 | | | | | | | | | | | | | | | | | | | (189) all_58_8 = e1 | all_58_14 = e1 % 152.37/22.80 | | | | | | | | | | | | | | | | | | | % 152.37/22.80 | | | | | | | | | | | | | | | | | | | BETA: splitting (189) gives: % 152.37/22.80 | | | | | | | | | | | | | | | | | | | % 152.37/22.80 | | | | | | | | | | | | | | | | | | | Case 1: % 152.37/22.80 | | | | | | | | | | | | | | | | | | | | % 152.37/22.80 | | | | | | | | | | | | | | | | | | | | (190) all_58_8 = e1 % 152.37/22.80 | | | | | | | | | | | | | | | | | | | | % 152.37/22.80 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (52), (174), (190) are inconsistent by sub-proof % 152.37/22.80 | | | | | | | | | | | | | | | | | | | | #621. % 152.37/22.80 | | | | | | | | | | | | | | | | | | | | % 152.37/22.80 | | | | | | | | | | | | | | | | | | | Case 2: % 152.37/22.80 | | | | | | | | | | | | | | | | | | | | % 152.37/22.80 | | | | | | | | | | | | | | | | | | | | (191) all_58_14 = e1 % 152.37/22.80 | | | | | | | | | | | | | | | | | | | | % 152.37/22.80 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (96), (191) imply: % 152.37/22.80 | | | | | | | | | | | | | | | | | | | | (192) all_52_11 = e1 % 152.37/22.80 | | | | | | | | | | | | | | | | | | | | % 152.37/22.80 | | | | | | | | | | | | | | | | | | | | REDUCE: (159), (192) imply: % 152.37/22.80 | | | | | | | | | | | | | | | | | | | | (193) $false % 152.37/22.80 | | | | | | | | | | | | | | | | | | | | % 152.37/22.80 | | | | | | | | | | | | | | | | | | | | CLOSE: (193) is inconsistent. % 152.37/22.80 | | | | | | | | | | | | | | | | | | | | % 152.37/22.80 | | | | | | | | | | | | | | | | | | | End of split % 152.37/22.80 | | | | | | | | | | | | | | | | | | | % 152.37/22.80 | | | | | | | | | | | | | | | | | | End of split % 152.37/22.80 | | | | | | | | | | | | | | | | | | % 152.37/22.80 | | | | | | | | | | | | | | | | | End of split % 152.37/22.80 | | | | | | | | | | | | | | | | | % 152.37/22.80 | | | | | | | | | | | | | | | | Case 2: % 152.37/22.80 | | | | | | | | | | | | | | | | | % 152.37/22.80 | | | | | | | | | | | | | | | | | (194) ~ (all_56_8 = all_56_9) & ~ (all_56_10 = % 152.37/22.80 | | | | | | | | | | | | | | | | | all_56_11) & ~ (all_56_12 = all_56_13) & ~ % 152.37/22.80 | | | | | | | | | | | | | | | | | (all_56_14 = all_56_15) % 152.37/22.80 | | | | | | | | | | | | | | | | | % 152.37/22.80 | | | | | | | | | | | | | | | | | ALPHA: (194) implies: % 152.37/22.80 | | | | | | | | | | | | | | | | | (195) ~ (all_56_14 = all_56_15) % 152.37/22.80 | | | | | | | | | | | | | | | | | % 152.37/22.80 | | | | | | | | | | | | | | | | | REDUCE: (38), (167), (195) imply: % 152.37/22.80 | | | | | | | | | | | | | | | | | (196) $false % 152.37/22.80 | | | | | | | | | | | | | | | | | % 152.37/22.80 | | | | | | | | | | | | | | | | | CLOSE: (196) is inconsistent. % 152.37/22.80 | | | | | | | | | | | | | | | | | % 152.37/22.80 | | | | | | | | | | | | | | | | End of split % 152.37/22.80 | | | | | | | | | | | | | | | | % 152.37/22.80 | | | | | | | | | | | | | | | Case 2: % 152.37/22.80 | | | | | | | | | | | | | | | | % 152.37/22.80 | | | | | | | | | | | | | | | | (197) ( ~ (all_56_16 = all_56_17) & ~ (all_56_18 = % 152.37/22.80 | | | | | | | | | | | | | | | | all_56_19) & ~ (all_56_20 = all_56_21) & ~ % 152.37/22.80 | | | | | | | | | | | | | | | | (all_56_22 = all_56_23)) | ( ~ (all_56_24 = % 152.37/22.80 | | | | | | | | | | | | | | | | all_56_25) & ~ (all_56_26 = all_56_27) & ~ % 152.37/22.80 | | | | | | | | | | | | | | | | (all_56_28 = all_56_29) & ~ (all_56_30 = % 152.37/22.80 | | | | | | | | | | | | | | | | all_56_31)) % 152.37/22.80 | | | | | | | | | | | | | | | | % 152.37/22.80 | | | | | | | | | | | | | | | | BETA: splitting (197) gives: % 152.37/22.80 | | | | | | | | | | | | | | | | % 152.37/22.80 | | | | | | | | | | | | | | | | Case 1: % 152.37/22.80 | | | | | | | | | | | | | | | | | % 152.37/22.80 | | | | | | | | | | | | | | | | | (198) ~ (all_56_16 = all_56_17) & ~ (all_56_18 = % 152.37/22.80 | | | | | | | | | | | | | | | | | all_56_19) & ~ (all_56_20 = all_56_21) & ~ % 152.37/22.80 | | | | | | | | | | | | | | | | | (all_56_22 = all_56_23) % 152.37/22.80 | | | | | | | | | | | | | | | | | % 152.37/22.80 | | | | | | | | | | | | | | | | | ALPHA: (198) implies: % 152.37/22.80 | | | | | | | | | | | | | | | | | (199) ~ (all_56_18 = all_56_19) % 152.37/22.80 | | | | | | | | | | | | | | | | | % 152.37/22.80 | | | | | | | | | | | | | | | | | REDUCE: (116), (141), (199) imply: % 152.37/22.80 | | | | | | | | | | | | | | | | | (200) $false % 152.37/22.80 | | | | | | | | | | | | | | | | | % 152.37/22.80 | | | | | | | | | | | | | | | | | CLOSE: (200) is inconsistent. % 152.37/22.80 | | | | | | | | | | | | | | | | | % 152.37/22.80 | | | | | | | | | | | | | | | | Case 2: % 152.37/22.80 | | | | | | | | | | | | | | | | | % 152.37/22.80 | | | | | | | | | | | | | | | | | (201) ~ (all_56_24 = all_56_25) & ~ (all_56_26 = % 152.37/22.80 | | | | | | | | | | | | | | | | | all_56_27) & ~ (all_56_28 = all_56_29) & ~ % 152.37/22.80 | | | | | | | | | | | | | | | | | (all_56_30 = all_56_31) % 152.37/22.80 | | | | | | | | | | | | | | | | | % 152.37/22.80 | | | | | | | | | | | | | | | | | ALPHA: (201) implies: % 152.37/22.80 | | | | | | | | | | | | | | | | | (202) ~ (all_56_30 = all_56_31) % 152.37/22.80 | | | | | | | | | | | | | | | | | % 152.37/22.80 | | | | | | | | | | | | | | | | | REDUCE: (69), (70), (202) imply: % 152.37/22.80 | | | | | | | | | | | | | | | | | (203) $false % 152.37/22.80 | | | | | | | | | | | | | | | | | % 152.37/22.80 | | | | | | | | | | | | | | | | | CLOSE: (203) is inconsistent. % 152.37/22.80 | | | | | | | | | | | | | | | | | % 152.37/22.80 | | | | | | | | | | | | | | | | End of split % 152.37/22.80 | | | | | | | | | | | | | | | | % 152.37/22.80 | | | | | | | | | | | | | | | End of split % 152.37/22.80 | | | | | | | | | | | | | | | % 152.37/22.80 | | | | | | | | | | | | | | Case 2: % 152.37/22.80 | | | | | | | | | | | | | | | % 152.37/22.80 | | | | | | | | | | | | | | | (204) ~ (all_58_1 = e1) % 152.37/22.80 | | | | | | | | | | | | | | | % 152.37/22.80 | | | | | | | | | | | | | | | REDUCE: (29), (204) imply: % 152.37/22.80 | | | | | | | | | | | | | | | (205) ~ (all_52_4 = e1) % 152.37/22.80 | | | | | | | | | | | | | | | % 152.37/22.80 | | | | | | | | | | | | | | | REF_CLOSE: (23), (41), (76), (107), (168), (205) are % 152.37/22.80 | | | | | | | | | | | | | | | inconsistent by sub-proof #717. % 152.37/22.80 | | | | | | | | | | | | | | | % 152.37/22.80 | | | | | | | | | | | | | | End of split % 152.37/22.80 | | | | | | | | | | | | | | % 152.37/22.80 | | | | | | | | | | | | | Case 2: % 152.37/22.80 | | | | | | | | | | | | | | % 152.37/22.80 | | | | | | | | | | | | | | (206) ~ (all_58_4 = e2) % 152.37/22.80 | | | | | | | | | | | | | | % 152.37/22.80 | | | | | | | | | | | | | | REDUCE: (16), (206) imply: % 152.37/22.80 | | | | | | | | | | | | | | (207) ~ (all_52_8 = e2) % 152.37/22.80 | | | | | | | | | | | | | | % 152.37/22.80 | | | | | | | | | | | | | | REF_CLOSE: (1), (23), (29), (31), (41), (66), (72), (76), % 152.37/22.80 | | | | | | | | | | | | | | (107), (138), (168), (207) are inconsistent by % 152.37/22.80 | | | | | | | | | | | | | | sub-proof #716. % 152.37/22.80 | | | | | | | | | | | | | | % 152.37/22.80 | | | | | | | | | | | | | End of split % 152.37/22.80 | | | | | | | | | | | | | % 152.37/22.80 | | | | | | | | | | | | Case 2: % 152.37/22.80 | | | | | | | | | | | | | % 152.37/22.80 | | | | | | | | | | | | | (208) ~ (all_58_13 = e2) % 152.37/22.80 | | | | | | | | | | | | | % 152.37/22.80 | | | | | | | | | | | | | REDUCE: (30), (208) imply: % 152.37/22.80 | | | | | | | | | | | | | (209) ~ (all_52_7 = e2) % 152.37/22.80 | | | | | | | | | | | | | % 152.37/22.80 | | | | | | | | | | | | | REF_CLOSE: (54), (71), (93), (120), (157), (209) are % 152.37/22.80 | | | | | | | | | | | | | inconsistent by sub-proof #620. % 152.37/22.80 | | | | | | | | | | | | | % 152.37/22.80 | | | | | | | | | | | | End of split % 152.37/22.80 | | | | | | | | | | | | % 152.37/22.80 | | | | | | | | | | | End of split % 152.37/22.80 | | | | | | | | | | | % 152.37/22.80 | | | | | | | | | | Case 2: % 152.37/22.80 | | | | | | | | | | | % 152.37/22.80 | | | | | | | | | | | (210) all_54_12 = e0 % 152.37/22.80 | | | | | | | | | | | % 152.37/22.80 | | | | | | | | | | | COMBINE_EQS: (13), (210) imply: % 152.37/22.80 | | | | | | | | | | | (211) all_52_3 = e0 % 152.37/22.80 | | | | | | | | | | | % 152.37/22.80 | | | | | | | | | | | REDUCE: (37), (211) imply: % 152.37/22.80 | | | | | | | | | | | (212) $false % 152.37/22.80 | | | | | | | | | | | % 152.37/22.80 | | | | | | | | | | | CLOSE: (212) is inconsistent. % 152.37/22.80 | | | | | | | | | | | % 152.37/22.80 | | | | | | | | | | End of split % 152.37/22.80 | | | | | | | | | | % 152.37/22.80 | | | | | | | | | End of split % 152.37/22.80 | | | | | | | | | % 152.37/22.80 | | | | | | | | End of split % 152.37/22.80 | | | | | | | | % 152.37/22.80 | | | | | | | Case 2: % 152.37/22.80 | | | | | | | | % 152.37/22.80 | | | | | | | | (213) ~ (all_58_2 = e3) % 152.37/22.80 | | | | | | | | % 152.37/22.80 | | | | | | | | REDUCE: (78), (213) imply: % 152.37/22.80 | | | | | | | | (214) ~ (all_52_1 = e3) % 152.37/22.80 | | | | | | | | % 152.37/22.80 | | | | | | | | BETA: splitting (47) gives: % 152.37/22.80 | | | | | | | | % 152.37/22.80 | | | | | | | | Case 1: % 152.37/22.80 | | | | | | | | | % 152.37/22.80 | | | | | | | | | (215) all_54_4 = e3 % 152.37/22.80 | | | | | | | | | % 152.37/22.80 | | | | | | | | | REF_CLOSE: (10), (214), (215) are inconsistent by sub-proof % 152.37/22.80 | | | | | | | | | #634. % 152.37/22.80 | | | | | | | | | % 152.37/22.80 | | | | | | | | Case 2: % 152.37/22.80 | | | | | | | | | % 152.37/22.80 | | | | | | | | | (216) all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0 % 152.37/22.80 | | | | | | | | | % 152.37/22.80 | | | | | | | | | BETA: splitting (216) gives: % 152.37/22.80 | | | | | | | | | % 152.37/22.80 | | | | | | | | | Case 1: % 152.37/22.80 | | | | | | | | | | % 152.37/22.80 | | | | | | | | | | (217) all_54_4 = e2 % 152.37/22.80 | | | | | | | | | | % 152.37/22.80 | | | | | | | | | | REF_CLOSE: (10), (97), (217) are inconsistent by sub-proof % 152.37/22.80 | | | | | | | | | | #633. % 152.37/22.80 | | | | | | | | | | % 152.37/22.80 | | | | | | | | | Case 2: % 152.37/22.80 | | | | | | | | | | % 152.37/22.80 | | | | | | | | | | (218) all_54_4 = e1 | all_54_4 = e0 % 152.37/22.80 | | | | | | | | | | % 152.37/22.80 | | | | | | | | | | BETA: splitting (218) gives: % 152.37/22.80 | | | | | | | | | | % 152.37/22.80 | | | | | | | | | | Case 1: % 152.37/22.80 | | | | | | | | | | | % 152.37/22.80 | | | | | | | | | | | (219) all_54_4 = e1 % 152.37/22.80 | | | | | | | | | | | % 152.37/22.80 | | | | | | | | | | | COMBINE_EQS: (10), (219) imply: % 152.37/22.80 | | | | | | | | | | | (220) all_52_1 = e1 % 152.37/22.80 | | | | | | | | | | | % 152.37/22.80 | | | | | | | | | | | SIMP: (220) implies: % 152.37/22.80 | | | | | | | | | | | (221) all_52_1 = e1 % 152.37/22.80 | | | | | | | | | | | % 152.37/22.80 | | | | | | | | | | | COMBINE_EQS: (99), (221) imply: % 152.37/22.80 | | | | | | | | | | | (222) all_56_9 = e1 % 152.37/22.80 | | | | | | | | | | | % 152.37/22.80 | | | | | | | | | | | REDUCE: (65), (221) imply: % 152.37/22.80 | | | | | | | | | | | (223) ~ (all_52_3 = e1) % 152.37/22.80 | | | | | | | | | | | % 152.37/22.80 | | | | | | | | | | | SIMP: (223) implies: % 152.37/22.80 | | | | | | | | | | | (224) ~ (all_52_3 = e1) % 152.37/22.80 | | | | | | | | | | | % 152.37/22.80 | | | | | | | | | | | REDUCE: (19), (221) imply: % 152.37/22.80 | | | | | | | | | | | (225) op(e3, e1) = all_56_8 % 152.37/22.80 | | | | | | | | | | | % 152.37/22.80 | | | | | | | | | | | BETA: splitting (43) gives: % 152.37/22.80 | | | | | | | | | | | % 152.37/22.80 | | | | | | | | | | | Case 1: % 152.37/22.80 | | | | | | | | | | | | % 152.37/22.80 | | | | | | | | | | | | (226) all_54_12 = e3 % 152.37/22.80 | | | | | | | | | | | | % 152.37/22.80 | | | | | | | | | | | | COMBINE_EQS: (13), (226) imply: % 152.37/22.80 | | | | | | | | | | | | (227) all_52_3 = e3 % 152.37/22.80 | | | | | | | | | | | | % 152.37/22.80 | | | | | | | | | | | | SIMP: (227) implies: % 152.37/22.80 | | | | | | | | | | | | (228) all_52_3 = e3 % 152.37/22.80 | | | | | | | | | | | | % 152.37/22.80 | | | | | | | | | | | | COMBINE_EQS: (111), (228) imply: % 152.37/22.80 | | | | | | | | | | | | (229) all_56_6 = e3 % 152.37/22.80 | | | | | | | | | | | | % 152.37/22.80 | | | | | | | | | | | | COMBINE_EQS: (100), (228) imply: % 152.37/22.80 | | | | | | | | | | | | (230) all_58_12 = e3 % 152.37/22.80 | | | | | | | | | | | | % 152.37/22.80 | | | | | | | | | | | | GROUND_INST: instantiating (33) with all_52_8, all_56_8, e1, % 152.37/22.80 | | | | | | | | | | | | e3, simplifying with (85), (225) gives: % 152.37/22.80 | | | | | | | | | | | | (231) all_56_8 = all_52_8 % 152.37/22.80 | | | | | | | | | | | | % 152.37/22.80 | | | | | | | | | | | | BETA: splitting (11) gives: % 152.37/22.80 | | | | | | | | | | | | % 152.37/22.80 | | | | | | | | | | | | Case 1: % 152.37/22.80 | | | | | | | | | | | | | % 152.37/22.80 | | | | | | | | | | | | | (232) all_58_4 = e2 % 152.37/22.80 | | | | | | | | | | | | | % 152.37/22.80 | | | | | | | | | | | | | COMBINE_EQS: (16), (232) imply: % 152.37/22.80 | | | | | | | | | | | | | (233) all_52_8 = e2 % 152.37/22.80 | | | | | | | | | | | | | % 152.37/22.80 | | | | | | | | | | | | | REDUCE: (1), (233) imply: % 152.37/22.80 | | | | | | | | | | | | | (234) ~ (all_52_4 = e2) % 152.37/22.80 | | | | | | | | | | | | | % 152.37/22.80 | | | | | | | | | | | | | REDUCE: (108), (233) imply: % 152.37/22.80 | | | | | | | | | | | | | (235) ~ (e3 = e2) % 152.37/22.80 | | | | | | | | | | | | | % 152.37/22.80 | | | | | | | | | | | | | SIMP: (235) implies: % 152.37/22.80 | | | | | | | | | | | | | (236) ~ (e3 = e2) % 152.37/22.80 | | | | | | | | | | | | | % 152.37/22.80 | | | | | | | | | | | | | REDUCE: (31), (233) imply: % 152.37/22.80 | | | | | | | | | | | | | (237) ~ (e2 = e0) % 152.37/22.80 | | | | | | | | | | | | | % 152.37/22.80 | | | | | | | | | | | | | BETA: splitting (20) gives: % 152.37/22.80 | | | | | | | | | | | | | % 152.37/22.80 | | | | | | | | | | | | | Case 1: % 152.37/22.80 | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | (238) all_58_1 = e2 % 152.37/22.81 | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | COMBINE_EQS: (29), (238) imply: % 152.37/22.81 | | | | | | | | | | | | | | (239) all_52_4 = e2 % 152.37/22.81 | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | REDUCE: (234), (239) imply: % 152.37/22.81 | | | | | | | | | | | | | | (240) $false % 152.37/22.81 | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | CLOSE: (240) is inconsistent. % 152.37/22.81 | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | Case 2: % 152.37/22.81 | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | (241) ~ (all_58_1 = e2) % 152.37/22.81 | | | | | | | | | | | | | | (242) all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2 % 152.37/22.81 | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | BETA: splitting (242) gives: % 152.37/22.81 | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | Case 1: % 152.37/22.81 | | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | | (243) all_58_3 = e2 % 152.37/22.81 | | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | | COMBINE_EQS: (56), (243) imply: % 152.37/22.81 | | | | | | | | | | | | | | | (244) e2 = e0 % 152.37/22.81 | | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | | REDUCE: (237), (244) imply: % 152.37/22.81 | | | | | | | | | | | | | | | (245) $false % 152.37/22.81 | | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | | CLOSE: (245) is inconsistent. % 152.37/22.81 | | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | Case 2: % 152.37/22.81 | | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | | (246) all_58_7 = e2 | all_58_13 = e2 % 152.37/22.81 | | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | | BETA: splitting (113) gives: % 152.37/22.81 | | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | | Case 1: % 152.37/22.81 | | | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | | | (247) all_54_1 = e2 % 152.37/22.81 | | | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | | | COMBINE_EQS: (23), (247) imply: % 152.37/22.81 | | | | | | | | | | | | | | | | (248) all_52_4 = e2 % 152.37/22.81 | | | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | | | REDUCE: (234), (248) imply: % 152.37/22.81 | | | | | | | | | | | | | | | | (249) $false % 152.37/22.81 | | | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | | | CLOSE: (249) is inconsistent. % 152.37/22.81 | | | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | | Case 2: % 152.37/22.81 | | | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | | | (250) all_54_1 = e1 | all_54_1 = e0 % 152.37/22.81 | | | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | | | BETA: splitting (250) gives: % 152.37/22.81 | | | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | | | Case 1: % 152.37/22.81 | | | | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | | | | (251) all_54_1 = e1 % 152.37/22.81 | | | | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | | | | COMBINE_EQS: (23), (251) imply: % 152.37/22.81 | | | | | | | | | | | | | | | | | (252) all_52_4 = e1 % 152.37/22.81 | | | | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | | | | REDUCE: (14), (252) imply: % 152.37/22.81 | | | | | | | | | | | | | | | | | (253) ~ (all_52_7 = e1) % 152.37/22.81 | | | | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | | | | SIMP: (253) implies: % 152.37/22.81 | | | | | | | | | | | | | | | | | (254) ~ (all_52_7 = e1) % 152.37/22.81 | | | | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | | | | REDUCE: (107), (252) imply: % 152.37/22.81 | | | | | | | | | | | | | | | | | (255) ~ (e3 = e1) % 152.37/22.81 | | | | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | | | | SIMP: (255) implies: % 152.37/22.81 | | | | | | | | | | | | | | | | | (256) ~ (e3 = e1) % 152.37/22.81 | | | | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | | | | BETA: splitting (81) gives: % 152.37/22.81 | | | | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | | | | Case 1: % 152.37/22.81 | | | | | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | | | | | (257) all_58_12 = e1 % 152.37/22.81 | | | | | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (230), (257) imply: % 152.37/22.81 | | | | | | | | | | | | | | | | | | (258) e3 = e1 % 152.37/22.81 | | | | | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | | | | | REDUCE: (256), (258) imply: % 152.37/22.81 | | | | | | | | | | | | | | | | | | (259) $false % 152.37/22.81 | | | | | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | | | | | CLOSE: (259) is inconsistent. % 152.37/22.81 | | | | | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | | | | Case 2: % 152.37/22.81 | | | | | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | | | | | (260) all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1 % 152.37/22.81 | | | | | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | | | | | BETA: splitting (246) gives: % 152.37/22.81 | | | | | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | | | | | Case 1: % 152.37/22.81 | | | | | | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | | | | | | (261) all_58_7 = e2 % 152.37/22.81 | | | | | | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (117), (261) imply: % 152.37/22.81 | | | | | | | | | | | | | | | | | | | (262) e3 = e2 % 152.37/22.81 | | | | | | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | | | | | | SIMP: (262) implies: % 152.37/22.81 | | | | | | | | | | | | | | | | | | | (263) e3 = e2 % 152.37/22.81 | | | | | | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | | | | | | REDUCE: (236), (263) imply: % 152.37/22.81 | | | | | | | | | | | | | | | | | | | (264) $false % 152.37/22.81 | | | | | | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | | | | | | CLOSE: (264) is inconsistent. % 152.37/22.81 | | | | | | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | | | | | Case 2: % 152.37/22.81 | | | | | | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | | | | | | (265) all_58_13 = e2 % 152.37/22.81 | | | | | | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (30), (265) imply: % 152.37/22.81 | | | | | | | | | | | | | | | | | | | (266) all_52_7 = e2 % 152.37/22.81 | | | | | | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (86), (266) imply: % 152.37/22.81 | | | | | | | | | | | | | | | | | | | (267) all_56_14 = e2 % 152.37/22.81 | | | | | | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | | | | | | BETA: splitting (27) gives: % 152.37/22.81 | | | | | | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | | | | | | Case 1: % 152.37/22.81 | | | | | | | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | | | | | | | (268) ( ~ (all_56_0 = all_56_1) & ~ (all_56_2 = % 152.37/22.81 | | | | | | | | | | | | | | | | | | | | all_56_3) & ~ (all_56_4 = all_56_5) & ~ % 152.37/22.81 | | | | | | | | | | | | | | | | | | | | (all_56_6 = all_56_7)) | ( ~ (all_56_8 = % 152.37/22.81 | | | | | | | | | | | | | | | | | | | | all_56_9) & ~ (all_56_10 = all_56_11) & ~ % 152.37/22.81 | | | | | | | | | | | | | | | | | | | | (all_56_12 = all_56_13) & ~ (all_56_14 = % 152.37/22.81 | | | | | | | | | | | | | | | | | | | | all_56_15)) % 152.37/22.81 | | | | | | | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | | | | | | | BETA: splitting (268) gives: % 152.37/22.81 | | | | | | | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | | | | | | | Case 1: % 152.37/22.81 | | | | | | | | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | | | | | | | | (269) ~ (all_56_0 = all_56_1) & ~ (all_56_2 = % 152.37/22.81 | | | | | | | | | | | | | | | | | | | | | all_56_3) & ~ (all_56_4 = all_56_5) & ~ % 152.37/22.81 | | | | | | | | | | | | | | | | | | | | | (all_56_6 = all_56_7) % 152.37/22.81 | | | | | | | | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | | | | | | | | ALPHA: (269) implies: % 152.37/22.81 | | | | | | | | | | | | | | | | | | | | | (270) ~ (all_56_6 = all_56_7) % 152.37/22.81 | | | | | | | | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | | | | | | | | REDUCE: (105), (229), (270) imply: % 152.37/22.81 | | | | | | | | | | | | | | | | | | | | | (271) $false % 152.37/22.81 | | | | | | | | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | | | | | | | | CLOSE: (271) is inconsistent. % 152.37/22.81 | | | | | | | | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | | | | | | | Case 2: % 152.37/22.81 | | | | | | | | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | | | | | | | | (272) ~ (all_56_8 = all_56_9) & ~ (all_56_10 = % 152.37/22.81 | | | | | | | | | | | | | | | | | | | | | all_56_11) & ~ (all_56_12 = all_56_13) & ~ % 152.37/22.81 | | | | | | | | | | | | | | | | | | | | | (all_56_14 = all_56_15) % 152.37/22.81 | | | | | | | | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | | | | | | | | ALPHA: (272) implies: % 152.37/22.81 | | | | | | | | | | | | | | | | | | | | | (273) ~ (all_56_14 = all_56_15) % 152.37/22.81 | | | | | | | | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | | | | | | | | REDUCE: (38), (267), (273) imply: % 152.37/22.81 | | | | | | | | | | | | | | | | | | | | | (274) $false % 152.37/22.81 | | | | | | | | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | | | | | | | | CLOSE: (274) is inconsistent. % 152.37/22.81 | | | | | | | | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | | | | | | | End of split % 152.37/22.81 | | | | | | | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | | | | | | Case 2: % 152.37/22.81 | | | | | | | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | | | | | | | (275) ( ~ (all_56_16 = all_56_17) & ~ (all_56_18 = % 152.37/22.81 | | | | | | | | | | | | | | | | | | | | all_56_19) & ~ (all_56_20 = all_56_21) & ~ % 152.37/22.81 | | | | | | | | | | | | | | | | | | | | (all_56_22 = all_56_23)) | ( ~ (all_56_24 = % 152.37/22.81 | | | | | | | | | | | | | | | | | | | | all_56_25) & ~ (all_56_26 = all_56_27) & ~ % 152.37/22.81 | | | | | | | | | | | | | | | | | | | | (all_56_28 = all_56_29) & ~ (all_56_30 = % 152.37/22.81 | | | | | | | | | | | | | | | | | | | | all_56_31)) % 152.37/22.81 | | | | | | | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | | | | | | | BETA: splitting (275) gives: % 152.37/22.81 | | | | | | | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | | | | | | | Case 1: % 152.37/22.81 | | | | | | | | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | | | | | | | | (276) ~ (all_56_16 = all_56_17) & ~ (all_56_18 = % 152.37/22.81 | | | | | | | | | | | | | | | | | | | | | all_56_19) & ~ (all_56_20 = all_56_21) & ~ % 152.37/22.81 | | | | | | | | | | | | | | | | | | | | | (all_56_22 = all_56_23) % 152.37/22.81 | | | | | | | | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | | | | | | | | ALPHA: (276) implies: % 152.37/22.81 | | | | | | | | | | | | | | | | | | | | | (277) ~ (all_56_22 = all_56_23) % 152.37/22.81 | | | | | | | | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | | | | | | | | REDUCE: (28), (110), (277) imply: % 152.37/22.81 | | | | | | | | | | | | | | | | | | | | | (278) ~ (all_52_11 = e1) % 152.37/22.81 | | | | | | | | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (260) gives: % 152.37/22.81 | | | | | | | | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.37/22.81 | | | | | | | | | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | | | | | | | | | (279) all_58_13 = e1 % 152.37/22.81 | | | | | | | | | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (30), (279) imply: % 152.37/22.81 | | | | | | | | | | | | | | | | | | | | | | (280) all_52_7 = e1 % 152.37/22.81 | | | | | | | | | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (254), (280) imply: % 152.37/22.81 | | | | | | | | | | | | | | | | | | | | | | (281) $false % 152.37/22.81 | | | | | | | | | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (281) is inconsistent. % 152.37/22.81 | | | | | | | | | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.37/22.81 | | | | | | | | | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | | | | | | | | | (282) all_58_14 = e1 | all_58_15 = e1 % 152.37/22.81 | | | | | | | | | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (50), (77), (96), (278), (282) are inconsistent by % 152.37/22.81 | | | | | | | | | | | | | | | | | | | | | | sub-proof #619. % 152.37/22.81 | | | | | | | | | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | | | | | | | | End of split % 152.37/22.81 | | | | | | | | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | | | | | | | Case 2: % 152.37/22.81 | | | | | | | | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | | | | | | | | (283) ~ (all_56_24 = all_56_25) & ~ (all_56_26 = % 152.37/22.81 | | | | | | | | | | | | | | | | | | | | | all_56_27) & ~ (all_56_28 = all_56_29) & ~ % 152.37/22.81 | | | | | | | | | | | | | | | | | | | | | (all_56_30 = all_56_31) % 152.37/22.81 | | | | | | | | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | | | | | | | | ALPHA: (283) implies: % 152.37/22.81 | | | | | | | | | | | | | | | | | | | | | (284) ~ (all_56_30 = all_56_31) % 152.37/22.81 | | | | | | | | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | | | | | | | | REDUCE: (69), (70), (284) imply: % 152.37/22.81 | | | | | | | | | | | | | | | | | | | | | (285) $false % 152.37/22.81 | | | | | | | | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | | | | | | | | CLOSE: (285) is inconsistent. % 152.37/22.81 | | | | | | | | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | | | | | | | End of split % 152.37/22.81 | | | | | | | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | | | | | | End of split % 152.37/22.81 | | | | | | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | | | | | End of split % 152.37/22.81 | | | | | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | | | | End of split % 152.37/22.81 | | | | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | | | Case 2: % 152.37/22.81 | | | | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | | | | (286) all_54_1 = e0 % 152.37/22.81 | | | | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | | | | COMBINE_EQS: (23), (286) imply: % 152.37/22.81 | | | | | | | | | | | | | | | | | (287) all_52_4 = e0 % 152.37/22.81 | | | | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | | | | REDUCE: (41), (287) imply: % 152.37/22.81 | | | | | | | | | | | | | | | | | (288) $false % 152.37/22.81 | | | | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | | | | CLOSE: (288) is inconsistent. % 152.37/22.81 | | | | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | | | End of split % 152.37/22.81 | | | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | | End of split % 152.37/22.81 | | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | End of split % 152.37/22.81 | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | End of split % 152.37/22.81 | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | Case 2: % 152.37/22.81 | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | (289) ~ (all_58_4 = e2) % 152.37/22.81 | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | REDUCE: (16), (289) imply: % 152.37/22.81 | | | | | | | | | | | | | (290) ~ (all_52_8 = e2) % 152.37/22.81 | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | BETA: splitting (138) gives: % 152.37/22.81 | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | Case 1: % 152.37/22.81 | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | (291) all_54_2 = e2 % 152.37/22.81 | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | COMBINE_EQS: (72), (291) imply: % 152.37/22.81 | | | | | | | | | | | | | | (292) all_52_8 = e2 % 152.37/22.81 | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | REDUCE: (290), (292) imply: % 152.37/22.81 | | | | | | | | | | | | | | (293) $false % 152.37/22.81 | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | CLOSE: (293) is inconsistent. % 152.37/22.81 | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | Case 2: % 152.37/22.81 | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | (294) all_54_2 = e1 | all_54_2 = e0 % 152.37/22.81 | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | BETA: splitting (294) gives: % 152.37/22.81 | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | Case 1: % 152.37/22.81 | | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | | (295) all_54_2 = e1 % 152.37/22.81 | | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | | COMBINE_EQS: (72), (295) imply: % 152.37/22.81 | | | | | | | | | | | | | | | (296) all_52_8 = e1 % 152.37/22.81 | | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | | COMBINE_EQS: (231), (296) imply: % 152.37/22.81 | | | | | | | | | | | | | | | (297) all_56_8 = e1 % 152.37/22.81 | | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | | REDUCE: (1), (296) imply: % 152.37/22.81 | | | | | | | | | | | | | | | (298) ~ (all_52_4 = e1) % 152.37/22.81 | | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | | BETA: splitting (113) gives: % 152.37/22.81 | | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | | Case 1: % 152.37/22.81 | | | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | | | (299) all_54_1 = e2 % 152.37/22.81 | | | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | | | COMBINE_EQS: (23), (299) imply: % 152.37/22.81 | | | | | | | | | | | | | | | | (300) all_52_4 = e2 % 152.37/22.81 | | | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | | | COMBINE_EQS: (133), (300) imply: % 152.37/22.81 | | | | | | | | | | | | | | | | (301) all_56_16 = e2 % 152.37/22.81 | | | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | | | BETA: splitting (27) gives: % 152.37/22.81 | | | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | | | Case 1: % 152.37/22.81 | | | | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | | | | (302) ( ~ (all_56_0 = all_56_1) & ~ (all_56_2 = % 152.37/22.81 | | | | | | | | | | | | | | | | | all_56_3) & ~ (all_56_4 = all_56_5) & ~ % 152.37/22.81 | | | | | | | | | | | | | | | | | (all_56_6 = all_56_7)) | ( ~ (all_56_8 = % 152.37/22.81 | | | | | | | | | | | | | | | | | all_56_9) & ~ (all_56_10 = all_56_11) & ~ % 152.37/22.81 | | | | | | | | | | | | | | | | | (all_56_12 = all_56_13) & ~ (all_56_14 = % 152.37/22.81 | | | | | | | | | | | | | | | | | all_56_15)) % 152.37/22.81 | | | | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | | | | BETA: splitting (302) gives: % 152.37/22.81 | | | | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | | | | Case 1: % 152.37/22.81 | | | | | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | | | | | (303) ~ (all_56_0 = all_56_1) & ~ (all_56_2 = % 152.37/22.81 | | | | | | | | | | | | | | | | | | all_56_3) & ~ (all_56_4 = all_56_5) & ~ % 152.37/22.81 | | | | | | | | | | | | | | | | | | (all_56_6 = all_56_7) % 152.37/22.81 | | | | | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | | | | | ALPHA: (303) implies: % 152.37/22.81 | | | | | | | | | | | | | | | | | | (304) ~ (all_56_6 = all_56_7) % 152.37/22.81 | | | | | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | | | | | REDUCE: (105), (229), (304) imply: % 152.37/22.81 | | | | | | | | | | | | | | | | | | (305) $false % 152.37/22.81 | | | | | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | | | | | CLOSE: (305) is inconsistent. % 152.37/22.81 | | | | | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | | | | Case 2: % 152.37/22.81 | | | | | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | | | | | (306) ~ (all_56_8 = all_56_9) & ~ (all_56_10 = % 152.37/22.81 | | | | | | | | | | | | | | | | | | all_56_11) & ~ (all_56_12 = all_56_13) & ~ % 152.37/22.81 | | | | | | | | | | | | | | | | | | (all_56_14 = all_56_15) % 152.37/22.81 | | | | | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | | | | | ALPHA: (306) implies: % 152.37/22.81 | | | | | | | | | | | | | | | | | | (307) ~ (all_56_8 = all_56_9) % 152.37/22.81 | | | | | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | | | | | REDUCE: (222), (297), (307) imply: % 152.37/22.81 | | | | | | | | | | | | | | | | | | (308) $false % 152.37/22.81 | | | | | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | | | | | CLOSE: (308) is inconsistent. % 152.37/22.81 | | | | | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | | | | End of split % 152.37/22.81 | | | | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | | | Case 2: % 152.37/22.81 | | | | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | | | | (309) ( ~ (all_56_16 = all_56_17) & ~ (all_56_18 = % 152.37/22.81 | | | | | | | | | | | | | | | | | all_56_19) & ~ (all_56_20 = all_56_21) & ~ % 152.37/22.81 | | | | | | | | | | | | | | | | | (all_56_22 = all_56_23)) | ( ~ (all_56_24 = % 152.37/22.81 | | | | | | | | | | | | | | | | | all_56_25) & ~ (all_56_26 = all_56_27) & ~ % 152.37/22.81 | | | | | | | | | | | | | | | | | (all_56_28 = all_56_29) & ~ (all_56_30 = % 152.37/22.81 | | | | | | | | | | | | | | | | | all_56_31)) % 152.37/22.81 | | | | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | | | | BETA: splitting (309) gives: % 152.37/22.81 | | | | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | | | | Case 1: % 152.37/22.81 | | | | | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | | | | | (310) ~ (all_56_16 = all_56_17) & ~ (all_56_18 = % 152.37/22.81 | | | | | | | | | | | | | | | | | | all_56_19) & ~ (all_56_20 = all_56_21) & ~ % 152.37/22.81 | | | | | | | | | | | | | | | | | | (all_56_22 = all_56_23) % 152.37/22.81 | | | | | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | | | | | ALPHA: (310) implies: % 152.37/22.81 | | | | | | | | | | | | | | | | | | (311) ~ (all_56_16 = all_56_17) % 152.37/22.81 | | | | | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | | | | | REDUCE: (128), (301), (311) imply: % 152.37/22.81 | | | | | | | | | | | | | | | | | | (312) $false % 152.37/22.81 | | | | | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | | | | | CLOSE: (312) is inconsistent. % 152.37/22.81 | | | | | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | | | | Case 2: % 152.37/22.81 | | | | | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | | | | | (313) ~ (all_56_24 = all_56_25) & ~ (all_56_26 = % 152.37/22.81 | | | | | | | | | | | | | | | | | | all_56_27) & ~ (all_56_28 = all_56_29) & ~ % 152.37/22.81 | | | | | | | | | | | | | | | | | | (all_56_30 = all_56_31) % 152.37/22.81 | | | | | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | | | | | ALPHA: (313) implies: % 152.37/22.81 | | | | | | | | | | | | | | | | | | (314) ~ (all_56_30 = all_56_31) % 152.37/22.81 | | | | | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | | | | | REDUCE: (69), (70), (314) imply: % 152.37/22.81 | | | | | | | | | | | | | | | | | | (315) $false % 152.37/22.81 | | | | | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | | | | | CLOSE: (315) is inconsistent. % 152.37/22.81 | | | | | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | | | | End of split % 152.37/22.81 | | | | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | | | End of split % 152.37/22.81 | | | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | | Case 2: % 152.37/22.81 | | | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | | | (316) all_54_1 = e1 | all_54_1 = e0 % 152.37/22.81 | | | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | | | REF_CLOSE: (23), (41), (298), (316) are inconsistent by % 152.37/22.81 | | | | | | | | | | | | | | | | sub-proof #628. % 152.37/22.81 | | | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | | End of split % 152.37/22.81 | | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | Case 2: % 152.37/22.81 | | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | | (317) all_54_2 = e0 % 152.37/22.81 | | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | | COMBINE_EQS: (72), (317) imply: % 152.37/22.81 | | | | | | | | | | | | | | | (318) all_52_8 = e0 % 152.37/22.81 | | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | | REDUCE: (31), (318) imply: % 152.37/22.81 | | | | | | | | | | | | | | | (319) $false % 152.37/22.81 | | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | | CLOSE: (319) is inconsistent. % 152.37/22.81 | | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | End of split % 152.37/22.81 | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | End of split % 152.37/22.81 | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | End of split % 152.37/22.81 | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | Case 2: % 152.37/22.81 | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | (320) all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0 % 152.37/22.81 | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | REF_CLOSE: (13), (37), (130), (224), (320) are inconsistent % 152.37/22.81 | | | | | | | | | | | | by sub-proof #615. % 152.37/22.81 | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | End of split % 152.37/22.81 | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | Case 2: % 152.37/22.81 | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | (321) all_54_4 = e0 % 152.37/22.81 | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | REF_CLOSE: (10), (60), (321) are inconsistent by sub-proof % 152.37/22.81 | | | | | | | | | | | #614. % 152.37/22.81 | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | End of split % 152.37/22.81 | | | | | | | | | | % 152.37/22.81 | | | | | | | | | End of split % 152.37/22.81 | | | | | | | | | % 152.37/22.81 | | | | | | | | End of split % 152.37/22.81 | | | | | | | | % 152.37/22.81 | | | | | | | End of split % 152.37/22.81 | | | | | | | % 152.37/22.81 | | | | | | End of split % 152.37/22.81 | | | | | | % 152.37/22.81 | | | | | Case 2: % 152.37/22.81 | | | | | | % 152.37/22.81 | | | | | | (322) all_54_8 = e1 | all_54_8 = e0 % 152.37/22.81 | | | | | | % 152.37/22.81 | | | | | | REF_CLOSE: (39), (57), (74), (322) are inconsistent by sub-proof % 152.37/22.81 | | | | | | #664. % 152.37/22.81 | | | | | | % 152.37/22.81 | | | | | End of split % 152.37/22.81 | | | | | % 152.37/22.81 | | | | End of split % 152.37/22.81 | | | | % 152.37/22.81 | | | Case 2: % 152.37/22.81 | | | | % 152.37/22.81 | | | | (323) all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0 % 152.37/22.81 | | | | % 152.37/22.81 | | | | BETA: splitting (323) gives: % 152.37/22.81 | | | | % 152.37/22.81 | | | | Case 1: % 152.37/22.81 | | | | | % 152.37/22.81 | | | | | (324) all_54_9 = e2 % 152.37/22.81 | | | | | % 152.37/22.81 | | | | | COMBINE_EQS: (3), (324) imply: % 152.37/22.81 | | | | | (325) all_52_6 = e2 % 152.37/22.81 | | | | | % 152.37/22.81 | | | | | REDUCE: (36), (325) imply: % 152.37/22.81 | | | | | (326) ~ (all_52_2 = e2) % 152.37/22.81 | | | | | % 152.37/22.81 | | | | | REDUCE: (95), (325) imply: % 152.37/22.81 | | | | | (327) ~ (all_52_4 = e2) % 152.37/22.81 | | | | | % 152.37/22.81 | | | | | REDUCE: (53), (325) imply: % 152.37/22.81 | | | | | (328) ~ (e2 = e0) % 152.37/22.81 | | | | | % 152.37/22.81 | | | | | REDUCE: (42), (325) imply: % 152.37/22.81 | | | | | (329) op(e1, e2) = e2 % 152.37/22.81 | | | | | % 152.37/22.81 | | | | | BETA: splitting (92) gives: % 152.37/22.81 | | | | | % 152.37/22.81 | | | | | Case 1: % 152.37/22.81 | | | | | | % 152.37/22.81 | | | | | | (330) all_54_8 = e3 % 152.37/22.81 | | | | | | % 152.37/22.81 | | | | | | COMBINE_EQS: (74), (330) imply: % 152.37/22.81 | | | | | | (331) all_52_2 = e3 % 152.37/22.81 | | | | | | % 152.37/22.81 | | | | | | REDUCE: (90), (331) imply: % 152.37/22.81 | | | | | | (332) ~ (all_52_1 = e3) % 152.37/22.81 | | | | | | % 152.37/22.81 | | | | | | REDUCE: (49), (331) imply: % 152.37/22.81 | | | | | | (333) op(e1, e3) = e3 % 152.37/22.81 | | | | | | % 152.37/22.81 | | | | | | BETA: splitting (47) gives: % 152.37/22.81 | | | | | | % 152.37/22.81 | | | | | | Case 1: % 152.37/22.81 | | | | | | | % 152.37/22.81 | | | | | | | (334) all_54_4 = e3 % 152.37/22.81 | | | | | | | % 152.37/22.81 | | | | | | | COMBINE_EQS: (10), (334) imply: % 152.37/22.81 | | | | | | | (335) all_52_1 = e3 % 152.37/22.81 | | | | | | | % 152.37/22.81 | | | | | | | REDUCE: (332), (335) imply: % 152.37/22.81 | | | | | | | (336) $false % 152.37/22.81 | | | | | | | % 152.37/22.81 | | | | | | | CLOSE: (336) is inconsistent. % 152.37/22.81 | | | | | | | % 152.37/22.81 | | | | | | Case 2: % 152.37/22.81 | | | | | | | % 152.37/22.81 | | | | | | | (337) ~ (all_54_4 = e3) % 152.37/22.81 | | | | | | | (338) all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0 % 152.37/22.81 | | | | | | | % 152.37/22.81 | | | | | | | BETA: splitting (94) gives: % 152.37/22.81 | | | | | | | % 152.37/22.81 | | | | | | | Case 1: % 152.37/22.81 | | | | | | | | % 152.37/22.81 | | | | | | | | (339) all_58_2 = e3 % 152.37/22.81 | | | | | | | | % 152.37/22.81 | | | | | | | | COMBINE_EQS: (78), (339) imply: % 152.37/22.81 | | | | | | | | (340) all_52_1 = e3 % 152.37/22.81 | | | | | | | | % 152.37/22.81 | | | | | | | | REDUCE: (332), (340) imply: % 152.37/22.81 | | | | | | | | (341) $false % 152.37/22.81 | | | | | | | | % 152.37/22.81 | | | | | | | | CLOSE: (341) is inconsistent. % 152.37/22.81 | | | | | | | | % 152.37/22.81 | | | | | | | Case 2: % 152.37/22.81 | | | | | | | | % 152.37/22.81 | | | | | | | | (342) all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3 % 152.37/22.81 | | | | | | | | % 152.37/22.81 | | | | | | | | BETA: splitting (12) gives: % 152.37/22.81 | | | | | | | | % 152.37/22.81 | | | | | | | | Case 1: % 152.37/22.81 | | | | | | | | | % 152.37/22.81 | | | | | | | | | (343) all_58_0 = e2 % 152.37/22.81 | | | | | | | | | % 152.37/22.81 | | | | | | | | | REF_CLOSE: (4), (37), (39), (60), (78), (91), (100), (328), % 152.37/22.81 | | | | | | | | | (343) are inconsistent by sub-proof #613. % 152.37/22.81 | | | | | | | | | % 152.37/22.81 | | | | | | | | Case 2: % 152.37/22.81 | | | | | | | | | % 152.37/22.81 | | | | | | | | | (344) all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2 % 152.37/22.81 | | | | | | | | | % 152.37/22.81 | | | | | | | | | BETA: splitting (344) gives: % 152.37/22.81 | | | | | | | | | % 152.37/22.81 | | | | | | | | | Case 1: % 152.37/22.81 | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | (345) all_58_1 = e2 % 152.37/22.81 | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | COMBINE_EQS: (29), (345) imply: % 152.37/22.81 | | | | | | | | | | (346) all_52_4 = e2 % 152.37/22.81 | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | REDUCE: (327), (346) imply: % 152.37/22.81 | | | | | | | | | | (347) $false % 152.37/22.81 | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | CLOSE: (347) is inconsistent. % 152.37/22.81 | | | | | | | | | | % 152.37/22.81 | | | | | | | | | Case 2: % 152.37/22.81 | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | (348) all_58_4 = e2 | all_58_9 = e2 % 152.37/22.81 | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | BETA: splitting (338) gives: % 152.37/22.81 | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | Case 1: % 152.37/22.81 | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | (349) all_54_4 = e2 % 152.37/22.81 | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | COMBINE_EQS: (10), (349) imply: % 152.37/22.81 | | | | | | | | | | | (350) all_52_1 = e2 % 152.37/22.81 | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | REDUCE: (97), (350) imply: % 152.37/22.81 | | | | | | | | | | | (351) $false % 152.37/22.81 | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | CLOSE: (351) is inconsistent. % 152.37/22.81 | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | Case 2: % 152.37/22.81 | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | (352) ~ (all_54_4 = e2) % 152.37/22.81 | | | | | | | | | | | (353) all_54_4 = e1 | all_54_4 = e0 % 152.37/22.81 | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | BETA: splitting (353) gives: % 152.37/22.81 | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | Case 1: % 152.37/22.81 | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | (354) all_54_4 = e1 % 152.37/22.81 | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | COMBINE_EQS: (10), (354) imply: % 152.37/22.81 | | | | | | | | | | | | (355) all_52_1 = e1 % 152.37/22.81 | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | REDUCE: (6), (355) imply: % 152.37/22.81 | | | | | | | | | | | | (356) ~ (all_52_9 = e1) % 152.37/22.81 | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | SIMP: (356) implies: % 152.37/22.81 | | | | | | | | | | | | (357) ~ (all_52_9 = e1) % 152.37/22.81 | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | REDUCE: (97), (355) imply: % 152.37/22.81 | | | | | | | | | | | | (358) ~ (e2 = e1) % 152.37/22.81 | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | SIMP: (358) implies: % 152.37/22.81 | | | | | | | | | | | | (359) ~ (e2 = e1) % 152.37/22.81 | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | REDUCE: (60), (355) imply: % 152.37/22.81 | | | | | | | | | | | | (360) ~ (e1 = e0) % 152.37/22.81 | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | BETA: splitting (21) gives: % 152.37/22.81 | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | Case 1: % 152.37/22.81 | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | (361) all_54_6 = e3 % 152.37/22.81 | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | COMBINE_EQS: (51), (361) imply: % 152.37/22.81 | | | | | | | | | | | | | (362) all_52_9 = e3 % 152.37/22.81 | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | SIMP: (362) implies: % 152.37/22.81 | | | | | | | | | | | | | (363) all_52_9 = e3 % 152.37/22.81 | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | COMBINE_EQS: (44), (363) imply: % 152.37/22.81 | | | | | | | | | | | | | (364) all_56_13 = e3 % 152.37/22.81 | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | REDUCE: (8), (363) imply: % 152.37/22.81 | | | | | | | | | | | | | (365) ~ (e3 = e2) % 152.37/22.81 | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | REDUCE: (357), (363) imply: % 152.37/22.81 | | | | | | | | | | | | | (366) ~ (e3 = e1) % 152.37/22.81 | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | REDUCE: (48), (363) imply: % 152.37/22.81 | | | | | | | | | | | | | (367) ~ (e3 = e0) % 152.37/22.81 | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | REDUCE: (84), (363) imply: % 152.37/22.81 | | | | | | | | | | | | | (368) op(e1, e3) = all_56_12 % 152.37/22.81 | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | BETA: splitting (348) gives: % 152.37/22.81 | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | Case 1: % 152.37/22.81 | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | (369) all_58_4 = e2 % 152.37/22.81 | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | COMBINE_EQS: (16), (369) imply: % 152.37/22.81 | | | | | | | | | | | | | | (370) all_52_8 = e2 % 152.37/22.81 | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | COMBINE_EQS: (55), (370) imply: % 152.37/22.81 | | | | | | | | | | | | | | (371) all_56_5 = e2 % 152.37/22.81 | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | REDUCE: (108), (370) imply: % 152.37/22.81 | | | | | | | | | | | | | | (372) ~ (e3 = e2) % 152.37/22.81 | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | REDUCE: (68), (370) imply: % 152.37/22.81 | | | | | | | | | | | | | | (373) op(e1, e2) = all_56_4 % 152.37/22.81 | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | BETA: splitting (62) gives: % 152.37/22.81 | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | Case 1: % 152.37/22.81 | | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | | (374) all_58_4 = e1 % 152.37/22.81 | | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | | COMBINE_EQS: (369), (374) imply: % 152.37/22.81 | | | | | | | | | | | | | | | (375) e2 = e1 % 152.37/22.81 | | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | | REDUCE: (359), (375) imply: % 152.37/22.81 | | | | | | | | | | | | | | | (376) $false % 152.37/22.81 | | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | | CLOSE: (376) is inconsistent. % 152.37/22.81 | | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | Case 2: % 152.37/22.81 | | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | | (377) all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1 % 152.37/22.81 | | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | | BETA: splitting (377) gives: % 152.37/22.81 | | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | | Case 1: % 152.37/22.81 | | | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | | | (378) all_58_5 = e1 % 152.37/22.81 | | | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | | | REF_CLOSE: (17), (56), (342), (365), (366), (367), (378) are % 152.37/22.81 | | | | | | | | | | | | | | | | inconsistent by sub-proof #611. % 152.37/22.81 | | | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | | Case 2: % 152.37/22.81 | | | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | | | (379) all_58_8 = e1 | all_58_14 = e1 % 152.37/22.81 | | | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | | | BETA: splitting (379) gives: % 152.37/22.81 | | | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | | | Case 1: % 152.37/22.81 | | | | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | | | | (380) all_58_8 = e1 % 152.37/22.81 | | | | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | | | | REF_CLOSE: (52), (360), (380) are inconsistent by sub-proof % 152.37/22.81 | | | | | | | | | | | | | | | | | #621. % 152.37/22.81 | | | | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | | | Case 2: % 152.37/22.81 | | | | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | | | | (381) all_58_14 = e1 % 152.37/22.81 | | | | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | | | | COMBINE_EQS: (96), (381) imply: % 152.37/22.81 | | | | | | | | | | | | | | | | | (382) all_52_11 = e1 % 152.37/22.81 | | | | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | | | | SIMP: (382) implies: % 152.37/22.81 | | | | | | | | | | | | | | | | | (383) all_52_11 = e1 % 152.37/22.81 | | | | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | | | | COMBINE_EQS: (110), (383) imply: % 152.37/22.81 | | | | | | | | | | | | | | | | | (384) all_56_22 = e1 % 152.37/22.81 | | | | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (33) with e2, all_56_4, e2, e1, % 152.37/22.81 | | | | | | | | | | | | | | | | | simplifying with (329), (373) gives: % 152.37/22.81 | | | | | | | | | | | | | | | | | (385) all_56_4 = e2 % 152.37/22.81 | | | | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (33) with e3, all_56_12, e3, e1, % 152.37/22.81 | | | | | | | | | | | | | | | | | simplifying with (333), (368) gives: % 152.37/22.81 | | | | | | | | | | | | | | | | | (386) all_56_12 = e3 % 152.37/22.81 | | | | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | | | | BETA: splitting (27) gives: % 152.37/22.81 | | | | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | | | | Case 1: % 152.37/22.81 | | | | | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | | | | | (387) ( ~ (all_56_0 = all_56_1) & ~ (all_56_2 = % 152.37/22.81 | | | | | | | | | | | | | | | | | | all_56_3) & ~ (all_56_4 = all_56_5) & ~ % 152.37/22.81 | | | | | | | | | | | | | | | | | | (all_56_6 = all_56_7)) | ( ~ (all_56_8 = % 152.37/22.81 | | | | | | | | | | | | | | | | | | all_56_9) & ~ (all_56_10 = all_56_11) & ~ % 152.37/22.81 | | | | | | | | | | | | | | | | | | (all_56_12 = all_56_13) & ~ (all_56_14 = % 152.37/22.81 | | | | | | | | | | | | | | | | | | all_56_15)) % 152.37/22.81 | | | | | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | | | | | BETA: splitting (387) gives: % 152.37/22.81 | | | | | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | | | | | Case 1: % 152.37/22.81 | | | | | | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | | | | | | (388) ~ (all_56_0 = all_56_1) & ~ (all_56_2 = % 152.37/22.81 | | | | | | | | | | | | | | | | | | | all_56_3) & ~ (all_56_4 = all_56_5) & ~ % 152.37/22.81 | | | | | | | | | | | | | | | | | | | (all_56_6 = all_56_7) % 152.37/22.81 | | | | | | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | | | | | | ALPHA: (388) implies: % 152.37/22.81 | | | | | | | | | | | | | | | | | | | (389) ~ (all_56_4 = all_56_5) % 152.37/22.81 | | | | | | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | | | | | | REDUCE: (371), (385), (389) imply: % 152.37/22.81 | | | | | | | | | | | | | | | | | | | (390) $false % 152.37/22.81 | | | | | | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | | | | | | CLOSE: (390) is inconsistent. % 152.37/22.81 | | | | | | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | | | | | Case 2: % 152.37/22.81 | | | | | | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | | | | | | (391) ~ (all_56_8 = all_56_9) & ~ (all_56_10 = % 152.37/22.81 | | | | | | | | | | | | | | | | | | | all_56_11) & ~ (all_56_12 = all_56_13) & ~ % 152.37/22.81 | | | | | | | | | | | | | | | | | | | (all_56_14 = all_56_15) % 152.37/22.81 | | | | | | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | | | | | | ALPHA: (391) implies: % 152.37/22.81 | | | | | | | | | | | | | | | | | | | (392) ~ (all_56_12 = all_56_13) % 152.37/22.81 | | | | | | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | | | | | | REDUCE: (364), (386), (392) imply: % 152.37/22.81 | | | | | | | | | | | | | | | | | | | (393) $false % 152.37/22.81 | | | | | | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | | | | | | CLOSE: (393) is inconsistent. % 152.37/22.81 | | | | | | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | | | | | End of split % 152.37/22.81 | | | | | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | | | | Case 2: % 152.37/22.81 | | | | | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | | | | | (394) ( ~ (all_56_16 = all_56_17) & ~ (all_56_18 = % 152.37/22.81 | | | | | | | | | | | | | | | | | | all_56_19) & ~ (all_56_20 = all_56_21) & ~ % 152.37/22.81 | | | | | | | | | | | | | | | | | | (all_56_22 = all_56_23)) | ( ~ (all_56_24 = % 152.37/22.81 | | | | | | | | | | | | | | | | | | all_56_25) & ~ (all_56_26 = all_56_27) & ~ % 152.37/22.81 | | | | | | | | | | | | | | | | | | (all_56_28 = all_56_29) & ~ (all_56_30 = % 152.37/22.81 | | | | | | | | | | | | | | | | | | all_56_31)) % 152.37/22.81 | | | | | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | | | | | BETA: splitting (394) gives: % 152.37/22.81 | | | | | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | | | | | Case 1: % 152.37/22.81 | | | | | | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | | | | | | (395) ~ (all_56_16 = all_56_17) & ~ (all_56_18 = % 152.37/22.81 | | | | | | | | | | | | | | | | | | | all_56_19) & ~ (all_56_20 = all_56_21) & ~ % 152.37/22.81 | | | | | | | | | | | | | | | | | | | (all_56_22 = all_56_23) % 152.37/22.81 | | | | | | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | | | | | | ALPHA: (395) implies: % 152.37/22.81 | | | | | | | | | | | | | | | | | | | (396) ~ (all_56_22 = all_56_23) % 152.37/22.81 | | | | | | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | | | | | | REDUCE: (28), (384), (396) imply: % 152.37/22.81 | | | | | | | | | | | | | | | | | | | (397) $false % 152.37/22.81 | | | | | | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | | | | | | CLOSE: (397) is inconsistent. % 152.37/22.81 | | | | | | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | | | | | Case 2: % 152.37/22.81 | | | | | | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | | | | | | (398) ~ (all_56_24 = all_56_25) & ~ (all_56_26 = % 152.37/22.81 | | | | | | | | | | | | | | | | | | | all_56_27) & ~ (all_56_28 = all_56_29) & ~ % 152.37/22.81 | | | | | | | | | | | | | | | | | | | (all_56_30 = all_56_31) % 152.37/22.81 | | | | | | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | | | | | | ALPHA: (398) implies: % 152.37/22.81 | | | | | | | | | | | | | | | | | | | (399) ~ (all_56_30 = all_56_31) % 152.37/22.81 | | | | | | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | | | | | | REDUCE: (69), (70), (399) imply: % 152.37/22.81 | | | | | | | | | | | | | | | | | | | (400) $false % 152.37/22.81 | | | | | | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | | | | | | CLOSE: (400) is inconsistent. % 152.37/22.81 | | | | | | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | | | | | End of split % 152.37/22.81 | | | | | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | | | | End of split % 152.37/22.81 | | | | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | | | End of split % 152.37/22.81 | | | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | | End of split % 152.37/22.81 | | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | End of split % 152.37/22.81 | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | Case 2: % 152.37/22.81 | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | (401) all_58_9 = e2 % 152.37/22.81 | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | COMBINE_EQS: (106), (401) imply: % 152.37/22.81 | | | | | | | | | | | | | | (402) e3 = e2 % 152.37/22.81 | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | REDUCE: (365), (402) imply: % 152.37/22.81 | | | | | | | | | | | | | | (403) $false % 152.37/22.81 | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | | CLOSE: (403) is inconsistent. % 152.37/22.81 | | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | End of split % 152.37/22.81 | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | Case 2: % 152.37/22.81 | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | (404) all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0 % 152.37/22.81 | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | | REF_CLOSE: (8), (48), (51), (357), (404) are inconsistent by % 152.37/22.81 | | | | | | | | | | | | | sub-proof #608. % 152.37/22.81 | | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | End of split % 152.37/22.81 | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | Case 2: % 152.37/22.81 | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | (405) all_54_4 = e0 % 152.37/22.81 | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | COMBINE_EQS: (10), (405) imply: % 152.37/22.81 | | | | | | | | | | | | (406) all_52_1 = e0 % 152.37/22.81 | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | REDUCE: (60), (406) imply: % 152.37/22.81 | | | | | | | | | | | | (407) $false % 152.37/22.81 | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | | CLOSE: (407) is inconsistent. % 152.37/22.81 | | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | | End of split % 152.37/22.81 | | | | | | | | | | | % 152.37/22.81 | | | | | | | | | | End of split % 152.37/22.81 | | | | | | | | | | % 152.37/22.81 | | | | | | | | | End of split % 152.37/22.81 | | | | | | | | | % 152.37/22.81 | | | | | | | | End of split % 152.37/22.81 | | | | | | | | % 152.37/22.81 | | | | | | | End of split % 152.37/22.81 | | | | | | | % 152.37/22.81 | | | | | | End of split % 152.37/22.81 | | | | | | % 152.37/22.81 | | | | | Case 2: % 152.37/22.81 | | | | | | % 152.37/22.81 | | | | | | (408) all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0 % 152.37/22.81 | | | | | | % 152.37/22.81 | | | | | | REF_CLOSE: (39), (57), (74), (326), (408) are inconsistent by % 152.37/22.81 | | | | | | sub-proof #663. % 152.37/22.81 | | | | | | % 152.37/22.81 | | | | | End of split % 152.37/22.81 | | | | | % 152.37/22.81 | | | | Case 2: % 152.37/22.81 | | | | | % 152.37/22.81 | | | | | (409) all_54_9 = e1 | all_54_9 = e0 % 152.37/22.81 | | | | | % 152.37/22.81 | | | | | REF_CLOSE: (3), (5), (53), (409) are inconsistent by sub-proof #678. % 152.37/22.81 | | | | | % 152.37/22.81 | | | | End of split % 152.37/22.81 | | | | % 152.37/22.81 | | | End of split % 152.37/22.81 | | | % 152.37/22.81 | | End of split % 152.37/22.81 | | % 152.37/22.81 | Case 2: % 152.37/22.81 | | % 152.37/22.81 | | (410) all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0 % 152.37/22.81 | | % 152.37/22.81 | | REF_CLOSE: (15), (34), (83), (87), (410) are inconsistent by sub-proof #654. % 152.37/22.81 | | % 152.37/22.81 | End of split % 152.37/22.81 | % 152.37/22.81 End of proof % 152.37/22.81 % 152.37/22.81 Sub-proof #608 shows that the following formulas are inconsistent: % 152.37/22.81 ---------------------------------------------------------------- % 152.37/22.81 (1) ~ (all_52_9 = e2) % 152.37/22.81 (2) ~ (all_52_9 = e0) % 152.37/22.81 (3) all_54_6 = all_52_9 % 152.37/22.81 (4) all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0 % 152.37/22.81 (5) ~ (all_52_9 = e1) % 152.37/22.81 % 152.37/22.81 Begin of proof % 152.37/22.81 | % 152.37/22.81 | BETA: splitting (4) gives: % 152.37/22.81 | % 152.37/22.81 | Case 1: % 152.37/22.81 | | % 152.37/22.81 | | (6) all_54_6 = e2 % 152.37/22.81 | | % 152.37/22.81 | | REF_CLOSE: (1), (3), (6) are inconsistent by sub-proof #610. % 152.37/22.81 | | % 152.37/22.81 | Case 2: % 152.37/22.81 | | % 152.37/22.81 | | (7) all_54_6 = e1 | all_54_6 = e0 % 152.37/22.81 | | % 152.37/22.81 | | BETA: splitting (7) gives: % 152.37/22.81 | | % 152.37/22.81 | | Case 1: % 152.37/22.81 | | | % 152.37/22.81 | | | (8) all_54_6 = e1 % 152.37/22.81 | | | % 152.37/22.81 | | | COMBINE_EQS: (3), (8) imply: % 152.37/22.81 | | | (9) all_52_9 = e1 % 152.37/22.81 | | | % 152.37/22.81 | | | SIMP: (9) implies: % 152.37/22.81 | | | (10) all_52_9 = e1 % 152.37/22.81 | | | % 152.37/22.81 | | | REDUCE: (5), (10) imply: % 152.37/22.81 | | | (11) $false % 152.37/22.81 | | | % 152.37/22.81 | | | CLOSE: (11) is inconsistent. % 152.37/22.81 | | | % 152.37/22.81 | | Case 2: % 152.37/22.81 | | | % 152.37/22.81 | | | (12) all_54_6 = e0 % 152.37/22.81 | | | % 152.37/22.81 | | | REF_CLOSE: (2), (3), (12) are inconsistent by sub-proof #609. % 152.37/22.81 | | | % 152.37/22.81 | | End of split % 152.37/22.81 | | % 152.37/22.81 | End of split % 152.37/22.81 | % 152.37/22.81 End of proof % 152.37/22.81 % 152.37/22.81 Sub-proof #609 shows that the following formulas are inconsistent: % 152.37/22.81 ---------------------------------------------------------------- % 152.37/22.81 (1) all_54_6 = all_52_9 % 152.37/22.81 (2) all_54_6 = e0 % 152.37/22.81 (3) ~ (all_52_9 = e0) % 152.37/22.81 % 152.37/22.81 Begin of proof % 152.37/22.81 | % 152.37/22.81 | COMBINE_EQS: (1), (2) imply: % 152.37/22.81 | (4) all_52_9 = e0 % 152.37/22.81 | % 152.37/22.81 | SIMP: (4) implies: % 152.37/22.81 | (5) all_52_9 = e0 % 152.37/22.81 | % 152.37/22.81 | REDUCE: (3), (5) imply: % 152.37/22.81 | (6) $false % 152.37/22.81 | % 152.37/22.81 | CLOSE: (6) is inconsistent. % 152.37/22.81 | % 152.37/22.81 End of proof % 152.37/22.81 % 152.37/22.81 Sub-proof #610 shows that the following formulas are inconsistent: % 152.37/22.81 ---------------------------------------------------------------- % 152.37/22.81 (1) all_54_6 = all_52_9 % 152.37/22.81 (2) all_54_6 = e2 % 152.37/22.81 (3) ~ (all_52_9 = e2) % 152.37/22.81 % 152.37/22.81 Begin of proof % 152.37/22.81 | % 152.37/22.81 | COMBINE_EQS: (1), (2) imply: % 152.37/22.81 | (4) all_52_9 = e2 % 152.37/22.81 | % 152.37/22.81 | SIMP: (4) implies: % 152.37/22.81 | (5) all_52_9 = e2 % 152.37/22.81 | % 152.37/22.81 | REDUCE: (3), (5) imply: % 152.37/22.81 | (6) $false % 152.37/22.81 | % 152.37/22.81 | CLOSE: (6) is inconsistent. % 152.37/22.81 | % 152.37/22.81 End of proof % 152.37/22.81 % 152.37/22.81 Sub-proof #611 shows that the following formulas are inconsistent: % 152.37/22.81 ---------------------------------------------------------------- % 152.37/22.81 (1) ~ (e3 = e0) % 152.37/22.81 (2) all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3 % 152.37/22.81 (3) ~ (e3 = e2) % 152.37/22.81 (4) all_58_10 = e2 % 152.37/22.81 (5) all_58_5 = e1 % 152.37/22.81 (6) all_58_3 = e0 % 152.37/22.81 (7) ~ (e3 = e1) % 152.37/22.81 % 152.37/22.81 Begin of proof % 152.37/22.81 | % 152.37/22.81 | BETA: splitting (2) gives: % 152.37/22.81 | % 152.37/22.81 | Case 1: % 152.37/22.81 | | % 152.37/22.81 | | (8) all_58_3 = e3 % 152.37/22.81 | | % 152.37/22.81 | | REF_CLOSE: (1), (6), (8) are inconsistent by sub-proof #632. % 152.37/22.81 | | % 152.37/22.81 | Case 2: % 152.37/22.81 | | % 152.37/22.81 | | (9) all_58_5 = e3 | all_58_10 = e3 % 152.37/22.81 | | % 152.37/22.81 | | REF_CLOSE: (3), (4), (5), (7), (9) are inconsistent by sub-proof #612. % 152.37/22.81 | | % 152.37/22.81 | End of split % 152.37/22.81 | % 152.37/22.81 End of proof % 152.37/22.81 % 152.37/22.81 Sub-proof #612 shows that the following formulas are inconsistent: % 152.37/22.81 ---------------------------------------------------------------- % 152.37/22.81 (1) ~ (e3 = e2) % 152.37/22.81 (2) all_58_10 = e2 % 152.37/22.81 (3) all_58_5 = e3 | all_58_10 = e3 % 152.37/22.81 (4) all_58_5 = e1 % 152.37/22.81 (5) ~ (e3 = e1) % 152.37/22.81 % 152.37/22.81 Begin of proof % 152.37/22.81 | % 152.37/22.81 | BETA: splitting (3) gives: % 152.37/22.81 | % 152.37/22.81 | Case 1: % 152.37/22.81 | | % 152.37/22.81 | | (6) all_58_5 = e3 % 152.37/22.81 | | % 152.37/22.81 | | COMBINE_EQS: (4), (6) imply: % 152.37/22.81 | | (7) e3 = e1 % 152.37/22.81 | | % 152.37/22.81 | | SIMP: (7) implies: % 152.37/22.81 | | (8) e3 = e1 % 152.37/22.81 | | % 152.37/22.81 | | REDUCE: (5), (8) imply: % 152.37/22.81 | | (9) $false % 152.37/22.81 | | % 152.37/22.81 | | CLOSE: (9) is inconsistent. % 152.37/22.81 | | % 152.37/22.81 | Case 2: % 152.37/22.81 | | % 152.37/22.81 | | (10) all_58_10 = e3 % 152.37/22.81 | | % 152.37/22.81 | | REF_CLOSE: (1), (2), (10) are inconsistent by sub-proof #635. % 152.37/22.81 | | % 152.37/22.81 | End of split % 152.37/22.81 | % 152.37/22.81 End of proof % 152.37/22.81 % 152.37/22.81 Sub-proof #613 shows that the following formulas are inconsistent: % 152.37/22.81 ---------------------------------------------------------------- % 152.37/22.81 (1) all_58_6 = all_52_2 % 152.37/22.81 (2) ~ (all_52_3 = e0) % 152.37/22.81 (3) ~ (all_52_2 = e0) % 152.37/22.81 (4) all_58_0 = e2 % 152.37/22.81 (5) ~ (all_52_1 = e0) % 152.37/22.81 (6) all_58_2 = all_52_1 % 152.37/22.81 (7) ~ (e2 = e0) % 152.37/22.81 (8) all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0 % 152.37/22.81 (9) all_58_12 = all_52_3 % 152.37/22.81 % 152.37/22.81 Begin of proof % 152.37/22.81 | % 152.37/22.81 | BETA: splitting (8) gives: % 152.37/22.81 | % 152.37/22.81 | Case 1: % 152.37/22.81 | | % 152.37/22.81 | | (10) all_58_0 = e0 % 152.37/22.81 | | % 152.37/22.81 | | COMBINE_EQS: (4), (10) imply: % 152.37/22.81 | | (11) e2 = e0 % 152.37/22.81 | | % 152.37/22.81 | | REDUCE: (7), (11) imply: % 152.37/22.81 | | (12) $false % 152.37/22.81 | | % 152.37/22.81 | | CLOSE: (12) is inconsistent. % 152.37/22.81 | | % 152.37/22.81 | Case 2: % 152.37/22.81 | | % 152.37/22.81 | | (13) all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0 % 152.37/22.81 | | % 152.37/22.81 | | REF_CLOSE: (1), (2), (3), (5), (6), (9), (13) are inconsistent by sub-proof % 152.37/22.81 | | #625. % 152.37/22.81 | | % 152.37/22.81 | End of split % 152.37/22.81 | % 152.37/22.81 End of proof % 152.37/22.81 % 152.37/22.81 Sub-proof #614 shows that the following formulas are inconsistent: % 152.37/22.81 ---------------------------------------------------------------- % 152.37/22.81 (1) all_54_4 = all_52_1 % 152.37/22.81 (2) all_54_4 = e0 % 152.37/22.81 (3) ~ (all_52_1 = e0) % 152.37/22.81 % 152.37/22.81 Begin of proof % 152.37/22.81 | % 152.37/22.81 | COMBINE_EQS: (1), (2) imply: % 152.37/22.81 | (4) all_52_1 = e0 % 152.37/22.81 | % 152.37/22.81 | SIMP: (4) implies: % 152.37/22.81 | (5) all_52_1 = e0 % 152.37/22.81 | % 152.37/22.81 | REDUCE: (3), (5) imply: % 152.37/22.81 | (6) $false % 152.37/22.81 | % 152.37/22.81 | CLOSE: (6) is inconsistent. % 152.37/22.81 | % 152.37/22.81 End of proof % 152.37/22.81 % 152.37/22.81 Sub-proof #615 shows that the following formulas are inconsistent: % 152.37/22.81 ---------------------------------------------------------------- % 152.37/22.81 (1) all_54_12 = all_52_3 % 152.37/22.81 (2) ~ (all_52_3 = e2) % 152.37/22.81 (3) ~ (all_52_3 = e0) % 152.37/22.81 (4) all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0 % 152.37/22.81 (5) ~ (all_52_3 = e1) % 152.37/22.81 % 152.37/22.81 Begin of proof % 152.37/22.81 | % 152.37/22.81 | BETA: splitting (4) gives: % 152.37/22.81 | % 152.37/22.81 | Case 1: % 152.37/22.81 | | % 152.37/22.81 | | (6) all_54_12 = e2 % 152.37/22.81 | | % 152.37/22.81 | | REF_CLOSE: (1), (2), (6) are inconsistent by sub-proof #618. % 152.37/22.81 | | % 152.37/22.81 | Case 2: % 152.37/22.81 | | % 152.37/22.81 | | (7) all_54_12 = e1 | all_54_12 = e0 % 152.37/22.81 | | % 152.37/22.81 | | REF_CLOSE: (1), (3), (5), (7) are inconsistent by sub-proof #616. % 152.37/22.81 | | % 152.37/22.81 | End of split % 152.37/22.81 | % 152.37/22.81 End of proof % 152.37/22.81 % 152.37/22.81 Sub-proof #616 shows that the following formulas are inconsistent: % 152.37/22.81 ---------------------------------------------------------------- % 152.37/22.81 (1) all_54_12 = e1 | all_54_12 = e0 % 152.37/22.81 (2) all_54_12 = all_52_3 % 152.37/22.81 (3) ~ (all_52_3 = e1) % 152.37/22.81 (4) ~ (all_52_3 = e0) % 152.37/22.81 % 152.37/22.81 Begin of proof % 152.37/22.81 | % 152.37/22.81 | BETA: splitting (1) gives: % 152.37/22.81 | % 152.37/22.81 | Case 1: % 152.37/22.81 | | % 152.37/22.81 | | (5) all_54_12 = e1 % 152.37/22.81 | | % 152.37/22.81 | | COMBINE_EQS: (2), (5) imply: % 152.37/22.81 | | (6) all_52_3 = e1 % 152.37/22.81 | | % 152.37/22.81 | | SIMP: (6) implies: % 152.37/22.82 | | (7) all_52_3 = e1 % 152.37/22.82 | | % 152.37/22.82 | | REDUCE: (3), (7) imply: % 152.37/22.82 | | (8) $false % 152.37/22.82 | | % 152.37/22.82 | | CLOSE: (8) is inconsistent. % 152.37/22.82 | | % 152.37/22.82 | Case 2: % 152.37/22.82 | | % 152.37/22.82 | | (9) all_54_12 = e0 % 152.37/22.82 | | % 152.37/22.82 | | REF_CLOSE: (2), (4), (9) are inconsistent by sub-proof #617. % 152.37/22.82 | | % 152.37/22.82 | End of split % 152.37/22.82 | % 152.37/22.82 End of proof % 152.37/22.82 % 152.37/22.82 Sub-proof #617 shows that the following formulas are inconsistent: % 152.37/22.82 ---------------------------------------------------------------- % 152.37/22.82 (1) all_54_12 = all_52_3 % 152.37/22.82 (2) all_54_12 = e0 % 152.37/22.82 (3) ~ (all_52_3 = e0) % 152.37/22.82 % 152.37/22.82 Begin of proof % 152.37/22.82 | % 152.37/22.82 | COMBINE_EQS: (1), (2) imply: % 152.37/22.82 | (4) all_52_3 = e0 % 152.37/22.82 | % 152.37/22.82 | SIMP: (4) implies: % 152.37/22.82 | (5) all_52_3 = e0 % 152.37/22.82 | % 152.37/22.82 | REDUCE: (3), (5) imply: % 152.37/22.82 | (6) $false % 152.37/22.82 | % 152.37/22.82 | CLOSE: (6) is inconsistent. % 152.37/22.82 | % 152.37/22.82 End of proof % 152.37/22.82 % 152.37/22.82 Sub-proof #618 shows that the following formulas are inconsistent: % 152.37/22.82 ---------------------------------------------------------------- % 152.37/22.82 (1) all_54_12 = all_52_3 % 152.37/22.82 (2) all_54_12 = e2 % 152.37/22.82 (3) ~ (all_52_3 = e2) % 152.37/22.82 % 152.37/22.82 Begin of proof % 152.37/22.82 | % 152.37/22.82 | COMBINE_EQS: (1), (2) imply: % 152.37/22.82 | (4) all_52_3 = e2 % 152.37/22.82 | % 152.37/22.82 | SIMP: (4) implies: % 152.37/22.82 | (5) all_52_3 = e2 % 152.37/22.82 | % 152.37/22.82 | REDUCE: (3), (5) imply: % 152.37/22.82 | (6) $false % 152.37/22.82 | % 152.37/22.82 | CLOSE: (6) is inconsistent. % 152.37/22.82 | % 152.37/22.82 End of proof % 152.37/22.82 % 152.37/22.82 Sub-proof #619 shows that the following formulas are inconsistent: % 152.37/22.82 ---------------------------------------------------------------- % 152.37/22.82 (1) all_58_14 = e1 | all_58_15 = e1 % 152.37/22.82 (2) ~ (all_4_2 = e1) % 152.37/22.82 (3) ~ (all_52_11 = e1) % 152.37/22.82 (4) all_58_15 = all_4_2 % 152.37/22.82 (5) all_58_14 = all_52_11 % 152.37/22.82 % 152.37/22.82 Begin of proof % 152.37/22.82 | % 152.37/22.82 | BETA: splitting (1) gives: % 152.37/22.82 | % 152.37/22.82 | Case 1: % 152.37/22.82 | | % 152.37/22.82 | | (6) all_58_14 = e1 % 152.37/22.82 | | % 152.37/22.82 | | REF_CLOSE: (3), (5), (6) are inconsistent by sub-proof #699. % 152.37/22.82 | | % 152.37/22.82 | Case 2: % 152.37/22.82 | | % 152.37/22.82 | | (7) all_58_15 = e1 % 152.37/22.82 | | % 152.37/22.82 | | COMBINE_EQS: (4), (7) imply: % 152.37/22.82 | | (8) all_4_2 = e1 % 152.37/22.82 | | % 152.37/22.82 | | REDUCE: (2), (8) imply: % 152.37/22.82 | | (9) $false % 152.37/22.82 | | % 152.37/22.82 | | CLOSE: (9) is inconsistent. % 152.37/22.82 | | % 152.37/22.82 | End of split % 152.37/22.82 | % 152.37/22.82 End of proof % 152.37/22.82 % 152.37/22.82 Sub-proof #620 shows that the following formulas are inconsistent: % 152.37/22.82 ---------------------------------------------------------------- % 152.37/22.82 (1) ~ (all_52_7 = e2) % 152.37/22.82 (2) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0 % 152.37/22.82 (3) ~ (all_52_7 = e1) % 152.37/22.82 (4) all_54_13 = all_52_7 % 152.37/22.82 (5) ~ (all_52_7 = e3) % 152.37/22.82 (6) ~ (all_52_7 = e0) % 152.37/22.82 % 152.37/22.82 Begin of proof % 152.37/22.82 | % 152.37/22.82 | BETA: splitting (2) gives: % 152.37/22.82 | % 152.37/22.82 | Case 1: % 152.37/22.82 | | % 152.37/22.82 | | (7) all_54_13 = e3 % 152.37/22.82 | | % 152.37/22.82 | | COMBINE_EQS: (4), (7) imply: % 152.37/22.82 | | (8) all_52_7 = e3 % 152.37/22.82 | | % 152.37/22.82 | | REDUCE: (5), (8) imply: % 152.37/22.82 | | (9) $false % 152.37/22.82 | | % 152.37/22.82 | | CLOSE: (9) is inconsistent. % 152.37/22.82 | | % 152.37/22.82 | Case 2: % 152.37/22.82 | | % 152.37/22.82 | | (10) all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0 % 152.37/22.82 | | % 152.37/22.82 | | REF_CLOSE: (1), (3), (4), (6), (10) are inconsistent by sub-proof #710. % 152.37/22.82 | | % 152.37/22.82 | End of split % 152.37/22.82 | % 152.37/22.82 End of proof % 152.37/22.82 % 152.37/22.82 Sub-proof #621 shows that the following formulas are inconsistent: % 152.37/22.82 ---------------------------------------------------------------- % 152.37/22.82 (1) all_58_8 = e1 % 152.37/22.82 (2) all_58_8 = e0 % 152.37/22.82 (3) ~ (e1 = e0) % 152.37/22.82 % 152.37/22.82 Begin of proof % 152.37/22.82 | % 152.37/22.82 | COMBINE_EQS: (1), (2) imply: % 152.37/22.82 | (4) e1 = e0 % 152.37/22.82 | % 152.37/22.82 | SIMP: (4) implies: % 152.37/22.82 | (5) e1 = e0 % 152.37/22.82 | % 152.37/22.82 | REDUCE: (3), (5) imply: % 152.37/22.82 | (6) $false % 152.37/22.82 | % 152.37/22.82 | CLOSE: (6) is inconsistent. % 152.37/22.82 | % 152.37/22.82 End of proof % 152.37/22.82 % 152.37/22.82 Sub-proof #622 shows that the following formulas are inconsistent: % 152.37/22.82 ---------------------------------------------------------------- % 152.37/22.82 (1) all_58_12 = e2 % 152.37/22.82 (2) all_58_12 = e1 % 152.37/22.82 (3) ~ (e2 = e1) % 152.37/22.82 % 152.37/22.82 Begin of proof % 152.37/22.82 | % 152.37/22.82 | COMBINE_EQS: (1), (2) imply: % 152.37/22.82 | (4) e2 = e1 % 152.37/22.82 | % 152.37/22.82 | SIMP: (4) implies: % 152.37/22.82 | (5) e2 = e1 % 152.37/22.82 | % 152.37/22.82 | REDUCE: (3), (5) imply: % 152.37/22.82 | (6) $false % 152.37/22.82 | % 152.37/22.82 | CLOSE: (6) is inconsistent. % 152.37/22.82 | % 152.37/22.82 End of proof % 152.37/22.82 % 152.37/22.82 Sub-proof #623 shows that the following formulas are inconsistent: % 152.37/22.82 ---------------------------------------------------------------- % 152.37/22.82 (1) all_58_6 = all_52_2 % 152.37/22.82 (2) all_58_4 = all_52_8 % 152.37/22.82 (3) ~ (all_52_11 = e0) % 152.37/22.82 (4) all_58_5 = all_52_9 % 152.37/22.82 (5) all_58_4 = e0 | all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0 % 152.37/22.82 (6) ~ (all_6_2 = e0) % 152.37/22.82 (7) ~ (all_52_3 = e0) % 152.37/22.82 (8) ~ (all_58_6 = e0) % 152.37/22.82 (9) ~ (all_52_9 = e0) % 152.37/22.82 (10) all_58_8 = all_6_2 % 152.37/22.82 (11) ~ (all_52_8 = all_10_2) % 152.37/22.82 (12) ~ (all_52_1 = e0) % 152.37/22.82 (13) all_58_2 = all_52_1 % 152.37/22.82 (14) all_58_0 = all_10_2 % 152.37/22.82 (15) all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0 % 152.37/22.82 (16) all_58_14 = all_52_11 % 152.37/22.82 (17) all_58_12 = all_52_3 % 152.37/22.82 % 152.37/22.82 Begin of proof % 152.37/22.82 | % 152.37/22.82 | REDUCE: (1), (8) imply: % 152.37/22.82 | (18) ~ (all_52_2 = e0) % 152.37/22.82 | % 152.37/22.82 | BETA: splitting (5) gives: % 152.37/22.82 | % 152.37/22.82 | Case 1: % 152.37/22.82 | | % 152.37/22.82 | | (19) all_58_4 = e0 % 152.37/22.82 | | % 152.37/22.82 | | COMBINE_EQS: (2), (19) imply: % 152.37/22.82 | | (20) all_52_8 = e0 % 152.37/22.82 | | % 152.37/22.82 | | REDUCE: (11), (20) imply: % 152.37/22.82 | | (21) ~ (all_10_2 = e0) % 152.37/22.82 | | % 152.37/22.82 | | REF_CLOSE: (1), (7), (12), (13), (14), (15), (17), (18), (21) are % 152.37/22.82 | | inconsistent by sub-proof #624. % 152.37/22.82 | | % 152.37/22.82 | Case 2: % 152.37/22.82 | | % 152.37/22.82 | | (22) all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0 % 152.37/22.82 | | % 152.37/22.82 | | REF_CLOSE: (3), (4), (6), (9), (10), (16), (22) are inconsistent by % 152.37/22.82 | | sub-proof #626. % 152.37/22.82 | | % 152.37/22.82 | End of split % 152.37/22.82 | % 152.37/22.82 End of proof % 152.37/22.82 % 152.37/22.82 Sub-proof #624 shows that the following formulas are inconsistent: % 152.37/22.82 ---------------------------------------------------------------- % 152.37/22.82 (1) all_58_6 = all_52_2 % 152.37/22.82 (2) ~ (all_10_2 = e0) % 152.37/22.82 (3) ~ (all_52_3 = e0) % 152.37/22.82 (4) ~ (all_52_2 = e0) % 152.37/22.82 (5) ~ (all_52_1 = e0) % 152.37/22.82 (6) all_58_2 = all_52_1 % 152.37/22.82 (7) all_58_0 = all_10_2 % 152.37/22.82 (8) all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0 % 152.37/22.82 (9) all_58_12 = all_52_3 % 152.37/22.82 % 152.37/22.82 Begin of proof % 152.37/22.82 | % 152.37/22.82 | SIMP: (2) implies: % 152.37/22.82 | (10) ~ (all_10_2 = e0) % 152.37/22.82 | % 152.37/22.82 | BETA: splitting (8) gives: % 152.37/22.82 | % 152.37/22.82 | Case 1: % 152.37/22.82 | | % 152.37/22.82 | | (11) all_58_0 = e0 % 152.37/22.82 | | % 152.37/22.82 | | COMBINE_EQS: (7), (11) imply: % 152.37/22.82 | | (12) all_10_2 = e0 % 152.37/22.82 | | % 152.37/22.82 | | REDUCE: (10), (12) imply: % 152.37/22.82 | | (13) $false % 152.37/22.82 | | % 152.37/22.82 | | CLOSE: (13) is inconsistent. % 152.37/22.82 | | % 152.37/22.82 | Case 2: % 152.37/22.82 | | % 152.37/22.82 | | (14) all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0 % 152.37/22.82 | | % 152.37/22.82 | | REF_CLOSE: (1), (3), (4), (5), (6), (9), (14) are inconsistent by sub-proof % 152.37/22.82 | | #625. % 152.37/22.82 | | % 152.37/22.82 | End of split % 152.37/22.82 | % 152.37/22.82 End of proof % 152.37/22.82 % 152.37/22.82 Sub-proof #625 shows that the following formulas are inconsistent: % 152.37/22.82 ---------------------------------------------------------------- % 152.37/22.82 (1) all_58_6 = all_52_2 % 152.37/22.82 (2) all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0 % 152.37/22.82 (3) ~ (all_52_3 = e0) % 152.37/22.82 (4) ~ (all_52_2 = e0) % 152.37/22.82 (5) ~ (all_52_1 = e0) % 152.37/22.82 (6) all_58_2 = all_52_1 % 152.37/22.82 (7) all_58_12 = all_52_3 % 152.37/22.82 % 152.37/22.82 Begin of proof % 152.37/22.82 | % 152.37/22.82 | BETA: splitting (2) gives: % 152.37/22.82 | % 152.37/22.82 | Case 1: % 152.37/22.82 | | % 152.37/22.82 | | (8) all_58_2 = e0 % 152.37/22.82 | | % 152.37/22.82 | | COMBINE_EQS: (6), (8) imply: % 152.37/22.82 | | (9) all_52_1 = e0 % 152.37/22.82 | | % 152.37/22.82 | | REDUCE: (5), (9) imply: % 152.37/22.82 | | (10) $false % 152.37/22.82 | | % 152.37/22.82 | | CLOSE: (10) is inconsistent. % 152.37/22.82 | | % 152.37/22.82 | Case 2: % 152.37/22.82 | | % 152.37/22.82 | | (11) all_58_6 = e0 | all_58_12 = e0 % 152.37/22.82 | | % 152.37/22.82 | | BETA: splitting (11) gives: % 152.37/22.82 | | % 152.37/22.82 | | Case 1: % 152.37/22.82 | | | % 152.37/22.82 | | | (12) all_58_6 = e0 % 152.37/22.82 | | | % 152.37/22.82 | | | COMBINE_EQS: (1), (12) imply: % 152.37/22.82 | | | (13) all_52_2 = e0 % 152.37/22.82 | | | % 152.37/22.82 | | | REDUCE: (4), (13) imply: % 152.37/22.82 | | | (14) $false % 152.37/22.82 | | | % 152.37/22.82 | | | CLOSE: (14) is inconsistent. % 152.37/22.82 | | | % 152.37/22.82 | | Case 2: % 152.37/22.82 | | | % 152.37/22.82 | | | (15) all_58_12 = e0 % 152.37/22.82 | | | % 152.37/22.82 | | | COMBINE_EQS: (7), (15) imply: % 152.37/22.82 | | | (16) all_52_3 = e0 % 152.37/22.82 | | | % 152.37/22.82 | | | REDUCE: (3), (16) imply: % 152.37/22.82 | | | (17) $false % 152.37/22.82 | | | % 152.37/22.82 | | | CLOSE: (17) is inconsistent. % 152.37/22.82 | | | % 152.37/22.82 | | End of split % 152.37/22.82 | | % 152.37/22.82 | End of split % 152.37/22.82 | % 152.37/22.82 End of proof % 152.37/22.82 % 152.37/22.82 Sub-proof #626 shows that the following formulas are inconsistent: % 152.37/22.82 ---------------------------------------------------------------- % 152.37/22.82 (1) ~ (all_52_11 = e0) % 152.37/22.82 (2) all_58_5 = all_52_9 % 152.37/22.82 (3) ~ (all_6_2 = e0) % 152.37/22.82 (4) ~ (all_52_9 = e0) % 152.37/22.82 (5) all_58_8 = all_6_2 % 152.37/22.82 (6) all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0 % 152.37/22.82 (7) all_58_14 = all_52_11 % 152.37/22.82 % 152.37/22.82 Begin of proof % 152.37/22.82 | % 152.37/22.82 | BETA: splitting (6) gives: % 152.37/22.82 | % 152.37/22.82 | Case 1: % 152.37/22.82 | | % 152.37/22.82 | | (8) all_58_5 = e0 % 152.37/22.82 | | % 152.37/22.82 | | COMBINE_EQS: (2), (8) imply: % 152.37/22.82 | | (9) all_52_9 = e0 % 152.37/22.82 | | % 152.37/22.82 | | REDUCE: (4), (9) imply: % 152.37/22.82 | | (10) $false % 152.37/22.82 | | % 152.37/22.82 | | CLOSE: (10) is inconsistent. % 152.37/22.82 | | % 152.37/22.82 | Case 2: % 152.37/22.82 | | % 152.37/22.82 | | (11) all_58_8 = e0 | all_58_14 = e0 % 152.37/22.82 | | % 152.37/22.82 | | REF_CLOSE: (1), (3), (5), (7), (11) are inconsistent by sub-proof #627. % 152.37/22.82 | | % 152.37/22.82 | End of split % 152.37/22.82 | % 152.37/22.82 End of proof % 152.37/22.82 % 152.37/22.82 Sub-proof #627 shows that the following formulas are inconsistent: % 152.37/22.82 ---------------------------------------------------------------- % 152.37/22.82 (1) ~ (all_52_11 = e0) % 152.37/22.82 (2) all_58_8 = e0 | all_58_14 = e0 % 152.37/22.82 (3) ~ (all_6_2 = e0) % 152.37/22.82 (4) all_58_8 = all_6_2 % 152.37/22.82 (5) all_58_14 = all_52_11 % 152.37/22.82 % 152.37/22.82 Begin of proof % 152.37/22.82 | % 152.37/22.82 | BETA: splitting (2) gives: % 152.37/22.82 | % 152.37/22.82 | Case 1: % 152.37/22.82 | | % 152.37/22.82 | | (6) all_58_8 = e0 % 152.37/22.82 | | % 152.37/22.82 | | COMBINE_EQS: (4), (6) imply: % 152.37/22.82 | | (7) all_6_2 = e0 % 152.37/22.82 | | % 152.37/22.82 | | REDUCE: (3), (7) imply: % 152.37/22.82 | | (8) $false % 152.37/22.82 | | % 152.37/22.82 | | CLOSE: (8) is inconsistent. % 152.37/22.82 | | % 152.37/22.82 | Case 2: % 152.37/22.82 | | % 152.37/22.82 | | (9) all_58_14 = e0 % 152.37/22.82 | | % 152.37/22.82 | | REF_CLOSE: (1), (5), (9) are inconsistent by sub-proof #639. % 152.37/22.82 | | % 152.37/22.82 | End of split % 152.37/22.82 | % 152.37/22.82 End of proof % 152.37/22.82 % 152.37/22.82 Sub-proof #628 shows that the following formulas are inconsistent: % 152.37/22.82 ---------------------------------------------------------------- % 152.37/22.82 (1) all_54_1 = e1 | all_54_1 = e0 % 152.37/22.82 (2) all_54_1 = all_52_4 % 152.37/22.82 (3) ~ (all_52_4 = e1) % 152.37/22.82 (4) ~ (all_52_4 = e0) % 152.37/22.82 % 152.37/22.82 Begin of proof % 152.37/22.82 | % 152.37/22.82 | BETA: splitting (1) gives: % 152.37/22.82 | % 152.37/22.82 | Case 1: % 152.37/22.82 | | % 152.37/22.82 | | (5) all_54_1 = e1 % 152.37/22.82 | | % 152.37/22.82 | | REF_CLOSE: (2), (3), (5) are inconsistent by sub-proof #720. % 152.37/22.82 | | % 152.37/22.82 | Case 2: % 152.37/22.82 | | % 152.37/22.82 | | (6) all_54_1 = e0 % 152.37/22.82 | | % 152.37/22.82 | | REF_CLOSE: (2), (4), (6) are inconsistent by sub-proof #719. % 152.37/22.82 | | % 152.37/22.82 | End of split % 152.37/22.82 | % 152.37/22.82 End of proof % 152.37/22.82 % 152.37/22.82 Sub-proof #629 shows that the following formulas are inconsistent: % 152.37/22.82 ---------------------------------------------------------------- % 152.37/22.82 (1) all_58_14 = all_52_11 % 152.37/22.82 (2) all_58_14 = e2 % 152.37/22.82 (3) ~ (all_52_11 = e2) % 152.37/22.82 % 152.37/22.82 Begin of proof % 152.37/22.82 | % 152.37/22.82 | COMBINE_EQS: (1), (2) imply: % 152.37/22.82 | (4) all_52_11 = e2 % 152.37/22.82 | % 152.37/22.82 | SIMP: (4) implies: % 152.37/22.82 | (5) all_52_11 = e2 % 152.37/22.82 | % 152.37/22.82 | REDUCE: (3), (5) imply: % 152.37/22.82 | (6) $false % 152.37/22.82 | % 152.37/22.82 | CLOSE: (6) is inconsistent. % 152.37/22.82 | % 152.37/22.82 End of proof % 152.37/22.82 % 152.37/22.82 Sub-proof #630 shows that the following formulas are inconsistent: % 152.37/22.82 ---------------------------------------------------------------- % 152.37/22.82 (1) all_58_4 = e2 % 152.37/22.82 (2) all_58_4 = e0 % 152.37/22.82 (3) ~ (e2 = e0) % 152.37/22.82 % 152.37/22.82 Begin of proof % 152.37/22.82 | % 152.37/22.82 | COMBINE_EQS: (1), (2) imply: % 152.37/22.82 | (4) e2 = e0 % 152.37/22.82 | % 152.37/22.82 | SIMP: (4) implies: % 152.37/22.82 | (5) e2 = e0 % 152.37/22.82 | % 152.37/22.82 | REDUCE: (3), (5) imply: % 152.37/22.82 | (6) $false % 152.37/22.82 | % 152.37/22.82 | CLOSE: (6) is inconsistent. % 152.37/22.82 | % 152.37/22.82 End of proof % 152.37/22.82 % 152.37/22.82 Sub-proof #631 shows that the following formulas are inconsistent: % 152.37/22.82 ---------------------------------------------------------------- % 152.37/22.82 (1) all_58_2 = e2 % 152.37/22.82 (2) all_58_2 = e1 % 152.37/22.82 (3) ~ (e2 = e1) % 152.37/22.82 % 152.37/22.82 Begin of proof % 152.37/22.82 | % 152.37/22.82 | COMBINE_EQS: (1), (2) imply: % 152.37/22.82 | (4) e2 = e1 % 152.37/22.82 | % 152.37/22.82 | SIMP: (4) implies: % 152.37/22.82 | (5) e2 = e1 % 152.37/22.82 | % 152.37/22.82 | REDUCE: (3), (5) imply: % 152.37/22.82 | (6) $false % 152.37/22.82 | % 152.37/22.82 | CLOSE: (6) is inconsistent. % 152.37/22.82 | % 152.37/22.82 End of proof % 152.37/22.82 % 152.37/22.82 Sub-proof #632 shows that the following formulas are inconsistent: % 152.37/22.82 ---------------------------------------------------------------- % 152.37/22.82 (1) all_58_3 = e3 % 152.37/22.82 (2) all_58_3 = e0 % 152.37/22.82 (3) ~ (e3 = e0) % 152.37/22.82 % 152.37/22.82 Begin of proof % 152.37/22.82 | % 152.37/22.82 | COMBINE_EQS: (1), (2) imply: % 152.37/22.82 | (4) e3 = e0 % 152.37/22.82 | % 152.37/22.82 | SIMP: (4) implies: % 152.37/22.82 | (5) e3 = e0 % 152.37/22.82 | % 152.37/22.82 | REDUCE: (3), (5) imply: % 152.37/22.82 | (6) $false % 152.37/22.82 | % 152.37/22.82 | CLOSE: (6) is inconsistent. % 152.37/22.82 | % 152.37/22.82 End of proof % 152.37/22.82 % 152.37/22.82 Sub-proof #633 shows that the following formulas are inconsistent: % 152.37/22.82 ---------------------------------------------------------------- % 152.37/22.82 (1) all_54_4 = all_52_1 % 152.37/22.82 (2) all_54_4 = e2 % 152.37/22.82 (3) ~ (all_52_1 = e2) % 152.37/22.82 % 152.37/22.82 Begin of proof % 152.37/22.82 | % 152.37/22.82 | COMBINE_EQS: (1), (2) imply: % 152.37/22.82 | (4) all_52_1 = e2 % 152.37/22.82 | % 152.37/22.82 | SIMP: (4) implies: % 152.37/22.82 | (5) all_52_1 = e2 % 152.37/22.82 | % 152.37/22.82 | REDUCE: (3), (5) imply: % 152.37/22.82 | (6) $false % 152.37/22.82 | % 152.37/22.82 | CLOSE: (6) is inconsistent. % 152.37/22.82 | % 152.37/22.82 End of proof % 152.37/22.82 % 152.37/22.82 Sub-proof #634 shows that the following formulas are inconsistent: % 152.37/22.82 ---------------------------------------------------------------- % 152.37/22.82 (1) all_54_4 = all_52_1 % 152.37/22.82 (2) all_54_4 = e3 % 152.37/22.82 (3) ~ (all_52_1 = e3) % 152.37/22.82 % 152.37/22.82 Begin of proof % 152.37/22.82 | % 152.37/22.82 | COMBINE_EQS: (1), (2) imply: % 152.37/22.82 | (4) all_52_1 = e3 % 152.37/22.82 | % 152.37/22.82 | SIMP: (4) implies: % 152.37/22.82 | (5) all_52_1 = e3 % 152.37/22.82 | % 152.37/22.82 | REDUCE: (3), (5) imply: % 152.37/22.82 | (6) $false % 152.37/22.82 | % 152.37/22.82 | CLOSE: (6) is inconsistent. % 152.37/22.82 | % 152.37/22.82 End of proof % 152.37/22.82 % 152.37/22.82 Sub-proof #635 shows that the following formulas are inconsistent: % 152.37/22.82 ---------------------------------------------------------------- % 152.37/22.82 (1) all_58_10 = e3 % 152.37/22.82 (2) all_58_10 = e2 % 152.37/22.82 (3) ~ (e3 = e2) % 152.37/22.82 % 152.37/22.82 Begin of proof % 152.37/22.82 | % 152.37/22.82 | COMBINE_EQS: (1), (2) imply: % 152.37/22.82 | (4) e3 = e2 % 152.37/22.82 | % 152.37/22.82 | SIMP: (4) implies: % 152.37/22.82 | (5) e3 = e2 % 152.37/22.82 | % 152.37/22.82 | REDUCE: (3), (5) imply: % 152.37/22.82 | (6) $false % 152.37/22.82 | % 152.37/22.82 | CLOSE: (6) is inconsistent. % 152.37/22.82 | % 152.37/22.82 End of proof % 152.37/22.82 % 152.37/22.82 Sub-proof #636 shows that the following formulas are inconsistent: % 152.37/22.82 ---------------------------------------------------------------- % 152.37/22.82 (1) all_58_8 = e3 | all_58_11 = e3 % 152.37/22.82 (2) ~ (all_6_2 = e3) % 152.37/22.82 (3) ~ (all_52_14 = e3) % 152.37/22.82 (4) all_58_8 = all_6_2 % 152.37/22.82 (5) all_58_11 = all_52_14 % 152.37/22.82 % 152.37/22.82 Begin of proof % 152.37/22.82 | % 152.37/22.82 | BETA: splitting (1) gives: % 152.37/22.82 | % 152.37/22.82 | Case 1: % 152.37/22.82 | | % 152.37/22.82 | | (6) all_58_8 = e3 % 152.37/22.82 | | % 152.37/22.82 | | COMBINE_EQS: (4), (6) imply: % 152.37/22.82 | | (7) all_6_2 = e3 % 152.37/22.82 | | % 152.37/22.82 | | REDUCE: (2), (7) imply: % 152.37/22.82 | | (8) $false % 152.37/22.82 | | % 152.37/22.82 | | CLOSE: (8) is inconsistent. % 152.37/22.82 | | % 152.37/22.82 | Case 2: % 152.37/22.82 | | % 152.37/22.82 | | (9) all_58_11 = e3 % 152.37/22.82 | | % 152.37/22.82 | | COMBINE_EQS: (5), (9) imply: % 152.37/22.82 | | (10) all_52_14 = e3 % 152.37/22.82 | | % 152.37/22.82 | | REDUCE: (3), (10) imply: % 152.37/22.82 | | (11) $false % 152.37/22.82 | | % 152.37/22.82 | | CLOSE: (11) is inconsistent. % 152.37/22.82 | | % 152.37/22.82 | End of split % 152.37/22.82 | % 152.37/22.82 End of proof % 152.37/22.82 % 152.37/22.82 Sub-proof #637 shows that the following formulas are inconsistent: % 152.37/22.82 ---------------------------------------------------------------- % 152.37/22.82 (1) ~ (all_52_4 = all_52_8) % 152.37/22.82 (2) op(e2, all_52_4) = all_56_2 % 152.37/22.82 (3) op(e2, e0) = e3 % 152.37/22.82 (4) all_58_4 = all_52_8 % 152.37/22.82 (5) ~ (all_52_11 = e0) % 152.37/22.82 (6) all_54_1 = all_52_4 % 152.37/22.82 (7) ~ (all_52_4 = e1) % 152.37/22.82 (8) all_58_4 = e0 | all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0 % 152.37/22.82 (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 152.37/22.82 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 152.37/22.82 (10) all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0 % 152.37/22.82 (11) all_58_8 = all_6_2 % 152.37/22.82 (12) op(e2, all_6_2) = all_8_0 % 152.37/22.82 (13) all_58_5 = e2 % 152.37/22.82 (14) ~ (all_8_0 = e3) % 152.37/22.82 (15) ~ (all_52_4 = e2) % 152.37/22.82 (16) all_58_14 = all_52_11 % 152.37/22.82 % 152.37/22.82 Begin of proof % 152.37/22.82 | % 152.37/22.82 | BETA: splitting (10) gives: % 152.37/22.82 | % 152.37/22.82 | Case 1: % 152.37/22.82 | | % 152.37/22.82 | | (17) all_54_1 = e2 % 152.37/22.82 | | % 152.37/22.82 | | REF_CLOSE: (6), (15), (17) are inconsistent by sub-proof #721. % 152.37/22.82 | | % 152.37/22.82 | Case 2: % 152.37/22.82 | | % 152.37/22.82 | | (18) ~ (all_54_1 = e2) % 152.37/22.82 | | (19) all_54_1 = e1 | all_54_1 = e0 % 152.37/22.82 | | % 152.37/22.82 | | BETA: splitting (19) gives: % 152.37/22.82 | | % 152.37/22.82 | | Case 1: % 152.37/22.82 | | | % 152.37/22.82 | | | (20) all_54_1 = e1 % 152.37/22.82 | | | % 152.37/22.82 | | | REF_CLOSE: (6), (7), (20) are inconsistent by sub-proof #720. % 152.37/22.82 | | | % 152.37/22.82 | | Case 2: % 152.37/22.82 | | | % 152.37/22.82 | | | (21) all_54_1 = e0 % 152.37/22.82 | | | % 152.37/22.82 | | | COMBINE_EQS: (6), (21) imply: % 152.37/22.82 | | | (22) all_52_4 = e0 % 152.37/22.82 | | | % 152.37/22.82 | | | SIMP: (22) implies: % 152.37/22.82 | | | (23) all_52_4 = e0 % 152.37/22.82 | | | % 152.37/22.82 | | | REDUCE: (1), (23) imply: % 152.37/22.82 | | | (24) ~ (all_52_8 = e0) % 152.37/22.82 | | | % 152.37/22.82 | | | SIMP: (24) implies: % 152.37/22.82 | | | (25) ~ (all_52_8 = e0) % 152.37/22.82 | | | % 152.37/22.82 | | | REDUCE: (15), (23) imply: % 152.37/22.82 | | | (26) ~ (e2 = e0) % 152.37/22.82 | | | % 152.37/22.82 | | | SIMP: (26) implies: % 152.37/22.82 | | | (27) ~ (e2 = e0) % 152.37/22.82 | | | % 152.37/22.82 | | | REDUCE: (2), (23) imply: % 152.37/22.82 | | | (28) op(e2, e0) = all_56_2 % 152.37/22.82 | | | % 152.37/22.82 | | | REF_CLOSE: (3), (4), (5), (8), (9), (11), (12), (13), (14), (16), (25), % 152.37/22.82 | | | (27), (28) are inconsistent by sub-proof #638. % 152.37/22.82 | | | % 152.37/22.82 | | End of split % 152.37/22.82 | | % 152.37/22.82 | End of split % 152.37/22.82 | % 152.37/22.82 End of proof % 152.37/22.82 % 152.37/22.82 Sub-proof #638 shows that the following formulas are inconsistent: % 152.37/22.82 ---------------------------------------------------------------- % 152.37/22.82 (1) op(e2, e0) = e3 % 152.37/22.82 (2) all_58_4 = all_52_8 % 152.37/22.82 (3) ~ (all_52_11 = e0) % 152.37/22.82 (4) op(e2, e0) = all_56_2 % 152.37/22.82 (5) all_58_4 = e0 | all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0 % 152.37/22.82 (6) ~ (all_52_8 = e0) % 152.37/22.82 (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 152.37/22.82 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 152.37/22.82 (8) all_58_8 = all_6_2 % 152.37/22.82 (9) op(e2, all_6_2) = all_8_0 % 152.37/22.82 (10) all_58_5 = e2 % 152.37/22.82 (11) ~ (all_8_0 = e3) % 152.37/22.82 (12) ~ (e2 = e0) % 152.37/22.82 (13) all_58_14 = all_52_11 % 152.37/22.82 % 152.37/22.82 Begin of proof % 152.37/22.82 | % 152.37/22.82 | BETA: splitting (5) gives: % 152.37/22.82 | % 152.37/22.82 | Case 1: % 152.37/22.82 | | % 152.37/22.82 | | (14) all_58_4 = e0 % 152.37/22.82 | | % 152.37/22.82 | | COMBINE_EQS: (2), (14) imply: % 152.37/22.82 | | (15) all_52_8 = e0 % 152.37/22.82 | | % 152.37/22.82 | | SIMP: (15) implies: % 152.37/22.82 | | (16) all_52_8 = e0 % 152.37/22.82 | | % 152.37/22.82 | | REDUCE: (6), (16) imply: % 152.37/22.82 | | (17) $false % 152.37/22.82 | | % 152.37/22.82 | | CLOSE: (17) is inconsistent. % 152.37/22.82 | | % 152.37/22.82 | Case 2: % 152.37/22.82 | | % 152.37/22.82 | | (18) all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0 % 152.37/22.82 | | % 152.37/22.82 | | BETA: splitting (18) gives: % 152.37/22.82 | | % 152.37/22.82 | | Case 1: % 152.37/22.82 | | | % 152.37/22.82 | | | (19) all_58_5 = e0 % 152.37/22.82 | | | % 152.37/22.82 | | | COMBINE_EQS: (10), (19) imply: % 152.37/22.82 | | | (20) e2 = e0 % 152.37/22.82 | | | % 152.37/22.82 | | | SIMP: (20) implies: % 152.37/22.82 | | | (21) e2 = e0 % 152.37/22.82 | | | % 152.37/22.82 | | | REDUCE: (12), (21) imply: % 152.37/22.82 | | | (22) $false % 152.37/22.82 | | | % 152.37/22.82 | | | CLOSE: (22) is inconsistent. % 152.37/22.82 | | | % 152.37/22.82 | | Case 2: % 152.37/22.82 | | | % 152.37/22.82 | | | (23) all_58_8 = e0 | all_58_14 = e0 % 152.37/22.82 | | | % 152.37/22.82 | | | BETA: splitting (23) gives: % 152.37/22.82 | | | % 152.37/22.82 | | | Case 1: % 152.37/22.82 | | | | % 152.37/22.82 | | | | (24) all_58_8 = e0 % 152.37/22.82 | | | | % 152.37/22.82 | | | | COMBINE_EQS: (8), (24) imply: % 152.37/22.82 | | | | (25) all_6_2 = e0 % 152.37/22.82 | | | | % 152.37/22.82 | | | | SIMP: (25) implies: % 152.37/22.82 | | | | (26) all_6_2 = e0 % 152.37/22.82 | | | | % 152.37/22.82 | | | | REDUCE: (9), (26) imply: % 152.37/22.82 | | | | (27) op(e2, e0) = all_8_0 % 152.37/22.82 | | | | % 152.37/22.82 | | | | GROUND_INST: instantiating (7) with e3, all_56_2, e0, e2, simplifying % 152.37/22.82 | | | | with (1), (4) gives: % 152.37/22.82 | | | | (28) all_56_2 = e3 % 152.37/22.82 | | | | % 152.37/22.82 | | | | GROUND_INST: instantiating (7) with all_8_0, all_56_2, e0, e2, % 152.37/22.82 | | | | simplifying with (4), (27) gives: % 152.37/22.82 | | | | (29) all_56_2 = all_8_0 % 152.37/22.82 | | | | % 152.37/22.82 | | | | COMBINE_EQS: (28), (29) imply: % 152.37/22.82 | | | | (30) all_8_0 = e3 % 152.37/22.82 | | | | % 152.37/22.82 | | | | REDUCE: (11), (30) imply: % 152.37/22.82 | | | | (31) $false % 152.37/22.82 | | | | % 152.37/22.82 | | | | CLOSE: (31) is inconsistent. % 152.37/22.82 | | | | % 152.37/22.82 | | | Case 2: % 152.37/22.82 | | | | % 152.37/22.82 | | | | (32) all_58_14 = e0 % 152.37/22.82 | | | | % 152.37/22.82 | | | | REF_CLOSE: (3), (13), (32) are inconsistent by sub-proof #639. % 152.37/22.82 | | | | % 152.37/22.82 | | | End of split % 152.37/22.82 | | | % 152.37/22.82 | | End of split % 152.37/22.82 | | % 152.37/22.82 | End of split % 152.37/22.82 | % 152.37/22.82 End of proof % 152.37/22.82 % 152.37/22.82 Sub-proof #639 shows that the following formulas are inconsistent: % 152.37/22.82 ---------------------------------------------------------------- % 152.37/22.82 (1) all_58_14 = all_52_11 % 152.37/22.82 (2) all_58_14 = e0 % 152.37/22.82 (3) ~ (all_52_11 = e0) % 152.37/22.82 % 152.37/22.82 Begin of proof % 152.37/22.82 | % 152.37/22.82 | COMBINE_EQS: (1), (2) imply: % 152.37/22.82 | (4) all_52_11 = e0 % 152.37/22.82 | % 152.37/22.82 | SIMP: (4) implies: % 152.37/22.82 | (5) all_52_11 = e0 % 152.37/22.82 | % 152.37/22.82 | REDUCE: (3), (5) imply: % 152.37/22.82 | (6) $false % 152.37/22.82 | % 152.37/22.82 | CLOSE: (6) is inconsistent. % 152.37/22.82 | % 152.37/22.82 End of proof % 152.37/22.82 % 152.37/22.82 Sub-proof #640 shows that the following formulas are inconsistent: % 152.37/22.82 ---------------------------------------------------------------- % 152.37/22.82 (1) all_56_11 = all_8_2 % 152.37/22.82 (2) ~ (all_52_11 = all_6_2) % 152.37/22.82 (3) ~ (all_52_4 = all_52_8) % 152.37/22.82 (4) ~ (all_52_7 = all_52_11) % 152.37/22.82 (5) all_54_9 = all_52_6 % 152.37/22.82 (6) all_58_6 = all_52_2 % 152.37/22.82 (7) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0 % 152.37/22.82 (8) all_54_10 = all_6_2 % 152.37/22.82 (9) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0 % 152.37/22.82 (10) ~ (all_6_1 = e2) % 152.37/22.82 (11) ~ (all_52_13 = all_8_2) % 152.37/22.82 (12) ~ (all_8_2 = e1) % 152.37/22.82 (13) ~ (all_56_21 = e2) | all_56_19 = e1 % 152.37/22.82 (14) all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2 % 152.37/22.82 (15) all_54_0 = all_10_2 % 152.37/22.82 (16) ~ (all_52_14 = all_4_2) % 152.37/22.82 (17) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0 % 152.37/22.82 (18) all_54_12 = all_52_3 % 152.37/22.82 (19) ~ (all_52_12 = all_52_13) % 152.37/22.82 (20) ~ (all_52_4 = all_52_7) % 152.37/22.82 (21) op(e0, e0) = all_4_2 % 152.37/22.82 (22) all_58_4 = all_52_8 % 152.37/22.82 (23) all_54_5 = all_8_2 % 152.37/22.82 (24) ~ (all_52_13 = e0) % 152.37/22.82 (25) ~ (all_10_2 = e1) % 152.37/22.82 (26) ~ (all_6_1 = e3) % 152.37/22.82 (27) ~ (all_52_6 = all_52_14) % 152.37/22.82 (28) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 152.37/22.82 (29) ~ (all_6_0 = e2) % 152.37/22.82 (30) ~ (all_52_11 = e0) % 152.37/22.82 (31) all_54_15 = all_4_2 % 152.37/22.82 (32) all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1 % 152.37/22.82 (33) ~ (all_10_1 = e1) % 152.37/22.82 (34) all_56_21 = all_6_2 % 152.37/22.82 (35) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 152.37/22.82 (36) ~ (all_52_7 = all_8_2) % 152.37/22.82 (37) all_56_1 = all_10_2 % 152.37/22.82 (38) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0 % 152.37/22.82 (39) all_58_5 = all_52_9 % 152.37/22.82 (40) all_54_1 = all_52_4 % 152.37/22.82 (41) all_56_17 = all_52_2 % 152.37/22.82 (42) all_58_9 = all_52_12 % 152.37/22.82 (43) op(e1, e0) = all_52_14 % 152.37/22.82 (44) all_54_14 = all_52_11 % 152.37/22.82 (45) ~ (all_10_2 = e2) % 152.37/22.82 (46) ( ~ (all_56_0 = all_56_1) & ~ (all_56_2 = all_56_3) & ~ (all_56_4 = % 152.37/22.82 all_56_5) & ~ (all_56_6 = all_56_7)) | ( ~ (all_56_8 = all_56_9) & % 152.37/22.82 ~ (all_56_10 = all_56_11) & ~ (all_56_12 = all_56_13) & ~ (all_56_14 % 152.37/22.82 = all_56_15)) | ( ~ (all_56_16 = all_56_17) & ~ (all_56_18 = % 152.37/22.82 all_56_19) & ~ (all_56_20 = all_56_21) & ~ (all_56_22 = % 152.37/22.82 all_56_23)) | ( ~ (all_56_24 = all_56_25) & ~ (all_56_26 = % 152.37/22.82 all_56_27) & ~ (all_56_28 = all_56_29) & ~ (all_56_30 = % 152.37/22.82 all_56_31)) % 152.37/22.82 (47) all_58_1 = all_52_4 % 152.37/22.82 (48) all_58_13 = all_52_7 % 152.37/22.82 (49) op(e2, all_8_2) = all_56_10 % 152.37/22.82 (50) op(e3, e3) = all_10_2 % 152.37/22.82 (51) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0 % 152.37/22.82 (52) all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1 % 152.37/22.82 (53) ~ (all_56_21 = e3) | all_56_17 = e1 % 152.37/22.82 (54) all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2 % 152.37/22.82 (55) ~ (all_52_1 = all_8_2) % 152.37/22.82 (56) all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2 % 152.37/22.82 (57) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 152.37/22.82 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 152.37/22.82 (58) ~ (all_52_3 = all_10_2) % 152.37/22.82 (59) all_54_3 = all_52_12 % 152.37/22.82 (60) all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0 % 152.37/22.82 (61) ~ (all_52_3 = all_52_7) % 152.37/22.82 (62) ~ (all_52_2 = all_52_6) % 152.37/22.82 (63) ~ (all_52_3 = e0) % 152.37/22.82 (64) all_56_7 = all_52_12 % 152.37/22.82 (65) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0 % 152.37/22.82 (66) ~ (all_4_2 = e1) % 152.37/22.82 (67) ~ (all_52_8 = all_10_2) % 152.37/22.82 (68) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0 % 152.37/22.82 (69) ~ (all_56_1 = e0) | all_56_7 = e3 % 152.37/22.82 (70) ~ (all_8_2 = e3) % 152.37/22.82 (71) ~ (all_4_2 = e2) % 152.37/22.82 (72) ~ (all_52_2 = all_52_3) % 152.37/22.82 (73) op(e1, all_6_1) = all_6_0 % 152.37/22.82 (74) all_58_3 = all_8_2 % 152.37/22.82 (75) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0 % 152.37/22.82 (76) all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1 % 152.37/22.82 (77) ~ (all_52_6 = all_52_7) % 152.37/22.82 (78) all_56_31 = all_4_2 % 152.37/22.82 (79) all_58_11 = all_52_14 % 152.37/22.82 (80) all_56_30 = e0 % 152.37/22.82 (81) ~ (all_52_2 = all_52_14) % 152.37/22.82 (82) all_54_7 = all_52_13 % 152.37/22.82 (83) all_56_31 = e0 % 152.37/22.82 (84) op(all_6_2, all_6_2) = all_6_1 % 152.37/22.82 (85) all_56_1 = e3 | all_56_11 = e2 | all_56_21 = e1 | all_56_31 = e0 % 152.37/22.82 (86) ~ (all_52_14 = e0) % 152.37/22.82 (87) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0 % 152.37/22.82 (88) ~ (all_52_8 = all_52_11) % 152.37/22.82 (89) all_54_13 = all_52_7 % 152.37/22.82 (90) all_54_2 = all_52_8 % 152.37/22.82 (91) ~ (all_52_13 = all_52_14) % 152.37/22.82 (92) all_56_23 = all_52_14 % 152.37/22.82 (93) all_54_8 = all_52_2 % 152.37/22.82 (94) op(e1, e1) = all_6_2 % 152.37/22.82 (95) ~ (all_52_6 = all_8_2) % 152.37/22.82 (96) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0 % 152.37/22.82 (97) all_58_15 = all_4_2 % 152.37/22.82 (98) all_58_2 = all_52_1 % 152.37/22.82 (99) ~ (all_4_2 = e3) % 152.37/22.82 (100) all_58_10 = all_52_13 % 152.37/22.82 (101) ~ (all_52_12 = all_4_2) % 152.37/22.82 (102) op(all_10_2, all_10_2) = all_10_1 % 152.37/22.82 (103) all_58_0 = all_10_2 % 152.37/22.82 (104) op(e1, all_6_2) = all_56_20 % 152.37/22.82 (105) all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1 % 152.37/22.82 (106) ~ (all_52_12 = all_52_14) % 152.37/22.82 (107) op(e1, all_52_9) = all_56_12 % 152.37/22.82 (108) ~ (all_52_12 = e0) % 152.37/22.82 (109) op(e2, e2) = all_8_2 % 152.37/22.82 (110) ~ (all_52_4 = all_52_12) % 152.37/22.82 (111) ~ (all_52_2 = all_6_2) % 152.37/22.82 (112) ~ (all_52_8 = all_52_12) % 152.37/22.82 (113) ~ (all_56_21 = e0) | all_56_23 = e1 % 152.37/22.82 (114) ~ (all_52_6 = all_6_2) % 152.37/22.82 (115) ~ (all_8_2 = e0) % 152.37/22.82 (116) op(e3, all_10_2) = all_56_0 % 152.37/22.82 (117) ~ (all_52_14 = all_6_2) % 152.37/22.82 (118) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0 % 152.37/22.82 (119) ~ (all_52_7 = e0) % 152.37/22.82 (120) ~ (all_52_2 = all_10_2) % 152.37/22.82 (121) ~ (all_52_4 = all_10_2) % 152.37/22.82 (122) ~ (all_52_4 = all_8_2) % 152.37/22.83 (123) op(all_8_2, all_8_2) = all_8_1 % 152.37/22.83 (124) ~ (all_52_4 = all_52_6) % 152.37/22.83 (125) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 152.37/22.83 (126) all_58_14 = all_52_11 % 152.37/22.83 (127) all_56_19 = all_52_6 % 152.37/22.83 (128) ~ (all_52_12 = all_10_2) % 152.37/22.83 (129) ~ (all_52_1 = all_10_2) % 152.37/22.83 (130) all_58_12 = all_52_3 % 152.37/22.83 (131) all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2 % 152.37/22.83 (132) all_54_11 = all_52_14 % 152.37/22.83 % 152.37/22.83 Begin of proof % 152.37/22.83 | % 152.37/22.83 | BETA: splitting (125) gives: % 152.37/22.83 | % 152.37/22.83 | Case 1: % 152.37/22.83 | | % 152.37/22.83 | | (133) all_54_5 = e3 % 152.37/22.83 | | % 152.37/22.83 | | REF_CLOSE: (23), (70), (133) are inconsistent by sub-proof #737. % 152.37/22.83 | | % 152.37/22.83 | Case 2: % 152.37/22.83 | | % 152.37/22.83 | | (134) ~ (all_54_5 = e3) % 152.37/22.83 | | (135) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 152.37/22.83 | | % 152.37/22.83 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), % 152.37/22.83 | | (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23), % 152.37/22.83 | | (24), (25), (26), (27), (28), (29), (30), (31), (32), (33), (34), % 152.37/22.83 | | (35), (36), (37), (38), (39), (40), (41), (42), (43), (44), (45), % 152.37/22.83 | | (46), (47), (48), (49), (50), (51), (52), (53), (54), (55), (56), % 152.37/22.83 | | (57), (58), (59), (60), (61), (62), (63), (64), (65), (66), (67), % 152.37/22.83 | | (68), (69), (70), (71), (72), (73), (74), (75), (76), (77), (78), % 152.37/22.83 | | (79), (80), (81), (82), (83), (84), (85), (86), (87), (88), (89), % 152.37/22.83 | | (90), (91), (92), (93), (94), (95), (96), (97), (98), (99), % 152.37/22.83 | | (100), (101), (102), (103), (104), (105), (106), (107), (108), % 152.37/22.83 | | (109), (110), (111), (112), (113), (114), (115), (116), (117), % 152.37/22.83 | | (118), (119), (120), (121), (122), (123), (124), (125), (126), % 152.37/22.83 | | (127), (128), (129), (130), (131), (132), (135) are inconsistent % 152.37/22.83 | | by sub-proof #641. % 152.37/22.83 | | % 152.37/22.83 | End of split % 152.37/22.83 | % 152.37/22.83 End of proof % 152.37/22.83 % 152.37/22.83 Sub-proof #641 shows that the following formulas are inconsistent: % 152.37/22.83 ---------------------------------------------------------------- % 152.37/22.83 (1) all_56_11 = all_8_2 % 152.37/22.83 (2) ~ (all_52_11 = all_6_2) % 152.37/22.83 (3) ~ (all_52_4 = all_52_8) % 152.37/22.83 (4) ~ (all_52_7 = all_52_11) % 152.37/22.83 (5) all_54_9 = all_52_6 % 152.37/22.83 (6) all_58_6 = all_52_2 % 152.37/22.83 (7) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0 % 152.37/22.83 (8) all_54_10 = all_6_2 % 152.37/22.83 (9) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0 % 152.37/22.83 (10) ~ (all_6_1 = e2) % 152.37/22.83 (11) ~ (all_52_13 = all_8_2) % 152.37/22.83 (12) ~ (all_8_2 = e1) % 152.37/22.83 (13) ~ (all_56_21 = e2) | all_56_19 = e1 % 152.37/22.83 (14) all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2 % 152.37/22.83 (15) all_54_0 = all_10_2 % 152.37/22.83 (16) ~ (all_52_14 = all_4_2) % 152.37/22.83 (17) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0 % 152.37/22.83 (18) all_54_12 = all_52_3 % 152.37/22.83 (19) ~ (all_52_12 = all_52_13) % 152.37/22.83 (20) ~ (all_52_4 = all_52_7) % 152.37/22.83 (21) op(e0, e0) = all_4_2 % 152.37/22.83 (22) all_58_4 = all_52_8 % 152.37/22.83 (23) all_54_5 = all_8_2 % 152.37/22.83 (24) ~ (all_52_13 = e0) % 152.37/22.83 (25) ~ (all_10_2 = e1) % 152.37/22.83 (26) ~ (all_6_1 = e3) % 152.37/22.83 (27) ~ (all_52_6 = all_52_14) % 152.37/22.83 (28) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 152.37/22.83 (29) ~ (all_6_0 = e2) % 152.37/22.83 (30) ~ (all_52_11 = e0) % 152.37/22.83 (31) all_54_15 = all_4_2 % 152.37/22.83 (32) all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1 % 152.37/22.83 (33) ~ (all_10_1 = e1) % 152.37/22.83 (34) all_56_21 = all_6_2 % 152.37/22.83 (35) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 152.37/22.83 (36) ~ (all_52_7 = all_8_2) % 152.37/22.83 (37) all_56_1 = all_10_2 % 152.37/22.83 (38) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0 % 152.37/22.83 (39) all_58_5 = all_52_9 % 152.37/22.83 (40) all_54_1 = all_52_4 % 152.37/22.83 (41) all_56_17 = all_52_2 % 152.37/22.83 (42) all_58_9 = all_52_12 % 152.37/22.83 (43) op(e1, e0) = all_52_14 % 152.37/22.83 (44) all_54_14 = all_52_11 % 152.37/22.83 (45) ~ (all_10_2 = e2) % 152.37/22.83 (46) ( ~ (all_56_0 = all_56_1) & ~ (all_56_2 = all_56_3) & ~ (all_56_4 = % 152.37/22.83 all_56_5) & ~ (all_56_6 = all_56_7)) | ( ~ (all_56_8 = all_56_9) & % 152.37/22.83 ~ (all_56_10 = all_56_11) & ~ (all_56_12 = all_56_13) & ~ (all_56_14 % 152.37/22.83 = all_56_15)) | ( ~ (all_56_16 = all_56_17) & ~ (all_56_18 = % 152.37/22.83 all_56_19) & ~ (all_56_20 = all_56_21) & ~ (all_56_22 = % 152.37/22.83 all_56_23)) | ( ~ (all_56_24 = all_56_25) & ~ (all_56_26 = % 152.37/22.83 all_56_27) & ~ (all_56_28 = all_56_29) & ~ (all_56_30 = % 152.37/22.83 all_56_31)) % 152.37/22.83 (47) all_58_1 = all_52_4 % 152.37/22.83 (48) all_58_13 = all_52_7 % 152.37/22.83 (49) op(e2, all_8_2) = all_56_10 % 152.37/22.83 (50) op(e3, e3) = all_10_2 % 152.37/22.83 (51) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0 % 152.37/22.83 (52) all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1 % 152.37/22.83 (53) ~ (all_56_21 = e3) | all_56_17 = e1 % 152.37/22.83 (54) all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2 % 152.37/22.83 (55) ~ (all_52_1 = all_8_2) % 152.37/22.83 (56) all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2 % 152.37/22.83 (57) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 152.37/22.83 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 152.37/22.83 (58) ~ (all_52_3 = all_10_2) % 152.37/22.83 (59) all_54_3 = all_52_12 % 152.37/22.83 (60) all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0 % 152.37/22.83 (61) ~ (all_52_3 = all_52_7) % 152.37/22.83 (62) ~ (all_52_2 = all_52_6) % 152.37/22.83 (63) ~ (all_52_3 = e0) % 152.37/22.83 (64) all_56_7 = all_52_12 % 152.37/22.83 (65) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0 % 152.37/22.83 (66) ~ (all_4_2 = e1) % 152.37/22.83 (67) ~ (all_52_8 = all_10_2) % 152.37/22.83 (68) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0 % 152.37/22.83 (69) ~ (all_56_1 = e0) | all_56_7 = e3 % 152.37/22.83 (70) ~ (all_8_2 = e3) % 152.37/22.83 (71) ~ (all_4_2 = e2) % 152.37/22.83 (72) ~ (all_52_2 = all_52_3) % 152.37/22.83 (73) op(e1, all_6_1) = all_6_0 % 152.37/22.83 (74) all_58_3 = all_8_2 % 152.37/22.83 (75) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0 % 152.37/22.83 (76) all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1 % 152.37/22.83 (77) ~ (all_52_6 = all_52_7) % 152.37/22.83 (78) all_56_31 = all_4_2 % 152.37/22.83 (79) all_58_11 = all_52_14 % 152.37/22.83 (80) all_56_30 = e0 % 152.37/22.83 (81) ~ (all_52_2 = all_52_14) % 152.37/22.83 (82) all_54_7 = all_52_13 % 152.37/22.83 (83) all_56_31 = e0 % 152.37/22.83 (84) op(all_6_2, all_6_2) = all_6_1 % 152.37/22.83 (85) all_56_1 = e3 | all_56_11 = e2 | all_56_21 = e1 | all_56_31 = e0 % 152.37/22.83 (86) ~ (all_52_14 = e0) % 152.37/22.83 (87) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0 % 152.37/22.83 (88) ~ (all_52_8 = all_52_11) % 152.37/22.83 (89) all_54_13 = all_52_7 % 152.37/22.83 (90) all_54_2 = all_52_8 % 152.37/22.83 (91) ~ (all_52_13 = all_52_14) % 152.37/22.83 (92) all_56_23 = all_52_14 % 152.37/22.83 (93) all_54_8 = all_52_2 % 152.37/22.83 (94) op(e1, e1) = all_6_2 % 152.37/22.83 (95) ~ (all_52_6 = all_8_2) % 152.37/22.83 (96) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0 % 152.37/22.83 (97) all_58_15 = all_4_2 % 152.37/22.83 (98) all_58_2 = all_52_1 % 152.37/22.83 (99) ~ (all_4_2 = e3) % 152.37/22.83 (100) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 152.37/22.83 (101) all_58_10 = all_52_13 % 152.48/22.83 (102) ~ (all_52_12 = all_4_2) % 152.48/22.83 (103) op(all_10_2, all_10_2) = all_10_1 % 152.48/22.83 (104) all_58_0 = all_10_2 % 152.48/22.83 (105) op(e1, all_6_2) = all_56_20 % 152.48/22.83 (106) all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1 % 152.48/22.83 (107) ~ (all_52_12 = all_52_14) % 152.48/22.83 (108) op(e1, all_52_9) = all_56_12 % 152.48/22.83 (109) ~ (all_52_12 = e0) % 152.48/22.83 (110) op(e2, e2) = all_8_2 % 152.48/22.83 (111) ~ (all_52_4 = all_52_12) % 152.48/22.83 (112) ~ (all_52_2 = all_6_2) % 152.48/22.83 (113) ~ (all_52_8 = all_52_12) % 152.48/22.83 (114) ~ (all_56_21 = e0) | all_56_23 = e1 % 152.48/22.83 (115) ~ (all_52_6 = all_6_2) % 152.48/22.83 (116) ~ (all_8_2 = e0) % 152.48/22.83 (117) op(e3, all_10_2) = all_56_0 % 152.48/22.83 (118) ~ (all_52_14 = all_6_2) % 152.48/22.83 (119) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0 % 152.48/22.83 (120) ~ (all_52_7 = e0) % 152.48/22.83 (121) ~ (all_52_2 = all_10_2) % 152.48/22.83 (122) ~ (all_52_4 = all_10_2) % 152.48/22.83 (123) ~ (all_52_4 = all_8_2) % 152.48/22.83 (124) op(all_8_2, all_8_2) = all_8_1 % 152.48/22.83 (125) ~ (all_52_4 = all_52_6) % 152.48/22.83 (126) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 152.48/22.83 (127) all_58_14 = all_52_11 % 152.48/22.83 (128) all_56_19 = all_52_6 % 152.48/22.83 (129) ~ (all_52_12 = all_10_2) % 152.48/22.83 (130) ~ (all_52_1 = all_10_2) % 152.48/22.83 (131) all_58_12 = all_52_3 % 152.48/22.83 (132) all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2 % 152.48/22.83 (133) all_54_11 = all_52_14 % 152.48/22.83 % 152.48/22.83 Begin of proof % 152.48/22.83 | % 152.48/22.83 | BETA: splitting (100) gives: % 152.48/22.83 | % 152.48/22.83 | Case 1: % 152.48/22.83 | | % 152.48/22.83 | | (134) all_54_5 = e2 % 152.48/22.83 | | % 152.48/22.83 | | COMBINE_EQS: (23), (134) imply: % 152.48/22.83 | | (135) all_8_2 = e2 % 152.48/22.83 | | % 152.48/22.83 | | SIMP: (135) implies: % 152.48/22.83 | | (136) all_8_2 = e2 % 152.48/22.83 | | % 152.48/22.83 | | COMBINE_EQS: (1), (136) imply: % 152.48/22.83 | | (137) all_56_11 = e2 % 152.48/22.83 | | % 152.48/22.83 | | REDUCE: (55), (136) imply: % 152.48/22.83 | | (138) ~ (all_52_1 = e2) % 152.48/22.83 | | % 152.48/22.83 | | REDUCE: (123), (136) imply: % 152.48/22.83 | | (139) ~ (all_52_4 = e2) % 152.48/22.83 | | % 152.48/22.83 | | REDUCE: (95), (136) imply: % 152.48/22.83 | | (140) ~ (all_52_6 = e2) % 152.48/22.83 | | % 152.48/22.83 | | REDUCE: (36), (136) imply: % 152.48/22.83 | | (141) ~ (all_52_7 = e2) % 152.48/22.83 | | % 152.48/22.83 | | REDUCE: (11), (136) imply: % 152.48/22.83 | | (142) ~ (all_52_13 = e2) % 152.48/22.83 | | % 152.48/22.83 | | REDUCE: (124), (136) imply: % 152.48/22.83 | | (143) op(e2, e2) = all_8_1 % 152.48/22.83 | | % 152.48/22.83 | | REDUCE: (49), (136) imply: % 152.48/22.83 | | (144) op(e2, e2) = all_56_10 % 152.48/22.83 | | % 152.48/22.83 | | REDUCE: (110), (136) imply: % 152.48/22.83 | | (145) op(e2, e2) = e2 % 152.48/22.83 | | % 152.48/22.83 | | GROUND_INST: instantiating (57) with all_8_1, all_56_10, e2, e2, simplifying % 152.48/22.83 | | with (143), (144) gives: % 152.48/22.83 | | (146) all_56_10 = all_8_1 % 152.48/22.83 | | % 152.48/22.83 | | GROUND_INST: instantiating (57) with e2, all_56_10, e2, e2, simplifying with % 152.48/22.83 | | (144), (145) gives: % 152.48/22.83 | | (147) all_56_10 = e2 % 152.48/22.83 | | % 152.48/22.83 | | COMBINE_EQS: (146), (147) imply: % 152.48/22.83 | | (148) all_8_1 = e2 % 152.48/22.83 | | % 152.48/22.83 | | BETA: splitting (114) gives: % 152.48/22.83 | | % 152.48/22.83 | | Case 1: % 152.48/22.83 | | | % 152.48/22.83 | | | (149) ~ (all_56_21 = e0) % 152.48/22.83 | | | % 152.48/22.83 | | | REDUCE: (34), (149) imply: % 152.48/22.83 | | | (150) ~ (all_6_2 = e0) % 152.48/22.83 | | | % 152.48/22.83 | | | BETA: splitting (53) gives: % 152.48/22.83 | | | % 152.48/22.83 | | | Case 1: % 152.48/22.83 | | | | % 152.48/22.83 | | | | (151) ~ (all_56_21 = e3) % 152.48/22.83 | | | | % 152.48/22.83 | | | | REDUCE: (34), (151) imply: % 152.48/22.83 | | | | (152) ~ (all_6_2 = e3) % 152.48/22.83 | | | | % 152.48/22.83 | | | | BETA: splitting (13) gives: % 152.48/22.83 | | | | % 152.48/22.83 | | | | Case 1: % 152.48/22.83 | | | | | % 152.48/22.83 | | | | | (153) ~ (all_56_21 = e2) % 152.48/22.83 | | | | | % 152.48/22.83 | | | | | REDUCE: (34), (153) imply: % 152.48/22.83 | | | | | (154) ~ (all_6_2 = e2) % 152.48/22.83 | | | | | % 152.48/22.83 | | | | | BETA: splitting (35) gives: % 152.48/22.83 | | | | | % 152.48/22.83 | | | | | Case 1: % 152.48/22.83 | | | | | | % 152.48/22.83 | | | | | | (155) all_54_10 = e3 % 152.48/22.83 | | | | | | % 152.48/22.83 | | | | | | REF_CLOSE: (8), (152), (155) are inconsistent by sub-proof #736. % 152.48/22.83 | | | | | | % 152.48/22.83 | | | | | Case 2: % 152.48/22.83 | | | | | | % 152.48/22.83 | | | | | | (156) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 152.48/22.83 | | | | | | % 152.48/22.83 | | | | | | BETA: splitting (156) gives: % 152.48/22.83 | | | | | | % 152.48/22.83 | | | | | | Case 1: % 152.48/22.83 | | | | | | | % 152.48/22.83 | | | | | | | (157) all_54_10 = e2 % 152.48/22.83 | | | | | | | % 152.48/22.83 | | | | | | | REF_CLOSE: (8), (154), (157) are inconsistent by sub-proof #735. % 152.48/22.83 | | | | | | | % 152.48/22.83 | | | | | | Case 2: % 152.48/22.83 | | | | | | | % 152.48/22.83 | | | | | | | (158) all_54_10 = e1 | all_54_10 = e0 % 152.48/22.83 | | | | | | | % 152.48/22.83 | | | | | | | BETA: splitting (158) gives: % 152.48/22.83 | | | | | | | % 152.48/22.83 | | | | | | | Case 1: % 152.48/22.83 | | | | | | | | % 152.48/22.83 | | | | | | | | (159) all_54_10 = e1 % 152.48/22.83 | | | | | | | | % 152.48/22.83 | | | | | | | | COMBINE_EQS: (8), (159) imply: % 152.48/22.83 | | | | | | | | (160) all_6_2 = e1 % 152.48/22.83 | | | | | | | | % 152.48/22.83 | | | | | | | | SIMP: (160) implies: % 152.48/22.83 | | | | | | | | (161) all_6_2 = e1 % 152.48/22.83 | | | | | | | | % 152.48/22.83 | | | | | | | | COMBINE_EQS: (34), (161) imply: % 152.48/22.83 | | | | | | | | (162) all_56_21 = e1 % 152.48/22.83 | | | | | | | | % 152.48/22.83 | | | | | | | | REDUCE: (2), (161) imply: % 152.48/22.83 | | | | | | | | (163) ~ (all_52_11 = e1) % 152.48/22.83 | | | | | | | | % 152.48/22.83 | | | | | | | | REDUCE: (105), (161) imply: % 152.48/22.83 | | | | | | | | (164) op(e1, e1) = all_56_20 % 152.48/22.83 | | | | | | | | % 152.48/22.83 | | | | | | | | REDUCE: (94), (161) imply: % 152.48/22.83 | | | | | | | | (165) op(e1, e1) = e1 % 152.48/22.83 | | | | | | | | % 152.48/22.83 | | | | | | | | GROUND_INST: instantiating (57) with e1, all_56_20, e1, e1, % 152.48/22.83 | | | | | | | | simplifying with (164), (165) gives: % 152.48/22.83 | | | | | | | | (166) all_56_20 = e1 % 152.48/22.83 | | | | | | | | % 152.48/22.83 | | | | | | | | BETA: splitting (46) gives: % 152.48/22.83 | | | | | | | | % 152.48/22.83 | | | | | | | | Case 1: % 152.48/22.83 | | | | | | | | | % 152.48/22.83 | | | | | | | | | (167) ( ~ (all_56_0 = all_56_1) & ~ (all_56_2 = all_56_3) % 152.48/22.83 | | | | | | | | | & ~ (all_56_4 = all_56_5) & ~ (all_56_6 = % 152.48/22.83 | | | | | | | | | all_56_7)) | ( ~ (all_56_8 = all_56_9) & ~ % 152.48/22.83 | | | | | | | | | (all_56_10 = all_56_11) & ~ (all_56_12 = % 152.48/22.83 | | | | | | | | | all_56_13) & ~ (all_56_14 = all_56_15)) % 152.48/22.83 | | | | | | | | | % 152.48/22.83 | | | | | | | | | BETA: splitting (167) gives: % 152.48/22.83 | | | | | | | | | % 152.48/22.83 | | | | | | | | | Case 1: % 152.48/22.83 | | | | | | | | | | % 152.48/22.83 | | | | | | | | | | (168) ~ (all_56_0 = all_56_1) & ~ (all_56_2 = all_56_3) % 152.48/22.83 | | | | | | | | | | & ~ (all_56_4 = all_56_5) & ~ (all_56_6 = % 152.48/22.83 | | | | | | | | | | all_56_7) % 152.48/22.83 | | | | | | | | | | % 152.48/22.83 | | | | | | | | | | ALPHA: (168) implies: % 152.48/22.83 | | | | | | | | | | (169) ~ (all_56_0 = all_56_1) % 152.48/22.83 | | | | | | | | | | % 152.48/22.83 | | | | | | | | | | REDUCE: (37), (169) imply: % 152.48/22.83 | | | | | | | | | | (170) ~ (all_56_0 = all_10_2) % 152.48/22.83 | | | | | | | | | | % 152.48/22.83 | | | | | | | | | | BETA: splitting (69) gives: % 152.48/22.83 | | | | | | | | | | % 152.48/22.83 | | | | | | | | | | Case 1: % 152.48/22.83 | | | | | | | | | | | % 152.48/22.83 | | | | | | | | | | | (171) ~ (all_56_1 = e0) % 152.48/22.83 | | | | | | | | | | | % 152.48/22.83 | | | | | | | | | | | REDUCE: (37), (171) imply: % 152.48/22.83 | | | | | | | | | | | (172) ~ (all_10_2 = e0) % 152.48/22.83 | | | | | | | | | | | % 152.48/22.83 | | | | | | | | | | | BETA: splitting (28) gives: % 152.48/22.83 | | | | | | | | | | | % 152.48/22.83 | | | | | | | | | | | Case 1: % 152.48/22.83 | | | | | | | | | | | | % 152.48/22.83 | | | | | | | | | | | | (173) all_54_0 = e3 % 152.48/22.83 | | | | | | | | | | | | % 152.48/22.83 | | | | | | | | | | | | COMBINE_EQS: (15), (173) imply: % 152.48/22.83 | | | | | | | | | | | | (174) all_10_2 = e3 % 152.48/22.83 | | | | | | | | | | | | % 152.48/22.83 | | | | | | | | | | | | SIMP: (174) implies: % 152.48/22.83 | | | | | | | | | | | | (175) all_10_2 = e3 % 152.48/22.83 | | | | | | | | | | | | % 152.48/22.83 | | | | | | | | | | | | REDUCE: (170), (175) imply: % 152.48/22.83 | | | | | | | | | | | | (176) ~ (all_56_0 = e3) % 152.48/22.83 | | | | | | | | | | | | % 152.48/22.83 | | | | | | | | | | | | REDUCE: (117), (175) imply: % 152.48/22.83 | | | | | | | | | | | | (177) op(e3, e3) = all_56_0 % 152.48/22.83 | | | | | | | | | | | | % 152.48/22.83 | | | | | | | | | | | | REDUCE: (50), (175) imply: % 152.48/22.83 | | | | | | | | | | | | (178) op(e3, e3) = e3 % 152.48/22.83 | | | | | | | | | | | | % 152.48/22.83 | | | | | | | | | | | | GROUND_INST: instantiating (57) with e3, all_56_0, e3, e3, % 152.48/22.83 | | | | | | | | | | | | simplifying with (177), (178) gives: % 152.48/22.83 | | | | | | | | | | | | (179) all_56_0 = e3 % 152.48/22.83 | | | | | | | | | | | | % 152.48/22.83 | | | | | | | | | | | | REDUCE: (176), (179) imply: % 152.48/22.83 | | | | | | | | | | | | (180) $false % 152.48/22.83 | | | | | | | | | | | | % 152.48/22.83 | | | | | | | | | | | | CLOSE: (180) is inconsistent. % 152.48/22.83 | | | | | | | | | | | | % 152.48/22.83 | | | | | | | | | | | Case 2: % 152.48/22.83 | | | | | | | | | | | | % 152.48/22.83 | | | | | | | | | | | | (181) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 152.48/22.83 | | | | | | | | | | | | % 152.48/22.83 | | | | | | | | | | | | REF_CLOSE: (15), (25), (45), (172), (181) are inconsistent by % 152.48/22.83 | | | | | | | | | | | | sub-proof #731. % 152.48/22.83 | | | | | | | | | | | | % 152.48/22.83 | | | | | | | | | | | End of split % 152.48/22.83 | | | | | | | | | | | % 152.48/22.83 | | | | | | | | | | Case 2: % 152.48/22.83 | | | | | | | | | | | % 152.48/22.83 | | | | | | | | | | | (182) all_56_7 = e3 % 152.48/22.83 | | | | | | | | | | | (183) all_56_1 = e0 % 152.48/22.83 | | | | | | | | | | | % 152.48/22.83 | | | | | | | | | | | COMBINE_EQS: (37), (183) imply: % 152.48/22.83 | | | | | | | | | | | (184) all_10_2 = e0 % 152.48/22.83 | | | | | | | | | | | % 152.48/22.83 | | | | | | | | | | | SIMP: (184) implies: % 152.48/22.83 | | | | | | | | | | | (185) all_10_2 = e0 % 152.48/22.83 | | | | | | | | | | | % 152.48/22.83 | | | | | | | | | | | COMBINE_EQS: (64), (182) imply: % 152.48/22.83 | | | | | | | | | | | (186) all_52_12 = e3 % 152.48/22.83 | | | | | | | | | | | % 152.48/22.83 | | | | | | | | | | | COMBINE_EQS: (104), (185) imply: % 152.48/22.83 | | | | | | | | | | | (187) all_58_0 = e0 % 152.48/22.83 | | | | | | | | | | | % 152.48/22.83 | | | | | | | | | | | REDUCE: (111), (186) imply: % 152.48/22.83 | | | | | | | | | | | (188) ~ (all_52_4 = e3) % 152.48/22.83 | | | | | | | | | | | % 152.48/22.83 | | | | | | | | | | | REDUCE: (122), (185) imply: % 152.48/22.83 | | | | | | | | | | | (189) ~ (all_52_4 = e0) % 152.48/22.83 | | | | | | | | | | | % 152.48/22.83 | | | | | | | | | | | REDUCE: (113), (186) imply: % 152.48/22.83 | | | | | | | | | | | (190) ~ (all_52_8 = e3) % 152.48/22.83 | | | | | | | | | | | % 152.48/22.83 | | | | | | | | | | | REDUCE: (67), (185) imply: % 152.48/22.83 | | | | | | | | | | | (191) ~ (all_52_8 = e0) % 152.48/22.83 | | | | | | | | | | | % 152.48/22.83 | | | | | | | | | | | REDUCE: (25), (185) imply: % 152.48/22.83 | | | | | | | | | | | (192) ~ (e1 = e0) % 152.48/22.83 | | | | | | | | | | | % 152.48/22.83 | | | | | | | | | | | SIMP: (192) implies: % 152.48/22.83 | | | | | | | | | | | (193) ~ (e1 = e0) % 152.48/22.83 | | | | | | | | | | | % 152.48/22.83 | | | | | | | | | | | BETA: splitting (52) gives: % 152.48/22.83 | | | | | | | | | | | % 152.48/22.83 | | | | | | | | | | | Case 1: % 152.48/22.83 | | | | | | | | | | | | % 152.48/22.83 | | | | | | | | | | | | (194) all_58_0 = e1 % 152.48/22.83 | | | | | | | | | | | | % 152.48/22.83 | | | | | | | | | | | | REF_CLOSE: (187), (193), (194) are inconsistent by sub-proof % 152.48/22.83 | | | | | | | | | | | | #730. % 152.48/22.83 | | | | | | | | | | | | % 152.48/22.83 | | | | | | | | | | | Case 2: % 152.48/22.83 | | | | | | | | | | | | % 152.48/22.83 | | | | | | | | | | | | (195) all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1 % 152.48/22.83 | | | | | | | | | | | | % 152.48/22.83 | | | | | | | | | | | | BETA: splitting (195) gives: % 152.48/22.83 | | | | | | | | | | | | % 152.48/22.83 | | | | | | | | | | | | Case 1: % 152.48/22.83 | | | | | | | | | | | | | % 152.48/22.83 | | | | | | | | | | | | | (196) all_58_1 = e1 % 152.48/22.83 | | | | | | | | | | | | | % 152.48/22.83 | | | | | | | | | | | | | COMBINE_EQS: (47), (196) imply: % 152.48/22.83 | | | | | | | | | | | | | (197) all_52_4 = e1 % 152.48/22.83 | | | | | | | | | | | | | % 152.48/22.83 | | | | | | | | | | | | | REDUCE: (20), (197) imply: % 152.48/22.83 | | | | | | | | | | | | | (198) ~ (all_52_7 = e1) % 152.48/22.83 | | | | | | | | | | | | | % 152.48/22.83 | | | | | | | | | | | | | SIMP: (198) implies: % 152.48/22.83 | | | | | | | | | | | | | (199) ~ (all_52_7 = e1) % 152.48/22.83 | | | | | | | | | | | | | % 152.48/22.83 | | | | | | | | | | | | | BETA: splitting (68) gives: % 152.48/22.83 | | | | | | | | | | | | | % 152.48/22.83 | | | | | | | | | | | | | Case 1: % 152.48/22.83 | | | | | | | | | | | | | | % 152.48/22.83 | | | | | | | | | | | | | | (200) all_54_13 = e3 % 152.48/22.83 | | | | | | | | | | | | | | % 152.48/22.83 | | | | | | | | | | | | | | COMBINE_EQS: (89), (200) imply: % 152.48/22.83 | | | | | | | | | | | | | | (201) all_52_7 = e3 % 152.48/22.83 | | | | | | | | | | | | | | % 152.48/22.83 | | | | | | | | | | | | | | SIMP: (201) implies: % 152.48/22.83 | | | | | | | | | | | | | | (202) all_52_7 = e3 % 152.48/22.83 | | | | | | | | | | | | | | % 152.48/22.83 | | | | | | | | | | | | | | REDUCE: (4), (202) imply: % 152.48/22.83 | | | | | | | | | | | | | | (203) ~ (all_52_11 = e3) % 152.48/22.83 | | | | | | | | | | | | | | % 152.48/22.83 | | | | | | | | | | | | | | SIMP: (203) implies: % 152.48/22.83 | | | | | | | | | | | | | | (204) ~ (all_52_11 = e3) % 152.48/22.83 | | | | | | | | | | | | | | % 152.48/22.83 | | | | | | | | | | | | | | BETA: splitting (7) gives: % 152.48/22.83 | | | | | | | | | | | | | | % 152.48/22.83 | | | | | | | | | | | | | | Case 1: % 152.48/22.83 | | | | | | | | | | | | | | | % 152.48/22.83 | | | | | | | | | | | | | | | (205) all_54_14 = e3 % 152.48/22.83 | | | | | | | | | | | | | | | % 152.48/22.83 | | | | | | | | | | | | | | | REF_CLOSE: (44), (204), (205) are inconsistent by sub-proof % 152.48/22.83 | | | | | | | | | | | | | | | #729. % 152.48/22.83 | | | | | | | | | | | | | | | % 152.48/22.83 | | | | | | | | | | | | | | Case 2: % 152.48/22.83 | | | | | | | | | | | | | | | % 152.48/22.83 | | | | | | | | | | | | | | | (206) all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0 % 152.48/22.83 | | | | | | | | | | | | | | | % 152.48/22.83 | | | | | | | | | | | | | | | BETA: splitting (51) gives: % 152.48/22.83 | | | | | | | | | | | | | | | % 152.48/22.83 | | | | | | | | | | | | | | | Case 1: % 152.48/22.83 | | | | | | | | | | | | | | | | % 152.48/22.83 | | | | | | | | | | | | | | | | (207) all_54_2 = e3 % 152.48/22.83 | | | | | | | | | | | | | | | | % 152.48/22.83 | | | | | | | | | | | | | | | | REF_CLOSE: (90), (190), (207) are inconsistent by sub-proof % 152.48/22.83 | | | | | | | | | | | | | | | | #728. % 152.48/22.83 | | | | | | | | | | | | | | | | % 152.48/22.83 | | | | | | | | | | | | | | | Case 2: % 152.48/22.83 | | | | | | | | | | | | | | | | % 152.48/22.83 | | | | | | | | | | | | | | | | (208) all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0 % 152.48/22.83 | | | | | | | | | | | | | | | | % 152.48/22.83 | | | | | | | | | | | | | | | | BETA: splitting (206) gives: % 152.48/22.83 | | | | | | | | | | | | | | | | % 152.48/22.83 | | | | | | | | | | | | | | | | Case 1: % 152.48/22.83 | | | | | | | | | | | | | | | | | % 152.48/22.83 | | | | | | | | | | | | | | | | | (209) all_54_14 = e2 % 152.48/22.83 | | | | | | | | | | | | | | | | | % 152.48/22.83 | | | | | | | | | | | | | | | | | COMBINE_EQS: (44), (209) imply: % 152.48/22.83 | | | | | | | | | | | | | | | | | (210) all_52_11 = e2 % 152.48/22.83 | | | | | | | | | | | | | | | | | % 152.48/22.83 | | | | | | | | | | | | | | | | | SIMP: (210) implies: % 152.48/22.83 | | | | | | | | | | | | | | | | | (211) all_52_11 = e2 % 152.48/22.83 | | | | | | | | | | | | | | | | | % 152.48/22.83 | | | | | | | | | | | | | | | | | REDUCE: (88), (211) imply: % 152.48/22.83 | | | | | | | | | | | | | | | | | (212) ~ (all_52_8 = e2) % 152.48/22.83 | | | | | | | | | | | | | | | | | % 152.48/22.83 | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (40), (47), (76), (90), (96), (139), (188), % 152.48/22.83 | | | | | | | | | | | | | | | | | (189), (191), (208), (212) are inconsistent by % 152.48/22.83 | | | | | | | | | | | | | | | | | sub-proof #716. % 152.48/22.83 | | | | | | | | | | | | | | | | | % 152.48/22.83 | | | | | | | | | | | | | | | | Case 2: % 152.48/22.83 | | | | | | | | | | | | | | | | | % 152.48/22.83 | | | | | | | | | | | | | | | | | (213) all_54_14 = e1 | all_54_14 = e0 % 152.48/22.83 | | | | | | | | | | | | | | | | | % 152.48/22.83 | | | | | | | | | | | | | | | | | REF_CLOSE: (30), (44), (163), (213) are inconsistent by % 152.48/22.83 | | | | | | | | | | | | | | | | | sub-proof #714. % 152.48/22.83 | | | | | | | | | | | | | | | | | % 152.48/22.83 | | | | | | | | | | | | | | | | End of split % 152.48/22.83 | | | | | | | | | | | | | | | | % 152.48/22.83 | | | | | | | | | | | | | | | End of split % 152.48/22.83 | | | | | | | | | | | | | | | % 152.48/22.83 | | | | | | | | | | | | | | End of split % 152.48/22.83 | | | | | | | | | | | | | | % 152.48/22.83 | | | | | | | | | | | | | Case 2: % 152.48/22.83 | | | | | | | | | | | | | | % 152.48/22.83 | | | | | | | | | | | | | | (214) all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0 % 152.48/22.83 | | | | | | | | | | | | | | % 152.48/22.83 | | | | | | | | | | | | | | REF_CLOSE: (89), (120), (141), (199), (214) are inconsistent % 152.48/22.83 | | | | | | | | | | | | | | by sub-proof #710. % 152.48/22.83 | | | | | | | | | | | | | | % 152.48/22.83 | | | | | | | | | | | | | End of split % 152.48/22.83 | | | | | | | | | | | | | % 152.48/22.83 | | | | | | | | | | | | Case 2: % 152.48/22.83 | | | | | | | | | | | | | % 152.48/22.83 | | | | | | | | | | | | | (215) ~ (all_58_1 = e1) % 152.48/22.83 | | | | | | | | | | | | | % 152.48/22.83 | | | | | | | | | | | | | REDUCE: (47), (215) imply: % 152.48/22.83 | | | | | | | | | | | | | (216) ~ (all_52_4 = e1) % 152.48/22.83 | | | | | | | | | | | | | % 152.48/22.83 | | | | | | | | | | | | | REF_CLOSE: (15), (25), (28), (37), (40), (45), (64), (69), % 152.48/22.83 | | | | | | | | | | | | | (96), (111), (122), (139), (189), (216) are % 152.48/22.83 | | | | | | | | | | | | | inconsistent by sub-proof #706. % 152.48/22.83 | | | | | | | | | | | | | % 152.48/22.83 | | | | | | | | | | | | End of split % 152.48/22.83 | | | | | | | | | | | | % 152.48/22.83 | | | | | | | | | | | End of split % 152.48/22.83 | | | | | | | | | | | % 152.48/22.83 | | | | | | | | | | End of split % 152.48/22.83 | | | | | | | | | | % 152.48/22.83 | | | | | | | | | Case 2: % 152.48/22.83 | | | | | | | | | | % 152.48/22.83 | | | | | | | | | | (217) ~ (all_56_8 = all_56_9) & ~ (all_56_10 = % 152.48/22.83 | | | | | | | | | | all_56_11) & ~ (all_56_12 = all_56_13) & ~ % 152.48/22.83 | | | | | | | | | | (all_56_14 = all_56_15) % 152.48/22.83 | | | | | | | | | | % 152.48/22.83 | | | | | | | | | | ALPHA: (217) implies: % 152.48/22.83 | | | | | | | | | | (218) ~ (all_56_10 = all_56_11) % 152.48/22.83 | | | | | | | | | | % 152.48/22.83 | | | | | | | | | | REDUCE: (137), (147), (218) imply: % 152.48/22.83 | | | | | | | | | | (219) $false % 152.48/22.83 | | | | | | | | | | % 152.48/22.83 | | | | | | | | | | CLOSE: (219) is inconsistent. % 152.48/22.83 | | | | | | | | | | % 152.48/22.83 | | | | | | | | | End of split % 152.48/22.83 | | | | | | | | | % 152.48/22.83 | | | | | | | | Case 2: % 152.48/22.83 | | | | | | | | | % 152.48/22.83 | | | | | | | | | (220) ( ~ (all_56_16 = all_56_17) & ~ (all_56_18 = % 152.48/22.83 | | | | | | | | | all_56_19) & ~ (all_56_20 = all_56_21) & ~ % 152.48/22.83 | | | | | | | | | (all_56_22 = all_56_23)) | ( ~ (all_56_24 = % 152.48/22.83 | | | | | | | | | all_56_25) & ~ (all_56_26 = all_56_27) & ~ % 152.48/22.83 | | | | | | | | | (all_56_28 = all_56_29) & ~ (all_56_30 = % 152.48/22.83 | | | | | | | | | all_56_31)) % 152.48/22.83 | | | | | | | | | % 152.48/22.83 | | | | | | | | | BETA: splitting (220) gives: % 152.48/22.83 | | | | | | | | | % 152.48/22.83 | | | | | | | | | Case 1: % 152.48/22.83 | | | | | | | | | | % 152.48/22.83 | | | | | | | | | | (221) ~ (all_56_16 = all_56_17) & ~ (all_56_18 = % 152.48/22.83 | | | | | | | | | | all_56_19) & ~ (all_56_20 = all_56_21) & ~ % 152.48/22.83 | | | | | | | | | | (all_56_22 = all_56_23) % 152.48/22.83 | | | | | | | | | | % 152.48/22.83 | | | | | | | | | | ALPHA: (221) implies: % 152.48/22.83 | | | | | | | | | | (222) ~ (all_56_20 = all_56_21) % 152.48/22.83 | | | | | | | | | | % 152.48/22.83 | | | | | | | | | | REDUCE: (162), (166), (222) imply: % 152.48/22.83 | | | | | | | | | | (223) $false % 152.48/22.83 | | | | | | | | | | % 152.48/22.83 | | | | | | | | | | CLOSE: (223) is inconsistent. % 152.48/22.83 | | | | | | | | | | % 152.48/22.83 | | | | | | | | | Case 2: % 152.48/22.83 | | | | | | | | | | % 152.48/22.83 | | | | | | | | | | (224) ~ (all_56_24 = all_56_25) & ~ (all_56_26 = % 152.48/22.83 | | | | | | | | | | all_56_27) & ~ (all_56_28 = all_56_29) & ~ % 152.48/22.83 | | | | | | | | | | (all_56_30 = all_56_31) % 152.48/22.83 | | | | | | | | | | % 152.48/22.83 | | | | | | | | | | ALPHA: (224) implies: % 152.48/22.83 | | | | | | | | | | (225) ~ (all_56_30 = all_56_31) % 152.48/22.83 | | | | | | | | | | % 152.48/22.83 | | | | | | | | | | REDUCE: (80), (83), (225) imply: % 152.48/22.83 | | | | | | | | | | (226) $false % 152.48/22.83 | | | | | | | | | | % 152.48/22.83 | | | | | | | | | | CLOSE: (226) is inconsistent. % 152.48/22.83 | | | | | | | | | | % 152.48/22.83 | | | | | | | | | End of split % 152.48/22.83 | | | | | | | | | % 152.48/22.83 | | | | | | | | End of split % 152.48/22.83 | | | | | | | | % 152.48/22.83 | | | | | | | Case 2: % 152.48/22.83 | | | | | | | | % 152.48/22.83 | | | | | | | | (227) all_54_10 = e0 % 152.48/22.83 | | | | | | | | % 152.48/22.83 | | | | | | | | REF_CLOSE: (8), (150), (227) are inconsistent by sub-proof #705. % 152.48/22.83 | | | | | | | | % 152.48/22.83 | | | | | | | End of split % 152.48/22.83 | | | | | | | % 152.48/22.83 | | | | | | End of split % 152.48/22.83 | | | | | | % 152.48/22.83 | | | | | End of split % 152.48/22.83 | | | | | % 152.48/22.83 | | | | Case 2: % 152.48/22.83 | | | | | % 152.48/22.83 | | | | | (228) all_56_21 = e2 % 152.48/22.83 | | | | | (229) all_56_19 = e1 % 152.48/22.83 | | | | | % 152.48/22.83 | | | | | COMBINE_EQS: (128), (229) imply: % 152.48/22.83 | | | | | (230) all_52_6 = e1 % 152.48/22.83 | | | | | % 152.48/22.83 | | | | | SIMP: (230) implies: % 152.48/22.83 | | | | | (231) all_52_6 = e1 % 152.48/22.83 | | | | | % 152.48/22.83 | | | | | COMBINE_EQS: (34), (228) imply: % 152.48/22.83 | | | | | (232) all_6_2 = e2 % 152.48/22.83 | | | | | % 152.48/22.83 | | | | | SIMP: (232) implies: % 152.48/22.83 | | | | | (233) all_6_2 = e2 % 152.48/22.83 | | | | | % 152.48/22.83 | | | | | REDUCE: (112), (233) imply: % 152.48/22.83 | | | | | (234) ~ (all_52_2 = e2) % 152.48/22.83 | | | | | % 152.48/22.83 | | | | | REDUCE: (125), (231) imply: % 152.48/22.83 | | | | | (235) ~ (all_52_4 = e1) % 152.48/22.83 | | | | | % 152.48/22.83 | | | | | REDUCE: (77), (231) imply: % 152.48/22.83 | | | | | (236) ~ (all_52_7 = e1) % 152.48/22.83 | | | | | % 152.48/22.83 | | | | | SIMP: (236) implies: % 152.48/22.83 | | | | | (237) ~ (all_52_7 = e1) % 152.48/22.83 | | | | | % 152.48/22.83 | | | | | REDUCE: (27), (231) imply: % 152.48/22.83 | | | | | (238) ~ (all_52_14 = e1) % 152.48/22.83 | | | | | % 152.48/22.83 | | | | | SIMP: (238) implies: % 152.48/22.83 | | | | | (239) ~ (all_52_14 = e1) % 152.48/22.83 | | | | | % 152.48/22.83 | | | | | REDUCE: (140), (231) imply: % 152.48/22.83 | | | | | (240) ~ (e2 = e1) % 152.48/22.83 | | | | | % 152.48/22.83 | | | | | SIMP: (240) implies: % 152.48/22.83 | | | | | (241) ~ (e2 = e1) % 152.48/22.83 | | | | | % 152.48/22.83 | | | | | REDUCE: (118), (233) imply: % 152.48/22.83 | | | | | (242) ~ (all_52_14 = e2) % 152.48/22.83 | | | | | % 152.48/22.83 | | | | | BETA: splitting (17) gives: % 152.48/22.83 | | | | | % 152.48/22.83 | | | | | Case 1: % 152.48/22.83 | | | | | | % 152.48/22.83 | | | | | | (243) all_54_11 = e3 % 152.48/22.83 | | | | | | % 152.48/22.83 | | | | | | COMBINE_EQS: (133), (243) imply: % 152.48/22.83 | | | | | | (244) all_52_14 = e3 % 152.48/22.83 | | | | | | % 152.48/22.83 | | | | | | REDUCE: (107), (244) imply: % 152.48/22.83 | | | | | | (245) ~ (all_52_12 = e3) % 152.48/22.83 | | | | | | % 152.48/22.83 | | | | | | BETA: splitting (69) gives: % 152.48/22.83 | | | | | | % 152.48/22.83 | | | | | | Case 1: % 152.48/22.83 | | | | | | | % 152.48/22.83 | | | | | | | (246) ~ (all_56_1 = e0) % 152.48/22.83 | | | | | | | % 152.48/22.83 | | | | | | | REDUCE: (37), (246) imply: % 152.48/22.83 | | | | | | | (247) ~ (all_10_2 = e0) % 152.48/22.83 | | | | | | | % 152.48/22.83 | | | | | | | REF_CLOSE: (3), (6), (14), (15), (22), (25), (28), (31), (40), % 152.48/22.83 | | | | | | | (42), (47), (48), (51), (52), (54), (66), (71), (79), % 152.48/22.83 | | | | | | | (87), (88), (90), (96), (97), (98), (99), (101), (102), % 152.48/22.83 | | | | | | | (104), (106), (111), (113), (122), (127), (129), (131), % 152.48/22.83 | | | | | | | (132), (138), (142), (234), (235), (237), (241), (242), % 152.48/22.83 | | | | | | | (247) are inconsistent by sub-proof #692. % 152.48/22.83 | | | | | | | % 152.48/22.83 | | | | | | Case 2: % 152.48/22.83 | | | | | | | % 152.48/22.83 | | | | | | | (248) all_56_7 = e3 % 152.48/22.83 | | | | | | | % 152.48/22.83 | | | | | | | REF_CLOSE: (64), (245), (248) are inconsistent by sub-proof #691. % 152.48/22.83 | | | | | | | % 152.48/22.83 | | | | | | End of split % 152.48/22.83 | | | | | | % 152.48/22.83 | | | | | Case 2: % 152.48/22.83 | | | | | | % 152.48/22.83 | | | | | | (249) all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0 % 152.48/22.83 | | | | | | % 152.48/22.83 | | | | | | REF_CLOSE: (86), (133), (239), (242), (249) are inconsistent by % 152.48/22.83 | | | | | | sub-proof #687. % 152.48/22.83 | | | | | | % 152.48/22.83 | | | | | End of split % 152.48/22.83 | | | | | % 152.48/22.83 | | | | End of split % 152.48/22.83 | | | | % 152.48/22.83 | | | Case 2: % 152.48/22.83 | | | | % 152.48/22.83 | | | | (250) all_56_21 = e3 % 152.48/22.83 | | | | (251) all_56_17 = e1 % 152.48/22.83 | | | | % 152.48/22.83 | | | | REF_CLOSE: (1), (5), (10), (15), (16), (17), (19), (21), (26), (27), % 152.48/22.83 | | | | (28), (29), (32), (33), (34), (37), (39), (41), (42), (43), % 152.48/22.83 | | | | (50), (57), (60), (62), (64), (69), (73), (74), (75), (78), % 152.48/22.83 | | | | (79), (81), (84), (85), (91), (95), (97), (98), (101), (103), % 152.48/22.83 | | | | (107), (108), (112), (115), (116), (121), (130), (133), % 152.48/22.83 | | | | (250), (251) are inconsistent by sub-proof #669. % 152.48/22.83 | | | | % 152.48/22.83 | | | End of split % 152.48/22.83 | | | % 152.48/22.83 | | Case 2: % 152.48/22.83 | | | % 152.48/22.83 | | | (252) all_56_23 = e1 % 152.48/22.83 | | | (253) all_56_21 = e0 % 152.48/22.83 | | | % 152.48/22.83 | | | COMBINE_EQS: (34), (253) imply: % 152.48/22.83 | | | (254) all_6_2 = e0 % 152.48/22.83 | | | % 152.48/22.83 | | | SIMP: (254) implies: % 152.48/22.83 | | | (255) all_6_2 = e0 % 152.48/22.83 | | | % 152.48/22.83 | | | COMBINE_EQS: (92), (252) imply: % 152.48/22.83 | | | (256) all_52_14 = e1 % 152.48/22.83 | | | % 152.48/22.83 | | | SIMP: (256) implies: % 152.48/22.83 | | | (257) all_52_14 = e1 % 152.48/22.83 | | | % 152.48/22.83 | | | REDUCE: (81), (257) imply: % 152.48/22.83 | | | (258) ~ (all_52_2 = e1) % 152.48/22.83 | | | % 152.48/22.83 | | | REDUCE: (112), (255) imply: % 152.48/22.83 | | | (259) ~ (all_52_2 = e0) % 152.48/22.83 | | | % 152.48/22.83 | | | REDUCE: (27), (257) imply: % 152.48/22.83 | | | (260) ~ (all_52_6 = e1) % 152.48/22.83 | | | % 152.48/22.83 | | | REDUCE: (115), (255) imply: % 152.48/22.83 | | | (261) ~ (all_52_6 = e0) % 152.48/22.83 | | | % 152.48/22.83 | | | REDUCE: (107), (257) imply: % 152.48/22.83 | | | (262) ~ (all_52_12 = e1) % 152.48/22.83 | | | % 152.48/22.83 | | | REDUCE: (91), (257) imply: % 152.48/22.83 | | | (263) ~ (all_52_13 = e1) % 152.48/22.83 | | | % 152.48/22.83 | | | BETA: splitting (75) gives: % 152.48/22.83 | | | % 152.48/22.83 | | | Case 1: % 152.48/22.83 | | | | % 152.48/22.83 | | | | (264) all_54_9 = e3 % 152.48/22.83 | | | | % 152.48/22.83 | | | | COMBINE_EQS: (5), (264) imply: % 152.48/22.83 | | | | (265) all_52_6 = e3 % 152.48/22.83 | | | | % 152.48/22.83 | | | | SIMP: (265) implies: % 152.48/22.83 | | | | (266) all_52_6 = e3 % 152.48/22.83 | | | | % 152.48/22.83 | | | | REDUCE: (77), (266) imply: % 152.48/22.83 | | | | (267) ~ (all_52_7 = e3) % 152.48/22.83 | | | | % 152.48/22.83 | | | | SIMP: (267) implies: % 152.48/22.83 | | | | (268) ~ (all_52_7 = e3) % 152.48/22.83 | | | | % 152.48/22.83 | | | | REDUCE: (140), (266) imply: % 152.48/22.83 | | | | (269) ~ (e3 = e2) % 152.48/22.83 | | | | % 152.48/22.83 | | | | BETA: splitting (14) gives: % 152.48/22.83 | | | | % 152.48/22.83 | | | | Case 1: % 152.48/22.83 | | | | | % 152.48/22.83 | | | | | (270) all_58_9 = e2 % 152.48/22.83 | | | | | % 152.48/22.84 | | | | | COMBINE_EQS: (42), (270) imply: % 152.48/22.84 | | | | | (271) all_52_12 = e2 % 152.48/22.84 | | | | | % 152.48/22.84 | | | | | COMBINE_EQS: (64), (271) imply: % 152.48/22.84 | | | | | (272) all_56_7 = e2 % 152.48/22.84 | | | | | % 152.48/22.84 | | | | | REDUCE: (129), (271) imply: % 152.48/22.84 | | | | | (273) ~ (all_10_2 = e2) % 152.48/22.84 | | | | | % 152.48/22.84 | | | | | BETA: splitting (69) gives: % 152.48/22.84 | | | | | % 152.48/22.84 | | | | | Case 1: % 152.48/22.84 | | | | | | % 152.48/22.84 | | | | | | (274) ~ (all_56_1 = e0) % 152.48/22.84 | | | | | | % 152.48/22.84 | | | | | | REDUCE: (37), (274) imply: % 152.48/22.84 | | | | | | (275) ~ (all_10_2 = e0) % 152.48/22.84 | | | | | | % 152.48/22.84 | | | | | | BETA: splitting (28) gives: % 152.48/22.84 | | | | | | % 152.48/22.84 | | | | | | Case 1: % 152.48/22.84 | | | | | | | % 152.48/22.84 | | | | | | | (276) all_54_0 = e3 % 152.48/22.84 | | | | | | | % 152.48/22.84 | | | | | | | COMBINE_EQS: (15), (276) imply: % 152.48/22.84 | | | | | | | (277) all_10_2 = e3 % 152.48/22.84 | | | | | | | % 152.48/22.84 | | | | | | | SIMP: (277) implies: % 152.48/22.84 | | | | | | | (278) all_10_2 = e3 % 152.48/22.84 | | | | | | | % 152.48/22.84 | | | | | | | REDUCE: (121), (278) imply: % 152.48/22.84 | | | | | | | (279) ~ (all_52_2 = e3) % 152.48/22.84 | | | | | | | % 152.48/22.84 | | | | | | | REDUCE: (58), (278) imply: % 152.48/22.84 | | | | | | | (280) ~ (all_52_3 = e3) % 152.48/22.84 | | | | | | | % 152.48/22.84 | | | | | | | REF_CLOSE: (6), (18), (56), (61), (63), (65), (68), (72), (89), % 152.48/22.84 | | | | | | | (93), (119), (120), (141), (258), (259), (268), (279), % 152.48/22.84 | | | | | | | (280) are inconsistent by sub-proof #661. % 152.48/22.84 | | | | | | | % 152.48/22.84 | | | | | | Case 2: % 152.48/22.84 | | | | | | | % 152.48/22.84 | | | | | | | (281) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 152.48/22.84 | | | | | | | % 152.48/22.84 | | | | | | | REF_CLOSE: (15), (25), (45), (275), (281) are inconsistent by % 152.48/22.84 | | | | | | | sub-proof #731. % 152.48/22.84 | | | | | | | % 152.48/22.84 | | | | | | End of split % 152.48/22.84 | | | | | | % 152.48/22.84 | | | | | Case 2: % 152.48/22.84 | | | | | | % 152.48/22.84 | | | | | | (282) all_56_7 = e3 % 152.48/22.84 | | | | | | % 152.48/22.84 | | | | | | REF_CLOSE: (269), (272), (282) are inconsistent by sub-proof #660. % 152.48/22.84 | | | | | | % 152.48/22.84 | | | | | End of split % 152.48/22.84 | | | | | % 152.48/22.84 | | | | Case 2: % 152.48/22.84 | | | | | % 152.48/22.84 | | | | | (283) ~ (all_58_9 = e2) % 152.48/22.84 | | | | | % 152.48/22.84 | | | | | REDUCE: (42), (283) imply: % 152.48/22.84 | | | | | (284) ~ (all_52_12 = e2) % 152.48/22.84 | | | | | % 152.48/22.84 | | | | | BETA: splitting (38) gives: % 152.48/22.84 | | | | | % 152.48/22.84 | | | | | Case 1: % 152.48/22.84 | | | | | | % 152.48/22.84 | | | | | | (285) all_54_7 = e3 % 152.48/22.84 | | | | | | % 152.48/22.84 | | | | | | COMBINE_EQS: (82), (285) imply: % 152.48/22.84 | | | | | | (286) all_52_13 = e3 % 152.48/22.84 | | | | | | % 152.48/22.84 | | | | | | SIMP: (286) implies: % 152.48/22.84 | | | | | | (287) all_52_13 = e3 % 152.48/22.84 | | | | | | % 152.48/22.84 | | | | | | REDUCE: (19), (287) imply: % 152.48/22.84 | | | | | | (288) ~ (all_52_12 = e3) % 152.48/22.84 | | | | | | % 152.48/22.84 | | | | | | REF_CLOSE: (9), (59), (109), (262), (284), (288) are inconsistent by % 152.48/22.84 | | | | | | sub-proof #653. % 152.48/22.84 | | | | | | % 152.48/22.84 | | | | | Case 2: % 152.48/22.84 | | | | | | % 152.48/22.84 | | | | | | (289) all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0 % 152.48/22.84 | | | | | | % 152.48/22.84 | | | | | | REF_CLOSE: (24), (82), (142), (263), (289) are inconsistent by % 152.48/22.84 | | | | | | sub-proof #649. % 152.48/22.84 | | | | | | % 152.48/22.84 | | | | | End of split % 152.48/22.84 | | | | | % 152.48/22.84 | | | | End of split % 152.48/22.84 | | | | % 152.48/22.84 | | | Case 2: % 152.48/22.84 | | | | % 152.48/22.84 | | | | (290) all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0 % 152.48/22.84 | | | | % 152.48/22.84 | | | | REF_CLOSE: (5), (12), (23), (70), (95), (116), (126), (260), (261), % 152.48/22.84 | | | | (290) are inconsistent by sub-proof #642. % 152.48/22.84 | | | | % 152.48/22.84 | | | End of split % 152.48/22.84 | | | % 152.48/22.84 | | End of split % 152.48/22.84 | | % 152.48/22.84 | Case 2: % 152.48/22.84 | | % 152.48/22.84 | | (291) all_54_5 = e1 | all_54_5 = e0 % 152.48/22.84 | | % 152.48/22.84 | | REF_CLOSE: (12), (23), (116), (291) are inconsistent by sub-proof #645. % 152.48/22.84 | | % 152.48/22.84 | End of split % 152.48/22.84 | % 152.48/22.84 End of proof % 152.48/22.84 % 152.48/22.84 Sub-proof #642 shows that the following formulas are inconsistent: % 152.48/22.84 ---------------------------------------------------------------- % 152.48/22.84 (1) all_54_9 = all_52_6 % 152.48/22.84 (2) ~ (all_52_6 = e1) % 152.48/22.84 (3) ~ (all_8_2 = e1) % 152.48/22.84 (4) all_54_5 = all_8_2 % 152.48/22.84 (5) ~ (all_52_6 = e0) % 152.48/22.84 (6) ~ (all_8_2 = e3) % 152.48/22.84 (7) ~ (all_52_6 = all_8_2) % 152.48/22.84 (8) all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0 % 152.48/22.84 (9) ~ (all_8_2 = e0) % 152.48/22.84 (10) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 152.48/22.84 % 152.48/22.84 Begin of proof % 152.48/22.84 | % 152.48/22.84 | BETA: splitting (8) gives: % 152.48/22.84 | % 152.48/22.84 | Case 1: % 152.48/22.84 | | % 152.48/22.84 | | (11) all_54_9 = e2 % 152.48/22.84 | | % 152.48/22.84 | | COMBINE_EQS: (1), (11) imply: % 152.48/22.84 | | (12) all_52_6 = e2 % 152.48/22.84 | | % 152.48/22.84 | | REDUCE: (7), (12) imply: % 152.48/22.84 | | (13) ~ (all_8_2 = e2) % 152.48/22.84 | | % 152.48/22.84 | | REF_CLOSE: (3), (4), (6), (9), (10), (13) are inconsistent by sub-proof % 152.48/22.84 | | #643. % 152.48/22.84 | | % 152.48/22.84 | Case 2: % 152.48/22.84 | | % 152.48/22.84 | | (14) all_54_9 = e1 | all_54_9 = e0 % 152.48/22.84 | | % 152.48/22.84 | | REF_CLOSE: (1), (2), (5), (14) are inconsistent by sub-proof #678. % 152.48/22.84 | | % 152.48/22.84 | End of split % 152.48/22.84 | % 152.48/22.84 End of proof % 152.48/22.84 % 152.48/22.84 Sub-proof #643 shows that the following formulas are inconsistent: % 152.48/22.84 ---------------------------------------------------------------- % 152.48/22.84 (1) ~ (all_8_2 = e1) % 152.48/22.84 (2) all_54_5 = all_8_2 % 152.48/22.84 (3) ~ (all_8_2 = e3) % 152.48/22.84 (4) ~ (all_8_2 = e0) % 152.48/22.84 (5) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 152.48/22.84 (6) ~ (all_8_2 = e2) % 152.48/22.84 % 152.48/22.84 Begin of proof % 152.48/22.84 | % 152.48/22.84 | SIMP: (6) implies: % 152.48/22.84 | (7) ~ (all_8_2 = e2) % 152.48/22.84 | % 152.48/22.84 | BETA: splitting (5) gives: % 152.48/22.84 | % 152.48/22.84 | Case 1: % 152.48/22.84 | | % 152.48/22.84 | | (8) all_54_5 = e3 % 152.48/22.84 | | % 152.48/22.84 | | REF_CLOSE: (2), (3), (8) are inconsistent by sub-proof #737. % 152.48/22.84 | | % 152.48/22.84 | Case 2: % 152.48/22.84 | | % 152.48/22.84 | | (9) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 152.48/22.84 | | % 152.48/22.84 | | REF_CLOSE: (1), (2), (4), (7), (9) are inconsistent by sub-proof #644. % 152.48/22.84 | | % 152.48/22.84 | End of split % 152.48/22.84 | % 152.48/22.84 End of proof % 152.48/22.84 % 152.48/22.84 Sub-proof #644 shows that the following formulas are inconsistent: % 152.48/22.84 ---------------------------------------------------------------- % 152.48/22.84 (1) ~ (all_8_2 = e1) % 152.48/22.84 (2) all_54_5 = all_8_2 % 152.48/22.84 (3) ~ (all_8_2 = e2) % 152.48/22.84 (4) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 152.48/22.84 (5) ~ (all_8_2 = e0) % 152.48/22.84 % 152.48/22.84 Begin of proof % 152.48/22.84 | % 152.48/22.84 | BETA: splitting (4) gives: % 152.48/22.84 | % 152.48/22.84 | Case 1: % 152.48/22.84 | | % 152.48/22.84 | | (6) all_54_5 = e2 % 152.48/22.84 | | % 152.48/22.84 | | REF_CLOSE: (2), (3), (6) are inconsistent by sub-proof #648. % 152.48/22.84 | | % 152.48/22.84 | Case 2: % 152.48/22.84 | | % 152.48/22.84 | | (7) all_54_5 = e1 | all_54_5 = e0 % 152.48/22.84 | | % 152.48/22.84 | | REF_CLOSE: (1), (2), (5), (7) are inconsistent by sub-proof #645. % 152.48/22.84 | | % 152.48/22.84 | End of split % 152.48/22.84 | % 152.48/22.84 End of proof % 152.48/22.84 % 152.48/22.84 Sub-proof #645 shows that the following formulas are inconsistent: % 152.48/22.84 ---------------------------------------------------------------- % 152.48/22.84 (1) all_54_5 = e1 | all_54_5 = e0 % 152.48/22.84 (2) all_54_5 = all_8_2 % 152.48/22.84 (3) ~ (all_8_2 = e1) % 152.48/22.84 (4) ~ (all_8_2 = e0) % 152.48/22.84 % 152.48/22.84 Begin of proof % 152.48/22.84 | % 152.48/22.84 | BETA: splitting (1) gives: % 152.48/22.84 | % 152.48/22.84 | Case 1: % 152.48/22.84 | | % 152.48/22.84 | | (5) all_54_5 = e1 % 152.48/22.84 | | % 152.48/22.84 | | REF_CLOSE: (2), (3), (5) are inconsistent by sub-proof #647. % 152.48/22.84 | | % 152.48/22.84 | Case 2: % 152.48/22.84 | | % 152.48/22.84 | | (6) all_54_5 = e0 % 152.48/22.84 | | % 152.48/22.84 | | REF_CLOSE: (2), (4), (6) are inconsistent by sub-proof #646. % 152.48/22.84 | | % 152.48/22.84 | End of split % 152.48/22.84 | % 152.48/22.84 End of proof % 152.48/22.84 % 152.48/22.84 Sub-proof #646 shows that the following formulas are inconsistent: % 152.48/22.84 ---------------------------------------------------------------- % 152.48/22.84 (1) all_54_5 = all_8_2 % 152.48/22.84 (2) all_54_5 = e0 % 152.48/22.84 (3) ~ (all_8_2 = e0) % 152.48/22.84 % 152.48/22.84 Begin of proof % 152.48/22.84 | % 152.48/22.84 | COMBINE_EQS: (1), (2) imply: % 152.48/22.84 | (4) all_8_2 = e0 % 152.48/22.84 | % 152.48/22.84 | SIMP: (4) implies: % 152.48/22.84 | (5) all_8_2 = e0 % 152.48/22.84 | % 152.48/22.84 | REDUCE: (3), (5) imply: % 152.48/22.84 | (6) $false % 152.48/22.84 | % 152.48/22.84 | CLOSE: (6) is inconsistent. % 152.48/22.84 | % 152.48/22.84 End of proof % 152.48/22.84 % 152.48/22.84 Sub-proof #647 shows that the following formulas are inconsistent: % 152.48/22.84 ---------------------------------------------------------------- % 152.48/22.84 (1) all_54_5 = all_8_2 % 152.48/22.84 (2) all_54_5 = e1 % 152.48/22.84 (3) ~ (all_8_2 = e1) % 152.48/22.84 % 152.48/22.84 Begin of proof % 152.48/22.84 | % 152.48/22.84 | COMBINE_EQS: (1), (2) imply: % 152.48/22.84 | (4) all_8_2 = e1 % 152.48/22.84 | % 152.48/22.84 | SIMP: (4) implies: % 152.48/22.84 | (5) all_8_2 = e1 % 152.48/22.84 | % 152.48/22.84 | REDUCE: (3), (5) imply: % 152.48/22.84 | (6) $false % 152.48/22.84 | % 152.48/22.84 | CLOSE: (6) is inconsistent. % 152.48/22.84 | % 152.48/22.84 End of proof % 152.48/22.84 % 152.48/22.84 Sub-proof #648 shows that the following formulas are inconsistent: % 152.48/22.84 ---------------------------------------------------------------- % 152.48/22.84 (1) all_54_5 = all_8_2 % 152.48/22.84 (2) all_54_5 = e2 % 152.48/22.84 (3) ~ (all_8_2 = e2) % 152.48/22.84 % 152.48/22.84 Begin of proof % 152.48/22.84 | % 152.48/22.84 | COMBINE_EQS: (1), (2) imply: % 152.48/22.84 | (4) all_8_2 = e2 % 152.48/22.84 | % 152.48/22.84 | SIMP: (4) implies: % 152.48/22.84 | (5) all_8_2 = e2 % 152.48/22.84 | % 152.48/22.84 | REDUCE: (3), (5) imply: % 152.48/22.84 | (6) $false % 152.48/22.84 | % 152.48/22.84 | CLOSE: (6) is inconsistent. % 152.48/22.84 | % 152.48/22.84 End of proof % 152.48/22.84 % 152.48/22.84 Sub-proof #649 shows that the following formulas are inconsistent: % 152.48/22.84 ---------------------------------------------------------------- % 152.48/22.84 (1) ~ (all_52_13 = e1) % 152.48/22.84 (2) ~ (all_52_13 = e0) % 152.48/22.84 (3) all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0 % 152.48/22.84 (4) ~ (all_52_13 = e2) % 152.48/22.84 (5) all_54_7 = all_52_13 % 152.48/22.84 % 152.48/22.84 Begin of proof % 152.48/22.84 | % 152.48/22.84 | BETA: splitting (3) gives: % 152.48/22.84 | % 152.48/22.84 | Case 1: % 152.48/22.84 | | % 152.48/22.84 | | (6) all_54_7 = e2 % 152.48/22.84 | | % 152.48/22.84 | | REF_CLOSE: (4), (5), (6) are inconsistent by sub-proof #652. % 152.48/22.84 | | % 152.48/22.84 | Case 2: % 152.48/22.84 | | % 152.48/22.84 | | (7) all_54_7 = e1 | all_54_7 = e0 % 152.48/22.84 | | % 152.48/22.84 | | BETA: splitting (7) gives: % 152.48/22.84 | | % 152.48/22.84 | | Case 1: % 152.48/22.84 | | | % 152.48/22.84 | | | (8) all_54_7 = e1 % 152.48/22.84 | | | % 152.48/22.84 | | | REF_CLOSE: (1), (5), (8) are inconsistent by sub-proof #651. % 152.48/22.84 | | | % 152.48/22.84 | | Case 2: % 152.48/22.84 | | | % 152.48/22.84 | | | (9) all_54_7 = e0 % 152.48/22.84 | | | % 152.48/22.84 | | | REF_CLOSE: (2), (5), (9) are inconsistent by sub-proof #650. % 152.48/22.84 | | | % 152.48/22.84 | | End of split % 152.48/22.84 | | % 152.48/22.84 | End of split % 152.48/22.84 | % 152.48/22.84 End of proof % 152.48/22.84 % 152.48/22.84 Sub-proof #650 shows that the following formulas are inconsistent: % 152.48/22.84 ---------------------------------------------------------------- % 152.48/22.84 (1) all_54_7 = all_52_13 % 152.48/22.84 (2) all_54_7 = e0 % 152.48/22.84 (3) ~ (all_52_13 = e0) % 152.48/22.84 % 152.48/22.84 Begin of proof % 152.48/22.84 | % 152.48/22.84 | COMBINE_EQS: (1), (2) imply: % 152.48/22.84 | (4) all_52_13 = e0 % 152.48/22.84 | % 152.48/22.84 | SIMP: (4) implies: % 152.48/22.84 | (5) all_52_13 = e0 % 152.48/22.84 | % 152.48/22.84 | REDUCE: (3), (5) imply: % 152.48/22.84 | (6) $false % 152.48/22.84 | % 152.48/22.84 | CLOSE: (6) is inconsistent. % 152.48/22.84 | % 152.48/22.84 End of proof % 152.48/22.84 % 152.48/22.84 Sub-proof #651 shows that the following formulas are inconsistent: % 152.48/22.84 ---------------------------------------------------------------- % 152.48/22.84 (1) all_54_7 = all_52_13 % 152.48/22.84 (2) all_54_7 = e1 % 152.48/22.84 (3) ~ (all_52_13 = e1) % 152.48/22.84 % 152.48/22.84 Begin of proof % 152.48/22.84 | % 152.48/22.84 | COMBINE_EQS: (1), (2) imply: % 152.48/22.84 | (4) all_52_13 = e1 % 152.48/22.84 | % 152.48/22.84 | SIMP: (4) implies: % 152.48/22.84 | (5) all_52_13 = e1 % 152.48/22.84 | % 152.48/22.84 | REDUCE: (3), (5) imply: % 152.48/22.84 | (6) $false % 152.48/22.84 | % 152.48/22.84 | CLOSE: (6) is inconsistent. % 152.48/22.84 | % 152.48/22.84 End of proof % 152.48/22.84 % 152.48/22.84 Sub-proof #652 shows that the following formulas are inconsistent: % 152.48/22.84 ---------------------------------------------------------------- % 152.48/22.84 (1) all_54_7 = all_52_13 % 152.48/22.84 (2) all_54_7 = e2 % 152.48/22.84 (3) ~ (all_52_13 = e2) % 152.48/22.84 % 152.48/22.84 Begin of proof % 152.48/22.84 | % 152.48/22.84 | COMBINE_EQS: (1), (2) imply: % 152.48/22.84 | (4) all_52_13 = e2 % 152.48/22.84 | % 152.48/22.84 | SIMP: (4) implies: % 152.48/22.84 | (5) all_52_13 = e2 % 152.48/22.84 | % 152.48/22.84 | REDUCE: (3), (5) imply: % 152.48/22.84 | (6) $false % 152.48/22.84 | % 152.48/22.84 | CLOSE: (6) is inconsistent. % 152.48/22.84 | % 152.48/22.84 End of proof % 152.48/22.84 % 152.48/22.84 Sub-proof #653 shows that the following formulas are inconsistent: % 152.48/22.84 ---------------------------------------------------------------- % 152.48/22.84 (1) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0 % 152.48/22.84 (2) ~ (all_52_12 = e2) % 152.48/22.84 (3) all_54_3 = all_52_12 % 152.48/22.84 (4) ~ (all_52_12 = e3) % 152.48/22.84 (5) ~ (all_52_12 = e1) % 152.48/22.84 (6) ~ (all_52_12 = e0) % 152.48/22.84 % 152.48/22.84 Begin of proof % 152.48/22.84 | % 152.48/22.84 | BETA: splitting (1) gives: % 152.48/22.84 | % 152.48/22.84 | Case 1: % 152.48/22.84 | | % 152.48/22.84 | | (7) all_54_3 = e3 % 152.48/22.84 | | % 152.48/22.84 | | REF_CLOSE: (3), (4), (7) are inconsistent by sub-proof #659. % 152.48/22.84 | | % 152.48/22.84 | Case 2: % 152.48/22.84 | | % 152.48/22.84 | | (8) all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0 % 152.48/22.84 | | % 152.48/22.84 | | REF_CLOSE: (2), (3), (5), (6), (8) are inconsistent by sub-proof #654. % 152.48/22.84 | | % 152.48/22.84 | End of split % 152.48/22.84 | % 152.48/22.84 End of proof % 152.48/22.84 % 152.48/22.84 Sub-proof #654 shows that the following formulas are inconsistent: % 152.48/22.84 ---------------------------------------------------------------- % 152.48/22.84 (1) ~ (all_52_12 = e2) % 152.48/22.84 (2) all_54_3 = all_52_12 % 152.48/22.84 (3) all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0 % 152.48/22.84 (4) ~ (all_52_12 = e1) % 152.48/22.84 (5) ~ (all_52_12 = e0) % 152.48/22.84 % 152.48/22.84 Begin of proof % 152.48/22.84 | % 152.48/22.84 | BETA: splitting (3) gives: % 152.48/22.84 | % 152.48/22.84 | Case 1: % 152.48/22.84 | | % 152.48/22.84 | | (6) all_54_3 = e2 % 152.48/22.84 | | % 152.48/22.84 | | REF_CLOSE: (1), (2), (6) are inconsistent by sub-proof #658. % 152.48/22.84 | | % 152.48/22.84 | Case 2: % 152.48/22.84 | | % 152.48/22.84 | | (7) all_54_3 = e1 | all_54_3 = e0 % 152.48/22.84 | | % 152.48/22.84 | | REF_CLOSE: (2), (4), (5), (7) are inconsistent by sub-proof #655. % 152.48/22.84 | | % 152.48/22.84 | End of split % 152.48/22.84 | % 152.48/22.84 End of proof % 152.48/22.84 % 152.48/22.84 Sub-proof #655 shows that the following formulas are inconsistent: % 152.48/22.84 ---------------------------------------------------------------- % 152.48/22.84 (1) all_54_3 = e1 | all_54_3 = e0 % 152.48/22.84 (2) all_54_3 = all_52_12 % 152.48/22.84 (3) ~ (all_52_12 = e1) % 152.48/22.84 (4) ~ (all_52_12 = e0) % 152.48/22.84 % 152.48/22.84 Begin of proof % 152.48/22.84 | % 152.48/22.84 | BETA: splitting (1) gives: % 152.48/22.84 | % 152.48/22.84 | Case 1: % 152.48/22.84 | | % 152.48/22.84 | | (5) all_54_3 = e1 % 152.48/22.84 | | % 152.48/22.84 | | REF_CLOSE: (2), (3), (5) are inconsistent by sub-proof #657. % 152.48/22.84 | | % 152.48/22.84 | Case 2: % 152.48/22.84 | | % 152.48/22.84 | | (6) all_54_3 = e0 % 152.48/22.84 | | % 152.48/22.84 | | REF_CLOSE: (2), (4), (6) are inconsistent by sub-proof #656. % 152.48/22.84 | | % 152.48/22.84 | End of split % 152.48/22.84 | % 152.48/22.84 End of proof % 152.48/22.84 % 152.48/22.84 Sub-proof #656 shows that the following formulas are inconsistent: % 152.48/22.84 ---------------------------------------------------------------- % 152.48/22.84 (1) all_54_3 = all_52_12 % 152.48/22.84 (2) all_54_3 = e0 % 152.48/22.84 (3) ~ (all_52_12 = e0) % 152.48/22.84 % 152.48/22.84 Begin of proof % 152.48/22.84 | % 152.48/22.84 | COMBINE_EQS: (1), (2) imply: % 152.48/22.84 | (4) all_52_12 = e0 % 152.48/22.84 | % 152.48/22.84 | SIMP: (4) implies: % 152.48/22.84 | (5) all_52_12 = e0 % 152.48/22.84 | % 152.48/22.84 | REDUCE: (3), (5) imply: % 152.48/22.84 | (6) $false % 152.48/22.84 | % 152.48/22.84 | CLOSE: (6) is inconsistent. % 152.48/22.84 | % 152.48/22.84 End of proof % 152.48/22.84 % 152.48/22.84 Sub-proof #657 shows that the following formulas are inconsistent: % 152.48/22.84 ---------------------------------------------------------------- % 152.48/22.84 (1) all_54_3 = all_52_12 % 152.48/22.84 (2) all_54_3 = e1 % 152.48/22.84 (3) ~ (all_52_12 = e1) % 152.48/22.84 % 152.48/22.84 Begin of proof % 152.48/22.84 | % 152.48/22.84 | COMBINE_EQS: (1), (2) imply: % 152.48/22.84 | (4) all_52_12 = e1 % 152.48/22.84 | % 152.48/22.84 | SIMP: (4) implies: % 152.48/22.84 | (5) all_52_12 = e1 % 152.48/22.84 | % 152.48/22.84 | REDUCE: (3), (5) imply: % 152.48/22.84 | (6) $false % 152.48/22.84 | % 152.48/22.84 | CLOSE: (6) is inconsistent. % 152.48/22.84 | % 152.48/22.84 End of proof % 152.48/22.84 % 152.48/22.84 Sub-proof #658 shows that the following formulas are inconsistent: % 152.48/22.84 ---------------------------------------------------------------- % 152.48/22.84 (1) all_54_3 = all_52_12 % 152.48/22.84 (2) all_54_3 = e2 % 152.48/22.84 (3) ~ (all_52_12 = e2) % 152.48/22.84 % 152.48/22.84 Begin of proof % 152.48/22.84 | % 152.48/22.84 | COMBINE_EQS: (1), (2) imply: % 152.48/22.84 | (4) all_52_12 = e2 % 152.48/22.84 | % 152.48/22.84 | SIMP: (4) implies: % 152.48/22.84 | (5) all_52_12 = e2 % 152.48/22.84 | % 152.48/22.84 | REDUCE: (3), (5) imply: % 152.48/22.84 | (6) $false % 152.48/22.84 | % 152.48/22.84 | CLOSE: (6) is inconsistent. % 152.48/22.84 | % 152.48/22.84 End of proof % 152.48/22.84 % 152.48/22.84 Sub-proof #659 shows that the following formulas are inconsistent: % 152.48/22.84 ---------------------------------------------------------------- % 152.48/22.84 (1) all_54_3 = all_52_12 % 152.48/22.84 (2) all_54_3 = e3 % 152.48/22.84 (3) ~ (all_52_12 = e3) % 152.48/22.84 % 152.48/22.84 Begin of proof % 152.48/22.84 | % 152.48/22.84 | COMBINE_EQS: (1), (2) imply: % 152.48/22.84 | (4) all_52_12 = e3 % 152.48/22.84 | % 152.48/22.84 | SIMP: (4) implies: % 152.48/22.84 | (5) all_52_12 = e3 % 152.48/22.84 | % 152.48/22.84 | REDUCE: (3), (5) imply: % 152.48/22.84 | (6) $false % 152.48/22.84 | % 152.48/22.84 | CLOSE: (6) is inconsistent. % 152.48/22.84 | % 152.48/22.84 End of proof % 152.48/22.84 % 152.48/22.84 Sub-proof #660 shows that the following formulas are inconsistent: % 152.48/22.84 ---------------------------------------------------------------- % 152.48/22.84 (1) all_56_7 = e3 % 152.48/22.84 (2) all_56_7 = e2 % 152.48/22.84 (3) ~ (e3 = e2) % 152.48/22.84 % 152.48/22.84 Begin of proof % 152.48/22.84 | % 152.48/22.84 | COMBINE_EQS: (1), (2) imply: % 152.48/22.84 | (4) e3 = e2 % 152.48/22.84 | % 152.48/22.84 | SIMP: (4) implies: % 152.48/22.84 | (5) e3 = e2 % 152.48/22.84 | % 152.48/22.84 | REDUCE: (3), (5) imply: % 152.48/22.84 | (6) $false % 152.48/22.84 | % 152.48/22.84 | CLOSE: (6) is inconsistent. % 152.48/22.84 | % 152.48/22.84 End of proof % 152.48/22.84 % 152.48/22.84 Sub-proof #661 shows that the following formulas are inconsistent: % 152.48/22.84 ---------------------------------------------------------------- % 152.48/22.84 (1) ~ (all_52_2 = e3) % 152.48/22.84 (2) all_58_6 = all_52_2 % 152.48/22.84 (3) ~ (all_52_7 = e2) % 152.48/22.84 (4) all_54_12 = all_52_3 % 152.48/22.84 (5) all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2 % 152.48/22.84 (6) ~ (all_52_3 = all_52_7) % 152.48/22.84 (7) ~ (all_52_3 = e0) % 152.48/22.84 (8) ~ (all_52_2 = e0) % 152.48/22.84 (9) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0 % 152.48/22.84 (10) ~ (all_52_3 = e3) % 152.48/22.84 (11) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0 % 152.48/22.84 (12) ~ (all_52_2 = e1) % 152.48/22.84 (13) ~ (all_52_2 = all_52_3) % 152.48/22.84 (14) all_54_13 = all_52_7 % 152.48/22.84 (15) all_54_8 = all_52_2 % 152.48/22.84 (16) ~ (all_52_7 = e3) % 152.48/22.84 (17) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0 % 152.48/22.84 (18) ~ (all_52_7 = e0) % 152.48/22.84 % 152.48/22.84 Begin of proof % 152.48/22.84 | % 152.48/22.84 | BETA: splitting (11) gives: % 152.48/22.84 | % 152.48/22.84 | Case 1: % 152.48/22.84 | | % 152.48/22.84 | | (19) all_54_13 = e3 % 152.48/22.84 | | % 152.48/22.84 | | REF_CLOSE: (14), (16), (19) are inconsistent by sub-proof #668. % 152.48/22.84 | | % 152.48/22.84 | Case 2: % 152.48/22.84 | | % 152.48/22.84 | | (20) all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0 % 152.48/22.84 | | % 152.48/22.84 | | BETA: splitting (5) gives: % 152.48/22.84 | | % 152.48/22.84 | | Case 1: % 152.48/22.84 | | | % 152.48/22.84 | | | (21) all_58_6 = e2 % 152.48/22.84 | | | % 152.48/22.84 | | | COMBINE_EQS: (2), (21) imply: % 152.48/22.84 | | | (22) all_52_2 = e2 % 152.48/22.84 | | | % 152.48/22.84 | | | SIMP: (22) implies: % 152.48/22.84 | | | (23) all_52_2 = e2 % 152.48/22.84 | | | % 152.48/22.84 | | | REDUCE: (13), (23) imply: % 152.48/22.84 | | | (24) ~ (all_52_3 = e2) % 152.48/22.84 | | | % 152.48/22.84 | | | SIMP: (24) implies: % 152.48/22.84 | | | (25) ~ (all_52_3 = e2) % 152.48/22.84 | | | % 152.48/22.84 | | | BETA: splitting (9) gives: % 152.48/22.84 | | | % 152.48/22.84 | | | Case 1: % 152.48/22.84 | | | | % 152.48/22.84 | | | | (26) all_54_12 = e3 % 152.48/22.84 | | | | % 152.48/22.84 | | | | REF_CLOSE: (4), (10), (26) are inconsistent by sub-proof #667. % 152.48/22.84 | | | | % 152.48/22.84 | | | Case 2: % 152.48/22.84 | | | | % 152.48/22.84 | | | | (27) all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0 % 152.48/22.84 | | | | % 152.48/22.84 | | | | BETA: splitting (27) gives: % 152.48/22.84 | | | | % 152.48/22.84 | | | | Case 1: % 152.48/22.84 | | | | | % 152.48/22.84 | | | | | (28) all_54_12 = e2 % 152.48/22.84 | | | | | % 152.48/22.84 | | | | | COMBINE_EQS: (4), (28) imply: % 152.48/22.84 | | | | | (29) all_52_3 = e2 % 152.48/22.84 | | | | | % 152.48/22.84 | | | | | REDUCE: (25), (29) imply: % 152.48/22.84 | | | | | (30) $false % 152.48/22.84 | | | | | % 152.48/22.84 | | | | | CLOSE: (30) is inconsistent. % 152.48/22.84 | | | | | % 152.48/22.84 | | | | Case 2: % 152.48/22.84 | | | | | % 152.48/22.84 | | | | | (31) all_54_12 = e1 | all_54_12 = e0 % 152.48/22.84 | | | | | % 152.48/22.84 | | | | | BETA: splitting (31) gives: % 152.48/22.84 | | | | | % 152.48/22.84 | | | | | Case 1: % 152.48/22.84 | | | | | | % 152.48/22.84 | | | | | | (32) all_54_12 = e1 % 152.48/22.84 | | | | | | % 152.48/22.84 | | | | | | COMBINE_EQS: (4), (32) imply: % 152.48/22.84 | | | | | | (33) all_52_3 = e1 % 152.48/22.84 | | | | | | % 152.48/22.84 | | | | | | REDUCE: (6), (33) imply: % 152.48/22.84 | | | | | | (34) ~ (all_52_7 = e1) % 152.48/22.84 | | | | | | % 152.48/22.84 | | | | | | SIMP: (34) implies: % 152.48/22.84 | | | | | | (35) ~ (all_52_7 = e1) % 152.48/22.84 | | | | | | % 152.48/22.84 | | | | | | REF_CLOSE: (3), (14), (18), (20), (35) are inconsistent by sub-proof % 152.48/22.84 | | | | | | #710. % 152.48/22.84 | | | | | | % 152.48/22.84 | | | | | Case 2: % 152.48/22.84 | | | | | | % 152.48/22.84 | | | | | | (36) all_54_12 = e0 % 152.48/22.84 | | | | | | % 152.48/22.84 | | | | | | COMBINE_EQS: (4), (36) imply: % 152.48/22.84 | | | | | | (37) all_52_3 = e0 % 152.48/22.84 | | | | | | % 152.48/22.84 | | | | | | REDUCE: (7), (37) imply: % 152.48/22.84 | | | | | | (38) $false % 152.48/22.84 | | | | | | % 152.48/22.84 | | | | | | CLOSE: (38) is inconsistent. % 152.48/22.84 | | | | | | % 152.48/22.84 | | | | | End of split % 152.48/22.84 | | | | | % 152.48/22.84 | | | | End of split % 152.48/22.84 | | | | % 152.48/22.84 | | | End of split % 152.48/22.84 | | | % 152.48/22.84 | | Case 2: % 152.48/22.84 | | | % 152.48/22.84 | | | (39) ~ (all_58_6 = e2) % 152.48/22.84 | | | % 152.48/22.84 | | | REDUCE: (2), (39) imply: % 152.48/22.84 | | | (40) ~ (all_52_2 = e2) % 152.48/22.84 | | | % 152.48/22.84 | | | REF_CLOSE: (1), (8), (12), (15), (17), (40) are inconsistent by sub-proof % 152.48/22.84 | | | #662. % 152.48/22.84 | | | % 152.48/22.84 | | End of split % 152.48/22.84 | | % 152.48/22.84 | End of split % 152.48/22.84 | % 152.48/22.84 End of proof % 152.48/22.84 % 152.48/22.84 Sub-proof #662 shows that the following formulas are inconsistent: % 152.48/22.84 ---------------------------------------------------------------- % 152.48/22.84 (1) ~ (all_52_2 = e3) % 152.48/22.84 (2) ~ (all_52_2 = e0) % 152.48/22.84 (3) ~ (all_52_2 = e1) % 152.48/22.84 (4) ~ (all_52_2 = e2) % 152.48/22.84 (5) all_54_8 = all_52_2 % 152.48/22.84 (6) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0 % 152.48/22.84 % 152.48/22.84 Begin of proof % 152.48/22.84 | % 152.48/22.84 | BETA: splitting (6) gives: % 152.48/22.84 | % 152.48/22.84 | Case 1: % 152.48/22.84 | | % 152.48/22.84 | | (7) all_54_8 = e3 % 152.48/22.84 | | % 152.48/22.84 | | COMBINE_EQS: (5), (7) imply: % 152.48/22.84 | | (8) all_52_2 = e3 % 152.48/22.84 | | % 152.48/22.84 | | REDUCE: (1), (8) imply: % 152.48/22.84 | | (9) $false % 152.48/22.84 | | % 152.48/22.84 | | CLOSE: (9) is inconsistent. % 152.48/22.84 | | % 152.48/22.84 | Case 2: % 152.48/22.84 | | % 152.48/22.84 | | (10) all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0 % 152.48/22.84 | | % 152.48/22.84 | | REF_CLOSE: (2), (3), (4), (5), (10) are inconsistent by sub-proof #663. % 152.48/22.84 | | % 152.48/22.84 | End of split % 152.48/22.84 | % 152.48/22.84 End of proof % 152.48/22.84 % 152.48/22.84 Sub-proof #663 shows that the following formulas are inconsistent: % 152.48/22.84 ---------------------------------------------------------------- % 152.48/22.84 (1) all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0 % 152.48/22.84 (2) ~ (all_52_2 = e0) % 152.48/22.84 (3) ~ (all_52_2 = e1) % 152.48/22.84 (4) ~ (all_52_2 = e2) % 152.48/22.84 (5) all_54_8 = all_52_2 % 152.48/22.84 % 152.48/22.84 Begin of proof % 152.48/22.84 | % 152.48/22.84 | BETA: splitting (1) gives: % 152.48/22.84 | % 152.48/22.84 | Case 1: % 152.48/22.84 | | % 152.48/22.84 | | (6) all_54_8 = e2 % 152.48/22.84 | | % 152.48/22.84 | | REF_CLOSE: (4), (5), (6) are inconsistent by sub-proof #666. % 152.48/22.84 | | % 152.48/22.84 | Case 2: % 152.48/22.84 | | % 152.48/22.84 | | (7) all_54_8 = e1 | all_54_8 = e0 % 152.48/22.84 | | % 152.48/22.84 | | REF_CLOSE: (2), (3), (5), (7) are inconsistent by sub-proof #664. % 152.48/22.84 | | % 152.48/22.84 | End of split % 152.48/22.84 | % 152.48/22.84 End of proof % 152.48/22.84 % 152.48/22.84 Sub-proof #664 shows that the following formulas are inconsistent: % 152.48/22.84 ---------------------------------------------------------------- % 152.48/22.84 (1) all_54_8 = e1 | all_54_8 = e0 % 152.48/22.84 (2) all_54_8 = all_52_2 % 152.48/22.84 (3) ~ (all_52_2 = e1) % 152.48/22.84 (4) ~ (all_52_2 = e0) % 152.48/22.84 % 152.48/22.84 Begin of proof % 152.48/22.84 | % 152.48/22.84 | BETA: splitting (1) gives: % 152.48/22.84 | % 152.48/22.84 | Case 1: % 152.48/22.84 | | % 152.48/22.84 | | (5) all_54_8 = e1 % 152.48/22.84 | | % 152.48/22.84 | | REF_CLOSE: (2), (3), (5) are inconsistent by sub-proof #665. % 152.48/22.84 | | % 152.48/22.84 | Case 2: % 152.48/22.84 | | % 152.48/22.84 | | (6) all_54_8 = e0 % 152.48/22.84 | | % 152.48/22.84 | | COMBINE_EQS: (2), (6) imply: % 152.48/22.84 | | (7) all_52_2 = e0 % 152.48/22.84 | | % 152.48/22.84 | | SIMP: (7) implies: % 152.48/22.84 | | (8) all_52_2 = e0 % 152.48/22.84 | | % 152.48/22.84 | | REDUCE: (4), (8) imply: % 152.48/22.84 | | (9) $false % 152.48/22.84 | | % 152.48/22.84 | | CLOSE: (9) is inconsistent. % 152.48/22.84 | | % 152.48/22.84 | End of split % 152.48/22.84 | % 152.48/22.84 End of proof % 152.48/22.84 % 152.48/22.84 Sub-proof #665 shows that the following formulas are inconsistent: % 152.48/22.84 ---------------------------------------------------------------- % 152.48/22.84 (1) all_54_8 = all_52_2 % 152.48/22.84 (2) all_54_8 = e1 % 152.48/22.84 (3) ~ (all_52_2 = e1) % 152.48/22.84 % 152.48/22.84 Begin of proof % 152.48/22.84 | % 152.48/22.84 | COMBINE_EQS: (1), (2) imply: % 152.48/22.84 | (4) all_52_2 = e1 % 152.48/22.84 | % 152.48/22.84 | SIMP: (4) implies: % 152.48/22.84 | (5) all_52_2 = e1 % 152.48/22.84 | % 152.48/22.84 | REDUCE: (3), (5) imply: % 152.48/22.84 | (6) $false % 152.48/22.84 | % 152.48/22.84 | CLOSE: (6) is inconsistent. % 152.48/22.84 | % 152.48/22.84 End of proof % 152.48/22.84 % 152.48/22.84 Sub-proof #666 shows that the following formulas are inconsistent: % 152.48/22.84 ---------------------------------------------------------------- % 152.48/22.84 (1) all_54_8 = all_52_2 % 152.48/22.84 (2) all_54_8 = e2 % 152.48/22.84 (3) ~ (all_52_2 = e2) % 152.48/22.84 % 152.48/22.84 Begin of proof % 152.48/22.84 | % 152.48/22.84 | COMBINE_EQS: (1), (2) imply: % 152.48/22.84 | (4) all_52_2 = e2 % 152.48/22.84 | % 152.48/22.84 | SIMP: (4) implies: % 152.48/22.84 | (5) all_52_2 = e2 % 152.48/22.84 | % 152.48/22.84 | REDUCE: (3), (5) imply: % 152.48/22.84 | (6) $false % 152.48/22.84 | % 152.48/22.84 | CLOSE: (6) is inconsistent. % 152.48/22.84 | % 152.48/22.84 End of proof % 152.48/22.84 % 152.48/22.84 Sub-proof #667 shows that the following formulas are inconsistent: % 152.48/22.84 ---------------------------------------------------------------- % 152.48/22.84 (1) all_54_12 = all_52_3 % 152.48/22.84 (2) all_54_12 = e3 % 152.48/22.84 (3) ~ (all_52_3 = e3) % 152.48/22.84 % 152.48/22.84 Begin of proof % 152.48/22.84 | % 152.48/22.84 | COMBINE_EQS: (1), (2) imply: % 152.48/22.84 | (4) all_52_3 = e3 % 152.48/22.84 | % 152.48/22.84 | SIMP: (4) implies: % 152.48/22.84 | (5) all_52_3 = e3 % 152.48/22.84 | % 152.48/22.84 | REDUCE: (3), (5) imply: % 152.48/22.84 | (6) $false % 152.48/22.84 | % 152.48/22.84 | CLOSE: (6) is inconsistent. % 152.48/22.84 | % 152.48/22.84 End of proof % 152.48/22.84 % 152.48/22.84 Sub-proof #668 shows that the following formulas are inconsistent: % 152.48/22.84 ---------------------------------------------------------------- % 152.48/22.84 (1) all_54_13 = all_52_7 % 152.48/22.84 (2) all_54_13 = e3 % 152.48/22.84 (3) ~ (all_52_7 = e3) % 152.48/22.84 % 152.48/22.84 Begin of proof % 152.48/22.84 | % 152.48/22.84 | COMBINE_EQS: (1), (2) imply: % 152.48/22.84 | (4) all_52_7 = e3 % 152.48/22.84 | % 152.48/22.84 | SIMP: (4) implies: % 152.48/22.84 | (5) all_52_7 = e3 % 152.48/22.84 | % 152.48/22.84 | REDUCE: (3), (5) imply: % 152.48/22.84 | (6) $false % 152.48/22.84 | % 152.48/22.84 | CLOSE: (6) is inconsistent. % 152.48/22.84 | % 152.48/22.84 End of proof % 152.48/22.84 % 152.48/22.84 Sub-proof #669 shows that the following formulas are inconsistent: % 152.48/22.84 ---------------------------------------------------------------- % 152.48/22.84 (1) all_56_11 = all_8_2 % 152.48/22.84 (2) all_54_9 = all_52_6 % 152.48/22.84 (3) ~ (all_6_1 = e2) % 152.48/22.84 (4) all_54_0 = all_10_2 % 152.48/22.84 (5) all_56_21 = e3 % 152.48/22.84 (6) ~ (all_52_14 = all_4_2) % 152.48/22.84 (7) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0 % 152.48/22.84 (8) ~ (all_52_12 = all_52_13) % 152.48/22.84 (9) op(e0, e0) = all_4_2 % 152.48/22.84 (10) ~ (all_6_1 = e3) % 152.48/22.84 (11) ~ (all_52_6 = all_52_14) % 152.48/22.84 (12) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 152.48/22.84 (13) ~ (all_6_0 = e2) % 152.48/22.84 (14) all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1 % 152.48/22.84 (15) ~ (all_10_1 = e1) % 152.48/22.84 (16) all_56_21 = all_6_2 % 152.48/22.84 (17) all_56_1 = all_10_2 % 152.48/22.84 (18) all_58_5 = all_52_9 % 152.48/22.84 (19) all_56_17 = all_52_2 % 152.48/22.84 (20) all_58_9 = all_52_12 % 152.48/22.84 (21) op(e1, e0) = all_52_14 % 152.48/22.84 (22) op(e3, e3) = all_10_2 % 152.48/22.84 (23) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 152.48/22.84 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 152.48/22.84 (24) all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0 % 152.48/22.84 (25) ~ (all_52_2 = all_52_6) % 152.48/22.84 (26) all_56_7 = all_52_12 % 152.48/22.84 (27) ~ (all_56_1 = e0) | all_56_7 = e3 % 152.48/22.84 (28) op(e1, all_6_1) = all_6_0 % 152.48/22.84 (29) all_58_3 = all_8_2 % 152.48/22.84 (30) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0 % 152.48/22.84 (31) all_56_31 = all_4_2 % 152.48/22.84 (32) all_58_11 = all_52_14 % 152.48/22.84 (33) ~ (all_52_2 = all_52_14) % 152.48/22.84 (34) op(all_6_2, all_6_2) = all_6_1 % 152.48/22.84 (35) all_56_1 = e3 | all_56_11 = e2 | all_56_21 = e1 | all_56_31 = e0 % 152.48/22.84 (36) all_56_17 = e1 % 152.48/22.84 (37) ~ (all_52_13 = all_52_14) % 152.48/22.84 (38) ~ (all_52_6 = all_8_2) % 152.48/22.84 (39) all_58_15 = all_4_2 % 152.48/22.84 (40) all_58_2 = all_52_1 % 152.48/22.84 (41) all_58_10 = all_52_13 % 152.48/22.84 (42) op(all_10_2, all_10_2) = all_10_1 % 152.48/22.84 (43) ~ (all_52_12 = all_52_14) % 152.48/22.84 (44) op(e1, all_52_9) = all_56_12 % 152.48/22.84 (45) ~ (all_52_2 = all_6_2) % 152.48/22.84 (46) ~ (all_52_6 = all_6_2) % 152.48/22.84 (47) ~ (all_8_2 = e0) % 152.48/22.84 (48) ~ (all_52_2 = all_10_2) % 152.48/22.84 (49) ~ (all_52_1 = all_10_2) % 152.48/22.84 (50) all_54_11 = all_52_14 % 152.48/22.84 % 152.48/22.84 Begin of proof % 152.48/22.84 | % 152.48/22.84 | COMBINE_EQS: (19), (36) imply: % 152.48/22.84 | (51) all_52_2 = e1 % 152.53/22.84 | % 152.53/22.84 | SIMP: (51) implies: % 152.53/22.84 | (52) all_52_2 = e1 % 152.53/22.84 | % 152.53/22.84 | COMBINE_EQS: (5), (16) imply: % 152.53/22.84 | (53) all_6_2 = e3 % 152.53/22.84 | % 152.53/22.84 | SIMP: (53) implies: % 152.53/22.84 | (54) all_6_2 = e3 % 152.53/22.84 | % 152.53/22.84 | REDUCE: (25), (52) imply: % 152.53/22.84 | (55) ~ (all_52_6 = e1) % 152.53/22.84 | % 152.53/22.84 | SIMP: (55) implies: % 152.53/22.84 | (56) ~ (all_52_6 = e1) % 152.53/22.84 | % 152.53/22.84 | REDUCE: (33), (52) imply: % 152.53/22.84 | (57) ~ (all_52_14 = e1) % 152.53/22.84 | % 152.53/22.84 | SIMP: (57) implies: % 152.53/22.84 | (58) ~ (all_52_14 = e1) % 152.53/22.84 | % 152.53/22.84 | REDUCE: (48), (52) imply: % 152.53/22.84 | (59) ~ (all_10_2 = e1) % 152.53/22.84 | % 152.53/22.84 | SIMP: (59) implies: % 152.53/22.84 | (60) ~ (all_10_2 = e1) % 152.53/22.84 | % 152.53/22.84 | REDUCE: (45), (52), (54) imply: % 152.53/22.84 | (61) ~ (e3 = e1) % 152.53/22.84 | % 152.53/22.84 | SIMP: (61) implies: % 152.53/22.84 | (62) ~ (e3 = e1) % 152.53/22.84 | % 152.53/22.84 | REDUCE: (46), (54) imply: % 152.53/22.84 | (63) ~ (all_52_6 = e3) % 152.53/22.84 | % 152.53/22.84 | REDUCE: (34), (54) imply: % 152.53/22.84 | (64) op(e3, e3) = all_6_1 % 152.53/22.84 | % 152.53/22.84 | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), % 152.53/22.84 | (13), (14), (15), (17), (18), (20), (21), (22), (23), (24), (26), % 152.53/22.84 | (27), (28), (29), (30), (31), (32), (35), (37), (38), (39), (40), % 152.53/22.84 | (41), (42), (43), (44), (47), (49), (50), (56), (58), (60), (62), % 152.53/22.84 | (63), (64) are inconsistent by sub-proof #670. % 152.53/22.84 | % 152.53/22.84 End of proof % 152.53/22.84 % 152.53/22.84 Sub-proof #670 shows that the following formulas are inconsistent: % 152.53/22.84 ---------------------------------------------------------------- % 152.53/22.84 (1) all_56_11 = all_8_2 % 152.53/22.84 (2) all_54_9 = all_52_6 % 152.53/22.84 (3) ~ (all_52_6 = e1) % 152.53/22.84 (4) ~ (all_6_1 = e2) % 152.53/22.84 (5) all_54_0 = all_10_2 % 152.53/22.84 (6) all_56_21 = e3 % 152.53/22.84 (7) ~ (all_52_14 = all_4_2) % 152.53/22.84 (8) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0 % 152.53/22.84 (9) ~ (all_52_12 = all_52_13) % 152.53/22.84 (10) op(e0, e0) = all_4_2 % 152.53/22.84 (11) ~ (all_10_2 = e1) % 152.53/22.84 (12) ~ (all_6_1 = e3) % 152.53/22.84 (13) ~ (all_52_6 = all_52_14) % 152.53/22.85 (14) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 152.53/22.85 (15) ~ (all_6_0 = e2) % 152.53/22.85 (16) all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1 % 152.53/22.85 (17) ~ (all_10_1 = e1) % 152.53/22.85 (18) all_56_1 = all_10_2 % 152.53/22.85 (19) ~ (all_52_6 = e3) % 152.53/22.85 (20) all_58_5 = all_52_9 % 152.53/22.85 (21) all_58_9 = all_52_12 % 152.53/22.85 (22) op(e3, e3) = all_6_1 % 152.53/22.85 (23) op(e1, e0) = all_52_14 % 152.53/22.85 (24) op(e3, e3) = all_10_2 % 152.53/22.85 (25) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 152.53/22.85 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 152.53/22.85 (26) all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0 % 152.53/22.85 (27) ~ (all_52_14 = e1) % 152.53/22.85 (28) all_56_7 = all_52_12 % 152.53/22.85 (29) ~ (all_56_1 = e0) | all_56_7 = e3 % 152.53/22.85 (30) op(e1, all_6_1) = all_6_0 % 152.53/22.85 (31) all_58_3 = all_8_2 % 152.53/22.85 (32) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0 % 152.53/22.85 (33) all_56_31 = all_4_2 % 152.53/22.85 (34) all_58_11 = all_52_14 % 152.53/22.85 (35) all_56_1 = e3 | all_56_11 = e2 | all_56_21 = e1 | all_56_31 = e0 % 152.53/22.85 (36) ~ (all_52_13 = all_52_14) % 152.53/22.85 (37) ~ (all_52_6 = all_8_2) % 152.53/22.85 (38) all_58_15 = all_4_2 % 152.53/22.85 (39) all_58_2 = all_52_1 % 152.53/22.85 (40) all_58_10 = all_52_13 % 152.53/22.85 (41) op(all_10_2, all_10_2) = all_10_1 % 152.53/22.85 (42) ~ (all_52_12 = all_52_14) % 152.53/22.85 (43) op(e1, all_52_9) = all_56_12 % 152.53/22.85 (44) ~ (e3 = e1) % 152.53/22.85 (45) ~ (all_8_2 = e0) % 152.53/22.85 (46) ~ (all_52_1 = all_10_2) % 152.53/22.85 (47) all_54_11 = all_52_14 % 152.53/22.85 % 152.53/22.85 Begin of proof % 152.53/22.85 | % 152.53/22.85 | GROUND_INST: instantiating (25) with all_10_2, all_6_1, e3, e3, simplifying % 152.53/22.85 | with (22), (24) gives: % 152.53/22.85 | (48) all_10_2 = all_6_1 % 152.53/22.85 | % 152.53/22.85 | COMBINE_EQS: (5), (48) imply: % 152.53/22.85 | (49) all_54_0 = all_6_1 % 152.53/22.85 | % 152.53/22.85 | COMBINE_EQS: (18), (48) imply: % 152.53/22.85 | (50) all_56_1 = all_6_1 % 152.53/22.85 | % 152.53/22.85 | REDUCE: (46), (48) imply: % 152.53/22.85 | (51) ~ (all_52_1 = all_6_1) % 152.53/22.85 | % 152.53/22.85 | REDUCE: (11), (48) imply: % 152.53/22.85 | (52) ~ (all_6_1 = e1) % 152.53/22.85 | % 152.53/22.85 | REDUCE: (41), (48) imply: % 152.53/22.85 | (53) op(all_6_1, all_6_1) = all_10_1 % 152.53/22.85 | % 152.53/22.85 | BETA: splitting (14) gives: % 152.53/22.85 | % 152.53/22.85 | Case 1: % 152.53/22.85 | | % 152.53/22.85 | | (54) all_54_0 = e3 % 152.53/22.85 | | % 152.53/22.85 | | REF_CLOSE: (12), (49), (54) are inconsistent by sub-proof #686. % 152.53/22.85 | | % 152.53/22.85 | Case 2: % 152.53/22.85 | | % 152.53/22.85 | | (55) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 152.53/22.85 | | % 152.53/22.85 | | BETA: splitting (55) gives: % 152.53/22.85 | | % 152.53/22.85 | | Case 1: % 152.53/22.85 | | | % 152.53/22.85 | | | (56) all_54_0 = e2 % 152.53/22.85 | | | % 152.53/22.85 | | | REF_CLOSE: (4), (49), (56) are inconsistent by sub-proof #685. % 152.53/22.85 | | | % 152.53/22.85 | | Case 2: % 152.53/22.85 | | | % 152.53/22.85 | | | (57) all_54_0 = e1 | all_54_0 = e0 % 152.53/22.85 | | | % 152.53/22.85 | | | BETA: splitting (57) gives: % 152.53/22.85 | | | % 152.53/22.85 | | | Case 1: % 152.53/22.85 | | | | % 152.53/22.85 | | | | (58) all_54_0 = e1 % 152.53/22.85 | | | | % 152.53/22.85 | | | | REF_CLOSE: (49), (52), (58) are inconsistent by sub-proof #684. % 152.53/22.85 | | | | % 152.53/22.85 | | | Case 2: % 152.53/22.85 | | | | % 152.53/22.85 | | | | (59) all_54_0 = e0 % 152.53/22.85 | | | | % 152.53/22.85 | | | | COMBINE_EQS: (49), (59) imply: % 152.53/22.85 | | | | (60) all_6_1 = e0 % 152.53/22.85 | | | | % 152.53/22.85 | | | | SIMP: (60) implies: % 152.53/22.85 | | | | (61) all_6_1 = e0 % 152.53/22.85 | | | | % 152.53/22.85 | | | | COMBINE_EQS: (50), (61) imply: % 152.53/22.85 | | | | (62) all_56_1 = e0 % 152.53/22.85 | | | | % 152.53/22.85 | | | | REDUCE: (51), (61) imply: % 152.53/22.85 | | | | (63) ~ (all_52_1 = e0) % 152.53/22.85 | | | | % 152.53/22.85 | | | | REDUCE: (52), (61) imply: % 152.53/22.85 | | | | (64) ~ (e1 = e0) % 152.53/22.85 | | | | % 152.53/22.85 | | | | SIMP: (64) implies: % 152.53/22.85 | | | | (65) ~ (e1 = e0) % 152.53/22.85 | | | | % 152.53/22.85 | | | | REDUCE: (53), (61) imply: % 152.53/22.85 | | | | (66) op(e0, e0) = all_10_1 % 152.53/22.85 | | | | % 152.53/22.85 | | | | REDUCE: (30), (61) imply: % 152.53/22.85 | | | | (67) op(e1, e0) = all_6_0 % 152.53/22.85 | | | | % 152.53/22.85 | | | | BETA: splitting (29) gives: % 152.53/22.85 | | | | % 152.53/22.85 | | | | Case 1: % 152.53/22.85 | | | | | % 152.53/22.85 | | | | | (68) ~ (all_56_1 = e0) % 152.53/22.85 | | | | | % 152.53/22.85 | | | | | REDUCE: (62), (68) imply: % 152.53/22.85 | | | | | (69) $false % 152.53/22.85 | | | | | % 152.53/22.85 | | | | | CLOSE: (69) is inconsistent. % 152.53/22.85 | | | | | % 152.53/22.85 | | | | Case 2: % 152.53/22.85 | | | | | % 152.53/22.85 | | | | | (70) all_56_7 = e3 % 152.53/22.85 | | | | | % 152.53/22.85 | | | | | COMBINE_EQS: (28), (70) imply: % 152.53/22.85 | | | | | (71) all_52_12 = e3 % 152.53/22.85 | | | | | % 152.53/22.85 | | | | | COMBINE_EQS: (21), (71) imply: % 152.53/22.85 | | | | | (72) all_58_9 = e3 % 152.53/22.85 | | | | | % 152.53/22.85 | | | | | REDUCE: (9), (71) imply: % 152.53/22.85 | | | | | (73) ~ (all_52_13 = e3) % 152.53/22.85 | | | | | % 152.53/22.85 | | | | | SIMP: (73) implies: % 152.53/22.85 | | | | | (74) ~ (all_52_13 = e3) % 152.53/22.85 | | | | | % 152.53/22.85 | | | | | REDUCE: (42), (71) imply: % 152.53/22.85 | | | | | (75) ~ (all_52_14 = e3) % 152.53/22.85 | | | | | % 152.53/22.85 | | | | | SIMP: (75) implies: % 152.53/22.85 | | | | | (76) ~ (all_52_14 = e3) % 152.53/22.85 | | | | | % 152.53/22.85 | | | | | GROUND_INST: instantiating (25) with all_4_2, all_10_1, e0, e0, % 152.53/22.85 | | | | | simplifying with (10), (66) gives: % 152.53/22.85 | | | | | (77) all_10_1 = all_4_2 % 152.53/22.85 | | | | | % 152.53/22.85 | | | | | GROUND_INST: instantiating (25) with all_52_14, all_6_0, e0, e1, % 152.53/22.85 | | | | | simplifying with (23), (67) gives: % 152.53/22.85 | | | | | (78) all_52_14 = all_6_0 % 152.53/22.85 | | | | | % 152.53/22.85 | | | | | REDUCE: (17), (77) imply: % 152.53/22.85 | | | | | (79) ~ (all_4_2 = e1) % 152.53/22.85 | | | | | % 152.53/22.85 | | | | | REF_CLOSE: (1), (2), (3), (6), (7), (8), (13), (15), (16), (19), (20), % 152.53/22.85 | | | | | (23), (25), (26), (27), (31), (32), (33), (34), (35), (36), % 152.53/22.85 | | | | | (37), (38), (39), (40), (43), (44), (45), (47), (62), (63), % 152.53/22.85 | | | | | (65), (67), (72), (74), (76), (79) are inconsistent by % 152.53/22.85 | | | | | sub-proof #671. % 152.53/22.85 | | | | | % 152.53/22.85 | | | | End of split % 152.53/22.85 | | | | % 152.53/22.85 | | | End of split % 152.53/22.85 | | | % 152.53/22.85 | | End of split % 152.53/22.85 | | % 152.53/22.85 | End of split % 152.53/22.85 | % 152.53/22.85 End of proof % 152.53/22.85 % 152.53/22.85 Sub-proof #671 shows that the following formulas are inconsistent: % 152.53/22.85 ---------------------------------------------------------------- % 152.53/22.85 (1) all_56_11 = all_8_2 % 152.53/22.85 (2) all_54_9 = all_52_6 % 152.53/22.85 (3) ~ (all_52_6 = e1) % 152.53/22.85 (4) all_56_21 = e3 % 152.53/22.85 (5) ~ (all_52_14 = all_4_2) % 152.53/22.85 (6) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0 % 152.53/22.85 (7) all_58_9 = e3 % 152.53/22.85 (8) ~ (all_52_6 = all_52_14) % 152.53/22.85 (9) ~ (all_6_0 = e2) % 152.53/22.85 (10) all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1 % 152.53/22.85 (11) ~ (all_52_6 = e3) % 152.53/22.85 (12) all_58_5 = all_52_9 % 152.53/22.85 (13) op(e1, e0) = all_6_0 % 152.53/22.85 (14) op(e1, e0) = all_52_14 % 152.53/22.85 (15) ~ (e1 = e0) % 152.53/22.85 (16) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 152.53/22.85 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 152.53/22.85 (17) all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0 % 152.53/22.85 (18) ~ (all_52_14 = e1) % 152.53/22.85 (19) ~ (all_52_14 = e3) % 152.53/22.85 (20) ~ (all_4_2 = e1) % 152.53/22.85 (21) all_56_1 = e0 % 152.53/22.85 (22) ~ (all_52_1 = e0) % 152.53/22.85 (23) all_58_3 = all_8_2 % 152.53/22.85 (24) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0 % 152.53/22.85 (25) all_56_31 = all_4_2 % 152.53/22.85 (26) all_58_11 = all_52_14 % 152.53/22.85 (27) all_56_1 = e3 | all_56_11 = e2 | all_56_21 = e1 | all_56_31 = e0 % 152.53/22.85 (28) ~ (all_52_13 = all_52_14) % 152.53/22.85 (29) ~ (all_52_6 = all_8_2) % 152.53/22.85 (30) all_58_15 = all_4_2 % 152.53/22.85 (31) ~ (all_52_13 = e3) % 152.53/22.85 (32) all_58_2 = all_52_1 % 152.53/22.85 (33) all_58_10 = all_52_13 % 152.53/22.85 (34) op(e1, all_52_9) = all_56_12 % 152.53/22.85 (35) ~ (e3 = e1) % 152.53/22.85 (36) ~ (all_8_2 = e0) % 152.53/22.85 (37) all_54_11 = all_52_14 % 152.53/22.85 % 152.53/22.85 Begin of proof % 152.53/22.85 | % 152.53/22.85 | BETA: splitting (10) gives: % 152.53/22.85 | % 152.53/22.85 | Case 1: % 152.53/22.85 | | % 152.53/22.85 | | (38) all_58_9 = e1 % 152.53/22.85 | | % 152.53/22.85 | | COMBINE_EQS: (7), (38) imply: % 152.53/22.85 | | (39) e3 = e1 % 152.53/22.85 | | % 152.53/22.85 | | REDUCE: (35), (39) imply: % 152.53/22.85 | | (40) $false % 152.53/22.85 | | % 152.53/22.85 | | CLOSE: (40) is inconsistent. % 152.53/22.85 | | % 152.53/22.85 | Case 2: % 152.53/22.85 | | % 152.53/22.85 | | (41) all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1 % 152.53/22.85 | | % 152.53/22.85 | | BETA: splitting (41) gives: % 152.53/22.85 | | % 152.53/22.85 | | Case 1: % 152.53/22.85 | | | % 152.53/22.85 | | | (42) all_58_10 = e1 % 152.53/22.85 | | | % 152.53/22.85 | | | COMBINE_EQS: (33), (42) imply: % 152.53/22.85 | | | (43) all_52_13 = e1 % 152.53/22.85 | | | % 152.53/22.85 | | | REDUCE: (28), (43) imply: % 152.53/22.85 | | | (44) ~ (all_52_14 = e1) % 152.53/22.85 | | | % 152.53/22.85 | | | REDUCE: (31), (43) imply: % 152.53/22.85 | | | (45) ~ (e3 = e1) % 152.53/22.85 | | | % 152.53/22.85 | | | BETA: splitting (17) gives: % 152.53/22.85 | | | % 152.53/22.85 | | | Case 1: % 152.53/22.85 | | | | % 152.53/22.85 | | | | (46) all_58_2 = e0 % 152.53/22.85 | | | | % 152.53/22.85 | | | | COMBINE_EQS: (32), (46) imply: % 152.53/22.85 | | | | (47) all_52_1 = e0 % 152.53/22.85 | | | | % 152.53/22.85 | | | | REDUCE: (22), (47) imply: % 152.53/22.85 | | | | (48) $false % 152.53/22.85 | | | | % 152.53/22.85 | | | | CLOSE: (48) is inconsistent. % 152.53/22.85 | | | | % 152.53/22.85 | | | Case 2: % 152.53/22.85 | | | | % 152.53/22.85 | | | | (49) all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0 % 152.53/22.85 | | | | % 152.53/22.85 | | | | BETA: splitting (49) gives: % 152.53/22.85 | | | | % 152.53/22.85 | | | | Case 1: % 152.53/22.85 | | | | | % 152.53/22.85 | | | | | (50) all_58_3 = e0 % 152.53/22.85 | | | | | % 152.53/22.85 | | | | | COMBINE_EQS: (23), (50) imply: % 152.53/22.85 | | | | | (51) all_8_2 = e0 % 152.53/22.85 | | | | | % 152.53/22.85 | | | | | REDUCE: (36), (51) imply: % 152.53/22.85 | | | | | (52) $false % 152.53/22.85 | | | | | % 152.53/22.85 | | | | | CLOSE: (52) is inconsistent. % 152.53/22.85 | | | | | % 152.53/22.85 | | | | Case 2: % 152.53/22.85 | | | | | % 152.53/22.85 | | | | | (53) all_58_5 = e0 | all_58_10 = e0 % 152.53/22.85 | | | | | % 152.53/22.85 | | | | | BETA: splitting (53) gives: % 152.53/22.85 | | | | | % 152.53/22.85 | | | | | Case 1: % 152.53/22.85 | | | | | | % 152.53/22.85 | | | | | | (54) all_58_5 = e0 % 152.53/22.85 | | | | | | % 152.53/22.85 | | | | | | COMBINE_EQS: (12), (54) imply: % 152.53/22.85 | | | | | | (55) all_52_9 = e0 % 152.53/22.85 | | | | | | % 152.53/22.85 | | | | | | REDUCE: (34), (55) imply: % 152.53/22.85 | | | | | | (56) op(e1, e0) = all_56_12 % 152.53/22.85 | | | | | | % 152.53/22.85 | | | | | | GROUND_INST: instantiating (16) with all_52_14, all_56_12, e0, e1, % 152.53/22.85 | | | | | | simplifying with (14), (56) gives: % 152.53/22.85 | | | | | | (57) all_56_12 = all_52_14 % 152.53/22.85 | | | | | | % 152.53/22.85 | | | | | | GROUND_INST: instantiating (16) with all_6_0, all_56_12, e0, e1, % 152.53/22.85 | | | | | | simplifying with (13), (56) gives: % 152.53/22.85 | | | | | | (58) all_56_12 = all_6_0 % 152.53/22.85 | | | | | | % 152.53/22.85 | | | | | | COMBINE_EQS: (57), (58) imply: % 152.53/22.85 | | | | | | (59) all_52_14 = all_6_0 % 152.53/22.85 | | | | | | % 152.53/22.85 | | | | | | SIMP: (59) implies: % 152.53/22.85 | | | | | | (60) all_52_14 = all_6_0 % 152.53/22.85 | | | | | | % 152.53/22.85 | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (9), (11), (18), (19), % 152.53/22.85 | | | | | | (21), (24), (25), (27), (29), (35), (37), (60) are % 152.53/22.85 | | | | | | inconsistent by sub-proof #673. % 152.53/22.85 | | | | | | % 152.53/22.85 | | | | | Case 2: % 152.53/22.85 | | | | | | % 152.53/22.85 | | | | | | (61) all_58_10 = e0 % 152.53/22.85 | | | | | | % 152.53/22.85 | | | | | | COMBINE_EQS: (42), (61) imply: % 152.53/22.85 | | | | | | (62) e1 = e0 % 152.53/22.85 | | | | | | % 152.53/22.85 | | | | | | REDUCE: (15), (62) imply: % 152.53/22.85 | | | | | | (63) $false % 152.53/22.85 | | | | | | % 152.53/22.85 | | | | | | CLOSE: (63) is inconsistent. % 152.53/22.85 | | | | | | % 152.53/22.85 | | | | | End of split % 152.53/22.85 | | | | | % 152.53/22.85 | | | | End of split % 152.53/22.85 | | | | % 152.53/22.85 | | | End of split % 152.53/22.85 | | | % 152.53/22.85 | | Case 2: % 152.53/22.85 | | | % 152.53/22.85 | | | (64) all_58_11 = e1 | all_58_15 = e1 % 152.53/22.85 | | | % 152.53/22.85 | | | REF_CLOSE: (18), (20), (26), (30), (64) are inconsistent by sub-proof % 152.53/22.85 | | | #672. % 152.53/22.85 | | | % 152.53/22.85 | | End of split % 152.53/22.85 | | % 152.53/22.85 | End of split % 152.53/22.85 | % 152.53/22.85 End of proof % 152.53/22.85 % 152.53/22.85 Sub-proof #672 shows that the following formulas are inconsistent: % 152.53/22.85 ---------------------------------------------------------------- % 152.53/22.85 (1) all_58_11 = e1 | all_58_15 = e1 % 152.53/22.85 (2) ~ (all_52_14 = e1) % 152.53/22.85 (3) ~ (all_4_2 = e1) % 152.53/22.85 (4) all_58_11 = all_52_14 % 152.53/22.85 (5) all_58_15 = all_4_2 % 152.53/22.85 % 152.53/22.85 Begin of proof % 152.53/22.85 | % 152.53/22.85 | BETA: splitting (1) gives: % 152.53/22.85 | % 152.53/22.85 | Case 1: % 152.53/22.85 | | % 152.53/22.85 | | (6) all_58_11 = e1 % 152.53/22.85 | | % 152.53/22.85 | | COMBINE_EQS: (4), (6) imply: % 152.53/22.85 | | (7) all_52_14 = e1 % 152.53/22.85 | | % 152.53/22.85 | | REDUCE: (2), (7) imply: % 152.53/22.85 | | (8) $false % 152.53/22.85 | | % 152.53/22.85 | | CLOSE: (8) is inconsistent. % 152.53/22.85 | | % 152.53/22.85 | Case 2: % 152.53/22.85 | | % 152.53/22.85 | | (9) all_58_15 = e1 % 152.53/22.85 | | % 152.53/22.85 | | COMBINE_EQS: (5), (9) imply: % 152.53/22.85 | | (10) all_4_2 = e1 % 152.53/22.85 | | % 152.53/22.85 | | REDUCE: (3), (10) imply: % 152.53/22.85 | | (11) $false % 152.53/22.85 | | % 152.53/22.85 | | CLOSE: (11) is inconsistent. % 152.53/22.85 | | % 152.53/22.85 | End of split % 152.53/22.85 | % 152.53/22.85 End of proof % 152.53/22.85 % 152.53/22.85 Sub-proof #673 shows that the following formulas are inconsistent: % 152.53/22.85 ---------------------------------------------------------------- % 152.53/22.85 (1) all_56_11 = all_8_2 % 152.53/22.85 (2) all_54_9 = all_52_6 % 152.53/22.85 (3) ~ (all_52_6 = e1) % 152.53/22.85 (4) all_56_21 = e3 % 152.53/22.85 (5) ~ (all_52_14 = all_4_2) % 152.53/22.85 (6) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0 % 152.53/22.85 (7) ~ (all_52_6 = all_52_14) % 152.53/22.85 (8) ~ (all_6_0 = e2) % 152.53/22.85 (9) ~ (all_52_6 = e3) % 152.53/22.85 (10) ~ (all_52_14 = e1) % 152.53/22.85 (11) ~ (all_52_14 = e3) % 152.53/22.85 (12) all_52_14 = all_6_0 % 152.53/22.85 (13) all_56_1 = e0 % 152.53/22.85 (14) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0 % 152.53/22.85 (15) all_56_31 = all_4_2 % 152.53/22.85 (16) all_56_1 = e3 | all_56_11 = e2 | all_56_21 = e1 | all_56_31 = e0 % 152.53/22.85 (17) ~ (all_52_6 = all_8_2) % 152.53/22.85 (18) ~ (e3 = e1) % 152.53/22.85 (19) all_54_11 = all_52_14 % 152.53/22.85 % 152.53/22.85 Begin of proof % 152.53/22.85 | % 152.53/22.85 | COMBINE_EQS: (12), (19) imply: % 152.53/22.85 | (20) all_54_11 = all_6_0 % 152.53/22.85 | % 152.53/22.85 | REDUCE: (7), (12) imply: % 152.53/22.85 | (21) ~ (all_52_6 = all_6_0) % 152.53/22.85 | % 152.53/22.85 | REDUCE: (5), (12) imply: % 152.53/22.85 | (22) ~ (all_6_0 = all_4_2) % 152.53/22.85 | % 152.53/22.85 | REDUCE: (11), (12) imply: % 152.53/22.85 | (23) ~ (all_6_0 = e3) % 152.53/22.85 | % 152.53/22.85 | REDUCE: (10), (12) imply: % 152.53/22.85 | (24) ~ (all_6_0 = e1) % 152.53/22.85 | % 152.53/22.85 | BETA: splitting (6) gives: % 152.53/22.85 | % 152.53/22.85 | Case 1: % 152.53/22.85 | | % 152.53/22.85 | | (25) all_54_11 = e3 % 152.53/22.85 | | % 152.53/22.85 | | REF_CLOSE: (20), (23), (25) are inconsistent by sub-proof #683. % 152.53/22.85 | | % 152.53/22.85 | Case 2: % 152.53/22.85 | | % 152.53/22.85 | | (26) ~ (all_54_11 = e3) % 152.53/22.85 | | (27) all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0 % 152.53/22.85 | | % 152.53/22.85 | | BETA: splitting (27) gives: % 152.53/22.85 | | % 152.53/22.85 | | Case 1: % 152.53/22.85 | | | % 152.53/22.85 | | | (28) all_54_11 = e2 % 152.53/22.85 | | | % 152.53/22.85 | | | REF_CLOSE: (8), (20), (28) are inconsistent by sub-proof #682. % 152.53/22.85 | | | % 152.53/22.85 | | Case 2: % 152.53/22.85 | | | % 152.53/22.85 | | | (29) all_54_11 = e1 | all_54_11 = e0 % 152.53/22.85 | | | % 152.53/22.85 | | | BETA: splitting (29) gives: % 152.53/22.85 | | | % 152.53/22.85 | | | Case 1: % 152.53/22.85 | | | | % 152.53/22.85 | | | | (30) all_54_11 = e1 % 152.53/22.85 | | | | % 152.53/22.85 | | | | REF_CLOSE: (20), (24), (30) are inconsistent by sub-proof #681. % 152.53/22.85 | | | | % 152.53/22.85 | | | Case 2: % 152.53/22.85 | | | | % 152.53/22.85 | | | | (31) all_54_11 = e0 % 152.53/22.85 | | | | % 152.53/22.85 | | | | COMBINE_EQS: (20), (31) imply: % 152.53/22.85 | | | | (32) all_6_0 = e0 % 152.53/22.85 | | | | % 152.53/22.85 | | | | SIMP: (32) implies: % 152.53/22.85 | | | | (33) all_6_0 = e0 % 152.53/22.85 | | | | % 152.53/22.85 | | | | REDUCE: (21), (33) imply: % 152.53/22.85 | | | | (34) ~ (all_52_6 = e0) % 152.53/22.85 | | | | % 152.53/22.85 | | | | REDUCE: (22), (33) imply: % 152.53/22.85 | | | | (35) ~ (all_4_2 = e0) % 152.53/22.85 | | | | % 152.53/22.85 | | | | SIMP: (35) implies: % 152.53/22.85 | | | | (36) ~ (all_4_2 = e0) % 152.53/22.85 | | | | % 152.53/22.85 | | | | REDUCE: (23), (33) imply: % 152.53/22.85 | | | | (37) ~ (e3 = e0) % 152.53/22.85 | | | | % 152.53/22.85 | | | | SIMP: (37) implies: % 152.53/22.85 | | | | (38) ~ (e3 = e0) % 152.53/22.85 | | | | % 152.53/22.85 | | | | BETA: splitting (16) gives: % 152.53/22.85 | | | | % 152.53/22.85 | | | | Case 1: % 152.53/22.85 | | | | | % 152.53/22.85 | | | | | (39) all_56_1 = e3 % 152.53/22.85 | | | | | % 152.53/22.85 | | | | | COMBINE_EQS: (13), (39) imply: % 152.53/22.85 | | | | | (40) e3 = e0 % 152.53/22.85 | | | | | % 152.53/22.85 | | | | | REDUCE: (38), (40) imply: % 152.53/22.85 | | | | | (41) $false % 152.53/22.85 | | | | | % 152.53/22.85 | | | | | CLOSE: (41) is inconsistent. % 152.53/22.85 | | | | | % 152.53/22.85 | | | | Case 2: % 152.53/22.85 | | | | | % 152.53/22.85 | | | | | (42) all_56_11 = e2 | all_56_21 = e1 | all_56_31 = e0 % 152.53/22.85 | | | | | % 152.53/22.85 | | | | | BETA: splitting (42) gives: % 152.53/22.85 | | | | | % 152.53/22.85 | | | | | Case 1: % 152.53/22.85 | | | | | | % 152.53/22.85 | | | | | | (43) all_56_11 = e2 % 152.53/22.85 | | | | | | % 152.53/22.85 | | | | | | COMBINE_EQS: (1), (43) imply: % 152.53/22.85 | | | | | | (44) all_8_2 = e2 % 152.53/22.85 | | | | | | % 152.53/22.85 | | | | | | SIMP: (44) implies: % 152.53/22.85 | | | | | | (45) all_8_2 = e2 % 152.53/22.85 | | | | | | % 152.53/22.85 | | | | | | REDUCE: (17), (45) imply: % 152.53/22.85 | | | | | | (46) ~ (all_52_6 = e2) % 152.53/22.85 | | | | | | % 152.53/22.85 | | | | | | BETA: splitting (14) gives: % 152.53/22.85 | | | | | | % 152.53/22.85 | | | | | | Case 1: % 152.53/22.85 | | | | | | | % 152.53/22.85 | | | | | | | (47) all_54_9 = e3 % 152.53/22.85 | | | | | | | % 152.53/22.85 | | | | | | | REF_CLOSE: (2), (9), (47) are inconsistent by sub-proof #680. % 152.53/22.85 | | | | | | | % 152.53/22.85 | | | | | | Case 2: % 152.53/22.85 | | | | | | | % 152.53/22.85 | | | | | | | (48) all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0 % 152.53/22.85 | | | | | | | % 152.53/22.85 | | | | | | | REF_CLOSE: (2), (3), (34), (46), (48) are inconsistent by % 152.53/22.85 | | | | | | | sub-proof #677. % 152.53/22.85 | | | | | | | % 152.53/22.85 | | | | | | End of split % 152.53/22.85 | | | | | | % 152.53/22.85 | | | | | Case 2: % 152.53/22.85 | | | | | | % 152.53/22.85 | | | | | | (49) all_56_21 = e1 | all_56_31 = e0 % 152.53/22.85 | | | | | | % 152.53/22.85 | | | | | | REF_CLOSE: (4), (15), (18), (36), (49) are inconsistent by sub-proof % 152.53/22.85 | | | | | | #674. % 152.53/22.85 | | | | | | % 152.53/22.85 | | | | | End of split % 152.53/22.85 | | | | | % 152.53/22.85 | | | | End of split % 152.53/22.85 | | | | % 152.53/22.85 | | | End of split % 152.53/22.85 | | | % 152.53/22.85 | | End of split % 152.53/22.85 | | % 152.53/22.85 | End of split % 152.53/22.85 | % 152.53/22.85 End of proof % 152.53/22.85 % 152.53/22.85 Sub-proof #674 shows that the following formulas are inconsistent: % 152.53/22.85 ---------------------------------------------------------------- % 152.53/22.85 (1) all_56_21 = e3 % 152.53/22.85 (2) ~ (all_4_2 = e0) % 152.53/22.85 (3) all_56_31 = all_4_2 % 152.53/22.85 (4) all_56_21 = e1 | all_56_31 = e0 % 152.53/22.85 (5) ~ (e3 = e1) % 152.53/22.85 % 152.53/22.85 Begin of proof % 152.53/22.85 | % 152.53/22.85 | BETA: splitting (4) gives: % 152.53/22.85 | % 152.53/22.85 | Case 1: % 152.53/22.85 | | % 152.53/22.85 | | (6) all_56_21 = e1 % 152.53/22.85 | | % 152.53/22.85 | | REF_CLOSE: (1), (5), (6) are inconsistent by sub-proof #676. % 152.53/22.85 | | % 152.53/22.85 | Case 2: % 152.53/22.85 | | % 152.53/22.85 | | (7) all_56_31 = e0 % 152.53/22.85 | | % 152.53/22.85 | | REF_CLOSE: (2), (3), (7) are inconsistent by sub-proof #675. % 152.53/22.85 | | % 152.53/22.85 | End of split % 152.53/22.85 | % 152.53/22.85 End of proof % 152.53/22.85 % 152.53/22.85 Sub-proof #675 shows that the following formulas are inconsistent: % 152.53/22.85 ---------------------------------------------------------------- % 152.53/22.85 (1) all_56_31 = all_4_2 % 152.53/22.85 (2) all_56_31 = e0 % 152.53/22.85 (3) ~ (all_4_2 = e0) % 152.53/22.85 % 152.53/22.85 Begin of proof % 152.53/22.85 | % 152.53/22.85 | COMBINE_EQS: (1), (2) imply: % 152.53/22.85 | (4) all_4_2 = e0 % 152.53/22.85 | % 152.53/22.85 | SIMP: (4) implies: % 152.53/22.85 | (5) all_4_2 = e0 % 152.53/22.85 | % 152.53/22.85 | REDUCE: (3), (5) imply: % 152.53/22.85 | (6) $false % 152.53/22.85 | % 152.53/22.85 | CLOSE: (6) is inconsistent. % 152.53/22.85 | % 152.53/22.85 End of proof % 152.53/22.85 % 152.53/22.85 Sub-proof #676 shows that the following formulas are inconsistent: % 152.53/22.85 ---------------------------------------------------------------- % 152.53/22.85 (1) all_56_21 = e3 % 152.53/22.85 (2) all_56_21 = e1 % 152.53/22.85 (3) ~ (e3 = e1) % 152.53/22.85 % 152.53/22.85 Begin of proof % 152.53/22.85 | % 152.53/22.85 | COMBINE_EQS: (1), (2) imply: % 152.53/22.85 | (4) e3 = e1 % 152.53/22.85 | % 152.53/22.85 | SIMP: (4) implies: % 152.53/22.85 | (5) e3 = e1 % 152.53/22.85 | % 152.53/22.85 | REDUCE: (3), (5) imply: % 152.53/22.85 | (6) $false % 152.53/22.85 | % 152.53/22.85 | CLOSE: (6) is inconsistent. % 152.53/22.85 | % 152.53/22.85 End of proof % 152.53/22.85 % 152.53/22.85 Sub-proof #677 shows that the following formulas are inconsistent: % 152.53/22.85 ---------------------------------------------------------------- % 152.53/22.85 (1) all_54_9 = all_52_6 % 152.53/22.85 (2) ~ (all_52_6 = e1) % 152.53/22.85 (3) ~ (all_52_6 = e0) % 152.53/22.85 (4) ~ (all_52_6 = e2) % 152.53/22.85 (5) all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0 % 152.53/22.85 % 152.53/22.85 Begin of proof % 152.53/22.85 | % 152.53/22.85 | BETA: splitting (5) gives: % 152.53/22.85 | % 152.53/22.85 | Case 1: % 152.53/22.85 | | % 152.53/22.85 | | (6) all_54_9 = e2 % 152.53/22.85 | | % 152.53/22.85 | | COMBINE_EQS: (1), (6) imply: % 152.53/22.85 | | (7) all_52_6 = e2 % 152.53/22.85 | | % 152.53/22.85 | | REDUCE: (4), (7) imply: % 152.53/22.85 | | (8) $false % 152.53/22.85 | | % 152.53/22.85 | | CLOSE: (8) is inconsistent. % 152.53/22.85 | | % 152.53/22.85 | Case 2: % 152.53/22.85 | | % 152.53/22.85 | | (9) all_54_9 = e1 | all_54_9 = e0 % 152.53/22.85 | | % 152.53/22.85 | | REF_CLOSE: (1), (2), (3), (9) are inconsistent by sub-proof #678. % 152.53/22.85 | | % 152.53/22.85 | End of split % 152.53/22.85 | % 152.53/22.85 End of proof % 152.53/22.85 % 152.53/22.85 Sub-proof #678 shows that the following formulas are inconsistent: % 152.53/22.85 ---------------------------------------------------------------- % 152.53/22.85 (1) all_54_9 = e1 | all_54_9 = e0 % 152.53/22.85 (2) all_54_9 = all_52_6 % 152.53/22.85 (3) ~ (all_52_6 = e1) % 152.53/22.85 (4) ~ (all_52_6 = e0) % 152.53/22.85 % 152.53/22.85 Begin of proof % 152.53/22.85 | % 152.53/22.85 | BETA: splitting (1) gives: % 152.53/22.85 | % 152.53/22.85 | Case 1: % 152.53/22.85 | | % 152.53/22.85 | | (5) all_54_9 = e1 % 152.53/22.85 | | % 152.53/22.85 | | REF_CLOSE: (2), (3), (5) are inconsistent by sub-proof #679. % 152.53/22.85 | | % 152.53/22.85 | Case 2: % 152.53/22.85 | | % 152.53/22.85 | | (6) all_54_9 = e0 % 152.53/22.85 | | % 152.53/22.85 | | COMBINE_EQS: (2), (6) imply: % 152.53/22.85 | | (7) all_52_6 = e0 % 152.53/22.85 | | % 152.53/22.85 | | SIMP: (7) implies: % 152.53/22.85 | | (8) all_52_6 = e0 % 152.53/22.85 | | % 152.53/22.85 | | REDUCE: (4), (8) imply: % 152.53/22.85 | | (9) $false % 152.53/22.85 | | % 152.53/22.85 | | CLOSE: (9) is inconsistent. % 152.53/22.85 | | % 152.53/22.85 | End of split % 152.53/22.85 | % 152.53/22.85 End of proof % 152.53/22.85 % 152.53/22.85 Sub-proof #679 shows that the following formulas are inconsistent: % 152.53/22.85 ---------------------------------------------------------------- % 152.53/22.85 (1) all_54_9 = all_52_6 % 152.53/22.85 (2) all_54_9 = e1 % 152.53/22.85 (3) ~ (all_52_6 = e1) % 152.53/22.85 % 152.53/22.85 Begin of proof % 152.53/22.85 | % 152.53/22.85 | COMBINE_EQS: (1), (2) imply: % 152.53/22.85 | (4) all_52_6 = e1 % 152.53/22.85 | % 152.53/22.85 | SIMP: (4) implies: % 152.53/22.85 | (5) all_52_6 = e1 % 152.53/22.85 | % 152.53/22.85 | REDUCE: (3), (5) imply: % 152.53/22.85 | (6) $false % 152.53/22.85 | % 152.53/22.85 | CLOSE: (6) is inconsistent. % 152.53/22.85 | % 152.53/22.85 End of proof % 152.53/22.85 % 152.53/22.85 Sub-proof #680 shows that the following formulas are inconsistent: % 152.53/22.85 ---------------------------------------------------------------- % 152.53/22.85 (1) all_54_9 = all_52_6 % 152.53/22.85 (2) all_54_9 = e3 % 152.53/22.85 (3) ~ (all_52_6 = e3) % 152.53/22.85 % 152.53/22.85 Begin of proof % 152.53/22.85 | % 152.53/22.85 | COMBINE_EQS: (1), (2) imply: % 152.53/22.85 | (4) all_52_6 = e3 % 152.53/22.85 | % 152.53/22.85 | SIMP: (4) implies: % 152.53/22.85 | (5) all_52_6 = e3 % 152.53/22.85 | % 152.53/22.85 | REDUCE: (3), (5) imply: % 152.53/22.85 | (6) $false % 152.53/22.85 | % 152.53/22.85 | CLOSE: (6) is inconsistent. % 152.53/22.85 | % 152.53/22.85 End of proof % 152.53/22.85 % 152.53/22.85 Sub-proof #681 shows that the following formulas are inconsistent: % 152.53/22.85 ---------------------------------------------------------------- % 152.53/22.85 (1) all_54_11 = all_6_0 % 152.53/22.85 (2) all_54_11 = e1 % 152.53/22.85 (3) ~ (all_6_0 = e1) % 152.53/22.85 % 152.53/22.85 Begin of proof % 152.53/22.85 | % 152.53/22.85 | COMBINE_EQS: (1), (2) imply: % 152.53/22.85 | (4) all_6_0 = e1 % 152.53/22.85 | % 152.53/22.85 | SIMP: (4) implies: % 152.53/22.85 | (5) all_6_0 = e1 % 152.53/22.85 | % 152.53/22.85 | REDUCE: (3), (5) imply: % 152.53/22.85 | (6) $false % 152.53/22.85 | % 152.53/22.85 | CLOSE: (6) is inconsistent. % 152.53/22.85 | % 152.53/22.85 End of proof % 152.53/22.85 % 152.53/22.85 Sub-proof #682 shows that the following formulas are inconsistent: % 152.53/22.85 ---------------------------------------------------------------- % 152.53/22.85 (1) all_54_11 = all_6_0 % 152.53/22.85 (2) all_54_11 = e2 % 152.53/22.85 (3) ~ (all_6_0 = e2) % 152.53/22.85 % 152.53/22.85 Begin of proof % 152.53/22.85 | % 152.53/22.85 | COMBINE_EQS: (1), (2) imply: % 152.53/22.85 | (4) all_6_0 = e2 % 152.53/22.85 | % 152.53/22.85 | SIMP: (4) implies: % 152.53/22.85 | (5) all_6_0 = e2 % 152.53/22.85 | % 152.53/22.85 | REDUCE: (3), (5) imply: % 152.53/22.85 | (6) $false % 152.53/22.85 | % 152.53/22.85 | CLOSE: (6) is inconsistent. % 152.53/22.85 | % 152.53/22.85 End of proof % 152.53/22.85 % 152.53/22.85 Sub-proof #683 shows that the following formulas are inconsistent: % 152.53/22.85 ---------------------------------------------------------------- % 152.53/22.85 (1) all_54_11 = all_6_0 % 152.53/22.85 (2) all_54_11 = e3 % 152.53/22.85 (3) ~ (all_6_0 = e3) % 152.53/22.85 % 152.53/22.85 Begin of proof % 152.53/22.85 | % 152.53/22.85 | COMBINE_EQS: (1), (2) imply: % 152.53/22.85 | (4) all_6_0 = e3 % 152.53/22.85 | % 152.53/22.85 | SIMP: (4) implies: % 152.53/22.85 | (5) all_6_0 = e3 % 152.53/22.85 | % 152.53/22.85 | REDUCE: (3), (5) imply: % 152.53/22.85 | (6) $false % 152.53/22.85 | % 152.53/22.85 | CLOSE: (6) is inconsistent. % 152.53/22.85 | % 152.53/22.85 End of proof % 152.53/22.85 % 152.53/22.85 Sub-proof #684 shows that the following formulas are inconsistent: % 152.53/22.85 ---------------------------------------------------------------- % 152.53/22.85 (1) all_54_0 = all_6_1 % 152.53/22.85 (2) all_54_0 = e1 % 152.53/22.85 (3) ~ (all_6_1 = e1) % 152.53/22.85 % 152.53/22.85 Begin of proof % 152.53/22.85 | % 152.53/22.85 | COMBINE_EQS: (1), (2) imply: % 152.53/22.85 | (4) all_6_1 = e1 % 152.53/22.85 | % 152.53/22.85 | SIMP: (4) implies: % 152.53/22.85 | (5) all_6_1 = e1 % 152.53/22.85 | % 152.53/22.85 | REDUCE: (3), (5) imply: % 152.53/22.85 | (6) $false % 152.53/22.85 | % 152.53/22.85 | CLOSE: (6) is inconsistent. % 152.53/22.85 | % 152.53/22.85 End of proof % 152.53/22.85 % 152.53/22.85 Sub-proof #685 shows that the following formulas are inconsistent: % 152.53/22.85 ---------------------------------------------------------------- % 152.53/22.85 (1) all_54_0 = all_6_1 % 152.53/22.85 (2) all_54_0 = e2 % 152.53/22.85 (3) ~ (all_6_1 = e2) % 152.53/22.85 % 152.53/22.85 Begin of proof % 152.53/22.85 | % 152.53/22.85 | COMBINE_EQS: (1), (2) imply: % 152.53/22.85 | (4) all_6_1 = e2 % 152.53/22.85 | % 152.53/22.85 | SIMP: (4) implies: % 152.53/22.85 | (5) all_6_1 = e2 % 152.53/22.85 | % 152.53/22.85 | REDUCE: (3), (5) imply: % 152.53/22.85 | (6) $false % 152.53/22.85 | % 152.53/22.85 | CLOSE: (6) is inconsistent. % 152.53/22.85 | % 152.53/22.85 End of proof % 152.53/22.85 % 152.53/22.85 Sub-proof #686 shows that the following formulas are inconsistent: % 152.53/22.85 ---------------------------------------------------------------- % 152.53/22.85 (1) all_54_0 = all_6_1 % 152.53/22.85 (2) all_54_0 = e3 % 152.53/22.85 (3) ~ (all_6_1 = e3) % 152.53/22.85 % 152.53/22.85 Begin of proof % 152.53/22.85 | % 152.53/22.85 | COMBINE_EQS: (1), (2) imply: % 152.53/22.85 | (4) all_6_1 = e3 % 152.53/22.85 | % 152.53/22.85 | SIMP: (4) implies: % 152.53/22.85 | (5) all_6_1 = e3 % 152.53/22.85 | % 152.53/22.85 | REDUCE: (3), (5) imply: % 152.53/22.85 | (6) $false % 152.53/22.85 | % 152.53/22.85 | CLOSE: (6) is inconsistent. % 152.53/22.85 | % 152.53/22.85 End of proof % 152.53/22.85 % 152.53/22.85 Sub-proof #687 shows that the following formulas are inconsistent: % 152.53/22.85 ---------------------------------------------------------------- % 152.53/22.85 (1) ~ (all_52_14 = e2) % 152.53/22.85 (2) ~ (all_52_14 = e1) % 152.53/22.85 (3) all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0 % 152.53/22.85 (4) ~ (all_52_14 = e0) % 152.53/22.85 (5) all_54_11 = all_52_14 % 152.53/22.85 % 152.53/22.85 Begin of proof % 152.53/22.85 | % 152.53/22.85 | BETA: splitting (3) gives: % 152.53/22.85 | % 152.53/22.85 | Case 1: % 152.53/22.85 | | % 152.53/22.85 | | (6) all_54_11 = e2 % 152.53/22.85 | | % 152.53/22.85 | | REF_CLOSE: (1), (5), (6) are inconsistent by sub-proof #690. % 152.53/22.85 | | % 152.53/22.85 | Case 2: % 152.53/22.85 | | % 152.53/22.85 | | (7) all_54_11 = e1 | all_54_11 = e0 % 152.53/22.85 | | % 152.53/22.85 | | REF_CLOSE: (2), (4), (5), (7) are inconsistent by sub-proof #688. % 152.53/22.85 | | % 152.53/22.85 | End of split % 152.53/22.85 | % 152.53/22.85 End of proof % 152.53/22.85 % 152.53/22.85 Sub-proof #688 shows that the following formulas are inconsistent: % 152.53/22.85 ---------------------------------------------------------------- % 152.53/22.85 (1) all_54_11 = e1 | all_54_11 = e0 % 152.53/22.85 (2) all_54_11 = all_52_14 % 152.53/22.85 (3) ~ (all_52_14 = e1) % 152.53/22.85 (4) ~ (all_52_14 = e0) % 152.53/22.85 % 152.53/22.85 Begin of proof % 152.53/22.85 | % 152.53/22.85 | BETA: splitting (1) gives: % 152.53/22.85 | % 152.53/22.85 | Case 1: % 152.53/22.85 | | % 152.53/22.85 | | (5) all_54_11 = e1 % 152.53/22.85 | | % 152.53/22.85 | | REF_CLOSE: (2), (3), (5) are inconsistent by sub-proof #689. % 152.53/22.85 | | % 152.53/22.85 | Case 2: % 152.53/22.85 | | % 152.53/22.85 | | (6) all_54_11 = e0 % 152.53/22.85 | | % 152.53/22.85 | | COMBINE_EQS: (2), (6) imply: % 152.53/22.85 | | (7) all_52_14 = e0 % 152.53/22.85 | | % 152.53/22.85 | | SIMP: (7) implies: % 152.53/22.85 | | (8) all_52_14 = e0 % 152.53/22.85 | | % 152.53/22.85 | | REDUCE: (4), (8) imply: % 152.53/22.85 | | (9) $false % 152.53/22.85 | | % 152.53/22.85 | | CLOSE: (9) is inconsistent. % 152.53/22.85 | | % 152.53/22.85 | End of split % 152.53/22.85 | % 152.53/22.85 End of proof % 152.53/22.85 % 152.53/22.85 Sub-proof #689 shows that the following formulas are inconsistent: % 152.53/22.85 ---------------------------------------------------------------- % 152.53/22.85 (1) all_54_11 = all_52_14 % 152.53/22.85 (2) all_54_11 = e1 % 152.53/22.85 (3) ~ (all_52_14 = e1) % 152.53/22.85 % 152.53/22.85 Begin of proof % 152.53/22.85 | % 152.53/22.85 | COMBINE_EQS: (1), (2) imply: % 152.53/22.85 | (4) all_52_14 = e1 % 152.53/22.85 | % 152.53/22.85 | SIMP: (4) implies: % 152.53/22.85 | (5) all_52_14 = e1 % 152.53/22.85 | % 152.53/22.85 | REDUCE: (3), (5) imply: % 152.53/22.85 | (6) $false % 152.53/22.85 | % 152.53/22.85 | CLOSE: (6) is inconsistent. % 152.53/22.85 | % 152.53/22.85 End of proof % 152.53/22.85 % 152.53/22.85 Sub-proof #690 shows that the following formulas are inconsistent: % 152.53/22.85 ---------------------------------------------------------------- % 152.53/22.85 (1) all_54_11 = all_52_14 % 152.53/22.85 (2) all_54_11 = e2 % 152.53/22.85 (3) ~ (all_52_14 = e2) % 152.53/22.85 % 152.53/22.85 Begin of proof % 152.53/22.85 | % 152.53/22.85 | COMBINE_EQS: (1), (2) imply: % 152.53/22.85 | (4) all_52_14 = e2 % 152.53/22.85 | % 152.53/22.85 | SIMP: (4) implies: % 152.53/22.85 | (5) all_52_14 = e2 % 152.53/22.85 | % 152.53/22.85 | REDUCE: (3), (5) imply: % 152.53/22.85 | (6) $false % 152.53/22.85 | % 152.53/22.85 | CLOSE: (6) is inconsistent. % 152.53/22.85 | % 152.53/22.85 End of proof % 152.53/22.85 % 152.53/22.85 Sub-proof #691 shows that the following formulas are inconsistent: % 152.53/22.85 ---------------------------------------------------------------- % 152.53/22.85 (1) all_56_7 = all_52_12 % 152.53/22.85 (2) all_56_7 = e3 % 152.53/22.85 (3) ~ (all_52_12 = e3) % 152.53/22.85 % 152.53/22.85 Begin of proof % 152.53/22.85 | % 152.53/22.85 | COMBINE_EQS: (1), (2) imply: % 152.53/22.85 | (4) all_52_12 = e3 % 152.53/22.85 | % 152.53/22.85 | SIMP: (4) implies: % 152.53/22.85 | (5) all_52_12 = e3 % 152.53/22.85 | % 152.53/22.85 | REDUCE: (3), (5) imply: % 152.53/22.85 | (6) $false % 152.53/22.85 | % 152.53/22.85 | CLOSE: (6) is inconsistent. % 152.53/22.86 | % 152.53/22.86 End of proof % 152.53/22.86 % 152.53/22.86 Sub-proof #692 shows that the following formulas are inconsistent: % 152.53/22.86 ---------------------------------------------------------------- % 152.53/22.86 (1) ~ (all_52_4 = all_52_8) % 152.53/22.86 (2) all_58_6 = all_52_2 % 152.53/22.86 (3) all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2 % 152.53/22.86 (4) all_54_0 = all_10_2 % 152.53/22.86 (5) all_58_4 = all_52_8 % 152.53/22.86 (6) ~ (all_10_2 = e1) % 152.53/22.86 (7) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 152.53/22.86 (8) all_54_15 = all_4_2 % 152.53/22.86 (9) ~ (all_52_14 = e2) % 152.53/22.86 (10) all_54_1 = all_52_4 % 152.53/22.86 (11) ~ (all_52_13 = e2) % 152.53/22.86 (12) all_58_9 = all_52_12 % 152.53/22.86 (13) ~ (all_52_4 = e1) % 152.53/22.86 (14) all_58_1 = all_52_4 % 152.53/22.86 (15) all_58_13 = all_52_7 % 152.53/22.86 (16) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0 % 152.53/22.86 (17) all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1 % 152.53/22.86 (18) all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2 % 152.53/22.86 (19) ~ (all_4_2 = e1) % 152.53/22.86 (20) ~ (all_4_2 = e2) % 152.53/22.86 (21) ~ (e2 = e1) % 152.53/22.86 (22) all_58_11 = all_52_14 % 152.53/22.86 (23) ~ (all_52_2 = e2) % 152.53/22.86 (24) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0 % 152.53/22.86 (25) ~ (all_52_7 = e1) % 152.53/22.86 (26) ~ (all_52_8 = all_52_11) % 152.53/22.86 (27) all_54_2 = all_52_8 % 152.53/22.86 (28) ~ (all_10_2 = e0) % 152.53/22.86 (29) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0 % 152.53/22.86 (30) all_58_15 = all_4_2 % 152.53/22.86 (31) all_58_2 = all_52_1 % 152.53/22.86 (32) ~ (all_4_2 = e3) % 152.53/22.86 (33) all_58_10 = all_52_13 % 152.53/22.86 (34) ~ (all_52_12 = all_4_2) % 152.53/22.86 (35) all_58_0 = all_10_2 % 152.53/22.86 (36) all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1 % 152.53/22.86 (37) ~ (all_52_4 = all_52_12) % 152.53/22.86 (38) ~ (all_52_8 = all_52_12) % 152.53/22.86 (39) ~ (all_52_4 = all_10_2) % 152.53/22.86 (40) all_58_14 = all_52_11 % 152.53/22.86 (41) ~ (all_52_1 = e2) % 152.53/22.86 (42) ~ (all_52_12 = all_10_2) % 152.53/22.86 (43) all_58_12 = all_52_3 % 152.53/22.86 (44) all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2 % 152.53/22.86 % 152.53/22.86 Begin of proof % 152.53/22.86 | % 152.53/22.86 | BETA: splitting (3) gives: % 152.53/22.86 | % 152.53/22.86 | Case 1: % 152.53/22.86 | | % 152.53/22.86 | | (45) all_58_9 = e2 % 152.53/22.86 | | % 152.53/22.86 | | COMBINE_EQS: (12), (45) imply: % 152.53/22.86 | | (46) all_52_12 = e2 % 152.53/22.86 | | % 152.53/22.86 | | REDUCE: (37), (46) imply: % 152.53/22.86 | | (47) ~ (all_52_4 = e2) % 152.53/22.86 | | % 152.53/22.86 | | REDUCE: (38), (46) imply: % 152.53/22.86 | | (48) ~ (all_52_8 = e2) % 152.53/22.86 | | % 152.53/22.86 | | REDUCE: (42), (46) imply: % 152.53/22.86 | | (49) ~ (all_10_2 = e2) % 152.53/22.86 | | % 152.53/22.86 | | SIMP: (49) implies: % 152.53/22.86 | | (50) ~ (all_10_2 = e2) % 152.53/22.86 | | % 152.53/22.86 | | REDUCE: (34), (46) imply: % 152.53/22.86 | | (51) ~ (all_4_2 = e2) % 152.53/22.86 | | % 152.53/22.86 | | BETA: splitting (7) gives: % 152.53/22.86 | | % 152.53/22.86 | | Case 1: % 152.53/22.86 | | | % 152.53/22.86 | | | (52) all_54_0 = e3 % 152.53/22.86 | | | % 152.53/22.86 | | | COMBINE_EQS: (4), (52) imply: % 152.53/22.86 | | | (53) all_10_2 = e3 % 152.53/22.86 | | | % 152.53/22.86 | | | SIMP: (53) implies: % 152.53/22.86 | | | (54) all_10_2 = e3 % 152.53/22.86 | | | % 152.53/22.86 | | | COMBINE_EQS: (35), (54) imply: % 152.53/22.86 | | | (55) all_58_0 = e3 % 152.53/22.86 | | | % 152.53/22.86 | | | REDUCE: (39), (54) imply: % 152.53/22.86 | | | (56) ~ (all_52_4 = e3) % 152.53/22.86 | | | % 152.53/22.86 | | | REDUCE: (50), (54) imply: % 152.53/22.86 | | | (57) ~ (e3 = e2) % 152.53/22.86 | | | % 152.53/22.86 | | | REDUCE: (6), (54) imply: % 152.53/22.86 | | | (58) ~ (e3 = e1) % 152.53/22.86 | | | % 152.53/22.86 | | | BETA: splitting (24) gives: % 152.53/22.86 | | | % 152.53/22.86 | | | Case 1: % 152.53/22.86 | | | | % 152.53/22.86 | | | | (59) all_54_15 = e3 % 152.53/22.86 | | | | % 152.53/22.86 | | | | REF_CLOSE: (8), (32), (59) are inconsistent by sub-proof #740. % 152.53/22.86 | | | | % 152.53/22.86 | | | Case 2: % 152.53/22.86 | | | | % 152.53/22.86 | | | | (60) all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0 % 152.53/22.86 | | | | % 152.53/22.86 | | | | BETA: splitting (60) gives: % 152.53/22.86 | | | | % 152.53/22.86 | | | | Case 1: % 152.53/22.86 | | | | | % 152.53/22.86 | | | | | (61) all_54_15 = e2 % 152.53/22.86 | | | | | % 152.53/22.86 | | | | | REF_CLOSE: (8), (20), (61) are inconsistent by sub-proof #739. % 152.53/22.86 | | | | | % 152.53/22.86 | | | | Case 2: % 152.53/22.86 | | | | | % 152.53/22.86 | | | | | (62) all_54_15 = e1 | all_54_15 = e0 % 152.53/22.86 | | | | | % 152.53/22.86 | | | | | BETA: splitting (44) gives: % 152.53/22.86 | | | | | % 152.53/22.86 | | | | | Case 1: % 152.53/22.86 | | | | | | % 152.53/22.86 | | | | | | (63) all_58_12 = e2 % 152.53/22.86 | | | | | | % 152.53/22.86 | | | | | | BETA: splitting (29) gives: % 152.53/22.86 | | | | | | % 152.53/22.86 | | | | | | Case 1: % 152.53/22.86 | | | | | | | % 152.53/22.86 | | | | | | | (64) all_54_1 = e3 % 152.53/22.86 | | | | | | | % 152.53/22.86 | | | | | | | REF_CLOSE: (10), (56), (64) are inconsistent by sub-proof #722. % 152.53/22.86 | | | | | | | % 152.53/22.86 | | | | | | Case 2: % 152.53/22.86 | | | | | | | % 152.53/22.86 | | | | | | | (65) all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0 % 152.53/22.86 | | | | | | | % 152.53/22.86 | | | | | | | BETA: splitting (65) gives: % 152.53/22.86 | | | | | | | % 152.53/22.86 | | | | | | | Case 1: % 152.53/22.86 | | | | | | | | % 152.53/22.86 | | | | | | | | (66) all_54_1 = e2 % 152.53/22.86 | | | | | | | | % 152.53/22.86 | | | | | | | | REF_CLOSE: (10), (47), (66) are inconsistent by sub-proof #721. % 152.53/22.86 | | | | | | | | % 152.53/22.86 | | | | | | | Case 2: % 152.53/22.86 | | | | | | | | % 152.53/22.86 | | | | | | | | (67) ~ (all_54_1 = e2) % 152.53/22.86 | | | | | | | | (68) all_54_1 = e1 | all_54_1 = e0 % 152.53/22.86 | | | | | | | | % 152.53/22.86 | | | | | | | | BETA: splitting (36) gives: % 152.53/22.86 | | | | | | | | % 152.53/22.86 | | | | | | | | Case 1: % 152.53/22.86 | | | | | | | | | % 152.53/22.86 | | | | | | | | | (69) all_58_12 = e1 % 152.53/22.86 | | | | | | | | | % 152.53/22.86 | | | | | | | | | COMBINE_EQS: (63), (69) imply: % 152.53/22.86 | | | | | | | | | (70) e2 = e1 % 152.53/22.86 | | | | | | | | | % 152.53/22.86 | | | | | | | | | REDUCE: (21), (70) imply: % 152.53/22.86 | | | | | | | | | (71) $false % 152.53/22.86 | | | | | | | | | % 152.53/22.86 | | | | | | | | | CLOSE: (71) is inconsistent. % 152.53/22.86 | | | | | | | | | % 152.53/22.86 | | | | | | | | Case 2: % 152.53/22.86 | | | | | | | | | % 152.53/22.86 | | | | | | | | | (72) ~ (all_58_12 = e1) % 152.53/22.86 | | | | | | | | | (73) all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1 % 152.53/22.86 | | | | | | | | | % 152.53/22.86 | | | | | | | | | BETA: splitting (73) gives: % 152.53/22.86 | | | | | | | | | % 152.53/22.86 | | | | | | | | | Case 1: % 152.53/22.86 | | | | | | | | | | % 152.53/22.86 | | | | | | | | | | (74) all_58_13 = e1 % 152.53/22.86 | | | | | | | | | | % 152.53/22.86 | | | | | | | | | | REF_CLOSE: (15), (25), (74) are inconsistent by sub-proof % 152.53/22.86 | | | | | | | | | | #704. % 152.53/22.86 | | | | | | | | | | % 152.53/22.86 | | | | | | | | | Case 2: % 152.53/22.86 | | | | | | | | | | % 152.53/22.86 | | | | | | | | | | (75) all_58_14 = e1 | all_58_15 = e1 % 152.53/22.86 | | | | | | | | | | % 152.53/22.86 | | | | | | | | | | BETA: splitting (17) gives: % 152.53/22.86 | | | | | | | | | | % 152.53/22.86 | | | | | | | | | | Case 1: % 152.53/22.86 | | | | | | | | | | | % 152.53/22.86 | | | | | | | | | | | (76) all_58_0 = e1 % 152.53/22.86 | | | | | | | | | | | % 152.53/22.86 | | | | | | | | | | | COMBINE_EQS: (55), (76) imply: % 152.53/22.86 | | | | | | | | | | | (77) e3 = e1 % 152.53/22.86 | | | | | | | | | | | % 152.53/22.86 | | | | | | | | | | | REDUCE: (58), (77) imply: % 152.53/22.86 | | | | | | | | | | | (78) $false % 152.53/22.86 | | | | | | | | | | | % 152.53/22.86 | | | | | | | | | | | CLOSE: (78) is inconsistent. % 152.53/22.86 | | | | | | | | | | | % 152.53/22.86 | | | | | | | | | | Case 2: % 152.53/22.86 | | | | | | | | | | | % 152.53/22.86 | | | | | | | | | | | (79) ~ (all_58_0 = e1) % 152.53/22.86 | | | | | | | | | | | (80) all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1 % 152.53/22.86 | | | | | | | | | | | % 152.53/22.86 | | | | | | | | | | | BETA: splitting (68) gives: % 152.53/22.86 | | | | | | | | | | | % 152.53/22.86 | | | | | | | | | | | Case 1: % 152.53/22.86 | | | | | | | | | | | | % 152.53/22.86 | | | | | | | | | | | | (81) all_54_1 = e1 % 152.53/22.86 | | | | | | | | | | | | % 152.53/22.86 | | | | | | | | | | | | REF_CLOSE: (10), (13), (81) are inconsistent by sub-proof % 152.53/22.86 | | | | | | | | | | | | #720. % 152.53/22.86 | | | | | | | | | | | | % 152.53/22.86 | | | | | | | | | | | Case 2: % 152.53/22.86 | | | | | | | | | | | | % 152.53/22.86 | | | | | | | | | | | | (82) all_54_1 = e0 % 152.53/22.86 | | | | | | | | | | | | % 152.53/22.86 | | | | | | | | | | | | COMBINE_EQS: (10), (82) imply: % 152.53/22.86 | | | | | | | | | | | | (83) all_52_4 = e0 % 152.53/22.86 | | | | | | | | | | | | % 152.53/22.86 | | | | | | | | | | | | SIMP: (83) implies: % 152.53/22.86 | | | | | | | | | | | | (84) all_52_4 = e0 % 152.53/22.86 | | | | | | | | | | | | % 152.53/22.86 | | | | | | | | | | | | REDUCE: (1), (84) imply: % 152.53/22.86 | | | | | | | | | | | | (85) ~ (all_52_8 = e0) % 152.53/22.86 | | | | | | | | | | | | % 152.53/22.86 | | | | | | | | | | | | SIMP: (85) implies: % 152.53/22.86 | | | | | | | | | | | | (86) ~ (all_52_8 = e0) % 152.53/22.86 | | | | | | | | | | | | % 152.53/22.86 | | | | | | | | | | | | BETA: splitting (16) gives: % 152.53/22.86 | | | | | | | | | | | | % 152.53/22.86 | | | | | | | | | | | | Case 1: % 152.53/22.86 | | | | | | | | | | | | | % 152.53/22.86 | | | | | | | | | | | | | (87) all_54_2 = e3 % 152.53/22.86 | | | | | | | | | | | | | % 152.53/22.86 | | | | | | | | | | | | | REF_CLOSE: (5), (10), (13), (14), (21), (27), (45), (47), % 152.53/22.86 | | | | | | | | | | | | | (58), (65), (80), (87) are inconsistent by % 152.53/22.86 | | | | | | | | | | | | | sub-proof #700. % 152.53/22.86 | | | | | | | | | | | | | % 152.53/22.86 | | | | | | | | | | | | Case 2: % 152.53/22.86 | | | | | | | | | | | | | % 152.53/22.86 | | | | | | | | | | | | | (88) all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0 % 152.53/22.86 | | | | | | | | | | | | | % 152.53/22.86 | | | | | | | | | | | | | REF_CLOSE: (8), (19), (26), (27), (30), (40), (48), (62), % 152.53/22.86 | | | | | | | | | | | | | (75), (86), (88) are inconsistent by sub-proof % 152.53/22.86 | | | | | | | | | | | | | #697. % 152.53/22.86 | | | | | | | | | | | | | % 152.53/22.86 | | | | | | | | | | | | End of split % 152.53/22.86 | | | | | | | | | | | | % 152.53/22.86 | | | | | | | | | | | End of split % 152.53/22.86 | | | | | | | | | | | % 152.53/22.86 | | | | | | | | | | End of split % 152.53/22.86 | | | | | | | | | | % 152.53/22.86 | | | | | | | | | End of split % 152.53/22.86 | | | | | | | | | % 152.53/22.86 | | | | | | | | End of split % 152.53/22.86 | | | | | | | | % 152.53/22.86 | | | | | | | End of split % 152.53/22.86 | | | | | | | % 152.53/22.86 | | | | | | End of split % 152.53/22.86 | | | | | | % 152.53/22.86 | | | | | Case 2: % 152.53/22.86 | | | | | | % 152.53/22.86 | | | | | | (89) ~ (all_58_12 = e2) % 152.53/22.86 | | | | | | % 152.53/22.86 | | | | | | REDUCE: (43), (89) imply: % 152.53/22.86 | | | | | | (90) ~ (all_52_3 = e2) % 152.53/22.86 | | | | | | % 152.53/22.86 | | | | | | REF_CLOSE: (2), (18), (23), (31), (41), (43), (55), (57), (90) are % 152.53/22.86 | | | | | | inconsistent by sub-proof #694. % 152.53/22.86 | | | | | | % 152.53/22.86 | | | | | End of split % 152.53/22.86 | | | | | % 152.53/22.86 | | | | End of split % 152.53/22.86 | | | | % 152.53/22.86 | | | End of split % 152.53/22.86 | | | % 152.53/22.86 | | Case 2: % 152.53/22.86 | | | % 152.53/22.86 | | | (91) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 152.53/22.86 | | | % 152.53/22.86 | | | REF_CLOSE: (4), (6), (28), (50), (91) are inconsistent by sub-proof #731. % 152.53/22.86 | | | % 152.53/22.86 | | End of split % 152.53/22.86 | | % 152.53/22.86 | Case 2: % 152.53/22.86 | | % 152.53/22.86 | | (92) all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2 % 152.53/22.86 | | % 152.53/22.86 | | REF_CLOSE: (9), (11), (20), (22), (30), (33), (92) are inconsistent by % 152.53/22.86 | | sub-proof #693. % 152.53/22.86 | | % 152.53/22.86 | End of split % 152.53/22.86 | % 152.53/22.86 End of proof % 152.53/22.86 % 152.53/22.86 Sub-proof #693 shows that the following formulas are inconsistent: % 152.53/22.86 ---------------------------------------------------------------- % 152.53/22.86 (1) ~ (all_52_14 = e2) % 152.53/22.86 (2) ~ (all_52_13 = e2) % 152.53/22.86 (3) ~ (all_4_2 = e2) % 152.53/22.86 (4) all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2 % 152.53/22.86 (5) all_58_11 = all_52_14 % 152.53/22.86 (6) all_58_15 = all_4_2 % 152.53/22.86 (7) all_58_10 = all_52_13 % 152.53/22.86 % 152.53/22.86 Begin of proof % 152.53/22.86 | % 152.53/22.86 | BETA: splitting (4) gives: % 152.53/22.86 | % 152.53/22.86 | Case 1: % 152.53/22.86 | | % 152.53/22.86 | | (8) all_58_10 = e2 % 152.53/22.86 | | % 152.53/22.86 | | COMBINE_EQS: (7), (8) imply: % 152.53/22.86 | | (9) all_52_13 = e2 % 152.53/22.86 | | % 152.53/22.86 | | REDUCE: (2), (9) imply: % 152.53/22.86 | | (10) $false % 152.53/22.86 | | % 152.53/22.86 | | CLOSE: (10) is inconsistent. % 152.53/22.86 | | % 152.53/22.86 | Case 2: % 152.53/22.86 | | % 152.53/22.86 | | (11) all_58_11 = e2 | all_58_15 = e2 % 152.53/22.86 | | % 152.53/22.86 | | BETA: splitting (11) gives: % 152.53/22.86 | | % 152.53/22.86 | | Case 1: % 152.53/22.86 | | | % 152.53/22.86 | | | (12) all_58_11 = e2 % 152.53/22.86 | | | % 152.53/22.86 | | | COMBINE_EQS: (5), (12) imply: % 152.53/22.86 | | | (13) all_52_14 = e2 % 152.53/22.86 | | | % 152.53/22.86 | | | REDUCE: (1), (13) imply: % 152.53/22.86 | | | (14) $false % 152.53/22.86 | | | % 152.53/22.86 | | | CLOSE: (14) is inconsistent. % 152.53/22.86 | | | % 152.53/22.86 | | Case 2: % 152.53/22.86 | | | % 152.53/22.86 | | | (15) all_58_15 = e2 % 152.53/22.86 | | | % 152.53/22.86 | | | COMBINE_EQS: (6), (15) imply: % 152.53/22.86 | | | (16) all_4_2 = e2 % 152.53/22.86 | | | % 152.53/22.86 | | | REDUCE: (3), (16) imply: % 152.53/22.86 | | | (17) $false % 152.53/22.86 | | | % 152.53/22.86 | | | CLOSE: (17) is inconsistent. % 152.53/22.86 | | | % 152.53/22.86 | | End of split % 152.53/22.86 | | % 152.53/22.86 | End of split % 152.53/22.86 | % 152.53/22.86 End of proof % 152.53/22.86 % 152.53/22.86 Sub-proof #694 shows that the following formulas are inconsistent: % 152.53/22.86 ---------------------------------------------------------------- % 152.53/22.86 (1) all_58_6 = all_52_2 % 152.53/22.86 (2) ~ (e3 = e2) % 152.53/22.86 (3) ~ (all_52_3 = e2) % 152.53/22.86 (4) all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2 % 152.53/22.86 (5) ~ (all_52_2 = e2) % 152.53/22.86 (6) all_58_2 = all_52_1 % 152.53/22.86 (7) all_58_0 = e3 % 152.53/22.86 (8) ~ (all_52_1 = e2) % 152.53/22.86 (9) all_58_12 = all_52_3 % 152.53/22.86 % 152.53/22.86 Begin of proof % 152.53/22.86 | % 152.53/22.86 | BETA: splitting (4) gives: % 152.53/22.86 | % 152.53/22.86 | Case 1: % 152.53/22.86 | | % 152.53/22.86 | | (10) all_58_0 = e2 % 152.53/22.86 | | % 152.53/22.86 | | COMBINE_EQS: (7), (10) imply: % 152.53/22.86 | | (11) e3 = e2 % 152.53/22.86 | | % 152.53/22.86 | | REDUCE: (2), (11) imply: % 152.53/22.86 | | (12) $false % 152.53/22.86 | | % 152.53/22.86 | | CLOSE: (12) is inconsistent. % 152.53/22.86 | | % 152.53/22.86 | Case 2: % 152.53/22.86 | | % 152.53/22.86 | | (13) all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2 % 152.53/22.86 | | % 152.53/22.86 | | REF_CLOSE: (1), (3), (5), (6), (8), (9), (13) are inconsistent by sub-proof % 152.53/22.86 | | #695. % 152.53/22.86 | | % 152.53/22.86 | End of split % 152.53/22.86 | % 152.53/22.86 End of proof % 152.53/22.86 % 152.53/22.86 Sub-proof #695 shows that the following formulas are inconsistent: % 152.53/22.86 ---------------------------------------------------------------- % 152.53/22.86 (1) all_58_6 = all_52_2 % 152.53/22.86 (2) ~ (all_52_3 = e2) % 152.53/22.86 (3) all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2 % 152.53/22.86 (4) ~ (all_52_2 = e2) % 152.53/22.86 (5) all_58_2 = all_52_1 % 152.53/22.86 (6) ~ (all_52_1 = e2) % 152.53/22.86 (7) all_58_12 = all_52_3 % 152.53/22.86 % 152.53/22.86 Begin of proof % 152.53/22.86 | % 152.53/22.86 | BETA: splitting (3) gives: % 152.53/22.86 | % 152.53/22.86 | Case 1: % 152.53/22.86 | | % 152.53/22.86 | | (8) all_58_2 = e2 % 152.53/22.86 | | % 152.53/22.86 | | COMBINE_EQS: (5), (8) imply: % 152.53/22.86 | | (9) all_52_1 = e2 % 152.53/22.86 | | % 152.53/22.86 | | REDUCE: (6), (9) imply: % 152.53/22.86 | | (10) $false % 152.53/22.86 | | % 152.53/22.86 | | CLOSE: (10) is inconsistent. % 152.53/22.86 | | % 152.53/22.86 | Case 2: % 152.53/22.86 | | % 152.53/22.86 | | (11) all_58_6 = e2 | all_58_12 = e2 % 152.53/22.86 | | % 152.53/22.86 | | REF_CLOSE: (1), (2), (4), (7), (11) are inconsistent by sub-proof #696. % 152.53/22.86 | | % 152.53/22.86 | End of split % 152.53/22.86 | % 152.53/22.86 End of proof % 152.53/22.86 % 152.53/22.86 Sub-proof #696 shows that the following formulas are inconsistent: % 152.53/22.86 ---------------------------------------------------------------- % 152.53/22.86 (1) all_58_6 = all_52_2 % 152.53/22.86 (2) ~ (all_52_3 = e2) % 152.53/22.86 (3) ~ (all_52_2 = e2) % 152.53/22.86 (4) all_58_6 = e2 | all_58_12 = e2 % 152.53/22.86 (5) all_58_12 = all_52_3 % 152.53/22.86 % 152.53/22.86 Begin of proof % 152.53/22.86 | % 152.53/22.86 | BETA: splitting (4) gives: % 152.53/22.86 | % 152.53/22.86 | Case 1: % 152.53/22.86 | | % 152.53/22.86 | | (6) all_58_6 = e2 % 152.53/22.86 | | % 152.53/22.86 | | COMBINE_EQS: (1), (6) imply: % 152.53/22.86 | | (7) all_52_2 = e2 % 152.53/22.86 | | % 152.53/22.86 | | REDUCE: (3), (7) imply: % 152.53/22.86 | | (8) $false % 152.53/22.86 | | % 152.53/22.86 | | CLOSE: (8) is inconsistent. % 152.53/22.86 | | % 152.53/22.86 | Case 2: % 152.53/22.86 | | % 152.53/22.86 | | (9) all_58_12 = e2 % 152.53/22.86 | | % 152.53/22.86 | | COMBINE_EQS: (5), (9) imply: % 152.53/22.86 | | (10) all_52_3 = e2 % 152.53/22.86 | | % 152.53/22.86 | | REDUCE: (2), (10) imply: % 152.53/22.86 | | (11) $false % 152.53/22.86 | | % 152.53/22.86 | | CLOSE: (11) is inconsistent. % 152.53/22.86 | | % 152.53/22.86 | End of split % 152.53/22.86 | % 152.53/22.86 End of proof % 152.53/22.86 % 152.53/22.86 Sub-proof #697 shows that the following formulas are inconsistent: % 152.53/22.86 ---------------------------------------------------------------- % 152.53/22.86 (1) ~ (all_52_8 = e2) % 152.53/22.86 (2) all_58_14 = e1 | all_58_15 = e1 % 152.53/22.86 (3) all_54_15 = all_4_2 % 152.53/22.86 (4) ~ (all_52_8 = e0) % 152.53/22.86 (5) ~ (all_4_2 = e1) % 152.53/22.86 (6) all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0 % 152.53/22.86 (7) ~ (all_52_8 = all_52_11) % 152.53/22.86 (8) all_54_2 = all_52_8 % 152.53/22.86 (9) all_58_15 = all_4_2 % 152.53/22.86 (10) all_58_14 = all_52_11 % 152.53/22.86 (11) all_54_15 = e1 | all_54_15 = e0 % 152.53/22.86 % 152.53/22.86 Begin of proof % 152.53/22.86 | % 152.53/22.86 | BETA: splitting (6) gives: % 152.53/22.86 | % 152.53/22.86 | Case 1: % 152.53/22.86 | | % 152.53/22.86 | | (12) all_54_2 = e2 % 152.53/22.86 | | % 152.53/22.86 | | REF_CLOSE: (1), (8), (12) are inconsistent by sub-proof #727. % 152.53/22.86 | | % 152.53/22.86 | Case 2: % 152.53/22.86 | | % 152.53/22.86 | | (13) all_54_2 = e1 | all_54_2 = e0 % 152.53/22.86 | | % 152.53/22.86 | | BETA: splitting (13) gives: % 152.53/22.86 | | % 152.53/22.86 | | Case 1: % 152.53/22.86 | | | % 152.53/22.86 | | | (14) all_54_2 = e1 % 152.53/22.86 | | | % 152.53/22.86 | | | COMBINE_EQS: (8), (14) imply: % 152.53/22.86 | | | (15) all_52_8 = e1 % 152.53/22.86 | | | % 152.53/22.86 | | | SIMP: (15) implies: % 152.53/22.86 | | | (16) all_52_8 = e1 % 152.53/22.86 | | | % 152.53/22.86 | | | REDUCE: (7), (16) imply: % 152.53/22.86 | | | (17) ~ (all_52_11 = e1) % 152.53/22.86 | | | % 152.53/22.86 | | | SIMP: (17) implies: % 152.53/22.86 | | | (18) ~ (all_52_11 = e1) % 152.53/22.86 | | | % 152.53/22.86 | | | BETA: splitting (11) gives: % 152.53/22.86 | | | % 152.53/22.86 | | | Case 1: % 152.53/22.86 | | | | % 152.53/22.86 | | | | (19) all_54_15 = e1 % 152.53/22.86 | | | | % 152.53/22.86 | | | | REF_CLOSE: (3), (5), (19) are inconsistent by sub-proof #738. % 152.53/22.86 | | | | % 152.53/22.86 | | | Case 2: % 152.53/22.86 | | | | % 152.53/22.86 | | | | (20) all_54_15 = e0 % 152.53/22.86 | | | | % 152.53/22.86 | | | | COMBINE_EQS: (3), (20) imply: % 152.53/22.86 | | | | (21) all_4_2 = e0 % 152.53/22.86 | | | | % 152.53/22.86 | | | | SIMP: (21) implies: % 152.53/22.86 | | | | (22) all_4_2 = e0 % 152.53/22.86 | | | | % 152.53/22.86 | | | | COMBINE_EQS: (9), (22) imply: % 152.53/22.86 | | | | (23) all_58_15 = e0 % 152.53/22.86 | | | | % 152.53/22.86 | | | | REDUCE: (5), (22) imply: % 152.53/22.86 | | | | (24) ~ (e1 = e0) % 152.53/22.86 | | | | % 152.53/22.86 | | | | SIMP: (24) implies: % 152.53/22.86 | | | | (25) ~ (e1 = e0) % 152.53/22.86 | | | | % 152.53/22.86 | | | | BETA: splitting (2) gives: % 152.53/22.86 | | | | % 152.53/22.86 | | | | Case 1: % 152.53/22.86 | | | | | % 152.53/22.86 | | | | | (26) all_58_14 = e1 % 152.53/22.86 | | | | | % 152.53/22.86 | | | | | REF_CLOSE: (10), (18), (26) are inconsistent by sub-proof #699. % 152.53/22.86 | | | | | % 152.53/22.86 | | | | Case 2: % 152.53/22.86 | | | | | % 152.53/22.86 | | | | | (27) all_58_15 = e1 % 152.53/22.86 | | | | | % 152.53/22.86 | | | | | REF_CLOSE: (23), (25), (27) are inconsistent by sub-proof #698. % 152.53/22.86 | | | | | % 152.53/22.86 | | | | End of split % 152.53/22.86 | | | | % 152.53/22.86 | | | End of split % 152.53/22.86 | | | % 152.53/22.86 | | Case 2: % 152.53/22.86 | | | % 152.53/22.86 | | | (28) all_54_2 = e0 % 152.53/22.86 | | | % 152.53/22.86 | | | REF_CLOSE: (4), (8), (28) are inconsistent by sub-proof #725. % 152.53/22.86 | | | % 152.53/22.86 | | End of split % 152.53/22.86 | | % 152.53/22.86 | End of split % 152.53/22.86 | % 152.53/22.86 End of proof % 152.53/22.86 % 152.53/22.86 Sub-proof #698 shows that the following formulas are inconsistent: % 152.53/22.86 ---------------------------------------------------------------- % 152.53/22.86 (1) all_58_15 = e1 % 152.53/22.86 (2) all_58_15 = e0 % 152.53/22.86 (3) ~ (e1 = e0) % 152.53/22.86 % 152.53/22.86 Begin of proof % 152.53/22.86 | % 152.53/22.86 | COMBINE_EQS: (1), (2) imply: % 152.53/22.86 | (4) e1 = e0 % 152.53/22.86 | % 152.53/22.86 | SIMP: (4) implies: % 152.53/22.86 | (5) e1 = e0 % 152.53/22.86 | % 152.53/22.86 | REDUCE: (3), (5) imply: % 152.53/22.86 | (6) $false % 152.53/22.86 | % 152.53/22.86 | CLOSE: (6) is inconsistent. % 152.53/22.86 | % 152.53/22.86 End of proof % 152.53/22.86 % 152.53/22.86 Sub-proof #699 shows that the following formulas are inconsistent: % 152.53/22.86 ---------------------------------------------------------------- % 152.53/22.86 (1) all_58_14 = all_52_11 % 152.53/22.86 (2) all_58_14 = e1 % 152.53/22.86 (3) ~ (all_52_11 = e1) % 152.53/22.86 % 152.53/22.86 Begin of proof % 152.53/22.86 | % 152.53/22.86 | COMBINE_EQS: (1), (2) imply: % 152.53/22.86 | (4) all_52_11 = e1 % 152.53/22.86 | % 152.53/22.86 | SIMP: (4) implies: % 152.53/22.86 | (5) all_52_11 = e1 % 152.53/22.86 | % 152.53/22.86 | REDUCE: (3), (5) imply: % 152.53/22.86 | (6) $false % 152.53/22.86 | % 152.53/22.86 | CLOSE: (6) is inconsistent. % 152.53/22.86 | % 152.53/22.86 End of proof % 152.53/22.86 % 152.53/22.86 Sub-proof #700 shows that the following formulas are inconsistent: % 152.53/22.86 ---------------------------------------------------------------- % 152.53/22.86 (1) all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1 % 152.53/22.86 (2) all_58_4 = all_52_8 % 152.53/22.86 (3) all_54_1 = all_52_4 % 152.53/22.86 (4) ~ (all_52_4 = e1) % 152.53/22.86 (5) all_58_1 = all_52_4 % 152.53/22.86 (6) all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0 % 152.53/22.86 (7) all_54_2 = e3 % 152.53/22.86 (8) all_58_9 = e2 % 152.53/22.86 (9) ~ (e2 = e1) % 152.53/22.86 (10) ~ (all_52_4 = e2) % 152.53/22.86 (11) all_54_2 = all_52_8 % 152.53/22.86 (12) ~ (e3 = e1) % 152.53/22.86 % 152.53/22.86 Begin of proof % 152.53/22.86 | % 152.53/22.86 | COMBINE_EQS: (7), (11) imply: % 152.53/22.86 | (13) all_52_8 = e3 % 152.53/22.86 | % 152.53/22.86 | SIMP: (13) implies: % 152.53/22.86 | (14) all_52_8 = e3 % 152.53/22.86 | % 152.53/22.86 | COMBINE_EQS: (2), (14) imply: % 152.53/22.86 | (15) all_58_4 = e3 % 152.53/22.86 | % 152.53/22.86 | REF_CLOSE: (1), (3), (4), (5), (6), (8), (9), (10), (12), (15) are % 152.53/22.86 | inconsistent by sub-proof #701. % 152.53/22.86 | % 152.53/22.86 End of proof % 152.53/22.86 % 152.53/22.86 Sub-proof #701 shows that the following formulas are inconsistent: % 152.53/22.86 ---------------------------------------------------------------- % 152.53/22.86 (1) all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1 % 152.53/22.86 (2) all_54_1 = all_52_4 % 152.53/22.86 (3) ~ (all_52_4 = e1) % 152.53/22.86 (4) all_58_1 = all_52_4 % 152.53/22.86 (5) all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0 % 152.53/22.86 (6) all_58_9 = e2 % 152.53/22.86 (7) ~ (e2 = e1) % 152.53/22.86 (8) ~ (all_52_4 = e2) % 152.53/22.86 (9) ~ (e3 = e1) % 152.53/22.86 (10) all_58_4 = e3 % 152.53/22.86 % 152.53/22.86 Begin of proof % 152.53/22.86 | % 152.53/22.86 | BETA: splitting (5) gives: % 152.53/22.86 | % 152.53/22.86 | Case 1: % 152.53/22.86 | | % 152.53/22.86 | | (11) all_54_1 = e2 % 152.53/22.86 | | % 152.53/22.86 | | REF_CLOSE: (2), (8), (11) are inconsistent by sub-proof #721. % 152.53/22.86 | | % 152.53/22.86 | Case 2: % 152.53/22.86 | | % 152.53/22.86 | | (12) all_54_1 = e1 | all_54_1 = e0 % 152.53/22.86 | | % 152.53/22.86 | | BETA: splitting (12) gives: % 152.53/22.86 | | % 152.53/22.86 | | Case 1: % 152.53/22.86 | | | % 152.53/22.86 | | | (13) all_54_1 = e1 % 152.53/22.86 | | | % 152.53/22.86 | | | REF_CLOSE: (2), (3), (13) are inconsistent by sub-proof #720. % 152.53/22.86 | | | % 152.53/22.86 | | Case 2: % 152.53/22.86 | | | % 152.53/22.86 | | | (14) all_54_1 = e0 % 152.53/22.86 | | | % 152.53/22.86 | | | COMBINE_EQS: (2), (14) imply: % 152.53/22.86 | | | (15) all_52_4 = e0 % 152.53/22.86 | | | % 152.53/22.86 | | | SIMP: (15) implies: % 152.53/22.86 | | | (16) all_52_4 = e0 % 152.53/22.86 | | | % 152.53/22.86 | | | COMBINE_EQS: (4), (16) imply: % 152.53/22.86 | | | (17) all_58_1 = e0 % 152.53/22.86 | | | % 152.53/22.86 | | | REDUCE: (3), (16) imply: % 152.53/22.86 | | | (18) ~ (e1 = e0) % 152.53/22.86 | | | % 152.53/22.86 | | | SIMP: (18) implies: % 152.53/22.86 | | | (19) ~ (e1 = e0) % 152.53/22.86 | | | % 152.53/22.86 | | | REF_CLOSE: (1), (6), (7), (9), (10), (17), (19) are inconsistent by % 152.53/22.86 | | | sub-proof #702. % 152.53/22.86 | | | % 152.53/22.86 | | End of split % 152.53/22.86 | | % 152.53/22.86 | End of split % 152.53/22.86 | % 152.53/22.86 End of proof % 152.53/22.86 % 152.53/22.86 Sub-proof #702 shows that the following formulas are inconsistent: % 152.53/22.86 ---------------------------------------------------------------- % 152.53/22.86 (1) all_58_1 = e0 % 152.53/22.86 (2) all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1 % 152.53/22.86 (3) ~ (e1 = e0) % 152.53/22.86 (4) all_58_9 = e2 % 152.53/22.86 (5) ~ (e2 = e1) % 152.53/22.86 (6) ~ (e3 = e1) % 152.53/22.86 (7) all_58_4 = e3 % 152.53/22.86 % 152.53/22.86 Begin of proof % 152.53/22.86 | % 152.53/22.86 | BETA: splitting (2) gives: % 152.53/22.86 | % 152.53/22.86 | Case 1: % 152.53/22.86 | | % 152.53/22.86 | | (8) all_58_1 = e1 % 152.53/22.86 | | % 152.53/22.86 | | REF_CLOSE: (1), (3), (8) are inconsistent by sub-proof #703. % 152.53/22.86 | | % 152.53/22.86 | Case 2: % 152.53/22.86 | | % 152.53/22.86 | | (9) all_58_4 = e1 | all_58_9 = e1 % 152.53/22.86 | | % 152.53/22.86 | | BETA: splitting (9) gives: % 152.53/22.86 | | % 152.53/22.86 | | Case 1: % 152.53/22.86 | | | % 152.53/22.86 | | | (10) all_58_4 = e1 % 152.53/22.86 | | | % 152.53/22.86 | | | COMBINE_EQS: (7), (10) imply: % 152.53/22.86 | | | (11) e3 = e1 % 152.53/22.86 | | | % 152.53/22.86 | | | REDUCE: (6), (11) imply: % 152.53/22.86 | | | (12) $false % 152.53/22.86 | | | % 152.53/22.86 | | | CLOSE: (12) is inconsistent. % 152.53/22.86 | | | % 152.53/22.86 | | Case 2: % 152.53/22.86 | | | % 152.53/22.86 | | | (13) all_58_9 = e1 % 152.53/22.86 | | | % 152.53/22.86 | | | COMBINE_EQS: (4), (13) imply: % 152.53/22.86 | | | (14) e2 = e1 % 152.53/22.86 | | | % 152.53/22.86 | | | REDUCE: (5), (14) imply: % 152.53/22.86 | | | (15) $false % 152.53/22.86 | | | % 152.53/22.86 | | | CLOSE: (15) is inconsistent. % 152.53/22.86 | | | % 152.53/22.86 | | End of split % 152.53/22.86 | | % 152.53/22.86 | End of split % 152.53/22.86 | % 152.53/22.86 End of proof % 152.53/22.86 % 152.53/22.86 Sub-proof #703 shows that the following formulas are inconsistent: % 152.53/22.86 ---------------------------------------------------------------- % 152.53/22.86 (1) all_58_1 = e1 % 152.53/22.86 (2) all_58_1 = e0 % 152.53/22.86 (3) ~ (e1 = e0) % 152.53/22.86 % 152.53/22.86 Begin of proof % 152.53/22.86 | % 152.53/22.86 | COMBINE_EQS: (1), (2) imply: % 152.53/22.86 | (4) e1 = e0 % 152.53/22.86 | % 152.53/22.86 | SIMP: (4) implies: % 152.53/22.86 | (5) e1 = e0 % 152.53/22.86 | % 152.53/22.86 | REDUCE: (3), (5) imply: % 152.53/22.86 | (6) $false % 152.53/22.86 | % 152.53/22.86 | CLOSE: (6) is inconsistent. % 152.53/22.86 | % 152.53/22.86 End of proof % 152.53/22.86 % 152.53/22.86 Sub-proof #704 shows that the following formulas are inconsistent: % 152.53/22.86 ---------------------------------------------------------------- % 152.53/22.86 (1) all_58_13 = all_52_7 % 152.53/22.86 (2) all_58_13 = e1 % 152.53/22.86 (3) ~ (all_52_7 = e1) % 152.53/22.86 % 152.53/22.86 Begin of proof % 152.53/22.86 | % 152.53/22.86 | COMBINE_EQS: (1), (2) imply: % 152.53/22.86 | (4) all_52_7 = e1 % 152.53/22.86 | % 152.53/22.86 | SIMP: (4) implies: % 152.53/22.86 | (5) all_52_7 = e1 % 152.53/22.86 | % 152.53/22.86 | REDUCE: (3), (5) imply: % 152.53/22.86 | (6) $false % 152.53/22.86 | % 152.53/22.86 | CLOSE: (6) is inconsistent. % 152.53/22.86 | % 152.53/22.86 End of proof % 152.53/22.86 % 152.53/22.86 Sub-proof #705 shows that the following formulas are inconsistent: % 152.53/22.86 ---------------------------------------------------------------- % 152.53/22.86 (1) all_54_10 = all_6_2 % 152.53/22.86 (2) all_54_10 = e0 % 152.53/22.86 (3) ~ (all_6_2 = e0) % 152.53/22.86 % 152.53/22.86 Begin of proof % 152.53/22.86 | % 152.53/22.86 | COMBINE_EQS: (1), (2) imply: % 152.53/22.86 | (4) all_6_2 = e0 % 152.53/22.86 | % 152.53/22.86 | SIMP: (4) implies: % 152.53/22.86 | (5) all_6_2 = e0 % 152.53/22.86 | % 152.53/22.86 | REDUCE: (3), (5) imply: % 152.53/22.86 | (6) $false % 152.53/22.86 | % 152.53/22.86 | CLOSE: (6) is inconsistent. % 152.53/22.86 | % 152.53/22.86 End of proof % 152.53/22.86 % 152.53/22.86 Sub-proof #706 shows that the following formulas are inconsistent: % 152.53/22.86 ---------------------------------------------------------------- % 152.53/22.86 (1) all_54_0 = all_10_2 % 152.53/22.86 (2) ~ (all_10_2 = e1) % 152.53/22.86 (3) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 152.53/22.86 (4) all_56_1 = all_10_2 % 152.53/22.86 (5) all_54_1 = all_52_4 % 152.53/22.86 (6) ~ (all_52_4 = e1) % 152.53/22.86 (7) ~ (all_10_2 = e2) % 152.53/22.86 (8) all_56_7 = all_52_12 % 152.53/22.86 (9) ~ (all_52_4 = e0) % 152.53/22.86 (10) ~ (all_56_1 = e0) | all_56_7 = e3 % 152.53/22.86 (11) ~ (all_52_4 = e2) % 152.53/22.86 (12) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0 % 152.53/22.86 (13) ~ (all_52_4 = all_52_12) % 152.53/22.86 (14) ~ (all_52_4 = all_10_2) % 152.53/22.86 % 152.53/22.86 Begin of proof % 152.53/22.86 | % 152.53/22.86 | BETA: splitting (12) gives: % 152.53/22.86 | % 152.53/22.86 | Case 1: % 152.53/22.86 | | % 152.53/22.86 | | (15) all_54_1 = e3 % 152.53/22.86 | | % 152.53/22.86 | | COMBINE_EQS: (5), (15) imply: % 152.53/22.86 | | (16) all_52_4 = e3 % 152.53/22.86 | | % 152.53/22.86 | | SIMP: (16) implies: % 152.53/22.86 | | (17) all_52_4 = e3 % 152.53/22.86 | | % 152.53/22.86 | | REDUCE: (13), (17) imply: % 152.53/22.86 | | (18) ~ (all_52_12 = e3) % 152.53/22.86 | | % 152.53/22.86 | | SIMP: (18) implies: % 152.53/22.86 | | (19) ~ (all_52_12 = e3) % 152.53/22.86 | | % 152.53/22.86 | | REDUCE: (14), (17) imply: % 152.53/22.86 | | (20) ~ (all_10_2 = e3) % 152.53/22.86 | | % 152.53/22.86 | | SIMP: (20) implies: % 152.53/22.86 | | (21) ~ (all_10_2 = e3) % 152.53/22.86 | | % 152.53/22.86 | | REF_CLOSE: (1), (2), (3), (4), (7), (8), (10), (19), (21) are inconsistent % 152.53/22.86 | | by sub-proof #707. % 152.53/22.86 | | % 152.53/22.86 | Case 2: % 152.53/22.86 | | % 152.53/22.86 | | (22) all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0 % 152.53/22.86 | | % 152.53/22.86 | | REF_CLOSE: (5), (6), (9), (11), (22) are inconsistent by sub-proof #718. % 152.53/22.86 | | % 152.53/22.86 | End of split % 152.53/22.86 | % 152.53/22.86 End of proof % 152.53/22.86 % 152.53/22.86 Sub-proof #707 shows that the following formulas are inconsistent: % 152.53/22.86 ---------------------------------------------------------------- % 152.53/22.86 (1) all_54_0 = all_10_2 % 152.53/22.86 (2) ~ (all_10_2 = e1) % 152.53/22.86 (3) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 152.53/22.86 (4) all_56_1 = all_10_2 % 152.53/22.86 (5) ~ (all_10_2 = e2) % 152.53/22.86 (6) all_56_7 = all_52_12 % 152.53/22.86 (7) ~ (all_52_12 = e3) % 152.53/22.86 (8) ~ (all_56_1 = e0) | all_56_7 = e3 % 152.53/22.86 (9) ~ (all_10_2 = e3) % 152.53/22.86 % 152.53/22.86 Begin of proof % 152.53/22.86 | % 152.53/22.86 | BETA: splitting (8) gives: % 152.53/22.86 | % 152.53/22.86 | Case 1: % 152.53/22.86 | | % 152.53/22.86 | | (10) ~ (all_56_1 = e0) % 152.53/22.86 | | % 152.53/22.86 | | REDUCE: (4), (10) imply: % 152.53/22.86 | | (11) ~ (all_10_2 = e0) % 152.53/22.86 | | % 152.53/22.86 | | REF_CLOSE: (1), (2), (3), (5), (9), (11) are inconsistent by sub-proof #708. % 152.53/22.86 | | % 152.53/22.86 | Case 2: % 152.53/22.86 | | % 152.53/22.86 | | (12) all_56_7 = e3 % 152.53/22.86 | | % 152.53/22.86 | | COMBINE_EQS: (6), (12) imply: % 152.53/22.86 | | (13) all_52_12 = e3 % 152.53/22.86 | | % 152.53/22.86 | | REDUCE: (7), (13) imply: % 152.53/22.86 | | (14) $false % 152.53/22.86 | | % 152.53/22.86 | | CLOSE: (14) is inconsistent. % 152.53/22.86 | | % 152.53/22.86 | End of split % 152.53/22.86 | % 152.53/22.86 End of proof % 152.53/22.86 % 152.53/22.86 Sub-proof #708 shows that the following formulas are inconsistent: % 152.53/22.86 ---------------------------------------------------------------- % 152.53/22.86 (1) all_54_0 = all_10_2 % 152.53/22.86 (2) ~ (all_10_2 = e1) % 152.53/22.86 (3) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 152.53/22.86 (4) ~ (all_10_2 = e2) % 152.53/22.86 (5) ~ (all_10_2 = e0) % 152.53/22.86 (6) ~ (all_10_2 = e3) % 152.53/22.86 % 152.53/22.86 Begin of proof % 152.53/22.86 | % 152.53/22.86 | BETA: splitting (3) gives: % 152.53/22.86 | % 152.53/22.86 | Case 1: % 152.53/22.86 | | % 152.53/22.86 | | (7) all_54_0 = e3 % 152.53/22.86 | | % 152.53/22.86 | | REF_CLOSE: (1), (6), (7) are inconsistent by sub-proof #709. % 152.53/22.86 | | % 152.53/22.86 | Case 2: % 152.53/22.86 | | % 152.53/22.86 | | (8) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 152.53/22.86 | | % 152.53/22.86 | | REF_CLOSE: (1), (2), (4), (5), (8) are inconsistent by sub-proof #731. % 152.53/22.86 | | % 152.53/22.86 | End of split % 152.53/22.86 | % 152.53/22.86 End of proof % 152.53/22.86 % 152.53/22.86 Sub-proof #709 shows that the following formulas are inconsistent: % 152.53/22.86 ---------------------------------------------------------------- % 152.53/22.86 (1) all_54_0 = all_10_2 % 152.53/22.86 (2) all_54_0 = e3 % 152.53/22.86 (3) ~ (all_10_2 = e3) % 152.53/22.86 % 152.53/22.86 Begin of proof % 152.53/22.86 | % 152.53/22.86 | COMBINE_EQS: (1), (2) imply: % 152.53/22.86 | (4) all_10_2 = e3 % 152.53/22.86 | % 152.53/22.86 | SIMP: (4) implies: % 152.53/22.86 | (5) all_10_2 = e3 % 152.53/22.86 | % 152.53/22.86 | REDUCE: (3), (5) imply: % 152.53/22.86 | (6) $false % 152.53/22.86 | % 152.53/22.86 | CLOSE: (6) is inconsistent. % 152.53/22.86 | % 152.53/22.86 End of proof % 152.53/22.86 % 152.53/22.86 Sub-proof #710 shows that the following formulas are inconsistent: % 152.53/22.86 ---------------------------------------------------------------- % 152.53/22.86 (1) ~ (all_52_7 = e2) % 152.53/22.86 (2) all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0 % 152.53/22.86 (3) ~ (all_52_7 = e1) % 152.53/22.86 (4) all_54_13 = all_52_7 % 152.53/22.86 (5) ~ (all_52_7 = e0) % 152.53/22.86 % 152.53/22.86 Begin of proof % 152.53/22.86 | % 152.53/22.86 | BETA: splitting (2) gives: % 152.53/22.86 | % 152.53/22.86 | Case 1: % 152.53/22.86 | | % 152.53/22.86 | | (6) all_54_13 = e2 % 152.53/22.86 | | % 152.53/22.86 | | COMBINE_EQS: (4), (6) imply: % 152.53/22.86 | | (7) all_52_7 = e2 % 152.53/22.86 | | % 152.53/22.86 | | REDUCE: (1), (7) imply: % 152.53/22.86 | | (8) $false % 152.53/22.86 | | % 152.53/22.86 | | CLOSE: (8) is inconsistent. % 152.53/22.86 | | % 152.53/22.86 | Case 2: % 152.53/22.86 | | % 152.53/22.86 | | (9) all_54_13 = e1 | all_54_13 = e0 % 152.53/22.86 | | % 152.53/22.86 | | REF_CLOSE: (3), (4), (5), (9) are inconsistent by sub-proof #711. % 152.53/22.86 | | % 152.53/22.86 | End of split % 152.53/22.86 | % 152.53/22.86 End of proof % 152.53/22.86 % 152.53/22.86 Sub-proof #711 shows that the following formulas are inconsistent: % 152.53/22.86 ---------------------------------------------------------------- % 152.53/22.86 (1) all_54_13 = e1 | all_54_13 = e0 % 152.53/22.86 (2) all_54_13 = all_52_7 % 152.53/22.86 (3) ~ (all_52_7 = e1) % 152.53/22.86 (4) ~ (all_52_7 = e0) % 152.53/22.86 % 152.53/22.86 Begin of proof % 152.53/22.86 | % 152.53/22.86 | BETA: splitting (1) gives: % 152.53/22.86 | % 152.53/22.86 | Case 1: % 152.53/22.86 | | % 152.53/22.86 | | (5) all_54_13 = e1 % 152.53/22.86 | | % 152.53/22.86 | | REF_CLOSE: (2), (3), (5) are inconsistent by sub-proof #713. % 152.53/22.86 | | % 152.53/22.86 | Case 2: % 152.53/22.86 | | % 152.53/22.86 | | (6) all_54_13 = e0 % 152.53/22.86 | | % 152.53/22.86 | | REF_CLOSE: (2), (4), (6) are inconsistent by sub-proof #712. % 152.53/22.86 | | % 152.53/22.86 | End of split % 152.53/22.86 | % 152.53/22.86 End of proof % 152.53/22.86 % 152.53/22.86 Sub-proof #712 shows that the following formulas are inconsistent: % 152.53/22.86 ---------------------------------------------------------------- % 152.53/22.86 (1) all_54_13 = all_52_7 % 152.53/22.86 (2) all_54_13 = e0 % 152.53/22.86 (3) ~ (all_52_7 = e0) % 152.53/22.86 % 152.53/22.86 Begin of proof % 152.53/22.86 | % 152.53/22.86 | COMBINE_EQS: (1), (2) imply: % 152.53/22.86 | (4) all_52_7 = e0 % 152.53/22.86 | % 152.53/22.86 | SIMP: (4) implies: % 152.53/22.86 | (5) all_52_7 = e0 % 152.53/22.86 | % 152.53/22.86 | REDUCE: (3), (5) imply: % 152.53/22.86 | (6) $false % 152.53/22.86 | % 152.53/22.86 | CLOSE: (6) is inconsistent. % 152.53/22.86 | % 152.53/22.86 End of proof % 152.53/22.86 % 152.53/22.86 Sub-proof #713 shows that the following formulas are inconsistent: % 152.53/22.86 ---------------------------------------------------------------- % 152.53/22.86 (1) all_54_13 = all_52_7 % 152.53/22.86 (2) all_54_13 = e1 % 152.53/22.86 (3) ~ (all_52_7 = e1) % 152.53/22.86 % 152.53/22.86 Begin of proof % 152.53/22.86 | % 152.53/22.86 | COMBINE_EQS: (1), (2) imply: % 152.53/22.86 | (4) all_52_7 = e1 % 152.53/22.86 | % 152.53/22.86 | SIMP: (4) implies: % 152.53/22.86 | (5) all_52_7 = e1 % 152.53/22.87 | % 152.53/22.87 | REDUCE: (3), (5) imply: % 152.53/22.87 | (6) $false % 152.53/22.87 | % 152.53/22.87 | CLOSE: (6) is inconsistent. % 152.53/22.87 | % 152.53/22.87 End of proof % 152.53/22.87 % 152.53/22.87 Sub-proof #714 shows that the following formulas are inconsistent: % 152.53/22.87 ---------------------------------------------------------------- % 152.53/22.87 (1) all_54_14 = e1 | all_54_14 = e0 % 152.53/22.87 (2) all_54_14 = all_52_11 % 152.53/22.87 (3) ~ (all_52_11 = e1) % 152.53/22.87 (4) ~ (all_52_11 = e0) % 152.53/22.87 % 152.53/22.87 Begin of proof % 152.53/22.87 | % 152.53/22.87 | BETA: splitting (1) gives: % 152.53/22.87 | % 152.53/22.87 | Case 1: % 152.53/22.87 | | % 152.53/22.87 | | (5) all_54_14 = e1 % 152.53/22.87 | | % 152.53/22.87 | | COMBINE_EQS: (2), (5) imply: % 152.53/22.87 | | (6) all_52_11 = e1 % 152.53/22.87 | | % 152.53/22.87 | | SIMP: (6) implies: % 152.53/22.87 | | (7) all_52_11 = e1 % 152.53/22.87 | | % 152.53/22.87 | | REDUCE: (3), (7) imply: % 152.53/22.87 | | (8) $false % 152.53/22.87 | | % 152.53/22.87 | | CLOSE: (8) is inconsistent. % 152.53/22.87 | | % 152.53/22.87 | Case 2: % 152.53/22.87 | | % 152.53/22.87 | | (9) all_54_14 = e0 % 152.53/22.87 | | % 152.53/22.87 | | REF_CLOSE: (2), (4), (9) are inconsistent by sub-proof #715. % 152.53/22.87 | | % 152.53/22.87 | End of split % 152.53/22.87 | % 152.53/22.87 End of proof % 152.53/22.87 % 152.53/22.87 Sub-proof #715 shows that the following formulas are inconsistent: % 152.53/22.87 ---------------------------------------------------------------- % 152.53/22.87 (1) all_54_14 = all_52_11 % 152.53/22.87 (2) all_54_14 = e0 % 152.53/22.87 (3) ~ (all_52_11 = e0) % 152.53/22.87 % 152.53/22.87 Begin of proof % 152.53/22.87 | % 152.53/22.87 | COMBINE_EQS: (1), (2) imply: % 152.53/22.87 | (4) all_52_11 = e0 % 152.53/22.87 | % 152.53/22.87 | SIMP: (4) implies: % 152.53/22.87 | (5) all_52_11 = e0 % 152.53/22.87 | % 152.53/22.87 | REDUCE: (3), (5) imply: % 152.53/22.87 | (6) $false % 152.53/22.87 | % 152.53/22.87 | CLOSE: (6) is inconsistent. % 152.53/22.87 | % 152.53/22.87 End of proof % 152.53/22.87 % 152.53/22.87 Sub-proof #716 shows that the following formulas are inconsistent: % 152.53/22.87 ---------------------------------------------------------------- % 152.53/22.87 (1) ~ (all_52_4 = all_52_8) % 152.53/22.87 (2) ~ (all_52_8 = e2) % 152.53/22.87 (3) all_54_1 = all_52_4 % 152.53/22.87 (4) all_58_1 = all_52_4 % 152.53/22.87 (5) ~ (all_52_8 = e0) % 152.53/22.87 (6) ~ (all_52_4 = e0) % 152.53/22.87 (7) all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0 % 152.53/22.87 (8) all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1 % 152.53/22.87 (9) ~ (all_52_4 = e2) % 152.53/22.87 (10) all_54_2 = all_52_8 % 152.53/22.87 (11) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0 % 152.53/22.87 (12) ~ (all_52_4 = e3) % 152.53/22.87 % 152.53/22.87 Begin of proof % 152.53/22.87 | % 152.53/22.87 | BETA: splitting (8) gives: % 152.53/22.87 | % 152.53/22.87 | Case 1: % 152.53/22.87 | | % 152.53/22.87 | | (13) all_58_1 = e1 % 152.53/22.87 | | % 152.53/22.87 | | COMBINE_EQS: (4), (13) imply: % 152.53/22.87 | | (14) all_52_4 = e1 % 152.53/22.87 | | % 152.53/22.87 | | REDUCE: (1), (14) imply: % 152.53/22.87 | | (15) ~ (all_52_8 = e1) % 152.53/22.87 | | % 152.53/22.87 | | SIMP: (15) implies: % 152.53/22.87 | | (16) ~ (all_52_8 = e1) % 152.53/22.87 | | % 152.53/22.87 | | REF_CLOSE: (2), (5), (7), (10), (16) are inconsistent by sub-proof #723. % 152.53/22.87 | | % 152.53/22.87 | Case 2: % 152.53/22.87 | | % 152.53/22.87 | | (17) ~ (all_58_1 = e1) % 152.53/22.87 | | % 152.53/22.87 | | REDUCE: (4), (17) imply: % 152.53/22.87 | | (18) ~ (all_52_4 = e1) % 152.53/22.87 | | % 152.53/22.87 | | REF_CLOSE: (3), (6), (9), (11), (12), (18) are inconsistent by sub-proof % 152.53/22.87 | | #717. % 152.53/22.87 | | % 152.53/22.87 | End of split % 152.53/22.87 | % 152.53/22.87 End of proof % 152.53/22.87 % 152.53/22.87 Sub-proof #717 shows that the following formulas are inconsistent: % 152.53/22.87 ---------------------------------------------------------------- % 152.53/22.87 (1) all_54_1 = all_52_4 % 152.53/22.87 (2) ~ (all_52_4 = e1) % 152.53/22.87 (3) ~ (all_52_4 = e0) % 152.53/22.87 (4) ~ (all_52_4 = e2) % 152.53/22.87 (5) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0 % 152.53/22.87 (6) ~ (all_52_4 = e3) % 152.53/22.87 % 152.53/22.87 Begin of proof % 152.53/22.87 | % 152.53/22.87 | BETA: splitting (5) gives: % 152.53/22.87 | % 152.53/22.87 | Case 1: % 152.53/22.87 | | % 152.53/22.87 | | (7) all_54_1 = e3 % 152.53/22.87 | | % 152.53/22.87 | | REF_CLOSE: (1), (6), (7) are inconsistent by sub-proof #722. % 152.53/22.87 | | % 152.53/22.87 | Case 2: % 152.53/22.87 | | % 152.53/22.87 | | (8) all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0 % 152.53/22.87 | | % 152.53/22.87 | | REF_CLOSE: (1), (2), (3), (4), (8) are inconsistent by sub-proof #718. % 152.53/22.87 | | % 152.53/22.87 | End of split % 152.53/22.87 | % 152.53/22.87 End of proof % 152.53/22.87 % 152.53/22.87 Sub-proof #718 shows that the following formulas are inconsistent: % 152.53/22.87 ---------------------------------------------------------------- % 152.53/22.87 (1) all_54_1 = all_52_4 % 152.53/22.87 (2) ~ (all_52_4 = e1) % 152.53/22.87 (3) all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0 % 152.53/22.87 (4) ~ (all_52_4 = e0) % 152.53/22.87 (5) ~ (all_52_4 = e2) % 152.53/22.87 % 152.53/22.87 Begin of proof % 152.53/22.87 | % 152.53/22.87 | BETA: splitting (3) gives: % 152.53/22.87 | % 152.53/22.87 | Case 1: % 152.53/22.87 | | % 152.53/22.87 | | (6) all_54_1 = e2 % 152.53/22.87 | | % 152.53/22.87 | | REF_CLOSE: (1), (5), (6) are inconsistent by sub-proof #721. % 152.53/22.87 | | % 152.53/22.87 | Case 2: % 152.53/22.87 | | % 152.53/22.87 | | (7) all_54_1 = e1 | all_54_1 = e0 % 152.53/22.87 | | % 152.53/22.87 | | BETA: splitting (7) gives: % 152.53/22.87 | | % 152.53/22.87 | | Case 1: % 152.53/22.87 | | | % 152.53/22.87 | | | (8) all_54_1 = e1 % 152.53/22.87 | | | % 152.53/22.87 | | | REF_CLOSE: (1), (2), (8) are inconsistent by sub-proof #720. % 152.53/22.87 | | | % 152.53/22.87 | | Case 2: % 152.53/22.87 | | | % 152.53/22.87 | | | (9) all_54_1 = e0 % 152.53/22.87 | | | % 152.53/22.87 | | | REF_CLOSE: (1), (4), (9) are inconsistent by sub-proof #719. % 152.53/22.87 | | | % 152.53/22.87 | | End of split % 152.53/22.87 | | % 152.53/22.87 | End of split % 152.53/22.87 | % 152.53/22.87 End of proof % 152.53/22.87 % 152.53/22.87 Sub-proof #719 shows that the following formulas are inconsistent: % 152.53/22.87 ---------------------------------------------------------------- % 152.53/22.87 (1) all_54_1 = all_52_4 % 152.53/22.87 (2) all_54_1 = e0 % 152.53/22.87 (3) ~ (all_52_4 = e0) % 152.53/22.87 % 152.53/22.87 Begin of proof % 152.53/22.87 | % 152.53/22.87 | COMBINE_EQS: (1), (2) imply: % 152.53/22.87 | (4) all_52_4 = e0 % 152.53/22.87 | % 152.53/22.87 | SIMP: (4) implies: % 152.53/22.87 | (5) all_52_4 = e0 % 152.53/22.87 | % 152.53/22.87 | REDUCE: (3), (5) imply: % 152.53/22.87 | (6) $false % 152.53/22.87 | % 152.53/22.87 | CLOSE: (6) is inconsistent. % 152.53/22.87 | % 152.53/22.87 End of proof % 152.53/22.87 % 152.53/22.87 Sub-proof #720 shows that the following formulas are inconsistent: % 152.53/22.87 ---------------------------------------------------------------- % 152.53/22.87 (1) all_54_1 = all_52_4 % 152.53/22.87 (2) all_54_1 = e1 % 152.53/22.87 (3) ~ (all_52_4 = e1) % 152.53/22.87 % 152.53/22.87 Begin of proof % 152.53/22.87 | % 152.53/22.87 | COMBINE_EQS: (1), (2) imply: % 152.53/22.87 | (4) all_52_4 = e1 % 152.53/22.87 | % 152.53/22.87 | SIMP: (4) implies: % 152.53/22.87 | (5) all_52_4 = e1 % 152.53/22.87 | % 152.53/22.87 | REDUCE: (3), (5) imply: % 152.53/22.87 | (6) $false % 152.53/22.87 | % 152.53/22.87 | CLOSE: (6) is inconsistent. % 152.53/22.87 | % 152.53/22.87 End of proof % 152.53/22.87 % 152.53/22.87 Sub-proof #721 shows that the following formulas are inconsistent: % 152.53/22.87 ---------------------------------------------------------------- % 152.53/22.87 (1) all_54_1 = all_52_4 % 152.53/22.87 (2) all_54_1 = e2 % 152.53/22.87 (3) ~ (all_52_4 = e2) % 152.53/22.87 % 152.53/22.87 Begin of proof % 152.53/22.87 | % 152.53/22.87 | COMBINE_EQS: (1), (2) imply: % 152.53/22.87 | (4) all_52_4 = e2 % 152.53/22.87 | % 152.53/22.87 | SIMP: (4) implies: % 152.53/22.87 | (5) all_52_4 = e2 % 152.53/22.87 | % 152.53/22.87 | REDUCE: (3), (5) imply: % 152.53/22.87 | (6) $false % 152.53/22.87 | % 152.53/22.87 | CLOSE: (6) is inconsistent. % 152.53/22.87 | % 152.53/22.87 End of proof % 152.53/22.87 % 152.53/22.87 Sub-proof #722 shows that the following formulas are inconsistent: % 152.53/22.87 ---------------------------------------------------------------- % 152.53/22.87 (1) all_54_1 = all_52_4 % 152.53/22.87 (2) all_54_1 = e3 % 152.53/22.87 (3) ~ (all_52_4 = e3) % 152.53/22.87 % 152.53/22.87 Begin of proof % 152.53/22.87 | % 152.53/22.87 | COMBINE_EQS: (1), (2) imply: % 152.53/22.87 | (4) all_52_4 = e3 % 152.53/22.87 | % 152.53/22.87 | SIMP: (4) implies: % 152.53/22.87 | (5) all_52_4 = e3 % 152.53/22.87 | % 152.53/22.87 | REDUCE: (3), (5) imply: % 152.53/22.87 | (6) $false % 152.53/22.87 | % 152.53/22.87 | CLOSE: (6) is inconsistent. % 152.53/22.87 | % 152.53/22.87 End of proof % 152.53/22.87 % 152.53/22.87 Sub-proof #723 shows that the following formulas are inconsistent: % 152.53/22.87 ---------------------------------------------------------------- % 152.53/22.87 (1) ~ (all_52_8 = e2) % 152.53/22.87 (2) ~ (all_52_8 = e0) % 152.53/22.87 (3) all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0 % 152.53/22.87 (4) ~ (all_52_8 = e1) % 152.53/22.87 (5) all_54_2 = all_52_8 % 152.53/22.87 % 152.53/22.87 Begin of proof % 152.53/22.87 | % 152.53/22.87 | BETA: splitting (3) gives: % 152.53/22.87 | % 152.53/22.87 | Case 1: % 152.53/22.87 | | % 152.53/22.87 | | (6) all_54_2 = e2 % 152.53/22.87 | | % 152.53/22.87 | | REF_CLOSE: (1), (5), (6) are inconsistent by sub-proof #727. % 152.53/22.87 | | % 152.53/22.87 | Case 2: % 152.53/22.87 | | % 152.53/22.87 | | (7) all_54_2 = e1 | all_54_2 = e0 % 152.53/22.87 | | % 152.53/22.87 | | REF_CLOSE: (2), (4), (5), (7) are inconsistent by sub-proof #724. % 152.53/22.87 | | % 152.53/22.87 | End of split % 152.53/22.87 | % 152.53/22.87 End of proof % 152.53/22.87 % 152.53/22.87 Sub-proof #724 shows that the following formulas are inconsistent: % 152.53/22.87 ---------------------------------------------------------------- % 152.53/22.87 (1) all_54_2 = e1 | all_54_2 = e0 % 152.53/22.87 (2) all_54_2 = all_52_8 % 152.53/22.87 (3) ~ (all_52_8 = e1) % 152.53/22.87 (4) ~ (all_52_8 = e0) % 152.53/22.87 % 152.53/22.87 Begin of proof % 152.53/22.87 | % 152.53/22.87 | BETA: splitting (1) gives: % 152.53/22.87 | % 152.53/22.87 | Case 1: % 152.53/22.87 | | % 152.53/22.87 | | (5) all_54_2 = e1 % 152.53/22.87 | | % 152.53/22.87 | | REF_CLOSE: (2), (3), (5) are inconsistent by sub-proof #726. % 152.53/22.87 | | % 152.53/22.87 | Case 2: % 152.53/22.87 | | % 152.53/22.87 | | (6) all_54_2 = e0 % 152.53/22.87 | | % 152.53/22.87 | | REF_CLOSE: (2), (4), (6) are inconsistent by sub-proof #725. % 152.53/22.87 | | % 152.53/22.87 | End of split % 152.53/22.87 | % 152.53/22.87 End of proof % 152.53/22.87 % 152.53/22.87 Sub-proof #725 shows that the following formulas are inconsistent: % 152.53/22.87 ---------------------------------------------------------------- % 152.53/22.87 (1) all_54_2 = all_52_8 % 152.53/22.87 (2) all_54_2 = e0 % 152.53/22.87 (3) ~ (all_52_8 = e0) % 152.53/22.87 % 152.53/22.87 Begin of proof % 152.53/22.87 | % 152.53/22.87 | COMBINE_EQS: (1), (2) imply: % 152.53/22.87 | (4) all_52_8 = e0 % 152.53/22.87 | % 152.53/22.87 | SIMP: (4) implies: % 152.53/22.87 | (5) all_52_8 = e0 % 152.53/22.87 | % 152.53/22.87 | REDUCE: (3), (5) imply: % 152.53/22.87 | (6) $false % 152.53/22.87 | % 152.53/22.87 | CLOSE: (6) is inconsistent. % 152.53/22.87 | % 152.53/22.87 End of proof % 152.53/22.87 % 152.53/22.87 Sub-proof #726 shows that the following formulas are inconsistent: % 152.53/22.87 ---------------------------------------------------------------- % 152.53/22.87 (1) all_54_2 = all_52_8 % 152.53/22.87 (2) all_54_2 = e1 % 152.53/22.87 (3) ~ (all_52_8 = e1) % 152.53/22.87 % 152.53/22.87 Begin of proof % 152.53/22.87 | % 152.53/22.87 | COMBINE_EQS: (1), (2) imply: % 152.53/22.87 | (4) all_52_8 = e1 % 152.53/22.87 | % 152.53/22.87 | SIMP: (4) implies: % 152.53/22.87 | (5) all_52_8 = e1 % 152.53/22.87 | % 152.53/22.87 | REDUCE: (3), (5) imply: % 152.53/22.87 | (6) $false % 152.53/22.87 | % 152.53/22.87 | CLOSE: (6) is inconsistent. % 152.53/22.87 | % 152.53/22.87 End of proof % 152.53/22.87 % 152.53/22.87 Sub-proof #727 shows that the following formulas are inconsistent: % 152.53/22.87 ---------------------------------------------------------------- % 152.53/22.87 (1) all_54_2 = all_52_8 % 152.53/22.87 (2) all_54_2 = e2 % 152.53/22.87 (3) ~ (all_52_8 = e2) % 152.53/22.87 % 152.53/22.87 Begin of proof % 152.53/22.87 | % 152.53/22.87 | COMBINE_EQS: (1), (2) imply: % 152.53/22.87 | (4) all_52_8 = e2 % 152.53/22.87 | % 152.53/22.87 | SIMP: (4) implies: % 152.53/22.87 | (5) all_52_8 = e2 % 152.53/22.87 | % 152.53/22.87 | REDUCE: (3), (5) imply: % 152.53/22.87 | (6) $false % 152.53/22.87 | % 152.53/22.87 | CLOSE: (6) is inconsistent. % 152.53/22.87 | % 152.53/22.87 End of proof % 152.53/22.87 % 152.53/22.87 Sub-proof #728 shows that the following formulas are inconsistent: % 152.53/22.87 ---------------------------------------------------------------- % 152.53/22.87 (1) all_54_2 = all_52_8 % 152.53/22.87 (2) all_54_2 = e3 % 152.53/22.87 (3) ~ (all_52_8 = e3) % 152.53/22.87 % 152.53/22.87 Begin of proof % 152.53/22.87 | % 152.53/22.87 | COMBINE_EQS: (1), (2) imply: % 152.53/22.87 | (4) all_52_8 = e3 % 152.53/22.87 | % 152.53/22.87 | SIMP: (4) implies: % 152.53/22.87 | (5) all_52_8 = e3 % 152.53/22.87 | % 152.53/22.87 | REDUCE: (3), (5) imply: % 152.53/22.87 | (6) $false % 152.53/22.87 | % 152.53/22.87 | CLOSE: (6) is inconsistent. % 152.53/22.87 | % 152.53/22.87 End of proof % 152.53/22.87 % 152.53/22.87 Sub-proof #729 shows that the following formulas are inconsistent: % 152.53/22.87 ---------------------------------------------------------------- % 152.53/22.87 (1) all_54_14 = all_52_11 % 152.53/22.87 (2) all_54_14 = e3 % 152.53/22.87 (3) ~ (all_52_11 = e3) % 152.53/22.87 % 152.53/22.87 Begin of proof % 152.53/22.87 | % 152.53/22.87 | COMBINE_EQS: (1), (2) imply: % 152.53/22.87 | (4) all_52_11 = e3 % 152.53/22.87 | % 152.53/22.87 | SIMP: (4) implies: % 152.53/22.87 | (5) all_52_11 = e3 % 152.53/22.87 | % 152.53/22.87 | REDUCE: (3), (5) imply: % 152.53/22.87 | (6) $false % 152.53/22.87 | % 152.53/22.87 | CLOSE: (6) is inconsistent. % 152.53/22.87 | % 152.53/22.87 End of proof % 152.53/22.87 % 152.53/22.87 Sub-proof #730 shows that the following formulas are inconsistent: % 152.53/22.87 ---------------------------------------------------------------- % 152.53/22.87 (1) all_58_0 = e1 % 152.53/22.87 (2) all_58_0 = e0 % 152.53/22.87 (3) ~ (e1 = e0) % 152.53/22.87 % 152.53/22.87 Begin of proof % 152.53/22.87 | % 152.53/22.87 | COMBINE_EQS: (1), (2) imply: % 152.53/22.87 | (4) e1 = e0 % 152.53/22.87 | % 152.53/22.87 | SIMP: (4) implies: % 152.53/22.87 | (5) e1 = e0 % 152.53/22.87 | % 152.53/22.87 | REDUCE: (3), (5) imply: % 152.53/22.87 | (6) $false % 152.53/22.87 | % 152.53/22.87 | CLOSE: (6) is inconsistent. % 152.53/22.87 | % 152.53/22.87 End of proof % 152.53/22.87 % 152.53/22.87 Sub-proof #731 shows that the following formulas are inconsistent: % 152.53/22.87 ---------------------------------------------------------------- % 152.53/22.87 (1) all_54_0 = all_10_2 % 152.53/22.87 (2) ~ (all_10_2 = e1) % 152.53/22.87 (3) ~ (all_10_2 = e2) % 152.53/22.87 (4) ~ (all_10_2 = e0) % 152.53/22.87 (5) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 152.53/22.87 % 152.53/22.87 Begin of proof % 152.53/22.87 | % 152.53/22.87 | BETA: splitting (5) gives: % 152.53/22.87 | % 152.53/22.87 | Case 1: % 152.53/22.87 | | % 152.53/22.87 | | (6) all_54_0 = e2 % 152.53/22.87 | | % 152.53/22.87 | | REF_CLOSE: (1), (3), (6) are inconsistent by sub-proof #734. % 152.53/22.87 | | % 152.53/22.87 | Case 2: % 152.53/22.87 | | % 152.53/22.87 | | (7) all_54_0 = e1 | all_54_0 = e0 % 152.53/22.87 | | % 152.53/22.87 | | BETA: splitting (7) gives: % 152.53/22.87 | | % 152.53/22.87 | | Case 1: % 152.53/22.87 | | | % 152.53/22.87 | | | (8) all_54_0 = e1 % 152.53/22.87 | | | % 152.53/22.87 | | | REF_CLOSE: (1), (2), (8) are inconsistent by sub-proof #733. % 152.53/22.87 | | | % 152.53/22.87 | | Case 2: % 152.53/22.87 | | | % 152.53/22.87 | | | (9) all_54_0 = e0 % 152.53/22.87 | | | % 152.53/22.87 | | | REF_CLOSE: (1), (4), (9) are inconsistent by sub-proof #732. % 152.53/22.87 | | | % 152.53/22.87 | | End of split % 152.53/22.87 | | % 152.53/22.87 | End of split % 152.53/22.87 | % 152.53/22.87 End of proof % 152.53/22.87 % 152.53/22.87 Sub-proof #732 shows that the following formulas are inconsistent: % 152.53/22.87 ---------------------------------------------------------------- % 152.53/22.87 (1) all_54_0 = all_10_2 % 152.53/22.87 (2) all_54_0 = e0 % 152.53/22.87 (3) ~ (all_10_2 = e0) % 152.53/22.87 % 152.53/22.87 Begin of proof % 152.53/22.87 | % 152.53/22.87 | COMBINE_EQS: (1), (2) imply: % 152.53/22.87 | (4) all_10_2 = e0 % 152.53/22.87 | % 152.53/22.87 | SIMP: (4) implies: % 152.53/22.87 | (5) all_10_2 = e0 % 152.53/22.87 | % 152.53/22.87 | REDUCE: (3), (5) imply: % 152.53/22.87 | (6) $false % 152.53/22.87 | % 152.53/22.87 | CLOSE: (6) is inconsistent. % 152.53/22.87 | % 152.53/22.87 End of proof % 152.53/22.87 % 152.53/22.87 Sub-proof #733 shows that the following formulas are inconsistent: % 152.53/22.87 ---------------------------------------------------------------- % 152.53/22.87 (1) all_54_0 = all_10_2 % 152.53/22.87 (2) all_54_0 = e1 % 152.53/22.87 (3) ~ (all_10_2 = e1) % 152.53/22.87 % 152.53/22.87 Begin of proof % 152.53/22.87 | % 152.53/22.87 | COMBINE_EQS: (1), (2) imply: % 152.53/22.87 | (4) all_10_2 = e1 % 152.53/22.87 | % 152.53/22.87 | SIMP: (4) implies: % 152.53/22.87 | (5) all_10_2 = e1 % 152.53/22.87 | % 152.53/22.87 | REDUCE: (3), (5) imply: % 152.53/22.87 | (6) $false % 152.53/22.87 | % 152.53/22.87 | CLOSE: (6) is inconsistent. % 152.53/22.87 | % 152.53/22.87 End of proof % 152.53/22.87 % 152.53/22.87 Sub-proof #734 shows that the following formulas are inconsistent: % 152.53/22.87 ---------------------------------------------------------------- % 152.53/22.87 (1) all_54_0 = all_10_2 % 152.53/22.87 (2) all_54_0 = e2 % 152.53/22.87 (3) ~ (all_10_2 = e2) % 152.53/22.87 % 152.53/22.87 Begin of proof % 152.53/22.87 | % 152.53/22.87 | COMBINE_EQS: (1), (2) imply: % 152.53/22.87 | (4) all_10_2 = e2 % 152.53/22.87 | % 152.53/22.87 | SIMP: (4) implies: % 152.53/22.87 | (5) all_10_2 = e2 % 152.53/22.87 | % 152.53/22.87 | REDUCE: (3), (5) imply: % 152.53/22.87 | (6) $false % 152.53/22.87 | % 152.53/22.87 | CLOSE: (6) is inconsistent. % 152.53/22.87 | % 152.53/22.87 End of proof % 152.53/22.87 % 152.53/22.87 Sub-proof #735 shows that the following formulas are inconsistent: % 152.53/22.87 ---------------------------------------------------------------- % 152.53/22.87 (1) all_54_10 = all_6_2 % 152.53/22.87 (2) all_54_10 = e2 % 152.53/22.87 (3) ~ (all_6_2 = e2) % 152.53/22.87 % 152.53/22.87 Begin of proof % 152.53/22.87 | % 152.53/22.87 | COMBINE_EQS: (1), (2) imply: % 152.53/22.87 | (4) all_6_2 = e2 % 152.53/22.87 | % 152.53/22.87 | SIMP: (4) implies: % 152.53/22.87 | (5) all_6_2 = e2 % 152.53/22.87 | % 152.53/22.87 | REDUCE: (3), (5) imply: % 152.53/22.87 | (6) $false % 152.53/22.87 | % 152.53/22.87 | CLOSE: (6) is inconsistent. % 152.53/22.87 | % 152.53/22.87 End of proof % 152.53/22.87 % 152.53/22.87 Sub-proof #736 shows that the following formulas are inconsistent: % 152.53/22.87 ---------------------------------------------------------------- % 152.53/22.87 (1) all_54_10 = all_6_2 % 152.53/22.87 (2) all_54_10 = e3 % 152.53/22.87 (3) ~ (all_6_2 = e3) % 152.53/22.87 % 152.53/22.87 Begin of proof % 152.53/22.87 | % 152.53/22.87 | COMBINE_EQS: (1), (2) imply: % 152.53/22.87 | (4) all_6_2 = e3 % 152.53/22.87 | % 152.53/22.87 | SIMP: (4) implies: % 152.53/22.87 | (5) all_6_2 = e3 % 152.53/22.87 | % 152.53/22.87 | REDUCE: (3), (5) imply: % 152.53/22.87 | (6) $false % 152.53/22.87 | % 152.53/22.87 | CLOSE: (6) is inconsistent. % 152.53/22.87 | % 152.53/22.87 End of proof % 152.53/22.87 % 152.53/22.87 Sub-proof #737 shows that the following formulas are inconsistent: % 152.53/22.87 ---------------------------------------------------------------- % 152.53/22.87 (1) all_54_5 = all_8_2 % 152.53/22.87 (2) all_54_5 = e3 % 152.53/22.87 (3) ~ (all_8_2 = e3) % 152.53/22.87 % 152.53/22.87 Begin of proof % 152.53/22.87 | % 152.53/22.87 | COMBINE_EQS: (1), (2) imply: % 152.53/22.87 | (4) all_8_2 = e3 % 152.53/22.87 | % 152.53/22.87 | SIMP: (4) implies: % 152.53/22.87 | (5) all_8_2 = e3 % 152.53/22.87 | % 152.53/22.87 | REDUCE: (3), (5) imply: % 152.53/22.87 | (6) $false % 152.53/22.87 | % 152.53/22.87 | CLOSE: (6) is inconsistent. % 152.53/22.87 | % 152.53/22.87 End of proof % 152.53/22.87 % 152.53/22.87 Sub-proof #738 shows that the following formulas are inconsistent: % 152.53/22.87 ---------------------------------------------------------------- % 152.53/22.87 (1) all_54_15 = all_4_2 % 152.53/22.87 (2) all_54_15 = e1 % 152.53/22.87 (3) ~ (all_4_2 = e1) % 152.53/22.87 % 152.53/22.87 Begin of proof % 152.53/22.87 | % 152.53/22.87 | COMBINE_EQS: (1), (2) imply: % 152.53/22.87 | (4) all_4_2 = e1 % 152.53/22.87 | % 152.53/22.87 | SIMP: (4) implies: % 152.53/22.87 | (5) all_4_2 = e1 % 152.53/22.87 | % 152.53/22.87 | REDUCE: (3), (5) imply: % 152.53/22.87 | (6) $false % 152.53/22.87 | % 152.53/22.87 | CLOSE: (6) is inconsistent. % 152.53/22.87 | % 152.53/22.87 End of proof % 152.53/22.87 % 152.53/22.87 Sub-proof #739 shows that the following formulas are inconsistent: % 152.53/22.87 ---------------------------------------------------------------- % 152.53/22.87 (1) all_54_15 = all_4_2 % 152.53/22.87 (2) all_54_15 = e2 % 152.53/22.87 (3) ~ (all_4_2 = e2) % 152.53/22.87 % 152.53/22.87 Begin of proof % 152.53/22.87 | % 152.53/22.87 | COMBINE_EQS: (1), (2) imply: % 152.53/22.87 | (4) all_4_2 = e2 % 152.53/22.87 | % 152.53/22.87 | SIMP: (4) implies: % 152.53/22.87 | (5) all_4_2 = e2 % 152.53/22.87 | % 152.53/22.87 | REDUCE: (3), (5) imply: % 152.53/22.87 | (6) $false % 152.53/22.87 | % 152.53/22.87 | CLOSE: (6) is inconsistent. % 152.53/22.87 | % 152.53/22.87 End of proof % 152.53/22.87 % 152.53/22.87 Sub-proof #740 shows that the following formulas are inconsistent: % 152.53/22.87 ---------------------------------------------------------------- % 152.53/22.87 (1) all_54_15 = all_4_2 % 152.53/22.87 (2) all_54_15 = e3 % 152.53/22.87 (3) ~ (all_4_2 = e3) % 152.53/22.87 % 152.53/22.87 Begin of proof % 152.53/22.87 | % 152.53/22.87 | COMBINE_EQS: (1), (2) imply: % 152.53/22.87 | (4) all_4_2 = e3 % 152.53/22.87 | % 152.53/22.87 | SIMP: (4) implies: % 152.53/22.87 | (5) all_4_2 = e3 % 152.53/22.87 | % 152.53/22.87 | REDUCE: (3), (5) imply: % 152.53/22.87 | (6) $false % 152.53/22.87 | % 152.53/22.87 | CLOSE: (6) is inconsistent. % 152.53/22.87 | % 152.53/22.87 End of proof % 152.53/22.87 % SZS output end Proof for theBenchmark % 152.53/22.87 % 152.53/22.87 22236ms %------------------------------------------------------------------------------